\\\\sqrt{60 \\\\over 2 \\\\pi} \\\\, M_{\\\\rm P} \\\\approx 3.1 M_{\\\\rm\\n P} \\\\ , \\\\label{eq:2.11}\\n\\\\eeq\\nwhere $M_{\\\\rm P} \\\\equiv 1/\\\\sqrt{G} = 1.22 \\\\times 10^{19}$ GeV is\\nthe Planck mass. Although the value of the scalar field is\\nlarger than $M_{\\\\rm P}$, the energy density can be low compared\\nto the Planck scale: \\n\\\\beq\\n \\\\rho_0 = {1 \\\\over 2} m^2 \\\\phi_0^2 > {60 \\\\over 4 \\\\pi} M_{\\\\rm P}^2 m^2\\n \\\\ .\\n \\\\label{eq:2.12}\\n\\\\eeq\\nFor example, if $m = 10^{16}$ GeV, then the potential energy\\ndensity is only $3 \\\\times 10^{-6}\\\\, M_{\\\\rm P}^4$. Since it is\\npresumably the energy density that is relevant to gravity, one\\ndoes not expect this situation to lead to strong quantum gravity\\neffects.\\n\\n% Section III:\\n\\\\section{Evidence for Inflation}\\n\\\\setcounter{equation}{0}\\n\\nThe arguments in favor of inflation are pretty much the same no\\nmatter which form of inflation we are discussing. In my opinion,\\nthe evidence that our universe is the result of some form of\\ninflation is very solid. Since the term {\\\\it inflation}\\nencompasses a wide range of detailed theories, it is hard to\\nimagine any alternative. Let me review the basic arguments.\\n\\n\\\\subhead{1) The universe is big}\\n\\nFirst of all, we know that the universe is incredibly large. The\\nvisible part of it contains about $10^{90}$ particles. It is\\neasy, however, to take this fact for granted: of course the\\nuniverse is big, it's the whole universe! In ``standard''\\nFriedmann-Robertson-Walker cosmology, without inflation, one\\nsimply postulates that about $10^{90}$ or more particles were\\nhere from the start. If, however, we try to imagine a theory\\ndescribing the origin of the universe, it would have to somehow\\noutput this number of $10^{90}$ or more. That is a very big\\nnumber, and it is hard to imagine it ever coming out of a\\ncalculation in which the input consists only geometrical\\nquantities, quantities associated with simple dynamics, and\\nfactors of 2 and $\\\\pi$. In the inflationary model, the huge\\nnumber of particles is explained naturally by the exponential\\nexpansion, which reduces the problem to explaining 60 or 70\\ne-foldings of inflation. In fact, it is easy to construct\\nunderlying particle theories that will give far more than 70\\ne-foldings, suggesting that the observed universe is only a tiny\\nspeck within the universe as a whole.\\n\\n\\\\subhead{2) The Hubble expansion}\\n\\nThe Hubble expansion is also easy to take for granted, since it\\nis so familiar. In standard FRW cosmology, the Hubble expansion\\nis part of the list of postulates that define the initial\\nconditions. But inflation offers an explanation of how the\\nHubble expansion began. The repulsive gravity associated with\\nthe false vacuum is exactly the kind of force needed to propel\\nthe universe into a pattern of motion in which any two particles\\nare moving apart with a velocity proportional to their\\nseparation.\\n\\n\\\\subhead{3) Homogeneity and isotropy}\\n\\nThe degree of uniformity in the universe is startling. Through\\ncareful measurements of the cosmic background radiation, we know\\nthat the intensity of this radiation is the same in all\\ndirections to an accuracy of 1 part in 100,000. To get some\\nfeeling for how high this precision is, we can imagine a marble\\nthat is spherical to this accuracy. The surface of the\\nmarble would have to be shaped with a tolerance of about 1,000\\nangstroms, a quarter of the wavelength of light. \\n\\nAlthough precision lenses can be ground to quarter-wavelength\\naccuracy, we would nonetheless be shocked if we ever dug up a\\nstone from the ground that was round to this extraordinary\\naccuracy. If such a stone were somehow found, I am confident\\nthat we would not accept an explanation of its origin which\\nsimply proposed that the stone started out perfectly round. \\nSimilarly, in the current era, I do not think it makes sense to\\nconsider any theory of cosmogenesis that cannot offer some\\nexplanation of how the universe became so incredibly isotropic. \\n\\nThe uniformity of the cosmic background radiation implies that\\nthe observed universe had become uniform in temperature by about\\n300,000 years after the big bang, when the universe cooled enough\\nso that the opaque plasma neutralized into a transparent gas. In\\nstandard FRW cosmology, the uniformity could be established by\\nthis time only if signals could propagate 100 times faster than\\nlight, which is not possible. In inflationary cosmology,\\nhowever, the uniformity can be created initially on microscopic\\nscales, by normal thermal-equilibrium processes. Then inflation\\ntakes over and stretches the regions of uniformity to become\\nlarge enough to encompass the observed universe.\\n\\n\\\\subhead{4) The flatness problem}\\n\\nI find the flatness problem particularly impressive, because the\\nnumbers that it leads to are so extraordinary. The problem\\nconcerns the value of the ratio\\n\\\\beq\\n \\\\Omega_\\\\tot \\\\equiv {\\\\rho_\\\\tot \\\\over \\\\rho_c} \\\\ ,\\n \\\\label{eq:3.1}\\n\\\\eeq\\nwhere $\\\\rho_\\\\tot$ is the average total mass density of the\\nuniverse and $\\\\rho_c = 3 H^2 / 8 \\\\pi G$ is the critical density,\\nthe density that would make the universe spatially flat. \\n($\\\\rho_\\\\tot$ includes any vacuum energy $\\\\rho_{\\\\rm vac} =\\n\\\\Lambda/ 8 \\\\pi G$ associated with the cosmological constant\\n$\\\\Lambda$, if it is nonzero.)\\n\\nThe present value of $\\\\Omega_\\\\tot$ satisfies\\n\\\\beq\\n 0.1 \\\\lta \\\\Omega_{\\\\tot,0} \\\\lta 2 \\\\ ,\\n \\\\label{eq:3.2}\\n\\\\eeq\\nbut the precise value is not known. Despite the breadth of this\\nrange, the value of $\\\\Omega_\\\\tot$ at early times is highly\\nconstrained, since $\\\\Omega_\\\\tot=1$ is an unstable equilibrium\\npoint of the standard model evolution. If $\\\\Omega_\\\\tot$ was ever\\n{\\\\it exactly} equal to one, it would remain so forever. However,\\nif $\\\\Omega_\\\\tot$ differed slightly from 1 in the early universe,\\nthat difference---whether positive or negative---would be\\namplified with time. In particular, the FRW equations imply that\\n$\\\\Omega_\\\\tot - 1$ grows as\\n\\\\beq\\n \\\\Omega_\\\\tot - 1 \\\\propto \\\\cases{t &(during the\\n radiation-dominated era)\\\\cr \\n t^{2/3} &(during the matter-dominated era)\\\\ .\\\\cr}\\n \\\\label{eq:3.3}\\n\\\\eeq\\nAt $t=1$ sec, for example, Dicke and Peebles \\\\cite{dicke} pointed\\nout that $\\\\Omega_\\\\tot$ must have equaled one to an accuracy of\\none part in $10^{15}$. Classical cosmology provides no\\nexplanation for this fact---it is simply assumed as part of the\\ninitial conditions. In the context of modern particle theory,\\nwhere we try to push things all the way back to the Planck time,\\n$10^{-43}$ sec, the problem becomes even more extreme. At this\\ntime $\\\\Omega_\\\\tot$ must have equaled one to 58 decimal places!\\n\\nWhile this extraordinary flatness of the early universe has no\\nexplanation in classical FRW cosmology, it is a natural\\nprediction for inflationary cosmology. During the inflationary\\nperiod, instead of $\\\\Omega_\\\\tot$ being driven away from 1 as\\ndescribed by Eq.~(\\\\ref{eq:3.3}), $\\\\Omega_\\\\tot$ is driven towards\\n1, with exponential swiftness:\\n\\\\beq\\n \\\\Omega_\\\\tot - 1 \\\\propto e^{-2 H_{\\\\rm inf} t} \\\\ ,\\n \\\\label{eq:3.4}\\n\\\\eeq\\nwhere $H_{\\\\rm inf}$ is the Hubble parameter during inflation. \\nThus, as long as there is enough inflation, $\\\\Omega_\\\\tot$ can\\nstart at almost any value, and it will be driven to unity by the\\nexponential expansion. \\n\\n\\\\subhead{5) Absence of magnetic monopoles}\\n\\nAll grand unified theories predict that there should be, in the\\nspectrum of possible particles, extremely massive magnetic\\nmonopoles. By combining grand unified theories\\nwith classical cosmology without inflation, Preskill\\n\\\\cite{preskill} found that magnetic monopoles would be produced\\nso copiously that they would outweigh everything else in the\\nuniverse by a factor of about $10^{12}$. A mass density this\\nlarge would cause the inferred age of the universe to drop to\\nabout 30,000 years! In inflationary models, the monopoles can be\\neliminated simply by arranging the parameters so that inflation\\ntakes place after (or during) monopole production, so the\\nmonopole density is diluted to a completely negligible level.\\n\\n\\\\subhead{6) Anisotropy of the cosmic background radiation}\\n\\nThe process of inflation smooths the universe essentially\\ncompletely, but quantum fluctuations of the inflaton field can\\ngenerate density fluctuations as inflation ends. Generically\\nthese are adiabatic Gaussian fluctuations with a nearly\\nscale-invariant spectrum \\\\cite{Starobinsky2, GuthPi, Hawking1,\\nBST, BFM}. New data is arriving quickly, but so far the\\nobservations are in excellent agreement with the predictions of\\nthe simplest inflationary models. For a review, see for example\\nBond and Jaffe \\\\cite{bond-jaffe}, who find that the combined data\\ngive a slope of the primordial power spectrum within 5\\\\% of the\\npreferred scale-invariant value.\\n\\n\\n% Section IV:\\n\\\\section{Eternal Inflation: Mechanisms}\\n\\\\setcounter{equation}{0}\\n\\nHaving discussed the mechanisms and the motivation for inflation\\nitself, I now wish to move on the main issue that I want to\\nstress in this article---eternal inflation, the questions that it\\ncan answer, and the questions that it raises. In this section I\\nwill discuss the mechanisms that make eternal inflation possible,\\nleaving the other issues for the following sections. I will\\ndiscuss eternal inflation first in the context of new inflation,\\nand then in the context of chaotic inflation, where it is more\\nsubtle. \\n\\n\\\\subhead{Eternal New Inflation:}\\n\\nThe eternal nature of new inflation was first discovered by\\nSteinhardt \\\\cite{steinhardt-nuffield} and Vilenkin\\n\\\\cite{vilenkin-eternal} in 1983. Although the false vacuum is a\\nmetastable state, the decay of the false vacuum is an exponential\\nprocess, very much like the decay of any radioactive or unstable\\nsubstance. The probability of finding the inflaton field at the\\ntop of the plateau in its potential energy diagram does not fall\\nsharply to zero, but instead trails off exponentially with time\\n\\\\cite{guth-pi2}. However, unlike a normal radioactive substance\\nsuch as radium, the false vacuum exponentially expands at the\\nsame time that it decays. In fact, in any successful inflationary\\nmodel the rate of exponential expansion is always much faster\\nthan the rate of exponential decay. Therefore, even though the\\nfalse vacuum is decaying, it never disappears, and in fact the\\ntotal volume of the false vacuum, once inflation starts,\\ncontinues to grow exponentially with time, ad infinitum. \\n\\n\\\\begin{figure}[ht]\\n\\\\centerline{\\\\epsfbox{eternpr.eps}}\\n\\\\caption{A schematic illustration of eternal inflation.} \\n\\\\label{eternalline}\\n\\\\end{figure}\\n\\nFig.~\\\\ref{eternalline} shows a schematic diagram of an eternally\\ninflating universe. The top bar indicates a region of false\\nvacuum. The evolution of this region is shown by the successive\\nbars moving downward, except that I could not show the expansion\\nand still fit all the bars on the page. So the region is shown\\nas having a fixed size in comoving coordinates, while the scale\\nfactor, which is not shown, increases from each bar to the next. \\nAs a concrete example, suppose that the scale factor for each bar\\nis three times larger than for the previous bar. If we follow\\nthe region of false vacuum indicated by the top bar as it evolves\\ninto the second bar, in about one third of the region the scalar\\nfield rolls down the hill of the potential energy diagram,\\nprecipitating a local big bang that will evolve into something\\nthat will eventually appear to its inhabitants as a universe. \\nThis local big bang region is shown in gray and labeled\\n``Universe.'' Meanwhile, however, the space has expanded so much\\nthat each of the two remaining regions of false vacuum is the\\nsame size as the starting region. Thus, if we follow the region\\nfor another time interval of the same duration, each of these\\nregions of false vacuum will break up, with about one third of\\neach evolving into a local universe, as shown on the third bar\\nfrom the top. Now there are four remaining regions of false\\nvacuum, and again each is as large as the starting region. This\\nprocess will repeat itself literally forever, producing a kind of\\na fractal structure to the universe, resulting in an infinite\\nnumber of the local universes shown in gray. These local\\nuniverses are often called {\\\\it bubble universes,} but that\\nterminology conveys the unfortunate connotation that the local\\nuniverses are spherical. While bubbles formed in first-order\\nphase transitions are round \\\\cite{coleman-deluccia}, the local\\nuniverses formed in eternal new inflation are generally very\\nirregular, as can be seen for example in the two-dimensional\\nsimulation by Vanchurin, Vilenkin, and Winitzki in Fig.~2 of\\nRef.~\\\\cite{vvw}. I therefore prefer to call them {\\\\it pocket\\nuniverses,} to try to avoid the suggestion that they are round.\\n\\nThe diagram in Fig.~\\\\ref{eternalline} is of course an\\nidealization. The real universe is three dimensional, while the\\ndiagram illustrates a schematic one-dimensional universe. It is\\nalso important that the decay of the false vacuum is really a\\nrandom process, while I constructed the diagram to show a very\\nsystematic decay, because it is easier to draw and to think\\nabout. When these inaccuracies are corrected, we are still left\\nwith a scenario in which inflation leads asymptotically to a\\nfractal structure \\\\cite{aryal-vilenkin} in which the universe as\\na whole is populated by pocket universes on arbitrarily small\\ncomoving scales. Of course this fractal structure is entirely on\\ndistance scales much too large to be observed, so we cannot\\nexpect astronomers to actually find it. Nonetheless, one does\\nhave to think about the fractal structure if one wants to\\nunderstand the very large scale structure of the spacetime\\nproduced by inflation. \\n\\nMost important of all is the simple statement that once inflation\\nbegins, it produces not just one universe, but an infinite\\nnumber of universes. \\n\\n\\\\subhead{Eternal Chaotic Inflation:}\\n\\nThe eternal nature of new inflation depends crucially on the\\nscalar field lingering at the top of the plateau of\\nFig.~\\\\ref{newinf}. Since the potential function for chaotic\\ninflation, Fig.~\\\\ref{chaoticinf}, has no plateau, it does not\\nseem likely that eternal inflation can happen in this context. \\nNonetheless, Andrei Linde \\\\cite{linde-eternal} showed in 1986\\nthat chaotic inflation can also be eternal. \\n\\nThe key to eternal chaotic inflation is the role of quantum\\nfluctuations, which is very significant in all inflationary\\nmodels. Quantum fluctuations are invariably important on very\\nsmall scales, and with inflation these very small scales are\\nrapidly stretched to become macroscopic and even astronomical. \\nThus the quantum fluctuations of the inflaton field can have very\\nnoticeable effects.\\n\\n\\\\begin{figure}[ht]\\n\\\\epsfxsize=275pt % Reduced 69.4%\\n\\\\centerline{\\\\epsfbox{eipot2.eps}}\\n\\\\caption{Evolution of the inflaton field during eternal chaotic\\ninflation.} \\n\\\\label{chaotic-eternal}\\n\\\\end{figure}\\n\\nWhen the mass of the scalar field is small compared to the Hubble\\nparameter $H$, these quantum evolution of the scalar field is\\naccurately described as a random walk. It is useful to divide\\nspace into regions of physical size $H^{-1}$, and to discuss the\\naverage value of the scalar field $\\\\phi$ within a given region. \\nIn a time $H^{-1}$, the quantum fluctuations cause the scalar\\nfield to undergo a random Gaussian jump of zero mean and a\\nroot-mean-squared magnitude\\n\\\\cite{random-vil-ford,random-linde,Starobinsky2,random-starobinsky}\\ngiven by\\n\\\\beq\\n \\\\Delta \\\\phi_{\\\\rm qu} = {H \\\\over 2 \\\\pi} \\\\ .\\n \\\\label{eq:4.1}\\n\\\\eeq\\nThis random quantum jump is superimposed on the classical motion,\\nas indicated in Fig.~(\\\\ref{chaotic-eternal}).\\n\\nTo illustrate how eternal inflation happens in the simplest\\ncontext, let us consider again the free scalar field described by\\nthe potential function of Eq.~(\\\\ref{eq:2.1}). We consider a\\nregion of physical radius $H^{-1}$, in which the field has an\\naverage value $\\\\phi$. Using Eq.~(\\\\ref{eq:2.9}) along with\\nEqs.~(\\\\ref{eq:2.8}) and (\\\\ref{eq:2.1}), one finds that the\\nmagnitude of the classical change that the field will undergo in\\na time $H^{-1}$ is given in by\\n\\\\beq\\n \\\\Delta \\\\phi_{\\\\rm cl} = {M_{\\\\rm P} m \\\\over \\\\sqrt{12 \\\\pi}} \\\\, H^{-1} =\\n {1 \\\\over 4 \\\\pi} {M_{\\\\rm P}^2 \\\\over \\\\phi} \\\\ .\\n \\\\label{eq:4.2}\\n\\\\eeq\\nLet $\\\\phi^*$ denote the value of $\\\\phi$ which is\\nlarge enough so that\\n\\\\beq\\n \\\\Delta \\\\phi_{\\\\rm qu} (\\\\phi^*) = \\\\Delta \\\\phi_{\\\\rm cl}(\\\\phi^*) \\\\ ,\\n \\\\label{eq:4.3}\\n\\\\eeq\\nwhich implies that\\n\\\\beq\\n \\\\phi^* = \\\\left( {3 \\\\over 16 \\\\pi} \\\\right)^{1/4} {M_{\\\\rm P}^{3/2} \\\\over\\n m^{1/2}} \\\\ .\\n \\\\label{eq:4.4}\\n\\\\eeq\\n\\nNow consider what happens to a region for which the initial\\naverage value of $\\\\phi$ is equal to $\\\\phi^*$. In a time interval\\n$H^{-1}$, the volume of the region will increase by $e^3 \\\\approx\\n20$. At the end of the time interval we can divide the original\\nregion into 20 regions of the same volume as the original, and in\\neach region the average scalar field can be written as\\n\\\\beq\\n \\\\phi = \\\\phi^* + \\\\Delta \\\\phi_{\\\\rm cl} + \\\\delta \\\\phi \\\\ ,\\n \\\\label{eq:4.5}\\n\\\\eeq\\nwhere $\\\\delta \\\\phi$ denotes the random quantum jump, which is\\ndrawn from a Gaussian probability distribution with standard\\ndeviation $\\\\Delta \\\\phi_{\\\\rm qu} = \\\\Delta \\\\phi_{\\\\rm cl}$. \\nGaussian statistics imply that there is a 15.9\\\\% chance that a\\nGaussian random variable will exceed its mean by more than one\\nstandard deviation, and therefore there is a 15.9\\\\% chance that\\nthe net change in $\\\\phi$ will be positive. Since there are now\\n20 regions of the original volume, on average the value of $\\\\phi$\\nwill exceed the original value in 3.2 of these regions. Thus the\\nvolume for which $\\\\phi \\\\ge \\\\phi^*$ does not (on average)\\ndecrease, but instead increases by more than a factor of 3. \\nSince this argument can be repeated, the expectation value of the\\nvolume for which $\\\\phi \\\\ge \\\\phi^*$ increases exponentially with\\ntime. Typically, therefore, inflation never ends, but instead\\nthe volume of the inflating region grows exponentially without\\nbound. The minimum field value for eternal inflation is a little\\nbelow $\\\\phi^*$, since a volume increase by a factor of 3.2 is\\nmore than necessary---any factor greater than one would be\\nsufficient. A short calculation shows that the minimal value for\\neternal inflation is $0.78 \\\\phi^*$.\\n\\nWhile the value of $\\\\phi^*$ is larger than Planck scale, again we\\nfind that this is not true of the energy density:\\n\\\\beq\\n V(\\\\phi^*) = {1 \\\\over 2} m^2 \\\\phi^{*2} = \\\\sqrt{3 \\\\over 64 \\\\pi}\\n \\\\, m M_{\\\\rm P}^3 \\\\ ,\\n \\\\label{eq:4.6}\\n\\\\eeq\\nwhich for $m = 10^{16}$ GeV gives an energy density of $1 \\\\times\\n10^{-4} \\\\, M_{\\\\rm P}^4$. \\n\\nIf one carries out the same analysis with a potential function\\n\\\\beq\\n V(\\\\phi) = {1 \\\\over 4} \\\\lambda \\\\phi^4 \\\\ ,\\n \\\\label{eq:4.7}\\n\\\\eeq\\none finds \\\\cite{linde-book} that\\n\\\\beq\\n \\\\phi^* = \\\\left( 3 \\\\over 2 \\\\pi \\\\lambda \\\\right)^{1/6} M_{\\\\rm P} \\\\ ,\\n \\\\label{eq:4.8}\\n\\\\eeq\\nand\\n\\\\beq\\n V(\\\\phi^*) = \\\\left( 3 \\\\over 16 \\\\pi \\\\right)^{2/3} \\\\lambda^{1/3}\\n M_{\\\\rm P}^4 \\\\ .\\n \\\\label{eq:4.9}\\n\\\\eeq\\nSince $\\\\lambda$ must be very small in any case so that\\ndensity perturbations are not too large, one finds again that\\neternal inflation is predicted to happen at an energy density well\\nbelow the Planck scale.\\n\\n% Section V:\\n\\\\section{Eternal Inflation: Implications}\\n\\\\setcounter{equation}{0}\\n\\\\label{implications}\\n\\nWhen I told Rocky Kolb that I was going to be talking about\\neternal inflation, he said, ``That's OK, we can talk about\\nphysics later.'' So that's the point I'd like to address here. \\nIn spite of the fact that the other universes created by eternal\\ninflation are too remote to imagine observing directly, I still\\nbelieve that eternal inflation has real consequences in terms of\\nthe way we extract predictions from theoretical models. \\nSpecifically, there are four consequences of eternal inflation\\nthat I will highlight.\\n \\n\\\\subhead{1) Unobservability of initial conditions}\\n\\nFirst, eternal inflation implies that all hypotheses about the\\nultimate initial conditions for the universe---such as the\\nHartle-Hawking \\\\cite{hartle-hawking} no boundary proposal, the\\ntunneling proposals by Vilenkin \\\\cite{tunnel-vilenkin} or Linde\\n\\\\cite{tunnel-linde}, or the more recent Hawking-Turok instanton\\n\\\\cite{hawking-turok}---become totally divorced from observation.\\nThat is, one would expect that if inflation is to continue\\narbitrarily far into the future with the production of an\\ninfinite number of pocket universes, then the statistical\\nproperties of the inflating region should approach a steady state\\nwhich is independent of the initial conditions. Unfortunately,\\nattempts to quantitatively study this steady state are severely\\nlimited by several factors. First, there are ambiguities in\\ndefining probabilities, which will be discussed later. In\\naddition, the steady state properties seem to depend strongly on\\nsuper-Planckian physics which we do not understand. That is, the\\nsame quantum fluctuations that make eternal chaotic inflation\\npossible tend to drive the scalar field further and further up\\nthe potential energy curve, so attempts to quantify the steady\\nstate probability distribution \\\\cite{LLM,GBLinde} require the\\nimposition of some kind of a boundary condition at large $\\\\phi$. \\nAlthough these problems remain unsolved, I still believe that it\\nis reasonable to assume that in the course of its perpetual\\nevolution, an eternally inflating universe would lose all memory\\nof the state in which it started.\\n\\nAlthough the ultimate origin of the universe would become\\nunobservable, I would not expect that the question of how the\\nuniverse began would lose its interest. While eternally\\ninflating universes continue forever once they start, they are\\npresumably not eternal into the past. (The word {\\\\it eternal} is\\ntherefore not technically correct---it would be more precise to\\ncall this scenario {\\\\it semi-eternal} or {\\\\it future-eternal}.) \\nWhile the issue is not completely settled, it appears likely that\\neternally inflating universes must necessarily have a beginning. \\nBorde and Vilenkin \\\\cite{borde-vilenkin} have shown, provided\\nthat certain conditions are met, that spacetimes which are\\nfuture-eternal must have an initial singularity, in the sense\\nthat they cannot be past null geodesically complete. The proof,\\nhowever, requires the weak energy condition, which is classically\\nvalid but quantum-mechanically violated \\\\cite{borde-vilenkin2}. \\nIn any case, I am not aware of any viable model without a\\nbeginning, and certainly nothing that we know can rule out the\\npossibility of a beginning. The possibility of a quantum origin\\nof the universe is very attractive, and will no doubt be a\\nsubject of interest for some time. Eternal inflation, however,\\nseems to imply that the entire study will have to be conducted\\nwith literally no input from observation. \\n\\n\\\\subhead{2) Irrelevance of initial probability}\\n\\nA second consequence of eternal inflation is that the\\nprobability of the onset of inflation becomes totally\\nirrelevant, provided that the probability is not identically zero.\\nVarious authors in the past have argued that one type of\\ninflation is more plausible than another, because the initial\\nconditions that it requires appear more likely to have occurred. \\nIn the context of eternal inflation, however, such arguments have\\nno significance.\\n\\nTo illustrate the insignificance of the probability of the onset\\nof inflation, I will use a numerical example. We will imagine\\ncomparing two different versions of inflation, which I will call\\nType A and Type B\\\\relax. They are both eternally inflating---but\\nType A will have a higher probability of starting, while Type B\\nwill be a little faster in its exponential expansion rate. Since\\nI am trying to show that the higher starting probability of Type\\nA is irrelevant, I will choose my numbers to be extremely\\ngenerous to Type A\\\\relax. First, we must choose a number for how\\nmuch more probable it is for Type A inflation to begin, relative\\nto type B\\\\relax. A googol, $10^{100}$, is usually considered a\\nlarge number---it is some 20 orders of magnitude larger than the\\ntotal number of baryons in the visible universe. But I will be\\nmore generous: I will assume that Type A inflation is more likely\\nto start than type B inflation by a factor of $10^{1,000,000}$. \\nType B inflation, however, expands just a little bit faster, say\\nby 0.001\\\\%. We need to choose a time constant for the\\nexponential expansion, which I will take to be a typical grand\\nunified theory scale, $\\\\tau = 10^{-37}$ sec. ($\\\\tau$ represents\\nthe time constant for the overall expansion factor, which takes\\ninto account both the inflationary expansion and the exponential\\ndecay of the false vacuum.) Finally, we need to choose a length\\nof time to let the system evolve. In principle this time\\ninterval is infinite (the inflation is eternal into the future),\\nbut to be conservative we will watch the system for only one\\nsecond.\\n\\nWe imagine setting up a statistical ensemble of universes at\\n$t=0$, with an expectation value for the volume of Type A\\ninflation exceeding that of Type B inflation by $10^{1,000,000}$. \\nFor brevity, let the term ``weight'' to refer to the ensemble\\nexpectation value of the volume. Thus, the weights of Type A\\ninflation and Type B inflation will begin with the ratio\\n\\\\beq\\n \\\\left.{W_B \\\\over W_A}\\\\right|_{t=0} = 10^{-1,000,000} \\\\ .\\n \\\\label{eq:5.1}\\n\\\\eeq\\nAfter one second of evolution, the expansion factors for Type A\\nand Type B inflation will be\\n\\\\begin{eqnarray}\\n \\\\label{eq:5.2}\\n Z_A & = & e^{t/\\\\tau} = e^{10^{37}} \\\\\\\\\\n \\\\label{eq:5.3}\\n Z_B & = & e^{1.00001\\\\,t/\\\\tau} = e^{0.00001\\\\,t/\\\\tau} Z_A\\n \\\\nonumber \\\\\\\\\\n & = & e^{10^{32}} Z_A \\\\approx 10^{4.3 \\\\times 10^{31}} Z_A \\n \\\\ .\\n\\\\end{eqnarray}\\nThe weights at the end of one second are proportional to these\\nexpansion factors, so\\n\\\\beq\\n \\\\left.{W_B \\\\over W_A}\\\\right|_{t=1\\\\ \\\\rm sec} = 10^{\\\\left(4.3\\n \\\\times 10^{31} - 1,000,000\\\\right)} \\\\ .\\n \\\\label{eq:5.4}\\n\\\\eeq\\nThus, the initial ratio of $10^{1,000,000}$ is vastly superseded\\nby the difference in exponential expansion factors. In fact, we\\nwould have to calculate the exponent of Eq.~(\\\\ref{eq:5.4}) to an\\naccuracy of 25 significant figures to be able to barely detect\\nthe effect of the initial factor of $10^{1,000,000}$. \\n\\nOne might criticize the above argument for being naive, as the\\nconcept of time was invoked without any discussion of how the\\nequal-time hypersurfaces are to be chosen. I do not know a\\ndecisive answer to this objection; as I will discuss later, there\\nare unresolved questions concerning the calculation of\\nprobabilities in eternally inflating spacetimes. Nonetheless,\\ngiven that there is actually an infinity of time available, it is\\nseems reasonable to believe that the form of inflation that\\nexpands the fastest will always dominate over the slower forms by\\nan infinite factor.\\n\\nA corollary to this argument is that new inflation is not dead. \\nWhile the initial conditions necessary for new inflation cannot\\nbe justified on the basis of thermal equilibrium, as proposed in\\nthe original papers \\\\cite{Linde1,Albrecht-Steinhardt1}, in the\\ncontext of eternal inflation it is sufficient to conclude that\\nthe probability for the required initial conditions is nonzero. \\nSince the resulting scenario does not depend on the words that\\nare used to justify the initial state, the standard treatment of\\nnew inflation remains valid.\\n\\n\\\\subhead{3) Inevitability of eternal inflation}\\n\\nThird, I'd like to claim that, since it appears that a universe\\nis in principle capable of eternally reproducing, it is hard to\\nbelieve that any other description can make sense at all. To\\nclarify this point, let me raise the analogy of rabbits. We all\\nknow that rabbits can reproduce---in fact, they reproduce like\\nrabbits. Suppose that you went out into the woods and found a\\nrabbit that had characteristics indicating that it did not belong\\nto any known rabbit species. Then you would have to theorize\\nabout how the rabbit originated. You might entertain the notion\\nthat the rabbit was created by some unique, mysterious, cosmic\\nevent that you hope to someday understand better. Or you could\\nassume that the rabbit was created by the process of rabbit\\nreproduction that we all know so well. I think that we would all\\nconsider the latter possibility to be far more plausible. So, I\\nclaim that once we become convinced that universes can reproduce\\nlike rabbits, then the situations are similar. When we notice\\nthat there is a universe and ask how it originated, the same\\ninferences that we made for the rabbit question should apply to\\nthis one.\\n\\n\\\\subhead{4) Possibility of restoring the uniqueness of\\ntheoretical predictions}\\n\\nA fourth consequence of eternal inflation is the possibility that\\nit offers to rescue the predictive power of theoretical physics. \\nAll the indications suggest that string theory or M theory\\ndescribes an elegantly unique theoretical structure, but\\nnonetheless it seem unlikely that the theory possesses a unique\\nvacuum. Since predictions will ultimately depend on the\\nproperties of the vacuum, the predictive power of string/M theory\\nmay be limited. Eternal inflation, however, provides a hope that\\nthis problem can be remedied. Even if many types of vacua are\\nequally stable, it may turn out that a unique state produces the\\nmaximum possible rate of inflation. If so, then this state will\\ndominate the universe, even if its expansion rate is only\\ninfinitesimally larger than the other possibilities. Thus,\\neternal inflation might allow physicists to extract unique\\npredictions, in spite of the multiplicity of stable vacua.\\n\\n% Section VI:\\n\\\\section{Difficulties in Calculating Probabilities}\\n\\\\setcounter{equation}{0}\\n\\nIn an eternally inflating universe, anything that can happen will\\nhappen; in fact, it will happen an infinite number of times. Thus,\\nthe question of what is possible becomes trivial---anything is\\npossible, unless it violates some absolute conservation law. To\\nextract predictions from the theory, we must therefore learn to\\ndistinguish the probable from the improbable.\\n\\nHowever, as soon as one attempts to define probabilities in an\\neternally inflating spacetime, one discovers ambiguities. Since\\nan eternally inflating universe produces an infinite number of\\npocket universes, the sample space is infinite. The fraction of\\nuniverses with any particular property is given by the\\nmeaningless ratio of infinity divided by infinity. To obtain a\\nwell-defined answer, one needs to invoke some method of\\nregularization. The most straightforward form of regularization\\nconsists of truncating the space to a finite subspace, and then\\ntaking a limit in which the subspace becomes larger and larger.\\n\\nTo understand the nature of the problem, it is useful to think\\nabout the integers as a model system with an infinite number of\\nentities. We can ask, for example, what fraction of the integers\\nare odd. Most people would presumably say that the answer is\\n$1/2$, since the integers alternate between odd and even. That\\nis, if the string of integers is truncated after the $N$th, then\\nthe fraction of odd integers in the string is exactly $1/2$ if\\n$N$ is even, and is $(N+1)/2N$ if $N$ is odd. In any case, the\\nfraction approaches $1/2$ as $N$ approaches infinity.\\n\\nHowever, the ambiguity of the answer can be seen if one imagines\\nother orderings for the integers. One could, if one wished,\\norder the integers as \\n\\\\beq\\n 1,3,\\\\ 2,\\\\ 5,7,\\\\ 4,\\\\ 9,11,\\\\ 6\\\\ ,\\\\ldots, \\n \\\\label{eq:6.1}\\n\\\\eeq\\nalways writing two odd integers followed by one even integer. \\nThis series includes each integer exactly once, just like the\\nusual sequence ($1,2,3,4, \\\\ldots$). The integers are just\\narranged in an unusual order. However, if we truncate the\\nsequence shown in Eq.~(\\\\ref{eq:6.1}) after the $N$th entry, and\\nthen take the limit $N \\\\to \\\\infty$, we would conclude that 2/3 of\\nthe integers are odd. Thus, we see that probabilities can\\ndepend nontrivially on the method of regularization that is used.\\n\\nIn the case of eternally inflating spacetimes, one might consider\\na regularization defined by ordering the pocket universes in the\\nsequence in which they form, and then truncating after the $N$th. \\nHowever, each pocket universe fills its own future light cone, so\\nno pocket universe forms in the future light cone of another. \\nAny two pocket universes are spacelike separated from each other,\\nso different observers can disagree about which formed first. \\nOne can arbitrarily choose equal-time surfaces that foliate the\\nspacetime, and then truncate at some value of $t$, but this\\nrecipe is far from unique. In practice, different ways of\\nchoosing equal-time surfaces give different results. \\n\\n% Section VII\\n\\\\section{The Youngness Paradox}\\n\\\\setcounter{equation}{0}\\n\\nIf one chooses a regularization in the most naive way, one is led\\nto a set of very peculiar results which I call the {\\\\it youngness\\nparadox.} \\n\\nSpecifically, suppose that one constructs a Robertson-Walker\\ncoordinate system while the model universe is still in the false\\nvacuum (de Sitter) phase, before any pocket universes have\\nformed. One can then propagate this coordinate system forward\\nwith a synchronous gauge condition,\\\\footnote{By a synchronous\\ngauge condition, I mean that each equal-time hypersurface is\\nobtained by propagating every point on the previous hypersurface\\nby a fixed infinitesimal time interval $\\\\Delta t$ in the\\ndirection normal to the hypersurface.} and one can define\\nprobabilities by truncating at a fixed value $t_f$ of the\\nsynchronous time coordinate $t$. That is, the probability of any\\nparticular property can be taken to be proportional to the volume\\non the $t = t_f$ hypersurface which has that property. This\\nmethod of defining probabilities was studied in detail by Linde,\\nLinde, and Mezhlumian, in a paper with the memorable title ``Do\\nwe live in the center of the world?'' \\\\cite{center-world}. I\\nwill refer to probabilities defined in this way as synchronous\\ngauge probabilities.\\n\\nThe youngness paradox is caused by the fact that the volume of\\nfalse vacuum is growing exponentially with time with an\\nextraordinarily short time constant, in the vicinity of\\n$10^{-37}$ sec. Since the rate at which pocket universes form is\\nproportional to the volume of false vacuum, this rate is\\nincreasing exponentially with the same time constant. That means\\nthat in each second the number of pocket universes that exist is\\nmultiplied by a factor of $\\\\exp\\\\left\\\\{10^{37}\\\\right\\\\}$. At any\\ngiven time, therefore, almost all of the pocket universes that\\nexist are universes that formed very very recently, within the\\nlast several time constants. The population of pocket universes\\nis therefore an incredibly youth-dominated society, in which the\\nmature universes are vastly outnumbered by universes that have\\njust barely begun to evolve. Although a mature universe has a\\nlarger volume then a young one, this multiplicative factor is of\\nlittle importance, since in synchronous coordinates the volume no\\nlonger grows exponentially once the pocket universe forms.\\n\\nProbability calculations in this youth-dominated ensemble lead to\\npeculiar results, as discussed in Ref.~\\\\cite{center-world}. These\\nauthors considered the expected behavior of the mass density in\\nour vicinity, concluding that we should find ourselves very near\\nthe center of a spherical low-density region. Here I would like\\nto discuss a less physical but simpler question, just to\\nillustrate the paradoxes associated with synchronous gauge\\nprobabilities. Specifically, I will consider the question: ``Are\\nthere any other civilizations in the visible universe that are\\nmore advanced than ours?''. Intuitively I would not expect\\ninflation to make any predictions about this question, but I will\\nargue that the synchronous gauge probability distribution\\nstrongly implies that there is no civilization in the visible\\nuniverse more advanced than we are.\\n\\nSuppose that we have reached some level of advancement, and\\nsuppose that $t_{\\\\rm min}$ represents the minimum amount of time\\nneeded for a civilization as advanced as we are to evolve,\\nstarting from the moment of the decay of the false vacuum---the\\nstart of the big bang. The reader might object on the grounds\\nthat there are many possible measures of advancement, but I would\\nrespond by inviting the reader to pick any measure she chooses;\\nthe argument that I am about to give should apply to all of them. \\nThe reader might alternatively claim that there is no sharp\\nminimum $t_{\\\\rm min}$, but instead we should describe the problem\\nin terms of a function which gives the probability that, for any\\ngiven region within a pocket universe of the size of our visible\\nuniverse, a civilization as advanced as we are would develop by\\ntime $t$. I believe, however, that the introduction of such a\\nprobability distribution would merely complicate the argument,\\nwithout changing the result. So, for simplicity of discussion, I\\nwill assume that there is some sharply defined minimum time\\n$t_{\\\\rm min}$ required for a civilization as advanced as ours to\\ndevelop.\\n\\nSince we exist, our pocket universe must have an age $t_0$\\nsatisfying \\n\\\\beq\\n t_0 \\\\ge t_{\\\\rm min} \\\\ . \\n \\\\label{eq:7.1}\\n\\\\eeq\\nSuppose, however, that there is some civilization\\nin our visible universe that is more advanced than we are, let us\\nsay by 1 second. In that case Eq.~(\\\\ref{eq:7.1}) is not\\nsufficient, but instead the age of our pocket universe would have\\nto satisfy\\n\\\\beq\\n t_0 \\\\ge t_{\\\\rm min} + 1 \\\\hbox{\\\\ second}\\\\ . \\n \\\\label{eq:7.2}\\n\\\\eeq\\nHowever, in the synchronous gauge probability distribution,\\nuniverses that satisfy Eq.~(\\\\ref{eq:7.2}) are outnumbered by\\nuniverses that satisfy Eq.~(\\\\ref{eq:7.1}) by a factor of\\napproximately $\\\\exp\\\\left\\\\{10^{37}\\\\right\\\\}$. Thus, if we know\\nonly that we are living in a pocket universe that satisfies\\nEq.~(\\\\ref{eq:7.1}), the probability that it also satisfies\\nEq.~(\\\\ref{eq:7.2}) is approximately\\n$\\\\exp\\\\left\\\\{-10^{37}\\\\right\\\\}$. We would conclude, therefore,\\nthat it is extraordinarily improbable that there is a\\ncivilization in our visible universe that is at least 1 second\\nmore advanced than we are.\\n\\nPerhaps this argument explains why SETI has not found any signals\\nfrom alien civilizations, but I find it more plausible that it is\\nmerely a symptom that the synchronous gauge probability\\ndistribution is not the right one.\\n\\n% Section VIII\\n\\\\section{Toy Model of Eternal Inflation}\\n\\\\setcounter{equation}{0}\\n\\nThe conceptual issue involved in the youngness paradox can\\nperhaps be clarified by considering a toy model of a highly\\nsimplified eternally inflating universe. Suppose that the\\nuniverse as a whole can be labeled with a global time variable\\n$t$, and that it consists of a countably infinite set of pocket\\nuniverses, each of which is labeled by an index $i$. For\\nsimplicity, we let each pocket universe have zero spatial\\ndimensions, so a spacetime point is fully specified by the time\\n$t$ and the index $i$ which indicates the pocket universe in\\nwhich it is located. We assume that each pocket universe $i$\\nforms at some time $t_i = n_i \\\\tau$, where $n_i$ is an integer and\\n$\\\\tau$ is a fixed time constant characterizing the entire\\nuniverse. Let the number of pocket universes that form at time\\n$t = n \\\\tau$ be equal to $2^n$, for each nonnegative integer $n$. \\nAssume that each pocket universe exists for a time $T \\\\gg \\\\tau$,\\nand then disappears, and that within each pocket universe the\\ninterval from the time of formation to disappearance is uniformly\\npopulated with ``sentient beings.'' Within each pocket universe\\nwe can define a relative time, $t_{\\\\rm rel} \\\\equiv t - t_i$,\\nwhich measures the amount of time since the formation of the\\npocket universe. \\n\\nThe difficult question, then, is the following: At what relative\\ntime $t_{\\\\rm rel}$ does a {\\\\it typical} sentient being live? If\\none answers this question by truncating the spacetime by the\\ncriterion\\n\\\\beq\\n t \\\\le t_c \\\\ , \\n \\\\label{eq:8.1}\\n\\\\eeq\\nfor some cut-off time $t_c = n_c \\\\tau$, then one finds that most\\nof the pocket universes in the truncated spacetime formed within\\nthe past few time constants. As $t_c \\\\to \\\\infty$, the mean value\\nof $t_{\\\\rm rel}$ approaches $\\\\tau$. This method is analogous to\\nthe synchronous gauge cut-off discussed above. If, however, one\\ntruncates the spacetime by including all pocket universes for\\nwhich the time of formation\\n\\\\beq\\n t_i \\\\le t_c \\\\ , \\n \\\\label{eq:8.2}\\n\\\\eeq\\nthen the mean value of $t_{\\\\rm rel}$ is equal to $T/2$ for any\\n$t_c$. The truncation method of Eq.~(\\\\ref{eq:8.1}) leads to the\\nyoungness paradox, in which the probability sample is strongly\\ndominated by universes that are extremely young, while the\\ntruncation method of Eq.~(\\\\ref{eq:8.2}) does not.\\n\\nAt this point, I have to admit that I do not understand how to\\nresolve the ambiguities associated with this toy model. It is\\nconceivable that there is no meaningful method of regularization,\\nand that $t_{\\\\rm rel}$ is somehow not susceptible to\\nprobabilistic predictions. It is also conceivable that there is\\nsomething wrong with either the truncation (\\\\ref{eq:8.1}) or\\n(\\\\ref{eq:8.2}) or both, and that a correct analysis would lead to\\na unique probability calculation. It is also conceivable that\\nthe regularization has to be specified as part of the theory, so\\nthat the truncations (\\\\ref{eq:8.1}) and (\\\\ref{eq:8.2}) represent\\ntwo distinct theories, each of which is logically consistent.\\n\\n% Section IX\\n\\\\section{An Alternative Probability Prescription}\\n\\\\setcounter{equation}{0}\\n\\nSince the probability measure depends on the method used to\\nregulate the infinite spacetime of eternal inflation, we are not\\nforced to accept the consequences of the synchronous gauge\\nprobabilities. A very attractive alternative has been proposed\\nby Vilenkin \\\\cite{vilenkin-proposal}, and developed further by\\nVanchurin, Vilenkin, and Winitzki \\\\cite{vvw}. This procedure is,\\nroughly speaking, analogous to the truncation of\\nEq.~(\\\\ref{eq:8.2}). \\n\\nThe key idea of the Vilenkin proposal is to define probabilities\\nwithin a single pocket universe (which he describes more\\nprecisely as a connected, thermalized domain). Thus, unlike the\\nsynchronous gauge method, there is no comparison between old\\npocket universes and young ones. To justify this approach it is\\ncrucial to recognize that each pocket universe is infinite, even\\nif one starts the model with a finite region of de Sitter space. \\nThe infinite volume arises in the same way as it does for the\\nspecial case of Coleman-de Luccia bubbles\\n\\\\cite{coleman-deluccia}, the interior of which are open\\nRobertson-Walker universes. From the outside one often describes\\nsuch bubbles in a coordinate system in which they are finite at\\nany fixed time, but in which they grow without bound. On the\\ninside, however, the natural coordinate system is the one that\\nreflects the intrinsic homogeneity, in which the space is\\ninfinite at any given time. The infinity of time, as seen from\\nthe outside, becomes an infinity of spatial extent as seen on the\\ninside. Thus, at least for continuously variable parameters, a\\nsingle pocket universe provides an infinite sample space which\\ncan be used to define probabilities. The second key idea of\\nVilenkin's method is to use the inflaton field itself as the time\\nvariable, rather than the synchronous time variable discussed in\\nthe previous section.\\n\\nThis approach can be used, for example, to discuss the\\nprobability distribution for $\\\\Omega$ in open inflationary\\nmodels, or to discuss the probability distribution for some\\narbitrary field that has a flat potential energy function. If,\\nhowever, the vacuum has a discrete parameter which is homogeneous\\nwithin each pocket universe, but which takes on different values\\nin different pocket universes, then this method does not apply. \\n\\n\\\\begin{figure}[ht]\\n\\\\centerline{\\\\epsfbox{vilsp2.eps}}\\n\\\\caption{A schematic picture of a pocket universe, illustrating\\nVilenkin's proposal for the calculation of probabilities.} \\n\\\\label{vilenkin-space}\\n\\\\end{figure}\\n\\nThe proposal can be described in terms of\\nFig.~\\\\ref{vilenkin-space}. We suppose that the theory includes\\nan inflaton field $\\\\phi$ of the new inflation type, and some set\\nof fields $\\\\chi_i$ which have flat potentials. The goal is to\\nfind the probability distribution for the fields $\\\\chi_i$. We\\nassume that the evolution of the inflaton $\\\\phi$ can be divided\\ninto three regimes, as shown on the figure. $\\\\phi < \\\\phi_1$\\ndescribes the eternally inflating regime, in which the evolution\\nis governed by quantum diffusion. For $\\\\phi_1 < \\\\phi < \\\\phi_{\\\\rm\\nend}$, the evolution is described classically in a slow-roll\\napproximation, so that $\\\\dot \\\\phi \\\\equiv {\\\\rm d} \\\\phi / {\\\\rm d}\\nt$ can be expressed as a function of $\\\\phi$. For $\\\\phi >\\n\\\\phi_{\\\\rm end}$ inflation is over, and the $\\\\phi$ field no longer\\nplays an important role in the evolution. The $\\\\chi_i$ fields\\nare assumed to have a finite range of values, such as angular\\nvariables, so that a flat probability distribution is\\nnormalizable. They are assumed to have a flat potential energy\\nfunction for $\\\\phi > \\\\phi_{\\\\rm end}$, so that they could settle\\nat any value. They are also assumed to have a flat potential\\nenergy function for $\\\\phi < \\\\phi_1$, although they might interact\\nwith $\\\\phi$ during the slow-roll regime, however, so that they\\ncan affect the rate of inflation. \\n\\nSince the potential for the $\\\\chi_i$ is flat for $\\\\phi < \\\\phi_1$,\\nwe can assume that they begin with a flat probability\\ndistribution $P_0(\\\\chi_i) \\\\equiv P(\\\\chi_i, \\\\phi_1)$ on the $\\\\phi\\n= \\\\phi_1$ hypersurface. If the kinetic energy function for the\\n$\\\\chi_i$ is of the standard form, we take $P_0(\\\\chi_i) = const$. \\nIf, however, the kinetic energy is nonstandard,\\n\\\\beq\\n {\\\\cal L}_{\\\\rm kinetic} = g^{ij}(\\\\chi) \\\\partial_\\\\mu \\\\chi_i\\n \\\\partial^\\\\mu \\\\chi_j \\\\ ,\\n \\\\label{eq:9.1}\\n\\\\eeq\\nas is plausible for a field described in angular variables, then\\nthe initial probability distribution is assumed to take the\\nreparameterization-invariant form\\n\\\\beq\\n P_0(\\\\chi_i) \\\\propto \\\\sqrt{ \\\\det g} \\\\ .\\n \\\\label{eq:9.2}\\n\\\\eeq\\nDuring the slow-roll era, it is assumed that the $\\\\chi_i$ fields\\nevolve classically, so one can calculate the number of e-folds of\\ninflation $N(\\\\chi_i)$ as a function of the final value of the\\n$\\\\chi_i$ (i.e., the value of $\\\\chi_i$ on the $\\\\phi = \\\\phi_{\\\\rm\\nend}$ hypersurface). One can also calculate the final values\\n$\\\\chi_i$ in terms of the initial values $\\\\chi_i^0$ (i.e., the\\nvalue of $\\\\chi_i$ on the $\\\\phi=\\\\phi_1$ hypersurface). One then\\nassumes that the probability density is enhanced by the volume\\ninflation factor $e^{3 N (\\\\chi_i)}$. The evolution from\\n$\\\\chi_i^0$ to $\\\\chi_i$ results in a Jacobian factor. The\\n(unnormalized) final probability distribution is thus given by\\n\\\\beq\\n P(\\\\chi_i, \\\\phi_{\\\\rm end}) = P_0(\\\\chi_i^0) e^{3 N (\\\\chi_i)} \\\\,\\n \\\\det {\\\\partial \\\\chi_j^0 \\\\over \\\\partial \\\\chi_k} \\\\ .\\n \\\\label{eq:9.3}\\n\\\\eeq\\nAlternatively, if the evolution of the $\\\\chi_i$ during the\\nslow-roll era is subject to quantum fluctuations, Ref.~\\\\cite{vvw}\\nshows how to write a Fokker-Planck equation which is equivalent\\nto averaging the result of Eq.~(\\\\ref{eq:9.3}) over a collection of\\npaths that result from interactions with a noise term.\\n\\nThe Vilenkin proposal sidesteps the youngness paradox by defining\\nprobabilities by the comparison of volumes within one pocket\\nuniverse. The youngness paradox, in contrast, arose when one\\nconsidered a probability ensemble of all pocket universes at a\\nfixed value of the synchronous gauge time coordinate---an\\nensemble that is overwhelmingly dominated by very young pocket\\nuniverses.\\n\\nThe proposal has the drawback, however, that it cannot be used to\\ncompare the probabilities of discretely different alternatives. \\nFurthermore, although the results of this method seem\\nreasonable, I do not at this point find them compelling. That\\nis, it is not clear what principles of physics or probability\\ntheory ensure that this particular method of regularizing the\\nspacetime is the one that leads to correct predictions. Perhaps\\nthere is no way to answer this question, so we may be forced to\\naccept this proposal, or something similar to it, as a postulate.\\n\\n% Section X\\n\\\\section{Probabilities with only one universe?}\\n\\nIn discussing a probabilistic approach to cosmology, we need to\\nknow whether it makes sense to talk about a probability\\ndistribution for a cosmic parameter such as $\\\\Omega$, for which\\nwe have only one example to measure. I have certainly heard more\\nthan one physicist say that he or she doesn't think that one can\\nmeaningfully talk about probabilities for an experiment that can\\nbe done only once. The notion that probability requires\\nrepetition is very widespread, and I am sure that it is\\nincorporated into many books about probability theory. \\nNonetheless, I would like to argue that repetition is not at all\\nnecessary to make use of probability theory. Instead, I will\\nargue that probability is meaningful whenever one has a {\\\\it\\nstrong} probabilistic prediction, by which I mean a prediction\\nthat the probability for some discernible event is either very\\nclose to zero or very close to one.\\n\\nThus, if a cosmological theory predicts a probability\\ndistribution for $\\\\Omega$ which is reasonably flat, then there is\\nno strong prediction, and the implications of the theory for\\n$\\\\Omega$ do not provide a way of testing the theory. However, if\\nthe theory predicts that the probability of $\\\\Omega$ lying\\noutside the range of 0.99 to 1.01 is $10^{-6}$, then I would\\nclaim that the prediction is meaningful and can be used to test\\nthe theory.\\n\\nMy point of view can be explained most easily by considering coin\\nflips. If a flip of an unbiased coin is repeated 20 times, the\\nprobability of getting 20 successive heads is a very small\\nnumber, about $10^{-6}$. This is an example of what I call a\\nstrong prediction. Many common examples of strong predictions\\ninvolve repetition. However, if 20 unbiased coins are flipped\\nsimultaneously in a single experiment, the probability that all\\nwill come up heads is identical, about $10^{-6}$. Since the\\nprobability of these two results---20 successive heads or 20\\nsimultaneous heads---are both equally small, I would draw the\\nobvious conclusion that we should be equally surprised if either\\nresult occurred. It does not matter that the first result\\ninvolved repetition, while the second did not. Some might argue\\nthat the 20 simultaneous coin flips involved the replication of\\nidentical experiments, even if they were not performed in\\nsuccession, so I will take the analogy one step further. Suppose\\nwe constructed a roulette wheel that was so finely ruled that\\nthe probability of the ball landing on 0 was only $10^{-6}$. \\nAgain, we should be just as surprised if this result occurred as\\nwe would be if 20 successive coins landed heads.\\n\\nSimilarly, if our cosmological theory predicted that the\\nprobability of $\\\\Omega$ lying outside the range of 0.99 to 1.01\\nis $10^{-6}$, we should be just as surprised if this outcome\\noccurred as we would be if 20 consecutive coins came up heads. \\nIn both cases, we would have good cause to question the\\nassumptions that went into calculating the prediction.\\n\\n% Section X\\n\\\\section{Conclusion}\\n\\\\setcounter{equation}{0}\\n\\nIn this paper I have summarized the workings of inflation, and\\nthe arguments that strongly suggest that our universe is the\\nproduct of inflation. I argued that inflation can explain the \\nsize, the Hubble expansion, the homogeneity, the isotropy, and the\\nflatness of our universe, as well as the absence of magnetic\\nmonopoles, and even the characteristics of the nonuniformities. \\nThe detailed observations of the cosmic background radiation\\nanisotropies continue to fall in line with inflationary\\nexpectations, and the evidence for an accelerating universe fits\\nwell with the inflationary preference for a flat universe.\\n\\nNext I turned to the question of eternal inflation, claiming\\nthat essentially all inflationary models are eternal. In my opinion\\nthis makes inflation very robust: if it starts anywhere,\\nat any time in all of eternity, it produces an infinite number of\\npocket universes. Eternal inflation has the very attractive\\nfeature, from my point of view, that it offers the possibility of\\nallowing unique predictions even if the underlying string theory\\ndoes not have a unique vacuum. I have also emphasized, however,\\nthat there are important problems in understanding the\\nimplications of eternal inflation. First, there is the problem\\nthat we do not know how to treat the situation in which the\\nscalar field climbs upward to the Planck energy scale. Second,\\nthe definition of probabilities in an eternally inflating\\nspacetime is not yet a closed issue, although important progress\\nhas been made. And third, I might add that the entire present\\napproach is at best semiclassical. A better treatment may not be\\npossible until we have a much better handle on quantum gravity,\\nbut eventually this issue will have to be faced.\\n\\n\\\\section*{Acknowledgments}\\n\\nThe author particularly thanks Andrei Linde, Alexander Vilenkin,\\nNeil Turok, and other participants in the Isaac Newton Institute\\nprogramme {\\\\it Structure Formation in the Universe} for very\\nhelpful conversations. This work is supported in part by funds\\nprovided by the U.S. Department of Energy (D.O.E.) under\\ncooperative research agreement \\\\#DF-FC02-94ER40818, and in part\\nby funds provided by NM Rothschild \\\\& Sons Ltd and by the EPSRC.\\n\\n% Macros that control the format for all references:\\n\\\\newcommand{\\\\jf}{\\\\it} % Journal name font\\n\\\\newcommand{\\\\jt}{\\\\/} % Journal name spacing correction\\n % Replace by {} if Journal name font is not italics\\n\\\\newcommand{\\\\VPY}[3]{{\\\\bf #1}, #2 (#3)} % Volume Page Year\\n\\\\newcommand{\\\\ispace}{\\\\thinspace} % Space between multiple initials\\n\\n% Macro to implement the \\\\. command for spacing \\\\ispace between initials\\n% LaTeX uses \\\\.{o} for an o with an overdot, but I want to use \\\\. for\\n% periods separating multiple initials. Use \\\\U{o} for an o with an \\n% overdot:\\n\\\\let\\\\U=\\\\.\\n\\\\def\\\\.{.\\\\nobreak\\\\ispace\\\\ignorespaces}\\n\\n% Macros for individual journal names:\\n\\\\newcommand{\\\\IJMODPHYS}[3]{{\\\\jf Int. J. Mod. Phys.\\\\jt} \\\\VPY{#1}{#2}{#3}}\\n\\\\newcommand{\\\\JETP}[3]{{\\\\jf JETP Lett.\\\\jt} \\\\VPY{#1}{#2}{#3}}\\n\\\\newcommand{\\\\MPL}[3]{{\\\\jf Mod. Phys. Lett.\\\\jt} \\\\VPY{#1}{#2}{#3}}\\n\\\\newcommand{\\\\NC}[3]{{\\\\jf Nuovo Cim.\\\\jt} \\\\VPY{#1}{#2}{#3}}\\n\\\\newcommand{\\\\NP}[3]{{\\\\jf Nucl. Phys.\\\\jt} \\\\VPY{#1}{#2}{#3}}\\n\\\\newcommand{\\\\PHYREP}[3]{{\\\\jf Phys. Rept.\\\\jt} \\\\VPY{#1}{#2}{#3}}\\n\\\\newcommand{\\\\PL}[3]{{\\\\jf Phys. Lett.\\\\jt} \\\\VPY{#1}{#2}{#3}}\\n\\\\newcommand{\\\\PRD}[3]{{\\\\jf Phys. Rev. D\\\\jt} \\\\VPY{#1}{#2}{#3}}\\n\\\\newcommand{\\\\PRL}[3]{{\\\\jf Phys. Rev. Lett.\\\\jt} \\\\VPY{#1}{#2}{#3}}\\n\\\\newcommand{\\\\PTRSLA}[3]{{\\\\jf Phil. Trans. R. Soc. Lond.\\\\jt\\\\ A}\\n\\\\VPY{#1}{#2}{#3}}\\n\\\\newcommand{\\\\ZhETF}[3]{{\\\\jf Zh. Eksp. Teor. Fiz.\\\\jt} \\\\VPY{#1}{#2}{#3}}\\n\\n\\\\begin{thebibliography}{99}\\n\\n\\\\bibitem{Linde1}\\nA\\\\.D.~Linde, \\\\PL{108B}{389--393}{1982}.\\n% A New Inflationary Universe Scenario: A Possible Solution of the\\n% Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole\\n% Problems\\n\\n\\\\bibitem{Albrecht-Steinhardt1}\\nA.~Albrecht and P\\\\.J.~Steinhardt, \\\\PRL{48}{1220--1223}{1982}.\\n% Cosmology for Grand Unified Theories with Radiatively Induced\\n% Symmetry Breaking\\n\\n\\\\bibitem{chaotic}\\nA\\\\.D.~Linde, \\\\ZhETF{38}{149--151}{1983} [\\\\JETP{38}{176--179}{1983}];\\n% Chaotic inflating universe\\nA\\\\.D.~Linde, \\\\PL{129B}{177--181}{1983}.\\n% Chaotic inflation\\n\\n\\\\bibitem{hyb1} \\nA\\\\.D.~Linde, \\\\PL{B259}{38--47}{1991}.\\n% Axions in Inflationary Cosmology\\n\\n\\\\bibitem{hyb2}\\nA\\\\.R.~Liddle and D\\\\.H.~Lyth, \\\\PHYREP{231}{1--105}{1993},\\nastro-ph/9303019.\\n% The Cold Dark Matter Density Perturbation\\n\\n\\\\bibitem{hyb3}\\nA\\\\.D.~Linde, \\\\PRD{49}{748--754}{1994}, astro-ph/9307002.\\n% Hybrid Inflation\\n\\n\\\\bibitem{hyb4}\\nE\\\\.J.~Copeland, A\\\\.R.~Liddle, D\\\\.H.~Lyth, E\\\\.D.~Stewart, and\\nD.~Wands, \\\\PRD{49}{6410-6433}{1994}, astro-ph/9401011.\\n% False Vacuum Inflation with Einstein Gravity\\n\\n\\\\bibitem{hyb5}\\nE.~Stewart, \\\\PL{B345}{414--415}{1995}, astro-ph/9407040.\\n% Mutated Hybrid Inflation\\n\\n\\\\bibitem{RSG}\\nL.~Randall, M.~Solja\\\\v{c}i\\\\'{c}, and A\\\\.H.~Guth,\\n\\\\NP{B472}{377--408}{1996}, hep-ph/9512439; also hep-ph/9601296.\\n% Supernatural Inflation: Inflation from Supersymmetry\\n% with No (Very) Small Parameters\\n% Supernatural Inflation (hep-ph/9601296).\\n\\n\\\\bibitem{Guth1}\\nA\\\\.H.~Guth, \\\\PRD{23}{347--356}{1981}.\\n% The Inflationary Universe: A Possible Solution to the Horizon\\n% and Flatness Problems\\n\\n\\\\bibitem{Starobinsky}\\nA\\\\.A.~Starobinsky, \\\\ZhETF{30}{719}{1979} [\\\\JETP{30}{682}{1979}];\\nA\\\\.A.~Starobinsky, \\\\PL{91B}{99--102}{1980}.\\n% A New Type of Isotropic Cosmological Models without Singularity\\n% (yes, that really is ``Models''; reprinted in Abbott & Pi)\\n\\n\\\\bibitem{Coleman}\\nS.~Coleman, \\\\PRD{15}{2929--2936}{1977} [see errata\\n\\\\VPY{16}{1248}{1977}];\\n% The Fate of the False Vacuum. 1. Semiclassical Theory\\nC\\\\.G.~Callan and S.~Coleman,\\n\\\\PRD{16}{1762--1768}{1977}.\\n% The Fate of the False Vacuum. 2. First Quantum Corrections\\n\\n\\\\bibitem{HMS}\\nS\\\\.W.~Hawking, I\\\\.G.~Moss, and J\\\\.M.~Stewart,\\n\\\\PRD{26}{2681--2693}{1982}.\\n% Bubble Collisions in the Very Early Universe\\n\\n\\\\bibitem{GuthWeinberg}\\nA\\\\.H.~Guth and E\\\\.J.~Weinberg, \\\\NP{B212}{321--364}{1983}.\\n% Could the Universe Have Recovered from a Slow First Order Phase\\n% Transition?\\n\\n\\\\bibitem{Jensen-Stein-Schabes}\\nL\\\\.G. Jensen and J\\\\.A. Stein-Schabes, \\\\PRD{35}{1146--1150}{1987},\\nand references therein.\\n% Is inflation natural?\\n% Lars Gerhard Jensen and Jaime A. Stein-Schabes \\n\\n\\\\bibitem{Starobinsky2}\\nA\\\\.A.~Starobinsky, \\\\PL{117B}{175--178}{1982}.\\n% Dynamics of phase transition in the new inflationary universe\\n% scenario and generation of perturbations\\n\\n\\\\bibitem{GuthPi}\\nA\\\\.H.~Guth and S.-Y.~Pi, \\\\PRL{49}{1110--1113}{1982}.\\n% Fluctuations in the new inflationary universe\\n\\n\\\\bibitem{Hawking1}\\nS\\\\.W.~Hawking, \\\\PL{115B}{295--297}{1982}.\\n% The development of irregularities in a single bubble\\n% inflationary universe\\n\\n\\\\bibitem{BST}\\nJ\\\\.M.~Bardeen, P\\\\.J.~Steinhardt, and M\\\\.S.~Turner,\\n\\\\PRD{28}{679--693}{1983}.\\n% Spontaneous creation of almost scale-free density perturbations\\n% in an inflationary universe\\n\\n\\\\bibitem{BFM}\\nFor a modern review, see\\nV\\\\.F.~Mukhanov, H\\\\.A.~Feldman, and R\\\\.H.~Brandenberger,\\n\\\\PHYREP{215}{203--333}{1992}.\\n% Theory of Cosmological Perturbations\\n\\n\\\\bibitem{Guth-RS}\\nA\\\\.H.~Guth, \\\\PTRSLA{307}{141--148}{1982}.\\n% Phase transitions in the embryo universe\\n\\n\\\\bibitem{dicke}\\nR\\\\.H.~Dicke and P\\\\.J\\\\.E.~Peebles, in {\\\\bf General\\nRelativity: An Einstein Centenary Survey}, eds: S\\\\.W.~Hawking and\\nW.~Israel (Cambridge University Press, 1979).\\n\\n\\\\bibitem{preskill}\\nJ\\\\.P.~Preskill, \\\\PRL{43}{1365--1368}{1979}.\\n% Cosmological production of superheavy magnetic monopoles\\n\\n\\\\bibitem{bond-jaffe}\\nJ\\\\.R.~Bond and A\\\\.H.~Jaffe, talk given at Royal Society Meeting\\non {\\\\bf The Development of Large Scale Structure in the\\nUniverse,} London, England, 25-26 Mar 1998, submitted to {\\\\jf\\nPhil. Trans. Roy. Soc. Lond. A}, astro-ph/9809043.\\n\\n\\\\bibitem{steinhardt-nuffield}\\nP\\\\.J. Steinhardt, in {\\\\bf The Very Early Universe}, Proceedings\\nof the Nuffield Workshop, Cambridge, 21 June -- 9 July, 1982,\\neds: G\\\\.W.~Gibbons, S\\\\.W.~Hawking, and S\\\\.T\\\\.C.~Siklos (Cambridge\\nUniversity Press, 1983), pp. 251--266.\\n% Natural Inflation\\n\\n\\\\bibitem{vilenkin-eternal}\\nA.~Vilenkin, \\\\PRD{27}{2848--2855}{1983}.\\n% The Birth of Inflationary Universes.\\n\\n\\\\bibitem{guth-pi2}\\nA\\\\.H.~Guth and S.-Y.~Pi, \\\\PRD{32}{1899--1920}{1985}.\\n% Quantum Mechanics of the Scalar Field in the New Inflationary\\n% Universe\\n\\n\\\\bibitem{coleman-deluccia}\\nS.~Coleman \\\\& F.~De~Luccia, \\\\PRD{21}{3305--3315}{1980}.\\n% Gravitational effects on and of vacuum decay\\n\\n\\\\bibitem{vvw}\\nV.~Vanchurin, A.~Vilenkin, \\\\& S.~Winitzki, gr-qc/9905097.\\n% Predictability crisis in inflationary cosmology and its\\n% resolution\\n\\n\\\\bibitem{aryal-vilenkin}\\nM.~Aryal and A.~Vilenkin, \\\\PL{199B}{351--357}{1987}.\\n% The Fractal Dimension of Inflationary Universe.\\n% Mukunda Aryal\\n\\n\\\\bibitem{linde-eternal}\\nA\\\\.D.~Linde, \\\\MPL{A1}{81}{1986};\\n% Eternal Chaotic Inflation\\nA\\\\.D.~Linde, \\\\PL{175B}{395--400}{1986};\\n% Eternally Existing Selfreproducing Chaotic Inflationary Universe\\nA\\\\.S.~Goncharov, A\\\\.D.~Linde, and V\\\\.F.~Mukhanov,\\n\\\\IJMODPHYS{A2}{561--591}{1987}.\\n% The Global Structure of the Inflationary Universe.\\n\\n\\\\bibitem{random-vil-ford}\\nA.~Vilenkin and L\\\\.H.~Ford, \\\\PRD{26}{1231--1241}{1982}.\\n% Gravitational Effects Upon Cosmological Phase Transitions.\\n\\n\\\\bibitem{random-linde}\\nA\\\\.D.~Linde, \\\\PL{B116}{335}{1982}.\\n% Scalar Field Fluctuations in Expanding Universe and the New\\n% Inflationary Universe Scenario.\\n\\n\\\\bibitem{random-starobinsky}\\nA.~Starobinsky, in {\\\\bf Field Theory, Quantum Gravity and\\nStrings}, eds: H.J. de Vega \\\\& N. S\\\\'anchez, {\\\\jf Lecture Notes\\nin Physics\\\\jt} (Springer Verlag) Vol.~246, pp.~107--126 (1986).\\n\\n\\\\bibitem{linde-book}\\nSee for example A\\\\.D.~Linde, {\\\\bf Particle Physics and\\nInflationary Cosmology} (Harwood Academic Publishers, Chur,\\nSwitzerland, 1990) Secs.~1.7--1.8.\\n\\n\\\\bibitem{hartle-hawking}\\nJ\\\\.B.~Hartle \\\\& S\\\\.W.~Hawking, \\\\PRD{28}{2960--2975}{1983}.\\n% Wave Function of the Universe\\n\\n\\\\bibitem{tunnel-vilenkin}\\nA.~Vilenkin, \\\\PRD{30}{509--511}{1984};\\n% Quantum Creation of Universes\\nA.~Vilenkin, \\\\PRD{33}{3560--3569}{1986};\\n% Boundary Conditions in Quantum Cosmology\\nA.~Vilenkin, gr-qc/9812027, to be published in {\\\\bf Proceedings\\nof COSMO 98}, Monterey, CA, 15-20 November, 1998.\\n% The Quantum Cosmology Debate\\n\\n\\\\bibitem{tunnel-linde}\\nA\\\\.D. Linde, \\\\NC{39}{401--405}{1984};\\n% Quantum Creation of the Inflationary Universe\\nA\\\\.D. Linde, \\\\PRD{58}{083514}{1998}, gr-qc/9802038.\\n% Quantum Creation of an Open Inflationary Universe\\n\\n\\\\bibitem{hawking-turok}\\nS\\\\.W.~Hawking \\\\& N\\\\.G.~Turok, \\\\PL{B425}{25--32}{1998}, hep-th/9802030.\\n% Open Inflation Without False Vacua.\\n\\n\\\\bibitem{LLM}\\nA.~Linde, D.~Linde, \\\\& A.~Mezhlumian, \\\\PRD{49}{1783--1826}{1994},\\ngr-qc/9306035.\\n% From the Big Bang Theory to the Theory of a Stationary\\n% Universe\\n\\n\\\\bibitem{GBLinde}\\nJ.~Garcia-Bellido \\\\& A.~Linde, \\\\PRD{51}{429--443}{1995},\\nhep-th/9408023.\\n% Stationarity of Inflation and Predictions of Quantum Cosmology\\n\\n\\\\bibitem{borde-vilenkin}\\nA.~Borde \\\\& A.~Vilenkin, \\\\PRL{72}{3305--3309}{1994}, gr-qc/9312022.\\n% Eternal inflation and the initial singularity\\n\\n\\\\bibitem{borde-vilenkin2}\\nA.~Borde \\\\& A.~Vilenkin, \\\\PRD{56}{717--723}{1997}, gr-qc/9702019.\\n% Violations of the Weak Energy Condition in Inflating\\n% Space-Times.\\n\\n\\\\bibitem{center-world}\\nA.~Linde, D.~Linde, \\\\& A.~Mezhlumian, \\\\PL{B345}{203--210}{1995},\\nhep-th/9411111.\\n\\n\\\\bibitem{vilenkin-proposal}\\nA.~Vilenkin, \\\\PRL{81}{5501--5504}{1998}, hep-th/9806185.\\n% Unambiguous Probabilities in an Eternally Inflating Universe\\n\\n\\\\end{thebibliography}\\n\\n\\\\end{document}\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002188.extracted_bib","string":"\\begin{thebibliography}{99}\n\n\\bibitem{Linde1}\nA\\.D.~Linde, \\PL{108B}{389--393}{1982}.\n% A New Inflationary Universe Scenario: A Possible Solution of the\n% Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole\n% Problems\n\n\\bibitem{Albrecht-Steinhardt1}\nA.~Albrecht and P\\.J.~Steinhardt, \\PRL{48}{1220--1223}{1982}.\n% Cosmology for Grand Unified Theories with Radiatively Induced\n% Symmetry Breaking\n\n\\bibitem{chaotic}\nA\\.D.~Linde, \\ZhETF{38}{149--151}{1983} [\\JETP{38}{176--179}{1983}];\n% Chaotic inflating universe\nA\\.D.~Linde, \\PL{129B}{177--181}{1983}.\n% Chaotic inflation\n\n\\bibitem{hyb1} \nA\\.D.~Linde, \\PL{B259}{38--47}{1991}.\n% Axions in Inflationary Cosmology\n\n\\bibitem{hyb2}\nA\\.R.~Liddle and D\\.H.~Lyth, \\PHYREP{231}{1--105}{1993},\nastro-ph/9303019.\n% The Cold Dark Matter Density Perturbation\n\n\\bibitem{hyb3}\nA\\.D.~Linde, \\PRD{49}{748--754}{1994}, astro-ph/9307002.\n% Hybrid Inflation\n\n\\bibitem{hyb4}\nE\\.J.~Copeland, A\\.R.~Liddle, D\\.H.~Lyth, E\\.D.~Stewart, and\nD.~Wands, \\PRD{49}{6410-6433}{1994}, astro-ph/9401011.\n% False Vacuum Inflation with Einstein Gravity\n\n\\bibitem{hyb5}\nE.~Stewart, \\PL{B345}{414--415}{1995}, astro-ph/9407040.\n% Mutated Hybrid Inflation\n\n\\bibitem{RSG}\nL.~Randall, M.~Solja\\v{c}i\\'{c}, and A\\.H.~Guth,\n\\NP{B472}{377--408}{1996}, hep-ph/9512439; also hep-ph/9601296.\n% Supernatural Inflation: Inflation from Supersymmetry\n% with No (Very) Small Parameters\n% Supernatural Inflation (hep-ph/9601296).\n\n\\bibitem{Guth1}\nA\\.H.~Guth, \\PRD{23}{347--356}{1981}.\n% The Inflationary Universe: A Possible Solution to the Horizon\n% and Flatness Problems\n\n\\bibitem{Starobinsky}\nA\\.A.~Starobinsky, \\ZhETF{30}{719}{1979} [\\JETP{30}{682}{1979}];\nA\\.A.~Starobinsky, \\PL{91B}{99--102}{1980}.\n% A New Type of Isotropic Cosmological Models without Singularity\n% (yes, that really is ``Models''; reprinted in Abbott & Pi)\n\n\\bibitem{Coleman}\nS.~Coleman, \\PRD{15}{2929--2936}{1977} [see errata\n\\VPY{16}{1248}{1977}];\n% The Fate of the False Vacuum. 1. Semiclassical Theory\nC\\.G.~Callan and S.~Coleman,\n\\PRD{16}{1762--1768}{1977}.\n% The Fate of the False Vacuum. 2. First Quantum Corrections\n\n\\bibitem{HMS}\nS\\.W.~Hawking, I\\.G.~Moss, and J\\.M.~Stewart,\n\\PRD{26}{2681--2693}{1982}.\n% Bubble Collisions in the Very Early Universe\n\n\\bibitem{GuthWeinberg}\nA\\.H.~Guth and E\\.J.~Weinberg, \\NP{B212}{321--364}{1983}.\n% Could the Universe Have Recovered from a Slow First Order Phase\n% Transition?\n\n\\bibitem{Jensen-Stein-Schabes}\nL\\.G. Jensen and J\\.A. Stein-Schabes, \\PRD{35}{1146--1150}{1987},\nand references therein.\n% Is inflation natural?\n% Lars Gerhard Jensen and Jaime A. Stein-Schabes \n\n\\bibitem{Starobinsky2}\nA\\.A.~Starobinsky, \\PL{117B}{175--178}{1982}.\n% Dynamics of phase transition in the new inflationary universe\n% scenario and generation of perturbations\n\n\\bibitem{GuthPi}\nA\\.H.~Guth and S.-Y.~Pi, \\PRL{49}{1110--1113}{1982}.\n% Fluctuations in the new inflationary universe\n\n\\bibitem{Hawking1}\nS\\.W.~Hawking, \\PL{115B}{295--297}{1982}.\n% The development of irregularities in a single bubble\n% inflationary universe\n\n\\bibitem{BST}\nJ\\.M.~Bardeen, P\\.J.~Steinhardt, and M\\.S.~Turner,\n\\PRD{28}{679--693}{1983}.\n% Spontaneous creation of almost scale-free density perturbations\n% in an inflationary universe\n\n\\bibitem{BFM}\nFor a modern review, see\nV\\.F.~Mukhanov, H\\.A.~Feldman, and R\\.H.~Brandenberger,\n\\PHYREP{215}{203--333}{1992}.\n% Theory of Cosmological Perturbations\n\n\\bibitem{Guth-RS}\nA\\.H.~Guth, \\PTRSLA{307}{141--148}{1982}.\n% Phase transitions in the embryo universe\n\n\\bibitem{dicke}\nR\\.H.~Dicke and P\\.J\\.E.~Peebles, in {\\bf General\nRelativity: An Einstein Centenary Survey}, eds: S\\.W.~Hawking and\nW.~Israel (Cambridge University Press, 1979).\n\n\\bibitem{preskill}\nJ\\.P.~Preskill, \\PRL{43}{1365--1368}{1979}.\n% Cosmological production of superheavy magnetic monopoles\n\n\\bibitem{bond-jaffe}\nJ\\.R.~Bond and A\\.H.~Jaffe, talk given at Royal Society Meeting\non {\\bf The Development of Large Scale Structure in the\nUniverse,} London, England, 25-26 Mar 1998, submitted to {\\jf\nPhil. Trans. Roy. Soc. Lond. A}, astro-ph/9809043.\n\n\\bibitem{steinhardt-nuffield}\nP\\.J. Steinhardt, in {\\bf The Very Early Universe}, Proceedings\nof the Nuffield Workshop, Cambridge, 21 June -- 9 July, 1982,\neds: G\\.W.~Gibbons, S\\.W.~Hawking, and S\\.T\\.C.~Siklos (Cambridge\nUniversity Press, 1983), pp. 251--266.\n% Natural Inflation\n\n\\bibitem{vilenkin-eternal}\nA.~Vilenkin, \\PRD{27}{2848--2855}{1983}.\n% The Birth of Inflationary Universes.\n\n\\bibitem{guth-pi2}\nA\\.H.~Guth and S.-Y.~Pi, \\PRD{32}{1899--1920}{1985}.\n% Quantum Mechanics of the Scalar Field in the New Inflationary\n% Universe\n\n\\bibitem{coleman-deluccia}\nS.~Coleman \\& F.~De~Luccia, \\PRD{21}{3305--3315}{1980}.\n% Gravitational effects on and of vacuum decay\n\n\\bibitem{vvw}\nV.~Vanchurin, A.~Vilenkin, \\& S.~Winitzki, gr-qc/9905097.\n% Predictability crisis in inflationary cosmology and its\n% resolution\n\n\\bibitem{aryal-vilenkin}\nM.~Aryal and A.~Vilenkin, \\PL{199B}{351--357}{1987}.\n% The Fractal Dimension of Inflationary Universe.\n% Mukunda Aryal\n\n\\bibitem{linde-eternal}\nA\\.D.~Linde, \\MPL{A1}{81}{1986};\n% Eternal Chaotic Inflation\nA\\.D.~Linde, \\PL{175B}{395--400}{1986};\n% Eternally Existing Selfreproducing Chaotic Inflationary Universe\nA\\.S.~Goncharov, A\\.D.~Linde, and V\\.F.~Mukhanov,\n\\IJMODPHYS{A2}{561--591}{1987}.\n% The Global Structure of the Inflationary Universe.\n\n\\bibitem{random-vil-ford}\nA.~Vilenkin and L\\.H.~Ford, \\PRD{26}{1231--1241}{1982}.\n% Gravitational Effects Upon Cosmological Phase Transitions.\n\n\\bibitem{random-linde}\nA\\.D.~Linde, \\PL{B116}{335}{1982}.\n% Scalar Field Fluctuations in Expanding Universe and the New\n% Inflationary Universe Scenario.\n\n\\bibitem{random-starobinsky}\nA.~Starobinsky, in {\\bf Field Theory, Quantum Gravity and\nStrings}, eds: H.J. de Vega \\& N. S\\'anchez, {\\jf Lecture Notes\nin Physics\\jt} (Springer Verlag) Vol.~246, pp.~107--126 (1986).\n\n\\bibitem{linde-book}\nSee for example A\\.D.~Linde, {\\bf Particle Physics and\nInflationary Cosmology} (Harwood Academic Publishers, Chur,\nSwitzerland, 1990) Secs.~1.7--1.8.\n\n\\bibitem{hartle-hawking}\nJ\\.B.~Hartle \\& S\\.W.~Hawking, \\PRD{28}{2960--2975}{1983}.\n% Wave Function of the Universe\n\n\\bibitem{tunnel-vilenkin}\nA.~Vilenkin, \\PRD{30}{509--511}{1984};\n% Quantum Creation of Universes\nA.~Vilenkin, \\PRD{33}{3560--3569}{1986};\n% Boundary Conditions in Quantum Cosmology\nA.~Vilenkin, gr-qc/9812027, to be published in {\\bf Proceedings\nof COSMO 98}, Monterey, CA, 15-20 November, 1998.\n% The Quantum Cosmology Debate\n\n\\bibitem{tunnel-linde}\nA\\.D. Linde, \\NC{39}{401--405}{1984};\n% Quantum Creation of the Inflationary Universe\nA\\.D. Linde, \\PRD{58}{083514}{1998}, gr-qc/9802038.\n% Quantum Creation of an Open Inflationary Universe\n\n\\bibitem{hawking-turok}\nS\\.W.~Hawking \\& N\\.G.~Turok, \\PL{B425}{25--32}{1998}, hep-th/9802030.\n% Open Inflation Without False Vacua.\n\n\\bibitem{LLM}\nA.~Linde, D.~Linde, \\& A.~Mezhlumian, \\PRD{49}{1783--1826}{1994},\ngr-qc/9306035.\n% From the Big Bang Theory to the Theory of a Stationary\n% Universe\n\n\\bibitem{GBLinde}\nJ.~Garcia-Bellido \\& A.~Linde, \\PRD{51}{429--443}{1995},\nhep-th/9408023.\n% Stationarity of Inflation and Predictions of Quantum Cosmology\n\n\\bibitem{borde-vilenkin}\nA.~Borde \\& A.~Vilenkin, \\PRL{72}{3305--3309}{1994}, gr-qc/9312022.\n% Eternal inflation and the initial singularity\n\n\\bibitem{borde-vilenkin2}\nA.~Borde \\& A.~Vilenkin, \\PRD{56}{717--723}{1997}, gr-qc/9702019.\n% Violations of the Weak Energy Condition in Inflating\n% Space-Times.\n\n\\bibitem{center-world}\nA.~Linde, D.~Linde, \\& A.~Mezhlumian, \\PL{B345}{203--210}{1995},\nhep-th/9411111.\n\n\\bibitem{vilenkin-proposal}\nA.~Vilenkin, \\PRL{81}{5501--5504}{1998}, hep-th/9806185.\n% Unambiguous Probabilities in an Eternally Inflating Universe\n\n\\end{thebibliography}"}],"string":"[\n {\n \"name\": \"astro-ph0002188.extracted_bib\",\n \"string\": \"\\\\begin{thebibliography}{99}\\n\\n\\\\bibitem{Linde1}\\nA\\\\.D.~Linde, \\\\PL{108B}{389--393}{1982}.\\n% A New Inflationary Universe Scenario: A Possible Solution of the\\n% Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole\\n% Problems\\n\\n\\\\bibitem{Albrecht-Steinhardt1}\\nA.~Albrecht and P\\\\.J.~Steinhardt, \\\\PRL{48}{1220--1223}{1982}.\\n% Cosmology for Grand Unified Theories with Radiatively Induced\\n% Symmetry Breaking\\n\\n\\\\bibitem{chaotic}\\nA\\\\.D.~Linde, \\\\ZhETF{38}{149--151}{1983} [\\\\JETP{38}{176--179}{1983}];\\n% Chaotic inflating universe\\nA\\\\.D.~Linde, \\\\PL{129B}{177--181}{1983}.\\n% Chaotic inflation\\n\\n\\\\bibitem{hyb1} \\nA\\\\.D.~Linde, \\\\PL{B259}{38--47}{1991}.\\n% Axions in Inflationary Cosmology\\n\\n\\\\bibitem{hyb2}\\nA\\\\.R.~Liddle and D\\\\.H.~Lyth, \\\\PHYREP{231}{1--105}{1993},\\nastro-ph/9303019.\\n% The Cold Dark Matter Density Perturbation\\n\\n\\\\bibitem{hyb3}\\nA\\\\.D.~Linde, \\\\PRD{49}{748--754}{1994}, astro-ph/9307002.\\n% Hybrid Inflation\\n\\n\\\\bibitem{hyb4}\\nE\\\\.J.~Copeland, A\\\\.R.~Liddle, D\\\\.H.~Lyth, E\\\\.D.~Stewart, and\\nD.~Wands, \\\\PRD{49}{6410-6433}{1994}, astro-ph/9401011.\\n% False Vacuum Inflation with Einstein Gravity\\n\\n\\\\bibitem{hyb5}\\nE.~Stewart, \\\\PL{B345}{414--415}{1995}, astro-ph/9407040.\\n% Mutated Hybrid Inflation\\n\\n\\\\bibitem{RSG}\\nL.~Randall, M.~Solja\\\\v{c}i\\\\'{c}, and A\\\\.H.~Guth,\\n\\\\NP{B472}{377--408}{1996}, hep-ph/9512439; also hep-ph/9601296.\\n% Supernatural Inflation: Inflation from Supersymmetry\\n% with No (Very) Small Parameters\\n% Supernatural Inflation (hep-ph/9601296).\\n\\n\\\\bibitem{Guth1}\\nA\\\\.H.~Guth, \\\\PRD{23}{347--356}{1981}.\\n% The Inflationary Universe: A Possible Solution to the Horizon\\n% and Flatness Problems\\n\\n\\\\bibitem{Starobinsky}\\nA\\\\.A.~Starobinsky, \\\\ZhETF{30}{719}{1979} [\\\\JETP{30}{682}{1979}];\\nA\\\\.A.~Starobinsky, \\\\PL{91B}{99--102}{1980}.\\n% A New Type of Isotropic Cosmological Models without Singularity\\n% (yes, that really is ``Models''; reprinted in Abbott & Pi)\\n\\n\\\\bibitem{Coleman}\\nS.~Coleman, \\\\PRD{15}{2929--2936}{1977} [see errata\\n\\\\VPY{16}{1248}{1977}];\\n% The Fate of the False Vacuum. 1. Semiclassical Theory\\nC\\\\.G.~Callan and S.~Coleman,\\n\\\\PRD{16}{1762--1768}{1977}.\\n% The Fate of the False Vacuum. 2. First Quantum Corrections\\n\\n\\\\bibitem{HMS}\\nS\\\\.W.~Hawking, I\\\\.G.~Moss, and J\\\\.M.~Stewart,\\n\\\\PRD{26}{2681--2693}{1982}.\\n% Bubble Collisions in the Very Early Universe\\n\\n\\\\bibitem{GuthWeinberg}\\nA\\\\.H.~Guth and E\\\\.J.~Weinberg, \\\\NP{B212}{321--364}{1983}.\\n% Could the Universe Have Recovered from a Slow First Order Phase\\n% Transition?\\n\\n\\\\bibitem{Jensen-Stein-Schabes}\\nL\\\\.G. Jensen and J\\\\.A. Stein-Schabes, \\\\PRD{35}{1146--1150}{1987},\\nand references therein.\\n% Is inflation natural?\\n% Lars Gerhard Jensen and Jaime A. Stein-Schabes \\n\\n\\\\bibitem{Starobinsky2}\\nA\\\\.A.~Starobinsky, \\\\PL{117B}{175--178}{1982}.\\n% Dynamics of phase transition in the new inflationary universe\\n% scenario and generation of perturbations\\n\\n\\\\bibitem{GuthPi}\\nA\\\\.H.~Guth and S.-Y.~Pi, \\\\PRL{49}{1110--1113}{1982}.\\n% Fluctuations in the new inflationary universe\\n\\n\\\\bibitem{Hawking1}\\nS\\\\.W.~Hawking, \\\\PL{115B}{295--297}{1982}.\\n% The development of irregularities in a single bubble\\n% inflationary universe\\n\\n\\\\bibitem{BST}\\nJ\\\\.M.~Bardeen, P\\\\.J.~Steinhardt, and M\\\\.S.~Turner,\\n\\\\PRD{28}{679--693}{1983}.\\n% Spontaneous creation of almost scale-free density perturbations\\n% in an inflationary universe\\n\\n\\\\bibitem{BFM}\\nFor a modern review, see\\nV\\\\.F.~Mukhanov, H\\\\.A.~Feldman, and R\\\\.H.~Brandenberger,\\n\\\\PHYREP{215}{203--333}{1992}.\\n% Theory of Cosmological Perturbations\\n\\n\\\\bibitem{Guth-RS}\\nA\\\\.H.~Guth, \\\\PTRSLA{307}{141--148}{1982}.\\n% Phase transitions in the embryo universe\\n\\n\\\\bibitem{dicke}\\nR\\\\.H.~Dicke and P\\\\.J\\\\.E.~Peebles, in {\\\\bf General\\nRelativity: An Einstein Centenary Survey}, eds: S\\\\.W.~Hawking and\\nW.~Israel (Cambridge University Press, 1979).\\n\\n\\\\bibitem{preskill}\\nJ\\\\.P.~Preskill, \\\\PRL{43}{1365--1368}{1979}.\\n% Cosmological production of superheavy magnetic monopoles\\n\\n\\\\bibitem{bond-jaffe}\\nJ\\\\.R.~Bond and A\\\\.H.~Jaffe, talk given at Royal Society Meeting\\non {\\\\bf The Development of Large Scale Structure in the\\nUniverse,} London, England, 25-26 Mar 1998, submitted to {\\\\jf\\nPhil. Trans. Roy. Soc. Lond. A}, astro-ph/9809043.\\n\\n\\\\bibitem{steinhardt-nuffield}\\nP\\\\.J. Steinhardt, in {\\\\bf The Very Early Universe}, Proceedings\\nof the Nuffield Workshop, Cambridge, 21 June -- 9 July, 1982,\\neds: G\\\\.W.~Gibbons, S\\\\.W.~Hawking, and S\\\\.T\\\\.C.~Siklos (Cambridge\\nUniversity Press, 1983), pp. 251--266.\\n% Natural Inflation\\n\\n\\\\bibitem{vilenkin-eternal}\\nA.~Vilenkin, \\\\PRD{27}{2848--2855}{1983}.\\n% The Birth of Inflationary Universes.\\n\\n\\\\bibitem{guth-pi2}\\nA\\\\.H.~Guth and S.-Y.~Pi, \\\\PRD{32}{1899--1920}{1985}.\\n% Quantum Mechanics of the Scalar Field in the New Inflationary\\n% Universe\\n\\n\\\\bibitem{coleman-deluccia}\\nS.~Coleman \\\\& F.~De~Luccia, \\\\PRD{21}{3305--3315}{1980}.\\n% Gravitational effects on and of vacuum decay\\n\\n\\\\bibitem{vvw}\\nV.~Vanchurin, A.~Vilenkin, \\\\& S.~Winitzki, gr-qc/9905097.\\n% Predictability crisis in inflationary cosmology and its\\n% resolution\\n\\n\\\\bibitem{aryal-vilenkin}\\nM.~Aryal and A.~Vilenkin, \\\\PL{199B}{351--357}{1987}.\\n% The Fractal Dimension of Inflationary Universe.\\n% Mukunda Aryal\\n\\n\\\\bibitem{linde-eternal}\\nA\\\\.D.~Linde, \\\\MPL{A1}{81}{1986};\\n% Eternal Chaotic Inflation\\nA\\\\.D.~Linde, \\\\PL{175B}{395--400}{1986};\\n% Eternally Existing Selfreproducing Chaotic Inflationary Universe\\nA\\\\.S.~Goncharov, A\\\\.D.~Linde, and V\\\\.F.~Mukhanov,\\n\\\\IJMODPHYS{A2}{561--591}{1987}.\\n% The Global Structure of the Inflationary Universe.\\n\\n\\\\bibitem{random-vil-ford}\\nA.~Vilenkin and L\\\\.H.~Ford, \\\\PRD{26}{1231--1241}{1982}.\\n% Gravitational Effects Upon Cosmological Phase Transitions.\\n\\n\\\\bibitem{random-linde}\\nA\\\\.D.~Linde, \\\\PL{B116}{335}{1982}.\\n% Scalar Field Fluctuations in Expanding Universe and the New\\n% Inflationary Universe Scenario.\\n\\n\\\\bibitem{random-starobinsky}\\nA.~Starobinsky, in {\\\\bf Field Theory, Quantum Gravity and\\nStrings}, eds: H.J. de Vega \\\\& N. S\\\\'anchez, {\\\\jf Lecture Notes\\nin Physics\\\\jt} (Springer Verlag) Vol.~246, pp.~107--126 (1986).\\n\\n\\\\bibitem{linde-book}\\nSee for example A\\\\.D.~Linde, {\\\\bf Particle Physics and\\nInflationary Cosmology} (Harwood Academic Publishers, Chur,\\nSwitzerland, 1990) Secs.~1.7--1.8.\\n\\n\\\\bibitem{hartle-hawking}\\nJ\\\\.B.~Hartle \\\\& S\\\\.W.~Hawking, \\\\PRD{28}{2960--2975}{1983}.\\n% Wave Function of the Universe\\n\\n\\\\bibitem{tunnel-vilenkin}\\nA.~Vilenkin, \\\\PRD{30}{509--511}{1984};\\n% Quantum Creation of Universes\\nA.~Vilenkin, \\\\PRD{33}{3560--3569}{1986};\\n% Boundary Conditions in Quantum Cosmology\\nA.~Vilenkin, gr-qc/9812027, to be published in {\\\\bf Proceedings\\nof COSMO 98}, Monterey, CA, 15-20 November, 1998.\\n% The Quantum Cosmology Debate\\n\\n\\\\bibitem{tunnel-linde}\\nA\\\\.D. Linde, \\\\NC{39}{401--405}{1984};\\n% Quantum Creation of the Inflationary Universe\\nA\\\\.D. Linde, \\\\PRD{58}{083514}{1998}, gr-qc/9802038.\\n% Quantum Creation of an Open Inflationary Universe\\n\\n\\\\bibitem{hawking-turok}\\nS\\\\.W.~Hawking \\\\& N\\\\.G.~Turok, \\\\PL{B425}{25--32}{1998}, hep-th/9802030.\\n% Open Inflation Without False Vacua.\\n\\n\\\\bibitem{LLM}\\nA.~Linde, D.~Linde, \\\\& A.~Mezhlumian, \\\\PRD{49}{1783--1826}{1994},\\ngr-qc/9306035.\\n% From the Big Bang Theory to the Theory of a Stationary\\n% Universe\\n\\n\\\\bibitem{GBLinde}\\nJ.~Garcia-Bellido \\\\& A.~Linde, \\\\PRD{51}{429--443}{1995},\\nhep-th/9408023.\\n% Stationarity of Inflation and Predictions of Quantum Cosmology\\n\\n\\\\bibitem{borde-vilenkin}\\nA.~Borde \\\\& A.~Vilenkin, \\\\PRL{72}{3305--3309}{1994}, gr-qc/9312022.\\n% Eternal inflation and the initial singularity\\n\\n\\\\bibitem{borde-vilenkin2}\\nA.~Borde \\\\& A.~Vilenkin, \\\\PRD{56}{717--723}{1997}, gr-qc/9702019.\\n% Violations of the Weak Energy Condition in Inflating\\n% Space-Times.\\n\\n\\\\bibitem{center-world}\\nA.~Linde, D.~Linde, \\\\& A.~Mezhlumian, \\\\PL{B345}{203--210}{1995},\\nhep-th/9411111.\\n\\n\\\\bibitem{vilenkin-proposal}\\nA.~Vilenkin, \\\\PRL{81}{5501--5504}{1998}, hep-th/9806185.\\n% Unambiguous Probabilities in an Eternally Inflating Universe\\n\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":186,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002189"},"title":{"kind":"string","value":"Spatially-resolved spectra of the accretion disc of the novalike UU Aquarii"},"authors":{"kind":"list like","value":[{"author":"Raymundo Baptista$^1$"},{"author":"C. Silveira$^1$"},{"author":"J.E. Steiner$^2$ and Keith Horne$^3$"},{"author":"% and Knox Long$^4$"},{"author":"$^1$ Departamento de F\\'\\i sica"},{"author":"Universidade Federal de Santa Catarina"},{"author":"Campus Trindade"},{"author":"88040-900"},{"author":"Florian\\'opolis - SC"},{"author":"Brazil"},{"author":"$^2$ Laborat\\'orio Nacional de Astrof\\'\\i sica-LNA/CNPq"},{"author":"CP 21"},{"author":"37500-000"},{"author":"Itajub\\'a"},{"author":"$^3$ School of Physics \\& Astronomy"},{"author":"Andrews"},{"author":"North Haugh"},{"author":"St.\\"},{"author":"Fife"},{"author":"KY16 9SS"},{"author":"Scotland"},{"author":"3700 San Martin Drive"},{"author":"Baltimore"},{"author":"% MD 21218"},{"author":"USA"}],"string":"[\n {\n \"author\": \"Raymundo Baptista$^1$\"\n },\n {\n \"author\": \"C. Silveira$^1$\"\n },\n {\n \"author\": \"J.E. Steiner$^2$ and Keith Horne$^3$\"\n },\n {\n \"author\": \"% and Knox Long$^4$\"\n },\n {\n \"author\": \"$^1$ Departamento de F\\\\'\\\\i sica\"\n },\n {\n \"author\": \"Universidade Federal de Santa Catarina\"\n },\n {\n \"author\": \"Campus Trindade\"\n },\n {\n \"author\": \"88040-900\"\n },\n {\n \"author\": \"Florian\\\\'opolis - SC\"\n },\n {\n \"author\": \"Brazil\"\n },\n {\n \"author\": \"$^2$ Laborat\\\\'orio Nacional de Astrof\\\\'\\\\i sica-LNA/CNPq\"\n },\n {\n \"author\": \"CP 21\"\n },\n {\n \"author\": \"37500-000\"\n },\n {\n \"author\": \"Itajub\\\\'a\"\n },\n {\n \"author\": \"$^3$ School of Physics \\\\& Astronomy\"\n },\n {\n \"author\": \"Andrews\"\n },\n {\n \"author\": \"North Haugh\"\n },\n {\n \"author\": \"St.\\\\\"\n },\n {\n \"author\": \"Fife\"\n },\n {\n \"author\": \"KY16 9SS\"\n },\n {\n \"author\": \"Scotland\"\n },\n {\n \"author\": \"3700 San Martin Drive\"\n },\n {\n \"author\": \"Baltimore\"\n },\n {\n \"author\": \"% MD 21218\"\n },\n {\n \"author\": \"USA\"\n }\n]"},"abstract":{"kind":"string","value":"Time-resolved spectroscopy of the novalike variable UU Aquarii is analyzed with eclipse mapping techniques to produce spatially resolved spectra of its accretion disc and gas stream as a function of distance from disc centre in the range 3600-6900 \\AA. The spatially-resolved spectra show that the continuum emission becomes progressively fainter and redder for increasing disc radius -- reflecting the radial temperature gradient -- and reveal that the H\\,I and He\\,I lines appear as deep, narrow absorption features in the inner disc regions transitioning to emission with P Cyg profiles for intermediate and large disc radii. The spectrum of the uneclipsed component has strong H\\,I and He\\,I emission lines plus a Balmer jump in emission and is explained as optically thin emission from a vertically extended disc chromosphere + wind. Most of the line emission probably arises from the wind. The spatially-resolved spectra also suggest the existence of gas stream ``disk-skimming'' overflow in UU~Aqr, which can be seen down to $R\\simeq 0.2\\; R_{L1}$. The comparison of our eclipse maps with those of Baptista, Steiner \\& Horne (1996) suggests that the asymmetric structure in the outer disc previously identified as the bright spot may be the signature of an elliptical disc similar to those possibly present in SU~UMa stars during superoutbursts."},"latex":{"kind":"list like","value":[{"name":"uu3.tex","string":"%\tSpatially-resolved spectra of the accretion disc of UU Aqr (paper 3)\n%\tBaptista, Silveira, Steiner & Horne\n%\tlast update: 21/08/99\n\n\\documentstyle[psfig]{mn}\n\\topmargin -20 mm\n\n% If your system has the AMS fonts version 2.0 installed, MN.sty can be\n% made to use them by uncommenting the line: %\\AMStwofontstrue\n%\n% By doing this, you will be able to obtain upright Greek characters.\n% e.g. \\umu, \\upi etc. See the section on \"Upright Greek characters\" in\n% this guide for further information.\n%\n% If you are using AMS 2.0 fonts, bold math letters/symbols are available\n% at a larger range of sizes for NFSS release 1 and 2 (using \\boldmath or\n% preferably \\bmath).\n\n\\newif\\ifAMStwofonts\n%\\AMStwofontstrue\n\n%%%%% AUTHORS - PLACE YOUR OWN MACROS HERE %%%%%\n\n% Useful symbols\n\\def\\simlt{\\lower.5ex\\hbox{$\\; \\buildrel < \\over \\sim \\;$}}\n\\def\\simgt{\\lower.5ex\\hbox{$\\; \\buildrel > \\over \\sim \\;$}}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\ifoldfss\n %\n \\newcommand{\\rmn}[1] {{\\rm #1}}\n \\newcommand{\\itl}[1] {{\\it #1}}\n \\newcommand{\\bld}[1] {{\\bf #1}}\n %\n \\ifCUPmtlplainloaded \\else\n \\NewTextAlphabet{textbfit} {cmbxti10} {}\n \\NewTextAlphabet{textbfss} {cmssbx10} {}\n \\NewMathAlphabet{mathbfit} {cmbxti10} {} % for math mode\n \\NewMathAlphabet{mathbfss} {cmssbx10} {} % \" \" \"\n \\fi\n %\n \\ifAMStwofonts\n %\n \\ifCUPmtlplainloaded \\else\n \\NewSymbolFont{upmath} {eurm10}\n \\NewSymbolFont{AMSa} {msam10}\n \\NewMathSymbol{\\upi} {0}{upmath}{19}\n \\NewMathSymbol{\\umu} {0}{upmath}{16}\n \\NewMathSymbol{\\upartial}{0}{upmath}{40}\n \\NewMathSymbol{\\leqslant}{3}{AMSa}{36}\n \\NewMathSymbol{\\geqslant}{3}{AMSa}{3E}\n \\let\\oldle=\\le \\let\\oldleq=\\leq\n \\let\\oldge=\\ge \\let\\oldgeq=\\geq\n \\let\\leq=\\leqslant \\let\\le=\\leqslant\n \\let\\geq=\\geqslant \\let\\ge=\\geqslant\n \\fi\n %\n \\fi\n%\n\\fi % End of OFSS\n\n\\ifnfssone\n %\n \\newmathalphabet{\\mathit}\n \\addtoversion{normal}{\\mathit}{cmr}{m}{it}\n \\addtoversion{bold}{\\mathit}{cmr}{bx}{it}\n %\n \\newcommand{\\rmn}[1] {\\mathrm{#1}}\n \\newcommand{\\itl}[1] {\\mathit{#1}}\n \\newcommand{\\bld}[1] {\\mathbf{#1}}\n %\n \\def\\textbfit{\\protect\\txtbfit}\n \\def\\textbfss{\\protect\\txtbfss}\n \\long\\def\\txtbfit#1{{\\fontfamily{cmr}\\fontseries{bx}\\fontshape{it}%\n \\selectfont #1}}\n \\long\\def\\txtbfss#1{{\\fontfamily{cmss}\\fontseries{bx}\\fontshape{n}%\n \\selectfont #1}}\n %\n \\newmathalphabet{\\mathbfit} % math mode version of \\textbfit{..}\n \\addtoversion{normal}{\\mathbfit}{cmr}{bx}{it}\n \\addtoversion{bold}{\\mathbfit}{cmr}{bx}{it}\n %\n \\newmathalphabet{\\mathbfss} % math mode version of \\textbfss{..}\n \\addtoversion{normal}{\\mathbfss}{cmss}{bx}{n}\n \\addtoversion{bold}{\\mathbfss}{cmss}{bx}{n}\n %\n \\ifAMStwofonts\n %\n \\ifCUPmtlplainloaded \\else\n %\n % Make NFSS 1 use the extra sizes available for bold math italic and\n % bold math symbol. 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Baptista et~al.]\n\t{Raymundo Baptista$^1$, C. Silveira$^1$, J.E. Steiner$^2$\n\tand Keith Horne$^3$ \\\\\n%\tand Knox Long$^4$ \\\\\n\t$^1$ Departamento de F\\'\\i sica, Universidade Federal de Santa Catarina,\n Campus Trindade, 88040-900, Florian\\'opolis - SC, Brazil, \\\\\n ~ email: bap@fsc.ufsc.br, silveira@fsc.ufsc.br \\\\\n\t$^2$ Laborat\\'orio Nacional de Astrof\\'\\i sica-LNA/CNPq, CP 21, 37500-000,\n\tItajub\\'a, Brazil, email: steiner@lna.br \\\\\n\t$^3$ School of Physics \\& Astronomy, University of St.\\,Andrews,\n\tNorth Haugh, St.\\,Andrews, Fife, KY16 9SS, Scotland, \\\\\n ~ email: kdh1@st-and.ac.uk \\\\\n% $^4$ Space Telescope Science Institute, 3700 San Martin Drive, Baltimore,\n% MD 21218, USA, email: long@stsci.edu \n\t}\n\\date{Accepted for publication at Monthly Notices of the Royal Astronomical\n\t\tSociety}\n\n\\pagerange{1-13}\n\\pubyear{2000}\n\n\\begin{document}\n\n\\maketitle\n\n\\begin{abstract}\n\nTime-resolved spectroscopy of the novalike variable UU Aquarii is analyzed\nwith eclipse mapping techniques to produce spatially resolved spectra\nof its accretion disc and gas stream as a function of distance from disc\ncentre in the range 3600-6900 \\AA. The spatially-resolved spectra show\nthat the continuum emission becomes progressively fainter and redder for\nincreasing disc radius -- reflecting the radial temperature gradient --\nand reveal that the H\\,I and He\\,I lines appear as deep, narrow absorption\nfeatures in the inner disc regions transitioning to emission with P Cyg\nprofiles for intermediate and large disc radii. The spectrum of the\nuneclipsed component has strong H\\,I and He\\,I emission lines plus a Balmer\njump in emission and is explained as optically thin emission from a\nvertically extended disc chromosphere + wind. \nMost of the line emission probably arises from the wind.\nThe spatially-resolved spectra also suggest the existence of gas stream \n``disk-skimming'' overflow in UU~Aqr, which can be seen down to\n$R\\simeq 0.2\\; R_{L1}$. The comparison of our eclipse maps with those \nof Baptista, Steiner \\& Horne (1996) suggests that the asymmetric structure \nin the outer disc previously identified as the bright spot may be the \nsignature of an elliptical disc similar to those possibly present in \nSU~UMa stars during superoutbursts.\n\n\\end{abstract}\n\n\\begin{keywords}\nbinaries: close -- novae, cataclysmic variables -- eclipses -- accretion\ndiscs -- stars: individual: (UU Aquarii).\n\\end{keywords}\n\n\n\\section{Introduction}\n\nThe standard picture of a novalike system is that of a close binary in\nwhich a late type star fills its Roche lobe and transfers matter to a\ncompanion white dwarf via an accretion disc. A bright spot is expected \nto form where the gas stream from the donor star hits the edge of the\naccretion disc.\n\nThe SW Sex stars (Thorstensen et~al. 1991) form a sub-class of the\nnovalikes with orbital periods in the range 3-4 hs that do not seem to\nfit within the above standard picture, displaying a range of peculiarities:\n(1) single peaked asymmetric emission lines showing little eclipse, \n(2) large ($\\sim 70\\degr$) phase shifts between photometric and\nspectroscopic conjunction, \n(3) orbital phase-dependent absorption in the Balmer lines,\n(4) Doppler tomograms bright in the lower-left quadrant with small\nor no sign of disc emission, and\n(5) v-shaped continuum eclipses implying in flat radial temperature \nprofiles in the inner disc (e.g., Warner 1995 and references therein).\nEarlier proposals to explain the phenomenon include accretion disc winds\n(Honeycutt, Schlegel \\& Kaitchuck 1986), magnetic white dwarfs\ndisrupting the inner disc (Williams 1989), and gas stream overflow\n(Hellier \\& Robinson 1994). The two most recent models proposed to\nexplain the phenomenology of the SW Sex stars are the disc-anchored\nmagnetic propeller (Horne 1999) and a combination of stream overflow\n+ disc winds (Hellier 1999).\n\nUU~Aqr is an eclipsing novalike (P$_{\\rm orb}= 3.9$\\,hr) whose \nspectrum is dominated by single-peaked strong Balmer and He\\,I emission\nlines (e.g., Downes \\& Keyes 1988). H$\\alpha$ spectroscopy revealed\nthat the line profile is highly asymmetric and phase-dependent \nand that the spectroscopic conjunction lags mid-eclipse\nby $\\sim 0.15$ cycle (Haefner 1989; Diaz \\& Steiner 1991).\nThe lack of the rotational disturbance typical of emitting accretion\ndiscs during eclipse in H$\\beta$ led Hessman (1990) to the suggestion\nthat the emission lines have a non-disc origin.\n\nBaptista, Steiner \\& Cieslinski (1994; hereafter BSC94) derived a\nphotometric model for the binary with $q= 0.30$, M$_1 = 0.67\\:\n{\\rm M}_{\\odot}$, an inclination of $i= 78$ degrees.\nFrom the analysis of mid-eclipse fluxes they suggested that the Balmer\nlines are formed in an extended region only partially occulted during\neclipse, possibly in a wind emanating from the inner disc.\nThey also found that UU Aqr presents long-term brightness variations of\nlow amplitude ($\\simeq 0.3$ mags) on timescales of years.\n\nThe eclipse mapping study of Baptista, Steiner \\& Horne (1996;\nthereafter BSH96) indicates that the inner disc of UU Aqr is\noptically thick, resulting in a distance estimate of 200 pc.\nTemperatures in the disc range from $\\sim 6000$\\,K in the outer \nregions to $\\sim 16000$\\,K near the white dwarf at disc centre.\nThe radial temperature profiles in the high state follow the\nT$\\:\\propto R^{-3/4}$ law in the outer and intermediate disc regions\nbut flattens off in the inner disc, leading to mass accretion rates\nof $10^{-9.2}\\:{\\rm M_{\\odot}\\,yr}^{-1}$ at $R= 0.1\\: R_{\\rm L1}$\nand $10^{-8.8}\\:{\\rm M_{\\odot}\\,yr}^{-1}$ at $R= 0.3\\: R_{\\rm L1}$\n($R_{\\rm L1}$ is the distance from disc centre to the inner Lagrangian\npoint). Together with other characteristics, this led BSH96 to suggest\nthat UU Aqr was an SW Sex star.\nThe comparison of eclipse maps of the low and high states revealed that\nthe differences are due to changes in the structure of the outer parts\nof the disc, the most noticeable effect being the appearance of a\nconspicuous red, bright structure at disc rim, which the authors\nidentified with the bright spot.\n\nAccording to BSH96, the \\.{M} of UU Aqr is barely above the critical\nlimit for disc instability to set in. Warner (1997) noted that the\nouter disc temperature is only 6000 K and remarked that small variations\nin \\.{M} could lead to dwarf novae type outbursts.\nHoneycutt, Robertson \\& Turner (1998) performed a long-term photometric\nmonitoring of UU Aqr which confirmed the high and low brightness states\nof BSC94 and revealed the existence of small amplitude ($\\simlt 1.0$ mag)\nbrightness variations on timescales of a few days, which they called\n`stunted outbursts'.\n\nThe detailed spectroscopic study of Hoard et~al. (1998) reinforced the\nclassification of UU Aqr as an SW Sex star.\nThey found evidences for the presence of a bright spot at the impact site\nof the gas stream with the edge of the disc, and a non-axisymmetric,\nvertically and azimuthally extended absorbing structure in the disc.\nThey proposed an explanation for the absorbing structure as well as for\nthe other spectroscopic features of UU Aqr in terms of the explosive\nimpact of the accretion stream with the disc.\nOptical and ultraviolet spectroscopy by Kaitchuck et~al. (1998)\nshows a secondary eclipse at phase 0.4 in the optical and Balmer lines\n(but not in the UV continuum or lines) which they suggested may be\ncaused by an occultation of the bright spot and stream region by material\nsuspended above the inner disc.\n\nIn this paper we report on the analysis of time-resolved spectroscopy\nof UU Aqr with multi-wavelength eclipse mapping techniques to derive \nspatially-resolved spectra of the accretion flow in this binary.\nSection~\\ref{data} describes the observations and data reduction procedures,\nwhile section~\\ref{analise} describes the analysis of the light curves with\neclipse mapping techniques.\nSection~\\ref{resultados} presents eclipse maps at selected wavelengths,\nthe radial intensity and brightness temperature distributions,\nspatially resolved spectra of the accretion disc and gas stream as well\nas the spectrum of the uneclipsed component.\nThe results are discussed in section~\\ref{discussao} and summarized in section~\\ref{conclusao}.\n\n\n\\section{Observations} \\label{data}\n\nTime-resolved spectroscopy covering 5 eclipses of UU~Aqr was obtained\nwith the 2.1-m telescope at the Kitt Peak National Observatory (KPNO) on\nJuly-August 1993 in the spectral range 3500--6900 \\AA\\ (spectral\nresolution of $\\Delta\\lambda= 1.5$ \\AA\\ pixel$^{-1}$).\nThe observations consist of 5 sets of $\\simeq 100$ short exposure\n($\\Delta t=30s$) spectra at a time resolution of 50\\,s. A close comparison\nstar (star C1 of BSC94) was included in the slit to allow correction of sky\ntransparency variations and slit losses. The observations (summarized in\nTable~\\ref{tab1}) were performed under good (cloud-free) sky conditions and\nat small to moderate air masses ($X \\leq 1.4$) except for run 1, which\nstarted while the object was still at a reasonably high zenith angle\n($X= 2.2$).\n%\n% ############################### TABLE 1 #################################\n\\begin{table*}\n \\centering\n \\begin{minipage}{120mm}\n \\caption{Journal of the observations.}\n \\label{tab1}\n\\begin{tabular}{@{}lccccccc@{}}\n~~Date & Run & \\multicolumn{2}{c}{UT} & No. of & Spectral & Cycle &\nPhase range \\\\ [-0.5ex]\n~(1993) && start & end & spectra & range (\\AA) & number & (cycle) \\\\ [1ex]\n22 July & 1 & 05:56 & 07:33 & 105 & 3564.0--6766.5 & 17389 & $-0.20,+0.21$ \\\\\n27 July & 2 & 07:59 & 09:40 & 111 & 3601.6--6805.5 & 17420 & $-0.11,+0.32$ \\\\\n13 August & 3 & 07:52 & 09:25 & 101 & 3646.5--6850.5 & 17524 & $-0.22,+0.17$ \\\\ \n15 August & 4 & 07:01 & 08:37 & 106 & 3649.5--6853.5 & 17536 & $-0.20,+0.20$ \\\\\n16 August & 5 & 06:18 & 08:18 & 110 & 3649.5--6853.5 & 17542 & $-0.27,+0.24$ \\\\ \n\\end{tabular}\n\\end{minipage}\n\\end{table*}\n% #########################################################################\n\n\nThe data were bias-subtracted and corrected for flat-field and slit\nillumination effects using standard {\\sc iraf} procedures.\n1-D spectra of both variable and comparison star were extracted\nwith the optimal extraction algorithm of Horne (1986). \nThe individual spectra were checked for the presence of possible cosmic\nrays and, when appropriate, were corrected by interpolation from the\nneighboring wavelengths. Arc-lamp observations were used to calibrate the\nwavelength scale (accuracy of 0.15 \\AA). Observations of the standard spectrophotometric stars\nBD+28\\,4211 and G191\\,B2B (Massey et~al. 1988) were used to derive the\ninstrumental sensitivity function and to flux calibrate the set of extracted\nspectra on each night. Error bars were computed taking into account the photon\ncount noise and the sensitivity response of the instrument.\n\nThe reduced spectra were combined to produce trailed spectrograms of the\nvariable and the comparison star for each night. The display of the trailed\nspectrograms of the comparison star shows that there were non negligible sky\ntransparency variations and/or time-dependent slit losses along the runs.\nWe defined a reference spectrum of the comparison star by computing an average\nof 40 spectra on night 5 corresponding to the time for which the star was\nclosest to zenith.\nWe normalized the spectrograms of the comparison star by dividing each\nspectrum by the reference spectrum. A 2-D cubic spline fit was used to\nproduce a smoothed version of the normalized spectrograms.\nThe sky transparency variations and variable slit losses were corrected\nby dividing the spectrogram of the variable by the smoothed, normalized\nspectrogram of the comparison star on each night (a procedure analogous\nto the flat-field correction).\nThe reference spectrum is consistent with the UBVRI photometry of star C1\n(BSC94) at the 1-$\\sigma$ level. Therefore, the absolute photometric accuracy\nof these observations should be better than 10 per cent.\n\nFig.\\,\\ref{fig1} shows average out-of-eclipse and mid-eclipse spectra of\nUU~Aqr on 1995 August 13. The spectra are dominated by strong single-peaked\nBalmer emission lines but also show He\\,I lines and the blend of\nC\\,III, N\\,III and He\\,II lines at $\\sim 4650$ \\AA. The emission lines\nhave asymmetrical shapes, the red side of the line being stronger --\nin accordance with the results of Hessman (1990) and Diaz \\& Steiner (1991).\nThe He\\,I lines and the higher energy Balmer lines show a possible double\npeak structure suggesting either classical double-peaked emission from a\nhighly inclined disc or single peaked emission with a central absorption\ncomponent. While the continuum is reduced by a factor\n$\\simeq 3$ during eclipse, the emission lines\nsuffer a much smaller reduction in flux suggesting that they possibly\narise from a vertically-extended source larger than the accretion disc\n(responsible for the continuum emission), in accordance with inferences\ndrawn by BSC94.\n%\n% ############################## FIGURE 1 #################################\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig01.ps,angle=-90,width=10.5cm,rheight=7.5cm}}\n\\caption{Average out-of-eclipse (black, phase range $-0.22$ to $-0.06$ cycle)\nand mid-eclipse (light gray, phase range $-0.025$ to 0.025 cycle) spectra of\nUU~Aqr on 1995 August 13. Major emission features are indicated by vertical\ndotted lines.}\n\\label{fig1}\n\\end{figure}\n\n\nFig.\\,\\ref{fig2} shows lightcurves of the 5 runs in the broad band $5000-\n6500$ \\AA. The gap in run 5 is due to\nan interruption of the observations to check the telescope focus.\nThe lightcurves have similar eclipse shapes and out of eclipse flux levels,\nwith variations at the level of $\\simlt 20$\\ per cent between the runs.\nIndications that the observations were performed while UU~Aqr was in its\nhigh brightness state come from the eclipse shape and average out of eclipse\nflux level. The latter suggests that the object was even slightly brighter\nthan the typical high brightness state of BSC94.\nThese remarks are in agreement with the historical lightcurve of Honeycutt\net~al. (1998, see their fig.\\,1), which shows that UU~Aqr reached a maximum\nof its long-term average brightness level during 1993, the epoch of our\nobservations. The spectral range of the lightcurves in Fig.\\,1 corresponds\nroughly to the $V$ band.\nThe average out of eclipse level of all runs yields an approximate mean\nmagnitude of $V= 13.2 \\pm 0.2$ mag, consistent with the value drawn from\nthe lightcurve of Honeycutt et~al. (1998), of $V= 13.4 \\pm 0.6$ mag.\n%\n% ############################## FIGURE 2 #################################\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig02.ps,width=10cm,rheight=12cm}}\n\\caption{Broad band lightcurves of the UU Aqr dataset. The curves are\nprogressively displaced upwards by 20 mJy for visualization purposes.\nHorizontal lines at mid-eclipse show the true zero level in each case.}\n\\label{fig2}\n\\end{figure}\n\n\n\\section{Data analysis} \\label{analise}\n\n\\subsection{Light curve construction}\n\nThe spectra were divided into 226 passbands of 15 \\AA\\ in the continuum and\nfainter lines, and $\\simeq 500\\; km\\,s^{-1}$ across the most prominent lines.\nFor each passband a lightcurve was extracted by computing the average flux\non the corresponding wavelength range and phase folding the resulting data\naccording to the ephemeris of BSC94. A phase correction of $-0.003$ cycle was\nfurther applied to the data to make the centre of the white dwarf eclipse\ncoincident with phase zero. For those passbands including emission lines\nthe light curves comprise the total flux at the corresponding bin with\nno subtraction of a possible underlying continuum contribution.\n\nSince the dataset correspond to the same brightness level it was possible\nto combine the lightcurves of all runs to produce average lightcurves for\neach passband. This is helpful to increase the signal-to-noise ratio of the\nlightcurves and to reduce the influence of flickering in the eclipse shape.\nFor each passband, we first normalized the individual lightcurves by\nfitting a spline function to the phases outside eclipse and dividing the\nlightcurve by the fitted spline. The normalized lightcurves were combined by\nseparating the data into phase bins of 0.0038~cycle and computing the median\nfor each bin. The median of the absolute deviations with respect to the\nmedian is taken as the corresponding uncertainty.\nThe resulting lightcurve is scaled back to flux units by multiplying the\ncombined lightcurve by the median flux of the spline functions at phase zero.\nThis procedure removes orbital variations outside eclipse with\nonly minor effects on the eclipse shape itself.\n\n\n\\subsection{Eclipse mapping}\n\\label{mem}\n\nThe eclipse mapping method was used to solve for a map of the disc\nbrightness distribution and for the flux of an additional uneclipsed\ncomponent in each passband. For the details of the method the reader\nis referred to Horne (1985, 1993), Baptista \\& Steiner (1993) and\nRutten et al. (1994).\n\nFor our analysis we adopted the same eclipse map of BSH96, a $51 \\times 51$\npixel grid centred on the primary star with side $2 \\:R_{L1}$ where\n$R_{L1}$ is the distance from the disc centre to the inner Lagrangian point.\nThis choice provides maps with a nominal spatial resolution of $0.039 \\:\nR_{L1}$, comparable to the expected size of the white dwarf in UU~Aqr\n($\\simeq 0.032\\: R_{L1}$). The eclipse geometry is specified by the mass\nratio $q$ and the inclination $i$. We adopted the parameters of BSC94,\n$i= 78\\degr$ and $q=0.3$.\nThe specific intensities in the eclipse map were computed assuming\nR$_{L1}= 0.74 \\; R_\\odot$ (BSC94) and a distance of 200 pc (BSH96).\n\nThe statistical uncertainties of the eclipse maps were estimated with a\nMonte Carlo procedure (e.g., Rutten et al. 1992; Baptista et~al. 1995).\nFor a given narrow-band lightcurve a set of 10 artificial lightcurves is\ngenerated, in which the data points are independently and randomly\nvaried according to a Gaussian distribution with standard deviation\nequal to the uncertainty at that point. The lightcurves are fitted\nwith the eclipse mapping algorithm to produce a set of randomized\neclipse maps. These are combined to produce an average map and a map\nof the residuals with respect to the average, which yields the statistical\nuncertainty at each pixel.\nThe uncertainties obtained with this procedure will be used when\nestimating the errors in the derived radial temperature and intensity\nprofiles as well as in the spatially-resolved spectra.\n\nAverage light curves, fitted models, and eclipse maps at selected passbands\nare show in Figs.\\,\\ref{fig3} and \\ref{fig4}. These will be discussed in\ndetail in section\\,\\ref{resultados}.\n\n\n\\section{Results} \\label{resultados}\n\n\\subsection{Accretion disc structure}\n\\label{estrutura}\n\nIn this section we compare eclipse maps at selected passbands in order\nto study the structure of the accretion disc at different wavelengths.\n\nFig.\\,\\ref{fig3} shows lightcurves (left panels) and eclipse maps (right\npanels) of 4 selected continuum passbands close to the Johnson-Cousins\nUBVR effective wavelengths in order to allow a comparison with\nthe results of BSH96.\nDashed horizontal lines depict the uneclipsed component in each case.\nThe continuum lightcurves show a deep eclipse with a slightly asymmetric\negress shoulder which is more pronounced for longer wavelengths.\nThis results in eclipse maps with brightness distributions concentrated\ntowards disc centre and asymmetric structures in the trailing quadrant of\nthe disc closest to the secondary star (the upper right quadrant in the\neclipse maps of Fig.\\,\\ref{fig3}).\nThe uneclipsed component at $\\lambda 3657$ is perceptibly \nlarger than at $\\lambda 4411$, suggesting that the Balmer jump is\nin emission and that the uneclipsed light has an important contribution\nfrom optically thin gas. This is in line with previous results by\nBSC94 and BSH96.\nThe eclipse shapes and out of eclipse levels resemble those\nof the high brightness state observed by BSH96, although with a less\npronounced asymmetry at eclipse egress. Accordingly, the eclipse maps\nclearly lack the noticeable asymmetric structure at disc edge which was\nthe main characteristic of the high state (BSH96, see their Fig.\\,3).\nWe will return to this point in section\\,\\ref{discussao}.\n%\n% ############################## FIGURE 3 #################################\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig03.ps,width=11cm,rheight=13.5cm}}\n\\caption{ Lightcurves (left) and eclipse maps (right) at selected continuum\n\tpassbands. Data lightcurves are shown as gray dots with error bars and\n\tthe fitted models appear as solid black lines. A horizontal dashed line\n\tdepicts the uneclipsed component in each case. Labels indicate the\n\tcentral wavelength of each passband. Eclipse maps are shown to the right\n\tin a logarithmic grayscale: dark regions are brighter; white corresponds\n\tto $\\log I_\\nu= -6.5$, and black to $\\log I_\\nu= -3.1$. Dotted curves\n\tshow the projection of the primary Roche lobe onto the orbital plane\n\tand the theoretical gas stream trajectory; the secondary star is to the\n\tright of each panel and the stars rotate counter-clockwise. }\n\\label{fig3}\n\\end{figure}\n\nFig.\\,\\ref{fig4} shows lightcurves and eclipse maps for the line centre\npassbands of H$\\alpha$, H$\\beta$, H$\\gamma$ and He\\,I $\\lambda$5876.\nWe remark that the line lightcurves include the total flux at the \ncorresponding wavelength range with no subtraction of an interpolated\ncontinuum. The eclipses are shallow, leading to brightness distributions\nwhich are flatter than those of the continuum. \nSimilar to the continuum maps, the asymmetry in the egress shoulder is\nmore pronounced for the lines at longer wavelengths.\nThe uneclipsed components are considerably larger than in the continuum,\nindicating that the uneclipsed spectrum has strong Balmer and He\\,I\nemission lines.\nThe large error bars of the H$\\alpha$ centre lightcurve is due not to\nlow signal-to-noise ratio but to the variability of the eclipse shape at\nthis wavelength. This effect is also seen, although to a lesser extent,\nin H$\\beta$ and H$\\gamma$.\n%\n% ############################## FIGURE 4 #################################\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig04.ps,width=11cm,rheight=13.5cm}}\n\\caption{ Lightcurves (left) and eclipse maps (right) for the H$\\alpha$,\n\tH$\\beta$, H$\\gamma$ and He\\,I $\\lambda 5876$ line centre passbands.\n\tThe notation and logarithmic grayscale are the same as in\n\tfigure\\,\\ref{fig3}. }\n\\label{fig4}\n\\end{figure}\n\n\nFig.\\,\\ref{fig5} shows (Doppler) velocity-resolved lightcurves (left) and\neclipse maps (right) across the H$\\beta$ line.\nThere is marginal evidence of rotational disturbance: the minimum of the\nblue bin lightcurve ($- 494 \\; km \\;s^{-1}$) is slightly displaced towards \nnegative phases while that of the red bin lightcurve ($+ 494 \\; km \\;s^{-1}$)\nis correspondingly displaced towards positive phases, suggesting that the\nline emitting gas rotates in the prograde sense.\nHowever, the eclipse maps in the symmetric velocity bins do not show the\nmirror symmetry (over the line joining both stars) expected for line\nemission from a Keplerian disc around the white dwarf.\nEqually remarkable are the facts that the lightcurve in the red bin has a\nmuch larger out-of-eclipse flux than its blue counterpart and that the\ncorresponding eclipse map is perceptibly brighter than that of the blue\nbin anywhere. A similar behaviour is found in the other lines for which\nvelocity-resolved maps were obtained.\nThis cannot be attributed to the underlying continuum since the\ninterpolated continuum has essentially a constant level across each line.\nIt seems clear that most of the line emission does not arise from a\ndisc in Keplerian rotation.\n%\n% ############################## FIGURE 5 #################################\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig05.ps,width=10cm,rheight=12.2cm}}\n\\caption{ H$\\beta$ velocity-resolved lightcurves (left) and eclipse maps\n\t(right) at velocities of $-494,\\; 0,\\; {\\rm and}\\; +494\t\\;km \\;s^{-1}$.\n\tThe notation and logarithmic grayscale are the same as in\n\tfigure\\,\\ref{fig3}. }\n\\label{fig5}\n\\end{figure}\n\n\n\\subsection{Radial temperature distribution and mass accretion rate estimate}\n\nThe simplest way of testing theoretical disc models is to convert the\nintensities in the eclipse maps to blackbody brightness temperatures,\nwhich can then be compared to the radial run of the effective temperature\npredicted by steady state, optically thick disc models. However, as\ndiscussed by Baptista et~al. (1998), a relation between the effective\ntemperature and a monochromatic brightness temperature is non-trivial,\nand can only be properly obtained by constructing self-consistent models\nof the vertical structure of the disc. Therefore, our analysis here\nis meant as preliminary, and should be complemented by detailed disc\nspectrum modeling in a future paper.\n\nFig.\\,\\ref{fig6} shows brightness temperature radial distributions for\nthe continuum maps of Fig.\\,\\ref{fig3} in a logarithmic scale.\nEach temperature shown is the blackbody brightness temperature that\nreproduces the observed surface brightness at the corresponding pixel\nassuming a distance of 200~pc to UU~Aqr (BSH96). Steady-state disc models\nfor mass accretion rates of $10^{-8.5}$, $10^{-9}$, $10^{-9.5}$ and\n$10^{-10}\\; M_\\odot \\; yr^{-1}$ are plotted as dotted lines for comparison.\nThese models assume M$_1= 0.67 \\; M_\\odot$ and $R_1= 0.012 \\; R_\\odot$\n(BSC94).\n\nThe distributions resemble those obtained by BSH96 for the high brightness\nstate of UU Aqr, closely following the $T\\propto R^{-3/4}$ law for steady\naccretion in the intermediate and outer disc regions ($R \\geq 0.2\\; \nR_{\\rm L1}$) but displaying a noticeable flattening in the inner disc\n($R < 0.1\\; R_{\\rm L1}$).\nTemperatures range from $\\sim 18000$ K in the inner disc to 6000 K in the\nouter disc regions, leading to inferred mass accretion rates of \\.{M}=\n$10^{-9.0 \\pm 0.3}\\; M_\\odot \\, yr^{-1}$ at $R= 0.1\\; R_{\\rm L1}$ and\n$10^{-8.7 \\pm 0.2} \\; M_\\odot \\, yr^{-1}$ at $R= 0.3\\; R_{\\rm L1}$ --- in\ngood agreement with the results of BSH96 for the high brightness state.\nThe quoted errors on \\.{M} account for the statistical uncertainties in the\neclipse maps, obtained from the Monte Carlo procedure described in\nsection\\,\\ref{mem}, and the scatter in the temperatures of maps at\ndifferent wavelengths.\nThe eclipse map at $\\lambda 3657$ leads to temperatures which are\nsystematically higher than those of the other continuum maps of Fig.\\,3,\nin an example of the limitations of using brightness temperatures to\nestimate the mass accretion rate. This difference reflects the fact that\nthe Balmer jump appears in emission for the intermediate and outer disc\nregions, as will be seen in section\\,\\ref{spectra}.\n%\n% ############################## FIGURE 6 #################################\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig06.ps,angle=-90,width=11cm,rheight=7.5cm}}\n\\caption{ Brightness temperature radial distributions of the UU Aqr accretion\n\tdisc for the continuum maps of figure\\,\\ref{fig3}, calculated assuming\n\ta distance of 200 pc to the system (BSH96). Dotted lines correspond to\n\tsteady-state disc models for mass accretion rates of \\.{M}$= 10^{-8.5}$,\n\t$10^{-9}$, $10^{-9.5}$ and $10^{-10}\\; M_\\odot \\; yr^{-1}$, assuming\n\tM$_1= 0.67 \\; M_\\odot$ and $R_1= 0.012 \\; R_\\odot$ (BSC94). Abscissae\n\tare in units of the distance from disc centre to the inner Lagrangian\n\tpoint (R$_{\\rm L1}$). }\n\\label{fig6}\n\\end{figure}\n\n\n\\subsection{Radial line intensity distributions}\n\nLeft panel in Fig.\\,\\ref{fig7} shows radial intensity distributions for\nthe most prominent lines (solid) and adjacent continuum (dotted) in a\nlogarithmic scale. The line distributions were obtained from the average\nof all eclipse maps across the line region, while the continuum\ndistributions were obtained from the average of eclipse maps on\nboth sides of each line. \nNet line emission distributions were computed by subtracting the\ndistributions of the adjacent continuum from those of the lines,\nand are shown in the right panel.\nIn the external map regions ($R \\simgt 0.7\\; R_{\\rm L1}$) the intensities\nof both line and continuum drop by a factor $\\sim 10^3$ with respect\nto the inner disc regions, making the computation of the net emission\nquite noisy and unreliable.\nH$\\alpha$ is seen in emission (intensities larger than those at the\nadjacent continuum) at all disc radii and up to $R \\simeq 0.6\\; R_{\\rm L1}$. \nThe other lines are in absorption in the inner disc and transition to\nemission at intermediate ($R \\sim 0.2\\; R_{\\rm L1}$) disc radius.\nThis behaviour is noticeably different from that observed at the low\nbrightness state, where H$\\alpha$ is seen in emission in the inner disc\nand disappears into the continuum for $R \\simeq 0.3\\; R_{\\rm L1}$ (BSH96).\nThis result suggests that the line emission region increases in size\nfrom the low to the high brightness state, possibly in response to changes\nin mass accretion rate.\nThe transition from absorption to emission occurs at larger disc radii for\nlines of higher excitation. This can be explained, for the Balmer lines,\nby the increase in continuum emission at the inner disc for shorter\nwavelengths.\n%\n% ############################## FIGURE 7 #################################\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig07.ps,width=10cm,rheight=12cm}}\n\\caption{ Radial line intensity profiles for the most prominent lines,\n\tcalculated assuming a distance of 200 pc to the system (BSH96). \n\tAbscissae are in units of the distance from disc centre to the inner\n\tLagrangian point (R$_{\\rm L1}$). Right panels show net line emission \n\tradial distributions. Dotted lines depict the slope of the expected\n\trelation $I \\propto R^{-1.5}$. }\n\\label{fig7}\n\\end{figure}\n\nA set of dotted lines in the right panel indicate the slope of the empirical\nradial dependency of the line emissivity in accretion discs, $I \\propto\nR^{-1.5}$, as inferred from Doppler Tomography by assuming a Keplerian\ndistribution of velocities for the emitting gas (Marsh et al. 1990).\nFor H$\\gamma$ and He\\,I $\\lambda$5876, the net emission occurs for a narrow range of radii making a comparison with the empirical law difficult.\nThe derived radial distributions for H$\\alpha$ and H$\\beta$ are clearly\ndifferent from the empirical $I \\propto R^{-1.5}$ law; in particular,\nthe H$\\alpha$ distribution is flat at inner and intermediate disc radii\n($R <0.3\\; R_{\\rm L1}$).\nThis remark suggests that the line emitting regions on the disc surface\nare not in Keplerian orbits or that a substantial fraction of the emission\nlines does not arise from the accretion disc, in line with the inferences\ndrawn by the comparison of velocity-resolved eclipse maps in\nsection\\,\\ref{estrutura}.\nThe latter hypothesis is consistent with the significant uneclipsed\ncomponents inferred for the Balmer and He\\,I lines (section\n\\,\\ref{uneclipsed}).\n\n\n\\subsection{Spatially resolved spectra}\n\\label{spectra}\n\nEach of the eclipse maps yields spatially-resolved information about\nthe emitting region on a specific wavelength range. By combining all\nnarrow-band eclipse maps we are able to isolate the spectrum of the\neclipsed region at any desired position (e.g., Rutten et~al. 1994;\nBaptista et~al. 1998).\n\nTo investigate the possible influence of the gas stream on the disc\nemission and motivated by the observed asymmetries in the eclipse maps\nshown in section\\,\\ref{estrutura}, we divided the disc into two major\nazimuthal regions to extract spatially-resolved spectra: the gas stream\nregion (upper right quadrant in the eclipse maps of Figs.\\,3 and 4) and\nthe disc region (the remaining 3/4 of the eclipse map). \nFor each of these regions, we divided the maps into a set of 6 concentric\nannuli centred on the white dwarf of width $0.1\\: R_{L1}$ and with radius increasing in steps of $0.1\\: R_{L1}$.\nEach spectrum is obtained by averaging the intensity of all pixels\ninside the corresponding annulus and the statistical uncertainties\naffecting the average intensities are estimated with the Monte Carlo\nprocedure described in section\\,\\ref{mem}.\n\n\n\\subsubsection{Disc spectra}\n\\label{disc}\n\nFig.\\,\\ref{fig8} shows spatially-resolved spectra of the disc region in\na logarithmic scale. The inner annular region is at the top and each\nspectrum is at its true intensity level. The spectrum of the uneclipsed\ncomponent is shown in the lower panel and will be discussed in detail in\nsection\\,\\ref{uneclipsed}.\n%\n% ############################## FIGURE 8 #################################\n%\n\\begin{figure*}\n\\centerline{\\psfig{figure=xfig08.ps,angle=-90,width=21cm,rheight=15cm}}\n\t\\caption{ Spatially resolved spectra of the UU Aqr accretion disc.\n\tThe spectra were computed for a set of concentric annular sections\n\t(radius range indicated on the right, in units of $R_{L1}$).\n\tThe lower panel shows the spectrum of the uneclipsed light.\n\tThe most prominent line transitions are indicated by vertical dotted\n\tlines. Error bars were derived via Monte Carlo simulations with the\n\teclipse lightcurves. }\n\\label{fig8}\n\\end{figure*}\n%\nThe spectrum of the inner disc is characterized by a blue and bright\ncontinuum filled with deep and narrow absorption lines. The continuum\nemission becomes progressively fainter and redder for increasing disc radius\nwhile the lines transition from absorption to emission showing clear P~Cygni\nprofiles on all lines mapped at higher spectral resolution. The Balmer jump\nappears in absorption in the inner disc and weakly in emission in the\nintermediate and outer disc regions suggesting that the outer disc in\nUU~Aqr is optically thin. The change in the slope and intensity\nof the continuum with increasing disc radius reflects the temperature\ngradient in the accretion disc, with the effective temperature decreasing\noutwards.\n\nThe spatially resolved spectra of the disc are plotted in\nFig.\\,\\ref{fig9} as a function of velocity for the H$\\alpha$, H$\\beta$\nand H$\\gamma$ regions. Vertical dotted lines mark line centre and the\nmaximum blueshift/redshift velocity expected for gas in Keplerian\norbits around a $0.67 M_\\odot$ white dwarf as seen from an inclination of\n$i=78\\degr$ ($v \\sin i= 3200 \\;km \\;s^{-1}$) [BSC94].\n%\t\n% ############################## FIGURE 9 #################################\n%\n\\begin{figure}[h]\n\\centerline{\\psfig{figure=xfig09.ps,width=9.5cm,rheight=11cm}}\n\t\\caption{ Spatially resolved spectra in the H$\\alpha$, H$\\beta$ and\n\tH$\\gamma$ regions as a function of velocity. The notation is the same\n\tas in figure\\,\\ref{fig8}. Dotted vertical lines mark line centre and\n\tthe maximum blueshift/redshift velocity expected for gas in Keplerian\n\torbits around a $0.67 M_\\odot$ white dwarf seen at an inclination of\n\t$i=78\\degr$ ($v \\sin i= 3200 \\;km \\;s^{-1}$). }\n\\label{fig9}\n\\end{figure}\n% \nThe absorption lines at disc centre are perceptibly narrower than expected\nfor emission from either the white dwarf atmosphere or from disc gas in\nKeplerian orbits around the white dwarf. The discrepancy increases if the\nlarger mass estimates of Diaz \\& Steiner (1991) and Kaitchuck et~al (1998)\nare assumed for the white dwarf. Moreover, the absorption lines at disc\ncentre are deep, while lines produced in a white dwarf atmosphere or\ninnermost disc regions should be broad and shallow. The width of the lines\nindicate a velocity dispersion of $\\simeq 1500 \\;km \\;s^{-1}$ for the line\nemitting region in the line of sight to the disc centre and higher\nvelocities ($\\sim 2000 \\;km \\;s^{-1}$) for the gas in the outer disc at\n$R \\simeq 0.5\\; R_{\\rm L1}$.\nThis is in clear disagreement with the expected behaviour of line emission\nfrom gas in a Keplerian disc and provide additional evidence that these\nlines do not arise from the disc atmosphere.\nOn the other hand, the lines at intermediate and outer disc regions\n($R \\simgt 0.2\\; R_{\\rm L1}$) show clear P~Cygni profiles indicating origin\nin an outflowing gas, probably the disc wind.\n\nWe note that the H$\\alpha$ line shows a redshifted ($v \\sim 1800 \\;km\\;\ns^{-1}$) absorption component in spectra of the outer disc regions ($R >\n0.3\\; R_{L1}$). Comparison of disc spectra at different azimuths shows\nthat this absorption is produced in the front side of the disc, but an\norigin in the gas stream can possibly be ruled out since the absorption\ncomponent is seen with similar strengths in the leading and trailing\n(the one containing the gas stream) quadrants.\nThe interpretation of this feature is not straightforward and deserves a\nbit of caution, since it is not clearly seen in any other line and also\nbecause the surface brightness in the corresponding disc region is only\na few percent of the intensities in the inner disc.\n\n\n\\subsubsection{The uneclipsed spectrum}\n\\label{uneclipsed}\n\nThe spectrum of the uneclipsed light (lower panel of Fig.\\,\\ref{fig8})\nshow prominent Balmer and He\\,I emission lines. The Balmer jump is clearly\nin emission and the optical continuum rises towards longer wavelengths\nsuggesting that the Paschen jump is also in emission. These results\nare consistent with the findings of BSH96 and indicate that the uneclipsed\nlight has an important contribution from optically thin gas from outside\nthe orbital plane. The Balmer lines mapped at higher spectral resolution\nshow broad asymmetric profiles, with line peaks displaced to the red\nside and wings extending up to $\\simeq 1500 \\;km \\;s^{-1}$. The observed\nasymmetry is consistent with that previously seen in the integrated spectra\nof Diaz \\& Steiner (1991) and Hessman (1990) and is similar to that\nobserved in the resonant ultraviolet lines of UX~UMa, where the uneclipsed\ncomponent was attributed to emission in a vertically-extended disc wind\n(Baptista et~al. 1995; 1998; Knigge \\& Drew 1997).\n\nThe fractional contribution of the uneclipsed component to the total flux\nwas obtained by dividing the flux of the uneclipsed light by the average\nout of eclipse level at each passband. The result is shown in \nFig.\\,\\ref{fig10}. The fractional contribution of the uneclipsed light\nis very significant for the optical emission lines, reaching 40-60\\ per cent\nat the Balmer lines and 20-40\\ per cent at the He\\,I lines, and decreases\nsteadily along the Balmer series. \nThe difference in fractional contribution between the Balmer\nand He\\,I lines and among the Balmer lines indicates the existence of\na vertical temperature gradient in the material above/below the disc,\nwith the He\\,I lines (which require higher excitation energies)\nbeing produced closer to the orbital plane. In any case, a substantial \nfraction of the light at these lines does not arise from the orbital\nplane and is not occulted during eclipse.\nThe uneclipsed component gives significant contribution also to the\ncontinuum emission. About 20\\ per cent of the flux at the Balmer continuum\nand similar fraction of the continuum emission at the red end\nof the spectrum arise from regions outside the orbital plane.\n%\t\n% ############################# FIGURE 10 #################################\n%\n\\begin{figure}[h]\n\\centerline{\\psfig{figure=xfig11.ps,angle=-90,width=10cm,rheight=7.5cm}}\n\t\\caption{ Fractional contribution of the uneclipsed component to\n\tthe total flux as a function of wavelength. The values were obtained\n\tby dividing the flux of the uneclipsed component by the average out\n\tof eclipse level for each passband. }\n\\label{fig10}\n\\end{figure}\n\n\n\\subsubsection{The gas stream region}\n\\label{stream}\n\nFig.\\,\\ref{fig11} shows the ratio between the spectrum of the gas stream\nregion and the disc region at same radius as a function of radius.\nA dotted line marks the unity level for each panel. \nThe comparison shows that the spectrum of the gas stream is noticeably\ndifferent from the disc spectrum in the outer disc regions (where one\nexpects a bright spot to form due to the shock between the inflowing\nstream and the outer disc rim), but also reveals systematic differences\nbetween stream and disc spectra in a range of radii. In all cases,\nthe stream emission is stronger than that of the adjacent disc.\n%\t\n% ############################# FIGURE 11 #################################\n%\n\\begin{figure*}\n\\centerline{\\psfig{figure=xfig10.ps,width=14cm,rheight=17cm}}\n\t\\caption{ Ratio of the gas stream spectrum and the disc spectrum \n\tfor the same set of annular regions of figure\\,\\ref{fig8}. Dashed\n\tlines mark the unity level for each panel. The notation is the same\n\tas in fig.\\,\\ref{fig8}.}\n\\label{fig11}\n\\end{figure*}\n\nThis result suggests that the material in the gas stream continues to flow\ndownstream beyond the bright spot position. In this regard, there are three\npotential cases: (1) stream overflow that arcs high above/below the disc\nuntil it hits the disc surface again at a downstream position closer to \nthe white dwarf (hereafter called the ``classical stream overflow''); \n(2) stream overflow that continuously skims the disc surface (hereafter\ncalled the ``disc-skimming overflow''); and (3) the stream drills into the\ndisc at the impact site (hereafter named the ``disc stream penetration'').\nThe latter case seems physically unrealistic and is not supported by hydrodynamic calculations of stream-disc interaction (Armitage \\& Livio\n1996, 1998). \nThe fact that there is enhanced emission in the stream region extending\nall the way from the outer disc down to $R\\simeq 0.2\\; R_{L1}$ argues in\nfavor of an interpretation in terms of disc-skimming overflow instead of\nthe classical stream overflow -- as has been suggested to explain the\nbehaviour of SW~Sex stars (Hellier \\& Robinson 1994; Hellier 1996) --\nsince the latter would produce enhanced emission only at the position of\nthe two spots, at the initial impact site in the outer disc edge and at\nthe re-impact site much closer to disc centre (Lubow 1989).\n\nThe spectrum of the ratio becomes redder for decreasing disc radius,\npossibly a combination of the disc emission becoming bluer as one moves\ninwards and the gas stream emission becoming redder while its energy is\ncontinuously lost in the shock with disc material along the inward stream\ntrajectory.\nThis is reminiscent of what was seen in ultraviolet eclipse observations\nof the dwarf novae IP~Peg in quiescence, which revealed a compact blue\nbright spot with an extended red tail (Baptista et~al. 1993). \n\n\n\\section{Discussion} \\label{discussao}\n\nIn this section we present and discuss some possible interpretations for\nthe results of section\\,\\ref{resultados} in the context of the current\nmodels for the SW Sex stars.\n\n\\subsection{Where do the lines come from?}\n\nIn previous sections we have accumulated evidences that the behaviour\nof the UU Aqr lines in its high state is not consistent with emission\nin a disc atmosphere, namely: \n(i) negligible rotational disturbance, (ii) no mirror symmetry between\neclipse maps in symmetric velocity bins; (iii) H$\\alpha$ line emission\ndistribution much flatter than the empirical $I \\propto R^{-1.5}$ law;\n(iv) significant uneclipsed components, and (v) presence of P~Cygni\nprofiles in the disc spectra at intermediate and large disc radii.\nIf the lines do not arise in the disc atmosphere, where do they come from?\n\nThe most compelling interpretation is that the lines are produced in a\ndisc chromosphere + wind. This region is hot, dense, opaque and has low\nexpansion velocities close to the orbital plane in order to produce the\nobserved deep, narrow absorption lines in the line of sight to the inner\ndisc. Most of the high excitation lines are produced close to the disc\nplane. The density and temperature decrease with height above/below the\ndisc as the outflowing gas spreads over an increasing surface area.\nOptically thin emission from this extended region is\nprobably responsible for the Balmer jump (and lines) in emission observed\nin the uneclipsed spectrum. Support in favor of this scenario comes from\nthe recent detailed modeling of the C\\,{\\sc IV} wind line of eclipsing\nnova-likes by Schlosman, Vitello \\& Mauche (1996) and Knigge \\& Drew\n(1997). Their results suggest the existence of a relatively dense ($n_e\n\\sim 4 \\times 10^{12}$~cm$^{-3}$) and vertically extended chromosphere\nbetween the disc surface and the fast-moving parts of the wind, which\ncould produce significant amounts of optically thin emission.\nAt orbital phases around eclipse, gas outflowing in the direction of the\nsecondary star will be seen along the line of sight to the bright underlying\naccretion disc as blueshifted absorption features, while gas expelled in\nthe direction away from the secondary star should contribute with\nredshifted emission.\n\nWe tested this scenario by \ncomparing spatially resolved spectra of the disc lune closest to the\nsecondary star (the right hemisphere of the disc in the eclipse maps of\nFig.\\,\\ref{fig3}, hereafter called the ``front'' side) and of the disc\nlune farthest away from the secondary star (the left hemisphere of the\ndisc in Fig.\\,\\ref{fig3}, hereafter called the ``back'' side). \nFor this purpose, we defined two opposite azimuthal disc regions of width\n$30\\degr$ along the major axis of the binary, and extracted spatially\nresolved spectra for the same set of annuli as above. These spatially\nresolved spectra are noisier than those of Figs.\\,\\ref{fig8} and\n\\ref{fig9} because in this case the average intensity of each annulus\nis computed from a significantly smaller number of pixels. The results\nare shown in Fig.\\,\\ref{fig9A} for the H$\\beta$ and H$\\gamma$ regions\nand are consistent with our interpretation:\nThe blueshifted absorption component is seen mainly in the front side of\nthe disc while the redshifted emission is generally more prominent in\nspectra of the back side of the disc.\nThe fact that the blueshifted absorption can still be seen projected along\nthe line of sight at the outer regions of the disc favours a more spherical\nor equatorial geometry for the outflowing gas instead of a highly collimated,\npolar jet.\n%\t\n% ############################## FIGURE 12 ################################\n%\n\\begin{figure}\n\\vspace*{7cm}\n%\\centerline{\\psfig{figure=xfig12.ps,angle=-90,width=10.5cm,rheight=7cm}}\n\t\\caption{ Comparison of spatially resolved spectra of the front and\n\tback side of the disc (see text) in the H$\\beta$ and H$\\gamma$ regions.\n\tThe notation is the same as in figure\\,\\ref{fig9}. For clarity, only\n\tthe H$\\gamma$ spectra of two annuli are shown. }\n\\label{fig9A}\n\\end{figure}\n\nThe chromosphere + disc wind interpretation satisfactorily accounts for all\nthe features listed above and also gives a plausible explanation for \n(1) the distinct semi-amplitude of the radial velocity $K$ and systemic\nvelocity $\\gamma$ as inferred from different emission lines and \n(2) the time dependent $K$ and $\\gamma$ values (Hoard et~al. 1998). \nThe centroid of lines of different excitation level will occur at different\nlocations in the primary lobe and will sample different velocities \nalong the line of sight. With respect to (2), \nthe comparison of the H$\\alpha$ map of BSH96 (which corresponds to the low\nbrightness state) with that of Fig.\\,\\ref{fig4} (the high state) reveals\nthat in the latter the emission extends over a much larger region of the\nprimary lobe with a pronounced asymmetry in the stream region,\nsuggesting that the wind emission is variable in time and is intimately\nconnected with the mass accretion rate. \nThis remark gives additional support to the suggestion\nby Hoard et~al. (1998) that the observed time dependence of the $K$ and\n$\\gamma$ velocities might be due to variability of a wind component\nin UU Aqr.\n\nAn alternative possibility is to consider the deep absorption lines\nseen towards the line of sight to the disc centre as being produced by\nabsorption in a vertically extended disc rim. Although this scenario\naccounts for the narrow absorption lines,\nit is not able to explain the large velocities inferred from the line\nwidth for intermediate and large disc radius nor the P~Cygni profiles.\nFurthermore, it should result in a perceptible front-back asymmetry in\nthe disc surface brightness (namely, the back side of the disc should be\nbrighter) which is not seen in the eclipse maps.\n\nRecently, Horne (1999) proposed that most of the features of the SW Sex\nstars could be explained in terms of a disc-anchored magnetic propeller,\nin which energy and angular momentum are extracted from the magnetic field\nof the inner disc regions to fling part of the material in the gas stream\nout of the binary towards the back side of the disc. \nAlthough this model is able to explain many of the observed features of\nUU Aqr, it can only account for the observed P Cygni profiles if the gas\ntrapped by the inner disc magnetic field is expelled in all directions\nand not only towards the back of the disc.\nWe note that, in this case, there is no significant difference between\nthe propeller and the disc wind models and, in fact, the former could\npossibly work as the underlying physical mechanism driving the latter.\n\nIf disk-skimming overflow does occur, we might expect that \ndissipation of energy in the collision between the gas stream and the\ndisc material gives rise to a bulge extending along the stream trajectory\nover and under the disc. This bulge will appear in front of the\nchromosphere + wind line emitting region at the inner disc when seen\nalong the line of sight at orbital phases 0.5-0.9.\nThis may explain the phase-dependent absorption lines, observed from\nphases 0.5-0.9 and with maximum at phase $\\sim 0.8$ (Heafner 1989;\nHoard et~al. 1998). The enhanced line emission along the gas stream\n(see Fig.\\,\\ref{fig4}) is possibly responsible for the phase offset\nbetween photometric and spectroscopic conjunction\n(Diaz \\& Steiner 1991; Hoard et~al. 1998). \n\nIn summary, the picture which emerges from our results is consistent\nwith the results from the Doppler tomography and the model proposed\nfor UU Aqr by Hoard et~al. (1998).\n\n\n\\subsection{Where has the bright spot gone?}\n\nAlthough our observations correspond to the high brightness state of\nUU Aqr, our eclipse maps do not show the conspicuous asymmetric structure\nseen in the high state eclipse maps of BSH96 and which was interpreted\nas being the bright spot.\nThe explanation for the `disappearance' of the bright spot may be\nconnected with the stunted outbursts found by Honeycutt et~al. (1998).\n\nBSH96 pointed out that the inferred accretion rate of UU Aqr\nis close to the critical mass accretion rate for disc instability\nto occur and remarked that the long-term lightcurves of accretion\ndiscs with mass transfer rates near their critical limit might display\nlow-amplitude ($\\simlt 1.0$ mag) outbursts caused by thermal\ninstabilities in the outer disc regions (e.g., Lin, Papaloizou \\&\nFaulkner 1985). In this case the outburst is restricted to the outer\n1/3 of the disc extent while the inner disc remains in a high viscosity,\nsteady state.\nHoneycutt et~al (1998) suggested that such dwarf-nova type instabilities\ncould be an explanation for the stunted outbursts of UU Aqr if a\nmechanism can be identified to make the amplitudes appear small. \nWe note that the observed low amplitudes can be easily accounted for\nby the reduced contrast of the light from the outbursting outer\nregions -- where the efficiency in transforming gravitational potential\nenergy in radiation is relatively low -- in comparison to the bright,\noptically thick and steady inner disc.\n\nIf the observed stunted outbursts of UU Aqr are caused by thermal\ninstabilities in its outer disc, the disc radius is expected to\nincrease during the outburst and will eventually reach the 3:1 tidal\nresonance radius leading to an elliptical precessing disc reminiscent\nof what possibly happens in SU UMa stars in superoutburst\n(e.g., Warner 1995 and references therein). \nWe suggest that the azimuthally elongated structure seen in the\neclipse maps of BSH96 is the signature of such an elliptical disc\nand not the bright spot. Following this line of reasoning, this\nstructure should not be present when the disc radius is smaller than\nthe tidal resonance radius. Support for this interpretation comes from\nthe comparison of disc radius in the high state eclipse maps of BSH96\nand our eclipse maps. \nFrom BSH96 data we estimate a disc radius of $R_d \\simeq 0.7 \\; \nR_{\\rm L1}$, comparable to the 3:1 tidal resonance radius for a\nmass ratio of $q=0.3$. Our eclipse maps lead to a smaller value of\n$R_d = 0.65 \\; R_{\\rm L1}$. Therefore, we suggest that UU Aqr was in an \noccasional superhumper state during the high brightness state observations\nof BSC94.\n\nIn the model of Hoard et~al. (1998), after the explosive impact of the\nhigh \\.{M} accretion stream with the edge of the disc, the incomming gas \nforms an optically thick absorbing bulge on the disc that either follows \nroughly the stream trajectory or runs along the rim of the disc, producing\nthe absorption features seen at phases 0.4-0.9. It may alternatively be\npossible that the structure seen in the eclipse maps of BSH96 is the\nsignature of such post-impact stream material running along the edge of\nthe disc. In this scenario, the azimuthally extended bulge would be present\nor not depending on the (variable) mass accretion rate and the resulting\norbital hump would remain fixed in phase.\n\nIt would be interesting (although outside the scope of this paper) to\nreanalize the data of BSC94 to see if the orbital hump present in the high\nstate precesses in phase in a similar manner as superhumps in superoutbursts\n(supporting the elliptical disc scenario) or if its maximum occurs always\nat the same orbital phase range about 0.8 - 0.9 cycle (favouring the\npost-impact bulge scenario).\n\n\n\\section{Conclusions} \\label{conclusao}\n\nWe used time-resolved spectroscopy to study the structure and spectra\nof the accretion disc and gas stream of the novalike UU~Aquarii in\nthe optical range. The main results of this analysis can be summarized\nas follows:\n\n\\begin{itemize}\n\n\\item The spectrum of the inner disc shows a blue continuum filled with deep,\nnarrow absorption lines which transition to emission with clear P~Cygni\nprofiles at intermediate and large radii ($R\\simgt 0.2 \\; R_{L1}$).\n\n\\item The spectrum of the uneclipsed light has strong H\\,I and He\\,I\nemission lines and a Balmer jump in emission indicating a significant\ncontribution from optically thin regions outside the orbital plane.\n\n\\item Velocity-resolved eclipse maps and spectra indicate that most\nof the line emission probably arises in a vertically-extended disc\nchromosphere + wind.\n\n\\item Differences in fractional contribution among emission lines suggests\na vertical temperature gradient in the material above/below the disc.\n\n\\item The comparison of the spectrum of the gas stream region and the\ndisc region at the same radius as a function of radius gives evidence \nof gas stream disc-skimming overflow down to $R\\simeq 0.2\\; R_{L1}$.\nThis may explain the phase-dependent absorption in emission lines.\n\n\\item The comparison of our eclipse maps with those of BSH96 suggests that\nthe asymmetric structure in the outer disc previously identified as\nthe bright spot may be the signature of an elliptical precessing disc\nsimilar to those possibly present in SU UMa stars during superoutbursts.\n\n\\end{itemize}\n\n\n\\section*{Acknowledgments}\n\nWe gratefully acknowledge the director of KPNO for granting telescope time\nfor this project at the Summer Queue Program, Tod Boroson and the team\nof observers at KPNO for their kind effort in collecting the data, \nKnox Long and the director of STScI for financial support through\nthe Director Discretionary fund, Susan Keener for helping with the data\nreduction at STScI, and an anonymous referee for valuable comments and\nsuggestions that helped to improve the presentation of the results.\nRB acknowledges financial support from CNPq/Brazil through grant no. 300\\,354/96-7. 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AJ, 96, 777\n\\bibitem {9} Haefner R., 1989. Inf. Bull. Var. Stars, 3397\n\\bibitem {10} Hellier C., 1996. ApJ, 471, 949\n\\bibitem {11} Hellier C., 1999. in Warner Symposium on Cataclysmic Variables,\n\t\tNew Astronomy Reviews, in press (astro-ph/9906089).\n\\bibitem {12} Hellier C., Robinson E. L., 1994. ApJ, 431, L107\n\\bibitem {13} Hessman F. V., 1990. in Reviews in Modern Astrophysics:\n\t\tAccretion and Winds, ed. G. Klare, Springer, Berlin\n\\bibitem [Hoard et al, 1998]{Hoard} Hoard D. W., Still M.D., Skzody P., \n Smith R.C., Buckley D.A.H., 1998. MNRAS, 294, 689\n\\bibitem [Honeycutt et al, 1998]{Honey}\n\t\tHoneycutt R. K., Robertson J. W., Turner G. W., 1998. AJ, 115, 2527\n\\bibitem {Honey2} Honeycutt R. K., Schlegel E. M., Kaitchuck R. H., 1986.\n\t\tApJ, 302, 388\n\\bibitem [Horne 1985]{Horne} Horne K., 1985. MNRAS, 213, 129\n\\bibitem {14} Horne K., 1986. PASP, 98, 609\n\\bibitem {15} Horne K., 1993. in Accretion Disks in Compact Stellar Systems,\n\t\ted. J. C. Wheeler, World Scientific Publ. Co., p. 117\n\\bibitem {16} Horne K., 1999. in Magnetic Cataclysmic Variables, ASP Conf.\n\t\tSeries Vol.\\ 157, eds. K. Mukai \\& C. Hellier, ASP, San Francisco,\n\t\tp. 349\n\\bibitem {20} Kaitchuck R. H., Schlegel E. M., White II J. C., Mansperger\n\t\tC. S., 1998. ApJ, 499, 444\n\\bibitem {21} Knigge C., Drew J. E., 1997. ApJ, 486, 445\n\\bibitem {22} Lin D. N. C., Papaloizou J., Faulkner J., 1985. MNRAS, 212, 105\n\\bibitem {23} Lubow S. H., 1989. ApJ, 340, 1064\n\\bibitem {25} Marsh T. R., Horne K., Schlegel E.M., Honeycutt K., \n\t\tKaitchuck R.H., 1990. ApJ, 364, 637\n\\bibitem {30} Massey P., Strobel K., Barnes J. V., Anderson E., 1988.\n\t\tApJ, 328, 315\n\\bibitem {39} Rutten R. G. M., van Paradijs J., Tinbergen J., 1992. A\\&A,\n\t\t260, 213\n\\bibitem {40} Rutten R. G. M., Dhillon V. S., Horne K., Kuulkers E,. 1994.\n\t\tA\\&A, 283, 441\n\\bibitem {45} Schlosman I., Vitello, P. A. J., Mauche C. W., 1996. \n\t\tApJ, 461, 377\n\\bibitem {47} Thorstensen J. R., et~al., 1991. AJ, 102, 272\n\\bibitem {50} Warner B., 1995. Cataclysmic Variable Stars, Cambridge\n\t\tUniversity Press, Cambridge\n\\bibitem {51} Warner B., 1997. IAU Colloquium 163, Accretion Phenomena \n\t\tand Related Outflows, ASP Conf. Series 121, ed. D. T. Wickramasinghe,\n\t\tG. V. Bicknell \\& L. Ferrario, ASP, San Francisco, p. 133\n\\bibitem {52} Williams R. E., 1989. AJ, 97, 1752\n\n\\end{thebibliography}\n\n\\bsp\n\\end{document}\n"}],"string":"[\n {\n \"name\": \"uu3.tex\",\n \"string\": \"%\\tSpatially-resolved spectra of the accretion disc of UU Aqr (paper 3)\\n%\\tBaptista, Silveira, Steiner & Horne\\n%\\tlast update: 21/08/99\\n\\n\\\\documentstyle[psfig]{mn}\\n\\\\topmargin -20 mm\\n\\n% If your system has the AMS fonts version 2.0 installed, MN.sty can be\\n% made to use them by uncommenting the line: %\\\\AMStwofontstrue\\n%\\n% By doing this, you will be able to obtain upright Greek characters.\\n% e.g. \\\\umu, \\\\upi etc. See the section on \\\"Upright Greek characters\\\" in\\n% this guide for further information.\\n%\\n% If you are using AMS 2.0 fonts, bold math letters/symbols are available\\n% at a larger range of sizes for NFSS release 1 and 2 (using \\\\boldmath or\\n% preferably \\\\bmath).\\n\\n\\\\newif\\\\ifAMStwofonts\\n%\\\\AMStwofontstrue\\n\\n%%%%% AUTHORS - PLACE YOUR OWN MACROS HERE %%%%%\\n\\n% Useful symbols\\n\\\\def\\\\simlt{\\\\lower.5ex\\\\hbox{$\\\\; \\\\buildrel < \\\\over \\\\sim \\\\;$}}\\n\\\\def\\\\simgt{\\\\lower.5ex\\\\hbox{$\\\\; \\\\buildrel > \\\\over \\\\sim \\\\;$}}\\n\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\\\ifoldfss\\n %\\n \\\\newcommand{\\\\rmn}[1] {{\\\\rm #1}}\\n \\\\newcommand{\\\\itl}[1] {{\\\\it #1}}\\n \\\\newcommand{\\\\bld}[1] {{\\\\bf #1}}\\n %\\n \\\\ifCUPmtlplainloaded \\\\else\\n \\\\NewTextAlphabet{textbfit} {cmbxti10} {}\\n \\\\NewTextAlphabet{textbfss} {cmssbx10} {}\\n \\\\NewMathAlphabet{mathbfit} {cmbxti10} {} % for math mode\\n \\\\NewMathAlphabet{mathbfss} {cmssbx10} {} % \\\" \\\" \\\"\\n \\\\fi\\n %\\n \\\\ifAMStwofonts\\n %\\n \\\\ifCUPmtlplainloaded \\\\else\\n \\\\NewSymbolFont{upmath} {eurm10}\\n \\\\NewSymbolFont{AMSa} {msam10}\\n \\\\NewMathSymbol{\\\\upi} {0}{upmath}{19}\\n \\\\NewMathSymbol{\\\\umu} {0}{upmath}{16}\\n \\\\NewMathSymbol{\\\\upartial}{0}{upmath}{40}\\n \\\\NewMathSymbol{\\\\leqslant}{3}{AMSa}{36}\\n \\\\NewMathSymbol{\\\\geqslant}{3}{AMSa}{3E}\\n \\\\let\\\\oldle=\\\\le \\\\let\\\\oldleq=\\\\leq\\n \\\\let\\\\oldge=\\\\ge \\\\let\\\\oldgeq=\\\\geq\\n \\\\let\\\\leq=\\\\leqslant \\\\let\\\\le=\\\\leqslant\\n \\\\let\\\\geq=\\\\geqslant \\\\let\\\\ge=\\\\geqslant\\n \\\\fi\\n %\\n \\\\fi\\n%\\n\\\\fi % End of OFSS\\n\\n\\\\ifnfssone\\n %\\n \\\\newmathalphabet{\\\\mathit}\\n \\\\addtoversion{normal}{\\\\mathit}{cmr}{m}{it}\\n \\\\addtoversion{bold}{\\\\mathit}{cmr}{bx}{it}\\n %\\n \\\\newcommand{\\\\rmn}[1] {\\\\mathrm{#1}}\\n \\\\newcommand{\\\\itl}[1] {\\\\mathit{#1}}\\n \\\\newcommand{\\\\bld}[1] {\\\\mathbf{#1}}\\n %\\n \\\\def\\\\textbfit{\\\\protect\\\\txtbfit}\\n \\\\def\\\\textbfss{\\\\protect\\\\txtbfss}\\n \\\\long\\\\def\\\\txtbfit#1{{\\\\fontfamily{cmr}\\\\fontseries{bx}\\\\fontshape{it}%\\n \\\\selectfont #1}}\\n \\\\long\\\\def\\\\txtbfss#1{{\\\\fontfamily{cmss}\\\\fontseries{bx}\\\\fontshape{n}%\\n \\\\selectfont #1}}\\n %\\n \\\\newmathalphabet{\\\\mathbfit} % math mode version of \\\\textbfit{..}\\n \\\\addtoversion{normal}{\\\\mathbfit}{cmr}{bx}{it}\\n \\\\addtoversion{bold}{\\\\mathbfit}{cmr}{bx}{it}\\n %\\n \\\\newmathalphabet{\\\\mathbfss} % math mode version of \\\\textbfss{..}\\n \\\\addtoversion{normal}{\\\\mathbfss}{cmss}{bx}{n}\\n \\\\addtoversion{bold}{\\\\mathbfss}{cmss}{bx}{n}\\n %\\n \\\\ifAMStwofonts\\n %\\n \\\\ifCUPmtlplainloaded \\\\else\\n %\\n % Make NFSS 1 use the extra sizes available for bold math italic and\\n % bold math symbol. 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Baptista et~al.]\\n\\t{Raymundo Baptista$^1$, C. Silveira$^1$, J.E. Steiner$^2$\\n\\tand Keith Horne$^3$ \\\\\\\\\\n%\\tand Knox Long$^4$ \\\\\\\\\\n\\t$^1$ Departamento de F\\\\'\\\\i sica, Universidade Federal de Santa Catarina,\\n Campus Trindade, 88040-900, Florian\\\\'opolis - SC, Brazil, \\\\\\\\\\n ~ email: bap@fsc.ufsc.br, silveira@fsc.ufsc.br \\\\\\\\\\n\\t$^2$ Laborat\\\\'orio Nacional de Astrof\\\\'\\\\i sica-LNA/CNPq, CP 21, 37500-000,\\n\\tItajub\\\\'a, Brazil, email: steiner@lna.br \\\\\\\\\\n\\t$^3$ School of Physics \\\\& Astronomy, University of St.\\\\,Andrews,\\n\\tNorth Haugh, St.\\\\,Andrews, Fife, KY16 9SS, Scotland, \\\\\\\\\\n ~ email: kdh1@st-and.ac.uk \\\\\\\\\\n% $^4$ Space Telescope Science Institute, 3700 San Martin Drive, Baltimore,\\n% MD 21218, USA, email: long@stsci.edu \\n\\t}\\n\\\\date{Accepted for publication at Monthly Notices of the Royal Astronomical\\n\\t\\tSociety}\\n\\n\\\\pagerange{1-13}\\n\\\\pubyear{2000}\\n\\n\\\\begin{document}\\n\\n\\\\maketitle\\n\\n\\\\begin{abstract}\\n\\nTime-resolved spectroscopy of the novalike variable UU Aquarii is analyzed\\nwith eclipse mapping techniques to produce spatially resolved spectra\\nof its accretion disc and gas stream as a function of distance from disc\\ncentre in the range 3600-6900 \\\\AA. The spatially-resolved spectra show\\nthat the continuum emission becomes progressively fainter and redder for\\nincreasing disc radius -- reflecting the radial temperature gradient --\\nand reveal that the H\\\\,I and He\\\\,I lines appear as deep, narrow absorption\\nfeatures in the inner disc regions transitioning to emission with P Cyg\\nprofiles for intermediate and large disc radii. The spectrum of the\\nuneclipsed component has strong H\\\\,I and He\\\\,I emission lines plus a Balmer\\njump in emission and is explained as optically thin emission from a\\nvertically extended disc chromosphere + wind. \\nMost of the line emission probably arises from the wind.\\nThe spatially-resolved spectra also suggest the existence of gas stream \\n``disk-skimming'' overflow in UU~Aqr, which can be seen down to\\n$R\\\\simeq 0.2\\\\; R_{L1}$. The comparison of our eclipse maps with those \\nof Baptista, Steiner \\\\& Horne (1996) suggests that the asymmetric structure \\nin the outer disc previously identified as the bright spot may be the \\nsignature of an elliptical disc similar to those possibly present in \\nSU~UMa stars during superoutbursts.\\n\\n\\\\end{abstract}\\n\\n\\\\begin{keywords}\\nbinaries: close -- novae, cataclysmic variables -- eclipses -- accretion\\ndiscs -- stars: individual: (UU Aquarii).\\n\\\\end{keywords}\\n\\n\\n\\\\section{Introduction}\\n\\nThe standard picture of a novalike system is that of a close binary in\\nwhich a late type star fills its Roche lobe and transfers matter to a\\ncompanion white dwarf via an accretion disc. A bright spot is expected \\nto form where the gas stream from the donor star hits the edge of the\\naccretion disc.\\n\\nThe SW Sex stars (Thorstensen et~al. 1991) form a sub-class of the\\nnovalikes with orbital periods in the range 3-4 hs that do not seem to\\nfit within the above standard picture, displaying a range of peculiarities:\\n(1) single peaked asymmetric emission lines showing little eclipse, \\n(2) large ($\\\\sim 70\\\\degr$) phase shifts between photometric and\\nspectroscopic conjunction, \\n(3) orbital phase-dependent absorption in the Balmer lines,\\n(4) Doppler tomograms bright in the lower-left quadrant with small\\nor no sign of disc emission, and\\n(5) v-shaped continuum eclipses implying in flat radial temperature \\nprofiles in the inner disc (e.g., Warner 1995 and references therein).\\nEarlier proposals to explain the phenomenon include accretion disc winds\\n(Honeycutt, Schlegel \\\\& Kaitchuck 1986), magnetic white dwarfs\\ndisrupting the inner disc (Williams 1989), and gas stream overflow\\n(Hellier \\\\& Robinson 1994). The two most recent models proposed to\\nexplain the phenomenology of the SW Sex stars are the disc-anchored\\nmagnetic propeller (Horne 1999) and a combination of stream overflow\\n+ disc winds (Hellier 1999).\\n\\nUU~Aqr is an eclipsing novalike (P$_{\\\\rm orb}= 3.9$\\\\,hr) whose \\nspectrum is dominated by single-peaked strong Balmer and He\\\\,I emission\\nlines (e.g., Downes \\\\& Keyes 1988). H$\\\\alpha$ spectroscopy revealed\\nthat the line profile is highly asymmetric and phase-dependent \\nand that the spectroscopic conjunction lags mid-eclipse\\nby $\\\\sim 0.15$ cycle (Haefner 1989; Diaz \\\\& Steiner 1991).\\nThe lack of the rotational disturbance typical of emitting accretion\\ndiscs during eclipse in H$\\\\beta$ led Hessman (1990) to the suggestion\\nthat the emission lines have a non-disc origin.\\n\\nBaptista, Steiner \\\\& Cieslinski (1994; hereafter BSC94) derived a\\nphotometric model for the binary with $q= 0.30$, M$_1 = 0.67\\\\:\\n{\\\\rm M}_{\\\\odot}$, an inclination of $i= 78$ degrees.\\nFrom the analysis of mid-eclipse fluxes they suggested that the Balmer\\nlines are formed in an extended region only partially occulted during\\neclipse, possibly in a wind emanating from the inner disc.\\nThey also found that UU Aqr presents long-term brightness variations of\\nlow amplitude ($\\\\simeq 0.3$ mags) on timescales of years.\\n\\nThe eclipse mapping study of Baptista, Steiner \\\\& Horne (1996;\\nthereafter BSH96) indicates that the inner disc of UU Aqr is\\noptically thick, resulting in a distance estimate of 200 pc.\\nTemperatures in the disc range from $\\\\sim 6000$\\\\,K in the outer \\nregions to $\\\\sim 16000$\\\\,K near the white dwarf at disc centre.\\nThe radial temperature profiles in the high state follow the\\nT$\\\\:\\\\propto R^{-3/4}$ law in the outer and intermediate disc regions\\nbut flattens off in the inner disc, leading to mass accretion rates\\nof $10^{-9.2}\\\\:{\\\\rm M_{\\\\odot}\\\\,yr}^{-1}$ at $R= 0.1\\\\: R_{\\\\rm L1}$\\nand $10^{-8.8}\\\\:{\\\\rm M_{\\\\odot}\\\\,yr}^{-1}$ at $R= 0.3\\\\: R_{\\\\rm L1}$\\n($R_{\\\\rm L1}$ is the distance from disc centre to the inner Lagrangian\\npoint). Together with other characteristics, this led BSH96 to suggest\\nthat UU Aqr was an SW Sex star.\\nThe comparison of eclipse maps of the low and high states revealed that\\nthe differences are due to changes in the structure of the outer parts\\nof the disc, the most noticeable effect being the appearance of a\\nconspicuous red, bright structure at disc rim, which the authors\\nidentified with the bright spot.\\n\\nAccording to BSH96, the \\\\.{M} of UU Aqr is barely above the critical\\nlimit for disc instability to set in. Warner (1997) noted that the\\nouter disc temperature is only 6000 K and remarked that small variations\\nin \\\\.{M} could lead to dwarf novae type outbursts.\\nHoneycutt, Robertson \\\\& Turner (1998) performed a long-term photometric\\nmonitoring of UU Aqr which confirmed the high and low brightness states\\nof BSC94 and revealed the existence of small amplitude ($\\\\simlt 1.0$ mag)\\nbrightness variations on timescales of a few days, which they called\\n`stunted outbursts'.\\n\\nThe detailed spectroscopic study of Hoard et~al. (1998) reinforced the\\nclassification of UU Aqr as an SW Sex star.\\nThey found evidences for the presence of a bright spot at the impact site\\nof the gas stream with the edge of the disc, and a non-axisymmetric,\\nvertically and azimuthally extended absorbing structure in the disc.\\nThey proposed an explanation for the absorbing structure as well as for\\nthe other spectroscopic features of UU Aqr in terms of the explosive\\nimpact of the accretion stream with the disc.\\nOptical and ultraviolet spectroscopy by Kaitchuck et~al. (1998)\\nshows a secondary eclipse at phase 0.4 in the optical and Balmer lines\\n(but not in the UV continuum or lines) which they suggested may be\\ncaused by an occultation of the bright spot and stream region by material\\nsuspended above the inner disc.\\n\\nIn this paper we report on the analysis of time-resolved spectroscopy\\nof UU Aqr with multi-wavelength eclipse mapping techniques to derive \\nspatially-resolved spectra of the accretion flow in this binary.\\nSection~\\\\ref{data} describes the observations and data reduction procedures,\\nwhile section~\\\\ref{analise} describes the analysis of the light curves with\\neclipse mapping techniques.\\nSection~\\\\ref{resultados} presents eclipse maps at selected wavelengths,\\nthe radial intensity and brightness temperature distributions,\\nspatially resolved spectra of the accretion disc and gas stream as well\\nas the spectrum of the uneclipsed component.\\nThe results are discussed in section~\\\\ref{discussao} and summarized in section~\\\\ref{conclusao}.\\n\\n\\n\\\\section{Observations} \\\\label{data}\\n\\nTime-resolved spectroscopy covering 5 eclipses of UU~Aqr was obtained\\nwith the 2.1-m telescope at the Kitt Peak National Observatory (KPNO) on\\nJuly-August 1993 in the spectral range 3500--6900 \\\\AA\\\\ (spectral\\nresolution of $\\\\Delta\\\\lambda= 1.5$ \\\\AA\\\\ pixel$^{-1}$).\\nThe observations consist of 5 sets of $\\\\simeq 100$ short exposure\\n($\\\\Delta t=30s$) spectra at a time resolution of 50\\\\,s. A close comparison\\nstar (star C1 of BSC94) was included in the slit to allow correction of sky\\ntransparency variations and slit losses. The observations (summarized in\\nTable~\\\\ref{tab1}) were performed under good (cloud-free) sky conditions and\\nat small to moderate air masses ($X \\\\leq 1.4$) except for run 1, which\\nstarted while the object was still at a reasonably high zenith angle\\n($X= 2.2$).\\n%\\n% ############################### TABLE 1 #################################\\n\\\\begin{table*}\\n \\\\centering\\n \\\\begin{minipage}{120mm}\\n \\\\caption{Journal of the observations.}\\n \\\\label{tab1}\\n\\\\begin{tabular}{@{}lccccccc@{}}\\n~~Date & Run & \\\\multicolumn{2}{c}{UT} & No. of & Spectral & Cycle &\\nPhase range \\\\\\\\ [-0.5ex]\\n~(1993) && start & end & spectra & range (\\\\AA) & number & (cycle) \\\\\\\\ [1ex]\\n22 July & 1 & 05:56 & 07:33 & 105 & 3564.0--6766.5 & 17389 & $-0.20,+0.21$ \\\\\\\\\\n27 July & 2 & 07:59 & 09:40 & 111 & 3601.6--6805.5 & 17420 & $-0.11,+0.32$ \\\\\\\\\\n13 August & 3 & 07:52 & 09:25 & 101 & 3646.5--6850.5 & 17524 & $-0.22,+0.17$ \\\\\\\\ \\n15 August & 4 & 07:01 & 08:37 & 106 & 3649.5--6853.5 & 17536 & $-0.20,+0.20$ \\\\\\\\\\n16 August & 5 & 06:18 & 08:18 & 110 & 3649.5--6853.5 & 17542 & $-0.27,+0.24$ \\\\\\\\ \\n\\\\end{tabular}\\n\\\\end{minipage}\\n\\\\end{table*}\\n% #########################################################################\\n\\n\\nThe data were bias-subtracted and corrected for flat-field and slit\\nillumination effects using standard {\\\\sc iraf} procedures.\\n1-D spectra of both variable and comparison star were extracted\\nwith the optimal extraction algorithm of Horne (1986). \\nThe individual spectra were checked for the presence of possible cosmic\\nrays and, when appropriate, were corrected by interpolation from the\\nneighboring wavelengths. Arc-lamp observations were used to calibrate the\\nwavelength scale (accuracy of 0.15 \\\\AA). Observations of the standard spectrophotometric stars\\nBD+28\\\\,4211 and G191\\\\,B2B (Massey et~al. 1988) were used to derive the\\ninstrumental sensitivity function and to flux calibrate the set of extracted\\nspectra on each night. Error bars were computed taking into account the photon\\ncount noise and the sensitivity response of the instrument.\\n\\nThe reduced spectra were combined to produce trailed spectrograms of the\\nvariable and the comparison star for each night. The display of the trailed\\nspectrograms of the comparison star shows that there were non negligible sky\\ntransparency variations and/or time-dependent slit losses along the runs.\\nWe defined a reference spectrum of the comparison star by computing an average\\nof 40 spectra on night 5 corresponding to the time for which the star was\\nclosest to zenith.\\nWe normalized the spectrograms of the comparison star by dividing each\\nspectrum by the reference spectrum. A 2-D cubic spline fit was used to\\nproduce a smoothed version of the normalized spectrograms.\\nThe sky transparency variations and variable slit losses were corrected\\nby dividing the spectrogram of the variable by the smoothed, normalized\\nspectrogram of the comparison star on each night (a procedure analogous\\nto the flat-field correction).\\nThe reference spectrum is consistent with the UBVRI photometry of star C1\\n(BSC94) at the 1-$\\\\sigma$ level. Therefore, the absolute photometric accuracy\\nof these observations should be better than 10 per cent.\\n\\nFig.\\\\,\\\\ref{fig1} shows average out-of-eclipse and mid-eclipse spectra of\\nUU~Aqr on 1995 August 13. The spectra are dominated by strong single-peaked\\nBalmer emission lines but also show He\\\\,I lines and the blend of\\nC\\\\,III, N\\\\,III and He\\\\,II lines at $\\\\sim 4650$ \\\\AA. The emission lines\\nhave asymmetrical shapes, the red side of the line being stronger --\\nin accordance with the results of Hessman (1990) and Diaz \\\\& Steiner (1991).\\nThe He\\\\,I lines and the higher energy Balmer lines show a possible double\\npeak structure suggesting either classical double-peaked emission from a\\nhighly inclined disc or single peaked emission with a central absorption\\ncomponent. While the continuum is reduced by a factor\\n$\\\\simeq 3$ during eclipse, the emission lines\\nsuffer a much smaller reduction in flux suggesting that they possibly\\narise from a vertically-extended source larger than the accretion disc\\n(responsible for the continuum emission), in accordance with inferences\\ndrawn by BSC94.\\n%\\n% ############################## FIGURE 1 #################################\\n%\\n\\\\begin{figure}\\n\\\\centerline{\\\\psfig{figure=xfig01.ps,angle=-90,width=10.5cm,rheight=7.5cm}}\\n\\\\caption{Average out-of-eclipse (black, phase range $-0.22$ to $-0.06$ cycle)\\nand mid-eclipse (light gray, phase range $-0.025$ to 0.025 cycle) spectra of\\nUU~Aqr on 1995 August 13. Major emission features are indicated by vertical\\ndotted lines.}\\n\\\\label{fig1}\\n\\\\end{figure}\\n\\n\\nFig.\\\\,\\\\ref{fig2} shows lightcurves of the 5 runs in the broad band $5000-\\n6500$ \\\\AA. The gap in run 5 is due to\\nan interruption of the observations to check the telescope focus.\\nThe lightcurves have similar eclipse shapes and out of eclipse flux levels,\\nwith variations at the level of $\\\\simlt 20$\\\\ per cent between the runs.\\nIndications that the observations were performed while UU~Aqr was in its\\nhigh brightness state come from the eclipse shape and average out of eclipse\\nflux level. The latter suggests that the object was even slightly brighter\\nthan the typical high brightness state of BSC94.\\nThese remarks are in agreement with the historical lightcurve of Honeycutt\\net~al. (1998, see their fig.\\\\,1), which shows that UU~Aqr reached a maximum\\nof its long-term average brightness level during 1993, the epoch of our\\nobservations. The spectral range of the lightcurves in Fig.\\\\,1 corresponds\\nroughly to the $V$ band.\\nThe average out of eclipse level of all runs yields an approximate mean\\nmagnitude of $V= 13.2 \\\\pm 0.2$ mag, consistent with the value drawn from\\nthe lightcurve of Honeycutt et~al. (1998), of $V= 13.4 \\\\pm 0.6$ mag.\\n%\\n% ############################## FIGURE 2 #################################\\n%\\n\\\\begin{figure}\\n\\\\centerline{\\\\psfig{figure=xfig02.ps,width=10cm,rheight=12cm}}\\n\\\\caption{Broad band lightcurves of the UU Aqr dataset. The curves are\\nprogressively displaced upwards by 20 mJy for visualization purposes.\\nHorizontal lines at mid-eclipse show the true zero level in each case.}\\n\\\\label{fig2}\\n\\\\end{figure}\\n\\n\\n\\\\section{Data analysis} \\\\label{analise}\\n\\n\\\\subsection{Light curve construction}\\n\\nThe spectra were divided into 226 passbands of 15 \\\\AA\\\\ in the continuum and\\nfainter lines, and $\\\\simeq 500\\\\; km\\\\,s^{-1}$ across the most prominent lines.\\nFor each passband a lightcurve was extracted by computing the average flux\\non the corresponding wavelength range and phase folding the resulting data\\naccording to the ephemeris of BSC94. A phase correction of $-0.003$ cycle was\\nfurther applied to the data to make the centre of the white dwarf eclipse\\ncoincident with phase zero. For those passbands including emission lines\\nthe light curves comprise the total flux at the corresponding bin with\\nno subtraction of a possible underlying continuum contribution.\\n\\nSince the dataset correspond to the same brightness level it was possible\\nto combine the lightcurves of all runs to produce average lightcurves for\\neach passband. This is helpful to increase the signal-to-noise ratio of the\\nlightcurves and to reduce the influence of flickering in the eclipse shape.\\nFor each passband, we first normalized the individual lightcurves by\\nfitting a spline function to the phases outside eclipse and dividing the\\nlightcurve by the fitted spline. The normalized lightcurves were combined by\\nseparating the data into phase bins of 0.0038~cycle and computing the median\\nfor each bin. The median of the absolute deviations with respect to the\\nmedian is taken as the corresponding uncertainty.\\nThe resulting lightcurve is scaled back to flux units by multiplying the\\ncombined lightcurve by the median flux of the spline functions at phase zero.\\nThis procedure removes orbital variations outside eclipse with\\nonly minor effects on the eclipse shape itself.\\n\\n\\n\\\\subsection{Eclipse mapping}\\n\\\\label{mem}\\n\\nThe eclipse mapping method was used to solve for a map of the disc\\nbrightness distribution and for the flux of an additional uneclipsed\\ncomponent in each passband. For the details of the method the reader\\nis referred to Horne (1985, 1993), Baptista \\\\& Steiner (1993) and\\nRutten et al. (1994).\\n\\nFor our analysis we adopted the same eclipse map of BSH96, a $51 \\\\times 51$\\npixel grid centred on the primary star with side $2 \\\\:R_{L1}$ where\\n$R_{L1}$ is the distance from the disc centre to the inner Lagrangian point.\\nThis choice provides maps with a nominal spatial resolution of $0.039 \\\\:\\nR_{L1}$, comparable to the expected size of the white dwarf in UU~Aqr\\n($\\\\simeq 0.032\\\\: R_{L1}$). The eclipse geometry is specified by the mass\\nratio $q$ and the inclination $i$. We adopted the parameters of BSC94,\\n$i= 78\\\\degr$ and $q=0.3$.\\nThe specific intensities in the eclipse map were computed assuming\\nR$_{L1}= 0.74 \\\\; R_\\\\odot$ (BSC94) and a distance of 200 pc (BSH96).\\n\\nThe statistical uncertainties of the eclipse maps were estimated with a\\nMonte Carlo procedure (e.g., Rutten et al. 1992; Baptista et~al. 1995).\\nFor a given narrow-band lightcurve a set of 10 artificial lightcurves is\\ngenerated, in which the data points are independently and randomly\\nvaried according to a Gaussian distribution with standard deviation\\nequal to the uncertainty at that point. The lightcurves are fitted\\nwith the eclipse mapping algorithm to produce a set of randomized\\neclipse maps. These are combined to produce an average map and a map\\nof the residuals with respect to the average, which yields the statistical\\nuncertainty at each pixel.\\nThe uncertainties obtained with this procedure will be used when\\nestimating the errors in the derived radial temperature and intensity\\nprofiles as well as in the spatially-resolved spectra.\\n\\nAverage light curves, fitted models, and eclipse maps at selected passbands\\nare show in Figs.\\\\,\\\\ref{fig3} and \\\\ref{fig4}. These will be discussed in\\ndetail in section\\\\,\\\\ref{resultados}.\\n\\n\\n\\\\section{Results} \\\\label{resultados}\\n\\n\\\\subsection{Accretion disc structure}\\n\\\\label{estrutura}\\n\\nIn this section we compare eclipse maps at selected passbands in order\\nto study the structure of the accretion disc at different wavelengths.\\n\\nFig.\\\\,\\\\ref{fig3} shows lightcurves (left panels) and eclipse maps (right\\npanels) of 4 selected continuum passbands close to the Johnson-Cousins\\nUBVR effective wavelengths in order to allow a comparison with\\nthe results of BSH96.\\nDashed horizontal lines depict the uneclipsed component in each case.\\nThe continuum lightcurves show a deep eclipse with a slightly asymmetric\\negress shoulder which is more pronounced for longer wavelengths.\\nThis results in eclipse maps with brightness distributions concentrated\\ntowards disc centre and asymmetric structures in the trailing quadrant of\\nthe disc closest to the secondary star (the upper right quadrant in the\\neclipse maps of Fig.\\\\,\\\\ref{fig3}).\\nThe uneclipsed component at $\\\\lambda 3657$ is perceptibly \\nlarger than at $\\\\lambda 4411$, suggesting that the Balmer jump is\\nin emission and that the uneclipsed light has an important contribution\\nfrom optically thin gas. This is in line with previous results by\\nBSC94 and BSH96.\\nThe eclipse shapes and out of eclipse levels resemble those\\nof the high brightness state observed by BSH96, although with a less\\npronounced asymmetry at eclipse egress. Accordingly, the eclipse maps\\nclearly lack the noticeable asymmetric structure at disc edge which was\\nthe main characteristic of the high state (BSH96, see their Fig.\\\\,3).\\nWe will return to this point in section\\\\,\\\\ref{discussao}.\\n%\\n% ############################## FIGURE 3 #################################\\n%\\n\\\\begin{figure}\\n\\\\centerline{\\\\psfig{figure=xfig03.ps,width=11cm,rheight=13.5cm}}\\n\\\\caption{ Lightcurves (left) and eclipse maps (right) at selected continuum\\n\\tpassbands. Data lightcurves are shown as gray dots with error bars and\\n\\tthe fitted models appear as solid black lines. A horizontal dashed line\\n\\tdepicts the uneclipsed component in each case. Labels indicate the\\n\\tcentral wavelength of each passband. Eclipse maps are shown to the right\\n\\tin a logarithmic grayscale: dark regions are brighter; white corresponds\\n\\tto $\\\\log I_\\\\nu= -6.5$, and black to $\\\\log I_\\\\nu= -3.1$. Dotted curves\\n\\tshow the projection of the primary Roche lobe onto the orbital plane\\n\\tand the theoretical gas stream trajectory; the secondary star is to the\\n\\tright of each panel and the stars rotate counter-clockwise. }\\n\\\\label{fig3}\\n\\\\end{figure}\\n\\nFig.\\\\,\\\\ref{fig4} shows lightcurves and eclipse maps for the line centre\\npassbands of H$\\\\alpha$, H$\\\\beta$, H$\\\\gamma$ and He\\\\,I $\\\\lambda$5876.\\nWe remark that the line lightcurves include the total flux at the \\ncorresponding wavelength range with no subtraction of an interpolated\\ncontinuum. The eclipses are shallow, leading to brightness distributions\\nwhich are flatter than those of the continuum. \\nSimilar to the continuum maps, the asymmetry in the egress shoulder is\\nmore pronounced for the lines at longer wavelengths.\\nThe uneclipsed components are considerably larger than in the continuum,\\nindicating that the uneclipsed spectrum has strong Balmer and He\\\\,I\\nemission lines.\\nThe large error bars of the H$\\\\alpha$ centre lightcurve is due not to\\nlow signal-to-noise ratio but to the variability of the eclipse shape at\\nthis wavelength. This effect is also seen, although to a lesser extent,\\nin H$\\\\beta$ and H$\\\\gamma$.\\n%\\n% ############################## FIGURE 4 #################################\\n%\\n\\\\begin{figure}\\n\\\\centerline{\\\\psfig{figure=xfig04.ps,width=11cm,rheight=13.5cm}}\\n\\\\caption{ Lightcurves (left) and eclipse maps (right) for the H$\\\\alpha$,\\n\\tH$\\\\beta$, H$\\\\gamma$ and He\\\\,I $\\\\lambda 5876$ line centre passbands.\\n\\tThe notation and logarithmic grayscale are the same as in\\n\\tfigure\\\\,\\\\ref{fig3}. }\\n\\\\label{fig4}\\n\\\\end{figure}\\n\\n\\nFig.\\\\,\\\\ref{fig5} shows (Doppler) velocity-resolved lightcurves (left) and\\neclipse maps (right) across the H$\\\\beta$ line.\\nThere is marginal evidence of rotational disturbance: the minimum of the\\nblue bin lightcurve ($- 494 \\\\; km \\\\;s^{-1}$) is slightly displaced towards \\nnegative phases while that of the red bin lightcurve ($+ 494 \\\\; km \\\\;s^{-1}$)\\nis correspondingly displaced towards positive phases, suggesting that the\\nline emitting gas rotates in the prograde sense.\\nHowever, the eclipse maps in the symmetric velocity bins do not show the\\nmirror symmetry (over the line joining both stars) expected for line\\nemission from a Keplerian disc around the white dwarf.\\nEqually remarkable are the facts that the lightcurve in the red bin has a\\nmuch larger out-of-eclipse flux than its blue counterpart and that the\\ncorresponding eclipse map is perceptibly brighter than that of the blue\\nbin anywhere. A similar behaviour is found in the other lines for which\\nvelocity-resolved maps were obtained.\\nThis cannot be attributed to the underlying continuum since the\\ninterpolated continuum has essentially a constant level across each line.\\nIt seems clear that most of the line emission does not arise from a\\ndisc in Keplerian rotation.\\n%\\n% ############################## FIGURE 5 #################################\\n%\\n\\\\begin{figure}\\n\\\\centerline{\\\\psfig{figure=xfig05.ps,width=10cm,rheight=12.2cm}}\\n\\\\caption{ H$\\\\beta$ velocity-resolved lightcurves (left) and eclipse maps\\n\\t(right) at velocities of $-494,\\\\; 0,\\\\; {\\\\rm and}\\\\; +494\\t\\\\;km \\\\;s^{-1}$.\\n\\tThe notation and logarithmic grayscale are the same as in\\n\\tfigure\\\\,\\\\ref{fig3}. }\\n\\\\label{fig5}\\n\\\\end{figure}\\n\\n\\n\\\\subsection{Radial temperature distribution and mass accretion rate estimate}\\n\\nThe simplest way of testing theoretical disc models is to convert the\\nintensities in the eclipse maps to blackbody brightness temperatures,\\nwhich can then be compared to the radial run of the effective temperature\\npredicted by steady state, optically thick disc models. However, as\\ndiscussed by Baptista et~al. (1998), a relation between the effective\\ntemperature and a monochromatic brightness temperature is non-trivial,\\nand can only be properly obtained by constructing self-consistent models\\nof the vertical structure of the disc. Therefore, our analysis here\\nis meant as preliminary, and should be complemented by detailed disc\\nspectrum modeling in a future paper.\\n\\nFig.\\\\,\\\\ref{fig6} shows brightness temperature radial distributions for\\nthe continuum maps of Fig.\\\\,\\\\ref{fig3} in a logarithmic scale.\\nEach temperature shown is the blackbody brightness temperature that\\nreproduces the observed surface brightness at the corresponding pixel\\nassuming a distance of 200~pc to UU~Aqr (BSH96). Steady-state disc models\\nfor mass accretion rates of $10^{-8.5}$, $10^{-9}$, $10^{-9.5}$ and\\n$10^{-10}\\\\; M_\\\\odot \\\\; yr^{-1}$ are plotted as dotted lines for comparison.\\nThese models assume M$_1= 0.67 \\\\; M_\\\\odot$ and $R_1= 0.012 \\\\; R_\\\\odot$\\n(BSC94).\\n\\nThe distributions resemble those obtained by BSH96 for the high brightness\\nstate of UU Aqr, closely following the $T\\\\propto R^{-3/4}$ law for steady\\naccretion in the intermediate and outer disc regions ($R \\\\geq 0.2\\\\; \\nR_{\\\\rm L1}$) but displaying a noticeable flattening in the inner disc\\n($R < 0.1\\\\; R_{\\\\rm L1}$).\\nTemperatures range from $\\\\sim 18000$ K in the inner disc to 6000 K in the\\nouter disc regions, leading to inferred mass accretion rates of \\\\.{M}=\\n$10^{-9.0 \\\\pm 0.3}\\\\; M_\\\\odot \\\\, yr^{-1}$ at $R= 0.1\\\\; R_{\\\\rm L1}$ and\\n$10^{-8.7 \\\\pm 0.2} \\\\; M_\\\\odot \\\\, yr^{-1}$ at $R= 0.3\\\\; R_{\\\\rm L1}$ --- in\\ngood agreement with the results of BSH96 for the high brightness state.\\nThe quoted errors on \\\\.{M} account for the statistical uncertainties in the\\neclipse maps, obtained from the Monte Carlo procedure described in\\nsection\\\\,\\\\ref{mem}, and the scatter in the temperatures of maps at\\ndifferent wavelengths.\\nThe eclipse map at $\\\\lambda 3657$ leads to temperatures which are\\nsystematically higher than those of the other continuum maps of Fig.\\\\,3,\\nin an example of the limitations of using brightness temperatures to\\nestimate the mass accretion rate. This difference reflects the fact that\\nthe Balmer jump appears in emission for the intermediate and outer disc\\nregions, as will be seen in section\\\\,\\\\ref{spectra}.\\n%\\n% ############################## FIGURE 6 #################################\\n%\\n\\\\begin{figure}\\n\\\\centerline{\\\\psfig{figure=xfig06.ps,angle=-90,width=11cm,rheight=7.5cm}}\\n\\\\caption{ Brightness temperature radial distributions of the UU Aqr accretion\\n\\tdisc for the continuum maps of figure\\\\,\\\\ref{fig3}, calculated assuming\\n\\ta distance of 200 pc to the system (BSH96). Dotted lines correspond to\\n\\tsteady-state disc models for mass accretion rates of \\\\.{M}$= 10^{-8.5}$,\\n\\t$10^{-9}$, $10^{-9.5}$ and $10^{-10}\\\\; M_\\\\odot \\\\; yr^{-1}$, assuming\\n\\tM$_1= 0.67 \\\\; M_\\\\odot$ and $R_1= 0.012 \\\\; R_\\\\odot$ (BSC94). Abscissae\\n\\tare in units of the distance from disc centre to the inner Lagrangian\\n\\tpoint (R$_{\\\\rm L1}$). }\\n\\\\label{fig6}\\n\\\\end{figure}\\n\\n\\n\\\\subsection{Radial line intensity distributions}\\n\\nLeft panel in Fig.\\\\,\\\\ref{fig7} shows radial intensity distributions for\\nthe most prominent lines (solid) and adjacent continuum (dotted) in a\\nlogarithmic scale. The line distributions were obtained from the average\\nof all eclipse maps across the line region, while the continuum\\ndistributions were obtained from the average of eclipse maps on\\nboth sides of each line. \\nNet line emission distributions were computed by subtracting the\\ndistributions of the adjacent continuum from those of the lines,\\nand are shown in the right panel.\\nIn the external map regions ($R \\\\simgt 0.7\\\\; R_{\\\\rm L1}$) the intensities\\nof both line and continuum drop by a factor $\\\\sim 10^3$ with respect\\nto the inner disc regions, making the computation of the net emission\\nquite noisy and unreliable.\\nH$\\\\alpha$ is seen in emission (intensities larger than those at the\\nadjacent continuum) at all disc radii and up to $R \\\\simeq 0.6\\\\; R_{\\\\rm L1}$. \\nThe other lines are in absorption in the inner disc and transition to\\nemission at intermediate ($R \\\\sim 0.2\\\\; R_{\\\\rm L1}$) disc radius.\\nThis behaviour is noticeably different from that observed at the low\\nbrightness state, where H$\\\\alpha$ is seen in emission in the inner disc\\nand disappears into the continuum for $R \\\\simeq 0.3\\\\; R_{\\\\rm L1}$ (BSH96).\\nThis result suggests that the line emission region increases in size\\nfrom the low to the high brightness state, possibly in response to changes\\nin mass accretion rate.\\nThe transition from absorption to emission occurs at larger disc radii for\\nlines of higher excitation. This can be explained, for the Balmer lines,\\nby the increase in continuum emission at the inner disc for shorter\\nwavelengths.\\n%\\n% ############################## FIGURE 7 #################################\\n%\\n\\\\begin{figure}\\n\\\\centerline{\\\\psfig{figure=xfig07.ps,width=10cm,rheight=12cm}}\\n\\\\caption{ Radial line intensity profiles for the most prominent lines,\\n\\tcalculated assuming a distance of 200 pc to the system (BSH96). \\n\\tAbscissae are in units of the distance from disc centre to the inner\\n\\tLagrangian point (R$_{\\\\rm L1}$). Right panels show net line emission \\n\\tradial distributions. Dotted lines depict the slope of the expected\\n\\trelation $I \\\\propto R^{-1.5}$. }\\n\\\\label{fig7}\\n\\\\end{figure}\\n\\nA set of dotted lines in the right panel indicate the slope of the empirical\\nradial dependency of the line emissivity in accretion discs, $I \\\\propto\\nR^{-1.5}$, as inferred from Doppler Tomography by assuming a Keplerian\\ndistribution of velocities for the emitting gas (Marsh et al. 1990).\\nFor H$\\\\gamma$ and He\\\\,I $\\\\lambda$5876, the net emission occurs for a narrow range of radii making a comparison with the empirical law difficult.\\nThe derived radial distributions for H$\\\\alpha$ and H$\\\\beta$ are clearly\\ndifferent from the empirical $I \\\\propto R^{-1.5}$ law; in particular,\\nthe H$\\\\alpha$ distribution is flat at inner and intermediate disc radii\\n($R <0.3\\\\; R_{\\\\rm L1}$).\\nThis remark suggests that the line emitting regions on the disc surface\\nare not in Keplerian orbits or that a substantial fraction of the emission\\nlines does not arise from the accretion disc, in line with the inferences\\ndrawn by the comparison of velocity-resolved eclipse maps in\\nsection\\\\,\\\\ref{estrutura}.\\nThe latter hypothesis is consistent with the significant uneclipsed\\ncomponents inferred for the Balmer and He\\\\,I lines (section\\n\\\\,\\\\ref{uneclipsed}).\\n\\n\\n\\\\subsection{Spatially resolved spectra}\\n\\\\label{spectra}\\n\\nEach of the eclipse maps yields spatially-resolved information about\\nthe emitting region on a specific wavelength range. By combining all\\nnarrow-band eclipse maps we are able to isolate the spectrum of the\\neclipsed region at any desired position (e.g., Rutten et~al. 1994;\\nBaptista et~al. 1998).\\n\\nTo investigate the possible influence of the gas stream on the disc\\nemission and motivated by the observed asymmetries in the eclipse maps\\nshown in section\\\\,\\\\ref{estrutura}, we divided the disc into two major\\nazimuthal regions to extract spatially-resolved spectra: the gas stream\\nregion (upper right quadrant in the eclipse maps of Figs.\\\\,3 and 4) and\\nthe disc region (the remaining 3/4 of the eclipse map). \\nFor each of these regions, we divided the maps into a set of 6 concentric\\nannuli centred on the white dwarf of width $0.1\\\\: R_{L1}$ and with radius increasing in steps of $0.1\\\\: R_{L1}$.\\nEach spectrum is obtained by averaging the intensity of all pixels\\ninside the corresponding annulus and the statistical uncertainties\\naffecting the average intensities are estimated with the Monte Carlo\\nprocedure described in section\\\\,\\\\ref{mem}.\\n\\n\\n\\\\subsubsection{Disc spectra}\\n\\\\label{disc}\\n\\nFig.\\\\,\\\\ref{fig8} shows spatially-resolved spectra of the disc region in\\na logarithmic scale. The inner annular region is at the top and each\\nspectrum is at its true intensity level. The spectrum of the uneclipsed\\ncomponent is shown in the lower panel and will be discussed in detail in\\nsection\\\\,\\\\ref{uneclipsed}.\\n%\\n% ############################## FIGURE 8 #################################\\n%\\n\\\\begin{figure*}\\n\\\\centerline{\\\\psfig{figure=xfig08.ps,angle=-90,width=21cm,rheight=15cm}}\\n\\t\\\\caption{ Spatially resolved spectra of the UU Aqr accretion disc.\\n\\tThe spectra were computed for a set of concentric annular sections\\n\\t(radius range indicated on the right, in units of $R_{L1}$).\\n\\tThe lower panel shows the spectrum of the uneclipsed light.\\n\\tThe most prominent line transitions are indicated by vertical dotted\\n\\tlines. Error bars were derived via Monte Carlo simulations with the\\n\\teclipse lightcurves. }\\n\\\\label{fig8}\\n\\\\end{figure*}\\n%\\nThe spectrum of the inner disc is characterized by a blue and bright\\ncontinuum filled with deep and narrow absorption lines. The continuum\\nemission becomes progressively fainter and redder for increasing disc radius\\nwhile the lines transition from absorption to emission showing clear P~Cygni\\nprofiles on all lines mapped at higher spectral resolution. The Balmer jump\\nappears in absorption in the inner disc and weakly in emission in the\\nintermediate and outer disc regions suggesting that the outer disc in\\nUU~Aqr is optically thin. The change in the slope and intensity\\nof the continuum with increasing disc radius reflects the temperature\\ngradient in the accretion disc, with the effective temperature decreasing\\noutwards.\\n\\nThe spatially resolved spectra of the disc are plotted in\\nFig.\\\\,\\\\ref{fig9} as a function of velocity for the H$\\\\alpha$, H$\\\\beta$\\nand H$\\\\gamma$ regions. Vertical dotted lines mark line centre and the\\nmaximum blueshift/redshift velocity expected for gas in Keplerian\\norbits around a $0.67 M_\\\\odot$ white dwarf as seen from an inclination of\\n$i=78\\\\degr$ ($v \\\\sin i= 3200 \\\\;km \\\\;s^{-1}$) [BSC94].\\n%\\t\\n% ############################## FIGURE 9 #################################\\n%\\n\\\\begin{figure}[h]\\n\\\\centerline{\\\\psfig{figure=xfig09.ps,width=9.5cm,rheight=11cm}}\\n\\t\\\\caption{ Spatially resolved spectra in the H$\\\\alpha$, H$\\\\beta$ and\\n\\tH$\\\\gamma$ regions as a function of velocity. The notation is the same\\n\\tas in figure\\\\,\\\\ref{fig8}. Dotted vertical lines mark line centre and\\n\\tthe maximum blueshift/redshift velocity expected for gas in Keplerian\\n\\torbits around a $0.67 M_\\\\odot$ white dwarf seen at an inclination of\\n\\t$i=78\\\\degr$ ($v \\\\sin i= 3200 \\\\;km \\\\;s^{-1}$). }\\n\\\\label{fig9}\\n\\\\end{figure}\\n% \\nThe absorption lines at disc centre are perceptibly narrower than expected\\nfor emission from either the white dwarf atmosphere or from disc gas in\\nKeplerian orbits around the white dwarf. The discrepancy increases if the\\nlarger mass estimates of Diaz \\\\& Steiner (1991) and Kaitchuck et~al (1998)\\nare assumed for the white dwarf. Moreover, the absorption lines at disc\\ncentre are deep, while lines produced in a white dwarf atmosphere or\\ninnermost disc regions should be broad and shallow. The width of the lines\\nindicate a velocity dispersion of $\\\\simeq 1500 \\\\;km \\\\;s^{-1}$ for the line\\nemitting region in the line of sight to the disc centre and higher\\nvelocities ($\\\\sim 2000 \\\\;km \\\\;s^{-1}$) for the gas in the outer disc at\\n$R \\\\simeq 0.5\\\\; R_{\\\\rm L1}$.\\nThis is in clear disagreement with the expected behaviour of line emission\\nfrom gas in a Keplerian disc and provide additional evidence that these\\nlines do not arise from the disc atmosphere.\\nOn the other hand, the lines at intermediate and outer disc regions\\n($R \\\\simgt 0.2\\\\; R_{\\\\rm L1}$) show clear P~Cygni profiles indicating origin\\nin an outflowing gas, probably the disc wind.\\n\\nWe note that the H$\\\\alpha$ line shows a redshifted ($v \\\\sim 1800 \\\\;km\\\\;\\ns^{-1}$) absorption component in spectra of the outer disc regions ($R >\\n0.3\\\\; R_{L1}$). Comparison of disc spectra at different azimuths shows\\nthat this absorption is produced in the front side of the disc, but an\\norigin in the gas stream can possibly be ruled out since the absorption\\ncomponent is seen with similar strengths in the leading and trailing\\n(the one containing the gas stream) quadrants.\\nThe interpretation of this feature is not straightforward and deserves a\\nbit of caution, since it is not clearly seen in any other line and also\\nbecause the surface brightness in the corresponding disc region is only\\na few percent of the intensities in the inner disc.\\n\\n\\n\\\\subsubsection{The uneclipsed spectrum}\\n\\\\label{uneclipsed}\\n\\nThe spectrum of the uneclipsed light (lower panel of Fig.\\\\,\\\\ref{fig8})\\nshow prominent Balmer and He\\\\,I emission lines. The Balmer jump is clearly\\nin emission and the optical continuum rises towards longer wavelengths\\nsuggesting that the Paschen jump is also in emission. These results\\nare consistent with the findings of BSH96 and indicate that the uneclipsed\\nlight has an important contribution from optically thin gas from outside\\nthe orbital plane. The Balmer lines mapped at higher spectral resolution\\nshow broad asymmetric profiles, with line peaks displaced to the red\\nside and wings extending up to $\\\\simeq 1500 \\\\;km \\\\;s^{-1}$. The observed\\nasymmetry is consistent with that previously seen in the integrated spectra\\nof Diaz \\\\& Steiner (1991) and Hessman (1990) and is similar to that\\nobserved in the resonant ultraviolet lines of UX~UMa, where the uneclipsed\\ncomponent was attributed to emission in a vertically-extended disc wind\\n(Baptista et~al. 1995; 1998; Knigge \\\\& Drew 1997).\\n\\nThe fractional contribution of the uneclipsed component to the total flux\\nwas obtained by dividing the flux of the uneclipsed light by the average\\nout of eclipse level at each passband. The result is shown in \\nFig.\\\\,\\\\ref{fig10}. The fractional contribution of the uneclipsed light\\nis very significant for the optical emission lines, reaching 40-60\\\\ per cent\\nat the Balmer lines and 20-40\\\\ per cent at the He\\\\,I lines, and decreases\\nsteadily along the Balmer series. \\nThe difference in fractional contribution between the Balmer\\nand He\\\\,I lines and among the Balmer lines indicates the existence of\\na vertical temperature gradient in the material above/below the disc,\\nwith the He\\\\,I lines (which require higher excitation energies)\\nbeing produced closer to the orbital plane. In any case, a substantial \\nfraction of the light at these lines does not arise from the orbital\\nplane and is not occulted during eclipse.\\nThe uneclipsed component gives significant contribution also to the\\ncontinuum emission. About 20\\\\ per cent of the flux at the Balmer continuum\\nand similar fraction of the continuum emission at the red end\\nof the spectrum arise from regions outside the orbital plane.\\n%\\t\\n% ############################# FIGURE 10 #################################\\n%\\n\\\\begin{figure}[h]\\n\\\\centerline{\\\\psfig{figure=xfig11.ps,angle=-90,width=10cm,rheight=7.5cm}}\\n\\t\\\\caption{ Fractional contribution of the uneclipsed component to\\n\\tthe total flux as a function of wavelength. The values were obtained\\n\\tby dividing the flux of the uneclipsed component by the average out\\n\\tof eclipse level for each passband. }\\n\\\\label{fig10}\\n\\\\end{figure}\\n\\n\\n\\\\subsubsection{The gas stream region}\\n\\\\label{stream}\\n\\nFig.\\\\,\\\\ref{fig11} shows the ratio between the spectrum of the gas stream\\nregion and the disc region at same radius as a function of radius.\\nA dotted line marks the unity level for each panel. \\nThe comparison shows that the spectrum of the gas stream is noticeably\\ndifferent from the disc spectrum in the outer disc regions (where one\\nexpects a bright spot to form due to the shock between the inflowing\\nstream and the outer disc rim), but also reveals systematic differences\\nbetween stream and disc spectra in a range of radii. In all cases,\\nthe stream emission is stronger than that of the adjacent disc.\\n%\\t\\n% ############################# FIGURE 11 #################################\\n%\\n\\\\begin{figure*}\\n\\\\centerline{\\\\psfig{figure=xfig10.ps,width=14cm,rheight=17cm}}\\n\\t\\\\caption{ Ratio of the gas stream spectrum and the disc spectrum \\n\\tfor the same set of annular regions of figure\\\\,\\\\ref{fig8}. Dashed\\n\\tlines mark the unity level for each panel. The notation is the same\\n\\tas in fig.\\\\,\\\\ref{fig8}.}\\n\\\\label{fig11}\\n\\\\end{figure*}\\n\\nThis result suggests that the material in the gas stream continues to flow\\ndownstream beyond the bright spot position. In this regard, there are three\\npotential cases: (1) stream overflow that arcs high above/below the disc\\nuntil it hits the disc surface again at a downstream position closer to \\nthe white dwarf (hereafter called the ``classical stream overflow''); \\n(2) stream overflow that continuously skims the disc surface (hereafter\\ncalled the ``disc-skimming overflow''); and (3) the stream drills into the\\ndisc at the impact site (hereafter named the ``disc stream penetration'').\\nThe latter case seems physically unrealistic and is not supported by hydrodynamic calculations of stream-disc interaction (Armitage \\\\& Livio\\n1996, 1998). \\nThe fact that there is enhanced emission in the stream region extending\\nall the way from the outer disc down to $R\\\\simeq 0.2\\\\; R_{L1}$ argues in\\nfavor of an interpretation in terms of disc-skimming overflow instead of\\nthe classical stream overflow -- as has been suggested to explain the\\nbehaviour of SW~Sex stars (Hellier \\\\& Robinson 1994; Hellier 1996) --\\nsince the latter would produce enhanced emission only at the position of\\nthe two spots, at the initial impact site in the outer disc edge and at\\nthe re-impact site much closer to disc centre (Lubow 1989).\\n\\nThe spectrum of the ratio becomes redder for decreasing disc radius,\\npossibly a combination of the disc emission becoming bluer as one moves\\ninwards and the gas stream emission becoming redder while its energy is\\ncontinuously lost in the shock with disc material along the inward stream\\ntrajectory.\\nThis is reminiscent of what was seen in ultraviolet eclipse observations\\nof the dwarf novae IP~Peg in quiescence, which revealed a compact blue\\nbright spot with an extended red tail (Baptista et~al. 1993). \\n\\n\\n\\\\section{Discussion} \\\\label{discussao}\\n\\nIn this section we present and discuss some possible interpretations for\\nthe results of section\\\\,\\\\ref{resultados} in the context of the current\\nmodels for the SW Sex stars.\\n\\n\\\\subsection{Where do the lines come from?}\\n\\nIn previous sections we have accumulated evidences that the behaviour\\nof the UU Aqr lines in its high state is not consistent with emission\\nin a disc atmosphere, namely: \\n(i) negligible rotational disturbance, (ii) no mirror symmetry between\\neclipse maps in symmetric velocity bins; (iii) H$\\\\alpha$ line emission\\ndistribution much flatter than the empirical $I \\\\propto R^{-1.5}$ law;\\n(iv) significant uneclipsed components, and (v) presence of P~Cygni\\nprofiles in the disc spectra at intermediate and large disc radii.\\nIf the lines do not arise in the disc atmosphere, where do they come from?\\n\\nThe most compelling interpretation is that the lines are produced in a\\ndisc chromosphere + wind. This region is hot, dense, opaque and has low\\nexpansion velocities close to the orbital plane in order to produce the\\nobserved deep, narrow absorption lines in the line of sight to the inner\\ndisc. Most of the high excitation lines are produced close to the disc\\nplane. The density and temperature decrease with height above/below the\\ndisc as the outflowing gas spreads over an increasing surface area.\\nOptically thin emission from this extended region is\\nprobably responsible for the Balmer jump (and lines) in emission observed\\nin the uneclipsed spectrum. Support in favor of this scenario comes from\\nthe recent detailed modeling of the C\\\\,{\\\\sc IV} wind line of eclipsing\\nnova-likes by Schlosman, Vitello \\\\& Mauche (1996) and Knigge \\\\& Drew\\n(1997). Their results suggest the existence of a relatively dense ($n_e\\n\\\\sim 4 \\\\times 10^{12}$~cm$^{-3}$) and vertically extended chromosphere\\nbetween the disc surface and the fast-moving parts of the wind, which\\ncould produce significant amounts of optically thin emission.\\nAt orbital phases around eclipse, gas outflowing in the direction of the\\nsecondary star will be seen along the line of sight to the bright underlying\\naccretion disc as blueshifted absorption features, while gas expelled in\\nthe direction away from the secondary star should contribute with\\nredshifted emission.\\n\\nWe tested this scenario by \\ncomparing spatially resolved spectra of the disc lune closest to the\\nsecondary star (the right hemisphere of the disc in the eclipse maps of\\nFig.\\\\,\\\\ref{fig3}, hereafter called the ``front'' side) and of the disc\\nlune farthest away from the secondary star (the left hemisphere of the\\ndisc in Fig.\\\\,\\\\ref{fig3}, hereafter called the ``back'' side). \\nFor this purpose, we defined two opposite azimuthal disc regions of width\\n$30\\\\degr$ along the major axis of the binary, and extracted spatially\\nresolved spectra for the same set of annuli as above. These spatially\\nresolved spectra are noisier than those of Figs.\\\\,\\\\ref{fig8} and\\n\\\\ref{fig9} because in this case the average intensity of each annulus\\nis computed from a significantly smaller number of pixels. The results\\nare shown in Fig.\\\\,\\\\ref{fig9A} for the H$\\\\beta$ and H$\\\\gamma$ regions\\nand are consistent with our interpretation:\\nThe blueshifted absorption component is seen mainly in the front side of\\nthe disc while the redshifted emission is generally more prominent in\\nspectra of the back side of the disc.\\nThe fact that the blueshifted absorption can still be seen projected along\\nthe line of sight at the outer regions of the disc favours a more spherical\\nor equatorial geometry for the outflowing gas instead of a highly collimated,\\npolar jet.\\n%\\t\\n% ############################## FIGURE 12 ################################\\n%\\n\\\\begin{figure}\\n\\\\vspace*{7cm}\\n%\\\\centerline{\\\\psfig{figure=xfig12.ps,angle=-90,width=10.5cm,rheight=7cm}}\\n\\t\\\\caption{ Comparison of spatially resolved spectra of the front and\\n\\tback side of the disc (see text) in the H$\\\\beta$ and H$\\\\gamma$ regions.\\n\\tThe notation is the same as in figure\\\\,\\\\ref{fig9}. For clarity, only\\n\\tthe H$\\\\gamma$ spectra of two annuli are shown. }\\n\\\\label{fig9A}\\n\\\\end{figure}\\n\\nThe chromosphere + disc wind interpretation satisfactorily accounts for all\\nthe features listed above and also gives a plausible explanation for \\n(1) the distinct semi-amplitude of the radial velocity $K$ and systemic\\nvelocity $\\\\gamma$ as inferred from different emission lines and \\n(2) the time dependent $K$ and $\\\\gamma$ values (Hoard et~al. 1998). \\nThe centroid of lines of different excitation level will occur at different\\nlocations in the primary lobe and will sample different velocities \\nalong the line of sight. With respect to (2), \\nthe comparison of the H$\\\\alpha$ map of BSH96 (which corresponds to the low\\nbrightness state) with that of Fig.\\\\,\\\\ref{fig4} (the high state) reveals\\nthat in the latter the emission extends over a much larger region of the\\nprimary lobe with a pronounced asymmetry in the stream region,\\nsuggesting that the wind emission is variable in time and is intimately\\nconnected with the mass accretion rate. \\nThis remark gives additional support to the suggestion\\nby Hoard et~al. (1998) that the observed time dependence of the $K$ and\\n$\\\\gamma$ velocities might be due to variability of a wind component\\nin UU Aqr.\\n\\nAn alternative possibility is to consider the deep absorption lines\\nseen towards the line of sight to the disc centre as being produced by\\nabsorption in a vertically extended disc rim. Although this scenario\\naccounts for the narrow absorption lines,\\nit is not able to explain the large velocities inferred from the line\\nwidth for intermediate and large disc radius nor the P~Cygni profiles.\\nFurthermore, it should result in a perceptible front-back asymmetry in\\nthe disc surface brightness (namely, the back side of the disc should be\\nbrighter) which is not seen in the eclipse maps.\\n\\nRecently, Horne (1999) proposed that most of the features of the SW Sex\\nstars could be explained in terms of a disc-anchored magnetic propeller,\\nin which energy and angular momentum are extracted from the magnetic field\\nof the inner disc regions to fling part of the material in the gas stream\\nout of the binary towards the back side of the disc. \\nAlthough this model is able to explain many of the observed features of\\nUU Aqr, it can only account for the observed P Cygni profiles if the gas\\ntrapped by the inner disc magnetic field is expelled in all directions\\nand not only towards the back of the disc.\\nWe note that, in this case, there is no significant difference between\\nthe propeller and the disc wind models and, in fact, the former could\\npossibly work as the underlying physical mechanism driving the latter.\\n\\nIf disk-skimming overflow does occur, we might expect that \\ndissipation of energy in the collision between the gas stream and the\\ndisc material gives rise to a bulge extending along the stream trajectory\\nover and under the disc. This bulge will appear in front of the\\nchromosphere + wind line emitting region at the inner disc when seen\\nalong the line of sight at orbital phases 0.5-0.9.\\nThis may explain the phase-dependent absorption lines, observed from\\nphases 0.5-0.9 and with maximum at phase $\\\\sim 0.8$ (Heafner 1989;\\nHoard et~al. 1998). The enhanced line emission along the gas stream\\n(see Fig.\\\\,\\\\ref{fig4}) is possibly responsible for the phase offset\\nbetween photometric and spectroscopic conjunction\\n(Diaz \\\\& Steiner 1991; Hoard et~al. 1998). \\n\\nIn summary, the picture which emerges from our results is consistent\\nwith the results from the Doppler tomography and the model proposed\\nfor UU Aqr by Hoard et~al. (1998).\\n\\n\\n\\\\subsection{Where has the bright spot gone?}\\n\\nAlthough our observations correspond to the high brightness state of\\nUU Aqr, our eclipse maps do not show the conspicuous asymmetric structure\\nseen in the high state eclipse maps of BSH96 and which was interpreted\\nas being the bright spot.\\nThe explanation for the `disappearance' of the bright spot may be\\nconnected with the stunted outbursts found by Honeycutt et~al. (1998).\\n\\nBSH96 pointed out that the inferred accretion rate of UU Aqr\\nis close to the critical mass accretion rate for disc instability\\nto occur and remarked that the long-term lightcurves of accretion\\ndiscs with mass transfer rates near their critical limit might display\\nlow-amplitude ($\\\\simlt 1.0$ mag) outbursts caused by thermal\\ninstabilities in the outer disc regions (e.g., Lin, Papaloizou \\\\&\\nFaulkner 1985). In this case the outburst is restricted to the outer\\n1/3 of the disc extent while the inner disc remains in a high viscosity,\\nsteady state.\\nHoneycutt et~al (1998) suggested that such dwarf-nova type instabilities\\ncould be an explanation for the stunted outbursts of UU Aqr if a\\nmechanism can be identified to make the amplitudes appear small. \\nWe note that the observed low amplitudes can be easily accounted for\\nby the reduced contrast of the light from the outbursting outer\\nregions -- where the efficiency in transforming gravitational potential\\nenergy in radiation is relatively low -- in comparison to the bright,\\noptically thick and steady inner disc.\\n\\nIf the observed stunted outbursts of UU Aqr are caused by thermal\\ninstabilities in its outer disc, the disc radius is expected to\\nincrease during the outburst and will eventually reach the 3:1 tidal\\nresonance radius leading to an elliptical precessing disc reminiscent\\nof what possibly happens in SU UMa stars in superoutburst\\n(e.g., Warner 1995 and references therein). \\nWe suggest that the azimuthally elongated structure seen in the\\neclipse maps of BSH96 is the signature of such an elliptical disc\\nand not the bright spot. Following this line of reasoning, this\\nstructure should not be present when the disc radius is smaller than\\nthe tidal resonance radius. Support for this interpretation comes from\\nthe comparison of disc radius in the high state eclipse maps of BSH96\\nand our eclipse maps. \\nFrom BSH96 data we estimate a disc radius of $R_d \\\\simeq 0.7 \\\\; \\nR_{\\\\rm L1}$, comparable to the 3:1 tidal resonance radius for a\\nmass ratio of $q=0.3$. Our eclipse maps lead to a smaller value of\\n$R_d = 0.65 \\\\; R_{\\\\rm L1}$. Therefore, we suggest that UU Aqr was in an \\noccasional superhumper state during the high brightness state observations\\nof BSC94.\\n\\nIn the model of Hoard et~al. (1998), after the explosive impact of the\\nhigh \\\\.{M} accretion stream with the edge of the disc, the incomming gas \\nforms an optically thick absorbing bulge on the disc that either follows \\nroughly the stream trajectory or runs along the rim of the disc, producing\\nthe absorption features seen at phases 0.4-0.9. It may alternatively be\\npossible that the structure seen in the eclipse maps of BSH96 is the\\nsignature of such post-impact stream material running along the edge of\\nthe disc. In this scenario, the azimuthally extended bulge would be present\\nor not depending on the (variable) mass accretion rate and the resulting\\norbital hump would remain fixed in phase.\\n\\nIt would be interesting (although outside the scope of this paper) to\\nreanalize the data of BSC94 to see if the orbital hump present in the high\\nstate precesses in phase in a similar manner as superhumps in superoutbursts\\n(supporting the elliptical disc scenario) or if its maximum occurs always\\nat the same orbital phase range about 0.8 - 0.9 cycle (favouring the\\npost-impact bulge scenario).\\n\\n\\n\\\\section{Conclusions} \\\\label{conclusao}\\n\\nWe used time-resolved spectroscopy to study the structure and spectra\\nof the accretion disc and gas stream of the novalike UU~Aquarii in\\nthe optical range. The main results of this analysis can be summarized\\nas follows:\\n\\n\\\\begin{itemize}\\n\\n\\\\item The spectrum of the inner disc shows a blue continuum filled with deep,\\nnarrow absorption lines which transition to emission with clear P~Cygni\\nprofiles at intermediate and large radii ($R\\\\simgt 0.2 \\\\; R_{L1}$).\\n\\n\\\\item The spectrum of the uneclipsed light has strong H\\\\,I and He\\\\,I\\nemission lines and a Balmer jump in emission indicating a significant\\ncontribution from optically thin regions outside the orbital plane.\\n\\n\\\\item Velocity-resolved eclipse maps and spectra indicate that most\\nof the line emission probably arises in a vertically-extended disc\\nchromosphere + wind.\\n\\n\\\\item Differences in fractional contribution among emission lines suggests\\na vertical temperature gradient in the material above/below the disc.\\n\\n\\\\item The comparison of the spectrum of the gas stream region and the\\ndisc region at the same radius as a function of radius gives evidence \\nof gas stream disc-skimming overflow down to $R\\\\simeq 0.2\\\\; R_{L1}$.\\nThis may explain the phase-dependent absorption in emission lines.\\n\\n\\\\item The comparison of our eclipse maps with those of BSH96 suggests that\\nthe asymmetric structure in the outer disc previously identified as\\nthe bright spot may be the signature of an elliptical precessing disc\\nsimilar to those possibly present in SU UMa stars during superoutbursts.\\n\\n\\\\end{itemize}\\n\\n\\n\\\\section*{Acknowledgments}\\n\\nWe gratefully acknowledge the director of KPNO for granting telescope time\\nfor this project at the Summer Queue Program, Tod Boroson and the team\\nof observers at KPNO for their kind effort in collecting the data, \\nKnox Long and the director of STScI for financial support through\\nthe Director Discretionary fund, Susan Keener for helping with the data\\nreduction at STScI, and an anonymous referee for valuable comments and\\nsuggestions that helped to improve the presentation of the results.\\nRB acknowledges financial support from CNPq/Brazil through grant no. 300\\\\,354/96-7. 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M., Dhillon V. S., Horne K., Kuulkers E,. 1994.\\n\\t\\tA\\\\&A, 283, 441\\n\\\\bibitem {45} Schlosman I., Vitello, P. A. J., Mauche C. W., 1996. \\n\\t\\tApJ, 461, 377\\n\\\\bibitem {47} Thorstensen J. R., et~al., 1991. AJ, 102, 272\\n\\\\bibitem {50} Warner B., 1995. Cataclysmic Variable Stars, Cambridge\\n\\t\\tUniversity Press, Cambridge\\n\\\\bibitem {51} Warner B., 1997. IAU Colloquium 163, Accretion Phenomena \\n\\t\\tand Related Outflows, ASP Conf. Series 121, ed. D. T. Wickramasinghe,\\n\\t\\tG. V. Bicknell \\\\& L. Ferrario, ASP, San Francisco, p. 133\\n\\\\bibitem {52} Williams R. E., 1989. AJ, 97, 1752\\n\\n\\\\end{thebibliography}\\n\\n\\\\bsp\\n\\\\end{document}\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002189.extracted_bib","string":"\\begin{thebibliography}{99}\n\\bibitem {1} Armitage P.J., Livio M., 1996. ApJ, 470, 1024\n\\bibitem {2} Armitage P.J., Livio M., 1998. ApJ, 493, 898\n\\bibitem {3} Baptista R., et~al., 1993. in Interacting Binary Stars, ASP\n\t\tConf. Series Vol.\\ 56, ed. A. Shafter, ASP, San Francisco, p. 259\n\\bibitem {4} Baptista R., Horne K., Hilditch R., Mason K. O., Drew J. E.,\n\t\t1995. ApJ, 448, 395\n\\bibitem {5} Baptista R., Horne K., Wade R. A., Hubeny I., Long K. S.,\n\t\tRutten R. G. M., 1998. MNRAS, 298, 1079\n\\bibitem {6} Baptista R., Steiner J. E., 1993. A\\&A, 277, 331\n\\bibitem [Baptista et al, 1994]{BSC94}\n\t\tBaptista R., Steiner J. E., Cieslinski D., 1994. ApJ, 433, 332\n\\bibitem [Baptista et al, 1996]{BSH96}\n\t\tBaptista R., Steiner J. E., Horne K., 1996. MNRAS, 282, 99\n\\bibitem {7} Diaz M. P., Steiner J. E., 1991. AJ, 102, 1417\n\\bibitem {8} Downes R. A., Keyes C. D., 1988. AJ, 96, 777\n\\bibitem {9} Haefner R., 1989. Inf. Bull. Var. Stars, 3397\n\\bibitem {10} Hellier C., 1996. ApJ, 471, 949\n\\bibitem {11} Hellier C., 1999. in Warner Symposium on Cataclysmic Variables,\n\t\tNew Astronomy Reviews, in press (astro-ph/9906089).\n\\bibitem {12} Hellier C., Robinson E. L., 1994. ApJ, 431, L107\n\\bibitem {13} Hessman F. V., 1990. in Reviews in Modern Astrophysics:\n\t\tAccretion and Winds, ed. G. Klare, Springer, Berlin\n\\bibitem [Hoard et al, 1998]{Hoard} Hoard D. W., Still M.D., Skzody P., \n Smith R.C., Buckley D.A.H., 1998. MNRAS, 294, 689\n\\bibitem [Honeycutt et al, 1998]{Honey}\n\t\tHoneycutt R. K., Robertson J. W., Turner G. W., 1998. AJ, 115, 2527\n\\bibitem {Honey2} Honeycutt R. K., Schlegel E. M., Kaitchuck R. H., 1986.\n\t\tApJ, 302, 388\n\\bibitem [Horne 1985]{Horne} Horne K., 1985. MNRAS, 213, 129\n\\bibitem {14} Horne K., 1986. PASP, 98, 609\n\\bibitem {15} Horne K., 1993. in Accretion Disks in Compact Stellar Systems,\n\t\ted. J. C. Wheeler, World Scientific Publ. Co., p. 117\n\\bibitem {16} Horne K., 1999. in Magnetic Cataclysmic Variables, ASP Conf.\n\t\tSeries Vol.\\ 157, eds. K. Mukai \\& C. Hellier, ASP, San Francisco,\n\t\tp. 349\n\\bibitem {20} Kaitchuck R. H., Schlegel E. M., White II J. C., Mansperger\n\t\tC. S., 1998. ApJ, 499, 444\n\\bibitem {21} Knigge C., Drew J. E., 1997. ApJ, 486, 445\n\\bibitem {22} Lin D. N. C., Papaloizou J., Faulkner J., 1985. MNRAS, 212, 105\n\\bibitem {23} Lubow S. H., 1989. ApJ, 340, 1064\n\\bibitem {25} Marsh T. R., Horne K., Schlegel E.M., Honeycutt K., \n\t\tKaitchuck R.H., 1990. ApJ, 364, 637\n\\bibitem {30} Massey P., Strobel K., Barnes J. V., Anderson E., 1988.\n\t\tApJ, 328, 315\n\\bibitem {39} Rutten R. G. M., van Paradijs J., Tinbergen J., 1992. A\\&A,\n\t\t260, 213\n\\bibitem {40} Rutten R. G. M., Dhillon V. S., Horne K., Kuulkers E,. 1994.\n\t\tA\\&A, 283, 441\n\\bibitem {45} Schlosman I., Vitello, P. A. J., Mauche C. W., 1996. \n\t\tApJ, 461, 377\n\\bibitem {47} Thorstensen J. R., et~al., 1991. 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S.,\\n\\t\\tRutten R. G. M., 1998. MNRAS, 298, 1079\\n\\\\bibitem {6} Baptista R., Steiner J. E., 1993. A\\\\&A, 277, 331\\n\\\\bibitem [Baptista et al, 1994]{BSC94}\\n\\t\\tBaptista R., Steiner J. E., Cieslinski D., 1994. ApJ, 433, 332\\n\\\\bibitem [Baptista et al, 1996]{BSH96}\\n\\t\\tBaptista R., Steiner J. E., Horne K., 1996. MNRAS, 282, 99\\n\\\\bibitem {7} Diaz M. P., Steiner J. E., 1991. AJ, 102, 1417\\n\\\\bibitem {8} Downes R. A., Keyes C. D., 1988. AJ, 96, 777\\n\\\\bibitem {9} Haefner R., 1989. Inf. Bull. Var. Stars, 3397\\n\\\\bibitem {10} Hellier C., 1996. ApJ, 471, 949\\n\\\\bibitem {11} Hellier C., 1999. in Warner Symposium on Cataclysmic Variables,\\n\\t\\tNew Astronomy Reviews, in press (astro-ph/9906089).\\n\\\\bibitem {12} Hellier C., Robinson E. L., 1994. ApJ, 431, L107\\n\\\\bibitem {13} Hessman F. V., 1990. in Reviews in Modern Astrophysics:\\n\\t\\tAccretion and Winds, ed. G. Klare, Springer, Berlin\\n\\\\bibitem [Hoard et al, 1998]{Hoard} Hoard D. 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Ferrario, ASP, San Francisco, p. 133\\n\\\\bibitem {52} Williams R. E., 1989. AJ, 97, 1752\\n\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":187,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002190"},"title":{"kind":"string","value":"Constraining the Lifetime of Quasars from their Spatial Clustering"},"authors":{"kind":"list like","value":[{"author":"Zolt\\'an Haiman\\altaffilmark{1}"}],"string":"[\n {\n \"author\": \"Zolt\\\\'an Haiman\\\\altaffilmark{1}\"\n }\n]"},"abstract":{"kind":"string","value":"The lifetime of the luminous phase of quasars is constrained by current observations to be $10^{6} \\lsim t_Q \\lsim 10^8$ years, but is otherwise unkown. We model the quasar luminosity function in detail in the optical and X--ray bands using the Press--Schechter formalism, and show that the expected clustering of quasars depends strongly on their assumed lifetime $t_Q$. %within this range. %If quasars are short lived, their duty cycle is small, and they %must reside in abundant, low--mass dark matter halos. Conversely, if quasars %live longer, they must be hosted by rarer, more massive and more strongly %clustered halos. We quantify the resulting dependence of clustering on the We quantify this dependence, and find that existing measurements of the correlation length of quasars are consistent with the range $10^{6} \\lsim t_Q \\lsim 10^8$. We then show that future measurements of the power spectrum of quasars out to $z\\sim 3$, from the 2dF or Sloan Digital Sky Survey, can significantly improve this constraint, and in principle allow a precise determination of $t_Q$. We estimate the systematic errors introduced by uncertainties in the modeling of the quasar-halo relationship, as well as by the possible existence of obscured quasars."},"latex":{"kind":"list like","value":[{"name":"msrev.tex","string":"%\\documentstyle[aasms4]{article}\n\\documentstyle[emulateapj]{article}\n\n\n\\def\\gsim{\\;\\rlap{\\lower 2.5pt\n \\hbox{$\\sim$}}\\raise 1.5pt\\hbox{$>$}\\;}\n\\def\\lsim{\\;\\rlap{\\lower 2.5pt\n \\hbox{$\\sim$}}\\raise 1.5pt\\hbox{$<$}\\;}\n\\def\\msun{{\\rm\\,M_\\odot}}\n\\def\\yr{{\\rm\\,yr}}\n\\def\\au{{\\rm\\,AU}}\n\\def\\del{{\\partial}}\n\\def\\gm{{\\rm\\,g}}\n\\def\\cm{{\\rm\\,cm}}\n\\def\\sec{{\\rm\\,s}}\n\\def\\erg{{\\rm\\,erg}}\n\\def\\kev{{\\rm\\,keV}}\n\\def\\ev{{\\rm\\,eV}}\n\\def\\K{{\\rm\\,K}}\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\def\\lta{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar''218$}}\n \\raise 2.0pt\\hbox{$\\mathchar''13C$}}}\n\\def\\gta{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar''218$}}\n \\raise 2.0pt\\hbox{$\\mathchar''13E$}}}\n\\newcommand{\\beq}{\\begin{equation}}\n\\newcommand{\\eeq}{\\end{equation}}\n\n\\lefthead{HAIMAN \\& HUI}\n\\righthead{QSO CLUSTERING}\n\n\\begin{document}\n\\title{Constraining the Lifetime of Quasars from their Spatial Clustering}\n\\author{Zolt\\'an Haiman\\altaffilmark{1}}\n\\affil{Princeton University Observatory, Princeton, NJ 08544, USA \\\\email: zoltan@astro.princeton.edu}\n\\and\n\\author{Lam Hui}\n\\affil{Institute for Advanced Study, Olden Lane, Princeton, NJ 08544, USA \\\\\nemail: lhui@ias.edu}\n\n\\altaffiltext{1}{Hubble Fellow}\n\n\\vspace{0.75\\baselineskip}\n\\submitted{ApJ, in press (submitted on Feb. 8. 2000)}\n\n\\begin{abstract}\n\nThe lifetime of the luminous phase of quasars is constrained by current\nobservations to be $10^{6} \\lsim t_Q \\lsim 10^8$ years, but is otherwise\nunkown. We model the quasar luminosity function in detail in the optical and\nX--ray bands using the Press--Schechter formalism, and show that the expected\nclustering of quasars depends strongly on their assumed lifetime $t_Q$.\n%within this range.\n%If quasars are short lived, their duty cycle is small, and they\n%must reside in abundant, low--mass dark matter halos. Conversely, if quasars\n%live longer, they must be hosted by rarer, more massive and more strongly\n%clustered halos. We quantify the resulting dependence of clustering on the\nWe quantify this dependence, and find that existing measurements of the\ncorrelation length of quasars are consistent with the range $10^{6} \\lsim t_Q\n\\lsim 10^8$. We then show that future measurements of the power spectrum of\nquasars out to $z\\sim 3$, from the 2dF or Sloan Digital Sky Survey, can\nsignificantly improve this constraint, and in principle allow a precise\ndetermination of $t_Q$. We estimate the systematic errors introduced by\nuncertainties in the modeling of the quasar-halo relationship, as well as by\nthe possible existence of obscured quasars.\n\\end{abstract}\n\n\\keywords{cosmology: theory -- cosmology: observation -- quasars: formation -- large scale structure}\n\n\\section{Introduction}\n\\label{section:introduction}\n\nA long outstanding problem in cosmology is the synchronized evolution of the\nquasar population over the redshift range $0\\lsim z\\lsim 5$. Observations in\nthe optical (Pei 1995) and radio (Shaver et al. 1994) show a pronounced peak in\nthe abundance of bright quasars at $z\\approx 2.5$; recent X--ray observations\n(Miyaji et al. 2000) confirm the rapid rise from $z=0$ towards $z\\approx 2$,\nbut have not shown evidence for a decline at still higher redshifts.\nIndividual quasars are widely understood to consist of supermassive black holes\n(BHs) powered by accretion (Lynden-Bell 1967; Rees 1984). A plausible\ntimescale for quasar activity is then the Eddington time, $4\\times10^7$\n($\\epsilon$/0.1) yr, the e-folding time for the growth of a BH accreting mass\nat a rate $\\dot M$, while shining at the Eddington luminosity with a radiative\nefficiency of $L=L_{\\rm Edd}=\\epsilon\\dot M c^2$. The lifetime $t_Q$ of the\nluminous phase of quasars can be estimated directly, by considering the space\ndensity of quasars and galaxies. At $z\\sim 2$, the ratio $n_Q/n_G \\sim 3\\times\n10^{-3}$ implies the reassuringly close value of $t_Q\\sim t_{\\rm Hub}\nn_Q/n_G\\sim 10^7$ yr (Blandford 1999 and references therein). These lifetimes\nare significantly shorter than the Hubble time, suggesting that the quasar\npopulation evolves on cosmic time--scales by some mechanism other than local\naccretion physics near the BH.\n\nIt is tempting to identify quasars with halos condensing in a cold dark matter\n(CDM) dominated universe, as the halo population naturally evolves on cosmic\ntime--scales (Efstathiou \\& Rees 1988; Haiman \\& Loeb 1998; Kauffmann \\&\nHaehnelt 2000). Furthermore, quasars reside in a subset of all galaxies, while\nthe redshift--evolution of the galaxy population as a whole (qualitatively\nsimilar to that of bright quasars) has been successfully described by\nassociating galaxies with dark halos (e.g. Lacey \\& Cole 1993; Kauffmann \\&\nWhite 1993). A further link between galaxies and quasars comes from the recent\ndetection, and measurements of the masses of massive BHs at the centers of\nnearby galaxies (Magorrian et al. 1998; van der Marel 1999).\n\nThese arguments suggest that the evolution of the quasar population can indeed\nbe described by ``semi--analytic'' models, associating quasars with dark matter\nhalos. In this type of modeling, the quasar lifetime plays an important role.\nThe quasar phase in a single halo could last longer ($t_{\\rm Q}\\sim10^8$yr),\nwith correspondingly small $M_{\\rm bh}/M_{\\rm halo}$ ratios, or last shorter\n($t_{\\rm Q}\\sim10^6$yr), with larger BH formation efficiencies (Haiman \\& Loeb\n1998; Haehnelt et al. 1998). Note that although recent studies have\nestablished a correlation between the bulge mass $M_{\\rm bulge}$ and BH mass\n$M_{\\rm bh}$, this correlation leaves a considerable uncertainty in the\nrelation between $M_{\\rm bh}$ and the mass $M_{\\rm halo}$ of its host halo. If\nthe initial density fluctuations are Gaussian with a CDM power spectrum, the\nclustering of collapsed halos is a function of their mass -- rarer, more\nmassive halos cluster more strongly (Kaiser 1984; Mo \\& White 1996). Hence,\nmeasurements of quasar clustering are a potentially useful probe of both BH\nformation efficiencies and quasar lifetimes (La Franca et al. 1998, Haehnelt et\nal. 1998).\n\nIn this paper, we assess the feasibility of breaking the above degeneracy, and\ninferring quasar lifetimes, from the statistics of clustering that will be\navailable from the Sloan Digital Sky Survey (SDSS, Gunn \\& Weinberg 1995) and\nAnglo-Australian Telescope Two-Degree-Field (2dF, Boyle et al. 1999). Previous\nworks (e.g. Stephens et al. 1997; Sabbey et al. 1999) have yielded estimates\nsuggesting that quasars are clustered more strongly than galaxies. However, the\ncurrent uncertainties are large, especially at higher redshifts, where\nclustering has been found to decrease (Iovino \\& Shaver 1988; Iovino et\nal. 1991), to stay constant (Andreani \\& Cristiani 1992; Croom \\& Shanks 1996),\nor to increase with redshift (La Franca et al. 1998). As a result, no strong\nconstraints on the life--time can be obtained yet. The key advance of\nforthcoming surveys over previous efforts is two--fold. Because of their sheer\nsize, i.e. the large number of quasars covering a large fraction of the sky,\nboth shot--noise and sample variance can be beaten down, significantly reducing\nthe statistical uncertainties. Furthermore, the large sample-size will\neliminate the need to combine data from different surveys with different\nselection criteria, hence allowing cleaner interpretation.\n\nRecent measurements of the local massive black hole density have stimulated\ndiscussions of a radiative efficiency which is much lower than the usual $\\sim\n0.1$ (e.g. Haehnelt et al. 1999). A convincing constraint on the lifetime of\nquasars could be therefore highly interesting, as this might have implications\nfor the local accretion physics near the BH.\n\nThis paper is organized as follows. In \\S~\\ref{section:models}, we summarize\nour models for the quasar luminosity function, and in\n\\S~\\ref{section:clustering} we compute the quasar correlation function in these\nmodels. In \\S~\\ref{section:present}, we compare the model predictions with\npresently available data, and in \\S~\\ref{section:future} we assess the ability\nof future optical redshift surveys to discriminate between the various models.\nIn \\S~\\ref{section:xray}, we repeat our analysis in the soft X--ray band, and\nexamine the contribution of quasars to the X-ray background, and its\nauto--correlation. In \\S~\\ref{section:discussion}, we address some of the\ncaveats arising from our assumptions, and in \\S~\\ref{section:conclusions} we\nsummarize our conclusions and the implications of this work.\n\n\\section{Models for the Quasar Luminosity Function}\n\\label{section:models}\n\nIn this section, we briefly summarize our model for the luminosity function\n(LF) of quasars, based on associating quasar BHs with dark halos. Our\ntreatment is similar to previous works (Haiman \\& Loeb 1998; Haehnelt et\nal. 1998), although differs in some of the details. A more extensive treatment\nis provided in the Appendix. The main assumption is that there is, on average,\na direct monotonic relation between halo mass $M_{\\rm halo}$ and average quasar\nluminosity $L_{M,z}$, which we parameterize using the simple\npower--law ansatz:\n\n\\beq \\bar L_{M,z}= x_0(z) M_{\\rm halo} \\left(\\frac{M_{\\rm\nhalo}}{M_0}\\right)^{\\alpha(z)}.\n\\label{eq:params00}\n\\eeq\n\nHere $x_0(z)$ and $\\alpha(z)$ are ``free functions'', whose values are found by\nthe requirement that the resulting luminosity function agrees with\nobservations. As explained in the Appendix, our model has one free parameter,\nthe lifetime $t_Q$, which uniquely determines $x_0(z)$ and $\\alpha(z)$ in any\ngiven background cosmology. We assume the background cosmology to be either\nflat ($\\Lambda$CDM) with $(\\Omega_\\Lambda,\\Omega_{\\rm m},h,\\sigma_{\\rm\n8h^{-1}},n)=(0.7,0.3,0.65,1.0,1.0)$ or open (OCDM) with\n$(\\Omega_\\Lambda,\\Omega_{\\rm m},h,\\sigma_{\\rm\n8h^{-1}},n)=(0,0.3,0.65,0.82,1.3)$. In LCDM, we find $(-\\log[x_0/{\\rm L_\\odot\nM_\\odot^{-1}}],\\alpha) \\approx (1,0.4)$ and $\\approx (-0.2, -0.1)$ for\nlifetimes of $t_Q=10^{8}$ and $t_Q=10^{6.5}$yr, respectively. Similarly, in\nOCDM, we find $(-\\log[x_0/{\\rm L_\\odot M_\\odot^{-1}}],\\alpha) \\approx (1,0.25)$\nand $\\approx (-0.2, -0.25)$ for these two lifetimes.\n\nIn Figure~\\ref{fig:LFfits}, we demonstrate the agreement between the LF\ncomputed in our models with the observational data at two different redshifts,\n$z=2$ and $z=3$. For reference, the upper labels in this figure show the\napparent magnitudes in the SDSS $g^\\prime$ band, assuming that the intrinsic\nquasar spectrum is the same as the mean spectrum in the Elvis et al. (1994)\nquasar sample. The photometric detection threshold\\footnote{See\nhttp://www.sdss.org/science/tech\\_summary.html.} of SDSS is $g^\\prime \\approx\n22.6$, corresponding to a BH mass of $\\approx 10^{8} {\\rm M_\\odot}$ at $z=3$\nand a three times smaller mass at $z=2$. As the figure shows, the overall\nquality of the fits is excellent; for reference, the dashed lines show the\nad--hoc empirical fitting formulae from Pei (1995). Similarly accurate match\nto the quasar LF is achieved at different redshifts, and in the models assuming\nan OCDM cosmology. Figure~\\ref{fig:LFfits} shows, in particular, that the fits\nobtained from the power--law ansatz adopting either a short (solid lines) or a\nlong (dotted lines) lifetime are nearly indistinguishable; hence modeling the\nLF by itself does not constrain the quasar lifetime within the limits\n$10^{6.5}$ yr $\\lsim t_Q \\lsim 10^8$ yr.\n\nBefore considering constraints on the lifetime from clustering, it is useful to\npoint out that estimates for both upper and lower limits on $t_Q$ follow from\nthe observed luminosity function alone.\n\n{\\it Lower limit on $t_Q$.} A halo of mass $M_{\\rm halo}$ is unlikely to harbor\na BH more massive than $\\approx 6\\times10^{-3} (\\Omega_{b}/\\Omega_{0}) M_{\\rm\nhalo} = 6\\times 10^{-4} M_{\\rm halo}$, where $\\approx 6\\times10^{-3}$ is the\nratio $M_{\\rm bh}/M_{\\rm bulge}$ found in nearby galaxies (Magorrian et\nal. 1998) because $M_{\\rm bulge}$ cannot be larger than\n$(\\Omega_{b}/\\Omega_{0}) M_{\\rm halo}$. This maximal BH could at best emit\n$\\approx 10\\%$ of the Eddington luminosity in the B--band, implying $L/M_{\\rm\nhalo} \\lsim 3~{\\rm L_\\odot/M_\\odot}$. We find (cf. Fig.~\\ref{fig:params}) that\nour short lifetime model with $t_Q=10^{6.5}$ yr nearly reaches this limit;\nmodels with shorter lifetimes would require unrealistically large $L/M_{\\rm\nhalo}$ ratios.\n\n{\\it Upper limit on $t_Q$.} Long lifetimes, on the other hand, require the\nratio $L/M_{\\rm halo}$ to be small; this can lead to unrealistically large halo\nmasses. The brightest quasars detected at redshifts $z\\approx 2-3$ have\nluminosities as large as $L\\approx 10^{14} {\\rm L_\\odot}$ (Pei 1995). We find\n(cf. Fig.~\\ref{fig:params}) that in order to avoid the host halo masses of\nthese bright quasars to exceed $\\sim 10^{15}~{\\rm M_\\odot}$, the lifetime\ncannot be longer than $\\sim 10^8$ yr. An alternative, standard argument goes as\nfollows. The black hole mass grows during the quasar phase as $e^{t_Q/t_E}$\nwhere $t_E = 4\\times10^7 (\\epsilon/0.1)$ yr is the Eddington time. Assuming a\nconservative initial black hole mass of $1 M_{\\odot}$, a lifetime longer than\n$10^9$ yr would give final black hole masses that are unacceptably large.\n\n\\vspace{2\\baselineskip}\n\n\\section{The Clustering of Quasars}\n\\label{section:clustering}\n\nAs demonstrated in the previous section, equally good fits can be obtained to\nthe luminosity function of quasars, assuming either a short or a long lifetime,\nand a power-law dependence of the mean quasar luminosity on the halo mass $\\bar\nL\\propto M^\\alpha$. In this section, we derive the clustering of quasars in\nour models, and demonstrate that they depend significantly on the assumed\nlifetime.\n\nThe halos are a biased tracer of the underlying mass distribution, customarily\nexpressed by $P_{\\rm halo} (k) = b^2 P(k)$ where $P_{\\rm halo}$ and $P$ are the\nhalo and mass power spectra as a function of wavenumber $k$. The bias parameter\nfor halos of a given mass $M$ at a given redshift $z$ is given by (Mo \\& White\n1996)\n\n\\beq\nb(M,z)= 1 + \\frac{1}{\\delta_c}\\left[\n\\left(\\frac{\\delta_c}{\\sigma(M)D(z)}\\right)^2-1\\right],\n\\label{eq:biasM}\n\\eeq\n\nwhere $D(z)$ is the linear growth function, $\\sigma(M)$ is the r.m.s. mass\nfluctuation on mass--scale $M$ (using the power spectrum of Eisenstein \\& Hu\n1999), and $\\delta_c\\approx 1.68$ is the usual critical overdensity in the\nPress--Schechter formalism (see Jing 1999 and Sheth \\& Tormen 1999 for more\naccurate expressions for $b(M,z)$ for low $M$, which we find not to affect our\nresults here). The bias associated with quasars with luminosity $L$ in our\nmodels is given by averaging over halos of different masses associated with\nthis luminosity. Following equation \\ref{eq:matchdiff}, we obtain\n\n\\begin{eqnarray}\nb(L,z) = && \\hspace{-0.5cm}\\left[\\frac{d\\phi}{dL}(L,z)\\right]^{-1} \\times\n\\int_0^\\infty dM \\frac{dN}{dM}(M,z) \\\\\n\\nonumber && b(M,z) \\frac{dg}{dL}(L,\\bar L_{M,z}) f_{\\rm on}(M,z).\n\\label{eq:biasL}\n\\end{eqnarray}\n\nWe show in Figure~\\ref{fig:bias} the resulting bias parameter $b(L,z)$ in the\nmodels corresponding to Figure~\\ref{fig:LFfits}, with short and long lifetimes,\nand at redshifts $z=2$ and 3. As expected, quasars are more highly biased in\nthe long lifetime model, by a ratio $b$(long)/$b$(short)$\\gsim 2$. In the\n$\\Lambda$CDM case, at the detection threshold of SDSS, we find\n$b$(long)$\\approx 3$ at $z=3$ and $b$(long)$\\approx2$ at $z=2$. Bright quasars\nwith $g^\\prime=17$ are predicted to have a bias at $z=3$ as large as $b=10$.\nFor reference, we also show in this figure the bias parameters obtained in the\nOCDM cosmology, which are significantly lower than in the $\\Lambda$CDM case.\nThe number of quasars observed at a fixed flux implies an intrinsically larger\nnumber of sources if OCDM is assumed, because the volume per unit redshift and\nsolid angle in an open universe is smaller. This lowers the corresponding halo\nmass and therefore the bias.\n\n\\section{Comparison with Available Data}\n\\label{section:present}\n\nAs emphasized in \\S~\\ref{section:introduction}, the presently available data\nleave considerable uncertainties in the clustering of quasars. Nevertheless, it\nis interesting to contrast the results of the previous section with preliminary\nresults from the already relatively large, homogeneous sample of high--redshift\nquasars in the 2dF survey (Boyle et al. 2000). Our predictions are obtained by\nrelating the apparent magnitude limit to a minimum absolute luminosity at a\ngiven redshift: $\\log [L_{\\rm min}(z)/L_{B,\\odot}] = 0.4[5.48- B + 5\\log(d_{\\rm\nL}(z)/{\\rm pc})-5]$. This relation assumes no K--correction, justified by the\nnearly flat quasar spectra ($\\nu F_\\nu = $ const) at the relevant wavelengths\n(e.g. Elvis et al. 1994; Pei 1995). In our model, the correlation length $r_0$\nis given implicitly by\n\n\\beq\n\\xi_q(r_0)\\equiv \\bar b^2(z) D^2(z) \\xi_m(r_0) = 1,\n\\label{eq:xiq}\n\\eeq\n\nwhere $\\xi_m(r)$ is the usual dark matter correlation function, and $\\bar b(z)$\nis the value of the bias parameter $b(L,z)$ as determined in the previous\nsection, but now averaged over all quasars with magnitudes brighter than the\ndetection limit,\n\n\\beq\n\\bar b(z) = \\left[\\int_{L_{\\rm min}(z)}^\\infty dL \\frac{d\\phi}{dL} \\right]^{-1}\n\\int_{L_{\\rm min}(z)}^\\infty dL \\frac{d\\phi}{dL} b(L,z).\n\\label{eq:bave}\n\\eeq\n\nIn Figure~\\ref{fig:r0} we show the resulting correlation lengths in the long\nand short lifetime models. Also shown is a preliminary data--point with\n1$\\sigma$ error--bars from the 2dF survey, based on $\\approx$3000 quasars with\napparent magnitudes $B < 20.85$ (Croom et al. 1999). The upper panel shows the\nresults in our fiducial $\\Lambda$CDM model with predictions for this magnitude\ncut. The published results for $r_0$ are cosmology dependent, and we have\nsimply converted them for our cosmological models by taking the corresponding\naverage of the redshift-distance and angular-diameter-distance -- this crude\ntreatment is adequate given the large measurement errors. Our models\ngenerically predict a gradual increase of the correlation length with redshift\n(``positive evolution''). The clustering is dominated by the faintest quasars\nnear the threshold luminosity; as a result, the fixed magnitude-cut of\n$B=20.85$ corresponds to more massive, and more highly clustered halos at\nhigher redshifts. There are two additional effects that determine the\nredshift--evolution of clustering: (1) quasars of a fixed luminosity are more\nabundant towards high--$z$, requiring smaller halo masses to match their number\ndensity, and (2) halos with a fixed mass are more highly clustered towards\nhigh-$z$. We find, however, that these effects are less important than the\nincrease in $M_{\\rm halo}$ caused by fixing the apparent magnitude threshold,\nwhich gives rise to the overall positive evolution.\n\nThe clustering in the long--lifetime model is stronger, and evolves more\nrapidly than in the short--lifetime case. As we can see, the present\nmeasurement error-bars are large -- the whole range of life-times from\n$10^{6.5}$ to $10^8$ yr is broadly consistent with the data, to within $\\sim 2\n\\sigma$. For the $\\Lambda$CDM model, the 2dF data-point is consistent with a\nlifetime of around $10^{7.7 \\pm 0.8}$ yr; in the OCDM model the lifetime is\nsomewhat higher, $10^{8 \\pm 0.8}$ yr. It is worth emphasizing here that the\nconstraints on lifetime from clustering depends on the underlying cosmological\nparameters one assumes, which future large scale structure measurements (from\ne.g. the microwave background, galaxy surveys and the Lyman--$\\alpha$ forest)\nwill hopefully pin down to the accuracy required here.\n\nLastly, we note that observational results on $r_0$ are commonly obtained by a\nfit to the two-point correlation of the form $\\xi (r) =\n(r/r_0)^{-\\gamma}$. Since $r_0$ is the correlation length where the correlation\nis unity, we expect our formalism to begin to fail on such a scale, because\nneither linear fluctuation growth nor linear biasing holds. On the other hand,\nit is also unclear whether $r_0$ as presently measured from a 2-parameter fit\nto the still rather noisy observed two-point correlation necessarily\ncorresponds to the true correlation length. While our crude comparison with\nexisting data in Figure~\\ref{fig:r0} suffices given the large measurement\nerrors, superior data in the near future demand a more refined treatment, which\nis the subject of the next section.\n\n\\section{Expectations from the SDSS and 2dF}\n\\label{section:future}\n\nAlthough existing quasar clustering measurements still allow a wide range of\nquasar lifetimes, and do not provide tight constraints on our models,\nforthcoming large quasar samples from SDSS or the complete 2dF survey are\nideally suited for this purpose. Here we estimate the statistical uncertainties\non the derived lifetimes, using the three--dimensional quasar power spectrum\n$P_Q(k)$ derived from these surveys.\n\nThe variance of the power spectrum is computed by\n\n\\beq \n\\langle \\delta P_{\\rm Q}^2 (k) \\rangle = n_k^{-1} [\\bar b^2 P(k) + \\bar n]^2,\n\\label{eq:variance}\n\\eeq \n\nwhere the large scale fluctuations are assumed to be Gaussian, $n_k$ is the\nnumber of independent modes, $\\bar n$ is the mean number density of observed\nquasars, $P_Q(k) = \\bar b^2 P(k)$ is the quasar power spectrum and $P(k)$ is\nthe mass power spectrum (Feldman, Kaiser \\& Peacock 1994). For a survey of\nvolume $V$, and a $k$-bin of size $\\Delta k$, we use $n_k = k^2 \\Delta k V / 4\n\\pi^2$. The fractional variance is therefore $n_k^{-1} \\{1 + 1/[\\bar n \\bar b\nP(k)]\\}^2$. In terms of minimizing this error, increasing the luminosity cut of\na survey has the advantage of raising the bias $\\bar b$, but has the\ndisadvantage of decreasing the abundance $\\bar n$. In practice, $\\bar b$\nchanges relatively slowly with mass (slower than $\\bar b\\propto M$) whereas\n$\\bar n$ varies with mass much more rapidly ($\\bar n \\sim 1/M$, or steeper if\n$M>M_\\star$). As a result, we find that for our purpose of determining the\nclustering and the quasar lifetime, it is better to include more (fainter)\nquasars.\n\nThe power spectrum $P_Q(k)$ of quasars in $\\Lambda$CDM is shown in\nFigure~\\ref{fig:sdsslcdm} at two different redshifts near the peak of the\ncomoving quasar abundance, $z=2$ and $z=3$. We assume that redshift slices are\ntaken centered at each redshift with a width of $\\Delta z = 0.5$ (which enters\ninto the volume $V$ above). Results are shown in the long and short lifetime\nmodels, together with the expected $1\\sigma$ error bars from SDSS (crosses).\nAlso shown in the lower panel are the expected error bars from 2dF (open\nsquares), which are slightly larger because of the smaller volume (for SDSS, we\nassume an angular coverage of $\\pi$ steradians, and for 2dF, an area of $0.23$\nsteradians). We do not show error bars for 2dF beyond $k \\sim 0.01 {\\, \\rm\nMpc/h}$ because larger scales would likely be affected by the survey window.\nWe also only show scales where the mass power spectrum and biasing are believed\nto be linear.\n\nAs these figures show, the long and short $t_Q$ models are easily\ndistinguishable with the expected uncertainties both from the SDSS and the 2dF\ndata, out to a scale of $\\sim 100$Mpc. The measurement errors at different\nscales are independent (under the Gaussian assumption), and hence, when\ncombined, give powerful constraints e.g. formally, even models with lifetimes\ndiffering by a few percent can be distinguished with high confidence using the\nSDSS. However, systematic errors due to the theoretical modeling are expected\nto be important at this level, which we will discuss in \\S\n\\ref{section:discussion}.\n\nIn Figure~\\ref{fig:sdsslcdm}, we have used the magnitude cuts for spectroscopy,\ni.e. $B=20.85$ for 2dF and $B=20.4$ ($g^\\prime\\approx 19$) for SDSS. If\nphotometric redshifts of quasars are sufficiently accurate, the magnitude cuts\ncan be pushed fainter, further decreasing the error-bars -- although it is\nlikely that the photometric redshift errors will be large enough that one can\nonly measure the clustering in projection, in some well-defined redshift-bin\npicked out using color information. Color selection of $z > 3$ quasars has\nalready proven to be highly effective (Fan et al. 1999); a high redshift sample\ncan give valuable information on the evolution of the quasar clustering (see\nFig. \\ref{fig:r0}).\n\n\\section{Quasar Clustering in X-ray}\n\\label{section:xray}\n\nBoth the luminosity function (e.g. Miyaji et al. 2000), and the clustering of\nquasars (e.g. Carrera et al. 1998) has been studied in the X--ray band,\nanalogously to the optical observations described above. At present, the\naccuracy of both quantities are inferior to that in the optical. Nevertheless,\nit is interesting to consider the clustering of quasars in the X--ray regime,\nbecause (1) applying the exercise outlined above to a different wavelength band\nprovides a useful consistency check on our results, (2) observations with the\n{\\it Chandra X--ray Observatory (CXO)} and {\\it XMM} can potentially\\footnote{\nsee http://asc.harvard.edu and http://xmm.vilspa.esa.es, respectively} probe\nquasars at redshifts higher than currently reached in the optical, and (3)\nX-ray observations are free from complications due to dust extinction, although\nother forms of obscuration are possible (see \\S \\ref {section:discussion}). In\naddition, we will consider here the auto--correlation of the soft X--ray\nbackground (XRB) as another potential probe of quasar clustering and lifetime.\n\nThe formalism we presented in \\S~\\ref{section:models} and\n\\S~\\ref{section:clustering} is quite general, and we here apply it to the soft\nX--ray luminosity function (XRLF) from Miyaji et al. (2000). The details of\nthe fitting procedure are given in the Appendix. In analogy with the optical\ncase, we find that the clustering of X-ray selected quasars depends strongly on\nthe lifetime. As an example, including all quasars whose observed flux is\nabove $3 \\times 10^{-14} {\\, \\rm erg \\, cm^{-2}\\, s^{-1}}$, we find the\ncorrelation length at $z=2$ to be $\\approx 4h^{-1}$Mpc in the short lifetime,\nand $\\approx 11h^{-1}$Mpc in the long lifetime case ($\\Lambda$CDM). Current\ndata probes the clustering of X-ray quasars only at low redshifts ($z\\lsim 1$,\nsee Carrera et al. 1998), where our models suffer from significant\nuncertainties due to the subhalo problem discussed in \\S\n\\ref{section:discussion}. Constraints at $z\\gsim 2$ could be available in the\nfuture from {\\it CXO} and {\\it XMM}, provided that a large area of the sky is\nsurveyed at the improved sensitivities of these instruments.\n\nWe next focus on the quasar contribution to the soft X--ray background and its\nauto--correlation, which as we will see is dominated by quasar contributions at\nsomewhat higher redshifts. The mean comoving emissivity at energy $E$ from all\nquasars at redshift $z$, typically in units of ${\\rm keV \\, cm^{-3} \\, s^{-1}\n\\, sr^{-1}}$, is given in our models by\n\n\\beq\n\\bar j(E,z) = \\frac{1}{4\\pi} \\int_0^\\infty dL \\frac{d\\phi}{dL} L_X(E,L),\n\\label{eq:jxray}\n\\eeq where $L_X(E,L)$ is the luminosity (in ${\\rm keV \\, s^{-1} \\, keV^{-1}}$)\nat the energy $E$ of a quasar whose luminosity at $(1+z)$ keV is $L$. We have\nused the mean spectrum of Elvis et al. (1994) to include a small K--correction\nwhen computing the background at observed energies $E\\ne 1$keV. The mean\nbackground is the integral of the emissivity over redshift,\n\n\\begin{equation}\n\\bar I(E) = \\int_0^\\infty \\frac{d\\chi}{(1+z)} \\bar j(E_z,\\chi),\n\\label{eq:xrb}\n\\end{equation}\nwhere $\\bar I$ is typically given in units of ${\\rm keV \\, cm^{-2} \\, s^{-1} \\,\nsr^{-1} \\, keV^{-1}}$, $E_z = E (1+z)$, and $\\chi$ is the comoving distance\nalong the line of sight.\n\nIf $\\delta(z)$ is the mass fluctuation at some position at redshift $z$, then\nthe fluctuation of the emissivity at the same position and redshift is given by\n$b_X(z) \\delta(z) \\bar j(E_z, z)$, where we have defined the X-ray\nemission--weighted bias $\\bar b_X(z)$ as\n\n\\beq\n\\bar b_X(z) = \\frac{1}{\\bar j(E_z,z)} \n\\frac{1}{4\\pi} \\int_0^\\infty dL \\frac{d\\phi}{dL} L_X(E_z,L) b_X(L,z).\n\\label{eq:biasx}\n\\eeq\n\nFor simplicity, we compute the auto--correlation $w_\\theta$ of the XRB using\nthe Limber approximation, together with the small angle approximation, as:\n\n\\begin{eqnarray}\n\\label{eq:Clwtheta}\nC_\\ell(E) &=& {\\bar I(E)}^{-2} \\int \\frac{d\\chi}{r_\\chi^2}\nW^2(E_\\chi,\\chi) P_0(\\ell/r_\\chi) \\\\ \n\\nonumber w_\\theta(E) &=& \n\\int {\\ell d\\ell \\over 2\\pi} C_\\ell(E) J_0 (\\ell \\theta),\n\\end{eqnarray}\n\nwhere $C_\\ell$ is the angular power spectrum, $J_0$ is the zeroth order Bessel\nfunction, $P_0(\\ell/r_\\chi)$ is the linear mass power spectrum today, $r_\\chi$\nis the angular diameter distance ($=\\chi$ for a flat universe), and\n$W(E_\\chi,\\chi) = \\bar j(E_z,z) \\bar b_X(z) D(z)/(1+z)$. When the power\nspectrum is measured in practice, shot-noise has to be subtracted or should be\nincluded in the theoretical prediction, whereas the same is not necessary for\nthe angular correlation except at zero-lag.\n\nOur models predicts the correct mean background spectrum $\\bar I(E)$, computed\nfrom equation~\\ref{eq:xrb}, at $E=1$ keV. We have included all quasars down to\nthe observed 1 keV flux of $2\\times10^{-17}~{\\rm erg~cm^{-2}~s^{-1}}$, i.e. we\nused our models to extrapolate the XRLF to two orders of magnitude fainter than\nthe ROSAT detection threshold for discrete sources (Hasinger \\& Zamorani 1997),\nto make up the remaining $\\sim 50\\%$ of the XRB at 1keV. Our models predict a\nfaint--end slope that is steeper than the Miyaji et al. (2000) fitting\nformulae, allowing faint quasars to contribute half of the background. The\nemissivities peak at $z\\approx 2$, coinciding with the peak of the XRLF,\nimplying that our model produces most of the XRB, as well as its\nauto--correlation signal at $z\\approx 2$. Note that the known contribution\nfrom nearby galaxy clusters is $\\sim 10\\%$ (Gilli et al. 1999), which we ignore\nhere.\n\nIn Figure \\ref{fig:xrb}, we show our predictions for the two point angular\ncorrelation $w_\\theta$ of the XRB from quasars at 1 keV. Most measurements at\nthe soft X-ray bands have yielded only upper limits, which are consistent with\nour predictions (e.g. variance at $\\lsim 0.12$ at a scale of $10$ arcmin. and\n$E = 0.9 - 2$keV, from Carrera et al. 1998; see also references therein).\nSoltan et al. (1999) obtained angular correlations significantly higher than\nprevious results (dashed curve), which, taken at face value, would imply quasar\nlifetimes $t_Q \\gg 10^8$ yr. However, the results of Soltan et al. (1999)\ncould be partially explained by galactic contamination (Barcons et\nal. 2000). We therefore view this measurement as an upper limit, which is\nconsistent with models using both lifetimes we considered. Figure \\ref{fig:xrb}\nshows that $w_\\theta$ predicted in the long and short lifetime models differ by\na factor of $\\sim 2$ on angular scales of 0.1-1 degrees, offering another\npotential probe of quasar lifetimes, provided that $w_\\theta$ can be measured\nmore accurately in the future, and that the contribution to the clustering\nsignal from nearby non-quasar sources (e.g. clusters) is small or can be\nsubtracted out. Finally, we note that there have been detections of of\nclustering on several-degree-scales at the hard X-ray bands ($2 - 10$ keV) from\nthe HEAO satellite (Treyer et al. 1998) -- while a prediction for such energies\nwould be interesting (see also Lahav et al. 1997), it would require an\nextrapolation of the X-ray spectrum, since we normalize by fitting to the\nsoft-Xray luminosity function.\n\n\\section{Further Considerations}\n\\label{section:discussion}\n\nWe have shown above that the quasar lifetime could be measured to high\nprecision, using the soon available large samples of quasars at $z\\lsim 3$;\neither from the 2dF or the SDSS survey. This precision, however, reflects only\nthe statistical errors in the simple model we have adopted for relating quasars\nto dark matter halos. The main hindrance in determining the quasar lifetime\nwill likely be systematic errors; here we discuss how several potential\ncomplications could affect the derived lifetime.\n\n\\vspace{\\baselineskip} {\\em Obscured sources.} Considerations of the hard\nX--ray background have led several authors to suggest the presence of a large\npopulation of ``absorbed'' quasars, necessary to fit the hard slope and overall\namplitude of the background. Although not a unique explanation for the XRB,\nthis would imply that the true number of quasars near the faint end of both the\noptical and soft X--ray LF is $\\sim10$ times larger than what is observed; 90\\%\nbeing undetected due to large absorbing columns of dust in the optical, and\nneutral hydrogen in the soft X--rays (see, e.g. Gilli et al. 1999). Unless the\noptically bright and dust--obscured phases occur within the same object (Fabian\n\\& Iwasawa 1999), this increase would have a direct effect on our results,\nsince we would then need to adjust our fitting parameters to match a $\\sim10$\ntimes higher quasar abundance. We find that this is easily achieved by leaving\n$x_0$ and $\\alpha$ unchanged, and instead raising the lifetime from $10^{6.5}$\nto $10^{7.5}$ yr in the short lifetime model, and from $10^{8}$ to $10^{8.6}$\nyr in the long lifetime model. In the latter case, a 10-fold increase in the\nduty cycle requires only an increase in $t_Q$ by a factor of $\\approx 4$, owing\nto the shape of the age distribution $dp_a/dt$ (Lacey \\& Cole 1993). Our\nresults would then hold as before, but they would describe the two cases of\n$t_Q=10^{7.5}$ and $10^{8.6}$ yr. Interestingly, this scenario would imply\nthat the quasar lifetime could not be shorter than $t_Q\\approx10^{7.5}$ yr,\nsimply based on the abundance of quasars (cf. \\S~\\ref{section:models}). Future\ninfrared and hard X-ray observations should help constrain the abundance of\nobscured sources, and reduce this systematic uncertainty.\n\n\\vspace{\\baselineskip} {\\em Multiple BH's in a single halo.} A possibility\nthat could modify the simple picture adopted above is that a single halo might\nhost several quasar black holes. A massive (e.g. $10^{14}~{\\rm M_\\odot}$) halo\ncorresponds to a cluster of galaxies; while the Press--Schechter formalism\ncounts this halo as a single object. If quasar activity is triggered by\ngalaxy--galaxy mergers, a massive Press-Schechter halo, known to contain\nseveral galaxies, could equally well host several quasars (e.g. Cavaliere \\&\nVittorini 1998). There is some observational evidence of perhaps merger driven\ndouble quasar activity (Owen et al. 1985; Comins \\& Owen 1991). One could\ntherefore envision that quasars reside in the sub--halos of massive ``parent''\nhalos -- a scenario that would modify the predicted clustering. To address\nthese issues in detail, one needs to know the mass--function of sub--halos\nwithin a given parent halo, as well as the rate at which they merge and turn\non. In principle, this information can be extracted from Monte Carlo\nrealizations of the formation history of halos in the extended Press--Schechter\nformalism (i.e. the so called merger tree) together with some estimate of the\ntime-scale for mergers of sub--halos based on, for instance, dynamical friction\n(e.g. Kauffmann \\& Haehnelt 2000). Here, we consider two toy models that we\nhope can bracket the plausible range of clustering predictions.\n\nTo simplify matters, we ignore the scatter in $L$--$M$ in the following\ndiscussion. Suppose one is interested in quasars of a luminosity $L$ at\nredshift $z_0$, which correspond to Press-Schechter halos of mass $M_0$ in our\nformalism as laid out in \\S \\ref{section:models}. This choice of $M_0$ matches\nthe abundance of quasars, expressed approximately as $L(d\\Phi/dL)\\approx\nM_0[dN(M_0, z_0)/dM_0] (t_Q/t_{\\rm Hub})$ (the merger, or activation rate of\nhalos is approximated as $\\sim t_{\\rm Hub}^{-1}$, where $t_{\\rm Hub}$ is the\nHubble time), and implies the bias $b_0(L)\\approx b(M_0,z_0)$.\n\nIn model A, we suppose the Press-Schechter halos are identified at some earlier\nredshift $z_1$ -- these would be sub--halos of those Press-Schechter halos\nidentified at $z_0$. Quasars of luminosity $L$ now correspond to sub--halos of\nmass $M_1$. The abundance of these sub-halos is given by the Press-Schechter\nmass function $dN(M_1, z_1)/dM_1$, which is related to the mass function at\n$z_0$ by $dN(M_1, z_1)/dM_1 = \\int_{M_1}^\\infty dM [dN(M, z_0)/dM] [d{\\cal\nN}(M_1, z_1 | M, z_0) / dM_1]$ where $dM_1 \\times d{\\cal N}(M_1, z_1 | M, z_0)\n/ dM_1$ is the average number of $M_1 \\pm dM_1/2$ sub--halos within parent\nhalos of mass $M$, given by (e.g. Sheth \\& Lemson 1999)\n\n\\begin{eqnarray}\n\\label{eq:condPS}\n&& d{\\cal N}(M_1, z_1 | M, z_0) / dM_1 = \\\\ \\nonumber\n&& \\quad \\quad {M\\over M_1} {1\\over \\sqrt{2\\pi}} \n{{\\delta_1 - \\delta_0}\\over {[\\sigma^2 (M_1) - \\sigma^2 (M)]^{3/2}}} \\\\ \\nonumber\n&& \\quad \\quad\n{\\, \\rm exp} \\left\\{ -{(\\delta_1 - \\delta_0)^2 \\over {2[\\sigma^2 (M_1)-\\sigma^2 (M)]}}\\right\\}\n{d \\sigma^2 (M_1) \\over dM_1},\n\\end{eqnarray}\n\nwhere $\\delta_1 = \\delta_c/D(z_1)$ and $\\delta_0 = \\delta_c/D(z_0)$ (see\neq. \\ref{eq:biasM}).\n\nTo match the abundance of quasars at luminosity $L$, we impose the condition\nthat $M_1 [dN(M_1, z_1)/dM_1] \\approx$ $M_0[dN(M_0, z_0)/dM_0]$ , which\ndetermines $M_1$ given $z_1$, $M_0$ and $z_0$. The bias of the quasars is no\nlonger $b_0 (L) \\approx b(M_0, z_0)$, but is instead given by\n\n\\begin{eqnarray}\n\\label{eq:beff}\n&& b_{\\rm eff}^A (L,z_1) = \\left[{dN(M_1, z_1) \\over dM_1}\\right]^{-1} \\\\ \\nonumber \n&& \\quad \\int_{M_1}^\\infty dM {dN(M, z_0) \\over dM} {d{\\cal N}\n(M_1, z_1 | M, z_0) \\over dM_1} b(M, z_0).\n\\end{eqnarray}\n\nWe show in Fig. \\ref{fig:comparebiasPS} the ratio of $b_{\\rm eff}^A (L,z_1)/b_0\n(L)$ as a function of $z_1$, for $z_0 = 3$ and $z_0 = 2$ respectively, and for\na range of masses $M_0$ which are representative of the halos that dominate our\nclustering signal in previous discussions. It is interesting how the bias\n$b_{\\rm eff}^A (L,z_1)$ is not necessarily larger than our original bias $b_0\n(L)$, despite the fact that the bias of sub--halos should be boosted by their\ntaking residence in bigger halos. This is because the relevant masses here\n(e.g. $M_0$) are generally large, and we find that the number of halos of mass\n$M_0$ at $z_1$ is always {\\it smaller} than the number of halos of the same\nmass at $z_0 < z_1$. Hence, to match the observed abundance of quasars at the\nsame $L$, $M_1$ must be chosen to be smaller than $M_0$. As\nFig. \\ref{fig:comparebiasPS} shows, this could, in some cases, more than\ncompensate the increase in clustering due to massive parent halos. Because of\nthese two opposing effects, the bias does not change by more than about $50 \\%$\neven if one considers $z_1$ as high as $10$. This translates into a factor of\n$\\sim 2$ uncertainty in our predictions for the quasar power spectrum. Our\nclustering predictions for the short and long lifetime models differ by about a\nfactor of $\\sim 5$, implying that the lifetime can still be usefully\nconstrained at $z\\gsim 2$. As we can see from Fig. \\ref{fig:comparebiasPS}, at\nlower redshifts, or equivalently lower $M_0/M_\\star$, our predictions for the\nquasar power spectrum should be more uncertain.\n\nOne might imagine modifying the above model by allowing mergers to take place\npreferentially in massive parents, and therefore boosting the predicted bias.\nIn model B, we adopt a more general procedure of matching the observed quasar\nabundance by $L (d\\Phi/dL) = M_1 \\int_{M_1}^\\infty dM [dN(M, z_0)/dM] [d{\\cal\nN}(M_1, z_1 | M, z_0) / dM_1]$ $(t_Q/t_{\\rm Hub}) f(M_1, M) $ where\n$(t_Q/t_{\\rm Hub}) f(M_1, M)$ is the probability that an $M_1$ sub--halo\nresiding within a parent halo of $M_0$ harbors an active quasar of luminosity\n$L$. It is conceivable that $f$ increases with the parent mass $M_0$ -- a more\nmassive parent might encourage more quasar activity by having a higher fraction\nof mergers or collisions. The following heuristic argument shows that one\nmight expect $[d{\\cal N}(M_1, z_1 | M, z_0) / dM_1] f(M_1, M)$ to scale\napproximately as $\\sim M^{4/3}$. Let $N_h$ be the number of sub--halos inside a\nparent halo of mass $M$. The rate of collisions is given by $N_h^2 v_h \\sigma_h\n/R^3$ where $v_h$ is the velocity of the sub--halos, $\\sigma_h$ is their\ncross-section and $R^3$ is the volume of the parent halo. Using $N_h \\propto M$\n(which can be obtained from eq. \\ref{eq:condPS} in the large $M$ limit), $v_h\n\\propto \\sqrt{M/R}$ (virial theorem) and $R^3 \\propto M$ (fixed overdensity of\n$\\sim 200$ at the redshift of formation), the rate of collisions scales with\nthe parent mass as $M^{4/3}$, if one ignores the possibility that $\\sigma_h$\nmight depend on the parent mass as well. A similar scaling of $M^{1.3}$ has\nbeen observed in simulations of the star-burst model for Lyman-break objects\n(Kolatt et al. 1999, Weschler et al. 1999).\n\nTo model the enhanced rate of collisions inside massive parent halos, we can\nsimply modify model A by using $f(M_1, M) = (M/M_1)^{1/3}$. The effective\nbias is given by\n\n\\begin{eqnarray}\n&& b_{\\rm eff}^B (L,z_1) = \\\\ \\nonumber\n&& \\left[\\int_{M_1}^\\infty dM {dN(M, z_0) \\over dM} {d{\\cal N}\n(M_1, z_1 | M, z_0) \\over dM_1} \\left({M\\over M_1}\n\\right)^{1\\over 3} \\right]^{-1} \\\\ \\nonumber &&\n\\times\\int_{M_1}^\\infty dM {dN(M, z_0) \\over dM} {d{\\cal N}\n(M_1, z_1 | M, z_0) \\over dM_1} \\left({M \\over M_1}\\right)^{1\\over 3} \nb(M,z_0).\n\\label{eq:beffB}\n\\end{eqnarray}\n\nWe find that the above prescription does not significantly alter our\nconclusions following from model A: the $M^{1/3}$ enhancement of the activation\nrate inside massive parent halos turns out to be relatively shallow, and\ntranslate to a small effect in the bias. Finally, we note that $z_1$ above\ncould in principle depend on $M_0$ and $M_1$, a possibility that would require\nfurther modeling and is not pursued here.\n\n\\vspace{\\baselineskip} {\\em Galaxies without BH's.} Another possibility that\ncould modify our picture is that only a fraction $f<1$ of the halos harbor\nBH's; the duty cycle could then reflect this fraction, rather than the lifetime\nof quasars. Although there is evidence (e.g. Magorrian et al. 1998) that most\n{\\it nearby} galaxies harbor a central BH, this is not necessarily the case at\nredshifts $z=2-3$: the fraction $f$ of galaxies hosting BH's at $z=2-3$ could,\nin principle have merged with the fraction $1-f$ of galaxies without BH's,\nsatisfying the local constraint.\n\nUsing the extended Press--Schechter formalism (Lacey \\& Cole 1993), one can\ncompute the rate of mergers between halos of various masses. On galaxy--mass\nscales, the merger rates at $z=2-3$ are comparable to the reciprocal of the\nHubble time (cf. Fig. 5 in Haiman \\& Menou 2000), implying that a typical\ngalaxy did not go through numerous major mergers between $z=2-3$ and $z=0$,\ni.e. that the fraction $f$ cannot be significantly less than unity at $z=2-3$.\nA more detailed consideration of this issue is beyond the scope of this paper;\nwe simply note that the lifetimes derived here scale approximately as $1/f$,\nwhere $f$ is likely of order unity.\n\n\\vspace{\\baselineskip} {\\em Larger scatter in $L/M$.} The scatter $\\sigma$ we\nassumed around the mean relation between quasar luminosity and halo mass is\nmotivated by the scatter found empirically for the $M_{\\rm bh}-M_{\\rm bulge}$\nrelation (Magorrian et al. 1998). It is interesting to consider the\nsensitivity of our conclusions to an increased $\\sigma$. In general, scatter\nraises the number of quasars predicted by our models, by an amount that depends\non the slope of the underlying mass function $dN/dM$. As a result, increasing\n$\\sigma$ raises, and flattens the predicted LF. We find that an increase of\n$\\sigma$ from 0.5 to 1 (an additional order of magnitude of scatter) can be\ncompensated by a steeper $\\bar L_M$ relation, typically replacing $\\alpha$ with\n$\\approx \\alpha-0.5$. As a result of the increase in $\\sigma$, quasars with a\nfixed $L$ are, on average, associated with larger, and more highly biased\nhalos.\n\nNevertheless, we find that the mean bias $\\bar b$ of all sources above a fixed\nflux (cf. eq.~\\ref{eq:bave}), and therefore the correlation length $r_0$, is\nunchanged by the increased scatter (at the level of $\\sim 3\\%$). The reason\nfor the insensitivity of $r_0$ to the amplitude of the scatter can be\nunderstood as follows. The mean bias $\\bar b$ of all sources with $L>L_{\\rm\nmin}$ is dominated by the bias $b(L)$ of sources near the threshold $L_{\\rm\nmin}$. The latter is obtained by averaging $b(M)$ over halos of different\nmasses (cf. eq.~\\ref{eq:biasL}), and it is dominated by the bias of the\nsmallest halos within the width of the scatter, i.e. of halos with mass $M_{\\rm\nmin} \\approx \\bar M / 10^\\sigma$, where $\\bar M$ defines the mean relation\nbetween $L_{\\rm min}$ and halo mass i.e. $L_{\\rm min}$ = $\\bar L(\\bar M)$, and\n$\\sigma$ quantifies the scatter (see eq. \\ref{eq:scatter}). As mentioned\nbefore, increasing the scatter makes the luminosity function flatter, which\nmeans to match the observed abundance of halos at a fixed luminosity $L_{\\rm\nmin}$, one has to choose a higher $\\bar M$. In other words, $\\bar M$ scales up\nwith the scatter, and it turns out to scale up approximately as $10^\\sigma$,\nmaking $M_{\\rm min}$ and hence the effective bias roughly independent of\nscatter.\n\nWe note that the relation between quasar luminosity and halo mass can, in\nprinciple be derived from observations, by measuring $M_{\\rm halo}$ for the\nhosts of quasars (e.g. by weak lensing, or by finding test particles around\nquasars, such as nearby satellite galaxies).\n\n\\vspace{\\baselineskip} {\\em Mass and redshift dependent lifetime.} In all of\nthe above, we have assumed that the quasar lifetime is a single parameter,\nindependent of the halo mass. This is not unreasonable if the Eddington time,\nthe timescale for the growth of black hole mass, is indeed the relevant\ntime--scale, $4\\times10^7$ ($\\epsilon$/0.1) yr. Implicit in such reasoning is\nthat the active phase of the quasar is coincident with the phase where the\nblack hole gains most of its mass. This is not the only possibility; see\nHaehnelt et al. (1999) for more discussions. One can attempt to explore how\n$t_Q$ depends on halo mass by applying our method to quasars grouped into\ndifferent absolute luminosity ranges, but the intrinsic scatter in the\nmass-luminosity relation should be kept in mind. We emphasize, however, since\nwe fit the luminosity function and clustering data at the same redshift, there\nis no need within our formalism to assume a redshift independent lifetime. In\nfact, performing our exercise as a function of redshift could give interesting\nconstraints on how $t_Q$ evolves with redshift.\n\n\\section{Conclusions}\n\\label{section:conclusions}\n\nIn this paper, we have modeled the quasar luminosity function in detail in the\noptical and X--ray bands using the Press--Schechter formalism. The lifetime of\nquasars $t_Q$ enters into our analysis through the duty--cycle of quasars, and\nwe find that matching the observed quasar LF to dark matter halos yields the\nconstraint $10^6 \\lsim t_Q \\lsim 10^8$ yr: smaller lifetimes would imply overly\nmassive BH's, while longer lifetimes would necessitate overly massive halos.\nThis range reassuringly brackets the Eddington timescale of $4\\times10^7$\n($\\epsilon$/0.1) yr.\n\nThe main conclusion of this paper is that the lifetime (and hence $\\epsilon$,\nif the Eddington time is the relevant timescale for quasar activity) can be\nfurther constrained within this range using the clustering of quasars: for\nquasars with a fixed luminosity, longer $t_Q$ implies larger host halo masses,\nand higher bias. We find that as a result, the correlation length $r_0$ varies\nstrongly with the assumed lifetime. Preliminary data from the 2dF survey\nalready sets mild constraints on the lifetime. Depending on the assumed\ncosmology, we find $t_Q=10^{7.7\\pm 0.8}$ yr ($\\Lambda$CDM) or $t_Q=10^{8\\pm\n0.8}$ yr (OCDM) to within $1\\sigma$ statistical uncertainty. These values are\nalso found to satisfy upper limits on the auto--correlation function of the\nsoft X--ray background.\n\nForthcoming large quasar samples from SDSS or the complete 2dF survey are\nideally suited for a study of quasar clustering, and they can, in principle\nconstrain the quasar lifetime to high accuracy, with small statistical\nerrors. We expect the modeling of the quasar--halo relation, as well as the\npossible presence of obscured quasars, to be the dominant sources of systematic\nuncertainty. Not discussed in depth in this paper is the possibility of using\nhigher moments (such as skewness), which our models also make definite\npredictions for, and will be considered in a future publication. Remarkably,\nour best determination of the lifetime of quasars might come from the\nstatistics of high--redshift quasars, rather than the study of individual\nobjects.\n\n\\acknowledgments \n\nNear the completion of this work, we became aware of a similar, independent\nstudy by P. Martini \\& D. Weinberg. We thank M. Haehnelt, K. Menou,\nE. Quataert, U-L. Pen., U. Seljak, R. Sheth and D. Spergel for useful\ndiscussions, T. Miyaji for his advice on the X--ray luminosity function, and\nT. Shanks and S. Croom for discussions on the 2dF survey. 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We adopt the\nparameterization of the observational LF in the optical B band, given in the\nredshift range $0$}\\\\;}\\n\\\\def\\\\lsim{\\\\;\\\\rlap{\\\\lower 2.5pt\\n \\\\hbox{$\\\\sim$}}\\\\raise 1.5pt\\\\hbox{$<$}\\\\;}\\n\\\\def\\\\msun{{\\\\rm\\\\,M_\\\\odot}}\\n\\\\def\\\\yr{{\\\\rm\\\\,yr}}\\n\\\\def\\\\au{{\\\\rm\\\\,AU}}\\n\\\\def\\\\del{{\\\\partial}}\\n\\\\def\\\\gm{{\\\\rm\\\\,g}}\\n\\\\def\\\\cm{{\\\\rm\\\\,cm}}\\n\\\\def\\\\sec{{\\\\rm\\\\,s}}\\n\\\\def\\\\erg{{\\\\rm\\\\,erg}}\\n\\\\def\\\\kev{{\\\\rm\\\\,keV}}\\n\\\\def\\\\ev{{\\\\rm\\\\,eV}}\\n\\\\def\\\\K{{\\\\rm\\\\,K}}\\n\\\\def\\\\spose#1{\\\\hbox to 0pt{#1\\\\hss}}\\n\\\\def\\\\lta{\\\\mathrel{\\\\spose{\\\\lower 3pt\\\\hbox{$\\\\mathchar''218$}}\\n \\\\raise 2.0pt\\\\hbox{$\\\\mathchar''13C$}}}\\n\\\\def\\\\gta{\\\\mathrel{\\\\spose{\\\\lower 3pt\\\\hbox{$\\\\mathchar''218$}}\\n \\\\raise 2.0pt\\\\hbox{$\\\\mathchar''13E$}}}\\n\\\\newcommand{\\\\beq}{\\\\begin{equation}}\\n\\\\newcommand{\\\\eeq}{\\\\end{equation}}\\n\\n\\\\lefthead{HAIMAN \\\\& HUI}\\n\\\\righthead{QSO CLUSTERING}\\n\\n\\\\begin{document}\\n\\\\title{Constraining the Lifetime of Quasars from their Spatial Clustering}\\n\\\\author{Zolt\\\\'an Haiman\\\\altaffilmark{1}}\\n\\\\affil{Princeton University Observatory, Princeton, NJ 08544, USA \\\\\\\\email: zoltan@astro.princeton.edu}\\n\\\\and\\n\\\\author{Lam Hui}\\n\\\\affil{Institute for Advanced Study, Olden Lane, Princeton, NJ 08544, USA \\\\\\\\\\nemail: lhui@ias.edu}\\n\\n\\\\altaffiltext{1}{Hubble Fellow}\\n\\n\\\\vspace{0.75\\\\baselineskip}\\n\\\\submitted{ApJ, in press (submitted on Feb. 8. 2000)}\\n\\n\\\\begin{abstract}\\n\\nThe lifetime of the luminous phase of quasars is constrained by current\\nobservations to be $10^{6} \\\\lsim t_Q \\\\lsim 10^8$ years, but is otherwise\\nunkown. We model the quasar luminosity function in detail in the optical and\\nX--ray bands using the Press--Schechter formalism, and show that the expected\\nclustering of quasars depends strongly on their assumed lifetime $t_Q$.\\n%within this range.\\n%If quasars are short lived, their duty cycle is small, and they\\n%must reside in abundant, low--mass dark matter halos. Conversely, if quasars\\n%live longer, they must be hosted by rarer, more massive and more strongly\\n%clustered halos. We quantify the resulting dependence of clustering on the\\nWe quantify this dependence, and find that existing measurements of the\\ncorrelation length of quasars are consistent with the range $10^{6} \\\\lsim t_Q\\n\\\\lsim 10^8$. We then show that future measurements of the power spectrum of\\nquasars out to $z\\\\sim 3$, from the 2dF or Sloan Digital Sky Survey, can\\nsignificantly improve this constraint, and in principle allow a precise\\ndetermination of $t_Q$. We estimate the systematic errors introduced by\\nuncertainties in the modeling of the quasar-halo relationship, as well as by\\nthe possible existence of obscured quasars.\\n\\\\end{abstract}\\n\\n\\\\keywords{cosmology: theory -- cosmology: observation -- quasars: formation -- large scale structure}\\n\\n\\\\section{Introduction}\\n\\\\label{section:introduction}\\n\\nA long outstanding problem in cosmology is the synchronized evolution of the\\nquasar population over the redshift range $0\\\\lsim z\\\\lsim 5$. Observations in\\nthe optical (Pei 1995) and radio (Shaver et al. 1994) show a pronounced peak in\\nthe abundance of bright quasars at $z\\\\approx 2.5$; recent X--ray observations\\n(Miyaji et al. 2000) confirm the rapid rise from $z=0$ towards $z\\\\approx 2$,\\nbut have not shown evidence for a decline at still higher redshifts.\\nIndividual quasars are widely understood to consist of supermassive black holes\\n(BHs) powered by accretion (Lynden-Bell 1967; Rees 1984). A plausible\\ntimescale for quasar activity is then the Eddington time, $4\\\\times10^7$\\n($\\\\epsilon$/0.1) yr, the e-folding time for the growth of a BH accreting mass\\nat a rate $\\\\dot M$, while shining at the Eddington luminosity with a radiative\\nefficiency of $L=L_{\\\\rm Edd}=\\\\epsilon\\\\dot M c^2$. The lifetime $t_Q$ of the\\nluminous phase of quasars can be estimated directly, by considering the space\\ndensity of quasars and galaxies. At $z\\\\sim 2$, the ratio $n_Q/n_G \\\\sim 3\\\\times\\n10^{-3}$ implies the reassuringly close value of $t_Q\\\\sim t_{\\\\rm Hub}\\nn_Q/n_G\\\\sim 10^7$ yr (Blandford 1999 and references therein). These lifetimes\\nare significantly shorter than the Hubble time, suggesting that the quasar\\npopulation evolves on cosmic time--scales by some mechanism other than local\\naccretion physics near the BH.\\n\\nIt is tempting to identify quasars with halos condensing in a cold dark matter\\n(CDM) dominated universe, as the halo population naturally evolves on cosmic\\ntime--scales (Efstathiou \\\\& Rees 1988; Haiman \\\\& Loeb 1998; Kauffmann \\\\&\\nHaehnelt 2000). Furthermore, quasars reside in a subset of all galaxies, while\\nthe redshift--evolution of the galaxy population as a whole (qualitatively\\nsimilar to that of bright quasars) has been successfully described by\\nassociating galaxies with dark halos (e.g. Lacey \\\\& Cole 1993; Kauffmann \\\\&\\nWhite 1993). A further link between galaxies and quasars comes from the recent\\ndetection, and measurements of the masses of massive BHs at the centers of\\nnearby galaxies (Magorrian et al. 1998; van der Marel 1999).\\n\\nThese arguments suggest that the evolution of the quasar population can indeed\\nbe described by ``semi--analytic'' models, associating quasars with dark matter\\nhalos. In this type of modeling, the quasar lifetime plays an important role.\\nThe quasar phase in a single halo could last longer ($t_{\\\\rm Q}\\\\sim10^8$yr),\\nwith correspondingly small $M_{\\\\rm bh}/M_{\\\\rm halo}$ ratios, or last shorter\\n($t_{\\\\rm Q}\\\\sim10^6$yr), with larger BH formation efficiencies (Haiman \\\\& Loeb\\n1998; Haehnelt et al. 1998). Note that although recent studies have\\nestablished a correlation between the bulge mass $M_{\\\\rm bulge}$ and BH mass\\n$M_{\\\\rm bh}$, this correlation leaves a considerable uncertainty in the\\nrelation between $M_{\\\\rm bh}$ and the mass $M_{\\\\rm halo}$ of its host halo. If\\nthe initial density fluctuations are Gaussian with a CDM power spectrum, the\\nclustering of collapsed halos is a function of their mass -- rarer, more\\nmassive halos cluster more strongly (Kaiser 1984; Mo \\\\& White 1996). Hence,\\nmeasurements of quasar clustering are a potentially useful probe of both BH\\nformation efficiencies and quasar lifetimes (La Franca et al. 1998, Haehnelt et\\nal. 1998).\\n\\nIn this paper, we assess the feasibility of breaking the above degeneracy, and\\ninferring quasar lifetimes, from the statistics of clustering that will be\\navailable from the Sloan Digital Sky Survey (SDSS, Gunn \\\\& Weinberg 1995) and\\nAnglo-Australian Telescope Two-Degree-Field (2dF, Boyle et al. 1999). Previous\\nworks (e.g. Stephens et al. 1997; Sabbey et al. 1999) have yielded estimates\\nsuggesting that quasars are clustered more strongly than galaxies. However, the\\ncurrent uncertainties are large, especially at higher redshifts, where\\nclustering has been found to decrease (Iovino \\\\& Shaver 1988; Iovino et\\nal. 1991), to stay constant (Andreani \\\\& Cristiani 1992; Croom \\\\& Shanks 1996),\\nor to increase with redshift (La Franca et al. 1998). As a result, no strong\\nconstraints on the life--time can be obtained yet. The key advance of\\nforthcoming surveys over previous efforts is two--fold. Because of their sheer\\nsize, i.e. the large number of quasars covering a large fraction of the sky,\\nboth shot--noise and sample variance can be beaten down, significantly reducing\\nthe statistical uncertainties. Furthermore, the large sample-size will\\neliminate the need to combine data from different surveys with different\\nselection criteria, hence allowing cleaner interpretation.\\n\\nRecent measurements of the local massive black hole density have stimulated\\ndiscussions of a radiative efficiency which is much lower than the usual $\\\\sim\\n0.1$ (e.g. Haehnelt et al. 1999). A convincing constraint on the lifetime of\\nquasars could be therefore highly interesting, as this might have implications\\nfor the local accretion physics near the BH.\\n\\nThis paper is organized as follows. In \\\\S~\\\\ref{section:models}, we summarize\\nour models for the quasar luminosity function, and in\\n\\\\S~\\\\ref{section:clustering} we compute the quasar correlation function in these\\nmodels. In \\\\S~\\\\ref{section:present}, we compare the model predictions with\\npresently available data, and in \\\\S~\\\\ref{section:future} we assess the ability\\nof future optical redshift surveys to discriminate between the various models.\\nIn \\\\S~\\\\ref{section:xray}, we repeat our analysis in the soft X--ray band, and\\nexamine the contribution of quasars to the X-ray background, and its\\nauto--correlation. In \\\\S~\\\\ref{section:discussion}, we address some of the\\ncaveats arising from our assumptions, and in \\\\S~\\\\ref{section:conclusions} we\\nsummarize our conclusions and the implications of this work.\\n\\n\\\\section{Models for the Quasar Luminosity Function}\\n\\\\label{section:models}\\n\\nIn this section, we briefly summarize our model for the luminosity function\\n(LF) of quasars, based on associating quasar BHs with dark halos. Our\\ntreatment is similar to previous works (Haiman \\\\& Loeb 1998; Haehnelt et\\nal. 1998), although differs in some of the details. A more extensive treatment\\nis provided in the Appendix. The main assumption is that there is, on average,\\na direct monotonic relation between halo mass $M_{\\\\rm halo}$ and average quasar\\nluminosity $L_{M,z}$, which we parameterize using the simple\\npower--law ansatz:\\n\\n\\\\beq \\\\bar L_{M,z}= x_0(z) M_{\\\\rm halo} \\\\left(\\\\frac{M_{\\\\rm\\nhalo}}{M_0}\\\\right)^{\\\\alpha(z)}.\\n\\\\label{eq:params00}\\n\\\\eeq\\n\\nHere $x_0(z)$ and $\\\\alpha(z)$ are ``free functions'', whose values are found by\\nthe requirement that the resulting luminosity function agrees with\\nobservations. As explained in the Appendix, our model has one free parameter,\\nthe lifetime $t_Q$, which uniquely determines $x_0(z)$ and $\\\\alpha(z)$ in any\\ngiven background cosmology. We assume the background cosmology to be either\\nflat ($\\\\Lambda$CDM) with $(\\\\Omega_\\\\Lambda,\\\\Omega_{\\\\rm m},h,\\\\sigma_{\\\\rm\\n8h^{-1}},n)=(0.7,0.3,0.65,1.0,1.0)$ or open (OCDM) with\\n$(\\\\Omega_\\\\Lambda,\\\\Omega_{\\\\rm m},h,\\\\sigma_{\\\\rm\\n8h^{-1}},n)=(0,0.3,0.65,0.82,1.3)$. In LCDM, we find $(-\\\\log[x_0/{\\\\rm L_\\\\odot\\nM_\\\\odot^{-1}}],\\\\alpha) \\\\approx (1,0.4)$ and $\\\\approx (-0.2, -0.1)$ for\\nlifetimes of $t_Q=10^{8}$ and $t_Q=10^{6.5}$yr, respectively. Similarly, in\\nOCDM, we find $(-\\\\log[x_0/{\\\\rm L_\\\\odot M_\\\\odot^{-1}}],\\\\alpha) \\\\approx (1,0.25)$\\nand $\\\\approx (-0.2, -0.25)$ for these two lifetimes.\\n\\nIn Figure~\\\\ref{fig:LFfits}, we demonstrate the agreement between the LF\\ncomputed in our models with the observational data at two different redshifts,\\n$z=2$ and $z=3$. For reference, the upper labels in this figure show the\\napparent magnitudes in the SDSS $g^\\\\prime$ band, assuming that the intrinsic\\nquasar spectrum is the same as the mean spectrum in the Elvis et al. (1994)\\nquasar sample. The photometric detection threshold\\\\footnote{See\\nhttp://www.sdss.org/science/tech\\\\_summary.html.} of SDSS is $g^\\\\prime \\\\approx\\n22.6$, corresponding to a BH mass of $\\\\approx 10^{8} {\\\\rm M_\\\\odot}$ at $z=3$\\nand a three times smaller mass at $z=2$. As the figure shows, the overall\\nquality of the fits is excellent; for reference, the dashed lines show the\\nad--hoc empirical fitting formulae from Pei (1995). Similarly accurate match\\nto the quasar LF is achieved at different redshifts, and in the models assuming\\nan OCDM cosmology. Figure~\\\\ref{fig:LFfits} shows, in particular, that the fits\\nobtained from the power--law ansatz adopting either a short (solid lines) or a\\nlong (dotted lines) lifetime are nearly indistinguishable; hence modeling the\\nLF by itself does not constrain the quasar lifetime within the limits\\n$10^{6.5}$ yr $\\\\lsim t_Q \\\\lsim 10^8$ yr.\\n\\nBefore considering constraints on the lifetime from clustering, it is useful to\\npoint out that estimates for both upper and lower limits on $t_Q$ follow from\\nthe observed luminosity function alone.\\n\\n{\\\\it Lower limit on $t_Q$.} A halo of mass $M_{\\\\rm halo}$ is unlikely to harbor\\na BH more massive than $\\\\approx 6\\\\times10^{-3} (\\\\Omega_{b}/\\\\Omega_{0}) M_{\\\\rm\\nhalo} = 6\\\\times 10^{-4} M_{\\\\rm halo}$, where $\\\\approx 6\\\\times10^{-3}$ is the\\nratio $M_{\\\\rm bh}/M_{\\\\rm bulge}$ found in nearby galaxies (Magorrian et\\nal. 1998) because $M_{\\\\rm bulge}$ cannot be larger than\\n$(\\\\Omega_{b}/\\\\Omega_{0}) M_{\\\\rm halo}$. This maximal BH could at best emit\\n$\\\\approx 10\\\\%$ of the Eddington luminosity in the B--band, implying $L/M_{\\\\rm\\nhalo} \\\\lsim 3~{\\\\rm L_\\\\odot/M_\\\\odot}$. We find (cf. Fig.~\\\\ref{fig:params}) that\\nour short lifetime model with $t_Q=10^{6.5}$ yr nearly reaches this limit;\\nmodels with shorter lifetimes would require unrealistically large $L/M_{\\\\rm\\nhalo}$ ratios.\\n\\n{\\\\it Upper limit on $t_Q$.} Long lifetimes, on the other hand, require the\\nratio $L/M_{\\\\rm halo}$ to be small; this can lead to unrealistically large halo\\nmasses. The brightest quasars detected at redshifts $z\\\\approx 2-3$ have\\nluminosities as large as $L\\\\approx 10^{14} {\\\\rm L_\\\\odot}$ (Pei 1995). We find\\n(cf. Fig.~\\\\ref{fig:params}) that in order to avoid the host halo masses of\\nthese bright quasars to exceed $\\\\sim 10^{15}~{\\\\rm M_\\\\odot}$, the lifetime\\ncannot be longer than $\\\\sim 10^8$ yr. An alternative, standard argument goes as\\nfollows. The black hole mass grows during the quasar phase as $e^{t_Q/t_E}$\\nwhere $t_E = 4\\\\times10^7 (\\\\epsilon/0.1)$ yr is the Eddington time. Assuming a\\nconservative initial black hole mass of $1 M_{\\\\odot}$, a lifetime longer than\\n$10^9$ yr would give final black hole masses that are unacceptably large.\\n\\n\\\\vspace{2\\\\baselineskip}\\n\\n\\\\section{The Clustering of Quasars}\\n\\\\label{section:clustering}\\n\\nAs demonstrated in the previous section, equally good fits can be obtained to\\nthe luminosity function of quasars, assuming either a short or a long lifetime,\\nand a power-law dependence of the mean quasar luminosity on the halo mass $\\\\bar\\nL\\\\propto M^\\\\alpha$. In this section, we derive the clustering of quasars in\\nour models, and demonstrate that they depend significantly on the assumed\\nlifetime.\\n\\nThe halos are a biased tracer of the underlying mass distribution, customarily\\nexpressed by $P_{\\\\rm halo} (k) = b^2 P(k)$ where $P_{\\\\rm halo}$ and $P$ are the\\nhalo and mass power spectra as a function of wavenumber $k$. The bias parameter\\nfor halos of a given mass $M$ at a given redshift $z$ is given by (Mo \\\\& White\\n1996)\\n\\n\\\\beq\\nb(M,z)= 1 + \\\\frac{1}{\\\\delta_c}\\\\left[\\n\\\\left(\\\\frac{\\\\delta_c}{\\\\sigma(M)D(z)}\\\\right)^2-1\\\\right],\\n\\\\label{eq:biasM}\\n\\\\eeq\\n\\nwhere $D(z)$ is the linear growth function, $\\\\sigma(M)$ is the r.m.s. mass\\nfluctuation on mass--scale $M$ (using the power spectrum of Eisenstein \\\\& Hu\\n1999), and $\\\\delta_c\\\\approx 1.68$ is the usual critical overdensity in the\\nPress--Schechter formalism (see Jing 1999 and Sheth \\\\& Tormen 1999 for more\\naccurate expressions for $b(M,z)$ for low $M$, which we find not to affect our\\nresults here). The bias associated with quasars with luminosity $L$ in our\\nmodels is given by averaging over halos of different masses associated with\\nthis luminosity. Following equation \\\\ref{eq:matchdiff}, we obtain\\n\\n\\\\begin{eqnarray}\\nb(L,z) = && \\\\hspace{-0.5cm}\\\\left[\\\\frac{d\\\\phi}{dL}(L,z)\\\\right]^{-1} \\\\times\\n\\\\int_0^\\\\infty dM \\\\frac{dN}{dM}(M,z) \\\\\\\\\\n\\\\nonumber && b(M,z) \\\\frac{dg}{dL}(L,\\\\bar L_{M,z}) f_{\\\\rm on}(M,z).\\n\\\\label{eq:biasL}\\n\\\\end{eqnarray}\\n\\nWe show in Figure~\\\\ref{fig:bias} the resulting bias parameter $b(L,z)$ in the\\nmodels corresponding to Figure~\\\\ref{fig:LFfits}, with short and long lifetimes,\\nand at redshifts $z=2$ and 3. As expected, quasars are more highly biased in\\nthe long lifetime model, by a ratio $b$(long)/$b$(short)$\\\\gsim 2$. In the\\n$\\\\Lambda$CDM case, at the detection threshold of SDSS, we find\\n$b$(long)$\\\\approx 3$ at $z=3$ and $b$(long)$\\\\approx2$ at $z=2$. Bright quasars\\nwith $g^\\\\prime=17$ are predicted to have a bias at $z=3$ as large as $b=10$.\\nFor reference, we also show in this figure the bias parameters obtained in the\\nOCDM cosmology, which are significantly lower than in the $\\\\Lambda$CDM case.\\nThe number of quasars observed at a fixed flux implies an intrinsically larger\\nnumber of sources if OCDM is assumed, because the volume per unit redshift and\\nsolid angle in an open universe is smaller. This lowers the corresponding halo\\nmass and therefore the bias.\\n\\n\\\\section{Comparison with Available Data}\\n\\\\label{section:present}\\n\\nAs emphasized in \\\\S~\\\\ref{section:introduction}, the presently available data\\nleave considerable uncertainties in the clustering of quasars. Nevertheless, it\\nis interesting to contrast the results of the previous section with preliminary\\nresults from the already relatively large, homogeneous sample of high--redshift\\nquasars in the 2dF survey (Boyle et al. 2000). Our predictions are obtained by\\nrelating the apparent magnitude limit to a minimum absolute luminosity at a\\ngiven redshift: $\\\\log [L_{\\\\rm min}(z)/L_{B,\\\\odot}] = 0.4[5.48- B + 5\\\\log(d_{\\\\rm\\nL}(z)/{\\\\rm pc})-5]$. This relation assumes no K--correction, justified by the\\nnearly flat quasar spectra ($\\\\nu F_\\\\nu = $ const) at the relevant wavelengths\\n(e.g. Elvis et al. 1994; Pei 1995). In our model, the correlation length $r_0$\\nis given implicitly by\\n\\n\\\\beq\\n\\\\xi_q(r_0)\\\\equiv \\\\bar b^2(z) D^2(z) \\\\xi_m(r_0) = 1,\\n\\\\label{eq:xiq}\\n\\\\eeq\\n\\nwhere $\\\\xi_m(r)$ is the usual dark matter correlation function, and $\\\\bar b(z)$\\nis the value of the bias parameter $b(L,z)$ as determined in the previous\\nsection, but now averaged over all quasars with magnitudes brighter than the\\ndetection limit,\\n\\n\\\\beq\\n\\\\bar b(z) = \\\\left[\\\\int_{L_{\\\\rm min}(z)}^\\\\infty dL \\\\frac{d\\\\phi}{dL} \\\\right]^{-1}\\n\\\\int_{L_{\\\\rm min}(z)}^\\\\infty dL \\\\frac{d\\\\phi}{dL} b(L,z).\\n\\\\label{eq:bave}\\n\\\\eeq\\n\\nIn Figure~\\\\ref{fig:r0} we show the resulting correlation lengths in the long\\nand short lifetime models. Also shown is a preliminary data--point with\\n1$\\\\sigma$ error--bars from the 2dF survey, based on $\\\\approx$3000 quasars with\\napparent magnitudes $B < 20.85$ (Croom et al. 1999). The upper panel shows the\\nresults in our fiducial $\\\\Lambda$CDM model with predictions for this magnitude\\ncut. The published results for $r_0$ are cosmology dependent, and we have\\nsimply converted them for our cosmological models by taking the corresponding\\naverage of the redshift-distance and angular-diameter-distance -- this crude\\ntreatment is adequate given the large measurement errors. Our models\\ngenerically predict a gradual increase of the correlation length with redshift\\n(``positive evolution''). The clustering is dominated by the faintest quasars\\nnear the threshold luminosity; as a result, the fixed magnitude-cut of\\n$B=20.85$ corresponds to more massive, and more highly clustered halos at\\nhigher redshifts. There are two additional effects that determine the\\nredshift--evolution of clustering: (1) quasars of a fixed luminosity are more\\nabundant towards high--$z$, requiring smaller halo masses to match their number\\ndensity, and (2) halos with a fixed mass are more highly clustered towards\\nhigh-$z$. We find, however, that these effects are less important than the\\nincrease in $M_{\\\\rm halo}$ caused by fixing the apparent magnitude threshold,\\nwhich gives rise to the overall positive evolution.\\n\\nThe clustering in the long--lifetime model is stronger, and evolves more\\nrapidly than in the short--lifetime case. As we can see, the present\\nmeasurement error-bars are large -- the whole range of life-times from\\n$10^{6.5}$ to $10^8$ yr is broadly consistent with the data, to within $\\\\sim 2\\n\\\\sigma$. For the $\\\\Lambda$CDM model, the 2dF data-point is consistent with a\\nlifetime of around $10^{7.7 \\\\pm 0.8}$ yr; in the OCDM model the lifetime is\\nsomewhat higher, $10^{8 \\\\pm 0.8}$ yr. It is worth emphasizing here that the\\nconstraints on lifetime from clustering depends on the underlying cosmological\\nparameters one assumes, which future large scale structure measurements (from\\ne.g. the microwave background, galaxy surveys and the Lyman--$\\\\alpha$ forest)\\nwill hopefully pin down to the accuracy required here.\\n\\nLastly, we note that observational results on $r_0$ are commonly obtained by a\\nfit to the two-point correlation of the form $\\\\xi (r) =\\n(r/r_0)^{-\\\\gamma}$. Since $r_0$ is the correlation length where the correlation\\nis unity, we expect our formalism to begin to fail on such a scale, because\\nneither linear fluctuation growth nor linear biasing holds. On the other hand,\\nit is also unclear whether $r_0$ as presently measured from a 2-parameter fit\\nto the still rather noisy observed two-point correlation necessarily\\ncorresponds to the true correlation length. While our crude comparison with\\nexisting data in Figure~\\\\ref{fig:r0} suffices given the large measurement\\nerrors, superior data in the near future demand a more refined treatment, which\\nis the subject of the next section.\\n\\n\\\\section{Expectations from the SDSS and 2dF}\\n\\\\label{section:future}\\n\\nAlthough existing quasar clustering measurements still allow a wide range of\\nquasar lifetimes, and do not provide tight constraints on our models,\\nforthcoming large quasar samples from SDSS or the complete 2dF survey are\\nideally suited for this purpose. Here we estimate the statistical uncertainties\\non the derived lifetimes, using the three--dimensional quasar power spectrum\\n$P_Q(k)$ derived from these surveys.\\n\\nThe variance of the power spectrum is computed by\\n\\n\\\\beq \\n\\\\langle \\\\delta P_{\\\\rm Q}^2 (k) \\\\rangle = n_k^{-1} [\\\\bar b^2 P(k) + \\\\bar n]^2,\\n\\\\label{eq:variance}\\n\\\\eeq \\n\\nwhere the large scale fluctuations are assumed to be Gaussian, $n_k$ is the\\nnumber of independent modes, $\\\\bar n$ is the mean number density of observed\\nquasars, $P_Q(k) = \\\\bar b^2 P(k)$ is the quasar power spectrum and $P(k)$ is\\nthe mass power spectrum (Feldman, Kaiser \\\\& Peacock 1994). For a survey of\\nvolume $V$, and a $k$-bin of size $\\\\Delta k$, we use $n_k = k^2 \\\\Delta k V / 4\\n\\\\pi^2$. The fractional variance is therefore $n_k^{-1} \\\\{1 + 1/[\\\\bar n \\\\bar b\\nP(k)]\\\\}^2$. In terms of minimizing this error, increasing the luminosity cut of\\na survey has the advantage of raising the bias $\\\\bar b$, but has the\\ndisadvantage of decreasing the abundance $\\\\bar n$. In practice, $\\\\bar b$\\nchanges relatively slowly with mass (slower than $\\\\bar b\\\\propto M$) whereas\\n$\\\\bar n$ varies with mass much more rapidly ($\\\\bar n \\\\sim 1/M$, or steeper if\\n$M>M_\\\\star$). As a result, we find that for our purpose of determining the\\nclustering and the quasar lifetime, it is better to include more (fainter)\\nquasars.\\n\\nThe power spectrum $P_Q(k)$ of quasars in $\\\\Lambda$CDM is shown in\\nFigure~\\\\ref{fig:sdsslcdm} at two different redshifts near the peak of the\\ncomoving quasar abundance, $z=2$ and $z=3$. We assume that redshift slices are\\ntaken centered at each redshift with a width of $\\\\Delta z = 0.5$ (which enters\\ninto the volume $V$ above). Results are shown in the long and short lifetime\\nmodels, together with the expected $1\\\\sigma$ error bars from SDSS (crosses).\\nAlso shown in the lower panel are the expected error bars from 2dF (open\\nsquares), which are slightly larger because of the smaller volume (for SDSS, we\\nassume an angular coverage of $\\\\pi$ steradians, and for 2dF, an area of $0.23$\\nsteradians). We do not show error bars for 2dF beyond $k \\\\sim 0.01 {\\\\, \\\\rm\\nMpc/h}$ because larger scales would likely be affected by the survey window.\\nWe also only show scales where the mass power spectrum and biasing are believed\\nto be linear.\\n\\nAs these figures show, the long and short $t_Q$ models are easily\\ndistinguishable with the expected uncertainties both from the SDSS and the 2dF\\ndata, out to a scale of $\\\\sim 100$Mpc. The measurement errors at different\\nscales are independent (under the Gaussian assumption), and hence, when\\ncombined, give powerful constraints e.g. formally, even models with lifetimes\\ndiffering by a few percent can be distinguished with high confidence using the\\nSDSS. However, systematic errors due to the theoretical modeling are expected\\nto be important at this level, which we will discuss in \\\\S\\n\\\\ref{section:discussion}.\\n\\nIn Figure~\\\\ref{fig:sdsslcdm}, we have used the magnitude cuts for spectroscopy,\\ni.e. $B=20.85$ for 2dF and $B=20.4$ ($g^\\\\prime\\\\approx 19$) for SDSS. If\\nphotometric redshifts of quasars are sufficiently accurate, the magnitude cuts\\ncan be pushed fainter, further decreasing the error-bars -- although it is\\nlikely that the photometric redshift errors will be large enough that one can\\nonly measure the clustering in projection, in some well-defined redshift-bin\\npicked out using color information. Color selection of $z > 3$ quasars has\\nalready proven to be highly effective (Fan et al. 1999); a high redshift sample\\ncan give valuable information on the evolution of the quasar clustering (see\\nFig. \\\\ref{fig:r0}).\\n\\n\\\\section{Quasar Clustering in X-ray}\\n\\\\label{section:xray}\\n\\nBoth the luminosity function (e.g. Miyaji et al. 2000), and the clustering of\\nquasars (e.g. Carrera et al. 1998) has been studied in the X--ray band,\\nanalogously to the optical observations described above. At present, the\\naccuracy of both quantities are inferior to that in the optical. Nevertheless,\\nit is interesting to consider the clustering of quasars in the X--ray regime,\\nbecause (1) applying the exercise outlined above to a different wavelength band\\nprovides a useful consistency check on our results, (2) observations with the\\n{\\\\it Chandra X--ray Observatory (CXO)} and {\\\\it XMM} can potentially\\\\footnote{\\nsee http://asc.harvard.edu and http://xmm.vilspa.esa.es, respectively} probe\\nquasars at redshifts higher than currently reached in the optical, and (3)\\nX-ray observations are free from complications due to dust extinction, although\\nother forms of obscuration are possible (see \\\\S \\\\ref {section:discussion}). In\\naddition, we will consider here the auto--correlation of the soft X--ray\\nbackground (XRB) as another potential probe of quasar clustering and lifetime.\\n\\nThe formalism we presented in \\\\S~\\\\ref{section:models} and\\n\\\\S~\\\\ref{section:clustering} is quite general, and we here apply it to the soft\\nX--ray luminosity function (XRLF) from Miyaji et al. (2000). The details of\\nthe fitting procedure are given in the Appendix. In analogy with the optical\\ncase, we find that the clustering of X-ray selected quasars depends strongly on\\nthe lifetime. As an example, including all quasars whose observed flux is\\nabove $3 \\\\times 10^{-14} {\\\\, \\\\rm erg \\\\, cm^{-2}\\\\, s^{-1}}$, we find the\\ncorrelation length at $z=2$ to be $\\\\approx 4h^{-1}$Mpc in the short lifetime,\\nand $\\\\approx 11h^{-1}$Mpc in the long lifetime case ($\\\\Lambda$CDM). Current\\ndata probes the clustering of X-ray quasars only at low redshifts ($z\\\\lsim 1$,\\nsee Carrera et al. 1998), where our models suffer from significant\\nuncertainties due to the subhalo problem discussed in \\\\S\\n\\\\ref{section:discussion}. Constraints at $z\\\\gsim 2$ could be available in the\\nfuture from {\\\\it CXO} and {\\\\it XMM}, provided that a large area of the sky is\\nsurveyed at the improved sensitivities of these instruments.\\n\\nWe next focus on the quasar contribution to the soft X--ray background and its\\nauto--correlation, which as we will see is dominated by quasar contributions at\\nsomewhat higher redshifts. The mean comoving emissivity at energy $E$ from all\\nquasars at redshift $z$, typically in units of ${\\\\rm keV \\\\, cm^{-3} \\\\, s^{-1}\\n\\\\, sr^{-1}}$, is given in our models by\\n\\n\\\\beq\\n\\\\bar j(E,z) = \\\\frac{1}{4\\\\pi} \\\\int_0^\\\\infty dL \\\\frac{d\\\\phi}{dL} L_X(E,L),\\n\\\\label{eq:jxray}\\n\\\\eeq where $L_X(E,L)$ is the luminosity (in ${\\\\rm keV \\\\, s^{-1} \\\\, keV^{-1}}$)\\nat the energy $E$ of a quasar whose luminosity at $(1+z)$ keV is $L$. We have\\nused the mean spectrum of Elvis et al. (1994) to include a small K--correction\\nwhen computing the background at observed energies $E\\\\ne 1$keV. The mean\\nbackground is the integral of the emissivity over redshift,\\n\\n\\\\begin{equation}\\n\\\\bar I(E) = \\\\int_0^\\\\infty \\\\frac{d\\\\chi}{(1+z)} \\\\bar j(E_z,\\\\chi),\\n\\\\label{eq:xrb}\\n\\\\end{equation}\\nwhere $\\\\bar I$ is typically given in units of ${\\\\rm keV \\\\, cm^{-2} \\\\, s^{-1} \\\\,\\nsr^{-1} \\\\, keV^{-1}}$, $E_z = E (1+z)$, and $\\\\chi$ is the comoving distance\\nalong the line of sight.\\n\\nIf $\\\\delta(z)$ is the mass fluctuation at some position at redshift $z$, then\\nthe fluctuation of the emissivity at the same position and redshift is given by\\n$b_X(z) \\\\delta(z) \\\\bar j(E_z, z)$, where we have defined the X-ray\\nemission--weighted bias $\\\\bar b_X(z)$ as\\n\\n\\\\beq\\n\\\\bar b_X(z) = \\\\frac{1}{\\\\bar j(E_z,z)} \\n\\\\frac{1}{4\\\\pi} \\\\int_0^\\\\infty dL \\\\frac{d\\\\phi}{dL} L_X(E_z,L) b_X(L,z).\\n\\\\label{eq:biasx}\\n\\\\eeq\\n\\nFor simplicity, we compute the auto--correlation $w_\\\\theta$ of the XRB using\\nthe Limber approximation, together with the small angle approximation, as:\\n\\n\\\\begin{eqnarray}\\n\\\\label{eq:Clwtheta}\\nC_\\\\ell(E) &=& {\\\\bar I(E)}^{-2} \\\\int \\\\frac{d\\\\chi}{r_\\\\chi^2}\\nW^2(E_\\\\chi,\\\\chi) P_0(\\\\ell/r_\\\\chi) \\\\\\\\ \\n\\\\nonumber w_\\\\theta(E) &=& \\n\\\\int {\\\\ell d\\\\ell \\\\over 2\\\\pi} C_\\\\ell(E) J_0 (\\\\ell \\\\theta),\\n\\\\end{eqnarray}\\n\\nwhere $C_\\\\ell$ is the angular power spectrum, $J_0$ is the zeroth order Bessel\\nfunction, $P_0(\\\\ell/r_\\\\chi)$ is the linear mass power spectrum today, $r_\\\\chi$\\nis the angular diameter distance ($=\\\\chi$ for a flat universe), and\\n$W(E_\\\\chi,\\\\chi) = \\\\bar j(E_z,z) \\\\bar b_X(z) D(z)/(1+z)$. When the power\\nspectrum is measured in practice, shot-noise has to be subtracted or should be\\nincluded in the theoretical prediction, whereas the same is not necessary for\\nthe angular correlation except at zero-lag.\\n\\nOur models predicts the correct mean background spectrum $\\\\bar I(E)$, computed\\nfrom equation~\\\\ref{eq:xrb}, at $E=1$ keV. We have included all quasars down to\\nthe observed 1 keV flux of $2\\\\times10^{-17}~{\\\\rm erg~cm^{-2}~s^{-1}}$, i.e. we\\nused our models to extrapolate the XRLF to two orders of magnitude fainter than\\nthe ROSAT detection threshold for discrete sources (Hasinger \\\\& Zamorani 1997),\\nto make up the remaining $\\\\sim 50\\\\%$ of the XRB at 1keV. Our models predict a\\nfaint--end slope that is steeper than the Miyaji et al. (2000) fitting\\nformulae, allowing faint quasars to contribute half of the background. The\\nemissivities peak at $z\\\\approx 2$, coinciding with the peak of the XRLF,\\nimplying that our model produces most of the XRB, as well as its\\nauto--correlation signal at $z\\\\approx 2$. Note that the known contribution\\nfrom nearby galaxy clusters is $\\\\sim 10\\\\%$ (Gilli et al. 1999), which we ignore\\nhere.\\n\\nIn Figure \\\\ref{fig:xrb}, we show our predictions for the two point angular\\ncorrelation $w_\\\\theta$ of the XRB from quasars at 1 keV. Most measurements at\\nthe soft X-ray bands have yielded only upper limits, which are consistent with\\nour predictions (e.g. variance at $\\\\lsim 0.12$ at a scale of $10$ arcmin. and\\n$E = 0.9 - 2$keV, from Carrera et al. 1998; see also references therein).\\nSoltan et al. (1999) obtained angular correlations significantly higher than\\nprevious results (dashed curve), which, taken at face value, would imply quasar\\nlifetimes $t_Q \\\\gg 10^8$ yr. However, the results of Soltan et al. (1999)\\ncould be partially explained by galactic contamination (Barcons et\\nal. 2000). We therefore view this measurement as an upper limit, which is\\nconsistent with models using both lifetimes we considered. Figure \\\\ref{fig:xrb}\\nshows that $w_\\\\theta$ predicted in the long and short lifetime models differ by\\na factor of $\\\\sim 2$ on angular scales of 0.1-1 degrees, offering another\\npotential probe of quasar lifetimes, provided that $w_\\\\theta$ can be measured\\nmore accurately in the future, and that the contribution to the clustering\\nsignal from nearby non-quasar sources (e.g. clusters) is small or can be\\nsubtracted out. Finally, we note that there have been detections of of\\nclustering on several-degree-scales at the hard X-ray bands ($2 - 10$ keV) from\\nthe HEAO satellite (Treyer et al. 1998) -- while a prediction for such energies\\nwould be interesting (see also Lahav et al. 1997), it would require an\\nextrapolation of the X-ray spectrum, since we normalize by fitting to the\\nsoft-Xray luminosity function.\\n\\n\\\\section{Further Considerations}\\n\\\\label{section:discussion}\\n\\nWe have shown above that the quasar lifetime could be measured to high\\nprecision, using the soon available large samples of quasars at $z\\\\lsim 3$;\\neither from the 2dF or the SDSS survey. This precision, however, reflects only\\nthe statistical errors in the simple model we have adopted for relating quasars\\nto dark matter halos. The main hindrance in determining the quasar lifetime\\nwill likely be systematic errors; here we discuss how several potential\\ncomplications could affect the derived lifetime.\\n\\n\\\\vspace{\\\\baselineskip} {\\\\em Obscured sources.} Considerations of the hard\\nX--ray background have led several authors to suggest the presence of a large\\npopulation of ``absorbed'' quasars, necessary to fit the hard slope and overall\\namplitude of the background. Although not a unique explanation for the XRB,\\nthis would imply that the true number of quasars near the faint end of both the\\noptical and soft X--ray LF is $\\\\sim10$ times larger than what is observed; 90\\\\%\\nbeing undetected due to large absorbing columns of dust in the optical, and\\nneutral hydrogen in the soft X--rays (see, e.g. Gilli et al. 1999). Unless the\\noptically bright and dust--obscured phases occur within the same object (Fabian\\n\\\\& Iwasawa 1999), this increase would have a direct effect on our results,\\nsince we would then need to adjust our fitting parameters to match a $\\\\sim10$\\ntimes higher quasar abundance. We find that this is easily achieved by leaving\\n$x_0$ and $\\\\alpha$ unchanged, and instead raising the lifetime from $10^{6.5}$\\nto $10^{7.5}$ yr in the short lifetime model, and from $10^{8}$ to $10^{8.6}$\\nyr in the long lifetime model. In the latter case, a 10-fold increase in the\\nduty cycle requires only an increase in $t_Q$ by a factor of $\\\\approx 4$, owing\\nto the shape of the age distribution $dp_a/dt$ (Lacey \\\\& Cole 1993). Our\\nresults would then hold as before, but they would describe the two cases of\\n$t_Q=10^{7.5}$ and $10^{8.6}$ yr. Interestingly, this scenario would imply\\nthat the quasar lifetime could not be shorter than $t_Q\\\\approx10^{7.5}$ yr,\\nsimply based on the abundance of quasars (cf. \\\\S~\\\\ref{section:models}). Future\\ninfrared and hard X-ray observations should help constrain the abundance of\\nobscured sources, and reduce this systematic uncertainty.\\n\\n\\\\vspace{\\\\baselineskip} {\\\\em Multiple BH's in a single halo.} A possibility\\nthat could modify the simple picture adopted above is that a single halo might\\nhost several quasar black holes. A massive (e.g. $10^{14}~{\\\\rm M_\\\\odot}$) halo\\ncorresponds to a cluster of galaxies; while the Press--Schechter formalism\\ncounts this halo as a single object. If quasar activity is triggered by\\ngalaxy--galaxy mergers, a massive Press-Schechter halo, known to contain\\nseveral galaxies, could equally well host several quasars (e.g. Cavaliere \\\\&\\nVittorini 1998). There is some observational evidence of perhaps merger driven\\ndouble quasar activity (Owen et al. 1985; Comins \\\\& Owen 1991). One could\\ntherefore envision that quasars reside in the sub--halos of massive ``parent''\\nhalos -- a scenario that would modify the predicted clustering. To address\\nthese issues in detail, one needs to know the mass--function of sub--halos\\nwithin a given parent halo, as well as the rate at which they merge and turn\\non. In principle, this information can be extracted from Monte Carlo\\nrealizations of the formation history of halos in the extended Press--Schechter\\nformalism (i.e. the so called merger tree) together with some estimate of the\\ntime-scale for mergers of sub--halos based on, for instance, dynamical friction\\n(e.g. Kauffmann \\\\& Haehnelt 2000). Here, we consider two toy models that we\\nhope can bracket the plausible range of clustering predictions.\\n\\nTo simplify matters, we ignore the scatter in $L$--$M$ in the following\\ndiscussion. Suppose one is interested in quasars of a luminosity $L$ at\\nredshift $z_0$, which correspond to Press-Schechter halos of mass $M_0$ in our\\nformalism as laid out in \\\\S \\\\ref{section:models}. This choice of $M_0$ matches\\nthe abundance of quasars, expressed approximately as $L(d\\\\Phi/dL)\\\\approx\\nM_0[dN(M_0, z_0)/dM_0] (t_Q/t_{\\\\rm Hub})$ (the merger, or activation rate of\\nhalos is approximated as $\\\\sim t_{\\\\rm Hub}^{-1}$, where $t_{\\\\rm Hub}$ is the\\nHubble time), and implies the bias $b_0(L)\\\\approx b(M_0,z_0)$.\\n\\nIn model A, we suppose the Press-Schechter halos are identified at some earlier\\nredshift $z_1$ -- these would be sub--halos of those Press-Schechter halos\\nidentified at $z_0$. Quasars of luminosity $L$ now correspond to sub--halos of\\nmass $M_1$. The abundance of these sub-halos is given by the Press-Schechter\\nmass function $dN(M_1, z_1)/dM_1$, which is related to the mass function at\\n$z_0$ by $dN(M_1, z_1)/dM_1 = \\\\int_{M_1}^\\\\infty dM [dN(M, z_0)/dM] [d{\\\\cal\\nN}(M_1, z_1 | M, z_0) / dM_1]$ where $dM_1 \\\\times d{\\\\cal N}(M_1, z_1 | M, z_0)\\n/ dM_1$ is the average number of $M_1 \\\\pm dM_1/2$ sub--halos within parent\\nhalos of mass $M$, given by (e.g. Sheth \\\\& Lemson 1999)\\n\\n\\\\begin{eqnarray}\\n\\\\label{eq:condPS}\\n&& d{\\\\cal N}(M_1, z_1 | M, z_0) / dM_1 = \\\\\\\\ \\\\nonumber\\n&& \\\\quad \\\\quad {M\\\\over M_1} {1\\\\over \\\\sqrt{2\\\\pi}} \\n{{\\\\delta_1 - \\\\delta_0}\\\\over {[\\\\sigma^2 (M_1) - \\\\sigma^2 (M)]^{3/2}}} \\\\\\\\ \\\\nonumber\\n&& \\\\quad \\\\quad\\n{\\\\, \\\\rm exp} \\\\left\\\\{ -{(\\\\delta_1 - \\\\delta_0)^2 \\\\over {2[\\\\sigma^2 (M_1)-\\\\sigma^2 (M)]}}\\\\right\\\\}\\n{d \\\\sigma^2 (M_1) \\\\over dM_1},\\n\\\\end{eqnarray}\\n\\nwhere $\\\\delta_1 = \\\\delta_c/D(z_1)$ and $\\\\delta_0 = \\\\delta_c/D(z_0)$ (see\\neq. \\\\ref{eq:biasM}).\\n\\nTo match the abundance of quasars at luminosity $L$, we impose the condition\\nthat $M_1 [dN(M_1, z_1)/dM_1] \\\\approx$ $M_0[dN(M_0, z_0)/dM_0]$ , which\\ndetermines $M_1$ given $z_1$, $M_0$ and $z_0$. The bias of the quasars is no\\nlonger $b_0 (L) \\\\approx b(M_0, z_0)$, but is instead given by\\n\\n\\\\begin{eqnarray}\\n\\\\label{eq:beff}\\n&& b_{\\\\rm eff}^A (L,z_1) = \\\\left[{dN(M_1, z_1) \\\\over dM_1}\\\\right]^{-1} \\\\\\\\ \\\\nonumber \\n&& \\\\quad \\\\int_{M_1}^\\\\infty dM {dN(M, z_0) \\\\over dM} {d{\\\\cal N}\\n(M_1, z_1 | M, z_0) \\\\over dM_1} b(M, z_0).\\n\\\\end{eqnarray}\\n\\nWe show in Fig. \\\\ref{fig:comparebiasPS} the ratio of $b_{\\\\rm eff}^A (L,z_1)/b_0\\n(L)$ as a function of $z_1$, for $z_0 = 3$ and $z_0 = 2$ respectively, and for\\na range of masses $M_0$ which are representative of the halos that dominate our\\nclustering signal in previous discussions. It is interesting how the bias\\n$b_{\\\\rm eff}^A (L,z_1)$ is not necessarily larger than our original bias $b_0\\n(L)$, despite the fact that the bias of sub--halos should be boosted by their\\ntaking residence in bigger halos. This is because the relevant masses here\\n(e.g. $M_0$) are generally large, and we find that the number of halos of mass\\n$M_0$ at $z_1$ is always {\\\\it smaller} than the number of halos of the same\\nmass at $z_0 < z_1$. Hence, to match the observed abundance of quasars at the\\nsame $L$, $M_1$ must be chosen to be smaller than $M_0$. As\\nFig. \\\\ref{fig:comparebiasPS} shows, this could, in some cases, more than\\ncompensate the increase in clustering due to massive parent halos. Because of\\nthese two opposing effects, the bias does not change by more than about $50 \\\\%$\\neven if one considers $z_1$ as high as $10$. This translates into a factor of\\n$\\\\sim 2$ uncertainty in our predictions for the quasar power spectrum. Our\\nclustering predictions for the short and long lifetime models differ by about a\\nfactor of $\\\\sim 5$, implying that the lifetime can still be usefully\\nconstrained at $z\\\\gsim 2$. As we can see from Fig. \\\\ref{fig:comparebiasPS}, at\\nlower redshifts, or equivalently lower $M_0/M_\\\\star$, our predictions for the\\nquasar power spectrum should be more uncertain.\\n\\nOne might imagine modifying the above model by allowing mergers to take place\\npreferentially in massive parents, and therefore boosting the predicted bias.\\nIn model B, we adopt a more general procedure of matching the observed quasar\\nabundance by $L (d\\\\Phi/dL) = M_1 \\\\int_{M_1}^\\\\infty dM [dN(M, z_0)/dM] [d{\\\\cal\\nN}(M_1, z_1 | M, z_0) / dM_1]$ $(t_Q/t_{\\\\rm Hub}) f(M_1, M) $ where\\n$(t_Q/t_{\\\\rm Hub}) f(M_1, M)$ is the probability that an $M_1$ sub--halo\\nresiding within a parent halo of $M_0$ harbors an active quasar of luminosity\\n$L$. It is conceivable that $f$ increases with the parent mass $M_0$ -- a more\\nmassive parent might encourage more quasar activity by having a higher fraction\\nof mergers or collisions. The following heuristic argument shows that one\\nmight expect $[d{\\\\cal N}(M_1, z_1 | M, z_0) / dM_1] f(M_1, M)$ to scale\\napproximately as $\\\\sim M^{4/3}$. Let $N_h$ be the number of sub--halos inside a\\nparent halo of mass $M$. The rate of collisions is given by $N_h^2 v_h \\\\sigma_h\\n/R^3$ where $v_h$ is the velocity of the sub--halos, $\\\\sigma_h$ is their\\ncross-section and $R^3$ is the volume of the parent halo. Using $N_h \\\\propto M$\\n(which can be obtained from eq. \\\\ref{eq:condPS} in the large $M$ limit), $v_h\\n\\\\propto \\\\sqrt{M/R}$ (virial theorem) and $R^3 \\\\propto M$ (fixed overdensity of\\n$\\\\sim 200$ at the redshift of formation), the rate of collisions scales with\\nthe parent mass as $M^{4/3}$, if one ignores the possibility that $\\\\sigma_h$\\nmight depend on the parent mass as well. A similar scaling of $M^{1.3}$ has\\nbeen observed in simulations of the star-burst model for Lyman-break objects\\n(Kolatt et al. 1999, Weschler et al. 1999).\\n\\nTo model the enhanced rate of collisions inside massive parent halos, we can\\nsimply modify model A by using $f(M_1, M) = (M/M_1)^{1/3}$. The effective\\nbias is given by\\n\\n\\\\begin{eqnarray}\\n&& b_{\\\\rm eff}^B (L,z_1) = \\\\\\\\ \\\\nonumber\\n&& \\\\left[\\\\int_{M_1}^\\\\infty dM {dN(M, z_0) \\\\over dM} {d{\\\\cal N}\\n(M_1, z_1 | M, z_0) \\\\over dM_1} \\\\left({M\\\\over M_1}\\n\\\\right)^{1\\\\over 3} \\\\right]^{-1} \\\\\\\\ \\\\nonumber &&\\n\\\\times\\\\int_{M_1}^\\\\infty dM {dN(M, z_0) \\\\over dM} {d{\\\\cal N}\\n(M_1, z_1 | M, z_0) \\\\over dM_1} \\\\left({M \\\\over M_1}\\\\right)^{1\\\\over 3} \\nb(M,z_0).\\n\\\\label{eq:beffB}\\n\\\\end{eqnarray}\\n\\nWe find that the above prescription does not significantly alter our\\nconclusions following from model A: the $M^{1/3}$ enhancement of the activation\\nrate inside massive parent halos turns out to be relatively shallow, and\\ntranslate to a small effect in the bias. Finally, we note that $z_1$ above\\ncould in principle depend on $M_0$ and $M_1$, a possibility that would require\\nfurther modeling and is not pursued here.\\n\\n\\\\vspace{\\\\baselineskip} {\\\\em Galaxies without BH's.} Another possibility that\\ncould modify our picture is that only a fraction $f<1$ of the halos harbor\\nBH's; the duty cycle could then reflect this fraction, rather than the lifetime\\nof quasars. Although there is evidence (e.g. Magorrian et al. 1998) that most\\n{\\\\it nearby} galaxies harbor a central BH, this is not necessarily the case at\\nredshifts $z=2-3$: the fraction $f$ of galaxies hosting BH's at $z=2-3$ could,\\nin principle have merged with the fraction $1-f$ of galaxies without BH's,\\nsatisfying the local constraint.\\n\\nUsing the extended Press--Schechter formalism (Lacey \\\\& Cole 1993), one can\\ncompute the rate of mergers between halos of various masses. On galaxy--mass\\nscales, the merger rates at $z=2-3$ are comparable to the reciprocal of the\\nHubble time (cf. Fig. 5 in Haiman \\\\& Menou 2000), implying that a typical\\ngalaxy did not go through numerous major mergers between $z=2-3$ and $z=0$,\\ni.e. that the fraction $f$ cannot be significantly less than unity at $z=2-3$.\\nA more detailed consideration of this issue is beyond the scope of this paper;\\nwe simply note that the lifetimes derived here scale approximately as $1/f$,\\nwhere $f$ is likely of order unity.\\n\\n\\\\vspace{\\\\baselineskip} {\\\\em Larger scatter in $L/M$.} The scatter $\\\\sigma$ we\\nassumed around the mean relation between quasar luminosity and halo mass is\\nmotivated by the scatter found empirically for the $M_{\\\\rm bh}-M_{\\\\rm bulge}$\\nrelation (Magorrian et al. 1998). It is interesting to consider the\\nsensitivity of our conclusions to an increased $\\\\sigma$. In general, scatter\\nraises the number of quasars predicted by our models, by an amount that depends\\non the slope of the underlying mass function $dN/dM$. As a result, increasing\\n$\\\\sigma$ raises, and flattens the predicted LF. We find that an increase of\\n$\\\\sigma$ from 0.5 to 1 (an additional order of magnitude of scatter) can be\\ncompensated by a steeper $\\\\bar L_M$ relation, typically replacing $\\\\alpha$ with\\n$\\\\approx \\\\alpha-0.5$. As a result of the increase in $\\\\sigma$, quasars with a\\nfixed $L$ are, on average, associated with larger, and more highly biased\\nhalos.\\n\\nNevertheless, we find that the mean bias $\\\\bar b$ of all sources above a fixed\\nflux (cf. eq.~\\\\ref{eq:bave}), and therefore the correlation length $r_0$, is\\nunchanged by the increased scatter (at the level of $\\\\sim 3\\\\%$). The reason\\nfor the insensitivity of $r_0$ to the amplitude of the scatter can be\\nunderstood as follows. The mean bias $\\\\bar b$ of all sources with $L>L_{\\\\rm\\nmin}$ is dominated by the bias $b(L)$ of sources near the threshold $L_{\\\\rm\\nmin}$. The latter is obtained by averaging $b(M)$ over halos of different\\nmasses (cf. eq.~\\\\ref{eq:biasL}), and it is dominated by the bias of the\\nsmallest halos within the width of the scatter, i.e. of halos with mass $M_{\\\\rm\\nmin} \\\\approx \\\\bar M / 10^\\\\sigma$, where $\\\\bar M$ defines the mean relation\\nbetween $L_{\\\\rm min}$ and halo mass i.e. $L_{\\\\rm min}$ = $\\\\bar L(\\\\bar M)$, and\\n$\\\\sigma$ quantifies the scatter (see eq. \\\\ref{eq:scatter}). As mentioned\\nbefore, increasing the scatter makes the luminosity function flatter, which\\nmeans to match the observed abundance of halos at a fixed luminosity $L_{\\\\rm\\nmin}$, one has to choose a higher $\\\\bar M$. In other words, $\\\\bar M$ scales up\\nwith the scatter, and it turns out to scale up approximately as $10^\\\\sigma$,\\nmaking $M_{\\\\rm min}$ and hence the effective bias roughly independent of\\nscatter.\\n\\nWe note that the relation between quasar luminosity and halo mass can, in\\nprinciple be derived from observations, by measuring $M_{\\\\rm halo}$ for the\\nhosts of quasars (e.g. by weak lensing, or by finding test particles around\\nquasars, such as nearby satellite galaxies).\\n\\n\\\\vspace{\\\\baselineskip} {\\\\em Mass and redshift dependent lifetime.} In all of\\nthe above, we have assumed that the quasar lifetime is a single parameter,\\nindependent of the halo mass. This is not unreasonable if the Eddington time,\\nthe timescale for the growth of black hole mass, is indeed the relevant\\ntime--scale, $4\\\\times10^7$ ($\\\\epsilon$/0.1) yr. Implicit in such reasoning is\\nthat the active phase of the quasar is coincident with the phase where the\\nblack hole gains most of its mass. This is not the only possibility; see\\nHaehnelt et al. (1999) for more discussions. One can attempt to explore how\\n$t_Q$ depends on halo mass by applying our method to quasars grouped into\\ndifferent absolute luminosity ranges, but the intrinsic scatter in the\\nmass-luminosity relation should be kept in mind. We emphasize, however, since\\nwe fit the luminosity function and clustering data at the same redshift, there\\nis no need within our formalism to assume a redshift independent lifetime. In\\nfact, performing our exercise as a function of redshift could give interesting\\nconstraints on how $t_Q$ evolves with redshift.\\n\\n\\\\section{Conclusions}\\n\\\\label{section:conclusions}\\n\\nIn this paper, we have modeled the quasar luminosity function in detail in the\\noptical and X--ray bands using the Press--Schechter formalism. The lifetime of\\nquasars $t_Q$ enters into our analysis through the duty--cycle of quasars, and\\nwe find that matching the observed quasar LF to dark matter halos yields the\\nconstraint $10^6 \\\\lsim t_Q \\\\lsim 10^8$ yr: smaller lifetimes would imply overly\\nmassive BH's, while longer lifetimes would necessitate overly massive halos.\\nThis range reassuringly brackets the Eddington timescale of $4\\\\times10^7$\\n($\\\\epsilon$/0.1) yr.\\n\\nThe main conclusion of this paper is that the lifetime (and hence $\\\\epsilon$,\\nif the Eddington time is the relevant timescale for quasar activity) can be\\nfurther constrained within this range using the clustering of quasars: for\\nquasars with a fixed luminosity, longer $t_Q$ implies larger host halo masses,\\nand higher bias. We find that as a result, the correlation length $r_0$ varies\\nstrongly with the assumed lifetime. Preliminary data from the 2dF survey\\nalready sets mild constraints on the lifetime. Depending on the assumed\\ncosmology, we find $t_Q=10^{7.7\\\\pm 0.8}$ yr ($\\\\Lambda$CDM) or $t_Q=10^{8\\\\pm\\n0.8}$ yr (OCDM) to within $1\\\\sigma$ statistical uncertainty. These values are\\nalso found to satisfy upper limits on the auto--correlation function of the\\nsoft X--ray background.\\n\\nForthcoming large quasar samples from SDSS or the complete 2dF survey are\\nideally suited for a study of quasar clustering, and they can, in principle\\nconstrain the quasar lifetime to high accuracy, with small statistical\\nerrors. We expect the modeling of the quasar--halo relation, as well as the\\npossible presence of obscured quasars, to be the dominant sources of systematic\\nuncertainty. Not discussed in depth in this paper is the possibility of using\\nhigher moments (such as skewness), which our models also make definite\\npredictions for, and will be considered in a future publication. Remarkably,\\nour best determination of the lifetime of quasars might come from the\\nstatistics of high--redshift quasars, rather than the study of individual\\nobjects.\\n\\n\\\\acknowledgments \\n\\nNear the completion of this work, we became aware of a similar, independent\\nstudy by P. Martini \\\\& D. Weinberg. We thank M. Haehnelt, K. Menou,\\nE. Quataert, U-L. Pen., U. Seljak, R. Sheth and D. Spergel for useful\\ndiscussions, T. Miyaji for his advice on the X--ray luminosity function, and\\nT. Shanks and S. Croom for discussions on the 2dF survey. 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Lebrun, in press, astro-ph/9910359\\n\\\\end{thebibliography}\\n\\n\\\\section*{Appendix}\\n\\nIn this Appendix, we describe our models for the luminosity function (LF) of\\nquasars, based on associating quasar BHs with dark halos. Our main assumption\\nis that there is, on average, a direct monotonic relation between halo mass and\\nquasar light. Our treatment is similar to previous works (Haiman \\\\& Loeb 1998;\\nHaehnelt et al. 1998), but differs in some of the details. We adopt the\\nparameterization of the observational LF in the optical B band, given in the\\nredshift range $0 \\:$}\n\\newcommand{\\lta}{$\\leq $}\n\\newcommand{\\gta}{$\\geq $}\n\\newcommand{\\Bmu}{\\rm $\\mu_B \\:$}\n\\newcommand{\\Rmu}{\\rm $\\mu_R \\:$}\n\\newcommand{\\Imu}{\\rm $\\mu_I \\:$}\n\\newcommand{\\Umu}{\\rm $\\mu_U \\:$}\n\\newcommand{\\Vmu}{\\rm $\\mu_V \\:$}\n\\newcommand{\\Bmo}{\\rm ${\\mu _B}$(0) }\n\\newcommand{\\Imo}{\\rm ${\\mu _I}$(0) }\n\\newcommand{\\Vmo}{\\rm ${\\mu _V}$(0) }\n\\newcommand{\\Ho}{\\rm H$_0$ }\n\\newcommand{\\Bmag}{\\rm B$\\rm _{mag}$ }\n\\newcommand{\\Bt}{\\rm B$\\rm _T$(0) }\n\\newcommand{\\mt}{\\rm m$\\rm _T$ }\n\\newcommand{\\muo}{\\rm ${\\mu}$(0) }\n\\newcommand{\\rts}{\\rm $\\rm r_{27}$ }\n\\newcommand{\\rtf}{\\rm $\\rm r_{25}$ }\n\\newcommand{\\Vc}{{V$_{circ}$\\ }}\n\\newcommand{\\Halp}{H$_{\\alpha}$\\ }\n\\newcommand{\\alp}{$\\alpha$\\ }\n\\newcommand{\\etal}{{\\it et.al.}}\n\\newcommand{\\degree}{$^{\\circ}$ }\n\\newcommand{\\arcs}{\\rm arcsec$^2$}\n\\newcommand{\\teff}{\\rm T$_{eff}$\\ }\n\\newcommand{\\kmsec}{km sec$^{-1}$\\ }\n\\newcommand{\\kms}{km sec$^{-1}$\\ }\n\\newcommand{\\app}{$\\sim$}\n\\newcommand{\\eg}{{\\em e.\\ g.\\ }}\n\\newcommand{\\ie}{{\\em i.\\ e.\\ }}\n\\newcommand{\\mn}{{\\em MNRAS\\ }}\n\\newcommand{\\solarm}{$M_{\\odot}$\\ }\n\\newcommand{\\Msol}{$M_{\\odot}$\\ }\n\\newcommand{\\Zsol}{$Z_{\\odot}$\\ }\n\\newcommand{\\Lsol}{$L_{\\odot}$\\ }\n\\newcommand{\\fivesixco}{$^{56}$Co\\ }\n\\newcommand{\\chisq}{${\\chi}^{2}$\\ }\n\\newcommand{\\chinusq}{${\\chi}_{\\nu}^{2}$\\ }\n\\newcommand{\\bvzero}{\\rm (B-V)$_{\\circ}$\\ }\n\\newcommand{\\feh}{\\rm [Fe/H]\\ }\n\\newcommand{\\lsb}{\\rm low surface brightness}\n\\newcommand{\\hsb}{\\rm high surface brightness}\n\\newcommand{\\lsbg}{\\rm low surface brightness galaxy}\n\\newcommand{\\lsbgs}{\\rm low surface brightness galaxies}\n\\newcommand{\\PMO}{\\rm Pine Mountain Observatory}\n\n\\usepackage{apjfonts}\n\\usepackage{float}\n\\usepackage{multicol}\n\\usepackage{epsfig}\n\n\\textwidth=17.5cm\n\\textheight=23.5cm\n\\voffset=-2.5cm\n\\hoffset=-2.54cm\n\n\\columnsep=7mm\n\\evensidemargin=25mm\n\\oddsidemargin=21mm\n\n\\renewcommand{\\baselinestretch}{0.87}\n\\renewcommand{\\topfraction}{0.99}\n\\renewcommand{\\bottomfraction}{0.99}\n\\renewcommand{\\textfraction}{0.01}\n\n\\begin{document}\n\n\\twocolumn[\n\\null\n\\vspace{-1cm}\n\n\\begin{center}\n\\noindent\n\n{\\Large \\bf Star Formation and Tidal Encounters with the Low Surface\nBrightness Galaxy UGC 12695 and Companions}\n\n\\vspace{1cm}\n\nK. O'Neil$^1$, M.A.W. Verheijen$^2$, S.S. McGaugh$^3$ \\\\\n\n\\end{center}\n\n\\vspace{1cm}\n\n$^1$Arecibo Observatory, HC03 Box 53995, Arecibo, PR 00612, email:koneil@naic.edu \\\\\n$^2$National Radio Astronomy Observatory, Box 0, Socorro, NM 87801, email:mverheij@nrao.edu \\\\\n$^3$Department of Astronomy, University of Maryland, College Park, MD 20742, email:ssm@astro.umd.edu \\\\\n\n\\vspace{0.5cm}\n\n\\begin{flushright}\n\n\\parbox{13.3cm}{{\\large\\noindent{\\bf\\sf ABSTRACT-- }}\nWe present VLA H I observations of the low surface brightness galaxy UGC\n12695 and its two companions, UGC 12687 and a newly discovered dwarf\ngalaxy 2333+1234. UGC 12695 shows solid body rotation but has a very\nlopsided morphology of the H I disk, with the majority of the H I lying\nin the southern arm of the galaxy. The H I column density distribution\nof this very blue, LSB galaxy coincides in detail with its light\ndistribution. Comparing the H I column density of UGC 12695 with the\nempirical (but not well understood) value of $\\Sigma_c$ = 10$^{21}$\natoms cm$^{-2}$ found in, i.e., Skillman's 1986 paper shows the star\nformation to be a local affair, occurring only in those regions where\nthe column density is above this star formation threshold. The low\nsurface brightness nature of this galaxy could thus be attributed to an\ninsufficient gas surface density, inhibiting star formation on a more\nglobal scale. Significantly, though, the Toomre criterion places a\nmuch lower critical density on the galaxy ($\\sim$10$^{20}$ atoms\ncm$^{-2}$), which is shown by the galaxy's low SFR to not be applicable.\n\nWithin a projected distance of 300 kpc/30 \\kms\\ of UGC 12695 lie two\ncompanion galaxies -- UGC 12687, a high surface brightness barred spiral\ngalaxy, and 2333+1234, a dwarf galaxy discovered during this\ninvestigation. The close proximity of the three galaxies, combined with\nUGC 12695's extremely blue color and regions of localized starburst and\nUGC 12687's UV excess bring to mind mutually induced star formation\nthrough tidal activity. } \n\\end{flushright} \n\n\\vspace{0.5cm}\n\n\\noindent\n{\\it Subject headings:} \ngalaxies: individual(UGC 12695, UGC 12687, 2333+1234) \n-- galaxies: spiral\n-- galaxies: evolution \n-- galaxies: interactions\n-- galaxies: kinematics and dynamics\n-- galaxies: structure\n\n\\null\n\\vspace{0.5cm}\n]\n\n\\setcounter{footnote}{0}\n\\footnotetext{To be published in The Astronomical Journal, May 2000}\n\n\\newpage\n\n\n\\begin{figure*}[t]\n\\begin{center}\n\\epsfig{file=ovm.fig1bmp.ps,width=17cm}\n\\caption{H I contours of all three galaxies overlaid on a POSS-II\nimage.}\n\\label{fig:Allposs2HI}\n\\end{center}\n\\end{figure*}\n\n\n\\section{Introduction}\n\nAttempts to understand star formation in low surface brightness (LSB)\ngalaxies has resulted in a large number of theories being discarded and\nfew alternatives being offered. As a result we have considerable\nknowledge on what these enigmatic systems are not. LSB galaxies are\n{\\em not}:\n\n\\begin{itemize}\n\n\\item simply the faded version of high surface brightness (HSB)\ngalaxies. Although some red LSB galaxies have been found which may be\nthe end product of the faint blue galaxies, the majority of LSB galaxies\nhave very blue colors and low metallicities (i.e. Ferguson \\& McGaugh\n1995; O'Neil, \\etal 1997a; McGaugh 1994; Schombert, \\etal 1990; De Blok\n\\& Van der Hulst 1998), arguing against any fading scenario. \n\n\\item lacking the neutral hydrogen necessary to form stars, as many LSB\ngalaxies contain more than 10$^9$ \\Msol of H I and LSB galaxies include\nsome of the highest M$_{HI}$/L$_B$ galaxies known (O'Neil, Bothun, \\&\nSchombert 1999). \n\n\\item a completely new type of galaxy. The transition from HSB to LSB\ngalaxies is smooth, with LSB galaxies covering the entire color and\nmorphological spectrum of HSB galaxies (i.e. O'Neil, \\etal 1997b;\nMatthews \\& Gallagher 1997)\n\n\\end{itemize}\n\nUGC 12695 is a relatively nearby (z=0.021) low surface brightness galaxy\nwith an absolute blue magnitude of M$_B$=$-$18.9. Previous studies of\nUGC 12695 (McGaugh, 1994; O'Neil \\etal, 1998) have shown it to be very\nremarkable. The galaxy is of an exceedingly transparent nature,\nevidenced by the many background galaxies seen through its elusive disk,\nand it contains a reasonably high gas fraction (M$_{HI}$/L$_B$ = 2.6\n\\Msol/\\Lsol) while having a very low metallicity and an extremely blue\ncolor for a galaxy ($U-I$ = $-0.2$) (Table 1). \n\nBecause UGC 12695 was thought to be fairly isolated, with the nearest\ngalaxy (UGC 12687) lying more than 277 kpc away\n(Figure~\\ref{fig:Allposs2HI}), it provides a good opportunity for\nstudying star formation and evolution in LSB galaxies. To this end, and\nwith the above points in mind, we undertook to observe UGC 12695 with\nthe Very Large Array (VLA) in the C configuration. The results of these\nobservations are described in this paper, as follows: Section 2\ndescribes the observations and data reduction; Section 3 examines the H\nI morphology and kinematics of UGC 12695 and its companions -- UGC\n12687, and 2333+1234; Section 4 looks at the dark and visible mass of\nUGC 12695; Section 5 examines the star formation potential of UGC\n12695; Finally, section 6 examines the possibility of a recent tidal\nencounter between the UGC galaxies. \n\n\\begin{table}[ht]\n\\begin{center}\n\\caption{Global properties of UGC~12695 and UGC~12687.}\n\\begin{tabular}{lccc}\n\\noalign{\\vspace{0.8mm}}\n\\hline\n\\hline\n\\noalign{\\vspace{0.8mm}}\n & & UGC~12695 & UGC~12687 \\\\\n\\hline\n\\noalign{\\vspace{0.8mm}}\nType & & Sm$^1$ & SBbc$^1$\\\\\nV$_{hel}$ & km s$^{-1}$& 6186$^2$& 6150$^2$\\\\\nM$_B$ & mag & -18.9$^3$& -20.3$^1$\\\\\n$B-V$ & & 0.26$^3$ & 0.70$^4$\\\\\n$\\mu_B(0)$ &mag/arcsec$^{2}$& 23.8$^3$ & - \\\\\nr$_{25}$ & kpc & 0.79$^1$ & 0.87$^1$\\\\\nM$_{HI}$ & M$_\\odot$ & 7.5$\\times$10$^9$ $^2$& 1.2$\\times$10$^{10}$ $^2$\\\\\nM$_{HI}$/L$_B$ & M$_\\odot$/L$_\\odot$ & 2.62$^2$ & 1.18$^2$ \\\\\n\\noalign{\\vspace{0.8mm}}\n\\hline\n\\multicolumn{4}{l}{$^1$De Vaucouleurs, \\etal 1991}\\\\\n\\multicolumn{4}{l}{$^2$This paper}\\\\\n\\multicolumn{4}{l}{$^3$O'Neil, \\etal 1998}\\\\\n\\multicolumn{4}{l}{$^4$Prugniel \\& Heraudeau 1998}\\\\\n\\noalign{\\vspace{0.8mm}}\n\\hline\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n\\begin{table}[ht]\n\\caption{VLA observing parameters}\n\\begin{tabular}{lr}\n\\noalign{\\vspace{0.8mm}}\n\\hline\n\\hline\n\\noalign{\\vspace{0.8mm}}\nConfiguration & C-short \\\\\nCorrelator mode & 2AC-normal \\\\\nTotal integration time \\hfill (hours) & 15.5 \\\\\nDates of observation & 15Jan99 \\\\\n\\multicolumn{2}{r}{16Jan99} \\\\\nField center, $\\alpha$(B1950) & 23:33:30 \\\\\n\\phantom{Field center, }$\\delta$(B1950) & 12:35:53 \\\\\nCentral frequency \\hfill (MHz) & 1391.64 \\\\\n$V_{\\rm hel}$ of central channel \\hfill (km$\\:$s$^{-1}$) & 6170 \\\\\nPrimary beam FWHM \\hfill (arcmin) & 32.4 \\\\\nSynthesized beam ($\\alpha$$\\times$$\\delta$) \\hfill (arcsec) & 16.2$\\times$14.1 \\\\\nBandwidth \\hfill (MHz) & 1.5625 \\\\\nNumber of channels & 256 \\\\\nChannel separation \\hfill (km$\\:$s$^{-1}$) & 1.31 \\\\\nVelocity resolution \\hfill (km$\\:$s$^{-1}$) & 1.58 \\\\\nrms noise in one channel \\hfill (K) & 2.63 \\\\\nK-mJy conversion, & \\\\\n\\phantom{K-}equiv. of 1mJy/beam \\hfill (K) & 2.76 \\\\\n\\noalign{\\vspace{0.8mm}}\n\\hline\n\\hline\n\\end{tabular}\n\\end{table}\n\n\\section{The Data -- Observations and Reduction} \n\nH I spectral line synthesis observations of UGC 12695 and its companions\nwere done in two runs with the VLA in its new C-short configuration and\nare specified in Table~2. The primary calibrator 3C48 was observed\nthree times per run and the secondary phase calibrator 2340+135 was\nobserved every 35 minutes. \n\nCalibration, flagging, concatenation and Fourier transformation of the\nUV data was done with the AIPS package. A robust R=0 weighting of the\nUV data points was applied and the entire primary beam was imaged with a\n512 x 512 map of 5 arcsecond pixels. The dirty maps and corresponding\nantenna patterns were exported into the GIPSY package which was used for\nfurther data reduction and analysis as described below. \n\nThe number of velocity channels was reduced by averaging adjacent pairs\nof channel maps which resulted in a data cube of 127 nearly independent\nchannels, each 2.68 \\kms\\ wide. The dirty maps were cleaned down to\nhalf the rms noise level with channel dependent search areas using the\nstandard H\\\"ogbom algorithm. The clean components were restored with a\nGaussian beam of FWHM 16.2$\\times$14.1 arcsec at a position angle of\n$-$54 degrees. The data cube was then Hanning smoothed in velocity\nwhich resulted in a velocity resolution of 5.3 \\kms. \n\nNo continuum emission was detected in the averaged line-free channels at\nthe positions of UGC 12695 and 2333+1234. Due to a steep rotation\ncurve, the line emission at the center of UGC 12687 spans the entire\nbandpass, leaving only 4 line-free continuum channels at the high\nvelocity end of the data cube while some line emission at the low\nvelocity edge of the bandpass is severely affected by the high noise\nlevel. No continuum emission could be detected in the line-free\nchannels at the position of the disk of UGC 12687. Therefore, no\ncontinuum map was subtracted to avoid the unnecessary addition of noise\nto the channel maps and the nuclear continuum emission of UGC 12687 was\nremoved at a later stage. \n\nThe areas of H I emission were isolated in each channel map and the\npixels outside these areas were set to zero. Global H I profiles were\nderived by measuring the total flux in the isolated areas, corrected for\nprimary beam attenuation. In the case of UGC 12687, a 2.9 mJy baseline\nwas subtracted from the global profile. \n\nIntegrated H I maps of the galaxies were constructed by summing the\nprimary beam corrected, isolated areas of H I emission. At the position\nof the nucleus of UGC 12687, 7 channels at the high velocity end of the\ndata cube are free from line emission and those were averaged to obtain\na map of the central continuum source. A Gaussian beam was fitted to\nthis source, giving a primary beam corrected flux density of 2.9$\\pm$0.2\nmJy at the position $23^{\\rm h}32^{\\rm m}45^{\\rm s}.4$ and $23^{\\rm\nd}32^\\prime53^{\\prime\\prime}$ (B1950). Subsequently, this fitted\nGaussian was subtracted from the integrated H I map.\n\nVelocity fields were constructed by fitting a single Gaussian to each\nprofile and rotation curves for UGC 12695 and UGC 12687 were derived by\nfitting tilted rings of 11 arcsec width to their velocity fields. \n\nOptical images were taken from the Hubble Space Telescope Wide Field\nPlanetary Camera-2 (WFPC2) images of O'Neil, \\etal (1998), the MDM 1.3m\nMcGraw Hill telescope (McGaugh, Schombert, \\& Bothun 1995), and from the\nSpace Telescope Science Institute Digital Sky Survey. The metallicity\nstudies of UGC 12695 are from McGaugh (1994). \n\nH$_0$ is 75 km s$^{-1}$ Mpc$^{-1}$ throughout this paper, and a \nVirgo-centric infall of 300 km s$^{-1}$ is assumed. B1950 coordinates\nare used throughout this paper.\n\n\n\n\\section{H I morphology and kinematics}\n\nThe following subsections contain detailed descriptions of the overall\nproperties of the neutral hydrogen gas in UGC 12695 and its companions\nUGC 12687 and 2333+1234 which are illustrated in\nFigures~\\ref{fig:U12695}, \\ref{fig:U12687}, \\ref{fig:2333},\nrespectively. The beam size is 16.2'' $\\times$ 14.1'', or 6.4 kpc\n$\\times$ 5.6 kpc at 82 Mpc. \n\n\\subsection{UGC 12695}\n\n\n\\begin{figure*}[p]\n\\epsfig{file=ovm.fig2bmp.ps,width=16cm}\n\\caption{UGC 12695. See section 3.1 for explanations.}\n\\label{fig:U12695}\n\\end{figure*}\n\n\nFigure~\\ref{fig:U12695} presents the data of UGC 12695. The upper left\npanel displays the HST WFPC2 F814W image of O'Neil, \\etal\\ (1998). It\nshows a relatively smooth triangular inner region and an irregular outer\ndisk dominated by several large star forming H$\\alpha$ regions. Several\nbackground galaxies can be seen through the disk, evidencing its\nextremely transparent nature. The southern spiral arm seems to be\nsharply outlined while the northern arm is extremely diffuse. Smoothing\nthe WFPC2 image to a 1$^{\\prime\\prime}$ resolution and fitting an\nellipse to the faintest isophotes indicates a position angle of\n88$^\\circ$, an inclination of 43$^\\circ$ and a central position at\n(23$^{\\rm h}$33$^{\\rm m}$30.4$^{\\rm s}$,\n12$^\\circ$36$^\\prime$1$^{\\prime\\prime}$).\n\nThe upper right panel shows the global H I profile obtained by measuring\nthe flux in the individual channel maps. The width at the 20\\% level of\nthe peak flux is 79.4 \\kms\\ and the width at the 50\\% level of the peak\nflux is 62.2 \\kms. The integrated flux density is 4.7 Jy km s$^{-1}$\nwhich corresponds to a total H I mass of 7.5$\\times$10$^9$ M$_\\odot$ for\na distance of 82 Mpc (v=6186 km s$^{-1}$ (Table 1) and H$_0$=75 km\ns$^{-1}$ Mpc$^{-1}$). The shape of the profile suggests a global\nlopsidedness of the H I distribution and or kinematics. The vertical\narrow indicates the systemic velocity as derived from the H I velocity\nfield. It should be noted that the H I profile of UGC 12695 was\npreviously determined both by Theureau, \\etal\\ (1998) using the\nNan\\c{c}ay telescope and Schneider, \\etal (1990) using the Arecibo\ntelescope. Although both of the earlier observations match our\nvelocity widths, the Nan\\c{c}ay result list a 40\\% smaller total flux. \nAs our results match those of Schneider, \\etal, we believe the data\ndifferences to be the result of uncertain beam shapes and primary beam\ncorrections in the Nan\\c{c}ay data.\n\nThe middle left panel presents the integrated H I column density map\nwith the size of the synthesized beam in the lower left corner. This H\nI map is at the same scale as the WFPC2 image above. Contour levels are\ndrawn at 0.5, 1, 2, 4, 6, 8, 10 and 12$\\times$10$^{20}$ atoms cm$^{-2}$.\n Overall, the neutral hydrogen distribution of UGC 12695 appears to\nmatch the optical morphology quite well, including the fact that the H I\ndistribution is very lopsided with a high column density ridge running\nthrough the southern part of the disk. The cross corresponds to the\nposition of the cross in the WFPC2 image and indicates the central\noptical concentration. Fitting an ellipse to the lowest H I contours\nindicates a position angle of 80$^\\circ$, an inclination of 37$^\\circ$\nafter a first order beam smearing correction, and puts the center of the\nH I disk at (23$^{\\rm h}$33$^{\\rm m}$30.0$^{\\rm s}$,\n12$^\\circ$36$^\\prime$4$^{\\prime\\prime}$), 7 arcseconds ($<$ 1 beam\nwidth) north of the central optical concentration. \n\nThe middle right panel shows the radial H I column density distribution,\nazimuthally averaged over the northern and southern sides separately.\nClearly, the H I surface density falls off more sharply at the southern\nedge, going from 10 to 0.5 x 10$^{20}$ atoms cm$^{-2}$ within two beam\nwidths. \n\nThe lower left panel shows the H I velocity field. Apart from some\nobvious wrinkles due to non-circular or streaming motions, the velocity\nfield is dominated by solid body rotation. This makes it impossible to\ndetermine the dynamical center and inclination from the velocity field\nand therefore the optical center (cross) was adopted as the dynamical\ncenter. The thick line indicates the adopted systemic isovelocity\ncontour at 6185.7 \\kms\\ while the black contours indicate the\napproaching side and the white contours the receding side of the galaxy.\n The isovelocity contour intervals are set at $\\pm$n$\\times$5 \\kms. \n\nThe lower right panel presents the position-velocity diagram along the\nkinematic major axis. Contours are drawn at -4, -2 (dashed), 2, 4, 8,\n12, 16 and 20 times the rms noise level. The vertical dashed line\ncorresponds to the position of the cross in the left panels, the\nhorizontal dashed line corresponds to the adopted systemic velocity. \nThe cross in the lower left corner indicates the beam. All profiles in\nthe vertical direction can be well described by single Gaussians. No\ndouble profiles are observed. The solid points show the derived\nrotation curve projected onto the position-velocity diagram. The\nrotation curve was derived by fitting full tilted rings to the velocity\nfield, effectively azimuthally averaging the wrinkles. Consequently,\nthis azimuthally averaged rotation curve might deviate locally from the\nposition-velocity slice. \n\nThe rotation curve of UGC 12695 is tabulated in Table~3. Fitting a\nsingle, galaxy wide ring to the entire velocity field gives a position\nangle of the kinematic major axis of 62 degree. The short thin lines\noutside the velocity field indicate this average kinematic major axis. \nNote the significant difference of 18 degrees between the kinematic and\nmorphological position angles of the outer H I disk. An inclination of\n40$^\\circ$ is adopted which is the average of the optical and H I\ninclinations. Given this rather face-on orientation of the disk, the\nuncertainty in the position of the dynamical center and the obvious\ndeviations from circular motions, we estimate the uncertainties in the\nrotation curve at some 20\\%. \n\n\n\\subsection {UGC 12687}\n\n\\begin{figure*}[p]\n\\epsfig{file=ovm.fig3.ps,width=16cm}\n\\caption{UGC 12687. See section 3.2 for explanations.}\n\\label{fig:U12687}\n\\end{figure*}\n\n\\begin{figure*}[p]\n\\epsfig{file=ovm.fig4.ps,width=16cm}\n\\caption{2333+1234. See section 3.3 for explanations.}\n\\label{fig:2333}\n\\end{figure*}\n\nThe upper left panel of Figure~\\ref{fig:U12687} shows the blue POSS-II\nimage of UGC 12687, a strongly barred two-armed spiral. The bar\ndynamics efficiently feeds gas to the nuclear region where a radio\ncontinuum source with a peak flux of 4.0$\\pm$0.6 mJy is found at 1.4 GHz\n(Condon {\\it et al}, 1998). An ultra-violet excess has been reported by\nKazarian \\& Kazarian (1985), suggesting a high level of star formation\nactivity. Nevertheless, the B$-$V=0.70 color from Prugniel \\& Heraudeau\n(1998) of UGC 12687 is considerably redder than that of UGC 12695. \n\nThe upper right panel shows the global H I profile which displays the\nclassical double-horned shape. Fluxes were measured in individual\nchannel maps including the central continuum source. Afterwards, a\n2.9~mJy/beam continuum baseline was subtracted from the global profile. \nUnfortunately, H I emission at the lower velocities is lost in the edge\nof the passband. To estimate total fluxes and line widths, the high\nvelocity edge was mirrored and, as an educated guess, put in place of\nthe missing low velocity side of the profile. This technique gives an\nintegrated flux density of 7.5 Jy km s$^{-1}$ or a total H I mass of\n1.2$\\times$10$^{10}$ M$_\\odot$. The inferred line widths are 296.7\n\\kms\\ at the 20\\% level and 255.4 \\kms\\ at the 50\\% level. Like UGC\n12695, UGC 12687 was imaged by Theureau, \\etal\\ (1998) with the\nNan\\c{c}ay telescope, with similar results -- the velocity widths of the\n Nan\\c{c}ay data matched ours well, but the total flux reported by \nTheureau, \\etal\\ was only 80\\% of our result. To check our data, we\nobtained a 5 minute ON/OFF pair with the Arecibo telescope using the\nL-narrow receiver. The Arecibo data and our VLA data again matched to\nwithin 5\\% in total flux.\n\nThe middle left panel displays the integrated column density map of UGC\n12687 constructed by adding the individual channel maps, including the\ncentral continuum source which was removed by subtracting a 2.9 mJy/beam\ncentral point source. Contour levels are drawn at 0.5, 1, 2, 4, 6, 8,\n10, 12, 14, 16 and 18$\\times$10$^{20}$ atoms cm$^{-2}$. The central\nhole in the H I map might be due to a slight overestimation of the\ncontinuum flux or might be caused by H I seen in absorption. \nFurthermore, the approaching south-eastern side of the galaxy is missing\nsome flux in the integrated H I map due to the bandpass effect mentioned\nabove. Nevertheless, it is clear that the H I gas in UGC 12687 is\nconcentrated near the tips of the bar and to some extent along both\noptically visible spiral arms. Fitting an ellipse to the outer H I\ncontours gives an axis ratio of (b/a)=0.72 and a position angle of 129.8\ndegrees centered on (23$^{\\rm h}$32$^{\\rm m}$45.2$^{\\rm s}$,\n12$^\\circ$38$^\\prime$54$^{\\prime\\prime}$). \n\nThe middle right panel shows the azimuthally averaged radial H I surface\ndensity profiles of the receding and approaching sides separately. Note\nthat the approaching side misses some flux around a radius of 1\narcminute. \n\nThe lower left panel shows the velocity field which suggests, at least\nin projection, a declining rotation curve in the inner regions. Fitting\ntilted rings gives a dynamical center at (23$^{\\rm h}$32$^{\\rm\nm}$45.4$^{\\rm s}$, 12$^\\circ$38$^\\prime$52$^{\\prime\\prime}$), a systemic\nvelocity of 6150.2 \\kms\\ (thick line), an inclination of 43$^\\circ$ and\na position angle of 297$^\\circ$. However, due to the strong bar,\nnon-circular motions are certainly present. No significant warp could\nbe detected. The isovelocity contours are plotted at intervals of\n$\\pm$n$\\times$20 \\kms. The inferred rotation curve of UGC 12687 is\ntabulated in Table~3.\n\nThe lower right panel shows the position-velocity diagram over the\nentire observed bandwidth along the kinematic major axis. The central\ncontinuum source has not been removed. Note how the low velocity gas is\nlost in the edge of the bandpass as well as the limited number of line\nfree channels at the high velocity side. Also note the occasional double\nprofiles. \n\n\\subsection{2333+1234}\n\nIn the VLA data cube, the H I emission of a tiny irregular dwarf low\nsurface brightness galaxy was discovered. Having discovered it first in\nH I, we were then able to discern the galaxy as a barely visible smudge\non the POSS-II plate (left panel of Figure~\\ref{fig:2333}). Fitting an\nellipse to the faintest POSS-II isophotes yields a size of\n17.5$\\times$7.2 arcsec and a position angle of 58$^\\circ$, centered on\n(23$^{\\rm h}$33$^{\\rm m}$8.9$^{\\rm s}$,\n12$^\\circ$34$^\\prime$39$^{\\prime\\prime}$). \n\nThe upper right panel shows the measured global H I profile with an\nintegrated flux of 0.33 Jy km s$^{-1}$ or a total H I mass of\n5.2$\\times$10$^8$ M$_\\odot$. The line widths are 92 \\kms\\ at the 20\\%\nlevel and 75 \\kms\\ at the 50\\% level.\n\nThe middle left panel shows the resolved integrated H I column density\nmap which seems to be slightly offset from the optical image. H I\ncontours are plotted at 0.5, 1, 2, 4 and 6$\\times$10$^{20}$ atoms\ncm$^{-2}$\n\nThe middle right panel shows the barely resolved radial H I surface\ndensity profile. No deconvolution attempt was made. \n\nThe lower left panel shows the velocity field which clearly indicates a\nvelocity gradient along the optical major axis. The optical center was\ntaken to be the dynamical center and a systemic velocity of 6192.5 \\kms\\\nwas inferred. Isovelocity contours are plotted in steps of\n$\\pm$n$\\times$10 \\kms. Obviously, trying to derive a rotation curve by\nfitting tilted rings is futile. \n\nThe lower right panel displays the position-velocity diagram through the\noptical center along the kinematic major axis, however, and the sign of\nsolid body rotation is evident. \n\n\n\\section{Dark and Visible Matter in UGC 12695}\n\n\\begin{table}[t]\n\\begin{center}\n\\caption{Inclination corrected rotation curves of UGC~12695 and\nUGC~12687.}\n\\begin{tabular}{ccccccc}\n\\noalign{\\vspace{0.8mm}}\n\\hline\n\\hline\n\\noalign{\\vspace{0.8mm}}\n &\\multicolumn{3}{c}{UGC~12695} & \\multicolumn{3}{c}{UGC~12687} \\\\\nR & V$_{\\rm rot}$ & incl. & P.A. & V$_{\\rm rot}$ & incl. & P.A. \\\\\n$\\prime\\prime$ & km/s & $\\circ$ & $\\circ$ & km/s & $\\circ$ & $\\circ$ \\\\\n\\hline\n\\noalign{\\vspace{0.8mm}}\n 10.7 & 17 & 40 & 62 & 195 & 43 & 297 \\\\\n 21.3 & 26 & 40 & 62 & 195 & 43 & 297 \\\\\n 32.0 & 32 & 40 & 62 & 195 & 43 & 297 \\\\\n 42.7 & 38 & 40 & 62 & 195 & 43 & 297 \\\\\n 53.3 & 45 & 40 & 62 & 179 & 43 & 297 \\\\\n 64.0 & 52 & 40 & 62 & 174 & 43 & 297 \\\\\n 74.7 & & & & 171 & 43 & 297 \\\\\n\\noalign{\\vspace{0.8mm}}\n\\hline\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\nPrevious studies of the dark and visible matter of LSB galaxies have\nshown them to be extremely dark matter dominated with respect to\n``normal'' HSB galaxies (i.e. Van Zee, \\etal 1997; De Blok \\& McGaugh\n1997, 1998). Thus, although the lack of any turn-over in UGC 12695's\nrotation curve makes it clear that we have not come close to determining\nthe full gravitational potential of the galaxy, it is still a worthwhile\nexercise to look at UGC 12695's total mass.\n\n\n\\begin{figure}[t]\n\\epsfig{file=ovm.fig5.ps,width=8.5cm}\n\\caption{LSB galaxy Tully-Fisher relation. The \nlines are the 1$\\sigma$ and 2$\\sigma$ fits to the data of Zwaan, \\etal\n(1995), and the circles are recent observations of LSB galaxies in the \nPegasus and Cancer groups from O'Neil, Bothun, \\& Schombert (1999). UGC \n12695 (using {\\it i} = 40\\degree) is shown as a diamond.}\n\\label{fig:tf}\n\\end{figure}\n\n\nClassic Newtonian mechanics states that the dynamical mass of a\nrotating, gravitationally bound object is simply\n\\[M_{dyn}\\:=\\:{{v^2\\:R}\\over{G\\:\\sin^2{\\it i}}}\\] where G is the\ngravitational constant. Using the maximum known velocity of UGC 12695\n(33/sin(40\\degree) km s$^{-1}$ at r=64''), this gives a total dynamical\nmass of 16 x 10$^{9}$\\Msol, while the determined H I flux gives a total\nH I mass of M$_{HI}$ = 7.5 x 10$^{9}$\\Msol. Although at first glance\nthese numbers hardly seem remarkable, they imply a considerable absence\nof dark matter for a LSB galaxy. Assuming a minimal disk scenario\n(M$_*$/L$_B$ = 0), and letting all the gas in the galaxy be neutral\nhydrogen and helium (M$_{gas}$ = 1.47$\\times$M$_{HI}$ =\n11$\\times$10$^9$\\Msol), gives a dark-to-total mass ratio of only\nM$_{DM}$/M$_{dyn}$ = 0.30. Using somewhat more realistic numbers by\nletting M$_*$/L$_B$ = 1, (a low-to-average LSB maximal disk value from\nVan Zee, \\etal\\ 1997 \\& De Blok \\& McGaugh 1997) reduces the dark matter\ncontribution to only 12\\% of the total dynamical mass of UGC 12695. \n(The luminosity value, L$_B$ = 2.86 $\\times$ 10$^9$ \\Msol, is derived\nfrom the value given in O'Neil, \\etal, 1998 which used integrated\naperatures. The error in L$_B$ is less than 1\\%.) For comparison, the\naverage M$_{DM}$/M$_{dyn}$ values for LSB galaxies from De Blok \\&\nMcGaugh is 0.6 for maximum disk scenarios, and for Van Zee, \\etal\\\n(1997) \\lb~M$_{DM}$/M$_{dyn}$\\gb = 0.7. Additionally, if the stellar\nmass-to-light ratio of UGC 12695 is increased to 1.7, a reasonable value\nfor both HSB and LSB galaxies, there is no need to invoke any dark\nmatter to explain the maximum {\\it observed} rotational velocity at the\nlast measured point of UGC 12695's rotation curve. It should be noted\nthat we were not able to observe any turn-over in UGC 12695's rotation\ncurve. Thus, unlike the Van Zee, \\etal\\ and De Blok \\& McGaugh samples\nwe are not determining the dynamical mass from the flat portion of the\nrotation curve but instead from the still rising portion. As such, it is\nextremely likely that dark matter will play a large role in UGC 12695's \nouter regions.\n\nIt should also be noted that the {\\it observed} velocity width of UGC\n12695 causes it to fall well off the standard Tully-Fisher relation,\nlying approximately 2.5 magnitudes (3$\\sigma$) above the LSB galaxy line\ndefined by Zwaan, \\etal\\ (1995) (Figure~\\ref{fig:tf}). This may be the\nconsequence of the apparent lack of dark matter in the observed portion\nof UGC 12695. On the other hand, it is quite likely that there is\nsignificant dark matter outside the observed radius (else the rotation\ncurve would show some turn over), and thus we are merely viewing a\nlower limit of the galaxy's rotational velocity. The uncertainty in UGC\n12695's inclination (see the next section) also makes the current\nlocation of UGC 12695 on the Tully-Fisher relation suspect and if the\ninclination is less than 40\\degree, UGC 12695 could move onto (or even\nto the right of) the Tully-Fisher relation of Zwaan, \\etal.\n\n\\section{Star Formation in UGC 12695}\n\n\\begin{figure*}[t] \n\\epsfig{file=ovm.fig6bmp.ps,width=17.5cm}\n\\caption{Left panel: HI contours of U12695 overlaid on the HST WFPC2\nF814W image. Right panel: HI contours of U12695 overlaid on the\nH$\\alpha$ image. The red contours indicate the critical HI column\ndensity of 1.6$\\times$10$^{20}$ and 6.0$\\times$10$^{20}$ cm$^{-2}$ above\nwhich star formation is expected based on Toomre's criterion (for {\\it\ni} = 40\\degree \\& 10\\degree, respectively), while the green contours are\nthe 10$^{21}$ cm$^{-2}$ level.}\n\\label{fig:U12695optHI}\n\\end{figure*} \n\nIt was demonstrated by Toomre (1964) that a thin, {\\it collisionless}\nstellar disk in circular motion becomes unstable if the surface mass\ndensity exceeds a critical value of \\[\\Sigma_c\\:=\\:\\alpha\\:{{\\kappa\n\\sigma}\\over{3.36 G}}\\] where $\\Sigma_c$ is the critical density,\n$\\sigma$ is the velocity dispersion, \\alp is a dimensionless constant\nnear 1, and $\\kappa$ is the epicyclic frequency of the gas, also written\nas \\[\\kappa\\:=\\:1.41\\:{V\\over R}\\:\\left(1\\:+\\:{R \\over\nV}{{dV}\\over{dR}}\\right)^{1/2}.\\] Cowie (1981) showed that this\ncriterion is also applicable to instabilities in a gaseous disk if\nembedded in a more massive stellar disk. Kennicutt (1989) determined an\nempirical value for \\alp of about 2/3. Typical HSB galaxies exceed this\ncritical surface density and form stars throughout most of their stellar\ndisks. \n\nAs an LSB galaxy which appears to be in the midst of considerable but\nlocalized star formation, UGC 12695 is an ideal case on which to test\nthis star formation threshold theory. Before this can be done, though,\n$\\kappa$ and $\\sigma$ must be determined. From the rotation curve of\nUGC 12695 it is apparent that its near solid body rotation makes\ndetermining $\\kappa$ relatively easy. Approximating the rotation curve\nas pure solid body with an inclination corrected amplitude of 57 \\kms\\ \nat a radius of 22 kpc yields $\\kappa$=5.2 \\kms\\ kpc$^{-1}$ (using the\nfact that for a gas disk in pure solid body rotation,\n${{dV}\\over{dR}}={V\\over R}$ and $\\kappa={{2V}\\over{R}}$). Due to beam\nsmearing the velocity dispersion is hard to measure from the data and a\ncanonical dispersion of $\\sim$8 \\kms\\ is assumed as an average estimate\n(8 \\kms\\ is also observed in several highly resolved face-on gas disks).\n This leads to a critical surface mass density of\n$\\Sigma_c\\:=\\:4.0\\times10^{-3}$ kg m$^{-2}$. Taking a 32\\% helium mass\nfraction into account, this corresponds to a critical H I column density\nof 1.6$\\times$10$^{20}$ atoms cm$^{-2}$ (i.e. between the 1st and 2nd\ncontours in Figure~\\ref{fig:U12695optHI}) above which star formation is\nto be expected. This implies that everywhere throughout the disk of UGC\n12695 star formation should occur. \n\n\\begin{figure*}[t]\n\\epsfig{file=ovm.fig7.ps,width=17.5cm}\n\\caption{The azimuthally averaged observed gas \ndensity, Toomre star formation threshold, and rotation curves of UGC\n12695 for an assumed galaxy inclination of 40\\degree, 25\\degree, and\n10\\degree (left to right).}\n\\label{fig:azav}\n\\end{figure*}\n\nHowever, we only observe star formation in a limited number of localized\nregions near the very peaks of the H I column density distribution where\nit reaches levels of 1$\\times$10$^{21}$ atoms cm$^{-2}$. This is\nillustrated in Figure~\\ref{fig:U12695optHI} which shows in the left\npanel the HI column density map overlaid on a false-color WFPC2 F814W\nimage and in the right panel the same H I contours overlaid on a\ngreyscale MDM-1.3m H$\\alpha$ image. The lower red contour indicates the\ncritical column density of 1.6$\\times$10$^{20}$ atoms/cm$^2$. Obviously,\nthe theoretically derived and empirically adjusted critical surface\ndensity is clearly not applicable to the low metallicity, irregular gas\ndisk of UGC 12695. \n\nOne of the more curious aspects of the Kennicutt-Cowie-Toomre star\nformation criterion is that it successfully works at all, considering\nthe number of physical processes which affect the value of $\\Sigma_c$. \nFor example, disks are not infinitely thin but have a certain thickness\nwhich could increase or decrease the column density thresholds and alter\nthe radial instabilities. That is, if the volume gas density is\nsignificantly different than the surface gas density of UGC 12695, a\nvolume-density dependent Schmidt law would be more appropriate than the\nKennicutt/Cowie/Toomre star formation criterion used above (i.e.\nFerguson, \\etal\\ 1998). Additionally, there is energy dissipation,\nmagnetic field lines, etc. which should also affect $\\Sigma_c$ (i.e.\nHunter, Elmegreen, \\& Hunter 1998). Thus it is not surprising that UGC\n12695, and in fact many LSB galaxies, do not adhere to the Toomre\ncriterion (i.e. Van Zee, \\etal\\ 1997; Van der Hulst, \\etal\\ 1993).\n\nWhat is interesting is that UGC 12695, like many LSB and dwarf galaxies,\nforms stars only where the local H I column density exceeds 10$^{21}$\natoms cm$^{-2}$. In fact, Skillman (1986) pointed out that the actually\nobserved {\\em local} H I column density threshold for star formation, at\na resolution of 500 pc, is about 1$\\times$10$^{21}$ atoms cm$^{-2}$ and\nroughly 5$\\times$10$^{21}$ atoms cm$^{-2}$ for star formation events of\nthe order of 30 Doradus. This local H I column density threshold\nappears to be in better agreement with the observations of UGC 12695\n(i.e. note the green contours in Figure~\\ref{fig:U12695optHI}), although\nthe beam size makes a detailed analysis impossible. (The H$\\alpha$ data\nof McGaugh 1994 is not photometric, making determination of UGC 12695's\nH II luminosity difficult. It should be noted, though, that attempts to\ndetect faint diffuse H-$\\alpha$ regions have not been successful,\nmaking it unlikely that any widespread component of faint star-forming\nregions has been missed.)\n\nUnlike our sample, a previous study by Van der Hulst, \\etal\\ (1993)\nfound their sample of low surface galaxies to be generally consistent\nwith the Kennicutt-Toomre criterion for star formation. Perhaps the\nmost important difference between this study of UGC 12695 and the Van\nder Hulst, \\etal\\ results is that Van Der Hulst, \\etal\\ used azimuthally\naveraged radial H I surface density profiles. Figure~\\ref{fig:azav}\nshows the results of applying Van der Hulst, \\etal's method to UGC 12695\nfor a variety of possible inclinations (see below). As can be seen, even\nby ignoring the extremely asymmetric nature of UGC 12695, only the most\nextreme case ({\\it i}=10\\degree) does UGC 12695 come close to falling\nbelow the critical density for star formation anywhere but in the\noutermost isophotes. This sort of study, though, disallows for any\nanalysis of the local star forming potential of UGC 12695 while hiding\nthe exceptionally asymmetric nature of galaxy.\n\n\n\\begin{figure*}[p]\n\\hspace{-1cm}\n\\epsfig{file=ovm.fig8bmp.ps,width=18.5cm}\n\\caption{Zooming in on the main star formation regions in in UGC~12695.\nThe upper row shows the star formation complexes in the eastern side of\nthe galaxy. Those in the western side are shown in the bottom row. The\nwhite contours are from the VLA H I map while the yellow contours are\nfrom the MDM-1.3m H$\\alpha$ image.}\n\\label{fig:U12695SFs}\n\\end{figure*}\n\n\nAt this point, it is important to consider the uncertainties involved\nin calculating $\\Sigma_C$. Most notably, we should take another look at\nUGC 12695's assumed inclination. It is certainly possible that UGC\n12695's shape truly is circular, thus validating the inclination value\nused in the previous calculations (40\\degree). If, however, UGC 12695\nhas recently tidally interacted with UGC 12687, as discussed below, the\nperceived inclination may be overestimated in that UGC 12695 may have\nbeen distorted (and `flattened') by the interaction (e.g. see Figure 2\nof Mihos, \\etal, 1997). In this case the true inclination of UGC 12695\nmay be considerably less than we have assumed, thereby raising the \nvalue of $\\Sigma_C$. As an example, if UGC 12695's true inclination is\n10\\degree, the critical density will increase to\n$\\Sigma_C\\:=\\:6\\times10^{20}$ atoms cm$^{-2}$. In this case, although\nthe critical density and the density at which star formation is observed\nstill would not precisely coincide, they would lie considerably closer \ntogether (i.e. the higher red contour in Figure~\\ref{fig:U12695optHI}). \nIf, in addition to the above correction to {\\it i}, our estimate of\n$\\kappa$ is off by a factor of 60\\% (3$\\sigma$) due to inclination\nuncertainties and the rotation curve shape, the critical density would\nreadily be raised to 10$^{21}$ atoms cm$^{-2}$, the observed local H I\ncolumn density threshold for star formation of Skillman (1986). Of\ncourse, if the inclination correction is off in the other direction, \nand {\\it i}=50\\degree, $\\Sigma_C$ would be reduced even more, raising\nagain the question of why UGC 12695 is LSB.\n\nIt is noteworthy to point out that the three local peaks in the neutral\nhydrogen of UGC 12695 lie near, but not on top, the primary star\nformation regions of the galaxy, as defined by the H-\\alp image of\nMcGaugh (1994). This is illustrated in Figure~\\ref{fig:U12695SFs} which\ndisplays in the left panels the white VLA H I contours on the color\nWFPC2 F814W image, in the middle panels the yellow MDM-1.3m H$\\alpha$\ncontours on the WFPC2 image and in the right panels the combined H I and\nH$\\alpha$ contours on the WFPC2 image.\n\nFigure~\\ref{fig:U12695SFs} shows that there seems to be a clear offset\nbetween the highest peaks in the H I column density at 1.2 x 10$^{21}$\ncm$^{-2}$ and the location of the primary H$\\alpha$ complexes. The\nlargest star clusters seem to surround the regions with the highest HI\ncolumn densities. However, the relatively poor spatial resolution of\nthe current H I observations is insufficient to draw any further\nconclusions on the relation between the H I peaks and the H$\\alpha$\nregions.\n \nThe colors of those regions, as provided by the WFPC2 images, also put\nthe star-formation peaks away from the H I peaks, with the left two H I\npeaks having F300W $-$ F814W = $-$0.06 and $-$2.82, versus $-$3.27 and\n$-$3.14 for the corresponding H-\\alp peaks (top and bottom,\nrespectively). (These colors roughly correspond to U $-$ I colors of\n1.42, $-$1.34, $-$1.79. and $-$1.66, respectively (i.e. O'Neil, \\etal\n1998).) The third H I peak, at the bottom right of\nFigure~\\ref{fig:U12695optHI}, lies in the extremely noisy PC chip of the\nWFPC2 image, making the determination of colors in that region extremely\ndifficult. Thus the neutral hydrogen is behaving as expected -- as star\nformation occurs the surrounding gas is ionized, shifting the peak in\nthe neutral hydrogen distribution to the edge of the star forming\nregions. \n\n\n\\section{Are UGC~12695 and UGC~12687 Ti-dally Interacting?}\n\nThe close proximity of UGC 12695 and UGC 12687 in redshift space, the\nlopsided morphology of UGC 12695 and its slightly skewed kinematics, \nimmediately brings to mind the possibility of a tidal interaction\n(Figure~\\ref{fig:Allposs2HI}). Additionally, the presence of 2333+1234\nlying between the two galaxies suggests it may have been formed as a\ntidal remnant. (Of course, 2333+1234 may simply be a naturally\noccurring representative of the faint-end of the luminosity function.) \n\nIn 1997 Mihos, McGaugh, \\& De Blok argued that LSB and HSB galaxies of\nthe same total mass are equally susceptible to local disk instabilities\nbut that LSB galaxies are far less responsive to global instabilities\nthan their HSB counterparts. This difference is mainly due to the\nstabilizing nature of the relatively more massive dark matter halo in\nwhich the LSB disk is embedded. To test their hypothesis, they modeled\na strong prograde tidal encounter between an LSB and an HSB disk galaxy\nof similar mass. After the encounter the HSB galaxy exhibited two\ndefinitive spiral arms, a central inflow of gas and an oval central\nregion. Presumably, the HSB system was in the midst of, or had recently\nundergone, a large burst of star formation in its core. Being more\nstable than its HSB counterpart, the LSB galaxy displayed a milder, yet\nsignificant response. Although the encounter strongly perturbed the LSB\ngalaxy, it did not result in a central gas inflow. However, it did\ninduce long-lived spiral arms, an overall lopsided distortion of the\ngalaxy, and possibly localized compressions and instabilities in the\ndisk. \n\nThe observed morphologies of UGC 12695 and UGC 12687 show a striking\nresemblance to the numerical simulations of Mihos \\etal\\ at the time\nstamp T=36 (see their Figure~2). Their HSB system (UGC 12687 in our\ncase) shows a strong bar from which two well defined spiral arms emerge.\n UGC~12687's observed morphology is in close agreement with their\nresults while its central continuum emission and UV-excess indicate a\nconsiderable nuclear star formation activity, hinting at well developed\nbar kinematics efficient in fueling H I to the central region. In the\ncase of the LSB galaxy, the numerical simulations display a sharp\nstellar edge on one side of the disk and a more diffuse gradient on the\nother side while a highly variable structure in the mass surface density\nhints at strong local instabilities. Observationally, UGC 12695's\nextremely blue colors, highly asymmetric gas and star distribution, and\nregions of intense local star formation also match the model predictions\nextremely well. In fact, without relying on some sort of external\ntrigger the observed morphology and color of UGC 12695 is extremely\ndifficult to explain. \n\nIn spite of the above assertions, a number of arguments against any\nmajor tidal encounter between these two galaxies must be considered. \nThe first, and perhaps most obvious of these is the apparently settled\nkinematics of both UGC 12695 and UGC 12687. At first glance it would\nseem that if the two galaxies have interacted recently enough for the\ntidally-induced star formation to be at, or near, its peak the galaxies\nwould still exhibit highly agitated kinematics. A study by V\\'azquez\nand Scalo (1989), though, has shown that starbursts do not typically\noccur during the gas compression stage but in fact occur well after the\ngas has re-established. In other words, the V\\'azquez and Scalo model\nsuggests that disks can have tidally induced star formation well after\nthe gas has kinematically re-settled. \n\nA second argument which could be put forward against the idea of the two\ngalaxies having recently undergone a tidal interaction is simply this --\nif UGC 12695 is experiencing a burst of localized star formation due to\na recent tidal encounter, should it not be experiencing a corresponding\nrise in central surface brightness? A recent paper by O'Neil, Bothun, \\&\nSchombert (1998) tested this idea through modeling a wide variety of LSB\ngalaxies experiencing localized starbursts. Their results were quite\ndefinitive -- if a galaxy forms as a LSB galaxy, due to a high angular\nmomentum giving rise to a low gas surface density etc., it will remain a\nLSB galaxy barring any major encounter catastrophe. Thus it is quite\nbelievable that UGC 12695 could be undergoing significant localized star\nformation activity and yet not be undergoing any significant change in\nits global surface brightness. \n\nThe final argument against UGC 12695 and UGC 12687 having undergone a\nsignificant tidal interaction in the recent past comes from examining\nthe smoothed data cube. Not a trace of extended H I gas above a minimal\ndetectable column density of 2$\\times$10$^{19}$ atoms cm$^{-2}$\n(3$\\sigma$) can be found besides the rotating gas disks of the three\nidentified galaxies. This leads to the conclusion that no major tidal\ntails were ever formed in any past interaction between the two systems. \n\n\n\\section{Conclusion}\n \nUGC 12695 is an intriguing low surface brightness galaxy of a very\ntransparent nature, having an extremely blue color, a highly asymmetric\nappearance and very localized bursts of star formation near the peaks in\nthe H I column density distribution.\n\nMany of the properties of both UGC 12687 and UGC 12695 can be explained\nas being induced by such a tidal interaction, including the bar of UGC\n12687 and its central radio continuum emission and UV excess as well as\nthe lopsided appearance of UGC 12695 and the offset between its\nmorphological and kinematic major axes. Furthermore, the localized\nbursts of star formation in UGC 12695 could very well be induced by such\nan interaction, giving rise to local instabilities in the LSB disk as\ndemonstrated by Mihos \\etal (1997). \n\nIt is likely that UGC 12695 could have been living a fairly quiescent\nexistence, its low surface gas density keeping its star formation rate\nquite low, and just now it is experiencing a period of localized but\nvigorous star formation triggered by a mild tidal interaction which\nmight lead to a major morphological transition. \n\nWithin all this, though, it is easy to overlook one important fact. \nAlthough many of the properties of UGC 12695 and UGC 12687 can readily\nbe explained through an ongoing tidal encounter, the two galaxies are\nstill fundamentally distinct. UGC 12695 is not simply a fainter, or\nmore `stretched-out', or more quickly rotating version of UGC 12687. \nWere any of these the case the behavior of the two galaxies after the\ntidal encounter would be similar, and UGC 12695 would have experienced a\ncentral gas inflow with the majority of its star formation now occurring\nnot in the outlying regions (as it is), but in the galaxy's core. Thus\nthe fundamental question of why UGC 12695 is an LSB galaxy, and UGC\n12687 is not remains unanswered. \n\n\n\\section{Acknowledgments}\n\nThe Very Large Array is a facility of the National Radio Astronomy\nObservatory, a facility of the National Science Foundation operated\nunder cooperative agreement by Associated Universities, Inc. The\nDigitized Sky Surveys were produced at the Space Telescope Science\nInstitute under U.S. Government grant NAG W-2166. The images of these\nsurveys are based on photographic data obtained using the Oschin Schmidt\nTelescope on Palomar Mountain and the UK Schmidt Telescope. The plates\nwere processed into the present compressed digital form with the\npermission of these institutions. \n\n\n\\section*{References}\n\n\\noindent\n Condon, \\etal, 1998, AJ, 115, 1693\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Cowie, L., 1981, ApJ, 245, 66\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n De Blok, W.J.G. \\& Van der Hulst, J.M., 1998, A\\&A, 336, 49\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n De Blok, W.J.G. \\& McGaugh, S., 1998, ApJ, 499, 41\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n De Blok, W.J.G. \\& McGaugh, S., 1997, MNRAS, 290, 533\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Ferguson, H., \\& McGaugh, S., 1995, ApJ, 440, 470\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Ferguson, A. \\etal, 1998, ApJ, 506, L19\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Kazarian, M.A. \\& Kazarian, E.S., 1985, Afz, 22, 431\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Kennicutt, R., 1989, ApJ, 344, 685\\\\ \n\n\\vspace{-3.5mm}\n\\noindent\n Hunter, D., Elmegreen, B. \\& Baker, A., 1998, ApJ, 493, 595\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Matthews, L., \\& Gallagher, J., 1997, AJ, 114, 1899\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n McGaugh, S., 1994, ApJ, 426, 135\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Mihos, C., McGaugh, S., \\& De Blok, W.J.G, 1997, ApJ, 477L, 79\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n O'Neil, K, Bothun, G., \\& Schombert, J., 1999, AJ, in press\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n O'Neil, K., Bothun, G., \\& Schombert, 1998, AJ, 116, 2776\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n O'Neil, K., \\etal, 1998, AJ, 116, 657\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n O'Neil, K., Bothun, G., \\& Cornell M., 1997b, AJ, 113, 1212\\\\ \n\n\\vspace{-3.5mm}\n\\noindent\n O'Neil, K., \\etal, 1997a, AJ, 113, 1212\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Prugniel, P. \\& Heraudeau, P., 1998, A\\&AS, 128, 299\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Schombert, J. \\etal, 1990, AJ, 100, 1533\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Skillman, E.D., 1986, in \"{\\it Star Formation in Galaxies}\", C.J. Lonsdale (ed), NASA Conference Publication 2466, 263\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Theureau, G., \\etal, 1998, A\\&AS, 130, 333\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Schneider, S., \\etal, 1990, ApJS, 72, 245\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Toomre, A., 1964, ApJ, 139, 1217\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n De Vaucouleurs, G. \\etal, 1991, {\\it The Third Reference Catalog of Bright Galaxies}, Springer-Verlag: New York\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Van der Hulst, J.M., \\etal, 1993, AJ, 106, 548\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Van Zee, L., \\etal, 1997, AJ, 113, 1618\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n V\\'azquez, E. \\& Scalo, J.M., 1989, ApJ, 343, 644\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Zwaan, M., Van der Hulst, J., De Blok, W., \\& McGaugh, S.S., 1995, MNRAS, 273, L35\\\\\n\n\n\\end{document}\n"}],"string":"[\n {\n \"name\": \"ovm.astroph.tex\",\n \"string\": \"\\\\documentclass[11pt]{article}\\n\\n\\\\newcommand{\\\\vcirc}{$\\\\rm v_{circ}$ }\\n\\\\newcommand{\\\\elec}{$\\\\rm e^{-}$ }\\n\\\\newcommand{\\\\rarr}{$\\\\rightarrow$ }\\n\\\\newcommand{\\\\larr}{$\\\\leftarrow$ }\\n\\\\newcommand{\\\\Delt}{$\\\\rm \\\\Delta$}\\n\\\\newcommand{\\\\emo}{$\\\\rm \\\\mu _{814} (0)$}\\n\\\\newcommand{\\\\emu}{$\\\\rm \\\\mu _{814}$}\\n\\\\newcommand{\\\\tmo}{$\\\\rm \\\\mu _{300}$}\\n\\\\newcommand{\\\\mo}{$\\\\rm \\\\mu _{0}$}\\n\\\\newcommand{\\\\MgL}{\\\\rm $\\\\rm M_{gas}/L_T$ }\\n\\\\newcommand{\\\\ML}{\\\\rm $\\\\rm M_T/L_T$ }\\n\\\\newcommand{\\\\MgM}{\\\\rm $\\\\rm M_{gas}/M_T$ }\\n\\\\newcommand{\\\\Lt}{\\\\rm $\\\\rm L_T$}\\n\\\\newcommand{\\\\mss}{mag arcsec$^{-2}$}\\n\\\\newcommand{\\\\Bmoi}{\\\\rm ${\\\\mu_{B_{i}}}$(0) }\\n\\\\newcommand{\\\\plm}{$\\\\pm$ }\\n\\\\newcommand{\\\\lb}{$\\\\langle \\\\:$}\\n\\\\newcommand{\\\\gb}{$\\\\rangle \\\\:$}\\n\\\\newcommand{\\\\lt}{$< \\\\:$}\\n\\\\newcommand{\\\\gt}{$> \\\\:$}\\n\\\\newcommand{\\\\lta}{$\\\\leq $}\\n\\\\newcommand{\\\\gta}{$\\\\geq $}\\n\\\\newcommand{\\\\Bmu}{\\\\rm $\\\\mu_B \\\\:$}\\n\\\\newcommand{\\\\Rmu}{\\\\rm $\\\\mu_R \\\\:$}\\n\\\\newcommand{\\\\Imu}{\\\\rm $\\\\mu_I \\\\:$}\\n\\\\newcommand{\\\\Umu}{\\\\rm $\\\\mu_U \\\\:$}\\n\\\\newcommand{\\\\Vmu}{\\\\rm $\\\\mu_V \\\\:$}\\n\\\\newcommand{\\\\Bmo}{\\\\rm ${\\\\mu _B}$(0) }\\n\\\\newcommand{\\\\Imo}{\\\\rm ${\\\\mu _I}$(0) }\\n\\\\newcommand{\\\\Vmo}{\\\\rm ${\\\\mu _V}$(0) }\\n\\\\newcommand{\\\\Ho}{\\\\rm H$_0$ }\\n\\\\newcommand{\\\\Bmag}{\\\\rm B$\\\\rm _{mag}$ }\\n\\\\newcommand{\\\\Bt}{\\\\rm B$\\\\rm _T$(0) }\\n\\\\newcommand{\\\\mt}{\\\\rm m$\\\\rm _T$ }\\n\\\\newcommand{\\\\muo}{\\\\rm ${\\\\mu}$(0) }\\n\\\\newcommand{\\\\rts}{\\\\rm $\\\\rm r_{27}$ }\\n\\\\newcommand{\\\\rtf}{\\\\rm $\\\\rm r_{25}$ }\\n\\\\newcommand{\\\\Vc}{{V$_{circ}$\\\\ }}\\n\\\\newcommand{\\\\Halp}{H$_{\\\\alpha}$\\\\ }\\n\\\\newcommand{\\\\alp}{$\\\\alpha$\\\\ }\\n\\\\newcommand{\\\\etal}{{\\\\it et.al.}}\\n\\\\newcommand{\\\\degree}{$^{\\\\circ}$ }\\n\\\\newcommand{\\\\arcs}{\\\\rm arcsec$^2$}\\n\\\\newcommand{\\\\teff}{\\\\rm T$_{eff}$\\\\ }\\n\\\\newcommand{\\\\kmsec}{km sec$^{-1}$\\\\ }\\n\\\\newcommand{\\\\kms}{km sec$^{-1}$\\\\ }\\n\\\\newcommand{\\\\app}{$\\\\sim$}\\n\\\\newcommand{\\\\eg}{{\\\\em e.\\\\ g.\\\\ }}\\n\\\\newcommand{\\\\ie}{{\\\\em i.\\\\ e.\\\\ }}\\n\\\\newcommand{\\\\mn}{{\\\\em MNRAS\\\\ }}\\n\\\\newcommand{\\\\solarm}{$M_{\\\\odot}$\\\\ }\\n\\\\newcommand{\\\\Msol}{$M_{\\\\odot}$\\\\ }\\n\\\\newcommand{\\\\Zsol}{$Z_{\\\\odot}$\\\\ }\\n\\\\newcommand{\\\\Lsol}{$L_{\\\\odot}$\\\\ }\\n\\\\newcommand{\\\\fivesixco}{$^{56}$Co\\\\ }\\n\\\\newcommand{\\\\chisq}{${\\\\chi}^{2}$\\\\ }\\n\\\\newcommand{\\\\chinusq}{${\\\\chi}_{\\\\nu}^{2}$\\\\ }\\n\\\\newcommand{\\\\bvzero}{\\\\rm (B-V)$_{\\\\circ}$\\\\ }\\n\\\\newcommand{\\\\feh}{\\\\rm [Fe/H]\\\\ }\\n\\\\newcommand{\\\\lsb}{\\\\rm low surface brightness}\\n\\\\newcommand{\\\\hsb}{\\\\rm high surface brightness}\\n\\\\newcommand{\\\\lsbg}{\\\\rm low surface brightness galaxy}\\n\\\\newcommand{\\\\lsbgs}{\\\\rm low surface brightness galaxies}\\n\\\\newcommand{\\\\PMO}{\\\\rm Pine Mountain Observatory}\\n\\n\\\\usepackage{apjfonts}\\n\\\\usepackage{float}\\n\\\\usepackage{multicol}\\n\\\\usepackage{epsfig}\\n\\n\\\\textwidth=17.5cm\\n\\\\textheight=23.5cm\\n\\\\voffset=-2.5cm\\n\\\\hoffset=-2.54cm\\n\\n\\\\columnsep=7mm\\n\\\\evensidemargin=25mm\\n\\\\oddsidemargin=21mm\\n\\n\\\\renewcommand{\\\\baselinestretch}{0.87}\\n\\\\renewcommand{\\\\topfraction}{0.99}\\n\\\\renewcommand{\\\\bottomfraction}{0.99}\\n\\\\renewcommand{\\\\textfraction}{0.01}\\n\\n\\\\begin{document}\\n\\n\\\\twocolumn[\\n\\\\null\\n\\\\vspace{-1cm}\\n\\n\\\\begin{center}\\n\\\\noindent\\n\\n{\\\\Large \\\\bf Star Formation and Tidal Encounters with the Low Surface\\nBrightness Galaxy UGC 12695 and Companions}\\n\\n\\\\vspace{1cm}\\n\\nK. O'Neil$^1$, M.A.W. Verheijen$^2$, S.S. McGaugh$^3$ \\\\\\\\\\n\\n\\\\end{center}\\n\\n\\\\vspace{1cm}\\n\\n$^1$Arecibo Observatory, HC03 Box 53995, Arecibo, PR 00612, email:koneil@naic.edu \\\\\\\\\\n$^2$National Radio Astronomy Observatory, Box 0, Socorro, NM 87801, email:mverheij@nrao.edu \\\\\\\\\\n$^3$Department of Astronomy, University of Maryland, College Park, MD 20742, email:ssm@astro.umd.edu \\\\\\\\\\n\\n\\\\vspace{0.5cm}\\n\\n\\\\begin{flushright}\\n\\n\\\\parbox{13.3cm}{{\\\\large\\\\noindent{\\\\bf\\\\sf ABSTRACT-- }}\\nWe present VLA H I observations of the low surface brightness galaxy UGC\\n12695 and its two companions, UGC 12687 and a newly discovered dwarf\\ngalaxy 2333+1234. UGC 12695 shows solid body rotation but has a very\\nlopsided morphology of the H I disk, with the majority of the H I lying\\nin the southern arm of the galaxy. The H I column density distribution\\nof this very blue, LSB galaxy coincides in detail with its light\\ndistribution. Comparing the H I column density of UGC 12695 with the\\nempirical (but not well understood) value of $\\\\Sigma_c$ = 10$^{21}$\\natoms cm$^{-2}$ found in, i.e., Skillman's 1986 paper shows the star\\nformation to be a local affair, occurring only in those regions where\\nthe column density is above this star formation threshold. The low\\nsurface brightness nature of this galaxy could thus be attributed to an\\ninsufficient gas surface density, inhibiting star formation on a more\\nglobal scale. Significantly, though, the Toomre criterion places a\\nmuch lower critical density on the galaxy ($\\\\sim$10$^{20}$ atoms\\ncm$^{-2}$), which is shown by the galaxy's low SFR to not be applicable.\\n\\nWithin a projected distance of 300 kpc/30 \\\\kms\\\\ of UGC 12695 lie two\\ncompanion galaxies -- UGC 12687, a high surface brightness barred spiral\\ngalaxy, and 2333+1234, a dwarf galaxy discovered during this\\ninvestigation. The close proximity of the three galaxies, combined with\\nUGC 12695's extremely blue color and regions of localized starburst and\\nUGC 12687's UV excess bring to mind mutually induced star formation\\nthrough tidal activity. } \\n\\\\end{flushright} \\n\\n\\\\vspace{0.5cm}\\n\\n\\\\noindent\\n{\\\\it Subject headings:} \\ngalaxies: individual(UGC 12695, UGC 12687, 2333+1234) \\n-- galaxies: spiral\\n-- galaxies: evolution \\n-- galaxies: interactions\\n-- galaxies: kinematics and dynamics\\n-- galaxies: structure\\n\\n\\\\null\\n\\\\vspace{0.5cm}\\n]\\n\\n\\\\setcounter{footnote}{0}\\n\\\\footnotetext{To be published in The Astronomical Journal, May 2000}\\n\\n\\\\newpage\\n\\n\\n\\\\begin{figure*}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=ovm.fig1bmp.ps,width=17cm}\\n\\\\caption{H I contours of all three galaxies overlaid on a POSS-II\\nimage.}\\n\\\\label{fig:Allposs2HI}\\n\\\\end{center}\\n\\\\end{figure*}\\n\\n\\n\\\\section{Introduction}\\n\\nAttempts to understand star formation in low surface brightness (LSB)\\ngalaxies has resulted in a large number of theories being discarded and\\nfew alternatives being offered. As a result we have considerable\\nknowledge on what these enigmatic systems are not. LSB galaxies are\\n{\\\\em not}:\\n\\n\\\\begin{itemize}\\n\\n\\\\item simply the faded version of high surface brightness (HSB)\\ngalaxies. Although some red LSB galaxies have been found which may be\\nthe end product of the faint blue galaxies, the majority of LSB galaxies\\nhave very blue colors and low metallicities (i.e. Ferguson \\\\& McGaugh\\n1995; O'Neil, \\\\etal 1997a; McGaugh 1994; Schombert, \\\\etal 1990; De Blok\\n\\\\& Van der Hulst 1998), arguing against any fading scenario. \\n\\n\\\\item lacking the neutral hydrogen necessary to form stars, as many LSB\\ngalaxies contain more than 10$^9$ \\\\Msol of H I and LSB galaxies include\\nsome of the highest M$_{HI}$/L$_B$ galaxies known (O'Neil, Bothun, \\\\&\\nSchombert 1999). \\n\\n\\\\item a completely new type of galaxy. The transition from HSB to LSB\\ngalaxies is smooth, with LSB galaxies covering the entire color and\\nmorphological spectrum of HSB galaxies (i.e. O'Neil, \\\\etal 1997b;\\nMatthews \\\\& Gallagher 1997)\\n\\n\\\\end{itemize}\\n\\nUGC 12695 is a relatively nearby (z=0.021) low surface brightness galaxy\\nwith an absolute blue magnitude of M$_B$=$-$18.9. Previous studies of\\nUGC 12695 (McGaugh, 1994; O'Neil \\\\etal, 1998) have shown it to be very\\nremarkable. The galaxy is of an exceedingly transparent nature,\\nevidenced by the many background galaxies seen through its elusive disk,\\nand it contains a reasonably high gas fraction (M$_{HI}$/L$_B$ = 2.6\\n\\\\Msol/\\\\Lsol) while having a very low metallicity and an extremely blue\\ncolor for a galaxy ($U-I$ = $-0.2$) (Table 1). \\n\\nBecause UGC 12695 was thought to be fairly isolated, with the nearest\\ngalaxy (UGC 12687) lying more than 277 kpc away\\n(Figure~\\\\ref{fig:Allposs2HI}), it provides a good opportunity for\\nstudying star formation and evolution in LSB galaxies. To this end, and\\nwith the above points in mind, we undertook to observe UGC 12695 with\\nthe Very Large Array (VLA) in the C configuration. The results of these\\nobservations are described in this paper, as follows: Section 2\\ndescribes the observations and data reduction; Section 3 examines the H\\nI morphology and kinematics of UGC 12695 and its companions -- UGC\\n12687, and 2333+1234; Section 4 looks at the dark and visible mass of\\nUGC 12695; Section 5 examines the star formation potential of UGC\\n12695; Finally, section 6 examines the possibility of a recent tidal\\nencounter between the UGC galaxies. \\n\\n\\\\begin{table}[ht]\\n\\\\begin{center}\\n\\\\caption{Global properties of UGC~12695 and UGC~12687.}\\n\\\\begin{tabular}{lccc}\\n\\\\noalign{\\\\vspace{0.8mm}}\\n\\\\hline\\n\\\\hline\\n\\\\noalign{\\\\vspace{0.8mm}}\\n & & UGC~12695 & UGC~12687 \\\\\\\\\\n\\\\hline\\n\\\\noalign{\\\\vspace{0.8mm}}\\nType & & Sm$^1$ & SBbc$^1$\\\\\\\\\\nV$_{hel}$ & km s$^{-1}$& 6186$^2$& 6150$^2$\\\\\\\\\\nM$_B$ & mag & -18.9$^3$& -20.3$^1$\\\\\\\\\\n$B-V$ & & 0.26$^3$ & 0.70$^4$\\\\\\\\\\n$\\\\mu_B(0)$ &mag/arcsec$^{2}$& 23.8$^3$ & - \\\\\\\\\\nr$_{25}$ & kpc & 0.79$^1$ & 0.87$^1$\\\\\\\\\\nM$_{HI}$ & M$_\\\\odot$ & 7.5$\\\\times$10$^9$ $^2$& 1.2$\\\\times$10$^{10}$ $^2$\\\\\\\\\\nM$_{HI}$/L$_B$ & M$_\\\\odot$/L$_\\\\odot$ & 2.62$^2$ & 1.18$^2$ \\\\\\\\\\n\\\\noalign{\\\\vspace{0.8mm}}\\n\\\\hline\\n\\\\multicolumn{4}{l}{$^1$De Vaucouleurs, \\\\etal 1991}\\\\\\\\\\n\\\\multicolumn{4}{l}{$^2$This paper}\\\\\\\\\\n\\\\multicolumn{4}{l}{$^3$O'Neil, \\\\etal 1998}\\\\\\\\\\n\\\\multicolumn{4}{l}{$^4$Prugniel \\\\& Heraudeau 1998}\\\\\\\\\\n\\\\noalign{\\\\vspace{0.8mm}}\\n\\\\hline\\n\\\\hline\\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\end{table}\\n\\n\\n\\\\begin{table}[ht]\\n\\\\caption{VLA observing parameters}\\n\\\\begin{tabular}{lr}\\n\\\\noalign{\\\\vspace{0.8mm}}\\n\\\\hline\\n\\\\hline\\n\\\\noalign{\\\\vspace{0.8mm}}\\nConfiguration & C-short \\\\\\\\\\nCorrelator mode & 2AC-normal \\\\\\\\\\nTotal integration time \\\\hfill (hours) & 15.5 \\\\\\\\\\nDates of observation & 15Jan99 \\\\\\\\\\n\\\\multicolumn{2}{r}{16Jan99} \\\\\\\\\\nField center, $\\\\alpha$(B1950) & 23:33:30 \\\\\\\\\\n\\\\phantom{Field center, }$\\\\delta$(B1950) & 12:35:53 \\\\\\\\\\nCentral frequency \\\\hfill (MHz) & 1391.64 \\\\\\\\\\n$V_{\\\\rm hel}$ of central channel \\\\hfill (km$\\\\:$s$^{-1}$) & 6170 \\\\\\\\\\nPrimary beam FWHM \\\\hfill (arcmin) & 32.4 \\\\\\\\\\nSynthesized beam ($\\\\alpha$$\\\\times$$\\\\delta$) \\\\hfill (arcsec) & 16.2$\\\\times$14.1 \\\\\\\\\\nBandwidth \\\\hfill (MHz) & 1.5625 \\\\\\\\\\nNumber of channels & 256 \\\\\\\\\\nChannel separation \\\\hfill (km$\\\\:$s$^{-1}$) & 1.31 \\\\\\\\\\nVelocity resolution \\\\hfill (km$\\\\:$s$^{-1}$) & 1.58 \\\\\\\\\\nrms noise in one channel \\\\hfill (K) & 2.63 \\\\\\\\\\nK-mJy conversion, & \\\\\\\\\\n\\\\phantom{K-}equiv. of 1mJy/beam \\\\hfill (K) & 2.76 \\\\\\\\\\n\\\\noalign{\\\\vspace{0.8mm}}\\n\\\\hline\\n\\\\hline\\n\\\\end{tabular}\\n\\\\end{table}\\n\\n\\\\section{The Data -- Observations and Reduction} \\n\\nH I spectral line synthesis observations of UGC 12695 and its companions\\nwere done in two runs with the VLA in its new C-short configuration and\\nare specified in Table~2. The primary calibrator 3C48 was observed\\nthree times per run and the secondary phase calibrator 2340+135 was\\nobserved every 35 minutes. \\n\\nCalibration, flagging, concatenation and Fourier transformation of the\\nUV data was done with the AIPS package. A robust R=0 weighting of the\\nUV data points was applied and the entire primary beam was imaged with a\\n512 x 512 map of 5 arcsecond pixels. The dirty maps and corresponding\\nantenna patterns were exported into the GIPSY package which was used for\\nfurther data reduction and analysis as described below. \\n\\nThe number of velocity channels was reduced by averaging adjacent pairs\\nof channel maps which resulted in a data cube of 127 nearly independent\\nchannels, each 2.68 \\\\kms\\\\ wide. The dirty maps were cleaned down to\\nhalf the rms noise level with channel dependent search areas using the\\nstandard H\\\\\\\"ogbom algorithm. The clean components were restored with a\\nGaussian beam of FWHM 16.2$\\\\times$14.1 arcsec at a position angle of\\n$-$54 degrees. The data cube was then Hanning smoothed in velocity\\nwhich resulted in a velocity resolution of 5.3 \\\\kms. \\n\\nNo continuum emission was detected in the averaged line-free channels at\\nthe positions of UGC 12695 and 2333+1234. Due to a steep rotation\\ncurve, the line emission at the center of UGC 12687 spans the entire\\nbandpass, leaving only 4 line-free continuum channels at the high\\nvelocity end of the data cube while some line emission at the low\\nvelocity edge of the bandpass is severely affected by the high noise\\nlevel. No continuum emission could be detected in the line-free\\nchannels at the position of the disk of UGC 12687. Therefore, no\\ncontinuum map was subtracted to avoid the unnecessary addition of noise\\nto the channel maps and the nuclear continuum emission of UGC 12687 was\\nremoved at a later stage. \\n\\nThe areas of H I emission were isolated in each channel map and the\\npixels outside these areas were set to zero. Global H I profiles were\\nderived by measuring the total flux in the isolated areas, corrected for\\nprimary beam attenuation. In the case of UGC 12687, a 2.9 mJy baseline\\nwas subtracted from the global profile. \\n\\nIntegrated H I maps of the galaxies were constructed by summing the\\nprimary beam corrected, isolated areas of H I emission. At the position\\nof the nucleus of UGC 12687, 7 channels at the high velocity end of the\\ndata cube are free from line emission and those were averaged to obtain\\na map of the central continuum source. A Gaussian beam was fitted to\\nthis source, giving a primary beam corrected flux density of 2.9$\\\\pm$0.2\\nmJy at the position $23^{\\\\rm h}32^{\\\\rm m}45^{\\\\rm s}.4$ and $23^{\\\\rm\\nd}32^\\\\prime53^{\\\\prime\\\\prime}$ (B1950). Subsequently, this fitted\\nGaussian was subtracted from the integrated H I map.\\n\\nVelocity fields were constructed by fitting a single Gaussian to each\\nprofile and rotation curves for UGC 12695 and UGC 12687 were derived by\\nfitting tilted rings of 11 arcsec width to their velocity fields. \\n\\nOptical images were taken from the Hubble Space Telescope Wide Field\\nPlanetary Camera-2 (WFPC2) images of O'Neil, \\\\etal (1998), the MDM 1.3m\\nMcGraw Hill telescope (McGaugh, Schombert, \\\\& Bothun 1995), and from the\\nSpace Telescope Science Institute Digital Sky Survey. The metallicity\\nstudies of UGC 12695 are from McGaugh (1994). \\n\\nH$_0$ is 75 km s$^{-1}$ Mpc$^{-1}$ throughout this paper, and a \\nVirgo-centric infall of 300 km s$^{-1}$ is assumed. B1950 coordinates\\nare used throughout this paper.\\n\\n\\n\\n\\\\section{H I morphology and kinematics}\\n\\nThe following subsections contain detailed descriptions of the overall\\nproperties of the neutral hydrogen gas in UGC 12695 and its companions\\nUGC 12687 and 2333+1234 which are illustrated in\\nFigures~\\\\ref{fig:U12695}, \\\\ref{fig:U12687}, \\\\ref{fig:2333},\\nrespectively. The beam size is 16.2'' $\\\\times$ 14.1'', or 6.4 kpc\\n$\\\\times$ 5.6 kpc at 82 Mpc. \\n\\n\\\\subsection{UGC 12695}\\n\\n\\n\\\\begin{figure*}[p]\\n\\\\epsfig{file=ovm.fig2bmp.ps,width=16cm}\\n\\\\caption{UGC 12695. See section 3.1 for explanations.}\\n\\\\label{fig:U12695}\\n\\\\end{figure*}\\n\\n\\nFigure~\\\\ref{fig:U12695} presents the data of UGC 12695. The upper left\\npanel displays the HST WFPC2 F814W image of O'Neil, \\\\etal\\\\ (1998). It\\nshows a relatively smooth triangular inner region and an irregular outer\\ndisk dominated by several large star forming H$\\\\alpha$ regions. Several\\nbackground galaxies can be seen through the disk, evidencing its\\nextremely transparent nature. The southern spiral arm seems to be\\nsharply outlined while the northern arm is extremely diffuse. Smoothing\\nthe WFPC2 image to a 1$^{\\\\prime\\\\prime}$ resolution and fitting an\\nellipse to the faintest isophotes indicates a position angle of\\n88$^\\\\circ$, an inclination of 43$^\\\\circ$ and a central position at\\n(23$^{\\\\rm h}$33$^{\\\\rm m}$30.4$^{\\\\rm s}$,\\n12$^\\\\circ$36$^\\\\prime$1$^{\\\\prime\\\\prime}$).\\n\\nThe upper right panel shows the global H I profile obtained by measuring\\nthe flux in the individual channel maps. The width at the 20\\\\% level of\\nthe peak flux is 79.4 \\\\kms\\\\ and the width at the 50\\\\% level of the peak\\nflux is 62.2 \\\\kms. The integrated flux density is 4.7 Jy km s$^{-1}$\\nwhich corresponds to a total H I mass of 7.5$\\\\times$10$^9$ M$_\\\\odot$ for\\na distance of 82 Mpc (v=6186 km s$^{-1}$ (Table 1) and H$_0$=75 km\\ns$^{-1}$ Mpc$^{-1}$). The shape of the profile suggests a global\\nlopsidedness of the H I distribution and or kinematics. The vertical\\narrow indicates the systemic velocity as derived from the H I velocity\\nfield. It should be noted that the H I profile of UGC 12695 was\\npreviously determined both by Theureau, \\\\etal\\\\ (1998) using the\\nNan\\\\c{c}ay telescope and Schneider, \\\\etal (1990) using the Arecibo\\ntelescope. Although both of the earlier observations match our\\nvelocity widths, the Nan\\\\c{c}ay result list a 40\\\\% smaller total flux. \\nAs our results match those of Schneider, \\\\etal, we believe the data\\ndifferences to be the result of uncertain beam shapes and primary beam\\ncorrections in the Nan\\\\c{c}ay data.\\n\\nThe middle left panel presents the integrated H I column density map\\nwith the size of the synthesized beam in the lower left corner. This H\\nI map is at the same scale as the WFPC2 image above. Contour levels are\\ndrawn at 0.5, 1, 2, 4, 6, 8, 10 and 12$\\\\times$10$^{20}$ atoms cm$^{-2}$.\\n Overall, the neutral hydrogen distribution of UGC 12695 appears to\\nmatch the optical morphology quite well, including the fact that the H I\\ndistribution is very lopsided with a high column density ridge running\\nthrough the southern part of the disk. The cross corresponds to the\\nposition of the cross in the WFPC2 image and indicates the central\\noptical concentration. Fitting an ellipse to the lowest H I contours\\nindicates a position angle of 80$^\\\\circ$, an inclination of 37$^\\\\circ$\\nafter a first order beam smearing correction, and puts the center of the\\nH I disk at (23$^{\\\\rm h}$33$^{\\\\rm m}$30.0$^{\\\\rm s}$,\\n12$^\\\\circ$36$^\\\\prime$4$^{\\\\prime\\\\prime}$), 7 arcseconds ($<$ 1 beam\\nwidth) north of the central optical concentration. \\n\\nThe middle right panel shows the radial H I column density distribution,\\nazimuthally averaged over the northern and southern sides separately.\\nClearly, the H I surface density falls off more sharply at the southern\\nedge, going from 10 to 0.5 x 10$^{20}$ atoms cm$^{-2}$ within two beam\\nwidths. \\n\\nThe lower left panel shows the H I velocity field. Apart from some\\nobvious wrinkles due to non-circular or streaming motions, the velocity\\nfield is dominated by solid body rotation. This makes it impossible to\\ndetermine the dynamical center and inclination from the velocity field\\nand therefore the optical center (cross) was adopted as the dynamical\\ncenter. The thick line indicates the adopted systemic isovelocity\\ncontour at 6185.7 \\\\kms\\\\ while the black contours indicate the\\napproaching side and the white contours the receding side of the galaxy.\\n The isovelocity contour intervals are set at $\\\\pm$n$\\\\times$5 \\\\kms. \\n\\nThe lower right panel presents the position-velocity diagram along the\\nkinematic major axis. Contours are drawn at -4, -2 (dashed), 2, 4, 8,\\n12, 16 and 20 times the rms noise level. The vertical dashed line\\ncorresponds to the position of the cross in the left panels, the\\nhorizontal dashed line corresponds to the adopted systemic velocity. \\nThe cross in the lower left corner indicates the beam. All profiles in\\nthe vertical direction can be well described by single Gaussians. No\\ndouble profiles are observed. The solid points show the derived\\nrotation curve projected onto the position-velocity diagram. The\\nrotation curve was derived by fitting full tilted rings to the velocity\\nfield, effectively azimuthally averaging the wrinkles. Consequently,\\nthis azimuthally averaged rotation curve might deviate locally from the\\nposition-velocity slice. \\n\\nThe rotation curve of UGC 12695 is tabulated in Table~3. Fitting a\\nsingle, galaxy wide ring to the entire velocity field gives a position\\nangle of the kinematic major axis of 62 degree. The short thin lines\\noutside the velocity field indicate this average kinematic major axis. \\nNote the significant difference of 18 degrees between the kinematic and\\nmorphological position angles of the outer H I disk. An inclination of\\n40$^\\\\circ$ is adopted which is the average of the optical and H I\\ninclinations. Given this rather face-on orientation of the disk, the\\nuncertainty in the position of the dynamical center and the obvious\\ndeviations from circular motions, we estimate the uncertainties in the\\nrotation curve at some 20\\\\%. \\n\\n\\n\\\\subsection {UGC 12687}\\n\\n\\\\begin{figure*}[p]\\n\\\\epsfig{file=ovm.fig3.ps,width=16cm}\\n\\\\caption{UGC 12687. See section 3.2 for explanations.}\\n\\\\label{fig:U12687}\\n\\\\end{figure*}\\n\\n\\\\begin{figure*}[p]\\n\\\\epsfig{file=ovm.fig4.ps,width=16cm}\\n\\\\caption{2333+1234. See section 3.3 for explanations.}\\n\\\\label{fig:2333}\\n\\\\end{figure*}\\n\\nThe upper left panel of Figure~\\\\ref{fig:U12687} shows the blue POSS-II\\nimage of UGC 12687, a strongly barred two-armed spiral. The bar\\ndynamics efficiently feeds gas to the nuclear region where a radio\\ncontinuum source with a peak flux of 4.0$\\\\pm$0.6 mJy is found at 1.4 GHz\\n(Condon {\\\\it et al}, 1998). An ultra-violet excess has been reported by\\nKazarian \\\\& Kazarian (1985), suggesting a high level of star formation\\nactivity. Nevertheless, the B$-$V=0.70 color from Prugniel \\\\& Heraudeau\\n(1998) of UGC 12687 is considerably redder than that of UGC 12695. \\n\\nThe upper right panel shows the global H I profile which displays the\\nclassical double-horned shape. Fluxes were measured in individual\\nchannel maps including the central continuum source. Afterwards, a\\n2.9~mJy/beam continuum baseline was subtracted from the global profile. \\nUnfortunately, H I emission at the lower velocities is lost in the edge\\nof the passband. To estimate total fluxes and line widths, the high\\nvelocity edge was mirrored and, as an educated guess, put in place of\\nthe missing low velocity side of the profile. This technique gives an\\nintegrated flux density of 7.5 Jy km s$^{-1}$ or a total H I mass of\\n1.2$\\\\times$10$^{10}$ M$_\\\\odot$. The inferred line widths are 296.7\\n\\\\kms\\\\ at the 20\\\\% level and 255.4 \\\\kms\\\\ at the 50\\\\% level. Like UGC\\n12695, UGC 12687 was imaged by Theureau, \\\\etal\\\\ (1998) with the\\nNan\\\\c{c}ay telescope, with similar results -- the velocity widths of the\\n Nan\\\\c{c}ay data matched ours well, but the total flux reported by \\nTheureau, \\\\etal\\\\ was only 80\\\\% of our result. To check our data, we\\nobtained a 5 minute ON/OFF pair with the Arecibo telescope using the\\nL-narrow receiver. The Arecibo data and our VLA data again matched to\\nwithin 5\\\\% in total flux.\\n\\nThe middle left panel displays the integrated column density map of UGC\\n12687 constructed by adding the individual channel maps, including the\\ncentral continuum source which was removed by subtracting a 2.9 mJy/beam\\ncentral point source. Contour levels are drawn at 0.5, 1, 2, 4, 6, 8,\\n10, 12, 14, 16 and 18$\\\\times$10$^{20}$ atoms cm$^{-2}$. The central\\nhole in the H I map might be due to a slight overestimation of the\\ncontinuum flux or might be caused by H I seen in absorption. \\nFurthermore, the approaching south-eastern side of the galaxy is missing\\nsome flux in the integrated H I map due to the bandpass effect mentioned\\nabove. Nevertheless, it is clear that the H I gas in UGC 12687 is\\nconcentrated near the tips of the bar and to some extent along both\\noptically visible spiral arms. Fitting an ellipse to the outer H I\\ncontours gives an axis ratio of (b/a)=0.72 and a position angle of 129.8\\ndegrees centered on (23$^{\\\\rm h}$32$^{\\\\rm m}$45.2$^{\\\\rm s}$,\\n12$^\\\\circ$38$^\\\\prime$54$^{\\\\prime\\\\prime}$). \\n\\nThe middle right panel shows the azimuthally averaged radial H I surface\\ndensity profiles of the receding and approaching sides separately. Note\\nthat the approaching side misses some flux around a radius of 1\\narcminute. \\n\\nThe lower left panel shows the velocity field which suggests, at least\\nin projection, a declining rotation curve in the inner regions. Fitting\\ntilted rings gives a dynamical center at (23$^{\\\\rm h}$32$^{\\\\rm\\nm}$45.4$^{\\\\rm s}$, 12$^\\\\circ$38$^\\\\prime$52$^{\\\\prime\\\\prime}$), a systemic\\nvelocity of 6150.2 \\\\kms\\\\ (thick line), an inclination of 43$^\\\\circ$ and\\na position angle of 297$^\\\\circ$. However, due to the strong bar,\\nnon-circular motions are certainly present. No significant warp could\\nbe detected. The isovelocity contours are plotted at intervals of\\n$\\\\pm$n$\\\\times$20 \\\\kms. The inferred rotation curve of UGC 12687 is\\ntabulated in Table~3.\\n\\nThe lower right panel shows the position-velocity diagram over the\\nentire observed bandwidth along the kinematic major axis. The central\\ncontinuum source has not been removed. Note how the low velocity gas is\\nlost in the edge of the bandpass as well as the limited number of line\\nfree channels at the high velocity side. Also note the occasional double\\nprofiles. \\n\\n\\\\subsection{2333+1234}\\n\\nIn the VLA data cube, the H I emission of a tiny irregular dwarf low\\nsurface brightness galaxy was discovered. Having discovered it first in\\nH I, we were then able to discern the galaxy as a barely visible smudge\\non the POSS-II plate (left panel of Figure~\\\\ref{fig:2333}). Fitting an\\nellipse to the faintest POSS-II isophotes yields a size of\\n17.5$\\\\times$7.2 arcsec and a position angle of 58$^\\\\circ$, centered on\\n(23$^{\\\\rm h}$33$^{\\\\rm m}$8.9$^{\\\\rm s}$,\\n12$^\\\\circ$34$^\\\\prime$39$^{\\\\prime\\\\prime}$). \\n\\nThe upper right panel shows the measured global H I profile with an\\nintegrated flux of 0.33 Jy km s$^{-1}$ or a total H I mass of\\n5.2$\\\\times$10$^8$ M$_\\\\odot$. The line widths are 92 \\\\kms\\\\ at the 20\\\\%\\nlevel and 75 \\\\kms\\\\ at the 50\\\\% level.\\n\\nThe middle left panel shows the resolved integrated H I column density\\nmap which seems to be slightly offset from the optical image. H I\\ncontours are plotted at 0.5, 1, 2, 4 and 6$\\\\times$10$^{20}$ atoms\\ncm$^{-2}$\\n\\nThe middle right panel shows the barely resolved radial H I surface\\ndensity profile. No deconvolution attempt was made. \\n\\nThe lower left panel shows the velocity field which clearly indicates a\\nvelocity gradient along the optical major axis. The optical center was\\ntaken to be the dynamical center and a systemic velocity of 6192.5 \\\\kms\\\\\\nwas inferred. Isovelocity contours are plotted in steps of\\n$\\\\pm$n$\\\\times$10 \\\\kms. Obviously, trying to derive a rotation curve by\\nfitting tilted rings is futile. \\n\\nThe lower right panel displays the position-velocity diagram through the\\noptical center along the kinematic major axis, however, and the sign of\\nsolid body rotation is evident. \\n\\n\\n\\\\section{Dark and Visible Matter in UGC 12695}\\n\\n\\\\begin{table}[t]\\n\\\\begin{center}\\n\\\\caption{Inclination corrected rotation curves of UGC~12695 and\\nUGC~12687.}\\n\\\\begin{tabular}{ccccccc}\\n\\\\noalign{\\\\vspace{0.8mm}}\\n\\\\hline\\n\\\\hline\\n\\\\noalign{\\\\vspace{0.8mm}}\\n &\\\\multicolumn{3}{c}{UGC~12695} & \\\\multicolumn{3}{c}{UGC~12687} \\\\\\\\\\nR & V$_{\\\\rm rot}$ & incl. & P.A. & V$_{\\\\rm rot}$ & incl. & P.A. \\\\\\\\\\n$\\\\prime\\\\prime$ & km/s & $\\\\circ$ & $\\\\circ$ & km/s & $\\\\circ$ & $\\\\circ$ \\\\\\\\\\n\\\\hline\\n\\\\noalign{\\\\vspace{0.8mm}}\\n 10.7 & 17 & 40 & 62 & 195 & 43 & 297 \\\\\\\\\\n 21.3 & 26 & 40 & 62 & 195 & 43 & 297 \\\\\\\\\\n 32.0 & 32 & 40 & 62 & 195 & 43 & 297 \\\\\\\\\\n 42.7 & 38 & 40 & 62 & 195 & 43 & 297 \\\\\\\\\\n 53.3 & 45 & 40 & 62 & 179 & 43 & 297 \\\\\\\\\\n 64.0 & 52 & 40 & 62 & 174 & 43 & 297 \\\\\\\\\\n 74.7 & & & & 171 & 43 & 297 \\\\\\\\\\n\\\\noalign{\\\\vspace{0.8mm}}\\n\\\\hline\\n\\\\hline\\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\end{table}\\n\\n\\nPrevious studies of the dark and visible matter of LSB galaxies have\\nshown them to be extremely dark matter dominated with respect to\\n``normal'' HSB galaxies (i.e. Van Zee, \\\\etal 1997; De Blok \\\\& McGaugh\\n1997, 1998). Thus, although the lack of any turn-over in UGC 12695's\\nrotation curve makes it clear that we have not come close to determining\\nthe full gravitational potential of the galaxy, it is still a worthwhile\\nexercise to look at UGC 12695's total mass.\\n\\n\\n\\\\begin{figure}[t]\\n\\\\epsfig{file=ovm.fig5.ps,width=8.5cm}\\n\\\\caption{LSB galaxy Tully-Fisher relation. The \\nlines are the 1$\\\\sigma$ and 2$\\\\sigma$ fits to the data of Zwaan, \\\\etal\\n(1995), and the circles are recent observations of LSB galaxies in the \\nPegasus and Cancer groups from O'Neil, Bothun, \\\\& Schombert (1999). UGC \\n12695 (using {\\\\it i} = 40\\\\degree) is shown as a diamond.}\\n\\\\label{fig:tf}\\n\\\\end{figure}\\n\\n\\nClassic Newtonian mechanics states that the dynamical mass of a\\nrotating, gravitationally bound object is simply\\n\\\\[M_{dyn}\\\\:=\\\\:{{v^2\\\\:R}\\\\over{G\\\\:\\\\sin^2{\\\\it i}}}\\\\] where G is the\\ngravitational constant. Using the maximum known velocity of UGC 12695\\n(33/sin(40\\\\degree) km s$^{-1}$ at r=64''), this gives a total dynamical\\nmass of 16 x 10$^{9}$\\\\Msol, while the determined H I flux gives a total\\nH I mass of M$_{HI}$ = 7.5 x 10$^{9}$\\\\Msol. Although at first glance\\nthese numbers hardly seem remarkable, they imply a considerable absence\\nof dark matter for a LSB galaxy. Assuming a minimal disk scenario\\n(M$_*$/L$_B$ = 0), and letting all the gas in the galaxy be neutral\\nhydrogen and helium (M$_{gas}$ = 1.47$\\\\times$M$_{HI}$ =\\n11$\\\\times$10$^9$\\\\Msol), gives a dark-to-total mass ratio of only\\nM$_{DM}$/M$_{dyn}$ = 0.30. Using somewhat more realistic numbers by\\nletting M$_*$/L$_B$ = 1, (a low-to-average LSB maximal disk value from\\nVan Zee, \\\\etal\\\\ 1997 \\\\& De Blok \\\\& McGaugh 1997) reduces the dark matter\\ncontribution to only 12\\\\% of the total dynamical mass of UGC 12695. \\n(The luminosity value, L$_B$ = 2.86 $\\\\times$ 10$^9$ \\\\Msol, is derived\\nfrom the value given in O'Neil, \\\\etal, 1998 which used integrated\\naperatures. The error in L$_B$ is less than 1\\\\%.) For comparison, the\\naverage M$_{DM}$/M$_{dyn}$ values for LSB galaxies from De Blok \\\\&\\nMcGaugh is 0.6 for maximum disk scenarios, and for Van Zee, \\\\etal\\\\\\n(1997) \\\\lb~M$_{DM}$/M$_{dyn}$\\\\gb = 0.7. Additionally, if the stellar\\nmass-to-light ratio of UGC 12695 is increased to 1.7, a reasonable value\\nfor both HSB and LSB galaxies, there is no need to invoke any dark\\nmatter to explain the maximum {\\\\it observed} rotational velocity at the\\nlast measured point of UGC 12695's rotation curve. It should be noted\\nthat we were not able to observe any turn-over in UGC 12695's rotation\\ncurve. Thus, unlike the Van Zee, \\\\etal\\\\ and De Blok \\\\& McGaugh samples\\nwe are not determining the dynamical mass from the flat portion of the\\nrotation curve but instead from the still rising portion. As such, it is\\nextremely likely that dark matter will play a large role in UGC 12695's \\nouter regions.\\n\\nIt should also be noted that the {\\\\it observed} velocity width of UGC\\n12695 causes it to fall well off the standard Tully-Fisher relation,\\nlying approximately 2.5 magnitudes (3$\\\\sigma$) above the LSB galaxy line\\ndefined by Zwaan, \\\\etal\\\\ (1995) (Figure~\\\\ref{fig:tf}). This may be the\\nconsequence of the apparent lack of dark matter in the observed portion\\nof UGC 12695. On the other hand, it is quite likely that there is\\nsignificant dark matter outside the observed radius (else the rotation\\ncurve would show some turn over), and thus we are merely viewing a\\nlower limit of the galaxy's rotational velocity. The uncertainty in UGC\\n12695's inclination (see the next section) also makes the current\\nlocation of UGC 12695 on the Tully-Fisher relation suspect and if the\\ninclination is less than 40\\\\degree, UGC 12695 could move onto (or even\\nto the right of) the Tully-Fisher relation of Zwaan, \\\\etal.\\n\\n\\\\section{Star Formation in UGC 12695}\\n\\n\\\\begin{figure*}[t] \\n\\\\epsfig{file=ovm.fig6bmp.ps,width=17.5cm}\\n\\\\caption{Left panel: HI contours of U12695 overlaid on the HST WFPC2\\nF814W image. Right panel: HI contours of U12695 overlaid on the\\nH$\\\\alpha$ image. The red contours indicate the critical HI column\\ndensity of 1.6$\\\\times$10$^{20}$ and 6.0$\\\\times$10$^{20}$ cm$^{-2}$ above\\nwhich star formation is expected based on Toomre's criterion (for {\\\\it\\ni} = 40\\\\degree \\\\& 10\\\\degree, respectively), while the green contours are\\nthe 10$^{21}$ cm$^{-2}$ level.}\\n\\\\label{fig:U12695optHI}\\n\\\\end{figure*} \\n\\nIt was demonstrated by Toomre (1964) that a thin, {\\\\it collisionless}\\nstellar disk in circular motion becomes unstable if the surface mass\\ndensity exceeds a critical value of \\\\[\\\\Sigma_c\\\\:=\\\\:\\\\alpha\\\\:{{\\\\kappa\\n\\\\sigma}\\\\over{3.36 G}}\\\\] where $\\\\Sigma_c$ is the critical density,\\n$\\\\sigma$ is the velocity dispersion, \\\\alp is a dimensionless constant\\nnear 1, and $\\\\kappa$ is the epicyclic frequency of the gas, also written\\nas \\\\[\\\\kappa\\\\:=\\\\:1.41\\\\:{V\\\\over R}\\\\:\\\\left(1\\\\:+\\\\:{R \\\\over\\nV}{{dV}\\\\over{dR}}\\\\right)^{1/2}.\\\\] Cowie (1981) showed that this\\ncriterion is also applicable to instabilities in a gaseous disk if\\nembedded in a more massive stellar disk. Kennicutt (1989) determined an\\nempirical value for \\\\alp of about 2/3. Typical HSB galaxies exceed this\\ncritical surface density and form stars throughout most of their stellar\\ndisks. \\n\\nAs an LSB galaxy which appears to be in the midst of considerable but\\nlocalized star formation, UGC 12695 is an ideal case on which to test\\nthis star formation threshold theory. Before this can be done, though,\\n$\\\\kappa$ and $\\\\sigma$ must be determined. From the rotation curve of\\nUGC 12695 it is apparent that its near solid body rotation makes\\ndetermining $\\\\kappa$ relatively easy. Approximating the rotation curve\\nas pure solid body with an inclination corrected amplitude of 57 \\\\kms\\\\ \\nat a radius of 22 kpc yields $\\\\kappa$=5.2 \\\\kms\\\\ kpc$^{-1}$ (using the\\nfact that for a gas disk in pure solid body rotation,\\n${{dV}\\\\over{dR}}={V\\\\over R}$ and $\\\\kappa={{2V}\\\\over{R}}$). Due to beam\\nsmearing the velocity dispersion is hard to measure from the data and a\\ncanonical dispersion of $\\\\sim$8 \\\\kms\\\\ is assumed as an average estimate\\n(8 \\\\kms\\\\ is also observed in several highly resolved face-on gas disks).\\n This leads to a critical surface mass density of\\n$\\\\Sigma_c\\\\:=\\\\:4.0\\\\times10^{-3}$ kg m$^{-2}$. Taking a 32\\\\% helium mass\\nfraction into account, this corresponds to a critical H I column density\\nof 1.6$\\\\times$10$^{20}$ atoms cm$^{-2}$ (i.e. between the 1st and 2nd\\ncontours in Figure~\\\\ref{fig:U12695optHI}) above which star formation is\\nto be expected. This implies that everywhere throughout the disk of UGC\\n12695 star formation should occur. \\n\\n\\\\begin{figure*}[t]\\n\\\\epsfig{file=ovm.fig7.ps,width=17.5cm}\\n\\\\caption{The azimuthally averaged observed gas \\ndensity, Toomre star formation threshold, and rotation curves of UGC\\n12695 for an assumed galaxy inclination of 40\\\\degree, 25\\\\degree, and\\n10\\\\degree (left to right).}\\n\\\\label{fig:azav}\\n\\\\end{figure*}\\n\\nHowever, we only observe star formation in a limited number of localized\\nregions near the very peaks of the H I column density distribution where\\nit reaches levels of 1$\\\\times$10$^{21}$ atoms cm$^{-2}$. This is\\nillustrated in Figure~\\\\ref{fig:U12695optHI} which shows in the left\\npanel the HI column density map overlaid on a false-color WFPC2 F814W\\nimage and in the right panel the same H I contours overlaid on a\\ngreyscale MDM-1.3m H$\\\\alpha$ image. The lower red contour indicates the\\ncritical column density of 1.6$\\\\times$10$^{20}$ atoms/cm$^2$. Obviously,\\nthe theoretically derived and empirically adjusted critical surface\\ndensity is clearly not applicable to the low metallicity, irregular gas\\ndisk of UGC 12695. \\n\\nOne of the more curious aspects of the Kennicutt-Cowie-Toomre star\\nformation criterion is that it successfully works at all, considering\\nthe number of physical processes which affect the value of $\\\\Sigma_c$. \\nFor example, disks are not infinitely thin but have a certain thickness\\nwhich could increase or decrease the column density thresholds and alter\\nthe radial instabilities. That is, if the volume gas density is\\nsignificantly different than the surface gas density of UGC 12695, a\\nvolume-density dependent Schmidt law would be more appropriate than the\\nKennicutt/Cowie/Toomre star formation criterion used above (i.e.\\nFerguson, \\\\etal\\\\ 1998). Additionally, there is energy dissipation,\\nmagnetic field lines, etc. which should also affect $\\\\Sigma_c$ (i.e.\\nHunter, Elmegreen, \\\\& Hunter 1998). Thus it is not surprising that UGC\\n12695, and in fact many LSB galaxies, do not adhere to the Toomre\\ncriterion (i.e. Van Zee, \\\\etal\\\\ 1997; Van der Hulst, \\\\etal\\\\ 1993).\\n\\nWhat is interesting is that UGC 12695, like many LSB and dwarf galaxies,\\nforms stars only where the local H I column density exceeds 10$^{21}$\\natoms cm$^{-2}$. In fact, Skillman (1986) pointed out that the actually\\nobserved {\\\\em local} H I column density threshold for star formation, at\\na resolution of 500 pc, is about 1$\\\\times$10$^{21}$ atoms cm$^{-2}$ and\\nroughly 5$\\\\times$10$^{21}$ atoms cm$^{-2}$ for star formation events of\\nthe order of 30 Doradus. This local H I column density threshold\\nappears to be in better agreement with the observations of UGC 12695\\n(i.e. note the green contours in Figure~\\\\ref{fig:U12695optHI}), although\\nthe beam size makes a detailed analysis impossible. (The H$\\\\alpha$ data\\nof McGaugh 1994 is not photometric, making determination of UGC 12695's\\nH II luminosity difficult. It should be noted, though, that attempts to\\ndetect faint diffuse H-$\\\\alpha$ regions have not been successful,\\nmaking it unlikely that any widespread component of faint star-forming\\nregions has been missed.)\\n\\nUnlike our sample, a previous study by Van der Hulst, \\\\etal\\\\ (1993)\\nfound their sample of low surface galaxies to be generally consistent\\nwith the Kennicutt-Toomre criterion for star formation. Perhaps the\\nmost important difference between this study of UGC 12695 and the Van\\nder Hulst, \\\\etal\\\\ results is that Van Der Hulst, \\\\etal\\\\ used azimuthally\\naveraged radial H I surface density profiles. Figure~\\\\ref{fig:azav}\\nshows the results of applying Van der Hulst, \\\\etal's method to UGC 12695\\nfor a variety of possible inclinations (see below). As can be seen, even\\nby ignoring the extremely asymmetric nature of UGC 12695, only the most\\nextreme case ({\\\\it i}=10\\\\degree) does UGC 12695 come close to falling\\nbelow the critical density for star formation anywhere but in the\\noutermost isophotes. This sort of study, though, disallows for any\\nanalysis of the local star forming potential of UGC 12695 while hiding\\nthe exceptionally asymmetric nature of galaxy.\\n\\n\\n\\\\begin{figure*}[p]\\n\\\\hspace{-1cm}\\n\\\\epsfig{file=ovm.fig8bmp.ps,width=18.5cm}\\n\\\\caption{Zooming in on the main star formation regions in in UGC~12695.\\nThe upper row shows the star formation complexes in the eastern side of\\nthe galaxy. Those in the western side are shown in the bottom row. The\\nwhite contours are from the VLA H I map while the yellow contours are\\nfrom the MDM-1.3m H$\\\\alpha$ image.}\\n\\\\label{fig:U12695SFs}\\n\\\\end{figure*}\\n\\n\\nAt this point, it is important to consider the uncertainties involved\\nin calculating $\\\\Sigma_C$. Most notably, we should take another look at\\nUGC 12695's assumed inclination. It is certainly possible that UGC\\n12695's shape truly is circular, thus validating the inclination value\\nused in the previous calculations (40\\\\degree). If, however, UGC 12695\\nhas recently tidally interacted with UGC 12687, as discussed below, the\\nperceived inclination may be overestimated in that UGC 12695 may have\\nbeen distorted (and `flattened') by the interaction (e.g. see Figure 2\\nof Mihos, \\\\etal, 1997). In this case the true inclination of UGC 12695\\nmay be considerably less than we have assumed, thereby raising the \\nvalue of $\\\\Sigma_C$. As an example, if UGC 12695's true inclination is\\n10\\\\degree, the critical density will increase to\\n$\\\\Sigma_C\\\\:=\\\\:6\\\\times10^{20}$ atoms cm$^{-2}$. In this case, although\\nthe critical density and the density at which star formation is observed\\nstill would not precisely coincide, they would lie considerably closer \\ntogether (i.e. the higher red contour in Figure~\\\\ref{fig:U12695optHI}). \\nIf, in addition to the above correction to {\\\\it i}, our estimate of\\n$\\\\kappa$ is off by a factor of 60\\\\% (3$\\\\sigma$) due to inclination\\nuncertainties and the rotation curve shape, the critical density would\\nreadily be raised to 10$^{21}$ atoms cm$^{-2}$, the observed local H I\\ncolumn density threshold for star formation of Skillman (1986). Of\\ncourse, if the inclination correction is off in the other direction, \\nand {\\\\it i}=50\\\\degree, $\\\\Sigma_C$ would be reduced even more, raising\\nagain the question of why UGC 12695 is LSB.\\n\\nIt is noteworthy to point out that the three local peaks in the neutral\\nhydrogen of UGC 12695 lie near, but not on top, the primary star\\nformation regions of the galaxy, as defined by the H-\\\\alp image of\\nMcGaugh (1994). This is illustrated in Figure~\\\\ref{fig:U12695SFs} which\\ndisplays in the left panels the white VLA H I contours on the color\\nWFPC2 F814W image, in the middle panels the yellow MDM-1.3m H$\\\\alpha$\\ncontours on the WFPC2 image and in the right panels the combined H I and\\nH$\\\\alpha$ contours on the WFPC2 image.\\n\\nFigure~\\\\ref{fig:U12695SFs} shows that there seems to be a clear offset\\nbetween the highest peaks in the H I column density at 1.2 x 10$^{21}$\\ncm$^{-2}$ and the location of the primary H$\\\\alpha$ complexes. The\\nlargest star clusters seem to surround the regions with the highest HI\\ncolumn densities. However, the relatively poor spatial resolution of\\nthe current H I observations is insufficient to draw any further\\nconclusions on the relation between the H I peaks and the H$\\\\alpha$\\nregions.\\n \\nThe colors of those regions, as provided by the WFPC2 images, also put\\nthe star-formation peaks away from the H I peaks, with the left two H I\\npeaks having F300W $-$ F814W = $-$0.06 and $-$2.82, versus $-$3.27 and\\n$-$3.14 for the corresponding H-\\\\alp peaks (top and bottom,\\nrespectively). (These colors roughly correspond to U $-$ I colors of\\n1.42, $-$1.34, $-$1.79. and $-$1.66, respectively (i.e. O'Neil, \\\\etal\\n1998).) The third H I peak, at the bottom right of\\nFigure~\\\\ref{fig:U12695optHI}, lies in the extremely noisy PC chip of the\\nWFPC2 image, making the determination of colors in that region extremely\\ndifficult. Thus the neutral hydrogen is behaving as expected -- as star\\nformation occurs the surrounding gas is ionized, shifting the peak in\\nthe neutral hydrogen distribution to the edge of the star forming\\nregions. \\n\\n\\n\\\\section{Are UGC~12695 and UGC~12687 Ti-dally Interacting?}\\n\\nThe close proximity of UGC 12695 and UGC 12687 in redshift space, the\\nlopsided morphology of UGC 12695 and its slightly skewed kinematics, \\nimmediately brings to mind the possibility of a tidal interaction\\n(Figure~\\\\ref{fig:Allposs2HI}). Additionally, the presence of 2333+1234\\nlying between the two galaxies suggests it may have been formed as a\\ntidal remnant. (Of course, 2333+1234 may simply be a naturally\\noccurring representative of the faint-end of the luminosity function.) \\n\\nIn 1997 Mihos, McGaugh, \\\\& De Blok argued that LSB and HSB galaxies of\\nthe same total mass are equally susceptible to local disk instabilities\\nbut that LSB galaxies are far less responsive to global instabilities\\nthan their HSB counterparts. This difference is mainly due to the\\nstabilizing nature of the relatively more massive dark matter halo in\\nwhich the LSB disk is embedded. To test their hypothesis, they modeled\\na strong prograde tidal encounter between an LSB and an HSB disk galaxy\\nof similar mass. After the encounter the HSB galaxy exhibited two\\ndefinitive spiral arms, a central inflow of gas and an oval central\\nregion. Presumably, the HSB system was in the midst of, or had recently\\nundergone, a large burst of star formation in its core. Being more\\nstable than its HSB counterpart, the LSB galaxy displayed a milder, yet\\nsignificant response. Although the encounter strongly perturbed the LSB\\ngalaxy, it did not result in a central gas inflow. However, it did\\ninduce long-lived spiral arms, an overall lopsided distortion of the\\ngalaxy, and possibly localized compressions and instabilities in the\\ndisk. \\n\\nThe observed morphologies of UGC 12695 and UGC 12687 show a striking\\nresemblance to the numerical simulations of Mihos \\\\etal\\\\ at the time\\nstamp T=36 (see their Figure~2). Their HSB system (UGC 12687 in our\\ncase) shows a strong bar from which two well defined spiral arms emerge.\\n UGC~12687's observed morphology is in close agreement with their\\nresults while its central continuum emission and UV-excess indicate a\\nconsiderable nuclear star formation activity, hinting at well developed\\nbar kinematics efficient in fueling H I to the central region. In the\\ncase of the LSB galaxy, the numerical simulations display a sharp\\nstellar edge on one side of the disk and a more diffuse gradient on the\\nother side while a highly variable structure in the mass surface density\\nhints at strong local instabilities. Observationally, UGC 12695's\\nextremely blue colors, highly asymmetric gas and star distribution, and\\nregions of intense local star formation also match the model predictions\\nextremely well. In fact, without relying on some sort of external\\ntrigger the observed morphology and color of UGC 12695 is extremely\\ndifficult to explain. \\n\\nIn spite of the above assertions, a number of arguments against any\\nmajor tidal encounter between these two galaxies must be considered. \\nThe first, and perhaps most obvious of these is the apparently settled\\nkinematics of both UGC 12695 and UGC 12687. At first glance it would\\nseem that if the two galaxies have interacted recently enough for the\\ntidally-induced star formation to be at, or near, its peak the galaxies\\nwould still exhibit highly agitated kinematics. A study by V\\\\'azquez\\nand Scalo (1989), though, has shown that starbursts do not typically\\noccur during the gas compression stage but in fact occur well after the\\ngas has re-established. In other words, the V\\\\'azquez and Scalo model\\nsuggests that disks can have tidally induced star formation well after\\nthe gas has kinematically re-settled. \\n\\nA second argument which could be put forward against the idea of the two\\ngalaxies having recently undergone a tidal interaction is simply this --\\nif UGC 12695 is experiencing a burst of localized star formation due to\\na recent tidal encounter, should it not be experiencing a corresponding\\nrise in central surface brightness? A recent paper by O'Neil, Bothun, \\\\&\\nSchombert (1998) tested this idea through modeling a wide variety of LSB\\ngalaxies experiencing localized starbursts. Their results were quite\\ndefinitive -- if a galaxy forms as a LSB galaxy, due to a high angular\\nmomentum giving rise to a low gas surface density etc., it will remain a\\nLSB galaxy barring any major encounter catastrophe. Thus it is quite\\nbelievable that UGC 12695 could be undergoing significant localized star\\nformation activity and yet not be undergoing any significant change in\\nits global surface brightness. \\n\\nThe final argument against UGC 12695 and UGC 12687 having undergone a\\nsignificant tidal interaction in the recent past comes from examining\\nthe smoothed data cube. Not a trace of extended H I gas above a minimal\\ndetectable column density of 2$\\\\times$10$^{19}$ atoms cm$^{-2}$\\n(3$\\\\sigma$) can be found besides the rotating gas disks of the three\\nidentified galaxies. This leads to the conclusion that no major tidal\\ntails were ever formed in any past interaction between the two systems. \\n\\n\\n\\\\section{Conclusion}\\n \\nUGC 12695 is an intriguing low surface brightness galaxy of a very\\ntransparent nature, having an extremely blue color, a highly asymmetric\\nappearance and very localized bursts of star formation near the peaks in\\nthe H I column density distribution.\\n\\nMany of the properties of both UGC 12687 and UGC 12695 can be explained\\nas being induced by such a tidal interaction, including the bar of UGC\\n12687 and its central radio continuum emission and UV excess as well as\\nthe lopsided appearance of UGC 12695 and the offset between its\\nmorphological and kinematic major axes. Furthermore, the localized\\nbursts of star formation in UGC 12695 could very well be induced by such\\nan interaction, giving rise to local instabilities in the LSB disk as\\ndemonstrated by Mihos \\\\etal (1997). \\n\\nIt is likely that UGC 12695 could have been living a fairly quiescent\\nexistence, its low surface gas density keeping its star formation rate\\nquite low, and just now it is experiencing a period of localized but\\nvigorous star formation triggered by a mild tidal interaction which\\nmight lead to a major morphological transition. \\n\\nWithin all this, though, it is easy to overlook one important fact. \\nAlthough many of the properties of UGC 12695 and UGC 12687 can readily\\nbe explained through an ongoing tidal encounter, the two galaxies are\\nstill fundamentally distinct. UGC 12695 is not simply a fainter, or\\nmore `stretched-out', or more quickly rotating version of UGC 12687. \\nWere any of these the case the behavior of the two galaxies after the\\ntidal encounter would be similar, and UGC 12695 would have experienced a\\ncentral gas inflow with the majority of its star formation now occurring\\nnot in the outlying regions (as it is), but in the galaxy's core. Thus\\nthe fundamental question of why UGC 12695 is an LSB galaxy, and UGC\\n12687 is not remains unanswered. \\n\\n\\n\\\\section{Acknowledgments}\\n\\nThe Very Large Array is a facility of the National Radio Astronomy\\nObservatory, a facility of the National Science Foundation operated\\nunder cooperative agreement by Associated Universities, Inc. The\\nDigitized Sky Surveys were produced at the Space Telescope Science\\nInstitute under U.S. Government grant NAG W-2166. The images of these\\nsurveys are based on photographic data obtained using the Oschin Schmidt\\nTelescope on Palomar Mountain and the UK Schmidt Telescope. The plates\\nwere processed into the present compressed digital form with the\\npermission of these institutions. \\n\\n\\n\\\\section*{References}\\n\\n\\\\noindent\\n Condon, \\\\etal, 1998, AJ, 115, 1693\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n Cowie, L., 1981, ApJ, 245, 66\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n De Blok, W.J.G. \\\\& Van der Hulst, J.M., 1998, A\\\\&A, 336, 49\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n De Blok, W.J.G. \\\\& McGaugh, S., 1998, ApJ, 499, 41\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n De Blok, W.J.G. \\\\& McGaugh, S., 1997, MNRAS, 290, 533\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n Ferguson, H., \\\\& McGaugh, S., 1995, ApJ, 440, 470\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n Ferguson, A. \\\\etal, 1998, ApJ, 506, L19\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n Kazarian, M.A. \\\\& Kazarian, E.S., 1985, Afz, 22, 431\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n Kennicutt, R., 1989, ApJ, 344, 685\\\\\\\\ \\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n Hunter, D., Elmegreen, B. \\\\& Baker, A., 1998, ApJ, 493, 595\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n Matthews, L., \\\\& Gallagher, J., 1997, AJ, 114, 1899\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n McGaugh, S., 1994, ApJ, 426, 135\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n Mihos, C., McGaugh, S., \\\\& De Blok, W.J.G, 1997, ApJ, 477L, 79\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n O'Neil, K, Bothun, G., \\\\& Schombert, J., 1999, AJ, in press\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n O'Neil, K., Bothun, G., \\\\& Schombert, 1998, AJ, 116, 2776\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n O'Neil, K., \\\\etal, 1998, AJ, 116, 657\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n O'Neil, K., Bothun, G., \\\\& Cornell M., 1997b, AJ, 113, 1212\\\\\\\\ \\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n O'Neil, K., \\\\etal, 1997a, AJ, 113, 1212\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n Prugniel, P. \\\\& Heraudeau, P., 1998, A\\\\&AS, 128, 299\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n Schombert, J. \\\\etal, 1990, AJ, 100, 1533\\\\\\\\\\n\\n\\\\vspace{-3.5mm}\\n\\\\noindent\\n Skillman, E.D., 1986, in \\\"{\\\\it Star Formation in Galaxies}\\\", C.J. 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Rayner\\altaffilmark{2,3}"},{"author":"David L. Jauncey\\altaffilmark{2}"}],"string":"[\n {\n \"author\": \"J-P Macquart\\\\altaffilmark{1}\"\n },\n {\n \"author\": \"Lucyna Kedziora-Chudczer\\\\altaffilmark{1,2}\"\n },\n {\n \"author\": \"David P. Rayner\\\\altaffilmark{2,3}\"\n },\n {\n \"author\": \"David L. Jauncey\\\\altaffilmark{2}\"\n }\n]"},"abstract":{"kind":"string","value":"We report strong variability in the circular and linear polarization of the intraday variable source PKS~1519-273. The circular polarization varies on a timescale of hours to days at frequencies between 1.4 and 8.6~GHz, and is strongly correlated with variations in the total intensity at 4.8 and 8.6~GHz. We argue that the variability is due to interstellar scintillation of a highly compact ($15-35 \\mu$as) component of the source with $-3.8\\pm 0.4$\\% circular polarization at 4.8~GHz. We find that no simple model for the circular polarization can account for both the high magnitude and the frequency dependence in PKS~1519-273 at centimeter wavelengths."},"latex":{"kind":"list like","value":[{"name":"C1519em.tex","string":"\\documentclass[10pt]{article}\n\\usepackage[]{emulateapj}\n\\usepackage[]{psfig}\n\n%\\documentstyle[10pt,emulateapj,psfig]{article}\n%\\documentstyle[12pt,aasms4]{article}\n\n\n\\begin{document}\n\\submitted{}\n\n\\title{Strong, Variable Circular Polarization in PKS~1519-273}\n\n\\author{J-P Macquart\\altaffilmark{1}, \nLucyna Kedziora-Chudczer\\altaffilmark{1,2}, David P. Rayner\\altaffilmark{2,3}, \nDavid L. Jauncey\\altaffilmark{2}}\n\\affil{$^1$Special Research Centre for Theoretical Astrophysics, School of \nPhysics, University of Sydney, New South Wales 2006, Australia.}\n\\affil{$^2$Australia Telescope National Facility, CSIRO, Epping, New \nSouth Wales 2121, Australia.}\n\\affil{$^3$School of Mathematics and Physics, University of Tasmania, \nHobart, Tasmania 7001, Australia.}\n\n% \\altaffiltext{1}{jpm@physics.usyd.edu.au}\n% \\altaffiltext{2}{lkedzior@antf.csiro.au}\n% \\altaffiltext{3}{d_rayner@postoffice.utas.edu.au}\n% \\altaffiltext{4}{djauncey@antf.csiro.au}\n\n\\begin{abstract}\nWe report strong variability in the circular and linear \npolarization of the intraday variable source PKS~1519-273.\nThe circular polarization varies on \na timescale of hours to days at frequencies between 1.4 and 8.6~GHz, and \nis strongly correlated with variations in the total intensity at 4.8 \nand 8.6~GHz. We argue that the variability is due to \ninterstellar scintillation of a highly compact \n($15-35 \\mu$as) component of the \nsource with $-3.8\\pm 0.4$\\% circular polarization at 4.8~GHz.\nWe find that no simple model for the circular polarization \ncan account for both the high magnitude and the frequency \ndependence in PKS~1519-273 at centimeter wavelengths. \n\\end{abstract}\n\n\\keywords{BL Lacertae objects: individual (PKS~1519-273) --- polarization --- \nradiation mechanisms: non-thermal --- scattering}\n\n\n\\section{Introduction}\n\nCircular polarization (CP) in extragalactic sources is very small, typically \n0.05\\% to 0.1\\% of the total source flux density (e.g. \nRoberts et al. 1975, Seaquist et al. 1974, Weiler and de Pater \n1983)\\markcite{Roberts75,Seaquist74,Weiler83} and sometimes variable \n(Komesaroff et al., 1984). Recent measurements of \nCP in extragalactic sources have\nrekindled debate as to its characteristics and origin. \nWardle et al. (1998)\\markcite{Wardle98} detected CP \nin 3C~279 and attributed it to the presence of a relativistic pair plasma. \nNew evidence has emerged that Sgr A$^*$, the AGN-like object at the \ncore of our own Galaxy, is also weakly circularly polarized (Bower et al. \n1999, Sault \\& Macquart 1999)\\markcite{Bower99,Sault99}.\n\nWe present Australia Telescope Compact Array (ATCA) measurements of the \ntimescale and magnitude of the variability of the CP \nin the extragalactic, intraday variable (IDV) BL Lac object, \nPKS~1519-273 (White et al. 1988)\\markcite{White88}. \nPKS~1519-273, at Galactic co-ordinates $l=339.5^{\\circ}, \\, b=24.5^{\\circ}$,\nis identified with a $m_V=18.5$ star-like object with a \nfeatureless optical spectrum. The lower limit on its redshift is $z=0.2$ \n(Veron-Cetty \\& Veron 1993)\\markcite{Veron93}. \nPKS~1519-273 is a compact high brightness temperature \nradio source (Linfield et al. 1989)\\markcite{Linfield89}. The ATCA IDV\nSurvey data shows strong IDV (Kedziora-Chudczer \n1998)\\markcite{KedzioraPhD} and IDV of the total and polarized \nflux densities at GHz frequencies has been \nfound during each of the 5 epochs of ATCA observations over the \npast 7 years.\n\nPKS~1519-273 has not been seen to exhibit IDV at \neither optical (Heidt \\& Wagner 1996)\\markcite{Heidt96} or mm \nwavelengths (Steppe et al. 1988, \nSteppe et al. 1995)\\markcite{Steppe88,Steppe95}. However, it does have a \nhigh degree ($5-12$\\%) of variable optical linear polarization (Impey and Tapia \n1988)\\markcite{Impey96}. PKS~1519-273 is a weak, soft X-ray source \nwith a flux density at 1~keV of 0.39~$\\mu$Jy \n(Urry et al. 1996)\\markcite{Urry96}. Its $\\gamma $-ray \nenergy output is less than \n$0.7\\times 10^{-7}$photons~cm$^{-2}$sec$^{-1}$ for energies \n$E>100$~MeV (Fichtel et al. 1994)\\markcite{Fichtel94}.\n \n\n\\section{Observations and Results}\nWe base our present report on PKS~1519-273 on the data obtained with ATCA \nover 5 days starting on 1998 September 9. Data were collected simultaneously for two \nfrequencies centered on either 1.384 and 2.496 GHz, or 4.800 and \n8.640 GHz each with a 128 MHz bandwidth. \nTo ensure high quality amplitude and phase calibration\nwe frequently observed both the standard primary flux density calibrator, \nPKS~1934-638, and a secondary calibrator, PKS~1514-241. \nThe primary calibrator was used to determine accurately the flux \ndensity scale and the instrumental \npolarization leakages (e.g. Sault, Killeen \\& Kesteven 1991)\\markcite{Sault91}. The \ntotal and polarized flux density lightcurves of \nPKS~1519-273 are presented in fig. 1. The circularly polarized emission, is unresolved on all ATCA baselines and is strongly variable at 4.8 and \n8.6~GHz. Comparison of the 2.5, 4.8 and 8.6~GHz Stokes $V$ measurements for \nPKS~1519-273 and the strong calibrator source PKS~1514-241, extensive \ntesting and consistency checks demonstrate that the observed CP and its \nvariations are not instrumental effects. \n\nThe most striking features of the 4.8 and 8.6~GHz light curves in \nfig. 1 are the exceptionally high level of CP \nand the large amplitude variability in all four Stokes \nparameters. The fractional variability of both the circularly and \nlinearly polarized flux density exceeds that of the total flux \ndensity. The high degree of correlation between the fluctuations in $I$ and \n$V$ (see figs. 1 \\& 2) suggests that the mechanism of variability of the \nCP is strongly related to that in $I$. Comparison of the \nfluctuations in $V$ with those in $I$ implies that, although the \noverall CP is only $\\sim 1$\\%, the\nCP of the variable component, $\\Delta V/\\Delta I$, is \n$-2.4 \\pm 1.3$\\%, $-3.8 \\pm 0.4$\\% and $-2.6 \\pm 0.5$\\% at 2.4, 4.8 and \n8.6~GHz respectively (see figs. 2 \\& 3(c)). The CP is \nweaker, $< 1.3$\\% at 1.4~GHz and its variability is less well-established.\n\n\n\\placefigure{fig:HIGH.PS}\n\\begin{figure*}\n \\begin{center}\n\\begin{tabular}{c}\n \\psfig{file=HIGH.PS,angle=270,width=120mm} \\\\\n \\psfig{file=LOW.PS,angle=270,width=120mm}\n\\end{tabular}\n\\end{center}\n\\caption{Variability of PKS~1519-273 in the total intensity ($I$), \nCP ($V$), and magnitude of the linear polarization ($P$),\nfor the four bands of the ATCA over 5 days. Each point \nrepresents a 10~min average, and is plotted with $1\\,\\sigma$ error bars. \nFluctuations in $I$ and $V$ are strongly correlated ($r=-0.90$ at \n4.8~GHz and $r=-0.80$ at 8.6~GHz).}\n\\end{figure*}\n\n\\placefigure{fig:v_vs_i_2496.eps}\n\\begin{figure*}\n\\begin{tabular}{c}\n \\psfig{file=v_vs_i_2496.eps,angle=270,width=60mm} \n \\psfig{file=v_vs_i_4800.eps,angle=270,width=60mm} \n \\psfig{file=v_vs_i_8640.eps,angle=270,width=60mm}\n\\end{tabular}\n\\caption{Plot \nof the correlation between $V$ and $I$. The best fit lines give \na fractional CP of $-2.4\\pm 1.3$\\%, $-3.8 \\pm 0.4$\\% \nand $-2.6 \\pm 0.5$\\% respectively at 2.5, 4.8 and 8.6~GHz for the \nvariable component of the source. The fluctuations in $I$ and $V$ do \nnot appear to be correlated at 1.4~GHz, indicating that we detect \n{\\it no} CP associated with the variable component \nat this frequency. We place an upper limit on the CP of \nthis component of 1.3\\%.}\n\\end{figure*}\n\n\\section{Discussion}\n\\subsection{Scintillation}\n\nWe attribute the short-timescale variability of this source to \nInterstellar Scintillation (ISS) in our Galaxy. ISS has already been \ninvoked to explain radio source IDV (Heeschen \\&\nRickett 1997)\\markcite{Heeschen97}, \nincluding the rapid variability of PKS~0405-385 (Kedziora-Chudczer et \nal. 1997)\\markcite{Ked97}. If intrinsic to the source, the total intensity \nvariations observed at 4.8~GHz imply a brightness temperature of $T_B \\gtrsim 3 \n\\times 10^{17}$~K for $z \\gtrsim 0.2$, based simply on light travel \ntimes. However, assuming that the \nvariations are intrinsic implies a source size that is necessarily \nsufficiently small to exhibit variability due to \nISS (Rickett et al. 1995)\\markcite{Rickett95}. This suggests that an \nexplanation based on ISS should be sought first.\n\nThe increase in modulation index (the rms normalized by the mean intensity), shown in fig. 3, and\nthe short variability timescale from 8.6 to 4.8~GHz, shown in fig. 1, \nare consistent with \nscintillation in the regime of weak scattering \n(e.g., Narayan 1992)\\markcite{Narayan92}, while the decrease in \nmodulation indices and the increasingly longer \nvariability timescales from 4.8 to 1.4~GHz \nare characteristic of refractive scintillation.\n\nAssuming that the density \ninhomogeneities in the ISM are located on a thin screen, the refractive scintillation at 1.4~GHz may be used to place a \nconstraint upon the distance to the scattering screen. The physical \nextent of the scattering disk at 1.4~GHz is the product of the long-period,\nrefractive variability \ntimescale, $t_{1.4}$, no \nless than 4 days (see fig. 1), and \nthe scintillation speed, $v$, of order 50~km/s (see Rickett et al. 1995). VSOP\nobservations at 1.7~GHz\\footnote{See \nhttp://www.vsop.isas.ac.jp/general/pr/1519-273.gif} indicate that the \nsource is unresolved, so we assume an\nangular size of no more than 0.3~mas. This implies an observer-screen distance of \n$D \\geq 390 (v/50~{\\rm km/s}) (t_{1.4}/4~{\\rm days})$~pc, or 390~pc in the\npresent case.\n\nHaving obtained a lower limit to the distance to the \nscattering screen, we may constrain the angular diameter of the source \nfrom the scintillation parameters in the weak scattering regime where \nthe scattering is quite sensitive to source size effects. The \nscintillation timescale of $\\sim 12$~hours at 4.8~GHz can be explained \neither in terms a scattering screen at large distance ($> 15$~kpc), or \nby a partially resolved source. For weak \nscattering, the source is resolved if the angular diameter of the \nsource, $\\theta_S$, exceeds the angular diameter of \nthe first Fresnel zone $\\theta_F = (k D)^{-1/2}$, where $k$ is the \nwavenumber. The \nscintillation timescale is then $t_{4.8} \\approx \\theta_S D/v$ for $\\theta_S >\n\\theta_F$ (Narayan 1992).\nA screen in our own Galaxy implies $D \\ll 15$~kpc, so the source must be partially resolved. \nAssuming the asymptotic results of weak scattering to be valid \nbetween the weak and strong scattering regimes, the scintillation timescale \nthen yields an {\\it estimate} of the intrinsic angular source size of \n$$\n\\theta_S \\approx 14.4 \\left(\\frac{t_{4.8}}{12~{\\rm hours}} \\right) \n\\left( \\frac{v}{50~{\\rm km/s} } \\right) \n\\left( \\frac{D}{1~{\\rm kpc}}\\right)^{-1}~\\mu{\\rm as}. \\eqno(1)\n$$\n\nFor a scintillating source of flux density $I_0$, the root-mean-square \nfluctuation is $I_{\\rm rms} = I_0 m(\\theta_S)$, where \n$m(\\theta_S)=(kD \\theta_S^2)^{7/12}$ is the modulation index expected for \na source of size $\\theta_S > \\theta_F$ (e.g. Narayan 1992)\\markcite{Narayan92}, \nand we have assumed that 4.8~GHz is near the \ntransition frequency between weak and strong scattering.\nGiven $I_{\\rm rms} = 0.11$~Jy and with the derived angular size of the \nscintillating component of the source, we estimate $I_0$ and derive \nits brightness temperature:\n{\\small\n$$\nT_b \\approx 2.0 \\times 10^{14} \\left( \\frac{D}{1~{\\rm kpc}} \n\\right)^{17/12} \n\\left( \\frac{t_{4.8}}{12~{\\rm hours}} \\right)^{-5/6} \n\\left( \\frac{v}{50~{\\rm km/s}} \\right)^{-5/6}~{\\rm K}. \\eqno(2)\n$$}\nUsing the limit of the distance to the scattering screen, the maximum \npossible angular size of the source for $t_{4.8}=12$~hours and \n$v=50$~km/s is $37\\,\\mu$as, the minimum brightness \ntemperature is $T_b=5 \\times 10^{13}$~K, consistent with incoherent synchrotron \nemission subject to relativistic beaming with a Doppler \nboosting factor $\\delta \\gtrsim 200 (1+z)$ \n(Readhead 1994)\\markcite{Readhead94}.\n\nHowever, if the CP observed at \n4.8~GHz is entirely due to the variable component, we may further \nconstrain $T_b$. From fig. 2 we have \n$I_0 = 0.35 \\pm 0.04$~Jy, implying $m(\\theta_S) \\approx 0.32$ \n(consistent with the modulation index observed in $V$: $0.32$) and hence an \nangular size of $9.8 (D/1\\, {\\rm kpc})^{-1/2} \\,\\mu$as. Comparing with \nequation (1), we have $v = 34 \\,(D/1\\,{\\rm kpc})^{1/2}$~km/s, implying \na brightness temperature of \n$3 \\times 10^{14} (D/1\\,{\\rm kpc}) (t_{4.8}/12\\,{\\rm hours})^{-5/6}$~K. \nA scintillation speed exceeding $50$~km/s therefore implies \na brightness temperature $T_b \\gtrsim 6 \\times 10^{14}$~K.\n% comparable \n% to that derived for PKS~0405-385 \n% (Kedziora-Chudczer et al. 1997)\\markcite{Kedzioraetal}.\n\n\\subsection{Circular Polarization}\nWe consider the origin of the CP in terms of intrinsic synchrotron \n(Legg \\& Westfold 1968)\\markcite{Legg68}, partial conversion of the linear \npolarization into CP due to ellipticity of the \nnatural wave modes of the cold background plasma (Pacholczyk \n1973)\\markcite{Pac73} or \nof the relativistic electron gas itself (e.g. Sazonov 1969, \nJones \\& O'Dell 1977a,b)\\markcite{Saz69,Jones77a,Jones77b}.\n\nIf the CP in \nthe scintillating component is due to \nsynchrotron emission then, following Legg \\& Westfold~(1968)\\markcite{Leg68}, \nthe Lorentz factor of the particles responsible for a CP \nof $m_c$ in a {\\it uniform} magnetic field \nis $\\gamma \\approx \\cot \\theta/m_c$, where \n$\\theta$ is the angle between the magnetic field\nand the line of sight. For $30^\\circ < \\theta < 60^\\circ$ this \nimplies Lorentz factors in the range $\\approx 15-45$ to\nexplain the CP at 4.8~GHz. Indeed, the observed (low) \nlevel of linear polarization suggests a\nnon-uniform magnetic field, indicating that \neven higher Lorentz factors are required. The \nmaximum brightness temperature of such emission is $T_B \\leq \n5.9 \\times 10^9 \\gamma$~K$=2.7 \\times 10^{11}$~K in the rest frame. Bulk motion with a \nDoppler boosting factor $\\delta \\gtrsim 200$ would account for the difference \nbetween the rest-frame and scintillation-derived brightness \ntemperatures. Such a Doppler factor, although very high, cannot be \nentirely ruled out. However the observed frequency dependence of the degree of \nCP is far from \nthe $\\nu^{-1/2}$ expected from synchrotron theory (see fig 3c); the \nCP {\\it decreases} sharply between 8.6 and 1.4~GHz.\nIt is therefore unlikely that the CP is due to synchrotron emission.\n\nAlternatively, the CP could be due to propagation \nthrough a relativistic pair plasma, such as may be present within the \nsource itself. The \nbirefringence induced in a medium by the presence of a pair plasma \nmay convert linear polarization to CP as \nfollows:\n$$\nV(\\nu) = U_{0}(\\nu) \\sin ( c^3 {\\rm RRM}/\\nu^3), \\eqno(3)\n$$\nwhere the relativistic rotation measure, RRM, depends upon the \ndensity of relativistic particles, the path length, the magnetic \nfield, and the minimum Lorentz factor of the pairs (e.g. Kennett \\& Melrose \n1998)\\markcite{Ken98}.\nThis effect operates only when the direction of the incident linear \npolarization is at an oblique angle to the projection of the magnetic \nfield on the plane orthogonal to the ray direction. The axes used to \ndefine the Stokes parameters may be chosen such that synchrotron \nemission has $Q \\neq 0, U=0$. With this choice, the effect occurs \nonly if the incident radiation has $U_0 \\neq 0$, requiring either \nFaraday rotation or that it \noriginate from a region of the source where the magnetic field is in a \ndifferent direction to that where the polarization \nconversion takes place. \n\nA characteristic of this model is a strong frequency dependence on the \nsign of $V$. If ${\\rm RRM}$ is high enough to produce the CP \nobserved at high frequency, this model predicts rapid changes \nin $V$ at low frequency: in particular, equation (3) yields the lower limit \n$|{\\rm RRM}| \\geq 6.2 \\times 10^2 \\, (1+z)^3\n/f_U(8.6\\,{\\rm GHz})$~rad/m$^3$ \nto explain the $-2.6$\\% CP at 8.6~GHz, where we write $f_U(8.6\\,{\\rm GHz}) =\n|(U_0(8.6\\,{\\rm GHz})/I(8.6\\,{\\rm GHz})|$. \nFor this lower limit, $\\lambda^3 {\\rm RRM}$ will vary by \n$0.88/f_U(8.6\\,{\\rm GHz})$~rad across 64~MHz\nbandwidth at 1.4~GHz and $0.08/f_U(8.6\\,{\\rm GHz})$~rad at 2.5~GHz. We \nsearched for frequency-dependent variations in $V$\nat all four frequencies by selecting two adjacent 32~MHz sub-bands at each \nfrequency. None were found. Although the Faraday rotation \n(RM $\\approx$ 69 rad/m$^2$)\nacross the band was clearly detected at 1.4 and 2.5~GHz, the variations in $V$ \nbetween sub-bands were less than 4\\% and 0.8\\% at these frequencies\nrespectively. This result appears inconsistent with the derived lower \nlimit on RRM, although the null result at \n1.4~GHz may result from an absence\nof CP in the scintillating component (which in turn implies\n$|U_0| /I \\sim |V|/I < 0.01$ at 1.4~GHz).\n\nThe fact that all detections of the CP are of same sign also argues \nagainst this model. If (i) $V$ does not change sign at any frequencies intermediate to those of our \nmeasurements (i.e. the spectrum is well-sampled) and (ii) $U_0$ does not \nchange sign in the range 1.4$-$8.6~GHz then equation (3) implies \n$\\lambda^3 {\\rm RRM} < 2 \\pi$ for \nall frequencies above 1.4~GHz (even if $V(1.4~{\\rm GHz})$, whose sign \nis uncertain, is positive).\nAt 1.4~GHz one then has \n$|{\\rm RRM}| < 6.2 \\times 10^2 \\, (1+z)^{3}$~rad/m$^3$, requiring \n$f_U(8.6\\,{\\rm GHz}) \\geq 100$\\% to be \nconsistent with the lower limit on ${\\rm RRM}$ obtained above. While \ndifficult to exclude entirely, we therefore conclude that the production of \nCP by a pair-dominated plasma is implausible.\n\nPolarization conversion may also occur in a medium containing a \nmixture of\ncold and relativistic pair plasma, in which case the fractional CP \nvaries as $m_c \\propto \\nu^{-1}$ Pacholczyk (1973). \nThis model appears implausible in light of the observed \n$\\nu^{0.7_{-0.3}^{+1.4}}$ frequency \ndependence of the CP from 1.4 to 4.8~GHz. \n\nThe presence of several distinct sub-components may \nalter the spectral properties of the observed CP.\nHowever, the scintillation characteristics argue against the existence of \nmultiple circularly polarized components, each with distinct $U_0$, RRM and \n$\\gamma$. The presence of multiple components with different $V/I$ \nwould lead to substructure in the lightcurve of $V$ compared to the lightcurve\nof $I$ as the scintillation selectively amplifies and deamplifies\nparts of the source differently. This would result in a loss of correlation \nbetween $V$ and $I$, particularly at 4.8 and 8.6~GHz, where the \nscintillation is most sensitive to small-scale structure. This \nis not observed in fig. 1 where \nthe correlation coefficients are close to unity. However, it is more \ndifficult to ascertain the presence of substructure in the variability \nat 1.4 and 2.5~GHz due to the long timescale of the fluctuations.\n \nJones \\& O'Dell (1977a, 1977b)\\markcite{Jones77a,Jones77b} \npresented a model for the CP of inhomogeneous \nsynchrotron sources, incorporating optical depth effects, mode \ncoupling and mode conversion due to the birefringence of the \nplasma. Below the self-absorption turnover \nfrequency, $\\nu_{\\rm SSA}$, mode coupling dominates, and the \nCP is typically less than 0.05\\%, and certainly \nnot more than 2\\%. Mode conversion dominates above $\\nu_{\\rm SSA}$, with the \nCP as high as 10\\% near $\\nu_{\\rm SSA}$, and \ndecreasing to less than $10^{-3}$ at frequencies a decade above\n$\\nu_{\\rm SSA}$. This model is viable only if $\\nu_{\\rm SSA}$ is\nwithin a factor $\\sim 1.4$ of the frequency at which the high (3.8\\%) \nCP was observed, at 4.8~GHz. This is difficult to \nverify as we do not know the intrinsic spectrum of the \nscintillating component and the frequency range of our observations is limited.\n\n\\placefigure{fig:FIG3N.PS}\n\\begin{figure*}\n\\begin{tabular}{c}\n \\psfig{file=FIG3N.PS,angle=270,width=70mm}\n\\end{tabular}\n\\caption{Various quantities derived from the data in \nfig. 1. (a) Spectra of the \ntotal intensity (circles) and CP (squares) in PKS~1519-273 for the four \nbands of ATCA averaged over the duration of the observations.\n(b) Modulation indices derived from the intensity \nfluctuations over the 5 days of observations. The long timescale of \nvariability makes it difficult to compare these values with the \nensemble-average quantities predicted by scintillation theory. This \nis particularly relevant at 2.5 and 1.4~GHz because the timescale of \nvariability is comparable to or exceeds the period of observation.\n(c) The spectrum of circularly polarized component derived by \ncomparing the magnitude of the fluctuations in $I$ with those in $V$ \n(see fig. 2).}\n\\end{figure*}\n\n\n\\section{Conclusion}\nThe variability detected in PKS~1519-273 in all four Stokes \nparameters at frequencies from 1.4 to 8.6~GHz is remarkable, but has a natural \ninterpretation in terms of ISS. The \nscintillation properties at 4.8~GHz constrain the brightness \ntemperature of the scintillating component to $T_b \\geq 5 \\times \n10^{13}$~K, although there is strong evidence to suggest it may be as \nhigh as $6 \\times 10^{14}$~K. Comparison of the fluctuations in \n$I$ and $V$ imply that \nthis component is exceptionally highly circularly polarized at 8.6 and \n4.8~GHz. Simple applications of synchrotron theory and models of \ncircular repolarization encounter difficulties with the spectral \nbehavior and magnitude of the CP. \nThe strong correlation between the fluctuations in $I$ and $V$ at 4.8 \nand 8.6~GHz and the high sensitivity of the scintillation to source \nstructure at these frequencies argue against a complex source, with different $V/I$ in each component.\nInclusion of effects due to small-scale inhomogeneity, mode coupling \nand optical depth effects may reproduce \nthe observed characteristics of the CP. However, \nthis model is only viable if the frequency at which the\nsource is observed to become optically thin is in the range \n$3.4\\,{\\rm GHz} \\lesssim \\nu \\lesssim 6.7\\,{\\rm GHz}$. This possibility is \npresently difficult to confirm. Even if correct, the puzzle \nremains as to why so few sources exhibit such high \nlevels of CP. \n\nFinally, in light of the extremely high brightness temperature of \nPKS~1519-273, we advance the possibility that the observed emission \nis not due to synchrotron emission at all and that high CP \nmay be a characteristic of a new emission mechanism.\n\n\n\\acknowledgments\nWe thank Don Melrose, Ron Ekers, Mark Walker, Jim Lovell, Dick \nHunstead and Lawrence Cram for valuable discussions. The \nAustralia Telescope is funded by the Commonwealth Government for \noperation as a national facility by the CSIRO.\n\n\\begin{references}\n\n\\reference{Bower99}\nBower, G.C., Falcke, H. \\& Backer, D.C., \n{1999}, \\apj, 1999, 523, L29\n\n% \\reference{Cordes86}\n% Cordes, J.M., 1986, \\apj, {311}, 183\n\n\\reference{Fichtel94}\nFichtel, C.E. et al., 1994, \\apjs, 94, 551\n\n% \\reference{Frater92}\n% Frater, R.H., Brooks, J.W. \\& Whiteoak, J.B., 1992, JEEEA,12, 103\n% JEEEA = Jnl of Electrical and Electronics Engineering, Australia\n\n\n\\reference{Heidt96}\nHeidt, J. \\& Wagner, S.J., 1996, \\aap, {305}, 42\n\n\\reference{Heeschen97}\nHeeschen, D.S., Rickett, B.J., 1997, \\aj, 93, 589\n\n\\reference{Impey96} Impey, C.D. \\& Tapia, S., 1996, \\apj, 333, 666\n\n\\reference{Jones77a}\nJones, T.W., O'Dell, S.L.,\n{1977a},\n\\apj,\n{214},\n552\n\n\n\\reference{Jones77b}\nJones, T.W., O'Dell, S.L.,\n{1977b},\n\\apj,\n{215},\n236.\n\n\n\\reference\n{KedzioraPhD}\nKedziora-Chudczer, L., Jauncey, D.L., Wieringa, M.H., Reynolds, J.E., Tzioumis,\nA.K. {1998} in ASP Conf. Ser. 144, Radio Emission from Galactic and Extragalactic Compact Radio\nSources, eds: J.A. Zensus, G.B. Taylor \\& J.M. Wrobel, 271\n\n\\reference\n{Kedzioraetal}\nKedziora-Chudczer, L., Jauncey, D.L., Wieringa, M.H., Walker, M.A., Nicolson,\nG.D., Reynolds, J.E. \\& Tzioumis, A.K.\n{1997},\n\\apj,\n{490},\nL9.\n\n\\reference{Ken98}\nKennett, M.P. \\& Melrose, D.B., 1998, {\\it Publ. Astron. Soc. Aust.}, 15, 211.\n\n\\reference{Kom84}\nKomesaroff,� M.�M., Roberts,� J.�A., Milne,� D.�K., Rayner, �P.�T., \nCooke, �D.�J.,\n{1984},\n\\mnras,\n{208},\n409.\n\n\\reference\n{Legg68}\nLegg, M.P.C., Westfold, K.C.,\n{1968},\n\\apj,\n{154},\n499\n\n\\reference{Linfield89} \nLinfield et al., 1989, \\apj, 336, 1105\n\n\n\\reference\n{Narayan92}\nNarayan, R.,\n{1992},\nPhil Trans R Soc Lond A,\n{341},\n151.\n\n\\reference\n{Pac73}\nPacholczyk, A.G.,\n{1973},\n\\mnras,\n{163},\n29P.\n\n\n\\reference{Readhead94}\nReadhead, A.C.S., 1994, \\apj, 426, 51\n\n\\reference{Rickett95}\nRickett, B.J., Quirrenbach, A., Wegner, R., Krichbaum, T.P. \\& Witzel, A., {1995},\n\\aap, {293}, 479\n\n\n\\reference\n{Roberts75}\nRoberts, J.A., Cooke, D.J., Murray, J.D., Cooper, B.F.C, Roger, R.S.,\nRibes, J.-C. \\& Biraud, F.,\n{1975}\nAuJPh,\n{28},\n325\n\n\\reference{Sault91} Sault, R.J., Killeen, N.E.B. \\& Kesteven, M.J., \n1991, ATNF Technical Document Series 39/015, ATNF \n\n\\reference{Sault99} Sault, R.J. \\& Macquart, J.-P., 1999, \\apj, 526, L85\n\n\\reference{Saz69}\nSazonov, V.N.,\n{1969},\nZh. Eksper Teor. Fiz.,\n{56},\n1074 (English transl. in Soviet Phys. -- JETP, {29}, 578).\n\n\\reference{Seaquist74}\nSeaquist, E.R, Gregory, P.C. \\& Clarke, T.R., 1974, \\aj, 79, 918\n\n\\reference{Steppe88}\nSteppe, H., Salter, C.J., Chini, R., Kreysa, E., Brunswig, W. \\& Lobato \nPerez, J., 1988, \\aaps, 75, 317\n\n\\reference{Steppe95}\nSteppe, H., Jeyakumar, S., Saikia, D.J. \\& Salter, C.J., 1995,\n\\aaps, 113, 409\n\n\\reference{Urry96}\nUrry, C.M., Sambruna, R.M., Worrall, D.M., Kollgaard, R.I., \nFeigelson, E.D., Perlman, E.S. \\& Stocke, J.T., 1996, \\apj, 463, 424\n\n\\reference{Veron93}\nVeron-Cetty, M.-P. \\& Veron, P., 1993, \\aaps, 100, 521\n\n% \\reference{Walker98}\n% Walker, M.A., 1998, \\mnras, 294, 307\n\n\\reference{Wardle98}\nWardle, J.F.C., Homan, D.C., Ojha, R. \\& Roberts, D.H.,\n{1998},\nNature,\n{395},\n457\n\n\\reference\n{Weiler83}\nWeiler, K. W \\& de Pater, I.,\n{1983},\n\\apjs,\n{52},\n293\n\n\\reference{White88} White, G.L., Jauncey, D.L., Savage, A., Wright, \nA.E, Batty, M.J., Peterson, B.A. \\& Gulkis, S., 1988, \\apj, 327, 561\n\n\\end{references}\n\n\n% \\figcaption[HIGH.PS,LOW.PS]{Variability of PKS~1519-273 in the total intensity ($I$), \n% CP ($V$), and magnitude of the linear polarization ($P$),\n% for the four bands of the ATCA over 5 days. Each point \n% represents a 10~min average, and is plotted with $1\\,\\sigma$ error bars. \n% Fluctuations in $I$ and $V$ are strongly correlated ($r=-0.90$ at \n% 4.8~GHz and $r=-0.80$ at 8.6~GHz).}\n% \\special{psfile=HIGH.PS angle=270 hscale=50 vscale=50}\n% \\vskip 2.8 in\n% \\special{psfile=LOW.PS angle=270 hscale=50 vscale=50}\n\n\n \n% \\figcaption[v_vs_i_2496.eps,v_vs_i_4800.eps,v_vs_i_8640.eps]{Plot \n% of the correlation between $V$ and $I$. The best fit lines give \n% a fractional CP of $-2.4\\pm 1.3$\\%, $-3.8 \\pm 0.4$\\% \n% and $-2.6 \\pm 0.5$\\% respectively at 2.5, 4.8 and 8.6~GHz for the \n% variable component of the source. The fluctuations in $I$ and $V$ do \n% not appear to be correlated at 1.4~GHz, indicating that we detect \n% {\\it no} CP associated with the variable component \n% at this frequency. We place an upper limit on the CP of \n% this component of 1.3\\%.}\n% \\special{psfile=v_vs_i_2496.eps angle=270 hscale=30 vscale=30}\n% \\vskip 2.2 in\n% \\special{psfile=v_vs_i_4800.eps angle=270 hscale=30 vscale=30}\n% \\vskip 2.2 in\n% \\special{psfile=v_vs_i_8640.eps angle=270 hscale=30 vscale=30}\n\n\n% \\figcaption[FIG3N.PS]{Various quantities derived from the data in \n% fig. 1. (a) Spectra of the \n% total intensity (circles) and CP (squares) in PKS~1519-273 for the four \n% bands of ATCA averaged over the duration of the observations.\n% (b) Modulation indices derived from the intensity \n% fluctuations over the 5 days of observations. The long timescale of \n% variability makes it difficult to compare these values with the \n% ensemble-average quantities predicted by scintillation theory. This \n% is particularly relevant at 2.5 and 1.4~GHz because the timescale of \n% variability is comparable to or exceeds the period of observation.\n% (c) The spectrum of circularly polarized component derived by \n% comparing the magnitude of the fluctuations in $I$ with those in $V$ \n% (see fig. 2).}\n% \\special{psfile=FIG3N.PS angle=270 hscale=80 vscale=80}\n\n\n\\end{document}\n\n\n"}],"string":"[\n {\n \"name\": \"C1519em.tex\",\n \"string\": \"\\\\documentclass[10pt]{article}\\n\\\\usepackage[]{emulateapj}\\n\\\\usepackage[]{psfig}\\n\\n%\\\\documentstyle[10pt,emulateapj,psfig]{article}\\n%\\\\documentstyle[12pt,aasms4]{article}\\n\\n\\n\\\\begin{document}\\n\\\\submitted{}\\n\\n\\\\title{Strong, Variable Circular Polarization in PKS~1519-273}\\n\\n\\\\author{J-P Macquart\\\\altaffilmark{1}, \\nLucyna Kedziora-Chudczer\\\\altaffilmark{1,2}, David P. Rayner\\\\altaffilmark{2,3}, \\nDavid L. Jauncey\\\\altaffilmark{2}}\\n\\\\affil{$^1$Special Research Centre for Theoretical Astrophysics, School of \\nPhysics, University of Sydney, New South Wales 2006, Australia.}\\n\\\\affil{$^2$Australia Telescope National Facility, CSIRO, Epping, New \\nSouth Wales 2121, Australia.}\\n\\\\affil{$^3$School of Mathematics and Physics, University of Tasmania, \\nHobart, Tasmania 7001, Australia.}\\n\\n% \\\\altaffiltext{1}{jpm@physics.usyd.edu.au}\\n% \\\\altaffiltext{2}{lkedzior@antf.csiro.au}\\n% \\\\altaffiltext{3}{d_rayner@postoffice.utas.edu.au}\\n% \\\\altaffiltext{4}{djauncey@antf.csiro.au}\\n\\n\\\\begin{abstract}\\nWe report strong variability in the circular and linear \\npolarization of the intraday variable source PKS~1519-273.\\nThe circular polarization varies on \\na timescale of hours to days at frequencies between 1.4 and 8.6~GHz, and \\nis strongly correlated with variations in the total intensity at 4.8 \\nand 8.6~GHz. We argue that the variability is due to \\ninterstellar scintillation of a highly compact \\n($15-35 \\\\mu$as) component of the \\nsource with $-3.8\\\\pm 0.4$\\\\% circular polarization at 4.8~GHz.\\nWe find that no simple model for the circular polarization \\ncan account for both the high magnitude and the frequency \\ndependence in PKS~1519-273 at centimeter wavelengths. \\n\\\\end{abstract}\\n\\n\\\\keywords{BL Lacertae objects: individual (PKS~1519-273) --- polarization --- \\nradiation mechanisms: non-thermal --- scattering}\\n\\n\\n\\\\section{Introduction}\\n\\nCircular polarization (CP) in extragalactic sources is very small, typically \\n0.05\\\\% to 0.1\\\\% of the total source flux density (e.g. \\nRoberts et al. 1975, Seaquist et al. 1974, Weiler and de Pater \\n1983)\\\\markcite{Roberts75,Seaquist74,Weiler83} and sometimes variable \\n(Komesaroff et al., 1984). Recent measurements of \\nCP in extragalactic sources have\\nrekindled debate as to its characteristics and origin. \\nWardle et al. (1998)\\\\markcite{Wardle98} detected CP \\nin 3C~279 and attributed it to the presence of a relativistic pair plasma. \\nNew evidence has emerged that Sgr A$^*$, the AGN-like object at the \\ncore of our own Galaxy, is also weakly circularly polarized (Bower et al. \\n1999, Sault \\\\& Macquart 1999)\\\\markcite{Bower99,Sault99}.\\n\\nWe present Australia Telescope Compact Array (ATCA) measurements of the \\ntimescale and magnitude of the variability of the CP \\nin the extragalactic, intraday variable (IDV) BL Lac object, \\nPKS~1519-273 (White et al. 1988)\\\\markcite{White88}. \\nPKS~1519-273, at Galactic co-ordinates $l=339.5^{\\\\circ}, \\\\, b=24.5^{\\\\circ}$,\\nis identified with a $m_V=18.5$ star-like object with a \\nfeatureless optical spectrum. The lower limit on its redshift is $z=0.2$ \\n(Veron-Cetty \\\\& Veron 1993)\\\\markcite{Veron93}. \\nPKS~1519-273 is a compact high brightness temperature \\nradio source (Linfield et al. 1989)\\\\markcite{Linfield89}. The ATCA IDV\\nSurvey data shows strong IDV (Kedziora-Chudczer \\n1998)\\\\markcite{KedzioraPhD} and IDV of the total and polarized \\nflux densities at GHz frequencies has been \\nfound during each of the 5 epochs of ATCA observations over the \\npast 7 years.\\n\\nPKS~1519-273 has not been seen to exhibit IDV at \\neither optical (Heidt \\\\& Wagner 1996)\\\\markcite{Heidt96} or mm \\nwavelengths (Steppe et al. 1988, \\nSteppe et al. 1995)\\\\markcite{Steppe88,Steppe95}. However, it does have a \\nhigh degree ($5-12$\\\\%) of variable optical linear polarization (Impey and Tapia \\n1988)\\\\markcite{Impey96}. PKS~1519-273 is a weak, soft X-ray source \\nwith a flux density at 1~keV of 0.39~$\\\\mu$Jy \\n(Urry et al. 1996)\\\\markcite{Urry96}. Its $\\\\gamma $-ray \\nenergy output is less than \\n$0.7\\\\times 10^{-7}$photons~cm$^{-2}$sec$^{-1}$ for energies \\n$E>100$~MeV (Fichtel et al. 1994)\\\\markcite{Fichtel94}.\\n \\n\\n\\\\section{Observations and Results}\\nWe base our present report on PKS~1519-273 on the data obtained with ATCA \\nover 5 days starting on 1998 September 9. Data were collected simultaneously for two \\nfrequencies centered on either 1.384 and 2.496 GHz, or 4.800 and \\n8.640 GHz each with a 128 MHz bandwidth. \\nTo ensure high quality amplitude and phase calibration\\nwe frequently observed both the standard primary flux density calibrator, \\nPKS~1934-638, and a secondary calibrator, PKS~1514-241. \\nThe primary calibrator was used to determine accurately the flux \\ndensity scale and the instrumental \\npolarization leakages (e.g. Sault, Killeen \\\\& Kesteven 1991)\\\\markcite{Sault91}. The \\ntotal and polarized flux density lightcurves of \\nPKS~1519-273 are presented in fig. 1. The circularly polarized emission, is unresolved on all ATCA baselines and is strongly variable at 4.8 and \\n8.6~GHz. Comparison of the 2.5, 4.8 and 8.6~GHz Stokes $V$ measurements for \\nPKS~1519-273 and the strong calibrator source PKS~1514-241, extensive \\ntesting and consistency checks demonstrate that the observed CP and its \\nvariations are not instrumental effects. \\n\\nThe most striking features of the 4.8 and 8.6~GHz light curves in \\nfig. 1 are the exceptionally high level of CP \\nand the large amplitude variability in all four Stokes \\nparameters. The fractional variability of both the circularly and \\nlinearly polarized flux density exceeds that of the total flux \\ndensity. The high degree of correlation between the fluctuations in $I$ and \\n$V$ (see figs. 1 \\\\& 2) suggests that the mechanism of variability of the \\nCP is strongly related to that in $I$. Comparison of the \\nfluctuations in $V$ with those in $I$ implies that, although the \\noverall CP is only $\\\\sim 1$\\\\%, the\\nCP of the variable component, $\\\\Delta V/\\\\Delta I$, is \\n$-2.4 \\\\pm 1.3$\\\\%, $-3.8 \\\\pm 0.4$\\\\% and $-2.6 \\\\pm 0.5$\\\\% at 2.4, 4.8 and \\n8.6~GHz respectively (see figs. 2 \\\\& 3(c)). The CP is \\nweaker, $< 1.3$\\\\% at 1.4~GHz and its variability is less well-established.\\n\\n\\n\\\\placefigure{fig:HIGH.PS}\\n\\\\begin{figure*}\\n \\\\begin{center}\\n\\\\begin{tabular}{c}\\n \\\\psfig{file=HIGH.PS,angle=270,width=120mm} \\\\\\\\\\n \\\\psfig{file=LOW.PS,angle=270,width=120mm}\\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\caption{Variability of PKS~1519-273 in the total intensity ($I$), \\nCP ($V$), and magnitude of the linear polarization ($P$),\\nfor the four bands of the ATCA over 5 days. Each point \\nrepresents a 10~min average, and is plotted with $1\\\\,\\\\sigma$ error bars. \\nFluctuations in $I$ and $V$ are strongly correlated ($r=-0.90$ at \\n4.8~GHz and $r=-0.80$ at 8.6~GHz).}\\n\\\\end{figure*}\\n\\n\\\\placefigure{fig:v_vs_i_2496.eps}\\n\\\\begin{figure*}\\n\\\\begin{tabular}{c}\\n \\\\psfig{file=v_vs_i_2496.eps,angle=270,width=60mm} \\n \\\\psfig{file=v_vs_i_4800.eps,angle=270,width=60mm} \\n \\\\psfig{file=v_vs_i_8640.eps,angle=270,width=60mm}\\n\\\\end{tabular}\\n\\\\caption{Plot \\nof the correlation between $V$ and $I$. The best fit lines give \\na fractional CP of $-2.4\\\\pm 1.3$\\\\%, $-3.8 \\\\pm 0.4$\\\\% \\nand $-2.6 \\\\pm 0.5$\\\\% respectively at 2.5, 4.8 and 8.6~GHz for the \\nvariable component of the source. The fluctuations in $I$ and $V$ do \\nnot appear to be correlated at 1.4~GHz, indicating that we detect \\n{\\\\it no} CP associated with the variable component \\nat this frequency. We place an upper limit on the CP of \\nthis component of 1.3\\\\%.}\\n\\\\end{figure*}\\n\\n\\\\section{Discussion}\\n\\\\subsection{Scintillation}\\n\\nWe attribute the short-timescale variability of this source to \\nInterstellar Scintillation (ISS) in our Galaxy. ISS has already been \\ninvoked to explain radio source IDV (Heeschen \\\\&\\nRickett 1997)\\\\markcite{Heeschen97}, \\nincluding the rapid variability of PKS~0405-385 (Kedziora-Chudczer et \\nal. 1997)\\\\markcite{Ked97}. If intrinsic to the source, the total intensity \\nvariations observed at 4.8~GHz imply a brightness temperature of $T_B \\\\gtrsim 3 \\n\\\\times 10^{17}$~K for $z \\\\gtrsim 0.2$, based simply on light travel \\ntimes. However, assuming that the \\nvariations are intrinsic implies a source size that is necessarily \\nsufficiently small to exhibit variability due to \\nISS (Rickett et al. 1995)\\\\markcite{Rickett95}. This suggests that an \\nexplanation based on ISS should be sought first.\\n\\nThe increase in modulation index (the rms normalized by the mean intensity), shown in fig. 3, and\\nthe short variability timescale from 8.6 to 4.8~GHz, shown in fig. 1, \\nare consistent with \\nscintillation in the regime of weak scattering \\n(e.g., Narayan 1992)\\\\markcite{Narayan92}, while the decrease in \\nmodulation indices and the increasingly longer \\nvariability timescales from 4.8 to 1.4~GHz \\nare characteristic of refractive scintillation.\\n\\nAssuming that the density \\ninhomogeneities in the ISM are located on a thin screen, the refractive scintillation at 1.4~GHz may be used to place a \\nconstraint upon the distance to the scattering screen. The physical \\nextent of the scattering disk at 1.4~GHz is the product of the long-period,\\nrefractive variability \\ntimescale, $t_{1.4}$, no \\nless than 4 days (see fig. 1), and \\nthe scintillation speed, $v$, of order 50~km/s (see Rickett et al. 1995). VSOP\\nobservations at 1.7~GHz\\\\footnote{See \\nhttp://www.vsop.isas.ac.jp/general/pr/1519-273.gif} indicate that the \\nsource is unresolved, so we assume an\\nangular size of no more than 0.3~mas. This implies an observer-screen distance of \\n$D \\\\geq 390 (v/50~{\\\\rm km/s}) (t_{1.4}/4~{\\\\rm days})$~pc, or 390~pc in the\\npresent case.\\n\\nHaving obtained a lower limit to the distance to the \\nscattering screen, we may constrain the angular diameter of the source \\nfrom the scintillation parameters in the weak scattering regime where \\nthe scattering is quite sensitive to source size effects. The \\nscintillation timescale of $\\\\sim 12$~hours at 4.8~GHz can be explained \\neither in terms a scattering screen at large distance ($> 15$~kpc), or \\nby a partially resolved source. For weak \\nscattering, the source is resolved if the angular diameter of the \\nsource, $\\\\theta_S$, exceeds the angular diameter of \\nthe first Fresnel zone $\\\\theta_F = (k D)^{-1/2}$, where $k$ is the \\nwavenumber. The \\nscintillation timescale is then $t_{4.8} \\\\approx \\\\theta_S D/v$ for $\\\\theta_S >\\n\\\\theta_F$ (Narayan 1992).\\nA screen in our own Galaxy implies $D \\\\ll 15$~kpc, so the source must be partially resolved. \\nAssuming the asymptotic results of weak scattering to be valid \\nbetween the weak and strong scattering regimes, the scintillation timescale \\nthen yields an {\\\\it estimate} of the intrinsic angular source size of \\n$$\\n\\\\theta_S \\\\approx 14.4 \\\\left(\\\\frac{t_{4.8}}{12~{\\\\rm hours}} \\\\right) \\n\\\\left( \\\\frac{v}{50~{\\\\rm km/s} } \\\\right) \\n\\\\left( \\\\frac{D}{1~{\\\\rm kpc}}\\\\right)^{-1}~\\\\mu{\\\\rm as}. \\\\eqno(1)\\n$$\\n\\nFor a scintillating source of flux density $I_0$, the root-mean-square \\nfluctuation is $I_{\\\\rm rms} = I_0 m(\\\\theta_S)$, where \\n$m(\\\\theta_S)=(kD \\\\theta_S^2)^{7/12}$ is the modulation index expected for \\na source of size $\\\\theta_S > \\\\theta_F$ (e.g. Narayan 1992)\\\\markcite{Narayan92}, \\nand we have assumed that 4.8~GHz is near the \\ntransition frequency between weak and strong scattering.\\nGiven $I_{\\\\rm rms} = 0.11$~Jy and with the derived angular size of the \\nscintillating component of the source, we estimate $I_0$ and derive \\nits brightness temperature:\\n{\\\\small\\n$$\\nT_b \\\\approx 2.0 \\\\times 10^{14} \\\\left( \\\\frac{D}{1~{\\\\rm kpc}} \\n\\\\right)^{17/12} \\n\\\\left( \\\\frac{t_{4.8}}{12~{\\\\rm hours}} \\\\right)^{-5/6} \\n\\\\left( \\\\frac{v}{50~{\\\\rm km/s}} \\\\right)^{-5/6}~{\\\\rm K}. \\\\eqno(2)\\n$$}\\nUsing the limit of the distance to the scattering screen, the maximum \\npossible angular size of the source for $t_{4.8}=12$~hours and \\n$v=50$~km/s is $37\\\\,\\\\mu$as, the minimum brightness \\ntemperature is $T_b=5 \\\\times 10^{13}$~K, consistent with incoherent synchrotron \\nemission subject to relativistic beaming with a Doppler \\nboosting factor $\\\\delta \\\\gtrsim 200 (1+z)$ \\n(Readhead 1994)\\\\markcite{Readhead94}.\\n\\nHowever, if the CP observed at \\n4.8~GHz is entirely due to the variable component, we may further \\nconstrain $T_b$. From fig. 2 we have \\n$I_0 = 0.35 \\\\pm 0.04$~Jy, implying $m(\\\\theta_S) \\\\approx 0.32$ \\n(consistent with the modulation index observed in $V$: $0.32$) and hence an \\nangular size of $9.8 (D/1\\\\, {\\\\rm kpc})^{-1/2} \\\\,\\\\mu$as. Comparing with \\nequation (1), we have $v = 34 \\\\,(D/1\\\\,{\\\\rm kpc})^{1/2}$~km/s, implying \\na brightness temperature of \\n$3 \\\\times 10^{14} (D/1\\\\,{\\\\rm kpc}) (t_{4.8}/12\\\\,{\\\\rm hours})^{-5/6}$~K. \\nA scintillation speed exceeding $50$~km/s therefore implies \\na brightness temperature $T_b \\\\gtrsim 6 \\\\times 10^{14}$~K.\\n% comparable \\n% to that derived for PKS~0405-385 \\n% (Kedziora-Chudczer et al. 1997)\\\\markcite{Kedzioraetal}.\\n\\n\\\\subsection{Circular Polarization}\\nWe consider the origin of the CP in terms of intrinsic synchrotron \\n(Legg \\\\& Westfold 1968)\\\\markcite{Legg68}, partial conversion of the linear \\npolarization into CP due to ellipticity of the \\nnatural wave modes of the cold background plasma (Pacholczyk \\n1973)\\\\markcite{Pac73} or \\nof the relativistic electron gas itself (e.g. Sazonov 1969, \\nJones \\\\& O'Dell 1977a,b)\\\\markcite{Saz69,Jones77a,Jones77b}.\\n\\nIf the CP in \\nthe scintillating component is due to \\nsynchrotron emission then, following Legg \\\\& Westfold~(1968)\\\\markcite{Leg68}, \\nthe Lorentz factor of the particles responsible for a CP \\nof $m_c$ in a {\\\\it uniform} magnetic field \\nis $\\\\gamma \\\\approx \\\\cot \\\\theta/m_c$, where \\n$\\\\theta$ is the angle between the magnetic field\\nand the line of sight. For $30^\\\\circ < \\\\theta < 60^\\\\circ$ this \\nimplies Lorentz factors in the range $\\\\approx 15-45$ to\\nexplain the CP at 4.8~GHz. Indeed, the observed (low) \\nlevel of linear polarization suggests a\\nnon-uniform magnetic field, indicating that \\neven higher Lorentz factors are required. The \\nmaximum brightness temperature of such emission is $T_B \\\\leq \\n5.9 \\\\times 10^9 \\\\gamma$~K$=2.7 \\\\times 10^{11}$~K in the rest frame. Bulk motion with a \\nDoppler boosting factor $\\\\delta \\\\gtrsim 200$ would account for the difference \\nbetween the rest-frame and scintillation-derived brightness \\ntemperatures. Such a Doppler factor, although very high, cannot be \\nentirely ruled out. However the observed frequency dependence of the degree of \\nCP is far from \\nthe $\\\\nu^{-1/2}$ expected from synchrotron theory (see fig 3c); the \\nCP {\\\\it decreases} sharply between 8.6 and 1.4~GHz.\\nIt is therefore unlikely that the CP is due to synchrotron emission.\\n\\nAlternatively, the CP could be due to propagation \\nthrough a relativistic pair plasma, such as may be present within the \\nsource itself. The \\nbirefringence induced in a medium by the presence of a pair plasma \\nmay convert linear polarization to CP as \\nfollows:\\n$$\\nV(\\\\nu) = U_{0}(\\\\nu) \\\\sin ( c^3 {\\\\rm RRM}/\\\\nu^3), \\\\eqno(3)\\n$$\\nwhere the relativistic rotation measure, RRM, depends upon the \\ndensity of relativistic particles, the path length, the magnetic \\nfield, and the minimum Lorentz factor of the pairs (e.g. Kennett \\\\& Melrose \\n1998)\\\\markcite{Ken98}.\\nThis effect operates only when the direction of the incident linear \\npolarization is at an oblique angle to the projection of the magnetic \\nfield on the plane orthogonal to the ray direction. The axes used to \\ndefine the Stokes parameters may be chosen such that synchrotron \\nemission has $Q \\\\neq 0, U=0$. With this choice, the effect occurs \\nonly if the incident radiation has $U_0 \\\\neq 0$, requiring either \\nFaraday rotation or that it \\noriginate from a region of the source where the magnetic field is in a \\ndifferent direction to that where the polarization \\nconversion takes place. \\n\\nA characteristic of this model is a strong frequency dependence on the \\nsign of $V$. If ${\\\\rm RRM}$ is high enough to produce the CP \\nobserved at high frequency, this model predicts rapid changes \\nin $V$ at low frequency: in particular, equation (3) yields the lower limit \\n$|{\\\\rm RRM}| \\\\geq 6.2 \\\\times 10^2 \\\\, (1+z)^3\\n/f_U(8.6\\\\,{\\\\rm GHz})$~rad/m$^3$ \\nto explain the $-2.6$\\\\% CP at 8.6~GHz, where we write $f_U(8.6\\\\,{\\\\rm GHz}) =\\n|(U_0(8.6\\\\,{\\\\rm GHz})/I(8.6\\\\,{\\\\rm GHz})|$. \\nFor this lower limit, $\\\\lambda^3 {\\\\rm RRM}$ will vary by \\n$0.88/f_U(8.6\\\\,{\\\\rm GHz})$~rad across 64~MHz\\nbandwidth at 1.4~GHz and $0.08/f_U(8.6\\\\,{\\\\rm GHz})$~rad at 2.5~GHz. We \\nsearched for frequency-dependent variations in $V$\\nat all four frequencies by selecting two adjacent 32~MHz sub-bands at each \\nfrequency. None were found. Although the Faraday rotation \\n(RM $\\\\approx$ 69 rad/m$^2$)\\nacross the band was clearly detected at 1.4 and 2.5~GHz, the variations in $V$ \\nbetween sub-bands were less than 4\\\\% and 0.8\\\\% at these frequencies\\nrespectively. This result appears inconsistent with the derived lower \\nlimit on RRM, although the null result at \\n1.4~GHz may result from an absence\\nof CP in the scintillating component (which in turn implies\\n$|U_0| /I \\\\sim |V|/I < 0.01$ at 1.4~GHz).\\n\\nThe fact that all detections of the CP are of same sign also argues \\nagainst this model. If (i) $V$ does not change sign at any frequencies intermediate to those of our \\nmeasurements (i.e. the spectrum is well-sampled) and (ii) $U_0$ does not \\nchange sign in the range 1.4$-$8.6~GHz then equation (3) implies \\n$\\\\lambda^3 {\\\\rm RRM} < 2 \\\\pi$ for \\nall frequencies above 1.4~GHz (even if $V(1.4~{\\\\rm GHz})$, whose sign \\nis uncertain, is positive).\\nAt 1.4~GHz one then has \\n$|{\\\\rm RRM}| < 6.2 \\\\times 10^2 \\\\, (1+z)^{3}$~rad/m$^3$, requiring \\n$f_U(8.6\\\\,{\\\\rm GHz}) \\\\geq 100$\\\\% to be \\nconsistent with the lower limit on ${\\\\rm RRM}$ obtained above. While \\ndifficult to exclude entirely, we therefore conclude that the production of \\nCP by a pair-dominated plasma is implausible.\\n\\nPolarization conversion may also occur in a medium containing a \\nmixture of\\ncold and relativistic pair plasma, in which case the fractional CP \\nvaries as $m_c \\\\propto \\\\nu^{-1}$ Pacholczyk (1973). \\nThis model appears implausible in light of the observed \\n$\\\\nu^{0.7_{-0.3}^{+1.4}}$ frequency \\ndependence of the CP from 1.4 to 4.8~GHz. \\n\\nThe presence of several distinct sub-components may \\nalter the spectral properties of the observed CP.\\nHowever, the scintillation characteristics argue against the existence of \\nmultiple circularly polarized components, each with distinct $U_0$, RRM and \\n$\\\\gamma$. The presence of multiple components with different $V/I$ \\nwould lead to substructure in the lightcurve of $V$ compared to the lightcurve\\nof $I$ as the scintillation selectively amplifies and deamplifies\\nparts of the source differently. This would result in a loss of correlation \\nbetween $V$ and $I$, particularly at 4.8 and 8.6~GHz, where the \\nscintillation is most sensitive to small-scale structure. This \\nis not observed in fig. 1 where \\nthe correlation coefficients are close to unity. However, it is more \\ndifficult to ascertain the presence of substructure in the variability \\nat 1.4 and 2.5~GHz due to the long timescale of the fluctuations.\\n \\nJones \\\\& O'Dell (1977a, 1977b)\\\\markcite{Jones77a,Jones77b} \\npresented a model for the CP of inhomogeneous \\nsynchrotron sources, incorporating optical depth effects, mode \\ncoupling and mode conversion due to the birefringence of the \\nplasma. Below the self-absorption turnover \\nfrequency, $\\\\nu_{\\\\rm SSA}$, mode coupling dominates, and the \\nCP is typically less than 0.05\\\\%, and certainly \\nnot more than 2\\\\%. Mode conversion dominates above $\\\\nu_{\\\\rm SSA}$, with the \\nCP as high as 10\\\\% near $\\\\nu_{\\\\rm SSA}$, and \\ndecreasing to less than $10^{-3}$ at frequencies a decade above\\n$\\\\nu_{\\\\rm SSA}$. This model is viable only if $\\\\nu_{\\\\rm SSA}$ is\\nwithin a factor $\\\\sim 1.4$ of the frequency at which the high (3.8\\\\%) \\nCP was observed, at 4.8~GHz. This is difficult to \\nverify as we do not know the intrinsic spectrum of the \\nscintillating component and the frequency range of our observations is limited.\\n\\n\\\\placefigure{fig:FIG3N.PS}\\n\\\\begin{figure*}\\n\\\\begin{tabular}{c}\\n \\\\psfig{file=FIG3N.PS,angle=270,width=70mm}\\n\\\\end{tabular}\\n\\\\caption{Various quantities derived from the data in \\nfig. 1. (a) Spectra of the \\ntotal intensity (circles) and CP (squares) in PKS~1519-273 for the four \\nbands of ATCA averaged over the duration of the observations.\\n(b) Modulation indices derived from the intensity \\nfluctuations over the 5 days of observations. The long timescale of \\nvariability makes it difficult to compare these values with the \\nensemble-average quantities predicted by scintillation theory. This \\nis particularly relevant at 2.5 and 1.4~GHz because the timescale of \\nvariability is comparable to or exceeds the period of observation.\\n(c) The spectrum of circularly polarized component derived by \\ncomparing the magnitude of the fluctuations in $I$ with those in $V$ \\n(see fig. 2).}\\n\\\\end{figure*}\\n\\n\\n\\\\section{Conclusion}\\nThe variability detected in PKS~1519-273 in all four Stokes \\nparameters at frequencies from 1.4 to 8.6~GHz is remarkable, but has a natural \\ninterpretation in terms of ISS. The \\nscintillation properties at 4.8~GHz constrain the brightness \\ntemperature of the scintillating component to $T_b \\\\geq 5 \\\\times \\n10^{13}$~K, although there is strong evidence to suggest it may be as \\nhigh as $6 \\\\times 10^{14}$~K. Comparison of the fluctuations in \\n$I$ and $V$ imply that \\nthis component is exceptionally highly circularly polarized at 8.6 and \\n4.8~GHz. Simple applications of synchrotron theory and models of \\ncircular repolarization encounter difficulties with the spectral \\nbehavior and magnitude of the CP. \\nThe strong correlation between the fluctuations in $I$ and $V$ at 4.8 \\nand 8.6~GHz and the high sensitivity of the scintillation to source \\nstructure at these frequencies argue against a complex source, with different $V/I$ in each component.\\nInclusion of effects due to small-scale inhomogeneity, mode coupling \\nand optical depth effects may reproduce \\nthe observed characteristics of the CP. However, \\nthis model is only viable if the frequency at which the\\nsource is observed to become optically thin is in the range \\n$3.4\\\\,{\\\\rm GHz} \\\\lesssim \\\\nu \\\\lesssim 6.7\\\\,{\\\\rm GHz}$. This possibility is \\npresently difficult to confirm. Even if correct, the puzzle \\nremains as to why so few sources exhibit such high \\nlevels of CP. \\n\\nFinally, in light of the extremely high brightness temperature of \\nPKS~1519-273, we advance the possibility that the observed emission \\nis not due to synchrotron emission at all and that high CP \\nmay be a characteristic of a new emission mechanism.\\n\\n\\n\\\\acknowledgments\\nWe thank Don Melrose, Ron Ekers, Mark Walker, Jim Lovell, Dick \\nHunstead and Lawrence Cram for valuable discussions. The \\nAustralia Telescope is funded by the Commonwealth Government for \\noperation as a national facility by the CSIRO.\\n\\n\\\\begin{references}\\n\\n\\\\reference{Bower99}\\nBower, G.C., Falcke, H. \\\\& Backer, D.C., \\n{1999}, \\\\apj, 1999, 523, L29\\n\\n% \\\\reference{Cordes86}\\n% Cordes, J.M., 1986, \\\\apj, {311}, 183\\n\\n\\\\reference{Fichtel94}\\nFichtel, C.E. et al., 1994, \\\\apjs, 94, 551\\n\\n% \\\\reference{Frater92}\\n% Frater, R.H., Brooks, J.W. \\\\& Whiteoak, J.B., 1992, JEEEA,12, 103\\n% JEEEA = Jnl of Electrical and Electronics Engineering, Australia\\n\\n\\n\\\\reference{Heidt96}\\nHeidt, J. \\\\& Wagner, S.J., 1996, \\\\aap, {305}, 42\\n\\n\\\\reference{Heeschen97}\\nHeeschen, D.S., Rickett, B.J., 1997, \\\\aj, 93, 589\\n\\n\\\\reference{Impey96} Impey, C.D. \\\\& Tapia, S., 1996, \\\\apj, 333, 666\\n\\n\\\\reference{Jones77a}\\nJones, T.W., O'Dell, S.L.,\\n{1977a},\\n\\\\apj,\\n{214},\\n552\\n\\n\\n\\\\reference{Jones77b}\\nJones, T.W., O'Dell, S.L.,\\n{1977b},\\n\\\\apj,\\n{215},\\n236.\\n\\n\\n\\\\reference\\n{KedzioraPhD}\\nKedziora-Chudczer, L., Jauncey, D.L., Wieringa, M.H., Reynolds, J.E., Tzioumis,\\nA.K. {1998} in ASP Conf. Ser. 144, Radio Emission from Galactic and Extragalactic Compact Radio\\nSources, eds: J.A. Zensus, G.B. Taylor \\\\& J.M. Wrobel, 271\\n\\n\\\\reference\\n{Kedzioraetal}\\nKedziora-Chudczer, L., Jauncey, D.L., Wieringa, M.H., Walker, M.A., Nicolson,\\nG.D., Reynolds, J.E. \\\\& Tzioumis, A.K.\\n{1997},\\n\\\\apj,\\n{490},\\nL9.\\n\\n\\\\reference{Ken98}\\nKennett, M.P. \\\\& Melrose, D.B., 1998, {\\\\it Publ. Astron. Soc. Aust.}, 15, 211.\\n\\n\\\\reference{Kom84}\\nKomesaroff,� M.�M., Roberts,� J.�A., Milne,� D.�K., Rayner, �P.�T., \\nCooke, �D.�J.,\\n{1984},\\n\\\\mnras,\\n{208},\\n409.\\n\\n\\\\reference\\n{Legg68}\\nLegg, M.P.C., Westfold, K.C.,\\n{1968},\\n\\\\apj,\\n{154},\\n499\\n\\n\\\\reference{Linfield89} \\nLinfield et al., 1989, \\\\apj, 336, 1105\\n\\n\\n\\\\reference\\n{Narayan92}\\nNarayan, R.,\\n{1992},\\nPhil Trans R Soc Lond A,\\n{341},\\n151.\\n\\n\\\\reference\\n{Pac73}\\nPacholczyk, A.G.,\\n{1973},\\n\\\\mnras,\\n{163},\\n29P.\\n\\n\\n\\\\reference{Readhead94}\\nReadhead, A.C.S., 1994, \\\\apj, 426, 51\\n\\n\\\\reference{Rickett95}\\nRickett, B.J., Quirrenbach, A., Wegner, R., Krichbaum, T.P. \\\\& Witzel, A., {1995},\\n\\\\aap, {293}, 479\\n\\n\\n\\\\reference\\n{Roberts75}\\nRoberts, J.A., Cooke, D.J., Murray, J.D., Cooper, B.F.C, Roger, R.S.,\\nRibes, J.-C. \\\\& Biraud, F.,\\n{1975}\\nAuJPh,\\n{28},\\n325\\n\\n\\\\reference{Sault91} Sault, R.J., Killeen, N.E.B. \\\\& Kesteven, M.J., \\n1991, ATNF Technical Document Series 39/015, ATNF \\n\\n\\\\reference{Sault99} Sault, R.J. \\\\& Macquart, J.-P., 1999, \\\\apj, 526, L85\\n\\n\\\\reference{Saz69}\\nSazonov, V.N.,\\n{1969},\\nZh. Eksper Teor. Fiz.,\\n{56},\\n1074 (English transl. in Soviet Phys. -- JETP, {29}, 578).\\n\\n\\\\reference{Seaquist74}\\nSeaquist, E.R, Gregory, P.C. \\\\& Clarke, T.R., 1974, \\\\aj, 79, 918\\n\\n\\\\reference{Steppe88}\\nSteppe, H., Salter, C.J., Chini, R., Kreysa, E., Brunswig, W. \\\\& Lobato \\nPerez, J., 1988, \\\\aaps, 75, 317\\n\\n\\\\reference{Steppe95}\\nSteppe, H., Jeyakumar, S., Saikia, D.J. \\\\& Salter, C.J., 1995,\\n\\\\aaps, 113, 409\\n\\n\\\\reference{Urry96}\\nUrry, C.M., Sambruna, R.M., Worrall, D.M., Kollgaard, R.I., \\nFeigelson, E.D., Perlman, E.S. \\\\& Stocke, J.T., 1996, \\\\apj, 463, 424\\n\\n\\\\reference{Veron93}\\nVeron-Cetty, M.-P. \\\\& Veron, P., 1993, \\\\aaps, 100, 521\\n\\n% \\\\reference{Walker98}\\n% Walker, M.A., 1998, \\\\mnras, 294, 307\\n\\n\\\\reference{Wardle98}\\nWardle, J.F.C., Homan, D.C., Ojha, R. \\\\& Roberts, D.H.,\\n{1998},\\nNature,\\n{395},\\n457\\n\\n\\\\reference\\n{Weiler83}\\nWeiler, K. W \\\\& de Pater, I.,\\n{1983},\\n\\\\apjs,\\n{52},\\n293\\n\\n\\\\reference{White88} White, G.L., Jauncey, D.L., Savage, A., Wright, \\nA.E, Batty, M.J., Peterson, B.A. \\\\& Gulkis, S., 1988, \\\\apj, 327, 561\\n\\n\\\\end{references}\\n\\n\\n% \\\\figcaption[HIGH.PS,LOW.PS]{Variability of PKS~1519-273 in the total intensity ($I$), \\n% CP ($V$), and magnitude of the linear polarization ($P$),\\n% for the four bands of the ATCA over 5 days. Each point \\n% represents a 10~min average, and is plotted with $1\\\\,\\\\sigma$ error bars. \\n% Fluctuations in $I$ and $V$ are strongly correlated ($r=-0.90$ at \\n% 4.8~GHz and $r=-0.80$ at 8.6~GHz).}\\n% \\\\special{psfile=HIGH.PS angle=270 hscale=50 vscale=50}\\n% \\\\vskip 2.8 in\\n% \\\\special{psfile=LOW.PS angle=270 hscale=50 vscale=50}\\n\\n\\n \\n% \\\\figcaption[v_vs_i_2496.eps,v_vs_i_4800.eps,v_vs_i_8640.eps]{Plot \\n% of the correlation between $V$ and $I$. The best fit lines give \\n% a fractional CP of $-2.4\\\\pm 1.3$\\\\%, $-3.8 \\\\pm 0.4$\\\\% \\n% and $-2.6 \\\\pm 0.5$\\\\% respectively at 2.5, 4.8 and 8.6~GHz for the \\n% variable component of the source. The fluctuations in $I$ and $V$ do \\n% not appear to be correlated at 1.4~GHz, indicating that we detect \\n% {\\\\it no} CP associated with the variable component \\n% at this frequency. We place an upper limit on the CP of \\n% this component of 1.3\\\\%.}\\n% \\\\special{psfile=v_vs_i_2496.eps angle=270 hscale=30 vscale=30}\\n% \\\\vskip 2.2 in\\n% \\\\special{psfile=v_vs_i_4800.eps angle=270 hscale=30 vscale=30}\\n% \\\\vskip 2.2 in\\n% \\\\special{psfile=v_vs_i_8640.eps angle=270 hscale=30 vscale=30}\\n\\n\\n% \\\\figcaption[FIG3N.PS]{Various quantities derived from the data in \\n% fig. 1. (a) Spectra of the \\n% total intensity (circles) and CP (squares) in PKS~1519-273 for the four \\n% bands of ATCA averaged over the duration of the observations.\\n% (b) Modulation indices derived from the intensity \\n% fluctuations over the 5 days of observations. The long timescale of \\n% variability makes it difficult to compare these values with the \\n% ensemble-average quantities predicted by scintillation theory. This \\n% is particularly relevant at 2.5 and 1.4~GHz because the timescale of \\n% variability is comparable to or exceeds the period of observation.\\n% (c) The spectrum of circularly polarized component derived by \\n% comparing the magnitude of the fluctuations in $I$ with those in $V$ \\n% (see fig. 2).}\\n% \\\\special{psfile=FIG3N.PS angle=270 hscale=80 vscale=80}\\n\\n\\n\\\\end{document}\\n\\n\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[],"string":"[]"}}},{"rowIdx":190,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002193"},"title":{"kind":"string","value":"A Theoretical Review of Axion\\footnote{Talk presented at cosmo-99, ICTP, Trieste, Italy, 28 September 1999.}"},"authors":{"kind":"list like","value":[{"author":"Jihn E. Kim"}],"string":"[\n {\n \"author\": \"Jihn E. Kim\"\n }\n]"},"abstract":{"kind":"string","value":"It is emphasized that the existence of a very light axion is consistent with the strong CP invariance and cosmological and astrophysical constraints. The attempt to embed the very light axion in superstring models is discussed."},"latex":{"kind":"list like","value":[{"name":"c99lanl.tex","string":"%%UNIX --- UPDATED ON 13/8/97 \n%====================================================================%\n% sprocl.tex 27-Feb-1995 %\n% This latex file rewritten from various sources for use in the %\n% preparation of the standard proceedings Volume, latest version %\n% by Susan Hezlet with acknowledgments to Lukas Nellen. %\n% Some changes are due to David Cassel. %\n%====================================================================%\n\n\\documentstyle[epsf,sprocl]{article}\n\n\\font\\eightrm=cmr8\n\n\\input{psfig.sty}\n\n\\bibliographystyle{unsrt} %for BibTeX - sorted numerical labels by\n %order of first citation.\n\n\\arraycolsep1.5pt\n\n% A useful Journal macro\n\\def\\Journal#1#2#3#4{{#1} {\\bf #2}, #3 (#4)}\n\n% Some useful journal names\n\\def\\NCA{\\em Nuovo Cimento}\n\\def\\NIM{\\em Nucl. Instrum. Methods}\n\\def\\NIMA{{\\em Nucl. Instrum. Methods} A}\n\\def\\NPB{{\\em Nucl. Phys.} B}\n\\def\\PLB{{\\em Phys. Lett.} B}\n\\def\\PRL{\\em Phys. Rev. Lett.}\n\\def\\PRD{{\\em Phys. Rev.} D}\n\\def\\ZPC{{\\em Z. Phys.} C}\n\n% Some other macros used in the sample text\n\\def\\st{\\scriptstyle}\n\\def\\sst{\\scriptscriptstyle}\n\\def\\mco{\\multicolumn}\n\\def\\epp{\\epsilon^{\\prime}}\n\\def\\vep{\\varepsilon}\n\\def\\ra{\\rightarrow}\n\\def\\ppg{\\pi^+\\pi^-\\gamma}\n\\def\\vp{{\\bf p}}\n\\def\\ko{K^0}\n\\def\\kb{\\bar{K^0}}\n\\def\\al{\\alpha}\n\\def\\ab{\\bar{\\alpha}}\n\\def\\be{\\begin{equation}}\n\\def\\ee{\\end{equation}}\n\\def\\bea{\\begin{eqnarray}}\n\\def\\eea{\\end{eqnarray}}\n\\def\\CPbar{\\hbox{{\\rm CP}\\hskip-1.80em{/}}}%temp replacemt due to no font\n\\def\\Dslash{D{\\hskip -0.22cm}\\slash} \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%BEGINNING OF TEXT \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{document}\n\n\\title{A Theoretical Review of Axion\\footnote{Talk presented at cosmo-99,\nICTP, Trieste, Italy, 28 September 1999.}}\n\n\\author{Jihn E. Kim}\n\n\\address{Department of Physics and Center for Theoretical Physics \\\\\nSeoul National University, Seoul 151-742, Korea } \n\n\\maketitle\\abstracts{It is emphasized that the existence of a very light \naxion is consistent with the strong CP invariance and cosmological\nand astrophysical constraints. The attempt to embed the very light axion\nin superstring models is discussed.}\n\n\\section{The Strong CP Problem}\n\nThe standard model $SU(3)\\times SU(2)\\times U(1)$ describes the\nweak and electromagnetic interactions very successfully. The strong\ninteraction part, quantum chromodynamics, is proven to be successful\nat perturbative level, but the study of nonperturbative effects are not \nso successful. Because of the lack of a calculational tool of the\nnonperturbative effects, the frequently used method for the study\nof QCD at low energy is the symmetry principle. At energy scales below\nthe confinement and chiral symmetry breaking scale, some symmetries\nof QCD are manifest in strong interaction dynamics. Baryon number is\nknown to be conserved. Chiral symmetry is broken. \n\nDiscrete symmetries are believed to be conserved in the process of\nconfinement. Here we are interested in CP. If QCD conserves CP,\nthe CP symmetry will be preserved in strong interactions at low energy.\nIf QCD violates CP, its effect will be shown in low energy strong\ninteraction dynamics. QCD before 1975 was described by\n\\begin{equation}\n{\\cal L}= -\\frac{1}{2g^2}{\\rm Tr\\ }F_{\\mu\\nu}F^{\\mu\\nu}\n+\\bar q(i\\Dslash-M_q)q\n\\end{equation} \nwhere $q$ and $M_q$ are quark and quark mass matricies, respectively.\nAfter the discovery of the instanton solution in non-Abelian gauge\ntheories,\\cite{bpst} it is known that the $\\theta$-term must be\nconsidered,\\cite{theta}\n\\begin{equation}\n{\\cal L}_\\theta=\\frac{\\theta}{16\\pi^2}{\\rm Tr}\\ F_{\\mu\\nu}\\tilde F^{\\mu\\nu}.\n\\end{equation}\nNote that ${\\cal L}_\\theta$ is odd uner P or T discrete transformation.\nTherefore, this term violates the CP invariance. Thus QCD contains a\nterm violating CP symmetry. If QCD violates the CP symmetry, it must be\nrevealed in strong interaction dynamics. For example, we may expect a \nCP violating static property of neutron, the electric dipole moment\nof neutron $d_n$. The experimental upper limit of $d_n$ is known to\nbe $0.63\\times 10^{-25}\\ e\\cdot$cm.\\cite{dn} On the other hand, if\nstrong interaction violates the CP invariance at the full strength,\nthen we expect $d_n\\sim 10^{-14}\\ e\\cdot$cm. Therefore, the vacuum\nangle is restricted to a tiny region\n\\begin{equation}\n|\\theta|< 10^{-9}.\n\\end{equation}\nThe question, $\\lq\\lq$Why is the vacuum angle so small\", is the\nstrong CP problem. If we treat $\\theta$ as O(1) parameter, then the\nabove observation excludes QCD as the theory of strong interactions.\nIn this case, different $\\theta$'s describe different universes. Since \nQCD is known to be so successful except for the strong CP problem, it is\nbetter to keep QCD as the theory of strong interactions. It is\ndesirable to resolve the strong CP problem with QCD untouched.\n\nThere have been several attempts toward the solution of the strong\nCP problem, one even incorrectly asserting that there is no\nstrong CP problem.\\cite{marshak}\\footnote{This reference~[4]\nstarts with an assumption on CPT invariant $|n\\rangle$ vacua and obtains\nthe CPT odd $|\\theta\\rangle$ vacuum. But in Yang-Mills theories,\n$|n\\rangle$ vacua are not CPT invariant, and the $|\\theta\\rangle$\nvacuum is CPT invariant.} \n\nOne class of solutions employs CP\nsymmetry at the Lagrangian level, and require the induced vacuum \nangle (in the process of introducing weak CP violation) sufficiently\nsmall.\\cite{natural} These are called natural solutions.\nHere, the weak CP violation is through spontaneous symmetry\nbreaking or soft breaking. Namely, the Kobayashi-Maskawa type\nweak CP violation is not possible except for the Nelson-Barr type.\nThe reason for a possible Kobayashi-Maskawa weak CP violation in\nthe Nelson-Barr type strong CP solution is that the spontaneous CP\nviolation here is introduced at a super high energy scale and\nhence at the electroweak scale CP is already violated as in the\nKobayashi-Maskawa model. In this class of models, at tree level\n$\\theta=0$, which implies $Arg\\ Det\\ M_q=0$. This is attained by\nassuming a CP invariant Lagrangian including the $\\theta$ term\nand specific symmetries. Possible symmetries used for this purpose\nare: left-right symmetry, $U(1)$ gauge symmetry, permutation symmetry,\nand other discrete symmetries.\n\nThe other solutions are the $m_u=0$ solution and the axion solution.\n\nHere, the most attractive solution is the axion solution, making\n$\\theta$ a dynamical variable. A dynamical $\\theta$ is equivalent to\na pseudoscalar field which we call axion. If the axion has a potential,\nthen in the evolving universe the minimum of the vacuum will be\nchosen. The axion solution guarantees that $\\theta=0$ is the\nminimum of the $\\theta$ potential, which is discussed below.\n\n\\section{The Peccei-Quinn Solution}\n\nThe axion solution is a dynamical solution. Peccei and Quinn~\\cite{pq}\nshowed that $\\theta=0$ at the point $dV/d\\theta=0$, which has been\nshown later by Vafa and Witten,\\cite{vw}\n\\begin{equation}\n{\\cal L}=-\\frac{1}{4}F^2+\\bar q(i\\Dslash-M_q)q+\\theta\\frac{g^2}{32\\pi^2}\nF\\tilde F\n\\end{equation}\nwhere we suppressed the Greek indices for space-time in $F$. Let us treat\n$\\theta$ as a coupling. After integrating the quark fields out, the\ngenerating functional in the Euclidian space is given by\n\\begin{equation}\n\\int [dA_\\mu]\\prod_i{\\rm Det}(\\Dslash+m_i)\n\\exp{\\{-\\int d^4x[\\frac{1}{4g^2}F^2-i\\theta\\frac{1}{32\\pi^2}F\\tilde F]\\}}.\n\\end{equation}\nNote that the resulting functional has a specific form of the $\\theta$\ndependence. In the Euclidian space, corresponding to the eigenstate\n$\\psi$ of $i\\Dslash$, $i\\Dslash\\psi=\\lambda\\psi$, there corresponds to\nthe other eigenstate of $i\\Dslash$, $i\\Dslash(\\gamma_5\\psi)=-\\lambda\n(\\gamma_5\\psi)$. Thus, the nonzero real eigenvalues of $i\\Dslash$ are\npaired with opposite sign and the identical magnitude. For $N_0$ number\nof zero modes, we can show that\n\\begin{equation}\n{\\rm Det\\ }(\\Dslash+m_i)=\\prod_i (-i\\lambda+m_i)=m_i^{N_0}(m_i^2+\n\\lambda^2)>0.\n\\end{equation}\nThus, the generating functional is bounded by usung the\nSchwarz inequality in view of Eq.~(6),\n\\begin{eqnarray}\n&\\exp[-\\int d^4x V[\\theta]]\\equiv |\\int[dA_\\mu]\\prod {\\rm Det\\ }\n(\\Dslash+m_i)\\exp(-\\int d^4x{\\cal L})|\\nonumber\\\\\n&\\le \\int [dA_\\mu]|\\prod {\\rm Det}(\\Dslash+m_i)\\exp(-\\int d^4x{\\cal L})\n|\\nonumber\\\\\n&=|\\int[dA_\\mu]\\prod{\\rm Det\\ }(\\Dslash+m_i)\\exp[-\\int d^4x\n{\\cal L}(\\theta=0)] |\\\\\n&=\\exp(-\\int d^4x V[0])\\nonumber\n\\end{eqnarray}\nwhere ${\\cal L}=(1/4g^2)F^2-i\\theta\\{F\\tilde F\\}$, and the simplified\nnotation $\\{\\ \\ \\}$ includes a factor $1/32\\pi^2$. The above\ninequality guarantees\n\\begin{equation}\nV[\\theta]\\ge V[0].\n\\end{equation}\nInstanton solutions have integer values for $\\int d^4x\\{F\\tilde F\\}$,\nhence $V[\\theta]$ is periodic with the $\\theta$ period of $2\\pi$,\n$\\theta\\rightarrow \\theta+2n\\pi$. The above agument is for a nonzero\nup quark mass. If $m_u=0$, $\\theta$ is unphysical and there is no\nstrong CP problem.\n\nAs a coupling, any $\\theta$ defines a good theory (or universe). The \nshape of $V$ as a function of $\\theta$ is\n\n\\begin{figure}\n\\epsfxsize=60mm\n\\centerline{\\epsfbox{c99kim1.eps}}\n\\end{figure}\n\\centerline{Fig.~1.\n{\\it Shape of $V[\\theta]$. The KM weak CP introduces}~\\cite{gr} \n$|\\theta| \\simeq 10^{-16}$.}\n\\vskip 0.3cm\nHere, the axion solution of the strong CP problem is transparent. If\nwe identify $\\theta$ as a pseudoscalar field,\n\\begin{equation}\n\\theta=\\frac{a}{F_a}\n\\end{equation}\nthe vacuum angle is chosen at $\\theta\\simeq 0$, realizing the\nalmost CP invariant QCD vacuum. Note the key ingredients of this\naxion solution. Firstly, the theory introduces an axion coupling\n$a\\{F\\tilde F\\}$. Second, there is no axion potential except\nthat coming from the $F\\tilde F$ term, otherwise our proof does not\ngo through. Third, there necessarily appears a mass parameter $F_a$,\nthe so-called axion decay constant. One possible example for \nthe axion is to introduce a\nGoldstone boson, using a global $U(1)$ symmetry.~\\cite{pq} As explained\nabove Peccei-Quinn showed that $\\theta=0$ is the minimum of the\npotential, which is meaningful only if there is a dynamical field\n$a$. Later, Weinberg and Wilczek explicitly showed that the model\ncontains the axion.~\\cite{ww} It was immediately known that the\nPQWW axion does not exist,\\cite{peccei} and hence there soon \nappeared a flurry of natural solutions.~\\cite{natural} \n\nTo have the anomalous coupling, the global symmetry must have a\ntriangle anomaly in $U(1)_{\\rm global}\\times SU(3)_c\\times SU(3)_c$.\nThis anomalous coupling introduces an axion decay constant which\ncan be large for the very light axion models.\\cite{invisible,dfsz}\nSoon after the invention of the very light axion, it has been\nknown that the astrophysical and cosmological bounds restrict \nthe axion decay constant in the region, $10^9{\\ \\rm GeV}\\le F_a\n\\le 10^{12}\\ {\\rm GeV}$.\\cite{astro,cos}\nAlso, it was known that a more ambitious composite axion can be \nconstructed.\\cite{comp}\n\nAnother interesting possibility is that there results an axion with\nthe above properties from a more fundamental theory such as from\nthe string theory. This possibility introduces a nonrenormalizable\ninteraction $aF\\tilde F$. Indeed, superstring models have a host\nof moduli fields which do not have potentials at the compactification\nscale. But some of the moduli have the desired anomalous \ncouplings,\\cite{witten} and becomes the axion. In this case, the \nso-called superstring axions are expected to have the decay constant \nnear the Planck scale. But the exact magnitude depends on the details\nof the model. \n\nThe mass of the very light axion is an important parameter in the\nevolving universe. The allowed range of the decay constant gives\ntens of micro-eV axion mass,\n\\begin{equation} \nm_a=0.6\\times 10^7\\ \\frac{\\rm eV}{F_a^{\\rm GeV}}\n\\end{equation}\nwhere $F_a^{\\rm GeV}=F_a/{\\rm GeV}$.\n\nThe neutron electric dipole moment in the $\\theta$ vacuum is\ngiven by~\\cite{quint}\n\\begin{equation}\n\\frac{d_n}{e}=O(1)\\frac{m_u\\sin\\theta}{f_\\pi^2[2Z\\cos\\theta+(\n1+Z)^2]^{1/2}}\n\\end{equation}\nwhere $Z=m_u/m_d$ is the ratio of the current quark masses.\nFor $m_u<2\\times 10^{-13}$~GeV, the neutron electric dipole \nmoment is satisfied even for O(1) $\\theta$.\n\nThe very light axion physics is closely connected to the study\nof the evolution of the universe. The domain wall problem~\\cite{sikivie}\nmust be studied in specific models. Usually, inflation needed in\nsupergravity models with the condition on the reheating temperature\n$T_R<10^9$~GeV \\cite{ekn} does not lead to the axionic domain\nwall problem.\n\nTheoretically, the introduction of the Peccei-Quinn U(1) global\nsymmetry is ad hoc. It is better if the axion arises from a\nfundamental theory. In this spirit, it is most important to\ndraw a very light axion from superstring theory. If we cannot,\nhow can we understand the strong CP problem?\n\n\\section{Embedding the Very Light Axion in Superstring}\n\nThe pseudoscalar moduli fields in D=10 superstring is $B_{MN}\\\n(M,N=0,\\cdots,9)$ among the bosonic fields $G_{MN}, B_{MN}$ and\nthe dilaton. Upon compactification to D=4, $B_{\\mu\\nu}\\ (\\mu,\\nu\n=0,\\cdots,3)$ turns out to be a pseudoscalar field. Dual \ntransformation of $B_{\\mu\\nu}$ defines a pseudoscalar $a$ as\n\\begin{equation}\n\\partial^\\sigma a\\propto\\epsilon^{\\mu\\nu\\rho\\sigma}H_{\\mu\\nu\\rho};\nH_{\\mu\\nu\\rho}={\\rm field\\ strength\\ of\\ }B_{\\mu\\nu}\\propto\n\\epsilon_{\\mu\\nu\\rho\\sigma}\\partial^\\sigma a.\n\\end{equation}\nOf course, $B_{\\mu\\nu}$ does not have renormalzable couplings to \nmatter fields, hence there is no potential for $a$ since the\npossible derivative coupling $\\partial^\\mu a\\psi\\gamma_\\mu\\gamma_5\n\\psi$ does not lead to a potential term. If we consider a field\nstrenth \n$H_{\\mu\\nu\\rho}$ to obtain couplings, it is invariant under\na shift $a\\rightarrow a+c$. This consideration does not lead to\nan anomalous coupling needed for an axion. \n\nHowever, the gauge invariant D=10 field strength of $B_{MN}$ is\nnot $H=dB$,\\footnote{In this paragraph we use the differential form.}\nbut is~\\cite{green}\n\\begin{equation}\nH=dB+\\omega^0_{3Y}-\\omega^0_{3L}\n\\end{equation} \nwhere the Yang-Mills Chern-Simmons form is tr$(AF-A^3/3)$ and the\nLorentz Chern-Simmons form is tr$(\\omega R-\\omega^3/3)$. The \nChern-Simmons forms satisfy $d\\omega^0_{3Y}={\\rm tr\\ }F^2$ and\n$d\\omega^0_{3L}={\\rm tr}\\ R^2$. Therefore,\n\\begin{equation}\ndH=-{\\rm tr\\ }F^2+{\\rm tr\\ }R^2,\n\\end{equation}\nand the equation of motion for $a$ is\n\\begin{equation}\n\\Box a=-\\frac{1}{M}[{\\rm Tr\\ }F_{\\mu\\nu}\\tilde F^{\\mu\\nu}\n-{\\rm Tr\\ }R_{\\mu\\nu}\\tilde R^{\\mu\\nu}]\n\\end{equation}\nwhich implies $aF\\tilde F$ coupling which is needed for the\naxion interpretation of $a$.\\cite{witten} This is the so-called\nmodel-independent axion. Here, $M$ is about the compactification\nscale suppressed by a factor and corresponds to the axion decay\nconstant.\\cite{choikim} \n\nTo cancel the Yang-Mills anomaly, one\nshould introduce the Green-Schwarz term,\\cite{green} $S_{GS}\\sim\n\\int(B{\\rm tr}F^4+\\cdots)$. The Green-Schwarz term gives the \nneeded anomalous coupling for pseudoscalars $B_{ij}\\ (i,j=4,\\cdots,\n9)$\n\\begin{equation}\nB_{ij}\\epsilon^{\\mu\\nu\\rho\\sigma}F_{\\mu\\nu}F_{\\rho\\sigma}\n\\langle F_{kl}\\rangle\\langle F_{pq}\\rangle\\epsilon^{ijklpq}.\n\\end{equation}\nHere, we have model-dependent axions $a_k\\sim \\epsilon_{ijk}B_{ij}$,\nthe number of which is the second Betti number.\\cite{witten1}\nUnlike the model-independent axion, the model-dependent axions receive\nnonvanishing superpotential terms from the world-sheet instanton effect,\n\\begin{equation}\n\\int_{\\Sigma_J} d^2z \\omega^I_{ij}(\\partial X^i\\underline\n\\partial X^{\\underline j}-\\underline\\partial X^i\\partial X^{\\underline\nj})=2\\alpha^\\prime\\delta_{IJ} \n\\end{equation}\nwhere $\\alpha^\\prime$ is the string tension, and $\\omega=4\\pi^2 {\\rm Re}\n(T_I)\\omega^I$. The internal space volume is given by\\cite{mth}\n$V_6=(1/3!)\\int \\omega\\land\\omega\\land\\omega\\approx \n(1/6)(4\\pi^2{\\rm Re}T)^3\n(2\\alpha^\\prime)^3$. So the model-dependent\naxion cannot be a candidate for the low energy QCD axion unless\nthe potential is sufficiently suppressed.\\cite{wen}\n\nThus, the model-independent axion is a good candidate for\nthe QCD axion. However, it has two serious problems:\n\\\\\n\\indent (A) The decay constant problem-- $F_a$ is too large, $\\sim \n10^{16}$~GeV,\\cite{choikim} and\\\\\n\\indent (B) The hidden sector problem-- We need a hidden sector confining\nforce for \nsupersymmetry breaking around $10^{10-13}$~GeV. If so, the\ndominant contribution \nto the model-independent axion comes from\nthe hidden sector anomaly, \n\\newpage\n\\begin{figure}\n\\epsfxsize=80mm\n\\centerline{\\epsfbox{c99kim2.eps}}\n\\end{figure}\n\\centerline{Fig. 2. {\\it The almost flat axion potential.}}\n\\vskip 0.3cm\n\\noindent $m_a\\simeq \\Lambda_h^2/F_a$. Then, this \ncannot be the needed axion for the strong CP problem. With two confining\nforces with scales of $\\Lambda_h$ and $\\Lambda_{QCD}$, the potential can\nbe written as\n\\begin{equation}\nV\\sim -\\Lambda^4_{QCD}\\cos(\\theta+\\alpha)-\\Lambda^4_h\\cos(\\theta_h+\\beta)\n\\end{equation}\nwhere $\\alpha$ and $\\beta$ are constants, and $\\Lambda_h\\gg\\Lambda_{QCD}$.\nTo settle both $\\theta_h$ and $\\theta$ dynamically at zero, we need\ntwo axions. But as shown above, we have only one axion for this \npurpose, the model-independent axion.\n\nBoth of the above problems are difficult to circumvent.\\footnote{See, \nhowever, Lalak et al.\\cite{lalak}} \n\nThe approximate global symmetries may be a way out from this dilemma.\n\\cite{shafi} Discrete symmetries may forbid sufficiently many terms so that\nthe Peccei-Quinn symmetry violating terms can appear only at $d\\ge 9$.\nOne such example is $Z_N$ symmetry (e.g. $N=3$) in theories without\nhidden sector quarks.\\cite{gkn} \n\n\\section{Cosmology with Axion}\n\nIn the hot cores of stellar objects, the axion production can occur\nthrough $\\gamma+e({\\rm or\\ }Z)\\rightarrow a+\ne({\\rm or\\ }Z)$, $n+n\\rightarrow n+n+a$, $\\gamma+e\\rightarrow a+e$,\n$e^++e^-\\rightarrow a+\\gamma$, etc. For a sufficiently large $F_a$,\naxions produced in the stellar core can escape the star since the \nrescattering cross section is small. If its production rate is too\nlarge $(\\sim 1/F_a^2)$, it takes out too much energy from the core. \nThus, there results the upper bounds on $F_a$ from star evolutions.\nThe best bound is obtained from the study of supernovae.\n\\cite{kang,astro,choikang} \nThus, the solar axion search may not succeed which\nneeds $F_a\\sim 10^7$~GeV.\n\nThe lifetime of $a$ is extremely long and hence can be treated in most cases\nas a stable particle. The classical coherent states of $a$ will \noscillate around the minimum $\\langle a\\rangle=0$. When can this \nhappen? It is around $T_1\\simeq 1$~GeV, not around the axion scale of \n$F_a$ since the axion potential is extremely flat.\nIts existence is felt when the expansion rate is smaller than the\noscillation rate of the classical axion field, viz. \n$3H0.\\n\\\\end{equation}\\nThus, the generating functional is bounded by usung the\\nSchwarz inequality in view of Eq.~(6),\\n\\\\begin{eqnarray}\\n&\\\\exp[-\\\\int d^4x V[\\\\theta]]\\\\equiv |\\\\int[dA_\\\\mu]\\\\prod {\\\\rm Det\\\\ }\\n(\\\\Dslash+m_i)\\\\exp(-\\\\int d^4x{\\\\cal L})|\\\\nonumber\\\\\\\\\\n&\\\\le \\\\int [dA_\\\\mu]|\\\\prod {\\\\rm Det}(\\\\Dslash+m_i)\\\\exp(-\\\\int d^4x{\\\\cal L})\\n|\\\\nonumber\\\\\\\\\\n&=|\\\\int[dA_\\\\mu]\\\\prod{\\\\rm Det\\\\ }(\\\\Dslash+m_i)\\\\exp[-\\\\int d^4x\\n{\\\\cal L}(\\\\theta=0)] |\\\\\\\\\\n&=\\\\exp(-\\\\int d^4x V[0])\\\\nonumber\\n\\\\end{eqnarray}\\nwhere ${\\\\cal L}=(1/4g^2)F^2-i\\\\theta\\\\{F\\\\tilde F\\\\}$, and the simplified\\nnotation $\\\\{\\\\ \\\\ \\\\}$ includes a factor $1/32\\\\pi^2$. The above\\ninequality guarantees\\n\\\\begin{equation}\\nV[\\\\theta]\\\\ge V[0].\\n\\\\end{equation}\\nInstanton solutions have integer values for $\\\\int d^4x\\\\{F\\\\tilde F\\\\}$,\\nhence $V[\\\\theta]$ is periodic with the $\\\\theta$ period of $2\\\\pi$,\\n$\\\\theta\\\\rightarrow \\\\theta+2n\\\\pi$. The above agument is for a nonzero\\nup quark mass. If $m_u=0$, $\\\\theta$ is unphysical and there is no\\nstrong CP problem.\\n\\nAs a coupling, any $\\\\theta$ defines a good theory (or universe). The \\nshape of $V$ as a function of $\\\\theta$ is\\n\\n\\\\begin{figure}\\n\\\\epsfxsize=60mm\\n\\\\centerline{\\\\epsfbox{c99kim1.eps}}\\n\\\\end{figure}\\n\\\\centerline{Fig.~1.\\n{\\\\it Shape of $V[\\\\theta]$. The KM weak CP introduces}~\\\\cite{gr} \\n$|\\\\theta| \\\\simeq 10^{-16}$.}\\n\\\\vskip 0.3cm\\nHere, the axion solution of the strong CP problem is transparent. If\\nwe identify $\\\\theta$ as a pseudoscalar field,\\n\\\\begin{equation}\\n\\\\theta=\\\\frac{a}{F_a}\\n\\\\end{equation}\\nthe vacuum angle is chosen at $\\\\theta\\\\simeq 0$, realizing the\\nalmost CP invariant QCD vacuum. Note the key ingredients of this\\naxion solution. Firstly, the theory introduces an axion coupling\\n$a\\\\{F\\\\tilde F\\\\}$. Second, there is no axion potential except\\nthat coming from the $F\\\\tilde F$ term, otherwise our proof does not\\ngo through. Third, there necessarily appears a mass parameter $F_a$,\\nthe so-called axion decay constant. One possible example for \\nthe axion is to introduce a\\nGoldstone boson, using a global $U(1)$ symmetry.~\\\\cite{pq} As explained\\nabove Peccei-Quinn showed that $\\\\theta=0$ is the minimum of the\\npotential, which is meaningful only if there is a dynamical field\\n$a$. Later, Weinberg and Wilczek explicitly showed that the model\\ncontains the axion.~\\\\cite{ww} It was immediately known that the\\nPQWW axion does not exist,\\\\cite{peccei} and hence there soon \\nappeared a flurry of natural solutions.~\\\\cite{natural} \\n\\nTo have the anomalous coupling, the global symmetry must have a\\ntriangle anomaly in $U(1)_{\\\\rm global}\\\\times SU(3)_c\\\\times SU(3)_c$.\\nThis anomalous coupling introduces an axion decay constant which\\ncan be large for the very light axion models.\\\\cite{invisible,dfsz}\\nSoon after the invention of the very light axion, it has been\\nknown that the astrophysical and cosmological bounds restrict \\nthe axion decay constant in the region, $10^9{\\\\ \\\\rm GeV}\\\\le F_a\\n\\\\le 10^{12}\\\\ {\\\\rm GeV}$.\\\\cite{astro,cos}\\nAlso, it was known that a more ambitious composite axion can be \\nconstructed.\\\\cite{comp}\\n\\nAnother interesting possibility is that there results an axion with\\nthe above properties from a more fundamental theory such as from\\nthe string theory. This possibility introduces a nonrenormalizable\\ninteraction $aF\\\\tilde F$. Indeed, superstring models have a host\\nof moduli fields which do not have potentials at the compactification\\nscale. But some of the moduli have the desired anomalous \\ncouplings,\\\\cite{witten} and becomes the axion. In this case, the \\nso-called superstring axions are expected to have the decay constant \\nnear the Planck scale. But the exact magnitude depends on the details\\nof the model. \\n\\nThe mass of the very light axion is an important parameter in the\\nevolving universe. The allowed range of the decay constant gives\\ntens of micro-eV axion mass,\\n\\\\begin{equation} \\nm_a=0.6\\\\times 10^7\\\\ \\\\frac{\\\\rm eV}{F_a^{\\\\rm GeV}}\\n\\\\end{equation}\\nwhere $F_a^{\\\\rm GeV}=F_a/{\\\\rm GeV}$.\\n\\nThe neutron electric dipole moment in the $\\\\theta$ vacuum is\\ngiven by~\\\\cite{quint}\\n\\\\begin{equation}\\n\\\\frac{d_n}{e}=O(1)\\\\frac{m_u\\\\sin\\\\theta}{f_\\\\pi^2[2Z\\\\cos\\\\theta+(\\n1+Z)^2]^{1/2}}\\n\\\\end{equation}\\nwhere $Z=m_u/m_d$ is the ratio of the current quark masses.\\nFor $m_u<2\\\\times 10^{-13}$~GeV, the neutron electric dipole \\nmoment is satisfied even for O(1) $\\\\theta$.\\n\\nThe very light axion physics is closely connected to the study\\nof the evolution of the universe. The domain wall problem~\\\\cite{sikivie}\\nmust be studied in specific models. Usually, inflation needed in\\nsupergravity models with the condition on the reheating temperature\\n$T_R<10^9$~GeV \\\\cite{ekn} does not lead to the axionic domain\\nwall problem.\\n\\nTheoretically, the introduction of the Peccei-Quinn U(1) global\\nsymmetry is ad hoc. It is better if the axion arises from a\\nfundamental theory. In this spirit, it is most important to\\ndraw a very light axion from superstring theory. If we cannot,\\nhow can we understand the strong CP problem?\\n\\n\\\\section{Embedding the Very Light Axion in Superstring}\\n\\nThe pseudoscalar moduli fields in D=10 superstring is $B_{MN}\\\\\\n(M,N=0,\\\\cdots,9)$ among the bosonic fields $G_{MN}, B_{MN}$ and\\nthe dilaton. Upon compactification to D=4, $B_{\\\\mu\\\\nu}\\\\ (\\\\mu,\\\\nu\\n=0,\\\\cdots,3)$ turns out to be a pseudoscalar field. Dual \\ntransformation of $B_{\\\\mu\\\\nu}$ defines a pseudoscalar $a$ as\\n\\\\begin{equation}\\n\\\\partial^\\\\sigma a\\\\propto\\\\epsilon^{\\\\mu\\\\nu\\\\rho\\\\sigma}H_{\\\\mu\\\\nu\\\\rho};\\nH_{\\\\mu\\\\nu\\\\rho}={\\\\rm field\\\\ strength\\\\ of\\\\ }B_{\\\\mu\\\\nu}\\\\propto\\n\\\\epsilon_{\\\\mu\\\\nu\\\\rho\\\\sigma}\\\\partial^\\\\sigma a.\\n\\\\end{equation}\\nOf course, $B_{\\\\mu\\\\nu}$ does not have renormalzable couplings to \\nmatter fields, hence there is no potential for $a$ since the\\npossible derivative coupling $\\\\partial^\\\\mu a\\\\psi\\\\gamma_\\\\mu\\\\gamma_5\\n\\\\psi$ does not lead to a potential term. If we consider a field\\nstrenth \\n$H_{\\\\mu\\\\nu\\\\rho}$ to obtain couplings, it is invariant under\\na shift $a\\\\rightarrow a+c$. This consideration does not lead to\\nan anomalous coupling needed for an axion. \\n\\nHowever, the gauge invariant D=10 field strength of $B_{MN}$ is\\nnot $H=dB$,\\\\footnote{In this paragraph we use the differential form.}\\nbut is~\\\\cite{green}\\n\\\\begin{equation}\\nH=dB+\\\\omega^0_{3Y}-\\\\omega^0_{3L}\\n\\\\end{equation} \\nwhere the Yang-Mills Chern-Simmons form is tr$(AF-A^3/3)$ and the\\nLorentz Chern-Simmons form is tr$(\\\\omega R-\\\\omega^3/3)$. The \\nChern-Simmons forms satisfy $d\\\\omega^0_{3Y}={\\\\rm tr\\\\ }F^2$ and\\n$d\\\\omega^0_{3L}={\\\\rm tr}\\\\ R^2$. Therefore,\\n\\\\begin{equation}\\ndH=-{\\\\rm tr\\\\ }F^2+{\\\\rm tr\\\\ }R^2,\\n\\\\end{equation}\\nand the equation of motion for $a$ is\\n\\\\begin{equation}\\n\\\\Box a=-\\\\frac{1}{M}[{\\\\rm Tr\\\\ }F_{\\\\mu\\\\nu}\\\\tilde F^{\\\\mu\\\\nu}\\n-{\\\\rm Tr\\\\ }R_{\\\\mu\\\\nu}\\\\tilde R^{\\\\mu\\\\nu}]\\n\\\\end{equation}\\nwhich implies $aF\\\\tilde F$ coupling which is needed for the\\naxion interpretation of $a$.\\\\cite{witten} This is the so-called\\nmodel-independent axion. Here, $M$ is about the compactification\\nscale suppressed by a factor and corresponds to the axion decay\\nconstant.\\\\cite{choikim} \\n\\nTo cancel the Yang-Mills anomaly, one\\nshould introduce the Green-Schwarz term,\\\\cite{green} $S_{GS}\\\\sim\\n\\\\int(B{\\\\rm tr}F^4+\\\\cdots)$. The Green-Schwarz term gives the \\nneeded anomalous coupling for pseudoscalars $B_{ij}\\\\ (i,j=4,\\\\cdots,\\n9)$\\n\\\\begin{equation}\\nB_{ij}\\\\epsilon^{\\\\mu\\\\nu\\\\rho\\\\sigma}F_{\\\\mu\\\\nu}F_{\\\\rho\\\\sigma}\\n\\\\langle F_{kl}\\\\rangle\\\\langle F_{pq}\\\\rangle\\\\epsilon^{ijklpq}.\\n\\\\end{equation}\\nHere, we have model-dependent axions $a_k\\\\sim \\\\epsilon_{ijk}B_{ij}$,\\nthe number of which is the second Betti number.\\\\cite{witten1}\\nUnlike the model-independent axion, the model-dependent axions receive\\nnonvanishing superpotential terms from the world-sheet instanton effect,\\n\\\\begin{equation}\\n\\\\int_{\\\\Sigma_J} d^2z \\\\omega^I_{ij}(\\\\partial X^i\\\\underline\\n\\\\partial X^{\\\\underline j}-\\\\underline\\\\partial X^i\\\\partial X^{\\\\underline\\nj})=2\\\\alpha^\\\\prime\\\\delta_{IJ} \\n\\\\end{equation}\\nwhere $\\\\alpha^\\\\prime$ is the string tension, and $\\\\omega=4\\\\pi^2 {\\\\rm Re}\\n(T_I)\\\\omega^I$. The internal space volume is given by\\\\cite{mth}\\n$V_6=(1/3!)\\\\int \\\\omega\\\\land\\\\omega\\\\land\\\\omega\\\\approx \\n(1/6)(4\\\\pi^2{\\\\rm Re}T)^3\\n(2\\\\alpha^\\\\prime)^3$. So the model-dependent\\naxion cannot be a candidate for the low energy QCD axion unless\\nthe potential is sufficiently suppressed.\\\\cite{wen}\\n\\nThus, the model-independent axion is a good candidate for\\nthe QCD axion. However, it has two serious problems:\\n\\\\\\\\\\n\\\\indent (A) The decay constant problem-- $F_a$ is too large, $\\\\sim \\n10^{16}$~GeV,\\\\cite{choikim} and\\\\\\\\\\n\\\\indent (B) The hidden sector problem-- We need a hidden sector confining\\nforce for \\nsupersymmetry breaking around $10^{10-13}$~GeV. If so, the\\ndominant contribution \\nto the model-independent axion comes from\\nthe hidden sector anomaly, \\n\\\\newpage\\n\\\\begin{figure}\\n\\\\epsfxsize=80mm\\n\\\\centerline{\\\\epsfbox{c99kim2.eps}}\\n\\\\end{figure}\\n\\\\centerline{Fig. 2. {\\\\it The almost flat axion potential.}}\\n\\\\vskip 0.3cm\\n\\\\noindent $m_a\\\\simeq \\\\Lambda_h^2/F_a$. Then, this \\ncannot be the needed axion for the strong CP problem. With two confining\\nforces with scales of $\\\\Lambda_h$ and $\\\\Lambda_{QCD}$, the potential can\\nbe written as\\n\\\\begin{equation}\\nV\\\\sim -\\\\Lambda^4_{QCD}\\\\cos(\\\\theta+\\\\alpha)-\\\\Lambda^4_h\\\\cos(\\\\theta_h+\\\\beta)\\n\\\\end{equation}\\nwhere $\\\\alpha$ and $\\\\beta$ are constants, and $\\\\Lambda_h\\\\gg\\\\Lambda_{QCD}$.\\nTo settle both $\\\\theta_h$ and $\\\\theta$ dynamically at zero, we need\\ntwo axions. But as shown above, we have only one axion for this \\npurpose, the model-independent axion.\\n\\nBoth of the above problems are difficult to circumvent.\\\\footnote{See, \\nhowever, Lalak et al.\\\\cite{lalak}} \\n\\nThe approximate global symmetries may be a way out from this dilemma.\\n\\\\cite{shafi} Discrete symmetries may forbid sufficiently many terms so that\\nthe Peccei-Quinn symmetry violating terms can appear only at $d\\\\ge 9$.\\nOne such example is $Z_N$ symmetry (e.g. $N=3$) in theories without\\nhidden sector quarks.\\\\cite{gkn} \\n\\n\\\\section{Cosmology with Axion}\\n\\nIn the hot cores of stellar objects, the axion production can occur\\nthrough $\\\\gamma+e({\\\\rm or\\\\ }Z)\\\\rightarrow a+\\ne({\\\\rm or\\\\ }Z)$, $n+n\\\\rightarrow n+n+a$, $\\\\gamma+e\\\\rightarrow a+e$,\\n$e^++e^-\\\\rightarrow a+\\\\gamma$, etc. For a sufficiently large $F_a$,\\naxions produced in the stellar core can escape the star since the \\nrescattering cross section is small. If its production rate is too\\nlarge $(\\\\sim 1/F_a^2)$, it takes out too much energy from the core. \\nThus, there results the upper bounds on $F_a$ from star evolutions.\\nThe best bound is obtained from the study of supernovae.\\n\\\\cite{kang,astro,choikang} \\nThus, the solar axion search may not succeed which\\nneeds $F_a\\\\sim 10^7$~GeV.\\n\\nThe lifetime of $a$ is extremely long and hence can be treated in most cases\\nas a stable particle. The classical coherent states of $a$ will \\noscillate around the minimum $\\\\langle a\\\\rangle=0$. When can this \\nhappen? It is around $T_1\\\\simeq 1$~GeV, not around the axion scale of \\n$F_a$ since the axion potential is extremely flat.\\nIts existence is felt when the expansion rate is smaller than the\\noscillation rate of the classical axion field, viz. \\n$3H\\varepsilon\\gamma (1-\\beta\\cos\n\\theta_c)$. For the photon energies at the peak of the Planck distribution,\n$\\varepsilon\\approx 2.82kT$, the latter condition can be rewritten as\n$4\\cdot 10^{-2}B_{12}(z)/(T_6\\gamma_3(1-\\beta\\cos\\theta_c))>1$, with\n$\\gamma_3\\equiv\\gamma/10^3$. Taking $T_6=0.5$, $\\gamma_3=3$, $B_{12}=0.1$\n(Zhang {\\it et al.} 1997, Fig. 1a), one can obtain that at $z=10R$ the\nleft-hand side of this inequality is $5\\cdot 10^{-5}$, while at $z=0$ it\nequals $3\\cdot 10^{-4}$. So even at the stellar surface most of the photons\nscatter in the Thomson regime rather than in the magnetic one. The rate of\nenergy loss out of the Thomson scattering is found to be\n$$\n\\frac{d\\gamma_T}{dt}=-30\\gamma T_6^4(1-\\beta\\cos\\theta_c)^3\\,{\\rm s}^{-1},\n\\eqno (4)$$\nshowing that this process is inefficient. Thus the resonant inverse Compton\nscattering is the only significant energy loss mechanism for the secondary\nparticles in pulsar magnetospheres.\n\nWe believe that the particles start deceleration just above the polar\ngap. In general the gap thickness is supposed to be of the order of the polar\ncap radius (Ruderman \\& Sutherland 1975) or even larger (Arons \\& Scharlemann\n1979). The energy loss of secondary particles due to the resonant\ninverse Compton scattering above the gap should certainly be influenced by\nthe adopted value of the gap height. In Fig. 2 we show the final\nLorentz-factors versus the gap height. One can see that the dependence is\nsufficiently weak, therefore, below we fix $z_0$ at $10^{-2}R$.\n\nIn contrast with the gap height, such pulsar parameters as the star temperature\nand magnetic field strength can influence particle deceleration essentially.\nIn Fig. 3 we present the dependences of the normalized final Lorentz-factor\non the neutron star temperature at various magnetic field strengths.\nApparently, at the temperatures $<10^5$ K the scattering is inefficient yet,\nwhile at higher temperatures it becomes significant. Note that at various\ninitial Lorentz-factors ($\\gamma_0=100$ and $3000$) the scattering efficiency\nversus magnetic field strength is essentially different. The particles with\n$\\gamma_0=100$ resonantly scatter the photons from the Wien region. Then the\nweaker the field strength, the lower is the energy of resonant photons and,\ncorrespondingly, the higher is the photon spectral density and the larger\nis the particle energy loss (see Fig. 3a). At $\\gamma_0=3000$ the resonant\nenergy lies in the Rayleigh-Jeans region. So the scattering is more efficient\nfor higher magnetic field strengths, since the photon spectral density\nincreases with the energy (see Fig. 3b).\n\nFor the resonant character of the scattering the particle energy loss\ndepends strongly on the initial Lorentz-factor. Figure 4 shows the final\nLorentz-factor versus the initial one for various neutron star temperatures\nand magnetic field strengths. At $\\gamma_0\\sim 10$ as well as at $\\gamma_0\n\\sim 10^4$ the resonant scattering appears to be inefficient. Provided that the\nscattering is intense ($\\gamma_0\\sim 10^2-10^3$), the final Lorentz-factor\nappears to be independent of the initial one. According to Fig. 4a, the length\nof the plateau increases with the star temperature. In fact, the higher\ntemperature implies the larger amount of photons at every energy, the\nscattering becoming more efficient. As can be seen from Fig. 4b, the increase\nof the magnetic field strength leads to the shift of the plateau toward a\nhigher energy; this is certainly consistent with the resonance condition (1).\n\n\\section{The distribution function of the secondary plasma as a result of\nresonant inverse Compton scattering}\nSince the energy loss depends essentially on the initial particle energy,\nwe are to investigate the evolution of the distribution function of\nsecondary particles as a result of the resonant inverse Compton scattering.\nConservation of the number of particles along a phase trajectory\nimplies that\n$$\nf(z,\\,\\gamma)d\\gamma=f(z_0,\\,\\gamma_0)d\\gamma_0\\,,$$\nwhere $f(z,\\,\\gamma)$ is the particle distribution function and the\nsubscript ''0'' refers to the initial values. So looking for the phase\ntrajectories of individual particles one can reconstruct the distribution\nfunction at any height $z$. We are particularly interested in the final\ndistribution function arising at distances, where the resonant scattering\nceases.\n\nLet us begin with the evolution of a waterbag distribution function:\n$$\nf(z_0,\\,\\gamma_0)=\n\\left\\{\n\\begin{array}{l}\n\\frac{1}{\\gamma_{max}-\\gamma_{min}},\\quad\\qquad\\qquad \\gamma_{min}\\leq\\gamma\\leq\n\\gamma_{max},\\\\\n0\\,,\\,\\quad\\qquad\\qquad\\qquad \\gamma <\\gamma_{min}\\,{\\rm and }\\,\\gamma >\\gamma_{max},\\\\\n\\end{array}\n\\right.$$\nwith $\\gamma_{min}=10$, $\\gamma_{max}=10^4$.\nThe final distribution functions\nat various pulsar\nparameters are plotted in Fig. 5. The particles with $\\gamma\\sim 10^2-10^3$\nare essentially decelerated due to the scattering, the final energies becoming\nequal (see also Fig. 4). These particles form the sharp peak at $\\gamma\n<10^2$. For the Lorentz-factors of a few thousand the scattering becomes\ninefficient and the distribution function remains almost unaltered. Thus,\nthe resonant inverse Compton scattering leads to the two-humped distribution\nfunction of the secondary plasma. At higher neutron star temperatures the\nmain peak of the function shifts towards the lower energies and the humps\nbecome more prominent. The magnetic field strength variation also results\nin the shift of the main peak. For the more realistic distribution function\nresembling that found by Arons (1980),\n$$\nf(\\gamma)=\n\\left\\{\n\\begin{array}{l}\n\\exp\\left(-10\\frac{\\gamma_m-\\gamma}{\\gamma_m}\\right),\\quad\\qquad\\qquad 10\\leq\\gamma\\leq\n\\gamma_m,\\\\\n(\\gamma/\\gamma_m)^{-3/2},\\,\\quad\\qquad\\qquad\\qquad \\gamma_m\\leq\\gamma\\leq\\gamma_c,\\\\\n(\\gamma_c/\\gamma_m)^{-3/2}\\exp\\left(-\\frac{\\gamma-\\gamma_c}{\\gamma_c}\\right),\n\\quad \\gamma_c\\leq\\gamma\\leq 10^4,\\\\\n\\end{array}\n\\right.\\eqno (5)$$\nwith $\\gamma_m=10^2$, $\\gamma_c=10^{3.5}$, the evolution on account of\nthe resonant inverse Compton scattering is qualitatively the same (see Fig. 6).\n\nWe next examine the dispersion properties of the plasma with the evolved\ndistribution function. For simplicity let us assume that the plasma consists\nof the two particle flows characterized by the number densities $n_a$,\n$n_b$ and by the Lorentz-factors $\\gamma_a$, $\\gamma_b$ ($\\gamma_a <\\gamma_b$).\nGiven the infinitely strong magnetic field, the dispersion relation is as\nfollows (see, {\\it e.g.} Lyubarskii 1995):\n$$\n\\frac{\\omega_{pa}^2}{(\\omega -kv_a)^2\\gamma_a^3}+\\frac{\\omega_{pb}^2}\n{(\\omega -kv_b)^2\\gamma_b^3}=1. \\eqno (6)$$\nHere $\\omega$ is the frequency, $k$ the wave number, $v_{a,b}$ are the\nparticle velocities, $\\omega_{pa,b}$ the plasma frequencies given by the\ncustomary expression:\n$$\n\\omega_{pa,b}=\\sqrt{\\frac{4\\pi n_{a,b}e^2}{m}}, \\eqno (7)$$\nwhere $e$ is the electron charge, $m$ the electron mass. As is evident from\nEq. (6), the dispersion properties of the plasma are mainly determined by one\nof the particle flows on condition that\n$$\n\\frac{n_a}{\\gamma_a^3}\\gg\\frac{n_b}{\\gamma_b^3}, \\eqno (8)$$\nrather than $n_a\\gg n_b$. This is because of the great inertia of the\nfast particles performing one-dimensional motion in the superstrong magnetic\nfield. For the distribution functions plotted in Fig. 5 and 6 $n_a$ and\n$n_b$ are comparable, while $\\gamma_a/\\gamma_b\\sim 10^{-1}-10^{-2}$. Therefore\nthe low-energy particles of the main peak almost completely determine the\ndispersion properties of the plasma.\n\nThe two-humped distribution function implies the possibility of the\ntwo-stream instability. Provided that the contribution of one of the plasma\nflows to the plasma dispersion is small ({\\it i.e.} Eq. (8) is valid), the\ngrowth rate of the instability takes the form (Lominadze \\& Mikhailovskii 1979,\nCheng \\& Ruderman 1980):\n$$\n{\\rm Im} \\omega\\approx\\left(\\frac{n_b}{n_a}\\right)^{1/3}\\frac{\\omega_{pa}}\n{\\gamma_a^{1/2}\\gamma_b}. \\eqno (9)$$\nThe two-stream instability results in an essential development of\ninitial perturbations on condition that\n$$\n\\frac{R_c}{c}{\\rm Im}\\omega> 10, \\eqno (10)$$\nwhere $R_c$ is the characteristic scale length for the increase of\nperturbations.\n\nIt is convenient to normalize the number density of the secondary plasma by\nthe Goldreich-Julian charge density:\n$$\nn=\\frac{\\kappa B}{Pce}, \\eqno (11)$$\nwhere $\\kappa$ is the multiplicity factor of the secondary plasma, $P$ the\npulsar period. The\nlatter equation can be rewritten as:\n$$\nn=6.25\\cdot 10^{13} P^{-1}\\kappa_3B_{12}(1+z/R)^{-3}\\, {\\rm cm^{-3}},\\eqno (12)$$\nwhere $\\kappa_3\\equiv\\kappa/10^3$. Using Eqs. (9) and (12) in Eq. (10) we\nreduce the condition for the efficient instability development to the form:\n$$\n\\frac{\\kappa_3B_{12}}{PR_{c7}\\gamma_{b3}^2\\gamma_{a2}}>4\\cdot 10^{-4}.\n\\eqno (13)$$\nHere $R_{c7}\\equiv R_c/10^7{\\rm cm}$, $\\gamma_{b3}\\equiv \\gamma_b/10^3$,\n$\\gamma_{a2}\\equiv\\gamma_a/10^2$ and it is assumed that $(n_b/n_a)^{1/3}\n\\approx 1$. As can be seen from Eq. (13), at typical pulsar parameters the\ntwo-stream instability can develop readily providing the increase of plasma\noscillations. The latter can be transformed into electromagnetic waves,\nthus giving rise to pulsar radio emission.\n\nIt should be mentioned that two-steram instability has always been one of\nthe most popular mechanisms for pulsar radio emission.\nFor more than two\ndecades a number of scenarios for the instability development were proposed.\nThe first and the most natural one involves the instability caused by\nthe flows of primary and secondary pulsar plasma (Ruderman \\& Sutherland 1975).\nHowever, the growth rate of this instability appears to be too small\nbecause of enormous inertia of the high-energy primary particles (Benford \\&\nBuschauer 1977). Cheng \\& Ruderman (1977) considered the two-stream\ninstability arising in the secondary plasma due to the difference in the\nvelocities of electrons and positrons moving along the curved magnetic lines.\nHowever, this difference is insufficient to cause the instability, since the\nparticle distribution functions are too broad (Buschauer \\& Benford 1977).\nLyubarskii (1993) suggested that current and charge density adjustment\nin pulsar\nmagnetosphere leads to the backward particle flow, which\ncauses intense two-stream instability. However, numerical simulations of the\nplasma flow in the open field line tube are necessary to prove this idea.\nGiven nonstationary generation of the secondary plasma the particles are\nconfined to the separate clouds, and the fastest particles of a cloud can\noutstrip the slower particles of the previous cloud giving rise to the\ntwo-stream instability (Usov 1987, Ursov \\& Usov 1988). Up to now it is not\nclear whether the instability initiated in such a way can account for pulsar\nradio emission, since the nonstationarity of plasma generation is not studied\nin detail yet.\nThe present\npaper suggests one more possibility of two-stream instability in pulsars,\nwhich is based on the selective energy loss of particles as a result of\nresonant inverse Compton scattering. Note that in this model the instability\narises naturally, with no additional assumptions being involved.\n\n\\section{Gamma-ray luminosity provided by resonantly\nupscattered Compton photons}\nThe photons produced by the resonant inverse Compton scattering have\nthe energies\n$$\nE\\sim\\gamma\\epsilon_Bmc^2\\sim B_{12}\\gamma_2\\,{\\rm MeV},\\eqno (14)$$\nso that typically $E\\sim 1-10$ MeV. Note that the curvature gamma-photons\nproduced in the polar gap as well as the photons upscattered by the primary\nparticles have essentially higher energies, $E\\sim 100$ MeV. Hence, the resonant\nscattering by secondary plasma results in an additional low-energy component in pulsar\ngamma-ray spectrum. The spectrum of this component in the case of some\nspecific distribution functions of the scattering particles is obtained\nby Daugherty \\& Harding (1989).\nIn general, the low-energy tail of this component spreads even to the\nX-ray band on account of the photons resonantly scattered at distances\n$z>R$, where the magnetic field strength decreases essentially. However,\nthese photons are very few, since at $z>R$ the scattering rate decreases\nsignificantly due to the shrinking of the solid angle subtended by the\nneutron star.\n\nGiven that the scattering is efficient, most of the energy of the secondary\nplasma should be transferred to the low-energy gamma-rays. The luminosity\nprovided by the upscattered photons can be estimated as follows:\n$$\nL=nSmc^3\\Delta\\gamma,\\eqno (15)$$\nwhere $S$ is the cross-sectional area of the open field line tube,\n$$\nS=\\frac{\\pi R^3}{R_L},\n\\eqno (16)$$\n$R_L$ is the light cylinder radius, $\\Delta\\gamma$ the difference between\nthe Lorentz-factors of the\nparticles, which mainly contribute to the final and initial plasma energy,\n$\\Delta\\gamma\\sim 10^2-10^3$. Substituting Eqs. (12) and (16) into Eq. (15)\nwe find:\n$$\nL=0.942\\cdot 10^{30}\\frac{B_{12}R_6^3\\kappa_3\\gamma_3}{P^2}\\, {\\rm ergs/s}.\n\\eqno (17)$$\n\nAlthough in the particle rest frame the photons are scattered in all\ndirections, in the laboratory frame they are beamed along the particle velocity.\nSo the opening angle of the gamma-ray beam is given by\n$\\varphi =3\\sqrt{R/R_L}.$\nThe averaged observed photon flux, $F$, is related to the luminosity as\n$$\nF=\\frac{L\\varphi}{2\\pi\\Omega d^2E\\Delta E},\\eqno (18)$$\nwhere $\\Omega =\\pi\\varphi^2/4$ is the solid angle occupied by the beam of\nupscattered photons,\n$d$ the distance to the pulsar, $\\Delta E$ the energy band. Taking into\naccount Eq. (17), Eq. (18) can be rewritten as\n$$\nF=3\\cdot 10^{-10}\\frac{B_{12}R_6^{5/2}\\gamma_3\\kappa_3}{P^{3/2}d_3^2 E_6^2}\\,\n{\\rm photons/(cm^2\\cdot s\\cdot keV)}, \\eqno (19)$$\nwhere $d_3\\equiv d/10^3\\,{\\rm pc}$, $E_6\\equiv E/1\\,{\\rm MeV}$.\n\nFor most pulsars the flux given by Eq. (19) is too low to be detected.\nAt present the detectors of the Compton gamma-ray observatory are the most\nsensitive to the low-energy gamma-ray emission (OSSE at 0.05--10 MeV and\nCOMPTEL at 1--30 MeV). At 1 MeV the source sensitivity of OSSE is only\n$2\\cdot 10^{-7}$ photons/(${\\rm cm^2\\cdot s\\cdot keV}$) (Gehrels \\&\nShrader 1996). In the observations reported by Kuiper {\\it et al.} (1996) the\nflux from Geminga in the band of 3--10 MeV was found to be $10^{-7}E_6^{-2}$\nphotons/(${\\rm cm^2\\cdot s\\cdot keV}$). Substituting Geminga parameters\n($P=0.237$ s, $B_{12}=3.3$, $d_3=0.15$) into Eq. (19) one can obtain the flux\nprovided by the upscattered Compton photons: $F=3.8\\cdot 10^{-7}\\kappa_3\n\\gamma_3R_6^{5/2}E_6^{-2}$ photons/(${\\rm cm^2\\cdot s\\cdot keV}$), which is\nconsistent with the one detected.\n\n\\section{Conclusions}\nWe have investigated resonant inverse Compton scattering by secondary\npulsar plasma. The process is found to cause the efficient energy loss of\nthe secondary particles given the neutron star temperatures $>10^5$ K, so\nthat our results are applicable to most pulsars. For the resonant\ncharacter of the scattering, the energy loss depends strongly on the initial\nparticle energy. At $\\gamma_0\\sim 10^2-10^3$ the scattering is the most\nessential, the final Lorentz-factors of the particles being independent of\nthe initial ones.\n \nThe distribution function of the secondary plasma is significantly altered by\nthe resonant inverse Compton scattering. It is shown that ultimately the\ndistribution function becomes two-humped. The main peak at $\\gamma\\sim 10^2$\nis very sharp. It is formed by particles which suffered severe energy\nloss on account of the scattering. Another hump is sufficiently broad. It is\nassociated with the particles, whose Lorentz-factors are almost unaltered by\nthe scattering. 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At neutron star\\ntemperatures higher than $10^5$ K the process appears to be an essential\\nenergy loss mechanism for the particles. The distribution function of the\\nsecondary plasma particles is found to be strongly affected by the scattering.\\nIt becomes two-humped implying the development of two-stream instability. The\\nresonantly upscattered Compton photons are found to gain energy of\\n1--10 MeV forming an additional component in the pulsar gamma-ray spectrum. The\\ncorresponding gamma-ray flux is estimated as well.\\n%\\\\keywords{plasmas---scattering---pulsars: general---gamma-rays: theory}\\n\\\\end{abstract}\\n\\n\\\\section{Introduction}\\nRotation of a highly magnetized neutron star is known to induce a strong\\nelectric field, which intensely accelerates charged particles. According to the\\ncustomary polar gap models (Ruderman \\\\& Sutherland 1975, Arons \\\\& Scharlemann\\n1979), the acceleration takes place near the neutron star surface above the polar\\ncap, the Lorentz-factor of the primary particles increasing up to $\\\\sim 10^6$.\\nThe particles move along the magnetic lines and emit curvature photons,\\nwhich initiate pair-production cascade. The first electron-positron\\npairs created screen the accelerating electric field, so that at higher altitudes the\\nparticle energy remains unaltered; the typical Lorentz-factors of the secondary\\nplasma are $\\\\sim 10-10^4$.\\n\\nRecent observations testify to thermal soft X-ray emission from some pulsars\\nindicating that the neutron stars can be rather hot, $T\\\\sim 5\\\\cdot 10^5$ K,\\nwhile the polar caps can have still higher temperatures scaling a few times\\n$10^6$ K (Cordova {\\\\it et al.} 1989, Ogelman 1991, Halpern \\\\& Holt 1992, Finley\\n{\\\\it et al.} 1992, Halpern \\\\& Ruderman 1993, Ogelman \\\\& Finley 1993,\\nOgelman {\\\\it et al.} 1993, Yancopoulos {\\\\it et al.} 1994, Ogelman 1995,\\nGreiveldinger {\\\\it et al.} 1996). Such high temperatures of the neutron star surface\\nare also predicted theoretically (Alpar {\\\\it et al.} 1984, Shibazaki \\\\& Lamb\\n1989, Van Riper 1991, Page \\\\& Applegate 1992, Umeda {\\\\it et al.} 1993, Halpern\\n\\\\& Ruderman 1993). The thermal X-ray photons should suffer inverse Compton\\nscattering off the primary particles in the polar gap. In the presence of a\\nstrong magnetic field the scattering cross-section is essentially enhanced,\\nif the photon energy in the particle rest frame equals the cyclotron energy\\n(Herold 1979, Xia {\\\\it et al.} 1985). For the pulsars with hot polar caps the\\nresonant Compton scattering in the polar gap was found to be rather efficient\\n(Kardashev {\\\\it et al.} 1984, Xia {\\\\it et al.} 1985, Daugherty \\\\& Harding\\n1989, Dermer 1990,\\nSturner 1995, Chang 1995). Firstly, it was recognized as an essential mechanism\\nfor energy loss of primary particles accelerating in the polar gap.\\nSecondly, inverse Compton scattering was found to condition the gap formation,\\nsince the pair production avalanche may be triggered by the upscattered\\nCompton photons rather than by curvature photons (Zhang \\\\& Qiao 1996, Qiao\\n\\\\& Zhang 1996, Luo 1996, Zhang {\\\\it et al.} 1997).\\n\\nAs shown by Sturner (1995), given typical values of neutron star temperature\\nand surface magnetic field, the resonant Compton scattering is the\\nstrongest for particle Lorentz-factors $\\\\sim 10^2-10^3$. Theoretical models\\n(Van Riper 1991, Page \\\\& Applegate 1992, Umeda {\\\\it et al.} 1993) suggest\\nthat the typical temperatures of the neutron star surface are as high as a few\\ntimes $10^5$ K. Hence, the scattering is likely to be essential for the\\nsecondary plasma in most of the pulsars. Daugherty \\\\&\\nHarding (1989), Zhang {\\\\it et al.} (1997)\\ntraced the evolution of the Lorentz-factor of secondary particles\\non account of magnetic inverse Compton scattering above the polar gap. Our\\naim is to investigate in more detail the influence of resonant inverse\\nCompton scattering on the parameters of secondary plasma. For the resonant\\ncharacter of the scattering, the evolution of particle Lorentz-factor with\\nthe distance depends strongly on the initial particle energy. Since the\\ndistribution function of the secondary plasma is generally believed to be\\nrather broad (the Lorentz-factor ranges from $10$ to $10^4$), its evolution\\non account of the Compton scattering is of a great interest. It will be\\nshown that only particles with Lorentz-factors between 100 and 1000 are\\nessentially decelerated in the course of\\nthe resonant scattering forming a sharp peak at low energies. Particles with\\nlarger Lorentz-factors are not decelerated at all. Thus,\\nthe resultant distribution function of secondary particles becomes\\ntwo-humped, giving rise to the two-stream instability.\\n\\nIn Sect. 2 we examine how the resonant inverse Compton scattering affects the\\nLorentz-factor of a secondary particle at various pulsar parameters. Section 3\\nis devoted to studying the evolution of the distribution function. The\\nconditions for the development of the two-stream instability are also\\ndiscussed. In Sect. 4 we estimate the gamma-ray luminosity caused by\\nthe upscattered Compton photons. Section 5 contains a brief summary.\\n\\n\\\\section{Deceleration of secondary particles due to resonant inverse Compton\\nscattering}\\nConsider the flow of secondary plasma streaming along the open magnetic field\\nlines above the polar gap. The neutron star is supposed to emit a blackbody\\nradiation, which is scattered by the plasma particles. In a strong magnetic\\nfield the scattering is particularly efficient, if the photon energy,\\n$\\\\varepsilon mc^2$, satisfies the resonance condition:\\n$$\\n\\\\varepsilon\\\\gamma (1-\\\\beta\\\\cos\\\\theta)=\\\\varepsilon_B, \\\\eqno (1)$$\\nwhere $\\\\gamma$ is the Lorentz-factor of the scattering particles, $\\\\beta$\\nthe particle velocity in units of $c$, $\\\\theta$ the angle the photon makes\\nwith the particle velocity, $\\\\varepsilon\\\\equiv B/B_{cr}$, with $B_{cr}=\\nm^2 c^3/\\\\hbar e=4.414\\\\cdot 10^{13}$ G.\\nAt the distance $z$ from the neutron star the rate of energy\\nloss due to the resonant inverse Compton scattering can be written as\\n(Sturner 1995):\\n$$\\n\\\\frac{d\\\\gamma}{dt}=4.92\\\\cdot 10^{11}\\\\frac{T_6B_{12}^2(z)}{\\\\beta\\\\gamma}\\n$$$$\\n\\\\times\\\\ln\\\\left[1-\\\\exp\\\\left(-\\\\frac{\\\\varepsilon_Bmc^2}\\n{\\\\gamma (1-\\\\beta\\\\cos\\\\theta_c(z))kT}\\\\right)\\\\right]{\\\\rm s}^{-1}.\\n\\\\eqno (2)$$\\nHere $T_6$ is the neutron star temperature in units of $10^6$ K, $B_{12}(z)$\\nthe magnetic field strength in units of $10^{12}$ G, $\\\\theta_c(z)$ the maximum\\nincident angle of photons,\\n$$\\n\\\\cos\\\\theta_c=\\\\sqrt{1-\\\\frac{1}{(1+z/R)^2}}, \\\\eqno (3)$$\\nwhere $R$ is the neutron star radius. Provided that the magnetic field is\\ndipolar, $B_{12}(z)\\\\propto (1+z/R)^{-3}$.\\n \\nNumerical solutions of Eq. (2) are presented in Fig. 1.\\n\\n\\n\\n\\n One can see that the\\nresonant inverse Compton scattering is significant up to $z\\\\sim R$ and it\\naffects the particle Lorentz-factor essentially. Note that the curves for\\ndifferent initial Lorentz-factors are not similar to each other. In agreement\\nwith Eq. (1), the larger the particle Lorentz-factor the lower is the energy\\nof resonantly scattered photons. At $\\\\gamma_0=3000$ the energy of the resonant\\nphotons is below $\\\\varepsilon_{max}=2.82kT/(mc^2)$, which corresponds to the\\nmaximum in the photon distribution. As $\\\\gamma$ is decreasing with the altitude,\\nthe resonant energy increases. Hence, the photon spectral density increases\\nand the scattering becomes more efficient. However, at distances $z\\\\sim R$ it\\nceases due to the essential shrinking of the solid angle subtended by the\\nneutron star. If the initial Lorentz-factor is $100$, the energy of resonant\\nphotons is above $\\\\varepsilon_{max}$ and further increases with the altitude,\\nso that the scattering gradually ceases.\\n\\nTheoretical models predict that the polar cap region should be significantly\\nhotter than the rest surface of the neutron star ({\\\\it e.g.} Cheng \\\\& Ruderman 1980,\\nArons 1981, Alpar {\\\\it et al.} 1984, Umeda {\\\\it et al.} 1993, Luo 1996).\\nHowever, the luminosities observed from the hot spots appear to be too small\\n(Finley {\\\\it et al.} 1992, Halpern \\\\& Ruderman 1993, Becker \\\\& Trumper 1993,\\nYancopoulos {\\\\it et al.} 1994, Greiveldinger {\\\\it et al.} 1996).\\nThe latter is usually interpreted as a consequence of small hot spot radii\\n({\\\\it e.g.} Yancopoulos {\\\\it et al.} 1994, Greiveldinger {\\\\it et al.} 1996).\\nAs is evident from Fig.1, for typical hot spot parameters\\nthe particle energy loss is mainly determined by the scattering\\nof the photons from the whole neutron star rather than by the scattering\\nof hot spot photons.\\nSo hereafter we take into account only the photons from the whole neutron star\\nsurface keeping in mind that the influence of hot spot photons can\\nsomehow alter our quantitative results, while the qualitative picture should\\nremain the same.\\n\\n\\nIt should be pointed out that the evolution of Lorentz-factor with the\\naltitude shown in Fig. 1 is somewhat different from that reported by\\nZhang {\\\\it et al.}(1997)(see their Fig. 1). These authors claim that\\nat distances $z\\\\sim{\\\\rm few} R$ the particles suffer severe nonresonant\\nmagnetized scattering, which leads to the drastic decrease of the\\nfinal Lorentz-factor. In fact, the rate of energy loss on account of\\nnonresonant magnetic scattering increases with decreasing the field strength\\nas $B_{12}^{-2}(z)$ (see Eq. (5) in Sturner 1995). However, this equation is\\napplicable only if in the particle rest frame the cyclotron energy exceeds\\nthe energy of most of photons, $\\\\varepsilon_B >\\\\varepsilon\\\\gamma (1-\\\\beta\\\\cos\\n\\\\theta_c)$. For the photon energies at the peak of the Planck distribution,\\n$\\\\varepsilon\\\\approx 2.82kT$, the latter condition can be rewritten as\\n$4\\\\cdot 10^{-2}B_{12}(z)/(T_6\\\\gamma_3(1-\\\\beta\\\\cos\\\\theta_c))>1$, with\\n$\\\\gamma_3\\\\equiv\\\\gamma/10^3$. Taking $T_6=0.5$, $\\\\gamma_3=3$, $B_{12}=0.1$\\n(Zhang {\\\\it et al.} 1997, Fig. 1a), one can obtain that at $z=10R$ the\\nleft-hand side of this inequality is $5\\\\cdot 10^{-5}$, while at $z=0$ it\\nequals $3\\\\cdot 10^{-4}$. So even at the stellar surface most of the photons\\nscatter in the Thomson regime rather than in the magnetic one. The rate of\\nenergy loss out of the Thomson scattering is found to be\\n$$\\n\\\\frac{d\\\\gamma_T}{dt}=-30\\\\gamma T_6^4(1-\\\\beta\\\\cos\\\\theta_c)^3\\\\,{\\\\rm s}^{-1},\\n\\\\eqno (4)$$\\nshowing that this process is inefficient. Thus the resonant inverse Compton\\nscattering is the only significant energy loss mechanism for the secondary\\nparticles in pulsar magnetospheres.\\n\\nWe believe that the particles start deceleration just above the polar\\ngap. In general the gap thickness is supposed to be of the order of the polar\\ncap radius (Ruderman \\\\& Sutherland 1975) or even larger (Arons \\\\& Scharlemann\\n1979). The energy loss of secondary particles due to the resonant\\ninverse Compton scattering above the gap should certainly be influenced by\\nthe adopted value of the gap height. In Fig. 2 we show the final\\nLorentz-factors versus the gap height. One can see that the dependence is\\nsufficiently weak, therefore, below we fix $z_0$ at $10^{-2}R$.\\n\\nIn contrast with the gap height, such pulsar parameters as the star temperature\\nand magnetic field strength can influence particle deceleration essentially.\\nIn Fig. 3 we present the dependences of the normalized final Lorentz-factor\\non the neutron star temperature at various magnetic field strengths.\\nApparently, at the temperatures $<10^5$ K the scattering is inefficient yet,\\nwhile at higher temperatures it becomes significant. Note that at various\\ninitial Lorentz-factors ($\\\\gamma_0=100$ and $3000$) the scattering efficiency\\nversus magnetic field strength is essentially different. The particles with\\n$\\\\gamma_0=100$ resonantly scatter the photons from the Wien region. Then the\\nweaker the field strength, the lower is the energy of resonant photons and,\\ncorrespondingly, the higher is the photon spectral density and the larger\\nis the particle energy loss (see Fig. 3a). At $\\\\gamma_0=3000$ the resonant\\nenergy lies in the Rayleigh-Jeans region. So the scattering is more efficient\\nfor higher magnetic field strengths, since the photon spectral density\\nincreases with the energy (see Fig. 3b).\\n\\nFor the resonant character of the scattering the particle energy loss\\ndepends strongly on the initial Lorentz-factor. Figure 4 shows the final\\nLorentz-factor versus the initial one for various neutron star temperatures\\nand magnetic field strengths. At $\\\\gamma_0\\\\sim 10$ as well as at $\\\\gamma_0\\n\\\\sim 10^4$ the resonant scattering appears to be inefficient. Provided that the\\nscattering is intense ($\\\\gamma_0\\\\sim 10^2-10^3$), the final Lorentz-factor\\nappears to be independent of the initial one. According to Fig. 4a, the length\\nof the plateau increases with the star temperature. In fact, the higher\\ntemperature implies the larger amount of photons at every energy, the\\nscattering becoming more efficient. As can be seen from Fig. 4b, the increase\\nof the magnetic field strength leads to the shift of the plateau toward a\\nhigher energy; this is certainly consistent with the resonance condition (1).\\n\\n\\\\section{The distribution function of the secondary plasma as a result of\\nresonant inverse Compton scattering}\\nSince the energy loss depends essentially on the initial particle energy,\\nwe are to investigate the evolution of the distribution function of\\nsecondary particles as a result of the resonant inverse Compton scattering.\\nConservation of the number of particles along a phase trajectory\\nimplies that\\n$$\\nf(z,\\\\,\\\\gamma)d\\\\gamma=f(z_0,\\\\,\\\\gamma_0)d\\\\gamma_0\\\\,,$$\\nwhere $f(z,\\\\,\\\\gamma)$ is the particle distribution function and the\\nsubscript ''0'' refers to the initial values. So looking for the phase\\ntrajectories of individual particles one can reconstruct the distribution\\nfunction at any height $z$. We are particularly interested in the final\\ndistribution function arising at distances, where the resonant scattering\\nceases.\\n\\nLet us begin with the evolution of a waterbag distribution function:\\n$$\\nf(z_0,\\\\,\\\\gamma_0)=\\n\\\\left\\\\{\\n\\\\begin{array}{l}\\n\\\\frac{1}{\\\\gamma_{max}-\\\\gamma_{min}},\\\\quad\\\\qquad\\\\qquad \\\\gamma_{min}\\\\leq\\\\gamma\\\\leq\\n\\\\gamma_{max},\\\\\\\\\\n0\\\\,,\\\\,\\\\quad\\\\qquad\\\\qquad\\\\qquad \\\\gamma <\\\\gamma_{min}\\\\,{\\\\rm and }\\\\,\\\\gamma >\\\\gamma_{max},\\\\\\\\\\n\\\\end{array}\\n\\\\right.$$\\nwith $\\\\gamma_{min}=10$, $\\\\gamma_{max}=10^4$.\\nThe final distribution functions\\nat various pulsar\\nparameters are plotted in Fig. 5. The particles with $\\\\gamma\\\\sim 10^2-10^3$\\nare essentially decelerated due to the scattering, the final energies becoming\\nequal (see also Fig. 4). These particles form the sharp peak at $\\\\gamma\\n<10^2$. For the Lorentz-factors of a few thousand the scattering becomes\\ninefficient and the distribution function remains almost unaltered. Thus,\\nthe resonant inverse Compton scattering leads to the two-humped distribution\\nfunction of the secondary plasma. At higher neutron star temperatures the\\nmain peak of the function shifts towards the lower energies and the humps\\nbecome more prominent. The magnetic field strength variation also results\\nin the shift of the main peak. For the more realistic distribution function\\nresembling that found by Arons (1980),\\n$$\\nf(\\\\gamma)=\\n\\\\left\\\\{\\n\\\\begin{array}{l}\\n\\\\exp\\\\left(-10\\\\frac{\\\\gamma_m-\\\\gamma}{\\\\gamma_m}\\\\right),\\\\quad\\\\qquad\\\\qquad 10\\\\leq\\\\gamma\\\\leq\\n\\\\gamma_m,\\\\\\\\\\n(\\\\gamma/\\\\gamma_m)^{-3/2},\\\\,\\\\quad\\\\qquad\\\\qquad\\\\qquad \\\\gamma_m\\\\leq\\\\gamma\\\\leq\\\\gamma_c,\\\\\\\\\\n(\\\\gamma_c/\\\\gamma_m)^{-3/2}\\\\exp\\\\left(-\\\\frac{\\\\gamma-\\\\gamma_c}{\\\\gamma_c}\\\\right),\\n\\\\quad \\\\gamma_c\\\\leq\\\\gamma\\\\leq 10^4,\\\\\\\\\\n\\\\end{array}\\n\\\\right.\\\\eqno (5)$$\\nwith $\\\\gamma_m=10^2$, $\\\\gamma_c=10^{3.5}$, the evolution on account of\\nthe resonant inverse Compton scattering is qualitatively the same (see Fig. 6).\\n\\nWe next examine the dispersion properties of the plasma with the evolved\\ndistribution function. For simplicity let us assume that the plasma consists\\nof the two particle flows characterized by the number densities $n_a$,\\n$n_b$ and by the Lorentz-factors $\\\\gamma_a$, $\\\\gamma_b$ ($\\\\gamma_a <\\\\gamma_b$).\\nGiven the infinitely strong magnetic field, the dispersion relation is as\\nfollows (see, {\\\\it e.g.} Lyubarskii 1995):\\n$$\\n\\\\frac{\\\\omega_{pa}^2}{(\\\\omega -kv_a)^2\\\\gamma_a^3}+\\\\frac{\\\\omega_{pb}^2}\\n{(\\\\omega -kv_b)^2\\\\gamma_b^3}=1. \\\\eqno (6)$$\\nHere $\\\\omega$ is the frequency, $k$ the wave number, $v_{a,b}$ are the\\nparticle velocities, $\\\\omega_{pa,b}$ the plasma frequencies given by the\\ncustomary expression:\\n$$\\n\\\\omega_{pa,b}=\\\\sqrt{\\\\frac{4\\\\pi n_{a,b}e^2}{m}}, \\\\eqno (7)$$\\nwhere $e$ is the electron charge, $m$ the electron mass. As is evident from\\nEq. (6), the dispersion properties of the plasma are mainly determined by one\\nof the particle flows on condition that\\n$$\\n\\\\frac{n_a}{\\\\gamma_a^3}\\\\gg\\\\frac{n_b}{\\\\gamma_b^3}, \\\\eqno (8)$$\\nrather than $n_a\\\\gg n_b$. This is because of the great inertia of the\\nfast particles performing one-dimensional motion in the superstrong magnetic\\nfield. For the distribution functions plotted in Fig. 5 and 6 $n_a$ and\\n$n_b$ are comparable, while $\\\\gamma_a/\\\\gamma_b\\\\sim 10^{-1}-10^{-2}$. Therefore\\nthe low-energy particles of the main peak almost completely determine the\\ndispersion properties of the plasma.\\n\\nThe two-humped distribution function implies the possibility of the\\ntwo-stream instability. Provided that the contribution of one of the plasma\\nflows to the plasma dispersion is small ({\\\\it i.e.} Eq. (8) is valid), the\\ngrowth rate of the instability takes the form (Lominadze \\\\& Mikhailovskii 1979,\\nCheng \\\\& Ruderman 1980):\\n$$\\n{\\\\rm Im} \\\\omega\\\\approx\\\\left(\\\\frac{n_b}{n_a}\\\\right)^{1/3}\\\\frac{\\\\omega_{pa}}\\n{\\\\gamma_a^{1/2}\\\\gamma_b}. \\\\eqno (9)$$\\nThe two-stream instability results in an essential development of\\ninitial perturbations on condition that\\n$$\\n\\\\frac{R_c}{c}{\\\\rm Im}\\\\omega> 10, \\\\eqno (10)$$\\nwhere $R_c$ is the characteristic scale length for the increase of\\nperturbations.\\n\\nIt is convenient to normalize the number density of the secondary plasma by\\nthe Goldreich-Julian charge density:\\n$$\\nn=\\\\frac{\\\\kappa B}{Pce}, \\\\eqno (11)$$\\nwhere $\\\\kappa$ is the multiplicity factor of the secondary plasma, $P$ the\\npulsar period. The\\nlatter equation can be rewritten as:\\n$$\\nn=6.25\\\\cdot 10^{13} P^{-1}\\\\kappa_3B_{12}(1+z/R)^{-3}\\\\, {\\\\rm cm^{-3}},\\\\eqno (12)$$\\nwhere $\\\\kappa_3\\\\equiv\\\\kappa/10^3$. Using Eqs. (9) and (12) in Eq. (10) we\\nreduce the condition for the efficient instability development to the form:\\n$$\\n\\\\frac{\\\\kappa_3B_{12}}{PR_{c7}\\\\gamma_{b3}^2\\\\gamma_{a2}}>4\\\\cdot 10^{-4}.\\n\\\\eqno (13)$$\\nHere $R_{c7}\\\\equiv R_c/10^7{\\\\rm cm}$, $\\\\gamma_{b3}\\\\equiv \\\\gamma_b/10^3$,\\n$\\\\gamma_{a2}\\\\equiv\\\\gamma_a/10^2$ and it is assumed that $(n_b/n_a)^{1/3}\\n\\\\approx 1$. As can be seen from Eq. (13), at typical pulsar parameters the\\ntwo-stream instability can develop readily providing the increase of plasma\\noscillations. The latter can be transformed into electromagnetic waves,\\nthus giving rise to pulsar radio emission.\\n\\nIt should be mentioned that two-steram instability has always been one of\\nthe most popular mechanisms for pulsar radio emission.\\nFor more than two\\ndecades a number of scenarios for the instability development were proposed.\\nThe first and the most natural one involves the instability caused by\\nthe flows of primary and secondary pulsar plasma (Ruderman \\\\& Sutherland 1975).\\nHowever, the growth rate of this instability appears to be too small\\nbecause of enormous inertia of the high-energy primary particles (Benford \\\\&\\nBuschauer 1977). Cheng \\\\& Ruderman (1977) considered the two-stream\\ninstability arising in the secondary plasma due to the difference in the\\nvelocities of electrons and positrons moving along the curved magnetic lines.\\nHowever, this difference is insufficient to cause the instability, since the\\nparticle distribution functions are too broad (Buschauer \\\\& Benford 1977).\\nLyubarskii (1993) suggested that current and charge density adjustment\\nin pulsar\\nmagnetosphere leads to the backward particle flow, which\\ncauses intense two-stream instability. However, numerical simulations of the\\nplasma flow in the open field line tube are necessary to prove this idea.\\nGiven nonstationary generation of the secondary plasma the particles are\\nconfined to the separate clouds, and the fastest particles of a cloud can\\noutstrip the slower particles of the previous cloud giving rise to the\\ntwo-stream instability (Usov 1987, Ursov \\\\& Usov 1988). Up to now it is not\\nclear whether the instability initiated in such a way can account for pulsar\\nradio emission, since the nonstationarity of plasma generation is not studied\\nin detail yet.\\nThe present\\npaper suggests one more possibility of two-stream instability in pulsars,\\nwhich is based on the selective energy loss of particles as a result of\\nresonant inverse Compton scattering. Note that in this model the instability\\narises naturally, with no additional assumptions being involved.\\n\\n\\\\section{Gamma-ray luminosity provided by resonantly\\nupscattered Compton photons}\\nThe photons produced by the resonant inverse Compton scattering have\\nthe energies\\n$$\\nE\\\\sim\\\\gamma\\\\epsilon_Bmc^2\\\\sim B_{12}\\\\gamma_2\\\\,{\\\\rm MeV},\\\\eqno (14)$$\\nso that typically $E\\\\sim 1-10$ MeV. Note that the curvature gamma-photons\\nproduced in the polar gap as well as the photons upscattered by the primary\\nparticles have essentially higher energies, $E\\\\sim 100$ MeV. Hence, the resonant\\nscattering by secondary plasma results in an additional low-energy component in pulsar\\ngamma-ray spectrum. The spectrum of this component in the case of some\\nspecific distribution functions of the scattering particles is obtained\\nby Daugherty \\\\& Harding (1989).\\nIn general, the low-energy tail of this component spreads even to the\\nX-ray band on account of the photons resonantly scattered at distances\\n$z>R$, where the magnetic field strength decreases essentially. However,\\nthese photons are very few, since at $z>R$ the scattering rate decreases\\nsignificantly due to the shrinking of the solid angle subtended by the\\nneutron star.\\n\\nGiven that the scattering is efficient, most of the energy of the secondary\\nplasma should be transferred to the low-energy gamma-rays. The luminosity\\nprovided by the upscattered photons can be estimated as follows:\\n$$\\nL=nSmc^3\\\\Delta\\\\gamma,\\\\eqno (15)$$\\nwhere $S$ is the cross-sectional area of the open field line tube,\\n$$\\nS=\\\\frac{\\\\pi R^3}{R_L},\\n\\\\eqno (16)$$\\n$R_L$ is the light cylinder radius, $\\\\Delta\\\\gamma$ the difference between\\nthe Lorentz-factors of the\\nparticles, which mainly contribute to the final and initial plasma energy,\\n$\\\\Delta\\\\gamma\\\\sim 10^2-10^3$. Substituting Eqs. (12) and (16) into Eq. (15)\\nwe find:\\n$$\\nL=0.942\\\\cdot 10^{30}\\\\frac{B_{12}R_6^3\\\\kappa_3\\\\gamma_3}{P^2}\\\\, {\\\\rm ergs/s}.\\n\\\\eqno (17)$$\\n\\nAlthough in the particle rest frame the photons are scattered in all\\ndirections, in the laboratory frame they are beamed along the particle velocity.\\nSo the opening angle of the gamma-ray beam is given by\\n$\\\\varphi =3\\\\sqrt{R/R_L}.$\\nThe averaged observed photon flux, $F$, is related to the luminosity as\\n$$\\nF=\\\\frac{L\\\\varphi}{2\\\\pi\\\\Omega d^2E\\\\Delta E},\\\\eqno (18)$$\\nwhere $\\\\Omega =\\\\pi\\\\varphi^2/4$ is the solid angle occupied by the beam of\\nupscattered photons,\\n$d$ the distance to the pulsar, $\\\\Delta E$ the energy band. Taking into\\naccount Eq. (17), Eq. (18) can be rewritten as\\n$$\\nF=3\\\\cdot 10^{-10}\\\\frac{B_{12}R_6^{5/2}\\\\gamma_3\\\\kappa_3}{P^{3/2}d_3^2 E_6^2}\\\\,\\n{\\\\rm photons/(cm^2\\\\cdot s\\\\cdot keV)}, \\\\eqno (19)$$\\nwhere $d_3\\\\equiv d/10^3\\\\,{\\\\rm pc}$, $E_6\\\\equiv E/1\\\\,{\\\\rm MeV}$.\\n\\nFor most pulsars the flux given by Eq. (19) is too low to be detected.\\nAt present the detectors of the Compton gamma-ray observatory are the most\\nsensitive to the low-energy gamma-ray emission (OSSE at 0.05--10 MeV and\\nCOMPTEL at 1--30 MeV). At 1 MeV the source sensitivity of OSSE is only\\n$2\\\\cdot 10^{-7}$ photons/(${\\\\rm cm^2\\\\cdot s\\\\cdot keV}$) (Gehrels \\\\&\\nShrader 1996). In the observations reported by Kuiper {\\\\it et al.} (1996) the\\nflux from Geminga in the band of 3--10 MeV was found to be $10^{-7}E_6^{-2}$\\nphotons/(${\\\\rm cm^2\\\\cdot s\\\\cdot keV}$). Substituting Geminga parameters\\n($P=0.237$ s, $B_{12}=3.3$, $d_3=0.15$) into Eq. (19) one can obtain the flux\\nprovided by the upscattered Compton photons: $F=3.8\\\\cdot 10^{-7}\\\\kappa_3\\n\\\\gamma_3R_6^{5/2}E_6^{-2}$ photons/(${\\\\rm cm^2\\\\cdot s\\\\cdot keV}$), which is\\nconsistent with the one detected.\\n\\n\\\\section{Conclusions}\\nWe have investigated resonant inverse Compton scattering by secondary\\npulsar plasma. The process is found to cause the efficient energy loss of\\nthe secondary particles given the neutron star temperatures $>10^5$ K, so\\nthat our results are applicable to most pulsars. For the resonant\\ncharacter of the scattering, the energy loss depends strongly on the initial\\nparticle energy. At $\\\\gamma_0\\\\sim 10^2-10^3$ the scattering is the most\\nessential, the final Lorentz-factors of the particles being independent of\\nthe initial ones.\\n \\nThe distribution function of the secondary plasma is significantly altered by\\nthe resonant inverse Compton scattering. It is shown that ultimately the\\ndistribution function becomes two-humped. The main peak at $\\\\gamma\\\\sim 10^2$\\nis very sharp. It is formed by particles which suffered severe energy\\nloss on account of the scattering. Another hump is sufficiently broad. It is\\nassociated with the particles, whose Lorentz-factors are almost unaltered by\\nthe scattering. The two-humped distribution function of the plasma particles is\\nknown to be unstable. It is shown that at pulsar conditions the two-stream\\ninstability develops readily and leads to an essential increase of plasma\\noscillations, which are likely to be transformed into radio emission.\\n\\nWe have also estimated the gamma-ray flux provided by the upscattered Compton\\nphotons. The resonantly scattered photons appear to gain the energies of\\n1--10 MeV forming an additional low-energy component in pulsar gamma-ray spectrum.\\n\\n\\\\begin{thebibliography}{}\\n\\\\bibitem{}\\nAlpar M.A. {\\\\it et al.}, 1984, ApJ 278, 791\\n\\n\\\\bibitem{}\\nArons J., 1980, In: Sieber W. \\\\& Wielebinski R. (eds.). Proc. IAU Symp.95,\\nPulsars: 13 Years of Research on Neutron Stars, 69\\n\\n\\\\bibitem{}\\nArons J., 1981, ApJ 248, 1099\\n\\n\\\\bibitem{}\\nArons J., Scharlemann E.T., 1979, ApJ 231, 854\\n\\n\\\\bibitem{}\\nBecker W., Trumper J., 1993, Nat 365, 528\\n\\n\\\\bibitem{}\\nBenford G., Buschauer R., 1977, MNRAS 179, 189\\n\\n\\\\bibitem{}\\nBuschauer R., Benford G., 1977, MNRAS 179, 99\\n\\n\\\\bibitem{}\\nChang H.-K., 1995, A\\\\&A 301, 456\\n\\n\\\\bibitem{}\\nCheng A.F., Ruderman M.A., 1977, ApJ 212, 800\\n\\n\\\\bibitem{}\\nCheng A.F., Ruderman M.A., 1980, ApJ 235, 576\\n\\n\\\\bibitem{}\\nCordova F.A. {\\\\it et al.}, 1989, ApJ 345, 451\\n\\n\\\\bibitem{}\\nDaugherty J.K., Harding A.K., 1989, ApJ 336, 861\\n\\n\\\\bibitem{}\\nDermer C.D., 1990, ApJ 360, 214\\n\\n\\\\bibitem{}\\nFinley J.P., Ogelman H., Kiziloglu U., 1992, ApJ 394, L21\\n\\n\\\\bibitem{}\\nGehrels N., Shrader C.R., 1996, A\\\\&AS 120, 1\\n\\n\\\\bibitem{}\\nGreiveldinger C. {\\\\it et al.}, 1996, ApJ 465, L35\\n\\n\\\\bibitem{}\\nHalpern J.P., Holt S.S., 1992, Nat 357, 222\\n\\n\\\\bibitem{}\\nHalpern J.P., Ruderman M.A., 1993, ApJ 415, 286\\n\\n\\\\bibitem{}\\nHerold H., 1979, Phys.Rev.D. 19, 2868\\n\\n\\\\bibitem{}\\nKardashev N.S., Mitrofanov I.G., Novikov I.D., 1984, Soviet Astron. 28, 651\\n\\n\\\\bibitem{}\\nKuiper L. {\\\\it et al.}, 1996, A\\\\&AS 120, 73\\n\\n\\\\bibitem{}\\nLominadze D.G., Mikhailovskii A.B., 1979, ZETPh 76, 959\\n\\n\\\\bibitem{}\\nLuo Q., 1996, ApJ 468, 338\\n\\n\\\\bibitem{}\\nLyubarskii Yu.E., 1993, Pis'ma v Astron. Zh. 19, 34\\n\\n\\n\\\\bibitem{}\\nLyubarskii Yu.E., 1995, Astrophys. \\\\& Space Phys.Rev. 9, pt.2, 1\\n\\n\\\\bibitem{}\\nOgelman H., 1991, In: Ventura J. \\\\& Pines D. (eds.). Neutron Stars: Theory\\nand observation, 87\\n\\n\\\\bibitem{}\\nOgelman H., 1995, In: Alpat M.A. {\\\\it et al.}(eds.). The Lives of Neutron\\nStars, 101\\n\\n\\\\bibitem{}\\nOgelman H., Finley J.P., 1993, ApJ 413, L31\\n\\n\\\\bibitem{}\\nOgelman H., Finley J.P., Zimmerman H.U., 1993, Nat 361, 136\\n\\n\\\\bibitem{}\\nPage D., Applegate J.H., 1992, ApJ 394, L17\\n\\n\\\\bibitem{}\\nQiao G.J., Zhang B., 1996, A\\\\&A 306, L5\\n\\n\\\\bibitem{}\\nRuderman M.A., Sutherland P.G., 1975, ApJ 196, 51\\n\\n\\\\bibitem{}\\nShibazaki N., Lamb F.K., 1989, ApJ 346, 808\\n\\n\\\\bibitem{}\\nSturner S.J., 1995, ApJ 446, 292\\n\\n\\\\bibitem{}\\nUlmer M.P. {\\\\it et al.}, 1994, ApJ 432, 228\\n\\n\\\\bibitem{}\\nUmeda H. {\\\\it et al.}, 1993, ApJ 408, 186\\n\\n\\\\bibitem{}\\nUsov V.V., 1987, ApJ 320, 333\\n\\n\\\\bibitem{}\\nUrsov V.N., Usov V.V., 1988, Ap\\\\&SS 140, 325\\n\\n\\\\bibitem{}\\nVan Riper K.A., 1991, ApJS 75, 449\\n\\n\\\\bibitem{}\\nXia X.Y. {\\\\it et al.}, 1985, A\\\\&A 152, 93\\n\\n\\\\bibitem{}\\nYancopoulos S., Hamilton T.T., Helfand D.J., 1994, ApJ 429, 832\\n\\n\\\\bibitem{}\\nZhang B., Qiao G.J., 1996, A\\\\&A 310, 135\\n\\n\\\\bibitem{}\\nZhang B., Qiao G.J., Han J.L., 1997, ApJ 491, 891\\n\\n\\n\\\\end{thebibliography}\\n\\n\\\\begin{figure}[htb]\\n%\\\\includegraphics[width=\\\\textwidth,keepaspectratio]{f1a.eps}\\n\\\\includegraphics[scale=0.4]{f1a.eps}\\n\\\\includegraphics[scale=0.4]{f1b.eps}\\n\\\\caption{\\n Evolution of particle Lorentz-factor with the distance for\\n initial Lorentz-factors, $\\\\gamma_0=100$ (a) and $\\\\gamma_0=3000$ (b);\\n $B_{12}=1$, $z_0/R=0.01$.The solid lines are plotted for the case\\nof scattering the photons from the whole neutron star surface with the\\ntemperature $5\\\\cdot 10^5$K, whereas the dashed lines refer to the case when the\\ncontribution of the hot spot photons is also taken into account(here the\\nhot spot radius is $5\\\\cdot 10^{-3}R$ and the temperature is $3\\\\cdot 10^6$K).\\n}\\n\\\\end{figure}\\n\\n\\\\begin{figure}[htb]\\n\\\\includegraphics[width=\\\\textwidth,keepaspectratio]{f2.eps}\\n%\\\\includegraphics[scale=0.4]{f1a.eps}\\n%\\\\includegraphics[scale=0.4]{f1b.eps}\\n\\\\caption{\\n Final Lorentz-factor versus the gap height for\\n$\\\\gamma_0=100$ (curve 1) and $\\\\gamma_0=3000$ (curve 2); $T_6=0.5$, $B_{12}=1$ \\n}\\n\\\\end{figure}\\n\\n\\\\begin{figure}[htb]\\n%\\\\includegraphics[width=\\\\textwidth,keepaspectratio]{f1a.eps}\\n\\\\includegraphics[scale=0.4]{f3a.eps}\\n\\\\includegraphics[scale=0.4]{f3b.eps}\\n\\\\caption{\\nFinal Lorentz-factor versus the temperature for various\\nmagnetic field strengths, $B_{12}$: {\\\\bf a} $\\\\gamma_0=100$, {\\\\bf b}\\n$\\\\gamma_0=3000$\\n}\\n\\\\end{figure}\\n\\n\\\\begin{figure}[htb]\\n%\\\\includegraphics[width=\\\\textwidth,keepaspectratio]{f1a.eps}\\n\\\\includegraphics[scale=0.4]{f4a.eps}\\n\\\\includegraphics[scale=0.4]{f4b.eps}\\n\\\\caption{\\n Final Lorentz-factor versus the initial one: {\\\\bf a}\\nfor various temperatures, $T_6$; $B_{12}=1$, {\\\\bf b} for various\\nmagnetic field strengths, $B_{12}$; $T_6=0.5$\\n}\\n\\\\end{figure}\\n\\n\\\\begin{figure}[htb]\\n%\\\\includegraphics[width=\\\\textwidth,keepaspectratio]{f1a.eps}\\n\\\\includegraphics[scale=0.4]{f5a.eps}\\n\\\\includegraphics[scale=0.4]{f5b.eps}\\n\\\\caption{\\n Evolution of the waterbag distribution function on account of\\nresonant inverse Compton scattering: {\\\\bf a} for various temperatures,\\n$T_6$; $B_{12}=1$, {\\\\bf b} for various magnetic field strengths,\\n$B_{12}$; $T_6=0.5$; the initial distribution function is shown by the dashed\\nline\\n}\\n\\\\end{figure}\\n\\n\\\\begin{figure}[htb]\\n%\\\\includegraphics[width=\\\\textwidth,keepaspectratio]{f1a.eps}\\n\\\\includegraphics[scale=0.4]{f6a.eps}\\n\\\\includegraphics[scale=0.4]{f6b.eps}\\n\\\\caption{\\n The same as in Fig. 5 for the initial distribution function (5).\\n}\\n\\\\end{figure}\\n\\n\\\\end{document}\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002194.extracted_bib","string":"\\begin{thebibliography}{}\n\\bibitem{}\nAlpar M.A. {\\it et al.}, 1984, ApJ 278, 791\n\n\\bibitem{}\nArons J., 1980, In: Sieber W. \\& Wielebinski R. (eds.). Proc. IAU Symp.95,\nPulsars: 13 Years of Research on Neutron Stars, 69\n\n\\bibitem{}\nArons J., 1981, ApJ 248, 1099\n\n\\bibitem{}\nArons J., Scharlemann E.T., 1979, ApJ 231, 854\n\n\\bibitem{}\nBecker W., Trumper J., 1993, Nat 365, 528\n\n\\bibitem{}\nBenford G., Buschauer R., 1977, MNRAS 179, 189\n\n\\bibitem{}\nBuschauer R., Benford G., 1977, MNRAS 179, 99\n\n\\bibitem{}\nChang H.-K., 1995, A\\&A 301, 456\n\n\\bibitem{}\nCheng A.F., Ruderman M.A., 1977, ApJ 212, 800\n\n\\bibitem{}\nCheng A.F., Ruderman M.A., 1980, ApJ 235, 576\n\n\\bibitem{}\nCordova F.A. {\\it et al.}, 1989, ApJ 345, 451\n\n\\bibitem{}\nDaugherty J.K., Harding A.K., 1989, ApJ 336, 861\n\n\\bibitem{}\nDermer C.D., 1990, ApJ 360, 214\n\n\\bibitem{}\nFinley J.P., Ogelman H., Kiziloglu U., 1992, ApJ 394, L21\n\n\\bibitem{}\nGehrels N., Shrader C.R., 1996, A\\&AS 120, 1\n\n\\bibitem{}\nGreiveldinger C. {\\it et al.}, 1996, ApJ 465, L35\n\n\\bibitem{}\nHalpern J.P., Holt S.S., 1992, Nat 357, 222\n\n\\bibitem{}\nHalpern J.P., Ruderman M.A., 1993, ApJ 415, 286\n\n\\bibitem{}\nHerold H., 1979, Phys.Rev.D. 19, 2868\n\n\\bibitem{}\nKardashev N.S., Mitrofanov I.G., Novikov I.D., 1984, Soviet Astron. 28, 651\n\n\\bibitem{}\nKuiper L. {\\it et al.}, 1996, A\\&AS 120, 73\n\n\\bibitem{}\nLominadze D.G., Mikhailovskii A.B., 1979, ZETPh 76, 959\n\n\\bibitem{}\nLuo Q., 1996, ApJ 468, 338\n\n\\bibitem{}\nLyubarskii Yu.E., 1993, Pis'ma v Astron. Zh. 19, 34\n\n\n\\bibitem{}\nLyubarskii Yu.E., 1995, Astrophys. \\& Space Phys.Rev. 9, pt.2, 1\n\n\\bibitem{}\nOgelman H., 1991, In: Ventura J. \\& Pines D. (eds.). Neutron Stars: Theory\nand observation, 87\n\n\\bibitem{}\nOgelman H., 1995, In: Alpat M.A. {\\it et al.}(eds.). The Lives of Neutron\nStars, 101\n\n\\bibitem{}\nOgelman H., Finley J.P., 1993, ApJ 413, L31\n\n\\bibitem{}\nOgelman H., Finley J.P., Zimmerman H.U., 1993, Nat 361, 136\n\n\\bibitem{}\nPage D., Applegate J.H., 1992, ApJ 394, L17\n\n\\bibitem{}\nQiao G.J., Zhang B., 1996, A\\&A 306, L5\n\n\\bibitem{}\nRuderman M.A., Sutherland P.G., 1975, ApJ 196, 51\n\n\\bibitem{}\nShibazaki N., Lamb F.K., 1989, ApJ 346, 808\n\n\\bibitem{}\nSturner S.J., 1995, ApJ 446, 292\n\n\\bibitem{}\nUlmer M.P. {\\it et al.}, 1994, ApJ 432, 228\n\n\\bibitem{}\nUmeda H. {\\it et al.}, 1993, ApJ 408, 186\n\n\\bibitem{}\nUsov V.V., 1987, ApJ 320, 333\n\n\\bibitem{}\nUrsov V.N., Usov V.V., 1988, Ap\\&SS 140, 325\n\n\\bibitem{}\nVan Riper K.A., 1991, ApJS 75, 449\n\n\\bibitem{}\nXia X.Y. {\\it et al.}, 1985, A\\&A 152, 93\n\n\\bibitem{}\nYancopoulos S., Hamilton T.T., Helfand D.J., 1994, ApJ 429, 832\n\n\\bibitem{}\nZhang B., Qiao G.J., 1996, A\\&A 310, 135\n\n\\bibitem{}\nZhang B., Qiao G.J., Han J.L., 1997, ApJ 491, 891\n\n\n\\end{thebibliography}"}],"string":"[\n {\n \"name\": \"astro-ph0002194.extracted_bib\",\n \"string\": \"\\\\begin{thebibliography}{}\\n\\\\bibitem{}\\nAlpar M.A. {\\\\it et al.}, 1984, ApJ 278, 791\\n\\n\\\\bibitem{}\\nArons J., 1980, In: Sieber W. \\\\& Wielebinski R. (eds.). Proc. IAU Symp.95,\\nPulsars: 13 Years of Research on Neutron Stars, 69\\n\\n\\\\bibitem{}\\nArons J., 1981, ApJ 248, 1099\\n\\n\\\\bibitem{}\\nArons J., Scharlemann E.T., 1979, ApJ 231, 854\\n\\n\\\\bibitem{}\\nBecker W., Trumper J., 1993, Nat 365, 528\\n\\n\\\\bibitem{}\\nBenford G., Buschauer R., 1977, MNRAS 179, 189\\n\\n\\\\bibitem{}\\nBuschauer R., Benford G., 1977, MNRAS 179, 99\\n\\n\\\\bibitem{}\\nChang H.-K., 1995, A\\\\&A 301, 456\\n\\n\\\\bibitem{}\\nCheng A.F., Ruderman M.A., 1977, ApJ 212, 800\\n\\n\\\\bibitem{}\\nCheng A.F., Ruderman M.A., 1980, ApJ 235, 576\\n\\n\\\\bibitem{}\\nCordova F.A. {\\\\it et al.}, 1989, ApJ 345, 451\\n\\n\\\\bibitem{}\\nDaugherty J.K., Harding A.K., 1989, ApJ 336, 861\\n\\n\\\\bibitem{}\\nDermer C.D., 1990, ApJ 360, 214\\n\\n\\\\bibitem{}\\nFinley J.P., Ogelman H., Kiziloglu U., 1992, ApJ 394, L21\\n\\n\\\\bibitem{}\\nGehrels N., Shrader C.R., 1996, A\\\\&AS 120, 1\\n\\n\\\\bibitem{}\\nGreiveldinger C. {\\\\it et al.}, 1996, ApJ 465, L35\\n\\n\\\\bibitem{}\\nHalpern J.P., Holt S.S., 1992, Nat 357, 222\\n\\n\\\\bibitem{}\\nHalpern J.P., Ruderman M.A., 1993, ApJ 415, 286\\n\\n\\\\bibitem{}\\nHerold H., 1979, Phys.Rev.D. 19, 2868\\n\\n\\\\bibitem{}\\nKardashev N.S., Mitrofanov I.G., Novikov I.D., 1984, Soviet Astron. 28, 651\\n\\n\\\\bibitem{}\\nKuiper L. {\\\\it et al.}, 1996, A\\\\&AS 120, 73\\n\\n\\\\bibitem{}\\nLominadze D.G., Mikhailovskii A.B., 1979, ZETPh 76, 959\\n\\n\\\\bibitem{}\\nLuo Q., 1996, ApJ 468, 338\\n\\n\\\\bibitem{}\\nLyubarskii Yu.E., 1993, Pis'ma v Astron. Zh. 19, 34\\n\\n\\n\\\\bibitem{}\\nLyubarskii Yu.E., 1995, Astrophys. \\\\& Space Phys.Rev. 9, pt.2, 1\\n\\n\\\\bibitem{}\\nOgelman H., 1991, In: Ventura J. \\\\& Pines D. (eds.). Neutron Stars: Theory\\nand observation, 87\\n\\n\\\\bibitem{}\\nOgelman H., 1995, In: Alpat M.A. {\\\\it et al.}(eds.). The Lives of Neutron\\nStars, 101\\n\\n\\\\bibitem{}\\nOgelman H., Finley J.P., 1993, ApJ 413, L31\\n\\n\\\\bibitem{}\\nOgelman H., Finley J.P., Zimmerman H.U., 1993, Nat 361, 136\\n\\n\\\\bibitem{}\\nPage D., Applegate J.H., 1992, ApJ 394, L17\\n\\n\\\\bibitem{}\\nQiao G.J., Zhang B., 1996, A\\\\&A 306, L5\\n\\n\\\\bibitem{}\\nRuderman M.A., Sutherland P.G., 1975, ApJ 196, 51\\n\\n\\\\bibitem{}\\nShibazaki N., Lamb F.K., 1989, ApJ 346, 808\\n\\n\\\\bibitem{}\\nSturner S.J., 1995, ApJ 446, 292\\n\\n\\\\bibitem{}\\nUlmer M.P. {\\\\it et al.}, 1994, ApJ 432, 228\\n\\n\\\\bibitem{}\\nUmeda H. {\\\\it et al.}, 1993, ApJ 408, 186\\n\\n\\\\bibitem{}\\nUsov V.V., 1987, ApJ 320, 333\\n\\n\\\\bibitem{}\\nUrsov V.N., Usov V.V., 1988, Ap\\\\&SS 140, 325\\n\\n\\\\bibitem{}\\nVan Riper K.A., 1991, ApJS 75, 449\\n\\n\\\\bibitem{}\\nXia X.Y. {\\\\it et al.}, 1985, A\\\\&A 152, 93\\n\\n\\\\bibitem{}\\nYancopoulos S., Hamilton T.T., Helfand D.J., 1994, ApJ 429, 832\\n\\n\\\\bibitem{}\\nZhang B., Qiao G.J., 1996, A\\\\&A 310, 135\\n\\n\\\\bibitem{}\\nZhang B., Qiao G.J., Han J.L., 1997, ApJ 491, 891\\n\\n\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":192,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002195"},"title":{"kind":"string","value":"ISO-SWS spectra of galaxies: continuum and features \\thanks{Based on observations with ISO, an ESA project with instruments funded by ESA member states (especially the PI countries: France, Germany, the Netherlands and the United Kingdom) and with participation of ISAS and NASA.}"},"authors":{"kind":"list like","value":[{"author":"E. Sturm \\inst{1,}\\inst{2}"},{"author":"{D. Lutz \\inst{1}}"},{"author":"{D. Tran \\inst{1}}"},{"author":"{H. Feuchtgruber \\inst{1}}"},{"author":"{R. Genzel \\inst{1}}"},{"author":"{D. Kunze \\inst{1}}"},{"author":"{A.F.M. Moorwood \\inst{3}}"},{"author":"{M.D. Thornley \\inst{4}}"}],"string":"[\n {\n \"author\": \"E. Sturm \\\\inst{1,}\\\\inst{2}\"\n },\n {\n \"author\": \"{D. Lutz \\\\inst{1}}\"\n },\n {\n \"author\": \"{D. Tran \\\\inst{1}}\"\n },\n {\n \"author\": \"{H. Feuchtgruber \\\\inst{1}}\"\n },\n {\n \"author\": \"{R. Genzel \\\\inst{1}}\"\n },\n {\n \"author\": \"{D. Kunze \\\\inst{1}}\"\n },\n {\n \"author\": \"{A.F.M. Moorwood \\\\inst{3}}\"\n },\n {\n \"author\": \"{M.D. Thornley \\\\inst{4}}\"\n }\n]"},"abstract":{"kind":"string","value":"We present an inventory of mid-infrared spectral features detected in high resolution (R$\\sim$1500) ISO-SWS 2.4--45$\\mu$m spectra of the galaxies \\object{M\\,82}, \\object{NGC\\,253}, \\object{Circinus}, \\object{NGC\\,1068}, and a position in the \\object{30\\,Doradus} region of the Large Magellanic Cloud. We discuss their identifications and highlight possible relations between these features and the physical state of the interstellar medium in galaxies. The spectral features vary considerably from source to source in presence and relative strength. Emission features are largely absent in the intense radiation field close to an AGN. Compared to normal infrared-selected starbursts, they also seem to be weaker in a low metallicity, intensely star forming environment. The large number of features beyond 13$\\mu$m is remarkable. Some of the features %are unambiguously detected for the first time in astronomical objects and have -- to our knowledge -- not been reported before in astronomical objects. In the 5--13$\\mu$m region, emission from unidentified infrared bands (UIBs), usually ascribed to aromatic molecules, and apparent silicate absorption dominate the spectrum. The density of features makes it difficult to determine the continuum, particularly in ground-based data of limited wavelength coverage. In fact the apparent depth of the 9.7$\\mu$m silicate absorption may be overestimated in the presence of UIB emission, as we demonstrate by comparing the spectrum of M\\,82 to the (absorption free) spectrum of the reflection nebula \\object{NGC\\,7023}. No strong silicate absorption is present in M\\,82. The (very small grain) dust continuum under the UIB emission in our starburst templates can be modeled by a simple power law, starting at wavelengths between 8 and 9$\\mu$m. We find broad H$_2$O-ice absorption features at 3.0$\\mu$m in M\\,82 and NGC\\,253. Their optical depths (relative to the visual extinction) indicate that the lines of sight towards these galaxies have similar properties as the line of sight towards the Galactic Center. %: a mixture of diffuse ISM and molecular cloud %extinction, with some %variance in the relative weight for different lines of sight. The active galaxy NGC\\,1068 exhibits a clearly different spectrum of absorption features, indicating different physical conditions in the obscuring regions of this AGN compared to the starburst templates. The spectra are valuable templates for future mid-infrared missions. We smooth our data to simulate low resolution spectra as obtained with ISOCAM-CVF, ISOPHOT-S, and in the future with the low resolution mode of SIRTF-IRS, and use our high spectral resolution information to highlight possible identification problems at low resolving power that are caused by coincidences of lines and features. The spectra are available in electronic form from the authors. \\keywords{ Infrared: ISM: continuum -- Infrared: ISM: lines and bands -- % Galaxies: ISM -- Galaxies: individual: M\\,82 -- Galaxies: individual: NGC\\,253 -- Galaxies: individual: Circinus -- Galaxies: individual: NGC\\,1068 }"},"latex":{"kind":"list like","value":[{"name":"sturm.tex","string":"\\documentclass{aa}\n%\\documentclass[referee]{aa}\n\\usepackage{graphics}\n\n\\begin{document}\n\n \\thesaurus{03\n (13.09.3);\n (13.09.4);\n% 11\n% (11.09.4);\n (11.09.1 M\\,82);\n (11.09.1 NGC\\,253);\n (11.09.1 Circinus);\n (11.09.1 NGC\\,1068)} \n%\n \\title{ISO-SWS spectra of galaxies: continuum and features\n \\thanks{Based on observations with ISO, an ESA project with\n instruments funded by ESA member states (especially\n the PI countries: France, Germany, the Netherlands and\n the United Kingdom) and with participation of ISAS and\n NASA.} }\n\n \\author{E. Sturm \\inst{1,}\\inst{2}\n \\and{D. Lutz \\inst{1}}\n \\and{D. Tran \\inst{1}}\n \\and{H. Feuchtgruber \\inst{1}}\n \\and{R. Genzel \\inst{1}}\n \\and{D. Kunze \\inst{1}}\n \\and{A.F.M. Moorwood \\inst{3}}\n \\and{M.D. Thornley \\inst{4}}}\n\n \\offprints{sturm@mpe.mpg.de}\n\n \\institute{Max-Planck-Institut f\\\"ur extraterrestrische Physik,\n Postfach 1603, D-85740 Garching, Germany\n \\and Infrared Processing and Analysis Center, \n MS 100-22, Pasadena, CA 91125, USA\n \\and European Southern Observatory,\n Karl-Schwarzschild-Str. 2, D-85748 Garching, Germany \n \\and National Radio Astronomy Observatory,\n 520 Edgemont Road, Charlottesville, VA 22903, USA}\n \n \\date{Received 19 October 1999 / Accepted 26 January 2000}\n\n \\maketitle\n\n \\begin{abstract}\n\nWe present an inventory of mid-infrared spectral features detected in\nhigh resolution (R$\\sim$1500) ISO-SWS 2.4--45$\\mu$m spectra of the \ngalaxies \\object{M\\,82}, \\object{NGC\\,253}, \\object{Circinus},\n\\object{NGC\\,1068}, and a position in the \\object{30\\,Doradus} region of the \nLarge Magellanic Cloud.\nWe discuss their identifications and highlight possible relations between\nthese features and the physical state of the interstellar medium in\ngalaxies. The spectral features vary considerably from source to source in \npresence and relative strength. Emission features are largely absent in \nthe intense radiation field close to an AGN. Compared to normal \ninfrared-selected starbursts, they also seem to be weaker in a\nlow metallicity, intensely star forming environment.\nThe large number of features beyond 13$\\mu$m is remarkable. \nSome of the features \n%are unambiguously detected for the first time in astronomical objects and \nhave -- to our knowledge -- not been \nreported before in astronomical objects. \n\nIn the 5--13$\\mu$m region, emission from unidentified infrared bands (UIBs),\nusually ascribed to\naromatic molecules, and apparent\nsilicate absorption dominate the spectrum. The density \nof features makes it\ndifficult to determine the continuum, particularly in ground-based data of \nlimited wavelength coverage. In fact \nthe apparent depth of the 9.7$\\mu$m\nsilicate absorption may be overestimated in the presence of UIB emission, as\nwe demonstrate by comparing the spectrum of M\\,82 to the (absorption free)\nspectrum of the reflection nebula \\object{NGC\\,7023}. \nNo strong silicate absorption is \npresent in M\\,82.\nThe (very small grain) dust continuum \nunder the UIB emission in our starburst templates \ncan be modeled by a simple power law, starting at wavelengths\nbetween 8 and 9$\\mu$m.\n\nWe find broad H$_2$O-ice absorption features at 3.0$\\mu$m in M\\,82 and \nNGC\\,253. Their optical depths (relative to the visual extinction) \nindicate that the lines of sight towards these galaxies have similar \nproperties as the line of sight\ntowards the Galactic Center.\n%: a mixture of diffuse ISM and molecular cloud\n%extinction, with some \n%variance in the relative weight for different lines of sight.\nThe active galaxy NGC\\,1068 exhibits a clearly different spectrum of \nabsorption features, indicating different\nphysical conditions in the obscuring regions of this AGN compared to the\nstarburst templates.\n\n\nThe spectra are valuable templates for future\nmid-infrared missions. \nWe smooth our data to simulate low resolution spectra as obtained\nwith ISOCAM-CVF, ISOPHOT-S, and in the future with the low resolution mode of\nSIRTF-IRS, and use our \nhigh\nspectral resolution information to highlight possible identification problems\nat low resolving power that are caused by coincidences of lines and features. \nThe spectra are available in electronic form from the authors.\n \\keywords{\n Infrared: ISM: continuum --\n Infrared: ISM: lines and bands --\n% Galaxies: ISM --\n Galaxies: individual: M\\,82 --\n Galaxies: individual: NGC\\,253 --\n Galaxies: individual: Circinus --\n Galaxies: individual: NGC\\,1068\n}\n\n \\end{abstract}\n\n%\n%________________________________________________________________\n\n\\section{Introduction}\nMid-infrared spectra of galaxies are rich in emission lines, and\ndisplay prominent broader emission and absorption features due to the presence\nof various solids and/or large molecules in their interstellar medium\n(ISM). Significant variation from source to source suggests \nthat these features may provide important\ndiagnostics of the ISM conditions in galaxies. \n\nThe ground based and Kuiper Airborne Observatory spectra of the \nprototypical starburst M\\,82 by Gillett et al. (1975) and Willner et al. (1977) \nfully established the existence of the\nmid-infrared `unidentified infrared bands' (UIB) at 6.2, 7.7, 8.6, \nand 11.3$\\mu$m\nin galaxy spectra. These emission bands are characteristic of C-C and C-H bonds\nin aromatic molecules. In this paper we will refer to them as \n`PAH features' \naccording to one of the most popular interpretations of their carrier, \npolycyclic aromatic hydrocarbon molecules\n\\footnote{Other suggested carriers include small grains of\nhydrogenated amorphous carbon (HACs), quenched carbonaceous composites (QCCs),\nor coal.}. \nThese detections and\nrelated work using the IRAS LRS (Cohen \\& Volk 1989) form the basic pre-ISO\nknowledge of mid-infrared spectral features in galaxies.\n\nConsiderable work has also been\ndone from the ground but has been limited to the features\nfound in atmospheric windows, mainly silicate absorption and PAH feature\nemission in the N band (e.g. Roche et al. 1991, and references therein) \nand the companion PAH feature\nin the L band (e.g. Moorwood 1986).\n%(e.g. Bridger, Wright \\& Geballe 1994).\nThe restriction\nto atmospheric windows increases problems in establishing the `continuum' on\nwhich the features are superposed. This is a nontrivial task, even with full\nwavelength coverage, due to the crowding of mid-infrared \nemission and absorption features (especially in the 10$\\mu$m region).\n\nWith the Short Wavelength Spectrometer SWS (de~Graauw et al. 1996) on\nboard\nthe Infrared Space Observatory ISO (Kessler et al. 1996) high spectral\nresolution observations with good signal-to-noise (S/N) were\nobtained for a number of bright galaxies. Their main\nadvantages lie in continuous wavelength coverage from 2.4 to 45$\\mu$m\nand in the possibility to clearly separate features from nearby\nemission lines.\n\nThe interpretation of\ngalaxy-integrated spectra strongly benefits from comparisons to similar\nobservations of galactic\nsources, sometimes spatially resolved, allowing\nbetter isolation of the physical mechanisms at work. Recent ISO spectra\n%which have been recently observed in\nof many galactic template objects, such as reflection\nnebulae (e.g. Boulanger et al. 1996, Cesarsky et al. 1996a, Verstraete et al.\n1996, Moutou et al. 1998), planetary nebulae and circumstellar regions\n(e.g. Beintema et al. 1996), and HII regions (Roelfsema et al. 1996,\nCesarsky et al. 1996b) have clearly demonstrated the importance of such\ntemplate spectra. They\n%provide a wealth of information and\nprove that PAHs\nare an ubiquitous part of the ISM. Additional information on emission features \nof crystalline silicates comes from similar template observations with ISO of \ne.g. planetary nebulae (Waters et al. 1998), evolved\nstars (Waters et al. 1996), young stars (Waelkens et al. 1996), or LBVs in \nthe LMC (Voors et al. 1999).\nAbsorption features (silicates, ices) have been found e.g. in the Galactic\ncenter (Lutz et al. 1996, Chiar et al. 2000), young stellar objects\n(d'Hendecourt et al. 1996, Whittet et al. 1996, Dartois et al. 1999), and \nin dark clouds in the solar neighborhood (Whittet et al. 1998).\n\nIn this paper we present an inventory of mid-infrared spectral features \ndetected in high resolution (R$\\sim$1500) ISO-SWS 2.4--45$\\mu$m spectra of the \nstarburst galaxies M\\,82 and NGC\\,253, the Seyfert 2 galaxies \nCircinus and NGC\\,1068, \nand a position in the 30\\,Doradus star forming region of the Large Magellanic \nCloud (Sect. \\ref{s:inventory}). \nWe briefly discuss possible feature identifications (Sect. \\ref{s:ident}) \nand highlight possible relations \nbetween these features and the physical state of the interstellar medium in\ngalaxies (Sect. \\ref{s:PAH_var}). \nWe also address the issue of the continuum determination and the \napparent depth of the silicate absorption at 9.7$\\mu$m (Sect. \n\\ref{s:continuum}). \nFinally (Sects. \\ref{s:lowres} and \\ref{s:conclusions}) we demonstrate\nthe use of these ISO spectra as templates for future \ninfrared missions such as SIRTF, with particular emphasis on \npotential identification problems\nat low resolving power that are caused by coincidences of lines and features.\n\nAll the spectra shown here exhibit a large number of atomic, ionic and\nmolecular emission lines. These have been or will be discussed elsewhere, \nalong with more details on observations and data processing\n(Circinus: Moorwood et al. 1996; M\\,82: Lutz et al. 1998b, Schreiber 1998;\nNGC\\,1068: Lutz et al. 2000; 30\\,Dor: Thornley et al., in prep.). \n\n%--------------------------------------------------------------------\n\n\\section{Observations and data reduction}\n\nThe objects discussed here have been observed as part of the ISO guaranteed \ntime project on bright galactic nuclei. Here we concentrate on full grating \nscans obtained in SWS01 mode, speed 4. This mode provides a full \n2.4--45$\\mu$m scan at resolving power of approximately 1000--2000.\nFor NGC\\,253, Circinus, and NGC\\,1068 the observations were centered on the\nnuclei. In the case of M\\,82 the observation was centered on the \nsouthwestern star formation \nlobe. For 30\\,Dor the apertures were lying roughly parallel to an ionized\nshell region, about 0.5\\arcmin\\/ away from the central stellar cluster.\nTable \\ref{tab:positions} summarizes the positions.\nNote that different parts of an SWS full grating scan are observed with\ndifferent aperture sizes\\footnote{The aperture sizes are\n14\\arcsec$\\times$20\\arcsec\\/ for 2.4--12.0$\\mu$m, 14\\arcsec$\\times$27\\arcsec\\/ \nfor 12.0--27.5$\\mu$m, 20\\arcsec$\\times$27\\arcsec\\/ for 27.5--29.0$\\mu$m, and\n20\\arcsec$\\times$33\\arcsec\\/ for 29.0--45$\\mu$m, with some wavelength overlap\nbetween the bands.}, varying between 14\\arcsec$\\times$20\\arcsec\\/ and \n20\\arcsec$\\times$33\\arcsec.\n\nWe have processed the data using the SWS Interactive Analysis (IA) system\n(Lahuis et al. 1998, Wieprecht et al. 1998) and the ISO Spectral Analysis\nPackage ISAP (Sturm et al. 1998). Dark current subtraction, scan direction \nmatching, and flatfielding have been done interactively, and noisy \ndetectors have been eliminated. In ISAP we clipped outliers and\naveraged the data of all 12 detectors for each AOT band, retaining the \ninstrumental resolution. For those wavelength ranges affected by fringes, the \naveraged spectra were defringed using the FFT or iterative sine fitting \noptions of the defringe module within ISAP. \n%More details about the observations and the data processing can be found\n%elsewhere (M\\,82: Schreiber 1998????; NGC\\,253: Thornley, in prep.; 30\\,Dor:\n%Thornley, in prep.; Circinus: Moorwood et al. 1996; NGC\\,1068: Lutz et al. \n%2000????).\n\n\\begin{table}\n\\caption[]{\\label{tab:positions} Summary of observed positions (J2000), \nand position angles.}\n%\\begin{footnotesize}\n%{\\scriptsize\n\\begin{flushleft}\n\\begin{tabular}{lllll}\n%\\begin{tabular}{llll}\n\\hline\\noalign{\\smallskip}\nObject & RA & Decl. & PA & remark\\\\\n%Object & RA & Decl. & \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nM\\,82 & 09$^h$55$^m$50.7$^s$ & 69\\degr40\\arcmin44.4\\arcsec & 245\\degr & 1 \\\\\nNGC\\,253 & 00$^h$47$^m$33.2$^s$ & -25\\degr17\\arcmin17.2\\arcsec & 28\\degr & 2 \\\\\n30\\,Dor & 05$^h$38$^m$46.0$^s$ & -69\\degr05\\arcmin07.9\\arcsec & 230\\degr & 3 \\\\\nCircinus & 14$^h$13$^m$09.7$^s$ & -65\\degr20\\arcmin21.5\\arcsec & 19\\degr & 2 \\\\\nNGC\\,1068 & 02$^h$42$^m$40.8$^s$ & -00\\degr00\\arcmin47.3\\arcsec & -11\\degr & 2 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n1 = SW lobe\\\\\n2 = nucleus\\\\\n3 = ionized shell\n\\end{table}\n\n\\begin{figure*}\n \\setcounter{figure}{0}\n% \\resizebox{\\hsize}{!}{\\includegraphics{fig1.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig1.ps}}\n \\caption{The full SWS01 spectra of the five extragalactic templates. x-axis:\n wavelength in $\\mu$m; y-axis: flux density in Jansky.}\n \\label{fig:m82}\n\\end{figure*} \n\nTo reduce noise for display purposes (Fig. 1), we have smoothed the data \nwith a gaussian filter to a uniform resolution of 1000. This\nbroadens slightly the line widths of the narrow atomic and ionic emission\nlines, but does not affect the broad emission and\nabsorption features discussed in this paper.\nWe did not remove the flux jumps at detector band limits. Part of\nthese jumps may be real because the sources are extended and because\nthe aperture sizes\nchange at some band edges (at approximately 12.0, 27.5 and 29.0$\\mu$m).\nAnother part simply reflects the flux calibration\nuncertainty, which is of the order of 20 per cent.\n\nWe carefully checked the reality of the features in the final spectra \nagainst the possibility of residual instrumental features from the \nRelative Spectral Response Function (RSRF), which might be caused \ne.g. by an improper dark current subtraction.\nFor example, the detector RSRF exhibits absorption features \nat 11.05 and 34$\\mu$m\nwhich might appear in emission in the calibrated spectrum. This is, however,\nat most an effect of the order of a few per cent of the continuum level. \nThe features\nwe see at these wavelengths in our spectra (see below) are stronger, so\nthat they must be real.\nFurthermore, we checked whether a feature\n%listed in the next section\nappears in both scan directions and in the majority of all\ndetectors. Additional confirmation\nwas possible for those features that lie in the overlap\nregion of two different AOT bands and appear in both bands.\nAt this stage of instrument calibration, we do not believe that any\nof the broad structures in band 3E (appr. 27.5--29.5 $\\mu$m) are real\nfeatures.\nAlso, features at the end of band 4 (43--45 $\\mu$m, e.g. in Circinus)\ncannot be trusted.\n\n%--------------------------------------------------------------------\n\n\\section{An inventory of features}\n\\label{s:inventory}\n\n\\begin{table}\n\\caption[]{\\label{tab:inventory} Summary of observed broad emission features\n(approximate peak positions in $\\mu$m). Uncertain detections are given in\nparentheses, nondetections are marked by a dash.} \n%\\begin{footnotesize}\n%{\\scriptsize\n\\begin{flushleft}\n\\begin{tabular}{llllll}\n%\\begin{tabular}{lll}\n\\hline\\noalign{\\smallskip}\nM\\,82 & NGC & 30\\,Dor & Circinus & NGC & nearby\\\\\n%\\multicolumn{5}{c}{ } & ionic lines\\\\ \n & 253 & & & 1068 & lines\\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\n3.25 & 3.25 & -- & 3.25 & -- & \\\\\n3.3 & 3.3 & 3.3 & 3.3 & 3.3 & Pf$_{\\delta}$\\\\\n3.4 & 3.4 & 3.4 & -- & -- & \\\\\n3.5 & (3.5) & 3.5 & -- & -- & \\\\\n-- & 3.75 & -- & 3.75 & -- & \\\\\n5.25 & -- & -- & -- & -- & \\\\\n5.65 & 5.65 & -- & -- & -- & \\\\\n6.0 & 6.0 & 6.0 & (6.0) & -- & \\\\\n6.2 & 6.2 & 6.2 & 6.2 & (6.2) & \\\\\n6.3 & 6.3 & 6.3 & 6.3 & -- & \\\\\n7.0 & 7.0 & (7.0) & -- & -- & H$_2$+\\\\\n & & & & & [Ar II]\\\\\n7.6 & 7.6 & 7.6 & 7.6 &(7.6) & Pf$_{\\alpha}$+\\\\\n & & & & & [Ne VI]\\\\\n7.8 & 7.8 & 7.8 & 7.8 & 7.8 & \\\\\n8.3 & -- & -- & -- & -- & \\\\\n8.6 & 8.6 & 8.6 & 8.6 & 8.6 & \\\\\n(10.6)& -- & -- & -- & -- & [S IV]\\\\\n11.05 & 11.05& 11.05 & 11.05 & 11.05 & \\\\\n11.25 & 11.2 & 11.25 & 11.25 & 11.25 & \\\\\n12.0 & 12.0 & 12.0 & -- & -- & \\\\\n12.7 & 12.7 & -- & 12.7 & (12.7)& [Ne II]\\\\\n13.55 & 13.55& (13.5) & 13.6 & 13.4 & \\\\\n14.25 & 14.25& 14.25 & 14.25 & -- & [Ne V]+\\\\\n & & & & & [Cl II]\\\\\n(14.8)&(14.8)&(14.8) &(14.8) & -- & \\\\\n15.7 & 15.7 & 15.7 & 15.85 & 15.9 & [Ne III]\\\\\n16.5 & 16.5 & 16.5 & -- & -- & \\\\\n(17.4)&(17.4)& -- & -- & -- & \\\\\n(18.0)& -- &(18.0) & -- & -- & \\\\\n20.5 &(20.3)&(20.4) & 20.2 & -- & \\\\\n-- & -- & -- & 21.7 & -- & \\\\\n%(27.9)&(28.0)& (27.9) & (27.8)& -- & \\\\\n34 & 34 & 34 & 34 & -- & [Si II]+\\\\\n & & & & & [S III]\\\\\n%-- & 36 & -- & -- & (36) & [Ne III]\\\\\n% & & & (44) & & \\\\\n% & & & & \\\\\n%\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n%\\end{footnotesize}\n%}\n\\end{table}\n\n\\begin{table}\n\\caption[]{\\label{tab:invent_abs} Summary of observed absorption features.\nUncertain detections are given in parentheses.} \n%\\begin{footnotesize}\n%{\\scriptsize\n\\begin{flushleft}\n\\begin{tabular}{llllll}\n%\\begin{tabular}{lll}\n\\hline\\noalign{\\smallskip}\nM\\,82 & NGC & 30\\,Dor & Circinus & NGC & species\\\\\n & 253 & & & 1068 & \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\n3.0 & 3.0 & -- & -- & -- & H$_2$O ice \\\\\n--$^1$ & --$^1$& --$^1$& --$^1$ & 3.4 & hydrocarbon \\\\\n%(--) & (--) & -- & -- & -- & 7.7$\\mu$m CH$_4$ \\\\\n(9.7) & (9.7) & -- & (9.7) & 9.4 & silicate \\\\\n(18.0 )& (18.0)& -- & (18.0) & -- & silicate \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n$^1$ could be filled in by PAH emission\n\\end{table}\n\n\n\\begin{table}\n\\caption[]{\\label{tab:PAH_flux1} Approximate absolute and relative fluxes of the \nprominent PAHs at 3.3 and 6.2$\\mu$m (see text for details).}\n%\\begin{footnotesize}\n%{\\scriptsize\n\\begin{flushleft}\n\\begin{tabular}{lllll}\n\\hline\\noalign{\\smallskip}\nObject & \\multicolumn{2}{c}{3.3$\\mu$m} & \\multicolumn{2}{c}{6.2$\\mu$m} \\\\ \n & flux$^1$ & relative flux$^2$ & flux$^1$ & relative flux$^2$ \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nM\\,82 & 3.3 & 0.2 & 37 & 2.7 \\\\\nNGC\\,253 & 1.0 & 0.1 & 13 & 1.7 \\\\\n30\\,Dor & 0.3 & 0.04& 1.5 & 0.2 \\\\\nCircinus & 0.7 & 0.06& 6.3 & 0.6 \\\\\nNGC\\,1068 & 0.3 & 0.02& 1.0 & 0.05\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n$^1$ [10$^{-18}$ W/cm$^2$] \\\\\n$^2$ PAH flux/continuum(11.6--11.9$\\mu$m)\n\\end{table}\n\n\\begin{table}\n\\caption[]{\\label{tab:PAH_flux2} Approximate absolute and relative fluxes of the \nprominent PAHs at 7.7 and 11.3$\\mu$m (see text for details).}\n%\\begin{footnotesize}\n%{\\scriptsize\n\\begin{flushleft}\n\\begin{tabular}{lllll}\n\\hline\\noalign{\\smallskip}\nObject & \\multicolumn{2}{c}{7.6--7.8$\\mu$m} & \\multicolumn{2}{c}{11.3$\\mu$m} \\\\ \n & flux$^1$ & relative flux$^2$ & flux$^1$ & relative flux$^2$ \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nM\\,82 & 99 & 7.2 & 16 & 1.2 \\\\\nNGC\\,253 & 39 & 5.0 & 7.2 & 0.9 \\\\\n30\\,Dor & 0.3 & 0.04& 1.7 & 0.2 \\\\\nCircinus & 21 & 1.9 & 3.9 & 0.4 \\\\\nNGC\\,1068 & 2.1 & 0.1 & 1.1 & 0.06\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n$^1$ [10$^{-18}$ W/cm$^2$] \\\\\n$^2$ PAH flux/continuum(11.6--11.9$\\mu$m)\n\\end{table}\n\nIn Tables \\ref{tab:inventory} and \\ref{tab:invent_abs} \nwe give an inventory of features that we believe to be reliable detections. \nWe consider a detection reliable if the feature has an amplitude of at least\n3$\\sigma$ of the noise level and if it fulfills the criteria described above.\nWe also list a few uncertain detections in parantheses, e.g. features in\ncompliance with the above criteria but with an amplitude of less than\n3$\\sigma$ (but note that the definition of the local noise level is in many \ncases somewhat uncertain).\nMost of these features have been described before in reports of ISO-SWS\nobservations of galactic template sources (e.g. Moutou et al. 1996, \nVerstraete et al. 1996, \nRoelfsema et al. 1996, Beintema et al. 1996). Here we highlight \na few of their characteristics, source by source. In Sect. \\ref{s:ident}\nwe briefly discuss possible identifications. Please note that many of \nthe features are severely blended and thus the peak wavelengths given here are \napproximate. \n\nWe also list the fluxes of four of the most prominent PAHs in\nTables \\ref{tab:PAH_flux1} and \\ref{tab:PAH_flux2}. To measure these fluxes\nwe defined continua by a linear interpolation between the following points: \n2.50 and 3.65$\\mu$m for the 3.3$\\mu$m feature, 5.9 and 10.9$\\mu$m for the\nfeatures at 6.2 and 7.7$\\mu$m, and 10.9 and 11.8$\\mu$m for the 11.3$\\mu$m\nfeature. We then obtained the fluxes by integrating between the following band\nlimits: 3.10--3.35$\\mu$m, 6.0--6.5$\\mu$m, 7.3--8.2$\\mu$m, and\n11.1--11.7$\\mu$m. To give an indication of the relative contribution of these\nfeatures to the infrared luminosity we also list their ratio to the continuum\nflux in the range 11.6--11.9$\\mu$m. Due to the uncertainties involved in this\nmeasuring process (continuum shape, feature profile, etc.) \nall absolute and relative fluxes are only approximate.\nBy definition, these fluxes ignore a possible, PAH-related `plateau' or\n`continuum' in the 6--9 and 10--13$\\mu$m range (e.g. Boulanger et al. 1996).\\\\\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n% \\resizebox{\\hsize}{!}{\\includegraphics{fig2a.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig2a.ps}}\n \\vspace*{0.05cm} \\caption{Details of the spectra. Wavelength in $\\mu$m, flux \n density in\n Jansky.}\n \\label{fig:details}\n\\end{figure*} \n\\begin{figure*}\n\\setcounter{figure}{1}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig2b.ps}}\n% \\resizebox{\\hsize}{!}{\\includegraphics{h1809.f2b}}\n \\vspace*{0.05cm} \\caption{{\\it continued} }\n\\end{figure*} \n\n%{\\vspace*{0.3cm} \\noindent \\bf M\\,82:} \n{\\noindent \\bf M\\,82:} \nM\\,82 is a small galaxy undergoing a very powerful\nstarburst, and is considered to be\na prototype of starburst activity.\nDue to its proximity (3.63 Mpc, Freedman et al. 1994) it is the\nbrightest galaxy in the infrared, with the infrared luminosity arising mainly\nfrom warm dust in the central region.\n%On the whole it is considered to be the prototypical starburst galaxy.\nEmission features\nat 8.7 and 11.3$\\mu$m were first detected by Gillett et al (1975), and the\n3.3, 6.2 and 7.6$\\mu$m features by Willner et al. (1977).\n%For more information on M\\,82 see e.g. Schreiber 1998????\n\nThe main PAH features are clearly seen in the\nmid-infrared spectrum of M\\,82, shown in its entirety in Fig. 1\nand in detail in the top panels of Fig 2. In addition,\nthe spectrum shows a large number of weaker features\nwhich have previously been detected with ISO only in\ngalactic template sources.\n\nThe 3.3$\\mu$m feature has satellites at 3.4 and 3.5$\\mu$m.\nIt also shows a blue asymmetry, which might be due to a feature at 3.25$\\mu$m\n(see Beintema et al. 1996).\nTwo weak features at 5.25 and 5.65$\\mu$m, that have been observed e.g. in\nthe planetary nebula NGC\\,7027 (Beintema et al. 1996) and the\nphotodissociation front of M\\,17 (Verstraete et al. 1996), are also present\nin M\\,82.\nThe 6.2$\\mu$m band has a red shoulder and\nshows an additional feature at 6.0$\\mu$m.\nThe 7.7$\\mu$m feature consists of two bands at 7.6 and 7.8$\\mu$m.\nA significant contribution of 7.7$\\mu$m solid methane absorption \n(e.g. Whittet et al. 1996, Lutz et al. 1996) to this strong dip between \n7.6 and 7.8$\\mu$m is unlikely, since in M\\,82 related icy absorption features \nare shallower and extinction is lower (Sect. \\ref{s:continuum}) than in the \nsources with clear methane absorptions.\nA weak feature is present at 10.6$\\mu$m, which is confirmed\nin the average starburst spectrum of Lutz et al. 1998a\n(their Fig. 1, independent ISOPHOT-S data), and probably related\nto a feature seen by Beintema et al. (1996) in the spectrum of NGC\\,7027. \nThe 11.3$\\mu$m feature peaks at 11.2$\\mu$m and shows the\nwell-known asymmetric shape towards longer wavelengths (Witteborn et al.\n1989).\nThere is an additional component around 11.05$\\mu$m, much too strong to be\nrelated to artifacts from the RSRF correction known to exist at this wavelength.\nA weak feature may be present near 12.0$\\mu$m. \nThe 12.7$\\mu$m feature is very prominent in M\\,82.\nMoutou et al. (1998) found two emission features at 15.8 and 16.4$\\mu$m in\nthe spectrum of the galactic reflection nebula NGC\\,7023. On the basis\nof their laboratory work, they\nattributed these features to PAH molecules.\nThese two features are clearly seen in M\\,82, and in some of our other \ntemplate spectra.\nMore emission features can be found at still longer wavelenghts\n(20.5 and 33-34$\\mu$m).\n\nIn addition we find two features that -- to our knowledge --\nhave not been reported before: at 7.0 and 8.3$\\mu$m.\nA feature around 7.0$\\mu$m is also present in NGC\\,253 (most clearly), and \nperhaps in 30\\,Dor.\nWe found the same feature in ISO-SWS \nspectra of the cool, dusty envelopes of the planetary nebula He\\,2-113\n(see e.g. Waters et al. 1998, their Fig. 2).\nThe average ISOPHOT-S spectra of starburst and normal galaxies (Lutz et al.\n1998a, Helou et al. 2000) also show hints of a weak feature, blended with\nH$_2$ S(5) 6.91$\\mu$m and [Ar II] 6.99$\\mu$m (see also Sect. \\ref{s:lowres}). \nThe 8.3 feature is also visible in\nthe galactic template spectrum of NGC\\,7023 (Fig. \\ref{fig:m82vsngc7023}),\nand perhaps in some of the compact HII regions shown in Roelfsema et al. (1996).\nWe also want to mention here the 14.3$\\mu$m band. An astronomical observation \nof this band has been reported only recently for the first time \n(Tielens et al. 1999). It is present in all \nour template spectra, with the\nexception of NGC\\,1068, in NGC\\,7023, and perhaps also in some of\nthe circumstellar PAH spectra shown in Beintema et al. (1996).\n%It is weak but important because it can be confused with the [Ne V] fine\n%structure line in spectra of low resolution (see Sec. \\ref{s:lowres}).\nOn the other hand, our spectra do not show some of the \nemission features that have been detected before \nin astronomical observations,\ne.g. at 4.65$\\mu$m (Verstraete et al. 1996) and \n13.3$\\mu$m (Moutou et al. 1998).\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n% \\resizebox{\\hsize}{!}{\\includegraphics{fig2c.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig2c.ps}}\n \\vspace*{0.05cm} \\caption{{\\it continued} }\n\\end{figure*} \n\\begin{figure*}\n\\setcounter{figure}{1}\n% \\resizebox{\\hsize}{!}{\\includegraphics{fig2d.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig2d.ps}}\n \\vspace*{0.05cm} \\caption{{\\it continued}. Broad features between 27.5 and \n 29.5$\\mu$m, and longward of 40$\\mu$m cannot be trusted.}\n\\end{figure*} \n\nThere are very few absorption features in our spectrum of M\\,82. The\ntrough around 10$\\mu$m looks like a strong 9.7$\\mu$m silicate feature.\nIn\nSect. \\ref{s:continuum} we argue, however, that the trough is mainly due \nto the strong PAH emission at 8.7 and 11.3$\\mu$m. \nAlso, there is no clear signature \nof a corresponding silicate absorption feature at 18$\\mu$m.\nA broad absorption feature around 3.0$\\mu$m is probably due to H$_2$O-ice.\nIts optical depth ($\\tau\\sim$0.2) is relatively small \ncompared e.g. to the Galactic center ($\\tau$=0.5, Lutz et al. 1996, \nChiar et al. 2000). However, \nsince the overall extinction estimates differ in the same sense,\nthis is consistent with the M\\,82 line of sight having properties similar to that\ntowards the Galactic center: a mixture of diffuse ISM and molecular cloud\nextinction, with some \nvariance in the relative weight for different lines of sight\n(Chiar et al. 2000). These properties seem to be quite typical for \nstarburst galaxies, as we find similar conditions in NGC\\,253 (see below) \nand in NGC\\,4945 (Spoon et al., in prep.).\n\nThe M\\,82 spectrum has the highest S/N ratio and\nshows the largest number of features in our sample.\nCombined with the ISO-LWS long wavelength spectrum (Colbert\net al. 1999) it will be an important template for future missions.\\\\\n\n\n{\\noindent \\bf NGC\\,253:}\nNGC\\,253 is a nearby, almost edge-on barred spiral galaxy with a high level \nof circumnuclear \nstarburst activity. At optical wavelengths the galaxy is heavily obscured by\ndust lanes in the central regions.\n%The ionic emission lines in NGC\\,253 are quite different from their \n%counterparts in M\\,82. E.g. the different [Ne III]/[Ne II] \n%ratios point to differences in the average radiation field \n%in these two starburst galaxies (Thornley et al. 2000).\nThe ionic emission lines in NGC\\,253 are of lower excitation (e.g. lower\n[Ne III]/[Ne II] ratio) than in M\\,82, suggesting a softer average\nradiation field (Thornley et al., in prep.). \nDespite these differences between the two galaxies, their \nspectra of broad emission features are \nremarkably similar. This is demonstrated in Fig. \\ref{fig:m82vsngc253}.\nOnly beyond 9$\\mu$m does a difference in the underlying continuum \nbecome obvious. NGC\\,253\n%, which has the stronger radiation field,\nhas a stronger continuum at these longer wavelengths. \nIn starburst galaxies this underlying continuum is usually attributed to \nvery small grains (VSG) of dust (e.g. D\\'esert et al. 1990). \nIn Sect. \\ref{s:continuum} we will use the difference in the continua of\nM\\,82 and NGC\\,253 to characterise the shape of the VSG continuum.\n\nTable \\ref{tab:inventory} shows that nearly all features of M\\,82 are also seen\nin NGC\\,253. The very few exceptions may simply be due to the lower\n%are probably just an issue of\nS/N ratio of the NGC\\,253 spectrum.\nThe red shoulder of the 6.2$\\mu$m band seen in M\\,82\nis more prominent in NGC\\,253 and is probably due to an additional feature at\n6.35$\\mu$m.\nThe 3.0$\\mu$m ice absorption is also present, having an optical depth of\n$\\tau\\sim$0.25.\\\\\n\n{\\noindent \\bf 30\\,Dor:}\nThe 30\\,Dor region in the LMC is the largest, most\nmassive, and most luminous H II region in the Local Group.\nAs a local template for massive star\nformation and its interaction with the interstellar medium, it is\ninstructive to compare its spectrum to the galaxy spectra in\nour sample.\nA more detailed study of the mid-infrared fine structure emission lines in\n30\\,Dor will be presented in an upcoming paper (Thornley et al., in prep.).\n%For an introduction to 30\\,Dor, more details about the ISO-SWS\n%observation, and a study of its mid-infrared\n%fine structure emission lines see Thornley et al. 2000????\n\nAn inspection of Fig. \\ref{fig:details} and Table \\ref{tab:inventory} shows\nthat the 30\\,Dor spectrum exhibits most of the PAH features found in the\ngalaxy spectra. Lower S/N may contribute to\nthe non-detection of some of the weak features.\nCompared to the two starburst galaxies, the features in 30\\,Dor are\nmuch weaker relative to the continuum (see also Tables \\ref{tab:PAH_flux1}\nand \\ref{tab:PAH_flux2}) and show different ratios.\nNote, for instance, the high 6.2/7.7$\\mu$m feature ratio, \nthe unusually high 3.4/3.3 ratio ($\\approx$ 0.5, see also Sect. \n\\ref{s:PAH_var}), the shape of the 7.6/7.8$\\mu$m features, or the complete\nabsence of the 12.7$\\mu$m feature.\nThese differences may be partly due to the fact, that the SWS apertures \ncovered only part of the entire 30\\,Dor complex. Verstraete et al. (1996)\nuse the case of M17 to demonstrate the strong variations in PAH spectra going\nfrom the center of an H\\,II region to the surrounding photodissociation region. \nOn the other hand, the similarity of the 30\\, Dor \nspectrum to the integrated ISOPHOT-S spectrum of the dwarf galaxy NGC\\,5253 \n(Rigopoulou et al. 1999) strongly suggests that the weakness of the PAHs is not\nan aperture effect but reflecting an intrinsic property of very active\nstar formation in a low metallicity environment.\n\nSilicate absorption at 9.7 and 18$\\mu$m is, if at all present, very weak.\nNo other absorption features can be detected. \\\\\n\n{\\noindent \\bf NGC\\,1068:}\nThe nearby, prototypical Seyfert 2 galaxy NGC\\,1068 is a key object in\nthe investigation and modeling of active galactic nuclei (AGNs).\nThe ISO-SWS observations were centered on the active nucleus, with the\naperture\ncovering very little of the\ncircumnuclear star forming `ring', which has a radius of $\\approx$15\\arcsec.\nIn stark contrast to the starburst templates we have shown, this active\nnucleus spectrum shows very little PAH emission.\nThe weaker features (e.g. 3.3, 6.2 or 12.7$\\mu$m)\nare barely visible, if at all. \n\nThe continuum around 10$\\mu$m is strong because of a central warm component\nheated by the AGN. Silicate absorption is clearly present, although centered\nat 9.4$\\mu$m rather than \nat 9.7$\\mu$m, but again surrounding weak PAH emission complicates its\ninterpretation. \nHydrocarbon absorption is seen at 3.4$\\mu$m (see also\nBridger et al. 1994), in contrast to our starburst templates, where\nit is not observed.\nNote, however, that in M\\,82 and NGC\\,253 a similar absorption feature\ncould plausibly\nexist if the analogy to the Galactic center holds, but be filled in by \nthe 3.3/3.4 PAH emission. On the other hand\nM\\,82 and NGC\\,253 show an H$_2$O ice absorption at 3.0$\\mu$m which is\ndefinitely absent in NGC\\,1068. \nThese differences in absorption features are entirely plausible because of the\ndifferent physical conditions in the obscuring regions. For the starbursts,\nthey likely include diffuse ISM as well as molecular clouds that can host icy\ngrains. Conversely, infrared polarimetry suggests that most of the \nnear-infrared obscuration in NGC\\,1068 occurs within a few parsecs from the \nnucleus, possibly in the torus (e.g. Packham et al. 1997). Such an energetic \nenvironment will be much less favourable for the existence of icy grains.\\\\\n\n{\\noindent \\bf Circinus:}\nThe Circinus Galaxy is a nearby spiral galaxy which shows Seyfert 2 activity\n(e.g. Moorwood \\& Glass 1984, Oliva et al. 1994, Moorwood et al. 1996,\nOliva et al. 1998). Due to its proximity (5 times closer than NGC\\,1068)\nit has become another template object for the study of AGNs.\nThe AGN is surrounded by circumnuclear\nstar-forming regions, as is often the case in Seyfert nuclei residing in\nspirals.\nThe ISO-SWS observations were centered on the active nucleus, but contrary to\nthe observations of NGC\\,1068 the apertures covered a significant amount of\nthis circumnuclear star formation.\nHence, most of the dust emission features seen in\nthe starburst templates are also found in\nCircinus, but with weaker line-to-continuum ratio (see the discussion in\nSect. \\ref{s:PAH_var}). A peculiarity of the Circinus spectrum are the\nvery pronounced features in the 20--22$\\mu$m region.\n\n\nThe observation was performed very early in the mission, when the\nobserving strategy was not yet fully optimized. For instance, exposures of\nthe internal flux calibration lamps, preceeding observations of the scientific\ntarget, caused memory effects in the immediately following scans.\nThe low flux level of band 4 ($\\lambda \\ge$ 29$\\mu$m),\nrelative to the preceding bands, is due to such a memory effect and an incorrect\ndark current subtraction. The same might be true for the apparent features near\n44$\\mu$m (which are not visible in the overlapping LWS spectrum). We did not \nattempt to improve the dark current subtraction further since this would \ninvolve subjective assumptions about the true dark current.\n\n%--------------------------------------------------------------------\n\\section{Mid-infrared features and the physical state of the ISM}\n\n%--------------------------------------------------------------------\n\n\\subsection{Identification}\n\\label{s:ident}\n\n\\subsubsection{The 2-13$\\mu$m region:}\n\nThe emission features in this wavelength range\nhave been extensively studied with ISO in galactic objects during the last few\nyears. Comprehensive discussions of their identifications and characteristics\ncan be found e.g. in Beintema et al. (1996), Moutou et al. (1998), Roelfsema\net al. (1996), and Verstraete et al. (1996).\nThey are most often attributed to PAH molecules. This is supported by\nrecent laboratory studies (e.g. Roelfsema et al. 1996, Moutou et al. 1996).\nThe only features in this range, \n%in Table \\ref{tab:inventory}, \nwhich have not\nbeen addressed in the\nliterature so far, are the ones at 7.0 and 8.3$\\mu$m. \nIn our sample of galaxies \nthey are\nunambiguously detected only in M\\,82 and NGC\\,253 (the 8.3$\\mu$m feature only\nin M\\,82), but as mentioned in Sect.\n\\ref{s:inventory} they seem to be present in other published spectra as well.\n%Here we will not attempt to identify its carrier but \nIt seems likely that they can be attributed to a PAH modes, too.\n\n\\subsubsection{Features between 13 and 20$\\mu$m:}\n\nFeatures in this range have attracted less attention in the past, because\nthey are intrinsically weak (but see e.g. Beintema et al. 1996).\nThese bands, however, are more sensitive to the molecular structure of PAHs,\nsince they\n%are due to skeletal vibration. \ninvolve the motion of the molecule as a whole, therefore depending on the \nexact species (L\\'eger et al. 1989).\nHence, their observation could help to better\nconstrain the composition of the interstellar mixture.\nThe 13.6, 15.8, and 16.5$\\mu$m features are\nalso visible in the spectra of NGC\\,7023 and have been attributed to PAH bands\nin the past by Moutou et al. (1998), based on their laboratory work.\nThe band at 14.3$\\mu$m has been tentatively attributed to a phenyl bending \nmode by Tielens et al. (1999). \nMoutou et al. (1996) list a feature at this wavelength in their composite\nlaboratory spectrum of a mixture of PAHs. Although weak, it might cause\nconfusion with [Ne V] in low resolution spectra (see Sect. \\ref{s:lowres}).\nFinally, the weak feature at 14.8$\\mu$m (if real) could be due to the smallest \nPAH, benzene (Tielens et al. 1999). \n\n\n\\subsubsection{Features in the 20 to 45 $\\mu$m region:}\n\nThe number of modes in the laboratory PAH spectra of Moutou et al. (1996) \ndecreases\nwith increasing wavelength. Few species show emission beyond 20$\\mu$m, \ne.g. near 21, 28 and 40$\\mu$m.\nIn this wavelength range other sources must be taken into\naccount. A number of recent papers have reported the detection of crystalline\nsilicates (olivines, fosterite, pyroxene, etc.) in objects like \nLuminous Blue Variables (Voors et al. 1999),\ndusty circumstellar disks (Waelkens et al. 1996, Waters et al. 1996), or\nPlanetary Nebulae (Waters et al. 1998).\nIn particular the feature at 34$\\mu$m\n%and 43$\\mu$m\ncould be attributed to\nthese kind of sources. However, one would expect to see emission\nfeatures at e.g. 23, 28, 40 and 43$\\mu$m, as well; none of these features are\nclearly detected in our spectra.\nOn the other hand, even in some of the galactic templates, such as the\nplanetary nebula NGC\\,6543 (e.g. Waters et al. 1996), not all of\nthese features are present.\n\nA feature near 20.5$\\mu$m shows a striking variation in shape and central\nwavelength between the galaxies. This is particularly surprising since \nthe galaxy spectra include a mixture of many different regions, and may suggest\na carrier occuring only transiently in very special conditions.\nIn Circinus this feature is most prominent, and peaks at the bluest wavelength \n(20.2$\\mu$m). Circinus also shows a second peak at 21.7$\\mu$m which \nis absent in the other spectra. \nA bump around 20.5$\\mu$m is also seen in ISO-SWS spectra of M supergiants \n(Voors et al. 1999, Molster et al. 1999). \nIt could be due to PAHs or alternatively metal\noxides like FeO (Waters et al. 1996, Henning et al. 1995).\nIRAS-LRS and ISO-SWS spectroscopy have also detected a broad feature, centered\nat approximately 20.1$\\mu$m, in carbon rich stars (Volk et al. 1999,\nGarc\\'{\\i}a-Lario et al. 1999, Szczerba et al. 1999). Possible candidates \nthat have\nbeen proposed include large PAH clusters or hydrogenated amorphous carbon\ngrains, hydrogenated fullerenes, and nano-diamonds (see references in\nVolk et al. 1999). However, compared to these detections, the\nfeatures\nin our spectra are much narrower.\n\nA mixture of fullerene molecules of different degree of hydrogenation (Webster\n1995) might also explain the second peak in Circinus around 21.7$\\mu$m, \nsince the emission\npeak shifts from 23 for fully hydrogenated fullerene (C$_{60}$H$_{60}$)\nto 19$\\mu$m for non-hydrogentated fullerene (C$_{60}$).\n%This second feature is observed in our sample in\n%the Circinus Galaxy only (OR IS IT IN 1068, too????). \nNone of the other galaxies exhibit this feature, but\n%However, the\nthe SWS01 spectrum of NML Cyg (Voors et al. 1999) and of the galaxy\nNGC4945 (S. Lord, private communication) also\nshow a weak emission feature around 21.6--22$\\mu$m.\n\nThe broad plateau at 33--34$\\mu$m, i.e. under the strong lines of [Si II]\nand [S III], could be affected by detector memory effects. To remove such a\npossible instrumental effect we treated the two\ndifferent scan directions of the SWS01 mode separately. \nThe trailing wings of each line profile, i.e. the blue\nwing for the scan with increasing wavelength, and the red wing for the scan\ndecreasing in wavelength, are much more distorted by memory effects than\nthe leading wings. Therefore, we cut out these trailing wings, before we\naveraged the spectra of the two scan directions.\nWe are\nhence confident that most of the remaining plateau is real. Such a feature\nhas been observed in many\ngalactic targets and is generally attributed to crystalline silicates\n(olivine, e.g. Waters et al. 1998).\n\n%A 44 FEATURE COULD ALSO BE H2O ICE\n%Features at 21, 22: seen in NML Cyg (Voors et al.), metal oxides? (Waters 96,\n%Henning 95). Nano-diamonds?\\\\\n%Feature at 34, 43: NGC6543, Waters 1996, also \n%NML Cyg (Justtanot, Waters 1996).\n%A pyroxene at 34 would also show 23.5 and 40 (Waters 1998).\n%43: crystalline ice, 34: olivine (Waters 1996)\\\\ \n%Feature at 36: seen in HD100546 (Waelkens 1996), but this one also shows\n%23.5 and 27 features, no 43. Unidentified/fosterite? (Waters 1996 \n%table2/figure2).\n%NGC6543 shows 34 and 43 but no 40 (Waters 96). NML Cyg shows 33, 40 and 43 \n%(plus 21, 22).\\\\\n%33 also seen in AG Car (Lamers 96). \n%Molinari: 43 ice feature should be more at 44-45. If there is no 62 um \n%feature it is probably amorphous ice not crystalline.\n%Waelkens: According to Koike et al. (1993) a 28$\\mu$m peak is characteristic\n%for all olivines. \n\n%No 4.65 um feature? No 13.1/13.3? (Verstraete/Moutou). No others????\n\n\n\n\n%--------------------------------------------------------------------\n\\subsection{Variation of PAH features}\n\\label{s:PAH_var}\n\nPublished mid-IR spectra of galactic template sources show a significant\nvariation of intrinsic\nPAH ratios from source to source. For instance Roelfsema et al.\n(1996) see a drastic change in the relative intensities of the 7.7 and 8.6\nbands with increasing intensity or hardness of the radiation field.\nSimilar changes are seen e.g. in different regions of M17\n(Verstraete et al. 1996) or - for the 8.6/11.3 ratio - in the\nreflection nebula NGC\\,1333 (Joblin et al. 1996).\nPAHs exposed to intense and hard radiation fields can be ionized, lose\nhydrogen atoms, or be photodissociated; any of these effects may contribute to\n% which in turn can cause\nthe observed variations in PAH ratios.\nAccording to Joblin et al. (1996) the ionization is best traced by the 3.4/3.3\nand 8.6/11.3 ratios. A good hydrogenation indicator is the (12+12.7)/11.3\nratio. For instance, these authors find a high 3.4/3.3 ratio \nof 0.1 in radiation fields that are 10$^5$ times the standard.\n\n\nAnother important factor that can alter observed\nPAH ratios is extinction. Extinction\nwill suppress the 6.2, 8.6 and 11.3$\\mu$m features with respect to \nthe one at 7.7$\\mu$m. \nThe 12.7/11.3 ratio is similarly affected, since the 11.3 feature is\nstill in the wing of the 9.7$\\mu$m silicate absorption. Details will depend\non the applicable extinction law (see e.g. the Galactic center, Lutz et al. \n1996). While extinction\nclearly affects PAH spectra in highly obscured sources like Ultraluminous \nInfrared Galaxies (ULIRGs, Lutz et al. 1998a) or the edge-on galaxy \nNGC\\,4945 (Spoon et al., in prep.), its\neffect will be less pronounced in the lower extinction sources of our sample.\n\nFinally, in active galaxies, such as NGC\\,1068 or the Circinus Galaxy, PAH\nfeatures can be diluted by an AGN-powered hot dust continuum.\nGenzel et al. (1998) and Lutz et al. (1998a) have used this as a diagnostic \nof the power sources of ULIRGs.\n\nOur sample of galaxy spectra exhibits a similar trend in relative PAH\nstrengths as the galactic templates.\nM\\,82 and NGC\\,253 have high\n3.4/3.3 ratios, consistent with them being active starburst galaxies.\n30\\,Dor seems to have an even higher 3.4/3.3 ratio, but the S/N ratio is not\nsufficient for a detailed analysis. However, a strong and hard, highly ionizing\nradiation field in 30\\,Dor is consistent with the results of Thornley et\nal. (1998), which are based on the ratios of fine structure emission lines,\nlike [Ne III]/[Ne II]. In that context it is interesting to note again\nthe complete absence of the 12.7$\\mu$m feature in 30\\,Dor.\nIn the two starburst galaxies\nM\\,82 and NGC\\,253 we see well-separated 7.6/7.8 and 8.6 features. The\n8.6 band is much weaker than the 7.6/7.8 band, just as observed in `normal'\nHII regions. In the Seyfert galaxy NGC\\,1068, however, the 8.6 band is similar\nin strength to the 7.7 band, as it is seen in the\nultracompact HII regions in M\\,17 (Cesarsky 1996b) or IRAS\\,18323-0242\n(Roelfsema et al. 1996), where the UV radiation field is\nextremely strong.\n\nNGC\\,1068, like many AGNs, shows an\nadditional component of warm dust in the 10$\\mu$m region. Unified models for\nSeyfert galaxies predict a dusty torus which would emit at these mid-infrared\nwavelengths (e.g. Pier \\& Krolik 1992). Hence, an alternative interpretation\nof the weak emission features on both sides of the silicate absorption might\nbe self-absorbed silicate emission from the torus, i.e. the emissions we \nidentified as PAH might simply be wings of a wide silicate emission maximum, \nthe center of which is suppressed by absorption.\nHowever, the observed double peaks at 7.7/8.6 and 11.05/11.25, as well as\nthe distinct rise in flux near 7.3$\\mu$m are not reproduced by torus models\nand show that there must be some\nreal, although weak, PAH emission on top of the continuum.\nThe weakness of the PAH emission can be understood in terms of dilution by the\nhot dust continuum and destruction by the intense AGN radiation field.\n\n\\begin{figure*}\n\\setcounter{figure}{2}\n% \\resizebox{\\hsize}{!}{\\includegraphics{m82vsngc253.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig3.ps}}\n \\caption{M\\,82 (full) versus NGC\\,253 (dash-dotted). In both spectra narrow\n emission lines have been masked out. Both spectra have been smoothed and \n corrected for zodiacal light and for their red shift. The spectrum of NGC\\,253\n has been multiplied by 2.6 to normalize the 7.6$\\mu$m PAH to the one in \n M\\,82.}\n \\label{fig:m82vsngc253}\n\\end{figure*} \n\\begin{figure*}\n \\setcounter{figure}{3}\n% \\resizebox{\\hsize}{!}{\\includegraphics{m82vsngc7023.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig4.ps}}\n \\caption{M\\,82 (full) versus the galactic reflection nebulae NGC\\,7023\n (dash-dotted). Both spectra have been corrected\n for zodiacal light and for their red shift. The spectrum of NGC\\,7023 \n has been smoothed and multiplied by 3.25 to normalize the 7.6$\\mu$m PAH to \n the one in M\\,82.}\n \\label{fig:m82vsngc7023}\n\\end{figure*} \n\\begin{figure*}\n \\setcounter{figure}{4}\n% \\resizebox{\\hsize}{!}{\\includegraphics{m82sim.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig5.ps}}\n \\caption{M\\,82 (full) versus NGC\\,7023 x 3.25 + power law (dashed).\n The spectra of NGC\\,7023 (dash-dotted) and M\\,82 have been smoothed. \n The power law component (dash-dotted) takes into account the aperture \n change at 12$\\mu$m (x 1.3).}\n \\label{fig:m82sim}\n\\end{figure*} \n\nNGC\\,1068 has a circumnuclear starburst region, and\nsome of the PAH emission might be picked up from this region by the large\nSWS aperture. The match in shape with the (small-aperture)\nground-based data of Roche et al. (1984) in the 8-13$\\mu$m range, and\ncomparisons to ground-based CO maps,\nsuggest that this effect is of minor importance here.\n\nIn the Circinus Galaxy the 7.7/8.6 ratio is somewhere in\nbetween the two extrema M\\,82 and NGC\\,1068.\nThe feature/continuum ratio of the PAH features,\nhowever, is much higher in Circinus than in NGC\\,1068. We attribute this to\nthe fact that in the case of Circinus the large SWS aperture\nindeed picked up parts of the well-known circumnuclear star forming region.\n%in Circinus.\n\n%Cesarsky (M17): a broad, smooth emission instead of the usual well-defined \n%7.7 and 8.6 bands is similar to M17 ultracompact HII region or protoplanetary \n%nebulae like IRAS 22273+5435 where the UV radiation field is extremely strong.\n%==> NGC\\,1068 does not pick up starburst ring, but shows PAHs in high radiation \n%environment (see also 1068 publication by Lutz).\n%While there exists an underlying continuum... another continuum starts at 15um\n%in regions of high radiation fields (see also Boulanger). Visible in 1068?\n \n%Roelfsema: The most dramatic change in relative intensities is seen \n%between the 7.6 and 8.6 bands. Similar to 8.6/11.3 (Joblin).\n%Non-compact PAHs enhance 8.6 relative to 7.6: less stable, occurs in sources\n%with higher luminosity/excitation. See their lab work.\n\n%--------------------------------------------------------------------\n\\section{Continuum placement and the depth of the silicate feature}\n\\label{s:continuum}\n\nAn important diagnostic in many extragalactic studies is the depth of the\nsilicate absorption feature at 9.7$\\mu$m and the extinction derived from it.\nHowever, the presence of strong PAH bands\non both sides of the 9.7$\\mu$m\nsilicate feature makes it very difficult to estimate the continuum level\nand the true depth of the silicate absorption.\nIn particular ground-based 8--13$\\mu$m data suffer from this problem.\nBecause of their continuous wavelength coverage ISO-SWS01 spectra are\nwell suited to shed more light on this question.\nIn the following we will discuss this issue using the example of M\\,82.\n\nFirstly, evidence against a strong 9.7$\\mu$m absorption comes \nfrom the absence of a strong 18$\\mu$m silicate absorption (see Fig. 1).\nAccording to Draine \\& Lee (1984) the expected ratio \n$\\tau_{sil}$(18$\\mu$m) / $\\tau_{sil}$(9.7$\\mu$m) is 0.4.\nFurthermore an analysis of hydrogen recombination lines in the ISO range\nyields a moderate A$_V$(gas)$\\approx$ 5 mag (for a uniform screen \nmodel - see Schreiber 1998). \n\nNext we come back to the comparison of the M\\,82 spectrum to the spectrum of\nNGC\\,253 (Fig.\n%\\ref{fig:m82vsngc253}\n3). The two galaxies are similar\nin A$_V$ and exhibit a very similar PAH spectrum. The only distinction appears\nto be a stronger VSG continuum in NGC\\,253. A strong\nrise of the continuum in this range is typical for regions of intense\nUV flux\n(e.g. D\\'esert et al. 1990, Vigroux et al. 1996) \\footnote{The spectrum of \nNGC\\,253 indicates lower ionization\n(e.g. low [Ne III]/[[Ne II]), but due to the compactness of the starburst in\nNGC\\,253 the radiation field here is more intense than in M\\,82.}.\nThe difference between both spectra\ncan be well fit by a power-law continuum that begins to rise at approximately\n8--9$\\mu$m.\n \nFinally, we\ncompare our spectrum\nof M\\,82 to the SWS01 spectrum of the galactic reflection nebula NGC 7023.\nLittle extinction is expected in the line of sight to this nebula.\nThe continuum under the PAH bands\nin NGC 7023 is very weak and starts to grow only beyond 20$\\mu$m (Moutou et\nal. 1998).\nThe flux density around 10$\\mu$m is almost on the same level as the flux\ndensity shortward of the 6$\\mu$m PAH band and at 15--20$\\mu$m.\n%(A similar behaviour is observed in many compact HII regions, Roelfsema et\n%al. 1996). \nIt could be explained by an underlying PAH plateau, or by\nthe wings of the 7.7/8.6 and 11.3 PAH\nfeatures (which can be represented by Lorentz profiles - Boulanger et al. 1998,\nMattila et al. 1999).\nWe therefore assume that in NGC\\,7023 this region consists\nmainly of emission bands, with little or no continuum and silicate absorption.\nIn Fig.\n%\\ref{fig:m82vsngc7023}\n4 we overplot the (smoothed) NGC\\,7023 spectrum on that of M\\,82. The NGC\\,7023\nspectrum has been multiplied by a factor 3.25 in order to normalize the\nPAH emission feature at 7.6$\\mu$m to the one in M\\,82.\nThe 3.3 and 11.3$\\mu$m bands\nin M\\,82 are weaker compared to NGC\\,7023. This might be explained\ne.g.\nby the harder radiation field in M\\,82 (Joblin et al. 1996, see \nSect. \\ref{s:PAH_var}).\n%Also, there might be a bit higher extinction in M\\,82, as indicated by the\n%slightly different 6.2$\\mu$m features (????).\nApart from this the two spectra are remarkably similar.\n%in the range up to 11$\\mu$m.\nOnly \n%beyond approximately 9$\\mu$m \nat higher wavelengths\na component of hot, small dust grains starts to add to the M\\,82\ncontinuum, as expected due to the much harder radiation field in M\\,82.\n\nIn view of these arguments we constructed a toy model in order to reproduce\nthe observed\nspectrum of M\\,82. The model simply consists of the scaled spectrum of\nNGC\\,7023 plus a power-law continuum which starts at 8.5$\\mu$m \n($f\\propto(\\lambda - 8.5)^{\\alpha}$).\nWe use a power-law rather than a black body curve for sake\nof simplicity. A power-law produces a very good fit to the continuum up to \n20 -- 25$\\mu$m. A black-body curve would be more problematic, because\nthe dust may not have a single temperature, and might not be in thermal \nequilibrium.\nM\\,82 is an extended source for the SWS apertures. There is a flux jump\naround 12$\\mu$m by a factor of about 1.3, corresponding to a similar change\nin aperture size. \nWe hence multiplied the power law continuum by 1.3 longward of 12$\\mu$m\n\\footnote{A more accurate correction for the change in aperture size would have\nto assume a light distribution (as a function of wavelength) and a model of\nthe instrument beam profile. Such a correction tool is not yet available.}.\nThe free parameters - the scaling factors for the\nNGC\\,7023 spectrum and the power law, plus the power law index - were adjusted \nby hand; we did not pursue a formal fit.\n%, since it is not needed for our purposes.\nFig.\n%\\ref{fig:m82sim}\n5 shows, that this simple model matches the observed\nspectrum remarkably well. There is no need to invoke any kind of extinction.\nDue to the uncertainties in the spectra, however, there is room for a moderate\nextinction,\nin accordance with the results from the recombination line studies (A$_V$ \n$\\approx$ 5 mag).\nA slightly different power-law, modified by a modest amount of extinction,\ncould fit the spectrum equally well.\nHowever,\na strong overall extinction, as deduced from the ground based 8-13$\\mu$m data\n(A$_V$ = 15--60 mag, Gillett et al. 1975), is clearly incompatible\nwith the new ISO data. This is an example of the potential danger of\noverestimating the silicate absorption depth in baseline-limited data.\n\n%--------------------------------------------------------------------\n\\section{The interpretation of low resolution spectra}\n\\label{s:lowres}\n\\begin{figure*}\n\\setcounter{figure}{5}\n% \\resizebox{\\hsize}{!}{\\includegraphics{fig6.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig6.ps}}\n% \\hfill\n% \\parbox[b]{55mm}{\n \\caption{The ISO-SWS spectra of M\\,82 and NGC\\,1068, \n smoothed to a resolution of 50 \n to simulate the ISOCAM-CVF and SIRTF-IRS (low resolution mode) spectrometers.\n Wavelength in $\\mu$m, flux density in\n Jansky.\n The feature at 14.3$\\mu$m in M\\,82 is NOT [Ne V] (see text).}\n \\label{fig:m82lowres}\n% }\n\\end{figure*} \n%\\begin{figure*}\n% \\setcounter{figure}{6}\n% \\resizebox{\\hsize}{!}{\\includegraphics{ngc1068lowres.eps}}\n% \\caption{The ISO-SWS spectrum of NGC\\,1068, smoothed to a resolution of 50 \n% to simulate the CAM-CVF and SIRTF-IRS (low resolution mode) spectrometer.}\n% \\label{fig:ngc1068lowres}\n%\\end{figure*} \nMany ISO spectra of galactic and extragalactic objects have been\ntaken in low resolution mode (ISOPHOT-S, ISOCAM-CVF). Also, surveys\nwith future mid- and far-infrared space missions, e.g. of galaxies at higher\nredshifts, will likely be\nperformed with a relatively low resolution. For example\nthe IRS spectrometer on board\nSIRTF will have a resolution of approximately 50--100 \n(plus a medium resolution mode of R=600) in a wavelength range similar to \nISO-SWS.\nIn this low resolution mode SIRTF-IRS, being much more sensitive \nthan ISO-SWS, will be a unique tool to detect emission features in spectra of \nfaint high-z galaxies.\nLow resolution spectra, however, suffer from possible identification\nand interpretation problems caused by coincidences of\natomic/ionic lines and solid state features.\nIn our high resolution SWS01 galaxy spectra lines and features are well\nseparated, and we can use these spectra as templates to identify and highlight\nthe importance of possible confusion problems.\nIn Fig. 6\n%\\ref{fig:m82lowres}\n%6 and\n%\\ref{fig:ngc1068lowres}\n%7 \nwe have smoothed and rebinned the M\\,82 and NGC\\,1068 spectra\nto a resolution of 50 to simulate e.g. an ISOCAM-CVF or a SIRTF-IRS spectrum.\n\n\\begin{table}\n\\caption[]{\\label{tab:ne2_vs_pah} The flux ratio of PAH 12.7 / [Ne II] 12.8}\n\\begin{flushleft}\n\\begin{tabular}{ll}\n\\hline\\noalign{\\smallskip}\nObject & PAH 12.7/[Ne II] 12.8\\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nM\\,82 & 0.96\\\\\nNGC\\,253 & 1.32\\\\\n30\\,Dor & 0.00\\\\\nCircinus & 6.17\\\\\nNGC\\,1068 & 0..1$^a$\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n\\begin{list}{}{}\n\\item[$^{\\rm a}$] exact value difficult to measure, due to the broad wing of \n the [Ne II] line and the relatively strong noise. \n\\end{list}\n\\end{table}\nIn Table \\ref{tab:inventory} we have indicated possible confusions with\nnearby molecular, atomic, and ionic lines. We want to mention three lines in \nparticular: \n[Ar II] at 6.99$\\mu$m, which might be \nconfused with the underlying PAH emission (and the nearby H$_2$ S(5) line), \n[Ne II] at 12.8$\\mu$m, which in \nfact has been confused in the past with the underlying 12.7$\\mu$m PAH feature,\nand [Ne V] at 14.3$\\mu$m, which also has been\nconfused in the past with the nearby PAH emission.\nTo get an indication of the relative contributions of the 12.7$\\mu$m \nPAH flux\nand the [Ne II] line flux to the combined (line plus feature) flux in low \nresolution spectra\nwe have measured both fluxes in our high resolution spectra.\nTable \\ref{tab:ne2_vs_pah} summarizes the ratios of\nPAH/[Ne II] in all 5 templates. The values\nvary widely: in 30\\,Dor\nthe flux is solely due to\n[Ne II], whereas in Circinus [Ne II] contributes \nonly about 15\\% of the combined flux. For the 7.0$\\mu$m feature,\nwe find that the broad feature contributes 25\\% of the combined flux of\nfeature, H$_2$, and [Ar II] in NGC\\,253.\n%varies in a wide range. In 30\\,Dor the flux is solely due to\n%[Ne II], whereas in Circinus [Ne II] contributes only about 15\\% to the\n%combined flux.\n%For the 7.0$\\mu$m feature we find a contribution of $\\approx$ 25\\% to the\n%combined flux of feature, H$_2$ and [Ar II] in NGC\\,253.\n\nIn the low resolution representation of\nM\\,82 in\nFig.\n%\\ref{fig:m82lowres}\n6 the shape of the 14.3$\\mu$m \nPAH resembles very much the shape of an unresolved\nline like the [Ne III] line\nat 15.5$\\mu$m and can be mistaken as [Ne V]. \nThe high resolution spectrum of M\\,82 (Fig. 2) clearly shows, that\nthere is no \\mbox{[Ne V]} at 14.32$\\mu$m but an \nemission feature plus a weak line of \\mbox{[Cl II]} 14.37$\\mu$m.\nOf all the strong fine structure emission lines\nonly few lines remain unambiguously detectable in low resolution\nspectra, like Br\\,$\\beta$, Br\\,$\\alpha$, [Ne III] 15$\\mu$m,\n\\mbox{[S III]} 18.7, 33.5$\\mu$m, and [Si II] 34.8$\\mu$m in M\\,82, or\n[O IV] 26$\\mu$m and perhaps [Ne V] 24$\\mu$m, and [S IV] 10.5$\\mu$m in \nNGC\\,1068.\nClearly, low resolution spectra are very well suited for PAH and continuum\nmeasurements. However, flux measurements of narrow lines, and -- in some cases\n-- even their identification, can be very difficult. For these purposes higher\nresolutions, as for instance provided by the R=600 mode of the SIRTF \nspectrometer, are definitely needed.\n\n\n%--------------------------------------------------------------------\n\\section{Conclusions}\n\\label{s:conclusions}\n\nWe have detected a large number of mid-infrared features in galaxy spectra, \nsome of them previously unobserved, and discussed the dependence of the\ndust features on ISM condition in galaxies.\nThe spectral features vary considerably from source to source in \npresence and relative strength. Emission features are largely absent in \nthe intense radiation field close to an AGN, and weak in a\nlow metallicity, intensely star forming environment.\nDifferences in the absorption spectra point to different\nphysical properties of the obscuring regions in starburst and active galaxies.\n\nThe spectra presented here will be valuable template spectra for future\nmid- and far-infrared space missions such as SIRTF, SOFIA or FIRST. \n%They can be used for simulations of observations and for estimating\n%exposure times.\nThey\nprovide important clues for the identification and interpretation of high\nredshift, dusty galaxies.\n%, which supposedly contain a large amount of dust.\nThe strongest PAH features can be used to provide redshift information in \nfar-infrared photometric\ngalaxy surveys (Simpson \\& Eisenhardt 1999, see also the example of\n21396+3623, Rigopoulou et al. 1999). Furthermore, they affect\ngalaxy number counts.\nFor instance, Xu et al. (1998) have constructed semi-empirical galaxy SEDs\nto model the considerable PAH effects on number counts and redshift distributions.\n%The improved data reductions\n%and additional sources presented here might help to further constrain, refine\n%and test this kind of models (e.g. Xu et al. assumed no 3.3 feature and no\n%features beyond 13$\\mu$m). \\\\\n%GEORGE: DO YOU THINK THIS IS RELEVANT???? DID YOU EVER TEST THESE MODELS\n%AGAINST CIRCINUS????\nFinally, the continuum and the PAH features can be used to distinguish \nbetween starburst activity and active nuclei in high redshift galaxies, as\nhas been demonstrated for local infrared bright galaxies (Genzel et al. 1998,\nLutz et al. 1998a, Rigopoulou et al. 1999).\n\nThe advantage of the wide wavelength coverage of the SWS spectra has been\nused to\nillustrate the problem of the continuum definition and the true depth of the\nsilicate absorption.\nWe find that in our starburst templates the hot VSG dust continuum begins to\nrise around 8 to 9$\\mu$m,\nand that it can be well fitted by a simple power-law up to 20...25$\\mu$m.\nFinally we have demonstrated possible line identification problems in low\nresolution spectra.\n\nThe spectra presented here are available in electronic form from the authors.\nWe want to note again, that different parts of the spectra were\nobserved through different aperture sizes, which should be taken into account\nfor a detailed use as template spectra.\n\n\n%--------------------------------------------------------------------\n\\begin{acknowledgements}\nWe wish to thank George Helou for very fruitful discussions, and Bernhard\nBrandl for support with the SIRTF-IRS simulations.\n SWS and the ISO Spectometer Data Center at MPE are supported by\n DLR under grants 50 QI 8610 8 and 50 QI 9402 3. \nThe ISO Spectral Analysis Package \n(ISAP) is a joint development by the LWS and SWS Instrument Teams and Data \nCenters. 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A., Bregman J. D., \n%Allamandola, L. J., Cohen, M., Wooden, D. H. \\& Graps, A. L. \net al. 1989, ApJ 341, 270 \n\n\\bibitem[Xu et al. 1998]{1998ApJ...508..576X} Xu C. , Hacking P. B., Fang F., \net al. 1998, ApJ 508, 576 \n\n\\end{thebibliography}\n\n\n\\end{document}\n"}],"string":"[\n {\n \"name\": \"sturm.tex\",\n \"string\": \"\\\\documentclass{aa}\\n%\\\\documentclass[referee]{aa}\\n\\\\usepackage{graphics}\\n\\n\\\\begin{document}\\n\\n \\\\thesaurus{03\\n (13.09.3);\\n (13.09.4);\\n% 11\\n% (11.09.4);\\n (11.09.1 M\\\\,82);\\n (11.09.1 NGC\\\\,253);\\n (11.09.1 Circinus);\\n (11.09.1 NGC\\\\,1068)} \\n%\\n \\\\title{ISO-SWS spectra of galaxies: continuum and features\\n \\\\thanks{Based on observations with ISO, an ESA project with\\n instruments funded by ESA member states (especially\\n the PI countries: France, Germany, the Netherlands and\\n the United Kingdom) and with participation of ISAS and\\n NASA.} }\\n\\n \\\\author{E. Sturm \\\\inst{1,}\\\\inst{2}\\n \\\\and{D. Lutz \\\\inst{1}}\\n \\\\and{D. Tran \\\\inst{1}}\\n \\\\and{H. Feuchtgruber \\\\inst{1}}\\n \\\\and{R. Genzel \\\\inst{1}}\\n \\\\and{D. Kunze \\\\inst{1}}\\n \\\\and{A.F.M. Moorwood \\\\inst{3}}\\n \\\\and{M.D. Thornley \\\\inst{4}}}\\n\\n \\\\offprints{sturm@mpe.mpg.de}\\n\\n \\\\institute{Max-Planck-Institut f\\\\\\\"ur extraterrestrische Physik,\\n Postfach 1603, D-85740 Garching, Germany\\n \\\\and Infrared Processing and Analysis Center, \\n MS 100-22, Pasadena, CA 91125, USA\\n \\\\and European Southern Observatory,\\n Karl-Schwarzschild-Str. 2, D-85748 Garching, Germany \\n \\\\and National Radio Astronomy Observatory,\\n 520 Edgemont Road, Charlottesville, VA 22903, USA}\\n \\n \\\\date{Received 19 October 1999 / Accepted 26 January 2000}\\n\\n \\\\maketitle\\n\\n \\\\begin{abstract}\\n\\nWe present an inventory of mid-infrared spectral features detected in\\nhigh resolution (R$\\\\sim$1500) ISO-SWS 2.4--45$\\\\mu$m spectra of the \\ngalaxies \\\\object{M\\\\,82}, \\\\object{NGC\\\\,253}, \\\\object{Circinus},\\n\\\\object{NGC\\\\,1068}, and a position in the \\\\object{30\\\\,Doradus} region of the \\nLarge Magellanic Cloud.\\nWe discuss their identifications and highlight possible relations between\\nthese features and the physical state of the interstellar medium in\\ngalaxies. The spectral features vary considerably from source to source in \\npresence and relative strength. Emission features are largely absent in \\nthe intense radiation field close to an AGN. Compared to normal \\ninfrared-selected starbursts, they also seem to be weaker in a\\nlow metallicity, intensely star forming environment.\\nThe large number of features beyond 13$\\\\mu$m is remarkable. \\nSome of the features \\n%are unambiguously detected for the first time in astronomical objects and \\nhave -- to our knowledge -- not been \\nreported before in astronomical objects. \\n\\nIn the 5--13$\\\\mu$m region, emission from unidentified infrared bands (UIBs),\\nusually ascribed to\\naromatic molecules, and apparent\\nsilicate absorption dominate the spectrum. The density \\nof features makes it\\ndifficult to determine the continuum, particularly in ground-based data of \\nlimited wavelength coverage. In fact \\nthe apparent depth of the 9.7$\\\\mu$m\\nsilicate absorption may be overestimated in the presence of UIB emission, as\\nwe demonstrate by comparing the spectrum of M\\\\,82 to the (absorption free)\\nspectrum of the reflection nebula \\\\object{NGC\\\\,7023}. \\nNo strong silicate absorption is \\npresent in M\\\\,82.\\nThe (very small grain) dust continuum \\nunder the UIB emission in our starburst templates \\ncan be modeled by a simple power law, starting at wavelengths\\nbetween 8 and 9$\\\\mu$m.\\n\\nWe find broad H$_2$O-ice absorption features at 3.0$\\\\mu$m in M\\\\,82 and \\nNGC\\\\,253. Their optical depths (relative to the visual extinction) \\nindicate that the lines of sight towards these galaxies have similar \\nproperties as the line of sight\\ntowards the Galactic Center.\\n%: a mixture of diffuse ISM and molecular cloud\\n%extinction, with some \\n%variance in the relative weight for different lines of sight.\\nThe active galaxy NGC\\\\,1068 exhibits a clearly different spectrum of \\nabsorption features, indicating different\\nphysical conditions in the obscuring regions of this AGN compared to the\\nstarburst templates.\\n\\n\\nThe spectra are valuable templates for future\\nmid-infrared missions. \\nWe smooth our data to simulate low resolution spectra as obtained\\nwith ISOCAM-CVF, ISOPHOT-S, and in the future with the low resolution mode of\\nSIRTF-IRS, and use our \\nhigh\\nspectral resolution information to highlight possible identification problems\\nat low resolving power that are caused by coincidences of lines and features. \\nThe spectra are available in electronic form from the authors.\\n \\\\keywords{\\n Infrared: ISM: continuum --\\n Infrared: ISM: lines and bands --\\n% Galaxies: ISM --\\n Galaxies: individual: M\\\\,82 --\\n Galaxies: individual: NGC\\\\,253 --\\n Galaxies: individual: Circinus --\\n Galaxies: individual: NGC\\\\,1068\\n}\\n\\n \\\\end{abstract}\\n\\n%\\n%________________________________________________________________\\n\\n\\\\section{Introduction}\\nMid-infrared spectra of galaxies are rich in emission lines, and\\ndisplay prominent broader emission and absorption features due to the presence\\nof various solids and/or large molecules in their interstellar medium\\n(ISM). Significant variation from source to source suggests \\nthat these features may provide important\\ndiagnostics of the ISM conditions in galaxies. \\n\\nThe ground based and Kuiper Airborne Observatory spectra of the \\nprototypical starburst M\\\\,82 by Gillett et al. (1975) and Willner et al. (1977) \\nfully established the existence of the\\nmid-infrared `unidentified infrared bands' (UIB) at 6.2, 7.7, 8.6, \\nand 11.3$\\\\mu$m\\nin galaxy spectra. These emission bands are characteristic of C-C and C-H bonds\\nin aromatic molecules. In this paper we will refer to them as \\n`PAH features' \\naccording to one of the most popular interpretations of their carrier, \\npolycyclic aromatic hydrocarbon molecules\\n\\\\footnote{Other suggested carriers include small grains of\\nhydrogenated amorphous carbon (HACs), quenched carbonaceous composites (QCCs),\\nor coal.}. \\nThese detections and\\nrelated work using the IRAS LRS (Cohen \\\\& Volk 1989) form the basic pre-ISO\\nknowledge of mid-infrared spectral features in galaxies.\\n\\nConsiderable work has also been\\ndone from the ground but has been limited to the features\\nfound in atmospheric windows, mainly silicate absorption and PAH feature\\nemission in the N band (e.g. Roche et al. 1991, and references therein) \\nand the companion PAH feature\\nin the L band (e.g. Moorwood 1986).\\n%(e.g. Bridger, Wright \\\\& Geballe 1994).\\nThe restriction\\nto atmospheric windows increases problems in establishing the `continuum' on\\nwhich the features are superposed. This is a nontrivial task, even with full\\nwavelength coverage, due to the crowding of mid-infrared \\nemission and absorption features (especially in the 10$\\\\mu$m region).\\n\\nWith the Short Wavelength Spectrometer SWS (de~Graauw et al. 1996) on\\nboard\\nthe Infrared Space Observatory ISO (Kessler et al. 1996) high spectral\\nresolution observations with good signal-to-noise (S/N) were\\nobtained for a number of bright galaxies. Their main\\nadvantages lie in continuous wavelength coverage from 2.4 to 45$\\\\mu$m\\nand in the possibility to clearly separate features from nearby\\nemission lines.\\n\\nThe interpretation of\\ngalaxy-integrated spectra strongly benefits from comparisons to similar\\nobservations of galactic\\nsources, sometimes spatially resolved, allowing\\nbetter isolation of the physical mechanisms at work. Recent ISO spectra\\n%which have been recently observed in\\nof many galactic template objects, such as reflection\\nnebulae (e.g. Boulanger et al. 1996, Cesarsky et al. 1996a, Verstraete et al.\\n1996, Moutou et al. 1998), planetary nebulae and circumstellar regions\\n(e.g. Beintema et al. 1996), and HII regions (Roelfsema et al. 1996,\\nCesarsky et al. 1996b) have clearly demonstrated the importance of such\\ntemplate spectra. They\\n%provide a wealth of information and\\nprove that PAHs\\nare an ubiquitous part of the ISM. Additional information on emission features \\nof crystalline silicates comes from similar template observations with ISO of \\ne.g. planetary nebulae (Waters et al. 1998), evolved\\nstars (Waters et al. 1996), young stars (Waelkens et al. 1996), or LBVs in \\nthe LMC (Voors et al. 1999).\\nAbsorption features (silicates, ices) have been found e.g. in the Galactic\\ncenter (Lutz et al. 1996, Chiar et al. 2000), young stellar objects\\n(d'Hendecourt et al. 1996, Whittet et al. 1996, Dartois et al. 1999), and \\nin dark clouds in the solar neighborhood (Whittet et al. 1998).\\n\\nIn this paper we present an inventory of mid-infrared spectral features \\ndetected in high resolution (R$\\\\sim$1500) ISO-SWS 2.4--45$\\\\mu$m spectra of the \\nstarburst galaxies M\\\\,82 and NGC\\\\,253, the Seyfert 2 galaxies \\nCircinus and NGC\\\\,1068, \\nand a position in the 30\\\\,Doradus star forming region of the Large Magellanic \\nCloud (Sect. \\\\ref{s:inventory}). \\nWe briefly discuss possible feature identifications (Sect. \\\\ref{s:ident}) \\nand highlight possible relations \\nbetween these features and the physical state of the interstellar medium in\\ngalaxies (Sect. \\\\ref{s:PAH_var}). \\nWe also address the issue of the continuum determination and the \\napparent depth of the silicate absorption at 9.7$\\\\mu$m (Sect. \\n\\\\ref{s:continuum}). \\nFinally (Sects. \\\\ref{s:lowres} and \\\\ref{s:conclusions}) we demonstrate\\nthe use of these ISO spectra as templates for future \\ninfrared missions such as SIRTF, with particular emphasis on \\npotential identification problems\\nat low resolving power that are caused by coincidences of lines and features.\\n\\nAll the spectra shown here exhibit a large number of atomic, ionic and\\nmolecular emission lines. These have been or will be discussed elsewhere, \\nalong with more details on observations and data processing\\n(Circinus: Moorwood et al. 1996; M\\\\,82: Lutz et al. 1998b, Schreiber 1998;\\nNGC\\\\,1068: Lutz et al. 2000; 30\\\\,Dor: Thornley et al., in prep.). \\n\\n%--------------------------------------------------------------------\\n\\n\\\\section{Observations and data reduction}\\n\\nThe objects discussed here have been observed as part of the ISO guaranteed \\ntime project on bright galactic nuclei. Here we concentrate on full grating \\nscans obtained in SWS01 mode, speed 4. This mode provides a full \\n2.4--45$\\\\mu$m scan at resolving power of approximately 1000--2000.\\nFor NGC\\\\,253, Circinus, and NGC\\\\,1068 the observations were centered on the\\nnuclei. In the case of M\\\\,82 the observation was centered on the \\nsouthwestern star formation \\nlobe. For 30\\\\,Dor the apertures were lying roughly parallel to an ionized\\nshell region, about 0.5\\\\arcmin\\\\/ away from the central stellar cluster.\\nTable \\\\ref{tab:positions} summarizes the positions.\\nNote that different parts of an SWS full grating scan are observed with\\ndifferent aperture sizes\\\\footnote{The aperture sizes are\\n14\\\\arcsec$\\\\times$20\\\\arcsec\\\\/ for 2.4--12.0$\\\\mu$m, 14\\\\arcsec$\\\\times$27\\\\arcsec\\\\/ \\nfor 12.0--27.5$\\\\mu$m, 20\\\\arcsec$\\\\times$27\\\\arcsec\\\\/ for 27.5--29.0$\\\\mu$m, and\\n20\\\\arcsec$\\\\times$33\\\\arcsec\\\\/ for 29.0--45$\\\\mu$m, with some wavelength overlap\\nbetween the bands.}, varying between 14\\\\arcsec$\\\\times$20\\\\arcsec\\\\/ and \\n20\\\\arcsec$\\\\times$33\\\\arcsec.\\n\\nWe have processed the data using the SWS Interactive Analysis (IA) system\\n(Lahuis et al. 1998, Wieprecht et al. 1998) and the ISO Spectral Analysis\\nPackage ISAP (Sturm et al. 1998). Dark current subtraction, scan direction \\nmatching, and flatfielding have been done interactively, and noisy \\ndetectors have been eliminated. In ISAP we clipped outliers and\\naveraged the data of all 12 detectors for each AOT band, retaining the \\ninstrumental resolution. For those wavelength ranges affected by fringes, the \\naveraged spectra were defringed using the FFT or iterative sine fitting \\noptions of the defringe module within ISAP. \\n%More details about the observations and the data processing can be found\\n%elsewhere (M\\\\,82: Schreiber 1998????; NGC\\\\,253: Thornley, in prep.; 30\\\\,Dor:\\n%Thornley, in prep.; Circinus: Moorwood et al. 1996; NGC\\\\,1068: Lutz et al. \\n%2000????).\\n\\n\\\\begin{table}\\n\\\\caption[]{\\\\label{tab:positions} Summary of observed positions (J2000), \\nand position angles.}\\n%\\\\begin{footnotesize}\\n%{\\\\scriptsize\\n\\\\begin{flushleft}\\n\\\\begin{tabular}{lllll}\\n%\\\\begin{tabular}{llll}\\n\\\\hline\\\\noalign{\\\\smallskip}\\nObject & RA & Decl. & PA & remark\\\\\\\\\\n%Object & RA & Decl. & \\\\\\\\\\n\\\\noalign{\\\\smallskip}\\n\\\\hline\\\\noalign{\\\\smallskip}\\nM\\\\,82 & 09$^h$55$^m$50.7$^s$ & 69\\\\degr40\\\\arcmin44.4\\\\arcsec & 245\\\\degr & 1 \\\\\\\\\\nNGC\\\\,253 & 00$^h$47$^m$33.2$^s$ & -25\\\\degr17\\\\arcmin17.2\\\\arcsec & 28\\\\degr & 2 \\\\\\\\\\n30\\\\,Dor & 05$^h$38$^m$46.0$^s$ & -69\\\\degr05\\\\arcmin07.9\\\\arcsec & 230\\\\degr & 3 \\\\\\\\\\nCircinus & 14$^h$13$^m$09.7$^s$ & -65\\\\degr20\\\\arcmin21.5\\\\arcsec & 19\\\\degr & 2 \\\\\\\\\\nNGC\\\\,1068 & 02$^h$42$^m$40.8$^s$ & -00\\\\degr00\\\\arcmin47.3\\\\arcsec & -11\\\\degr & 2 \\\\\\\\\\n\\\\noalign{\\\\smallskip}\\n\\\\hline\\n\\\\end{tabular}\\n\\\\end{flushleft}\\n1 = SW lobe\\\\\\\\\\n2 = nucleus\\\\\\\\\\n3 = ionized shell\\n\\\\end{table}\\n\\n\\\\begin{figure*}\\n \\\\setcounter{figure}{0}\\n% \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{fig1.eps}}\\n \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{sturm_fig1.ps}}\\n \\\\caption{The full SWS01 spectra of the five extragalactic templates. x-axis:\\n wavelength in $\\\\mu$m; y-axis: flux density in Jansky.}\\n \\\\label{fig:m82}\\n\\\\end{figure*} \\n\\nTo reduce noise for display purposes (Fig. 1), we have smoothed the data \\nwith a gaussian filter to a uniform resolution of 1000. This\\nbroadens slightly the line widths of the narrow atomic and ionic emission\\nlines, but does not affect the broad emission and\\nabsorption features discussed in this paper.\\nWe did not remove the flux jumps at detector band limits. Part of\\nthese jumps may be real because the sources are extended and because\\nthe aperture sizes\\nchange at some band edges (at approximately 12.0, 27.5 and 29.0$\\\\mu$m).\\nAnother part simply reflects the flux calibration\\nuncertainty, which is of the order of 20 per cent.\\n\\nWe carefully checked the reality of the features in the final spectra \\nagainst the possibility of residual instrumental features from the \\nRelative Spectral Response Function (RSRF), which might be caused \\ne.g. by an improper dark current subtraction.\\nFor example, the detector RSRF exhibits absorption features \\nat 11.05 and 34$\\\\mu$m\\nwhich might appear in emission in the calibrated spectrum. This is, however,\\nat most an effect of the order of a few per cent of the continuum level. \\nThe features\\nwe see at these wavelengths in our spectra (see below) are stronger, so\\nthat they must be real.\\nFurthermore, we checked whether a feature\\n%listed in the next section\\nappears in both scan directions and in the majority of all\\ndetectors. Additional confirmation\\nwas possible for those features that lie in the overlap\\nregion of two different AOT bands and appear in both bands.\\nAt this stage of instrument calibration, we do not believe that any\\nof the broad structures in band 3E (appr. 27.5--29.5 $\\\\mu$m) are real\\nfeatures.\\nAlso, features at the end of band 4 (43--45 $\\\\mu$m, e.g. in Circinus)\\ncannot be trusted.\\n\\n%--------------------------------------------------------------------\\n\\n\\\\section{An inventory of features}\\n\\\\label{s:inventory}\\n\\n\\\\begin{table}\\n\\\\caption[]{\\\\label{tab:inventory} Summary of observed broad emission features\\n(approximate peak positions in $\\\\mu$m). Uncertain detections are given in\\nparentheses, nondetections are marked by a dash.} \\n%\\\\begin{footnotesize}\\n%{\\\\scriptsize\\n\\\\begin{flushleft}\\n\\\\begin{tabular}{llllll}\\n%\\\\begin{tabular}{lll}\\n\\\\hline\\\\noalign{\\\\smallskip}\\nM\\\\,82 & NGC & 30\\\\,Dor & Circinus & NGC & nearby\\\\\\\\\\n%\\\\multicolumn{5}{c}{ } & ionic lines\\\\\\\\ \\n & 253 & & & 1068 & lines\\\\\\\\\\n\\\\noalign{\\\\smallskip}\\n\\\\hline\\\\noalign{\\\\smallskip}\\n3.25 & 3.25 & -- & 3.25 & -- & \\\\\\\\\\n3.3 & 3.3 & 3.3 & 3.3 & 3.3 & Pf$_{\\\\delta}$\\\\\\\\\\n3.4 & 3.4 & 3.4 & -- & -- & \\\\\\\\\\n3.5 & (3.5) & 3.5 & -- & -- & \\\\\\\\\\n-- & 3.75 & -- & 3.75 & -- & \\\\\\\\\\n5.25 & -- & -- & -- & -- & \\\\\\\\\\n5.65 & 5.65 & -- & -- & -- & \\\\\\\\\\n6.0 & 6.0 & 6.0 & (6.0) & -- & \\\\\\\\\\n6.2 & 6.2 & 6.2 & 6.2 & (6.2) & \\\\\\\\\\n6.3 & 6.3 & 6.3 & 6.3 & -- & \\\\\\\\\\n7.0 & 7.0 & (7.0) & -- & -- & H$_2$+\\\\\\\\\\n & & & & & [Ar II]\\\\\\\\\\n7.6 & 7.6 & 7.6 & 7.6 &(7.6) & Pf$_{\\\\alpha}$+\\\\\\\\\\n & & & & & [Ne VI]\\\\\\\\\\n7.8 & 7.8 & 7.8 & 7.8 & 7.8 & \\\\\\\\\\n8.3 & -- & -- & -- & -- & \\\\\\\\\\n8.6 & 8.6 & 8.6 & 8.6 & 8.6 & \\\\\\\\\\n(10.6)& -- & -- & -- & -- & [S IV]\\\\\\\\\\n11.05 & 11.05& 11.05 & 11.05 & 11.05 & \\\\\\\\\\n11.25 & 11.2 & 11.25 & 11.25 & 11.25 & \\\\\\\\\\n12.0 & 12.0 & 12.0 & -- & -- & \\\\\\\\\\n12.7 & 12.7 & -- & 12.7 & (12.7)& [Ne II]\\\\\\\\\\n13.55 & 13.55& (13.5) & 13.6 & 13.4 & \\\\\\\\\\n14.25 & 14.25& 14.25 & 14.25 & -- & [Ne V]+\\\\\\\\\\n & & & & & [Cl II]\\\\\\\\\\n(14.8)&(14.8)&(14.8) &(14.8) & -- & \\\\\\\\\\n15.7 & 15.7 & 15.7 & 15.85 & 15.9 & [Ne III]\\\\\\\\\\n16.5 & 16.5 & 16.5 & -- & -- & \\\\\\\\\\n(17.4)&(17.4)& -- & -- & -- & \\\\\\\\\\n(18.0)& -- &(18.0) & -- & -- & \\\\\\\\\\n20.5 &(20.3)&(20.4) & 20.2 & -- & \\\\\\\\\\n-- & -- & -- & 21.7 & -- & \\\\\\\\\\n%(27.9)&(28.0)& (27.9) & (27.8)& -- & \\\\\\\\\\n34 & 34 & 34 & 34 & -- & [Si II]+\\\\\\\\\\n & & & & & [S III]\\\\\\\\\\n%-- & 36 & -- & -- & (36) & [Ne III]\\\\\\\\\\n% & & & (44) & & \\\\\\\\\\n% & & & & \\\\\\\\\\n%\\n\\\\noalign{\\\\smallskip}\\n\\\\hline\\n\\\\end{tabular}\\n\\\\end{flushleft}\\n%\\\\end{footnotesize}\\n%}\\n\\\\end{table}\\n\\n\\\\begin{table}\\n\\\\caption[]{\\\\label{tab:invent_abs} Summary of observed absorption features.\\nUncertain detections are given in parentheses.} \\n%\\\\begin{footnotesize}\\n%{\\\\scriptsize\\n\\\\begin{flushleft}\\n\\\\begin{tabular}{llllll}\\n%\\\\begin{tabular}{lll}\\n\\\\hline\\\\noalign{\\\\smallskip}\\nM\\\\,82 & NGC & 30\\\\,Dor & Circinus & NGC & species\\\\\\\\\\n & 253 & & & 1068 & \\\\\\\\\\n\\\\noalign{\\\\smallskip}\\n\\\\hline\\\\noalign{\\\\smallskip}\\n3.0 & 3.0 & -- & -- & -- & H$_2$O ice \\\\\\\\\\n--$^1$ & --$^1$& --$^1$& --$^1$ & 3.4 & hydrocarbon \\\\\\\\\\n%(--) & (--) & -- & -- & -- & 7.7$\\\\mu$m CH$_4$ \\\\\\\\\\n(9.7) & (9.7) & -- & (9.7) & 9.4 & silicate \\\\\\\\\\n(18.0 )& (18.0)& -- & (18.0) & -- & silicate \\\\\\\\\\n\\\\noalign{\\\\smallskip}\\n\\\\hline\\n\\\\end{tabular}\\n\\\\end{flushleft}\\n$^1$ could be filled in by PAH emission\\n\\\\end{table}\\n\\n\\n\\\\begin{table}\\n\\\\caption[]{\\\\label{tab:PAH_flux1} Approximate absolute and relative fluxes of the \\nprominent PAHs at 3.3 and 6.2$\\\\mu$m (see text for details).}\\n%\\\\begin{footnotesize}\\n%{\\\\scriptsize\\n\\\\begin{flushleft}\\n\\\\begin{tabular}{lllll}\\n\\\\hline\\\\noalign{\\\\smallskip}\\nObject & \\\\multicolumn{2}{c}{3.3$\\\\mu$m} & \\\\multicolumn{2}{c}{6.2$\\\\mu$m} \\\\\\\\ \\n & flux$^1$ & relative flux$^2$ & flux$^1$ & relative flux$^2$ \\\\\\\\\\n\\\\noalign{\\\\smallskip}\\n\\\\hline\\\\noalign{\\\\smallskip}\\nM\\\\,82 & 3.3 & 0.2 & 37 & 2.7 \\\\\\\\\\nNGC\\\\,253 & 1.0 & 0.1 & 13 & 1.7 \\\\\\\\\\n30\\\\,Dor & 0.3 & 0.04& 1.5 & 0.2 \\\\\\\\\\nCircinus & 0.7 & 0.06& 6.3 & 0.6 \\\\\\\\\\nNGC\\\\,1068 & 0.3 & 0.02& 1.0 & 0.05\\\\\\\\\\n\\\\noalign{\\\\smallskip}\\n\\\\hline\\n\\\\end{tabular}\\n\\\\end{flushleft}\\n$^1$ [10$^{-18}$ W/cm$^2$] \\\\\\\\\\n$^2$ PAH flux/continuum(11.6--11.9$\\\\mu$m)\\n\\\\end{table}\\n\\n\\\\begin{table}\\n\\\\caption[]{\\\\label{tab:PAH_flux2} Approximate absolute and relative fluxes of the \\nprominent PAHs at 7.7 and 11.3$\\\\mu$m (see text for details).}\\n%\\\\begin{footnotesize}\\n%{\\\\scriptsize\\n\\\\begin{flushleft}\\n\\\\begin{tabular}{lllll}\\n\\\\hline\\\\noalign{\\\\smallskip}\\nObject & \\\\multicolumn{2}{c}{7.6--7.8$\\\\mu$m} & \\\\multicolumn{2}{c}{11.3$\\\\mu$m} \\\\\\\\ \\n & flux$^1$ & relative flux$^2$ & flux$^1$ & relative flux$^2$ \\\\\\\\\\n\\\\noalign{\\\\smallskip}\\n\\\\hline\\\\noalign{\\\\smallskip}\\nM\\\\,82 & 99 & 7.2 & 16 & 1.2 \\\\\\\\\\nNGC\\\\,253 & 39 & 5.0 & 7.2 & 0.9 \\\\\\\\\\n30\\\\,Dor & 0.3 & 0.04& 1.7 & 0.2 \\\\\\\\\\nCircinus & 21 & 1.9 & 3.9 & 0.4 \\\\\\\\\\nNGC\\\\,1068 & 2.1 & 0.1 & 1.1 & 0.06\\\\\\\\\\n\\\\noalign{\\\\smallskip}\\n\\\\hline\\n\\\\end{tabular}\\n\\\\end{flushleft}\\n$^1$ [10$^{-18}$ W/cm$^2$] \\\\\\\\\\n$^2$ PAH flux/continuum(11.6--11.9$\\\\mu$m)\\n\\\\end{table}\\n\\nIn Tables \\\\ref{tab:inventory} and \\\\ref{tab:invent_abs} \\nwe give an inventory of features that we believe to be reliable detections. \\nWe consider a detection reliable if the feature has an amplitude of at least\\n3$\\\\sigma$ of the noise level and if it fulfills the criteria described above.\\nWe also list a few uncertain detections in parantheses, e.g. features in\\ncompliance with the above criteria but with an amplitude of less than\\n3$\\\\sigma$ (but note that the definition of the local noise level is in many \\ncases somewhat uncertain).\\nMost of these features have been described before in reports of ISO-SWS\\nobservations of galactic template sources (e.g. Moutou et al. 1996, \\nVerstraete et al. 1996, \\nRoelfsema et al. 1996, Beintema et al. 1996). Here we highlight \\na few of their characteristics, source by source. In Sect. \\\\ref{s:ident}\\nwe briefly discuss possible identifications. Please note that many of \\nthe features are severely blended and thus the peak wavelengths given here are \\napproximate. \\n\\nWe also list the fluxes of four of the most prominent PAHs in\\nTables \\\\ref{tab:PAH_flux1} and \\\\ref{tab:PAH_flux2}. To measure these fluxes\\nwe defined continua by a linear interpolation between the following points: \\n2.50 and 3.65$\\\\mu$m for the 3.3$\\\\mu$m feature, 5.9 and 10.9$\\\\mu$m for the\\nfeatures at 6.2 and 7.7$\\\\mu$m, and 10.9 and 11.8$\\\\mu$m for the 11.3$\\\\mu$m\\nfeature. We then obtained the fluxes by integrating between the following band\\nlimits: 3.10--3.35$\\\\mu$m, 6.0--6.5$\\\\mu$m, 7.3--8.2$\\\\mu$m, and\\n11.1--11.7$\\\\mu$m. To give an indication of the relative contribution of these\\nfeatures to the infrared luminosity we also list their ratio to the continuum\\nflux in the range 11.6--11.9$\\\\mu$m. Due to the uncertainties involved in this\\nmeasuring process (continuum shape, feature profile, etc.) \\nall absolute and relative fluxes are only approximate.\\nBy definition, these fluxes ignore a possible, PAH-related `plateau' or\\n`continuum' in the 6--9 and 10--13$\\\\mu$m range (e.g. Boulanger et al. 1996).\\\\\\\\\\n\\n\\\\begin{figure*}\\n\\\\setcounter{figure}{1}\\n% \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{fig2a.eps}}\\n \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{sturm_fig2a.ps}}\\n \\\\vspace*{0.05cm} \\\\caption{Details of the spectra. Wavelength in $\\\\mu$m, flux \\n density in\\n Jansky.}\\n \\\\label{fig:details}\\n\\\\end{figure*} \\n\\\\begin{figure*}\\n\\\\setcounter{figure}{1}\\n \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{sturm_fig2b.ps}}\\n% \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{h1809.f2b}}\\n \\\\vspace*{0.05cm} \\\\caption{{\\\\it continued} }\\n\\\\end{figure*} \\n\\n%{\\\\vspace*{0.3cm} \\\\noindent \\\\bf M\\\\,82:} \\n{\\\\noindent \\\\bf M\\\\,82:} \\nM\\\\,82 is a small galaxy undergoing a very powerful\\nstarburst, and is considered to be\\na prototype of starburst activity.\\nDue to its proximity (3.63 Mpc, Freedman et al. 1994) it is the\\nbrightest galaxy in the infrared, with the infrared luminosity arising mainly\\nfrom warm dust in the central region.\\n%On the whole it is considered to be the prototypical starburst galaxy.\\nEmission features\\nat 8.7 and 11.3$\\\\mu$m were first detected by Gillett et al (1975), and the\\n3.3, 6.2 and 7.6$\\\\mu$m features by Willner et al. (1977).\\n%For more information on M\\\\,82 see e.g. Schreiber 1998????\\n\\nThe main PAH features are clearly seen in the\\nmid-infrared spectrum of M\\\\,82, shown in its entirety in Fig. 1\\nand in detail in the top panels of Fig 2. In addition,\\nthe spectrum shows a large number of weaker features\\nwhich have previously been detected with ISO only in\\ngalactic template sources.\\n\\nThe 3.3$\\\\mu$m feature has satellites at 3.4 and 3.5$\\\\mu$m.\\nIt also shows a blue asymmetry, which might be due to a feature at 3.25$\\\\mu$m\\n(see Beintema et al. 1996).\\nTwo weak features at 5.25 and 5.65$\\\\mu$m, that have been observed e.g. in\\nthe planetary nebula NGC\\\\,7027 (Beintema et al. 1996) and the\\nphotodissociation front of M\\\\,17 (Verstraete et al. 1996), are also present\\nin M\\\\,82.\\nThe 6.2$\\\\mu$m band has a red shoulder and\\nshows an additional feature at 6.0$\\\\mu$m.\\nThe 7.7$\\\\mu$m feature consists of two bands at 7.6 and 7.8$\\\\mu$m.\\nA significant contribution of 7.7$\\\\mu$m solid methane absorption \\n(e.g. Whittet et al. 1996, Lutz et al. 1996) to this strong dip between \\n7.6 and 7.8$\\\\mu$m is unlikely, since in M\\\\,82 related icy absorption features \\nare shallower and extinction is lower (Sect. \\\\ref{s:continuum}) than in the \\nsources with clear methane absorptions.\\nA weak feature is present at 10.6$\\\\mu$m, which is confirmed\\nin the average starburst spectrum of Lutz et al. 1998a\\n(their Fig. 1, independent ISOPHOT-S data), and probably related\\nto a feature seen by Beintema et al. (1996) in the spectrum of NGC\\\\,7027. \\nThe 11.3$\\\\mu$m feature peaks at 11.2$\\\\mu$m and shows the\\nwell-known asymmetric shape towards longer wavelengths (Witteborn et al.\\n1989).\\nThere is an additional component around 11.05$\\\\mu$m, much too strong to be\\nrelated to artifacts from the RSRF correction known to exist at this wavelength.\\nA weak feature may be present near 12.0$\\\\mu$m. \\nThe 12.7$\\\\mu$m feature is very prominent in M\\\\,82.\\nMoutou et al. (1998) found two emission features at 15.8 and 16.4$\\\\mu$m in\\nthe spectrum of the galactic reflection nebula NGC\\\\,7023. On the basis\\nof their laboratory work, they\\nattributed these features to PAH molecules.\\nThese two features are clearly seen in M\\\\,82, and in some of our other \\ntemplate spectra.\\nMore emission features can be found at still longer wavelenghts\\n(20.5 and 33-34$\\\\mu$m).\\n\\nIn addition we find two features that -- to our knowledge --\\nhave not been reported before: at 7.0 and 8.3$\\\\mu$m.\\nA feature around 7.0$\\\\mu$m is also present in NGC\\\\,253 (most clearly), and \\nperhaps in 30\\\\,Dor.\\nWe found the same feature in ISO-SWS \\nspectra of the cool, dusty envelopes of the planetary nebula He\\\\,2-113\\n(see e.g. Waters et al. 1998, their Fig. 2).\\nThe average ISOPHOT-S spectra of starburst and normal galaxies (Lutz et al.\\n1998a, Helou et al. 2000) also show hints of a weak feature, blended with\\nH$_2$ S(5) 6.91$\\\\mu$m and [Ar II] 6.99$\\\\mu$m (see also Sect. \\\\ref{s:lowres}). \\nThe 8.3 feature is also visible in\\nthe galactic template spectrum of NGC\\\\,7023 (Fig. \\\\ref{fig:m82vsngc7023}),\\nand perhaps in some of the compact HII regions shown in Roelfsema et al. (1996).\\nWe also want to mention here the 14.3$\\\\mu$m band. An astronomical observation \\nof this band has been reported only recently for the first time \\n(Tielens et al. 1999). It is present in all \\nour template spectra, with the\\nexception of NGC\\\\,1068, in NGC\\\\,7023, and perhaps also in some of\\nthe circumstellar PAH spectra shown in Beintema et al. (1996).\\n%It is weak but important because it can be confused with the [Ne V] fine\\n%structure line in spectra of low resolution (see Sec. \\\\ref{s:lowres}).\\nOn the other hand, our spectra do not show some of the \\nemission features that have been detected before \\nin astronomical observations,\\ne.g. at 4.65$\\\\mu$m (Verstraete et al. 1996) and \\n13.3$\\\\mu$m (Moutou et al. 1998).\\n\\n\\\\begin{figure*}\\n\\\\setcounter{figure}{1}\\n% \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{fig2c.eps}}\\n \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{sturm_fig2c.ps}}\\n \\\\vspace*{0.05cm} \\\\caption{{\\\\it continued} }\\n\\\\end{figure*} \\n\\\\begin{figure*}\\n\\\\setcounter{figure}{1}\\n% \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{fig2d.eps}}\\n \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{sturm_fig2d.ps}}\\n \\\\vspace*{0.05cm} \\\\caption{{\\\\it continued}. Broad features between 27.5 and \\n 29.5$\\\\mu$m, and longward of 40$\\\\mu$m cannot be trusted.}\\n\\\\end{figure*} \\n\\nThere are very few absorption features in our spectrum of M\\\\,82. The\\ntrough around 10$\\\\mu$m looks like a strong 9.7$\\\\mu$m silicate feature.\\nIn\\nSect. \\\\ref{s:continuum} we argue, however, that the trough is mainly due \\nto the strong PAH emission at 8.7 and 11.3$\\\\mu$m. \\nAlso, there is no clear signature \\nof a corresponding silicate absorption feature at 18$\\\\mu$m.\\nA broad absorption feature around 3.0$\\\\mu$m is probably due to H$_2$O-ice.\\nIts optical depth ($\\\\tau\\\\sim$0.2) is relatively small \\ncompared e.g. to the Galactic center ($\\\\tau$=0.5, Lutz et al. 1996, \\nChiar et al. 2000). However, \\nsince the overall extinction estimates differ in the same sense,\\nthis is consistent with the M\\\\,82 line of sight having properties similar to that\\ntowards the Galactic center: a mixture of diffuse ISM and molecular cloud\\nextinction, with some \\nvariance in the relative weight for different lines of sight\\n(Chiar et al. 2000). These properties seem to be quite typical for \\nstarburst galaxies, as we find similar conditions in NGC\\\\,253 (see below) \\nand in NGC\\\\,4945 (Spoon et al., in prep.).\\n\\nThe M\\\\,82 spectrum has the highest S/N ratio and\\nshows the largest number of features in our sample.\\nCombined with the ISO-LWS long wavelength spectrum (Colbert\\net al. 1999) it will be an important template for future missions.\\\\\\\\\\n\\n\\n{\\\\noindent \\\\bf NGC\\\\,253:}\\nNGC\\\\,253 is a nearby, almost edge-on barred spiral galaxy with a high level \\nof circumnuclear \\nstarburst activity. At optical wavelengths the galaxy is heavily obscured by\\ndust lanes in the central regions.\\n%The ionic emission lines in NGC\\\\,253 are quite different from their \\n%counterparts in M\\\\,82. E.g. the different [Ne III]/[Ne II] \\n%ratios point to differences in the average radiation field \\n%in these two starburst galaxies (Thornley et al. 2000).\\nThe ionic emission lines in NGC\\\\,253 are of lower excitation (e.g. lower\\n[Ne III]/[Ne II] ratio) than in M\\\\,82, suggesting a softer average\\nradiation field (Thornley et al., in prep.). \\nDespite these differences between the two galaxies, their \\nspectra of broad emission features are \\nremarkably similar. This is demonstrated in Fig. \\\\ref{fig:m82vsngc253}.\\nOnly beyond 9$\\\\mu$m does a difference in the underlying continuum \\nbecome obvious. NGC\\\\,253\\n%, which has the stronger radiation field,\\nhas a stronger continuum at these longer wavelengths. \\nIn starburst galaxies this underlying continuum is usually attributed to \\nvery small grains (VSG) of dust (e.g. D\\\\'esert et al. 1990). \\nIn Sect. \\\\ref{s:continuum} we will use the difference in the continua of\\nM\\\\,82 and NGC\\\\,253 to characterise the shape of the VSG continuum.\\n\\nTable \\\\ref{tab:inventory} shows that nearly all features of M\\\\,82 are also seen\\nin NGC\\\\,253. The very few exceptions may simply be due to the lower\\n%are probably just an issue of\\nS/N ratio of the NGC\\\\,253 spectrum.\\nThe red shoulder of the 6.2$\\\\mu$m band seen in M\\\\,82\\nis more prominent in NGC\\\\,253 and is probably due to an additional feature at\\n6.35$\\\\mu$m.\\nThe 3.0$\\\\mu$m ice absorption is also present, having an optical depth of\\n$\\\\tau\\\\sim$0.25.\\\\\\\\\\n\\n{\\\\noindent \\\\bf 30\\\\,Dor:}\\nThe 30\\\\,Dor region in the LMC is the largest, most\\nmassive, and most luminous H II region in the Local Group.\\nAs a local template for massive star\\nformation and its interaction with the interstellar medium, it is\\ninstructive to compare its spectrum to the galaxy spectra in\\nour sample.\\nA more detailed study of the mid-infrared fine structure emission lines in\\n30\\\\,Dor will be presented in an upcoming paper (Thornley et al., in prep.).\\n%For an introduction to 30\\\\,Dor, more details about the ISO-SWS\\n%observation, and a study of its mid-infrared\\n%fine structure emission lines see Thornley et al. 2000????\\n\\nAn inspection of Fig. \\\\ref{fig:details} and Table \\\\ref{tab:inventory} shows\\nthat the 30\\\\,Dor spectrum exhibits most of the PAH features found in the\\ngalaxy spectra. Lower S/N may contribute to\\nthe non-detection of some of the weak features.\\nCompared to the two starburst galaxies, the features in 30\\\\,Dor are\\nmuch weaker relative to the continuum (see also Tables \\\\ref{tab:PAH_flux1}\\nand \\\\ref{tab:PAH_flux2}) and show different ratios.\\nNote, for instance, the high 6.2/7.7$\\\\mu$m feature ratio, \\nthe unusually high 3.4/3.3 ratio ($\\\\approx$ 0.5, see also Sect. \\n\\\\ref{s:PAH_var}), the shape of the 7.6/7.8$\\\\mu$m features, or the complete\\nabsence of the 12.7$\\\\mu$m feature.\\nThese differences may be partly due to the fact, that the SWS apertures \\ncovered only part of the entire 30\\\\,Dor complex. Verstraete et al. (1996)\\nuse the case of M17 to demonstrate the strong variations in PAH spectra going\\nfrom the center of an H\\\\,II region to the surrounding photodissociation region. \\nOn the other hand, the similarity of the 30\\\\, Dor \\nspectrum to the integrated ISOPHOT-S spectrum of the dwarf galaxy NGC\\\\,5253 \\n(Rigopoulou et al. 1999) strongly suggests that the weakness of the PAHs is not\\nan aperture effect but reflecting an intrinsic property of very active\\nstar formation in a low metallicity environment.\\n\\nSilicate absorption at 9.7 and 18$\\\\mu$m is, if at all present, very weak.\\nNo other absorption features can be detected. \\\\\\\\\\n\\n{\\\\noindent \\\\bf NGC\\\\,1068:}\\nThe nearby, prototypical Seyfert 2 galaxy NGC\\\\,1068 is a key object in\\nthe investigation and modeling of active galactic nuclei (AGNs).\\nThe ISO-SWS observations were centered on the active nucleus, with the\\naperture\\ncovering very little of the\\ncircumnuclear star forming `ring', which has a radius of $\\\\approx$15\\\\arcsec.\\nIn stark contrast to the starburst templates we have shown, this active\\nnucleus spectrum shows very little PAH emission.\\nThe weaker features (e.g. 3.3, 6.2 or 12.7$\\\\mu$m)\\nare barely visible, if at all. \\n\\nThe continuum around 10$\\\\mu$m is strong because of a central warm component\\nheated by the AGN. Silicate absorption is clearly present, although centered\\nat 9.4$\\\\mu$m rather than \\nat 9.7$\\\\mu$m, but again surrounding weak PAH emission complicates its\\ninterpretation. \\nHydrocarbon absorption is seen at 3.4$\\\\mu$m (see also\\nBridger et al. 1994), in contrast to our starburst templates, where\\nit is not observed.\\nNote, however, that in M\\\\,82 and NGC\\\\,253 a similar absorption feature\\ncould plausibly\\nexist if the analogy to the Galactic center holds, but be filled in by \\nthe 3.3/3.4 PAH emission. On the other hand\\nM\\\\,82 and NGC\\\\,253 show an H$_2$O ice absorption at 3.0$\\\\mu$m which is\\ndefinitely absent in NGC\\\\,1068. \\nThese differences in absorption features are entirely plausible because of the\\ndifferent physical conditions in the obscuring regions. For the starbursts,\\nthey likely include diffuse ISM as well as molecular clouds that can host icy\\ngrains. Conversely, infrared polarimetry suggests that most of the \\nnear-infrared obscuration in NGC\\\\,1068 occurs within a few parsecs from the \\nnucleus, possibly in the torus (e.g. Packham et al. 1997). Such an energetic \\nenvironment will be much less favourable for the existence of icy grains.\\\\\\\\\\n\\n{\\\\noindent \\\\bf Circinus:}\\nThe Circinus Galaxy is a nearby spiral galaxy which shows Seyfert 2 activity\\n(e.g. Moorwood \\\\& Glass 1984, Oliva et al. 1994, Moorwood et al. 1996,\\nOliva et al. 1998). Due to its proximity (5 times closer than NGC\\\\,1068)\\nit has become another template object for the study of AGNs.\\nThe AGN is surrounded by circumnuclear\\nstar-forming regions, as is often the case in Seyfert nuclei residing in\\nspirals.\\nThe ISO-SWS observations were centered on the active nucleus, but contrary to\\nthe observations of NGC\\\\,1068 the apertures covered a significant amount of\\nthis circumnuclear star formation.\\nHence, most of the dust emission features seen in\\nthe starburst templates are also found in\\nCircinus, but with weaker line-to-continuum ratio (see the discussion in\\nSect. \\\\ref{s:PAH_var}). A peculiarity of the Circinus spectrum are the\\nvery pronounced features in the 20--22$\\\\mu$m region.\\n\\n\\nThe observation was performed very early in the mission, when the\\nobserving strategy was not yet fully optimized. For instance, exposures of\\nthe internal flux calibration lamps, preceeding observations of the scientific\\ntarget, caused memory effects in the immediately following scans.\\nThe low flux level of band 4 ($\\\\lambda \\\\ge$ 29$\\\\mu$m),\\nrelative to the preceding bands, is due to such a memory effect and an incorrect\\ndark current subtraction. The same might be true for the apparent features near\\n44$\\\\mu$m (which are not visible in the overlapping LWS spectrum). We did not \\nattempt to improve the dark current subtraction further since this would \\ninvolve subjective assumptions about the true dark current.\\n\\n%--------------------------------------------------------------------\\n\\\\section{Mid-infrared features and the physical state of the ISM}\\n\\n%--------------------------------------------------------------------\\n\\n\\\\subsection{Identification}\\n\\\\label{s:ident}\\n\\n\\\\subsubsection{The 2-13$\\\\mu$m region:}\\n\\nThe emission features in this wavelength range\\nhave been extensively studied with ISO in galactic objects during the last few\\nyears. Comprehensive discussions of their identifications and characteristics\\ncan be found e.g. in Beintema et al. (1996), Moutou et al. (1998), Roelfsema\\net al. (1996), and Verstraete et al. (1996).\\nThey are most often attributed to PAH molecules. This is supported by\\nrecent laboratory studies (e.g. Roelfsema et al. 1996, Moutou et al. 1996).\\nThe only features in this range, \\n%in Table \\\\ref{tab:inventory}, \\nwhich have not\\nbeen addressed in the\\nliterature so far, are the ones at 7.0 and 8.3$\\\\mu$m. \\nIn our sample of galaxies \\nthey are\\nunambiguously detected only in M\\\\,82 and NGC\\\\,253 (the 8.3$\\\\mu$m feature only\\nin M\\\\,82), but as mentioned in Sect.\\n\\\\ref{s:inventory} they seem to be present in other published spectra as well.\\n%Here we will not attempt to identify its carrier but \\nIt seems likely that they can be attributed to a PAH modes, too.\\n\\n\\\\subsubsection{Features between 13 and 20$\\\\mu$m:}\\n\\nFeatures in this range have attracted less attention in the past, because\\nthey are intrinsically weak (but see e.g. Beintema et al. 1996).\\nThese bands, however, are more sensitive to the molecular structure of PAHs,\\nsince they\\n%are due to skeletal vibration. \\ninvolve the motion of the molecule as a whole, therefore depending on the \\nexact species (L\\\\'eger et al. 1989).\\nHence, their observation could help to better\\nconstrain the composition of the interstellar mixture.\\nThe 13.6, 15.8, and 16.5$\\\\mu$m features are\\nalso visible in the spectra of NGC\\\\,7023 and have been attributed to PAH bands\\nin the past by Moutou et al. (1998), based on their laboratory work.\\nThe band at 14.3$\\\\mu$m has been tentatively attributed to a phenyl bending \\nmode by Tielens et al. (1999). \\nMoutou et al. (1996) list a feature at this wavelength in their composite\\nlaboratory spectrum of a mixture of PAHs. Although weak, it might cause\\nconfusion with [Ne V] in low resolution spectra (see Sect. \\\\ref{s:lowres}).\\nFinally, the weak feature at 14.8$\\\\mu$m (if real) could be due to the smallest \\nPAH, benzene (Tielens et al. 1999). \\n\\n\\n\\\\subsubsection{Features in the 20 to 45 $\\\\mu$m region:}\\n\\nThe number of modes in the laboratory PAH spectra of Moutou et al. (1996) \\ndecreases\\nwith increasing wavelength. Few species show emission beyond 20$\\\\mu$m, \\ne.g. near 21, 28 and 40$\\\\mu$m.\\nIn this wavelength range other sources must be taken into\\naccount. A number of recent papers have reported the detection of crystalline\\nsilicates (olivines, fosterite, pyroxene, etc.) in objects like \\nLuminous Blue Variables (Voors et al. 1999),\\ndusty circumstellar disks (Waelkens et al. 1996, Waters et al. 1996), or\\nPlanetary Nebulae (Waters et al. 1998).\\nIn particular the feature at 34$\\\\mu$m\\n%and 43$\\\\mu$m\\ncould be attributed to\\nthese kind of sources. However, one would expect to see emission\\nfeatures at e.g. 23, 28, 40 and 43$\\\\mu$m, as well; none of these features are\\nclearly detected in our spectra.\\nOn the other hand, even in some of the galactic templates, such as the\\nplanetary nebula NGC\\\\,6543 (e.g. Waters et al. 1996), not all of\\nthese features are present.\\n\\nA feature near 20.5$\\\\mu$m shows a striking variation in shape and central\\nwavelength between the galaxies. This is particularly surprising since \\nthe galaxy spectra include a mixture of many different regions, and may suggest\\na carrier occuring only transiently in very special conditions.\\nIn Circinus this feature is most prominent, and peaks at the bluest wavelength \\n(20.2$\\\\mu$m). Circinus also shows a second peak at 21.7$\\\\mu$m which \\nis absent in the other spectra. \\nA bump around 20.5$\\\\mu$m is also seen in ISO-SWS spectra of M supergiants \\n(Voors et al. 1999, Molster et al. 1999). \\nIt could be due to PAHs or alternatively metal\\noxides like FeO (Waters et al. 1996, Henning et al. 1995).\\nIRAS-LRS and ISO-SWS spectroscopy have also detected a broad feature, centered\\nat approximately 20.1$\\\\mu$m, in carbon rich stars (Volk et al. 1999,\\nGarc\\\\'{\\\\i}a-Lario et al. 1999, Szczerba et al. 1999). Possible candidates \\nthat have\\nbeen proposed include large PAH clusters or hydrogenated amorphous carbon\\ngrains, hydrogenated fullerenes, and nano-diamonds (see references in\\nVolk et al. 1999). However, compared to these detections, the\\nfeatures\\nin our spectra are much narrower.\\n\\nA mixture of fullerene molecules of different degree of hydrogenation (Webster\\n1995) might also explain the second peak in Circinus around 21.7$\\\\mu$m, \\nsince the emission\\npeak shifts from 23 for fully hydrogenated fullerene (C$_{60}$H$_{60}$)\\nto 19$\\\\mu$m for non-hydrogentated fullerene (C$_{60}$).\\n%This second feature is observed in our sample in\\n%the Circinus Galaxy only (OR IS IT IN 1068, too????). \\nNone of the other galaxies exhibit this feature, but\\n%However, the\\nthe SWS01 spectrum of NML Cyg (Voors et al. 1999) and of the galaxy\\nNGC4945 (S. Lord, private communication) also\\nshow a weak emission feature around 21.6--22$\\\\mu$m.\\n\\nThe broad plateau at 33--34$\\\\mu$m, i.e. under the strong lines of [Si II]\\nand [S III], could be affected by detector memory effects. To remove such a\\npossible instrumental effect we treated the two\\ndifferent scan directions of the SWS01 mode separately. \\nThe trailing wings of each line profile, i.e. the blue\\nwing for the scan with increasing wavelength, and the red wing for the scan\\ndecreasing in wavelength, are much more distorted by memory effects than\\nthe leading wings. Therefore, we cut out these trailing wings, before we\\naveraged the spectra of the two scan directions.\\nWe are\\nhence confident that most of the remaining plateau is real. Such a feature\\nhas been observed in many\\ngalactic targets and is generally attributed to crystalline silicates\\n(olivine, e.g. Waters et al. 1998).\\n\\n%A 44 FEATURE COULD ALSO BE H2O ICE\\n%Features at 21, 22: seen in NML Cyg (Voors et al.), metal oxides? (Waters 96,\\n%Henning 95). Nano-diamonds?\\\\\\\\\\n%Feature at 34, 43: NGC6543, Waters 1996, also \\n%NML Cyg (Justtanot, Waters 1996).\\n%A pyroxene at 34 would also show 23.5 and 40 (Waters 1998).\\n%43: crystalline ice, 34: olivine (Waters 1996)\\\\\\\\ \\n%Feature at 36: seen in HD100546 (Waelkens 1996), but this one also shows\\n%23.5 and 27 features, no 43. Unidentified/fosterite? (Waters 1996 \\n%table2/figure2).\\n%NGC6543 shows 34 and 43 but no 40 (Waters 96). NML Cyg shows 33, 40 and 43 \\n%(plus 21, 22).\\\\\\\\\\n%33 also seen in AG Car (Lamers 96). \\n%Molinari: 43 ice feature should be more at 44-45. If there is no 62 um \\n%feature it is probably amorphous ice not crystalline.\\n%Waelkens: According to Koike et al. (1993) a 28$\\\\mu$m peak is characteristic\\n%for all olivines. \\n\\n%No 4.65 um feature? No 13.1/13.3? (Verstraete/Moutou). No others????\\n\\n\\n\\n\\n%--------------------------------------------------------------------\\n\\\\subsection{Variation of PAH features}\\n\\\\label{s:PAH_var}\\n\\nPublished mid-IR spectra of galactic template sources show a significant\\nvariation of intrinsic\\nPAH ratios from source to source. For instance Roelfsema et al.\\n(1996) see a drastic change in the relative intensities of the 7.7 and 8.6\\nbands with increasing intensity or hardness of the radiation field.\\nSimilar changes are seen e.g. in different regions of M17\\n(Verstraete et al. 1996) or - for the 8.6/11.3 ratio - in the\\nreflection nebula NGC\\\\,1333 (Joblin et al. 1996).\\nPAHs exposed to intense and hard radiation fields can be ionized, lose\\nhydrogen atoms, or be photodissociated; any of these effects may contribute to\\n% which in turn can cause\\nthe observed variations in PAH ratios.\\nAccording to Joblin et al. (1996) the ionization is best traced by the 3.4/3.3\\nand 8.6/11.3 ratios. A good hydrogenation indicator is the (12+12.7)/11.3\\nratio. For instance, these authors find a high 3.4/3.3 ratio \\nof 0.1 in radiation fields that are 10$^5$ times the standard.\\n\\n\\nAnother important factor that can alter observed\\nPAH ratios is extinction. Extinction\\nwill suppress the 6.2, 8.6 and 11.3$\\\\mu$m features with respect to \\nthe one at 7.7$\\\\mu$m. \\nThe 12.7/11.3 ratio is similarly affected, since the 11.3 feature is\\nstill in the wing of the 9.7$\\\\mu$m silicate absorption. Details will depend\\non the applicable extinction law (see e.g. the Galactic center, Lutz et al. \\n1996). While extinction\\nclearly affects PAH spectra in highly obscured sources like Ultraluminous \\nInfrared Galaxies (ULIRGs, Lutz et al. 1998a) or the edge-on galaxy \\nNGC\\\\,4945 (Spoon et al., in prep.), its\\neffect will be less pronounced in the lower extinction sources of our sample.\\n\\nFinally, in active galaxies, such as NGC\\\\,1068 or the Circinus Galaxy, PAH\\nfeatures can be diluted by an AGN-powered hot dust continuum.\\nGenzel et al. (1998) and Lutz et al. (1998a) have used this as a diagnostic \\nof the power sources of ULIRGs.\\n\\nOur sample of galaxy spectra exhibits a similar trend in relative PAH\\nstrengths as the galactic templates.\\nM\\\\,82 and NGC\\\\,253 have high\\n3.4/3.3 ratios, consistent with them being active starburst galaxies.\\n30\\\\,Dor seems to have an even higher 3.4/3.3 ratio, but the S/N ratio is not\\nsufficient for a detailed analysis. However, a strong and hard, highly ionizing\\nradiation field in 30\\\\,Dor is consistent with the results of Thornley et\\nal. (1998), which are based on the ratios of fine structure emission lines,\\nlike [Ne III]/[Ne II]. In that context it is interesting to note again\\nthe complete absence of the 12.7$\\\\mu$m feature in 30\\\\,Dor.\\nIn the two starburst galaxies\\nM\\\\,82 and NGC\\\\,253 we see well-separated 7.6/7.8 and 8.6 features. The\\n8.6 band is much weaker than the 7.6/7.8 band, just as observed in `normal'\\nHII regions. In the Seyfert galaxy NGC\\\\,1068, however, the 8.6 band is similar\\nin strength to the 7.7 band, as it is seen in the\\nultracompact HII regions in M\\\\,17 (Cesarsky 1996b) or IRAS\\\\,18323-0242\\n(Roelfsema et al. 1996), where the UV radiation field is\\nextremely strong.\\n\\nNGC\\\\,1068, like many AGNs, shows an\\nadditional component of warm dust in the 10$\\\\mu$m region. Unified models for\\nSeyfert galaxies predict a dusty torus which would emit at these mid-infrared\\nwavelengths (e.g. Pier \\\\& Krolik 1992). Hence, an alternative interpretation\\nof the weak emission features on both sides of the silicate absorption might\\nbe self-absorbed silicate emission from the torus, i.e. the emissions we \\nidentified as PAH might simply be wings of a wide silicate emission maximum, \\nthe center of which is suppressed by absorption.\\nHowever, the observed double peaks at 7.7/8.6 and 11.05/11.25, as well as\\nthe distinct rise in flux near 7.3$\\\\mu$m are not reproduced by torus models\\nand show that there must be some\\nreal, although weak, PAH emission on top of the continuum.\\nThe weakness of the PAH emission can be understood in terms of dilution by the\\nhot dust continuum and destruction by the intense AGN radiation field.\\n\\n\\\\begin{figure*}\\n\\\\setcounter{figure}{2}\\n% \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{m82vsngc253.eps}}\\n \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{sturm_fig3.ps}}\\n \\\\caption{M\\\\,82 (full) versus NGC\\\\,253 (dash-dotted). In both spectra narrow\\n emission lines have been masked out. Both spectra have been smoothed and \\n corrected for zodiacal light and for their red shift. The spectrum of NGC\\\\,253\\n has been multiplied by 2.6 to normalize the 7.6$\\\\mu$m PAH to the one in \\n M\\\\,82.}\\n \\\\label{fig:m82vsngc253}\\n\\\\end{figure*} \\n\\\\begin{figure*}\\n \\\\setcounter{figure}{3}\\n% \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{m82vsngc7023.eps}}\\n \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{sturm_fig4.ps}}\\n \\\\caption{M\\\\,82 (full) versus the galactic reflection nebulae NGC\\\\,7023\\n (dash-dotted). Both spectra have been corrected\\n for zodiacal light and for their red shift. The spectrum of NGC\\\\,7023 \\n has been smoothed and multiplied by 3.25 to normalize the 7.6$\\\\mu$m PAH to \\n the one in M\\\\,82.}\\n \\\\label{fig:m82vsngc7023}\\n\\\\end{figure*} \\n\\\\begin{figure*}\\n \\\\setcounter{figure}{4}\\n% \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{m82sim.eps}}\\n \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{sturm_fig5.ps}}\\n \\\\caption{M\\\\,82 (full) versus NGC\\\\,7023 x 3.25 + power law (dashed).\\n The spectra of NGC\\\\,7023 (dash-dotted) and M\\\\,82 have been smoothed. \\n The power law component (dash-dotted) takes into account the aperture \\n change at 12$\\\\mu$m (x 1.3).}\\n \\\\label{fig:m82sim}\\n\\\\end{figure*} \\n\\nNGC\\\\,1068 has a circumnuclear starburst region, and\\nsome of the PAH emission might be picked up from this region by the large\\nSWS aperture. The match in shape with the (small-aperture)\\nground-based data of Roche et al. (1984) in the 8-13$\\\\mu$m range, and\\ncomparisons to ground-based CO maps,\\nsuggest that this effect is of minor importance here.\\n\\nIn the Circinus Galaxy the 7.7/8.6 ratio is somewhere in\\nbetween the two extrema M\\\\,82 and NGC\\\\,1068.\\nThe feature/continuum ratio of the PAH features,\\nhowever, is much higher in Circinus than in NGC\\\\,1068. We attribute this to\\nthe fact that in the case of Circinus the large SWS aperture\\nindeed picked up parts of the well-known circumnuclear star forming region.\\n%in Circinus.\\n\\n%Cesarsky (M17): a broad, smooth emission instead of the usual well-defined \\n%7.7 and 8.6 bands is similar to M17 ultracompact HII region or protoplanetary \\n%nebulae like IRAS 22273+5435 where the UV radiation field is extremely strong.\\n%==> NGC\\\\,1068 does not pick up starburst ring, but shows PAHs in high radiation \\n%environment (see also 1068 publication by Lutz).\\n%While there exists an underlying continuum... another continuum starts at 15um\\n%in regions of high radiation fields (see also Boulanger). Visible in 1068?\\n \\n%Roelfsema: The most dramatic change in relative intensities is seen \\n%between the 7.6 and 8.6 bands. Similar to 8.6/11.3 (Joblin).\\n%Non-compact PAHs enhance 8.6 relative to 7.6: less stable, occurs in sources\\n%with higher luminosity/excitation. See their lab work.\\n\\n%--------------------------------------------------------------------\\n\\\\section{Continuum placement and the depth of the silicate feature}\\n\\\\label{s:continuum}\\n\\nAn important diagnostic in many extragalactic studies is the depth of the\\nsilicate absorption feature at 9.7$\\\\mu$m and the extinction derived from it.\\nHowever, the presence of strong PAH bands\\non both sides of the 9.7$\\\\mu$m\\nsilicate feature makes it very difficult to estimate the continuum level\\nand the true depth of the silicate absorption.\\nIn particular ground-based 8--13$\\\\mu$m data suffer from this problem.\\nBecause of their continuous wavelength coverage ISO-SWS01 spectra are\\nwell suited to shed more light on this question.\\nIn the following we will discuss this issue using the example of M\\\\,82.\\n\\nFirstly, evidence against a strong 9.7$\\\\mu$m absorption comes \\nfrom the absence of a strong 18$\\\\mu$m silicate absorption (see Fig. 1).\\nAccording to Draine \\\\& Lee (1984) the expected ratio \\n$\\\\tau_{sil}$(18$\\\\mu$m) / $\\\\tau_{sil}$(9.7$\\\\mu$m) is 0.4.\\nFurthermore an analysis of hydrogen recombination lines in the ISO range\\nyields a moderate A$_V$(gas)$\\\\approx$ 5 mag (for a uniform screen \\nmodel - see Schreiber 1998). \\n\\nNext we come back to the comparison of the M\\\\,82 spectrum to the spectrum of\\nNGC\\\\,253 (Fig.\\n%\\\\ref{fig:m82vsngc253}\\n3). The two galaxies are similar\\nin A$_V$ and exhibit a very similar PAH spectrum. The only distinction appears\\nto be a stronger VSG continuum in NGC\\\\,253. A strong\\nrise of the continuum in this range is typical for regions of intense\\nUV flux\\n(e.g. D\\\\'esert et al. 1990, Vigroux et al. 1996) \\\\footnote{The spectrum of \\nNGC\\\\,253 indicates lower ionization\\n(e.g. low [Ne III]/[[Ne II]), but due to the compactness of the starburst in\\nNGC\\\\,253 the radiation field here is more intense than in M\\\\,82.}.\\nThe difference between both spectra\\ncan be well fit by a power-law continuum that begins to rise at approximately\\n8--9$\\\\mu$m.\\n \\nFinally, we\\ncompare our spectrum\\nof M\\\\,82 to the SWS01 spectrum of the galactic reflection nebula NGC 7023.\\nLittle extinction is expected in the line of sight to this nebula.\\nThe continuum under the PAH bands\\nin NGC 7023 is very weak and starts to grow only beyond 20$\\\\mu$m (Moutou et\\nal. 1998).\\nThe flux density around 10$\\\\mu$m is almost on the same level as the flux\\ndensity shortward of the 6$\\\\mu$m PAH band and at 15--20$\\\\mu$m.\\n%(A similar behaviour is observed in many compact HII regions, Roelfsema et\\n%al. 1996). \\nIt could be explained by an underlying PAH plateau, or by\\nthe wings of the 7.7/8.6 and 11.3 PAH\\nfeatures (which can be represented by Lorentz profiles - Boulanger et al. 1998,\\nMattila et al. 1999).\\nWe therefore assume that in NGC\\\\,7023 this region consists\\nmainly of emission bands, with little or no continuum and silicate absorption.\\nIn Fig.\\n%\\\\ref{fig:m82vsngc7023}\\n4 we overplot the (smoothed) NGC\\\\,7023 spectrum on that of M\\\\,82. The NGC\\\\,7023\\nspectrum has been multiplied by a factor 3.25 in order to normalize the\\nPAH emission feature at 7.6$\\\\mu$m to the one in M\\\\,82.\\nThe 3.3 and 11.3$\\\\mu$m bands\\nin M\\\\,82 are weaker compared to NGC\\\\,7023. This might be explained\\ne.g.\\nby the harder radiation field in M\\\\,82 (Joblin et al. 1996, see \\nSect. \\\\ref{s:PAH_var}).\\n%Also, there might be a bit higher extinction in M\\\\,82, as indicated by the\\n%slightly different 6.2$\\\\mu$m features (????).\\nApart from this the two spectra are remarkably similar.\\n%in the range up to 11$\\\\mu$m.\\nOnly \\n%beyond approximately 9$\\\\mu$m \\nat higher wavelengths\\na component of hot, small dust grains starts to add to the M\\\\,82\\ncontinuum, as expected due to the much harder radiation field in M\\\\,82.\\n\\nIn view of these arguments we constructed a toy model in order to reproduce\\nthe observed\\nspectrum of M\\\\,82. The model simply consists of the scaled spectrum of\\nNGC\\\\,7023 plus a power-law continuum which starts at 8.5$\\\\mu$m \\n($f\\\\propto(\\\\lambda - 8.5)^{\\\\alpha}$).\\nWe use a power-law rather than a black body curve for sake\\nof simplicity. A power-law produces a very good fit to the continuum up to \\n20 -- 25$\\\\mu$m. A black-body curve would be more problematic, because\\nthe dust may not have a single temperature, and might not be in thermal \\nequilibrium.\\nM\\\\,82 is an extended source for the SWS apertures. There is a flux jump\\naround 12$\\\\mu$m by a factor of about 1.3, corresponding to a similar change\\nin aperture size. \\nWe hence multiplied the power law continuum by 1.3 longward of 12$\\\\mu$m\\n\\\\footnote{A more accurate correction for the change in aperture size would have\\nto assume a light distribution (as a function of wavelength) and a model of\\nthe instrument beam profile. Such a correction tool is not yet available.}.\\nThe free parameters - the scaling factors for the\\nNGC\\\\,7023 spectrum and the power law, plus the power law index - were adjusted \\nby hand; we did not pursue a formal fit.\\n%, since it is not needed for our purposes.\\nFig.\\n%\\\\ref{fig:m82sim}\\n5 shows, that this simple model matches the observed\\nspectrum remarkably well. There is no need to invoke any kind of extinction.\\nDue to the uncertainties in the spectra, however, there is room for a moderate\\nextinction,\\nin accordance with the results from the recombination line studies (A$_V$ \\n$\\\\approx$ 5 mag).\\nA slightly different power-law, modified by a modest amount of extinction,\\ncould fit the spectrum equally well.\\nHowever,\\na strong overall extinction, as deduced from the ground based 8-13$\\\\mu$m data\\n(A$_V$ = 15--60 mag, Gillett et al. 1975), is clearly incompatible\\nwith the new ISO data. This is an example of the potential danger of\\noverestimating the silicate absorption depth in baseline-limited data.\\n\\n%--------------------------------------------------------------------\\n\\\\section{The interpretation of low resolution spectra}\\n\\\\label{s:lowres}\\n\\\\begin{figure*}\\n\\\\setcounter{figure}{5}\\n% \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{fig6.eps}}\\n \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{sturm_fig6.ps}}\\n% \\\\hfill\\n% \\\\parbox[b]{55mm}{\\n \\\\caption{The ISO-SWS spectra of M\\\\,82 and NGC\\\\,1068, \\n smoothed to a resolution of 50 \\n to simulate the ISOCAM-CVF and SIRTF-IRS (low resolution mode) spectrometers.\\n Wavelength in $\\\\mu$m, flux density in\\n Jansky.\\n The feature at 14.3$\\\\mu$m in M\\\\,82 is NOT [Ne V] (see text).}\\n \\\\label{fig:m82lowres}\\n% }\\n\\\\end{figure*} \\n%\\\\begin{figure*}\\n% \\\\setcounter{figure}{6}\\n% \\\\resizebox{\\\\hsize}{!}{\\\\includegraphics{ngc1068lowres.eps}}\\n% \\\\caption{The ISO-SWS spectrum of NGC\\\\,1068, smoothed to a resolution of 50 \\n% to simulate the CAM-CVF and SIRTF-IRS (low resolution mode) spectrometer.}\\n% \\\\label{fig:ngc1068lowres}\\n%\\\\end{figure*} \\nMany ISO spectra of galactic and extragalactic objects have been\\ntaken in low resolution mode (ISOPHOT-S, ISOCAM-CVF). Also, surveys\\nwith future mid- and far-infrared space missions, e.g. of galaxies at higher\\nredshifts, will likely be\\nperformed with a relatively low resolution. For example\\nthe IRS spectrometer on board\\nSIRTF will have a resolution of approximately 50--100 \\n(plus a medium resolution mode of R=600) in a wavelength range similar to \\nISO-SWS.\\nIn this low resolution mode SIRTF-IRS, being much more sensitive \\nthan ISO-SWS, will be a unique tool to detect emission features in spectra of \\nfaint high-z galaxies.\\nLow resolution spectra, however, suffer from possible identification\\nand interpretation problems caused by coincidences of\\natomic/ionic lines and solid state features.\\nIn our high resolution SWS01 galaxy spectra lines and features are well\\nseparated, and we can use these spectra as templates to identify and highlight\\nthe importance of possible confusion problems.\\nIn Fig. 6\\n%\\\\ref{fig:m82lowres}\\n%6 and\\n%\\\\ref{fig:ngc1068lowres}\\n%7 \\nwe have smoothed and rebinned the M\\\\,82 and NGC\\\\,1068 spectra\\nto a resolution of 50 to simulate e.g. an ISOCAM-CVF or a SIRTF-IRS spectrum.\\n\\n\\\\begin{table}\\n\\\\caption[]{\\\\label{tab:ne2_vs_pah} The flux ratio of PAH 12.7 / [Ne II] 12.8}\\n\\\\begin{flushleft}\\n\\\\begin{tabular}{ll}\\n\\\\hline\\\\noalign{\\\\smallskip}\\nObject & PAH 12.7/[Ne II] 12.8\\\\\\\\\\n\\\\noalign{\\\\smallskip}\\n\\\\hline\\\\noalign{\\\\smallskip}\\nM\\\\,82 & 0.96\\\\\\\\\\nNGC\\\\,253 & 1.32\\\\\\\\\\n30\\\\,Dor & 0.00\\\\\\\\\\nCircinus & 6.17\\\\\\\\\\nNGC\\\\,1068 & 0..1$^a$\\\\\\\\\\n\\\\noalign{\\\\smallskip}\\n\\\\hline\\n\\\\end{tabular}\\n\\\\end{flushleft}\\n\\\\begin{list}{}{}\\n\\\\item[$^{\\\\rm a}$] exact value difficult to measure, due to the broad wing of \\n the [Ne II] line and the relatively strong noise. \\n\\\\end{list}\\n\\\\end{table}\\nIn Table \\\\ref{tab:inventory} we have indicated possible confusions with\\nnearby molecular, atomic, and ionic lines. We want to mention three lines in \\nparticular: \\n[Ar II] at 6.99$\\\\mu$m, which might be \\nconfused with the underlying PAH emission (and the nearby H$_2$ S(5) line), \\n[Ne II] at 12.8$\\\\mu$m, which in \\nfact has been confused in the past with the underlying 12.7$\\\\mu$m PAH feature,\\nand [Ne V] at 14.3$\\\\mu$m, which also has been\\nconfused in the past with the nearby PAH emission.\\nTo get an indication of the relative contributions of the 12.7$\\\\mu$m \\nPAH flux\\nand the [Ne II] line flux to the combined (line plus feature) flux in low \\nresolution spectra\\nwe have measured both fluxes in our high resolution spectra.\\nTable \\\\ref{tab:ne2_vs_pah} summarizes the ratios of\\nPAH/[Ne II] in all 5 templates. The values\\nvary widely: in 30\\\\,Dor\\nthe flux is solely due to\\n[Ne II], whereas in Circinus [Ne II] contributes \\nonly about 15\\\\% of the combined flux. For the 7.0$\\\\mu$m feature,\\nwe find that the broad feature contributes 25\\\\% of the combined flux of\\nfeature, H$_2$, and [Ar II] in NGC\\\\,253.\\n%varies in a wide range. In 30\\\\,Dor the flux is solely due to\\n%[Ne II], whereas in Circinus [Ne II] contributes only about 15\\\\% to the\\n%combined flux.\\n%For the 7.0$\\\\mu$m feature we find a contribution of $\\\\approx$ 25\\\\% to the\\n%combined flux of feature, H$_2$ and [Ar II] in NGC\\\\,253.\\n\\nIn the low resolution representation of\\nM\\\\,82 in\\nFig.\\n%\\\\ref{fig:m82lowres}\\n6 the shape of the 14.3$\\\\mu$m \\nPAH resembles very much the shape of an unresolved\\nline like the [Ne III] line\\nat 15.5$\\\\mu$m and can be mistaken as [Ne V]. \\nThe high resolution spectrum of M\\\\,82 (Fig. 2) clearly shows, that\\nthere is no \\\\mbox{[Ne V]} at 14.32$\\\\mu$m but an \\nemission feature plus a weak line of \\\\mbox{[Cl II]} 14.37$\\\\mu$m.\\nOf all the strong fine structure emission lines\\nonly few lines remain unambiguously detectable in low resolution\\nspectra, like Br\\\\,$\\\\beta$, Br\\\\,$\\\\alpha$, [Ne III] 15$\\\\mu$m,\\n\\\\mbox{[S III]} 18.7, 33.5$\\\\mu$m, and [Si II] 34.8$\\\\mu$m in M\\\\,82, or\\n[O IV] 26$\\\\mu$m and perhaps [Ne V] 24$\\\\mu$m, and [S IV] 10.5$\\\\mu$m in \\nNGC\\\\,1068.\\nClearly, low resolution spectra are very well suited for PAH and continuum\\nmeasurements. However, flux measurements of narrow lines, and -- in some cases\\n-- even their identification, can be very difficult. For these purposes higher\\nresolutions, as for instance provided by the R=600 mode of the SIRTF \\nspectrometer, are definitely needed.\\n\\n\\n%--------------------------------------------------------------------\\n\\\\section{Conclusions}\\n\\\\label{s:conclusions}\\n\\nWe have detected a large number of mid-infrared features in galaxy spectra, \\nsome of them previously unobserved, and discussed the dependence of the\\ndust features on ISM condition in galaxies.\\nThe spectral features vary considerably from source to source in \\npresence and relative strength. Emission features are largely absent in \\nthe intense radiation field close to an AGN, and weak in a\\nlow metallicity, intensely star forming environment.\\nDifferences in the absorption spectra point to different\\nphysical properties of the obscuring regions in starburst and active galaxies.\\n\\nThe spectra presented here will be valuable template spectra for future\\nmid- and far-infrared space missions such as SIRTF, SOFIA or FIRST. \\n%They can be used for simulations of observations and for estimating\\n%exposure times.\\nThey\\nprovide important clues for the identification and interpretation of high\\nredshift, dusty galaxies.\\n%, which supposedly contain a large amount of dust.\\nThe strongest PAH features can be used to provide redshift information in \\nfar-infrared photometric\\ngalaxy surveys (Simpson \\\\& Eisenhardt 1999, see also the example of\\n21396+3623, Rigopoulou et al. 1999). Furthermore, they affect\\ngalaxy number counts.\\nFor instance, Xu et al. (1998) have constructed semi-empirical galaxy SEDs\\nto model the considerable PAH effects on number counts and redshift distributions.\\n%The improved data reductions\\n%and additional sources presented here might help to further constrain, refine\\n%and test this kind of models (e.g. Xu et al. assumed no 3.3 feature and no\\n%features beyond 13$\\\\mu$m). \\\\\\\\\\n%GEORGE: DO YOU THINK THIS IS RELEVANT???? DID YOU EVER TEST THESE MODELS\\n%AGAINST CIRCINUS????\\nFinally, the continuum and the PAH features can be used to distinguish \\nbetween starburst activity and active nuclei in high redshift galaxies, as\\nhas been demonstrated for local infrared bright galaxies (Genzel et al. 1998,\\nLutz et al. 1998a, Rigopoulou et al. 1999).\\n\\nThe advantage of the wide wavelength coverage of the SWS spectra has been\\nused to\\nillustrate the problem of the continuum definition and the true depth of the\\nsilicate absorption.\\nWe find that in our starburst templates the hot VSG dust continuum begins to\\nrise around 8 to 9$\\\\mu$m,\\nand that it can be well fitted by a simple power-law up to 20...25$\\\\mu$m.\\nFinally we have demonstrated possible line identification problems in low\\nresolution spectra.\\n\\nThe spectra presented here are available in electronic form from the authors.\\nWe want to note again, that different parts of the spectra were\\nobserved through different aperture sizes, which should be taken into account\\nfor a detailed use as template spectra.\\n\\n\\n%--------------------------------------------------------------------\\n\\\\begin{acknowledgements}\\nWe wish to thank George Helou for very fruitful discussions, and Bernhard\\nBrandl for support with the SIRTF-IRS simulations.\\n SWS and the ISO Spectometer Data Center at MPE are supported by\\n DLR under grants 50 QI 8610 8 and 50 QI 9402 3. \\nThe ISO Spectral Analysis Package \\n(ISAP) is a joint development by the LWS and SWS Instrument Teams and Data \\nCenters. 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B., Fang F., \\net al. 1998, ApJ 508, 576 \\n\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":193,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002196"},"title":{"kind":"string","value":"Neutrino Pair Annihilation in the Gravitation of Gamma Ray Burst Sources"},"authors":{"kind":"list like","value":[{"author":"Katsuaki Asano and Takeshi Fukuyama"}],"string":"[\n {\n \"author\": \"Katsuaki Asano and Takeshi Fukuyama\"\n }\n]"},"abstract":{"kind":"string","value":"We study semianalytically the gravitational effects on neutrino pair annihilation near the neutrinosphere and around the thin accretion disk. For the disk case, we assume that the accretion disk is isothermal and that the gravitational field is dominated by the Schwarzschild black hole. General relativistic effects are studied only near the rotation axis. The energy deposition rate is enhanced by the effect of orbital bending toward the center. However, the effects of the redshift and gravitational trapping of the deposited energy reduce the effective energy of the gamma ray bursts' source. Although each effect is substantial, the effects partly cancel one another. As a result, the gravitational effects do not substantially change the energy deposition rate for either the spherical symmetric case or the disk case."},"latex":{"kind":"list like","value":[{"name":"paper.TEX","string":"%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\n%\t Neutrino Pair Annihilation as a Source of Gamma Ray Bursts\n%\n%\n%\n%\n%\t Katsuaki ASANO & Takeshi FUKUYAMA\n%\n% 12nd June 1999\n%\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\documentstyle[12pt,aasms4]{article}\n%\\setlength{\\textwidth}{19cm}\n%\\setlength{\\oddsidemargin}{-1cm}\n\\begin{document}\n\n\n\\vspace*{0.5cm}\n\n\\title{Neutrino Pair Annihilation in the Gravitation of Gamma Ray Burst Sources}\n\n\\author{Katsuaki Asano and Takeshi Fukuyama}\n\n\n\\vspace{2cm}\n\n\\affil{Department of Physics, Ritsumeikan University\\\\\nKusatsu, Shiga 525-8577, Japan}\n\n\\affil{\\footnotesize e-mail: sph10001@se.ritsumei.ac.jp}\n\n\\vspace{2cm}\n\n\\baselineskip=16pt\n\n\\abstract{We study semianalytically\nthe gravitational effects on neutrino pair annihilation\nnear the neutrinosphere and around the thin accretion disk.\nFor the disk case, we assume that the accretion disk is isothermal\nand that the gravitational field is dominated by the Schwarzschild black hole.\nGeneral relativistic effects are studied only near the rotation axis.\nThe energy deposition rate is enhanced by\nthe effect of orbital bending toward the center.\nHowever, the effects of the redshift and gravitational trapping\nof the deposited energy reduce the effective energy of the gamma ray bursts' source.\nAlthough each effect is substantial,\nthe effects partly cancel one another.\nAs a result, the gravitational effects do not substantially change the\nenergy deposition rate for either the spherical symmetric case or the disk case.}\n\n\\vspace{0.5cm}\n\n\\noindent{\\it Subject headings}: accretion, accretion disks---black hole physics---gamma rays: bursts\n\n\n\\newpage\n\n\n\\section{INTRODUCTION}\n\n\\indent\n\nThe relativistic fireball (Shemi \\& Piran 1990; Rees \\& M\\'esz\\'aros 1992;\nM\\'esz\\'aros \\& Rees 1993; Sari \\& Piran 1995; Sari, Narayan \\& Piran 1996)\nis one of the most promising models of gamma ray bursts (GRBs).\nHowever, even if the fraction of the baryon rest energy is only $10^{-3}$\nin the fireball, the relativistic bulk flow, which is\nindispensable to GRBs, cannot be realized.\nNotwithstanding the very high energy phenomenon ($10^{52}$ ergs), the baryon\ndensity in the fireball must be extremely small.\nThis is the famous baryon contamination problem and still remains unsolved.\nThus the central engine of GRBs is still beyond\ndeep mist.\nThe source of GRBs may be one super massive\n(failed) supernovae (Woosley 1993; Paczy\\'nski 1998)\nor may be a merger of two neutron stars or of a neutron star and a black hole\n(e.g. Eichler et al. 1989; Narayan, Paczy\\'nski \\& Piran 1992;\nM\\'esz\\'aros \\& Rees 1992a; Katz 1997; Ruffert \\& Janka 1998, 1999).\n\nIn these compact high energy objects,\nthe neutrino-antineutrino annihilation\ninto electrons and positrons\n(hereafter neutrino pair annihilation)\nis a possible and important candidate to explain the energy source of GRBs\n(Paczy\\'nski 1990; M\\'esz\\'aros \\& Rees 1992b; Janka \\& Ruffert 1996;\nRuffert et al. 1997; Ruffert \\& Janka 1998, 1999).\nMotivated by the delayed explosion of Type II supernovae,\nthe energy deposition rate due\nto the neutrino pair annihilation above the neutrinosphere\nhas been calculated\n(Goodman, Dar \\& Nussinov 1987; Cooperstein, Van Den Horn \\& Baron 1987;\nBerezinsky \\& Prilutsky 1987).\nThe energy deposition rate is proportional to $r^{-8}$ ($r$\nis the distance from the center of the neutrinosphere) for a large $r$,\nand almost all deposition occurs near the neutrinosphere.\nAs they themselves noted in their paper,\nGoodman et al. (1987) neglected the general\nrelativistic effects on the energy deposition rate, which may change\ntheir numerical value seriously.\nIn simulations of the neutrino pair annihilation rate,\nit is very important to confirm whether or not the energy deposition\nrate is altered or not by the gravitational effects.\nIn the recent study, Salmonson \\& Wilson (1999)\nconcluded that the energy deposition rate in Type II\nsupernovae is enhanced about 4 times as a result of the gravitational effects.\nWe must check whether or not their results can be applied to the central engine\nof GRBs.\n\n\nOne of the most probable candidates for the central engine of GRBs\nis the accretion disk around a black hole (Woosley 1993; Popham, Woosley \\& Fryer 1999;\nMacFadyen \\& Woosley 1999; Ruffert \\& Janka 1999).\nThe system of an accretion disk and a black hole may be formed\nby the merging of two neutron stars,\nthe merging of a black hole and a neutron star,\nor the failed supernovae.\nIn general, the baryon density has the lowest value along the rotation axis\njust above the black hole (e.g. see Ruffert \\& Janka 1999).\nThis region might be a key to resolving the baryon contamination problem.\nThe hot accretion disk emits neutrinos and antineutrinos.\nThe energy deposited in the lowest density region is a candidate for\nthe central engine of GRBs.\nUsing hydrodynamic simulations,\nRuffert \\& Janka (1999) showed that the neutrino pair annihilation deposits \nenergy in the vicinity of the torus at a rate of $(3-5)\\times 10^{50}$ ergs ${\\rm s^{-1}}$.\nThey concluded that the gravitational effect on the energy deposition rate\naround the accretion disk is small.\nWe must supplement their results from the analytical side.\n\nIn various arguments on the energy deposition in the central engine of GRBs,\nthe order estimation of the deposited energy is sufficient, at least at present.\nIn this article, based on simple models, we study semianalytically\nthe gravitational effects on the energy deposition rate for two cases.\nIn one case neutrinos are emitted spherically symmetrically.\nIn the other case the hot accretion disk emits neutrinos.\nWe have derived the gravitational effects on the former case independently of\nSalmonson \\& Wilson (1999).\nSome differences of our work from Salmonson \\& Wilson in the formulation,\nthe interpretation of the energy deposition, and the additional factor are\nmentioned.\nAs for the disk case, we assume that the accretion disk is isothermal\nand that the gravitational field is dominated solely by the central\nSchwarzschild black hole.\nThese assumptions enable us to treat the energy deposition around the disk\nsemianalytically.\nThus, in both two cases gravitation is described by the Schwarzschild metric,\nand the essential differences between the two cases\ncome from the shape of the neutrino emitters.\n\nThe gravitational effects consist of three factors:\nthey are the bending of neutrino\ntrajectories, the gravitational redshift, and the trapping of deposited\nenergy into the central gravitational source.\nWe show that the energy deposition rate is indeed enhanced rather crucially by\nthe effect of neutrino bending.\nHowever, it is also shown that the gravitational redshift and the trapping\nof the deposited energy reduce this enhancement.\nAs a result, the gravitational effects do not substantially change the\nenergy deposition rate for either the spherical symmetric case or the disk case.\n\n\n\nThis paper is organized as follows. In section two we investigate\nneutrino pair annihilation near the neutrinosphere.\nThe same process around the accretion disk is\ndiscussed in section three. The last section is devoted to conclusions.\n\n\n\\section{NEUTRINO PAIR ANNIHILATION NEAR THE NEUTRINOSPHERE}\n\n\\indent\n\nIn this section we study the general relativistic effects on\nneutrino pair annihilation near the neutrinosphere.\nThis study has been already done by Salmonson \\& Wilson (1999).\nUsing another method, we formulate the same problem independently of\nthe work of Salmonson \\& Wilson.\nSome alterations in the interpretation of the energy deposition\nin Salmonson \\& Wilson are mentioned.\n\nThe number of reaction, $\\nu+\\bar{\\nu} \\to e^+ +e^-$,\nper unit volume per unit time (Goodman, Dar \\& Nussinov 1987) is written as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\frac{dN(\\mbox{\\boldmath$r$})}{dt dV}=\n\\int \\int f_{\\nu}(\\mbox{\\boldmath$p$}_{\\nu}, \\mbox{\\boldmath$r$})\nf_{\\bar{\\nu}}(\\mbox{\\boldmath$p$}_{\\bar{\\nu}}, \\mbox{\\boldmath$r$})\n\\sigma \\left| \\mbox{\\boldmath$v$}_{\\nu}-\\mbox{\\boldmath$v$}_{\\bar{\\nu}} \\right|\nd^3 \\mbox{\\boldmath$p$}_{\\nu} d^3 \\mbox{\\boldmath$p$}_{\\bar{\\nu}}.\n\\label{first}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%%\nHere $f_{\\nu}$ ($f_{\\bar{\\nu}}$) is the number density of neutrinos\n(antineutrinos) in phase space,\n$\\mbox{\\boldmath$v$}_{\\nu}$ ($\\mbox{\\boldmath$v$}_{\\bar{\\nu}}$)\nis the velocity of neutrinos (antineutrinos),\nand $\\sigma$ is the rest-frame cross section.\nThe left handside of equation (\\ref{first}) is Lorentz invariant,\nsince both the numerator, $dN$, and denominator, $dt dV=\\sqrt{-g} d^4 x$,\nare Lorentz invariant.\nSince $f_{\\nu}$ and $d^3 \\mbox{\\boldmath$p$}_{\\nu}/\\varepsilon_{\\nu}$\n(where $\\varepsilon_{\\nu}$ is the proper energy of neutrinos) of the right handside\nare also Lorentz invariant,\n$\\varepsilon_{\\nu} \\varepsilon_{\\bar{\\nu}}\n| \\mbox{\\boldmath$v$}_{\\nu}-\\mbox{\\boldmath$v$}_{\\bar{\\nu}} | \\sigma$\nshould be Lorentz invariant.\nThe latter is written in a manifest Lorentz-invariant form as\n$ \\sigma c^3 (p_{\\nu} \\cdot p_{\\bar{\\nu}})$,\nwhere $(p_{\\nu} \\cdot p_{\\bar{\\nu}})$ is the inner product of the 4-momenta.\nThe standard model predicts that the cross section is expressed as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\sigma=2 c^2 K G_{\\rm F}^2 (p_{\\nu} \\cdot p_{\\bar{\\nu}}),\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%%\nwhere the dimensionless parameter $K$ is written as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{eqnarray}\nK(\\nu_\\mu \\bar{\\nu_\\mu})&=&K(\\nu_\\tau \\bar{\\nu_\\tau})=\n\\frac{1-4 \\sin^2{\\theta_{\\rm W}}+8\\sin^4{\\theta_{\\rm W}}}{6 \\pi}, \\nonumber \\\\\nK(\\nu_{\\rm e} \\bar{\\nu_{\\rm e}})&=&\n\\frac{1+4 \\sin^2{\\theta_{\\rm W}}+8\\sin^4{\\theta_{\\rm W}}}{6 \\pi}.\n\\end{eqnarray}\n%%%%%%%%%%%%%%%%%%%%%%%%\nHere the Fermi constant $G_{\\rm F}^2=5.29 \\times 10^{-44} {\\rm cm^2\\, MeV^{-2}}$ and\nthe Weinberg angle $\\sin^2{\\theta_{\\rm W}}=0.23$.\n\nLet us incorporate the effects of gravitational force due to the neutron star\nor black hole on the neutrino pair annihilation rate.\nWe assume that the gravitational field is described by the Schwarzschild\nmetric:\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\nds^2=g_{i j} dx^i dx^j=\n\\left( 1-\\frac{r_{g}}{r} \\right) c^2 dt^2-\\frac{1}{1-\\frac{r_{g}}{r}} dr^2\n-r^2 \\left( d\\theta^2-\\sin^2{\\theta} d\\varphi^2 \\right),\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere $r_{g}=2GM/c^2$ is the Schwarzschild radius.\nIn this field the eikonal for a massless particle \n(Landau \\& Lifshitz 1979) is written as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\psi=-\\omega_0 t+L \\varphi+\\psi_r(r),\n\\label{eikonal}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere $\\omega_0$ and $L$ are constants.\n$\\psi_r(r)$ satisfies the equation\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\frac{\\partial \\psi_r(r)}{\\partial r}=\n\\sqrt{\\frac{\\omega_0^2}{c^2} \\left( 1-\\frac{r_{g}}{r} \\right)^{-2}-\\frac{L^2}{r^2}\n\\frac{1}{1-\\frac{r_{g}}{r}}}.\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nFrom equation (\\ref{eikonal}),\nwe can obtain the momentum of a neutrino by\n$p_{i}=\\hbar \\frac{\\partial \\psi}{\\partial x^i}$.\n\nLet us consider a neutrino and an antineutrino moving on the same surface,\n$\\theta=\\pi/2$.\nIn this case, the inner product of the two particles is written by\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{eqnarray}\n(p_{\\nu} \\cdot p_{\\bar{\\nu}})&=&g^{ij} p_{\\nu i} p_{\\bar{\\nu} j} \\\\\n&=& \\frac{\\varepsilon_{\\nu} \\varepsilon_{\\bar{\\nu}}}{c^2}\n\\left( 1-\\sqrt{1-\\left( \\frac{\\rho_{\\nu}}{r}\n\\right)^2 \\left( 1-\\frac{r_{g}}{r} \\right)}\n\\sqrt{1-\\left( \\frac{\\rho_{\\bar{\\nu}}}{r} \\right)^2\n\\left( 1-\\frac{r_{g}}{r} \\right)} \\right. \\nonumber \\\\\n&& \\left. -\\frac{\\rho_{\\nu} \\rho_{\\bar{\\nu}}}{r^2}\n\\left(1-\\frac{r_{g}}{r} \\right) \\right),\n\\label{product}\n\\end{eqnarray}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\rho_{\\nu} \\equiv \\frac{c L_\\nu}{\\omega_{0 \\nu}}.\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%%\nThe proper energy of the neutrino has been written as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\varepsilon_{\\nu} = \\frac{\\hbar \\omega_{0 \\nu}}{\\sqrt{1-\\frac{r_{g}}{r}}}\n\\equiv \\frac{\\varepsilon_{0 \\nu}}{\\sqrt{1-\\frac{r_{g}}{r}}},\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere $\\varepsilon_{0 \\nu}$ is the energy observed at infinity.\nThus the proper energy is redshifted, as is well known.\nIf we define an angle $\\theta_{\\nu}$ as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\sin{\\theta_{\\nu}} = \\frac{\\rho_{\\nu}}{r} \\sqrt{1-\\frac{r_{g}}{r}},\n\\label{sin}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nequation (\\ref{product}) becomes a simple and natural form,\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n(p_{\\nu} \\cdot p_{\\bar{\\nu}})=\\frac{\\varepsilon_{\\nu} \\varepsilon_{\\bar{\\nu}}}{c^2} \n\\left( 1-\\cos{(\\theta{\\nu}-\\theta{\\bar{\\nu}})} \\right).\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nThe angle $\\theta_{\\nu}$ ($\\theta_{\\bar{\\nu}}$)\nrepresents the angle between $\\mbox{\\boldmath$p$}_{\\nu}$ ($\\mbox{\\boldmath$p$}_{\\bar{\\nu}}$)\nand the position vector $\\mbox{\\boldmath$r$}$ (see Figure 1).\nWe assume that the neutrinosphere emits neutrinos and antineutrinos isotropically.\nThen we can write the number densities as\n$f_{\\nu}(\\mbox{\\boldmath$p$}_{\\nu}, \\mbox{\\boldmath$r$})\nd^3 \\mbox{\\boldmath$p$}_{\\nu}=n(\\varepsilon_{\\nu})\n\\varepsilon_{\\nu}^2 d \\varepsilon_{\\nu} d \\Omega$.\nBecause $\\rho_{\\nu}$ is constant along a neutrino ray,\nthe maximum angle, $\\theta_{\\rm M}$, is obtained by\nsubstituting $\\pi/2$ for $\\theta_{\\nu}$ at the radius of the\nneutrinosphere, $R_{\\nu}$, in equation (\\ref{sin}).\nThus we obtain\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\sin{\\theta_{\\rm M}}=\\frac{R_{\\nu}}{r} \\sqrt{\\frac{1-\\frac{r_{g}}{r}}\n{1-\\frac{r_{g}}{R_{\\nu}}}}.\n\\label{sM}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%%\nThe effect of the orbital bending is apparent in this equation.\nUntil now we have discussed the maximum angle on the surface of $\\theta=\\pi/2$.\nIn general cases, the angles between $\\mbox{\\boldmath$p$}_{\\nu}$\nand $\\mbox{\\boldmath$r$}$ or the inner product, $(p_{\\nu} \\cdot p_{\\bar{\\nu}})$,\nare expressed by the two angles, $\\theta_{\\nu}$\nand $\\varphi_{\\nu}$.\nFrom the symmetry, the behaviour of $\\theta_{\\rm M}$ is obviously\nthe same as described in equation (\\ref{sM}),\nand $\\varphi_{\\nu}$ varies from $0$ to $2 \\pi$.\n\nUsing the effective temperature of the neutrinosphere,\n$T_{\\rm eff}=T_0/\\sqrt{g_{00}}$ with a constant $T_0$,\nwe can write the density\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\nn(\\varepsilon_{\\nu})=\\frac{g_{\\nu}}{(hc)^3} \\frac{1}{\\exp{\\left( \n\\frac{\\varepsilon_{\\nu}}{k T_{\\rm eff}}\\right)}+1},\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere $g_{\\nu}$ is a statistical factor\n($g_{\\nu}=1$ for a neutrino).\n$\\varepsilon_{\\nu}/(k T_{\\rm eff})$ is constant along a neutrino ray,\nsince the redshift is cancelled out.\nThus $n(\\varepsilon_{\\nu})$ is conserved along a neutrino ray\nin accordance with Liouville's theorem in curved spacetime\n(Misner, Thorne \\& Wheeler 1975).\nFrom the above formulation, one can find\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\frac{dN(\\mbox{\\boldmath$r$})}{dt dV}=\n2 c K G_{\\rm F}^2 F(r) \\int \\int d \\varepsilon_{\\nu} d \\varepsilon_{\\bar{\\nu}}\nn(\\varepsilon_{\\nu}) n(\\varepsilon_{\\bar{\\nu}})\n\\varepsilon_{\\nu}^3 \\varepsilon_{\\bar{\\nu}}^3,\n\\label{num}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere the dimensionless factor $F(r)$ is written by\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{eqnarray}\nF(r)&=&\\int_0^{\\theta_{\\rm M}} d \\theta_{\\nu} \\sin{\\theta_{\\nu}}\n\\int_0^{\\theta_{\\rm M}} d \\theta_{\\bar{\\nu}} \\sin{\\theta_{\\bar{\\nu}}}\n\\int_0^{2 \\pi} d \\varphi_{\\nu} \\int_0^{2 \\pi} d \\varphi_{\\bar{\\nu}} \\nonumber \\\\\n&& \\times \\left( 1-\\sin{\\theta_{\\nu}} \\sin{\\theta_{\\bar{\\nu}}}\n\\cos{(\\varphi_{\\nu}-\\varphi_{\\bar{\\nu}})}-\\cos{\\theta_{\\nu}} \\cos{\\theta_{\\bar{\\nu}}}\n\\right)^2 \\label{Fr} \\\\\n&=& \\frac{2 \\pi^2 (1-X)^4}{3} (X^2+4X+5),\n\\end{eqnarray}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\nX = \\sqrt{1-\\left( \\frac{R_{\\nu}}{r} \\right)^2\n\\frac{1-\\frac{r_{g}}{r}}{1-\\frac{r_{g}}{R_{\\nu}}}}.\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nIn our assumption, the energy deposited by the neutrino pair annihilation\nis propagated outward as a fireball or a shock wave,\nand observed as a GRB by a distant observer.\nThus the energy we need to calculate is $\\varepsilon_{0 \\nu}$,\nnot the proper energy $\\varepsilon_{\\nu}$.\nIn this case the energy deposition rate is obtained by putting a factor\n$(\\varepsilon_{0 \\nu}+\\varepsilon_{0 \\bar{\\nu}})$ in the integrand\nin equation (\\ref{num});\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{eqnarray}\n\\frac{dE_0 (\\mbox{\\boldmath$r$})}{dt dV}&=&\n\\frac{2 c K G_{\\rm F}^2}{\\left( 1-\\frac{r_{g}}{r} \\right)^4}\n\\int_0^{\\infty} \\int_0^{\\infty} d \\varepsilon_{0 \\nu} d \\varepsilon_{0 \\bar{\\nu}}\n\\nonumber \\label{depo} \\\\\n&& \\times n(\\varepsilon_{0 \\nu}) n(\\varepsilon_{0 \\bar{\\nu}})\n\\varepsilon_{0 \\nu}^3 \\varepsilon_{0 \\bar{\\nu}}^3\n(\\varepsilon_{0 \\nu}+\\varepsilon_{0 \\bar{\\nu}}) F(r) \\\\\n&=& \\frac{21 \\pi^4}{4} \\zeta(5) \\frac{K G_{\\rm F}^2 g_{\\nu}^2}{h^6 c^5}\n\\frac{\\left( 1-\\frac{r_{g}}{R_{\\nu}} \\right)^{\\frac{9}{2}}}\n{\\left( 1-\\frac{r_{g}}{r} \\right)^4} (k T_{\\rm eff})^9 F(r).\n\\label{depo2}\n\\end{eqnarray}\n%%%%%%%%%%%%%%%%%%%%%%%\nThe integrals for $\\varepsilon_{0 \\nu}$ and $\\varepsilon_{0 \\bar{\\nu}}$\nshould be defined in the range in which the total energy\nproduced by the pair annihilation is larger than the mass of created electrons,\nand smaller than the masses of weak bosons.\nHere we have approximated the integrals as expressed in equation (\\ref{depo})\nin the same manner as Salmonson \\& Wilson (1999) did.\nThis is because the cross section decreases with the energy of neutrinos,\nand the number of neutrinos whose energy is larger than the masses of weak bosons\nis also very small in our assumption ($k T_{\\rm eff}$ is of the order of several MeV).\nThe factor $( 1-r_{g}/R_{\\nu})^{9/2} /( 1-r_{g}/r )^4$ represents\nthe effect of the gravitational redshift,\nand $F(r)$ includes the effect of the orbital bending.\n\nAs is understood from the Lorentz invariant, $dtdV=\\sqrt{-g} d^4 x$,\nif we integrate equation (\\ref{depo2}) over proper volume,\n$dV'=\\sqrt{-g_{rr} g_{\\theta \\theta} g_{\\varphi \\varphi}} dr d\\theta d\\varphi$,\nwe can obtain the total energy deposition per unit proper time,\n$d \\tau=\\sqrt{g_{00}} dt$.\nIt is natural to evaluate the energy deposition rate\nby the world time $dt$ for a distant observer.\nWe integrate over the volume,\n$dV=\\sqrt{g_{\\theta \\theta} g_{\\varphi \\varphi}} dr d\\theta d\\varphi$.\nThus the energy deposition per unit world time is expressed as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\frac{dE_0}{dt}=\n\\frac{21 \\pi^4}{4} \\zeta(5) \\frac{K G_{\\rm F}^2 g_{\\nu}^2}{h^6 c^5} (k T_{\\rm eff})^9\n\\left( 1-\\frac{r_{g}}{R_{\\nu}} \\right)^{\\frac{9}{2}}\n\\int_{R_{\\nu}}^{\\infty} dr 4 \\pi r^2\n\\frac{F(r)}{\\left( 1-\\frac{r_{g}}{r} \\right)^4} C(r),\n\\label{result}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere we have put a factor,\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\nC(r)=\\frac{1}{2} \\left( 1+\\sqrt{1-\\frac{27}{4} \\left( \\frac{r_{g}}{r} \\right)^2\n\\left( 1-\\frac{r_{g}}{r} \\right) } \\right),\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nin the integrand.\nThis is the escape probability of the deposited energy at $r$\nfrom the gravitational attraction\n(Chandrasekhar 1983; Shapiro \\& Teukolsky 1983; Ruffert \\& Janka 1999).\nThe electrons, positrons and photons which are captured by the gravitational attraction\ncannot contribute to the energy source of GRBs.\nApart from $C(r)$,\nthe radial profile in the integrand of equation (\\ref{result}) \nis different from those of Salmonson \\& Wilson (1999),\nsince Salmonson \\& Wilson calculated the proper energy deposition per\nunit proper time.\nOf course, the results of Salmonson \\& Wilson are not mistakes for the estimate of\nthe energy deposition rate in supernovae.\nFor the source of GRBs, however,\nequation (\\ref{result}) is adequate.\n\nLet us investigate the effects of the redshift, orbital bending and gravitational capture.\nWe integrate equation (\\ref{result}) and obtain\nthe energy deposition rate for $\\nu_{e}$ as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\frac{dE_0}{dt}=1.27 \\times 10^{42} \\left( \\frac{k T_{\\rm eff}}{1 {\\rm MeV}} \\right)^9\n\\left( \\frac{R_{\\nu}}{10 {\\rm km}} \\right)^3 f \\quad \\mbox{ergs ${\\rm s^{-1}}$},\n\\label{Gf}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere the dimensionless factor $f$ expresses the effects of the general relativity\n($f=1$ when we neglect the gravitation).\nThe energy deposition rates for $\\nu_{\\mu}$ and $\\nu_{\\tau}$ are 0.64 times\nequation (\\ref{Gf}).\nWe numerically estimate $f$ including the effects of the redshift only,\nthe orbital bending only, or both redshift and orbital bending.\nLast, the total effects of the redshift, orbital bending, and gravitational capture\nare calculated.\nThe results are listed in Table 1.\nAs Table 1 or equation (\\ref{result}) indicates,\nthe effect of the redshift reduces the energy deposition rate,\nand the effect of the orbital bending increases it.\nAlthough each effect, that of the redshift and that of orbital bending, is substantial,\nthe effects partly cancel each other.\nAs a result, the order of the energy deposition rate for\nthe most probable case, $R_{\\nu}/r_g=2.5$, is not altered.\nWhen we neglect the general relativistic effects, the energy deposition rate\nincreases by 1.3 times as $R_{\\nu}$ becomes 10\\%\nlarger, and also increases by 2.4 times as the temperature becomes 10\\%\nhigher.\nTherefore, the gravitational effects are not so large in comparison with\nthe errors due to the uncertainties of $R_{\\nu}$ or $T_{\\rm eff}$,\nand are overwhelmed by them.\nThe effect of the gravitational capture becomes important\nas $R_{\\nu}/r_g$ decreases.\nAs is plotted in Figure 2, in the cases of both the presence and absence\nof gravitation, the energy deposition mainly occurs near the neutrinosphere.\n\n\nSalmonson \\& Wilson (1999) concluded that the effects of gravity\nenhance the energy deposition rate up to a factor of more than\n4 for $R_{\\nu} \\le 2.5 r_g$. However, our results\nshow that the gravitational effects reduce the energy deposition rate.\nThis discrepancy survives even if we omit the escape factor $C(r)$.\nThe proper energy deposition per unit proper time is enhanced\nby both the effects of the redshift and that of orbital bending.\nAdditionally, Salmonson \\& Wilson expressed the general relativistic\neffects with the fixed neutrino luminosity at infinity $L_{\\infty}$,\nwhereas we have done so with the local physical quantity $T_{\\rm eff}$.\nTherefore, an additional factor coming from the redshift of the luminosity\n($L(R_{\\nu}) \\propto T_{\\rm eff}^4$, $L_{\\infty}=(1-{r_g/R_{\\nu}})L(R_{\\nu})$)\nenhances the energy deposition rate in the work of Salmonson \\& Wilson.\nHowever, the quantity $L_{\\infty}$ of GRBs is not directly observable at present.\nIt is more natural to study the effects for the given local parameters,\n$T_{\\rm eff}$ or $L(R_{\\nu})$,\nwhich is restricted or provided by models of the central engine.\n\n\\section{NEUTRINO PAIR ANNIHILATION AROUND THE ACCRETION DISK}\n\n\\indent\n\n\nIn this section we investigate the energy deposition rate around the accretion disk.\nIn order to simplify our formulation,\nwe assume that the accretion disk is isothermal\nand that the gravitational field is dominated\nby the central Schwarzschild black hole.\nWe neglect the rotation of the black hole.\nThe accretion disk is assumed to be thin, and its self-gravitational effects\nare neglected.\nOf course, these idealizations may be far from the case of the realistic accretion disk.\nHowever, we consider that this simple method is sufficient for qualitatively studying\nthe gravitational effects on the energy deposition rate.\nIn this case the equation of the energy deposition rate is\nthe same as equation (\\ref{depo2}) provided that $F(r)$\nis replaced by $F(r,\\theta)$ (it will be given below).\nThe effect of the gravitational redshift can be easily incorporated,\nwhereas the formulation of the neutrino bending is difficult to do\nbecause the accretion disk emits neutrinos anisotropically.\n\nFirst, we calculate the dimensionless factor $F(r, \\theta)$\nwithout the effect of gravity.\nThe accretion disk is placed on the equatorial plane, $\\theta=\\pi/2$.\nThe black hole is at the origin, and we consider\na point $P=(r,\\theta,0)$ where pair annihilations occur (see Figure 3).\nA neutrino is emitted from an arbitrary point on the disk $S=(R,\\pi/2,\\varphi)$,\nwhere $R$ is limited in the range from $R_{\\rm in}$ to $R_{\\rm out}$.\nThe neutrino emitted from $S$ travels straight and arrives at the point $P$.\nLet us denote the angle components of the vector joining $S$ and $P$\nby $(\\theta_{\\nu}, \\varphi_{\\nu})$.\nThey are given by\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\cos{\\theta_{\\nu}}=\\frac{r \\cos{\\theta}}{\\sqrt{r^2+R^2-2 r R \\sin{\\theta} \\cos{\\varphi}}},\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%\n%\\begin{equation}\n%\\sin{\\theta_{\\nu}}=\\frac{\\sqrt{r^2 \\sin^2{\\theta}+R^2-2 r R \\sin{\\theta} \\cos{\\varphi}}}\n%{\\sqrt{r^2+R^2-2 r R \\sin{\\theta} \\cos{\\varphi}}},\n%\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%\n%\\begin{equation}\n%\\cos{\\varphi_{\\nu}}=\\frac{r \\sin{\\theta}-R \\cos{\\varphi}}\n%{\\sqrt{r^2 \\sin^2{\\theta}+R^2-2 r R \\sin{\\theta} \\cos{\\varphi}}},\n%\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\sin{\\varphi_{\\nu}}=\\frac{-R \\sin{\\varphi}}\n{\\sqrt{r^2 \\sin^2{\\theta}+R^2-2 r R \\sin{\\theta} \\cos{\\varphi}}}.\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nThus $\\theta_{\\nu}$ and $\\varphi_{\\nu}$ are functions of $R$ and $\\varphi$\nfor fixed $r$ and $\\theta$.\nThe Jacobian $J \\equiv \\partial (\\theta_{\\nu}, \\varphi_{\\nu})/\\partial (R, \\varphi)$ is\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\nJ=\\frac{r R \\cos{\\theta}}\n{\\sqrt{r^2 \\sin^2{\\theta}+R^2-2 r R \\sin{\\theta} \\cos{\\varphi}}\n( r^2+R^2-2 r R \\sin{\\theta} \\cos{\\varphi})}.\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nConsequently, we obtain $F(r,\\theta)$ as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{eqnarray}\nF(r,\\theta)&=&\\int_{R_{\\rm in}}^{R_{\\rm out}} dR \\int_{R_{\\rm in}}^{R_{\\rm out}} dR'\n\\int_0^{2 \\pi} d \\varphi \\int_0^{2 \\pi} d \\varphi' J J' \\nonumber \\\\\n& \\times & \\sin{\\theta_{\\nu}} \\sin{\\theta_{\\bar{\\nu}}}\n\\left( 1-\\sin{\\theta_{\\nu}} \\sin{\\theta_{\\bar{\\nu}}}\n\\cos{(\\varphi_{\\nu}-\\varphi_{\\bar{\\nu}})}-\\cos{\\theta_{\\nu}} \\cos{\\theta_{\\bar{\\nu}}}\n\\right)^2.\n\\label{Frtheta}\n\\end{eqnarray}\n%%%%%%%%%%%%%%%%%%%%%%%\n\nIn equation (\\ref{Frtheta}) we adopt $R_{\\rm in}=3r_g$, the innermost stable orbit, and\n$R_{\\rm out}=10r_g$ as Woosely (1993) assumed. $F(r,\\theta)$ derived from\nthe numerical integral of equation (\\ref{Frtheta}) is plotted in Figure 4(a) and (b).\nAs is shown in these figures, the energy deposition rate is maximized in the\nvicinity of the accretion disk, where $F(r,\\theta) \\simeq 30-33$.\nThe simulation of a neutron star merger by Ruffert \\& Janka\n(1999) showed that the Paczy\\'nski-Wiita potential (Paczy\\'nski \\& Wiita 1980),\nwhich mimics the effects of the general relativity,\ngives a relatively more transparent disk for neutrinos than\nthat given by the Newtonian potential.\nThe profile of the energy deposition rate in the Paczy\\'nski-Wiita potential\nis similar to our analytical one depicted in Figure 4(a), which shows that the rate takes\nits maximum value on the surface of the disk.\nOn the other hand, the simulated deposition rate in the Newtonian potential\nis maximized near the rotation axis.\nLet us calculate the energy deposition rate near the rotation axis,\nwhere is the lowest baryon density region.\nThus we calculate in the region $\\theta \\leq \\pi/4$\nand obtain\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\frac{dE_0}{dt}=5.22 \\times 10^{43} \\left( \\frac{k T_{\\rm eff}}{1 {\\rm MeV}} \\right)^9\n\\left( \\frac{r_g}{10 {\\rm km}} \\right)^3 G f \\quad \\mbox{ergs ${\\rm s^{-1}}$},\n\\label{Gf2}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere the dimensionless quantity $G$ shows the relative contributions\nfrom various regions in the absence of gravitation.\n$G$ is normalized to unity when\nwe integrate over the volume for $\\theta \\leq \\pi /4$ and $r=2r_g-10r_g$.\nThe values of $G$ in the other regions are summarized in Table 2, from\nwhich we can obtain the energy deposition rate in the respective region.\nWe neglect the energy deposited inside $r=2 r_g$,\nsince the baryon density in this region is very high and\nthe energy contribution is small for the small volume and deposition rate.\nIn the case of the spherical emitter in section 2, the deposition rate decreases as\n$r^{-8}$.\nOn the other hand, around the accretion disk, as is seen from Table 2, there remains a\nmarginal deposition rate even at regions relatively distant from the center.\nOf course the deposition rate per unit volume at distant positions is small.\nHowever, large volume results in a non-negligible contribution at the regions\ndistant from the center.\n\nUntill now we have neglected the gravitational effects.\nIt is easy to incorporate the effects of the redshift and\ntrapping by the central gravitational source in the preceding arguments of this\nsection. However, the bending effect is difficult to treat, unlike the case\nof the neutrinosphere, since the accretion disk emits neutrinos anisotropically.\nThus we are forced to make some approximation.\nAs is shown in Figure 4(b), the $\\theta$ dependence of $F(r,\\theta)$ is weak for \nsmall $\\theta$.\nWe may set $F(r,\\theta) \\simeq F(r,0)$ for $\\theta \\leq \\pi/4$.\nIn the absence of gravitation if we adopt this\napproximation in the region $\\theta \\leq \\pi /4$ and $r=2r_g-10r_g$,\nwe obtain $G=0.81$.\nThe exact value of $G$ is unity, and this approximation is not\nnecessarily satisfactory. However, this approximation may be sufficient for the order\nestimate of the gravitational effects.\n\nWe can obtain $F(r,0)$ including the effect of orbital bending\nwith comparative ease,\nsince the geometry of this case maintain the symmetry.\nA neutrino is emitted from the disk at $R$ and $\\theta=\\pi/2$,\nand it arrives at a point at $r$ and $\\theta=0$.\nThe nearest distance, $r_0$,\nfrom the origin to the orbit of neutrinos (Landau \\& Lifshitz 1979)\nis numerically obtained from\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\pi/2=\\int_{\\rm C} \\frac{dr'}{r' \\sqrt{\\left( \\frac{r'}{r_0} \\right)^2\n\\left(1-\\frac{r_g}{r_0} \\right)-\\left(1-\\frac{r_g}{r'} \\right)}}.\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nHere, in the case in which a neutrino passes through $r_0$\nuntil it arrives at a point at $\\theta=0$,\nthe integration for $r'$ is performed from $r_0$ to $R$ and $r$.\nWhen the distance from the origin to the neutrino varies monotonically,\nthe integration is performed from the smaller\nto the larger of $r$ and $R$.\nWe can get $\\theta_{\\nu}$ at $\\theta=0$ numerically from $r_0$ and the following equation;\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\sin{\\theta_{\\nu}}=\\frac{r_0}{r} \\sqrt{\\frac{1-\\frac{r_g}{r}}{1-\\frac{r_g}{r_0}}}.\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nThe constant, $r_0$, or $\\theta_{\\nu}$, is a function of $r$ and $R$ in this case.\nAs is easily understood, a neutrino coming from $R_{\\rm in}$ forms $\\theta_{\\rm m}$,\nthe minimum value of $\\theta_{\\nu}$, at $\\theta=0$ and that from\n$R_{\\rm out}$ forms the maximum value of $\\theta$, $\\theta_{\\rm M}$.\nIntegrating equation (\\ref{Fr}) from $\\theta_{\\rm m}$ to $\\theta_{\\rm M}$,\nwe obtain $F(r,0)$ involving gravitational effects.\nIn Figure 5 we plot $F(r,0)$ for both the case when the bending is taken into\nconsideration and the case when it is not.\nIn comparison with the spherical case in Figure 2,\nthe deposited energy at distant regions in the disk case\nis marginally substantial.\nIn the presence of bending, the peak of the energy deposition rate is\nshifted to a little bit larger $r$ and the value of the rate at the peak\nis about twice as larger as values obtained in the absence of bending.\n\nAlthough the $\\theta$ dependence of the gravitational effects may not necessarily\nbe small, unlike $F(r,\\theta)$ in the absence of gravitation,\nwe assume it is small here. Using $F(r,0)$\nwith the bending effect, we calculate the energy deposition rate in the range\n$\\theta \\le \\pi/4$ and $r=2 r_g-10 r_g$.\nTable 3 lists the values of the factor $f$ that shows the gravitational effects.\nThe $\\theta$-dependence is neglected in our calculation\nexcept for the case involving the redshift only.\nThus $f$ is normalized to unity when $F(r,\\theta)$\n(in the case involving the effect of the redshift only)\nor $F(r,0)$ (in the other cases) is integrated over $r$ and $\\theta$\nin the absence of gravitation.\nAs is easily seen, the gravitational effects cancel one another out.\nThis is analogous to the neutrino sphere case in the previous section.\n%%%\nThis result strongly supports that of Ruffert \\& Janka (1999).\nThey treated the system of the accretion torus and a black hole unlike our\nsystem of the disk and a black hole.\nUsing an approximation similar to ours,\nthey analytically calculated\nthe energy deposition rate due to the neutrino pair annihilation.\nTheir result is that the gravitational effects reduce the deposition rate by a factor\nof $10-30\\%$.\nIt agrees well with our result.\n%%%\n\nIn order to circumvent the baryon contamination problem,\nthe energy fraction of baryonic matter in the fireball\nmust be less than about $10^{-5}$ (Shemi \\& Piran 1990).\nIf we adopt the duration time of the neutrino radiation to be $t_{\\rm\ndur}=0.1$s and $T_{\\rm eff}=10$MeV,\nthe highest mean mass densities $\\bar{\\rho}$ inside $\\theta=0-\\pi/3$ to resolve\nthe above problem are\n$10^6$g/${\\rm cm^3}$ for $r=2 r_g-5 r_g$,\n$10^5$g/${\\rm cm^3}$ for $r=5 r_g-10 r_g$ and\n$10^4$g/${\\rm cm^3}$ for $r=10 r_g-20 r_g$.\nSince some fraction of energy really\nescapes from the considered regions during the finite duration time,\nthe above restrictions may become more stringent.\n\n\n\n\n\\section{CONCLUSIONS}\n\n\\indent\n\nIn this article we have investigated semianalytically\nthe neutrino pair annihilation near\nthe neutrinosphere and around the thin accretion disk assuming that the\ngravitational sources in both cases are described by the Schwarzschild metric.\nThe accretion disk has been assumed to be a blackbody and isothermal.\nThese assumptions enable us to treat these two cases based in an almost\nunified fashion, which also clarifies the physical differences between these\ntwo cases.\nWe have studied the general relativistic effects only near the rotation axis,\nbecause that region is especially of interest to the source of GRBs\nand estimating the effect of orbital bending\nfor large $\\theta$ is difficult.\n\n\nThe general relativistic effects as a whole do not enhance the neutrino energy\ndeposition rate in either case.\nThe energy deposition rate is enhanced by\nthe effect of orbital bending toward the center.\nHowever, the enhancement is cancelled out by the effects of the redshift and\ncapture by the gravitational attraction.\nConsequently, numerical simulations of the neutrino energy\ndeposition rate in various models can correctly estimate\nthe order of the rate without considering the gravitational effects,\nsince it is supposed\nthat the thickness, shape, or temperature distribution of the disk or sphere\ndoes not greatly affect the gravitational effects themselves.\n%%%\nTaking into account also the results of Ruffert \\& Janka (1999), the\nconclusions mentioned above are strongly suggested to be valid in the following\ngeometrical forms of the neutrino source: sphere, thin disk and torus.\n%%%\nWe have also shown that the neutrinos emitted from the disk can\ndeposit energy at more distant regions than the neutrinos emitted\nfrom the sphere.\nThe importance in this article resides in\nthe qualitative properties of the general relativistic effects.\nThe quantitative calculations in this paper are not so important,\nand should be investigated on the basis of more sophisticated models and simulations.\n\n\n\n\n\n\n\n\n\n\\vspace{1.5cm}\n\n%We are grateful to A and the referee\n%for their helpful advice.\nWe appreciate the helpful advice of M. Ruffert.\nThis work was partly supported by a Research Fellowship of the Japan Society for\nthe Promotion of Science.\n%and\n%B\n%for C.\n%Lastly, we appreciate D for E.\n\n\\newpage\n\n\\begin{center}\n{\\bf \\LARGE References}\n\\end{center}\n\n\\medskip\n\n\\begin{description}\n\n\\item\nBerezinsky, V. S., \\& Prilutsky, O. F. 1987, A\\&A 175, 309\n\\item\nChandrasekhar, S. 1983, The Mathematical Theory of Black Holes\n(New York: Oxford)\n\\item\nCooperstein, J., Van Den Horn, L. J., \\& Baron, E. 1987, ApJ 321, L129\n\\item\nEichler, D., Livio, M., Piran, T., \\& Schramm, D. N. 1989, Nature 340, 126\n\\item\nGoodman, J., Dar, A., \\& Nussinov, S. 1987, ApJ 314, L7\n\\item\nJanka, H.-T., \\& Ruffert, M. 1996, A\\&A 307, L33\n\\item\nKatz, J. I. 1997, ApJ 490, 633\n\\item\nLandau, L. D., \\& Lifshitz, E. M. 1979, Classical Theory of Fields\n(London: Pergamon)\n\\item\nMacFadyen, A., \\& Woosley, S. E. 1999, ApJ 524, 262\n\\item\nM\\'esz\\'aros, P., \\& Rees, M. J. 1992a, ApJ 397, 570\n\\item\nM\\'esz\\'aros, P., \\& Rees, M. J. 1992b, MNRAS 257, 29p\n\\item\nM\\'esz\\'aros, P., \\& Rees, M. J. 1993, ApJ 405, 278\n\\item\nMisner, C. W., Thorne, K. S., \\& Wheeler, J. A. 1975,\nGravitation (New York: Freeman)\n\\item\nNarayan, R., Paczy\\'nski, B., \\& Piran, T. 1992, ApJ 395, L83\n\\item\nPaczy\\'nski, B. 1990, ApJ 363, 218\n\\item\nPaczy\\'nski, B. 1998, ApJ 494, L45\n\\item\nPaczy\\'nski, B., \\& Wiita, P. J. 1980, A\\&A 88, 23\n\\item\nPopham, R., Woosley, S. E., \\& Fryer, C. 1999, ApJ 518, 356\n\\item\nRees, M. J., \\& M\\'esz\\'aros, P. 1992, MNRAS 258, 41p\n\\item\nRuffert, M., \\& Janka, H.-T. 1998, A\\&A 338, 535\n\\item\nRuffert, M., \\& Janka, H.-T. 1999, A\\&A 344, 573\n\\item\nRuffert, M., Janka, H.-T., Takahashi, K., \\& Sch\\\"afer, G. 1997, A\\&A 319, 122\n\\item\nSalmonson, J. D., \\& Wilson, J. R. 1999, ApJ 517, 859\n\\item\nSari, R., Narayan, R., \\& Piran, T. 1996 ApJ 473, 204\n\\item\nSari, R., \\& Piran, T. 1995, ApJ 455, L143\n\\item\nShapiro, S. L., \\& Teukolsky, S. A. 1983, Black Holes, White Dwarfs and Neutron Stars\n(New York: Wiley)\n\\item\nShemi, A., \\& Piran, T. 1990, ApJ 365, L55\n\\item\nWoosley, S. E. 1993, ApJ 405, 273\n\n\n\n\n\\end{description}\n\\newpage\n\n\\begin{center}\n{\\bf \\large Figure captions}\n\\end{center}\n\n\n\\figcaption{Maximum angle $\\theta_{\\rm M}$ at a distance $r$ from the\ncenter formed by neutrinos emitted from the surface of the neutrinosphere.\nThe dashed line shows the orbit forming the maximum\nangle in the absence of gravitation.}\n\n\\figcaption{The plot of $F(r)$ against $r$ for $R_{\\nu}=2.5r_g$ when neutrinos are\nemitted isotropically.\nThe solid (dashed) line shows $F(r)$ for the case in the presence (absence) of\ngravitation. The origin is at $r=R_{\\nu}$.}\n\n\\figcaption{Geometry of neutrino's path.\nA neutrino is emitted from a point $S=(R,\\pi/2,\\varphi)$ on the disk and arrives at\n$P=(r,\\theta,0)$. The angular components of the vector joining $S$ and $P$ are\n$(\\theta_{\\nu}, \\varphi_{\\nu})$.\n$R$ (radius on the disk) is limited to the range from $R_{\\rm in}$ to $R_{\\rm out}$.}\n\n\\figcaption{Contour plot of $F(r,\\theta)$ where neutrinos are\nemitted from the disk. Here gravitation has been neglected.\n%%%\n(a) Plot in Cartesian coordinates $(r \\sin{\\theta},r \\cos{\\theta})$.\n(b) Plot in polar coordinates, $(r, \\theta)$.\n%%%\nThe contours\nare plotted at unit intervals except for the line of $F(r,\\theta)=0.1$;\n$\\theta=0$ and $\\theta=\\pi/2$ correspond to points on the rotation\naxis and on the disk, respectively.}\n\n\\figcaption{Diagram of $F(r,0)$ vs. $r$\nwhere neutrinos are emitted from the disk.\nThe solid (dashed) line shows $F(r,0)$ for the case in which we\nconsider (neglect) the effect of gravitational bending.}\n\n\n\n\\newpage\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline \\hline\n$R_{\\nu}/r_{g}$ & \\multicolumn{4}{c}{$f$} \\\\\n&Redshift Only & Bending Only & Redshift and Bending & Whole \\\\ \\hline\n1.5 & 0.32 & 4.7 & 0.97 & 0.57 \\\\\n2.5 & 0.60 & 1.6 & 0.87 & 0.73 \\\\\n5 & 0.81 & 1.2 & 0.93 & 0.89 \\\\ \\hline\n\\end{tabular}\n\\end{center}\n{\\footnotesize Table~1. The dimensionless factor $f$ represents\nthe general relativistic effects (see eq. [\\ref{Gf}])\nwhen neutrinos are emitted isotropically from the neutrinosphere;\n$f$ is normalized to unity in the absence of gravitation.\nThe column headings \"Redshift Only\" and so on indicate\nthe incorporated effects of gravitation;\n\"Whole\" over the last column means that we incorporate\nall gravitational effects, redshift, bending, and trapping.\nThe energy deposition rate is enhanced by orbital bending\nand reduced by the redshift and trapping.}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline \\hline\n$\\theta$ & $2 r_g-5 r_g$ & $5 r_g-10 r_g$ & $10 r_g-20 r_g$ \\\\ \\hline\n$0-\\pi/4$ & 0.35 & 0.65 & 0.22 \\\\\n$\\pi/4-\\pi/3$ & 0.32 & 0.77 & 0.17 \\\\ \\hline\n%$\\pi/3-\\pi/2$ & 2.27 & 0.21 \\\\ \\hline\n\\end{tabular}\n\\end{center}\n{\\footnotesize Table~2. The dimensionless factor $G$.\nIt represents the fraction of the energy deposition rate for each region\n(see eq. [\\ref{Gf2}])\nwhen neutrinos are emitted from the disk.\n$G$ is normalized to unity for the region surrounded by\n$r=2 r_g-10 r_g$ and $\\theta=0-\\pi/4$.\nHere we neglect the effects of gravitation.}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline \\hline\nrange & \\multicolumn{4}{c}{$f$} \\\\\n&redshift only & bending only & redshift and bending & whole \\\\ \\hline\n$2 r_g-5 r_g$ & 0.66 & 2.6 & 1.6 & 1.4 \\\\ \n$5 r_g-10 r_g$ & 0.31 & 2.5 & 0.78 & 0.75 \\\\ \\hline\n\\end{tabular}\n\\end{center}\n{\\footnotesize Table~3. The dimensionless factor $f$ for $\\theta=0-\\pi/4$\n(see equation [\\ref{Gf2}]).\nNeutrinos are emitted from the disk;\n$f$ is normalized to unity when $F(r,\\theta)$\n(in the case involving the effect of the redshift only)\nor $F(r,0)$ (in the other cases) is integrated over $r$ and $\\theta$\nin the absence of gravitation.}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\\begin{center}\n%\\begin{tabular}{cccc}\n%\\hline \\hline\n%$\\theta$ & $2 r_g-5 r_g$ & $5 r_g-10 r_g$ & $10 r_g-20 r_g$ \\\\ \\hline\n%$0-\\pi/4$ & $1.8 \\times 10^7$ & $2.5 \\times 10^6$ & $3.2 \\times 10^5$ \\\\\n%$\\pi/4-\\pi/3$ & $2.5 \\times 10^7$ & $3.4 \\times 10^6$ & $4.3 \\times 10^5$ \\\\ \\hline\n%\\end{tabular}\n%\\end{center}\n%{\\footnotesize Table~4. The highest mean density $\\bar{\\rho}$ for $\\eta \\geq 10^5$.\n%We assume $T_{\\rm eff}=10$ MeV.}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\end{document}"}],"string":"[\n {\n \"name\": \"paper.TEX\",\n \"string\": \"%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%\\n%\\t Neutrino Pair Annihilation as a Source of Gamma Ray Bursts\\n%\\n%\\n%\\n%\\n%\\t Katsuaki ASANO & Takeshi FUKUYAMA\\n%\\n% 12nd June 1999\\n%\\n%\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\documentstyle[12pt,aasms4]{article}\\n%\\\\setlength{\\\\textwidth}{19cm}\\n%\\\\setlength{\\\\oddsidemargin}{-1cm}\\n\\\\begin{document}\\n\\n\\n\\\\vspace*{0.5cm}\\n\\n\\\\title{Neutrino Pair Annihilation in the Gravitation of Gamma Ray Burst Sources}\\n\\n\\\\author{Katsuaki Asano and Takeshi Fukuyama}\\n\\n\\n\\\\vspace{2cm}\\n\\n\\\\affil{Department of Physics, Ritsumeikan University\\\\\\\\\\nKusatsu, Shiga 525-8577, Japan}\\n\\n\\\\affil{\\\\footnotesize e-mail: sph10001@se.ritsumei.ac.jp}\\n\\n\\\\vspace{2cm}\\n\\n\\\\baselineskip=16pt\\n\\n\\\\abstract{We study semianalytically\\nthe gravitational effects on neutrino pair annihilation\\nnear the neutrinosphere and around the thin accretion disk.\\nFor the disk case, we assume that the accretion disk is isothermal\\nand that the gravitational field is dominated by the Schwarzschild black hole.\\nGeneral relativistic effects are studied only near the rotation axis.\\nThe energy deposition rate is enhanced by\\nthe effect of orbital bending toward the center.\\nHowever, the effects of the redshift and gravitational trapping\\nof the deposited energy reduce the effective energy of the gamma ray bursts' source.\\nAlthough each effect is substantial,\\nthe effects partly cancel one another.\\nAs a result, the gravitational effects do not substantially change the\\nenergy deposition rate for either the spherical symmetric case or the disk case.}\\n\\n\\\\vspace{0.5cm}\\n\\n\\\\noindent{\\\\it Subject headings}: accretion, accretion disks---black hole physics---gamma rays: bursts\\n\\n\\n\\\\newpage\\n\\n\\n\\\\section{INTRODUCTION}\\n\\n\\\\indent\\n\\nThe relativistic fireball (Shemi \\\\& Piran 1990; Rees \\\\& M\\\\'esz\\\\'aros 1992;\\nM\\\\'esz\\\\'aros \\\\& Rees 1993; Sari \\\\& Piran 1995; Sari, Narayan \\\\& Piran 1996)\\nis one of the most promising models of gamma ray bursts (GRBs).\\nHowever, even if the fraction of the baryon rest energy is only $10^{-3}$\\nin the fireball, the relativistic bulk flow, which is\\nindispensable to GRBs, cannot be realized.\\nNotwithstanding the very high energy phenomenon ($10^{52}$ ergs), the baryon\\ndensity in the fireball must be extremely small.\\nThis is the famous baryon contamination problem and still remains unsolved.\\nThus the central engine of GRBs is still beyond\\ndeep mist.\\nThe source of GRBs may be one super massive\\n(failed) supernovae (Woosley 1993; Paczy\\\\'nski 1998)\\nor may be a merger of two neutron stars or of a neutron star and a black hole\\n(e.g. Eichler et al. 1989; Narayan, Paczy\\\\'nski \\\\& Piran 1992;\\nM\\\\'esz\\\\'aros \\\\& Rees 1992a; Katz 1997; Ruffert \\\\& Janka 1998, 1999).\\n\\nIn these compact high energy objects,\\nthe neutrino-antineutrino annihilation\\ninto electrons and positrons\\n(hereafter neutrino pair annihilation)\\nis a possible and important candidate to explain the energy source of GRBs\\n(Paczy\\\\'nski 1990; M\\\\'esz\\\\'aros \\\\& Rees 1992b; Janka \\\\& Ruffert 1996;\\nRuffert et al. 1997; Ruffert \\\\& Janka 1998, 1999).\\nMotivated by the delayed explosion of Type II supernovae,\\nthe energy deposition rate due\\nto the neutrino pair annihilation above the neutrinosphere\\nhas been calculated\\n(Goodman, Dar \\\\& Nussinov 1987; Cooperstein, Van Den Horn \\\\& Baron 1987;\\nBerezinsky \\\\& Prilutsky 1987).\\nThe energy deposition rate is proportional to $r^{-8}$ ($r$\\nis the distance from the center of the neutrinosphere) for a large $r$,\\nand almost all deposition occurs near the neutrinosphere.\\nAs they themselves noted in their paper,\\nGoodman et al. (1987) neglected the general\\nrelativistic effects on the energy deposition rate, which may change\\ntheir numerical value seriously.\\nIn simulations of the neutrino pair annihilation rate,\\nit is very important to confirm whether or not the energy deposition\\nrate is altered or not by the gravitational effects.\\nIn the recent study, Salmonson \\\\& Wilson (1999)\\nconcluded that the energy deposition rate in Type II\\nsupernovae is enhanced about 4 times as a result of the gravitational effects.\\nWe must check whether or not their results can be applied to the central engine\\nof GRBs.\\n\\n\\nOne of the most probable candidates for the central engine of GRBs\\nis the accretion disk around a black hole (Woosley 1993; Popham, Woosley \\\\& Fryer 1999;\\nMacFadyen \\\\& Woosley 1999; Ruffert \\\\& Janka 1999).\\nThe system of an accretion disk and a black hole may be formed\\nby the merging of two neutron stars,\\nthe merging of a black hole and a neutron star,\\nor the failed supernovae.\\nIn general, the baryon density has the lowest value along the rotation axis\\njust above the black hole (e.g. see Ruffert \\\\& Janka 1999).\\nThis region might be a key to resolving the baryon contamination problem.\\nThe hot accretion disk emits neutrinos and antineutrinos.\\nThe energy deposited in the lowest density region is a candidate for\\nthe central engine of GRBs.\\nUsing hydrodynamic simulations,\\nRuffert \\\\& Janka (1999) showed that the neutrino pair annihilation deposits \\nenergy in the vicinity of the torus at a rate of $(3-5)\\\\times 10^{50}$ ergs ${\\\\rm s^{-1}}$.\\nThey concluded that the gravitational effect on the energy deposition rate\\naround the accretion disk is small.\\nWe must supplement their results from the analytical side.\\n\\nIn various arguments on the energy deposition in the central engine of GRBs,\\nthe order estimation of the deposited energy is sufficient, at least at present.\\nIn this article, based on simple models, we study semianalytically\\nthe gravitational effects on the energy deposition rate for two cases.\\nIn one case neutrinos are emitted spherically symmetrically.\\nIn the other case the hot accretion disk emits neutrinos.\\nWe have derived the gravitational effects on the former case independently of\\nSalmonson \\\\& Wilson (1999).\\nSome differences of our work from Salmonson \\\\& Wilson in the formulation,\\nthe interpretation of the energy deposition, and the additional factor are\\nmentioned.\\nAs for the disk case, we assume that the accretion disk is isothermal\\nand that the gravitational field is dominated solely by the central\\nSchwarzschild black hole.\\nThese assumptions enable us to treat the energy deposition around the disk\\nsemianalytically.\\nThus, in both two cases gravitation is described by the Schwarzschild metric,\\nand the essential differences between the two cases\\ncome from the shape of the neutrino emitters.\\n\\nThe gravitational effects consist of three factors:\\nthey are the bending of neutrino\\ntrajectories, the gravitational redshift, and the trapping of deposited\\nenergy into the central gravitational source.\\nWe show that the energy deposition rate is indeed enhanced rather crucially by\\nthe effect of neutrino bending.\\nHowever, it is also shown that the gravitational redshift and the trapping\\nof the deposited energy reduce this enhancement.\\nAs a result, the gravitational effects do not substantially change the\\nenergy deposition rate for either the spherical symmetric case or the disk case.\\n\\n\\n\\nThis paper is organized as follows. In section two we investigate\\nneutrino pair annihilation near the neutrinosphere.\\nThe same process around the accretion disk is\\ndiscussed in section three. The last section is devoted to conclusions.\\n\\n\\n\\\\section{NEUTRINO PAIR ANNIHILATION NEAR THE NEUTRINOSPHERE}\\n\\n\\\\indent\\n\\nIn this section we study the general relativistic effects on\\nneutrino pair annihilation near the neutrinosphere.\\nThis study has been already done by Salmonson \\\\& Wilson (1999).\\nUsing another method, we formulate the same problem independently of\\nthe work of Salmonson \\\\& Wilson.\\nSome alterations in the interpretation of the energy deposition\\nin Salmonson \\\\& Wilson are mentioned.\\n\\nThe number of reaction, $\\\\nu+\\\\bar{\\\\nu} \\\\to e^+ +e^-$,\\nper unit volume per unit time (Goodman, Dar \\\\& Nussinov 1987) is written as\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\frac{dN(\\\\mbox{\\\\boldmath$r$})}{dt dV}=\\n\\\\int \\\\int f_{\\\\nu}(\\\\mbox{\\\\boldmath$p$}_{\\\\nu}, \\\\mbox{\\\\boldmath$r$})\\nf_{\\\\bar{\\\\nu}}(\\\\mbox{\\\\boldmath$p$}_{\\\\bar{\\\\nu}}, \\\\mbox{\\\\boldmath$r$})\\n\\\\sigma \\\\left| \\\\mbox{\\\\boldmath$v$}_{\\\\nu}-\\\\mbox{\\\\boldmath$v$}_{\\\\bar{\\\\nu}} \\\\right|\\nd^3 \\\\mbox{\\\\boldmath$p$}_{\\\\nu} d^3 \\\\mbox{\\\\boldmath$p$}_{\\\\bar{\\\\nu}}.\\n\\\\label{first}\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%%\\nHere $f_{\\\\nu}$ ($f_{\\\\bar{\\\\nu}}$) is the number density of neutrinos\\n(antineutrinos) in phase space,\\n$\\\\mbox{\\\\boldmath$v$}_{\\\\nu}$ ($\\\\mbox{\\\\boldmath$v$}_{\\\\bar{\\\\nu}}$)\\nis the velocity of neutrinos (antineutrinos),\\nand $\\\\sigma$ is the rest-frame cross section.\\nThe left handside of equation (\\\\ref{first}) is Lorentz invariant,\\nsince both the numerator, $dN$, and denominator, $dt dV=\\\\sqrt{-g} d^4 x$,\\nare Lorentz invariant.\\nSince $f_{\\\\nu}$ and $d^3 \\\\mbox{\\\\boldmath$p$}_{\\\\nu}/\\\\varepsilon_{\\\\nu}$\\n(where $\\\\varepsilon_{\\\\nu}$ is the proper energy of neutrinos) of the right handside\\nare also Lorentz invariant,\\n$\\\\varepsilon_{\\\\nu} \\\\varepsilon_{\\\\bar{\\\\nu}}\\n| \\\\mbox{\\\\boldmath$v$}_{\\\\nu}-\\\\mbox{\\\\boldmath$v$}_{\\\\bar{\\\\nu}} | \\\\sigma$\\nshould be Lorentz invariant.\\nThe latter is written in a manifest Lorentz-invariant form as\\n$ \\\\sigma c^3 (p_{\\\\nu} \\\\cdot p_{\\\\bar{\\\\nu}})$,\\nwhere $(p_{\\\\nu} \\\\cdot p_{\\\\bar{\\\\nu}})$ is the inner product of the 4-momenta.\\nThe standard model predicts that the cross section is expressed as\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\sigma=2 c^2 K G_{\\\\rm F}^2 (p_{\\\\nu} \\\\cdot p_{\\\\bar{\\\\nu}}),\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%%\\nwhere the dimensionless parameter $K$ is written as\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{eqnarray}\\nK(\\\\nu_\\\\mu \\\\bar{\\\\nu_\\\\mu})&=&K(\\\\nu_\\\\tau \\\\bar{\\\\nu_\\\\tau})=\\n\\\\frac{1-4 \\\\sin^2{\\\\theta_{\\\\rm W}}+8\\\\sin^4{\\\\theta_{\\\\rm W}}}{6 \\\\pi}, \\\\nonumber \\\\\\\\\\nK(\\\\nu_{\\\\rm e} \\\\bar{\\\\nu_{\\\\rm e}})&=&\\n\\\\frac{1+4 \\\\sin^2{\\\\theta_{\\\\rm W}}+8\\\\sin^4{\\\\theta_{\\\\rm W}}}{6 \\\\pi}.\\n\\\\end{eqnarray}\\n%%%%%%%%%%%%%%%%%%%%%%%%\\nHere the Fermi constant $G_{\\\\rm F}^2=5.29 \\\\times 10^{-44} {\\\\rm cm^2\\\\, MeV^{-2}}$ and\\nthe Weinberg angle $\\\\sin^2{\\\\theta_{\\\\rm W}}=0.23$.\\n\\nLet us incorporate the effects of gravitational force due to the neutron star\\nor black hole on the neutrino pair annihilation rate.\\nWe assume that the gravitational field is described by the Schwarzschild\\nmetric:\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\nds^2=g_{i j} dx^i dx^j=\\n\\\\left( 1-\\\\frac{r_{g}}{r} \\\\right) c^2 dt^2-\\\\frac{1}{1-\\\\frac{r_{g}}{r}} dr^2\\n-r^2 \\\\left( d\\\\theta^2-\\\\sin^2{\\\\theta} d\\\\varphi^2 \\\\right),\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nwhere $r_{g}=2GM/c^2$ is the Schwarzschild radius.\\nIn this field the eikonal for a massless particle \\n(Landau \\\\& Lifshitz 1979) is written as\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\psi=-\\\\omega_0 t+L \\\\varphi+\\\\psi_r(r),\\n\\\\label{eikonal}\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nwhere $\\\\omega_0$ and $L$ are constants.\\n$\\\\psi_r(r)$ satisfies the equation\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\frac{\\\\partial \\\\psi_r(r)}{\\\\partial r}=\\n\\\\sqrt{\\\\frac{\\\\omega_0^2}{c^2} \\\\left( 1-\\\\frac{r_{g}}{r} \\\\right)^{-2}-\\\\frac{L^2}{r^2}\\n\\\\frac{1}{1-\\\\frac{r_{g}}{r}}}.\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nFrom equation (\\\\ref{eikonal}),\\nwe can obtain the momentum of a neutrino by\\n$p_{i}=\\\\hbar \\\\frac{\\\\partial \\\\psi}{\\\\partial x^i}$.\\n\\nLet us consider a neutrino and an antineutrino moving on the same surface,\\n$\\\\theta=\\\\pi/2$.\\nIn this case, the inner product of the two particles is written by\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{eqnarray}\\n(p_{\\\\nu} \\\\cdot p_{\\\\bar{\\\\nu}})&=&g^{ij} p_{\\\\nu i} p_{\\\\bar{\\\\nu} j} \\\\\\\\\\n&=& \\\\frac{\\\\varepsilon_{\\\\nu} \\\\varepsilon_{\\\\bar{\\\\nu}}}{c^2}\\n\\\\left( 1-\\\\sqrt{1-\\\\left( \\\\frac{\\\\rho_{\\\\nu}}{r}\\n\\\\right)^2 \\\\left( 1-\\\\frac{r_{g}}{r} \\\\right)}\\n\\\\sqrt{1-\\\\left( \\\\frac{\\\\rho_{\\\\bar{\\\\nu}}}{r} \\\\right)^2\\n\\\\left( 1-\\\\frac{r_{g}}{r} \\\\right)} \\\\right. \\\\nonumber \\\\\\\\\\n&& \\\\left. -\\\\frac{\\\\rho_{\\\\nu} \\\\rho_{\\\\bar{\\\\nu}}}{r^2}\\n\\\\left(1-\\\\frac{r_{g}}{r} \\\\right) \\\\right),\\n\\\\label{product}\\n\\\\end{eqnarray}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nwhere\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\rho_{\\\\nu} \\\\equiv \\\\frac{c L_\\\\nu}{\\\\omega_{0 \\\\nu}}.\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%%\\nThe proper energy of the neutrino has been written as\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\varepsilon_{\\\\nu} = \\\\frac{\\\\hbar \\\\omega_{0 \\\\nu}}{\\\\sqrt{1-\\\\frac{r_{g}}{r}}}\\n\\\\equiv \\\\frac{\\\\varepsilon_{0 \\\\nu}}{\\\\sqrt{1-\\\\frac{r_{g}}{r}}},\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nwhere $\\\\varepsilon_{0 \\\\nu}$ is the energy observed at infinity.\\nThus the proper energy is redshifted, as is well known.\\nIf we define an angle $\\\\theta_{\\\\nu}$ as\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\sin{\\\\theta_{\\\\nu}} = \\\\frac{\\\\rho_{\\\\nu}}{r} \\\\sqrt{1-\\\\frac{r_{g}}{r}},\\n\\\\label{sin}\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nequation (\\\\ref{product}) becomes a simple and natural form,\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n(p_{\\\\nu} \\\\cdot p_{\\\\bar{\\\\nu}})=\\\\frac{\\\\varepsilon_{\\\\nu} \\\\varepsilon_{\\\\bar{\\\\nu}}}{c^2} \\n\\\\left( 1-\\\\cos{(\\\\theta{\\\\nu}-\\\\theta{\\\\bar{\\\\nu}})} \\\\right).\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nThe angle $\\\\theta_{\\\\nu}$ ($\\\\theta_{\\\\bar{\\\\nu}}$)\\nrepresents the angle between $\\\\mbox{\\\\boldmath$p$}_{\\\\nu}$ ($\\\\mbox{\\\\boldmath$p$}_{\\\\bar{\\\\nu}}$)\\nand the position vector $\\\\mbox{\\\\boldmath$r$}$ (see Figure 1).\\nWe assume that the neutrinosphere emits neutrinos and antineutrinos isotropically.\\nThen we can write the number densities as\\n$f_{\\\\nu}(\\\\mbox{\\\\boldmath$p$}_{\\\\nu}, \\\\mbox{\\\\boldmath$r$})\\nd^3 \\\\mbox{\\\\boldmath$p$}_{\\\\nu}=n(\\\\varepsilon_{\\\\nu})\\n\\\\varepsilon_{\\\\nu}^2 d \\\\varepsilon_{\\\\nu} d \\\\Omega$.\\nBecause $\\\\rho_{\\\\nu}$ is constant along a neutrino ray,\\nthe maximum angle, $\\\\theta_{\\\\rm M}$, is obtained by\\nsubstituting $\\\\pi/2$ for $\\\\theta_{\\\\nu}$ at the radius of the\\nneutrinosphere, $R_{\\\\nu}$, in equation (\\\\ref{sin}).\\nThus we obtain\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\sin{\\\\theta_{\\\\rm M}}=\\\\frac{R_{\\\\nu}}{r} \\\\sqrt{\\\\frac{1-\\\\frac{r_{g}}{r}}\\n{1-\\\\frac{r_{g}}{R_{\\\\nu}}}}.\\n\\\\label{sM}\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%%\\nThe effect of the orbital bending is apparent in this equation.\\nUntil now we have discussed the maximum angle on the surface of $\\\\theta=\\\\pi/2$.\\nIn general cases, the angles between $\\\\mbox{\\\\boldmath$p$}_{\\\\nu}$\\nand $\\\\mbox{\\\\boldmath$r$}$ or the inner product, $(p_{\\\\nu} \\\\cdot p_{\\\\bar{\\\\nu}})$,\\nare expressed by the two angles, $\\\\theta_{\\\\nu}$\\nand $\\\\varphi_{\\\\nu}$.\\nFrom the symmetry, the behaviour of $\\\\theta_{\\\\rm M}$ is obviously\\nthe same as described in equation (\\\\ref{sM}),\\nand $\\\\varphi_{\\\\nu}$ varies from $0$ to $2 \\\\pi$.\\n\\nUsing the effective temperature of the neutrinosphere,\\n$T_{\\\\rm eff}=T_0/\\\\sqrt{g_{00}}$ with a constant $T_0$,\\nwe can write the density\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\nn(\\\\varepsilon_{\\\\nu})=\\\\frac{g_{\\\\nu}}{(hc)^3} \\\\frac{1}{\\\\exp{\\\\left( \\n\\\\frac{\\\\varepsilon_{\\\\nu}}{k T_{\\\\rm eff}}\\\\right)}+1},\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nwhere $g_{\\\\nu}$ is a statistical factor\\n($g_{\\\\nu}=1$ for a neutrino).\\n$\\\\varepsilon_{\\\\nu}/(k T_{\\\\rm eff})$ is constant along a neutrino ray,\\nsince the redshift is cancelled out.\\nThus $n(\\\\varepsilon_{\\\\nu})$ is conserved along a neutrino ray\\nin accordance with Liouville's theorem in curved spacetime\\n(Misner, Thorne \\\\& Wheeler 1975).\\nFrom the above formulation, one can find\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\frac{dN(\\\\mbox{\\\\boldmath$r$})}{dt dV}=\\n2 c K G_{\\\\rm F}^2 F(r) \\\\int \\\\int d \\\\varepsilon_{\\\\nu} d \\\\varepsilon_{\\\\bar{\\\\nu}}\\nn(\\\\varepsilon_{\\\\nu}) n(\\\\varepsilon_{\\\\bar{\\\\nu}})\\n\\\\varepsilon_{\\\\nu}^3 \\\\varepsilon_{\\\\bar{\\\\nu}}^3,\\n\\\\label{num}\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nwhere the dimensionless factor $F(r)$ is written by\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{eqnarray}\\nF(r)&=&\\\\int_0^{\\\\theta_{\\\\rm M}} d \\\\theta_{\\\\nu} \\\\sin{\\\\theta_{\\\\nu}}\\n\\\\int_0^{\\\\theta_{\\\\rm M}} d \\\\theta_{\\\\bar{\\\\nu}} \\\\sin{\\\\theta_{\\\\bar{\\\\nu}}}\\n\\\\int_0^{2 \\\\pi} d \\\\varphi_{\\\\nu} \\\\int_0^{2 \\\\pi} d \\\\varphi_{\\\\bar{\\\\nu}} \\\\nonumber \\\\\\\\\\n&& \\\\times \\\\left( 1-\\\\sin{\\\\theta_{\\\\nu}} \\\\sin{\\\\theta_{\\\\bar{\\\\nu}}}\\n\\\\cos{(\\\\varphi_{\\\\nu}-\\\\varphi_{\\\\bar{\\\\nu}})}-\\\\cos{\\\\theta_{\\\\nu}} \\\\cos{\\\\theta_{\\\\bar{\\\\nu}}}\\n\\\\right)^2 \\\\label{Fr} \\\\\\\\\\n&=& \\\\frac{2 \\\\pi^2 (1-X)^4}{3} (X^2+4X+5),\\n\\\\end{eqnarray}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nwhere\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\nX = \\\\sqrt{1-\\\\left( \\\\frac{R_{\\\\nu}}{r} \\\\right)^2\\n\\\\frac{1-\\\\frac{r_{g}}{r}}{1-\\\\frac{r_{g}}{R_{\\\\nu}}}}.\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nIn our assumption, the energy deposited by the neutrino pair annihilation\\nis propagated outward as a fireball or a shock wave,\\nand observed as a GRB by a distant observer.\\nThus the energy we need to calculate is $\\\\varepsilon_{0 \\\\nu}$,\\nnot the proper energy $\\\\varepsilon_{\\\\nu}$.\\nIn this case the energy deposition rate is obtained by putting a factor\\n$(\\\\varepsilon_{0 \\\\nu}+\\\\varepsilon_{0 \\\\bar{\\\\nu}})$ in the integrand\\nin equation (\\\\ref{num});\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{eqnarray}\\n\\\\frac{dE_0 (\\\\mbox{\\\\boldmath$r$})}{dt dV}&=&\\n\\\\frac{2 c K G_{\\\\rm F}^2}{\\\\left( 1-\\\\frac{r_{g}}{r} \\\\right)^4}\\n\\\\int_0^{\\\\infty} \\\\int_0^{\\\\infty} d \\\\varepsilon_{0 \\\\nu} d \\\\varepsilon_{0 \\\\bar{\\\\nu}}\\n\\\\nonumber \\\\label{depo} \\\\\\\\\\n&& \\\\times n(\\\\varepsilon_{0 \\\\nu}) n(\\\\varepsilon_{0 \\\\bar{\\\\nu}})\\n\\\\varepsilon_{0 \\\\nu}^3 \\\\varepsilon_{0 \\\\bar{\\\\nu}}^3\\n(\\\\varepsilon_{0 \\\\nu}+\\\\varepsilon_{0 \\\\bar{\\\\nu}}) F(r) \\\\\\\\\\n&=& \\\\frac{21 \\\\pi^4}{4} \\\\zeta(5) \\\\frac{K G_{\\\\rm F}^2 g_{\\\\nu}^2}{h^6 c^5}\\n\\\\frac{\\\\left( 1-\\\\frac{r_{g}}{R_{\\\\nu}} \\\\right)^{\\\\frac{9}{2}}}\\n{\\\\left( 1-\\\\frac{r_{g}}{r} \\\\right)^4} (k T_{\\\\rm eff})^9 F(r).\\n\\\\label{depo2}\\n\\\\end{eqnarray}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nThe integrals for $\\\\varepsilon_{0 \\\\nu}$ and $\\\\varepsilon_{0 \\\\bar{\\\\nu}}$\\nshould be defined in the range in which the total energy\\nproduced by the pair annihilation is larger than the mass of created electrons,\\nand smaller than the masses of weak bosons.\\nHere we have approximated the integrals as expressed in equation (\\\\ref{depo})\\nin the same manner as Salmonson \\\\& Wilson (1999) did.\\nThis is because the cross section decreases with the energy of neutrinos,\\nand the number of neutrinos whose energy is larger than the masses of weak bosons\\nis also very small in our assumption ($k T_{\\\\rm eff}$ is of the order of several MeV).\\nThe factor $( 1-r_{g}/R_{\\\\nu})^{9/2} /( 1-r_{g}/r )^4$ represents\\nthe effect of the gravitational redshift,\\nand $F(r)$ includes the effect of the orbital bending.\\n\\nAs is understood from the Lorentz invariant, $dtdV=\\\\sqrt{-g} d^4 x$,\\nif we integrate equation (\\\\ref{depo2}) over proper volume,\\n$dV'=\\\\sqrt{-g_{rr} g_{\\\\theta \\\\theta} g_{\\\\varphi \\\\varphi}} dr d\\\\theta d\\\\varphi$,\\nwe can obtain the total energy deposition per unit proper time,\\n$d \\\\tau=\\\\sqrt{g_{00}} dt$.\\nIt is natural to evaluate the energy deposition rate\\nby the world time $dt$ for a distant observer.\\nWe integrate over the volume,\\n$dV=\\\\sqrt{g_{\\\\theta \\\\theta} g_{\\\\varphi \\\\varphi}} dr d\\\\theta d\\\\varphi$.\\nThus the energy deposition per unit world time is expressed as\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\frac{dE_0}{dt}=\\n\\\\frac{21 \\\\pi^4}{4} \\\\zeta(5) \\\\frac{K G_{\\\\rm F}^2 g_{\\\\nu}^2}{h^6 c^5} (k T_{\\\\rm eff})^9\\n\\\\left( 1-\\\\frac{r_{g}}{R_{\\\\nu}} \\\\right)^{\\\\frac{9}{2}}\\n\\\\int_{R_{\\\\nu}}^{\\\\infty} dr 4 \\\\pi r^2\\n\\\\frac{F(r)}{\\\\left( 1-\\\\frac{r_{g}}{r} \\\\right)^4} C(r),\\n\\\\label{result}\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nwhere we have put a factor,\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\nC(r)=\\\\frac{1}{2} \\\\left( 1+\\\\sqrt{1-\\\\frac{27}{4} \\\\left( \\\\frac{r_{g}}{r} \\\\right)^2\\n\\\\left( 1-\\\\frac{r_{g}}{r} \\\\right) } \\\\right),\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nin the integrand.\\nThis is the escape probability of the deposited energy at $r$\\nfrom the gravitational attraction\\n(Chandrasekhar 1983; Shapiro \\\\& Teukolsky 1983; Ruffert \\\\& Janka 1999).\\nThe electrons, positrons and photons which are captured by the gravitational attraction\\ncannot contribute to the energy source of GRBs.\\nApart from $C(r)$,\\nthe radial profile in the integrand of equation (\\\\ref{result}) \\nis different from those of Salmonson \\\\& Wilson (1999),\\nsince Salmonson \\\\& Wilson calculated the proper energy deposition per\\nunit proper time.\\nOf course, the results of Salmonson \\\\& Wilson are not mistakes for the estimate of\\nthe energy deposition rate in supernovae.\\nFor the source of GRBs, however,\\nequation (\\\\ref{result}) is adequate.\\n\\nLet us investigate the effects of the redshift, orbital bending and gravitational capture.\\nWe integrate equation (\\\\ref{result}) and obtain\\nthe energy deposition rate for $\\\\nu_{e}$ as\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\frac{dE_0}{dt}=1.27 \\\\times 10^{42} \\\\left( \\\\frac{k T_{\\\\rm eff}}{1 {\\\\rm MeV}} \\\\right)^9\\n\\\\left( \\\\frac{R_{\\\\nu}}{10 {\\\\rm km}} \\\\right)^3 f \\\\quad \\\\mbox{ergs ${\\\\rm s^{-1}}$},\\n\\\\label{Gf}\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nwhere the dimensionless factor $f$ expresses the effects of the general relativity\\n($f=1$ when we neglect the gravitation).\\nThe energy deposition rates for $\\\\nu_{\\\\mu}$ and $\\\\nu_{\\\\tau}$ are 0.64 times\\nequation (\\\\ref{Gf}).\\nWe numerically estimate $f$ including the effects of the redshift only,\\nthe orbital bending only, or both redshift and orbital bending.\\nLast, the total effects of the redshift, orbital bending, and gravitational capture\\nare calculated.\\nThe results are listed in Table 1.\\nAs Table 1 or equation (\\\\ref{result}) indicates,\\nthe effect of the redshift reduces the energy deposition rate,\\nand the effect of the orbital bending increases it.\\nAlthough each effect, that of the redshift and that of orbital bending, is substantial,\\nthe effects partly cancel each other.\\nAs a result, the order of the energy deposition rate for\\nthe most probable case, $R_{\\\\nu}/r_g=2.5$, is not altered.\\nWhen we neglect the general relativistic effects, the energy deposition rate\\nincreases by 1.3 times as $R_{\\\\nu}$ becomes 10\\\\%\\nlarger, and also increases by 2.4 times as the temperature becomes 10\\\\%\\nhigher.\\nTherefore, the gravitational effects are not so large in comparison with\\nthe errors due to the uncertainties of $R_{\\\\nu}$ or $T_{\\\\rm eff}$,\\nand are overwhelmed by them.\\nThe effect of the gravitational capture becomes important\\nas $R_{\\\\nu}/r_g$ decreases.\\nAs is plotted in Figure 2, in the cases of both the presence and absence\\nof gravitation, the energy deposition mainly occurs near the neutrinosphere.\\n\\n\\nSalmonson \\\\& Wilson (1999) concluded that the effects of gravity\\nenhance the energy deposition rate up to a factor of more than\\n4 for $R_{\\\\nu} \\\\le 2.5 r_g$. However, our results\\nshow that the gravitational effects reduce the energy deposition rate.\\nThis discrepancy survives even if we omit the escape factor $C(r)$.\\nThe proper energy deposition per unit proper time is enhanced\\nby both the effects of the redshift and that of orbital bending.\\nAdditionally, Salmonson \\\\& Wilson expressed the general relativistic\\neffects with the fixed neutrino luminosity at infinity $L_{\\\\infty}$,\\nwhereas we have done so with the local physical quantity $T_{\\\\rm eff}$.\\nTherefore, an additional factor coming from the redshift of the luminosity\\n($L(R_{\\\\nu}) \\\\propto T_{\\\\rm eff}^4$, $L_{\\\\infty}=(1-{r_g/R_{\\\\nu}})L(R_{\\\\nu})$)\\nenhances the energy deposition rate in the work of Salmonson \\\\& Wilson.\\nHowever, the quantity $L_{\\\\infty}$ of GRBs is not directly observable at present.\\nIt is more natural to study the effects for the given local parameters,\\n$T_{\\\\rm eff}$ or $L(R_{\\\\nu})$,\\nwhich is restricted or provided by models of the central engine.\\n\\n\\\\section{NEUTRINO PAIR ANNIHILATION AROUND THE ACCRETION DISK}\\n\\n\\\\indent\\n\\n\\nIn this section we investigate the energy deposition rate around the accretion disk.\\nIn order to simplify our formulation,\\nwe assume that the accretion disk is isothermal\\nand that the gravitational field is dominated\\nby the central Schwarzschild black hole.\\nWe neglect the rotation of the black hole.\\nThe accretion disk is assumed to be thin, and its self-gravitational effects\\nare neglected.\\nOf course, these idealizations may be far from the case of the realistic accretion disk.\\nHowever, we consider that this simple method is sufficient for qualitatively studying\\nthe gravitational effects on the energy deposition rate.\\nIn this case the equation of the energy deposition rate is\\nthe same as equation (\\\\ref{depo2}) provided that $F(r)$\\nis replaced by $F(r,\\\\theta)$ (it will be given below).\\nThe effect of the gravitational redshift can be easily incorporated,\\nwhereas the formulation of the neutrino bending is difficult to do\\nbecause the accretion disk emits neutrinos anisotropically.\\n\\nFirst, we calculate the dimensionless factor $F(r, \\\\theta)$\\nwithout the effect of gravity.\\nThe accretion disk is placed on the equatorial plane, $\\\\theta=\\\\pi/2$.\\nThe black hole is at the origin, and we consider\\na point $P=(r,\\\\theta,0)$ where pair annihilations occur (see Figure 3).\\nA neutrino is emitted from an arbitrary point on the disk $S=(R,\\\\pi/2,\\\\varphi)$,\\nwhere $R$ is limited in the range from $R_{\\\\rm in}$ to $R_{\\\\rm out}$.\\nThe neutrino emitted from $S$ travels straight and arrives at the point $P$.\\nLet us denote the angle components of the vector joining $S$ and $P$\\nby $(\\\\theta_{\\\\nu}, \\\\varphi_{\\\\nu})$.\\nThey are given by\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\cos{\\\\theta_{\\\\nu}}=\\\\frac{r \\\\cos{\\\\theta}}{\\\\sqrt{r^2+R^2-2 r R \\\\sin{\\\\theta} \\\\cos{\\\\varphi}}},\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\n%%%%%%%%%%%%%%%%%%%%%%%\\n%\\\\begin{equation}\\n%\\\\sin{\\\\theta_{\\\\nu}}=\\\\frac{\\\\sqrt{r^2 \\\\sin^2{\\\\theta}+R^2-2 r R \\\\sin{\\\\theta} \\\\cos{\\\\varphi}}}\\n%{\\\\sqrt{r^2+R^2-2 r R \\\\sin{\\\\theta} \\\\cos{\\\\varphi}}},\\n%\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\n%%%%%%%%%%%%%%%%%%%%%%%\\n%\\\\begin{equation}\\n%\\\\cos{\\\\varphi_{\\\\nu}}=\\\\frac{r \\\\sin{\\\\theta}-R \\\\cos{\\\\varphi}}\\n%{\\\\sqrt{r^2 \\\\sin^2{\\\\theta}+R^2-2 r R \\\\sin{\\\\theta} \\\\cos{\\\\varphi}}},\\n%\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\sin{\\\\varphi_{\\\\nu}}=\\\\frac{-R \\\\sin{\\\\varphi}}\\n{\\\\sqrt{r^2 \\\\sin^2{\\\\theta}+R^2-2 r R \\\\sin{\\\\theta} \\\\cos{\\\\varphi}}}.\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nThus $\\\\theta_{\\\\nu}$ and $\\\\varphi_{\\\\nu}$ are functions of $R$ and $\\\\varphi$\\nfor fixed $r$ and $\\\\theta$.\\nThe Jacobian $J \\\\equiv \\\\partial (\\\\theta_{\\\\nu}, \\\\varphi_{\\\\nu})/\\\\partial (R, \\\\varphi)$ is\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\nJ=\\\\frac{r R \\\\cos{\\\\theta}}\\n{\\\\sqrt{r^2 \\\\sin^2{\\\\theta}+R^2-2 r R \\\\sin{\\\\theta} \\\\cos{\\\\varphi}}\\n( r^2+R^2-2 r R \\\\sin{\\\\theta} \\\\cos{\\\\varphi})}.\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nConsequently, we obtain $F(r,\\\\theta)$ as\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{eqnarray}\\nF(r,\\\\theta)&=&\\\\int_{R_{\\\\rm in}}^{R_{\\\\rm out}} dR \\\\int_{R_{\\\\rm in}}^{R_{\\\\rm out}} dR'\\n\\\\int_0^{2 \\\\pi} d \\\\varphi \\\\int_0^{2 \\\\pi} d \\\\varphi' J J' \\\\nonumber \\\\\\\\\\n& \\\\times & \\\\sin{\\\\theta_{\\\\nu}} \\\\sin{\\\\theta_{\\\\bar{\\\\nu}}}\\n\\\\left( 1-\\\\sin{\\\\theta_{\\\\nu}} \\\\sin{\\\\theta_{\\\\bar{\\\\nu}}}\\n\\\\cos{(\\\\varphi_{\\\\nu}-\\\\varphi_{\\\\bar{\\\\nu}})}-\\\\cos{\\\\theta_{\\\\nu}} \\\\cos{\\\\theta_{\\\\bar{\\\\nu}}}\\n\\\\right)^2.\\n\\\\label{Frtheta}\\n\\\\end{eqnarray}\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\nIn equation (\\\\ref{Frtheta}) we adopt $R_{\\\\rm in}=3r_g$, the innermost stable orbit, and\\n$R_{\\\\rm out}=10r_g$ as Woosely (1993) assumed. $F(r,\\\\theta)$ derived from\\nthe numerical integral of equation (\\\\ref{Frtheta}) is plotted in Figure 4(a) and (b).\\nAs is shown in these figures, the energy deposition rate is maximized in the\\nvicinity of the accretion disk, where $F(r,\\\\theta) \\\\simeq 30-33$.\\nThe simulation of a neutron star merger by Ruffert \\\\& Janka\\n(1999) showed that the Paczy\\\\'nski-Wiita potential (Paczy\\\\'nski \\\\& Wiita 1980),\\nwhich mimics the effects of the general relativity,\\ngives a relatively more transparent disk for neutrinos than\\nthat given by the Newtonian potential.\\nThe profile of the energy deposition rate in the Paczy\\\\'nski-Wiita potential\\nis similar to our analytical one depicted in Figure 4(a), which shows that the rate takes\\nits maximum value on the surface of the disk.\\nOn the other hand, the simulated deposition rate in the Newtonian potential\\nis maximized near the rotation axis.\\nLet us calculate the energy deposition rate near the rotation axis,\\nwhere is the lowest baryon density region.\\nThus we calculate in the region $\\\\theta \\\\leq \\\\pi/4$\\nand obtain\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\frac{dE_0}{dt}=5.22 \\\\times 10^{43} \\\\left( \\\\frac{k T_{\\\\rm eff}}{1 {\\\\rm MeV}} \\\\right)^9\\n\\\\left( \\\\frac{r_g}{10 {\\\\rm km}} \\\\right)^3 G f \\\\quad \\\\mbox{ergs ${\\\\rm s^{-1}}$},\\n\\\\label{Gf2}\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nwhere the dimensionless quantity $G$ shows the relative contributions\\nfrom various regions in the absence of gravitation.\\n$G$ is normalized to unity when\\nwe integrate over the volume for $\\\\theta \\\\leq \\\\pi /4$ and $r=2r_g-10r_g$.\\nThe values of $G$ in the other regions are summarized in Table 2, from\\nwhich we can obtain the energy deposition rate in the respective region.\\nWe neglect the energy deposited inside $r=2 r_g$,\\nsince the baryon density in this region is very high and\\nthe energy contribution is small for the small volume and deposition rate.\\nIn the case of the spherical emitter in section 2, the deposition rate decreases as\\n$r^{-8}$.\\nOn the other hand, around the accretion disk, as is seen from Table 2, there remains a\\nmarginal deposition rate even at regions relatively distant from the center.\\nOf course the deposition rate per unit volume at distant positions is small.\\nHowever, large volume results in a non-negligible contribution at the regions\\ndistant from the center.\\n\\nUntill now we have neglected the gravitational effects.\\nIt is easy to incorporate the effects of the redshift and\\ntrapping by the central gravitational source in the preceding arguments of this\\nsection. However, the bending effect is difficult to treat, unlike the case\\nof the neutrinosphere, since the accretion disk emits neutrinos anisotropically.\\nThus we are forced to make some approximation.\\nAs is shown in Figure 4(b), the $\\\\theta$ dependence of $F(r,\\\\theta)$ is weak for \\nsmall $\\\\theta$.\\nWe may set $F(r,\\\\theta) \\\\simeq F(r,0)$ for $\\\\theta \\\\leq \\\\pi/4$.\\nIn the absence of gravitation if we adopt this\\napproximation in the region $\\\\theta \\\\leq \\\\pi /4$ and $r=2r_g-10r_g$,\\nwe obtain $G=0.81$.\\nThe exact value of $G$ is unity, and this approximation is not\\nnecessarily satisfactory. However, this approximation may be sufficient for the order\\nestimate of the gravitational effects.\\n\\nWe can obtain $F(r,0)$ including the effect of orbital bending\\nwith comparative ease,\\nsince the geometry of this case maintain the symmetry.\\nA neutrino is emitted from the disk at $R$ and $\\\\theta=\\\\pi/2$,\\nand it arrives at a point at $r$ and $\\\\theta=0$.\\nThe nearest distance, $r_0$,\\nfrom the origin to the orbit of neutrinos (Landau \\\\& Lifshitz 1979)\\nis numerically obtained from\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\pi/2=\\\\int_{\\\\rm C} \\\\frac{dr'}{r' \\\\sqrt{\\\\left( \\\\frac{r'}{r_0} \\\\right)^2\\n\\\\left(1-\\\\frac{r_g}{r_0} \\\\right)-\\\\left(1-\\\\frac{r_g}{r'} \\\\right)}}.\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nHere, in the case in which a neutrino passes through $r_0$\\nuntil it arrives at a point at $\\\\theta=0$,\\nthe integration for $r'$ is performed from $r_0$ to $R$ and $r$.\\nWhen the distance from the origin to the neutrino varies monotonically,\\nthe integration is performed from the smaller\\nto the larger of $r$ and $R$.\\nWe can get $\\\\theta_{\\\\nu}$ at $\\\\theta=0$ numerically from $r_0$ and the following equation;\\n%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{equation}\\n\\\\sin{\\\\theta_{\\\\nu}}=\\\\frac{r_0}{r} \\\\sqrt{\\\\frac{1-\\\\frac{r_g}{r}}{1-\\\\frac{r_g}{r_0}}}.\\n\\\\end{equation}\\n%%%%%%%%%%%%%%%%%%%%%%%\\nThe constant, $r_0$, or $\\\\theta_{\\\\nu}$, is a function of $r$ and $R$ in this case.\\nAs is easily understood, a neutrino coming from $R_{\\\\rm in}$ forms $\\\\theta_{\\\\rm m}$,\\nthe minimum value of $\\\\theta_{\\\\nu}$, at $\\\\theta=0$ and that from\\n$R_{\\\\rm out}$ forms the maximum value of $\\\\theta$, $\\\\theta_{\\\\rm M}$.\\nIntegrating equation (\\\\ref{Fr}) from $\\\\theta_{\\\\rm m}$ to $\\\\theta_{\\\\rm M}$,\\nwe obtain $F(r,0)$ involving gravitational effects.\\nIn Figure 5 we plot $F(r,0)$ for both the case when the bending is taken into\\nconsideration and the case when it is not.\\nIn comparison with the spherical case in Figure 2,\\nthe deposited energy at distant regions in the disk case\\nis marginally substantial.\\nIn the presence of bending, the peak of the energy deposition rate is\\nshifted to a little bit larger $r$ and the value of the rate at the peak\\nis about twice as larger as values obtained in the absence of bending.\\n\\nAlthough the $\\\\theta$ dependence of the gravitational effects may not necessarily\\nbe small, unlike $F(r,\\\\theta)$ in the absence of gravitation,\\nwe assume it is small here. Using $F(r,0)$\\nwith the bending effect, we calculate the energy deposition rate in the range\\n$\\\\theta \\\\le \\\\pi/4$ and $r=2 r_g-10 r_g$.\\nTable 3 lists the values of the factor $f$ that shows the gravitational effects.\\nThe $\\\\theta$-dependence is neglected in our calculation\\nexcept for the case involving the redshift only.\\nThus $f$ is normalized to unity when $F(r,\\\\theta)$\\n(in the case involving the effect of the redshift only)\\nor $F(r,0)$ (in the other cases) is integrated over $r$ and $\\\\theta$\\nin the absence of gravitation.\\nAs is easily seen, the gravitational effects cancel one another out.\\nThis is analogous to the neutrino sphere case in the previous section.\\n%%%\\nThis result strongly supports that of Ruffert \\\\& Janka (1999).\\nThey treated the system of the accretion torus and a black hole unlike our\\nsystem of the disk and a black hole.\\nUsing an approximation similar to ours,\\nthey analytically calculated\\nthe energy deposition rate due to the neutrino pair annihilation.\\nTheir result is that the gravitational effects reduce the deposition rate by a factor\\nof $10-30\\\\%$.\\nIt agrees well with our result.\\n%%%\\n\\nIn order to circumvent the baryon contamination problem,\\nthe energy fraction of baryonic matter in the fireball\\nmust be less than about $10^{-5}$ (Shemi \\\\& Piran 1990).\\nIf we adopt the duration time of the neutrino radiation to be $t_{\\\\rm\\ndur}=0.1$s and $T_{\\\\rm eff}=10$MeV,\\nthe highest mean mass densities $\\\\bar{\\\\rho}$ inside $\\\\theta=0-\\\\pi/3$ to resolve\\nthe above problem are\\n$10^6$g/${\\\\rm cm^3}$ for $r=2 r_g-5 r_g$,\\n$10^5$g/${\\\\rm cm^3}$ for $r=5 r_g-10 r_g$ and\\n$10^4$g/${\\\\rm cm^3}$ for $r=10 r_g-20 r_g$.\\nSince some fraction of energy really\\nescapes from the considered regions during the finite duration time,\\nthe above restrictions may become more stringent.\\n\\n\\n\\n\\n\\\\section{CONCLUSIONS}\\n\\n\\\\indent\\n\\nIn this article we have investigated semianalytically\\nthe neutrino pair annihilation near\\nthe neutrinosphere and around the thin accretion disk assuming that the\\ngravitational sources in both cases are described by the Schwarzschild metric.\\nThe accretion disk has been assumed to be a blackbody and isothermal.\\nThese assumptions enable us to treat these two cases based in an almost\\nunified fashion, which also clarifies the physical differences between these\\ntwo cases.\\nWe have studied the general relativistic effects only near the rotation axis,\\nbecause that region is especially of interest to the source of GRBs\\nand estimating the effect of orbital bending\\nfor large $\\\\theta$ is difficult.\\n\\n\\nThe general relativistic effects as a whole do not enhance the neutrino energy\\ndeposition rate in either case.\\nThe energy deposition rate is enhanced by\\nthe effect of orbital bending toward the center.\\nHowever, the enhancement is cancelled out by the effects of the redshift and\\ncapture by the gravitational attraction.\\nConsequently, numerical simulations of the neutrino energy\\ndeposition rate in various models can correctly estimate\\nthe order of the rate without considering the gravitational effects,\\nsince it is supposed\\nthat the thickness, shape, or temperature distribution of the disk or sphere\\ndoes not greatly affect the gravitational effects themselves.\\n%%%\\nTaking into account also the results of Ruffert \\\\& Janka (1999), the\\nconclusions mentioned above are strongly suggested to be valid in the following\\ngeometrical forms of the neutrino source: sphere, thin disk and torus.\\n%%%\\nWe have also shown that the neutrinos emitted from the disk can\\ndeposit energy at more distant regions than the neutrinos emitted\\nfrom the sphere.\\nThe importance in this article resides in\\nthe qualitative properties of the general relativistic effects.\\nThe quantitative calculations in this paper are not so important,\\nand should be investigated on the basis of more sophisticated models and simulations.\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\\\vspace{1.5cm}\\n\\n%We are grateful to A and the referee\\n%for their helpful advice.\\nWe appreciate the helpful advice of M. Ruffert.\\nThis work was partly supported by a Research Fellowship of the Japan Society for\\nthe Promotion of Science.\\n%and\\n%B\\n%for C.\\n%Lastly, we appreciate D for E.\\n\\n\\\\newpage\\n\\n\\\\begin{center}\\n{\\\\bf \\\\LARGE References}\\n\\\\end{center}\\n\\n\\\\medskip\\n\\n\\\\begin{description}\\n\\n\\\\item\\nBerezinsky, V. S., \\\\& Prilutsky, O. F. 1987, A\\\\&A 175, 309\\n\\\\item\\nChandrasekhar, S. 1983, The Mathematical Theory of Black Holes\\n(New York: Oxford)\\n\\\\item\\nCooperstein, J., Van Den Horn, L. J., \\\\& Baron, E. 1987, ApJ 321, L129\\n\\\\item\\nEichler, D., Livio, M., Piran, T., \\\\& Schramm, D. N. 1989, Nature 340, 126\\n\\\\item\\nGoodman, J., Dar, A., \\\\& Nussinov, S. 1987, ApJ 314, L7\\n\\\\item\\nJanka, H.-T., \\\\& Ruffert, M. 1996, A\\\\&A 307, L33\\n\\\\item\\nKatz, J. I. 1997, ApJ 490, 633\\n\\\\item\\nLandau, L. D., \\\\& Lifshitz, E. 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E. 1993, ApJ 405, 273\\n\\n\\n\\n\\n\\\\end{description}\\n\\\\newpage\\n\\n\\\\begin{center}\\n{\\\\bf \\\\large Figure captions}\\n\\\\end{center}\\n\\n\\n\\\\figcaption{Maximum angle $\\\\theta_{\\\\rm M}$ at a distance $r$ from the\\ncenter formed by neutrinos emitted from the surface of the neutrinosphere.\\nThe dashed line shows the orbit forming the maximum\\nangle in the absence of gravitation.}\\n\\n\\\\figcaption{The plot of $F(r)$ against $r$ for $R_{\\\\nu}=2.5r_g$ when neutrinos are\\nemitted isotropically.\\nThe solid (dashed) line shows $F(r)$ for the case in the presence (absence) of\\ngravitation. The origin is at $r=R_{\\\\nu}$.}\\n\\n\\\\figcaption{Geometry of neutrino's path.\\nA neutrino is emitted from a point $S=(R,\\\\pi/2,\\\\varphi)$ on the disk and arrives at\\n$P=(r,\\\\theta,0)$. The angular components of the vector joining $S$ and $P$ are\\n$(\\\\theta_{\\\\nu}, \\\\varphi_{\\\\nu})$.\\n$R$ (radius on the disk) is limited to the range from $R_{\\\\rm in}$ to $R_{\\\\rm out}$.}\\n\\n\\\\figcaption{Contour plot of $F(r,\\\\theta)$ where neutrinos are\\nemitted from the disk. Here gravitation has been neglected.\\n%%%\\n(a) Plot in Cartesian coordinates $(r \\\\sin{\\\\theta},r \\\\cos{\\\\theta})$.\\n(b) Plot in polar coordinates, $(r, \\\\theta)$.\\n%%%\\nThe contours\\nare plotted at unit intervals except for the line of $F(r,\\\\theta)=0.1$;\\n$\\\\theta=0$ and $\\\\theta=\\\\pi/2$ correspond to points on the rotation\\naxis and on the disk, respectively.}\\n\\n\\\\figcaption{Diagram of $F(r,0)$ vs. $r$\\nwhere neutrinos are emitted from the disk.\\nThe solid (dashed) line shows $F(r,0)$ for the case in which we\\nconsider (neglect) the effect of gravitational bending.}\\n\\n\\n\\n\\\\newpage\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{center}\\n\\\\begin{tabular}{ccccc}\\n\\\\hline \\\\hline\\n$R_{\\\\nu}/r_{g}$ & \\\\multicolumn{4}{c}{$f$} \\\\\\\\\\n&Redshift Only & Bending Only & Redshift and Bending & Whole \\\\\\\\ \\\\hline\\n1.5 & 0.32 & 4.7 & 0.97 & 0.57 \\\\\\\\\\n2.5 & 0.60 & 1.6 & 0.87 & 0.73 \\\\\\\\\\n5 & 0.81 & 1.2 & 0.93 & 0.89 \\\\\\\\ \\\\hline\\n\\\\end{tabular}\\n\\\\end{center}\\n{\\\\footnotesize Table~1. The dimensionless factor $f$ represents\\nthe general relativistic effects (see eq. [\\\\ref{Gf}])\\nwhen neutrinos are emitted isotropically from the neutrinosphere;\\n$f$ is normalized to unity in the absence of gravitation.\\nThe column headings \\\"Redshift Only\\\" and so on indicate\\nthe incorporated effects of gravitation;\\n\\\"Whole\\\" over the last column means that we incorporate\\nall gravitational effects, redshift, bending, and trapping.\\nThe energy deposition rate is enhanced by orbital bending\\nand reduced by the redshift and trapping.}\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{center}\\n\\\\begin{tabular}{cccc}\\n\\\\hline \\\\hline\\n$\\\\theta$ & $2 r_g-5 r_g$ & $5 r_g-10 r_g$ & $10 r_g-20 r_g$ \\\\\\\\ \\\\hline\\n$0-\\\\pi/4$ & 0.35 & 0.65 & 0.22 \\\\\\\\\\n$\\\\pi/4-\\\\pi/3$ & 0.32 & 0.77 & 0.17 \\\\\\\\ \\\\hline\\n%$\\\\pi/3-\\\\pi/2$ & 2.27 & 0.21 \\\\\\\\ \\\\hline\\n\\\\end{tabular}\\n\\\\end{center}\\n{\\\\footnotesize Table~2. The dimensionless factor $G$.\\nIt represents the fraction of the energy deposition rate for each region\\n(see eq. [\\\\ref{Gf2}])\\nwhen neutrinos are emitted from the disk.\\n$G$ is normalized to unity for the region surrounded by\\n$r=2 r_g-10 r_g$ and $\\\\theta=0-\\\\pi/4$.\\nHere we neglect the effects of gravitation.}\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{center}\\n\\\\begin{tabular}{ccccc}\\n\\\\hline \\\\hline\\nrange & \\\\multicolumn{4}{c}{$f$} \\\\\\\\\\n&redshift only & bending only & redshift and bending & whole \\\\\\\\ \\\\hline\\n$2 r_g-5 r_g$ & 0.66 & 2.6 & 1.6 & 1.4 \\\\\\\\ \\n$5 r_g-10 r_g$ & 0.31 & 2.5 & 0.78 & 0.75 \\\\\\\\ \\\\hline\\n\\\\end{tabular}\\n\\\\end{center}\\n{\\\\footnotesize Table~3. The dimensionless factor $f$ for $\\\\theta=0-\\\\pi/4$\\n(see equation [\\\\ref{Gf2}]).\\nNeutrinos are emitted from the disk;\\n$f$ is normalized to unity when $F(r,\\\\theta)$\\n(in the case involving the effect of the redshift only)\\nor $F(r,0)$ (in the other cases) is integrated over $r$ and $\\\\theta$\\nin the absence of gravitation.}\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%\\\\begin{center}\\n%\\\\begin{tabular}{cccc}\\n%\\\\hline \\\\hline\\n%$\\\\theta$ & $2 r_g-5 r_g$ & $5 r_g-10 r_g$ & $10 r_g-20 r_g$ \\\\\\\\ \\\\hline\\n%$0-\\\\pi/4$ & $1.8 \\\\times 10^7$ & $2.5 \\\\times 10^6$ & $3.2 \\\\times 10^5$ \\\\\\\\\\n%$\\\\pi/4-\\\\pi/3$ & $2.5 \\\\times 10^7$ & $3.4 \\\\times 10^6$ & $4.3 \\\\times 10^5$ \\\\\\\\ \\\\hline\\n%\\\\end{tabular}\\n%\\\\end{center}\\n%{\\\\footnotesize Table~4. The highest mean density $\\\\bar{\\\\rho}$ for $\\\\eta \\\\geq 10^5$.\\n%We assume $T_{\\\\rm eff}=10$ MeV.}\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\\\end{document}\"\n }\n]"},"bibtex":{"kind":"list like","value":[],"string":"[]"}}},{"rowIdx":194,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002197"},"title":{"kind":"string","value":"First VLT spectra of white dwarfs in a globular cluster"},"authors":{"kind":"list like","value":[{"author":"S.~Moehler\\inst{1}\\fnmsep\\thanks{Based on observations collected at the European Southern Observatory (ESO~N$^{\\b{o}}$~63.H-0348)}"},{"author":"U.~Heber\\inst{1}"},{"author":"R. Napiwotzki\\inst{1}"},{"author":"D. Koester\\inst{2}"},{"author":"A. Renzini\\inst{3}"}],"string":"[\n {\n \"author\": \"S.~Moehler\\\\inst{1}\\\\fnmsep\\\\thanks{Based on observations collected at the European Southern Observatory (ESO~N$^{\\\\b{o}}$~63.H-0348)}\"\n },\n {\n \"author\": \"U.~Heber\\\\inst{1}\"\n },\n {\n \"author\": \"R. Napiwotzki\\\\inst{1}\"\n },\n {\n \"author\": \"D. Koester\\\\inst{2}\"\n },\n {\n \"author\": \"A. Renzini\\\\inst{3}\"\n }\n]"},"abstract":{"kind":"string","value":"We present the first spectra obtained with the {\\em Very Large Telescope} for white dwarfs in a globular cluster. Estimates of atmospheric parameters are obtained and compared to evolutionary tracks. We discuss possible implications for the distance scale of globular clusters and white dwarf evolution and demonstrate how white dwarfs might be used to establish an independent distance scale to globular clusters."},"latex":{"kind":"list like","value":[{"name":"b1293.tex","string":"\\documentclass{aa}\n\\begin{document}\n\\newcommand\\bsec{\\hbox{$.\\!\\!{\\arcsec}$}}\n\\newcommand\\rsec{\\hbox{$.\\!\\!{^s}$}}\n\\newcommand\\RA[4]{#1$^{\\rm h}$#2$^{\\rm m}$#3\\rsec#4}\n\\newcommand\\DEC[3]{#1$^{\\circ}$#2\\arcmin#3\\arcsec}\n\\newcommand{\\magpt}[2]{\\mbox{$\\rm #1\\hspace{-0.25em}\\stackrel{m}{.}\n \\hspace{-1.0mm}#2$}} % magnitude \\magpt {}{}\n\\newcommand\\ebv{$E_{B-V}$} \n\\newcommand\\teff{$T_{\\rm eff}$} \n\\newcommand\\logt{$ \\log\\,T_{\\rm eff}$}\n\\newcommand\\logg{$ \\log\\,g$}\n\\newcommand\\loghe{$ \\log{\\frac{n_{\\rm He}}{n_{\\rm H}}}$}\n\\newcommand\\Msolar{${\\rm M_\\odot}$}\n\\thesaurus{01 (08.06.3, 08.16.3, 08.23.1, 10.07.3 NGC~6397)}\n\n\\title{First VLT spectra of white dwarfs in a globular cluster}\n\\author{S.~Moehler\\inst{1}\\fnmsep\\thanks{Based on observations collected at the \n European Southern Observatory (ESO~N$^{\\b{o}}$~63.H-0348)} \n \\and U.~Heber\\inst{1} \\and R. Napiwotzki\\inst{1} \\and\n D. Koester\\inst{2} \\and A. Renzini\\inst{3}}\n\\offprints{S.~Moehler}\n\\institute {Dr. Remeis-Sternwarte, Astronomisches Institut der Universit\\\"at\n Erlangen-N\\\"urnberg, Sternwartstr. 7, 96049 Bamberg, Germany \n (e-mail: moehler,heber,napiwotzki@sternwarte.uni-erlangen.de)\n\\and Institut f\\\"ur Theoretische Physik und Astrophysik, Abteilung \n Astrophysik, Leibnizstr. 15, D-24098 Kiel, Germany\n\\and European Southern Observatory, Karl Schwarzschild-Str. 2, D-85748 \nGarching bei M\\\"unchen, Germany\n}\n\\date{}\n%\\titlerunning{}\n\\maketitle\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% FOLLOWING TYPESETTING RULES SET OUT IN \"ASTRONOMY AND ASTROPHYSICS %%\n%% INSTRUCTIONS FOR AUTHORS\" -- ASTRON. ASTROPHYS. 341 (1) 1999 %% \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\begin{abstract}\nWe present the first spectra obtained with the {\\em Very Large Telescope}\nfor white dwarfs in a\nglobular cluster. Estimates of atmospheric parameters are obtained and\ncompared to evolutionary tracks. We discuss possible implications for the\ndistance scale of globular clusters and white dwarf evolution and\ndemonstrate how white dwarfs might be used to establish an independent\ndistance scale to globular clusters. \n\\end{abstract}\n\n\\keywords{Stars: fundamental parameters -- Stars: Population~II -- Stars: \n white dwarfs -- globular clusters: individual: NGC~6397}\n\n\\section{Introduction} \nWhite dwarfs are the final stage of all low-mass stars and therefore all\nsingle stars in a globular cluster that currently finish their\nnuclear-burning lifetimes are expected to evolve into white dwarfs. As this\nhas been the situation for many billions of years globular clusters should\ncontain many white dwarfs. However, these stars managed to evade detection\nuntil photometric white dwarf sequences in globular clusters were\ndiscovered recently by observations with the {\\em Hubble Space Telescope}\n(HST) (Paresce et al.\\ \\cite{pade95}, Richer et al.\\ \\cite{rifa95},\n\\cite{rifa97}, Cool et al.\\ \\cite{copi96}, Renzini et al.\\ \\cite{rebr96}).\nPhotometric observations contain only a limited amount of information: The\ntwo chemically distinct white dwarfs sequences (hydrogen-rich DA's and\nhelium-rich DB's) in principle can be distinguished by their photometric\nproperties alone in the temperature range $10,000\\,K \\leq T_{\\mathrm{eff}}\n\\leq 15,000$\\,K (see Bergeron et al.\\ \\cite{bewe95}). Renzini et al.\\\n(\\cite{rebr96}) classified two white dwarfs in NGC\\,6752 as DB's by this\nmethod. However, without a spectral classification, both stars can also be\nexplained as high mass DA white dwarfs, possibly a product of merging.\nRicher et al.\\ (\\cite{rifa97}) speculate that the brightest white dwarf in\nM\\,4 (V=22.08) might be a hot (27,000K) DB star. \n\\newline\\indent\nThe location of the white dwarf cooling sequence (and thus the brightness\nof the white dwarfs) is also sensitive to the white dwarf mass. Renzini et\nal.\\ (\\cite{rebr96}) argued that the white dwarf masses in globular\nclusters are constrained to the narrow range 0.51\\Msolar $\\leq {\\rm M_{WD}}\n\\leq$ 0.55\\Msolar, but some systematic differences between clusters are\nobvious: At a given metallicity some globular clusters (e.g.\\ NGC\\,6752)\npossess very blue horizontal branches (HB's) with HB star masses as low as\n0.50\\Msolar. Such extreme HB stars evolve directly to low-mass C/O white\ndwarfs (bypassing the AGB), shifting the mean white dwarf mass closer to\n0.51\\Msolar. Other clusters show only red HB stars, which will evolve to\nthe AGB and form preferably white dwarfs with masses of $\\approx$0.55\\Msolar. \n\\begin{figure}\n\\vspace{8cm}\n\\special{psfile=b1293.f1 hscale=100 vscale=100 hoffset=-130 voffset=-330\nangle=0}\n\\caption{Colour-magnitude diagram of NGC~6397 (King et al.\\ \\cite{kian98},\ntheir Fig.~2). Open circles mark the four white dwarfs for which spectra \ncould be obtained, the open square marks WF4-205 (see text).\\label{cmd}} \n\\end{figure}\nLow-mass white dwarfs (M$<$0.45\\Msolar) with a degenerate He core are\nproduced if the red giant branch evolution is terminated by binary\ninteraction before the helium core exceeds the minimum mass for helium\nburning. Recently, Cool et al.\\ (\\cite{cogr98}) found 3 faint UV-bright\nstars in NGC\\,6397 which they suggest could be He white dwarfs (supported\nby Edmonds et al.\\ \\cite{edgr99}). Massive white dwarfs may be produced\nfrom blue stragglers or by collisions of white dwarf-binaries with\nsubsequent merging (e.g. Marsh et al.\\ \\cite{madh95}). \n\\newline\\indent\nOnly a detailed spectroscopic investigation can provide masses and absolute\nluminosities of the individual globular cluster white dwarfs. This is also\nvery important for the use of white dwarfs as standard candles to derive\ndistances to globular clusters (Renzini et al.\\ \\cite{rebr96}): The basic\nidea is to fit the white dwarf cooling sequence of a globular cluster to an\nappropriate empirical cooling sequence of local white dwarfs with well\ndetermined trigonometric parallaxes. The procedure is analogous to the\nclassical main sequence fitting but avoids the complications with\nmetallicity -- white dwarfs have virtually metal free atmospheres. In\naddition they are locally much more abundant than metal-poor subdwarfs. The\narrival of the {\\sc Hipparcos} results as well as new metallicity\ndeterminations have rekindled the debate on globular cluster distances (see\nthe review by Reid \\cite{reid99} and references therein). A further check\non the distance is therefore urgently needed. \n\\newline\\indent\nWe started an observing programme at the ESO {\\em Very Large Telescope\n(VLT)} to obtain spectra of white dwarfs in globular clusters. The\nprogramme consists of two parts: First, low S/N ($\\approx 10$) spectra of\nthe white dwarf candidates are obtained to verify their spectral type and\nestimate their effective temperatures. In a second run we plan to observe\nhigher S/N ($\\approx 30$) spectra that will allow to derive \\logg\\ with an\ninternal error of $\\le 0.1$dex. Here we report on the very first results\nfor NGC~6397. \n\n\\begin{table}\n\\caption{Target coordinates and photometric data (Cool priv. comm.). \n\\label{targ}}\n\\begin{tabular}{lrrrr}\n\\hline\nStar & $\\alpha_{2000}$ & $\\delta_{2000}$ & $V$ & $V-I$\\\\\n\\hline\nWF4-358 & \\RA{17}{40}{58}{52} & \\DEC{$-$53}{42}{25.3} & \\magpt{22}{73} & \n\\magpt{+0}{02}\\\\\nWF2-479 & \\RA{17}{41}{07}{06} & \\DEC{$-$53}{44}{45.1} & \\magpt{23}{87} & \n\\magpt{+0}{22}\\\\\nWF4-205 & \\RA{17}{41}{01}{58} & \\DEC{$-$53}{43}{15.3} & \\magpt{23}{99} &\n\\magpt{+0}{30}\\\\\nWF2-51 & \\RA{17}{41}{04}{52} & \\DEC{$-$53}{43}{55.8} & \\magpt{24}{00} & \n\\magpt{+0}{28}\\\\\nWF2-846 & \\RA{17}{41}{01}{78} & \\DEC{$-$53}{44}{47.2} & \\magpt{24}{30} & \n\\magpt{+0}{33}\\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\\begin{figure}\n\\vspace{8.5cm}\n\\special{psfile=b1293.f2 hscale=43 vscale=43 hoffset=-10 voffset=-70\nangle=0}\n\\caption{Traces through the slits along the spatial axis. The lines mark \nthe white dwarf spectra (WF4-205 unfortunately lies on the wing of a much \nbrighter star).\\label{slits}} \n\\end{figure}\n\n\\begin{figure}\n\\vspace{8.5cm}\n\\special{psfile=b1293.f3 hscale=43 vscale=43 hoffset=-10 voffset=-70\nangle=0}\n\\caption{The (relatively flux-calibrated) spectra of the white dwarfs in \nNGC~6397. The spectra of the three faintest stars \nare offset from each other as they would otherwise overlap. WF4-358 has no \nadditional offset relative to WF2-479.\\label{spectra}} \n\\end{figure}\n\\section{Observations and Data Reduction}\nCool et al.\\ (\\cite{copi96}) discovered the white dwarfs using the {\\em\nWide Field and Planetary Camera~2} (WFPC2) onboard the HST to observe the\nglobular cluster NGC~6397. From the improved colour-magnitude diagram of\nKing et al.\\ (\\cite{kian98}) targets brighter than $V\\approx25^{\\rm m}$\nwere selected (see Fig.~\\ref{cmd}). The WFPC2 images were convolved to a\nseeing of 0\\bsec5 to select targets that are sufficiently uncrowded to be\nobservable from the ground (see Table~\\ref{targ} and Fig.~\\ref{slits}). The\nstars were observed with the {\\em FOcal Reducer/low dispersion\nSpectrograph} (FORS) at Unit Telescope 1 of the VLT using the high\nresolution collimator (0\\bsec1/pixel) to allow better extraction of the\nspectra and get a better handle on cosmic rays. We used the {\\em\nmulti-object spectroscopy} (MOS) mode with the grism 300V and a slit width\nof 0\\bsec8. The slit width was chosen to be larger than the required seeing\nto avoid slit losses due to imperfect pointing of the telescope. The data\nwere obtained in service mode under excellent conditions (seeing below\n0\\bsec55, no moon) with a total exposure time of 90 minutes. The final\nresolution as judged from a wavelength calibration spectrum obtained with a\n0\\bsec5 slit is $\\approx$11.5~\\AA. A trace along the spatial axis of the\nslitlets at about 4550~\\AA\\ is plotted in Fig.~\\ref{slits}. Unfortunately\nWF4-205 lies so close to a bright star that even at this excellent\nseeing its spectrum could not be extracted. \n\nDue to the use of slit blades instead of fibers or masks the MOS slitlets\nare very well defined and can be treated like long slits. The spectra were\ntherefore corrected for bias, flat-fielded, wavelength calibrated, and\nextracted as described by Moehler et al.\\ (\\cite{mohe97}). We find only a\ndiffuse and rather low sky background without any strong sky lines below\n5150~\\AA. The spectra were relatively flux calibrated using LTT~7987\n(Hamuy et al.\\ \\cite{hawa92}) and are plotted in Fig.~\\ref{spectra}. All\nfour stars display only strong broad Balmer lines, which is characteristic\nfor hydrogen-rich white dwarfs (DA stars). \n\n\\section{Atmospheric parameters}\nAlthough the white dwarf spectra have low signal-to-noise, they are\nsufficient for rough parameter estimates. The atmospheric parameters are\nobtained by simultaneously fitting profiles of the observed Balmer lines\nwith model spectra using the least-square algorithm of Bergeron et al.\\\n(\\cite{besa92}; see Napiwotzki et al.\\ 1999 for minor modifications).\nAnalyses were performed with Koester's LTE models as described in Finley et\nal.\\ (\\cite{fiko97}). As a check we repeated the analysis of the hottest\nstar in our sample (WF4-358) with the non-LTE grid described in Napiwotzki\net al.\\ (\\cite{nagr99}). Since the non-LTE code does not treat convection\nand ignores molecular opacities reliable atmospheric models cannot be\ncalculated for the three cooler white dwarfs. \n\n\\begin{figure}\n\\vspace{8.cm}\n\\special{psfile=b1293.f4 hscale=43 vscale=43 hoffset=-10 voffset=-10 angle=0}\n\\caption{Sample fits to the spectra of WF4-358 (\\teff\\ =\n18,200~K, \\logg\\ = 7.3) and WF2-479 (\\teff\\ = 11,000~K, \\logg\\= = 7.7).\n\\label{wd_fit}} \n\\end{figure}\n\n\\begin{table}[h]\n\\caption{Effective temperatures and $\\chi^2$ values for the white dwarfs\nfrom the fit of H$_\\delta$, H$_\\gamma$, H$_\\beta$ at fixed \\logg\\ (see text\nfor details). Also given are masses derived from theoretical tracks of\nBl\\\"ocker (\\cite{bloe95}) and Driebe et al.\\ (\\cite{drsch98}) and absolute\nmagnitudes (Bergeron et al.\\ \\cite{bewe95}). Using Bergeron et al.'s\n(\\cite{bewe95}) Table~3 we derived $T_{\\rm eff, (V-I)_0}$ from $(V-I)_0$,\nwhich was calculated from $V-I$ assuming $E_{V-I}$ = \\magpt{0}{225}.\n\\label{tab-results}} \n\\begin{tabular}{lrrrrr}\n\\hline\nstar & $\\chi^2$ & \\teff & $T_{\\rm eff, (V-I)_0}$ & M & $M_V$ \\\\\n & & [K] & [K] & [\\Msolar] & \\\\\n\\hline\n\\multicolumn{6}{c}{\\logg\\ = 7.5}\\\\\n\\hline\nWF4-358 & 1.04 & 18900 & & 0.42 & \\magpt{10}{0} \\\\\nWF2-479 & 1.15 & 10800 & & 0.39 & \\magpt{11}{1} \\\\\nWF2-51 & 1.46 & 10900 & & 0.39 & \\magpt{11}{1} \\\\\nWF2-846 & 0.71 & 10500 & & 0.38 & \\magpt{11}{2} \\\\\n\\hline\n\\multicolumn{6}{c}{\\logg\\ = 7.7}\\\\\n\\hline\nWF4-358 & 1.07 & 19500 & & 0.48 & \\magpt{10}{3} \\\\\nWF2-479 & 1.14 & 11000 & & 0.46 & \\magpt{11}{4} \\\\\nWF2-51 & 1.46 & 11100 & & 0.46 & \\magpt{11}{4} \\\\\nWF2-846 & 0.71 & 10600 & & 0.46 & \\magpt{11}{5} \\\\\n\\hline\n\\multicolumn{6}{c}{\\logg\\ = 8.0}\\\\\n\\hline\nWF4-358 & 1.13 & 20300 & 19400 & 0.62 & \\magpt{10}{7} \\\\\nWF2-479 & 1.14 & 11200 & 11500 & 0.59 & \\magpt{11}{8} \\\\\nWF2-51 & 1.47 & 11300 & 10800 & 0.59 & \\magpt{11}{8} \\\\\nWF2-846 & 0.71 & 10800 & 10300 & 0.59 & \\magpt{11}{9} \\\\\n\\hline\n\\end{tabular}\\\\\n\\end{table}\nFitting the lines H$_\\beta$ to H$_\\epsilon$ for WF4-358 (see\nFig.~\\ref{wd_fit}) gives 18,200$\\pm$1300~K and 7.30$\\pm$0.36 for \\teff\\ and\n\\logg, respectively ($\\chi^2$ = 0.93). The errors given here are 1$\\sigma$\nerrors obtained from the $\\chi^2$ fit. Omitting H$_\\epsilon$ from the fit\nresults in 17,800~K and 7.19 ($\\chi^2$ = 1.02) with more or less unchanged\nerrors. The results of the non-LTE analysis are essentially identical to\nthose obtained with Koester's models, differing only by small fractions of\nthe formal errors ($\\Delta$\\teff $\\approx$500\\,K, $\\Delta$\\logg $\\approx$\n0.07\\,dex). The surface gravity is surprisingly low and suggests that\nWF4-358 could be a bright ($M_V$=\\magpt{9}{7}) helium white dwarf of\n(0.36$\\pm$0.12)\\Msolar. Within the error bars, however, the derived\nparameters are also consistent with a low-mass C/O white dwarf. For the\nremaining three stars the S/N is too low to determine \\teff\\ and \\logg\\\nsimultaneously. We thus fitted H$_\\delta$, H$_\\gamma$, H$_\\beta$\n(H$_\\epsilon$ being too noisy) for WF2-51, WF2-479, and WF2-846 for three\nfixed values of \\logg\\ (8.0, 7.7, 7.5, see Fig.~\\ref{wd_fit} for an\nexample). These \\logg\\ values correspond to C/O white dwarfs of $\\approx$\n0.6\\Msolar, low-mass C/O white dwarfs of $\\approx$0.5\\Msolar, and He white\ndwarfs of $\\approx$0.4\\Msolar, respectively (see below). The formal errors\nare $\\approx$550~K (WF2-479), $\\approx$650~K (WF2-846, WF4-358), and\n$\\approx$790~K (WF2-51). The errors for the cooler stars are relatively\nsmall despite their low S/N because -- at fixed \\logg\\ -- the line profiles\nare much more sensitive to temperature variations at \\teff\n$\\approx$11,000~K than at \\teff $\\approx$18,000~K. The relatively large\n$\\chi^2$ value for WF2-51 suggests that either the noise in this spectrum\nhas been underestimated or that the spectrum contains additional features\nthat are not well described by the model spectra. The temperatures derived\nfrom the Balmer lines agree quite well with those obtained from $(V-I)_0$\nusing the theoretical colours of Bergeron et al.\\ (\\cite{bewe95}, \\logg\\ = \n8.0). \n\nThe masses given in Table~\\ref{tab-results} were derived by interpolation\nbetween the evolutionary tracks of C/O white dwarfs calculated by Bl\\\"ocker\n(\\cite{bloe95}) and the He white dwarf tracks of Driebe et al.\\\n(\\cite{drsch98}). Finally, absolute magnitudes $M_V$ were calculated for\neach parameter set with the photometric calibration of Bergeron et al.\\\n(\\cite{bewe95}). \n\n\\section{The distance to NGC\\,6397} \nThe old distance modulus to NGC\\,6397 was $(m-M)_0$ = \\magpt{11}{71} with a\nreddening of \\ebv\\ of \\magpt{0}{18} (Djorgovski \\cite{djor93}). Using local\nmetal-poor subdwarfs to fit the main sequence of NGC\\,6397 Reid \\& Gizis\n(\\cite{regi98}) obtained a mean distance modulus\nof $(m-M)_0$ = \\magpt{12}{20}$\\pm$\\magpt{0}{15} for\n\\ebv\\ = \\magpt{0}{19}. Thus NGC\\,6397 is a good example for the large\ndifferences between old and new distances to globular clusters. The\nabsolute magnitudes given in Table~\\ref{tab-results} for \\logg\\ = 7.5, 7.7,\n8.0 (M$_{\\rm WD}$ = 0.4\\Msolar, 0.5\\Msolar, 0.6\\Msolar) yield mean true\ndistance moduli (for \\ebv\\ = \\magpt{0}{18}) $(m-M)_0$ of \\magpt{12}{3},\n\\magpt{12}{0}, and \\magpt{11}{6}, respectively, with an r.m.s. error of\n\\magpt{0}{17}. Considering the error bars of the various distance\ndeterminations the long distance scale would be more consistent with white\ndwarf masses $\\le$0.5\\Msolar\\ and the short distance scale with masses\n$>$0.5\\Msolar. The longer distance moduli obtained for low-mass white\ndwarfs also result in masses for blue HB stars (Heber et al.\\\n\\cite{hemo97}) and a hot post-AGB star (ROB\\,162, Heber \\& Kudritzki\n\\cite{heku86}) that agree with canonical evolutionary theory. \n\nThe distance moduli derived for a given \\logg\\ from Tables~\\ref{targ} and\n\\ref{tab-results} show a systematic variation with the brightest star\n(WF4-358) yielding the smallest distance and the faintest star (WF2-846)\ngiving the largest distance. This variation could reflect the fact that the\nstars may not all have the same surface gravity: From their different\napparent magnitudes (i.e. different absolute magnitudes) it is plausible\nthat WF4-358 has the smallest \\logg\\ and WF2-846 the largest. The quality\nof the current data, however, does not allow to verify this idea. \n\n\\section{Conclusions} \nUsing VLT-FORS1 multi object spectroscopy we have confirmed four white\ndwarf candidates to be hydrogen-rich DA white dwarfs. The gravity\ndetermined for the brightest star, WF4-358, suggests that it could be a He\nwhite dwarf with a mass of (0.36$\\pm$0.12)\\Msolar, although the error bars\nare large enough to also accommodate a C/O white dwarf. Temperatures derived\nfor the three cooler and fainter stars for fixed \\logg\\ would put them near\nthe red edge of the ZZ Ceti instability strip, for which Bergeron et al.\\\n(\\cite{bewe95b}) determine a temperature range of 11,160~K to 12,460~K\nusing their preferred ML2/$\\alpha$=0.6 prescription for the treatment of\nconvection. Therefore, a search for photometric variability of WF2-479 and\nWF2-51 -- if successful -- could place important additional constraints on\nthese stars. The systematic variation of the distance moduli derived for a\ngiven \\logg\\ shows that the assumption of a constant mass for\nall white dwarfs in a globular cluster may bias a distance determination.\nHowever, due to the low S/N of the current data, these results are\npreliminary. Once higher quality spectra are available, which will allow\nmore accurate parameter (and thus mass) determinations, analyses of white\ndwarfs in globular clusters will become a powerful tool for independent\ndistance estimates. \n\n\\acknowledgements\nWe highly appreciate the work performed by the FORS team in building an\nexcellent instrument and the efforts of the staff at the ESO Paranal\nobservatory and ESO Garching that made these observations possible. We\nthank Dr.\\ A.\\ Cool for providing us with the photometry and coordinates of\nthe white dwarf candidates and an anonymous referee for valuable comments.\nS.M. acknowledges financial support from the DARA under grant\n50~OR~96029-ZA. \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% FOLLOWING TYPESETTING RULES SET OUT IN \"ASTRONOMY AND ASTROPHYSICS %%\n%% INSTRUCTIONS FOR AUTHORS\" -- ASTRON. ASTROPHYS. 341 (1) 1999; %%\n%% JOURNAL ACRONYMS CAN BE FOUND AT THE FOLLOWING TWO WEB SITES: %%\n%% http://adsdoc.harvard.edu/abs_doc/refereed.html %%\n%% http://adsdoc.harvard.edu/abs_doc/non_refereed.html %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{thebibliography}{}\n\\bibitem[1992]{besa92}\nBergeron P., Saffer R.A., Liebert J., 1992, ApJ 394, 228\n\\bibitem[1995a]{bewe95}\nBergeron P., Wesemael F., Beauchamp A., 1995a, PASP 107, 1047\n\\bibitem[1995b]{bewe95b}\nBergeron P., Wesemael F., Lamontagne R., et al., 1995b, ApJ 449, 258\n\\bibitem[1995]{bloe95}\nBl\\\"ocker T., 1995, A\\&A 299, 755\n\\bibitem[1996]{copi96}\nCool A.M., Piotto G., King I.R., 1996, ApJ 468, 655\n\\bibitem[1998]{cogr98}\nCool A.M., Grindlay J.E., Cohn H.N., Lugger P.M., Bailyn C.D., 1998, ApJ \n508, L75\n%\\bibitem[1995]{dbsc95}\n% de Boer K.S., Schmidt J.H.K., Heber U., 1995, A\\&A 303, 95 \n\\bibitem[1993]{djor93}\nDjorgovski S., 1993, in {\\it Structure and Dynamics of Globular Clusters},\n eds. 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Ser. 50 (San Francisco),\n p. 373\n\\bibitem[1998]{drsch98}\nDriebe T., Sch\\\"onberner D., Bl\\\"ocker T., Herwig F., 1998, A\\&A 339, 123\n\\bibitem[1999]{edgr99}\nEdmonds P.D., Grindlay J.E., Cool A., et al., 1999, ApJ 516, 250\n\\bibitem[1997]{fiko97}\nFinley D.S., Koester D., Basri G., 1997, ApJ 488, 375\n\\bibitem[1992]{hawa92}\nHamuy M., Walker A.R., Suntzeff N.B., et al., 1992, PASP 104, 533\n\\bibitem[1986]{heku86}\nHeber U., Kudritzki R.P., 1986, A\\&A 169, 244\n\\bibitem[1997]{hemo97}\nHeber U., Moehler S., Reid I.N., 1997, ESA SP-402, p.461 \n\\bibitem[1998]{kian98}\nKing I.R., Anderson J., Cool A.M., Piotto G., 1998, ApJ 492, L37\n\\bibitem[1995]{madh95}\nMarsh T.R., Dhillon V.S., Duck S.R., 1995, MNRAS 275, 828\n\\bibitem[1997]{mohe97}\nMoehler S., Heber U., Rupprecht G., 1997, A\\&A 319, 109\n\\bibitem[1999]{nagr99}\nNapiwotzki R., Green P.J., Saffer R.A., 1999, ApJ 517,399\n\\bibitem[1995]{pade95}\nParesce F., de Marchi G., Romaniello M., 1995, ApJ 440, 216\n\\bibitem[1999]{reid99}\nReid I.N., 1999, ARAA 37, 191\n\\bibitem[1998]{regi98}\nReid I.N., Gizis J.E., 1998, AJ 116, 2929\n\\bibitem[1996]{rebr96}\nRenzini A., Bragaglia A., Ferraro F.R., et al., 1996, ApJ 465, L23\n\\bibitem[1995]{rifa95}\nRicher H.B., Fahlmann G.G., Ibata R.A., et al., 1995, ApJ 451, L17\n\\bibitem[1997]{rifa97}\nRicher H.B., Fahlmann G.G., Ibata R.A., et al., 1997, ApJ 484, 741\n\\end{thebibliography}{}\n\\end{document}\n"}],"string":"[\n {\n \"name\": \"b1293.tex\",\n \"string\": \"\\\\documentclass{aa}\\n\\\\begin{document}\\n\\\\newcommand\\\\bsec{\\\\hbox{$.\\\\!\\\\!{\\\\arcsec}$}}\\n\\\\newcommand\\\\rsec{\\\\hbox{$.\\\\!\\\\!{^s}$}}\\n\\\\newcommand\\\\RA[4]{#1$^{\\\\rm h}$#2$^{\\\\rm m}$#3\\\\rsec#4}\\n\\\\newcommand\\\\DEC[3]{#1$^{\\\\circ}$#2\\\\arcmin#3\\\\arcsec}\\n\\\\newcommand{\\\\magpt}[2]{\\\\mbox{$\\\\rm #1\\\\hspace{-0.25em}\\\\stackrel{m}{.}\\n \\\\hspace{-1.0mm}#2$}} % magnitude \\\\magpt {}{}\\n\\\\newcommand\\\\ebv{$E_{B-V}$} \\n\\\\newcommand\\\\teff{$T_{\\\\rm eff}$} \\n\\\\newcommand\\\\logt{$ \\\\log\\\\,T_{\\\\rm eff}$}\\n\\\\newcommand\\\\logg{$ \\\\log\\\\,g$}\\n\\\\newcommand\\\\loghe{$ \\\\log{\\\\frac{n_{\\\\rm He}}{n_{\\\\rm H}}}$}\\n\\\\newcommand\\\\Msolar{${\\\\rm M_\\\\odot}$}\\n\\\\thesaurus{01 (08.06.3, 08.16.3, 08.23.1, 10.07.3 NGC~6397)}\\n\\n\\\\title{First VLT spectra of white dwarfs in a globular cluster}\\n\\\\author{S.~Moehler\\\\inst{1}\\\\fnmsep\\\\thanks{Based on observations collected at the \\n European Southern Observatory (ESO~N$^{\\\\b{o}}$~63.H-0348)} \\n \\\\and U.~Heber\\\\inst{1} \\\\and R. Napiwotzki\\\\inst{1} \\\\and\\n D. Koester\\\\inst{2} \\\\and A. Renzini\\\\inst{3}}\\n\\\\offprints{S.~Moehler}\\n\\\\institute {Dr. Remeis-Sternwarte, Astronomisches Institut der Universit\\\\\\\"at\\n Erlangen-N\\\\\\\"urnberg, Sternwartstr. 7, 96049 Bamberg, Germany \\n (e-mail: moehler,heber,napiwotzki@sternwarte.uni-erlangen.de)\\n\\\\and Institut f\\\\\\\"ur Theoretische Physik und Astrophysik, Abteilung \\n Astrophysik, Leibnizstr. 15, D-24098 Kiel, Germany\\n\\\\and European Southern Observatory, Karl Schwarzschild-Str. 2, D-85748 \\nGarching bei M\\\\\\\"unchen, Germany\\n}\\n\\\\date{}\\n%\\\\titlerunning{}\\n\\\\maketitle\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%% FOLLOWING TYPESETTING RULES SET OUT IN \\\"ASTRONOMY AND ASTROPHYSICS %%\\n%% INSTRUCTIONS FOR AUTHORS\\\" -- ASTRON. ASTROPHYS. 341 (1) 1999 %% \\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\n\\\\begin{abstract}\\nWe present the first spectra obtained with the {\\\\em Very Large Telescope}\\nfor white dwarfs in a\\nglobular cluster. Estimates of atmospheric parameters are obtained and\\ncompared to evolutionary tracks. We discuss possible implications for the\\ndistance scale of globular clusters and white dwarf evolution and\\ndemonstrate how white dwarfs might be used to establish an independent\\ndistance scale to globular clusters. \\n\\\\end{abstract}\\n\\n\\\\keywords{Stars: fundamental parameters -- Stars: Population~II -- Stars: \\n white dwarfs -- globular clusters: individual: NGC~6397}\\n\\n\\\\section{Introduction} \\nWhite dwarfs are the final stage of all low-mass stars and therefore all\\nsingle stars in a globular cluster that currently finish their\\nnuclear-burning lifetimes are expected to evolve into white dwarfs. As this\\nhas been the situation for many billions of years globular clusters should\\ncontain many white dwarfs. However, these stars managed to evade detection\\nuntil photometric white dwarf sequences in globular clusters were\\ndiscovered recently by observations with the {\\\\em Hubble Space Telescope}\\n(HST) (Paresce et al.\\\\ \\\\cite{pade95}, Richer et al.\\\\ \\\\cite{rifa95},\\n\\\\cite{rifa97}, Cool et al.\\\\ \\\\cite{copi96}, Renzini et al.\\\\ \\\\cite{rebr96}).\\nPhotometric observations contain only a limited amount of information: The\\ntwo chemically distinct white dwarfs sequences (hydrogen-rich DA's and\\nhelium-rich DB's) in principle can be distinguished by their photometric\\nproperties alone in the temperature range $10,000\\\\,K \\\\leq T_{\\\\mathrm{eff}}\\n\\\\leq 15,000$\\\\,K (see Bergeron et al.\\\\ \\\\cite{bewe95}). Renzini et al.\\\\\\n(\\\\cite{rebr96}) classified two white dwarfs in NGC\\\\,6752 as DB's by this\\nmethod. However, without a spectral classification, both stars can also be\\nexplained as high mass DA white dwarfs, possibly a product of merging.\\nRicher et al.\\\\ (\\\\cite{rifa97}) speculate that the brightest white dwarf in\\nM\\\\,4 (V=22.08) might be a hot (27,000K) DB star. \\n\\\\newline\\\\indent\\nThe location of the white dwarf cooling sequence (and thus the brightness\\nof the white dwarfs) is also sensitive to the white dwarf mass. Renzini et\\nal.\\\\ (\\\\cite{rebr96}) argued that the white dwarf masses in globular\\nclusters are constrained to the narrow range 0.51\\\\Msolar $\\\\leq {\\\\rm M_{WD}}\\n\\\\leq$ 0.55\\\\Msolar, but some systematic differences between clusters are\\nobvious: At a given metallicity some globular clusters (e.g.\\\\ NGC\\\\,6752)\\npossess very blue horizontal branches (HB's) with HB star masses as low as\\n0.50\\\\Msolar. Such extreme HB stars evolve directly to low-mass C/O white\\ndwarfs (bypassing the AGB), shifting the mean white dwarf mass closer to\\n0.51\\\\Msolar. Other clusters show only red HB stars, which will evolve to\\nthe AGB and form preferably white dwarfs with masses of $\\\\approx$0.55\\\\Msolar. \\n\\\\begin{figure}\\n\\\\vspace{8cm}\\n\\\\special{psfile=b1293.f1 hscale=100 vscale=100 hoffset=-130 voffset=-330\\nangle=0}\\n\\\\caption{Colour-magnitude diagram of NGC~6397 (King et al.\\\\ \\\\cite{kian98},\\ntheir Fig.~2). Open circles mark the four white dwarfs for which spectra \\ncould be obtained, the open square marks WF4-205 (see text).\\\\label{cmd}} \\n\\\\end{figure}\\nLow-mass white dwarfs (M$<$0.45\\\\Msolar) with a degenerate He core are\\nproduced if the red giant branch evolution is terminated by binary\\ninteraction before the helium core exceeds the minimum mass for helium\\nburning. Recently, Cool et al.\\\\ (\\\\cite{cogr98}) found 3 faint UV-bright\\nstars in NGC\\\\,6397 which they suggest could be He white dwarfs (supported\\nby Edmonds et al.\\\\ \\\\cite{edgr99}). Massive white dwarfs may be produced\\nfrom blue stragglers or by collisions of white dwarf-binaries with\\nsubsequent merging (e.g. Marsh et al.\\\\ \\\\cite{madh95}). \\n\\\\newline\\\\indent\\nOnly a detailed spectroscopic investigation can provide masses and absolute\\nluminosities of the individual globular cluster white dwarfs. This is also\\nvery important for the use of white dwarfs as standard candles to derive\\ndistances to globular clusters (Renzini et al.\\\\ \\\\cite{rebr96}): The basic\\nidea is to fit the white dwarf cooling sequence of a globular cluster to an\\nappropriate empirical cooling sequence of local white dwarfs with well\\ndetermined trigonometric parallaxes. The procedure is analogous to the\\nclassical main sequence fitting but avoids the complications with\\nmetallicity -- white dwarfs have virtually metal free atmospheres. In\\naddition they are locally much more abundant than metal-poor subdwarfs. The\\narrival of the {\\\\sc Hipparcos} results as well as new metallicity\\ndeterminations have rekindled the debate on globular cluster distances (see\\nthe review by Reid \\\\cite{reid99} and references therein). A further check\\non the distance is therefore urgently needed. \\n\\\\newline\\\\indent\\nWe started an observing programme at the ESO {\\\\em Very Large Telescope\\n(VLT)} to obtain spectra of white dwarfs in globular clusters. The\\nprogramme consists of two parts: First, low S/N ($\\\\approx 10$) spectra of\\nthe white dwarf candidates are obtained to verify their spectral type and\\nestimate their effective temperatures. In a second run we plan to observe\\nhigher S/N ($\\\\approx 30$) spectra that will allow to derive \\\\logg\\\\ with an\\ninternal error of $\\\\le 0.1$dex. Here we report on the very first results\\nfor NGC~6397. \\n\\n\\\\begin{table}\\n\\\\caption{Target coordinates and photometric data (Cool priv. comm.). \\n\\\\label{targ}}\\n\\\\begin{tabular}{lrrrr}\\n\\\\hline\\nStar & $\\\\alpha_{2000}$ & $\\\\delta_{2000}$ & $V$ & $V-I$\\\\\\\\\\n\\\\hline\\nWF4-358 & \\\\RA{17}{40}{58}{52} & \\\\DEC{$-$53}{42}{25.3} & \\\\magpt{22}{73} & \\n\\\\magpt{+0}{02}\\\\\\\\\\nWF2-479 & \\\\RA{17}{41}{07}{06} & \\\\DEC{$-$53}{44}{45.1} & \\\\magpt{23}{87} & \\n\\\\magpt{+0}{22}\\\\\\\\\\nWF4-205 & \\\\RA{17}{41}{01}{58} & \\\\DEC{$-$53}{43}{15.3} & \\\\magpt{23}{99} &\\n\\\\magpt{+0}{30}\\\\\\\\\\nWF2-51 & \\\\RA{17}{41}{04}{52} & \\\\DEC{$-$53}{43}{55.8} & \\\\magpt{24}{00} & \\n\\\\magpt{+0}{28}\\\\\\\\\\nWF2-846 & \\\\RA{17}{41}{01}{78} & \\\\DEC{$-$53}{44}{47.2} & \\\\magpt{24}{30} & \\n\\\\magpt{+0}{33}\\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\\\end{table}\\n\\\\begin{figure}\\n\\\\vspace{8.5cm}\\n\\\\special{psfile=b1293.f2 hscale=43 vscale=43 hoffset=-10 voffset=-70\\nangle=0}\\n\\\\caption{Traces through the slits along the spatial axis. The lines mark \\nthe white dwarf spectra (WF4-205 unfortunately lies on the wing of a much \\nbrighter star).\\\\label{slits}} \\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n\\\\vspace{8.5cm}\\n\\\\special{psfile=b1293.f3 hscale=43 vscale=43 hoffset=-10 voffset=-70\\nangle=0}\\n\\\\caption{The (relatively flux-calibrated) spectra of the white dwarfs in \\nNGC~6397. The spectra of the three faintest stars \\nare offset from each other as they would otherwise overlap. WF4-358 has no \\nadditional offset relative to WF2-479.\\\\label{spectra}} \\n\\\\end{figure}\\n\\\\section{Observations and Data Reduction}\\nCool et al.\\\\ (\\\\cite{copi96}) discovered the white dwarfs using the {\\\\em\\nWide Field and Planetary Camera~2} (WFPC2) onboard the HST to observe the\\nglobular cluster NGC~6397. From the improved colour-magnitude diagram of\\nKing et al.\\\\ (\\\\cite{kian98}) targets brighter than $V\\\\approx25^{\\\\rm m}$\\nwere selected (see Fig.~\\\\ref{cmd}). The WFPC2 images were convolved to a\\nseeing of 0\\\\bsec5 to select targets that are sufficiently uncrowded to be\\nobservable from the ground (see Table~\\\\ref{targ} and Fig.~\\\\ref{slits}). The\\nstars were observed with the {\\\\em FOcal Reducer/low dispersion\\nSpectrograph} (FORS) at Unit Telescope 1 of the VLT using the high\\nresolution collimator (0\\\\bsec1/pixel) to allow better extraction of the\\nspectra and get a better handle on cosmic rays. We used the {\\\\em\\nmulti-object spectroscopy} (MOS) mode with the grism 300V and a slit width\\nof 0\\\\bsec8. The slit width was chosen to be larger than the required seeing\\nto avoid slit losses due to imperfect pointing of the telescope. The data\\nwere obtained in service mode under excellent conditions (seeing below\\n0\\\\bsec55, no moon) with a total exposure time of 90 minutes. The final\\nresolution as judged from a wavelength calibration spectrum obtained with a\\n0\\\\bsec5 slit is $\\\\approx$11.5~\\\\AA. A trace along the spatial axis of the\\nslitlets at about 4550~\\\\AA\\\\ is plotted in Fig.~\\\\ref{slits}. Unfortunately\\nWF4-205 lies so close to a bright star that even at this excellent\\nseeing its spectrum could not be extracted. \\n\\nDue to the use of slit blades instead of fibers or masks the MOS slitlets\\nare very well defined and can be treated like long slits. The spectra were\\ntherefore corrected for bias, flat-fielded, wavelength calibrated, and\\nextracted as described by Moehler et al.\\\\ (\\\\cite{mohe97}). We find only a\\ndiffuse and rather low sky background without any strong sky lines below\\n5150~\\\\AA. The spectra were relatively flux calibrated using LTT~7987\\n(Hamuy et al.\\\\ \\\\cite{hawa92}) and are plotted in Fig.~\\\\ref{spectra}. All\\nfour stars display only strong broad Balmer lines, which is characteristic\\nfor hydrogen-rich white dwarfs (DA stars). \\n\\n\\\\section{Atmospheric parameters}\\nAlthough the white dwarf spectra have low signal-to-noise, they are\\nsufficient for rough parameter estimates. The atmospheric parameters are\\nobtained by simultaneously fitting profiles of the observed Balmer lines\\nwith model spectra using the least-square algorithm of Bergeron et al.\\\\\\n(\\\\cite{besa92}; see Napiwotzki et al.\\\\ 1999 for minor modifications).\\nAnalyses were performed with Koester's LTE models as described in Finley et\\nal.\\\\ (\\\\cite{fiko97}). As a check we repeated the analysis of the hottest\\nstar in our sample (WF4-358) with the non-LTE grid described in Napiwotzki\\net al.\\\\ (\\\\cite{nagr99}). Since the non-LTE code does not treat convection\\nand ignores molecular opacities reliable atmospheric models cannot be\\ncalculated for the three cooler white dwarfs. \\n\\n\\\\begin{figure}\\n\\\\vspace{8.cm}\\n\\\\special{psfile=b1293.f4 hscale=43 vscale=43 hoffset=-10 voffset=-10 angle=0}\\n\\\\caption{Sample fits to the spectra of WF4-358 (\\\\teff\\\\ =\\n18,200~K, \\\\logg\\\\ = 7.3) and WF2-479 (\\\\teff\\\\ = 11,000~K, \\\\logg\\\\= = 7.7).\\n\\\\label{wd_fit}} \\n\\\\end{figure}\\n\\n\\\\begin{table}[h]\\n\\\\caption{Effective temperatures and $\\\\chi^2$ values for the white dwarfs\\nfrom the fit of H$_\\\\delta$, H$_\\\\gamma$, H$_\\\\beta$ at fixed \\\\logg\\\\ (see text\\nfor details). Also given are masses derived from theoretical tracks of\\nBl\\\\\\\"ocker (\\\\cite{bloe95}) and Driebe et al.\\\\ (\\\\cite{drsch98}) and absolute\\nmagnitudes (Bergeron et al.\\\\ \\\\cite{bewe95}). Using Bergeron et al.'s\\n(\\\\cite{bewe95}) Table~3 we derived $T_{\\\\rm eff, (V-I)_0}$ from $(V-I)_0$,\\nwhich was calculated from $V-I$ assuming $E_{V-I}$ = \\\\magpt{0}{225}.\\n\\\\label{tab-results}} \\n\\\\begin{tabular}{lrrrrr}\\n\\\\hline\\nstar & $\\\\chi^2$ & \\\\teff & $T_{\\\\rm eff, (V-I)_0}$ & M & $M_V$ \\\\\\\\\\n & & [K] & [K] & [\\\\Msolar] & \\\\\\\\\\n\\\\hline\\n\\\\multicolumn{6}{c}{\\\\logg\\\\ = 7.5}\\\\\\\\\\n\\\\hline\\nWF4-358 & 1.04 & 18900 & & 0.42 & \\\\magpt{10}{0} \\\\\\\\\\nWF2-479 & 1.15 & 10800 & & 0.39 & \\\\magpt{11}{1} \\\\\\\\\\nWF2-51 & 1.46 & 10900 & & 0.39 & \\\\magpt{11}{1} \\\\\\\\\\nWF2-846 & 0.71 & 10500 & & 0.38 & \\\\magpt{11}{2} \\\\\\\\\\n\\\\hline\\n\\\\multicolumn{6}{c}{\\\\logg\\\\ = 7.7}\\\\\\\\\\n\\\\hline\\nWF4-358 & 1.07 & 19500 & & 0.48 & \\\\magpt{10}{3} \\\\\\\\\\nWF2-479 & 1.14 & 11000 & & 0.46 & \\\\magpt{11}{4} \\\\\\\\\\nWF2-51 & 1.46 & 11100 & & 0.46 & \\\\magpt{11}{4} \\\\\\\\\\nWF2-846 & 0.71 & 10600 & & 0.46 & \\\\magpt{11}{5} \\\\\\\\\\n\\\\hline\\n\\\\multicolumn{6}{c}{\\\\logg\\\\ = 8.0}\\\\\\\\\\n\\\\hline\\nWF4-358 & 1.13 & 20300 & 19400 & 0.62 & \\\\magpt{10}{7} \\\\\\\\\\nWF2-479 & 1.14 & 11200 & 11500 & 0.59 & \\\\magpt{11}{8} \\\\\\\\\\nWF2-51 & 1.47 & 11300 & 10800 & 0.59 & \\\\magpt{11}{8} \\\\\\\\\\nWF2-846 & 0.71 & 10800 & 10300 & 0.59 & \\\\magpt{11}{9} \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\\\\\\\\\n\\\\end{table}\\nFitting the lines H$_\\\\beta$ to H$_\\\\epsilon$ for WF4-358 (see\\nFig.~\\\\ref{wd_fit}) gives 18,200$\\\\pm$1300~K and 7.30$\\\\pm$0.36 for \\\\teff\\\\ and\\n\\\\logg, respectively ($\\\\chi^2$ = 0.93). The errors given here are 1$\\\\sigma$\\nerrors obtained from the $\\\\chi^2$ fit. Omitting H$_\\\\epsilon$ from the fit\\nresults in 17,800~K and 7.19 ($\\\\chi^2$ = 1.02) with more or less unchanged\\nerrors. The results of the non-LTE analysis are essentially identical to\\nthose obtained with Koester's models, differing only by small fractions of\\nthe formal errors ($\\\\Delta$\\\\teff $\\\\approx$500\\\\,K, $\\\\Delta$\\\\logg $\\\\approx$\\n0.07\\\\,dex). The surface gravity is surprisingly low and suggests that\\nWF4-358 could be a bright ($M_V$=\\\\magpt{9}{7}) helium white dwarf of\\n(0.36$\\\\pm$0.12)\\\\Msolar. Within the error bars, however, the derived\\nparameters are also consistent with a low-mass C/O white dwarf. For the\\nremaining three stars the S/N is too low to determine \\\\teff\\\\ and \\\\logg\\\\\\nsimultaneously. We thus fitted H$_\\\\delta$, H$_\\\\gamma$, H$_\\\\beta$\\n(H$_\\\\epsilon$ being too noisy) for WF2-51, WF2-479, and WF2-846 for three\\nfixed values of \\\\logg\\\\ (8.0, 7.7, 7.5, see Fig.~\\\\ref{wd_fit} for an\\nexample). These \\\\logg\\\\ values correspond to C/O white dwarfs of $\\\\approx$\\n0.6\\\\Msolar, low-mass C/O white dwarfs of $\\\\approx$0.5\\\\Msolar, and He white\\ndwarfs of $\\\\approx$0.4\\\\Msolar, respectively (see below). The formal errors\\nare $\\\\approx$550~K (WF2-479), $\\\\approx$650~K (WF2-846, WF4-358), and\\n$\\\\approx$790~K (WF2-51). The errors for the cooler stars are relatively\\nsmall despite their low S/N because -- at fixed \\\\logg\\\\ -- the line profiles\\nare much more sensitive to temperature variations at \\\\teff\\n$\\\\approx$11,000~K than at \\\\teff $\\\\approx$18,000~K. The relatively large\\n$\\\\chi^2$ value for WF2-51 suggests that either the noise in this spectrum\\nhas been underestimated or that the spectrum contains additional features\\nthat are not well described by the model spectra. The temperatures derived\\nfrom the Balmer lines agree quite well with those obtained from $(V-I)_0$\\nusing the theoretical colours of Bergeron et al.\\\\ (\\\\cite{bewe95}, \\\\logg\\\\ = \\n8.0). \\n\\nThe masses given in Table~\\\\ref{tab-results} were derived by interpolation\\nbetween the evolutionary tracks of C/O white dwarfs calculated by Bl\\\\\\\"ocker\\n(\\\\cite{bloe95}) and the He white dwarf tracks of Driebe et al.\\\\\\n(\\\\cite{drsch98}). Finally, absolute magnitudes $M_V$ were calculated for\\neach parameter set with the photometric calibration of Bergeron et al.\\\\\\n(\\\\cite{bewe95}). \\n\\n\\\\section{The distance to NGC\\\\,6397} \\nThe old distance modulus to NGC\\\\,6397 was $(m-M)_0$ = \\\\magpt{11}{71} with a\\nreddening of \\\\ebv\\\\ of \\\\magpt{0}{18} (Djorgovski \\\\cite{djor93}). Using local\\nmetal-poor subdwarfs to fit the main sequence of NGC\\\\,6397 Reid \\\\& Gizis\\n(\\\\cite{regi98}) obtained a mean distance modulus\\nof $(m-M)_0$ = \\\\magpt{12}{20}$\\\\pm$\\\\magpt{0}{15} for\\n\\\\ebv\\\\ = \\\\magpt{0}{19}. Thus NGC\\\\,6397 is a good example for the large\\ndifferences between old and new distances to globular clusters. The\\nabsolute magnitudes given in Table~\\\\ref{tab-results} for \\\\logg\\\\ = 7.5, 7.7,\\n8.0 (M$_{\\\\rm WD}$ = 0.4\\\\Msolar, 0.5\\\\Msolar, 0.6\\\\Msolar) yield mean true\\ndistance moduli (for \\\\ebv\\\\ = \\\\magpt{0}{18}) $(m-M)_0$ of \\\\magpt{12}{3},\\n\\\\magpt{12}{0}, and \\\\magpt{11}{6}, respectively, with an r.m.s. error of\\n\\\\magpt{0}{17}. Considering the error bars of the various distance\\ndeterminations the long distance scale would be more consistent with white\\ndwarf masses $\\\\le$0.5\\\\Msolar\\\\ and the short distance scale with masses\\n$>$0.5\\\\Msolar. The longer distance moduli obtained for low-mass white\\ndwarfs also result in masses for blue HB stars (Heber et al.\\\\\\n\\\\cite{hemo97}) and a hot post-AGB star (ROB\\\\,162, Heber \\\\& Kudritzki\\n\\\\cite{heku86}) that agree with canonical evolutionary theory. \\n\\nThe distance moduli derived for a given \\\\logg\\\\ from Tables~\\\\ref{targ} and\\n\\\\ref{tab-results} show a systematic variation with the brightest star\\n(WF4-358) yielding the smallest distance and the faintest star (WF2-846)\\ngiving the largest distance. This variation could reflect the fact that the\\nstars may not all have the same surface gravity: From their different\\napparent magnitudes (i.e. different absolute magnitudes) it is plausible\\nthat WF4-358 has the smallest \\\\logg\\\\ and WF2-846 the largest. The quality\\nof the current data, however, does not allow to verify this idea. \\n\\n\\\\section{Conclusions} \\nUsing VLT-FORS1 multi object spectroscopy we have confirmed four white\\ndwarf candidates to be hydrogen-rich DA white dwarfs. The gravity\\ndetermined for the brightest star, WF4-358, suggests that it could be a He\\nwhite dwarf with a mass of (0.36$\\\\pm$0.12)\\\\Msolar, although the error bars\\nare large enough to also accommodate a C/O white dwarf. Temperatures derived\\nfor the three cooler and fainter stars for fixed \\\\logg\\\\ would put them near\\nthe red edge of the ZZ Ceti instability strip, for which Bergeron et al.\\\\\\n(\\\\cite{bewe95b}) determine a temperature range of 11,160~K to 12,460~K\\nusing their preferred ML2/$\\\\alpha$=0.6 prescription for the treatment of\\nconvection. Therefore, a search for photometric variability of WF2-479 and\\nWF2-51 -- if successful -- could place important additional constraints on\\nthese stars. The systematic variation of the distance moduli derived for a\\ngiven \\\\logg\\\\ shows that the assumption of a constant mass for\\nall white dwarfs in a globular cluster may bias a distance determination.\\nHowever, due to the low S/N of the current data, these results are\\npreliminary. Once higher quality spectra are available, which will allow\\nmore accurate parameter (and thus mass) determinations, analyses of white\\ndwarfs in globular clusters will become a powerful tool for independent\\ndistance estimates. \\n\\n\\\\acknowledgements\\nWe highly appreciate the work performed by the FORS team in building an\\nexcellent instrument and the efforts of the staff at the ESO Paranal\\nobservatory and ESO Garching that made these observations possible. We\\nthank Dr.\\\\ A.\\\\ Cool for providing us with the photometry and coordinates of\\nthe white dwarf candidates and an anonymous referee for valuable comments.\\nS.M. acknowledges financial support from the DARA under grant\\n50~OR~96029-ZA. \\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%% FOLLOWING TYPESETTING RULES SET OUT IN \\\"ASTRONOMY AND ASTROPHYSICS %%\\n%% INSTRUCTIONS FOR AUTHORS\\\" -- ASTRON. ASTROPHYS. 341 (1) 1999; %%\\n%% JOURNAL ACRONYMS CAN BE FOUND AT THE FOLLOWING TWO WEB SITES: %%\\n%% http://adsdoc.harvard.edu/abs_doc/refereed.html %%\\n%% http://adsdoc.harvard.edu/abs_doc/non_refereed.html %%\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\begin{thebibliography}{}\\n\\\\bibitem[1992]{besa92}\\nBergeron P., Saffer R.A., Liebert J., 1992, ApJ 394, 228\\n\\\\bibitem[1995a]{bewe95}\\nBergeron P., Wesemael F., Beauchamp A., 1995a, PASP 107, 1047\\n\\\\bibitem[1995b]{bewe95b}\\nBergeron P., Wesemael F., Lamontagne R., et al., 1995b, ApJ 449, 258\\n\\\\bibitem[1995]{bloe95}\\nBl\\\\\\\"ocker T., 1995, A\\\\&A 299, 755\\n\\\\bibitem[1996]{copi96}\\nCool A.M., Piotto G., King I.R., 1996, ApJ 468, 655\\n\\\\bibitem[1998]{cogr98}\\nCool A.M., Grindlay J.E., Cohn H.N., Lugger P.M., Bailyn C.D., 1998, ApJ \\n508, L75\\n%\\\\bibitem[1995]{dbsc95}\\n% de Boer K.S., Schmidt J.H.K., Heber U., 1995, A\\\\&A 303, 95 \\n\\\\bibitem[1993]{djor93}\\nDjorgovski S., 1993, in {\\\\it Structure and Dynamics of Globular Clusters},\\n eds. S.G. Djorgovski \\\\& G. Meylan, ASP Conf. Ser. 50 (San Francisco),\\n p. 373\\n\\\\bibitem[1998]{drsch98}\\nDriebe T., Sch\\\\\\\"onberner D., Bl\\\\\\\"ocker T., Herwig F., 1998, A\\\\&A 339, 123\\n\\\\bibitem[1999]{edgr99}\\nEdmonds P.D., Grindlay J.E., Cool A., et al., 1999, ApJ 516, 250\\n\\\\bibitem[1997]{fiko97}\\nFinley D.S., Koester D., Basri G., 1997, ApJ 488, 375\\n\\\\bibitem[1992]{hawa92}\\nHamuy M., Walker A.R., Suntzeff N.B., et al., 1992, PASP 104, 533\\n\\\\bibitem[1986]{heku86}\\nHeber U., Kudritzki R.P., 1986, A\\\\&A 169, 244\\n\\\\bibitem[1997]{hemo97}\\nHeber U., Moehler S., Reid I.N., 1997, ESA SP-402, p.461 \\n\\\\bibitem[1998]{kian98}\\nKing I.R., Anderson J., Cool A.M., Piotto G., 1998, ApJ 492, L37\\n\\\\bibitem[1995]{madh95}\\nMarsh T.R., Dhillon V.S., Duck S.R., 1995, MNRAS 275, 828\\n\\\\bibitem[1997]{mohe97}\\nMoehler S., Heber U., Rupprecht G., 1997, A\\\\&A 319, 109\\n\\\\bibitem[1999]{nagr99}\\nNapiwotzki R., Green P.J., Saffer R.A., 1999, ApJ 517,399\\n\\\\bibitem[1995]{pade95}\\nParesce F., de Marchi G., Romaniello M., 1995, ApJ 440, 216\\n\\\\bibitem[1999]{reid99}\\nReid I.N., 1999, ARAA 37, 191\\n\\\\bibitem[1998]{regi98}\\nReid I.N., Gizis J.E., 1998, AJ 116, 2929\\n\\\\bibitem[1996]{rebr96}\\nRenzini A., Bragaglia A., Ferraro F.R., et al., 1996, ApJ 465, L23\\n\\\\bibitem[1995]{rifa95}\\nRicher H.B., Fahlmann G.G., Ibata R.A., et al., 1995, ApJ 451, L17\\n\\\\bibitem[1997]{rifa97}\\nRicher H.B., Fahlmann G.G., Ibata R.A., et al., 1997, ApJ 484, 741\\n\\\\end{thebibliography}{}\\n\\\\end{document}\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002197.extracted_bib","string":"\\begin{thebibliography}{}\n\\bibitem[1992]{besa92}\nBergeron P., Saffer R.A., Liebert J., 1992, ApJ 394, 228\n\\bibitem[1995a]{bewe95}\nBergeron P., Wesemael F., Beauchamp A., 1995a, PASP 107, 1047\n\\bibitem[1995b]{bewe95b}\nBergeron P., Wesemael F., Lamontagne R., et al., 1995b, ApJ 449, 258\n\\bibitem[1995]{bloe95}\nBl\\\"ocker T., 1995, A\\&A 299, 755\n\\bibitem[1996]{copi96}\nCool A.M., Piotto G., King I.R., 1996, ApJ 468, 655\n\\bibitem[1998]{cogr98}\nCool A.M., Grindlay J.E., Cohn H.N., Lugger P.M., Bailyn C.D., 1998, ApJ \n508, L75\n%\\bibitem[1995]{dbsc95}\n% de Boer K.S., Schmidt J.H.K., Heber U., 1995, A\\&A 303, 95 \n\\bibitem[1993]{djor93}\nDjorgovski S., 1993, in {\\it Structure and Dynamics of Globular Clusters},\n eds. S.G. Djorgovski \\& G. Meylan, ASP Conf. Ser. 50 (San Francisco),\n p. 373\n\\bibitem[1998]{drsch98}\nDriebe T., Sch\\\"onberner D., Bl\\\"ocker T., Herwig F., 1998, A\\&A 339, 123\n\\bibitem[1999]{edgr99}\nEdmonds P.D., Grindlay J.E., Cool A., et al., 1999, ApJ 516, 250\n\\bibitem[1997]{fiko97}\nFinley D.S., Koester D., Basri G., 1997, ApJ 488, 375\n\\bibitem[1992]{hawa92}\nHamuy M., Walker A.R., Suntzeff N.B., et al., 1992, PASP 104, 533\n\\bibitem[1986]{heku86}\nHeber U., Kudritzki R.P., 1986, A\\&A 169, 244\n\\bibitem[1997]{hemo97}\nHeber U., Moehler S., Reid I.N., 1997, ESA SP-402, p.461 \n\\bibitem[1998]{kian98}\nKing I.R., Anderson J., Cool A.M., Piotto G., 1998, ApJ 492, L37\n\\bibitem[1995]{madh95}\nMarsh T.R., Dhillon V.S., Duck S.R., 1995, MNRAS 275, 828\n\\bibitem[1997]{mohe97}\nMoehler S., Heber U., Rupprecht G., 1997, A\\&A 319, 109\n\\bibitem[1999]{nagr99}\nNapiwotzki R., Green P.J., Saffer R.A., 1999, ApJ 517,399\n\\bibitem[1995]{pade95}\nParesce F., de Marchi G., Romaniello M., 1995, ApJ 440, 216\n\\bibitem[1999]{reid99}\nReid I.N., 1999, ARAA 37, 191\n\\bibitem[1998]{regi98}\nReid I.N., Gizis J.E., 1998, AJ 116, 2929\n\\bibitem[1996]{rebr96}\nRenzini A., Bragaglia A., Ferraro F.R., et al., 1996, ApJ 465, L23\n\\bibitem[1995]{rifa95}\nRicher H.B., Fahlmann G.G., Ibata R.A., et al., 1995, ApJ 451, L17\n\\bibitem[1997]{rifa97}\nRicher H.B., Fahlmann G.G., Ibata R.A., et al., 1997, ApJ 484, 741\n\\end{thebibliography}"}],"string":"[\n {\n \"name\": \"astro-ph0002197.extracted_bib\",\n \"string\": \"\\\\begin{thebibliography}{}\\n\\\\bibitem[1992]{besa92}\\nBergeron P., Saffer R.A., Liebert J., 1992, ApJ 394, 228\\n\\\\bibitem[1995a]{bewe95}\\nBergeron P., Wesemael F., Beauchamp A., 1995a, PASP 107, 1047\\n\\\\bibitem[1995b]{bewe95b}\\nBergeron P., Wesemael F., Lamontagne R., et al., 1995b, ApJ 449, 258\\n\\\\bibitem[1995]{bloe95}\\nBl\\\\\\\"ocker T., 1995, A\\\\&A 299, 755\\n\\\\bibitem[1996]{copi96}\\nCool A.M., Piotto G., King I.R., 1996, ApJ 468, 655\\n\\\\bibitem[1998]{cogr98}\\nCool A.M., Grindlay J.E., Cohn H.N., Lugger P.M., Bailyn C.D., 1998, ApJ \\n508, L75\\n%\\\\bibitem[1995]{dbsc95}\\n% de Boer K.S., Schmidt J.H.K., Heber U., 1995, A\\\\&A 303, 95 \\n\\\\bibitem[1993]{djor93}\\nDjorgovski S., 1993, in {\\\\it Structure and Dynamics of Globular Clusters},\\n eds. S.G. Djorgovski \\\\& G. Meylan, ASP Conf. Ser. 50 (San Francisco),\\n p. 373\\n\\\\bibitem[1998]{drsch98}\\nDriebe T., Sch\\\\\\\"onberner D., Bl\\\\\\\"ocker T., Herwig F., 1998, A\\\\&A 339, 123\\n\\\\bibitem[1999]{edgr99}\\nEdmonds P.D., Grindlay J.E., Cool A., et al., 1999, ApJ 516, 250\\n\\\\bibitem[1997]{fiko97}\\nFinley D.S., Koester D., Basri G., 1997, ApJ 488, 375\\n\\\\bibitem[1992]{hawa92}\\nHamuy M., Walker A.R., Suntzeff N.B., et al., 1992, PASP 104, 533\\n\\\\bibitem[1986]{heku86}\\nHeber U., Kudritzki R.P., 1986, A\\\\&A 169, 244\\n\\\\bibitem[1997]{hemo97}\\nHeber U., Moehler S., Reid I.N., 1997, ESA SP-402, p.461 \\n\\\\bibitem[1998]{kian98}\\nKing I.R., Anderson J., Cool A.M., Piotto G., 1998, ApJ 492, L37\\n\\\\bibitem[1995]{madh95}\\nMarsh T.R., Dhillon V.S., Duck S.R., 1995, MNRAS 275, 828\\n\\\\bibitem[1997]{mohe97}\\nMoehler S., Heber U., Rupprecht G., 1997, A\\\\&A 319, 109\\n\\\\bibitem[1999]{nagr99}\\nNapiwotzki R., Green P.J., Saffer R.A., 1999, ApJ 517,399\\n\\\\bibitem[1995]{pade95}\\nParesce F., de Marchi G., Romaniello M., 1995, ApJ 440, 216\\n\\\\bibitem[1999]{reid99}\\nReid I.N., 1999, ARAA 37, 191\\n\\\\bibitem[1998]{regi98}\\nReid I.N., Gizis J.E., 1998, AJ 116, 2929\\n\\\\bibitem[1996]{rebr96}\\nRenzini A., Bragaglia A., Ferraro F.R., et al., 1996, ApJ 465, L23\\n\\\\bibitem[1995]{rifa95}\\nRicher H.B., Fahlmann G.G., Ibata R.A., et al., 1995, ApJ 451, L17\\n\\\\bibitem[1997]{rifa97}\\nRicher H.B., Fahlmann G.G., Ibata R.A., et al., 1997, ApJ 484, 741\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":195,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002198"},"title":{"kind":"string","value":"Improving the Resolution of X-Ray Telescopes with Occulting Satellites"},"authors":{"kind":"list like","value":[],"string":"[]"},"abstract":{"kind":"string","value":"One of the challenges of X-ray astronomy is how to both collect large numbers of photons yet attain high angular resolution. Because X-ray telescopes utilize grazing optics, to collect more photons requires a larger acceptance angle which in turn compromises the angular resolution. All X-ray telescopes thus have angular resolution far poorer than their diffraction limit. Although collecting more photons is a desirable goal, sometimes selective collecting fewer photons may yield more information. Natural (such as lunar) occultations have long been used to study sources on small angular scales. But natural occulters are of limited utility because of their large angular velocities relative to the telescope, and because of the serendipity of their transits. We describe here how one can make use of an X-ray Big Occulting Steerable Satellite (X-BOSS) to achieve very-high resolution of X-ray sources. An X-BOSS could significantly improve the resolution of existing X-ray facilities such as the Chandra telescope, or X-ray Multiple Mirror (XMM) satellite, and could vastly improve the resolution of some future X-ray telescopes, particularly Constellation X where sub-milliarcsecond resolution is possible for a wide range of sources. Similar occulting satellites could also be deployed in conjunction with planned space observatories for other wavebands."},"latex":{"kind":"list like","value":[{"name":"ms.tex","string":"%% For submission to apj use\n%\\documentclass{aastex}\n\\documentclass[preprint,12pt]{aastex}\n% To include figures\n\\usepackage{epsfig}\n% Include draftcopy to get ``draft date'' to appear on each page\n%\\usepackage{draftcopy}\n\n% $Id: ms.tex,v 1.9 2000/02/09 21:22:53 copi Exp $\n\n\\newcommand\\be{\\begin{equation}}\n\\newcommand\\ee{\\end{equation}}\n\n\\newcommand{\\mcommand}[1]{\\ifmmode #1\\else $#1$\\fi}\n\\newcommand{\\sci}[1]{\\mcommand{\\times 10^{#1}}}\n\n\\newcommand{\\unit}[1]{\\mcommand{\\;{\\rm #1}}}\n\\newcommand\\meter{\\unit{m}}\n\\newcommand\\second{\\unit{s}}\n\\newcommand\\as{\\unit{arcsecond}}\n\\newcommand\\mas{\\unit{mas}}\n\\newcommand\\parsec{\\unit{pc}}\n\\newcommand\\kpc{\\unit{kpc}}\n\\newcommand\\Mpc{\\unit{Mpc}}\n\\newcommand\\yr{\\unit{yr}}\n\\newcommand\\mps{\\unit{m\\;s^{-1}}}\n\\newcommand\\cm{\\unit{cm}}\n\\newcommand\\km{\\unit{km}}\n\\newcommand\\kmps{\\unit{km\\;s^{-1}}}\n\\newcommand\\pmsqs{\\unit{m^{-2}\\;s^{-1}}}\n\\newcommand\\gram{\\unit{g}}\n\\newcommand\\kg{\\unit{kg}}\n\\newcommand\\AU{\\unit{AU}}\n\\newcommand\\keV{\\unit{keV}}\n\n%\\def\\vec#1{\\mbox{\\boldmath$#1$\\unboldmath}}\n\n\\newcommand\\etal{et al.}\n\\newcommand\\etc{etc}\n\n\\newcommand\\ltsim{\\lesssim}\n\\newcommand\\gtsim{\\gtrsim}\n\n\n\\begin{document}\n\n\\title{Improving the Resolution of X-Ray Telescopes with Occulting Satellites}\n\\author{Craig J. Copi\\altaffilmark{1}\\email{cjc5@po.cwru.edu} \\and Glenn D. Starkman\\altaffilmark{1,2}\\email{gds6@po.cwru.edu}}\n\\affil{\nBOSS home page: \\tt\\url{http://boss.phys.cwru.edu/}}\n\\altaffiltext{1}{Department of Physics, Case Western Reserve\nUniversity, Cleveland, OH 44106-7079}\n\\altaffiltext{2}{Department of Astronomy, Case Western Reserve\nUniversity, Cleveland, OH 44106-7079}\n\\authoraddr{10900 Euclid Avenue\\\\ Cleveland, OH 44106-7079}\n\n\\shorttitle{Improving X-Ray Resolution with X-BOSS}\n\\shortauthors{Craig J. Copi and Glenn D. Starkman}\n\n\\begin{abstract}\nOne of the challenges of X-ray astronomy \nis how to both collect large numbers of photons yet \nattain high angular resolution. \nBecause X-ray telescopes utilize grazing optics, \nto collect more photons requires a larger acceptance angle \nwhich in turn compromises the angular resolution.\nAll X-ray telescopes thus have angular resolution\nfar poorer than their diffraction limit.\nAlthough collecting more photons is a desirable goal,\nsometimes selective collecting fewer photons may yield more information.\nNatural (such as lunar) occultations \nhave long been used to study sources on small angular scales.\nBut natural occulters are of limited utility because\nof their large angular velocities relative to the telescope,\nand because of the serendipity of their transits.\nWe describe here how one can make use of an \nX-ray Big Occulting Steerable Satellite (X-BOSS) \nto achieve very-high resolution of X-ray sources.\nAn X-BOSS could significantly improve the resolution of \nexisting X-ray facilities such as the Chandra telescope, \nor X-ray Multiple Mirror (XMM) satellite, \nand could vastly improve the resolution of some future\nX-ray telescopes, particularly Constellation X where sub-milliarcsecond\nresolution is possible for a wide range of sources.\nSimilar occulting satellites could also be deployed in conjunction \nwith planned space observatories for other wavebands.\n\\end{abstract} \n\n\\keywords{space vehicles---occultations---X-rays:general}\n\n\n\\slugcomment{\\small Preprint: {\\bf CWRU-P04-00}}\n% \\\\ Submitted to: \\em The Astrophysical Journal}\n\n\\section{Introduction}\n\nOne of the big challenges in doing X-ray astronomy\nis the relatively low photon fluxes from target sources.\nThe fact that X-ray mirrors operate only at grazing \nangles of incidence further exacerbates this problem.\nThus, while one might naively expect \nsuperb angular resolution from a $1.2\\meter$ aperture X-ray telescope \nsuch as the one on board the Chandra satellite,\nthe $0.5$ arcsecond reality is far from the \n0.3 milliarcsecond nominal diffraction limit,\nand considerably worse than what is routinely achieved in\nlonger wavelength bands. This situation is unlikely to \nchange in the near future. Indeed, current plans for\nfuture X-ray missions opt for increased acceptance\nangle (and thus increased photon count rate) at\nthe price of reduced angular resolution.\n\nBut it {\\em is} possible to achieve higher \nX-ray photon count rates and yet improve one's angular resolution. \nThe necessary step is to separate the collection of photons \nfrom the means of achieving high resolution.\nOne way to do this is well-known---occultation.\nWhen an astronomical body, such as the moon, transits the field\nof view of a telescope, it occults different sources within the\nfield of view at different times. By carefully measuring\nthe photon count rate as a function of time during the transit,\none can then reconstruct the projection of the surface brightness\nin the field of view onto the path of the occulter.\n\n\nNatural occulters {\\em have} been used to achieve high-resolution\nin X-ray observations; however, they have at least two distinct\ndisadvantages:\n\\begin{enumerate}\n\\item Although natural occultations can be predicted, they cannot be\n scheduled---target sources are therefore limited, and multiple\n occultations of the same source over the course of a few years\n are uncommon.\n\\item Natural occulters have large angular velocities relative to\n a telescope. The shorter the transit time, the fewer photons one\n collects, and so the lower the resolution. This is especially important\n for X-ray astronomy, where photon count rates are relatively low.\n\\end{enumerate}\nThere is however an alternative to natural occulters which can overcome\nboth of these disadvantages---a steerable occulting satellite. Deployment\nof large steerable occulting satellites has been discussed for optical and\nnear infra-red wavebands\n\\citep{Adams,Schneider,CS98,CS00},\nmostly for\nthe purpose of finding planet around nearby stars, but also for\nhigh-resolution astronomical observations. However, such satellites are\nnaturally well-suited for observations in the X-ray and far-UV\\@. In the\nlonger wavelength bands, minimization of diffractive losses pushes one to\nmake the satellite as large as feasible, and deploy it as far as possible\nfrom the telescope. In the X-ray waveband one is far into the geometric\noptic limit and diffraction of the X-ray photons around the satellite can\nessentially be neglected; thus the optimal size and placement of the satellite \nare determined by one's ability to accurately position the satellite with respect to the\ntelescope-star line-of-sight and to minimize the satellite's velocity\nperpendicular to that line-of-sight. The resolution delivered by the\ncombination of the X-ray telescope and the X-BOSS is determined by the\ncollecting area of the telescope (and thus the photon count rate for a\nsource) and by the accuracy with which one can match the X-BOSS and telescope\nvelocity. It is independent of the intrinsic resolution of the telescope.\n\nFor an X-ray telescope either in an eccentric high-Earth orbit (Chandra and XMM) or at the\nL2 point of the Earth-Sun system (Constellation-X) we discuss in section\n\\ref{sec:location} where to position X-BOSS relative to the satellite. In\nsection \\ref{sec:blocking} of this letter we discuss the X-ray blocking\nefficiency of a thick film and what it implies for the required thickness\nof the occulter. We also estimate in this section the required dimensions of an X-BOSS,\nwhich are determined mostly by limitations on telemetry.\nWe discuss the steering of the X-BOSS in section \\ref{sec:steer}. \nIn section \\ref{sec:resolve} we find the angular resolution that one\nobtains as a function of X-BOSS-telescope relative angular velocity, \nand of photon count rate. \nIn section~\\ref{sec:skycoverage} we discuss the the sky\ncoverage that one could obtain in each location. \nApplication of these techniques to specific sources is discussed briefly \nin section~\\ref{sec:results}. \nFinally, section~\\ref{sec:conclude} contains the conclusions.\n\n\\section{Locating an X-BOSS}\n\\label{sec:location}\n\nThe location of an X-BOSS is dictated by the location of the\ntelescope it is meant to occult. The Chandra X-ray telescope is\nin an elliptic orbit around the Earth with \nan apogee of $145,417\\km$ and a perigee of $16,026\\km$.\nThe X-ray Multiple Mirror (XMM) Telescope will also be inserted into\nan elliptic Earth orbit.\nOther X-ray telescopes, such as Constellation X, \nmay be located at the second Lagrangian point of the Earth-Sun system. \nThe orbital issues are entirely\ndifferent for these two locations; \nwe address each in turn below.\nFinally, some X-ray telescopes (Astro-E and XEUS) will be\nplaced in low earth orbit. Because orbital velocities\nare so high in low earth orbit, it is more difficult to make \nuse of the approach we advocate here; we will not discuss\nthese further.\n\n\\subsection{Eccentric high Earth-orbit}\n\\label{subsec:orbitearth}\n\nAs described above, the Chandra satellite is in an eccentric high altitude\nEarth orbit. The period of this orbit is 64 hours. The satellite\ntherefore has an average angular velocity of about 6 arcseconds per second. \nAn occulting satellite leading or following in Chandra's orbit would transit a source at\napproximately that rate. The planned X-ray Multiple Mirror Telescope (XMM)\nhas a similar orbit with a shorter 48 hour period.\nGiven that the attainable angular resolution is related to the angular \nvelocity of transit, \nthe resolution that one could achieve with these orbits is minimal.\n\nA great improvement is to place the X-BOSS in an orbit identical to that of\nthe telescope but slightly modified by shifting the apogee and perigee, by\nchanging the phase of the satellite in the orbit, or by rotating the orbit.\nIn all cases these modifications will put X-BOSS in an orbit with the same\nperiod as telescope. In such orbits the velocity perpendicular to the line\nof sight of X-BOSS and the telescope can be quite low. For example, consider\nplacing X-BOSS in an orbit identical to that of the telescope (in terms of\napogee, perigee, and orbital phase) but rotated about an axis through the center of the Earth\nin the plane of the orbit and perpendicular to the line connecting apogee and perigee. \nThe component of the relative velocity between X-BOSS and the telescope\nperpendicular to the line-of-sight between them is then zero throughout the\nentire orbit. Unfortunately, such an orbit intersects the telescope orbit at\ntwo points with disastrous consequences. The other orbital modifications\nmentioned above can alleviate this problem by enforcing a minimum\nseparation of, for example, $10\\km$ between the two spacecrafts. Although\n$10\\km$ may seem fairly close, note that each spacecraft is only a\nfew to tens of meters across; random errors therefore have a probability\nless than $10^{-9}$ per orbit crossing of causing catastrophic failure.\nThe importance of utilizing these orbit modifications is explained more\nfully in sections~\\ref{sec:steer} and \\ref{sec:skycoverage}.\n\n\\subsection{Orbit at L2}\n\\label{subsec:orbitL2}\n\nWe have previously discussed the orbital advantages of placing a large\nocculter at L2 in greater detail \\citep{CS00}. Here we will\nhighlight the important points.\nOrbits around L2, both in the plane of the ecliptic and oscillations\nperpendicular to this plane, have periods of about 6 months independent of\ntheir distance from L2 (for distances $\\ltsim 10^4\\km$). Therefore the\nlocal gravity is very small. Both the total velocity and acceleration of\norbits around L2 (relative to the L2 point) are on par with those we might attain\nthrough carefully \ntuning the orbit of X-BOSS relative to that of Chandra or XMM; \nthe relative velocity of the satellite and telescope due to the\nmotion of L2 about the Sun is of the same magnitude. If corrections are\nmade to the X-BOSS orbit to cancel these then the\nacceleration perpendicular to the line-of-sight is about\n$5\\sci{-10}\\meter\\second^{-2}$. Thus if the perpendicular velocity of\nX-BOSS relative to a particular line-of-sight between the telescope and some source\nis canceled by firing rockets, the perpendicular velocity will remain less than $10^{-4}\\mps$ for \nat least a day. Tuning the velocity of X-BOSS, therefore, can be done very \neasily at L2.\n\n\\section{Making an X-ray Occulter}\n\\label{sec:blocking}\n\n\\subsection{Thickness}\n\nThe attenuation length of X-ray photons in elemental matter\nis shown in figure~\\ref{fig:photonattenuation}.\nExcept in hydrogen, it is approximately $3\\times 10^{-4} \\gram \\cm^{-2}$ at\n$1\\keV$, and $10^{-2} \\gram\\cm^{-2}$ at $10\\keV$. \nThus a square $10\\meter$ on a side and one attenuation length\nthick has a mass of $0.3\\kg$ at $1\\keV$, and $10\\kg$ at $10\\keV$.\nAt a typical density of $3 \\gram \\cm^{-3}$, these represent thicknesses\nof just $1$ micron and $30$ microns respectively.\n\nA useful occulter would need to be $3\\hbox{--}5$ attenuation lengths thick,\nand so $3\\hbox{--}5$ microns and $1\\hbox{--}2\\kg$ to operate at $1\\keV$,\nand $100\\hbox{--}150$ microns and $30\\hbox{--}50\\kg$ to operate at $10\\keV$.\nEven at $100\\keV$ a $10\\meter\\times10\\meter$ lead film \n$0.6\\unit{mm}$ thick at a mass of $600\\kg$ would provide 3 attenuation \nlengths of occultation.\n\nIf positioning technology improved to the point where one could\nreduce the size of the occulter to $1\\hbox{--}2\\meter$, then even gamma ray\nocculters would be of reasonable mass.\n\n\\subsection{Size}\n\nThe size of the occulting satellite depend on\ntwo factors---the aperture of the telescope and \nthe accuracy with which one can position the occulter. \n\nThe apertures of typical X-ray satellites are about $1\\meter$.\nThis sets a lower bound on the dimensions of the occulter.\nOnce the occulter is larger than the aperture of the X-ray telescope,\nthere is essentially no effect on resolving power.\n\nNext we will estimate how well we can determine the position of X-BOSS \nin the plane perpendicular to the telescope-source line-of-sight \nit is meant to occult. \nConsider a telescope separated from the X-BOSS by a distance $r$. \nWe can mount a small diffraction-limited optical telescope of diameter $d$ \non the underside of the occulter. Using this telescope\nwe can establish the relative positions\nof the two satellite to within approximately\n\\be \n\\delta x = 1.2 r \\frac{\\lambda}{d} \n= 0.5 \\meter \\frac{r}{1000\\km} \\frac{\\lambda/400\\unit{nm}}{d/1\\meter}\n\\ee\nA $1\\meter$ positioning accuracy therefore requires\na $50\\unit{cm}$ finder scope at $1000\\unit{km}$ separation,\nproportionately smaller at smaller separations. \nThis is quite feasible, especially since the finder scope \nneed not have a full UV plane.\n\nAn important question is whether one will collect\nenough photons to reach the diffraction limit of the\nangular resolution. There are two principal\noptions---rely on reflected sunlight or \nshine a laser from the X-ray telescope onto the X-BOSS telescope.\nColumnation is not a significant problem, \nas seen by our calculation of the diffraction limit above. \nHowever, sunlight has an intensity of $1000\\unit{W}\\meter^{-2}$, \nwhich will be difficult to match with a laser anyway. \nAssuming isotropic scattering from the telescope,\nand a total reflecting area of $1\\meter^{2}$,\nthis results in a flux at the X-BOSS of $3\\sci{8}\\second^{-1}$,\nat $1000\\km$ (falling as $1/r^2$). Detailed studies\nof existing telescopes (Chandra, XMM) would be required\nto precisely quantify our ability to locate the\ntelescope relative to the X-BOSS, however, these\nestimates suggest that determining the relative\nposition to within $1\\hbox{--}3 \\meter$ is not unrealistic.\nIn the case of yet-to-be launched telescopes, \nthe mounting of a small reflector on\none or more corner of the telescope would be of\ndefinite benefit.\n\nAlthough we have argued that we can determine the\nrelative position of an X-BOSS and an X-ray telescope \nto within about a meter, we must also be able to reduce\nthe velocity to a fraction of a meter per second.\nThis can be done by a simple bootstrapping procedure.\nTwo position determinations each with error of $\\Delta x$,\nmade a time $t$ apart, determine the velocity within\n$\\Delta v \\simeq \\sqrt{2} \\Delta x/t$ (assuming the\nerror in $t$ to be negligible). If the relative velocity\ncan be canceled within errors by accurately firing rockets,\nthen the ability to reduce $\\Delta v$ is limited by \nthe time one can allow between position determinations, $t=\\Delta x/\\Delta v$.\nThis time is limited by the orbital accelerations, \nbut is thousands of seconds for the elliptic earth orbits of interest\n(cf.~subsection \\ref{subsec:earthorbit})\nand hundreds of thousands of seconds for orbits at L2.\n(cf.~subsection \\ref{subsec:L2orbits}).\nIn practice it may be desirable to gradually\nreduce the relative velocity using repeated position\ndeterminations and rocket firings.\n\n\n\\section{Steerability}\n\\label{sec:steer}\n\nIn order to successfully resolve objects it will be necessary\nto frequently change the velocity of the satellite. \nThese velocity changes will occur for two principal reasons:\nto move from one target source to another,\nand to match the velocity of the X-BOSS to that of the X-ray telescope.\nWhile solar radiation pressure might be used to some advantage,\nit will be necessary to make some velocity adjustments using rockets.\nThe number and size of such adjustments may be the limiting factor\non the useful lifetime of the X-BOSS.\n\n\nA change $\\Delta v$ in the satellite's velocity is related\nby momentum conservation to the mass of propellant ejected,\n$\\Delta m_{\\rm propellant}$, and the velocity of ejection $v_{\\rm ejection}$:\n\\be\n\\Delta v_{\\rm sat}\n= \\frac{\\Delta m_{\\rm propellant}{ v}_{\\rm ejection}}{m_{\\rm sat}} .\n\\ee\nIf $N$ is the number of desired major rocket-driven velocity changes,\nthen we must keep\n$(\\Delta m_{\\rm propellant}/m_{\\rm sat})\\leq N^{-1}$.\n(The mass of propellant ejected will of course vary on the particular\nmaneuver, but here $\\Delta m_{\\rm propellant}$ is taken to be some \ntypical mass of propellant expended per orbit reconfiguration.)\nWe therefore can accommodate only a limited number of such rocket firings:\n\\be\nN \\leq \\frac{v_{\\rm ejection}}{\\Delta{ v_{\\rm sat}}} .\n\\ee\nOff-the shelf, low-cost ion engines are currently available\nwith ejection velocities of $20 \\kmps$, and\nmore expensive systems with $30 \\kmps$ performance \nhave been developed, thus\n\\be\nN \\leq \\frac{30\\kmps}{\\Delta{ v_{\\rm sat}}} .\n\\label{eqn:Ncorrect}\n\\ee\n\nConsider first the need to match the velocities of the two spacecraft\nso that a long occultation can occur.\n$\\Delta{ v_{\\rm sat}}$ is then the relative velocity \nof the X-BOSS and the telescope in their orbits.\nIn determining the sky coverage for elliptic Earth orbits \nin section~\\ref{subsec:earthorbit} above, \nwe have considered only orbital configurations with relative velocities \nbetween the telescope and the X-BOSS of less than $10\\mps$.\n(Near L2, the relative velocities of relevance are typically \nconsiderably smaller than that.)\nIf $\\Delta{ v_{\\rm sat}}\\simeq 10\\mps$, then this implies \n$N\\leq 3000$,\nwhich is a reasonable quota of corrections for a mission with a 3--5 year\nlifetime, \ngiven the typical 2--3 day orbital period of Earth-orbiting\nX-ray telescopes. \n\nThe second type of velocity correction that will be required\nis target acquisition---the readjustment of the orbit\nof the occulter so as to allow the occultation of a new \ntarget source. \nFor satellites separated by $1000\\km$ near L2, relative velocities\nare only $v_{\\rm sat} = {\\cal O}(10^{-4}\\kmps)$,\nand the expression for\n$N$ (equation~\\ref{eqn:Ncorrect}) shows that any constraint on target\nchoice or order does not come from concerns about conserving\npropellant.\nFor telescopes in orbit about the Earth, \nthe matter is quite different.\nHere orbital velocities are $v_{\\rm sat} = {\\cal O}(1\\kmps)$,\nand so it is clear from the allowed number of orbital\ncorrections~(\\ref{eqn:Ncorrect}) that\none cannot indiscriminately rocket from one target to another on the sky.\nOne solution might have been to sail in the solar radiation pressure.\nHowever, the solar radiation pressure is approximately $P_{\\rm\n solar}=6\\times10^{-6}\\unit{Pa}$. \nFor an areal density of just $1.5\\times 10^{-3}\\gram\\cm^{-2}$\n(five attenuation lengths as $1\\keV$),\nthis results in an acceleration of only $4\\times10^{-4}\\meter\\second^{-2}$.\nAt this rate it takes about a month to change velocity by $1\\kmps$.\n\nClearly one cannot reposition randomly on the sky. \nHowever the velocity difference between two orbits which\nresult in occultation of target sources one degree apart are only\nof order $15\\mps$. Solar sailing can cause velocity changes\nof this order in under a day. \nMoreover, the allowed number of orbital corrections~(\\ref{eqn:Ncorrect})\nindicates that rocket driven\ncorrections of this magnitude can be made of order 1000 times.\nHow many corrections we can make, and how many sources we can\ntherefore target for occultation,\nclearly depends on exactly how we use the satellite. \nA reasonable program of observations certainly seems possible.\n\n\\section{Resolution}\n\\label{sec:resolve}\n\nWhen used in conjunction with an X-BOSS the telescope acts as a\nlight bucket. The angular resolution of the telescope itself is\nirrelevant; instead the collecting area is the important telescope\nparameter. The angular resolution of the system will come from probing the \nlightcurve as X-BOSS transits a source.\n\nTo study the angular resolution of X-BOSS we consider the simple case of\nidentifying a binary source. Let $f (\\vec x, t)$ be the normalized\nlightcurve (number of photons detected per second) generated as X-BOSS\nscans across a single source at a position\n$\\vec x$ in the plane of X-BOSS\\@. The lightcurve is the number of photons\ndetected as a function of time. It is normalized such that the value is\none (in the detector) when X-BOSS is not present. Since X-rays have\nextremely short\nwavelengths we can approximate the diffraction pattern produced by the\nsatellite simply by the geometric shadow projected on the telescope. This\nreduces the lightcurve to a calculation of the area of the telescope not\nunder the shadow of the occulter. We write the lightcurve of a single\nsource as\n\\be \nl_1 (\\vec x, t) = I_1 f (\\vec x, t)\n\\ee\nand the total lightcurve for two sources at $\\vec x_1$ and $\\vec x_2$\ncan be written as\n\\be\nl_2 (\\vec x_1, \\vec x_2, t) = I_2 \\left[ \\rho f (\\vec x_1, t) +\n (1-\\rho) f (\\vec x_2, t)\\right].\n\\ee\nHere $I_i$ is the total intensity of the system for $i=1$ or $2$ sources\nand $\\rho$ is\nthe intensity \nratio of the two sources. We would like to find the minimum separation of\ntwo sources that can be distinguished from a single source. An observation\nconsists of a sequence $\\left\\{O_j (\\vec x)\\slash j=1,...,n \\right\\}$\nof measurements of the integrated lightcurve between \ntimes $t_{j-1}$ and $t_j$:\n\\be \nO_j (\\vec x) = \\int_{t_{j-1}}^{t_j} dt\\; l_i (\\vec x, t).\n\\ee\nTo obtain\nlimits on the minimum separation we first evaluate the number of photons\nexpected between time $t_0$ and $t_k$\n\\be\nL_{i,k} (\\vec x) \\equiv \\int_{t_0}^{t_k} dt\\;l_i (\\vec x, t) =\n\\sum_{j=1}^k O_j (\\vec x)\n\\ee \nwhere $i$ is 1 or 2 as above.\nAssuming the counts in each time bin, $[t_{j-1},t_j)$, are Poisson distributed the\nlikelihood of a model with $i$ sources given an underlying model with 2\nsources is \n\\be \n{\\cal L}_i = \\prod_{k=1}^N \\left. e^{-L_{i,k}} \\left( L_{i,k} \\right)^{L_{2,k}}\n\\right/ \\left( L_{2,k}\\right)!.\n\\ee\nFinally the quantity\n\\be \nT = -2\\log \\left (\\frac{{\\cal L}_1}{{\\cal L}_2} \\right)\n\\ee\nis $\\chi^2$ distributed with 4 degrees of freedom ($t_0$, $x_2-x_1$, $I$,\nand $\\rho$) and allows us to\ncalculate the probability of misidentifying a binary source as a single source.\nThis probability depends on \n$\\mu_\\perp$, the angular velocity of X-BOSS as it transits the source.\nThe results for the 95\\% confidence limits as a function of the intensity\nin a $1.2\\meter$ aperture telescope for $\\rho=1$, $1/3$, and $1/10$ and for\n$\\mu_\\perp=10\\mas\\second^{-1}$, $\\mu_\\perp=1\\mas\\second^{-1}$, and\n$0.1\\mas\\second^{-1}$ are shown in figure~\\ref{fig:resolution}. In\nproducing figure~\\ref{fig:resolution} we assumed a uniform response over\nthe surface of the telescope. A more complicated response function may\nimprove resolution slightly.\n\nThe simple analysis employed here uses the edges of X-BOSS in a single\noccultation. In practice it would be necessary to obtain multiple\nprojections to resolve a source in two dimensions. This could be facilitated\nby putting slits at various angles in X-BOSS that allow for sources to be\nocculted by different regions of the satellite in different ways during a\nsingle transit.\n\n\n\\section{Sky Coverage}\n\\label{sec:skycoverage}\n\nThe issues of resolution and sky coverage are closely related. Here sky\ncoverage is the fraction of the sky for which a particular angular\nresolution can be obtained. While one can reposition X-BOSS to be in an\narbitrary direction on the sky relative to the X-ray telescope, this\nfrequently leads to large relative velocities and accelerations between the\nocculter and telescope perpendicular to the line-of-sight, thus leading to\npoor resolution (see figure~\\ref{fig:resolution}). Conversely, extremely\ngood resolution is possible if the relative velocity during the occultation\nis kept quite low; however this requires either special orbits (and thus\nvery little sky coverage) or expenditures of fuel. Here we will explore\nthe sky coverage that can be obtained subject to a number of constraints.\n\n\\subsection{Elliptic Earth Orbits}\n\\label{subsec:earthorbit}\n\nWe consider placing an X-BOSS in orbit around the Earth with nearly the\nsame orbital parameters as an X-ray telescope. As discussed in\nsection~\\ref{subsec:orbitearth} we then allow for small alterations in the\nX-BOSS orbit which change the direction of the line-of-sight from the\ntelescope to X-BOSS while keeping the X-BOSS period fixed.\nOur first constraint is that the\nminimum separation of the X-BOSS and telescope in their orbits must be larger than $10\\km$. \n(If this safety factor can be reduced then greater sky coverage may be possible.) \nWe then follow the two spacecrafts in their orbits to see what sky coverage \nthese orbits afford.\nTo limit the expenditure of propellant we \nconsider making observations only when the relative velocity of the\ntwo satellites perpendicular to the line-of-sight is sufficiently small,\nhere we require $v_\\perp^{\\rm orb} <\n10\\mps$ (see section~\\ref{sec:steer}). Prior to an observation this\nvelocity can be reduced to the desired range by firing the X-BOSS rockets\n(a small correction requiring acceptable use of consumables).\n\nAfter maneuvering to correct the perpendicular relative velocity between the\ntelescope and X-BOSS, they would still be accelerating relative to each\nother during the observation. The provides one limit on the total transit\ntime of the observation. There would also be some residual error in the\nvelocity correction, leaving X-BOSS with a component of its velocity perpendicular to the\nline-of-sight. This provides another limit on the total transit time of the\nobservation. Combining these two, the total transit time over which the\nobservation can made is\n\\be\nt_{\\rm obs} = \\min \\left(\\sqrt{\\frac{2w}{a_\\perp^{\\rm orb}}},\n \\frac{w}{\\mu_\\perp^{\\rm max} d} \\right).\n\\ee\nHere $a_\\perp^{\\rm orb}$ is the perpendicular linear acceleration, $w$ is the\nwidth of X-BOSS, $d$ is the distance between the two spacecrafts, and\n$\\mu_\\perp^{\\rm max}$ is the maximum angular velocity allowed to obtain a\nparticular resolution.\nIf we require that the angular velocity perpendicular to the line\nof sight at the end of the observation be less than the same maximum value,\n$\\mu_\\perp^{\\rm max}$, then we obtain the constraint\n\\be\na_\\perp^{\\rm orb} t_{\\rm obs} < \\mu_\\perp^{\\rm max} d.\n\\label{eqn:constraint1}\n\\ee\nOf course when we cancel $v_\\perp^{\\rm orb}$ before the observation we are\nalso making a small change to the orbit. This leads to an extra\nacceleration that must also be small. If we require that this acceleration\nalso not produce a large final velocity we obtain the constraint\n\\be\n\\frac{v_\\perp^{\\rm orb} t_{\\rm obs}^2}{r^3 d} < \\frac{\\mu_\\perp^{\\rm\n max}}{2g R_\\oplus^2},\n\\label{eqn:constraint2}\n\\ee\nwhere $r$ is the distance from X-BOSS to the (center of the) Earth,\n$g=9.8\\meter\\second^{-2}$, and $R_\\oplus$ is the radius of the Earth.\n\nThe sky coverage on each change of X-BOSS orbit is not large. To increase\nthe amount of sky\naccessible to observation we consider moving X-BOSS between orbits that are\nsimilar to the orbit of the X-ray telescope. Throughout we will consider\nmodifications of the X-BOSS orbit that leave the period unchanged. Over\nmany orbits this is a \ndesired feature since it prevents the times at which X-BOSS and the telescope\nachieve apogee and perigee from drifting apart, requiring a\nlarge expenditure of fuel to correct. The orbital modifications we\nconsider are increasing or decreasing the apogee distance (while preserving \nthe semi-major axis and thus the period), rotating the orbit\nabout all three axes, and introducing a phase shift (time of apogee) into the\norbit. For this study we taken the X-ray telescope to be the Chandra\nsatellite and allowed changes in apogee (and perigee) of\n$\\pm200\\km$, rotations about the two axes in the plane of the orbit of\n$\\pm1^\\circ$, rotations in the plane of the orbit of $\\pm0.4^\\circ$, and\ntime shifts of $\\pm100\\second$. All of these changes are relative to\nChandra's orbit. These changes can be accomplished using ion engines\nseveral thousand times before exhausting the supply of expendables (see\nsection~\\ref{sec:steer}). Since occultations are best done near apogee and \n1000 or so orbital periods is the Chandra mission lifetime, this rate of\nconsumption of expendable is acceptable.\n\nUsing Monte Carlo techniques,\nwe studied the orbits in this region of parameter space \nsubject to two constraints: the minimum separation of the X-BOSS and telescope \nmust be at least $10\\km$, and somewhere in the orbit the\nperpendicular velocity must be less than $10\\mps$. We generated $100,000$\norbits that satisfy these criteria. Next, for a variety of photon count rates\nand desired resolutions we used the resolution results show in \nfigure~(\\ref{fig:resolution}) to determine $\\mu_\\perp^{\\rm max}$. Finally\nwe checked which lines-of-sight satisfied the velocity and acceleration\nconstraints~(\\ref{eqn:constraint1}, \\ref{eqn:constraint2}) and thus which\nparts of the sky can be observed. The results are shown in\nfigure~\\ref{fig:skycoverage} assuming the width of X-BOSS is $10\\meter$. \nHere even for very intense sources (I=$10^5\\second^{-1}$) only 20\\%\nof the sky can be covered with a a resolution of\n$\\Delta\\theta=0.1\\as$. This tight constraint is due principally to the fact\nthat X-BOSS is accelerating during the time that both of the sources are\nocculted leading to a large velocity by the end of the observation which\noccurs when the transit is complete. \nTo counteract this we could use a narrower satellite, \nuse a satellite with slits in it so that we do not have to wait until the far\nedge starts unocculting the sources, or fire the rockets while both sources\nare occulted to cancel the velocity. To model these possibilities we have considered \na satellite that accelerates over only $2\\meter$ between the onset and end of\na transit. The results are shown in figure~\\ref{fig:skycoverage}b. \nHere we see a tremendous improvement in sky coverage and resolution. \nFor intense sources, $I=10^5\\second^{-1}$, we can obtain\n$\\Delta\\theta=0.1\\as$ over \n40\\% of the sky and $\\Delta\\theta=0.02\\as$ over 20\\% of the sky.\nLarger sky coverages would be obtained if we relaxed the criteria on the \norbital velocity difference between the Chandra and X-BOSS orbits.\nThis would be justified if the propellant velocities of ion engines\nrose about $30\\kmps$, or if we could make do with a smaller number of orbital \ncorrections.\n\n\\subsection{L2 Orbits}\n\\label{subsec:L2orbits}\n\nAs discussed above (section~\\ref{subsec:orbitL2}) the orbits at L2 are much \nsimpler to manage than orbits around the Earth. Full sky coverage can be\nobtained and the velocity perpendicular to the line-of-sight can be chosen\nas desired. Figure~\\ref{fig:resolution} best represents what can be\nachieved at L2. Since the perpendicular velocity can be chosen, extremely\nhigh angular resolution is possible. Even sub-milliarcsecond resolution is\npossible for many sources ($I\\gtsim 4\\sci{3}\\second^{-1}$) when\n$\\mu_\\perp=0.1\\mas\\second^{-1}$.\n\n\\section{Results}\n\\label{sec:results}\n\nThis is an exciting time for X-ray astronomy. Two new X-ray telescopes\n(the Chandra Advanced X-ray Astronomical Facility, and the X-ray Multiple\nMirror telescope (XMM)) have been successfully launched, while another\n(Astro-E) is being readied for launch. Of these three, Chandra and XMM are\nin highly elliptical high altitude earth orbits\n(cf.~Table~\\ref{tab:xray-telescopes}) while Astro-E is headed for a\ncircular low earth orbit. In addition, at least two major X-ray\nspace-observatories are being planned: Constellation X, with launch\nscheduled for 2003, and XEUS with a target date of 2007. Constellation X\nwill be placed at the L2 point of the Earth-Sun system, while XEUS, like\nAstro-E, will be placed in low Earth orbit.\n\nWhile this may seem a remarkable proliferation of X-ray telescopes, each\nmission has its own emphasis. In building an X-ray telescope there is a\ndirect competition between large effective area (and thus sensitivity) and\nsmall acceptance angle (and thus high angular resolution). Therefore one\nmust choose whether to build an instrument which aims for high\nangular-resolution or one which has a goal of achieving high sensitivity.\nChandra is the only high angular resolution instrument of the listed\nmissions, with a maximum resolution of $0.5\\as$ and thus has the relatively\nsmall effective area given above~(\\ref{eqn:AChandra}). The other\ninstruments all aim for large effective area, and so sacrifice angular\nresolution. XMM, which is already flying, has considerably larger\neffective area than Chandra (and thus much lower angular resolution).\nAstro-E will have even larger effective area. Constellation-X will consist\nof multiple X-ray telescopes flown in formation, with a total effective\narea considerably greater than either XMM or Astro-E; it too has relatively\nlow angular resolution compared to Chandra. Finally XEUS will have a huge\neffective area, and will be designed to be expandable. Its angular\nresolution is better than XMM, Astro-E, or Constellation-X but still not as\ngood as Chandra. The properties of the existing and planned\ntelescopes are shown in Table~\\ref{tab:xray-telescopes}.\n\nThroughout we have considered the photon rate in the detector, not at the\nsurface of the telescope. An X-ray telescope has an effective area, $\\cal\nA$, which includes the geometric collecting area (since grazing optics are\nused the collecting area is not the full beam) and the efficiency of the\nX-ray detector. As an example, with Chandra\n\\be \n {\\cal A}_{\\rm Chandra} \\approx 700 \\cm^2\n \\label{eqn:AChandra}\n\\ee\nfor $E\\approx 1\\keV$. This is the area to be used as the area of the\ntelescope, not the geometric area as in the case of optical telescopes.\nThe effective area for existing and planned X-ray telescopes is given in Table~\\ref{tab:xray-telescopes}.\n\nThe luminosity of X-ray sources varies greatly. Black holes in the cores\nof nearby galaxies have \n\\be \n{\\cal L}_{\\rm bh} \\approx 10^{38\\hbox{--}40}\\unit{erg}\\second^{-1} =\n6.2\\sci{46\\hbox{--}48} \\keV\\second^{-1}\n\\ee\nin the $0.2\\hbox{--}2.4\\keV$ energy range. This leads to a photon rate at\nthe surface of the detector of\n\\be\n\\Gamma_{\\rm bh} = (0.052\\hbox{--}5.2)\\sci{-2} \\left (\\frac{E}{\\keV}\\right) \n\\left ( \\frac{d}{1\\Mpc}\\right)^{-2}\n\\left (\\frac{\\cal A}{\\cm^2}\\right) \\second^ {-1},\n\\ee\nwhere the energy, $E$, we observe at is given in keV and $\\cal A$ is the\neffective area of the X-ray telescope as discussed above.\n\nAn active galactic nucleus (AGN), Seyfert galaxy, or the core of X-ray\nclusters can be much more luminous\n\\be \n{\\cal L}_{\\rm AGN} \\approx 10^{40\\hbox{--}44}\\unit{erg}\\second^{-1} =\n6.2\\sci{48\\hbox{--}52} \\keV\\second^{-1}.\n\\ee\nHowever, since they are approximately $100\\Mpc$ away the photon rate \nis only \n\\be\n\\Gamma_{\\rm AGN} = 5.2\\times (10^{-6}\\hbox{--}10^{-2})\\left\n (\\frac{E}{\\keV}\\right) \n\\left ( \\frac{d}{100\\Mpc}\\right)^{-2}\n\\left (\\frac{\\cal A}{\\cm^2}\\right) \\second^ {-1}.\n\\ee\nGalactic microquasars are somewhat less luminous\n\\be \n{\\cal L}_{\\rm microquasar} \\approx 10^{39}\\unit{erg}\\second^{-1} =\n6.2\\sci{47} \\keV\\second^{-1},\n\\ee\nsince they are in our own galaxy, though, the photon rate is fairly high\n\\be\n\\Gamma_{\\rm microquasar} = 52 \\left (\\frac{E}{\\keV} \\right) \n\\left ( \\frac{d}{10\\kpc}\\right)^{-2}\n\\left (\\frac{\\cal A}{\\cm^2}\\right) \\second^ {-1}.\n\\ee\n\nFor a $10\\meter$ X-BOSS employed in conjunction with Chandra we find\n(figure~\\ref{fig:skycoverage}a) that for the brightest sources (galactic \nmicroquasars) we can obtain $\\Delta\\theta=0.5\\as$ over about 30\\% of the\nsky with the sky coverage falling quickly until at $\\Delta\\theta=0.1\\as$\nvery little of the sky is accessible. This represents a modest gain over\nwhat can be obtained by Chandra without the aid of X-BOSS. For a $2\\meter$ \nX-BOSS (figure~\\ref{fig:skycoverage}b) the situation is much\nbetter. Here $\\Delta\\theta=0.5\\as$ can be obtained over about 50\\% of the\nsky, $\\Delta\\theta=0.1\\as$ over about 20\\% of the sky, and\n$\\Delta\\theta=0.05\\as$ over about 5\\% of the sky. Thus significant\nimprovements are attainable through the use of an X-BOSS with Chandra.\n\nFor an X-BOSS employed in conjunction with XMM the situation is similar.\nAlthough XMM has a shorter period than Chandra its has an effective area about\n$3$ times larger (Table~\\ref{tab:xray-telescopes}). For a $10\\meter$\nX-BOSS (figure~\\ref{fig:skycoverageXMM}a) the skycoverage that can be\nobtained for each incident photon rate, $\\Gamma$, is less than can be\nobtained by Chandra (compare to figure~\\ref{fig:skycoverage}a) even with\nthe factor of $3$ increase in effective area that XMM provides. For a\n$2\\meter$ X-BOSS (figure~\\ref{fig:skycoverageXMM}b) the sky coverage for\nXMM and Chandra are closer though Chandra is still superior. Note that for\nboth sizes of X-BOSS tremendous improvements over the nominal $15\\as$\nresolution for XMM are obtained.\n\nAt L2 the situation is even better. Since we can tune the velocity\nrelative to the line-of-sight more easily, great improvements in resolution \nare readily available (figure~\\ref{fig:resolution}). Sub-milliarcsecond\nresolution can be obtained for sources with photon rates $\\Gamma\\gtsim\n1000\\second^{-1}$. For a single Constellation X modules, which will have an \neffective area of about $15,000\\cm^2$, the brightest AGN's, X-ray cluster\ncores, and galactic black holes will have $\\Gamma\\approx 800\\second^{-1}$\nwe can obtain $\\Delta\\theta\\approx 2\\mas$.\n\n\\section{Conclusions}\n\\label{sec:conclude}\n\nWe have found that an X-BOSS used in conjunction with an X-ray telescope\ncan lead to tremendous improvements in angular resolution. \nThe trend of increasing the effective area of future X-ray telescopes at the\nexpense of angular resolution (Table~\\ref{tab:xray-telescopes}) meshes perfectly\nwith the benefits gained by including an X-BOSS in the mission. Indeed, an\nX-ray telescope to be used with an X-BOSS is treated as a light bucket with\nall the resolving power coming from the X-BOSS occulting the source. Thus\nan X-BOSS is an excellent addition to an X-ray telescope mission,\nparticularly one at L2, such as Constellation X where sub-milliarcsecond\nresolution can be attained for a wide range of sources.\n\nFor the Chandra X-ray telescope we found that moderate improvements in\nangular resolution over an appreciable fraction of the sky can be achieved\nthrough the use of an X-BOSS\\@. Similarly an X-BOSS employed in\nconjunction with XMM would provide tremendous improvements in the angular\nresolution that XMM could achieve allowing XMM to have angular resolution\ncomparable to Chandra. An X-BOSS launched for use with Chandra or XMM would\nalso provide an important test bed for the technology to be used with\nfuture missions.\n\n\\acknowledgements\nThe authors would like particularly to thank \nArt Chmielewski for financial and other support,\nA. Babul and M. Dragovan for many useful comments and suggestions,\nN. Choudhuri for helpful suggestions on statistical tests, and Paul\nGorenstein and William Zhang for comments on a preliminary version of the \nmanuscript.\nThis work was supported by \na CAREER grant to GDS from the National Science Foundation,\na DOE grant to the theoretical particle and astrophysics group at CWRU, \nby a grant from NASA's Jet Propulsion Laboratory,\nand by funds from CWRU.\n\n\\begin{thebibliography}{}\n\n\\bibitem[Adams \\etal (1988)]{Adams} Adams, D.J. \\etal~1988, \\apj, 327, L65\n\n\\bibitem[Copi \\& Starkman (1998)]{CS98} Copi, C.J. \\& Starkman, G.D.~1998, \nProceedings of SPIE, 3356, March 25, 1998, Kona, HI\n\n\\bibitem[Copi \\& Starkman (2000)]{CS00} Copi, C.J. \\& Starkman, G.D.~2000,\n \\apj, 534, too appear%,\n% preprint astro-ph/9904413\n \n\\bibitem[Schneider (1995)]{Schneider} Schneider, J.~1995, Proceeding of the\n workshop ``Detection and Study of Terrestrial Extra-solar Planets'', May\n 15--17, Boulder, CO\n\n\\end{thebibliography}\n\n\\begin{deluxetable}{lccl}\n\\tablecaption{Properties of existing and planned X-ray\n telescopes.\\label{tab:xray-telescopes}}\n\n\\tablehead{\n \\colhead{Satellite} & \\colhead{Effective} & \\colhead{Angular} &\n \\colhead{Orbit} \\\\ \n \\colhead{Name} & \\colhead{Area at $1\\keV$} & \\colhead{Resolution} &\n \\colhead{}\\\\ \n \\colhead{} & \\colhead{(cm$^2$)} & \\colhead{(arcsecond)} & \\colhead {}\n }\n\\startdata\nChandra (AXAF)\\tablenotemark{a} & \\phn\\phn\\phn\\phm{,}700 & 0.5 & eccentric\nhigh Earth orbit \\\\\nXMM & \\phn\\phn2,000 & 15 & eccentric high Earth orbit \\\\\nAstro-E & \\phn\\phn1,200 & 90 & low Earth orbit \\\\\nHETE-II\\tablenotemark{b} & \\phn\\phn\\phn\\phm{,}350 & 660 & low Earth orbit \\\\\nConstellation X & \\phn30,000\\tablenotemark{c} & 15 & L2 halo orbit \\\\\nXeus -- Phase I & \\phn60,000 & 2 & low Earth orbit \\\\\n\\phantom{Xeus}~-- Phase II& 300,000 & 2 & low Earth orbit \\\\\n\\enddata\n\\tablenotetext{a}{Effective area is for the AXAF CCD Imaging Spectrometer\n (ACIS)\\@. Angular resolution is for the High Resolution Camera (HRC)\\@.}\n\\tablenotetext{b}{These values are for the wide field X-ray monitor (WXM)\n instrument. The quoted effective area is for $2\\keV$ X-rays.}\n\\tablenotetext{c}{Total effective area for all modules.}\n\\tablerefs{\\\\\nChandra: http://asc.harvard.edu/\\\\\nXMM: http://xmm.vilspa.esa.es/\\\\\nHETE-II: http://space.mit.edu/HETE/\\\\\nAstro-E: http://heasarc.gsfc.nasa.gov/docs/astroe/overview.html\\\\\nConstellation X: http://constellation.gsfc.nasa.gov/\\\\\nXeus: http://astro.estec.esa.nl/SA-general/Projects/XEUS/web/mission.html\n}\n\n\\end{deluxetable}\n\n\\begin{figure}\n \\leavevmode\\center{\\epsfig{figure=photonattenuation.ps,height=5 in,width=8.5 in}}\n \\caption{The photon mass attenuation length $\\lambda=1/(\\mu/\\rho)$\nfor various elemental absorbers as a function of photon energy\n($\\rho$ is the density). The figure is obtained from the particle\ndata book, figure 23.11 (http://pdg.lbl.gov). \nThe data for $30{\\rm eV} < E < 1 {\\rm keV}$ are obtained from \nhttp://www-cxro.lbl.gov/optical\\_constants \n(courtesy of Eric M. Gullikson, LBNL).\nThe data for $1{\\rm keV} < E < 100 {\\rm GeV}$ are from \n\\protect\\url{http://physics.nist.gov/PhysRefData}, thru the courtesy of \nJohn H. Hubbel (NIST).\n}\n\\label{fig:photonattenuation}\n\\end{figure}\n\n\\begin{figure}\n \\leavevmode\\center{\\epsfig{figure=resolution.ps,height=6in,angle=-90}}\n \\caption{The minimum angular separation of two X-ray sources resolvable\n at the 95\\% confidence level. The limits are shown for intensity\n ratios, $\\rho=1$ (solid),\n $1/3$ (dashed), and $1/10$ (dashed-dotted). The upper set of three curves\n are for $\\mu_\\perp = 10\\mas\\second^{-1}$, the middle set of three curves are\n for $\\mu_\\perp = 1\\mas\\second^{-1}$, and the lower set of three curves\n are for $\\mu_\\perp = 0.1\\mas\\second^{-1}$. Note that the total photon\n rate is of photons detected in the telescope (without the presence\n X-BOSS), not photons incident on the telescope. Here $d$ is the\n distance between the telescope and X-BOSS in units of $10^3\\km$.\n }\n \\label{fig:resolution}\n\\end{figure}\n\n\\begin{figure}\n \\leavevmode\\center{\\epsfig{figure=skycoverage_10m.ps,height=4in,angle=-90}}\n \\leavevmode\\center{\\epsfig{figure=skycoverage_2m.ps,height=4in,angle=-90}}\n \\caption{The fraction of the sky that can be observed as a function of\n the desired resolution, $\\Delta\\theta$, and the photon rate in the\n detector (as in figure~\\protect\\ref{fig:resolution}), $\\Gamma$, for\n an X-BOSS used in conjunction with Chandra. (a) A satellite\n width of $10\\meter$ is assumed here. (b) A satellite\n width of $2\\meter$ is assumed here. A larger satellite can obtain\n these results if velocity corrections are made during the observation.\n See the text for details.\n }\n \\label{fig:skycoverage}\n\\end{figure}\n\n\\begin{figure}\n \\leavevmode\\center{\\epsfig{figure=skycoverage_XMM_10m.ps,height=4in,angle=-90}}\n \\leavevmode\\center{\\epsfig{figure=skycoverage_XMM_2m.ps,height=4in,angle=-90}}\n \\caption{\n The same as figure~\\protect\\ref{fig:skycoverage} for an X-BOSS used in\n conjunction with XMM\\@.\n }\n \\label{fig:skycoverageXMM}\n\\end{figure}\n\n\\end{document}\n"}],"string":"[\n {\n \"name\": \"ms.tex\",\n \"string\": \"%% For submission to apj use\\n%\\\\documentclass{aastex}\\n\\\\documentclass[preprint,12pt]{aastex}\\n% To include figures\\n\\\\usepackage{epsfig}\\n% Include draftcopy to get ``draft date'' to appear on each page\\n%\\\\usepackage{draftcopy}\\n\\n% $Id: ms.tex,v 1.9 2000/02/09 21:22:53 copi Exp $\\n\\n\\\\newcommand\\\\be{\\\\begin{equation}}\\n\\\\newcommand\\\\ee{\\\\end{equation}}\\n\\n\\\\newcommand{\\\\mcommand}[1]{\\\\ifmmode #1\\\\else $#1$\\\\fi}\\n\\\\newcommand{\\\\sci}[1]{\\\\mcommand{\\\\times 10^{#1}}}\\n\\n\\\\newcommand{\\\\unit}[1]{\\\\mcommand{\\\\;{\\\\rm #1}}}\\n\\\\newcommand\\\\meter{\\\\unit{m}}\\n\\\\newcommand\\\\second{\\\\unit{s}}\\n\\\\newcommand\\\\as{\\\\unit{arcsecond}}\\n\\\\newcommand\\\\mas{\\\\unit{mas}}\\n\\\\newcommand\\\\parsec{\\\\unit{pc}}\\n\\\\newcommand\\\\kpc{\\\\unit{kpc}}\\n\\\\newcommand\\\\Mpc{\\\\unit{Mpc}}\\n\\\\newcommand\\\\yr{\\\\unit{yr}}\\n\\\\newcommand\\\\mps{\\\\unit{m\\\\;s^{-1}}}\\n\\\\newcommand\\\\cm{\\\\unit{cm}}\\n\\\\newcommand\\\\km{\\\\unit{km}}\\n\\\\newcommand\\\\kmps{\\\\unit{km\\\\;s^{-1}}}\\n\\\\newcommand\\\\pmsqs{\\\\unit{m^{-2}\\\\;s^{-1}}}\\n\\\\newcommand\\\\gram{\\\\unit{g}}\\n\\\\newcommand\\\\kg{\\\\unit{kg}}\\n\\\\newcommand\\\\AU{\\\\unit{AU}}\\n\\\\newcommand\\\\keV{\\\\unit{keV}}\\n\\n%\\\\def\\\\vec#1{\\\\mbox{\\\\boldmath$#1$\\\\unboldmath}}\\n\\n\\\\newcommand\\\\etal{et al.}\\n\\\\newcommand\\\\etc{etc}\\n\\n\\\\newcommand\\\\ltsim{\\\\lesssim}\\n\\\\newcommand\\\\gtsim{\\\\gtrsim}\\n\\n\\n\\\\begin{document}\\n\\n\\\\title{Improving the Resolution of X-Ray Telescopes with Occulting Satellites}\\n\\\\author{Craig J. Copi\\\\altaffilmark{1}\\\\email{cjc5@po.cwru.edu} \\\\and Glenn D. Starkman\\\\altaffilmark{1,2}\\\\email{gds6@po.cwru.edu}}\\n\\\\affil{\\nBOSS home page: \\\\tt\\\\url{http://boss.phys.cwru.edu/}}\\n\\\\altaffiltext{1}{Department of Physics, Case Western Reserve\\nUniversity, Cleveland, OH 44106-7079}\\n\\\\altaffiltext{2}{Department of Astronomy, Case Western Reserve\\nUniversity, Cleveland, OH 44106-7079}\\n\\\\authoraddr{10900 Euclid Avenue\\\\\\\\ Cleveland, OH 44106-7079}\\n\\n\\\\shorttitle{Improving X-Ray Resolution with X-BOSS}\\n\\\\shortauthors{Craig J. Copi and Glenn D. Starkman}\\n\\n\\\\begin{abstract}\\nOne of the challenges of X-ray astronomy \\nis how to both collect large numbers of photons yet \\nattain high angular resolution. \\nBecause X-ray telescopes utilize grazing optics, \\nto collect more photons requires a larger acceptance angle \\nwhich in turn compromises the angular resolution.\\nAll X-ray telescopes thus have angular resolution\\nfar poorer than their diffraction limit.\\nAlthough collecting more photons is a desirable goal,\\nsometimes selective collecting fewer photons may yield more information.\\nNatural (such as lunar) occultations \\nhave long been used to study sources on small angular scales.\\nBut natural occulters are of limited utility because\\nof their large angular velocities relative to the telescope,\\nand because of the serendipity of their transits.\\nWe describe here how one can make use of an \\nX-ray Big Occulting Steerable Satellite (X-BOSS) \\nto achieve very-high resolution of X-ray sources.\\nAn X-BOSS could significantly improve the resolution of \\nexisting X-ray facilities such as the Chandra telescope, \\nor X-ray Multiple Mirror (XMM) satellite, \\nand could vastly improve the resolution of some future\\nX-ray telescopes, particularly Constellation X where sub-milliarcsecond\\nresolution is possible for a wide range of sources.\\nSimilar occulting satellites could also be deployed in conjunction \\nwith planned space observatories for other wavebands.\\n\\\\end{abstract} \\n\\n\\\\keywords{space vehicles---occultations---X-rays:general}\\n\\n\\n\\\\slugcomment{\\\\small Preprint: {\\\\bf CWRU-P04-00}}\\n% \\\\\\\\ Submitted to: \\\\em The Astrophysical Journal}\\n\\n\\\\section{Introduction}\\n\\nOne of the big challenges in doing X-ray astronomy\\nis the relatively low photon fluxes from target sources.\\nThe fact that X-ray mirrors operate only at grazing \\nangles of incidence further exacerbates this problem.\\nThus, while one might naively expect \\nsuperb angular resolution from a $1.2\\\\meter$ aperture X-ray telescope \\nsuch as the one on board the Chandra satellite,\\nthe $0.5$ arcsecond reality is far from the \\n0.3 milliarcsecond nominal diffraction limit,\\nand considerably worse than what is routinely achieved in\\nlonger wavelength bands. This situation is unlikely to \\nchange in the near future. Indeed, current plans for\\nfuture X-ray missions opt for increased acceptance\\nangle (and thus increased photon count rate) at\\nthe price of reduced angular resolution.\\n\\nBut it {\\\\em is} possible to achieve higher \\nX-ray photon count rates and yet improve one's angular resolution. \\nThe necessary step is to separate the collection of photons \\nfrom the means of achieving high resolution.\\nOne way to do this is well-known---occultation.\\nWhen an astronomical body, such as the moon, transits the field\\nof view of a telescope, it occults different sources within the\\nfield of view at different times. By carefully measuring\\nthe photon count rate as a function of time during the transit,\\none can then reconstruct the projection of the surface brightness\\nin the field of view onto the path of the occulter.\\n\\n\\nNatural occulters {\\\\em have} been used to achieve high-resolution\\nin X-ray observations; however, they have at least two distinct\\ndisadvantages:\\n\\\\begin{enumerate}\\n\\\\item Although natural occultations can be predicted, they cannot be\\n scheduled---target sources are therefore limited, and multiple\\n occultations of the same source over the course of a few years\\n are uncommon.\\n\\\\item Natural occulters have large angular velocities relative to\\n a telescope. The shorter the transit time, the fewer photons one\\n collects, and so the lower the resolution. This is especially important\\n for X-ray astronomy, where photon count rates are relatively low.\\n\\\\end{enumerate}\\nThere is however an alternative to natural occulters which can overcome\\nboth of these disadvantages---a steerable occulting satellite. Deployment\\nof large steerable occulting satellites has been discussed for optical and\\nnear infra-red wavebands\\n\\\\citep{Adams,Schneider,CS98,CS00},\\nmostly for\\nthe purpose of finding planet around nearby stars, but also for\\nhigh-resolution astronomical observations. However, such satellites are\\nnaturally well-suited for observations in the X-ray and far-UV\\\\@. In the\\nlonger wavelength bands, minimization of diffractive losses pushes one to\\nmake the satellite as large as feasible, and deploy it as far as possible\\nfrom the telescope. In the X-ray waveband one is far into the geometric\\noptic limit and diffraction of the X-ray photons around the satellite can\\nessentially be neglected; thus the optimal size and placement of the satellite \\nare determined by one's ability to accurately position the satellite with respect to the\\ntelescope-star line-of-sight and to minimize the satellite's velocity\\nperpendicular to that line-of-sight. The resolution delivered by the\\ncombination of the X-ray telescope and the X-BOSS is determined by the\\ncollecting area of the telescope (and thus the photon count rate for a\\nsource) and by the accuracy with which one can match the X-BOSS and telescope\\nvelocity. It is independent of the intrinsic resolution of the telescope.\\n\\nFor an X-ray telescope either in an eccentric high-Earth orbit (Chandra and XMM) or at the\\nL2 point of the Earth-Sun system (Constellation-X) we discuss in section\\n\\\\ref{sec:location} where to position X-BOSS relative to the satellite. In\\nsection \\\\ref{sec:blocking} of this letter we discuss the X-ray blocking\\nefficiency of a thick film and what it implies for the required thickness\\nof the occulter. We also estimate in this section the required dimensions of an X-BOSS,\\nwhich are determined mostly by limitations on telemetry.\\nWe discuss the steering of the X-BOSS in section \\\\ref{sec:steer}. \\nIn section \\\\ref{sec:resolve} we find the angular resolution that one\\nobtains as a function of X-BOSS-telescope relative angular velocity, \\nand of photon count rate. \\nIn section~\\\\ref{sec:skycoverage} we discuss the the sky\\ncoverage that one could obtain in each location. \\nApplication of these techniques to specific sources is discussed briefly \\nin section~\\\\ref{sec:results}. \\nFinally, section~\\\\ref{sec:conclude} contains the conclusions.\\n\\n\\\\section{Locating an X-BOSS}\\n\\\\label{sec:location}\\n\\nThe location of an X-BOSS is dictated by the location of the\\ntelescope it is meant to occult. The Chandra X-ray telescope is\\nin an elliptic orbit around the Earth with \\nan apogee of $145,417\\\\km$ and a perigee of $16,026\\\\km$.\\nThe X-ray Multiple Mirror (XMM) Telescope will also be inserted into\\nan elliptic Earth orbit.\\nOther X-ray telescopes, such as Constellation X, \\nmay be located at the second Lagrangian point of the Earth-Sun system. \\nThe orbital issues are entirely\\ndifferent for these two locations; \\nwe address each in turn below.\\nFinally, some X-ray telescopes (Astro-E and XEUS) will be\\nplaced in low earth orbit. Because orbital velocities\\nare so high in low earth orbit, it is more difficult to make \\nuse of the approach we advocate here; we will not discuss\\nthese further.\\n\\n\\\\subsection{Eccentric high Earth-orbit}\\n\\\\label{subsec:orbitearth}\\n\\nAs described above, the Chandra satellite is in an eccentric high altitude\\nEarth orbit. The period of this orbit is 64 hours. The satellite\\ntherefore has an average angular velocity of about 6 arcseconds per second. \\nAn occulting satellite leading or following in Chandra's orbit would transit a source at\\napproximately that rate. The planned X-ray Multiple Mirror Telescope (XMM)\\nhas a similar orbit with a shorter 48 hour period.\\nGiven that the attainable angular resolution is related to the angular \\nvelocity of transit, \\nthe resolution that one could achieve with these orbits is minimal.\\n\\nA great improvement is to place the X-BOSS in an orbit identical to that of\\nthe telescope but slightly modified by shifting the apogee and perigee, by\\nchanging the phase of the satellite in the orbit, or by rotating the orbit.\\nIn all cases these modifications will put X-BOSS in an orbit with the same\\nperiod as telescope. In such orbits the velocity perpendicular to the line\\nof sight of X-BOSS and the telescope can be quite low. For example, consider\\nplacing X-BOSS in an orbit identical to that of the telescope (in terms of\\napogee, perigee, and orbital phase) but rotated about an axis through the center of the Earth\\nin the plane of the orbit and perpendicular to the line connecting apogee and perigee. \\nThe component of the relative velocity between X-BOSS and the telescope\\nperpendicular to the line-of-sight between them is then zero throughout the\\nentire orbit. Unfortunately, such an orbit intersects the telescope orbit at\\ntwo points with disastrous consequences. The other orbital modifications\\nmentioned above can alleviate this problem by enforcing a minimum\\nseparation of, for example, $10\\\\km$ between the two spacecrafts. Although\\n$10\\\\km$ may seem fairly close, note that each spacecraft is only a\\nfew to tens of meters across; random errors therefore have a probability\\nless than $10^{-9}$ per orbit crossing of causing catastrophic failure.\\nThe importance of utilizing these orbit modifications is explained more\\nfully in sections~\\\\ref{sec:steer} and \\\\ref{sec:skycoverage}.\\n\\n\\\\subsection{Orbit at L2}\\n\\\\label{subsec:orbitL2}\\n\\nWe have previously discussed the orbital advantages of placing a large\\nocculter at L2 in greater detail \\\\citep{CS00}. Here we will\\nhighlight the important points.\\nOrbits around L2, both in the plane of the ecliptic and oscillations\\nperpendicular to this plane, have periods of about 6 months independent of\\ntheir distance from L2 (for distances $\\\\ltsim 10^4\\\\km$). Therefore the\\nlocal gravity is very small. Both the total velocity and acceleration of\\norbits around L2 (relative to the L2 point) are on par with those we might attain\\nthrough carefully \\ntuning the orbit of X-BOSS relative to that of Chandra or XMM; \\nthe relative velocity of the satellite and telescope due to the\\nmotion of L2 about the Sun is of the same magnitude. If corrections are\\nmade to the X-BOSS orbit to cancel these then the\\nacceleration perpendicular to the line-of-sight is about\\n$5\\\\sci{-10}\\\\meter\\\\second^{-2}$. Thus if the perpendicular velocity of\\nX-BOSS relative to a particular line-of-sight between the telescope and some source\\nis canceled by firing rockets, the perpendicular velocity will remain less than $10^{-4}\\\\mps$ for \\nat least a day. Tuning the velocity of X-BOSS, therefore, can be done very \\neasily at L2.\\n\\n\\\\section{Making an X-ray Occulter}\\n\\\\label{sec:blocking}\\n\\n\\\\subsection{Thickness}\\n\\nThe attenuation length of X-ray photons in elemental matter\\nis shown in figure~\\\\ref{fig:photonattenuation}.\\nExcept in hydrogen, it is approximately $3\\\\times 10^{-4} \\\\gram \\\\cm^{-2}$ at\\n$1\\\\keV$, and $10^{-2} \\\\gram\\\\cm^{-2}$ at $10\\\\keV$. \\nThus a square $10\\\\meter$ on a side and one attenuation length\\nthick has a mass of $0.3\\\\kg$ at $1\\\\keV$, and $10\\\\kg$ at $10\\\\keV$.\\nAt a typical density of $3 \\\\gram \\\\cm^{-3}$, these represent thicknesses\\nof just $1$ micron and $30$ microns respectively.\\n\\nA useful occulter would need to be $3\\\\hbox{--}5$ attenuation lengths thick,\\nand so $3\\\\hbox{--}5$ microns and $1\\\\hbox{--}2\\\\kg$ to operate at $1\\\\keV$,\\nand $100\\\\hbox{--}150$ microns and $30\\\\hbox{--}50\\\\kg$ to operate at $10\\\\keV$.\\nEven at $100\\\\keV$ a $10\\\\meter\\\\times10\\\\meter$ lead film \\n$0.6\\\\unit{mm}$ thick at a mass of $600\\\\kg$ would provide 3 attenuation \\nlengths of occultation.\\n\\nIf positioning technology improved to the point where one could\\nreduce the size of the occulter to $1\\\\hbox{--}2\\\\meter$, then even gamma ray\\nocculters would be of reasonable mass.\\n\\n\\\\subsection{Size}\\n\\nThe size of the occulting satellite depend on\\ntwo factors---the aperture of the telescope and \\nthe accuracy with which one can position the occulter. \\n\\nThe apertures of typical X-ray satellites are about $1\\\\meter$.\\nThis sets a lower bound on the dimensions of the occulter.\\nOnce the occulter is larger than the aperture of the X-ray telescope,\\nthere is essentially no effect on resolving power.\\n\\nNext we will estimate how well we can determine the position of X-BOSS \\nin the plane perpendicular to the telescope-source line-of-sight \\nit is meant to occult. \\nConsider a telescope separated from the X-BOSS by a distance $r$. \\nWe can mount a small diffraction-limited optical telescope of diameter $d$ \\non the underside of the occulter. Using this telescope\\nwe can establish the relative positions\\nof the two satellite to within approximately\\n\\\\be \\n\\\\delta x = 1.2 r \\\\frac{\\\\lambda}{d} \\n= 0.5 \\\\meter \\\\frac{r}{1000\\\\km} \\\\frac{\\\\lambda/400\\\\unit{nm}}{d/1\\\\meter}\\n\\\\ee\\nA $1\\\\meter$ positioning accuracy therefore requires\\na $50\\\\unit{cm}$ finder scope at $1000\\\\unit{km}$ separation,\\nproportionately smaller at smaller separations. \\nThis is quite feasible, especially since the finder scope \\nneed not have a full UV plane.\\n\\nAn important question is whether one will collect\\nenough photons to reach the diffraction limit of the\\nangular resolution. There are two principal\\noptions---rely on reflected sunlight or \\nshine a laser from the X-ray telescope onto the X-BOSS telescope.\\nColumnation is not a significant problem, \\nas seen by our calculation of the diffraction limit above. \\nHowever, sunlight has an intensity of $1000\\\\unit{W}\\\\meter^{-2}$, \\nwhich will be difficult to match with a laser anyway. \\nAssuming isotropic scattering from the telescope,\\nand a total reflecting area of $1\\\\meter^{2}$,\\nthis results in a flux at the X-BOSS of $3\\\\sci{8}\\\\second^{-1}$,\\nat $1000\\\\km$ (falling as $1/r^2$). Detailed studies\\nof existing telescopes (Chandra, XMM) would be required\\nto precisely quantify our ability to locate the\\ntelescope relative to the X-BOSS, however, these\\nestimates suggest that determining the relative\\nposition to within $1\\\\hbox{--}3 \\\\meter$ is not unrealistic.\\nIn the case of yet-to-be launched telescopes, \\nthe mounting of a small reflector on\\none or more corner of the telescope would be of\\ndefinite benefit.\\n\\nAlthough we have argued that we can determine the\\nrelative position of an X-BOSS and an X-ray telescope \\nto within about a meter, we must also be able to reduce\\nthe velocity to a fraction of a meter per second.\\nThis can be done by a simple bootstrapping procedure.\\nTwo position determinations each with error of $\\\\Delta x$,\\nmade a time $t$ apart, determine the velocity within\\n$\\\\Delta v \\\\simeq \\\\sqrt{2} \\\\Delta x/t$ (assuming the\\nerror in $t$ to be negligible). If the relative velocity\\ncan be canceled within errors by accurately firing rockets,\\nthen the ability to reduce $\\\\Delta v$ is limited by \\nthe time one can allow between position determinations, $t=\\\\Delta x/\\\\Delta v$.\\nThis time is limited by the orbital accelerations, \\nbut is thousands of seconds for the elliptic earth orbits of interest\\n(cf.~subsection \\\\ref{subsec:earthorbit})\\nand hundreds of thousands of seconds for orbits at L2.\\n(cf.~subsection \\\\ref{subsec:L2orbits}).\\nIn practice it may be desirable to gradually\\nreduce the relative velocity using repeated position\\ndeterminations and rocket firings.\\n\\n\\n\\\\section{Steerability}\\n\\\\label{sec:steer}\\n\\nIn order to successfully resolve objects it will be necessary\\nto frequently change the velocity of the satellite. \\nThese velocity changes will occur for two principal reasons:\\nto move from one target source to another,\\nand to match the velocity of the X-BOSS to that of the X-ray telescope.\\nWhile solar radiation pressure might be used to some advantage,\\nit will be necessary to make some velocity adjustments using rockets.\\nThe number and size of such adjustments may be the limiting factor\\non the useful lifetime of the X-BOSS.\\n\\n\\nA change $\\\\Delta v$ in the satellite's velocity is related\\nby momentum conservation to the mass of propellant ejected,\\n$\\\\Delta m_{\\\\rm propellant}$, and the velocity of ejection $v_{\\\\rm ejection}$:\\n\\\\be\\n\\\\Delta v_{\\\\rm sat}\\n= \\\\frac{\\\\Delta m_{\\\\rm propellant}{ v}_{\\\\rm ejection}}{m_{\\\\rm sat}} .\\n\\\\ee\\nIf $N$ is the number of desired major rocket-driven velocity changes,\\nthen we must keep\\n$(\\\\Delta m_{\\\\rm propellant}/m_{\\\\rm sat})\\\\leq N^{-1}$.\\n(The mass of propellant ejected will of course vary on the particular\\nmaneuver, but here $\\\\Delta m_{\\\\rm propellant}$ is taken to be some \\ntypical mass of propellant expended per orbit reconfiguration.)\\nWe therefore can accommodate only a limited number of such rocket firings:\\n\\\\be\\nN \\\\leq \\\\frac{v_{\\\\rm ejection}}{\\\\Delta{ v_{\\\\rm sat}}} .\\n\\\\ee\\nOff-the shelf, low-cost ion engines are currently available\\nwith ejection velocities of $20 \\\\kmps$, and\\nmore expensive systems with $30 \\\\kmps$ performance \\nhave been developed, thus\\n\\\\be\\nN \\\\leq \\\\frac{30\\\\kmps}{\\\\Delta{ v_{\\\\rm sat}}} .\\n\\\\label{eqn:Ncorrect}\\n\\\\ee\\n\\nConsider first the need to match the velocities of the two spacecraft\\nso that a long occultation can occur.\\n$\\\\Delta{ v_{\\\\rm sat}}$ is then the relative velocity \\nof the X-BOSS and the telescope in their orbits.\\nIn determining the sky coverage for elliptic Earth orbits \\nin section~\\\\ref{subsec:earthorbit} above, \\nwe have considered only orbital configurations with relative velocities \\nbetween the telescope and the X-BOSS of less than $10\\\\mps$.\\n(Near L2, the relative velocities of relevance are typically \\nconsiderably smaller than that.)\\nIf $\\\\Delta{ v_{\\\\rm sat}}\\\\simeq 10\\\\mps$, then this implies \\n$N\\\\leq 3000$,\\nwhich is a reasonable quota of corrections for a mission with a 3--5 year\\nlifetime, \\ngiven the typical 2--3 day orbital period of Earth-orbiting\\nX-ray telescopes. \\n\\nThe second type of velocity correction that will be required\\nis target acquisition---the readjustment of the orbit\\nof the occulter so as to allow the occultation of a new \\ntarget source. \\nFor satellites separated by $1000\\\\km$ near L2, relative velocities\\nare only $v_{\\\\rm sat} = {\\\\cal O}(10^{-4}\\\\kmps)$,\\nand the expression for\\n$N$ (equation~\\\\ref{eqn:Ncorrect}) shows that any constraint on target\\nchoice or order does not come from concerns about conserving\\npropellant.\\nFor telescopes in orbit about the Earth, \\nthe matter is quite different.\\nHere orbital velocities are $v_{\\\\rm sat} = {\\\\cal O}(1\\\\kmps)$,\\nand so it is clear from the allowed number of orbital\\ncorrections~(\\\\ref{eqn:Ncorrect}) that\\none cannot indiscriminately rocket from one target to another on the sky.\\nOne solution might have been to sail in the solar radiation pressure.\\nHowever, the solar radiation pressure is approximately $P_{\\\\rm\\n solar}=6\\\\times10^{-6}\\\\unit{Pa}$. \\nFor an areal density of just $1.5\\\\times 10^{-3}\\\\gram\\\\cm^{-2}$\\n(five attenuation lengths as $1\\\\keV$),\\nthis results in an acceleration of only $4\\\\times10^{-4}\\\\meter\\\\second^{-2}$.\\nAt this rate it takes about a month to change velocity by $1\\\\kmps$.\\n\\nClearly one cannot reposition randomly on the sky. \\nHowever the velocity difference between two orbits which\\nresult in occultation of target sources one degree apart are only\\nof order $15\\\\mps$. Solar sailing can cause velocity changes\\nof this order in under a day. \\nMoreover, the allowed number of orbital corrections~(\\\\ref{eqn:Ncorrect})\\nindicates that rocket driven\\ncorrections of this magnitude can be made of order 1000 times.\\nHow many corrections we can make, and how many sources we can\\ntherefore target for occultation,\\nclearly depends on exactly how we use the satellite. \\nA reasonable program of observations certainly seems possible.\\n\\n\\\\section{Resolution}\\n\\\\label{sec:resolve}\\n\\nWhen used in conjunction with an X-BOSS the telescope acts as a\\nlight bucket. The angular resolution of the telescope itself is\\nirrelevant; instead the collecting area is the important telescope\\nparameter. The angular resolution of the system will come from probing the \\nlightcurve as X-BOSS transits a source.\\n\\nTo study the angular resolution of X-BOSS we consider the simple case of\\nidentifying a binary source. Let $f (\\\\vec x, t)$ be the normalized\\nlightcurve (number of photons detected per second) generated as X-BOSS\\nscans across a single source at a position\\n$\\\\vec x$ in the plane of X-BOSS\\\\@. The lightcurve is the number of photons\\ndetected as a function of time. It is normalized such that the value is\\none (in the detector) when X-BOSS is not present. Since X-rays have\\nextremely short\\nwavelengths we can approximate the diffraction pattern produced by the\\nsatellite simply by the geometric shadow projected on the telescope. This\\nreduces the lightcurve to a calculation of the area of the telescope not\\nunder the shadow of the occulter. We write the lightcurve of a single\\nsource as\\n\\\\be \\nl_1 (\\\\vec x, t) = I_1 f (\\\\vec x, t)\\n\\\\ee\\nand the total lightcurve for two sources at $\\\\vec x_1$ and $\\\\vec x_2$\\ncan be written as\\n\\\\be\\nl_2 (\\\\vec x_1, \\\\vec x_2, t) = I_2 \\\\left[ \\\\rho f (\\\\vec x_1, t) +\\n (1-\\\\rho) f (\\\\vec x_2, t)\\\\right].\\n\\\\ee\\nHere $I_i$ is the total intensity of the system for $i=1$ or $2$ sources\\nand $\\\\rho$ is\\nthe intensity \\nratio of the two sources. We would like to find the minimum separation of\\ntwo sources that can be distinguished from a single source. An observation\\nconsists of a sequence $\\\\left\\\\{O_j (\\\\vec x)\\\\slash j=1,...,n \\\\right\\\\}$\\nof measurements of the integrated lightcurve between \\ntimes $t_{j-1}$ and $t_j$:\\n\\\\be \\nO_j (\\\\vec x) = \\\\int_{t_{j-1}}^{t_j} dt\\\\; l_i (\\\\vec x, t).\\n\\\\ee\\nTo obtain\\nlimits on the minimum separation we first evaluate the number of photons\\nexpected between time $t_0$ and $t_k$\\n\\\\be\\nL_{i,k} (\\\\vec x) \\\\equiv \\\\int_{t_0}^{t_k} dt\\\\;l_i (\\\\vec x, t) =\\n\\\\sum_{j=1}^k O_j (\\\\vec x)\\n\\\\ee \\nwhere $i$ is 1 or 2 as above.\\nAssuming the counts in each time bin, $[t_{j-1},t_j)$, are Poisson distributed the\\nlikelihood of a model with $i$ sources given an underlying model with 2\\nsources is \\n\\\\be \\n{\\\\cal L}_i = \\\\prod_{k=1}^N \\\\left. e^{-L_{i,k}} \\\\left( L_{i,k} \\\\right)^{L_{2,k}}\\n\\\\right/ \\\\left( L_{2,k}\\\\right)!.\\n\\\\ee\\nFinally the quantity\\n\\\\be \\nT = -2\\\\log \\\\left (\\\\frac{{\\\\cal L}_1}{{\\\\cal L}_2} \\\\right)\\n\\\\ee\\nis $\\\\chi^2$ distributed with 4 degrees of freedom ($t_0$, $x_2-x_1$, $I$,\\nand $\\\\rho$) and allows us to\\ncalculate the probability of misidentifying a binary source as a single source.\\nThis probability depends on \\n$\\\\mu_\\\\perp$, the angular velocity of X-BOSS as it transits the source.\\nThe results for the 95\\\\% confidence limits as a function of the intensity\\nin a $1.2\\\\meter$ aperture telescope for $\\\\rho=1$, $1/3$, and $1/10$ and for\\n$\\\\mu_\\\\perp=10\\\\mas\\\\second^{-1}$, $\\\\mu_\\\\perp=1\\\\mas\\\\second^{-1}$, and\\n$0.1\\\\mas\\\\second^{-1}$ are shown in figure~\\\\ref{fig:resolution}. In\\nproducing figure~\\\\ref{fig:resolution} we assumed a uniform response over\\nthe surface of the telescope. A more complicated response function may\\nimprove resolution slightly.\\n\\nThe simple analysis employed here uses the edges of X-BOSS in a single\\noccultation. In practice it would be necessary to obtain multiple\\nprojections to resolve a source in two dimensions. This could be facilitated\\nby putting slits at various angles in X-BOSS that allow for sources to be\\nocculted by different regions of the satellite in different ways during a\\nsingle transit.\\n\\n\\n\\\\section{Sky Coverage}\\n\\\\label{sec:skycoverage}\\n\\nThe issues of resolution and sky coverage are closely related. Here sky\\ncoverage is the fraction of the sky for which a particular angular\\nresolution can be obtained. While one can reposition X-BOSS to be in an\\narbitrary direction on the sky relative to the X-ray telescope, this\\nfrequently leads to large relative velocities and accelerations between the\\nocculter and telescope perpendicular to the line-of-sight, thus leading to\\npoor resolution (see figure~\\\\ref{fig:resolution}). Conversely, extremely\\ngood resolution is possible if the relative velocity during the occultation\\nis kept quite low; however this requires either special orbits (and thus\\nvery little sky coverage) or expenditures of fuel. Here we will explore\\nthe sky coverage that can be obtained subject to a number of constraints.\\n\\n\\\\subsection{Elliptic Earth Orbits}\\n\\\\label{subsec:earthorbit}\\n\\nWe consider placing an X-BOSS in orbit around the Earth with nearly the\\nsame orbital parameters as an X-ray telescope. As discussed in\\nsection~\\\\ref{subsec:orbitearth} we then allow for small alterations in the\\nX-BOSS orbit which change the direction of the line-of-sight from the\\ntelescope to X-BOSS while keeping the X-BOSS period fixed.\\nOur first constraint is that the\\nminimum separation of the X-BOSS and telescope in their orbits must be larger than $10\\\\km$. \\n(If this safety factor can be reduced then greater sky coverage may be possible.) \\nWe then follow the two spacecrafts in their orbits to see what sky coverage \\nthese orbits afford.\\nTo limit the expenditure of propellant we \\nconsider making observations only when the relative velocity of the\\ntwo satellites perpendicular to the line-of-sight is sufficiently small,\\nhere we require $v_\\\\perp^{\\\\rm orb} <\\n10\\\\mps$ (see section~\\\\ref{sec:steer}). Prior to an observation this\\nvelocity can be reduced to the desired range by firing the X-BOSS rockets\\n(a small correction requiring acceptable use of consumables).\\n\\nAfter maneuvering to correct the perpendicular relative velocity between the\\ntelescope and X-BOSS, they would still be accelerating relative to each\\nother during the observation. The provides one limit on the total transit\\ntime of the observation. There would also be some residual error in the\\nvelocity correction, leaving X-BOSS with a component of its velocity perpendicular to the\\nline-of-sight. This provides another limit on the total transit time of the\\nobservation. Combining these two, the total transit time over which the\\nobservation can made is\\n\\\\be\\nt_{\\\\rm obs} = \\\\min \\\\left(\\\\sqrt{\\\\frac{2w}{a_\\\\perp^{\\\\rm orb}}},\\n \\\\frac{w}{\\\\mu_\\\\perp^{\\\\rm max} d} \\\\right).\\n\\\\ee\\nHere $a_\\\\perp^{\\\\rm orb}$ is the perpendicular linear acceleration, $w$ is the\\nwidth of X-BOSS, $d$ is the distance between the two spacecrafts, and\\n$\\\\mu_\\\\perp^{\\\\rm max}$ is the maximum angular velocity allowed to obtain a\\nparticular resolution.\\nIf we require that the angular velocity perpendicular to the line\\nof sight at the end of the observation be less than the same maximum value,\\n$\\\\mu_\\\\perp^{\\\\rm max}$, then we obtain the constraint\\n\\\\be\\na_\\\\perp^{\\\\rm orb} t_{\\\\rm obs} < \\\\mu_\\\\perp^{\\\\rm max} d.\\n\\\\label{eqn:constraint1}\\n\\\\ee\\nOf course when we cancel $v_\\\\perp^{\\\\rm orb}$ before the observation we are\\nalso making a small change to the orbit. This leads to an extra\\nacceleration that must also be small. If we require that this acceleration\\nalso not produce a large final velocity we obtain the constraint\\n\\\\be\\n\\\\frac{v_\\\\perp^{\\\\rm orb} t_{\\\\rm obs}^2}{r^3 d} < \\\\frac{\\\\mu_\\\\perp^{\\\\rm\\n max}}{2g R_\\\\oplus^2},\\n\\\\label{eqn:constraint2}\\n\\\\ee\\nwhere $r$ is the distance from X-BOSS to the (center of the) Earth,\\n$g=9.8\\\\meter\\\\second^{-2}$, and $R_\\\\oplus$ is the radius of the Earth.\\n\\nThe sky coverage on each change of X-BOSS orbit is not large. To increase\\nthe amount of sky\\naccessible to observation we consider moving X-BOSS between orbits that are\\nsimilar to the orbit of the X-ray telescope. Throughout we will consider\\nmodifications of the X-BOSS orbit that leave the period unchanged. Over\\nmany orbits this is a \\ndesired feature since it prevents the times at which X-BOSS and the telescope\\nachieve apogee and perigee from drifting apart, requiring a\\nlarge expenditure of fuel to correct. The orbital modifications we\\nconsider are increasing or decreasing the apogee distance (while preserving \\nthe semi-major axis and thus the period), rotating the orbit\\nabout all three axes, and introducing a phase shift (time of apogee) into the\\norbit. For this study we taken the X-ray telescope to be the Chandra\\nsatellite and allowed changes in apogee (and perigee) of\\n$\\\\pm200\\\\km$, rotations about the two axes in the plane of the orbit of\\n$\\\\pm1^\\\\circ$, rotations in the plane of the orbit of $\\\\pm0.4^\\\\circ$, and\\ntime shifts of $\\\\pm100\\\\second$. All of these changes are relative to\\nChandra's orbit. These changes can be accomplished using ion engines\\nseveral thousand times before exhausting the supply of expendables (see\\nsection~\\\\ref{sec:steer}). Since occultations are best done near apogee and \\n1000 or so orbital periods is the Chandra mission lifetime, this rate of\\nconsumption of expendable is acceptable.\\n\\nUsing Monte Carlo techniques,\\nwe studied the orbits in this region of parameter space \\nsubject to two constraints: the minimum separation of the X-BOSS and telescope \\nmust be at least $10\\\\km$, and somewhere in the orbit the\\nperpendicular velocity must be less than $10\\\\mps$. We generated $100,000$\\norbits that satisfy these criteria. Next, for a variety of photon count rates\\nand desired resolutions we used the resolution results show in \\nfigure~(\\\\ref{fig:resolution}) to determine $\\\\mu_\\\\perp^{\\\\rm max}$. Finally\\nwe checked which lines-of-sight satisfied the velocity and acceleration\\nconstraints~(\\\\ref{eqn:constraint1}, \\\\ref{eqn:constraint2}) and thus which\\nparts of the sky can be observed. The results are shown in\\nfigure~\\\\ref{fig:skycoverage} assuming the width of X-BOSS is $10\\\\meter$. \\nHere even for very intense sources (I=$10^5\\\\second^{-1}$) only 20\\\\%\\nof the sky can be covered with a a resolution of\\n$\\\\Delta\\\\theta=0.1\\\\as$. This tight constraint is due principally to the fact\\nthat X-BOSS is accelerating during the time that both of the sources are\\nocculted leading to a large velocity by the end of the observation which\\noccurs when the transit is complete. \\nTo counteract this we could use a narrower satellite, \\nuse a satellite with slits in it so that we do not have to wait until the far\\nedge starts unocculting the sources, or fire the rockets while both sources\\nare occulted to cancel the velocity. To model these possibilities we have considered \\na satellite that accelerates over only $2\\\\meter$ between the onset and end of\\na transit. The results are shown in figure~\\\\ref{fig:skycoverage}b. \\nHere we see a tremendous improvement in sky coverage and resolution. \\nFor intense sources, $I=10^5\\\\second^{-1}$, we can obtain\\n$\\\\Delta\\\\theta=0.1\\\\as$ over \\n40\\\\% of the sky and $\\\\Delta\\\\theta=0.02\\\\as$ over 20\\\\% of the sky.\\nLarger sky coverages would be obtained if we relaxed the criteria on the \\norbital velocity difference between the Chandra and X-BOSS orbits.\\nThis would be justified if the propellant velocities of ion engines\\nrose about $30\\\\kmps$, or if we could make do with a smaller number of orbital \\ncorrections.\\n\\n\\\\subsection{L2 Orbits}\\n\\\\label{subsec:L2orbits}\\n\\nAs discussed above (section~\\\\ref{subsec:orbitL2}) the orbits at L2 are much \\nsimpler to manage than orbits around the Earth. Full sky coverage can be\\nobtained and the velocity perpendicular to the line-of-sight can be chosen\\nas desired. Figure~\\\\ref{fig:resolution} best represents what can be\\nachieved at L2. Since the perpendicular velocity can be chosen, extremely\\nhigh angular resolution is possible. Even sub-milliarcsecond resolution is\\npossible for many sources ($I\\\\gtsim 4\\\\sci{3}\\\\second^{-1}$) when\\n$\\\\mu_\\\\perp=0.1\\\\mas\\\\second^{-1}$.\\n\\n\\\\section{Results}\\n\\\\label{sec:results}\\n\\nThis is an exciting time for X-ray astronomy. Two new X-ray telescopes\\n(the Chandra Advanced X-ray Astronomical Facility, and the X-ray Multiple\\nMirror telescope (XMM)) have been successfully launched, while another\\n(Astro-E) is being readied for launch. Of these three, Chandra and XMM are\\nin highly elliptical high altitude earth orbits\\n(cf.~Table~\\\\ref{tab:xray-telescopes}) while Astro-E is headed for a\\ncircular low earth orbit. In addition, at least two major X-ray\\nspace-observatories are being planned: Constellation X, with launch\\nscheduled for 2003, and XEUS with a target date of 2007. Constellation X\\nwill be placed at the L2 point of the Earth-Sun system, while XEUS, like\\nAstro-E, will be placed in low Earth orbit.\\n\\nWhile this may seem a remarkable proliferation of X-ray telescopes, each\\nmission has its own emphasis. In building an X-ray telescope there is a\\ndirect competition between large effective area (and thus sensitivity) and\\nsmall acceptance angle (and thus high angular resolution). Therefore one\\nmust choose whether to build an instrument which aims for high\\nangular-resolution or one which has a goal of achieving high sensitivity.\\nChandra is the only high angular resolution instrument of the listed\\nmissions, with a maximum resolution of $0.5\\\\as$ and thus has the relatively\\nsmall effective area given above~(\\\\ref{eqn:AChandra}). The other\\ninstruments all aim for large effective area, and so sacrifice angular\\nresolution. XMM, which is already flying, has considerably larger\\neffective area than Chandra (and thus much lower angular resolution).\\nAstro-E will have even larger effective area. Constellation-X will consist\\nof multiple X-ray telescopes flown in formation, with a total effective\\narea considerably greater than either XMM or Astro-E; it too has relatively\\nlow angular resolution compared to Chandra. Finally XEUS will have a huge\\neffective area, and will be designed to be expandable. Its angular\\nresolution is better than XMM, Astro-E, or Constellation-X but still not as\\ngood as Chandra. The properties of the existing and planned\\ntelescopes are shown in Table~\\\\ref{tab:xray-telescopes}.\\n\\nThroughout we have considered the photon rate in the detector, not at the\\nsurface of the telescope. An X-ray telescope has an effective area, $\\\\cal\\nA$, which includes the geometric collecting area (since grazing optics are\\nused the collecting area is not the full beam) and the efficiency of the\\nX-ray detector. As an example, with Chandra\\n\\\\be \\n {\\\\cal A}_{\\\\rm Chandra} \\\\approx 700 \\\\cm^2\\n \\\\label{eqn:AChandra}\\n\\\\ee\\nfor $E\\\\approx 1\\\\keV$. This is the area to be used as the area of the\\ntelescope, not the geometric area as in the case of optical telescopes.\\nThe effective area for existing and planned X-ray telescopes is given in Table~\\\\ref{tab:xray-telescopes}.\\n\\nThe luminosity of X-ray sources varies greatly. Black holes in the cores\\nof nearby galaxies have \\n\\\\be \\n{\\\\cal L}_{\\\\rm bh} \\\\approx 10^{38\\\\hbox{--}40}\\\\unit{erg}\\\\second^{-1} =\\n6.2\\\\sci{46\\\\hbox{--}48} \\\\keV\\\\second^{-1}\\n\\\\ee\\nin the $0.2\\\\hbox{--}2.4\\\\keV$ energy range. This leads to a photon rate at\\nthe surface of the detector of\\n\\\\be\\n\\\\Gamma_{\\\\rm bh} = (0.052\\\\hbox{--}5.2)\\\\sci{-2} \\\\left (\\\\frac{E}{\\\\keV}\\\\right) \\n\\\\left ( \\\\frac{d}{1\\\\Mpc}\\\\right)^{-2}\\n\\\\left (\\\\frac{\\\\cal A}{\\\\cm^2}\\\\right) \\\\second^ {-1},\\n\\\\ee\\nwhere the energy, $E$, we observe at is given in keV and $\\\\cal A$ is the\\neffective area of the X-ray telescope as discussed above.\\n\\nAn active galactic nucleus (AGN), Seyfert galaxy, or the core of X-ray\\nclusters can be much more luminous\\n\\\\be \\n{\\\\cal L}_{\\\\rm AGN} \\\\approx 10^{40\\\\hbox{--}44}\\\\unit{erg}\\\\second^{-1} =\\n6.2\\\\sci{48\\\\hbox{--}52} \\\\keV\\\\second^{-1}.\\n\\\\ee\\nHowever, since they are approximately $100\\\\Mpc$ away the photon rate \\nis only \\n\\\\be\\n\\\\Gamma_{\\\\rm AGN} = 5.2\\\\times (10^{-6}\\\\hbox{--}10^{-2})\\\\left\\n (\\\\frac{E}{\\\\keV}\\\\right) \\n\\\\left ( \\\\frac{d}{100\\\\Mpc}\\\\right)^{-2}\\n\\\\left (\\\\frac{\\\\cal A}{\\\\cm^2}\\\\right) \\\\second^ {-1}.\\n\\\\ee\\nGalactic microquasars are somewhat less luminous\\n\\\\be \\n{\\\\cal L}_{\\\\rm microquasar} \\\\approx 10^{39}\\\\unit{erg}\\\\second^{-1} =\\n6.2\\\\sci{47} \\\\keV\\\\second^{-1},\\n\\\\ee\\nsince they are in our own galaxy, though, the photon rate is fairly high\\n\\\\be\\n\\\\Gamma_{\\\\rm microquasar} = 52 \\\\left (\\\\frac{E}{\\\\keV} \\\\right) \\n\\\\left ( \\\\frac{d}{10\\\\kpc}\\\\right)^{-2}\\n\\\\left (\\\\frac{\\\\cal A}{\\\\cm^2}\\\\right) \\\\second^ {-1}.\\n\\\\ee\\n\\nFor a $10\\\\meter$ X-BOSS employed in conjunction with Chandra we find\\n(figure~\\\\ref{fig:skycoverage}a) that for the brightest sources (galactic \\nmicroquasars) we can obtain $\\\\Delta\\\\theta=0.5\\\\as$ over about 30\\\\% of the\\nsky with the sky coverage falling quickly until at $\\\\Delta\\\\theta=0.1\\\\as$\\nvery little of the sky is accessible. This represents a modest gain over\\nwhat can be obtained by Chandra without the aid of X-BOSS. For a $2\\\\meter$ \\nX-BOSS (figure~\\\\ref{fig:skycoverage}b) the situation is much\\nbetter. Here $\\\\Delta\\\\theta=0.5\\\\as$ can be obtained over about 50\\\\% of the\\nsky, $\\\\Delta\\\\theta=0.1\\\\as$ over about 20\\\\% of the sky, and\\n$\\\\Delta\\\\theta=0.05\\\\as$ over about 5\\\\% of the sky. Thus significant\\nimprovements are attainable through the use of an X-BOSS with Chandra.\\n\\nFor an X-BOSS employed in conjunction with XMM the situation is similar.\\nAlthough XMM has a shorter period than Chandra its has an effective area about\\n$3$ times larger (Table~\\\\ref{tab:xray-telescopes}). For a $10\\\\meter$\\nX-BOSS (figure~\\\\ref{fig:skycoverageXMM}a) the skycoverage that can be\\nobtained for each incident photon rate, $\\\\Gamma$, is less than can be\\nobtained by Chandra (compare to figure~\\\\ref{fig:skycoverage}a) even with\\nthe factor of $3$ increase in effective area that XMM provides. For a\\n$2\\\\meter$ X-BOSS (figure~\\\\ref{fig:skycoverageXMM}b) the sky coverage for\\nXMM and Chandra are closer though Chandra is still superior. Note that for\\nboth sizes of X-BOSS tremendous improvements over the nominal $15\\\\as$\\nresolution for XMM are obtained.\\n\\nAt L2 the situation is even better. Since we can tune the velocity\\nrelative to the line-of-sight more easily, great improvements in resolution \\nare readily available (figure~\\\\ref{fig:resolution}). Sub-milliarcsecond\\nresolution can be obtained for sources with photon rates $\\\\Gamma\\\\gtsim\\n1000\\\\second^{-1}$. For a single Constellation X modules, which will have an \\neffective area of about $15,000\\\\cm^2$, the brightest AGN's, X-ray cluster\\ncores, and galactic black holes will have $\\\\Gamma\\\\approx 800\\\\second^{-1}$\\nwe can obtain $\\\\Delta\\\\theta\\\\approx 2\\\\mas$.\\n\\n\\\\section{Conclusions}\\n\\\\label{sec:conclude}\\n\\nWe have found that an X-BOSS used in conjunction with an X-ray telescope\\ncan lead to tremendous improvements in angular resolution. \\nThe trend of increasing the effective area of future X-ray telescopes at the\\nexpense of angular resolution (Table~\\\\ref{tab:xray-telescopes}) meshes perfectly\\nwith the benefits gained by including an X-BOSS in the mission. Indeed, an\\nX-ray telescope to be used with an X-BOSS is treated as a light bucket with\\nall the resolving power coming from the X-BOSS occulting the source. Thus\\nan X-BOSS is an excellent addition to an X-ray telescope mission,\\nparticularly one at L2, such as Constellation X where sub-milliarcsecond\\nresolution can be attained for a wide range of sources.\\n\\nFor the Chandra X-ray telescope we found that moderate improvements in\\nangular resolution over an appreciable fraction of the sky can be achieved\\nthrough the use of an X-BOSS\\\\@. Similarly an X-BOSS employed in\\nconjunction with XMM would provide tremendous improvements in the angular\\nresolution that XMM could achieve allowing XMM to have angular resolution\\ncomparable to Chandra. An X-BOSS launched for use with Chandra or XMM would\\nalso provide an important test bed for the technology to be used with\\nfuture missions.\\n\\n\\\\acknowledgements\\nThe authors would like particularly to thank \\nArt Chmielewski for financial and other support,\\nA. Babul and M. Dragovan for many useful comments and suggestions,\\nN. Choudhuri for helpful suggestions on statistical tests, and Paul\\nGorenstein and William Zhang for comments on a preliminary version of the \\nmanuscript.\\nThis work was supported by \\na CAREER grant to GDS from the National Science Foundation,\\na DOE grant to the theoretical particle and astrophysics group at CWRU, \\nby a grant from NASA's Jet Propulsion Laboratory,\\nand by funds from CWRU.\\n\\n\\\\begin{thebibliography}{}\\n\\n\\\\bibitem[Adams \\\\etal (1988)]{Adams} Adams, D.J. \\\\etal~1988, \\\\apj, 327, L65\\n\\n\\\\bibitem[Copi \\\\& Starkman (1998)]{CS98} Copi, C.J. \\\\& Starkman, G.D.~1998, \\nProceedings of SPIE, 3356, March 25, 1998, Kona, HI\\n\\n\\\\bibitem[Copi \\\\& Starkman (2000)]{CS00} Copi, C.J. \\\\& Starkman, G.D.~2000,\\n \\\\apj, 534, too appear%,\\n% preprint astro-ph/9904413\\n \\n\\\\bibitem[Schneider (1995)]{Schneider} Schneider, J.~1995, Proceeding of the\\n workshop ``Detection and Study of Terrestrial Extra-solar Planets'', May\\n 15--17, Boulder, CO\\n\\n\\\\end{thebibliography}\\n\\n\\\\begin{deluxetable}{lccl}\\n\\\\tablecaption{Properties of existing and planned X-ray\\n telescopes.\\\\label{tab:xray-telescopes}}\\n\\n\\\\tablehead{\\n \\\\colhead{Satellite} & \\\\colhead{Effective} & \\\\colhead{Angular} &\\n \\\\colhead{Orbit} \\\\\\\\ \\n \\\\colhead{Name} & \\\\colhead{Area at $1\\\\keV$} & \\\\colhead{Resolution} &\\n \\\\colhead{}\\\\\\\\ \\n \\\\colhead{} & \\\\colhead{(cm$^2$)} & \\\\colhead{(arcsecond)} & \\\\colhead {}\\n }\\n\\\\startdata\\nChandra (AXAF)\\\\tablenotemark{a} & \\\\phn\\\\phn\\\\phn\\\\phm{,}700 & 0.5 & eccentric\\nhigh Earth orbit \\\\\\\\\\nXMM & \\\\phn\\\\phn2,000 & 15 & eccentric high Earth orbit \\\\\\\\\\nAstro-E & \\\\phn\\\\phn1,200 & 90 & low Earth orbit \\\\\\\\\\nHETE-II\\\\tablenotemark{b} & \\\\phn\\\\phn\\\\phn\\\\phm{,}350 & 660 & low Earth orbit \\\\\\\\\\nConstellation X & \\\\phn30,000\\\\tablenotemark{c} & 15 & L2 halo orbit \\\\\\\\\\nXeus -- Phase I & \\\\phn60,000 & 2 & low Earth orbit \\\\\\\\\\n\\\\phantom{Xeus}~-- Phase II& 300,000 & 2 & low Earth orbit \\\\\\\\\\n\\\\enddata\\n\\\\tablenotetext{a}{Effective area is for the AXAF CCD Imaging Spectrometer\\n (ACIS)\\\\@. Angular resolution is for the High Resolution Camera (HRC)\\\\@.}\\n\\\\tablenotetext{b}{These values are for the wide field X-ray monitor (WXM)\\n instrument. The quoted effective area is for $2\\\\keV$ X-rays.}\\n\\\\tablenotetext{c}{Total effective area for all modules.}\\n\\\\tablerefs{\\\\\\\\\\nChandra: http://asc.harvard.edu/\\\\\\\\\\nXMM: http://xmm.vilspa.esa.es/\\\\\\\\\\nHETE-II: http://space.mit.edu/HETE/\\\\\\\\\\nAstro-E: http://heasarc.gsfc.nasa.gov/docs/astroe/overview.html\\\\\\\\\\nConstellation X: http://constellation.gsfc.nasa.gov/\\\\\\\\\\nXeus: http://astro.estec.esa.nl/SA-general/Projects/XEUS/web/mission.html\\n}\\n\\n\\\\end{deluxetable}\\n\\n\\\\begin{figure}\\n \\\\leavevmode\\\\center{\\\\epsfig{figure=photonattenuation.ps,height=5 in,width=8.5 in}}\\n \\\\caption{The photon mass attenuation length $\\\\lambda=1/(\\\\mu/\\\\rho)$\\nfor various elemental absorbers as a function of photon energy\\n($\\\\rho$ is the density). The figure is obtained from the particle\\ndata book, figure 23.11 (http://pdg.lbl.gov). \\nThe data for $30{\\\\rm eV} < E < 1 {\\\\rm keV}$ are obtained from \\nhttp://www-cxro.lbl.gov/optical\\\\_constants \\n(courtesy of Eric M. Gullikson, LBNL).\\nThe data for $1{\\\\rm keV} < E < 100 {\\\\rm GeV}$ are from \\n\\\\protect\\\\url{http://physics.nist.gov/PhysRefData}, thru the courtesy of \\nJohn H. Hubbel (NIST).\\n}\\n\\\\label{fig:photonattenuation}\\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n \\\\leavevmode\\\\center{\\\\epsfig{figure=resolution.ps,height=6in,angle=-90}}\\n \\\\caption{The minimum angular separation of two X-ray sources resolvable\\n at the 95\\\\% confidence level. The limits are shown for intensity\\n ratios, $\\\\rho=1$ (solid),\\n $1/3$ (dashed), and $1/10$ (dashed-dotted). The upper set of three curves\\n are for $\\\\mu_\\\\perp = 10\\\\mas\\\\second^{-1}$, the middle set of three curves are\\n for $\\\\mu_\\\\perp = 1\\\\mas\\\\second^{-1}$, and the lower set of three curves\\n are for $\\\\mu_\\\\perp = 0.1\\\\mas\\\\second^{-1}$. Note that the total photon\\n rate is of photons detected in the telescope (without the presence\\n X-BOSS), not photons incident on the telescope. Here $d$ is the\\n distance between the telescope and X-BOSS in units of $10^3\\\\km$.\\n }\\n \\\\label{fig:resolution}\\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n \\\\leavevmode\\\\center{\\\\epsfig{figure=skycoverage_10m.ps,height=4in,angle=-90}}\\n \\\\leavevmode\\\\center{\\\\epsfig{figure=skycoverage_2m.ps,height=4in,angle=-90}}\\n \\\\caption{The fraction of the sky that can be observed as a function of\\n the desired resolution, $\\\\Delta\\\\theta$, and the photon rate in the\\n detector (as in figure~\\\\protect\\\\ref{fig:resolution}), $\\\\Gamma$, for\\n an X-BOSS used in conjunction with Chandra. (a) A satellite\\n width of $10\\\\meter$ is assumed here. (b) A satellite\\n width of $2\\\\meter$ is assumed here. A larger satellite can obtain\\n these results if velocity corrections are made during the observation.\\n See the text for details.\\n }\\n \\\\label{fig:skycoverage}\\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n \\\\leavevmode\\\\center{\\\\epsfig{figure=skycoverage_XMM_10m.ps,height=4in,angle=-90}}\\n \\\\leavevmode\\\\center{\\\\epsfig{figure=skycoverage_XMM_2m.ps,height=4in,angle=-90}}\\n \\\\caption{\\n The same as figure~\\\\protect\\\\ref{fig:skycoverage} for an X-BOSS used in\\n conjunction with XMM\\\\@.\\n }\\n \\\\label{fig:skycoverageXMM}\\n\\\\end{figure}\\n\\n\\\\end{document}\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002198.extracted_bib","string":"\\begin{thebibliography}{}\n\n\\bibitem[Adams \\etal (1988)]{Adams} Adams, D.J. \\etal~1988, \\apj, 327, L65\n\n\\bibitem[Copi \\& Starkman (1998)]{CS98} Copi, C.J. \\& Starkman, G.D.~1998, \nProceedings of SPIE, 3356, March 25, 1998, Kona, HI\n\n\\bibitem[Copi \\& Starkman (2000)]{CS00} Copi, C.J. \\& Starkman, G.D.~2000,\n \\apj, 534, too appear%,\n% preprint astro-ph/9904413\n \n\\bibitem[Schneider (1995)]{Schneider} Schneider, J.~1995, Proceeding of the\n workshop ``Detection and Study of Terrestrial Extra-solar Planets'', May\n 15--17, Boulder, CO\n\n\\end{thebibliography}"}],"string":"[\n {\n \"name\": \"astro-ph0002198.extracted_bib\",\n \"string\": \"\\\\begin{thebibliography}{}\\n\\n\\\\bibitem[Adams \\\\etal (1988)]{Adams} Adams, D.J. \\\\etal~1988, \\\\apj, 327, L65\\n\\n\\\\bibitem[Copi \\\\& Starkman (1998)]{CS98} Copi, C.J. \\\\& Starkman, G.D.~1998, \\nProceedings of SPIE, 3356, March 25, 1998, Kona, HI\\n\\n\\\\bibitem[Copi \\\\& Starkman (2000)]{CS00} Copi, C.J. \\\\& Starkman, G.D.~2000,\\n \\\\apj, 534, too appear%,\\n% preprint astro-ph/9904413\\n \\n\\\\bibitem[Schneider (1995)]{Schneider} Schneider, J.~1995, Proceeding of the\\n workshop ``Detection and Study of Terrestrial Extra-solar Planets'', May\\n 15--17, Boulder, CO\\n\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":196,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002199"},"title":{"kind":"string","value":"The host galaxies of luminous radio-quiet quasars"},"authors":{"kind":"list like","value":[{"author":"W.J.Percival"},{"author":"$^{1,2}$ L.Miller"},{"author":"$^1$ R.J. McLure$^{2,1}$ and J.S. Dunlop$^2$"},{"author":"$^1$ Dept. of Physics"},{"author":"Nuclear \\& Astrophysics Laboratory"},{"author":"Keble Road"},{"author":"Oxford OX1 3RH"},{"author":"U.K."},{"author":"Royal Observatory"},{"author":"Blackford Hill"},{"author":"Edinburgh EH9 3HJ"}],"string":"[\n {\n \"author\": \"W.J.Percival\"\n },\n {\n \"author\": \"$^{1,2}$ L.Miller\"\n },\n {\n \"author\": \"$^1$ R.J. McLure$^{2,1}$ and J.S. Dunlop$^2$\"\n },\n {\n \"author\": \"$^1$ Dept. of Physics\"\n },\n {\n \"author\": \"Nuclear \\\\& Astrophysics Laboratory\"\n },\n {\n \"author\": \"Keble Road\"\n },\n {\n \"author\": \"Oxford OX1 3RH\"\n },\n {\n \"author\": \"U.K.\"\n },\n {\n \"author\": \"Royal Observatory\"\n },\n {\n \"author\": \"Blackford Hill\"\n },\n {\n \"author\": \"Edinburgh EH9 3HJ\"\n }\n]"},"abstract":{"kind":"string","value":"We present the results of a deep $K$-band imaging study which reveals the host galaxies around a sample of luminous radio-quiet quasars. The $K$-band images, obtained at UKIRT, are of sufficient quality to allow accurate modelling of the underlying host galaxy. Initially, the basic structure of the hosts is revealed using a modified Clean deconvolution routine optimised for this analysis. 2 of the 14 quasars are shown to have host galaxies with violently disturbed morphologies which cannot be modelled by smooth elliptical profiles. For the remainder of our sample, 2D models of the host and nuclear component are fitted to the images using the $\\chi^{2}$ statistic to determine goodness of fit. Host galaxies are detected around all of the quasars. The reliability of the modelling is extensively tested, and we find the host luminosity to be well constrained for 9 quasars. The derived average $K$-band absolute $K$-corrected host galaxy magnitude for these luminous radio-quiet quasars is $\\langle M_K \\rangle=-25.15\\pm0.04$, slightly more luminous than an $L^*$ galaxy. The spread of derived host galaxy luminosities is small, although the spread of nuclear-to-host ratios is not. These host luminosities are shown to be comparable to those derived from samples of quasars of lower total luminosity and we conclude that there is no correlation between host and nuclear luminosity for these quasars. Nuclear-to-host ratios break the lower limit previously suggested from studies of lower nuclear luminosity quasars and Seyfert galaxies. Morphologies are less certain but, on the scales probed by these images, some hosts appear to be dominated by spheroids but others appear to have disk-dominated profiles."},"latex":{"kind":"list like","value":[{"name":"ukirt_acc.tex","string":"\\documentstyle[epsf,graphics,epsfig]{mn}\n\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\def\\simlt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}}\n\\def\\simgt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}}\n\\newcommand{\\etal}{{\\it et~al.}}\n\\newcommand{\\msun}{\\thinspace\\hbox{$M_{\\odot}$}\\ }\n\n\\title[Quasar host galaxies]\n{The host galaxies of luminous radio-quiet quasars}\n\n\\author[W.J. Percival \\etal]{W.J.Percival,$^{1,2}$ L.Miller,$^1$\n\tR.J. McLure$^{2,1}$ and J.S. Dunlop$^2$\\\\\n $^1$ Dept. of Physics, University of Oxford, \n Nuclear \\& Astrophysics Laboratory, Keble Road, Oxford OX1 3RH, U.K.\\\\\n $^2$ Institute for Astronomy, University of Edinburgh, \n Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, U.K.\\\\}\n\n\\date{Submitted for publication in MNRAS}\n\\begin{document}\n\\maketitle\n\n\\begin{abstract} \nWe present the results of a deep $K$-band imaging study which reveals\nthe host galaxies around a sample of luminous radio-quiet quasars. The\n$K$-band images, obtained at UKIRT, are of sufficient quality to allow\naccurate modelling of the underlying host galaxy. Initially, the basic\nstructure of the hosts is revealed using a modified Clean\ndeconvolution routine optimised for this analysis. 2 of the 14 quasars\nare shown to have host galaxies with violently disturbed morphologies\nwhich cannot be modelled by smooth elliptical profiles. For the\nremainder of our sample, 2D models of the host and nuclear component\nare fitted to the images using the $\\chi^{2}$ statistic to determine\ngoodness of fit. Host galaxies are detected around all of the\nquasars. The reliability of the modelling is extensively tested, and\nwe find the host luminosity to be well constrained for 9 quasars. The\nderived average $K$-band absolute $K$-corrected host galaxy magnitude\nfor these luminous radio-quiet quasars is $\\langle M_K\n\\rangle=-25.15\\pm0.04$, slightly more luminous than an $L^*$\ngalaxy. The spread of derived host galaxy luminosities is small,\nalthough the spread of nuclear-to-host ratios is not. These host\nluminosities are shown to be comparable to those derived from samples\nof quasars of lower total luminosity and we conclude that there is no\ncorrelation between host and nuclear luminosity for these\nquasars. Nuclear-to-host ratios break the lower limit previously\nsuggested from studies of lower nuclear luminosity quasars and Seyfert\ngalaxies. Morphologies are less certain but, on the scales probed by\nthese images, some hosts appear to be dominated by spheroids but\nothers appear to have disk-dominated profiles.\n\\end{abstract}\n\n\\begin{keywords}\ngalaxies: active, quasars: general, infrared: galaxies\n\\end{keywords}\n\n\\section{Introduction}\nModels of the cosmological evolution of quasars often use galaxy\nmergers as the primary mechanism for quasar activation and require the\nmass of the structure within which a quasar is formed as a basic\nparameter \\cite{efrees,haehnelt,percival}. One step towards testing\nhypotheses about quasar initiation is to answer the question: Is a\nquasar's luminosity correlated with the luminosity of the structure\nwithin which it formed? Such a correlation has been shown to exist for\nlow redshift ($0$6.0 & spheroid \\\\\n 0244$-$012 & $<$0.25 & 0.61 & 1.62 & disk \\\\\n 0316$-$346 & 1.02 & 1.25 & 3.62 & ? \\\\\n 0956$-$073 & 0.71 & 0.92 & 1.21 & disk \\\\\n 1214+180 & $<$0.25 & 1.12 & $>$6.0 & ? \\\\\n 1216+069 & 1.44 & 2.73 & $>$6.0 & spheroid \\\\\n 1354+213 & 0.65 & 0.73 & 0.82 & disk \\\\\n 1543+489 & 0.49 & 0.67 & 0.90 & disk \\\\\n 2112+059 & $<$0.25 & 2.13 & $>$6.0 & ? \\\\\n 2233+134 & $<$0.25 & 0.64 & 1.21 & disk \\\\\n 2245+004 & 2.17 & 3.16 & 5.55 & spheroid \\\\\n \\hline \\end{tabular}\n\n \\caption{Table showing 68.3\\% confidence intervals for the best-fit\n host $\\beta$ parameters for the 12 quasars modelled using the 2D\n $\\chi^2$ minimising technique (Section~\\protect\\ref{sec:model}).\n Error bars were calculated as described in\n Section~\\protect\\ref{sec:bars} with $\\beta$ constrained to lie in\n the range $0.25<\\beta<6.0$. The morphology of the dominant\n contribution to the host galaxy is also presented, based on the best\n fit $\\beta$ parameter and associated confidence interval.}\n \\label{tab:beta}\n\\end{table}\n\n\\subsection{Axial ratios and angles} \\label{sec:axes}\n\nAnalysis of the parameter space reveals that the axial ratio and\nprojected angle of each host are better constrained than the other\nparameters. Fig.~\\ref{fig:histograms} shows histograms of these\nparameters for all quasars modelled. The distribution of axial ratios\nis small with $\\langle a/b\\rangle=0.79\\pm0.03$. This is in agreement\nwith those found by McLure \\etal\\ \\shortcite{mclure}, but higher than\nfound by Hooper, Impey \\& Foltz \\shortcite{hooper}. The projected\nangles are uniformly distributed as expected.\n\n\\begin{figure}\n \\centering \n \\resizebox{5.0cm}{5.0cm}{\\includegraphics{axis.eps}}\n \\vspace{5mm}\\\\\n \\resizebox{5.0cm}{5.0cm}{\\includegraphics{angle.eps}}\n \\caption{Histograms showing the distribution of axial ratios and\n projected angles of the host galaxies. These parameters were well\n constrained for all of the 12 quasars modelled, and are therefore\n plotted from all of the minima found. Axial ratios are tightly\n constrained with with $a/b>0.64$ for all hosts, and $\\langle\n a/b\\rangle=0.79\\pm0.03$. The distribution of projected angles is\n approximately uniformly distributed.}\n\\label{fig:histograms}\n\\end{figure}\n\n\\subsection{Highlighted results for selected quasars} \n \\label{sec:results-quasars}\n\n\\subsubsection{Quasar 0043+039}\nThe broad-absorption-line (BAL) quasar PG0043+039 has been subject to\n2 previous studies to determine host galaxy properties. It was\nobserved in the $i$ band by Veron-Cetty \\& Woltjer\n\\shortcite{veron-cetty} who determined $M_i=-23.9$ if the host is a\ndisk like ($\\beta=1$) galaxy, or $M_i=-24.7$ for a spheroidal\n($\\beta=4$) galaxy. This quasar was also observed using the wide-field\ncamera on HST by Boyce \\etal\\ \\shortcite{boyce}, who used a cross\ncorrelation technique to determine that the host was slightly better\nfit by a disk galaxy with $M_V=-21.6$. We also find that the dominant\nmorphology is disk-like and calculate $M_K=-25.29$. The old burst\nmodel of Bruzual \\& Charlot \\shortcite{bruzual} predicts $V-K=3.3$\nwhich is consistent with the derived $V-K=3.7$.\n\n\\subsubsection{Quasar 0316$-$346}\nThis quasar was previously observed using the wide field camera on HST\n\\cite{bahcall} and the host was found to reveal evidence of a merger,\nin particular tidal tails extending $\\sim20$\\,kpc west of the\nquasar. Bahcall \\etal\\ \\shortcite{bahcall} also provide a 2D fit to\nthe host properties and find that the best-fit host is disk galaxy\nwith $M_{V}=-22.3$. We also calculate a best-fit disk galaxy and find\n$M_K=-25.44$, giving $V-K=3.1$, again consistent with the old burst\nmodel of Bruzual \\& Charlot \\shortcite{bruzual} which predicts\n$V-K=3.3$.\n\n\\subsubsection{Quasar 1214+180}\nThere have been no previous attempts to determine the morphology of\nthe host galaxy around this quasar possibly due to the nearby star\nwhich was utilised in this work to obtain an accurate\npsf. Unfortunately in our images, a diffraction spike from this star\npassed close to the quasar reducing the area that could be used to\ncalculate $\\chi^2$. Although the modelling converged to give basic\ngalaxy parameters, further analysis of the parameter space revealed\nthat this minimum was not well constrained.\n\n\\subsubsection{Quasar 1216+069}\nOur analysis of this quasar benefited because the images were obtained\nusing the tip-tilt system and there is a nearby bright star which was\nplaced on the same frame as the quasar and used to obtain a psf\nmeasurement. Previously, `nebulosity' has been observed around this\nquasar \\cite{hutchings84}, and a more detailed HST study found a\nbest-fit spheroidal ($\\beta=4$) galaxy with $M_{V}=-22.3$\n\\cite{boyce}. We also find that the most likely host is a large\nspheroidal galaxy and obtain $M_K=-25.1$, giving $V-K=2.8$.\n\n\\subsubsection{Quasar 1354+213}\nUsing a psf subtraction technique, McLeod \\& Rieke\n\\shortcite{mcleod94b} found a residual host galaxy with $M_K=-25.6$\nwhen converted to our cosmology using the $K$-correction from\nGlazebrook \\etal\\ \\shortcite{glazebrook95} and the apparent colour\ncorrection $H-K=0.6$ (see Section~\\ref{sec:calc_lum}). Our best fit\nhost luminosity was $M_K=-25.2$. Analysis shows that the luminosity\nand the $\\beta$ parameter are both tightly constrained by the\nmodelling and the best-fit $\\beta=0.73$ suggests that the host is\ndominated by a disk component. The rest-frame nuclear-to-host ratio\nfor this quasar is only $6.8$ (the apparent nuclear-to-host ratio is\n$4.6$), which explains why the derived parameters have small error\nbars.\n\n\\subsubsection{Quasar 1636+384}\nWe are not aware of any previous attempts to determine the luminosity\nand morphology for the host galaxy of quasar 1636+384. Preliminary\ndeconvolution of the light revealed that the excess, non-central light\ndisplayed a morphology greatly disturbed from elliptical symmetry (as\nshown in Fig.~\\ref{fig:disturbed}). The structure includes an excess\nof light to the NW of the core which is interpreted as a merging\ncomponent as well as light around the central core which probably\noriginates from the host. From this image it was unclear how to\ndistinguish between the host and the interacting companion, so the\nluminosity of the host was estimated by summing pixel values excluding\nthe central pixel. This provided an approximate $K$-band absolute\nmagnitude of $M_K=-23.5$.\n\n\\subsubsection{Quasar 1700+518}\nQuasar 1700+518 is a bright BAL quasar of low redshift\n($z=0.29$). Such low redshift BAL objects are rare and hard to\ndiscover since the broad absorption lines are in the UV and\nconsequently quasar 1700+518 has received much interest: specific\nstudies of this quasar have been undertaken in many different\nwavebands \\cite{h92_1700,stockton,hines}. Because of the low redshift\nand the brightness of the quasar, 1700+518 has also been included in\nmany samples of quasars imaged to obtain details of their host\ngalaxies \\cite{neugebauer,mcleod94b}, although these have only\nprovided upper limits for the host magnitude. More recent imaging\nstudies have shown that the morphology of the underlying structure\nconsists of a disturbed host predominantly to the SW of the core\n\\cite{stockton} and a close interacting companion to the NE\n\\cite{h92_1700} which is most likely a ring galaxy \\cite{hines}.\nDeconvolution of the light from this quasar, as shown in\nFig.~\\ref{fig:disturbed}, confirms this picture of the structure. With\nthe disturbed morphology it is difficult to know how to split the\nlight in the central pixels into nuclear and host components. As for\nquasar 1636+384 the host luminosity was estimated by summing the\ncounts in the pixels surrounding the central one (ignoring those from\nthe NE companion). There will be errors caused by leakage of light\nfrom the nuclear component and from the contribution of the host to\nthe central pixel. An approximate $K$-band absolute magnitude of\n$-24.9$ was obtained for the host galaxy and $-24.4$ for the NE\ncompanion galaxy.\n\n\\subsubsection{Quasar 2233+134}\nBoth Smith \\etal\\ \\shortcite{smith} and Veron-Cetty \\& Woltjer\n\\shortcite{veron-cetty} included this quasar in their samples, but\nboth failed to resolve the host galaxy beyond obtaining upper limits\nfor the luminosity. Hutchings \\& Neff \\shortcite{hutchings92} did\nresolve the host galaxy and found the host to be best-fit by a\n$\\beta=4$ model, although they did not resolve further information\nabout the galaxy. However, we find that the most probable host has an\ndisk profile and calculate $M_K=-24.1$, the lowest luminosity host\nmodelled. If we constrain the host to have an elliptical profile, the\nbest fit luminosity becomes $M_K=-25.9$, although the half light\nradius is very small for this model ($R_{1/2}=1.5$\\,kpc) which places\nit a long way from the $K$-band Fundamental Plane of Pahre, Djorgovski\n\\& de Carvalho \\shortcite{pahre}. If the host parameters are\nconstrained to lie on this plane, then rerunning the modelling gives a\nbest fit host with $M_K=-24.6$. Neither of these changes would be\nsufficient to alter our conclusions.\n\n\\section{Simulated Data I - Single component galaxies} \\label{sec:mock}\n\nTrying to recover known host parameters from Monte-Carlo simulations\nof the actual data enables the distribution of recovered parameters\ngiven the true values to be determined. Note that the error bars\ncalculated using the $\\chi^2$ statistic are instead determined from\nthe distribution of possible true values given the data. These two\ndistributions are not necessarily equal. We need to determine the\ndistribution of recovered values in order to answer questions such as\n`Are our results biased towards low $\\beta$ values?'.\n\nIn view of the distribution of recovered $\\beta$ values, it was\ndecided to simulate data to match the images of quasars 0956$-$073 and\n1543+489. These quasars span the distribution of signal-to-noise of\nall the images, and 2D model fitting revealed evidence for disk\ndominated hosts in both cases. Verification of this result is\ninteresting as recent work has suggested that the hosts of luminous\nquasars should be dominated by the spheroidal component (see\nSection~\\ref{sec:discuss_morph}).\n\n\\subsection{Creating the mock data} \\label{sec:mock_noise}\n\n\\begin{table*}\n\\begin{minipage}{\\textwidth}\n \\centering \\begin{tabular}{ccccccccc} \\hline \n quasar & \\multicolumn{4}{c}{$\\beta$} & \n \\multicolumn{4}{c}{$L_{\\rm int}$ /adu} \\\\\n & true & min & average & max & true & min & average & max \\\\ \\hline\n\n 0956$-$073 & 1.0 & 0.74 & 1.14 & 2.28 & 300.0 & 262.1 & 323.7 & 510.0 \\\\\n 0956$-$073 & 4.0 & 1.93 & 3.77 & 7.42 & 300.0 & 213.6 & 288.3 & 463.1 \\\\\n 1543+489 & 1.0 & 0.79 & 1.08 & 1.69 & 300.0 & 260.1 & 324.7 & 512.2 \\\\\n 1543+489 & 4.0 & 2.13 & 4.04 & 7.25 & 300.0 & 209.6 & 302.2 & 469.8 \\\\\n \\hline \n \\end{tabular}\n\n \\caption{Table showing the mean and 68.3\\% confidence intervals for\n the recovered $\\beta$ and integrated host luminosity from the\n simulated data. 100 simulations were performed for each morphology\n for each quasar.} \\label{tab:mock_stat}\n\\end{minipage}\n\\end{table*}\n\n\\begin{figure*}\n\\begin{minipage}{\\textwidth}\n \\centering \\resizebox{10cm}{!}{\\includegraphics{mock_l.eps}}\n \\caption{The distribution of recovered luminosities from Monte-Carlo\n simulations of 100 $\\beta=1$ images and 100 $\\beta=4$ images. The\n $y$-axis gives the number of recovered values within each luminosity\n bin. Noise has been added to match observations of quasar (a)\n 0956$-$073 and (b) 1543+489, including a contribution from the error\n in the measured psf as described in\n Section~\\protect\\ref{sec:mock_noise}. The luminosity of each\n simulated galaxy, marked by the dotted line, was set at 300\\,adu.}\n \\label{fig:mock_lum}\n\\end{minipage}\n\\end{figure*}\n\nSimulated galaxies were created using the procedure outlined in\nSection~\\ref{sec:galaxy} and a single $\\delta$ function added to the\ncentre of each to create a `perfect unconvolved model'. The height of\nthe $\\delta$ function was chosen to match the total signal of the\noriginal images. These models were then convolved with the psf\nmeasured to match the quasar.\n\nGaussian noise was added with a radially dependent variance as given\nby the error profile calculated in Section~\\ref{sec:error} including\nthe best-fit host galaxy in the calculation. The error profiles used\nfor quasars 0956$-$073 and 1543+489 are given by the solid lines in\nFig.~\\ref{fig:epgal}. Differences between measured and true psf were\nincluded in this analysis, and are therefore included in the noise\nlevels added to the simulated data. This noise model assumes that the\nerrors in different pixels are independent (see\nSection~\\ref{sec:chisq}).\n\nWe have simulated 100 images with exact disk hosts, and 100 images\nwith exact spheroidal hosts for each of the two quasars chosen. The\ntrue integrated host luminosity was set at 300\\,adu for simulated data\nof both quasars. This conservative value is below the best-fit value\nobtained from the data for both quasars, providing a stringent test of\nthe modelling. This is particularly true for a $\\beta=4$ host:\nconstraining $\\beta=4$ when modelling the observed image would have\nresulted in a best-fit $L_{\\rm int}\\gg300$\\,adu. The simulated images\nwere analysed using exactly the same 2D modelling procedure described\nabove for the observed data. The range of recovered parameters is\nanalysed below.\n\n\\subsection{Results from the simulated data: luminosities}\n\nRecovered luminosities, presented in Fig.~\\ref{fig:mock_lum} reveal a\nskewed distribution, particularly for hosts with exact spheroidal\nprofiles where the recovered luminosity is biased towards a low\nvalue. This is consistent with the morphology being skewed towards a\nlow $\\beta$ value (see next Section): if $\\beta$ is decreased, the\nluminosity also has to decrease to keep the counts in the outer pixels\n(those most important for fitting the host) the same. The counts in\nthe centre of the galaxy are less important because of the additional\nnuclear component which is adjusted to match the data.\n\nThe mean and variance in the recovered luminosities are presented in\nTable~\\ref{tab:mock_stat}. Although the error bars reveal the extent\nof the skewed distribution, the mean is within 10\\% of the true value\nfor each quasar and morphology.\n\n\\subsection{Results from the simulated data: morphologies}\n\n\\begin{figure*}\n\\begin{minipage}{\\textwidth}\n \\centering \\resizebox{15cm}{!}{\\includegraphics{mock_b.eps}}\n\n \\caption{Evidence that the hosts of luminous radio-quiet quasars are\n not exclusively dominated by spheroidal components. The distribution\n of $\\beta$ values recovered from 2-D modelling of 100 simulated\n images created with hosts using exact disk or spheroidal profiles is\n presented. Noise has been added to these images to match\n observations of (a) quasar 0956$-$073 and (b) quasar 1543+489,\n including a contribution from the error in the measured psf as\n described in Section~\\protect\\ref{sec:mock_noise}. The dotted line\n shows the best-fit $\\beta$ value recovered from the images of these\n quasars. (c) For comparison the distribution of best-fit $\\beta$\n values obtained from all of our $K$-band images is also plotted. The\n probable morphology of the host was determined from the $\\chi^2$\n error bars derived for the true value given the data.}\n \\label{fig:mock_beta}\n\\end{minipage}\n\\end{figure*}\n\nThe skewed distribution observed in the error bars on the true host\n$\\beta$ value is mirrored by the distribution of $\\beta$ values\nrecovered using the standard modelling procedure described in\nSection~\\ref{sec:model}. Fig.~\\ref{fig:mock_beta} shows the relative\ndistribution of $\\beta$ values retrieved from the simulated images.\nLimits of $0.25<\\beta<8$ were placed on fitted $\\beta$ values. For\nquasar 0956$-$073, 16 of the simulated images created with exact\nspheroidal hosts, had recovered $\\beta>8$. For quasar 1543+489, this\nnumber was 14: these values are not included in\nFig.~\\ref{fig:mock_beta}. The distribution was used to calculate the\nmean and standard deviation given in Table~\\ref{tab:mock_stat},\nassuming all fits with $\\beta>8$ actually had $\\beta=8$.\n\nIf the host were a spheroidal galaxy with $\\beta=4$, the probability\nof recovering a best-fit value of $\\beta<1$ is $\\sim0.03$ for\n0956$-$073 and $\\sim0.01$ for 1543+489: the best-fit values from the\nimages were $\\beta=0.92$ and $\\beta=0.67$ respectively. The evidence\nfor the existence of hosts dominated by a disk component therefore\nappears to be strong. In Fig.~\\ref{fig:mock_beta}, the distribution of\nretrieved $\\beta$ values for the 12 quasars modelled is also\nshown. This distribution is inconsistent with the hypothesis that all\nthe hosts are dominated by spheroidal components on the scales probed\nby these measurements. The histogram is divided to show the probable\ndistribution of morphologies given the options $\\beta=1$ or\n$\\beta=4$. As can be seen, the modelling suggests that approximately\nhalf of the hosts are dominated by disk components.\n\n\\section{Simulated Data II - Two component galaxies} \\label{sec:mock2}\n\nIn order to constrain the potential importance of spheroidal cores in\nthe galaxies found to be dominated by disk-like profiles, we have\nanalysed synthetic quasars created with two host galaxy\ncomponents. Using the Fundamental-Plane (FP) relation between\n$R_{1/2}$ and $L_{\\rm int}$ found in the K-band by Pahre \\etal\\\n\\shortcite{pahre}, we have added extra spheroidal ($\\beta=4$)\ncomponents to the recovered best-fit host galaxy of quasar\n1543+489. Note that this best fit host had $\\beta=0.67$. We have tried\nthe same analysis using $\\beta=1$ and found no change in the effects\nproduced by the spheroidal core. After adding in the nuclear component\nand noise as described in Section~\\ref{sec:mock}, we have recovered\nthe best-fit host galaxy parameters using our single component\nmodelling. Spheroidal components were added with a variety of\ndifferent luminosities, and five different realisations of the\nadditional noise component were added to each. The resulting average\nrecovered $L_{\\rm int}$ \\& $\\beta$ are given in Table~\\ref{tab:2cmpt}.\n\n\\begin{table}\n \\centering\n \\begin{tabular}{cccccc} \\hline\n \\multicolumn{4}{c}{$L_{\\rm int}$ /adu} & $R_{1/2}$ & $\\beta$ \\\\\n spheroidal & total & recovered & diff & /kpc & \\\\ \\hline\n 0.0\t& 320.1 & 291.2 & -28.9 & 8.26 & 0.61 \t\\\\\n 40.0\t& 360.1 & 306.5 & -53.6 & 8.19 & 0.63 \t\\\\\n 80.0\t& 400.1 & 337.9 & -62.2 & 8.02 & 0.69\t\\\\\t\n 120.0\t& 440.1 & 382.7 & -57.4 & 7.71 & 0.81\t\\\\\n 160.0\t& 480.1 & 436.3 & -43.8 & 7.35 & 0.96\t\\\\\n 320.0\t& 640.1 & 785.8 & 145.7 & 5.45 & 1.93\t\\\\\n 480.0 & 800.1 & 1305.2 & 505.1 & 3.85 & 3.37 \t\\\\\n \\hline \\end{tabular}\n\n \\caption{Average recovered host parameters from single component\n fits to synthetic quasars with 2-component host\n galaxies. Uncorrelated Gaussian noise has been added to these models\n to match that of quasar 1543+489, and the average recovered values\n are given for 5 different realisations of this noise. The same noise\n was added to corresponding mock images created with different\n spheroidal luminosities, so there will be a systematic error because\n 5 realisations are not sufficient to fully sample the recovered\n parameters with the given noise level. The result of analysing a\n host with no spheroidal component shows that the results\n systematically underestimate $\\beta$ and $L_{\\rm int}$ and\n overestimate $R_{1/2}$ by small amounts. Note that the relative\n dependence of the recovered parameters on the spheroidal component\n will not be affected.} \\label{tab:2cmpt}\n\\end{table}\n\nBecause $R_{1/2}(\\rm spheroidal)$ and $L_{\\rm int}(\\rm spheroidal)$\nfollow a FP relation, the importance of this component is enhanced for\nlarge $L_{\\rm int}(\\rm spheroidal)$ and diminished for small $L_{\\rm\nint}(\\rm spheroidal)$. The recovered total luminosity for small\nspheroidal components is therefore very similar to that of the disk\nalone. For large spheroidal components, the modelling places an excess\nof host light in the core in order to simultaneously fit the outer\ndisk-like profile and the inner profile with a single, large $\\beta$\nvalue. This explains the behaviour of the difference between the\nactual and recovered $L_{\\rm int}$ values. Recovered $\\beta$\nmonotonically increases with the increasing luminosity of the\nspheroidal core, suggesting that the spheroidal core cannot be\ncompletely `hidden' without affecting the best fit galaxy. This adds\nto the evidence that the low $\\beta$ values recovered for some of the\nquasars implies that they do not contain strong spheroidal\ncomponents. Note that the recovered host luminosities are\napproximately correct for recovered values of $\\beta$ consistent with\na host dominated by a disk-like profile.\n\nFor the quasars which have best-fit hosts dominated by spheroidal\ncomponents, a disk-like profile at larger radii could have erroneously\nincreased the recovered total host luminosity. However, in order to\nsimultaneously fit these regions, small values of $R_{1/2}$ were\nrequired. For the quasars with hosts found to be dominated by\nspheroidal components, the relatively large values of $R_{1/2}$\nrecovered suggest that such a disk-like component is not present.\n\n\\section{Discussion}\n\n\\subsection{Luminosities} \\label{sec:discuss:lum}\n\nThe integrated host luminosities derived from our $K$-band images\nexhibit a low dispersion around a mean similar to that calculated in\nstudies of less luminous quasars. This is in accord with the work of\nMcLure \\etal\\ \\shortcite{mclure} who also found no evidence for an\nincreasing trend, although they had fewer data points at high nuclear\nluminosity.\n\nPrevious HST studies have found evidence that host luminosity\nincreases with nuclear luminosity \\cite{hooper}, although the trend\nobserved in this work could be due to incorrect nuclear component\nremoval: escaping nuclear light which increases in luminosity with the\ncore could be added to the host light. It has recently been stated\nthat the psf derived by packages such as {\\sc tinytim}, as used by\nHooper, Impey \\& Foltz \\shortcite{hooper} deviate from empirical\nWFPC~2 psfs at large radii ($\\ge2$ arcsec), due to scattering within\nthe camera \\cite{mclure}, and this could be the reason for an excess\nof nuclear light at larger radii which could be mistaken as host\nlight. This excess light could also be the reason the low axial ratios\nobserved in the Hooper, Impey \\& Foltz \\shortcite{hooper} work are not in\naccord with those derived in McLure \\etal\\ \\shortcite{mclure}, or in\nthis $K$-band study.\n\nThe triangular shape of the McLeod \\& Rieke points in\nFig.~\\ref{fig:hostvnuc} found for low redshift ($0$6.0 & spheroid \\\\\\\\\\n 0244$-$012 & $<$0.25 & 0.61 & 1.62 & disk \\\\\\\\\\n 0316$-$346 & 1.02 & 1.25 & 3.62 & ? \\\\\\\\\\n 0956$-$073 & 0.71 & 0.92 & 1.21 & disk \\\\\\\\\\n 1214+180 & $<$0.25 & 1.12 & $>$6.0 & ? \\\\\\\\\\n 1216+069 & 1.44 & 2.73 & $>$6.0 & spheroid \\\\\\\\\\n 1354+213 & 0.65 & 0.73 & 0.82 & disk \\\\\\\\\\n 1543+489 & 0.49 & 0.67 & 0.90 & disk \\\\\\\\\\n 2112+059 & $<$0.25 & 2.13 & $>$6.0 & ? \\\\\\\\\\n 2233+134 & $<$0.25 & 0.64 & 1.21 & disk \\\\\\\\\\n 2245+004 & 2.17 & 3.16 & 5.55 & spheroid \\\\\\\\\\n \\\\hline \\\\end{tabular}\\n\\n \\\\caption{Table showing 68.3\\\\% confidence intervals for the best-fit\\n host $\\\\beta$ parameters for the 12 quasars modelled using the 2D\\n $\\\\chi^2$ minimising technique (Section~\\\\protect\\\\ref{sec:model}).\\n Error bars were calculated as described in\\n Section~\\\\protect\\\\ref{sec:bars} with $\\\\beta$ constrained to lie in\\n the range $0.25<\\\\beta<6.0$. The morphology of the dominant\\n contribution to the host galaxy is also presented, based on the best\\n fit $\\\\beta$ parameter and associated confidence interval.}\\n \\\\label{tab:beta}\\n\\\\end{table}\\n\\n\\\\subsection{Axial ratios and angles} \\\\label{sec:axes}\\n\\nAnalysis of the parameter space reveals that the axial ratio and\\nprojected angle of each host are better constrained than the other\\nparameters. Fig.~\\\\ref{fig:histograms} shows histograms of these\\nparameters for all quasars modelled. The distribution of axial ratios\\nis small with $\\\\langle a/b\\\\rangle=0.79\\\\pm0.03$. This is in agreement\\nwith those found by McLure \\\\etal\\\\ \\\\shortcite{mclure}, but higher than\\nfound by Hooper, Impey \\\\& Foltz \\\\shortcite{hooper}. The projected\\nangles are uniformly distributed as expected.\\n\\n\\\\begin{figure}\\n \\\\centering \\n \\\\resizebox{5.0cm}{5.0cm}{\\\\includegraphics{axis.eps}}\\n \\\\vspace{5mm}\\\\\\\\\\n \\\\resizebox{5.0cm}{5.0cm}{\\\\includegraphics{angle.eps}}\\n \\\\caption{Histograms showing the distribution of axial ratios and\\n projected angles of the host galaxies. These parameters were well\\n constrained for all of the 12 quasars modelled, and are therefore\\n plotted from all of the minima found. Axial ratios are tightly\\n constrained with with $a/b>0.64$ for all hosts, and $\\\\langle\\n a/b\\\\rangle=0.79\\\\pm0.03$. The distribution of projected angles is\\n approximately uniformly distributed.}\\n\\\\label{fig:histograms}\\n\\\\end{figure}\\n\\n\\\\subsection{Highlighted results for selected quasars} \\n \\\\label{sec:results-quasars}\\n\\n\\\\subsubsection{Quasar 0043+039}\\nThe broad-absorption-line (BAL) quasar PG0043+039 has been subject to\\n2 previous studies to determine host galaxy properties. It was\\nobserved in the $i$ band by Veron-Cetty \\\\& Woltjer\\n\\\\shortcite{veron-cetty} who determined $M_i=-23.9$ if the host is a\\ndisk like ($\\\\beta=1$) galaxy, or $M_i=-24.7$ for a spheroidal\\n($\\\\beta=4$) galaxy. This quasar was also observed using the wide-field\\ncamera on HST by Boyce \\\\etal\\\\ \\\\shortcite{boyce}, who used a cross\\ncorrelation technique to determine that the host was slightly better\\nfit by a disk galaxy with $M_V=-21.6$. We also find that the dominant\\nmorphology is disk-like and calculate $M_K=-25.29$. The old burst\\nmodel of Bruzual \\\\& Charlot \\\\shortcite{bruzual} predicts $V-K=3.3$\\nwhich is consistent with the derived $V-K=3.7$.\\n\\n\\\\subsubsection{Quasar 0316$-$346}\\nThis quasar was previously observed using the wide field camera on HST\\n\\\\cite{bahcall} and the host was found to reveal evidence of a merger,\\nin particular tidal tails extending $\\\\sim20$\\\\,kpc west of the\\nquasar. Bahcall \\\\etal\\\\ \\\\shortcite{bahcall} also provide a 2D fit to\\nthe host properties and find that the best-fit host is disk galaxy\\nwith $M_{V}=-22.3$. We also calculate a best-fit disk galaxy and find\\n$M_K=-25.44$, giving $V-K=3.1$, again consistent with the old burst\\nmodel of Bruzual \\\\& Charlot \\\\shortcite{bruzual} which predicts\\n$V-K=3.3$.\\n\\n\\\\subsubsection{Quasar 1214+180}\\nThere have been no previous attempts to determine the morphology of\\nthe host galaxy around this quasar possibly due to the nearby star\\nwhich was utilised in this work to obtain an accurate\\npsf. Unfortunately in our images, a diffraction spike from this star\\npassed close to the quasar reducing the area that could be used to\\ncalculate $\\\\chi^2$. Although the modelling converged to give basic\\ngalaxy parameters, further analysis of the parameter space revealed\\nthat this minimum was not well constrained.\\n\\n\\\\subsubsection{Quasar 1216+069}\\nOur analysis of this quasar benefited because the images were obtained\\nusing the tip-tilt system and there is a nearby bright star which was\\nplaced on the same frame as the quasar and used to obtain a psf\\nmeasurement. Previously, `nebulosity' has been observed around this\\nquasar \\\\cite{hutchings84}, and a more detailed HST study found a\\nbest-fit spheroidal ($\\\\beta=4$) galaxy with $M_{V}=-22.3$\\n\\\\cite{boyce}. We also find that the most likely host is a large\\nspheroidal galaxy and obtain $M_K=-25.1$, giving $V-K=2.8$.\\n\\n\\\\subsubsection{Quasar 1354+213}\\nUsing a psf subtraction technique, McLeod \\\\& Rieke\\n\\\\shortcite{mcleod94b} found a residual host galaxy with $M_K=-25.6$\\nwhen converted to our cosmology using the $K$-correction from\\nGlazebrook \\\\etal\\\\ \\\\shortcite{glazebrook95} and the apparent colour\\ncorrection $H-K=0.6$ (see Section~\\\\ref{sec:calc_lum}). Our best fit\\nhost luminosity was $M_K=-25.2$. Analysis shows that the luminosity\\nand the $\\\\beta$ parameter are both tightly constrained by the\\nmodelling and the best-fit $\\\\beta=0.73$ suggests that the host is\\ndominated by a disk component. The rest-frame nuclear-to-host ratio\\nfor this quasar is only $6.8$ (the apparent nuclear-to-host ratio is\\n$4.6$), which explains why the derived parameters have small error\\nbars.\\n\\n\\\\subsubsection{Quasar 1636+384}\\nWe are not aware of any previous attempts to determine the luminosity\\nand morphology for the host galaxy of quasar 1636+384. Preliminary\\ndeconvolution of the light revealed that the excess, non-central light\\ndisplayed a morphology greatly disturbed from elliptical symmetry (as\\nshown in Fig.~\\\\ref{fig:disturbed}). The structure includes an excess\\nof light to the NW of the core which is interpreted as a merging\\ncomponent as well as light around the central core which probably\\noriginates from the host. From this image it was unclear how to\\ndistinguish between the host and the interacting companion, so the\\nluminosity of the host was estimated by summing pixel values excluding\\nthe central pixel. This provided an approximate $K$-band absolute\\nmagnitude of $M_K=-23.5$.\\n\\n\\\\subsubsection{Quasar 1700+518}\\nQuasar 1700+518 is a bright BAL quasar of low redshift\\n($z=0.29$). Such low redshift BAL objects are rare and hard to\\ndiscover since the broad absorption lines are in the UV and\\nconsequently quasar 1700+518 has received much interest: specific\\nstudies of this quasar have been undertaken in many different\\nwavebands \\\\cite{h92_1700,stockton,hines}. Because of the low redshift\\nand the brightness of the quasar, 1700+518 has also been included in\\nmany samples of quasars imaged to obtain details of their host\\ngalaxies \\\\cite{neugebauer,mcleod94b}, although these have only\\nprovided upper limits for the host magnitude. More recent imaging\\nstudies have shown that the morphology of the underlying structure\\nconsists of a disturbed host predominantly to the SW of the core\\n\\\\cite{stockton} and a close interacting companion to the NE\\n\\\\cite{h92_1700} which is most likely a ring galaxy \\\\cite{hines}.\\nDeconvolution of the light from this quasar, as shown in\\nFig.~\\\\ref{fig:disturbed}, confirms this picture of the structure. With\\nthe disturbed morphology it is difficult to know how to split the\\nlight in the central pixels into nuclear and host components. As for\\nquasar 1636+384 the host luminosity was estimated by summing the\\ncounts in the pixels surrounding the central one (ignoring those from\\nthe NE companion). There will be errors caused by leakage of light\\nfrom the nuclear component and from the contribution of the host to\\nthe central pixel. An approximate $K$-band absolute magnitude of\\n$-24.9$ was obtained for the host galaxy and $-24.4$ for the NE\\ncompanion galaxy.\\n\\n\\\\subsubsection{Quasar 2233+134}\\nBoth Smith \\\\etal\\\\ \\\\shortcite{smith} and Veron-Cetty \\\\& Woltjer\\n\\\\shortcite{veron-cetty} included this quasar in their samples, but\\nboth failed to resolve the host galaxy beyond obtaining upper limits\\nfor the luminosity. Hutchings \\\\& Neff \\\\shortcite{hutchings92} did\\nresolve the host galaxy and found the host to be best-fit by a\\n$\\\\beta=4$ model, although they did not resolve further information\\nabout the galaxy. However, we find that the most probable host has an\\ndisk profile and calculate $M_K=-24.1$, the lowest luminosity host\\nmodelled. If we constrain the host to have an elliptical profile, the\\nbest fit luminosity becomes $M_K=-25.9$, although the half light\\nradius is very small for this model ($R_{1/2}=1.5$\\\\,kpc) which places\\nit a long way from the $K$-band Fundamental Plane of Pahre, Djorgovski\\n\\\\& de Carvalho \\\\shortcite{pahre}. If the host parameters are\\nconstrained to lie on this plane, then rerunning the modelling gives a\\nbest fit host with $M_K=-24.6$. Neither of these changes would be\\nsufficient to alter our conclusions.\\n\\n\\\\section{Simulated Data I - Single component galaxies} \\\\label{sec:mock}\\n\\nTrying to recover known host parameters from Monte-Carlo simulations\\nof the actual data enables the distribution of recovered parameters\\ngiven the true values to be determined. Note that the error bars\\ncalculated using the $\\\\chi^2$ statistic are instead determined from\\nthe distribution of possible true values given the data. These two\\ndistributions are not necessarily equal. We need to determine the\\ndistribution of recovered values in order to answer questions such as\\n`Are our results biased towards low $\\\\beta$ values?'.\\n\\nIn view of the distribution of recovered $\\\\beta$ values, it was\\ndecided to simulate data to match the images of quasars 0956$-$073 and\\n1543+489. These quasars span the distribution of signal-to-noise of\\nall the images, and 2D model fitting revealed evidence for disk\\ndominated hosts in both cases. Verification of this result is\\ninteresting as recent work has suggested that the hosts of luminous\\nquasars should be dominated by the spheroidal component (see\\nSection~\\\\ref{sec:discuss_morph}).\\n\\n\\\\subsection{Creating the mock data} \\\\label{sec:mock_noise}\\n\\n\\\\begin{table*}\\n\\\\begin{minipage}{\\\\textwidth}\\n \\\\centering \\\\begin{tabular}{ccccccccc} \\\\hline \\n quasar & \\\\multicolumn{4}{c}{$\\\\beta$} & \\n \\\\multicolumn{4}{c}{$L_{\\\\rm int}$ /adu} \\\\\\\\\\n & true & min & average & max & true & min & average & max \\\\\\\\ \\\\hline\\n\\n 0956$-$073 & 1.0 & 0.74 & 1.14 & 2.28 & 300.0 & 262.1 & 323.7 & 510.0 \\\\\\\\\\n 0956$-$073 & 4.0 & 1.93 & 3.77 & 7.42 & 300.0 & 213.6 & 288.3 & 463.1 \\\\\\\\\\n 1543+489 & 1.0 & 0.79 & 1.08 & 1.69 & 300.0 & 260.1 & 324.7 & 512.2 \\\\\\\\\\n 1543+489 & 4.0 & 2.13 & 4.04 & 7.25 & 300.0 & 209.6 & 302.2 & 469.8 \\\\\\\\\\n \\\\hline \\n \\\\end{tabular}\\n\\n \\\\caption{Table showing the mean and 68.3\\\\% confidence intervals for\\n the recovered $\\\\beta$ and integrated host luminosity from the\\n simulated data. 100 simulations were performed for each morphology\\n for each quasar.} \\\\label{tab:mock_stat}\\n\\\\end{minipage}\\n\\\\end{table*}\\n\\n\\\\begin{figure*}\\n\\\\begin{minipage}{\\\\textwidth}\\n \\\\centering \\\\resizebox{10cm}{!}{\\\\includegraphics{mock_l.eps}}\\n \\\\caption{The distribution of recovered luminosities from Monte-Carlo\\n simulations of 100 $\\\\beta=1$ images and 100 $\\\\beta=4$ images. The\\n $y$-axis gives the number of recovered values within each luminosity\\n bin. Noise has been added to match observations of quasar (a)\\n 0956$-$073 and (b) 1543+489, including a contribution from the error\\n in the measured psf as described in\\n Section~\\\\protect\\\\ref{sec:mock_noise}. The luminosity of each\\n simulated galaxy, marked by the dotted line, was set at 300\\\\,adu.}\\n \\\\label{fig:mock_lum}\\n\\\\end{minipage}\\n\\\\end{figure*}\\n\\nSimulated galaxies were created using the procedure outlined in\\nSection~\\\\ref{sec:galaxy} and a single $\\\\delta$ function added to the\\ncentre of each to create a `perfect unconvolved model'. The height of\\nthe $\\\\delta$ function was chosen to match the total signal of the\\noriginal images. These models were then convolved with the psf\\nmeasured to match the quasar.\\n\\nGaussian noise was added with a radially dependent variance as given\\nby the error profile calculated in Section~\\\\ref{sec:error} including\\nthe best-fit host galaxy in the calculation. The error profiles used\\nfor quasars 0956$-$073 and 1543+489 are given by the solid lines in\\nFig.~\\\\ref{fig:epgal}. Differences between measured and true psf were\\nincluded in this analysis, and are therefore included in the noise\\nlevels added to the simulated data. This noise model assumes that the\\nerrors in different pixels are independent (see\\nSection~\\\\ref{sec:chisq}).\\n\\nWe have simulated 100 images with exact disk hosts, and 100 images\\nwith exact spheroidal hosts for each of the two quasars chosen. The\\ntrue integrated host luminosity was set at 300\\\\,adu for simulated data\\nof both quasars. This conservative value is below the best-fit value\\nobtained from the data for both quasars, providing a stringent test of\\nthe modelling. This is particularly true for a $\\\\beta=4$ host:\\nconstraining $\\\\beta=4$ when modelling the observed image would have\\nresulted in a best-fit $L_{\\\\rm int}\\\\gg300$\\\\,adu. The simulated images\\nwere analysed using exactly the same 2D modelling procedure described\\nabove for the observed data. The range of recovered parameters is\\nanalysed below.\\n\\n\\\\subsection{Results from the simulated data: luminosities}\\n\\nRecovered luminosities, presented in Fig.~\\\\ref{fig:mock_lum} reveal a\\nskewed distribution, particularly for hosts with exact spheroidal\\nprofiles where the recovered luminosity is biased towards a low\\nvalue. This is consistent with the morphology being skewed towards a\\nlow $\\\\beta$ value (see next Section): if $\\\\beta$ is decreased, the\\nluminosity also has to decrease to keep the counts in the outer pixels\\n(those most important for fitting the host) the same. The counts in\\nthe centre of the galaxy are less important because of the additional\\nnuclear component which is adjusted to match the data.\\n\\nThe mean and variance in the recovered luminosities are presented in\\nTable~\\\\ref{tab:mock_stat}. Although the error bars reveal the extent\\nof the skewed distribution, the mean is within 10\\\\% of the true value\\nfor each quasar and morphology.\\n\\n\\\\subsection{Results from the simulated data: morphologies}\\n\\n\\\\begin{figure*}\\n\\\\begin{minipage}{\\\\textwidth}\\n \\\\centering \\\\resizebox{15cm}{!}{\\\\includegraphics{mock_b.eps}}\\n\\n \\\\caption{Evidence that the hosts of luminous radio-quiet quasars are\\n not exclusively dominated by spheroidal components. The distribution\\n of $\\\\beta$ values recovered from 2-D modelling of 100 simulated\\n images created with hosts using exact disk or spheroidal profiles is\\n presented. Noise has been added to these images to match\\n observations of (a) quasar 0956$-$073 and (b) quasar 1543+489,\\n including a contribution from the error in the measured psf as\\n described in Section~\\\\protect\\\\ref{sec:mock_noise}. The dotted line\\n shows the best-fit $\\\\beta$ value recovered from the images of these\\n quasars. (c) For comparison the distribution of best-fit $\\\\beta$\\n values obtained from all of our $K$-band images is also plotted. The\\n probable morphology of the host was determined from the $\\\\chi^2$\\n error bars derived for the true value given the data.}\\n \\\\label{fig:mock_beta}\\n\\\\end{minipage}\\n\\\\end{figure*}\\n\\nThe skewed distribution observed in the error bars on the true host\\n$\\\\beta$ value is mirrored by the distribution of $\\\\beta$ values\\nrecovered using the standard modelling procedure described in\\nSection~\\\\ref{sec:model}. Fig.~\\\\ref{fig:mock_beta} shows the relative\\ndistribution of $\\\\beta$ values retrieved from the simulated images.\\nLimits of $0.25<\\\\beta<8$ were placed on fitted $\\\\beta$ values. For\\nquasar 0956$-$073, 16 of the simulated images created with exact\\nspheroidal hosts, had recovered $\\\\beta>8$. For quasar 1543+489, this\\nnumber was 14: these values are not included in\\nFig.~\\\\ref{fig:mock_beta}. The distribution was used to calculate the\\nmean and standard deviation given in Table~\\\\ref{tab:mock_stat},\\nassuming all fits with $\\\\beta>8$ actually had $\\\\beta=8$.\\n\\nIf the host were a spheroidal galaxy with $\\\\beta=4$, the probability\\nof recovering a best-fit value of $\\\\beta<1$ is $\\\\sim0.03$ for\\n0956$-$073 and $\\\\sim0.01$ for 1543+489: the best-fit values from the\\nimages were $\\\\beta=0.92$ and $\\\\beta=0.67$ respectively. The evidence\\nfor the existence of hosts dominated by a disk component therefore\\nappears to be strong. In Fig.~\\\\ref{fig:mock_beta}, the distribution of\\nretrieved $\\\\beta$ values for the 12 quasars modelled is also\\nshown. This distribution is inconsistent with the hypothesis that all\\nthe hosts are dominated by spheroidal components on the scales probed\\nby these measurements. The histogram is divided to show the probable\\ndistribution of morphologies given the options $\\\\beta=1$ or\\n$\\\\beta=4$. As can be seen, the modelling suggests that approximately\\nhalf of the hosts are dominated by disk components.\\n\\n\\\\section{Simulated Data II - Two component galaxies} \\\\label{sec:mock2}\\n\\nIn order to constrain the potential importance of spheroidal cores in\\nthe galaxies found to be dominated by disk-like profiles, we have\\nanalysed synthetic quasars created with two host galaxy\\ncomponents. Using the Fundamental-Plane (FP) relation between\\n$R_{1/2}$ and $L_{\\\\rm int}$ found in the K-band by Pahre \\\\etal\\\\\\n\\\\shortcite{pahre}, we have added extra spheroidal ($\\\\beta=4$)\\ncomponents to the recovered best-fit host galaxy of quasar\\n1543+489. Note that this best fit host had $\\\\beta=0.67$. We have tried\\nthe same analysis using $\\\\beta=1$ and found no change in the effects\\nproduced by the spheroidal core. After adding in the nuclear component\\nand noise as described in Section~\\\\ref{sec:mock}, we have recovered\\nthe best-fit host galaxy parameters using our single component\\nmodelling. Spheroidal components were added with a variety of\\ndifferent luminosities, and five different realisations of the\\nadditional noise component were added to each. The resulting average\\nrecovered $L_{\\\\rm int}$ \\\\& $\\\\beta$ are given in Table~\\\\ref{tab:2cmpt}.\\n\\n\\\\begin{table}\\n \\\\centering\\n \\\\begin{tabular}{cccccc} \\\\hline\\n \\\\multicolumn{4}{c}{$L_{\\\\rm int}$ /adu} & $R_{1/2}$ & $\\\\beta$ \\\\\\\\\\n spheroidal & total & recovered & diff & /kpc & \\\\\\\\ \\\\hline\\n 0.0\\t& 320.1 & 291.2 & -28.9 & 8.26 & 0.61 \\t\\\\\\\\\\n 40.0\\t& 360.1 & 306.5 & -53.6 & 8.19 & 0.63 \\t\\\\\\\\\\n 80.0\\t& 400.1 & 337.9 & -62.2 & 8.02 & 0.69\\t\\\\\\\\\\t\\n 120.0\\t& 440.1 & 382.7 & -57.4 & 7.71 & 0.81\\t\\\\\\\\\\n 160.0\\t& 480.1 & 436.3 & -43.8 & 7.35 & 0.96\\t\\\\\\\\\\n 320.0\\t& 640.1 & 785.8 & 145.7 & 5.45 & 1.93\\t\\\\\\\\\\n 480.0 & 800.1 & 1305.2 & 505.1 & 3.85 & 3.37 \\t\\\\\\\\\\n \\\\hline \\\\end{tabular}\\n\\n \\\\caption{Average recovered host parameters from single component\\n fits to synthetic quasars with 2-component host\\n galaxies. Uncorrelated Gaussian noise has been added to these models\\n to match that of quasar 1543+489, and the average recovered values\\n are given for 5 different realisations of this noise. The same noise\\n was added to corresponding mock images created with different\\n spheroidal luminosities, so there will be a systematic error because\\n 5 realisations are not sufficient to fully sample the recovered\\n parameters with the given noise level. The result of analysing a\\n host with no spheroidal component shows that the results\\n systematically underestimate $\\\\beta$ and $L_{\\\\rm int}$ and\\n overestimate $R_{1/2}$ by small amounts. Note that the relative\\n dependence of the recovered parameters on the spheroidal component\\n will not be affected.} \\\\label{tab:2cmpt}\\n\\\\end{table}\\n\\nBecause $R_{1/2}(\\\\rm spheroidal)$ and $L_{\\\\rm int}(\\\\rm spheroidal)$\\nfollow a FP relation, the importance of this component is enhanced for\\nlarge $L_{\\\\rm int}(\\\\rm spheroidal)$ and diminished for small $L_{\\\\rm\\nint}(\\\\rm spheroidal)$. The recovered total luminosity for small\\nspheroidal components is therefore very similar to that of the disk\\nalone. For large spheroidal components, the modelling places an excess\\nof host light in the core in order to simultaneously fit the outer\\ndisk-like profile and the inner profile with a single, large $\\\\beta$\\nvalue. This explains the behaviour of the difference between the\\nactual and recovered $L_{\\\\rm int}$ values. Recovered $\\\\beta$\\nmonotonically increases with the increasing luminosity of the\\nspheroidal core, suggesting that the spheroidal core cannot be\\ncompletely `hidden' without affecting the best fit galaxy. This adds\\nto the evidence that the low $\\\\beta$ values recovered for some of the\\nquasars implies that they do not contain strong spheroidal\\ncomponents. Note that the recovered host luminosities are\\napproximately correct for recovered values of $\\\\beta$ consistent with\\na host dominated by a disk-like profile.\\n\\nFor the quasars which have best-fit hosts dominated by spheroidal\\ncomponents, a disk-like profile at larger radii could have erroneously\\nincreased the recovered total host luminosity. However, in order to\\nsimultaneously fit these regions, small values of $R_{1/2}$ were\\nrequired. For the quasars with hosts found to be dominated by\\nspheroidal components, the relatively large values of $R_{1/2}$\\nrecovered suggest that such a disk-like component is not present.\\n\\n\\\\section{Discussion}\\n\\n\\\\subsection{Luminosities} \\\\label{sec:discuss:lum}\\n\\nThe integrated host luminosities derived from our $K$-band images\\nexhibit a low dispersion around a mean similar to that calculated in\\nstudies of less luminous quasars. This is in accord with the work of\\nMcLure \\\\etal\\\\ \\\\shortcite{mclure} who also found no evidence for an\\nincreasing trend, although they had fewer data points at high nuclear\\nluminosity.\\n\\nPrevious HST studies have found evidence that host luminosity\\nincreases with nuclear luminosity \\\\cite{hooper}, although the trend\\nobserved in this work could be due to incorrect nuclear component\\nremoval: escaping nuclear light which increases in luminosity with the\\ncore could be added to the host light. It has recently been stated\\nthat the psf derived by packages such as {\\\\sc tinytim}, as used by\\nHooper, Impey \\\\& Foltz \\\\shortcite{hooper} deviate from empirical\\nWFPC~2 psfs at large radii ($\\\\ge2$ arcsec), due to scattering within\\nthe camera \\\\cite{mclure}, and this could be the reason for an excess\\nof nuclear light at larger radii which could be mistaken as host\\nlight. This excess light could also be the reason the low axial ratios\\nobserved in the Hooper, Impey \\\\& Foltz \\\\shortcite{hooper} work are not in\\naccord with those derived in McLure \\\\etal\\\\ \\\\shortcite{mclure}, or in\\nthis $K$-band study.\\n\\nThe triangular shape of the McLeod \\\\& Rieke points in\\nFig.~\\\\ref{fig:hostvnuc} found for low redshift ($0$0.2 Jy. Due to the greater depth of the FSC only those samples\nconstructed from it will be considered here [5,6 hereafter RMS and FSXH]. In essence\nnone of these samples are truly compatible with the deeper ISO surveys because they\napply longer wavelength IRAS colour selection criteria and do not objectively classify\ngalaxies. Some of these samples additionally suffer from inaccurate source flux\nestimation, no correction for the overdensity due to large scale structure and\ninaccurate K-correction. Due to the lack of space here these latter two points are not\nconsidered although we refer the interested reader to [6,14] for excellent coverage of\nthese problems.\n\n\n\\subsection{The colour selection problem}\n\nSelecting objects at 12 $\\mu$m without colour selection will produce an abundance of\nstars over galaxies due to the Jeans tail of stellar emission. Without exception every\nextragalactic 12 $\\mu$m sample to date has had (the majority of) stars removed by\napplying longer wavelength IRAS colour criteria. This technique is clearly\nincompatible with ISO surveys where no colour criterium is applied and will cause a\nbias towards dusty galaxies. This also enforces that every galaxy must have a longer\nwavelength flux, producing incompleteness even within the selection boundaries. For\nexample, in RMS the primary selection is $f_{12}$$>$0.22 Jy but every galaxy must also\nhave $f_{60}$$>$0.5$f_{12}$ or $f_{100}$$>$$f_{12}$. However due to the completeness\nof FSC ($f_{60}$$>$0.2 Jy and $f_{100}$$>$0.6 Jy) this sample cannot be complete for\n$f_{12}$$<$0.4 Jy or $f_{12}$$<$0.6Jy respectively. \n\n\n\\subsection{The classification problem}\n\nTo produce accurate extragalactic luminosity functions and understand the galaxy\ncontributions to fainter source counts it is necessary to classify galaxies in an\nobjective way, the most common technique is with optical line ratios [7,8]. To date\nthe only classified 12 $\\mu$m sample is RMS although their classification was taken\nfrom various catalogues which differ in the definition of extragalactic type and\ncompleteness. As a comparison to this classification we have obtained line ratios from\nthe literature for 349 of the 483 RMS galaxies with $\\delta$$>$0 degrees. This gives\ncompletenesses of 72\\%, 78\\% and 93\\% for objects $f_{12}$$>$0.22, 0.3 and 0.5 Jy\nrespectively. Due to the spectroscopic incompleteness at lower fluxes and the colour\nselection incompleteness we only consider those of $f_{12}$$>$0.5 Jy here, see table\n1; our classification follows that of [7,9]. \n\n\n\\begin{table}\n\\centering\n\\caption{Extragalactic classification}\n\\renewcommand{\\arraystretch}{1.4}\n\\setlength\\tabcolsep{5pt}\n\\begin{tabular}{llllll}\n\\hline\\noalign{\\smallskip}\n & AGN & LINER & HII \\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nRMS & 13\\% & 15\\% & - \\\\\nAA & 16\\% & 24\\% & 60\\% \\\\\n\\hline\n\\end{tabular}\n\\label{Tab1a}\n\\end{table}\n\n\nAll galaxies are found to show H$\\alpha$ emission although for some galaxies\nW$_{\\lambda}$(H$\\alpha$)$<$1 angstrom and they would appear as absorption line objects\nin lower resolution/signal to noise spectra. Of the HII galaxies, 50\\% show evidence\nfor significant star formation (W$_{\\lambda}$(H$\\alpha$)$>$10 angstroms). RMS\nclassified an object as an AGN if it is present in an AGN catalogue. We find a good\nagreement in classification for this object class, the principal reason for the\nconstruction of the RMS sample. LINERs were classified in the RMS sample if they were\npresent in an AGN catalgoue and consequently this sample is thought to be incomplete. \nWe confirm this here. RMS did not classify HII galaxies although they considered those\ngalaxies not classified as a LINER or AGN, but with high infrared luminosities, to be\nstarburst galaxies and all other objects to be normal galaxies. \n\n\\subsection{The source flux problem}\n\nThe FSC detection algorithm has been optimised for unresolved sources therefore fluxes\nfor extended sources need to be calculated from the coaddition of scans (the ADDSCAN\ntechnique nowadays accessed via XSCANPI) [10]. However, if a source is unresolved, the\nflux calculation using this technique leads erroneously to a larger flux than the FSC\nflux [10]. Whilst FSXH carefully calculate the fluxes of extended and unresolved\nsources seperately, RMS treat all sources as extended and consequently overestimate\nthe fluxes of unresolved galaxies; due to the large beamsize of IRAS a large number of\ngalaxies can be overestimated. The magnitude of this effect can be estimated from\nISOCAM observations. Unfortunately only a few observations are available for the lw10\nfilter (the closest to the IRAS 12 $\\mu$m band) therefore in order to predict the IRAS\n12 $\\mu$m fluxes we have used observations in the lw2 (6.7 $\\mu$m) and lw3 (14.3\n$\\mu$m) bands and a spectral decomposition technique similar to that described in\n[11]. In this simple model the mid-infrared emission is produced by two components:\nHII regions (using M17 [12]) and photo-dissociation regions (PDR) (using NGC7023\n[13]). The ratio of HII to PDR is calculated from the ratio of lw2 to lw3 fluxes, a\nsynthetic spectra is produced and the IRAS 12 $\\mu$m flux is calculated. This\ntechnique will be somewhat imprecise due to the uncertainty of the CAM photometry and\nthe ability of the model to reproduce the galactic spectrum. Overall we estimate an\nuncertainty of $\\sim$20\\%, roughly equal to the worst error in the FSC photometry. In\nfigure 1 we plot our predicted fluxes against the FSC and RMS fluxes divided by the\npredicted flux (i.e. the relative errors in flux).\n\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=.6\\textwidth]{dma_fig1.eps}\n\\caption[]{12 $\\mu$m flux comparison}\n\\label{eps1}\n\\end{figure}\n\n\nOnly those galaxies with z$>$2,500 kms$^{-1}$ have been plotted as they should all be\nunresolved in the IRAS beam. In general a good agreement between the predicted flux\nand FSC flux is found leading us to believe that the true fluxes for these objects are\nclose to the FSC flux. Consequently RMS may be overpredicting the source flux for\n$\\sim$50\\% of their objects. This will have the effect of shifting galaxies from faint\nflux/luminosity bins to higher bins causing unpredictable effects in the source count\nand luminosity function determinations. \n\n\n\\section{A new IRAS 12 $\\mu$m sample}\n\nOur new IRAS 12 $\\mu$m sample aims to address these problems and create a local\ninfrared sample that is compatible with ISO surveys. The sample definition is close to\nthat of RMS: sources are taken from the FSC for those objects with $|$b$|$$>$25\ndegrees, $f_{12}$$>$0.2 Jy and a moderate or good quality detection (S/N$>$3). This\nselection results in 31002 objects, by comparison the RMS colour selection bias\nproduces $\\sim$1100 objects. \n\nOur sample provides an interesting complement to the PSC-z extragalactic survey [15]\nwhich selects those objects from the PSC with $f_{60}$$>$0.6 Jy. As with our sample\nthey do not apply colour selection criteria, stars are identified on Schmidt plates.\nIn terms of the extragalactic objects we would expect many galaxies in common although\nour sample should have a higher fraction of quasars and early type galaxies. \n\n\n\\subsection{The stellar infrared diagnostic correlation}\n\nBy not applying colour selection to distinguish galaxies from stars we have had to\ndevise an alternative technique. The key assumption in our technique is that stars\nhave, in the majority, predictable properties and therefore with the large and\ncomplete optical stellar databases currently available (in particular the Guide Star\nCatalogue [16], hereafter GSC) it is possible to find the majority of stars in our\nsample through positional cross correlation. An important factor here is in\ndetermining the completeness of an optical stellar catalgoue in an infrared sample,\nrequiring an understanding of the general optical and infrared characteristics of\nstars.\n \nTo determine these characteristics for our stars we have used SIMBAD, which provides\nstellar classifications, and produced a large sample ($\\sim$9000 objects) of\nclassified stars. When cross correlationing to optical positions we consider a star\ncorrelated if its optical position falls within 5$\\sigma$ of the IRAS position (the\nmean major and minor error ellipse axes are 16.9\" and 2.0\" respectively). The\nproperties of our classified stellar sample are shown in figure 2. We have only\nplotted those stars for which there are at least 10 objects in a classified class and\nonly a subset of these classes are shown here for clarity. A clear correlation between\nstellar type and flux ratio is found. The predicted black body colours for the\ndifferent stellar types follows a straight line passing close to the A1V to K5III\npoints. The interesting deviation observed for stars beyond type MOIII is {\\it\npossibly} due to an increasing amount of stellar absorption in the V band.\n\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=.6\\textwidth]{dma_fig2.eps}\n\\caption[]{Stellar infrared diagnostic diagram}\n\\label{eps1}\n\\end{figure}\n\n\nThese optical-infrared flux correlations provide an essential tool, the ability to\npredict the IRAS 12 $\\mu$m flux of a star for a given spectral type or B-V colour. In\nthe cases where we find an IRAS source associated with both a galaxy and a star we\nwill be able to predict the flux from the star and therefore estimate the flux from\nthe galaxy.\n\n\n\\subsection{Cross correlating stars}\n\nThe GSC is considered complete for 6$<$V$<$15 mags over the whole sky. Based on our\nstellar infrared diagnostic correlation this corresponds to a depth of $f_{12}$$>$0.2\nJy and therefore any stars earlier than a type M6III in our sample should be in the\nGSC. However, to accurately cross correlate the positions between the GSC and our\nsample requires accounting for proper motion. The Schmidt plates for the GSC were\ntaken in 1975 and 1982, by comparison the mean IRAS observation epoch is 1983.5. By\nanalysing a sub-sample of Hipparcos stars ($\\sim$4000 objects, selected by sky area)\nwe find a mean proper motion of 0.03\"yr$^{-1}$, with a one $\\sigma$ maximum of\n0.13\"yr$^{-1}$ (the maximum in the whole catalogue is 6\"yr$^{-1}$). Taking into\naccount the different observation epochs and the mean IRAS error ellipse, virtually\nall our stars should fall within 5$\\sigma$ of their GSC position. \n\nWe initially searched for associations by selecting all objects within 2' of the IRAS\nposition (2' corresponds to $\\sim$5$\\sigma$ of the mean positional uncertainty in the\nmajor axis direction) although we only consider a star cross-correlated if it falls\nwithin 5$\\sigma$ of an IRAS source. From this cross correlation we find that over that\n29000 of our IRAS sources are stars. Of these a small ($\\sim$0.5\\%), but significant,\nfraction show a considerable infrared excess ($f_{25}$$>$$f_{12}$) and warrant further\nstudy.\n\n\n\\subsection{Cross correlating galaxies}\n\nOur extragalactic cross correlation is performed in a similar manner although the\nproblems associated with correlating galaxies are somewhat different. Proper motion is\nnot a problem although the extended size of galaxies is as the peak mid-infrared\nposition can vary from the peak optical position and therefore some positional\nuncertainty must be included when trying to correlate an infrared galaxy to an optical\nsource. Although a 5$\\sigma$ positional uncertainty can correspond to 2' if the galaxy\nlies along the major axis of the IRAS error ellipse it can also correspond to just 10\"\nif the galaxy lies perpendicular to this direction. Therefore we only consider a\ngalaxy cross correlated if it falls within 10$\\sigma$ of an IRAS source. Due to the\noften unknown incompleteness of extragalactic catalogues it is not possible to\naccurately determine the completeness of our sample in extragalactic catalogues and\ntherefore we have simply used the largest (and most appropriate) databases. In the\ncross correlation presented here we have used the QIGC sample [17], which has just\nbecome available in electronic form, NED, SIMBAD and the FSC 25 $\\mu$m sample [18].\n\nUsing these databases we find that over 700 of our sources, not confirmed as stars,\nfall within our 10$\\sigma$ threshold. From these confirmed galaxies we find $\\sim$50\nare elliptical or S0 systems (not all are active galaxies) and $\\sim$150 have\n$f_{12}$$>$$f_{25}$ and are most probably PDR dominated galaxies. A number of galaxies\nhave $f_{12}$$>$2$f_{60}$ and would therefore not be picked up by RMS. One of these\ngalaxies is NGC 3115, a nearby bulge dominated galaxy of Hubble type S0. This galaxy\nis only detected at 12 $\\mu$m, the 25, 60 and 100 $\\mu$m fluxes are upper limits,\nalthough with a V band mag of $\\sim$8.9 it is bright optical galaxy. In terms of it's\nB-V (1.0) and B/12 (2.5) colours it corresponds to a K0III star. As a comparison we\nhave plotted a sample of our {\\it normal} infrared galaxies, see figure 3. \n\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=.6\\textwidth]{dma_fig3.eps}\n\\caption[]{Stellar and galactic colour plot. All confirmed stars are plotted as dots\nand a selection of normal infrared galaxies are plotted as filled circles. NGC 3115 is\nnot plotted here but would correspond to the position of a K0III star, see figure 2}\n\\label{eps1} \n\\end{figure}\n\n\n\\subsection{Further improvements}\n\nAlthough our initial cross correlation has been successful we have $\\sim$500 objects\nfor which we do not have an optical identification. These objects do not have IRAS\nCirrus/Confused flags or low 12 $\\mu$m fluxes although approximately 75\\% have upper\nlimit 60 $\\mu$m IRAS fluxes. Visual inspection of a number of these objects with the\nDigital Sky Survey shows them to be nearby bright stars, suggesting incompleteness in\nthe GSC at bright fluxes. However there is also probably a substantial population of\nstars not yet accounted for: those with V$>$15 mags (e.g. M7III and M8III stars),\ndark molecular clouds and planetary nebulae. We are currently compiling a list of\nadditional stellar objects to cross correlate to our sample to allow us to produce a\ndefinitive list of unidentified extragalactic sources.\n\n\n\\section{Further work}\n\nOur primary aim is to construct complete 12 $\\mu$m FSC selected samples of galaxies\nand stars. From this we will create accurate extragalactic source counts and\nclassified luminosity functions with optical slit spectroscopy. As many of our\nextragalactic objects will be extended we also intend to obtain integrated spectra to\nprovide a classification which is compatible with the distant objects found in ISO\nsurveys where the observed slit spectra will be produced by the majority of the\ngalaxy. With our stellar sample we wish to create a complete list of high galactic\nlatitude stars and sources to help constrain galactic models and provide further\ndiagnostics in distinguishing stars from galaxies in faint surveys (e.g. the Hubble\nDeep Field [3]). Both our galactic and stellar samples show objects that deviate from\nthe norm (i.e. galaxies with stellar colours and stars with galactic colours) and\nwarrant further study in their own right.\n\\\\~\\\\ \n{\\bf Acknowledgements} We thank I.Matute for assistance in producing the initial\ncatalogue and M.Moshir for fruitful discussions. We are grateful to O.Laurent and\nH.Roussel for providing the ISOCAM fluxes for some of the RMS sample sources. We\nacknowledge and thank the EC TMR extragalactic networks for postdoctoral grant\nsupport. 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(1981) PASP, 93, 5\n\n\\bibitem{} \nPoggianti, B.M., Smail, I., Dressler, A., Couch, W.J., Barger, A.J., et al. (1999)\nApJ, 518, 576\n\n\\bibitem{}\nHo, L., Filippenko, A.V., Sargent, W.L.W. (1997) ApJS, 326, 653\n\n\\bibitem{}\nMoshir, M., et al. (1992) Explanatory Supplement to the IRAS Faint Source Survey, Version\n2, Pasadena, JPL\n\n\\bibitem{}\nTran, Q.D. (1998) PhD thesis, University of Paris, Orsay, France\n\n\\bibitem{}\nCesarsky, D., Lequeux, J., Abergel, A., Perault, M., Palazzi, E., Madden, S., Tran, D.\n(1996) A\\&A, 315, L309\n\n\\bibitem{}\nCesarsky, D., Lequeux, J., Abergel, A., Perault, M., Palazzi, E., Madden, S., Tran, D.\n(1996) A\\&A, 315, L305\n\n\\bibitem{}\nXu, C., Hacking, P.B., Fang, F., Shupe, D.L., Lonsdale, C.J., et al. (1998) ApJ, 508,\n576\n\n\\bibitem{}\nSaunders, W., Oliver, S., Keeble, O., Rowan-Robinson, M., Canavezes, A., et al. (1997)\nin Maddox, S., Aragon-Salamanca, A., Wide Field Spectroscopy and the Distant Universe,\nWorld Scientific Press, Singapore\n\n\\bibitem{}\nLasker, B.M., Sturch, C.R., McLean, B.J., Russel, J.L., Jenker, H., Shara, M.M. (1990)\nAJ, 99, 2019\n\n\\bibitem{}\nLawrence, A., Rowan-Robinson, M., Ellis, R.S., Frenk. C.S., Efstathiou. G., et al. \n(1999) MNRAS, 308, 897\n\n\\bibitem{}\nShupe, D.L., Fang, F., Hacking, P.B., Huchra, J.P. (1998) ApJ, 501, 597\n\n\n\n\\end{thebibliography}\n\n%INDEX%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\clearpage\n\\addcontentsline{toc}{section}{Index}\n\\flushbottom\n\\printindex\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\end{document}\n"}],"string":"[\n {\n \"name\": \"dma_ringberg.tex\",\n \"string\": \"%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n% This is a sample input file for your contribution to a multi-\\n% author book to be published by Springer Verlag.\\n%\\n% Please use it as a template for your own input, and please\\n% follow the instructions for the formal editing of your\\n% manuscript as described in the file \\\"1readme\\\".\\n%\\n% Please send the Tex and figure files of your manuscript\\n% together with any additional style files as well as the\\n% PS file to the editor of your book.\\n%\\n% He or she will collect all contributions for the planned\\n% book, possibly compile them all in one go and pass the\\n% complete set of manuscripts on to Springer.\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\n\\n%RECOMMENDED%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\\\documentclass[runningheads]{cl2emult}\\n\\n\\\\usepackage{makeidx} % allows index generation\\n\\\\usepackage{graphicx} % standard LaTeX graphics tool\\n % for including eps-figure files\\n\\\\usepackage{subeqnar} % subnumbers individual equations\\n % within an array\\n\\\\usepackage{multicol} % used for the two-column index\\n\\\\usepackage{cropmark} % cropmarks for pages without\\n % pagenumbers\\n\\\\usepackage{lnp} % placeholder for figures\\n\\\\makeindex % used for the subject index\\n % please use the style sprmidx.sty with\\n % your makeindex program\\n\\n%upright Greek letters (example below: upright \\\"mu\\\")\\n\\\\newcommand{\\\\euler}[1]{{\\\\usefont{U}{eur}{m}{n}#1}}\\n\\\\newcommand{\\\\eulerbold}[1]{{\\\\usefont{U}{eur}{b}{n}#1}}\\n\\\\newcommand{\\\\umu}{\\\\mbox{\\\\euler{\\\\char22}}}\\n\\\\newcommand{\\\\umub}{\\\\mbox{\\\\eulerbold{\\\\char22}}}\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\n%OPTIONAL%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%\\n%\\\\usepackage{amstex} % useful for coding complex math\\n%\\\\mathindent\\\\parindent % needed in case \\\"Amstex\\\" is used\\n%\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n%AUTHOR_STYLES_AND_DEFINITIONS%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%\\n%Please reduce your own definitions and macros to an absolute\\n%minimum since otherwise it will become rather strenuous to\\n%compile all individual contributions to a single book file\\n%\\n%\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\\\begin{document}\\n%\\n\\\\title*{A local infrared perspective to deeper ISO surveys}\\n%\\n%\\n\\\\toctitle{A local infrared perspective to deeper ISO surveys}\\n% allows explicit linebreak for the table of content\\n%\\n%\\n\\\\titlerunning{A local infrared perspective}\\n% allows abbreviation of title, if the full title is too long\\n% to fit in the running head\\n%\\n\\\\author{D.M. Alexander\\\\inst{1}\\n\\\\and H. Aussel\\\\inst{2}}\\n%\\n\\\\authorrunning{Alexander and Aussel}\\n% if there are more than two authors,\\n% please abbreviate author list for running head\\n%\\n%\\n\\\\institute{International School for Advanced Studies, SISSA,\\nTrieste, Italy\\n\\\\and Osservatorio Astronomico di Padova, Padova, Italy}\\n\\n\\\\maketitle % typesets the title of the contribution\\n\\n\\\\begin{abstract}\\n\\nWe present new techniques to produce IRAS 12 $\\\\mu$m samples of galaxies and stars. We\\nshow that previous IRAS 12 $\\\\mu$m samples are incompatible for detailed comparison\\nwith ISO surveys and review their problems. We provide a stellar infrared diagnostic\\ndiagram to distinguish galaxies from stars without using longer wavelength IRAS colour\\ncriteria and produce complete 12 $\\\\mu$m samples of galaxies and stars. This new\\ntechnique allows us to estimate the contribution of non-dusty galaxies to the IRAS 12\\n$\\\\mu$m counts and produce a true local mid-infrared extragalactic sample compatible\\nwith ISO surveys. We present our initial analysis and results.\\n\\n\\\\end{abstract}\\n\\n\\\\section{The importance of the local infrared picture} \\n\\nThe recent ISO mission has produced a number of deep mid-infrared extragalactic\\nsurveys [1,2,3,4] many of which are presented elsewhere in these proceedings.\\nIn order to accurately evaluate the apparent source evolution found in these surveys\\nit is essential to have a stable and exact local infrared picture that is compatible\\nwith ISO surveys. \\n\\n\\n\\\\section{Previous work and problems}\\n\\nThere have been a number of previous IRAS 12 $\\\\mu$m extragalactic samples produced\\nfrom either the Point Source Catalog, hereafter PSC, or the Faint Source Catalog,\\nhereafter FSC. The FSC was constructed by co-adding the individual PSC scans and is\\nconsequently deeper at 12 $\\\\mu$m by approximately one mag; the FSC is considered\\ncomplete to $f_{12}$$>$0.2 Jy. Due to the greater depth of the FSC only those samples\\nconstructed from it will be considered here [5,6 hereafter RMS and FSXH]. In essence\\nnone of these samples are truly compatible with the deeper ISO surveys because they\\napply longer wavelength IRAS colour selection criteria and do not objectively classify\\ngalaxies. Some of these samples additionally suffer from inaccurate source flux\\nestimation, no correction for the overdensity due to large scale structure and\\ninaccurate K-correction. Due to the lack of space here these latter two points are not\\nconsidered although we refer the interested reader to [6,14] for excellent coverage of\\nthese problems.\\n\\n\\n\\\\subsection{The colour selection problem}\\n\\nSelecting objects at 12 $\\\\mu$m without colour selection will produce an abundance of\\nstars over galaxies due to the Jeans tail of stellar emission. Without exception every\\nextragalactic 12 $\\\\mu$m sample to date has had (the majority of) stars removed by\\napplying longer wavelength IRAS colour criteria. This technique is clearly\\nincompatible with ISO surveys where no colour criterium is applied and will cause a\\nbias towards dusty galaxies. This also enforces that every galaxy must have a longer\\nwavelength flux, producing incompleteness even within the selection boundaries. For\\nexample, in RMS the primary selection is $f_{12}$$>$0.22 Jy but every galaxy must also\\nhave $f_{60}$$>$0.5$f_{12}$ or $f_{100}$$>$$f_{12}$. However due to the completeness\\nof FSC ($f_{60}$$>$0.2 Jy and $f_{100}$$>$0.6 Jy) this sample cannot be complete for\\n$f_{12}$$<$0.4 Jy or $f_{12}$$<$0.6Jy respectively. \\n\\n\\n\\\\subsection{The classification problem}\\n\\nTo produce accurate extragalactic luminosity functions and understand the galaxy\\ncontributions to fainter source counts it is necessary to classify galaxies in an\\nobjective way, the most common technique is with optical line ratios [7,8]. To date\\nthe only classified 12 $\\\\mu$m sample is RMS although their classification was taken\\nfrom various catalogues which differ in the definition of extragalactic type and\\ncompleteness. As a comparison to this classification we have obtained line ratios from\\nthe literature for 349 of the 483 RMS galaxies with $\\\\delta$$>$0 degrees. This gives\\ncompletenesses of 72\\\\%, 78\\\\% and 93\\\\% for objects $f_{12}$$>$0.22, 0.3 and 0.5 Jy\\nrespectively. Due to the spectroscopic incompleteness at lower fluxes and the colour\\nselection incompleteness we only consider those of $f_{12}$$>$0.5 Jy here, see table\\n1; our classification follows that of [7,9]. \\n\\n\\n\\\\begin{table}\\n\\\\centering\\n\\\\caption{Extragalactic classification}\\n\\\\renewcommand{\\\\arraystretch}{1.4}\\n\\\\setlength\\\\tabcolsep{5pt}\\n\\\\begin{tabular}{llllll}\\n\\\\hline\\\\noalign{\\\\smallskip}\\n & AGN & LINER & HII \\\\\\\\\\n\\\\noalign{\\\\smallskip}\\n\\\\hline\\n\\\\noalign{\\\\smallskip}\\nRMS & 13\\\\% & 15\\\\% & - \\\\\\\\\\nAA & 16\\\\% & 24\\\\% & 60\\\\% \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\\\label{Tab1a}\\n\\\\end{table}\\n\\n\\nAll galaxies are found to show H$\\\\alpha$ emission although for some galaxies\\nW$_{\\\\lambda}$(H$\\\\alpha$)$<$1 angstrom and they would appear as absorption line objects\\nin lower resolution/signal to noise spectra. Of the HII galaxies, 50\\\\% show evidence\\nfor significant star formation (W$_{\\\\lambda}$(H$\\\\alpha$)$>$10 angstroms). RMS\\nclassified an object as an AGN if it is present in an AGN catalogue. We find a good\\nagreement in classification for this object class, the principal reason for the\\nconstruction of the RMS sample. LINERs were classified in the RMS sample if they were\\npresent in an AGN catalgoue and consequently this sample is thought to be incomplete. \\nWe confirm this here. RMS did not classify HII galaxies although they considered those\\ngalaxies not classified as a LINER or AGN, but with high infrared luminosities, to be\\nstarburst galaxies and all other objects to be normal galaxies. \\n\\n\\\\subsection{The source flux problem}\\n\\nThe FSC detection algorithm has been optimised for unresolved sources therefore fluxes\\nfor extended sources need to be calculated from the coaddition of scans (the ADDSCAN\\ntechnique nowadays accessed via XSCANPI) [10]. However, if a source is unresolved, the\\nflux calculation using this technique leads erroneously to a larger flux than the FSC\\nflux [10]. Whilst FSXH carefully calculate the fluxes of extended and unresolved\\nsources seperately, RMS treat all sources as extended and consequently overestimate\\nthe fluxes of unresolved galaxies; due to the large beamsize of IRAS a large number of\\ngalaxies can be overestimated. The magnitude of this effect can be estimated from\\nISOCAM observations. Unfortunately only a few observations are available for the lw10\\nfilter (the closest to the IRAS 12 $\\\\mu$m band) therefore in order to predict the IRAS\\n12 $\\\\mu$m fluxes we have used observations in the lw2 (6.7 $\\\\mu$m) and lw3 (14.3\\n$\\\\mu$m) bands and a spectral decomposition technique similar to that described in\\n[11]. In this simple model the mid-infrared emission is produced by two components:\\nHII regions (using M17 [12]) and photo-dissociation regions (PDR) (using NGC7023\\n[13]). The ratio of HII to PDR is calculated from the ratio of lw2 to lw3 fluxes, a\\nsynthetic spectra is produced and the IRAS 12 $\\\\mu$m flux is calculated. This\\ntechnique will be somewhat imprecise due to the uncertainty of the CAM photometry and\\nthe ability of the model to reproduce the galactic spectrum. Overall we estimate an\\nuncertainty of $\\\\sim$20\\\\%, roughly equal to the worst error in the FSC photometry. In\\nfigure 1 we plot our predicted fluxes against the FSC and RMS fluxes divided by the\\npredicted flux (i.e. the relative errors in flux).\\n\\n\\n\\\\begin{figure}\\n\\\\centering\\n\\\\includegraphics[width=.6\\\\textwidth]{dma_fig1.eps}\\n\\\\caption[]{12 $\\\\mu$m flux comparison}\\n\\\\label{eps1}\\n\\\\end{figure}\\n\\n\\nOnly those galaxies with z$>$2,500 kms$^{-1}$ have been plotted as they should all be\\nunresolved in the IRAS beam. In general a good agreement between the predicted flux\\nand FSC flux is found leading us to believe that the true fluxes for these objects are\\nclose to the FSC flux. Consequently RMS may be overpredicting the source flux for\\n$\\\\sim$50\\\\% of their objects. This will have the effect of shifting galaxies from faint\\nflux/luminosity bins to higher bins causing unpredictable effects in the source count\\nand luminosity function determinations. \\n\\n\\n\\\\section{A new IRAS 12 $\\\\mu$m sample}\\n\\nOur new IRAS 12 $\\\\mu$m sample aims to address these problems and create a local\\ninfrared sample that is compatible with ISO surveys. The sample definition is close to\\nthat of RMS: sources are taken from the FSC for those objects with $|$b$|$$>$25\\ndegrees, $f_{12}$$>$0.2 Jy and a moderate or good quality detection (S/N$>$3). This\\nselection results in 31002 objects, by comparison the RMS colour selection bias\\nproduces $\\\\sim$1100 objects. \\n\\nOur sample provides an interesting complement to the PSC-z extragalactic survey [15]\\nwhich selects those objects from the PSC with $f_{60}$$>$0.6 Jy. As with our sample\\nthey do not apply colour selection criteria, stars are identified on Schmidt plates.\\nIn terms of the extragalactic objects we would expect many galaxies in common although\\nour sample should have a higher fraction of quasars and early type galaxies. \\n\\n\\n\\\\subsection{The stellar infrared diagnostic correlation}\\n\\nBy not applying colour selection to distinguish galaxies from stars we have had to\\ndevise an alternative technique. The key assumption in our technique is that stars\\nhave, in the majority, predictable properties and therefore with the large and\\ncomplete optical stellar databases currently available (in particular the Guide Star\\nCatalogue [16], hereafter GSC) it is possible to find the majority of stars in our\\nsample through positional cross correlation. An important factor here is in\\ndetermining the completeness of an optical stellar catalgoue in an infrared sample,\\nrequiring an understanding of the general optical and infrared characteristics of\\nstars.\\n \\nTo determine these characteristics for our stars we have used SIMBAD, which provides\\nstellar classifications, and produced a large sample ($\\\\sim$9000 objects) of\\nclassified stars. When cross correlationing to optical positions we consider a star\\ncorrelated if its optical position falls within 5$\\\\sigma$ of the IRAS position (the\\nmean major and minor error ellipse axes are 16.9\\\" and 2.0\\\" respectively). The\\nproperties of our classified stellar sample are shown in figure 2. We have only\\nplotted those stars for which there are at least 10 objects in a classified class and\\nonly a subset of these classes are shown here for clarity. A clear correlation between\\nstellar type and flux ratio is found. The predicted black body colours for the\\ndifferent stellar types follows a straight line passing close to the A1V to K5III\\npoints. The interesting deviation observed for stars beyond type MOIII is {\\\\it\\npossibly} due to an increasing amount of stellar absorption in the V band.\\n\\n\\n\\\\begin{figure}\\n\\\\centering\\n\\\\includegraphics[width=.6\\\\textwidth]{dma_fig2.eps}\\n\\\\caption[]{Stellar infrared diagnostic diagram}\\n\\\\label{eps1}\\n\\\\end{figure}\\n\\n\\nThese optical-infrared flux correlations provide an essential tool, the ability to\\npredict the IRAS 12 $\\\\mu$m flux of a star for a given spectral type or B-V colour. In\\nthe cases where we find an IRAS source associated with both a galaxy and a star we\\nwill be able to predict the flux from the star and therefore estimate the flux from\\nthe galaxy.\\n\\n\\n\\\\subsection{Cross correlating stars}\\n\\nThe GSC is considered complete for 6$<$V$<$15 mags over the whole sky. Based on our\\nstellar infrared diagnostic correlation this corresponds to a depth of $f_{12}$$>$0.2\\nJy and therefore any stars earlier than a type M6III in our sample should be in the\\nGSC. However, to accurately cross correlate the positions between the GSC and our\\nsample requires accounting for proper motion. The Schmidt plates for the GSC were\\ntaken in 1975 and 1982, by comparison the mean IRAS observation epoch is 1983.5. By\\nanalysing a sub-sample of Hipparcos stars ($\\\\sim$4000 objects, selected by sky area)\\nwe find a mean proper motion of 0.03\\\"yr$^{-1}$, with a one $\\\\sigma$ maximum of\\n0.13\\\"yr$^{-1}$ (the maximum in the whole catalogue is 6\\\"yr$^{-1}$). Taking into\\naccount the different observation epochs and the mean IRAS error ellipse, virtually\\nall our stars should fall within 5$\\\\sigma$ of their GSC position. \\n\\nWe initially searched for associations by selecting all objects within 2' of the IRAS\\nposition (2' corresponds to $\\\\sim$5$\\\\sigma$ of the mean positional uncertainty in the\\nmajor axis direction) although we only consider a star cross-correlated if it falls\\nwithin 5$\\\\sigma$ of an IRAS source. From this cross correlation we find that over that\\n29000 of our IRAS sources are stars. Of these a small ($\\\\sim$0.5\\\\%), but significant,\\nfraction show a considerable infrared excess ($f_{25}$$>$$f_{12}$) and warrant further\\nstudy.\\n\\n\\n\\\\subsection{Cross correlating galaxies}\\n\\nOur extragalactic cross correlation is performed in a similar manner although the\\nproblems associated with correlating galaxies are somewhat different. Proper motion is\\nnot a problem although the extended size of galaxies is as the peak mid-infrared\\nposition can vary from the peak optical position and therefore some positional\\nuncertainty must be included when trying to correlate an infrared galaxy to an optical\\nsource. Although a 5$\\\\sigma$ positional uncertainty can correspond to 2' if the galaxy\\nlies along the major axis of the IRAS error ellipse it can also correspond to just 10\\\"\\nif the galaxy lies perpendicular to this direction. Therefore we only consider a\\ngalaxy cross correlated if it falls within 10$\\\\sigma$ of an IRAS source. Due to the\\noften unknown incompleteness of extragalactic catalogues it is not possible to\\naccurately determine the completeness of our sample in extragalactic catalogues and\\ntherefore we have simply used the largest (and most appropriate) databases. In the\\ncross correlation presented here we have used the QIGC sample [17], which has just\\nbecome available in electronic form, NED, SIMBAD and the FSC 25 $\\\\mu$m sample [18].\\n\\nUsing these databases we find that over 700 of our sources, not confirmed as stars,\\nfall within our 10$\\\\sigma$ threshold. From these confirmed galaxies we find $\\\\sim$50\\nare elliptical or S0 systems (not all are active galaxies) and $\\\\sim$150 have\\n$f_{12}$$>$$f_{25}$ and are most probably PDR dominated galaxies. A number of galaxies\\nhave $f_{12}$$>$2$f_{60}$ and would therefore not be picked up by RMS. One of these\\ngalaxies is NGC 3115, a nearby bulge dominated galaxy of Hubble type S0. This galaxy\\nis only detected at 12 $\\\\mu$m, the 25, 60 and 100 $\\\\mu$m fluxes are upper limits,\\nalthough with a V band mag of $\\\\sim$8.9 it is bright optical galaxy. In terms of it's\\nB-V (1.0) and B/12 (2.5) colours it corresponds to a K0III star. As a comparison we\\nhave plotted a sample of our {\\\\it normal} infrared galaxies, see figure 3. \\n\\n\\n\\\\begin{figure}\\n\\\\centering\\n\\\\includegraphics[width=.6\\\\textwidth]{dma_fig3.eps}\\n\\\\caption[]{Stellar and galactic colour plot. All confirmed stars are plotted as dots\\nand a selection of normal infrared galaxies are plotted as filled circles. NGC 3115 is\\nnot plotted here but would correspond to the position of a K0III star, see figure 2}\\n\\\\label{eps1} \\n\\\\end{figure}\\n\\n\\n\\\\subsection{Further improvements}\\n\\nAlthough our initial cross correlation has been successful we have $\\\\sim$500 objects\\nfor which we do not have an optical identification. These objects do not have IRAS\\nCirrus/Confused flags or low 12 $\\\\mu$m fluxes although approximately 75\\\\% have upper\\nlimit 60 $\\\\mu$m IRAS fluxes. Visual inspection of a number of these objects with the\\nDigital Sky Survey shows them to be nearby bright stars, suggesting incompleteness in\\nthe GSC at bright fluxes. However there is also probably a substantial population of\\nstars not yet accounted for: those with V$>$15 mags (e.g. M7III and M8III stars),\\ndark molecular clouds and planetary nebulae. We are currently compiling a list of\\nadditional stellar objects to cross correlate to our sample to allow us to produce a\\ndefinitive list of unidentified extragalactic sources.\\n\\n\\n\\\\section{Further work}\\n\\nOur primary aim is to construct complete 12 $\\\\mu$m FSC selected samples of galaxies\\nand stars. From this we will create accurate extragalactic source counts and\\nclassified luminosity functions with optical slit spectroscopy. As many of our\\nextragalactic objects will be extended we also intend to obtain integrated spectra to\\nprovide a classification which is compatible with the distant objects found in ISO\\nsurveys where the observed slit spectra will be produced by the majority of the\\ngalaxy. With our stellar sample we wish to create a complete list of high galactic\\nlatitude stars and sources to help constrain galactic models and provide further\\ndiagnostics in distinguishing stars from galaxies in faint surveys (e.g. the Hubble\\nDeep Field [3]). Both our galactic and stellar samples show objects that deviate from\\nthe norm (i.e. galaxies with stellar colours and stars with galactic colours) and\\nwarrant further study in their own right.\\n\\\\\\\\~\\\\\\\\ \\n{\\\\bf Acknowledgements} We thank I.Matute for assistance in producing the initial\\ncatalogue and M.Moshir for fruitful discussions. We are grateful to O.Laurent and\\nH.Roussel for providing the ISOCAM fluxes for some of the RMS sample sources. We\\nacknowledge and thank the EC TMR extragalactic networks for postdoctoral grant\\nsupport. This research has made use of the NASA/IPAC Extragalactic Database (NED)\\nwhich is operated by the Jet Propoulsion Laboratory, California Institute of\\nTechnology, under contact with NASA.\\n\\n\\n\\n\\\\begin{thebibliography}{7}\\n%\\n\\\\addcontentsline{toc}{section}{References}\\n\\n\\n\\\\bibitem{}\\nElbaz, D., Cesarsky, C., Fadda, D., Aussel, H., D\\\\'esert, F.-X., et al. (1999) A\\\\&A,\\n351, L37\\n\\n\\\\bibitem{}\\nOliver, S., Rowan-Robinson, M., Alexander, D.M., Almaini, O., Balcells, M., et al. \\n(1999), in press\\n\\n\\\\bibitem{}\\nAussel, H., Cesarsky, C., Elbaz, D., Starck, J. (1999) A\\\\&A, 342, 313\\n\\n\\\\bibitem{}\\nClements, D.L., D\\\\'esert, F.-X., Franceschini, A., Reach, W.T., Baker, A.C., Davies,\\nJ.K., Cesarsky, C. (1999) A\\\\&A, 346, 383\\n\\n\\\\bibitem{}\\nRush, B., Malkan, M.A., Spinoglio, L. (1993) ApJS, 89, 1 (RMS)\\n\\n\\\\bibitem{}\\nFang, F., Shupe, D.L., Xu, C., Hacking, P.B. (1998) ApJ, 500, 693 (FSXH)\\n\\n\\\\bibitem{}\\nBaldwin, J.A., Phillips, M.M., Terlevich, R. (1981) PASP, 93, 5\\n\\n\\\\bibitem{} \\nPoggianti, B.M., Smail, I., Dressler, A., Couch, W.J., Barger, A.J., et al. (1999)\\nApJ, 518, 576\\n\\n\\\\bibitem{}\\nHo, L., Filippenko, A.V., Sargent, W.L.W. (1997) ApJS, 326, 653\\n\\n\\\\bibitem{}\\nMoshir, M., et al. (1992) Explanatory Supplement to the IRAS Faint Source Survey, Version\\n2, Pasadena, JPL\\n\\n\\\\bibitem{}\\nTran, Q.D. (1998) PhD thesis, University of Paris, Orsay, France\\n\\n\\\\bibitem{}\\nCesarsky, D., Lequeux, J., Abergel, A., Perault, M., Palazzi, E., Madden, S., Tran, D.\\n(1996) A\\\\&A, 315, L309\\n\\n\\\\bibitem{}\\nCesarsky, D., Lequeux, J., Abergel, A., Perault, M., Palazzi, E., Madden, S., Tran, D.\\n(1996) A\\\\&A, 315, L305\\n\\n\\\\bibitem{}\\nXu, C., Hacking, P.B., Fang, F., Shupe, D.L., Lonsdale, C.J., et al. (1998) ApJ, 508,\\n576\\n\\n\\\\bibitem{}\\nSaunders, W., Oliver, S., Keeble, O., Rowan-Robinson, M., Canavezes, A., et al. (1997)\\nin Maddox, S., Aragon-Salamanca, A., Wide Field Spectroscopy and the Distant Universe,\\nWorld Scientific Press, Singapore\\n\\n\\\\bibitem{}\\nLasker, B.M., Sturch, C.R., McLean, B.J., Russel, J.L., Jenker, H., Shara, M.M. (1990)\\nAJ, 99, 2019\\n\\n\\\\bibitem{}\\nLawrence, A., Rowan-Robinson, M., Ellis, R.S., Frenk. C.S., Efstathiou. G., et al. \\n(1999) MNRAS, 308, 897\\n\\n\\\\bibitem{}\\nShupe, D.L., Fang, F., Hacking, P.B., Huchra, J.P. (1998) ApJ, 501, 597\\n\\n\\n\\n\\\\end{thebibliography}\\n\\n%INDEX%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\clearpage\\n\\\\addcontentsline{toc}{section}{Index}\\n\\\\flushbottom\\n\\\\printindex\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\\\end{document}\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002200.extracted_bib","string":"\\begin{thebibliography}{7}\n%\n\\addcontentsline{toc}{section}{References}\n\n\n\\bibitem{}\nElbaz, D., Cesarsky, C., Fadda, D., Aussel, H., D\\'esert, F.-X., et al. (1999) A\\&A,\n351, L37\n\n\\bibitem{}\nOliver, S., Rowan-Robinson, M., Alexander, D.M., Almaini, O., Balcells, M., et al. \n(1999), in press\n\n\\bibitem{}\nAussel, H., Cesarsky, C., Elbaz, D., Starck, J. (1999) A\\&A, 342, 313\n\n\\bibitem{}\nClements, D.L., D\\'esert, F.-X., Franceschini, A., Reach, W.T., Baker, A.C., Davies,\nJ.K., Cesarsky, C. (1999) A\\&A, 346, 383\n\n\\bibitem{}\nRush, B., Malkan, M.A., Spinoglio, L. (1993) ApJS, 89, 1 (RMS)\n\n\\bibitem{}\nFang, F., Shupe, D.L., Xu, C., Hacking, P.B. (1998) ApJ, 500, 693 (FSXH)\n\n\\bibitem{}\nBaldwin, J.A., Phillips, M.M., Terlevich, R. (1981) PASP, 93, 5\n\n\\bibitem{} \nPoggianti, B.M., Smail, I., Dressler, A., Couch, W.J., Barger, A.J., et al. (1999)\nApJ, 518, 576\n\n\\bibitem{}\nHo, L., Filippenko, A.V., Sargent, W.L.W. (1997) ApJS, 326, 653\n\n\\bibitem{}\nMoshir, M., et al. (1992) Explanatory Supplement to the IRAS Faint Source Survey, Version\n2, Pasadena, JPL\n\n\\bibitem{}\nTran, Q.D. (1998) PhD thesis, University of Paris, Orsay, France\n\n\\bibitem{}\nCesarsky, D., Lequeux, J., Abergel, A., Perault, M., Palazzi, E., Madden, S., Tran, D.\n(1996) A\\&A, 315, L309\n\n\\bibitem{}\nCesarsky, D., Lequeux, J., Abergel, A., Perault, M., Palazzi, E., Madden, S., Tran, D.\n(1996) A\\&A, 315, L305\n\n\\bibitem{}\nXu, C., Hacking, P.B., Fang, F., Shupe, D.L., Lonsdale, C.J., et al. (1998) ApJ, 508,\n576\n\n\\bibitem{}\nSaunders, W., Oliver, S., Keeble, O., Rowan-Robinson, M., Canavezes, A., et al. (1997)\nin Maddox, S., Aragon-Salamanca, A., Wide Field Spectroscopy and the Distant Universe,\nWorld Scientific Press, Singapore\n\n\\bibitem{}\nLasker, B.M., Sturch, C.R., McLean, B.J., Russel, J.L., Jenker, H., Shara, M.M. (1990)\nAJ, 99, 2019\n\n\\bibitem{}\nLawrence, A., Rowan-Robinson, M., Ellis, R.S., Frenk. C.S., Efstathiou. G., et al. \n(1999) MNRAS, 308, 897\n\n\\bibitem{}\nShupe, D.L., Fang, F., Hacking, P.B., Huchra, J.P. (1998) ApJ, 501, 597\n\n\n\n\\end{thebibliography}"}],"string":"[\n {\n \"name\": \"astro-ph0002200.extracted_bib\",\n \"string\": \"\\\\begin{thebibliography}{7}\\n%\\n\\\\addcontentsline{toc}{section}{References}\\n\\n\\n\\\\bibitem{}\\nElbaz, D., Cesarsky, C., Fadda, D., Aussel, H., D\\\\'esert, F.-X., et al. (1999) A\\\\&A,\\n351, L37\\n\\n\\\\bibitem{}\\nOliver, S., Rowan-Robinson, M., Alexander, D.M., Almaini, O., Balcells, M., et al. \\n(1999), in press\\n\\n\\\\bibitem{}\\nAussel, H., Cesarsky, C., Elbaz, D., Starck, J. (1999) A\\\\&A, 342, 313\\n\\n\\\\bibitem{}\\nClements, D.L., D\\\\'esert, F.-X., Franceschini, A., Reach, W.T., Baker, A.C., Davies,\\nJ.K., Cesarsky, C. (1999) A\\\\&A, 346, 383\\n\\n\\\\bibitem{}\\nRush, B., Malkan, M.A., Spinoglio, L. (1993) ApJS, 89, 1 (RMS)\\n\\n\\\\bibitem{}\\nFang, F., Shupe, D.L., Xu, C., Hacking, P.B. (1998) ApJ, 500, 693 (FSXH)\\n\\n\\\\bibitem{}\\nBaldwin, J.A., Phillips, M.M., Terlevich, R. (1981) PASP, 93, 5\\n\\n\\\\bibitem{} \\nPoggianti, B.M., Smail, I., Dressler, A., Couch, W.J., Barger, A.J., et al. (1999)\\nApJ, 518, 576\\n\\n\\\\bibitem{}\\nHo, L., Filippenko, A.V., Sargent, W.L.W. (1997) ApJS, 326, 653\\n\\n\\\\bibitem{}\\nMoshir, M., et al. (1992) Explanatory Supplement to the IRAS Faint Source Survey, Version\\n2, Pasadena, JPL\\n\\n\\\\bibitem{}\\nTran, Q.D. (1998) PhD thesis, University of Paris, Orsay, France\\n\\n\\\\bibitem{}\\nCesarsky, D., Lequeux, J., Abergel, A., Perault, M., Palazzi, E., Madden, S., Tran, D.\\n(1996) A\\\\&A, 315, L309\\n\\n\\\\bibitem{}\\nCesarsky, D., Lequeux, J., Abergel, A., Perault, M., Palazzi, E., Madden, S., Tran, D.\\n(1996) A\\\\&A, 315, L305\\n\\n\\\\bibitem{}\\nXu, C., Hacking, P.B., Fang, F., Shupe, D.L., Lonsdale, C.J., et al. (1998) ApJ, 508,\\n576\\n\\n\\\\bibitem{}\\nSaunders, W., Oliver, S., Keeble, O., Rowan-Robinson, M., Canavezes, A., et al. (1997)\\nin Maddox, S., Aragon-Salamanca, A., Wide Field Spectroscopy and the Distant Universe,\\nWorld Scientific Press, Singapore\\n\\n\\\\bibitem{}\\nLasker, B.M., Sturch, C.R., McLean, B.J., Russel, J.L., Jenker, H., Shara, M.M. (1990)\\nAJ, 99, 2019\\n\\n\\\\bibitem{}\\nLawrence, A., Rowan-Robinson, M., Ellis, R.S., Frenk. C.S., Efstathiou. G., et al. \\n(1999) MNRAS, 308, 897\\n\\n\\\\bibitem{}\\nShupe, D.L., Fang, F., Hacking, P.B., Huchra, J.P. (1998) ApJ, 501, 597\\n\\n\\n\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":198,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002201"},"title":{"kind":"string","value":"\\chandra~ uncovers a hidden Low-Luminosity AGN \\\\ in the radio galaxy Hydra~A (3C~218)"},"authors":{"kind":"list like","value":[{"author":"Rita M. Sambruna"},{"author":"George Chartas"},{"author":"and Michael Eracleous"}],"string":"[\n {\n \"author\": \"Rita M. Sambruna\"\n },\n {\n \"author\": \"George Chartas\"\n },\n {\n \"author\": \"and Michael Eracleous\"\n }\n]"},"abstract":{"kind":"string","value":"We report the detection with \\chandra ~of a Low-Luminosity AGN (LLAGN) in the Low Ionization Emission Line Region (LINER) hosted by Hydra~A, a nearby ($z$=0.0537) powerful FR~I radio galaxy with complex radio and optical morphology. In a 20 ks ACIS-S exposure during the calibration phase of the instrument, a point source is detected at energies $\\gtrsim$ 2 keV at the position of the compact radio core, embedded in diffuse thermal X-ray emission ($kT \\sim 1$ keV) at softer energies. The spectrum of the point source is well fitted by a heavily absorbed power law with intrinsic column density N$_H^{int} \\sim 3 \\times 10^{22}$ \\nh~ and photon index $\\Gamma \\sim 1.7$. The intrinsic (absorption-corrected) luminosity is $L_{2-10~keV} \\sim 1.3 \\times 10^{42}$ \\lum. These results provide strong evidence that an obscured AGN is present in the nuclear region of Hydra~A. We infer that the optical/UV emission of the AGN is mostly hidden by the heavy intrinsic reddening. In order to balance the photon budget of the nebula, we must either postulate that the ionizing spectrum includes a UV bump or invoke and additional power source (shocks in the cooling flow or interaction with the radio jets). Using an indirect estimate of the black hole mass and the X-ray luminosity, we infer that the accretion rate is low, suggesting that the accretion flow is advection dominated. %In this context, the %ionizing radiation from the AGN could power the LINER, if the spectral %energy distribution includes a ``UV bump''. Such a spectral feature %would not be inconsistent with an advection-dominated accretion flow. Finally, our results support current unification schemes for radio-loud sources, in particular the presence of the putative molecular torus in FR~Is. These observations underscore the power of the X-rays and of \\chandra~in the quest for black holes."},"latex":{"kind":"list like","value":[{"name":"hydra_rev.tex","string":"%\\documentstyle[12pt,aasms4]{article}\n%\\documentstyle[12pt,aasms4,flushrt]{article}\n\\documentstyle[11pt,aaspp4,flushrt]{article}\n% \\received{} \\accepted{~~}\n\n\\def\\oiii{[{\\sc O\\, iii}]}\n\\def\\oii{[{\\sc O\\, ii}]}\n\\def\\feka{Fe K$\\alpha$}\n\\def\\chandra{{\\it Chandra}} \n\\def\\asca{{\\it ASCA}} \n\\def\\rosat{{\\it ROSAT}} \n\\def\\lum{erg s$^{-1}$}\n\\def\\flux{erg cm$^{-2}$ s$^{-1}$}\n\\def\\nh{cm$^{-2}$}\n\n\\def\\cl{\\centerline}\n%\\input{psfig.tex}\n% in aasms4 use $\\gtrsim$ and $\\lesssim$\n\n\\begin{document}\n\n\\title{\\chandra~ uncovers a hidden Low-Luminosity AGN \\\\ \nin the radio galaxy Hydra~A (3C~218)}\n\n\\author{Rita M. Sambruna, George Chartas, and Michael Eracleous}\n\\affil{The Pennsylvania State University, Department of Astronomy and\nAstrophysics, 525 Davey Lab, State College, PA 16802 (email:\nrms@astro.psu.edu)} \n\n\\author{Richard F. Mushotzky}\n\\affil{NASA/GSFC, Code 662, Greenbelt, MD 20771}\n\n\\author{John A. Nousek} \n\\affil{The Pennsylvania State University, Department of Astronomy and\nAstrophysics, 525 Davey Lab, State College, PA 16802}\n\n\\begin{abstract}\n\nWe report the detection with \\chandra ~of a Low-Luminosity AGN (LLAGN)\nin the Low Ionization Emission Line Region (LINER) hosted by Hydra~A,\na nearby ($z$=0.0537) powerful FR~I radio galaxy with complex radio\nand optical morphology. In a 20 ks ACIS-S exposure during the\ncalibration phase of the instrument, a point source is detected at\nenergies $\\gtrsim$ 2 keV at the position of the compact radio core,\nembedded in diffuse thermal X-ray emission ($kT \\sim 1$ keV) at softer\nenergies. The spectrum of the point source is well fitted by a heavily\nabsorbed power law with intrinsic column density N$_H^{int} \\sim 3\n\\times 10^{22}$ \\nh~ and photon index $\\Gamma \\sim 1.7$. The intrinsic\n(absorption-corrected) luminosity is $L_{2-10~keV} \\sim 1.3 \\times\n10^{42}$ \\lum. These results provide strong evidence that an obscured\nAGN is present in the nuclear region of Hydra~A. We infer that the\noptical/UV emission of the AGN is mostly hidden by the heavy intrinsic\nreddening. In order to balance the photon budget of the nebula, we\nmust either postulate that the ionizing spectrum includes a UV bump or\ninvoke and additional power source (shocks in the cooling flow or\ninteraction with the radio jets). Using an indirect estimate of the\nblack hole mass and the X-ray luminosity, we infer that the accretion\nrate is low, suggesting that the accretion flow is advection\ndominated. %In this context, the\n%ionizing radiation from the AGN could power the LINER, if the spectral\n%energy distribution includes a ``UV bump''. Such a spectral feature\n%would not be inconsistent with an advection-dominated accretion flow.\nFinally, our results support current unification schemes for\nradio-loud sources, in particular the presence of the putative\nmolecular torus in FR~Is. These observations underscore the power of\nthe X-rays and of \\chandra~in the quest for black holes.\n\n\\end{abstract} \n\n\\noindent {\\underline{\\em Subject Headings:}} Galaxies: active --- \ngalaxies: individual (Hydra A, 3C~218) --- X-rays: galaxies. \n\n\\section{Introduction} \n\nRecent {\\it HST} and ground-based optical observations provided strong\nevidence that many nearby galaxies harbor supermassive black holes\n(e.g., Kormendy \\& Richstone 1995), possibly accreting at\nsub-Eddington luminosities (Fabian \\& Rees 1995). About 40\\% of nearby\nearly-type galaxies exhibit signs of mild nuclear activity, in the\nform of weak non-thermal radio cores (Sadler et al. 1989) and Low\nIonization Emission Lines (LINERs; Heckman 1986; Ho, Fillippenko, \\&\nSargent 1997a). These results collectively suggest that many nearby\ngalaxies may harbor weak nuclear activity in the form of a\nLow-Luminosity Active Galactic Nucleus (LLAGN; e.g., Ho 1999a).\n\nThanks to their high penetrating power, X-rays provide an optimal\nwindow to search for weak nuclear activity. Indeed, previous X-ray\n\\rosat~ images of a handful of galaxies show the presence of a central\nunresolved nucleus within the 5\\arcsec~ HRI resolution (e.g., Fabbiano\n1996). Indirect clues are provided by \\asca~ spectral constraints: a\nheavily absorbed power law component is often measured at energies\n$\\gtrsim 2$ keV, with intrinsic luminosities L$_{2-10~keV} \\sim\n10^{40-42}$ \\lum~, photon indices $\\Gamma_{2-10~keV} \\sim 1.5-1.7$,\nand a narrow Fe emission line at 6--7 keV in a few cases, suggestive\nof a LLAGN (Makishima et al. 1994; Ptak et al. 1999; Sambruna,\nEracleous, \\& Mushotzky 1999; Terashima et al. 1999). Within the\ncoarse angular resolution of these detectors, alternative scenarios\ncan not be ruled out in many cases (e.g., a starburst or X-ray\nbinaries). Unambiguous evidence for nuclear activity would be provided\nby the detection of a point source at the galaxy center. With its\nunprecedented angular resolution (0.5\\arcsec), wide-band coverage\n(0.2--10 keV), and high sensitivity, \\chandra~ is uniquely suited to\nthis task. \n\nIn this Letter, using recent \\chandra~calibration observations we\ndiscover a LLAGN in the LINER harbored by the nearby cD galaxy Hydra~A\n($z$=0.0537). Host of the powerful FR~I radio source 3C~218, Hydra~A\nis the dominant member of the poor cluster of galaxies A780, and\nfamous for its twin-jet radio morphology (Taylor et al. 1990).\n%and, in the local volume of space, is the second most powerful radio emitter\n%(second only to Cygnus~A). \nThe nuclear region contains a $\\sim$ 6\\arcsec~emission-line nebula\n(Baum et al. 1989; Heckman et al. 1989) and a disk of star formation\n%and lobes of excess blue light are present at $\\sim$ 2--3\\arcsec~on\n%either side of the core, probably due to active star formation\n(McNamara 1995; Melnick, Gopal-Krishna, \\& Terlevich 1997). At the\nposition of the nucleus, a LINER-like optical and UV spectrum is\nobserved (Hansen, J{\\o}rgensen, \\& N{\\o}rgaard-Nielsen 1995), which,\ntogether with the powerful lobe radio emission, led to the\nclassification of Hydra~A as a Weak Line Radio Galaxy (Tadhunter et\nal. 1998). The X-ray emission from Hydra~A in previous {\\it Einstein},\n\\rosat, and \\asca~ images is dominated by the cluster and the inner\n($\\lesssim$ 1.5\\arcmin) cooling flow, with $L^{cluster}_{0.5-4.5~keV}\n\\sim 2 \\times 10^{44}$ \\lum~ (David et al. 1990; Ikebe et al. 1997).\n\nIn the following, we assume a Friedman cosmology with $H_0=75$ km\ns$^{-1}$ Mpc$^{-1}$ and $q_0=0.5$. At the luminosity distance of\nHydra~A (217.46 Mpc), 1\\arcsec=0.95 kpc.\n\n\\section{Observations and Data analysis} \n\nHydra~A was observed with \\chandra~ ACIS-S for 20 ks on 1999 November\n11 at the aimpoint of S3 in faint telemetry mode with 5 CCDs turned\non. \n%For a description of the \\chandra~ payload and the ACIS\n%experiment, see O'Dell \\& Weisskopf (1998) and Lumb et al. (1993). \nThe data were analyzed using the \\verb+EventBrowser+ tool at Penn\nState, and the \\verb+CIAO+ software provided by the \\chandra~X-ray\nCenter. Only events for \\asca~ grades 0, 2, 3, 4, and 6 were\naccepted. The S3 background was rather stable during the observation.\n\nSpectral analysis was performed within \\verb+XSPEC+ v.10.0 using\nresponse files appropriate for the S3 aimpoint and for the epoch of\nthe present observation (\\verb+ccd7_c0.7.15.32.rmf+,\n\\verb+s3_c1_middle.arf+). The spectra were rebinned over the energy\nrange 0.2--6 keV to have a minimum of 20 counts in each bin, to\nvalidate the use of the $\\chi^2$ statistics. With a total count rate\nof $\\sim$ 0.02 c/s, pileup is not a concern. At this time of writing,\nthere appears to be an uncertainty of the order of 10\\% in the total\neffective area of the telescope mirror in the 1--2 keV energy\nrange. Fortunately, for the present analysis the energy range of\ninterest for the nuclear properties is restricted to energies above 2\nkeV, where the AGN component dominates. The errors in the on-axis\neffective area above 2 keV are of the order of 5\\% (Jerius et\nal. 2000). \n\nHydra~A was also observed with ACIS-I for 20 ks in 1999 October 30,\nafter the CCDs suffered radiation damage %due to exposure to collimated\n%high-energy protons from the Van Allen belts. \nresulting in a degradation of the gain and spectral resolution. \n%As a consequence of the increased Charge Transfer Inefficiency, the\n%gain and the spectral resolution of the ACIS-I CCDs were degraded,\n%making spectral analysis of these data difficult. \n%However, since the spectrum of the nucleus turned out to be\n%featureless in 2--6 keV in the ACIS-S data, \nTo improve the signal-to-noise ratio we extracted the ACIS-I spectrum\nof the nucleus in a region of similar size as for the ACIS-S\ndata, and analyzed the data using a position-dependent \n%Using calibration data, we built a position-dependent ACIS-I\nspectral response including an empirical CTI correction. The 2--6 keV\nACIS-I spectrum of the nucleus was fitted simultaneously to the ACIS-S\ndata leaving the intercalibration factors free to vary, giving a ratio\nof the two normalizations of $N_{ACIS-S}/N_{ACIS-I}=1.09 \\pm 0.22$.\n\n\\section{Results} \n\n%\\subsection{ACIS-S images} \n\nFigure 1 shows the S3 image of the central regions of Hydra~A in\n0.2--10 keV, with the VLA radio contours overlayed (Taylor et\nal. 1990). The ACIS-S data were adaptively smoothed using a Gaussian\nfunction with a kernel of 3.5\\arcsec~, and shifted by 3.6\\arcsec~to\nalign the X-ray and radio core and the other X-ray/radio morphology to\nbetter than 0.5\\arcsec. This shift is well within the range of\nuncertainties on the astrometry (0.5\\arcsec -- 5\\arcsec) measured in\nseveral other ACIS observations during the orbital activation and\ncheck-out phases. X-ray emission from the compact radio core is\nreadily apparent, embedded in diffuse soft X-ray emission. In the\n0.2--10 keV band, $\\sim$ 900 counts are detected within\n2.5\\arcsec~from the position of the radio core and the radial profile\nof the X-ray source is extended.\n%The presence of a diffuse soft component around the\n%nucleus in radio-loud sources is well established from previous\n%\\rosat~observations (Worrall \\& Birkinshaw 1994), extending from a few\n%kpc to cluster scales; a possible candidate is the halo of the host\n%galaxy. \nAt energies $\\gtrsim$ 2 keV, the radial profile is point-like and a\ntotal of $\\sim$ 150 counts are collected in 2--10 keV within\n1.5\\arcsec~ (or 80\\% of the total encircled energy). The hard X-ray\npoint source is also present in the 20 ks ACIS-I exposure. Thus, with\n\\chandra~we were able to detect a point-like X-ray source for the\nfirst time in Hydra~A at hard energies, indicating that the core radio\nemission is due to a hidden AGN. Interestingly, no X-ray emission is\ndetected from either the jets or lobes (Fig. 1). On the contrary, the\nextended radio structures appear to occupy regions relatively\ndeficient in X-ray photons. This is opposite to what recently detected\nwith \\chandra~ in the FR~II radio galaxy 3C~295 (Harris et al. 2000).\n\n%Also apparent in Figure 1 are two extended X-ray sources on the S-E\n%(source 1) and E (source 2) side of the nucleus, with source 1\n%matching faint radio emission. Source 1 has X-ray positions\n%$\\alpha^1_X$=09:18:6.2, $\\delta^1_X$=--12:05:47.3 (J2000), and $\\sim$\n%780 counts are detected in 0.2--10 keV within 2.5\\arcsec. Its optical\n%counterpart is a small nearby galaxy (Melnick et al. 1997). Note also\n%the embedded X-ray point source, most likely the ``second optical\n%nucleus'' reported by Ekers \\& Simkin (1983). Source 2 has\n%coordinates $\\alpha^2_X$=09:18:6.1, $\\delta^2_X$=--12:05:41.3 (J2000),\n%$\\sim$ 900 counts, and unclear optical counterpart.\n\nFigure 2 shows the inner 10\\arcsec~ region around the nucleus in\ncontour form, in 3.7--4.3 keV. The nuclear point source is apparent,\ntogether with extended faint emission elongated by $\\sim$ 3\\arcsec~ in\na N-W direction. Note the extension in the same direction in the radio\ncontours (Fig. 1). At roughly this distance, a spot of enhanced blue\nemission was observed in previous $B$ and $U$ band images, identified\nas the bluest edge of a star forming disk (McNamara 1995; Melnick et\nal. 1997). A total of $\\sim$ 260 counts are detected within 2\\arcsec~\nover the 0.2--10 keV band for this region. The study of the starburst\nand of the large-scale X-ray emission in Hydra~A are beyond the scope\nof this paper, and will not be discussed any further (see McNamara et\nal. 2000).\n \n%\\subsection{Nuclear X-ray spectrum} \n\nThe nuclear X-ray spectrum was extracted from a circular region with\nradius 1.5\\arcsec. The background was extracted in an annulus centered\non the nucleus with inner and outer radii 1\\arcmin~ and 1.3\\arcmin,\nrespectively. The cluster contribution in an area similar to the\nnuclear region is small, $\\sim$ 6\\%, while the instrumental and cosmic\nbackground is negligible, $\\sim 2 \\times 10^{-5}$ ph s$^{-1}$\narcsec$^{-2}$. The spectrum was fitted with a two-component model,\nincluding an absorbed power law at energies $\\gtrsim$ 2 keV, and a\nRaymond-Smith thermal plasma at softer energies. This model is a very\ngood description of the ACIS-S data, with $\\chi^2$=17 for 23 degrees\nof freedom. The data and residuals are shown in Figure 3. All\nspectral components in the fit were absorbed by the Galactic column\ndensity, N$_H^{Gal}=4.9 \\times 10^{20}$ cm$^{-2}$ (Dickey \\& Lockman\n1990).\n\n%In this small region, the X-ray contribution of the cooling flow is\n%small: converting from the \\rosat~surface brightness (Ikebe et\n%al. 1997), and assuming the gas is smoothly distributed in the inner\n%0.2\\arcmin~region, the ACIS-S surface brightness is $6.6 \\times\n%10^{-4}$ counts s$^{-1}$ arcsec$^{-2}$ in 0.2--10 keV, or $\\sim 4\n%\\times 10^{-3}$ counts s$^{-1}$ in a region of radius 1.5\\arcsec. This\n%is $\\sim$ 20\\% of the observed total ACIS-S count rate for the nuclear\n%region. \n\nThe fitted parameters of the absorbed power law are rest-frame column\ndensity N$_H^{int}=2.8^{+3.0}_{-1.4} \\times 10^{22}$ \\nh~ and photon\nindex $\\Gamma=1.75^{+1.14}_{-0.20}$ (uncertainties are 90\\% confidence\nfor one parameter of interest, $\\Delta\\chi^2$=2.7). This is the\nspectrum of the hard X-ray point source coincident with the radio core\nin Figure 1. The slope is consistent within 1$\\sigma$ with the average\nvalue measured with \\asca~for other Weak Line Radio Galaxies (WLRGs),\n$\\langle \\Gamma_{2-10~keV} \\rangle =1.49$ and dispersion\n$\\sigma_{\\Gamma}=0.30$ (Sambruna et al. 1999). The observed fluxes are\nF$_{0.2-2~keV} \\sim 9 \\times 10^{-15}$ and F$_{2-10~keV} \\sim 1.8\n\\times 10^{-13}$ \\flux. The intrinsic (absorption-corrected)\nluminosity is L$_{2-10~keV} \\sim 1.2 \\times 10^{42}$ \\lum, at the\nhigh-end of the distribution for WLRGs and LINERs.\n\nThe data require a thermal component at soft energies, with fitted\ntemperature $kT=1.05^{+0.32}_{-0.14}$ keV, consistent with the value\nmeasured for other radio sources with \\rosat~and \\asca~ (Worrall \\&\nBirkinshaw 1994; Sambruna et al. 1999). The abundance was fixed to the\nbest-fit value, 0.1 solar. The observed fluxes are F$_{0.2-2~keV}\n\\sim 3 \\times 10^{-14}$ and F$_{2-10~keV} \\sim 5 \\times 10^{-15}$\n\\flux. A possible origin of the thermal component is the halo of the\nhost galaxy. Indeed, the intrinsic luminosity is L$_{0.2-2~keV} \\sim 2\n\\times 10^{41}$ \\lum, consistent with the values measured for\nelliptical galaxies. Alternatively, the thermal component could be due\nto the cooling flow. \n%if the latter exhibits a local peak due to\n%small-scale ($\\lesssim$ 1.4 kpc) structures.\n\n%We also extracted the spectrum of the starburst component in Figure 2\n%and fitted it with a composite model including the same Raymond-Smith\n%model as for the nucleus, plus an additional thermal plasma component\n%described by \\verb+vmeka+ in \\verb+XSPEC+. The starburst spectrum is\n%very hot, $kT_{starb} \\gtrsim 5$ keV, and requires overabundant Ne\n%($A_{Ne} \\sim 34$ solar). This is similar to what measured with {\\it\n%SAX} for NGC~253 (Cappi et al. 1999). The spectral parameters are not\n%well determined as only $\\sim$ 260 counts were detected. The\n%absorption-corrected luminosities of the starburst are $L_{0.2-2~keV}\n%\\sim 1.5 \\times 10^{41}$ and $L_{2-10~keV} \\sim 2.7 \\times 10^{41}$\n%\\lum, respectively.\n\n\\section{Discussion and Conclusions}\n\nHydra~A is the second powerful radio galaxy observed with \\chandra,\nand the second instance where a nuclear X-ray point source is\ndetected. A luminous AGN was also discovered in an ACIS-S 20 ks image\nof the FR~II radio galaxy 3C~295 (Harris et al. 2000), with $\\Gamma\n\\sim 1.8$ and $L_{0.2-10~keV} \\sim 7 \\times 10^{43}$ \\lum. As in\nHydra~A, the AGN in 3C~295 resides in a cooling flow. These results\nconfirm that optically-weak, narrow-emission line radio sources harbor\ntrue AGNs as their brighter, broad-emission line Seyfert-like \ncounterparts. Thanks to \\chandra, a detailed study of the central\nengines of these systems becomes possible for the first time.\n\nThe large X-ray column density we measure in the nucleus of Hydra~A,\nN$_H^{int} \\sim 3 \\times 10^{22}$ \\nh, implies an optical extinction\n$A_V=10$, assuming galactic gas-to-dust ratios (Bohlin, Savage, \\&\nDrake 1978). This means that the optical and UV continuum from the AGN\nare strongly (factor $\\gtrsim 300$) suppressed, accounting for why the\nAGN was not previously detected at these wavelengths. The weak UV\ncontinuum detected in archival IUE spectra (Hansen et al. 1995 and our\nown inspection of an unpublished spectrum) cannot be due to the AGN;\nmost likely candidates are the starburst and/or the cooling flow.\nFuture {\\it HST} observations should detect only an extended thermal\ncomponent to the UV light.\n \nWe now turn to the issue of whether the LLAGN is capable of\nphotoionizing the emission-line nebula identified with the nucleus\n(Baum et al. 1989; Heckman et al. 1989). To make this assessment we\nfirst evaluate the total reddening to the nuclear emission-line\nsource, $E_{\\rm B-V}$. Since the nuclear spectrum resembles that of\nLINERs, we assume that the intrinsic Balmer decrement is\nH$\\alpha$/H$\\beta=3.1$ (e.g., Ho, Filippenko, \\& Sargent 1997b), leading\nto an estimate of $E_{\\rm B-V}\\approx 0.33$\\footnote{This is\nconsiderably higher than $E_{\\rm B-V}=0.15$ given by Hansen et\nal. (1995) based on the Ly$\\alpha$/H$\\beta$ ratio. Hansen et al. have\nprobably underestimated the reddening because the Ly$\\alpha$ flux was\nmeasured in the large IUE aperture which very likely includes a\ncontribution from the circumnuclear starburst region.}. With this\nvalue of the reddening and the H$\\beta$ flux measured by Hansen et\nal. (1995) we obtain the rate of emission of H$\\beta$ photons from the\nnebula as $Q_{\\rm H\\beta}=4.1\\times 10^{51}$~s$^{-1}$. If the H$\\beta$\nemission is the result of case~B recombination, then atomic physics\nimplies $Q_{\\rm H\\beta}=0.12\\; Q_{\\rm ion}$ (Osterbrock 1989), where\n$Q_{\\rm ion}$ is the ionizing photon rate from the active nucleus.\nThus, the observed H$\\beta$ flux requires that $Q_{\\rm ion}=(3.4\\times\n10^{52}/f_{\\rm c})$~s$^{-1}$, where $f_{\\rm c}$ is the covering\nfraction of the source by the nebula. In contrast, the observed\nionizing photon rate, assuming that the X-ray power-law spectrum\nextends all the way through the UV band, is $Q_{\\rm ion}=1.1\\times\n10^{52}$~s$^{-1}$, which falls short of the required rate by a\nconsiderable factor, even if $f_{\\rm c}=1$! In fact, if we model the\nspectral energy distribution (SED) of Hydra A after those observed in\nLINERs and other LLAGN, some of which are radio-loud (Ho 1999b), the\nproblem persists.\n\nIn order to balance the photon budget of the nebula, we must either\npostulate that the ionizing spectrum includes a UV bump or invoke and\nadditional power source. If we assume there is a UV bump, we can\nparameterize it following Mathews \\& Ferland (1987) and normalize the\nSED according to the \\chandra~ X-ray spectrum. We then find an\nionizing photon output rate of $Q_{\\rm ion}=6.4\\times\n10^{53}$~s$^{-1}$, which is more than enough to power the emission\nlines. \n% The UV bump may be somewhat weaker than the model of Mathews \\&\n% Ferland (1987) so as not to overproduce the rate of ionizing photons.\n% More specifically, if we adopt a covering factor for the\n% emission-line gas of $f_{\\rm c}=0.1$, then the UV bump must be about\n% a factor of 2 weaker than the model prescription. But even in this\n% case, the UV bump must be stronger than what is observed in the\n% LLAGNs of the Ho (1999b) collection. \nOn the other hand, one or more other power sources may contribute to\nthe ionization of the nebula. X-rays from shocks in the cooling flow\nare plausible (e.g., Heckman et al. 1989). Another possibility is\nmechanical interaction of the emission-line gas with the radio jets,\nwhich is particularly relevant since the images of Hansen et\nal. (1995) show superpositions of radio and emission-line knots.\n\nTo get a handle on the nature of the accretion flow, we compared the\nX-ray luminosity to the limiting Eddington luminosity through a rough\nestimate of the central black hole mass in Hydra~A, $M_{BH}$. The\napparent $V$ magnitude of the host galaxy in Hydra~A, $m_V=13.7$\n(Sandage 1973), and Figure 8 of Magorrian et al. (1998) imply $M_{BH}\n\\sim 4 \\times 10^9 M_{\\odot}$, consistent with the values dynamically\nmeasured in other giant ellipticals (e.g., Ford et al. 1994). The\nEddington luminosity is thus $L_{Edd} \\sim 5 \\times 10^{47}$\n\\lum. Assuming $L_X=0.1 L_{total}$, the luminosity relative to\nEddington is $L_{total}/L_{Edd} \\sim 2 \\times 10^{-5}$. This places\nHydra~A in the regime of an Advection-Dominated Accretion Flow (ADAF;\ne.g., Narayan, Mahadevan, \\& Quataert 1998), similar to other WLRGs\n(Sambruna et al. 1999). A powerful diagnostic of the accretion flow\nstructure in Hydra~A will be afforded by future higher-sensitivity\nX-ray observations, such as delivered by {\\it XMM}. The EPIC spectrum\nwill allow us to study in more detail the nuclear X-ray properties, in\nparticular whether an Fe line is present at 6--7 keV. The line energy\nand profile could allow us to discriminate between a standard\nSeyfert-like disk and an ADAF (e.g., Sambruna \\& Eracleous 1999).\n\n% The presence of an ADAF in Hydra~A does not preclude a modest UV\n% bump in the case where the transition radius between the ADAF and\n% the thin disk is rather small (of order a few tens of gravitational\n% radii; see the models of Gammie, Narayan \\& Blandford 1999). \n\nFinally, we note that the nuclear X-ray absorption in Hydra~A is much\nlarger (factor 10) than the optical/UV extinction to the emission-line\nnebula (see above), and consistent with the column measured in the\nradio toward the core (Taylor 1996). This suggests that the X-ray\nabsorber lies further in than the emission-line regions, close to the\ncentral black hole. A possible candidate is the molecular torus on\nparsec scales postulated by unification models (Urry \\& Padovani\n1995). Indeed, the radio and optical observations indicate an edge-on\ngeometry for Hydra~A (Taylor et al. 1990; Baum et al. 1989), such that\nthe torus intercepts the line of sight to the nucleus. Our results\nthus support current unification models for radio-loud sources and in\nparticular the presence of an obscuring torus in FR~I radio\ngalaxies. Clearly, large unbiased samples are needed to reach firmer\nconclusions, which we anticipate from \\chandra~in the next few years.\n\n%This result apparently contradicts a\n%recent claim, based on optical {\\it HST} data, that the nuclear\n%regions of FR~Is are not obscured (Chiaberge, Capetti, \\& Celotti\n%1999). Clearly, large unbiased samples are needed to reach firmer\n%conclusions, which we anticipate from \\chandra~in the next few years.\n\n%In conclusion, using \\chandra~data we discovered an obscured LLAGN in\n%the nearby LINER source Hydra~A. The AGN is bright enough to provide\n%at least half the photons needed to power the optical emission\n%lines. Our results support current unification models for radio-loud\n%sources and in particular the presence of an obscuring torus in FR~I\n%radio galaxies. \n\n% The present observations are a clear testimonial to the power of\n% X-rays in the quest for black holes. We can confidently anticipate\n% that in the next few years of operation, \\chandra~will truly\n% revolutionize our perception of nuclear activity in galaxies, with\n% profound implications for the AGN luminosity function, the origin of\n% the X-ray background, and the connection between AGNs and normal\n% galaxies.\n\n\\acknowledgements\n\nRMS acknowledges support from NASA contract NAS--38252. We are\ngrateful to Gordon Garmire and the ACIS team for making these\nobservations possible. We thank Joe Pesce for help with Figure 2, Niel\nBrandt for the \\verb+ASMOOTH+ routine, and Pat Broos and Scott Koch\nfor assistance with data retrieving and for the \\verb+TARA+ software.\nFinally, we are grateful to the referee, Yuichi Terashima, for his\nprompt and thoughtful comments and suggestions. \n\n\\newpage \n\n\\begin{references}\n\n\\reference {} Baum, S. A., Heckman, T. M., Bridle, A. H., van Breugel,\nW. J. M., \\& Miley, G. K. 1988, ApJS, 68, 833 \n\n\\reference {} Bohlin, R. 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M. \\& Birkinshaw, M. 1994, ApJ, 427, 134 \n\n\\end{references}\n\n\\newpage\n\n\\noindent{\\bf Figure Captions}\n\n\\begin{itemize}\n \n\\item\\noindent Figure 1: \\chandra~ACIS-S image in 0.2--10 keV of the\ncentral regions of Hydra~A, in a 20 ks calibration exposure. Radio VLA\ncontours at 6 cm are overlayed (Taylor et al. 1990). The ACIS-S image\nwas adaptively smoothed using a Gaussian function with a kernel of\n3.5\\arcsec, and shifted by 3.6\\arcsec~in declination to align the\nX-ray and radio core. X-ray emission from the compact radio core is\napparent, embedded in a diffuse halo, while the jets and lobes occupy\nregions deficient of X-rays. \n\n\\item\\noindent Figure 2: Contours of the inner region of Hydra~A at 4\nkeV. North is up and East is to the left. The intensity scale is\nlogarithmic with contour interval 0.4 or a factor 2.5 in\nintensity. The nuclear point source is apparent. A faint extended\nstructure is also present at $\\sim$ 3\\arcsec~ N-W of the nucleus,\nroughly at the position of the star formation region previously\ndetected in optical images (McNamara 1995; Melnick et al. 1997).\n\n\\item\\noindent Figure 3: The \\chandra~spectrum of the nuclear region\nin Hydra~A, extracted in a region of radius 1.5\\arcsec. The top panel\nshows the data convolved with the best-fit model, a highly absorbed\npower law at energies $\\gtrsim$ 2 keV and a soft thermal component\n(dotted lines). The bottom panel are the residuals in the form of\nratio of the data to the model. Crosses are ACIS-S data, asterisks are\nACIS-I data.\n\n\\end{itemize}\n\n\\end{document} \n\n\n"}],"string":"[\n {\n \"name\": \"hydra_rev.tex\",\n \"string\": \"%\\\\documentstyle[12pt,aasms4]{article}\\n%\\\\documentstyle[12pt,aasms4,flushrt]{article}\\n\\\\documentstyle[11pt,aaspp4,flushrt]{article}\\n% \\\\received{} \\\\accepted{~~}\\n\\n\\\\def\\\\oiii{[{\\\\sc O\\\\, iii}]}\\n\\\\def\\\\oii{[{\\\\sc O\\\\, ii}]}\\n\\\\def\\\\feka{Fe K$\\\\alpha$}\\n\\\\def\\\\chandra{{\\\\it Chandra}} \\n\\\\def\\\\asca{{\\\\it ASCA}} \\n\\\\def\\\\rosat{{\\\\it ROSAT}} \\n\\\\def\\\\lum{erg s$^{-1}$}\\n\\\\def\\\\flux{erg cm$^{-2}$ s$^{-1}$}\\n\\\\def\\\\nh{cm$^{-2}$}\\n\\n\\\\def\\\\cl{\\\\centerline}\\n%\\\\input{psfig.tex}\\n% in aasms4 use $\\\\gtrsim$ and $\\\\lesssim$\\n\\n\\\\begin{document}\\n\\n\\\\title{\\\\chandra~ uncovers a hidden Low-Luminosity AGN \\\\\\\\ \\nin the radio galaxy Hydra~A (3C~218)}\\n\\n\\\\author{Rita M. Sambruna, George Chartas, and Michael Eracleous}\\n\\\\affil{The Pennsylvania State University, Department of Astronomy and\\nAstrophysics, 525 Davey Lab, State College, PA 16802 (email:\\nrms@astro.psu.edu)} \\n\\n\\\\author{Richard F. Mushotzky}\\n\\\\affil{NASA/GSFC, Code 662, Greenbelt, MD 20771}\\n\\n\\\\author{John A. Nousek} \\n\\\\affil{The Pennsylvania State University, Department of Astronomy and\\nAstrophysics, 525 Davey Lab, State College, PA 16802}\\n\\n\\\\begin{abstract}\\n\\nWe report the detection with \\\\chandra ~of a Low-Luminosity AGN (LLAGN)\\nin the Low Ionization Emission Line Region (LINER) hosted by Hydra~A,\\na nearby ($z$=0.0537) powerful FR~I radio galaxy with complex radio\\nand optical morphology. In a 20 ks ACIS-S exposure during the\\ncalibration phase of the instrument, a point source is detected at\\nenergies $\\\\gtrsim$ 2 keV at the position of the compact radio core,\\nembedded in diffuse thermal X-ray emission ($kT \\\\sim 1$ keV) at softer\\nenergies. The spectrum of the point source is well fitted by a heavily\\nabsorbed power law with intrinsic column density N$_H^{int} \\\\sim 3\\n\\\\times 10^{22}$ \\\\nh~ and photon index $\\\\Gamma \\\\sim 1.7$. The intrinsic\\n(absorption-corrected) luminosity is $L_{2-10~keV} \\\\sim 1.3 \\\\times\\n10^{42}$ \\\\lum. These results provide strong evidence that an obscured\\nAGN is present in the nuclear region of Hydra~A. We infer that the\\noptical/UV emission of the AGN is mostly hidden by the heavy intrinsic\\nreddening. In order to balance the photon budget of the nebula, we\\nmust either postulate that the ionizing spectrum includes a UV bump or\\ninvoke and additional power source (shocks in the cooling flow or\\ninteraction with the radio jets). Using an indirect estimate of the\\nblack hole mass and the X-ray luminosity, we infer that the accretion\\nrate is low, suggesting that the accretion flow is advection\\ndominated. %In this context, the\\n%ionizing radiation from the AGN could power the LINER, if the spectral\\n%energy distribution includes a ``UV bump''. Such a spectral feature\\n%would not be inconsistent with an advection-dominated accretion flow.\\nFinally, our results support current unification schemes for\\nradio-loud sources, in particular the presence of the putative\\nmolecular torus in FR~Is. These observations underscore the power of\\nthe X-rays and of \\\\chandra~in the quest for black holes.\\n\\n\\\\end{abstract} \\n\\n\\\\noindent {\\\\underline{\\\\em Subject Headings:}} Galaxies: active --- \\ngalaxies: individual (Hydra A, 3C~218) --- X-rays: galaxies. \\n\\n\\\\section{Introduction} \\n\\nRecent {\\\\it HST} and ground-based optical observations provided strong\\nevidence that many nearby galaxies harbor supermassive black holes\\n(e.g., Kormendy \\\\& Richstone 1995), possibly accreting at\\nsub-Eddington luminosities (Fabian \\\\& Rees 1995). About 40\\\\% of nearby\\nearly-type galaxies exhibit signs of mild nuclear activity, in the\\nform of weak non-thermal radio cores (Sadler et al. 1989) and Low\\nIonization Emission Lines (LINERs; Heckman 1986; Ho, Fillippenko, \\\\&\\nSargent 1997a). These results collectively suggest that many nearby\\ngalaxies may harbor weak nuclear activity in the form of a\\nLow-Luminosity Active Galactic Nucleus (LLAGN; e.g., Ho 1999a).\\n\\nThanks to their high penetrating power, X-rays provide an optimal\\nwindow to search for weak nuclear activity. Indeed, previous X-ray\\n\\\\rosat~ images of a handful of galaxies show the presence of a central\\nunresolved nucleus within the 5\\\\arcsec~ HRI resolution (e.g., Fabbiano\\n1996). Indirect clues are provided by \\\\asca~ spectral constraints: a\\nheavily absorbed power law component is often measured at energies\\n$\\\\gtrsim 2$ keV, with intrinsic luminosities L$_{2-10~keV} \\\\sim\\n10^{40-42}$ \\\\lum~, photon indices $\\\\Gamma_{2-10~keV} \\\\sim 1.5-1.7$,\\nand a narrow Fe emission line at 6--7 keV in a few cases, suggestive\\nof a LLAGN (Makishima et al. 1994; Ptak et al. 1999; Sambruna,\\nEracleous, \\\\& Mushotzky 1999; Terashima et al. 1999). Within the\\ncoarse angular resolution of these detectors, alternative scenarios\\ncan not be ruled out in many cases (e.g., a starburst or X-ray\\nbinaries). Unambiguous evidence for nuclear activity would be provided\\nby the detection of a point source at the galaxy center. With its\\nunprecedented angular resolution (0.5\\\\arcsec), wide-band coverage\\n(0.2--10 keV), and high sensitivity, \\\\chandra~ is uniquely suited to\\nthis task. \\n\\nIn this Letter, using recent \\\\chandra~calibration observations we\\ndiscover a LLAGN in the LINER harbored by the nearby cD galaxy Hydra~A\\n($z$=0.0537). Host of the powerful FR~I radio source 3C~218, Hydra~A\\nis the dominant member of the poor cluster of galaxies A780, and\\nfamous for its twin-jet radio morphology (Taylor et al. 1990).\\n%and, in the local volume of space, is the second most powerful radio emitter\\n%(second only to Cygnus~A). \\nThe nuclear region contains a $\\\\sim$ 6\\\\arcsec~emission-line nebula\\n(Baum et al. 1989; Heckman et al. 1989) and a disk of star formation\\n%and lobes of excess blue light are present at $\\\\sim$ 2--3\\\\arcsec~on\\n%either side of the core, probably due to active star formation\\n(McNamara 1995; Melnick, Gopal-Krishna, \\\\& Terlevich 1997). At the\\nposition of the nucleus, a LINER-like optical and UV spectrum is\\nobserved (Hansen, J{\\\\o}rgensen, \\\\& N{\\\\o}rgaard-Nielsen 1995), which,\\ntogether with the powerful lobe radio emission, led to the\\nclassification of Hydra~A as a Weak Line Radio Galaxy (Tadhunter et\\nal. 1998). The X-ray emission from Hydra~A in previous {\\\\it Einstein},\\n\\\\rosat, and \\\\asca~ images is dominated by the cluster and the inner\\n($\\\\lesssim$ 1.5\\\\arcmin) cooling flow, with $L^{cluster}_{0.5-4.5~keV}\\n\\\\sim 2 \\\\times 10^{44}$ \\\\lum~ (David et al. 1990; Ikebe et al. 1997).\\n\\nIn the following, we assume a Friedman cosmology with $H_0=75$ km\\ns$^{-1}$ Mpc$^{-1}$ and $q_0=0.5$. At the luminosity distance of\\nHydra~A (217.46 Mpc), 1\\\\arcsec=0.95 kpc.\\n\\n\\\\section{Observations and Data analysis} \\n\\nHydra~A was observed with \\\\chandra~ ACIS-S for 20 ks on 1999 November\\n11 at the aimpoint of S3 in faint telemetry mode with 5 CCDs turned\\non. \\n%For a description of the \\\\chandra~ payload and the ACIS\\n%experiment, see O'Dell \\\\& Weisskopf (1998) and Lumb et al. (1993). \\nThe data were analyzed using the \\\\verb+EventBrowser+ tool at Penn\\nState, and the \\\\verb+CIAO+ software provided by the \\\\chandra~X-ray\\nCenter. Only events for \\\\asca~ grades 0, 2, 3, 4, and 6 were\\naccepted. The S3 background was rather stable during the observation.\\n\\nSpectral analysis was performed within \\\\verb+XSPEC+ v.10.0 using\\nresponse files appropriate for the S3 aimpoint and for the epoch of\\nthe present observation (\\\\verb+ccd7_c0.7.15.32.rmf+,\\n\\\\verb+s3_c1_middle.arf+). The spectra were rebinned over the energy\\nrange 0.2--6 keV to have a minimum of 20 counts in each bin, to\\nvalidate the use of the $\\\\chi^2$ statistics. With a total count rate\\nof $\\\\sim$ 0.02 c/s, pileup is not a concern. At this time of writing,\\nthere appears to be an uncertainty of the order of 10\\\\% in the total\\neffective area of the telescope mirror in the 1--2 keV energy\\nrange. Fortunately, for the present analysis the energy range of\\ninterest for the nuclear properties is restricted to energies above 2\\nkeV, where the AGN component dominates. The errors in the on-axis\\neffective area above 2 keV are of the order of 5\\\\% (Jerius et\\nal. 2000). \\n\\nHydra~A was also observed with ACIS-I for 20 ks in 1999 October 30,\\nafter the CCDs suffered radiation damage %due to exposure to collimated\\n%high-energy protons from the Van Allen belts. \\nresulting in a degradation of the gain and spectral resolution. \\n%As a consequence of the increased Charge Transfer Inefficiency, the\\n%gain and the spectral resolution of the ACIS-I CCDs were degraded,\\n%making spectral analysis of these data difficult. \\n%However, since the spectrum of the nucleus turned out to be\\n%featureless in 2--6 keV in the ACIS-S data, \\nTo improve the signal-to-noise ratio we extracted the ACIS-I spectrum\\nof the nucleus in a region of similar size as for the ACIS-S\\ndata, and analyzed the data using a position-dependent \\n%Using calibration data, we built a position-dependent ACIS-I\\nspectral response including an empirical CTI correction. The 2--6 keV\\nACIS-I spectrum of the nucleus was fitted simultaneously to the ACIS-S\\ndata leaving the intercalibration factors free to vary, giving a ratio\\nof the two normalizations of $N_{ACIS-S}/N_{ACIS-I}=1.09 \\\\pm 0.22$.\\n\\n\\\\section{Results} \\n\\n%\\\\subsection{ACIS-S images} \\n\\nFigure 1 shows the S3 image of the central regions of Hydra~A in\\n0.2--10 keV, with the VLA radio contours overlayed (Taylor et\\nal. 1990). The ACIS-S data were adaptively smoothed using a Gaussian\\nfunction with a kernel of 3.5\\\\arcsec~, and shifted by 3.6\\\\arcsec~to\\nalign the X-ray and radio core and the other X-ray/radio morphology to\\nbetter than 0.5\\\\arcsec. This shift is well within the range of\\nuncertainties on the astrometry (0.5\\\\arcsec -- 5\\\\arcsec) measured in\\nseveral other ACIS observations during the orbital activation and\\ncheck-out phases. X-ray emission from the compact radio core is\\nreadily apparent, embedded in diffuse soft X-ray emission. In the\\n0.2--10 keV band, $\\\\sim$ 900 counts are detected within\\n2.5\\\\arcsec~from the position of the radio core and the radial profile\\nof the X-ray source is extended.\\n%The presence of a diffuse soft component around the\\n%nucleus in radio-loud sources is well established from previous\\n%\\\\rosat~observations (Worrall \\\\& Birkinshaw 1994), extending from a few\\n%kpc to cluster scales; a possible candidate is the halo of the host\\n%galaxy. \\nAt energies $\\\\gtrsim$ 2 keV, the radial profile is point-like and a\\ntotal of $\\\\sim$ 150 counts are collected in 2--10 keV within\\n1.5\\\\arcsec~ (or 80\\\\% of the total encircled energy). The hard X-ray\\npoint source is also present in the 20 ks ACIS-I exposure. Thus, with\\n\\\\chandra~we were able to detect a point-like X-ray source for the\\nfirst time in Hydra~A at hard energies, indicating that the core radio\\nemission is due to a hidden AGN. Interestingly, no X-ray emission is\\ndetected from either the jets or lobes (Fig. 1). On the contrary, the\\nextended radio structures appear to occupy regions relatively\\ndeficient in X-ray photons. This is opposite to what recently detected\\nwith \\\\chandra~ in the FR~II radio galaxy 3C~295 (Harris et al. 2000).\\n\\n%Also apparent in Figure 1 are two extended X-ray sources on the S-E\\n%(source 1) and E (source 2) side of the nucleus, with source 1\\n%matching faint radio emission. Source 1 has X-ray positions\\n%$\\\\alpha^1_X$=09:18:6.2, $\\\\delta^1_X$=--12:05:47.3 (J2000), and $\\\\sim$\\n%780 counts are detected in 0.2--10 keV within 2.5\\\\arcsec. Its optical\\n%counterpart is a small nearby galaxy (Melnick et al. 1997). Note also\\n%the embedded X-ray point source, most likely the ``second optical\\n%nucleus'' reported by Ekers \\\\& Simkin (1983). Source 2 has\\n%coordinates $\\\\alpha^2_X$=09:18:6.1, $\\\\delta^2_X$=--12:05:41.3 (J2000),\\n%$\\\\sim$ 900 counts, and unclear optical counterpart.\\n\\nFigure 2 shows the inner 10\\\\arcsec~ region around the nucleus in\\ncontour form, in 3.7--4.3 keV. The nuclear point source is apparent,\\ntogether with extended faint emission elongated by $\\\\sim$ 3\\\\arcsec~ in\\na N-W direction. Note the extension in the same direction in the radio\\ncontours (Fig. 1). At roughly this distance, a spot of enhanced blue\\nemission was observed in previous $B$ and $U$ band images, identified\\nas the bluest edge of a star forming disk (McNamara 1995; Melnick et\\nal. 1997). A total of $\\\\sim$ 260 counts are detected within 2\\\\arcsec~\\nover the 0.2--10 keV band for this region. The study of the starburst\\nand of the large-scale X-ray emission in Hydra~A are beyond the scope\\nof this paper, and will not be discussed any further (see McNamara et\\nal. 2000).\\n \\n%\\\\subsection{Nuclear X-ray spectrum} \\n\\nThe nuclear X-ray spectrum was extracted from a circular region with\\nradius 1.5\\\\arcsec. The background was extracted in an annulus centered\\non the nucleus with inner and outer radii 1\\\\arcmin~ and 1.3\\\\arcmin,\\nrespectively. The cluster contribution in an area similar to the\\nnuclear region is small, $\\\\sim$ 6\\\\%, while the instrumental and cosmic\\nbackground is negligible, $\\\\sim 2 \\\\times 10^{-5}$ ph s$^{-1}$\\narcsec$^{-2}$. The spectrum was fitted with a two-component model,\\nincluding an absorbed power law at energies $\\\\gtrsim$ 2 keV, and a\\nRaymond-Smith thermal plasma at softer energies. This model is a very\\ngood description of the ACIS-S data, with $\\\\chi^2$=17 for 23 degrees\\nof freedom. The data and residuals are shown in Figure 3. All\\nspectral components in the fit were absorbed by the Galactic column\\ndensity, N$_H^{Gal}=4.9 \\\\times 10^{20}$ cm$^{-2}$ (Dickey \\\\& Lockman\\n1990).\\n\\n%In this small region, the X-ray contribution of the cooling flow is\\n%small: converting from the \\\\rosat~surface brightness (Ikebe et\\n%al. 1997), and assuming the gas is smoothly distributed in the inner\\n%0.2\\\\arcmin~region, the ACIS-S surface brightness is $6.6 \\\\times\\n%10^{-4}$ counts s$^{-1}$ arcsec$^{-2}$ in 0.2--10 keV, or $\\\\sim 4\\n%\\\\times 10^{-3}$ counts s$^{-1}$ in a region of radius 1.5\\\\arcsec. This\\n%is $\\\\sim$ 20\\\\% of the observed total ACIS-S count rate for the nuclear\\n%region. \\n\\nThe fitted parameters of the absorbed power law are rest-frame column\\ndensity N$_H^{int}=2.8^{+3.0}_{-1.4} \\\\times 10^{22}$ \\\\nh~ and photon\\nindex $\\\\Gamma=1.75^{+1.14}_{-0.20}$ (uncertainties are 90\\\\% confidence\\nfor one parameter of interest, $\\\\Delta\\\\chi^2$=2.7). This is the\\nspectrum of the hard X-ray point source coincident with the radio core\\nin Figure 1. The slope is consistent within 1$\\\\sigma$ with the average\\nvalue measured with \\\\asca~for other Weak Line Radio Galaxies (WLRGs),\\n$\\\\langle \\\\Gamma_{2-10~keV} \\\\rangle =1.49$ and dispersion\\n$\\\\sigma_{\\\\Gamma}=0.30$ (Sambruna et al. 1999). The observed fluxes are\\nF$_{0.2-2~keV} \\\\sim 9 \\\\times 10^{-15}$ and F$_{2-10~keV} \\\\sim 1.8\\n\\\\times 10^{-13}$ \\\\flux. The intrinsic (absorption-corrected)\\nluminosity is L$_{2-10~keV} \\\\sim 1.2 \\\\times 10^{42}$ \\\\lum, at the\\nhigh-end of the distribution for WLRGs and LINERs.\\n\\nThe data require a thermal component at soft energies, with fitted\\ntemperature $kT=1.05^{+0.32}_{-0.14}$ keV, consistent with the value\\nmeasured for other radio sources with \\\\rosat~and \\\\asca~ (Worrall \\\\&\\nBirkinshaw 1994; Sambruna et al. 1999). The abundance was fixed to the\\nbest-fit value, 0.1 solar. The observed fluxes are F$_{0.2-2~keV}\\n\\\\sim 3 \\\\times 10^{-14}$ and F$_{2-10~keV} \\\\sim 5 \\\\times 10^{-15}$\\n\\\\flux. A possible origin of the thermal component is the halo of the\\nhost galaxy. Indeed, the intrinsic luminosity is L$_{0.2-2~keV} \\\\sim 2\\n\\\\times 10^{41}$ \\\\lum, consistent with the values measured for\\nelliptical galaxies. Alternatively, the thermal component could be due\\nto the cooling flow. \\n%if the latter exhibits a local peak due to\\n%small-scale ($\\\\lesssim$ 1.4 kpc) structures.\\n\\n%We also extracted the spectrum of the starburst component in Figure 2\\n%and fitted it with a composite model including the same Raymond-Smith\\n%model as for the nucleus, plus an additional thermal plasma component\\n%described by \\\\verb+vmeka+ in \\\\verb+XSPEC+. The starburst spectrum is\\n%very hot, $kT_{starb} \\\\gtrsim 5$ keV, and requires overabundant Ne\\n%($A_{Ne} \\\\sim 34$ solar). This is similar to what measured with {\\\\it\\n%SAX} for NGC~253 (Cappi et al. 1999). The spectral parameters are not\\n%well determined as only $\\\\sim$ 260 counts were detected. The\\n%absorption-corrected luminosities of the starburst are $L_{0.2-2~keV}\\n%\\\\sim 1.5 \\\\times 10^{41}$ and $L_{2-10~keV} \\\\sim 2.7 \\\\times 10^{41}$\\n%\\\\lum, respectively.\\n\\n\\\\section{Discussion and Conclusions}\\n\\nHydra~A is the second powerful radio galaxy observed with \\\\chandra,\\nand the second instance where a nuclear X-ray point source is\\ndetected. A luminous AGN was also discovered in an ACIS-S 20 ks image\\nof the FR~II radio galaxy 3C~295 (Harris et al. 2000), with $\\\\Gamma\\n\\\\sim 1.8$ and $L_{0.2-10~keV} \\\\sim 7 \\\\times 10^{43}$ \\\\lum. As in\\nHydra~A, the AGN in 3C~295 resides in a cooling flow. These results\\nconfirm that optically-weak, narrow-emission line radio sources harbor\\ntrue AGNs as their brighter, broad-emission line Seyfert-like \\ncounterparts. Thanks to \\\\chandra, a detailed study of the central\\nengines of these systems becomes possible for the first time.\\n\\nThe large X-ray column density we measure in the nucleus of Hydra~A,\\nN$_H^{int} \\\\sim 3 \\\\times 10^{22}$ \\\\nh, implies an optical extinction\\n$A_V=10$, assuming galactic gas-to-dust ratios (Bohlin, Savage, \\\\&\\nDrake 1978). This means that the optical and UV continuum from the AGN\\nare strongly (factor $\\\\gtrsim 300$) suppressed, accounting for why the\\nAGN was not previously detected at these wavelengths. The weak UV\\ncontinuum detected in archival IUE spectra (Hansen et al. 1995 and our\\nown inspection of an unpublished spectrum) cannot be due to the AGN;\\nmost likely candidates are the starburst and/or the cooling flow.\\nFuture {\\\\it HST} observations should detect only an extended thermal\\ncomponent to the UV light.\\n \\nWe now turn to the issue of whether the LLAGN is capable of\\nphotoionizing the emission-line nebula identified with the nucleus\\n(Baum et al. 1989; Heckman et al. 1989). To make this assessment we\\nfirst evaluate the total reddening to the nuclear emission-line\\nsource, $E_{\\\\rm B-V}$. Since the nuclear spectrum resembles that of\\nLINERs, we assume that the intrinsic Balmer decrement is\\nH$\\\\alpha$/H$\\\\beta=3.1$ (e.g., Ho, Filippenko, \\\\& Sargent 1997b), leading\\nto an estimate of $E_{\\\\rm B-V}\\\\approx 0.33$\\\\footnote{This is\\nconsiderably higher than $E_{\\\\rm B-V}=0.15$ given by Hansen et\\nal. (1995) based on the Ly$\\\\alpha$/H$\\\\beta$ ratio. Hansen et al. have\\nprobably underestimated the reddening because the Ly$\\\\alpha$ flux was\\nmeasured in the large IUE aperture which very likely includes a\\ncontribution from the circumnuclear starburst region.}. With this\\nvalue of the reddening and the H$\\\\beta$ flux measured by Hansen et\\nal. (1995) we obtain the rate of emission of H$\\\\beta$ photons from the\\nnebula as $Q_{\\\\rm H\\\\beta}=4.1\\\\times 10^{51}$~s$^{-1}$. If the H$\\\\beta$\\nemission is the result of case~B recombination, then atomic physics\\nimplies $Q_{\\\\rm H\\\\beta}=0.12\\\\; Q_{\\\\rm ion}$ (Osterbrock 1989), where\\n$Q_{\\\\rm ion}$ is the ionizing photon rate from the active nucleus.\\nThus, the observed H$\\\\beta$ flux requires that $Q_{\\\\rm ion}=(3.4\\\\times\\n10^{52}/f_{\\\\rm c})$~s$^{-1}$, where $f_{\\\\rm c}$ is the covering\\nfraction of the source by the nebula. In contrast, the observed\\nionizing photon rate, assuming that the X-ray power-law spectrum\\nextends all the way through the UV band, is $Q_{\\\\rm ion}=1.1\\\\times\\n10^{52}$~s$^{-1}$, which falls short of the required rate by a\\nconsiderable factor, even if $f_{\\\\rm c}=1$! In fact, if we model the\\nspectral energy distribution (SED) of Hydra A after those observed in\\nLINERs and other LLAGN, some of which are radio-loud (Ho 1999b), the\\nproblem persists.\\n\\nIn order to balance the photon budget of the nebula, we must either\\npostulate that the ionizing spectrum includes a UV bump or invoke and\\nadditional power source. If we assume there is a UV bump, we can\\nparameterize it following Mathews \\\\& Ferland (1987) and normalize the\\nSED according to the \\\\chandra~ X-ray spectrum. We then find an\\nionizing photon output rate of $Q_{\\\\rm ion}=6.4\\\\times\\n10^{53}$~s$^{-1}$, which is more than enough to power the emission\\nlines. \\n% The UV bump may be somewhat weaker than the model of Mathews \\\\&\\n% Ferland (1987) so as not to overproduce the rate of ionizing photons.\\n% More specifically, if we adopt a covering factor for the\\n% emission-line gas of $f_{\\\\rm c}=0.1$, then the UV bump must be about\\n% a factor of 2 weaker than the model prescription. But even in this\\n% case, the UV bump must be stronger than what is observed in the\\n% LLAGNs of the Ho (1999b) collection. \\nOn the other hand, one or more other power sources may contribute to\\nthe ionization of the nebula. X-rays from shocks in the cooling flow\\nare plausible (e.g., Heckman et al. 1989). Another possibility is\\nmechanical interaction of the emission-line gas with the radio jets,\\nwhich is particularly relevant since the images of Hansen et\\nal. (1995) show superpositions of radio and emission-line knots.\\n\\nTo get a handle on the nature of the accretion flow, we compared the\\nX-ray luminosity to the limiting Eddington luminosity through a rough\\nestimate of the central black hole mass in Hydra~A, $M_{BH}$. The\\napparent $V$ magnitude of the host galaxy in Hydra~A, $m_V=13.7$\\n(Sandage 1973), and Figure 8 of Magorrian et al. (1998) imply $M_{BH}\\n\\\\sim 4 \\\\times 10^9 M_{\\\\odot}$, consistent with the values dynamically\\nmeasured in other giant ellipticals (e.g., Ford et al. 1994). The\\nEddington luminosity is thus $L_{Edd} \\\\sim 5 \\\\times 10^{47}$\\n\\\\lum. Assuming $L_X=0.1 L_{total}$, the luminosity relative to\\nEddington is $L_{total}/L_{Edd} \\\\sim 2 \\\\times 10^{-5}$. This places\\nHydra~A in the regime of an Advection-Dominated Accretion Flow (ADAF;\\ne.g., Narayan, Mahadevan, \\\\& Quataert 1998), similar to other WLRGs\\n(Sambruna et al. 1999). A powerful diagnostic of the accretion flow\\nstructure in Hydra~A will be afforded by future higher-sensitivity\\nX-ray observations, such as delivered by {\\\\it XMM}. The EPIC spectrum\\nwill allow us to study in more detail the nuclear X-ray properties, in\\nparticular whether an Fe line is present at 6--7 keV. The line energy\\nand profile could allow us to discriminate between a standard\\nSeyfert-like disk and an ADAF (e.g., Sambruna \\\\& Eracleous 1999).\\n\\n% The presence of an ADAF in Hydra~A does not preclude a modest UV\\n% bump in the case where the transition radius between the ADAF and\\n% the thin disk is rather small (of order a few tens of gravitational\\n% radii; see the models of Gammie, Narayan \\\\& Blandford 1999). \\n\\nFinally, we note that the nuclear X-ray absorption in Hydra~A is much\\nlarger (factor 10) than the optical/UV extinction to the emission-line\\nnebula (see above), and consistent with the column measured in the\\nradio toward the core (Taylor 1996). This suggests that the X-ray\\nabsorber lies further in than the emission-line regions, close to the\\ncentral black hole. A possible candidate is the molecular torus on\\nparsec scales postulated by unification models (Urry \\\\& Padovani\\n1995). Indeed, the radio and optical observations indicate an edge-on\\ngeometry for Hydra~A (Taylor et al. 1990; Baum et al. 1989), such that\\nthe torus intercepts the line of sight to the nucleus. Our results\\nthus support current unification models for radio-loud sources and in\\nparticular the presence of an obscuring torus in FR~I radio\\ngalaxies. Clearly, large unbiased samples are needed to reach firmer\\nconclusions, which we anticipate from \\\\chandra~in the next few years.\\n\\n%This result apparently contradicts a\\n%recent claim, based on optical {\\\\it HST} data, that the nuclear\\n%regions of FR~Is are not obscured (Chiaberge, Capetti, \\\\& Celotti\\n%1999). Clearly, large unbiased samples are needed to reach firmer\\n%conclusions, which we anticipate from \\\\chandra~in the next few years.\\n\\n%In conclusion, using \\\\chandra~data we discovered an obscured LLAGN in\\n%the nearby LINER source Hydra~A. The AGN is bright enough to provide\\n%at least half the photons needed to power the optical emission\\n%lines. Our results support current unification models for radio-loud\\n%sources and in particular the presence of an obscuring torus in FR~I\\n%radio galaxies. \\n\\n% The present observations are a clear testimonial to the power of\\n% X-rays in the quest for black holes. We can confidently anticipate\\n% that in the next few years of operation, \\\\chandra~will truly\\n% revolutionize our perception of nuclear activity in galaxies, with\\n% profound implications for the AGN luminosity function, the origin of\\n% the X-ray background, and the connection between AGNs and normal\\n% galaxies.\\n\\n\\\\acknowledgements\\n\\nRMS acknowledges support from NASA contract NAS--38252. We are\\ngrateful to Gordon Garmire and the ACIS team for making these\\nobservations possible. 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M. \\\\& Birkinshaw, M. 1994, ApJ, 427, 134 \\n\\n\\\\end{references}\\n\\n\\\\newpage\\n\\n\\\\noindent{\\\\bf Figure Captions}\\n\\n\\\\begin{itemize}\\n \\n\\\\item\\\\noindent Figure 1: \\\\chandra~ACIS-S image in 0.2--10 keV of the\\ncentral regions of Hydra~A, in a 20 ks calibration exposure. Radio VLA\\ncontours at 6 cm are overlayed (Taylor et al. 1990). The ACIS-S image\\nwas adaptively smoothed using a Gaussian function with a kernel of\\n3.5\\\\arcsec, and shifted by 3.6\\\\arcsec~in declination to align the\\nX-ray and radio core. X-ray emission from the compact radio core is\\napparent, embedded in a diffuse halo, while the jets and lobes occupy\\nregions deficient of X-rays. \\n\\n\\\\item\\\\noindent Figure 2: Contours of the inner region of Hydra~A at 4\\nkeV. North is up and East is to the left. The intensity scale is\\nlogarithmic with contour interval 0.4 or a factor 2.5 in\\nintensity. The nuclear point source is apparent. A faint extended\\nstructure is also present at $\\\\sim$ 3\\\\arcsec~ N-W of the nucleus,\\nroughly at the position of the star formation region previously\\ndetected in optical images (McNamara 1995; Melnick et al. 1997).\\n\\n\\\\item\\\\noindent Figure 3: The \\\\chandra~spectrum of the nuclear region\\nin Hydra~A, extracted in a region of radius 1.5\\\\arcsec. The top panel\\nshows the data convolved with the best-fit model, a highly absorbed\\npower law at energies $\\\\gtrsim$ 2 keV and a soft thermal component\\n(dotted lines). The bottom panel are the residuals in the form of\\nratio of the data to the model. Crosses are ACIS-S data, asterisks are\\nACIS-I data.\\n\\n\\\\end{itemize}\\n\\n\\\\end{document} \\n\\n\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[],"string":"[]"}}},{"rowIdx":199,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002202"},"title":{"kind":"string","value":"Recent Advances in Binary Star Formation Using SPH"},"authors":{"kind":"list like","value":[{"author":"M. R. Bate"}],"string":"[\n {\n \"author\": \"M. R. Bate\"\n }\n]"},"abstract":{"kind":"string","value":"We review recent advances in the study of binary star formation that have been made using the smoothed particle hydrodynamics technique."},"latex":{"kind":"list like","value":[{"name":"proc.tex","string":"%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% %\n% Proceedings of 20 years of Numerical Astrophysics Template %\n% You can use it with the academic press style file which %\n% can be found at (http://www.apnet.com/www/journal/cp.htm). %\n% %\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\documentclass{cjour}\n\\usepackage{epsfig}\n\\textheight= 22.0cm\n\\voffset=2.0mm\n\n\\def\\simless{\\mathbin{\\lower 2pt\\hbox\n {$\\rlap{\\raise 5pt\\hbox{$\\char'074$}}\\mathchar\"7218$}}} % < or of order\n\\def\\simgreat{\\mathbin{\\lower 2pt\\hbox\n {$\\rlap{\\raise 5pt\\hbox{$\\char'076$}}\\mathchar\"7218$}}} % > or of order\n\n\\authorrunninghead{M. R. Bate}\n\\titlerunninghead{Recent Advances in Binary Star Formation Using SPH}\n\n\\begin{document}\n\n\\title{Recent Advances in Binary Star Formation Using SPH}\n\n%\\subtitle{This is a subtitle if you wish to include one.}\n\n\\author{Matthew R. Bate}\n\\affil{Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, United Kingdom}\n\\email{mbate@ast.cam.ac.uk}\n%\\and\n%\\author{While The Second Author is}\n%\\affil{From Somewhere else.}\n%\\email{secondauthor@somewhere.else}\n\n\\abstract{We review recent advances in the study of binary star formation that have been made using the smoothed particle hydrodynamics technique.}\n\n\\begin{article}\n\n%% Section headings:\n\\section{Introduction}\n \nThe Smoothed Particle Hydrodynamics (SPH) numerical method \nwas introduced by Lucy \\cite{Lucy77} and \nGingold and Monaghan \\cite{GinMon77}. Its first application\nwas in the field of star formation, where it was used to \nstudy whether or not a rapidly-rotating polytrope could undergo\nfission to form a close binary system \\cite{Lucy77, GinMon78}.\nSince this initial application, SPH has been widely used in the\nstudy of star formation, for example \\cite{GinMon81, \nMiyHayNar84, Lattanzioetal85, Durisenetal86, SigKla97, \nBonBas91, BatBonPri95, Heller93, NelPap93, ArtLub94,\nLarwoodetal96, Nelsonetal98, VanCam98, \nChapmanetal92}.\n\nSPH is has many attributes which make it particularly \nwell suited to the study of star formation.\nSPH is Lagrangian and does not require a computational grid.\nThus, it can efficiently follow problems with large density \ncontrasts since computational effort is not wasted simulating \nthe low-density regions. Also, recent SPH implementations \n\\cite{Evrard88, HerKat89, Benz90, Monaghan92} use spatially \nand temporally varying smoothing lengths so that the resolution \nincreases automatically with increasing density; the complex \nmulti-grid and adaptive-grid schemes that are used for \nfinite difference methods are avoided.\n\nIn this proceedings, we review some of the recent advances\nin the study of binary star formation that have been made using \nSPH. In Section \\ref{jeansmass}, we discuss the importance of\nalways resolving the Jeans mass in numerical studies of self-gravitating\ngas. While this has been demonstrated using various types of \nhydrodynamic code, we concentrate specifically on the problems\nthat can arise if this criterion is not obeyed with SPH.\nIn Section \\ref{collstellar}, we demonstrate that, for the first time, \nit is now possible to perform three-dimensional hydrodynamic \ncalculations which follow the collapse of a molecular cloud \ncore to stellar densities. These calculations are performed with\nSPH. Finally, in Section \\ref{accretion}, \nwe discuss how SPH has been used to study the evolution of a \nprotobinary system as it accretes from an infalling gaseous \nenvelope and how this work can lead to predictions\nof the properties of binary stars.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig01.eps, width=13cm}\n\\caption{\\label{bate.forces} The ratio of the gravitational force \nto pressure force between two SPH particles in a Jeans-mass\nclump of gas of radius $R=h$. The gravitational softening length\nis $\\epsilon$ and the hydrodynamic smoothing length is $h$.}\n\\end{center}\n\\end{figure}\n\n\\section{The Importance of Resolving the Jeans Mass}\n\\label{jeansmass}\n\nIt has recently been realised that it is important that the Jeans\nmass/length is always resolved during a hydrodynamical calculation. \nThis has been demonstrated both with SPH \\cite{BatBur97, Whitworth98}\nand with grid-based codes \\cite{Trueloveetal97, Trueloveetal98, Boss98}. \nIf this criterion is not obeyed, artificial \nfragmentation can be induced, or fragmentation can be inhibited. \nEssentially this is because when the resolution length/mass \napproaches the Jeans length/mass, collapse is artificially delayed\ndue to viscous forces, softening of gravitational forces, or a combination\nof both. A good example is the collapse of an isothermal \nfilament \\cite{Trueloveetal97}. Such a filament should collapse\nwithout limit to a filamentary singularity without fragmenting. \nHowever, if the collapse perpendicular to the major-axis is delayed, small\ndensity perturbations along the filament may have enough time to grow \nto non-linear amplitudes and fragments may\nform along the bar.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig02.eps, width=10cm}\n\\caption{\\label{bate.massden} Maximum density versus time for during the\ncollapse of a molecular cloud core [8]. Three calculations were \nperformed using SPH with $\\epsilon=h$. The smoothing\nlengths were allowed to vary with time and space freely (solid line) or \nsubject to\na minimum length of 5\\% (dotted line) or 10 \\% (dashed line) of the\ninitial cloud radius. When the minimum Jeans length in the \ncalculation is less than or approximately equal to the smoothing/softening\nlength, the collapse is delayed.\n}\n\\end{center}\n\\end{figure}\n\nBate \\& Burkert \\cite{BatBur97} first demonstrated the need for the\nJeans mass criterion using self-gravitating SPH calculations. With\nSPH, the problem can be understood by considering the \ngravitational and pressure forces between two particles \nwithin a marginally Jeans-stable clump of gas of radius $R\\approx h$\n(Figure \\ref{bate.forces}). SPH codes typically soften \nthe gravitational forces between neighbouring particles, using either \nthe Plummer force law or kernel softening \n\\cite{GinMon77, HerKat89, Benz90}. The\ncharacteristic gravitational softening length, $\\epsilon$, \nmay or may not be equal to the SPH hydrodynamic smoothing \nlength, $h$, depending on the specific implementation.\nIf $\\epsilon=h$, the ratio of the gravitational and \npressure forces between two particles is approximately \nconstant for particle with separations $\\simless h$.\nThus, a Jeans-unstable clump of gas will collapse, while a \nJeans-stable clump will be supported. However, although the\nratio of the gravitational and pressure forces is approximately \nindependent of the separation of the particles, the magnitude \nof the gravitational force decreases with separation due to \nthe softening. Thus, while a Jeans-unstable clump of gas with \na size much larger than the resolution length, $h$, \nwill collapse at the correct rate, the collapse of clumps with \na size $\\approx h$ will be delayed. This is demonstrated\nin Figure \\ref{bate.massden}. \n\nUnfortunately, the effect is not always limited to a simple delay of \nthe collapse. Given the right problem, artificial fragmentation\ncan be induced (such as with the filament described above), \nor inhibited. In Figure \\ref{bate.80000} we show how the collapse\nof a particular molecular cloud core with an initial $m=2$ \ndensity perturbation results in a binary protostellar system\nwith a bar of gas between them. This calculation was performed\nwith $8\\times 10^4$ particles, enough to resolved the Jeans mass/length\nuntil after the binary had formed. However, performing\nthe same calculation with $1\\times 10^4$ particles gives a different\nresult: a single, dense bar of gas without the binary. In this \ncalculation, the Jeans mass becomes unresolved before $t=1.20$\nand the collapse of each of the two over-dense regions resulting from the \noriginal $m=2$ density perturbation is delayed. The collapse of the\nlarger-scale elongated region, however, continues, leading to \nthe formation of a bar rather than a binary.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig03.eps, width=12.5cm}\n\\vspace{0.25truecm}\n\\caption{\\label{bate.80000} Collapse and fragmentation of a \nmolecular cloud core to form a binary [8]. The initial cloud had an initial\n10\\% $m=2$ density perturbation. The local Jeans mass/length is unresolved\ninside the thick density contour. The calculation was performed\nwith $8\\times 10^4$ particles.\n}\n\\vspace{-0.5truecm}\n\\end{center}\n\\end{figure}\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig04.eps, width=12.5cm}\n\\vspace{0.25truecm}\n\\caption{\\label{bate.10000} Same as Figure 3, except that the calculation\nwas performed with $1\\times 10^4$ particles. When $t \\simgreat 1.20$,\nthe region within which the binary formed in the $8\\times 10^4$-particle\ncalculation becomes unresolved, collapse of the two over-dense\nregions is delayed, and the calculation eventually produces a dense\nbar instead of a binary.\n}\n\\vspace{-1.0truecm}\n\\end{center}\n\\end{figure}\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig05.eps, width=12.5cm}\n\\vspace{0.25truecm}\n\\caption{\\label{bate.10000eh} Same as Figure 4, except that the calculation\nwas performed with $\\epsilon=1.0\\times 10^{14}$ cm (i.e.~$e h$, the pressure forces\nbetween particles within a Jeans-unstable clump may exceed the \ngravitational forces and the clump will be artificially supported\nagainst collapse.\n\nClearly, the best SPH implementation is one where $\\epsilon=h$ always.\nIn this case, collapse of Jeans-unstable clumps with a size \nsimilar to that of the resolution length will still be \ndelayed, but the possibilities of\nartificial collapse within Jeans-stable clumps or the supporting\nof Jeans-unstable clumps against collapse are eliminated. Then,\nin order to avoid the collapse of Jeans-unstable clumps being\ndelayed significantly, enough particles should be used so that\nthe Jeans length/mass is always resolved. \n\nHow many particles\nare necessary to ensure that the Jeans length/mass is resolved?\nWith SPH, the spatial resolution \nis given by the smoothing length which is usually variable in \ntime and space. The smoothing lengths are set by ensuring that \neach particle contains a certain number of neighbours, \n$N_{\\rm neigh}$, or equivalently a fixed mass, within two \nsmoothing lengths. Thus, in contrast to a grid-based code \nwhich has spatially-limited resolution, SPH has mass-limited \nresolution which {\\it automatically} gives greater spatial \nresolution in regions of higher density. Therefore, with SPH,\nit is necessary to ensure that the minimum resolvable mass is \nalways less than the Jeans mass. In practice, Bate \\& Burkert \nfound that a Jeans mass should always \nbe represented by at least $\\approx 2 N_{\\rm neigh}$ particles. \n\\newpage\n\n\\section{Collapse of a Molecular Cloud to Stellar Densities}\n\\label{collstellar}\n\nThe mass-limited resolution of SPH is ideal for studying the \ncollapse and fragmentation of molecular cloud cores because \nthere is a minimum Jeans mass in the problem \n(Figure \\ref{bate.tmr}). By contrast,\nthere is no minimum Jeans length. This is a problem \nfor grid-based codes which must resort to nested or \nadaptive grids \\cite{ BurBod93, Trueloveetal97, Trueloveetal98}. \nWith SPH, if the number of \nparticles used is sufficient to resolve the minimum Jeans mass, a \ncalculation can be followed to arbitrary densities with the required\nspatial resolution given automatically with increasing density.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig06.eps, width=12cm}\n\\caption{\\label{bate.tmr} The gas temperature $T$ (solid line), Jeans \nmass $M_{\\rm J}$ (dotted line), and Jeans radius $R_{\\rm J}$ (dashed \nline), as a function of density in a collapsing molecular cloud core \n(adapted from Tohline [36]). The minimum Jeans mass of \n$ \\approx 4 \\times 10^{-4}~{\\rm M}_{\\odot}$ occurs \nat a density of $\\sim 10^{-3} {\\rm \\ g \\ cm}^{-3}$.}\n\\end{center}\n\\end{figure}\n\n\nRecently, this ability of SPH was used to perform the first \nthree-dimensional calculations ever to follow the collapse of\na molecular cloud core to stellar densities \\cite{Bate98}.\nThe calculations followed the collapse of an initially \nuniform-density molecular cloud core of mass $M=1 {\\rm \\ M}_\\odot$ and\nradius $R=7 \\times 10^{16} {\\rm \\ cm}$.\n\nThe minimum resolvable mass in the SPH code was \n$\\approx 2 N_{\\rm neigh} = 100$ particles. Thus, to enable the\nminimum Jeans mass during the calculation\n($\\approx 4 \\times 10^{-4}\\ {\\rm M}_{\\odot}$)\nto be resolved, the calculation used $3 \\times 10^5$ \nequal-mass particles.\n\nThe code did not include radiative transfer. Instead, to model \nthe behaviour of the gas during the different phases of collapse,\na piece-wise polytropic equation of state, $P=K \\rho^{\\gamma}$, was\nused, where $P$ is the pressure, $\\rho$ is the density, $K$ \ngives the entropy of the gas, and the ratio of specific heats, \n$\\gamma$, was varied as\n\\begin{equation}\n\\label{polytropic}\n\\gamma = \\cases {\\begin{array}{lll}\n1 & & \\rho \\leq 1.0 \\times 10^{-13} \\cr\n7/5 & \\ 1.0 \\times 10^{-13} < \\hspace{-6pt} & \\rho \\leq 5.7 \\times 10^{-8} \n\\cr\n1.15 & \\ 5.7 \\times 10^{-8\\ } < \\hspace{-6pt} & \\rho < 1.0 \\times 10^{-3} \\cr\n5/3 & & \\rho > 1.0 \\times 10^{-3} \\cr\n\\end{array}}\n\\end{equation}\nwhere the densities are in ${\\rm g\\ cm}^{-3}$ \n(see Figure \\ref{bate.tmr}).\nThe values of $\\gamma$ and the transition densities \nwere derived from Tohline \\cite{Tohline82}. The variable value of $\\gamma$ \nmimics the following behaviour of the gas. The\ncollapse is isothermal ($\\gamma=1$) until the gas becomes optically thick \nto infrared radiation \nat $\\rho \\approx 10^{-13} {\\rm \\ g \\ cm}^{-3}$, beyond which $\\gamma=7/5$\n(appropriate for a diatomic gas).\nWhen the gas reaches a temperature of $\\approx$ 2000 K \n($\\rho = 5.7 \\times 10^{-8} {\\rm \\ g \\ cm}^{-3}$), molecular \nhydrogen begins to dissociate and the temperature only slowly increases\nwith density. In this phase $\\gamma = 1.15$ is used to \nmodel {\\it both} the decreasing mean molecular weight and the slow increase \nof temperature with density, the latter of which has an effective \n$\\gamma \\approx 1.10$.\nFinally, when the gas has fully dissociated\n($\\rho \\approx 10^{-3} {\\rm \\ g \\ cm}^{-3}$), the gas is monatomic and\n$\\gamma=5/3$. The value of $K$ is\ndefined such that when the gas is isothermal, $K = c_{\\rm s}^2$\nwith $c_{\\rm s} = 2.0 \\times 10^4 {\\rm \\ cm\\ s^{-1}}$, and when $\\gamma$\nchanges the pressure is continuous.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig07.eps, width=12.5cm}\n\\caption{\\label{bate.static} Radial density and velocity profiles of \nthe collapsing molecular cloud core with the one-dimensional grid \ncode (solid) and the three-dimensional SPH code (dotted). \nThe profiles are compared when the central density in each calculation \nis a) $10^{-14}$, b) $10^{-11}$, c) $10^{-9}$, d) $10^{-6}$, \ne) $10^{-3}$, and f) $10^{-1}$ g cm$^{-3}$.}\n\\end{center}\n\\end{figure}\n\n\\subsection{Collapse of an initially-static cloud}\n\nTo test that the above equation of state captures the important elements\nof the gas's behaviour, spherically-symmetric,\none-dimensional (1-D), finite-difference calculations were performed\nof the collapse of an initially-static molecular cloud core \nwith the above parameters and equation of state.\nThe results are shown in Figure \\ref{bate.static} (solid line). \nThese results \nare in good agreement with the results from 1-D calculations \nincorporating radiative transfer \n(e.g.\\ Larson 1969; Winkler \\& Newman 1980a, b).\n\nThe three-dimensional (3-D) SPH code was also tested on the same \nproblem to check that the SPH code can indeed accurately resolve the \ncollapse down to stellar densities \n(Figure \\ref{bate.static}, dotted line). \nThere is excellent agreement between the results from the 1-D \nfinite-difference code and those from the 3-D SPH code.\n\n\n\\subsection{Collapse of a rotating cloud}\n\nThree-dimensional calculations are required if the molecular\ncloud core is rotating. In Figures \\ref{bate.rotmassdens} to\n\\ref{bate.finalstate2} we present results from the collapse\nof a cloud core which is identical to that in the previous \nsection, but which is initially in solid-body rotation with\nangular frequency $\\Omega=7.6 \\times 10^{-14}$ rad s$^{-1}$.\nThus, the ratio of rotational energy to the magnitude of the \ngravitational potential energy is $\\beta=0.005$ (i.e.~the cloud\nis rotating quite slowly).\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig08.eps, width=12cm}\n\\caption{\\label{bate.rotmassdens} Maximum density (solid line) \nand maximum temperature (dotted line) versus time for the collapsing \nmolecular cloud core. Time is given in units of the initial free-fall \ntime ($t_{\\rm ff}=1.785 \\times 10^{12}$ s). The right graph has \nexpanded axes to show the second collapse phase in greater detail.}\n\\end{center}\n\\end{figure}\n\n\\begin{figure}[b]\n\\begin{center}\n\\vspace{8.4truecm}\n%\\epsfig{file=fig09.eps, width=12cm}\n\\caption{\\label{bate.bar} A time sequence showing the density in \nthe plane perpendicular to the rotation axis during the dynamic, \nrotational, bar instability of the first hydrostatic core. The\npanels cover the period from $t\\approx 1.023-1.030$ t$_{\\rm ff}$.\nSee also the MPEG animation on this CD-ROM: bate1.mpg.\n}\n\\end{center}\n\\end{figure}\n\nThe evolution of the calculation is as follows \n(Figure \\ref{bate.rotmassdens}). \nThe initial collapse is isothermal. When the density surpasses\n$10^{-13}$ g cm$^{-3}$, the gas in the center \nis assumed to become optically thick\nto infrared radiation and begins to heat ($t=1.009~t_{\\rm ff}$).\nThe heating stops the collapse at the center and the first hydrostatic core\nis formed ($t=1.015~t_{\\rm ff}$) with maximum density \n$\\approx 2 \\times 10^{-11}$ g cm$^{-3}$, mass \n$\\approx 0.01 {\\rm \\ M}_\\odot$ ($\\approx 3 \\times 10^3$ particles), and radius \n$\\approx 7$ AU. As the first core accretes, its maximum\ndensity only slowly increases at first.\nHowever, the first core is rapidly rotating, oblate, and has \n$\\beta \\approx 0.34 > 0.274$, making it dynamically unstable to the\ngrowth of non-axisymmetric perturbations \n\\cite{Durisenetal86, ImaDurPic99}. \nAt $t \\approx 1.023~t_{\\rm ff}$, after about 3 rotations, \nthe first core becomes violently bar-unstable\nand forms trailing spiral arms (Figure \\ref{bate.bar}). This leads\nto a rapid increase in maximum density (Figure \\ref{bate.rotmassdens})\nas angular momentum is removed from\nthe central regions of the first core (now a disc with spiral structure) \nby gravitational torques ($t=1.023-1.030~t_{\\rm ff}$). An MPEG animation of \nthis bar instability is provided on this CD-ROM (bate1.mpg).\nWhen the maximum temperature reaches 2000 K, molecular hydrogen begins to\ndissociate, resulting in a rapid second collapse to stellar densities\n($t=1.030~t_{\\rm ff}$). The collapse is again halted at a density of \n$\\approx 0.007$ g cm$^{-3}$ with the formation of the second hydrostatic, \nor stellar, core. The initial mass and radius of the stellar core are \n$\\approx 0.0015 {\\rm \\ M}_\\odot$ ($\\approx 5 \\times 10^2$ particles) \nand $\\approx 0.8 {\\rm \\ R}_\\odot$, \nrespectively. Finally,\nan inner circumstellar disc begins to form around the stellar \nobject, within the region undergoing second collapse. The \ncalculation is stopped when the stellar object has a mass of \n$\\approx 0.004 {\\rm \\ M}_\\odot$ ($\\approx 1.2 \\times 10^3$ particles), \nthe inner circumstellar disc has extended out to $\\approx 0.1$ AU, \nand the outer disc (the remnant of the first hydrostatic core) contains \n$\\approx 0.08 {\\rm \\ M}_\\odot$ ($\\approx 2.4 \\times 10^4$ particles) \nand extends out to $\\approx 70$ AU. Note that the massive outer \ndisc forms {\\it before} the stellar core.\nThis final state is illustrated in Figures \\ref{bate.finalstate}\nand \\ref{bate.finalstate2}.\nIf the calculation was evolved further, the inner circumstellar disc would \ncontinue to grow in radius as gas with higher angular momentum fell in.\nEventually, the inner disc would meet the outer disc with only a\nsmall molecular dissociation region between the two.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig10.eps, width=12cm}\n\\caption{\\label{bate.finalstate} The state of the system at the end of \nthe calculation. The left graph gives the density (solid line) and \nsmoothing length (dashed line) as a function of radius and the mass \nenclosed within radius $r$ of the center of the stellar core (dotted line). \nThe right graph gives the radial (solid line) and rotational (dotted line) \nvelocities as functions of radius from the center of the stellar core. \nThe densities, smoothing lengths and velocities are the mean values in \nthe plane perpendicular to the rotation axis and through the stellar core. \nThe stellar core ($r<0.004$ AU), inner circumstellar disc \n($0.00460$ AU) are clearly visible.}\n\\end{center}\n\\end{figure}\n\n\\begin{figure}[t]\n\\begin{center}\n\\vspace{18.0truecm}\n%\\epsfig{file=fig11.eps, width=12.0cm}\n\\caption{\\label{bate.finalstate2} The state of the system at the end of \nthe calculation (not a time sequence). \nThe upper six panels give the density in the plane \nperpendicular to the rotation axis and through the stellar \ncore. The lower six panels give the density in a \nsection down the rotation axis. In each case, the six consecutive panels \ngive the structure on a spatial scale that is 10 times smaller than the \nprevious panel to resolve structure from 3000 AU to \n$\\approx 0.2~{\\rm R}_\\odot$. The remnant of the first hydrostatic \ncore (now a disc with spiral structure), the inner circumstellar disc, \nand the stellar core are all clearly visible. The logarithm of the \ndensity is plotted with the maximum and minimum \ndensities (in g~cm$^{-3}$) given under each panel. }\n\\vspace{-1.0truecm}\n\\end{center}\n\\end{figure}\n\n\n\\subsection{Close binary stellar systems}\n\nThe ability to perform three-dimensional calculations which follow\nthe collapse of molecular cloud cores to stellar densities allows\nus to study the formation of close ($\\simless 1$ AU) binary\nstellar systems. Currently, there is no accepted mechanism for \nforming close binaries; the proposal that close binary systems form\nvia the fission of a rapidly-rotating protostellar object \nhas been discredited by studies of rapidly-rotating \npolytropes \\cite{Durisenetal86}. Although fission\nitself appears not to operate, it is possible that fragmentation\ncan still occur due to the growth of non-axisymmetric perturbations\nin rotationally-supported objects. Only two studies have \nlooked at this possibility in detail \\cite{Boss87, BonBat94b}, and the\nlatter of these finds that fragmentation of a massive circumstellar\ndisc on scales ($\\simless 1$ AU) may be possible. However, in both\nthese studies, only the region inside the first hydrostatic\ncore was modelled and the initial conditions were chosen somewhat\nartificially. The ability to perform three-dimensional \ncalculations which follow the collapse of molecular cloud \ncores to stellar densities now allows us to study the formation of\nclose binaries from the collapse of larger-scale ($\\approx 10000$ AU)\nmolecular cloud cores.\n\n\n\\section{The evolution of an accreting protobinary system}\n\\label{accretion}\n\nThe favoured mechanism for the formation of most binary stellar\nsystems is the fragmentation of a collapsing molecular cloud core.\nFragmentation has been studied numerically for $\\approx 20$ years.\nThese calculations appear to show that it is possible to form binaries \nwith similar properties to those that are observed via fragmentation. \nHowever, they have not allowed us to predict the fundamental properties of \nstellar systems such as the fraction of stellar systems which \nare binary or the properties of binary \nsystems (e.g.~the distributions of mass ratios,\nseparations, and eccentricities and the properties of \ndiscs in pre-main-sequence systems).\n\n\nThere are two primary reasons for this lack of predictive power. \nFirst, the results of fragmentation calculations depend sensitively\non the initial conditions, which are poorly constrained.\nThe second problem is that of accretion. Fragmentation \ncalculations are typically stopped soon after the fragmentation\noccurs, when the binary or multiple protostellar system contains \nonly a small fraction of the total mass of the\noriginal cloud \\cite{Boss86, BonBat94b}. However, because much\nof the gas contained in the original cloud still has to fall on \nto the system and be accreted, \nthe final properties of the stellar system are \nunknown. Following the calculation significantly beyond the\npoint at which fragmentation occurs is extremely computationally \nintensive. Thus, it is impossible to perform the number of \ncalculations that are required to predict the statistical properties of \nbinary stellar systems -- even if we knew the distribution of the \ninitial conditions. On the other hand, if we can overcome this second\ndifficulty, we can make theoretical predictions about the properties\nof binary stars and, by comparing these predictions to the observed\nproperties of binary systems, we may be able to better constrain\nthe initial conditions for star formation.\n\n\\subsection{The Effects of Accretion on a Protobinary System}\n\nUsing SPH, Bate \\& Bonnell \\cite{BatBon97} studied and quantified how \nthe properties of a binary system are affected by the accretion \nof a small amount of gas from an infalling gaseous envelope. \nThey found that the effects depend primarily on the specific \nangular momentum of the gas and the binary's mass ratio \n(see also \\cite{Artymowicz83, Bate97}). Generally, accretion of gas \nwith low specific angular momentum decreases the mass ratio and \nseparation of the binary, while accretion of gas with high \nspecific angular momentum increases the separation and drives the \nmass ratio toward unity. From these results, they predicted \nthat closer binaries should have mass ratios that are biased \ntoward equal masses compared to wider systems, since the gas which\nfalls on to a closer system is likely to have more specific angular\nmomentum, relative to the binary, than for a wider system.\n\n\\begin{figure}[t]\n\\begin{center}\n\\vspace{9truecm}\n%\\epsfig{file=fig12.eps, width=13cm}\n\\caption{\\label{bate.accretion} The dependence of the \ndistribution of gas around an accreting protobinary system\non the specific angular momentum of the infalling gas \n(increasing from left-to-right and downward). For gas with low\nspecific angular momentum, only the primary forms a circumstellar\ndisc and the secondary accretes a small amount of gas via a\nBondi-Hoyle-type accretion stream. For gas with intermediate angular \nmomentum, both the primary and secondary form circumstellar discs.\nFor gas with high angular momentum, two circumstellar discs and\na circumbinary disc are formed. Finally, for the case with\nthe highest angular momentum, all the infalling gas settles into\na circumbinary disc. The\nbinary has a mass ratio of $q=0.6$ and the primary is on \nthe right.\n}\n\\end{center}\n\\end{figure}\n\nThey also studied the process of disc formation around an \naccreting protobinary system and found that for each protostar,\na circumstellar disc was only formed if the specific angular \nmomentum of the infalling gas was greater than the specific\norbital angular momentum of that protostar about the centre of\nmass of the binary (Figure \\ref{bate.accretion}). This is because,\nto be capture by one of the protostars, the gas much achieve the\nsame specific orbital angular momentum as that of the protostar.\nIf the gas has more specific angular momentum initially, some of its\nangular momentum goes into forming a disc around the protostar.\nHowever, if it has less specific angular momentum initially, there is\nno excess angular momentum to form a circumstellar\ndisc, and it must gain angular momentum even to be captured by\nthe protostar. In this case, the infalling gas gains angular \nmomentum as it falls on to the protostar in a Bondi-Hoyle-type accretion\nstream. In practice, \nthis means that a circumstellar disc is almost always formed around\nthe primary, but the secondary does not have a circumstellar disc\nunless the infalling gas has more specific angular momentum that\nsome critical value. In a similar way, the formation of a circumbinary \ndisc only begins when the specific angular momentum of the infalling\ngas is great enough for the gas to form a circular orbit at a radius\ngreater than that of the secondary from the centre of mass of the\nbinary.\n\n\n\\subsection{Development of a Protobinary Evolution Code}\n\nUsing the quantitative results of Bate \\& Bonnell \\cite{BatBon97}, \nBate \\cite{Bate2000} developed a protobinary evolution (PBE) code \nwhich follows the evolution of a protobinary system as it accretes \nfrom its initial to its final mass, but does so in far less time \nthan would be required for a full hydrodynamic calculation. \n\nThis code is based on the following model for the \nformation of binary stellar systems (Figure \\ref{bate.model}). \nThe model begins with a \nmolecular cloud core of known initial density and angular \nmomentum profile. It is assumed that this cloud begins to collapse\nand that a `seed' binary system\nis formed at the centre, presumably \nvia some sort of fragmentation. The `seed' binary has mass \nratio $q \\leq 1$,\nseparation $a$, and is assumed to have a circular orbit.\nIt initial consists of only a small fraction of the total mass of the core\nand is assumed to have formed from the gas that was originally\ncontained within a sphere of radius $r$, at the centre of the initial \ncloud (Figure \\ref{bate.model}). For the results presented in\nthis proceedings, the separation of the `seed' binary is set by assuming\nthat the angular momentum of the gas from which the binary \nforms is equal to the orbital angular momentum of the binary.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig13.eps, width=7cm}\n\\caption{\\label{bate.model} The model for studying the evolution of a \nprotobinary system that forms within a collapsing molecular cloud \ncore and is built up to its final mass by accreting the remaining \ngas as it falls on to the binary.}\n\\end{center}\n\\end{figure}\n\nSubsequently, the binary accretes the remainder of the initial \ncloud (which falls on to the binary) and the binary's \nproperties evolve due to the accretion. This evolution is calculated\nby taking a thin shell of gas of thickness d$r$ \n(Figure \\ref{bate.model}), surrounding the\nsphere from which the binary was formed, dividing the shell into \nsmall elements of gas, and calculating the effect that each \nelement of gas has on the protobinary when it is accreted\n(using the results of Bate \\& Bonnell \\cite{BatBon97}). \nThe binary's parameters (masses and separation) are updated,\nand the next shell of gas is considered until the whole cloud \nis accreted on to the binary. The amount of gas which settles \ninto a circumbinary disc is also recorded. In this way, the code\ncalculates the \nevolution of the binary from its initial to its final state when\nall of the original cloud's gas is contained\neither in one of the two stars or their surrounding discs.\n\n\n\\subsection{Testing the Protobinary Evolution Code}\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig14.eps, width=12.5cm}\n\\caption{\\label{bate.testcase1} First comparison of the results from \nthe protobinary evolution (PBE) code (solid lines) with those from a full SPH \ncalculation (dotted lines). \nThe graphs show the evolution of a protobinary system \nthat was formed in the centre of a collapsing molecular cloud core \nwhich initially had a uniform-density profile and was in solid-body \nrotation. The evolution of the (a; upper left) mass ratio, (b; upper \nright) separation, (c; lower) ratio of mass in a circumbinary disc \nto that of the binary are plotted \nas the binary accretes gas from the infalling envelope.}\n\\end{center}\n\\end{figure}\n\nTo test how accurately the PBE code describes the evolution \nof a `seed' binary as it accretes from its initial to \nits final mass, the PBE results were compared to those from \nfull SPH calculations. Two test cases were performed. The first \nfollowed the formation of a binary system from the collapse \nof an initially uniform-density, spherical molecular cloud \ncore in solid-body rotation. The `seed' binary was assumed \nto have a mass ratio of $q=0.6$ and a mass of $1/10$ the\ninitial cloud mass. The second test case was similar, except \nthat the progenitor cloud was centrally-condensed with a 1/r-density \ndistribution and the cloud had a total mass of only 5 times the\n`seed' binary's mass. A full discussion of the test cases\nis given by \\cite{Bate2000}.\n\n\n\\subsubsection{Test Case 1}\n\nThe evolution of the mass ratio, separation and amount of gas\nin the circumbinary disc are given for\nthe PBE code and for a full SPH calculation in Figure \n\\ref{bate.testcase1}. The curves are given as functions of the \namount of gas that has fallen on to the binary, $M_{\\rm acc}$, \nrelative to the binary's initial mass. \nIn addition, an MPEG animation of the\nSPH calculation is included on this CD-ROM as bate2.mpg.\nThe CPU time required to evolve the SPH\ncalculation until the entire cloud falls on to the binary in \nis prohibitively long, which, after all, is the reason that \nthe PBE code was developed in the first place. It takes \n$\\approx 60$ orbits for the binary to increase its mass by \na factor of 6 (i.e.~$\\approx 60$\\% of the total cloud was \naccreted). The SPH calculation took $\\approx 5$ months on \na 170 MHz Sun Ultra workstation with a GRAvity-PipE (GRAPE) board used\nto calculate the gravitational forces and neighbouring SPH particles. \nThe evolution with the PBE code took a few seconds!\n\nAlthough the SPH calculation did not run to completion, \nwe can compare the evolution as the binary's mass increases \nby a factor of 6 (Figure \\ref{bate.testcase1}). \nGenerally, there is good agreement \nbetween the PBE and SPH codes. The mass ratio is predicted \nto within 5\\% over the entire evolution and the separation \nto within 15\\%. In fact, as discussed in \\cite{Bate2000},\nthe small differences between the PBE and SPH results \nreflect unphysical treatment of the circumstellar discs\nby the SPH code rather than a problem with the PBE code.\nFor example, the slower rate of increase of the mass ratio\ninitially is due to the circumsecondary disc not being \nresolved correctly in the SPH calculation, and the larger\nseparation when $M_{\\rm acc}\\simgreat 3$ is due to \nunphysically-rapid viscous evolution of the \ncircumstellar discs which transfers angular momentum into\nthe binary's orbit too quickly. The greatest difference between\nthe PBE and SPH results is that the PBE code predicts that a \ncircumbinary disc should be formed around the binary whereas\nno circumbinary disc is formed in the SPH calculation. This is\ndue to the larger separation of the binary when $M_{\\rm acc}\\simgreat 3$ \nand the large shear viscosity in the SPH calculation.\n\n\n\\subsubsection{Test Case 2}\n\nUnlike test case 1, the PBE code predicts that a massive \ncircumbinary disc should be produced very early in the \nevolution of test case 2. Thus, test case 2 provides a \nbetter test of how well the PBE code predicts the formation\nof a circumbinary disc and its evolution. We note that,\nalthough the\nPBE code records the amount of gas which settles into a \ncircumbinary disc, it does not attempt to take account of the\ninteraction between the binary and the circumbinary disc. In\nreality, this interaction is expected to result in the \ntransfer of angular momentum from the orbit of the binary into\nthe gas of the circumbinary disc and, hence, in a smaller \nseparation. Furthermore, if the separation decreases, more \nof the infalling gas would be expected to settle into the \ncircumbinary disc and, for the same increase in the binary's\nmass, the mass ratio should increase more rapidly because the\ngas has a greater specific angular momentum relative to that of\nthe binary. Thus, if a massive circumbinary disc is formed, \nthe PBE code is expected to over-estimate the binary's separation, \nunder-estimate the mass in the circumbinary disc, and slightly\nunder-estimate the mass-ratio of the binary.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig15.eps, width=12.5cm}\n\\caption{\\label{bate.testcase2} Same as Figure 14, except that the \nprotobinary system was formed from a molecular cloud core \nwhich initially had a density profile of $\\rho \\propto 1/r$.}\n\\end{center}\n\\end{figure}\n\nThe evolution of the mass ratio, separation and amount of gas\nin the circumbinary disc are given for test case 2 in Figure \n\\ref{bate.testcase2}. An MPEG animation of the\nSPH calculation is included on this CD-ROM as bate3.mpg.\nTo avoid the problems that occurred due to the large shear viscosity\nin the SPH calculation for test case 1, the SPH calculation here\nuses a formulation with less shear viscosity (see \\cite{Bate2000}).\nAs with test case 1, due to the computational cost, the SPH \ncalculations were stopped before all of the gas had fallen on \nto the binary. The SPH calculation took $\\approx 4$ months \non a 300 MHz Sun Ultra workstation (using a binary tree, \nnot a GRAPE board). During the evolution, the \nbinary performed $\\approx 40$ orbits and $\\approx 60$\\%\nof the total mass was accreted by the binary or settled \ninto a circumbinary disc.\n\nThe agreement for the evolution of the mass ratio is even \nbetter than it was with test case 1 with differences between the PBE\nand SPH results of $\\simless 3$\\%. The separation\nfollows the prediction of the PBE code to better than $3$\\%\nuntil the circumbinary disc begins to form. Once the circumbinary\ndisc attains approximately 5\\% of the binary's mass, however,\nthe separation is always smaller than predicted by the PBE code.\nAs described above, this is expected because the PBE code\nneglects the separation-decreasing effect of the interaction \nbetween the binary and the circumbinary disc. This also explains\nwhy the PBE code slightly under-estimates the binary's mass ratio.\nHowever, it is pleasing to see that even neglecting the \ninteraction between the binary and the circumbinary disc, \nthe PBE code still predicts the mass of the circumbinary disc to \nwithin a factor of 2 of that given by the SPH code during the\nentire evolution.\n\n\n\\subsection{The Evolution of Accreting Protobinary Systems}\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig16.eps, width=12cm}\n\\vspace{0.5truecm}\n\\caption{\\label{bate.uniform} The evolution of protobinary systems \nformed in the centre of collapsing molecular cloud cores as they \naccrete from the gaseous envelope. The initial cores have uniform-density \nprofiles and are in solid-body rotation. The evolution of the mass ratio \n(a; upper left), separation (b; upper right), and ratio of the \ncircumbinary disc mass to that of the binary (c; lower left), and the \nrelative accretion rate (d; lower right) are given as functions of the \namount of gas that has been accreted from the envelope. The evolutionary\ncurves\nare given for `seed' binary systems with initial mass ratios of $q=0.1$ to \n$q=1.0$, with various different line types and/or widths for each. The \ncurves are all given by a thin dotted lines once the circumbinary \ndisc mass exceeds 5\\% of the binary's mass. Beyond this point, \nthe binary's mass ratio and the mass in the circumbinary disc are likely \nto be under-estimated, and the separation is likely to be over-estimated. }\n\\end{center}\n\\end{figure}\n\nAs we have seen, the PBE code gives a relatively accurate \ndescription of the evolution of an accreting protobinary, but does\nso $\\sim 10^6$ times faster than a full hydrodynamic SPH calculation.\nThis allows us to perform many calculations to \nstudy how the evolution of a binary as it accretes\nto its final mass depends on its initial mass ratio and on the\nproperties of the molecular cloud core from which it formed.\n\nAs examples, we give the evolution of `seed' binaries that form\nfrom two types of molecular cloud core. A greater range of\nmolecular cloud cores is considered in \\cite{Bate2000}.\nFigure \\ref{bate.uniform} presents the evolution of\nbinaries formed from molecular cloud cores which had\nuniform-density and were in solid-body rotation before they began\nto collapse dynamically. In Figure \\ref{bate.1r}, the \nmolecular cloud cores had radial density profiles of $\\rho \\propto 1/r$\nwith solid-body rotation, initially. \nEvolutionary curves are provided for `seed' binaries\nwith initial mass ratios ranging from $q=0.1-1.0$. \n\nIn all cases, the long-term evolution is towards a mass ratio \nof unity, since the material that falls in later has higher \nspecific angular momentum relative to that of the binary. \nThus, the more the binary accretes relative to its initial mass, \nthe stronger the tendency is for the mass ratio to be \ndriven to unity. Similarly, the more the binary accretes \nrelative to its initial mass, the more likely it is to be surrounded\nby a circumbinary disc. Note that, in the previous sections,\nwe found that when a massive circumbinary disc is formed, the PBE\ncode tends to over-estimate the separation, and under-estimate \nthe mass of the circumbinary disc and the binary's mass ratio.\nThus, if anything, the evolutionary curves in Figures \\ref{bate.uniform}\nand \\ref{bate.1r} tend to under-estimate the binary's mass ratio and \nthe mass of the circumbinary disc.\n\n\n\\subsection{The Properties of Binary Stars}\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig17.eps, width=12cm}\n\\vspace{0.5truecm}\n\\caption{\\label{bate.1r} Same as Figure 16, except that the \nprotobinary systems were formed from a molecular cloud cores \nwhich initially had a density profiles of $\\rho \\propto 1/r$.}\n\\end{center}\n\\end{figure}\n\nThe aim of developing the PBE code was to make it possible to predict\nsome of the properties of binary stars and, by comparing\nthese to the observed properties of binary systems, to constrain \nthe initial conditions for binary star formation. \n\nIn order to obtain predictions about the properties of binaries we \nnote that, generally, the initial mass of a `seed' binary is smaller \nfor those binaries with smaller separations. This relationship\nbetween a `seed' binary's mass and its separation is observed from\nfragmentation calculations \\cite{Boss86, BonBat94b} and\nis easily understood from a Jeans-mass argument \\cite{Bate2000}. \nIn order for\nfragmentation to occur, the Jeans length at the time of fragmentation\nmust be less than or approximately equal to the separation of the\nbinary which is formed. However, for a constant temperature,\nthe Jeans mass depends linearly on the Jeans length. Thus, the\nsmaller the separation of the `seed' binary, the smaller its initial\nmass. Generally, `seed' binaries with separations $\\simless 10$\nAU are expected to have masses $\\approx 0.01 {\\rm M}_{\\odot}$, while\nfor larger separations, the `seed' mass is expected to increase\napproximately linearly (i.e. `seed' binaries with separations of\n100-1000 AU should have initial masses of \n$\\approx 0.1-1.0 {\\rm M}_{\\odot}$).\n\nThis dependence of the initial mass on the separation means that\nto form binaries with the same final total mass, the closer systems\nneed to accrete more material, relative to their initial mass.\nTherefore, from the evolutionary curves of Figures \\ref{bate.uniform}\nand \\ref{bate.1r}, closer systems are more likely to have equal-mass\ncomponents than wider systems.\n\nThis prediction is supported by surveys of main-sequence \nG-dwarf stellar systems. Duquennoy \\& Mayor \\cite{DuqMay91} \nfound that the mass-ratio distribution, averaged over \nbinaries with all separations, increases toward small mass \nratios. However, there is mounting evidence that\nthe mass-ratio distributions differ between short and long-period\nsystems with the distribution for close binary systems ($P <\n3000$ days; $a \\simless 5$ AU) consistent with\na uniform distribution \\cite{Mazehetal92, HalMayUdr98}.\nThus, relative to wide systems, the close systems are biased toward\nmass ratios of unity.\n\nThe fraction by which the mass of a `seed' binary must\nbe increased in order for its mass ratio to approach unity depends\non the conditions in the molecular cloud core. Generally,\nthe less centrally-condensed a core is, the easier it is to \nform a binary system with a low mass ratio \n(c.f.~Figures \\ref{bate.uniform} and \\ref{bate.1r}).\nWe can use this dependence of the evolutionary curves on the \ntype of molecular cloud core to attempt to constrain the initial\nconditions for binary star formation.\n\nDuquennoy \\& Mayor \\cite{DuqMay91} found that binaries containing\nG-dwarfs with\nseparations $\\simgreat 30$ AU generally have unequal masses\n(typically $q\\approx 0.3$). Such binaries are likely to have\naccreted from a few to ten times there initial mass. For uniform-density\ncores (Figure \\ref{bate.uniform}), the observed mass-ratio \ndistribution can easily be obtained. Cores with $\\rho \\propto 1/r$\nresult in higher mass ratios than uniform-density cores, but it is\nstill possible to envisage a spectrum of `seed' mass ratios which gives\na final mass-ratio distribution which is consistent with the\nobservations of wide binaries.\n\nHowever, close binaries ($\\simless 5$ AU) have initial masses\nof $\\approx 0.01 {\\rm M}_{\\odot}$. Thus, they are expected to\nhave to accrete up to 100 times their initial mass from the infalling\ngaseous envelope before systems with G-dwarf primaries are obtained,\nyet the observed mass-ratio distribution is approximately flat\n(i.e.~approximately 1/2 the binaries have $q<0.5$). \nIt is effectively impossible for cores in solid-body rotation \nto produce such a mass ratio distribution if they are \nsignificantly centrally-condensed (Figure \\ref{bate.1r}). \nEven with uniform-density cores most of the `seed' binaries \nwould need to have mass ratios $q<0.1$, which is unlikely.\n\nHowever, the PBE code only evolves circular binaries whereas \nmost binaries have significant eccentricity \\cite{DuqMay91}.\nFor the same semi-major axis, eccentric binaries have less \nangular momentum than circular binaries meaning that the \nclouds from which they formed may be rotating more slowly\nand, thus, the gas in the envelope may have less angular momentum.\nThis would result in slower evolution toward equal masses for\neccentric binaries.\nTaking the effects of eccentricity into account, it is quite \npossible that the observed binary mass ratios could be \nproduced by the collapse of molecular cloud cores\nwith radial density profiles less centrally-condensed than $\\rho \n\\propto 1/r$. However, even accounting for eccentric binaries, \nit seems virtually impossible that the observed G-dwarf binary \nsystems could have been formed from molecular cloud cores with\ndensity profiles that were more centrally-condensed \nthan $\\rho \\propto 1/r$.\n\nThe above conclusion that closer binaries should have mass ratios\nthat are biased toward unity compared to wider systems with the\nsame total mass is just one of many predictions that may be\nderived using the PBE code (see \\cite{Bate2000}). \nOthers include: closer binaries are \nmore likely to have circumbinary discs than wider binaries; \nbrown dwarf companions to solar-type stars\nshould be very rare at separations $\\simless 5$ AU, but their\nfrequency should increase at larger separations. \n\n\n\\section{Conclusions}\n\nThe Lagrangian nature of SPH and its inherent ability to\nprovide finer spatial resolution in regions of higher density \nmake it a powerful tool which is ideally suited for \nstudying star formation.\n\nRecent advances in the study of binary star formation that \nhave been made using SPH include: the realisation that it is\nessential that the Jeans mass is always resolved in numerical \nstudies of self-gravitating gas; the ability to perform \nthree-dimensional hydrodynamic calculations which follow the \ncollapse of a molecular cloud core to stellar densities;\nthe study of the effects of accretion on a protobinary systems\nand the development of a code which enables the evolution of\naccreting binary systems to be followed $\\sim 10^6$ times \nfaster than a full hydrodynamic calculation. 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P., 1998, MNRAS, 296, 442\n\n\\end{references}\n\n\\end{article}\n\n\\end{document}\n\n\n"}],"string":"[\n {\n \"name\": \"proc.tex\",\n \"string\": \"%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n% %\\n% Proceedings of 20 years of Numerical Astrophysics Template %\\n% You can use it with the academic press style file which %\\n% can be found at (http://www.apnet.com/www/journal/cp.htm). %\\n% %\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\\\documentclass{cjour}\\n\\\\usepackage{epsfig}\\n\\\\textheight= 22.0cm\\n\\\\voffset=2.0mm\\n\\n\\\\def\\\\simless{\\\\mathbin{\\\\lower 2pt\\\\hbox\\n {$\\\\rlap{\\\\raise 5pt\\\\hbox{$\\\\char'074$}}\\\\mathchar\\\"7218$}}} % < or of order\\n\\\\def\\\\simgreat{\\\\mathbin{\\\\lower 2pt\\\\hbox\\n {$\\\\rlap{\\\\raise 5pt\\\\hbox{$\\\\char'076$}}\\\\mathchar\\\"7218$}}} % > or of order\\n\\n\\\\authorrunninghead{M. R. Bate}\\n\\\\titlerunninghead{Recent Advances in Binary Star Formation Using SPH}\\n\\n\\\\begin{document}\\n\\n\\\\title{Recent Advances in Binary Star Formation Using SPH}\\n\\n%\\\\subtitle{This is a subtitle if you wish to include one.}\\n\\n\\\\author{Matthew R. Bate}\\n\\\\affil{Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, United Kingdom}\\n\\\\email{mbate@ast.cam.ac.uk}\\n%\\\\and\\n%\\\\author{While The Second Author is}\\n%\\\\affil{From Somewhere else.}\\n%\\\\email{secondauthor@somewhere.else}\\n\\n\\\\abstract{We review recent advances in the study of binary star formation that have been made using the smoothed particle hydrodynamics technique.}\\n\\n\\\\begin{article}\\n\\n%% Section headings:\\n\\\\section{Introduction}\\n \\nThe Smoothed Particle Hydrodynamics (SPH) numerical method \\nwas introduced by Lucy \\\\cite{Lucy77} and \\nGingold and Monaghan \\\\cite{GinMon77}. Its first application\\nwas in the field of star formation, where it was used to \\nstudy whether or not a rapidly-rotating polytrope could undergo\\nfission to form a close binary system \\\\cite{Lucy77, GinMon78}.\\nSince this initial application, SPH has been widely used in the\\nstudy of star formation, for example \\\\cite{GinMon81, \\nMiyHayNar84, Lattanzioetal85, Durisenetal86, SigKla97, \\nBonBas91, BatBonPri95, Heller93, NelPap93, ArtLub94,\\nLarwoodetal96, Nelsonetal98, VanCam98, \\nChapmanetal92}.\\n\\nSPH is has many attributes which make it particularly \\nwell suited to the study of star formation.\\nSPH is Lagrangian and does not require a computational grid.\\nThus, it can efficiently follow problems with large density \\ncontrasts since computational effort is not wasted simulating \\nthe low-density regions. Also, recent SPH implementations \\n\\\\cite{Evrard88, HerKat89, Benz90, Monaghan92} use spatially \\nand temporally varying smoothing lengths so that the resolution \\nincreases automatically with increasing density; the complex \\nmulti-grid and adaptive-grid schemes that are used for \\nfinite difference methods are avoided.\\n\\nIn this proceedings, we review some of the recent advances\\nin the study of binary star formation that have been made using \\nSPH. In Section \\\\ref{jeansmass}, we discuss the importance of\\nalways resolving the Jeans mass in numerical studies of self-gravitating\\ngas. While this has been demonstrated using various types of \\nhydrodynamic code, we concentrate specifically on the problems\\nthat can arise if this criterion is not obeyed with SPH.\\nIn Section \\\\ref{collstellar}, we demonstrate that, for the first time, \\nit is now possible to perform three-dimensional hydrodynamic \\ncalculations which follow the collapse of a molecular cloud \\ncore to stellar densities. These calculations are performed with\\nSPH. Finally, in Section \\\\ref{accretion}, \\nwe discuss how SPH has been used to study the evolution of a \\nprotobinary system as it accretes from an infalling gaseous \\nenvelope and how this work can lead to predictions\\nof the properties of binary stars.\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=fig01.eps, width=13cm}\\n\\\\caption{\\\\label{bate.forces} The ratio of the gravitational force \\nto pressure force between two SPH particles in a Jeans-mass\\nclump of gas of radius $R=h$. The gravitational softening length\\nis $\\\\epsilon$ and the hydrodynamic smoothing length is $h$.}\\n\\\\end{center}\\n\\\\end{figure}\\n\\n\\\\section{The Importance of Resolving the Jeans Mass}\\n\\\\label{jeansmass}\\n\\nIt has recently been realised that it is important that the Jeans\\nmass/length is always resolved during a hydrodynamical calculation. \\nThis has been demonstrated both with SPH \\\\cite{BatBur97, Whitworth98}\\nand with grid-based codes \\\\cite{Trueloveetal97, Trueloveetal98, Boss98}. \\nIf this criterion is not obeyed, artificial \\nfragmentation can be induced, or fragmentation can be inhibited. \\nEssentially this is because when the resolution length/mass \\napproaches the Jeans length/mass, collapse is artificially delayed\\ndue to viscous forces, softening of gravitational forces, or a combination\\nof both. A good example is the collapse of an isothermal \\nfilament \\\\cite{Trueloveetal97}. Such a filament should collapse\\nwithout limit to a filamentary singularity without fragmenting. \\nHowever, if the collapse perpendicular to the major-axis is delayed, small\\ndensity perturbations along the filament may have enough time to grow \\nto non-linear amplitudes and fragments may\\nform along the bar.\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=fig02.eps, width=10cm}\\n\\\\caption{\\\\label{bate.massden} Maximum density versus time for during the\\ncollapse of a molecular cloud core [8]. Three calculations were \\nperformed using SPH with $\\\\epsilon=h$. The smoothing\\nlengths were allowed to vary with time and space freely (solid line) or \\nsubject to\\na minimum length of 5\\\\% (dotted line) or 10 \\\\% (dashed line) of the\\ninitial cloud radius. When the minimum Jeans length in the \\ncalculation is less than or approximately equal to the smoothing/softening\\nlength, the collapse is delayed.\\n}\\n\\\\end{center}\\n\\\\end{figure}\\n\\nBate \\\\& Burkert \\\\cite{BatBur97} first demonstrated the need for the\\nJeans mass criterion using self-gravitating SPH calculations. With\\nSPH, the problem can be understood by considering the \\ngravitational and pressure forces between two particles \\nwithin a marginally Jeans-stable clump of gas of radius $R\\\\approx h$\\n(Figure \\\\ref{bate.forces}). SPH codes typically soften \\nthe gravitational forces between neighbouring particles, using either \\nthe Plummer force law or kernel softening \\n\\\\cite{GinMon77, HerKat89, Benz90}. The\\ncharacteristic gravitational softening length, $\\\\epsilon$, \\nmay or may not be equal to the SPH hydrodynamic smoothing \\nlength, $h$, depending on the specific implementation.\\nIf $\\\\epsilon=h$, the ratio of the gravitational and \\npressure forces between two particles is approximately \\nconstant for particle with separations $\\\\simless h$.\\nThus, a Jeans-unstable clump of gas will collapse, while a \\nJeans-stable clump will be supported. However, although the\\nratio of the gravitational and pressure forces is approximately \\nindependent of the separation of the particles, the magnitude \\nof the gravitational force decreases with separation due to \\nthe softening. Thus, while a Jeans-unstable clump of gas with \\na size much larger than the resolution length, $h$, \\nwill collapse at the correct rate, the collapse of clumps with \\na size $\\\\approx h$ will be delayed. This is demonstrated\\nin Figure \\\\ref{bate.massden}. \\n\\nUnfortunately, the effect is not always limited to a simple delay of \\nthe collapse. Given the right problem, artificial fragmentation\\ncan be induced (such as with the filament described above), \\nor inhibited. In Figure \\\\ref{bate.80000} we show how the collapse\\nof a particular molecular cloud core with an initial $m=2$ \\ndensity perturbation results in a binary protostellar system\\nwith a bar of gas between them. This calculation was performed\\nwith $8\\\\times 10^4$ particles, enough to resolved the Jeans mass/length\\nuntil after the binary had formed. However, performing\\nthe same calculation with $1\\\\times 10^4$ particles gives a different\\nresult: a single, dense bar of gas without the binary. In this \\ncalculation, the Jeans mass becomes unresolved before $t=1.20$\\nand the collapse of each of the two over-dense regions resulting from the \\noriginal $m=2$ density perturbation is delayed. The collapse of the\\nlarger-scale elongated region, however, continues, leading to \\nthe formation of a bar rather than a binary.\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=fig03.eps, width=12.5cm}\\n\\\\vspace{0.25truecm}\\n\\\\caption{\\\\label{bate.80000} Collapse and fragmentation of a \\nmolecular cloud core to form a binary [8]. The initial cloud had an initial\\n10\\\\% $m=2$ density perturbation. The local Jeans mass/length is unresolved\\ninside the thick density contour. The calculation was performed\\nwith $8\\\\times 10^4$ particles.\\n}\\n\\\\vspace{-0.5truecm}\\n\\\\end{center}\\n\\\\end{figure}\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=fig04.eps, width=12.5cm}\\n\\\\vspace{0.25truecm}\\n\\\\caption{\\\\label{bate.10000} Same as Figure 3, except that the calculation\\nwas performed with $1\\\\times 10^4$ particles. When $t \\\\simgreat 1.20$,\\nthe region within which the binary formed in the $8\\\\times 10^4$-particle\\ncalculation becomes unresolved, collapse of the two over-dense\\nregions is delayed, and the calculation eventually produces a dense\\nbar instead of a binary.\\n}\\n\\\\vspace{-1.0truecm}\\n\\\\end{center}\\n\\\\end{figure}\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=fig05.eps, width=12.5cm}\\n\\\\vspace{0.25truecm}\\n\\\\caption{\\\\label{bate.10000eh} Same as Figure 4, except that the calculation\\nwas performed with $\\\\epsilon=1.0\\\\times 10^{14}$ cm (i.e.~$e h$, the pressure forces\\nbetween particles within a Jeans-unstable clump may exceed the \\ngravitational forces and the clump will be artificially supported\\nagainst collapse.\\n\\nClearly, the best SPH implementation is one where $\\\\epsilon=h$ always.\\nIn this case, collapse of Jeans-unstable clumps with a size \\nsimilar to that of the resolution length will still be \\ndelayed, but the possibilities of\\nartificial collapse within Jeans-stable clumps or the supporting\\nof Jeans-unstable clumps against collapse are eliminated. Then,\\nin order to avoid the collapse of Jeans-unstable clumps being\\ndelayed significantly, enough particles should be used so that\\nthe Jeans length/mass is always resolved. \\n\\nHow many particles\\nare necessary to ensure that the Jeans length/mass is resolved?\\nWith SPH, the spatial resolution \\nis given by the smoothing length which is usually variable in \\ntime and space. The smoothing lengths are set by ensuring that \\neach particle contains a certain number of neighbours, \\n$N_{\\\\rm neigh}$, or equivalently a fixed mass, within two \\nsmoothing lengths. Thus, in contrast to a grid-based code \\nwhich has spatially-limited resolution, SPH has mass-limited \\nresolution which {\\\\it automatically} gives greater spatial \\nresolution in regions of higher density. Therefore, with SPH,\\nit is necessary to ensure that the minimum resolvable mass is \\nalways less than the Jeans mass. In practice, Bate \\\\& Burkert \\nfound that a Jeans mass should always \\nbe represented by at least $\\\\approx 2 N_{\\\\rm neigh}$ particles. \\n\\\\newpage\\n\\n\\\\section{Collapse of a Molecular Cloud to Stellar Densities}\\n\\\\label{collstellar}\\n\\nThe mass-limited resolution of SPH is ideal for studying the \\ncollapse and fragmentation of molecular cloud cores because \\nthere is a minimum Jeans mass in the problem \\n(Figure \\\\ref{bate.tmr}). By contrast,\\nthere is no minimum Jeans length. This is a problem \\nfor grid-based codes which must resort to nested or \\nadaptive grids \\\\cite{ BurBod93, Trueloveetal97, Trueloveetal98}. \\nWith SPH, if the number of \\nparticles used is sufficient to resolve the minimum Jeans mass, a \\ncalculation can be followed to arbitrary densities with the required\\nspatial resolution given automatically with increasing density.\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=fig06.eps, width=12cm}\\n\\\\caption{\\\\label{bate.tmr} The gas temperature $T$ (solid line), Jeans \\nmass $M_{\\\\rm J}$ (dotted line), and Jeans radius $R_{\\\\rm J}$ (dashed \\nline), as a function of density in a collapsing molecular cloud core \\n(adapted from Tohline [36]). The minimum Jeans mass of \\n$ \\\\approx 4 \\\\times 10^{-4}~{\\\\rm M}_{\\\\odot}$ occurs \\nat a density of $\\\\sim 10^{-3} {\\\\rm \\\\ g \\\\ cm}^{-3}$.}\\n\\\\end{center}\\n\\\\end{figure}\\n\\n\\nRecently, this ability of SPH was used to perform the first \\nthree-dimensional calculations ever to follow the collapse of\\na molecular cloud core to stellar densities \\\\cite{Bate98}.\\nThe calculations followed the collapse of an initially \\nuniform-density molecular cloud core of mass $M=1 {\\\\rm \\\\ M}_\\\\odot$ and\\nradius $R=7 \\\\times 10^{16} {\\\\rm \\\\ cm}$.\\n\\nThe minimum resolvable mass in the SPH code was \\n$\\\\approx 2 N_{\\\\rm neigh} = 100$ particles. Thus, to enable the\\nminimum Jeans mass during the calculation\\n($\\\\approx 4 \\\\times 10^{-4}\\\\ {\\\\rm M}_{\\\\odot}$)\\nto be resolved, the calculation used $3 \\\\times 10^5$ \\nequal-mass particles.\\n\\nThe code did not include radiative transfer. Instead, to model \\nthe behaviour of the gas during the different phases of collapse,\\na piece-wise polytropic equation of state, $P=K \\\\rho^{\\\\gamma}$, was\\nused, where $P$ is the pressure, $\\\\rho$ is the density, $K$ \\ngives the entropy of the gas, and the ratio of specific heats, \\n$\\\\gamma$, was varied as\\n\\\\begin{equation}\\n\\\\label{polytropic}\\n\\\\gamma = \\\\cases {\\\\begin{array}{lll}\\n1 & & \\\\rho \\\\leq 1.0 \\\\times 10^{-13} \\\\cr\\n7/5 & \\\\ 1.0 \\\\times 10^{-13} < \\\\hspace{-6pt} & \\\\rho \\\\leq 5.7 \\\\times 10^{-8} \\n\\\\cr\\n1.15 & \\\\ 5.7 \\\\times 10^{-8\\\\ } < \\\\hspace{-6pt} & \\\\rho < 1.0 \\\\times 10^{-3} \\\\cr\\n5/3 & & \\\\rho > 1.0 \\\\times 10^{-3} \\\\cr\\n\\\\end{array}}\\n\\\\end{equation}\\nwhere the densities are in ${\\\\rm g\\\\ cm}^{-3}$ \\n(see Figure \\\\ref{bate.tmr}).\\nThe values of $\\\\gamma$ and the transition densities \\nwere derived from Tohline \\\\cite{Tohline82}. The variable value of $\\\\gamma$ \\nmimics the following behaviour of the gas. The\\ncollapse is isothermal ($\\\\gamma=1$) until the gas becomes optically thick \\nto infrared radiation \\nat $\\\\rho \\\\approx 10^{-13} {\\\\rm \\\\ g \\\\ cm}^{-3}$, beyond which $\\\\gamma=7/5$\\n(appropriate for a diatomic gas).\\nWhen the gas reaches a temperature of $\\\\approx$ 2000 K \\n($\\\\rho = 5.7 \\\\times 10^{-8} {\\\\rm \\\\ g \\\\ cm}^{-3}$), molecular \\nhydrogen begins to dissociate and the temperature only slowly increases\\nwith density. In this phase $\\\\gamma = 1.15$ is used to \\nmodel {\\\\it both} the decreasing mean molecular weight and the slow increase \\nof temperature with density, the latter of which has an effective \\n$\\\\gamma \\\\approx 1.10$.\\nFinally, when the gas has fully dissociated\\n($\\\\rho \\\\approx 10^{-3} {\\\\rm \\\\ g \\\\ cm}^{-3}$), the gas is monatomic and\\n$\\\\gamma=5/3$. The value of $K$ is\\ndefined such that when the gas is isothermal, $K = c_{\\\\rm s}^2$\\nwith $c_{\\\\rm s} = 2.0 \\\\times 10^4 {\\\\rm \\\\ cm\\\\ s^{-1}}$, and when $\\\\gamma$\\nchanges the pressure is continuous.\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=fig07.eps, width=12.5cm}\\n\\\\caption{\\\\label{bate.static} Radial density and velocity profiles of \\nthe collapsing molecular cloud core with the one-dimensional grid \\ncode (solid) and the three-dimensional SPH code (dotted). \\nThe profiles are compared when the central density in each calculation \\nis a) $10^{-14}$, b) $10^{-11}$, c) $10^{-9}$, d) $10^{-6}$, \\ne) $10^{-3}$, and f) $10^{-1}$ g cm$^{-3}$.}\\n\\\\end{center}\\n\\\\end{figure}\\n\\n\\\\subsection{Collapse of an initially-static cloud}\\n\\nTo test that the above equation of state captures the important elements\\nof the gas's behaviour, spherically-symmetric,\\none-dimensional (1-D), finite-difference calculations were performed\\nof the collapse of an initially-static molecular cloud core \\nwith the above parameters and equation of state.\\nThe results are shown in Figure \\\\ref{bate.static} (solid line). \\nThese results \\nare in good agreement with the results from 1-D calculations \\nincorporating radiative transfer \\n(e.g.\\\\ Larson 1969; Winkler \\\\& Newman 1980a, b).\\n\\nThe three-dimensional (3-D) SPH code was also tested on the same \\nproblem to check that the SPH code can indeed accurately resolve the \\ncollapse down to stellar densities \\n(Figure \\\\ref{bate.static}, dotted line). \\nThere is excellent agreement between the results from the 1-D \\nfinite-difference code and those from the 3-D SPH code.\\n\\n\\n\\\\subsection{Collapse of a rotating cloud}\\n\\nThree-dimensional calculations are required if the molecular\\ncloud core is rotating. In Figures \\\\ref{bate.rotmassdens} to\\n\\\\ref{bate.finalstate2} we present results from the collapse\\nof a cloud core which is identical to that in the previous \\nsection, but which is initially in solid-body rotation with\\nangular frequency $\\\\Omega=7.6 \\\\times 10^{-14}$ rad s$^{-1}$.\\nThus, the ratio of rotational energy to the magnitude of the \\ngravitational potential energy is $\\\\beta=0.005$ (i.e.~the cloud\\nis rotating quite slowly).\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=fig08.eps, width=12cm}\\n\\\\caption{\\\\label{bate.rotmassdens} Maximum density (solid line) \\nand maximum temperature (dotted line) versus time for the collapsing \\nmolecular cloud core. Time is given in units of the initial free-fall \\ntime ($t_{\\\\rm ff}=1.785 \\\\times 10^{12}$ s). The right graph has \\nexpanded axes to show the second collapse phase in greater detail.}\\n\\\\end{center}\\n\\\\end{figure}\\n\\n\\\\begin{figure}[b]\\n\\\\begin{center}\\n\\\\vspace{8.4truecm}\\n%\\\\epsfig{file=fig09.eps, width=12cm}\\n\\\\caption{\\\\label{bate.bar} A time sequence showing the density in \\nthe plane perpendicular to the rotation axis during the dynamic, \\nrotational, bar instability of the first hydrostatic core. The\\npanels cover the period from $t\\\\approx 1.023-1.030$ t$_{\\\\rm ff}$.\\nSee also the MPEG animation on this CD-ROM: bate1.mpg.\\n}\\n\\\\end{center}\\n\\\\end{figure}\\n\\nThe evolution of the calculation is as follows \\n(Figure \\\\ref{bate.rotmassdens}). \\nThe initial collapse is isothermal. When the density surpasses\\n$10^{-13}$ g cm$^{-3}$, the gas in the center \\nis assumed to become optically thick\\nto infrared radiation and begins to heat ($t=1.009~t_{\\\\rm ff}$).\\nThe heating stops the collapse at the center and the first hydrostatic core\\nis formed ($t=1.015~t_{\\\\rm ff}$) with maximum density \\n$\\\\approx 2 \\\\times 10^{-11}$ g cm$^{-3}$, mass \\n$\\\\approx 0.01 {\\\\rm \\\\ M}_\\\\odot$ ($\\\\approx 3 \\\\times 10^3$ particles), and radius \\n$\\\\approx 7$ AU. As the first core accretes, its maximum\\ndensity only slowly increases at first.\\nHowever, the first core is rapidly rotating, oblate, and has \\n$\\\\beta \\\\approx 0.34 > 0.274$, making it dynamically unstable to the\\ngrowth of non-axisymmetric perturbations \\n\\\\cite{Durisenetal86, ImaDurPic99}. \\nAt $t \\\\approx 1.023~t_{\\\\rm ff}$, after about 3 rotations, \\nthe first core becomes violently bar-unstable\\nand forms trailing spiral arms (Figure \\\\ref{bate.bar}). This leads\\nto a rapid increase in maximum density (Figure \\\\ref{bate.rotmassdens})\\nas angular momentum is removed from\\nthe central regions of the first core (now a disc with spiral structure) \\nby gravitational torques ($t=1.023-1.030~t_{\\\\rm ff}$). An MPEG animation of \\nthis bar instability is provided on this CD-ROM (bate1.mpg).\\nWhen the maximum temperature reaches 2000 K, molecular hydrogen begins to\\ndissociate, resulting in a rapid second collapse to stellar densities\\n($t=1.030~t_{\\\\rm ff}$). The collapse is again halted at a density of \\n$\\\\approx 0.007$ g cm$^{-3}$ with the formation of the second hydrostatic, \\nor stellar, core. The initial mass and radius of the stellar core are \\n$\\\\approx 0.0015 {\\\\rm \\\\ M}_\\\\odot$ ($\\\\approx 5 \\\\times 10^2$ particles) \\nand $\\\\approx 0.8 {\\\\rm \\\\ R}_\\\\odot$, \\nrespectively. Finally,\\nan inner circumstellar disc begins to form around the stellar \\nobject, within the region undergoing second collapse. The \\ncalculation is stopped when the stellar object has a mass of \\n$\\\\approx 0.004 {\\\\rm \\\\ M}_\\\\odot$ ($\\\\approx 1.2 \\\\times 10^3$ particles), \\nthe inner circumstellar disc has extended out to $\\\\approx 0.1$ AU, \\nand the outer disc (the remnant of the first hydrostatic core) contains \\n$\\\\approx 0.08 {\\\\rm \\\\ M}_\\\\odot$ ($\\\\approx 2.4 \\\\times 10^4$ particles) \\nand extends out to $\\\\approx 70$ AU. Note that the massive outer \\ndisc forms {\\\\it before} the stellar core.\\nThis final state is illustrated in Figures \\\\ref{bate.finalstate}\\nand \\\\ref{bate.finalstate2}.\\nIf the calculation was evolved further, the inner circumstellar disc would \\ncontinue to grow in radius as gas with higher angular momentum fell in.\\nEventually, the inner disc would meet the outer disc with only a\\nsmall molecular dissociation region between the two.\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=fig10.eps, width=12cm}\\n\\\\caption{\\\\label{bate.finalstate} The state of the system at the end of \\nthe calculation. The left graph gives the density (solid line) and \\nsmoothing length (dashed line) as a function of radius and the mass \\nenclosed within radius $r$ of the center of the stellar core (dotted line). \\nThe right graph gives the radial (solid line) and rotational (dotted line) \\nvelocities as functions of radius from the center of the stellar core. \\nThe densities, smoothing lengths and velocities are the mean values in \\nthe plane perpendicular to the rotation axis and through the stellar core. \\nThe stellar core ($r<0.004$ AU), inner circumstellar disc \\n($0.00460$ AU) are clearly visible.}\\n\\\\end{center}\\n\\\\end{figure}\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\vspace{18.0truecm}\\n%\\\\epsfig{file=fig11.eps, width=12.0cm}\\n\\\\caption{\\\\label{bate.finalstate2} The state of the system at the end of \\nthe calculation (not a time sequence). \\nThe upper six panels give the density in the plane \\nperpendicular to the rotation axis and through the stellar \\ncore. The lower six panels give the density in a \\nsection down the rotation axis. In each case, the six consecutive panels \\ngive the structure on a spatial scale that is 10 times smaller than the \\nprevious panel to resolve structure from 3000 AU to \\n$\\\\approx 0.2~{\\\\rm R}_\\\\odot$. The remnant of the first hydrostatic \\ncore (now a disc with spiral structure), the inner circumstellar disc, \\nand the stellar core are all clearly visible. The logarithm of the \\ndensity is plotted with the maximum and minimum \\ndensities (in g~cm$^{-3}$) given under each panel. }\\n\\\\vspace{-1.0truecm}\\n\\\\end{center}\\n\\\\end{figure}\\n\\n\\n\\\\subsection{Close binary stellar systems}\\n\\nThe ability to perform three-dimensional calculations which follow\\nthe collapse of molecular cloud cores to stellar densities allows\\nus to study the formation of close ($\\\\simless 1$ AU) binary\\nstellar systems. Currently, there is no accepted mechanism for \\nforming close binaries; the proposal that close binary systems form\\nvia the fission of a rapidly-rotating protostellar object \\nhas been discredited by studies of rapidly-rotating \\npolytropes \\\\cite{Durisenetal86}. Although fission\\nitself appears not to operate, it is possible that fragmentation\\ncan still occur due to the growth of non-axisymmetric perturbations\\nin rotationally-supported objects. Only two studies have \\nlooked at this possibility in detail \\\\cite{Boss87, BonBat94b}, and the\\nlatter of these finds that fragmentation of a massive circumstellar\\ndisc on scales ($\\\\simless 1$ AU) may be possible. However, in both\\nthese studies, only the region inside the first hydrostatic\\ncore was modelled and the initial conditions were chosen somewhat\\nartificially. The ability to perform three-dimensional \\ncalculations which follow the collapse of molecular cloud \\ncores to stellar densities now allows us to study the formation of\\nclose binaries from the collapse of larger-scale ($\\\\approx 10000$ AU)\\nmolecular cloud cores.\\n\\n\\n\\\\section{The evolution of an accreting protobinary system}\\n\\\\label{accretion}\\n\\nThe favoured mechanism for the formation of most binary stellar\\nsystems is the fragmentation of a collapsing molecular cloud core.\\nFragmentation has been studied numerically for $\\\\approx 20$ years.\\nThese calculations appear to show that it is possible to form binaries \\nwith similar properties to those that are observed via fragmentation. \\nHowever, they have not allowed us to predict the fundamental properties of \\nstellar systems such as the fraction of stellar systems which \\nare binary or the properties of binary \\nsystems (e.g.~the distributions of mass ratios,\\nseparations, and eccentricities and the properties of \\ndiscs in pre-main-sequence systems).\\n\\n\\nThere are two primary reasons for this lack of predictive power. \\nFirst, the results of fragmentation calculations depend sensitively\\non the initial conditions, which are poorly constrained.\\nThe second problem is that of accretion. Fragmentation \\ncalculations are typically stopped soon after the fragmentation\\noccurs, when the binary or multiple protostellar system contains \\nonly a small fraction of the total mass of the\\noriginal cloud \\\\cite{Boss86, BonBat94b}. However, because much\\nof the gas contained in the original cloud still has to fall on \\nto the system and be accreted, \\nthe final properties of the stellar system are \\nunknown. Following the calculation significantly beyond the\\npoint at which fragmentation occurs is extremely computationally \\nintensive. Thus, it is impossible to perform the number of \\ncalculations that are required to predict the statistical properties of \\nbinary stellar systems -- even if we knew the distribution of the \\ninitial conditions. On the other hand, if we can overcome this second\\ndifficulty, we can make theoretical predictions about the properties\\nof binary stars and, by comparing these predictions to the observed\\nproperties of binary systems, we may be able to better constrain\\nthe initial conditions for star formation.\\n\\n\\\\subsection{The Effects of Accretion on a Protobinary System}\\n\\nUsing SPH, Bate \\\\& Bonnell \\\\cite{BatBon97} studied and quantified how \\nthe properties of a binary system are affected by the accretion \\nof a small amount of gas from an infalling gaseous envelope. \\nThey found that the effects depend primarily on the specific \\nangular momentum of the gas and the binary's mass ratio \\n(see also \\\\cite{Artymowicz83, Bate97}). Generally, accretion of gas \\nwith low specific angular momentum decreases the mass ratio and \\nseparation of the binary, while accretion of gas with high \\nspecific angular momentum increases the separation and drives the \\nmass ratio toward unity. From these results, they predicted \\nthat closer binaries should have mass ratios that are biased \\ntoward equal masses compared to wider systems, since the gas which\\nfalls on to a closer system is likely to have more specific angular\\nmomentum, relative to the binary, than for a wider system.\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\vspace{9truecm}\\n%\\\\epsfig{file=fig12.eps, width=13cm}\\n\\\\caption{\\\\label{bate.accretion} The dependence of the \\ndistribution of gas around an accreting protobinary system\\non the specific angular momentum of the infalling gas \\n(increasing from left-to-right and downward). For gas with low\\nspecific angular momentum, only the primary forms a circumstellar\\ndisc and the secondary accretes a small amount of gas via a\\nBondi-Hoyle-type accretion stream. For gas with intermediate angular \\nmomentum, both the primary and secondary form circumstellar discs.\\nFor gas with high angular momentum, two circumstellar discs and\\na circumbinary disc are formed. Finally, for the case with\\nthe highest angular momentum, all the infalling gas settles into\\na circumbinary disc. The\\nbinary has a mass ratio of $q=0.6$ and the primary is on \\nthe right.\\n}\\n\\\\end{center}\\n\\\\end{figure}\\n\\nThey also studied the process of disc formation around an \\naccreting protobinary system and found that for each protostar,\\na circumstellar disc was only formed if the specific angular \\nmomentum of the infalling gas was greater than the specific\\norbital angular momentum of that protostar about the centre of\\nmass of the binary (Figure \\\\ref{bate.accretion}). This is because,\\nto be capture by one of the protostars, the gas much achieve the\\nsame specific orbital angular momentum as that of the protostar.\\nIf the gas has more specific angular momentum initially, some of its\\nangular momentum goes into forming a disc around the protostar.\\nHowever, if it has less specific angular momentum initially, there is\\nno excess angular momentum to form a circumstellar\\ndisc, and it must gain angular momentum even to be captured by\\nthe protostar. In this case, the infalling gas gains angular \\nmomentum as it falls on to the protostar in a Bondi-Hoyle-type accretion\\nstream. In practice, \\nthis means that a circumstellar disc is almost always formed around\\nthe primary, but the secondary does not have a circumstellar disc\\nunless the infalling gas has more specific angular momentum that\\nsome critical value. In a similar way, the formation of a circumbinary \\ndisc only begins when the specific angular momentum of the infalling\\ngas is great enough for the gas to form a circular orbit at a radius\\ngreater than that of the secondary from the centre of mass of the\\nbinary.\\n\\n\\n\\\\subsection{Development of a Protobinary Evolution Code}\\n\\nUsing the quantitative results of Bate \\\\& Bonnell \\\\cite{BatBon97}, \\nBate \\\\cite{Bate2000} developed a protobinary evolution (PBE) code \\nwhich follows the evolution of a protobinary system as it accretes \\nfrom its initial to its final mass, but does so in far less time \\nthan would be required for a full hydrodynamic calculation. \\n\\nThis code is based on the following model for the \\nformation of binary stellar systems (Figure \\\\ref{bate.model}). \\nThe model begins with a \\nmolecular cloud core of known initial density and angular \\nmomentum profile. It is assumed that this cloud begins to collapse\\nand that a `seed' binary system\\nis formed at the centre, presumably \\nvia some sort of fragmentation. The `seed' binary has mass \\nratio $q \\\\leq 1$,\\nseparation $a$, and is assumed to have a circular orbit.\\nIt initial consists of only a small fraction of the total mass of the core\\nand is assumed to have formed from the gas that was originally\\ncontained within a sphere of radius $r$, at the centre of the initial \\ncloud (Figure \\\\ref{bate.model}). For the results presented in\\nthis proceedings, the separation of the `seed' binary is set by assuming\\nthat the angular momentum of the gas from which the binary \\nforms is equal to the orbital angular momentum of the binary.\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=fig13.eps, width=7cm}\\n\\\\caption{\\\\label{bate.model} The model for studying the evolution of a \\nprotobinary system that forms within a collapsing molecular cloud \\ncore and is built up to its final mass by accreting the remaining \\ngas as it falls on to the binary.}\\n\\\\end{center}\\n\\\\end{figure}\\n\\nSubsequently, the binary accretes the remainder of the initial \\ncloud (which falls on to the binary) and the binary's \\nproperties evolve due to the accretion. This evolution is calculated\\nby taking a thin shell of gas of thickness d$r$ \\n(Figure \\\\ref{bate.model}), surrounding the\\nsphere from which the binary was formed, dividing the shell into \\nsmall elements of gas, and calculating the effect that each \\nelement of gas has on the protobinary when it is accreted\\n(using the results of Bate \\\\& Bonnell \\\\cite{BatBon97}). \\nThe binary's parameters (masses and separation) are updated,\\nand the next shell of gas is considered until the whole cloud \\nis accreted on to the binary. The amount of gas which settles \\ninto a circumbinary disc is also recorded. In this way, the code\\ncalculates the \\nevolution of the binary from its initial to its final state when\\nall of the original cloud's gas is contained\\neither in one of the two stars or their surrounding discs.\\n\\n\\n\\\\subsection{Testing the Protobinary Evolution Code}\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=fig14.eps, width=12.5cm}\\n\\\\caption{\\\\label{bate.testcase1} First comparison of the results from \\nthe protobinary evolution (PBE) code (solid lines) with those from a full SPH \\ncalculation (dotted lines). \\nThe graphs show the evolution of a protobinary system \\nthat was formed in the centre of a collapsing molecular cloud core \\nwhich initially had a uniform-density profile and was in solid-body \\nrotation. The evolution of the (a; upper left) mass ratio, (b; upper \\nright) separation, (c; lower) ratio of mass in a circumbinary disc \\nto that of the binary are plotted \\nas the binary accretes gas from the infalling envelope.}\\n\\\\end{center}\\n\\\\end{figure}\\n\\nTo test how accurately the PBE code describes the evolution \\nof a `seed' binary as it accretes from its initial to \\nits final mass, the PBE results were compared to those from \\nfull SPH calculations. Two test cases were performed. The first \\nfollowed the formation of a binary system from the collapse \\nof an initially uniform-density, spherical molecular cloud \\ncore in solid-body rotation. The `seed' binary was assumed \\nto have a mass ratio of $q=0.6$ and a mass of $1/10$ the\\ninitial cloud mass. The second test case was similar, except \\nthat the progenitor cloud was centrally-condensed with a 1/r-density \\ndistribution and the cloud had a total mass of only 5 times the\\n`seed' binary's mass. A full discussion of the test cases\\nis given by \\\\cite{Bate2000}.\\n\\n\\n\\\\subsubsection{Test Case 1}\\n\\nThe evolution of the mass ratio, separation and amount of gas\\nin the circumbinary disc are given for\\nthe PBE code and for a full SPH calculation in Figure \\n\\\\ref{bate.testcase1}. The curves are given as functions of the \\namount of gas that has fallen on to the binary, $M_{\\\\rm acc}$, \\nrelative to the binary's initial mass. \\nIn addition, an MPEG animation of the\\nSPH calculation is included on this CD-ROM as bate2.mpg.\\nThe CPU time required to evolve the SPH\\ncalculation until the entire cloud falls on to the binary in \\nis prohibitively long, which, after all, is the reason that \\nthe PBE code was developed in the first place. It takes \\n$\\\\approx 60$ orbits for the binary to increase its mass by \\na factor of 6 (i.e.~$\\\\approx 60$\\\\% of the total cloud was \\naccreted). The SPH calculation took $\\\\approx 5$ months on \\na 170 MHz Sun Ultra workstation with a GRAvity-PipE (GRAPE) board used\\nto calculate the gravitational forces and neighbouring SPH particles. \\nThe evolution with the PBE code took a few seconds!\\n\\nAlthough the SPH calculation did not run to completion, \\nwe can compare the evolution as the binary's mass increases \\nby a factor of 6 (Figure \\\\ref{bate.testcase1}). \\nGenerally, there is good agreement \\nbetween the PBE and SPH codes. The mass ratio is predicted \\nto within 5\\\\% over the entire evolution and the separation \\nto within 15\\\\%. In fact, as discussed in \\\\cite{Bate2000},\\nthe small differences between the PBE and SPH results \\nreflect unphysical treatment of the circumstellar discs\\nby the SPH code rather than a problem with the PBE code.\\nFor example, the slower rate of increase of the mass ratio\\ninitially is due to the circumsecondary disc not being \\nresolved correctly in the SPH calculation, and the larger\\nseparation when $M_{\\\\rm acc}\\\\simgreat 3$ is due to \\nunphysically-rapid viscous evolution of the \\ncircumstellar discs which transfers angular momentum into\\nthe binary's orbit too quickly. The greatest difference between\\nthe PBE and SPH results is that the PBE code predicts that a \\ncircumbinary disc should be formed around the binary whereas\\nno circumbinary disc is formed in the SPH calculation. This is\\ndue to the larger separation of the binary when $M_{\\\\rm acc}\\\\simgreat 3$ \\nand the large shear viscosity in the SPH calculation.\\n\\n\\n\\\\subsubsection{Test Case 2}\\n\\nUnlike test case 1, the PBE code predicts that a massive \\ncircumbinary disc should be produced very early in the \\nevolution of test case 2. Thus, test case 2 provides a \\nbetter test of how well the PBE code predicts the formation\\nof a circumbinary disc and its evolution. We note that,\\nalthough the\\nPBE code records the amount of gas which settles into a \\ncircumbinary disc, it does not attempt to take account of the\\ninteraction between the binary and the circumbinary disc. In\\nreality, this interaction is expected to result in the \\ntransfer of angular momentum from the orbit of the binary into\\nthe gas of the circumbinary disc and, hence, in a smaller \\nseparation. Furthermore, if the separation decreases, more \\nof the infalling gas would be expected to settle into the \\ncircumbinary disc and, for the same increase in the binary's\\nmass, the mass ratio should increase more rapidly because the\\ngas has a greater specific angular momentum relative to that of\\nthe binary. Thus, if a massive circumbinary disc is formed, \\nthe PBE code is expected to over-estimate the binary's separation, \\nunder-estimate the mass in the circumbinary disc, and slightly\\nunder-estimate the mass-ratio of the binary.\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=fig15.eps, width=12.5cm}\\n\\\\caption{\\\\label{bate.testcase2} Same as Figure 14, except that the \\nprotobinary system was formed from a molecular cloud core \\nwhich initially had a density profile of $\\\\rho \\\\propto 1/r$.}\\n\\\\end{center}\\n\\\\end{figure}\\n\\nThe evolution of the mass ratio, separation and amount of gas\\nin the circumbinary disc are given for test case 2 in Figure \\n\\\\ref{bate.testcase2}. An MPEG animation of the\\nSPH calculation is included on this CD-ROM as bate3.mpg.\\nTo avoid the problems that occurred due to the large shear viscosity\\nin the SPH calculation for test case 1, the SPH calculation here\\nuses a formulation with less shear viscosity (see \\\\cite{Bate2000}).\\nAs with test case 1, due to the computational cost, the SPH \\ncalculations were stopped before all of the gas had fallen on \\nto the binary. The SPH calculation took $\\\\approx 4$ months \\non a 300 MHz Sun Ultra workstation (using a binary tree, \\nnot a GRAPE board). During the evolution, the \\nbinary performed $\\\\approx 40$ orbits and $\\\\approx 60$\\\\%\\nof the total mass was accreted by the binary or settled \\ninto a circumbinary disc.\\n\\nThe agreement for the evolution of the mass ratio is even \\nbetter than it was with test case 1 with differences between the PBE\\nand SPH results of $\\\\simless 3$\\\\%. The separation\\nfollows the prediction of the PBE code to better than $3$\\\\%\\nuntil the circumbinary disc begins to form. Once the circumbinary\\ndisc attains approximately 5\\\\% of the binary's mass, however,\\nthe separation is always smaller than predicted by the PBE code.\\nAs described above, this is expected because the PBE code\\nneglects the separation-decreasing effect of the interaction \\nbetween the binary and the circumbinary disc. This also explains\\nwhy the PBE code slightly under-estimates the binary's mass ratio.\\nHowever, it is pleasing to see that even neglecting the \\ninteraction between the binary and the circumbinary disc, \\nthe PBE code still predicts the mass of the circumbinary disc to \\nwithin a factor of 2 of that given by the SPH code during the\\nentire evolution.\\n\\n\\n\\\\subsection{The Evolution of Accreting Protobinary Systems}\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=fig16.eps, width=12cm}\\n\\\\vspace{0.5truecm}\\n\\\\caption{\\\\label{bate.uniform} The evolution of protobinary systems \\nformed in the centre of collapsing molecular cloud cores as they \\naccrete from the gaseous envelope. The initial cores have uniform-density \\nprofiles and are in solid-body rotation. The evolution of the mass ratio \\n(a; upper left), separation (b; upper right), and ratio of the \\ncircumbinary disc mass to that of the binary (c; lower left), and the \\nrelative accretion rate (d; lower right) are given as functions of the \\namount of gas that has been accreted from the envelope. The evolutionary\\ncurves\\nare given for `seed' binary systems with initial mass ratios of $q=0.1$ to \\n$q=1.0$, with various different line types and/or widths for each. The \\ncurves are all given by a thin dotted lines once the circumbinary \\ndisc mass exceeds 5\\\\% of the binary's mass. Beyond this point, \\nthe binary's mass ratio and the mass in the circumbinary disc are likely \\nto be under-estimated, and the separation is likely to be over-estimated. }\\n\\\\end{center}\\n\\\\end{figure}\\n\\nAs we have seen, the PBE code gives a relatively accurate \\ndescription of the evolution of an accreting protobinary, but does\\nso $\\\\sim 10^6$ times faster than a full hydrodynamic SPH calculation.\\nThis allows us to perform many calculations to \\nstudy how the evolution of a binary as it accretes\\nto its final mass depends on its initial mass ratio and on the\\nproperties of the molecular cloud core from which it formed.\\n\\nAs examples, we give the evolution of `seed' binaries that form\\nfrom two types of molecular cloud core. A greater range of\\nmolecular cloud cores is considered in \\\\cite{Bate2000}.\\nFigure \\\\ref{bate.uniform} presents the evolution of\\nbinaries formed from molecular cloud cores which had\\nuniform-density and were in solid-body rotation before they began\\nto collapse dynamically. In Figure \\\\ref{bate.1r}, the \\nmolecular cloud cores had radial density profiles of $\\\\rho \\\\propto 1/r$\\nwith solid-body rotation, initially. \\nEvolutionary curves are provided for `seed' binaries\\nwith initial mass ratios ranging from $q=0.1-1.0$. \\n\\nIn all cases, the long-term evolution is towards a mass ratio \\nof unity, since the material that falls in later has higher \\nspecific angular momentum relative to that of the binary. \\nThus, the more the binary accretes relative to its initial mass, \\nthe stronger the tendency is for the mass ratio to be \\ndriven to unity. Similarly, the more the binary accretes \\nrelative to its initial mass, the more likely it is to be surrounded\\nby a circumbinary disc. Note that, in the previous sections,\\nwe found that when a massive circumbinary disc is formed, the PBE\\ncode tends to over-estimate the separation, and under-estimate \\nthe mass of the circumbinary disc and the binary's mass ratio.\\nThus, if anything, the evolutionary curves in Figures \\\\ref{bate.uniform}\\nand \\\\ref{bate.1r} tend to under-estimate the binary's mass ratio and \\nthe mass of the circumbinary disc.\\n\\n\\n\\\\subsection{The Properties of Binary Stars}\\n\\n\\\\begin{figure}[t]\\n\\\\begin{center}\\n\\\\epsfig{file=fig17.eps, width=12cm}\\n\\\\vspace{0.5truecm}\\n\\\\caption{\\\\label{bate.1r} Same as Figure 16, except that the \\nprotobinary systems were formed from a molecular cloud cores \\nwhich initially had a density profiles of $\\\\rho \\\\propto 1/r$.}\\n\\\\end{center}\\n\\\\end{figure}\\n\\nThe aim of developing the PBE code was to make it possible to predict\\nsome of the properties of binary stars and, by comparing\\nthese to the observed properties of binary systems, to constrain \\nthe initial conditions for binary star formation. \\n\\nIn order to obtain predictions about the properties of binaries we \\nnote that, generally, the initial mass of a `seed' binary is smaller \\nfor those binaries with smaller separations. This relationship\\nbetween a `seed' binary's mass and its separation is observed from\\nfragmentation calculations \\\\cite{Boss86, BonBat94b} and\\nis easily understood from a Jeans-mass argument \\\\cite{Bate2000}. \\nIn order for\\nfragmentation to occur, the Jeans length at the time of fragmentation\\nmust be less than or approximately equal to the separation of the\\nbinary which is formed. However, for a constant temperature,\\nthe Jeans mass depends linearly on the Jeans length. Thus, the\\nsmaller the separation of the `seed' binary, the smaller its initial\\nmass. Generally, `seed' binaries with separations $\\\\simless 10$\\nAU are expected to have masses $\\\\approx 0.01 {\\\\rm M}_{\\\\odot}$, while\\nfor larger separations, the `seed' mass is expected to increase\\napproximately linearly (i.e. `seed' binaries with separations of\\n100-1000 AU should have initial masses of \\n$\\\\approx 0.1-1.0 {\\\\rm M}_{\\\\odot}$).\\n\\nThis dependence of the initial mass on the separation means that\\nto form binaries with the same final total mass, the closer systems\\nneed to accrete more material, relative to their initial mass.\\nTherefore, from the evolutionary curves of Figures \\\\ref{bate.uniform}\\nand \\\\ref{bate.1r}, closer systems are more likely to have equal-mass\\ncomponents than wider systems.\\n\\nThis prediction is supported by surveys of main-sequence \\nG-dwarf stellar systems. Duquennoy \\\\& Mayor \\\\cite{DuqMay91} \\nfound that the mass-ratio distribution, averaged over \\nbinaries with all separations, increases toward small mass \\nratios. However, there is mounting evidence that\\nthe mass-ratio distributions differ between short and long-period\\nsystems with the distribution for close binary systems ($P <\\n3000$ days; $a \\\\simless 5$ AU) consistent with\\na uniform distribution \\\\cite{Mazehetal92, HalMayUdr98}.\\nThus, relative to wide systems, the close systems are biased toward\\nmass ratios of unity.\\n\\nThe fraction by which the mass of a `seed' binary must\\nbe increased in order for its mass ratio to approach unity depends\\non the conditions in the molecular cloud core. Generally,\\nthe less centrally-condensed a core is, the easier it is to \\nform a binary system with a low mass ratio \\n(c.f.~Figures \\\\ref{bate.uniform} and \\\\ref{bate.1r}).\\nWe can use this dependence of the evolutionary curves on the \\ntype of molecular cloud core to attempt to constrain the initial\\nconditions for binary star formation.\\n\\nDuquennoy \\\\& Mayor \\\\cite{DuqMay91} found that binaries containing\\nG-dwarfs with\\nseparations $\\\\simgreat 30$ AU generally have unequal masses\\n(typically $q\\\\approx 0.3$). Such binaries are likely to have\\naccreted from a few to ten times there initial mass. For uniform-density\\ncores (Figure \\\\ref{bate.uniform}), the observed mass-ratio \\ndistribution can easily be obtained. Cores with $\\\\rho \\\\propto 1/r$\\nresult in higher mass ratios than uniform-density cores, but it is\\nstill possible to envisage a spectrum of `seed' mass ratios which gives\\na final mass-ratio distribution which is consistent with the\\nobservations of wide binaries.\\n\\nHowever, close binaries ($\\\\simless 5$ AU) have initial masses\\nof $\\\\approx 0.01 {\\\\rm M}_{\\\\odot}$. Thus, they are expected to\\nhave to accrete up to 100 times their initial mass from the infalling\\ngaseous envelope before systems with G-dwarf primaries are obtained,\\nyet the observed mass-ratio distribution is approximately flat\\n(i.e.~approximately 1/2 the binaries have $q<0.5$). \\nIt is effectively impossible for cores in solid-body rotation \\nto produce such a mass ratio distribution if they are \\nsignificantly centrally-condensed (Figure \\\\ref{bate.1r}). \\nEven with uniform-density cores most of the `seed' binaries \\nwould need to have mass ratios $q<0.1$, which is unlikely.\\n\\nHowever, the PBE code only evolves circular binaries whereas \\nmost binaries have significant eccentricity \\\\cite{DuqMay91}.\\nFor the same semi-major axis, eccentric binaries have less \\nangular momentum than circular binaries meaning that the \\nclouds from which they formed may be rotating more slowly\\nand, thus, the gas in the envelope may have less angular momentum.\\nThis would result in slower evolution toward equal masses for\\neccentric binaries.\\nTaking the effects of eccentricity into account, it is quite \\npossible that the observed binary mass ratios could be \\nproduced by the collapse of molecular cloud cores\\nwith radial density profiles less centrally-condensed than $\\\\rho \\n\\\\propto 1/r$. However, even accounting for eccentric binaries, \\nit seems virtually impossible that the observed G-dwarf binary \\nsystems could have been formed from molecular cloud cores with\\ndensity profiles that were more centrally-condensed \\nthan $\\\\rho \\\\propto 1/r$.\\n\\nThe above conclusion that closer binaries should have mass ratios\\nthat are biased toward unity compared to wider systems with the\\nsame total mass is just one of many predictions that may be\\nderived using the PBE code (see \\\\cite{Bate2000}). \\nOthers include: closer binaries are \\nmore likely to have circumbinary discs than wider binaries; \\nbrown dwarf companions to solar-type stars\\nshould be very rare at separations $\\\\simless 5$ AU, but their\\nfrequency should increase at larger separations. \\n\\n\\n\\\\section{Conclusions}\\n\\nThe Lagrangian nature of SPH and its inherent ability to\\nprovide finer spatial resolution in regions of higher density \\nmake it a powerful tool which is ideally suited for \\nstudying star formation.\\n\\nRecent advances in the study of binary star formation that \\nhave been made using SPH include: the realisation that it is\\nessential that the Jeans mass is always resolved in numerical \\nstudies of self-gravitating gas; the ability to perform \\nthree-dimensional hydrodynamic calculations which follow the \\ncollapse of a molecular cloud core to stellar densities;\\nthe study of the effects of accretion on a protobinary systems\\nand the development of a code which enables the evolution of\\naccreting binary systems to be followed $\\\\sim 10^6$ times \\nfaster than a full hydrodynamic calculation. 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J., 1978, MNRAS, 184, 481\n\n\n\\bibitem{GinMon81}\n Gingold R. A., Monaghan J. J., 1981, MNRAS, 197, 461\n\n\n\\bibitem{HalMayUdr98}\n Halbwachs J. L., Mayor M., Udry S., 1998, in Rebolo R., Martin E. L., Zapatero Osorio M.R., eds., Brown Dwarfs and Extrasolar Planets (ASP Conf. Ser. 134). Brigham Young University, Provo, p. 308\n\n\n\\bibitem{Heller93}\n Heller, C. H., 1993, ApJ, 408, 337\n\n\n\\bibitem{HerKat89}\n Hernquist L., Katz N., 1989, ApJS, 70, 419\n\n\n\\bibitem{ImaDurPic99}\n Imamura J. N., Durisen R. H., Pickett B. K., 1999, ApJ, in press\n\n\n\\bibitem{Larwoodetal96}\n Larwood J. D., Nelson R. P., Papaloizou J. C. B., Terquem C., 1996, MNRAS, 282, 597\n\n\n\\bibitem{Lattanzioetal85}\n Lattanzio J. C., Monaghan J. J., Pongracic H., Schwarz M. P., 1985, MNRAS, 215, 125\n\n\n\\bibitem{Mazehetal92}\n Mazeh T., Goldberg D., Duquennoy A., Mayor M., 1992, ApJ, 401, 265\n\n\n\\bibitem{MiyHayNar84}\n Miyama S. M., Hayashi C., Narita S., 1984, ApJ, 279, 621\n\n\n\\bibitem{Monaghan92}\n Monaghan J. J., 1992, ARA\\&A, 30, 543\n\n\n\\bibitem{Nelsonetal98}\n Nelson A. F., Benz W., Adams F. C., Arnett D., ApJ, 502, 342\n\n\n\\bibitem{NelPap93}\n Nelson R., Papaloizou J. C., 1993, MNRAS, 265, 905\n\n\n\\bibitem{SigKla97}\n Sigalotti L. Di G., Klapp J., A\\&A, 319, 547\n\n\n\\bibitem{Tohline82}\n Tohline, J. E., 1982, Fund. Cos. Phys., 8, 1\n\n\n\\bibitem{Trueloveetal97}\n Truelove J. K., Klein R. I., McKee C. F., Holliman J. H. II, Howell L. H., Greenough J. A., 1997, ApJ, 489, L179\n\n\n\\bibitem{Trueloveetal98}\n Truelove J. K., Klein R. I., McKee C. F., Holliman J. H. II, Howell L. H. Greenough J. A., \\& Woods D. T., 1998, ApJ, 495, 821\n\n\n\\bibitem{VanCam98}\n Vanhala, H. A. T., Cameron A. G. W., 1998, ApJ, 508, 291\n\n\n\\bibitem{Whitworth98}\n Whitworth A. P., 1998, MNRAS, 296, 442\n\n"}],"string":"[\n {\n \"name\": \"astro-ph0002202.extracted_bib\",\n \"string\": \"\\\\bibitem{Artymowicz83}\\n Artymowicz P., 1983, Acta Astronomica, 33, 223\\n\\n\\n\\\\bibitem{ArtLub94}\\n Artymowicz P., Lubow S. H., 1994, ApJ, 421, 651\\n\\n\\n\\\\bibitem{Bate97}\\n Bate M. R., 1997, MNRAS, 285, 16\\n\\n\\n\\\\bibitem{Bate98}\\n Bate M. R., 1998, ApJ, 508, L95\\n\\n\\n\\\\bibitem{Bate2000}\\n Bate M. R., 2000, MNRAS, submitted\\n\\n\\n\\\\bibitem{BatBon97}\\n Bate M. R., Bonnell I. A., 1997, MNRAS, 285, 33\\n\\n\\n\\\\bibitem{BatBonPri95}\\n Bate M. R., Bonnell I. A., Price N. M., 1995, MNRAS, 277, 362\\n\\n\\n\\\\bibitem{BatBur97}\\n Bate M. R., Burkert A., 1997, MNRAS, 288, 1060\\n\\n\\n\\\\bibitem{Benz90}\\n Benz W., 1990, in Buchler J. R., ed., The Numerical Modeling of Nonlinear Stellar Pulsations: Problems and Prospects. Kluwer, Dordrecht, p. 269\\n\\n\\n\\\\bibitem{BonBas91}\\n Bonnell I. A., Bastien P., 1991, ApJ, 374, 610\\n\\n\\n\\\\bibitem{BonBat94b}\\n Bonnell I. A., Bate M. R., 1994, MNRAS, 271, 999\\n\\n\\n\\\\bibitem{Boss86}\\n Boss A. P., 1986, ApJS, 62, 519\\n\\n\\n\\\\bibitem{Boss87}\\n Boss A. P., 1987, ApJ, 319, 149\\n\\n\\n\\\\bibitem{Boss98}\\n Boss A. P., 1998, ApJ, 501, 77\\n\\n\\n\\\\bibitem{BurBod93}\\n Burkert A., Bodenheimer P., 1993, MNRAS, 264, 798\\n\\n\\n\\\\bibitem{Chapmanetal92}\\n Chapman S., Pongracic H., Disney M., Nelson A., Turner J., Whitworth A., 1992, Nature, 359, 207\\n\\n\\n\\\\bibitem{Durisenetal86}\\n Durisen R. H., Gingold R.A., Tohline J.E., Boss A.P., 1986, ApJ, 305, 281\\n\\n\\n\\\\bibitem{DuqMay91}\\n Duquennoy A., Mayor M., 1991, A\\\\&A, 248, 485\\n\\n\\n\\\\bibitem{Evrard88}\\n Evrard A. E., 1988, MNRAS, 235, 911\\n\\n\\n\\\\bibitem{Lucy77}\\n Lucy L., 1977, AJ, 82, 1013\\n\\n\\n\\\\bibitem{GinMon77}\\n Gingold R. A., Monaghan J. J., 1977, MNRAS, 181, 375\\n\\n\\n\\\\bibitem{GinMon78}\\n Gingold R. A., Monaghan J. J., 1978, MNRAS, 184, 481\\n\\n\\n\\\\bibitem{GinMon81}\\n Gingold R. A., Monaghan J. J., 1981, MNRAS, 197, 461\\n\\n\\n\\\\bibitem{HalMayUdr98}\\n Halbwachs J. L., Mayor M., Udry S., 1998, in Rebolo R., Martin E. L., Zapatero Osorio M.R., eds., Brown Dwarfs and Extrasolar Planets (ASP Conf. Ser. 134). Brigham Young University, Provo, p. 308\\n\\n\\n\\\\bibitem{Heller93}\\n Heller, C. H., 1993, ApJ, 408, 337\\n\\n\\n\\\\bibitem{HerKat89}\\n Hernquist L., Katz N., 1989, ApJS, 70, 419\\n\\n\\n\\\\bibitem{ImaDurPic99}\\n Imamura J. N., Durisen R. H., Pickett B. K., 1999, ApJ, in press\\n\\n\\n\\\\bibitem{Larwoodetal96}\\n Larwood J. D., Nelson R. P., Papaloizou J. C. B., Terquem C., 1996, MNRAS, 282, 597\\n\\n\\n\\\\bibitem{Lattanzioetal85}\\n Lattanzio J. C., Monaghan J. J., Pongracic H., Schwarz M. P., 1985, MNRAS, 215, 125\\n\\n\\n\\\\bibitem{Mazehetal92}\\n Mazeh T., Goldberg D., Duquennoy A., Mayor M., 1992, ApJ, 401, 265\\n\\n\\n\\\\bibitem{MiyHayNar84}\\n Miyama S. M., Hayashi C., Narita S., 1984, ApJ, 279, 621\\n\\n\\n\\\\bibitem{Monaghan92}\\n Monaghan J. J., 1992, ARA\\\\&A, 30, 543\\n\\n\\n\\\\bibitem{Nelsonetal98}\\n Nelson A. F., Benz W., Adams F. C., Arnett D., ApJ, 502, 342\\n\\n\\n\\\\bibitem{NelPap93}\\n Nelson R., Papaloizou J. C., 1993, MNRAS, 265, 905\\n\\n\\n\\\\bibitem{SigKla97}\\n Sigalotti L. Di G., Klapp J., A\\\\&A, 319, 547\\n\\n\\n\\\\bibitem{Tohline82}\\n Tohline, J. E., 1982, Fund. Cos. Phys., 8, 1\\n\\n\\n\\\\bibitem{Trueloveetal97}\\n Truelove J. K., Klein R. I., McKee C. F., Holliman J. H. II, Howell L. H., Greenough J. A., 1997, ApJ, 489, L179\\n\\n\\n\\\\bibitem{Trueloveetal98}\\n Truelove J. K., Klein R. I., McKee C. F., Holliman J. H. II, Howell L. H. Greenough J. A., \\\\& Woods D. T., 1998, ApJ, 495, 821\\n\\n\\n\\\\bibitem{VanCam98}\\n Vanhala, H. A. T., Cameron A. G. W., 1998, ApJ, 508, 291\\n\\n\\n\\\\bibitem{Whitworth98}\\n Whitworth A. 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astro-ph0002101
|
Red Companions to a z=2.15 Radio Loud Quasar
|
[
{
"author": "D.L. Clements$^{1,2,3}$"
},
{
"author": "$^1$Department of Physics and Astronomy"
},
{
"author": "PO Box 913"
},
{
"author": "Cardiff"
},
{
"author": "CF24 3YB"
},
{
"author": "$^2$Institut d'Astrophysique Spatiale"
},
{
"author": "B\\^atiment 121"
},
{
"author": "Universite Paris XI"
},
{
"author": "F-91405 ORSAY CEDEX"
},
{
"author": "France"
},
{
"author": "$^3$European Southern Observatory"
},
{
"author": "Karl-Schwarzschild-Strasse 2"
},
{
"author": "D-85748 Garching-bei-Munchen"
},
{
"author": "Germany"
}
] |
We have conducted observations of the environment around the z=2.15 radio loud quasar 1550-269 in search of distant galaxies associated either with it or the z=2.09 CIV absorber along its line of sight. Such objects will be distinguished by their red colours, R-K$>$4.5. We find five such objects in a 1.5 arcmin$^2$ field around the quasar, with typical K' magnitudes of $\sim$20.4 and no detected R band emission. We also find a sixth object with K=19.6$\pm$0.3, and undetected at R, just two arcseconds from the quasar. The nature of all these objects is currently unclear, and will remain so until we have determined their redshifts. We suggest that it is likely that they are associated with either the quasar or the CIV absorber, in which case their properties might be similar to those of the z=2.38 red Ly$\alpha$ emitting galaxies discovered by Francis et al. (1997). The small separation between the quasar and the brightest of our objects suggests that it may be the galaxy responsible for the CIV metal line absorption system. The closeness to the quasar and the red colour might have precluded similar objects from being uncovered in previous searches for emission from CIV and eg. damped absorbers.
|
[
{
"name": "rlqcomp.tex",
"string": "%\\documentstyle[doublespacing,psfig]{mn}\n\\documentstyle[psfig]{mn}\n\\def\\mic{\\,\\mu\\rm m}\n\\begin{document}\n\\title[z=2.15 Red Quasar Companions]{Red Companions to a z=2.15 Radio Loud Quasar}\n\\author[D.L. Clements]\n{D.L. Clements$^{1,2,3}$\\\\ $^1$Department of Physics and Astronomy,\nUniversity of Wales Cardiff, PO Box 913, Cardiff, CF24 3YB\\\\\n$^2$Institut d'Astrophysique Spatiale, B\\^atiment 121, Universite\nParis XI, F-91405 ORSAY CEDEX, France\\\\ $^3$European Southern Observatory,\nKarl-Schwarzschild-Strasse 2, D-85748 Garching-bei-Munchen, Germany}\n\n\\maketitle\n\n\\begin{abstract}\nWe have conducted observations of the environment around the z=2.15\nradio loud quasar 1550-269 in search of distant galaxies associated\neither with it or the z=2.09 CIV absorber along its line of\nsight. Such objects will be distinguished by their red colours,\nR-K$>$4.5. We find five such objects in a 1.5 arcmin$^2$ field around the\nquasar, with typical K' magnitudes of $\\sim$20.4 and no detected R band\nemission. We also find a sixth object with K=19.6$\\pm$0.3, and\nundetected at R, just two arcseconds from the quasar. The nature of all these\nobjects is currently unclear, and will remain so until we have determined\ntheir redshifts. We suggest that it is likely that they are associated with\neither the quasar or the CIV absorber, in which case their properties\nmight be similar to those of the z=2.38 red Ly$\\alpha$ emitting galaxies\ndiscovered by Francis et al. (1997). The small separation between\nthe quasar and the brightest of our objects suggests that it may be the\ngalaxy responsible for the CIV metal line absorption system. The closeness\nto the quasar and the red colour might have precluded similar objects from\nbeing uncovered in previous searches for emission from CIV\nand eg. damped absorbers.\n\\end{abstract}\n\n\\begin{keywords}\nquasars;absorption systems -- quasars;infrared -- galaxies;high redshift\n\\end{keywords}\n\n\\section{Introduction}\n\nThe selection of high redshift galaxies on the basis of their colours\nhas been a growth industry over the last 5 years. Much of this\nwork has concentrated on the selection of high (z$>$3) redshift\nobjects through `dropout' techniques. Such methods have had\nconsiderable success (eg. Steidel et al. 1999). However, many of these\ntechniques are reliant on emission in the rest-frame ultraviolet. The\nUV emission from a galaxy can easily be dominated by a small burst of\nstar formation, or alternatively obscured by a relatively small amount\nof dust. A population of older quiescent galaxies might thus coexist\nwith the UV selected high redshift objects. Studies of the stellar\npopulations in moderate redshift radio galaxies provide some support\nfor this idea. A number of authors (eg. Stockton et al. (1995),\nSpinrad et al. (1997)) have shown that several radio galaxies have\nages $>$3--5 Gyr at z$\\sim$1.5, indicating that they must have formed\nat z$>$5. These results have even been used (Dunlop et al. 1996) to\nargue that $\\Omega$ must be significantly less than 1.\n\nOld galaxies at moderate redshift, passively evolving from z$>$5 to\nz=1.5 -- 2.5, would appear as red objects, with R-K' colours\n$>$4.5. There has been considerable interest in such red objects. Much\nof this work has centred on red objects found in the fields of known\nhigh redshift AGN (eg. Hu \\& Ridgeway (1994), Yamada et al.,\n(1997)). A large survey of the environments of z=1--2 quasars (Hall et\nal., 1998) finds that such associations are quite common. The present\npaper attempts to push such studies above z=2. The alternative\napproach, to study red objects in the field, is also an active area\nwith several surveys dedicated to or capable of finding such objects.\nSee eg. Cohen et al. (1999), or Rigopoulou et al. (in preparation).\nRed objects need not be old, though. An alternative explanation is that they\nare heavily obscured, and may contain either a redenned AGN or massive\nstarburst (eg. Dey et al., 1999, Egami et al., 1996). In this context it is\ninteresting to note that several of the objects found in recent\ndeep submm surveys have been identified with very red objects (Smail\net al., 1999; Clements et al., in preparation).\n\nFinding emission from the putative galaxies responsible for metal and\ndamped-Ly$\\alpha$ absorption line systems has been the goal of\nnumerous observational programmes. At low redshift there has been\nconsiderable success in identifying the galaxies responsible for MgII\nabsorption systems (Bergeron \\& Boisse, 1991; Steidel et al., \n1997. At higher redshifts, interest has mostly focussed on the\ndamped-Ly$\\alpha$ absorption systems. Searches for line emission from\nsuch objects (eg. Bunker et al. 1999; Wolfe et al. 1992) has met with\nvarying success (Leibundgut \\& Robertson, 1999). Fewer observers have looked in the\ncontinuum, but there have been some successes there as well. For\nexample, Aragon-Salamanca et al. (1996) found close companions to 2\nout of 10 quasars with damped absorbers in a K band survey. As yet\nthere has been no spectroscopic confirmation of these identifications,\nbut the broad characteristics of these objects, and the small fraction\nof damped absorbers detected, is consistent with plausible models for\nthe evolution of the galaxies responsible (Mathlin et al., in\npreparation). Meanwhile, Aragon-Salamanca et al. (1994) looked for\ncounterparts to multiple CIV absorbers lying at z$\\sim$1.6, also using K band\nobservations. They found an excess of K band objects near to the quasars,\nconsistent with their being responsible for the CIV absorption. Once again,\nthere is no spectroscopic confirmation of the assumed redshifts.\n\nThe present paper presents the first results of a programme aimed at\nfinding quiescent objects at high redshift (z$\\sim$2--2.5) using\noptical/IR colour selection techniques. Among the targets observed in\nan initial test programme was the radio loud quasar 1550-2655,\nselected as an example radio loud object. The rest of the paper is\norganised as follows. Section 2 describes our observations, data\nanalysis and presents the results. Section 3 discusses these results\nand examines three possible origins for the red objects we have found\nto be associated with 1550-2655. Finally we draw our conclusions. We\nassume $\\Omega_M$ = 1, $\\Lambda$=0 and H$_0$=100 kms$^{-1}$Mpc$^{-1}$\nthroughout this paper.\n\n\n\\section{Observations and Results}\n\nAs part of a programme to examine the role of quiescent galaxies at\nz=2--2.5, we observed the field surrounding the radio loud quasar\n1550-2655. This object lies at a redshift of 2.15 and shows signs of\nassociated Ly$\\alpha$ absorption (Jauncey et al., 1984). Its spectrum\nalso contains a CIV absorber at z=2.09. Observations were made at\nthe 3.5m ESO NTT, and data reduction used standard IRAF and Eclipse\nroutines.\n\nThe optical observations, in R band, were conducted in service mode on\n20 August 1997 using the SUSI imager. This provides high resolution\nimages, with a pixel size of 0.13''. A total integration time of\n3600s was obtained on the source. This integration time was broken up\ninto 12 subintegrations of 300s each, whose relative positions were\nshifted by up to 40'' in a semi-random jitter pattern. These images\nwere bias subtracted, flat fielded using a sky flat made on the\ntwilight sky, then aligned and median combined to produce the final\nimage. A residual gradient going from left to right across the image\nwas apparent in the final data. This was removed by subtracting a\nlow-order polynomial fitted to each horizontal row of pixels once\ndetected objects had been masked off. The final R band image is shown\nin Figure 1a. Seeing was measured to be marginally subarcsecond on the\nfinal image.\n\nThe infrared data was obtained using the K' filter on the SOFI\ninfrared imager on 12 July 1998. The 3600s of integration were obtained\nin 60 one minute sub-integrations which themselves were the result of\nsix 10s integrations. The 60 one minute sub-integrations were shifted\nrelative to one another in a random 15'' size dithering pattern to\nallow for sky background determination and subtraction. The flat field\nwas obtained using a standard lamp ON $-$ lamp OFF dome flat. The\ndata were reduced using the Eclipse package by Nick Devillard\n(1997). The algorithms used for reducing dithered infrared data in\nthis package are detailed in Devillard (1999). In summary, the package allows\nfor flat fielding with the preprepared flat, and conducts sky\nsubtraction using a running average of 10 offset images. It then\nidentifies sources on each image and uses a correlation technique to\ncalculate the offsets between them. The separate subintegrations are\nthen offset and combined to produce the final image. Seeing was measured in\nthe final image to be $\\sim$ 0.9''.\n\nPhotometric calibration used the Landolt standard\n(Landolt, 1992) PG1633+099C in R band, and the faint IR standards\nP499E and S875C at K' (Cassali \\& Hawarden, 1992). Galactic extinction\nwas corrected using values obtained from the NASA Extragalactic\nDatabase (NED).\n\nAfter data reduction and flux calibration, the SUSI image, which has a\nresolution of 0.13''/pixel, was rebinned to match the 0.292''/pixel\nSOFI resolution, and the images were aligned. The final matched images\nwere 67 by 88 arcseconds in size. The main limiting factor on this\nsize was the small SUSI field of view and the dithering scheme used\nfor the optical observations. We then used SExtractor to select\nobjects detected at K' and to extract their photometric properties in\nmatched apertures in the two passbands. To qualify for detection, an\nobject had to have a 1.5$\\sigma$ significance flux in 10 connected\npixels in the K' band image (ie. $\\sim$ 5$\\sigma$ significance\noverall). This matched catalogue can then easily be searched for\nobjects with specific colour criteria. We detected a total of 75\nobjects in K' down to a limiting magnitude of $\\sim20.5$.\n\nThe catalogue was then searched for candidate red objects, with\nR-K'$>$4.5. We found five such objects in the catalogue, details of\nwhich are given in Table 1. Their positions are also shown in Figure 1,\nwhich shows both the R and K' band images of the quasar field.\n\n\\subsection{A Red Quasar Companion}\n\nComparison of the R and K' images of the quasar itself shows what would\nappear to be a red companion object --- apparent as an extension in K,\nbut absent in the R band image. The reality of this object was\ninvestigated by subtracting off the unresolved quasar contribution.\nThis was achieved by selecting a star, with no close companions, in\nthe observed field and using this as a PSF model. The central value of\nthe PSF image was scaled to match that in the quasar image, and then\nthe two images were subtracted. The companion was clearly visible in\nthe K'-band PSF subtracted image, but was entirely absent in the R-band\nPSF subtracted image. The companion is marginally resolved, having a\nsize of roughly 1.5 x 1 arcseconds, and is situated $\\sim$2 arcseconds\nfrom the quasar. R and K' magnitudes were extracted from the PSF\nsubtracted image, indicating that the quasar companion is also\nred. Its details are included in Table 1.\n\n\\vspace{1cm}\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{crrr} \\hline\nObject No.&Kmag&Rmag&R-K\\\\ \\hline\nR1&20.2$\\pm$0.1&$>$24.8&$>$4.6\\\\\nR2&20.2$\\pm$0.1&$>$25.3&$>$5.1\\\\\nR3&20.4$\\pm$0.1&$>$25.3&$>$4.9\\\\\nR4&20.3$\\pm$0.1&$>$24.9&$>$4.6\\\\\nR5&20.3$\\pm$0.1&$>$25.0&$>$4.7\\\\\nC1&19.5$\\pm$0.3&$>$24.5&$>$5.0\\\\ \\hline\n\\end{tabular}\n\\caption{Properties of red companions to the RLQ 1550-2655}\nAll limits given are 3$\\sigma$. The quasar companion is object C1.\n\\end{center}\n\\end{table}\n\n\\begin{figure*}\n\\begin{tabular}{cc}\n\\psfig{file=clementsd1_1.ps,width=8cm}\n\\psfig{file=clementsd1_2.ps,width=8cm}\\\\\n\\end{tabular}\n\\caption{R (left) and K' band (right) images of the quasar field.}\nThe red associates are indicated in each image. Note their clear detections\nin the K' image, and their non-detections in the deeper R band image.\n\\end{figure*}\n\n\n\\section{Discussion}\n\nUntil we can obtain spectroscopy for these objects, it is difficult to\nassess their importance or role in this system. There are three possible\norigins for these red objects: (1) they are associated with the quasar,\nlying at z=2.15; (2) they are associated with the CIV absorber at\nz=2.09; (3) they are foreground objects, unrelated to the quasar or CIV\nsystem. We will assess each of these alternatives in turn.\n\n\\subsection{Association with the Quasar}\n\nThe density of red objects in this field is surprisingly high -\n$\\sim 4\\pm1.5$ arcmin$^{-2}$ as opposed to the supposed global value of\n$\\sim 1\\pm0.3$ arcmin$^{-2}$ (Cohen et al. 1999). The density of red objects\nnear to the quasar is significantly higher, with three of the red\nobjects as well as the companion lying in a 0.25 arcmin$^{-2}$ region\nnear the quasar. This is certainly suggestive that there is some\nconnection between the red objects and the AGN (or CIV system). Other\nstudies have found a similar connection between red objects and AGN,\nespecially radio loud AGN. Perhaps the largest survey to date is that\nof Hall et al. (1999) who obtained images of 31 z=1 -- 2 radio loud\nquasars and found a significant excess of red galaxies around them.\nInterestingly they found two radial dependencies for this excess, one\nof which lies close to the quasar ($<$40'') and another more distant\n(40''--100''). This is perhaps reflected in the present study, with\ntwo red objects in the second class, further from the quasar, and the\nrest, including the close companion, within 40''. In this\ninterpretation, the close companion would be $\\sim$26kpc from the\nquasar, and would be about 20x15 kpc in size. Hydrogen in this object\nmight be responsible for the associated absorption seen in the quasar\nspectrum.\n\nIf we take the redshift of the companion galaxies to be the same as\nthe quasar, then the implied absolute magnitudes would be $\\sim$-24 to\n-25, ie. about L$^{*}$ (using the luminosity function of Mobasher et\nal., 1993 and converting to the assumed cosmology). This calculation\nof course ignores K-corrections, but these are expected to be quite\nlow in the K-band. Cowie et al (1994) calculate K-corrections at\nz$\\sim$2.1 to be less than 1 for all morphological classes from E to\nIrr. We also note that these results are not dissimilar to those of\nFrancis et al. (1997) who uncovered a group of similarly red objects\nat z=2.38 associated with a cluster of quasar absorption line\nsystems. K' magnitudes for these objects are similar to, or brighter\nthen, those of the objects discussed here. It is interesting to note\nthat the Francis et al. objects are all Ly$\\alpha$ emitters. If the\npresent red objects have similar properties, then such line emission\nwould make redshift determination much easier.\n\n\\subsection{Association with the CIV Absorber}\n\nMany of the same comments regarding direct association with the quasar\ncan be made regarding association with the CIV absorber: there is an\nunusually high density of red objects in this region suggesting some\nconnection between them. Of particular interest here is the closeness\nof the quasar companion to the quasar - only $\\sim$2'' away, or 26kpc\nat the redshift of the CIV absorber, and with a size similar to that 7 \n\ngiven above. To date little is known about the nature of CIV\nabsorbers, so the possible identification of the galaxy responsible\nfor one is rather interesting. Previous work looking for emission\nlines from objects associated with damped and CIV absorbers (Mannucci\net al., 1998) suggests that galaxies are more likely to cluster with\nabsorbers than with quasars. If correct, this would suggest that the\nobjects found here are more likely to be associated with the absorber\nthan the quasar.\n\nThere has been a long and largely unsuccessful history of searches for\nemission from absorption line systems in quasars at large\nredshift. These have largely concentrated on emission lines, whether\nLy$\\alpha$ (eg. Leibundgut \\& Robertson, 1999), H$\\alpha$, (eg. Bunker\net al., 1999), or others, though work in the infrared continuum has perhaps\nshown greater success (see eg. Aragon-Salamanca et al., 1996,\n1994). If the quasar companion in the present study is indeed\nresponsible for the CIV absorption, then we may have an explanation\nfor the failures. The object is both red and quite close to the\nquasar. Detection of the companion would require both good seeing\n(conditions for our own observations were sub-arcsecond) and\nobservations in the near-IR as well as the ability to subtract off the\nquasar contribution. Sensitive infrared detectors have only recently\nbecome available at most observatories, while subarcsecond seeing is\nonly rarely achieved. We might thus have been lucky in being able to\ndetect the companion. New instruments, such as UFTI at UKIRT, which\ncombines adaptive optics correction (regularly 0.5'') with a superb\ninfrared imager, can regularly make such observations. This will\nhopefully allow us to make significant advances in our understanding\nof high redshift absorption line systems.\n\n\\subsection{Foreground Contaminants}\n\nThe possibility that the red objects are at an entirely different\nredshift to the quasar and absorber must still be considered while we\ndo not have confirming redshift spectra. In this context it is\nsalutary to note the lesson of the first VRO discovered (Hu \\&\nRidgeway, 1994), known as HR10. This was found in the field of a\nz=3.79 quasar, but was later shown to have a redshift of 1.44 (Graham\n\\& Dey, 1996).\nHowever, the number density of red objects in their field was 0.9\narcmin$^{-2}$ which matches the field density of red objects discussed\nby Cohen et al. (1999), and is lower than that found here.\n\n\\section{Conclusions}\n\nAt present there are several deficiencies in our data. Firstly we have\nonly obtained limits on the objects R band magnitudes. We must detect\nthem and measure, rather than limit, their R band magnitudes before we\ncan properly determine their colours. Secondly we must obtain spectra\nfor the objects so that we can actually determine, rather than\nspeculate on, their redshift. However, the results presented here\nsuggest that a larger survey of quasar environments, both with and\nwithout absorbers, using infrared imagers with adaptive optics\ncorrection might shed new light on galaxy populations at large redshift.\n\\\\~\\\\\n{\\bf Acknowledgments} This paper is based on observations made at the\nEuropean Southern Observatory, Chile. It is a pleasure to thank Nick\nDevillard for his excellent Eclipse data reduction pipeline, and\nE. Bertin for SExtractor. This research has made use of the NASA/IPAC\nExtragalactic Database (NED) which is operated by the Jet Propulsion\nLaboratory, California Institute of Technology, under contract with\nthe National Aeronautics and Space Administration. I would like to\nthank Amanda Baker and Garry Mathlin for useful discussions, and the\nanonymous referee for helpful comments on an earlier version. This\nwork was supported in part by an ESO fellowship, EU TMR Network\nprogramme FMRX-CT96-0068 and by a PPARC postdoctoral grant.\n\n\\begin{thebibliography}{}\n\n\\bibitem[\\protect\\citename{Aragon-Salamanca et al. }1996]{a96}\nAragon-Salamanca, A., Ellis, R.S., O'Brien, K.S., 1996, MNRAS,\n281, 945\n\n\\bibitem[\\protect\\citename{Aragon-Salamanca et al. }1994]{a94}\nAragon-Salamanca, A., Ellis, R.S., Schwartzenberg, J.-M.,\nBergeron, J.A., 1994, ApJ., 421, 27\n\n\\bibitem[\\protect\\citename{Bergeron \\& Boisse, }1991]{b91}\nBergeron, J., Boisse, P., 1991, A\\&A, 243, 344\n\n\\bibitem[\\protect\\citename{Bunker et al. }1999]{b99}\nBunker, A.J., Warren, S.J., Clements, D.L., Williger, G.M., Hewitt, P.C., 1999, MNRAS, in press\n\n\\bibitem[\\protect\\citename{Cassali }1992]{c92}\nCassali, M.M., \\& Hawarden, T.G., 1992, JCMT-UKIRT Newsletter, NO. 3, August 1992, p33\n\n\\bibitem[\\protect\\citename{Cohen et al., }1999]{c99}\nCohen, J.G., Hogg, D.W., Blandford, R., Pahre, M.A., Shopbell, P.L.., 1999,\nin Astrophysics with Infrared Arrays: A prelude to SIRTF, p. 47, eds. Bicay, M.D.,\nBeichman, C.A., Cutri, R.M., Madore, B.F., pub. ASP\n\n\\bibitem[\\protect\\citename{Cowie et al., }1994]{c94}\nCowie, L.L., Gardner, J.P., Hu, E.M., Songaila, A., Hodapp, K-W.,\nWainscoat, R.J., 1994, ApJ., 434, 114\n\n\\bibitem[\\protect\\citename{Devillard, }1997]{d97}\nDevillard, N., \"The eclipse software\", The messenger No 87 - March 1997 \n\n\\bibitem[\\protect\\citename{Devillard, }1999]{d99a}\nDevillard, N., 1999, ESO Documentation, http://www.eso.org/projects/dfs/papers/jitter99/\n\n\\bibitem[\\protect\\citename{Dey et al., }1999]{d99b}\nDey, A., Graham, J.R., Ivison, R., Smail, I., Wright, G.S., Liu, M.C.,\n1999, ApJ., 610\n\n\\bibitem[\\protect\\citename{Dunlop et al. }1996]{d96}\nDunlop, J., Peacock, J., Spinrad, H., Dey, A., Jimenez, R., Stern, D., Windhorst, R.,\n1996, Nature, 381, 581\n\n\\bibitem[\\protect\\citename{Egami et al., }1996]{e96}\nEgami, E., Iwamurn, F., Maihara, T., Oya, S., Cowie, L.L., 1996, AJ, 112, 73\n\n\\bibitem[\\protect\\citename{Francis et al. }1997]{f97}\nFrancis, P.J., Woodgate, B.E., Danks, A.C., 1997, ApJ., 428, L25\n\n\\bibitem[\\protect\\citename{Graham et al., }1996]{g96}\nGraham, J.R., \\& Dey, A., 1996, ApJ., 471, 720\n\n\\bibitem[\\protect\\citename{Hall et al., }1998]{h98}\nHall, P.B., Green, R.F., 1998, ApJ., 507, 558\n\n\\bibitem[\\protect\\citename{Hu et al. }1994]{h94}\nHu, E.M., \\& Ridgeway, S.E., 1994, AJ., 107, 1303\n\n\\bibitem[\\protect\\citename{Jauncey et al. }1984]{j84}\nJauncey, D.L., Batty, M.J., Wright, A.E., Peterson, B.A., Savage, A.,\n1984, ApJ., 286, 498\n\n\\bibitem[\\protect\\citename{Landolt }1992]{l92}\nLandolt, A.U., 1992, AJ, 104, 340\n\n\\bibitem[\\protect\\citename{Leibundgut \\& Robertson }1999]{l99}\nLeibundgut, B., \\& Robertson, J.G., 1999, MNRAS, 303, 711\n\n\\bibitem[\\protect\\citename{Manucci et al. }1998]{m98}\nManucci, F., Thompson, D., Beckwith, S.V.W., Williger, G.M., 1998,\nApJ., 501, L11\n\n\\bibitem[\\protect\\citename{Mobasher et al. }1993]{m93}\nMobasher, B., Sharples, R.M., Ellis, R.S., 1993, MNRAS, 263, 560\n\n\\bibitem[\\protect\\citename{Smail et al., }1999]{sm99}\nSmail, I., et al., MNRAS, in press, astro-ph/9905246\n\n\\bibitem[\\protect\\citename{Spinrad et al. }1997]{s97}\nSpinrad, H., Dey, A., Stern, D., Dunlop, J., Peacock, J., Jimenez, R., Windhorst, R.,\n1997, ApJ., 484, 581\n\n\\bibitem[\\protect\\citename{Steidel et al. }1999]{s99}\nSteidel, C.C., Adelberger, K.L., Giavalisco, M., Dickinson, M., Pettini, M., \n1999, ApJ., 519, 1\n\n\\bibitem[\\protect\\citename{Steidel et al. }1997]{st97}\nSteidel, C.C., Dickinson, M., Meyer, D.M., Adelberger, K.L., Sembach, K.R.,\nApJ., 480, 568\n\n\\bibitem[\\protect\\citename{Stockton et al. }1995]{s95}\nStockton, A., Kellogg, M., Ridgeway, S.E., 1995, ApJ., 443, L69\n\n\\bibitem[\\protect\\citename{Wolfe et al. }1992]{w92}\nWolfe, A., Lanzetta, K.M., Turnshek, D.A., Oke, J.B., 1992, ApJ., 385, 151 \n\n\\bibitem[\\protect\\citename{Yamada et al. }1997]{y97}\nYamada, T., Tanaka, I., Aragon-Salamanca, A., Kodama, T., Ohta, K., Arimoto, N.,\n1997, ApJ., 487, L125 \n\n\\end{thebibliography}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002101.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[\\protect\\citename{Aragon-Salamanca et al. }1996]{a96}\nAragon-Salamanca, A., Ellis, R.S., O'Brien, K.S., 1996, MNRAS,\n281, 945\n\n\\bibitem[\\protect\\citename{Aragon-Salamanca et al. }1994]{a94}\nAragon-Salamanca, A., Ellis, R.S., Schwartzenberg, J.-M.,\nBergeron, J.A., 1994, ApJ., 421, 27\n\n\\bibitem[\\protect\\citename{Bergeron \\& Boisse, }1991]{b91}\nBergeron, J., Boisse, P., 1991, A\\&A, 243, 344\n\n\\bibitem[\\protect\\citename{Bunker et al. }1999]{b99}\nBunker, A.J., Warren, S.J., Clements, D.L., Williger, G.M., Hewitt, P.C., 1999, MNRAS, in press\n\n\\bibitem[\\protect\\citename{Cassali }1992]{c92}\nCassali, M.M., \\& Hawarden, T.G., 1992, JCMT-UKIRT Newsletter, NO. 3, August 1992, p33\n\n\\bibitem[\\protect\\citename{Cohen et al., }1999]{c99}\nCohen, J.G., Hogg, D.W., Blandford, R., Pahre, M.A., Shopbell, P.L.., 1999,\nin Astrophysics with Infrared Arrays: A prelude to SIRTF, p. 47, eds. Bicay, M.D.,\nBeichman, C.A., Cutri, R.M., Madore, B.F., pub. ASP\n\n\\bibitem[\\protect\\citename{Cowie et al., }1994]{c94}\nCowie, L.L., Gardner, J.P., Hu, E.M., Songaila, A., Hodapp, K-W.,\nWainscoat, R.J., 1994, ApJ., 434, 114\n\n\\bibitem[\\protect\\citename{Devillard, }1997]{d97}\nDevillard, N., \"The eclipse software\", The messenger No 87 - March 1997 \n\n\\bibitem[\\protect\\citename{Devillard, }1999]{d99a}\nDevillard, N., 1999, ESO Documentation, http://www.eso.org/projects/dfs/papers/jitter99/\n\n\\bibitem[\\protect\\citename{Dey et al., }1999]{d99b}\nDey, A., Graham, J.R., Ivison, R., Smail, I., Wright, G.S., Liu, M.C.,\n1999, ApJ., 610\n\n\\bibitem[\\protect\\citename{Dunlop et al. }1996]{d96}\nDunlop, J., Peacock, J., Spinrad, H., Dey, A., Jimenez, R., Stern, D., Windhorst, R.,\n1996, Nature, 381, 581\n\n\\bibitem[\\protect\\citename{Egami et al., }1996]{e96}\nEgami, E., Iwamurn, F., Maihara, T., Oya, S., Cowie, L.L., 1996, AJ, 112, 73\n\n\\bibitem[\\protect\\citename{Francis et al. }1997]{f97}\nFrancis, P.J., Woodgate, B.E., Danks, A.C., 1997, ApJ., 428, L25\n\n\\bibitem[\\protect\\citename{Graham et al., }1996]{g96}\nGraham, J.R., \\& Dey, A., 1996, ApJ., 471, 720\n\n\\bibitem[\\protect\\citename{Hall et al., }1998]{h98}\nHall, P.B., Green, R.F., 1998, ApJ., 507, 558\n\n\\bibitem[\\protect\\citename{Hu et al. }1994]{h94}\nHu, E.M., \\& Ridgeway, S.E., 1994, AJ., 107, 1303\n\n\\bibitem[\\protect\\citename{Jauncey et al. }1984]{j84}\nJauncey, D.L., Batty, M.J., Wright, A.E., Peterson, B.A., Savage, A.,\n1984, ApJ., 286, 498\n\n\\bibitem[\\protect\\citename{Landolt }1992]{l92}\nLandolt, A.U., 1992, AJ, 104, 340\n\n\\bibitem[\\protect\\citename{Leibundgut \\& Robertson }1999]{l99}\nLeibundgut, B., \\& Robertson, J.G., 1999, MNRAS, 303, 711\n\n\\bibitem[\\protect\\citename{Manucci et al. }1998]{m98}\nManucci, F., Thompson, D., Beckwith, S.V.W., Williger, G.M., 1998,\nApJ., 501, L11\n\n\\bibitem[\\protect\\citename{Mobasher et al. }1993]{m93}\nMobasher, B., Sharples, R.M., Ellis, R.S., 1993, MNRAS, 263, 560\n\n\\bibitem[\\protect\\citename{Smail et al., }1999]{sm99}\nSmail, I., et al., MNRAS, in press, astro-ph/9905246\n\n\\bibitem[\\protect\\citename{Spinrad et al. }1997]{s97}\nSpinrad, H., Dey, A., Stern, D., Dunlop, J., Peacock, J., Jimenez, R., Windhorst, R.,\n1997, ApJ., 484, 581\n\n\\bibitem[\\protect\\citename{Steidel et al. }1999]{s99}\nSteidel, C.C., Adelberger, K.L., Giavalisco, M., Dickinson, M., Pettini, M., \n1999, ApJ., 519, 1\n\n\\bibitem[\\protect\\citename{Steidel et al. }1997]{st97}\nSteidel, C.C., Dickinson, M., Meyer, D.M., Adelberger, K.L., Sembach, K.R.,\nApJ., 480, 568\n\n\\bibitem[\\protect\\citename{Stockton et al. }1995]{s95}\nStockton, A., Kellogg, M., Ridgeway, S.E., 1995, ApJ., 443, L69\n\n\\bibitem[\\protect\\citename{Wolfe et al. }1992]{w92}\nWolfe, A., Lanzetta, K.M., Turnshek, D.A., Oke, J.B., 1992, ApJ., 385, 151 \n\n\\bibitem[\\protect\\citename{Yamada et al. }1997]{y97}\nYamada, T., Tanaka, I., Aragon-Salamanca, A., Kodama, T., Ohta, K., Arimoto, N.,\n1997, ApJ., 487, L125 \n\n\\end{thebibliography}"
}
] |
astro-ph0002102
|
The NASA Astrophysics Data System: The Search Engine and its User Interface
|
[
{
"author": "G. Eichhorn"
},
{
"author": "M. J. Kurtz"
},
{
"author": "A. Accomazzi"
},
{
"author": "C. S. Grant"
},
{
"author": "S. S. Murray"
}
] |
The ADS Abstract and Article Services provide access to the astronomical literature through the World Wide Web (WWW). The forms based user interface provides access to sophisticated searching capabilities that allow our users to find references in the fields of Astronomy, Physics/Geophysics, and astronomical Instrumentation and Engineering. The returned information includes links to other on-line information sources, creating an extensive astronomical digital library. Other interfaces to the ADS databases provide direct access to the ADS data to allow developers of other data systems to integrate our data into their system. The search engine is a custom-built software system that is specifically tailored to search astronomical references. It includes an extensive synonym list that contains discipline specific knowledge about search term equivalences. Search request logs show the usage pattern of the various search system capabilities. Access logs show the world-wide distribution of ADS users. The ADS can be accessed at http://adswww.harvard.edu \keywords{ methods: data analysis -- databases: misc -- publications, bibliography -- sociology of astronomy}
|
[
{
"name": "ADS_search.tex",
"string": "\\documentclass[]{aa}\n\\usepackage{graphics}\n\n\n\n\\begin {document}\n\\title{The NASA Astrophysics Data System: The Search\nEngine and its User Interface}\n\n\\thesaurus{04(04.01.1)}\n\\author{G. Eichhorn\\and M. J. Kurtz\\and A. Accomazzi\\and C. S. Grant\n\\and S. S. Murray}\n\n\\institute{Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138}\n\n\n\\offprints{G. Eichhorn}\n\\mail{G. Eichhorn}\n\n\\date{Received / Accepted}\n\n\\titlerunning{}\n\\authorrunning{G. Eichhorn et al.}\n\n\\maketitle\n\n\\sloppy\n\n\\begin {abstract}\nThe ADS Abstract and Article Services provide access to the\nastronomical literature through the World Wide Web (WWW). The forms\nbased user interface provides access to sophisticated searching\ncapabilities that allow our users to find references in the fields of\nAstronomy, Physics/Geophysics, and astronomical Instrumentation and\nEngineering. The returned information includes links to other on-line\ninformation sources, creating an extensive astronomical digital\nlibrary. Other interfaces to the ADS databases provide direct access\nto the ADS data to allow developers of other data systems to integrate\nour data into their system.\n\nThe search engine is a custom-built software system that is\nspecifically tailored to search astronomical references. It includes\nan extensive synonym list that contains discipline specific knowledge\nabout search term equivalences.\n\nSearch request logs show the usage pattern of the various search\nsystem capabilities. Access logs show the world-wide distribution of\nADS users.\n\nThe ADS can be accessed at http://adswww.harvard.edu\n\n\\keywords{ methods: data analysis -- databases: misc -- publications,\nbibliography -- sociology of astronomy}\n\\end{abstract}\n\n\n\\section{Introduction}\n\nThe Astrophysics Data System (ADS) provides access to the astronomical\nliterature through the World Wide Web (WWW). It is widely used in the\nastronomical community. It is accessible to anybody world-wide\nthrough a forms based WWW interface. A detailed description of the\nhistory of the ADS is presented in the ADS Overview article\n(\\cite{adsoverview}, hereafter OVERVIEW). The system contains\ninformation from many sources (journals, other data centers,\nindividuals). A detailed description of the data that we get and how\nthey are included in the ADS is presented in the ADS Data article\n(\\cite{adsdata}, hereafter DATA). The incoming data are processed and\nindexed with custom-built software to take advantage of specialized\nknowledge of the data and the astronomical context. A description of\nthis processing is given in the ADS Architecture article\n(\\cite{adsarchitecture}, hereafter ARCHITECTURE). This article\ndescribes the development and the current status of the ADS Abstract\nService user interface and search engine.\n\nThe ADS was created as a system to provide access to astronomical data\n(\\cite{1992ald2.proc..387M}). In 1993 the ADS started to provide\naccess to a set of abstracts obtained from the NASA/STI (National\nAeronautics and Space Administration/Scientific and Technical\nInformation) project (\\cite{1993adass...2..132K}). The user interface\nwas built with the proprietary software system that the ADS used at\nthat time. The search engine of this first implementation used a\ncommercial database system. A description of the system at that time\nis in \\cite{1994ExA.....5..205E}.\n\nIn 1994, the World Wide Web (WWW, \\cite{www}) became widely useful\nthrough the NCSA Mosaic Web Browser (\\cite{mosaic}). The design of\nthe ADS Abstract Service with a clean separation between the user\ninterface and the search engine made it very easy to move the user\ninterface from the proprietary ADS system to the WWW. In February\n1994, a WWW interface to the ADS Abstract Service was made available\npublicly. The WWW interface to the ADS is described by\n\\cite{1995adass...4...28E} and \\cite{1995VA.....39..217E}. Within one\nmonth of the introduction of the WWW interface, the usage of the\nAbstract Service tripled, and it has continued to rise ever since\n(\\cite{1997Ap&SS.247..189E}).\n\nWith the increased usage of the system due to the easy access through\nthe WWW, severe limitations of the underlying commercial database\nsystem very quickly became apparent. We soon moved to an\nimplementation of the search engine that was custom-built and tailored\nto the specific requirements of the data that we used.\n\nIn January 1995 we started to provide access to scanned journal\narticles (\\cite{1996adass...5..558A}). The user interface to these\nscans provided the user with the capability to access the scans in\nvarious formats, both for viewing and for printing.\n\nWith time, other interfaces to the abstracts and scanned articles were\ndeveloped to provide other data systems the means to integrate ADS\ndata into their system (\\cite{1996adass...5..569E}).\n\nWith the adoption of the WWW user interface and the development of the\ncustom-built search engine, the current version of the ADS Abstract\nService was basically in place. The following sections describe the\ncurrent status of the different access capabilities\n(sections~\\ref{dataretrieval} and \\ref{cookies}), the search engine\n(sections~\\ref{searchengine} and \\ref{optimization}), access\nstatistics for the ADS system (section~\\ref{accessstats}), and future\nplans for the ADS interface and search engine (section~\\ref{future}).\n\n\n\\section{\\label {dataretrieval} Data Access}\n\n\nThe ADS services can be accessed through various interfaces. Some of\nthese interfaces use WWW based forms, others allow direct access to\nthe database and search system through Application Program Interfaces\n(APIs). This section describes the various interfaces and their use,\nas well as the returned results.\n\n\\subsection{Forms Based Interfaces}\n\n\\subsubsection{\\label {abstracts} Abstract Service}\n\na. User Interface\n\nThe main query forms\n(figures~\\ref{queryforma},~\\ref{queryformb},~\\ref{queryformc}) provide\naccess to the different abstract databases. These forms are generated\non demand by the ADS software. This allows the software to check the\nuser identification through the HTTP (HyperText Transfer Protocol)\ncookie mechanism (see section~\\ref{cookies}), so that the software can\nreturn a customized query form if one has been defined by the user.\nIt also adapts parts of the form according to the capabilities of the\nuser's web browser.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF1.eps}}\n\\caption[]{The ADS Abstract Service query form provides the capability to query the database by authors, object names, title and text words. }\n\\label{queryforma}\n\\end{figure}\n\t\t\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF2.eps}}\n\\caption[]{The Filter section of the query form allows selection of references that have specific properties. }\n\\label{queryformb}\n\\end{figure}\n\t\t\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF3.eps}}\n\\caption[]{The Settings section of the query form allows the user to customize the search. }\n\\label{queryformc}\n\\end{figure}\n\t\t\n\n\nThe query form allows the user to specify search terms in different\nfields. The input parameters in each query field can be combined in\ndifferent ways, as can the results obtained from the different fields\n(figure~\\ref{queryforma}). The user can specify how the results are\ncombined through settings on the query form\n(figure~\\ref{queryformc}). The combined results can then be filtered\naccording to various criteria (figure~\\ref{queryformb}).\n\nThe database can be queried for author names, astronomical objects\nnames, title words, and words in the abstract text. References can be\nselected according to the publication date. The author name, title,\nand text fields are case insensitive. The object field is case\nsensitive when the IAU (International Astronomical Union) Circulars\n(IAUC) object name database is searched, since the IAU object names\nare case sensitive. In the author and object name fields, the form\nexpects one search term per line since the terms can contain blanks.\nIn the title and text fields line breaks are not significant.\n\n\\medskip\n\n\\paragraph{Author Name Field}\n\nThe author names are indexed by last name and by a combination of last\nname and first initial, separated by a comma. To account for\ndifferences in the spelling of the same author name, the search system\ncontains a list of author names that are spelled differently but are\nin fact names of the same author. This allows for automatically\nretrieving all versions of common spelling differences. This is\nuseful for instance for German umlaut spelled as Muller and Mueller,\nor variations in the transliteration of names from non-English\nalphabets like Cyrillic. An example of such an entry in the author\nsynonym list is:\n\n\\begin{verbatim}\nAFANASJEV, V\nAFANAS'EV, V\nAFANAS'IEV, V\nAFANASEV, V\nAFANASYEV, V\nAFANS'IEV, V\nAFANSEV, V\n\\end{verbatim}\nWithout this synonym replacement capability, author searches would\nobviously be much less effective. On user request we also include\nname changes (e.g. due to marriage) in the author synonym list.\nCombinations of search results within the author field use ``OR'',\n``AND'', or simple logic (see below), depending on user selection.\n\nAuthor names are quite often spelled differently in different\npublications. First names are sometimes spelled out, sometimes only\nfirst initials are given, and sometimes middle initials are left out.\nThis makes it impossible to index all different spellings of a name\ntogether automatically. \n\nTo handle these different requirements, author names are indexed three\ntimes, once with the last name only, once with the last name and first\ninitial, and once with the complete name as it is specified in the\narticle.\n\nTo access these different indexes, we provide two user interfaces for\nauthor queries. The regular user interface allows the user to search\nfor either a last name or a last name combined with the first initial.\nThis allows for fairly discriminating author searches. It is a\ncompromise between the need to discriminate between different authors,\nand the need to find all instances of a given author. It\nidentifies all different versions of a given author quite reliably,\nbut it indexes together different authors with the same first initial.\nFor cases where this search method is not discriminating enough, we\nprovide a second user interface to the index of the full names, which\ndoes not attempt to index different spellings of the same author\ntogether. When the user selects ``Exact Author Search'' and specifies\nan author's last name or last name and first initial, a form is\nreturned with all distinct full author names that match the specified\nname. The user then selects all the different spellings of the\ndesired name and queries the database for articles that contain any\none of these different versions of an author's name. For instance\nspecifying:\n\\begin{verbatim}\nEichhorn, G\n\\end{verbatim}\n\nin the exact author name form returns the list:\n\\begin{verbatim}\nEICHHORN, G.\nEICHHORN, GERHARD\nEICHHORN, GUENTHER\nEICHHORN, GUNTHER\n\\end{verbatim}\n\nSelecting the first, third, and fourth author name from that list will\nreturn all articles by the first author of this article. Any articles\nby the second author containing only the first initial will also be\nreturned, but this is unavoidable.\n\n\\medskip\n\n\\paragraph{Object Name Field}\n\nThis field allows the user to query different databases for references\nwith different astronomical objects. The databases that provide\nobject information are: SIMBAD (Set of Identifications, Measurements\nand Bibliographies for Astronomical Data) at the Centre des Donn\\'ees\nAstronomique de Strasbourg (CDS), France (\\cite{simbad}); the NASA\nExtragalactic Database (NED) at the Infrared Processing and Analysis\nCenter (IPAC), Jet Propulsion Laboratory (JPL), Pasadena, CA\n(\\cite{1992adass...1...47M}); the IAU Circulars (IAUC) and the Minor\nPlanet Electronic Circulars (MPEC), both provided by the Central\nBureau for Astronomical Telegrams (CBAT) at the Harvard-Smithsonian\nCenter for Astrophysics in Cambridge, MA (\\cite{1980CeMec..22...63M});\nand a database with objects from publications from the Lunar and\nPlanetary Institute (LPI) in Houston (mainly Lunar sample numbers and\nmeteorite names). The user can select which of these databases should\nbe queried. If more than one database is searched, the results of\nthese queries are merged. The LPI database does not have any entries\nin common with the other databases. The SIMBAD, NED, and IAUC\ndatabases sometimes have information about the same objects.\n\n\\medskip\n\n\\paragraph{Title and Abstract Text Fields}\n\nThese fields query for words in the titles of articles or books, and\nin the abstracts of articles or descriptions of books respectively.\nThe words from the title of each reference are also indexed in the\ntext field so they will be found through either a title or a text\nsearch. Before querying the database the input in these fields is\nprocessed as follows:\n\n1. Apply translation rules. This step merges common expressions into\na single word so that they are searched as one expression. Regular\nexpression matching is used to convert the input into a standard\nformat that is used to search the database. For instance {\\it M 31}\n(with a space) is translated to {\\it M31} (without a space) for\nsearching as one search term. In order to make this general\ntranslation, a regular expression matching and substitution is\nperformed that translates all instances of an `M' followed by one or\nmore spaces or a hyphen followed by a number into `M' directly\nfollowed by the number. Other translation rules include the\nconversion of {\\it NGC 1234} to {\\it NGC1234}, contractions of {\\it T\nTauri, Be Star, Shoemaker Levy}, and several others (see ARCHITECTURE).\n\n2. Remove punctuation. In this step all non-alphanumeric characters\nare removed, unless they are significant (for instance symbols used in the\nsimple logic (see below), `+' and `--' before numbers, or `.' within numbers).\n\n3. Translate to uppercase. All information in the index files is in\nuppercase, except for object names from the IAU Circulars.\n\n4. Remove kill words. This step removes all non-significant words.\nThis includes words like `and', `although', `available', etc (for more\ndetails see ARCHITECTURE).\n\nIn the title and text fields, searching for phrases can be specified\nby enclosing several words in either single or double quotes, or\nconcatenating them with periods (`.') or hyphens (`--'). All these\naccomplish the same goal of searching the database for references that\ncontain specified sequences of words. The database is indexed for\ntwo-word phrases in addition to single words. Phrases with more than\ntwo words are treated as a search for sets of two-word phrases\ncontaining the first and second word in the first phrase, the second and\nthird word in the second phrase, etc.\n\n\\medskip\n\nb. Searching\n\nAfter the search terms are pre-processed, the databases of the\ndifferent fields are searched for the resulting list of words, the\nresults are combined according to the selected combination rules, and\nthe resulting score is calculated according to the selected scoring\ncriteria. These combination rules provide the means for improving the\nselectivity of a query.\n\n\\medskip\n\n\\paragraph{Search Word Selection}\n\nThe database is searched for the specified words as well as for words\nthat are synonymous with the specified term. One crucial part to\nsuccessful searches in a free text search system is the ability to not\nonly find words exactly as specified, but also similar words. This\nstarts with simply finding singular and plural forms of a word, but\nthen needs to be extended to different words with the same meaning in\nthe normal usage of words in a particular field of science. In\nAstronomy for instance ``spectrograph'' and ``spectroscope'' have\nbasically the same meaning and both need to be found when one of these\nwords is specified in the query. Even further reaching, more\ndiscipline-specific synonyms are necessary for efficient searches such\nas ``metallicity'' and ``abundance'' which have the same meaning in\nastronomical word usage. In order to exhaustively search the database\nfor a given term, it is important to search for all synonyms of a\ngiven word. The list of synonyms was developed manually by going\nthrough the list of words in the database and grouping them according\nto similar meanings. This synonym list is a very important part of\nthe ADS search system and is constantly being improved (see\nARCHITECTURE).\n\nThe list of synonyms also contains non-English words associated with\ntheir English translations. These words came from non-English\nreference titles that we included in the database. This allows searches\nwith either the English or non-English words to find references with\neither the English word or the non-English translation. We are in the\nprocess of extending this capability by including translations of most\nof the words in our database into several languages (German, French,\nItalian, Spanish). This will allow our users to phrase queries in any\nof these languages. We expect to complete this project sometime in 2000.\n\nBy default a search will return references that contain the search\nword or any of its synonyms. The user can choose to disable this\nfeature if for some reason a specific word needs to be found. The\nsynonym replacement can be turned off completely for a field in the\n``Settings'' section of the query form. This can be used to find a\nrare word that is a synonym of a much more frequent word, for\ninstance if you want to look for references to ``dateline'', which is a\nsynonym to ``date''. Synonym replacement can also be enabled or\ndisabled for individual words by prefixing a word with `=' to force an\nexact match without synonym replacement. When synonym replacement is\ndisabled for a field, it can be turned on for a particular word by\nprefixing it with `\\#'.\n\n\n\\paragraph{Selection Logic Within a Field}\n\nThere are four different types of combinations of results for searches\nwithin a field possible.\n\\begin{verbatim}\n1. OR\n2. AND\n3. Simple logic\n4. Full boolean logic\n\\end{verbatim}\n\n1. Combination by `OR':\nThe resulting list contains all references that contain at least one\nof the search terms.\n\n2. Combination by `AND':\nThe resulting list has only references that contain every one\nof the search terms.\n\n3. Combination by simple logic:\nThe default combination in this logic\nis by `OR'. Individual terms can be either required for selection by\nprefixing them with a `+', or can be selected against by prefixing\nthem with a `--'. In the latter case only references that do not\ncontain the search term are returned. If any of the terms in the\nsearch is prefixed by a `+', any other word without a prefix does not\ninfluence the resulting list of references. However, the final score\n(see below) for each reference will depend on whether the other search\nterms are present.\n\n4. Combination by full boolean logic:\nIn this setting, the user specifies a boolean expression containing\nthe search terms and the boolean operators `and', `or', and `not', as\nwell as parentheses for grouping. A boolean expression could for\ninstance look like:\n\n(pulsar or ``neutron star'') and (``red shift'' distance) and not 1987A\n\nThis expression searches for references that contain either the word\npulsar or the phrase ``neutron star'' and either the phrase ``red\nshift'' or the word distance (``or'' being the default), but not the\nword 1987A.\n\n\\medskip\n\n\\paragraph{Selection Logic Between Fields}\n\nIn the settings part of the query form, the user can specify fields\nthat will be required for selection. If a field is selected as\n``Required for Selection'' only references that were selected in the\nsearch specified in that field will be returned. If one field is\nselected as ``Required for Selection'', the searches in fields that are\nnot set as ``Required for Selection'' do not influence the resulting\nlist, but they influence the final score.\n\n\\medskip\n\nc. Scoring\n\nThe list of references resulting from a query is sorted according to a\n``score'' for each reference. This score is calculated according to how\nmany of the search items were matched. The user has the choice\nbetween two scoring algorithms:\n\\begin{verbatim}\n1. proportional scoring\n2. weighted scoring\n\\end{verbatim}\nThese scoring algorithms have been analyzed by \\cite{scoring}.\n\nIn proportional scoring, the score is directly proportional to the\nnumber of terms found in the reference. In weighted scoring, the\nscore is proportional to the inverse logarithm of the frequency of the\nmatched word. This weighting gives higher scores for words that are\nless frequent in the database and therefore presumably more important\nindicators of the relevance of a match. In the settings section of\nthe query form the user can select which type of scoring should be\nused for each query field separately. The default setting for title\nand text searches is the weighted scoring. For author searches\nproportional scoring is the default. Once the score for each query\nfield is calculated, the scores are normalized so that a reference\nthat matches all words in a field receives a score of 1.\n\nThe normalized scores from the different fields are then combined to\ncalculate a total score. Again the result is normalized so that a reference\nthat matches all words in each query field has a score of 1. The user\ncan influence this combining of scores from the different search\nfields by assigning weights to the different fields. This allows the\nuser to put more emphasis in the selection process on, for instance, the\nobject field by assigning a higher weight to that field. Another\nuse of the weight field is to select against a field. For instance\nspecifying an object name and an author name and selecting a negative\nweight to the author field will select articles about that object that\nwere {\\em not} written by the specified author.\n\nThe relative weights for the different search fields can be set by the\nuser. The ADS provides default weights as follows:\n\\begin{verbatim}\nAuthors: 1.0\nObjects: 1.0\nTitle: 0.3\nText: 3.0\n\\end{verbatim}\n\nThese default weights were determined on theoretical grounds, combined\nwith trial and error experimentation. We used different search inputs\nfrom known research fields and different weights and ranked the\nresulting lists according to how well they represented articles from\nthese research fields. The weights listed above gave the best\nresults.\n\n\n\\medskip\n\nd. Filtering of Selected References\n\nThe selected references can be filtered according to different\ncriteria (see section~\\ref{filters}) in order to reduce the number of\nreturned references. The user can select references according to\ntheir entry date in the database, a minimum score (see above), the\njournal they are published in, whether they have pointers to selected\nexternal data sources, or whether they belong to one or more of\nseveral groups of references. This allows a user for instance to\nselect only references from refereed journals or from one particular\njournal by specifying its abbreviation. It also allows a user to\nselect only references that have links to external data sets, on-line\narticles, or that have been scanned and are available through the ADS\nArticle Service.\n\n\\medskip\n\ne. Display of Search Results\n\nThe ADS system returns different amounts of information about a\nreference, depending on what the user request was. This section\ndescribes the different reference formats.\n\n\\medskip\n\n\\paragraph{Short Reference Display}\n\nThe list of references returned from a query is displayed in a\ntabular format. The returned references are sorted by score first.\nFor equal scores, the references are sorted by publication date with\nthe latest publications displayed first.\n\nA typical reference display is shown in figure~\\ref{referencedisp}. The\nfields in such a reference are shown in figure~\\ref{shortelements}.\nThey are as follows:\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF4.eps}}\n\\caption[]{Entries in the list of references returned by an ADS query contain the bibliographic code (1) the matching score (2), the publication date (3), a list of data links (4), the list of authors (5), and the title of the reference (6). }\n\\label{referencedisp}\n\\end{figure}\n\t\t\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF5.eps}}\n\\caption[]{Elements in the references returned from an ADS query. }\n\\label{shortelements}\n\\end{figure}\n\t\t\n\n\n1. Bibliographic Code: This code identifies the reference uniquely\n(see DATA and \\cite{1995ioda.book..259S}).\nTwo important properties of these codes are that they can be generated\nfrom a regular journal reference, and that they are human readable and\ncan be understood and interpreted.\n\n2. Score: The score is determined during the search according to\nhow well each reference fits the query.\n\n3. Date: The publication date of the reference is displayed as mm/yyyy.\n\n4. Links: The links are an extremely important aspect of the ADS. They\nprovide access to information correlated with the article.\nTable~\\ref{linkletters} shows the links that we currently provide\nwhen available.\n\n\\begin{table*}\n\\caption[]{Links types and their numbers in the ADS database.\n}\n\\label{linkletters}\n\\begin{tabular*}{7.0in}{llp{0.7\\linewidth}}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nLink & Resource & Description\n\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nA & Abstract & Full abstract of the article. These abstracts come\n from different sources.\\\\\n\nC & Citations & A list of articles that cite the current article.\n This list is not necessarily complete (see `R'\n References).\\\\\n\nD & On-line Data & Links to on-line data at other data centers.\\\\\n\nE & Electronic Article & Links to the on-line version of the article.\n These on-line versions are in HTML format for\n viewing on-screen, not for\n printing.$^{\\mathrm{a}}$\\\\\n\nF & Printable Article & Links to on-line articles in PDF or\n Postscript format for\n printing.$^{\\mathrm{a}}$\\\\\n \nG & Gif Images & Links to the images of scanned articles in the ADS\n Article Service.\\\\\n\nI & Author Comments & Links to author supplied additional\n\t\t\t\t\tinformation (e.g. corrections, additional\n\t references, links to data),\\\\\n\nL & Library Entries & Links to entries in the Library of Congress\n on-line system.\\\\\n\nM & Mail Order & Links to on-line document delivery systems at the\n publisher/owner of the article.\\\\\n\nN & NED Objects & Access to lists of objects for the current article\n in the NED database.\\\\\n\nO & Associated Articles & A list of articles that are associated\n with the current article. These can be errata or\n other articles in a series.\\\\\nP & Planetary Data System & Links to datasets at the Planetary Data\n\t\t\t\t\tSystem.\\\\\n\nR & References & A list of articles referred to in the current\n article. For older articles these lists are not\n necessarily complete, they contain only references\n to articles that are in the ADS database. For\n articles that are on-line in electronic form, the\n `R' link points to the on-line reference list, and\n therefore the complete list of references in that\n article.$^{\\mathrm{a}}$\\\\\n\nS & SIMBAD Objects & Access to lists of objects for the current\n article in the SIMBAD database.\\\\\n\nT & Table of Contents & Links to the list of articles in a books or\n\t\t\t\t\tproceedings volume.\\\\\n\nX & Planetary Nebulae & Links to datasets in the Galactic Planetary\n\t\t\t\t\tNebulae Database.\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\begin{list}{}{}\n\\item[$^{\\mathrm{a}}$]There\nis generally access control at the site that serves these on-line articles\n\\end{list}{}{}\n\\end{table*}\n\n\n\nA more detailed description of resources in the ADS that these links\npoint to is provided in DATA.\n\nSome of these links (for instance the `D' links) can point to more\nthan one external information provider. In such cases the link points\nto a page that lists the available choices of data sources. The user\ncan then select the more convenient site for that resource, depending\non the connectivity between the user site and the data site.\n\n5. Authors: This is the list of authors for the reference. Generally\nthese lists are complete. For some of the older abstracts that we\nreceived from NASA/STI, the author lists were truncated at 5 or 10\nauthors, but every effort has been made to correct these abbreviated\nauthor lists (see DATA).\n\n6. Title: The complete title of the reference.\n\nThe reference lists are returned as forms if table display is selected\n(see section~\\ref{cookies}). The user can select some or all of the\nreferences from that list to be returned in any one of several formats:\n\ni. HTML format: The HTML (HyperText Markup Language) format is for\n screen viewing of the formatted record.\n\nii. Portable Format: This is the format that the ADS uses internally\n and for exchanging references with other data centers. A\n description of this format is available on-line at:\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/abs_doc/\n abstract_format.html\n\\end{verbatim}\n\niii. BibTeX format: This is a standard format that is used to build\n reference lists for TeX (a typesetting language especially suited\n for mathematical formulas) formatted articles.\n\niv. ASCII format: This is a straight ASCII text version of the\n abstract. All formatting is done with spaces, not with tabs.\n\nv. User Specified Format: This allows the user to specify in which\n format to return the reference. The default format for this\n selection is the bibitem format from the AASTeX macro package.\n The user can specify an often used format string in the user\n preferences (see section~\\ref{cookies}). This format string\n will then be used as the default in future queries.\n\nThe user can select whether to return the selected abstracts to the\nbrowser, a printer, a local file for storage, or email it to a\nspecified address.\n\n\\medskip\n\n\\paragraph{Full Abstract Display}\n\nIn addition to the information in the short reference list, the full\nabstract display (see figure~\\ref{abstract}) includes, where available,\nthe journal information, author affiliations, language, objects, keywords,\nabstract category, comments, origin of the reference, a copyright\nnotice, and the full abstract. It also includes all the links\ndescribed above.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF6.eps}}\n\\caption[]{The full abstract display contains (where available) the title, author list, journal information, author affiliations, publication date, keywords, the origin of the reference, the bibliographic code, the abstract, object names, abstract category, and a copyright notice. }\n\\label{abstract}\n\\end{figure}\n\t\t\n\n\nFor abstracts that are displayed as a result of a search, the system\nwill highlight all search terms that are present in the returned\nabstract. This makes it easy to locate the relevant parts in an\nabstract. Since the highlighting is somewhat resource intensive, it\ncan be turned off in the user preference settings (see\nsection~\\ref{cookies}).\n\nFor convenience, the returned abstract contains links that allow the\nuser to directly retrieve the BibTex or the custom formatted version of\nthe abstract.\n\nThe full abstract display also includes a form that provides the\ncapability to use selected information from the reference to build a\nnew query to find similar abstracts. The query feedback mechanism\nmakes in-depth literature searches quick and easy. The user can\nselect which parts of the reference to use for the feedback query\n(e.g. authors, title, or abstract). The feedback query can either be\nexecuted directly, or be returned as a query form for further\nmodification before executing it, for instance to change the\npublication date range or limit the search to specific journals. This\nquery feedback mechanism is a very powerful means to do exhaustive\nliterature searches and distinguishes the ADS system from most other\nsearch systems. A query feedback ranks the database against the\nrecord used for the feedback and sorts it according to how relevant\neach reference is to the search record. The query feedback can be\ndone across databases. For instance a reference from the Astronomy\ndatabase can be used as query feedback in the preprint database to see\nthe latest work in the field of this article.\n\nIf the article for the current reference has been scanned and is available\nthrough the ADS Article Service (see below), printing options are\navailable in the abstract display as well. These printing options\nallow the printing of the article without having to retrieve the\narticle in the viewer first.\n\n\n\\subsubsection{Article Service}\n\nThis part of the ADS provides access to the scanned images of\narticles. We have received permission from most astronomy journals to\nscan their volumes and make them available on-line free of charge. A\nmore detailed description of these data is in the DATA.\n\nThe most common access to the scanned articles is through the ADS\nAbstract Service via the `G'-links (see above). However they can also\nbe accessed directly through the article query page by\npublication year and month or by volume and page at:\n\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/article_service.html\n\\end{verbatim}\n\nThis form returns the specified article in the user specified format\n(see section~\\ref{cookies}). If a page within an article is\nspecified, and the single page display is selected, the specified page\nwithin the article is returned with the links to the other available pages\nas usual. \n\nThe article display normally shows the first page\n(figure~\\ref{articlegif}) of an article at the selected resolution and\nquality (see section~\\ref{cookies}). The user can select resolutions\nof 75, 100, or 150 dots per inch (dpi) and image qualities of 1, 2, 3,\nor 4 bits of greyscale per pixel. These gif images are produced on\ndemand from the stored tiff images (see DATA). The default version of\nthe gif images (100 dpi, 3 bit greyscale) is cached on disk. The\ncache of these gif images is managed to stay below a maximum size.\nAny time the size of the cached gif images exceeds the preset cache\nsize, the gif images of pages that have not been accessed recently\nare deleted.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF7.eps}}\n\\caption[]{The article display shows a gif image of the selected journal page with the resolution selected in the user preferences. }\n\\label{articlegif}\n\\end{figure}\n\t\t\n\n\nBelow the page image on the returned page are links to every page of\nthe article individually. This allows the user to directly access any\npage in the article. Wherever possible, plates that have been printed\nseparately in the back of the journal volume have been bundled with\nthe articles to which they belong for ease of access. The next part\nof the displayed document provides access to plates in that volume\nif the plates for this journal are separate from the articles.\nAnother link retrieves the abstract for this article.\n\nThe next part of the page allows the printing of the article. If the\nbrowser works with HTTP persistent cookies (see\nsection~\\ref{cookies}), there is just one print button in that section\nwith a selection to print either the whole paper or individual pages.\nThis print button will print the article in the format that the user\nhas specified in the user preferences. If the browser does not handle\ncookies, several of the more commonly used print options are made\navailable here.\n\nAll possible printing options can be accessed through the next link\ncalled ``More Article Retrieval Options''. This page allows the user to\nselect all possible retrieval options. These include:\n\ni. Postscript: Access to two resolutions is provided (200 dpi and 600\ndpi). For compatibility with older printers, there is also an option\nto retrieve Postscript Level 1 files.\n\nii. PCL (Printer Control Language): This language is for printing on\nPCL printers such as the HP desk jets and compatibles.\n\niii. PDF (Portable Document Format): PDF can be viewed with the Adobe\nAcrobat reader (\\cite{acrobat}). From the Acrobat reader the article\ncan be printed.\n\niv. TIFF (Tagged Image File Format): The original images can be\nretrieved for local storage. This would allow further processing like\nextraction of figures, or Optical Character Recognition (OCR) in order\nto translate the article into ASCII text.\n\nv. Fax retrieval: Within the USA, articles can be retrieved via\nfax at no cost. Again, the retrieval is greatly facilitated through\nthe preferences setting capability. The preferences allow the user to\nstore a fax number that will be used for the fax service.\n\nvi. Email retrieval: Articles can be retrieved through email instead\nof through a WWW browser. MIME (Multipurpose Internet Mail Extension,\n\\cite{mime}) capable email systems should be able to send the\nretrieved images directly to the printer, to a file, or to a viewer,\ndepending on what retrieval option was selected by the user.\n\n\\medskip\n\nFor most of the retrieval options, the data can optionally be compressed\nbefore they are sent to the user. Unix compress and GNU gzip are\nsupported compression algorithms.\n\nInstead of displaying the first page of an article together with the\nother retrieval links, the user has the option (selected through the\npreferences system, see section~\\ref{cookies}) to display thumbnails\nof all article pages simultaneously. This allows an overview of the\nwhole article at once. One can easily find specific figures or\nsections within an article without having to download every page.\nThis should be especially useful for users with slow connections to\nthe Internet. Each thumbnail image ranges in size from only 700 bytes\nto 3000 bytes, depending on the user selected thumbnail image quality.\nThe rest of this type of article page is the same as for the\npage-by-page display option.\n\n\n\\subsubsection{Other Forms Based User Interfaces}\n\nThere are several forms available to directly access references or\narticles and other relevant information. All abstract query forms\nreturn the short reference format as described above. One form allows\naccess to references through bibliographic codes:\n\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/bib_abs.html\n\\end{verbatim}\n\nThis form allows the user to retrieve abstracts by specifying directly\na bibliographic code or the individual parts of a bibliographic (year,\njournal, volume, page). This can be very useful in retrieving\nreferences from article reference lists, since such reference lists\ngenerally contain enough information to build the bibliographic codes\nfor the references. This form also accepts partial codes and returns\nall references that match the partial code. It accepts the wildcard\ncharacter `?'. The `?' wildcard stands for one character in the code.\nFor partial codes that are shorter than 19 characters, matching is\ndone on the first part of the bibliographic codes. For instance:\n\n1989ApJ...341?...1\n\\noindent\nwill retrieve the articles on page 1 of the ApJ (Astrophysical\nJournal) and ApJ Letters volume 341, regardless of the author name.\n\nAnother form allows access to the Tables of Contents (ToCs) of selected\njournals by month/year or volume:\n\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/toc_service.html\n\\end{verbatim}\n\nOne option on that form is to retrieve the latest published issue of a\nparticular journal. Access to the last volumes of a set of journals\nis also available though a page with a graphical display of selected\njournals' cover pages:\n\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/tocs.html\n\\end{verbatim}\n\nBy clicking on a journal cover page either the last published volume\nof that journal or the last volume that the user has not yet read is\nreturned, depending on the user preference settings (see\nsection~\\ref{cookies}). The information necessary for that service is\nstored with the user preferences in our internal user preferences\ndatabase.\n\nA customized ToC query page is available at:\n\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/custom_toc.html\n\\end{verbatim}\n\nIt will display only icons for journals that have issues available\nthat have not been read by the user. This allows a user to see at a\nglance which new issues for this set of journals have been published.\nThe set of journals that is included in the customized ToC query page\ncan be specified in the user preferences (see section~\\ref{cookies}).\n\nAs mentioned in section~\\ref{abstracts} and in ARCHITECTURE, one\nimportant aspect of the ADS search system is the list of synonyms.\nSometimes it is important for our users to be able to see what words\nare in a particular synonym group to properly interpret the search\nresults. Another question that is asked is what words are in the\ndatabase and how often. The list query page (linked to the words\n``Authors'', ``Title Words'', and ``Text Words'' above the\ncorresponding entry fields on the main query form) allows the user to\nfind synonym groups and words in the database. The user can specify\neither a complete word in order to find its synonyms, or a partial\nword with wildcard characters to find all matching words in the\ndatabase. When a word without wildcard characters is specified, the\nlist query form returns all of its synonyms (if any).\n\nTo find words matching a given pattern, the users can specify a\npartial word with either or both of two wildcard characters. The\nquestion mark `?' stands for any single character, the asterisk `*'\nstands for zero or more characters (see section~\\ref{wildcard}). For a\nwildcard search, the list query form returns all words in the database\nthat match the specified pattern, together with the frequencies of\nthese words in the database.\n\n\\subsubsection{Journal specific access forms}\n\nThe regular query forms search the complete database. The user can\nselect the return of only specific journals in the ``Filter'' section\nof the query form. In order to allow different journals to use the\nADS system for searching their references, journal specific pages are\navailable. The URL (Uniform Resource Locator) for an abstract search\npage for a specific journal is:\n\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/Journals/\n search/bibstem\n\\end{verbatim}\n\nThe page for retrieving scanned articles of a specific journal is:\n\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/Journals/\n articles/bibstem\n\\end{verbatim}\n\nand the page for retrieving the tables of contents by volume or\npublication date is:\n\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/Journals/toc/bibstem\n\\end{verbatim}\n\nIn each case, bibstem is the abbreviation for the selected journal.\nFor instance:\n\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/Journals/search/ApJ\n\\end{verbatim}\n\nreturns a query form for searching only references of the Astrophysical\nJournal. These forms are available for linking by anybody.\n\n\n\\subsection{Direct Access Interfaces}\n\nBoth abstracts and articles can be accessed directly though HTML\nhyperlinks. The references are identified through the bibliographic\ncodes (or bibcodes for short) mentioned above and described in detail\nin DATA. The syntax for such links to access\nabstracts is:\n\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/cgi-bin/\n bib_query?bibcode=1989ApJ...342L..71R\n\\end{verbatim}\n\nScanned articles can be accessed directly through links of the form:\n\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/cgi-bin/\n article_query?bibcode=1989ApJ...342L..71R\n\\end{verbatim}\n\nThese links will return the abstract or scanned article respectively\nfor the specified bibliographic code. They are guaranteed to\nwork in this form. You may see other URLs while you use the ADS.\nThese are internal addresses that are not guaranteed to work in the\nfuture. They may change names or parameters. Please use only links\nof the form described above to directly access abstracts and articles.\n\n\n\\subsection{Embedded Queries}\n\nEmbedded queries can be used to build hyperlinks that return the\nresults of a pre-formulated query. One frequently used example is a\nlink that returns all articles written by a specific user. The syntax\nfor such a link is:\n\n\\begin{verbatim}\n<a href=\"http://adsabs.harvard.edu/cgi-bin/\n abs_connect?return_req=no_params&\n param1=val1¶m2=val2&...\">...</a>\n\\end{verbatim}\n\nThere are no spaces allowed in a URL. All blanks need to be encoded\nas `+'. The parameter return\\_req=no\\_params sets all the default\nsettings. Individual settings can be changed by including the name of\nthe specific setting and its value after the return\\_req=no\\_params\nparameter in the URL. A list of available parameters can be accessed\nat:\n\n\\begin{verbatim}\nhttp://adsdoc.harvard.edu/cgi-bin/\n get_field_names.pl\n\\end{verbatim}\n\nWe try to make changes to parameters backward compatible, but that is\nnot always possible. We encourage you to use this capability, but it\nis advisable to use only the more basic parameters.\n\nThis type of interface allows users to link to the ADS for a\ncomprehensive list of references on a specific topic. Many users use\nthis to provide an up-to-date publication list for themselves by\nencoding an author query into an embedded query.\n\n\n\\subsection{\\label{perlaccess} Perl Script Queries}\n\nThe ADS database can be used by other systems to include ADS data in\ndocuments returned from that site. This allows programmers at other\nsites to dynamically include the latest available information in their\npages. An example is the interface that SPIE (the International\nSociety for Optical Engineering) provides to our database. It is\navailable at:\n\n\\begin{verbatim}\nhttp://www.spie.org/incite/\n\\end{verbatim}\n\nThis site uses Perl scripts to query our database and format the\nresults according to their conventions. These Perl scripts are\navailable at:\n\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/www/adswww-lib/\n\\end{verbatim}\n\nThe Perl scripts allow the programmer to specify all the regular\nparameters. The results are returned in Perl arrays.\nIf you use these scripts, we would appreciate it if you would credit\nthe ADS somewhere on your pages.\n\n\n\\subsection{\\label{email} Email Interface}\n\nThe ADS Abstract Service can be accessed through an email interface.\nThis service is somewhat difficult to use since it involves an\ninterface between two relatively incompatible interface paradigms.\nThis makes describing it quite difficult as well. It is intended for\nusers who do not have access to web browsers. If you have questions\nabout how to use this access, please contact the ADS at\nads@cfa.harvard.edu.\n\nTo get information about this capability, send email to:\n\nadsquery@cfa.harvard.edu\n\nwith the word ``help'' in the message body.\n\nThis interface accepts email messages with commands in the message\nbody. The subject line is ignored. The commands that are available\nare:\n\\begin{verbatim}\n1) help (see above)\n2) action=URL\n\\end{verbatim}\n\nThe second command allows a user to retrieve a document at the\nspecified URL. Three qualifiers allow the user to specify what\nretrieval method to use, what format to return, and to which address\nto return the results:\n\\begin{verbatim}\na) method=`method'\nb) return=`return-type'\nc) address=`e-mail-address'\n\\end{verbatim}\n\na. `method' is either `get' or `post' (without the quotes). This\ndetermines what kind of query will be executed. To retrieve a form\nfor further queries, use the `get' method. To execute a forms query\nyou need to know what type of query the server can handle. If you\nexecute a forms query after retrieving the form through this service,\nthe correct method line will already be in place. Default method is\n`get'.\n\nb. `return-type' is either `text', `form', or `raw' (without the\nquotes). If text return is requested, only the text of the query\nresult is returned, formatted as if viewed by a WWW browser. If form\nreturn is requested, the text of the result is returned as well as a\ntemplate of the form that can again be executed with this service. If\nraw return is requested, the original document is returned without any\nprocessing. Default return is `form'. The capability to return MIME\nencoded files is in preparation.\n\nc. `e-mail-address' specifies to which e-mail address the result\nshould be sent. This line is optional. If no address is specified,\nthe result is sent to the address from where the request came.\n\nTo execute a query via email, the user first retrieves the abstract\nquery form with:\n\n\\begin{verbatim}\naction=http://adsabs.harvard.edu/\n abstract_service.html\n\\end{verbatim}\n\nThis will return an executable form. This form can be returned to the\nADS in an email message to execute the query. The user enters input\nfor the different fields as required in the forms template. For forms\ntags like checkboxes or radio buttons, the user can uncomment the\nappropriate line in the form. Comments in the form that are included\nwith each forms field provide guidance for completing the form before\nsubmission. The text part of the form is formatted as comment lines\nso that the user does not have to modify any irrelevant parts of the\nform. The retrieval method is already set appropriately.\n\n\n\n\n\\subsection{Z39.50 Interface}\n\n\\fussy\nThe recently implemented Z39.50 interface (\\cite{z3950}) conforms to\nthe Library of Congress Z39.50 conventions\n(http://lcweb.loc.gov/z3950/lcserver.html). This allows any library\nthat uses this protocol to access the ADS through their interface.\nThe databases supported through this interface are listed in\ntable~\\ref{z3950db}, search fields supported are listed in\ntable~\\ref{z3950use}, supported relationship attributes are listed in\ntable~\\ref{z3950rel} and the supported structure attributes are listed\nin table~\\ref{z3950strct}. Table~\\ref{z3950recfmt} lists the\nsupported record formats and table~\\ref{z3950recsyn} shows the\nsupported record syntax.\n\\sloppy\n\n\\begin{table}\n\\caption[]{Database Names Supported in the ADS database. }\n\\label{z3950db}\n\\begin{tabular*}{3.4in}{lp{0.8\\linewidth}}\n\n\\hline\n\\noalign{\\smallskip}\n\nValue & Description\\\\\n\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nAST & Astronomy Database. Contains references from\n Astronomy related articles\\\\\nINST & Instrumentation Database. Contains references from\n articles related to Space Instrumentation\\\\\nPHY & Physics Database. Contains references from\n Physics related articles\\\\\nPRE & Preprint Database. Contains references from\n the Los Alamos preprint server related to Astronomy\\\\\nGEN & General Database. Contains references from\n articles unrelated to the other databases\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\end{table}\n\n\n\n\\begin{table}\n\\caption[]{Use Attributes Supported in the ADS database. }\n\\label{z3950use}\n\\begin{tabular*}{3.4in}{ll}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nValue & Description\n\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n1 & Personal name$^{\\mathrm{a}}$\\\\\n1003 & Author$^{\\mathrm{a}}$\\\\\n4 & Title\\\\\n5 & Title series$^{\\mathrm{b}}$\\\\\n62 & Abstract\\\\\n31 & Publication Date\\\\\n1011 & Entry Date in Database\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\begin{list}{}{}\n\\item[$^{\\mathrm{a}}$]These attributes search the same field\n\\item[$^{\\mathrm{b}}$]This attribute limits searches to the journal specified\n\\end{list}{}{}\n\\end{table}\n\n\n\n\\begin{table}\n\\caption[]{Relation Attributes Supported in the ADS database.\n}\n\\label{z3950rel}\n\\begin{tabular*}{3.4in}{llp{0.4\\linewidth}}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nValue & Description & Fields Supporting\n\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n3 & Equal$^{\\mathrm{a}}$ & All\\\\\n2 & Less than or Equal & Publication Date\\\\\n4 & Greater than or Equal & Publication Date, Entry Date\\\\\n102 & Relevance$^{\\mathrm{b}}$ & Title, Abstract, Author\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\begin{list}{}{}\n\\item[$^{\\mathrm{a}}$]Relation Equal searches for exact words.\n\\item[$^{\\mathrm{b}}$]Relation Relevance searches for words and their synonyms.\n\\end{list}{}{}\n\\end{table}\n\n\n\n\\begin{table}\n\\caption[]{Structure Attributes Supported in the ADS database.\n}\n\\label{z3950strct}\n\\begin{tabular*}{3.4in}{lll}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nValue & Description & Fields Supporting\n\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n1 & quoted phrase & Title, Abstract\\\\\n2 & word & Title, Abstract, Author, Series\\\\\n6 & word list & Title, Abstract, Author, Series\\\\\n5 & date & Publication Date, Entry Date\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\end{table}\n\n\n\n\\begin{table}\n\\caption[]{Record Format Supported in the ADS database. }\n\\label{z3950recfmt}\n\\begin{tabular*}{3.4in}{ll}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nValue & Description\n\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nB & Brief Records (Title, Authors)\\\\\nF & Full Records (all available information)\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\end{table}\n\n\n\n\\begin{table}\n\\caption[]{Record Syntax Supported in the ADS database. }\n\\label{z3950recsyn}\n\\begin{tabular*}{3.4in}{ll}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nValue & Description\n\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n1.2.840.10003.5.101 & SUTRS Records\\\\\n1.2.840.10003.5.109.3 & HTML Records\\\\\n1.2.840.10003.5.1000.147.1 & ADS Tagged Records\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\end{table}\n\n\n\nEach table notes which search fields support which attribute. The\nrelationship attributes `equal' and `relevance' are used to search\nwithout and with synonym replacement respectively. If the structure\nattribute `Phrase' is selected, the input is considered to be one\nphrase and is not separated into individual words. If the structure\nattribute `Word' is selected and several words are specified, the\ninput is treated as if the structure attribute `Word List' were\nspecified.\n\nAs output, brief and full records are supported. These record formats\nare the same as in the short results list and in the full abstract\ndisplay as described above. The supported record syntax is either\nSUTRS (Simple Unstructured Text Record Syntax), HTML (HyperText Markup\nLanguage), or the ADS tagged format. In the HTML record syntax, links\nto other supported ADS internal and external data sources are\nincluded.\n\nA description of this interface is available on-line at:\n\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/abs_doc/ads_server.html\n\\end{verbatim}\n\nAn example of the ADS Z39.50 interface can be accessed from the\nLibrary of Congress Z39.50 Gateway at:\n\n\\begin{verbatim}\nhttp://lcweb.loc.gov/z3950/\n\\end{verbatim}\n\n\n\\section{\\label {cookies} Preferences}\n\nThe ADS user interface is customized through the use of so-called HTTP\npersistent cookies (see \\cite{cookies}). These ``cookies'' are a\nmeans of identifying individual users. They are strings that are\ncreated by the server software. Web browsers that accept cookies\nstore these identification strings locally on the user's computer.\nAnytime a user makes a request, the ADS software checks whether the\nrequesting browser is capable of accepting cookies. If so, it sends a\nunique string to the browser and asks it to store this string as an\nidentifier for that user. From then on, every time the same user\naccesses the ADS from that account, the browser sends this cookie back\nto the ADS server. The ADS software contains a database with a data\nstructure for each cookie that the ADS has issued. The data structure\nassociated with each cookie contains information such as the type of\ndisplay the user prefers, whether tables should be used to format\ndata, which mirror sites the user prefers for certain external data\nproviders, the preferred printing format for ADS articles, and which\njournal volumes the user has read. It also can store the email\naddress of the user and a fax number, in case the user wants to\nretrieve articles via email or fax.\n\nThe preference settings form includes a field for the user name as\nwell as the email address. However, neither is necessary for the\nfunctioning of any of the features of the ADS. The system is\ncompletely anonymous. None of the information stored through this\ncookie system is made available to anybody outside the ADS. There is\nno open interface to this database and the database files are not\naccessible through the WWW. Any particular user can only access their\nown preferences, not the preferences set by any other user.\n\nMost of these preferences can be set by the user through a WWW forms\ninterface. Some fields in a user's preference record are for ADS\ninternal use only. For instance the system is being used to display\nannouncements to users in a pop-up window. The cookie database\nremembers when the message was last displayed, so that each message is\ndisplayed only once to each user.\n\nThis preference saving system also allows each user to store a query\nform with filled-in fields. This enables users to quickly query the\nADS for a frequently used set of criteria.\n\nThe cookie identification system is implemented as a Berkeley DBM\n(DataBase Manager) database with the cookie as the record key. The\ndata block that is stored in the database is a C structure. The\nbinary settings (e.g. ``Use Tables'', or ``Use graphical ToC Page'')\nare stored as bits in several preference bytes. Other preferences are\nstored as bytes, short integer, or long integer, depending on their\ndynamic range.\n\nHTTP cookies are based on host names. Whenever a particular host is\naccessed by the browser, the browser sends the cookie for that host to\nthe server software. Since the ADS uses several host names as well as\nmirror sites, we developed software that, on first contact between a\nnew user and the ADS, sets the same cookie for all our host names at\nthe main sites, as well as for the mirror hosts. This is essential in\norder to provide a seamless system with different servers handling\ndifferent tasks.\n\n\n\n\\section{\\label {searchengine} Search Engine Details}\n\n\\subsection{General}\n\nThe search engine software is written in C. It accepts as input a\nstructure that contains all the search fields and flags for the user\nspecified settings and filters. For each search field that contains\nuser input a separate POSIX (Portable Operating System Interface)\nthread is started that searches the database for the terms specified\nin that field. The results obtained for each term in that field are\ncombined in the thread according to the specified combination logic.\nThe resulting list of references is returned to the main thread. The\nmain thread combines the results from the different field searches and\ncalculates the final score for each reference. The final combined\nlist with the scores is returned to the user interface routines that\nformat the results according to the user specified output format.\n\n\\subsection{\\label {searchalgorithm} Searching}\n\n\\subsubsection{Database Files}\n\nThe abstracts are indexed in separate fields: Author names, titles,\nabstract text, and objects. Each of these fields is indexed\nsimilarly into an index file and a list file (see ARCHITECTURE). The\nindex file contains a list of all terms in the field together with the\nfrequency of the term in the database, and the position and length of\ntwo blocks of data in the list file. One block contains all\nreferences that include the exact word as specified. The other block\ncontains all references that contain either the word or any of its\nsynonyms.\n\nA search for a particular word in the index file is done through a\nbinary search in the index. The indexes are resident in memory,\nloaded during boot time (see section~\\ref{optimization}). Once the\nword is found in the index, the position and length of the data block\nis used to directly access the data block in the list file. This data\nblock contains the identifier for each reference that contains the\nsearch word.\n\nIf a quick update has occurred (see ARCHITECTURE) since the list file\nwas last built (indicated by a negative in part of the last\nidentifier), an auxiliary block of reference identifiers is read. Its\nposition is contained in the structure of the last reference\nidentifier. This auxiliary block is merged with the original one.\n\nThe identifier for each reference is the position of the bibliographic\ncode for that reference in the list of all bibliographic codes. This\nsystem saves one lookup of the identifier in a list of identifiers,\nsince the number can be used directly as an index in the array of\nbibliographic codes.\n\n\n\\subsubsection{Synonym Searches}\n\nAs mentioned above, the index files contain information about two\nblocks of data, the data for the individual word and for the synonym\ngroup to which this word belongs. When a search with synonym lookup\nenabled is requested, the block of data for the whole synonym group is\nused, otherwise the data for only the individual word is returned.\nAll the processing that enables these two types of searches is done\nduring indexing time, therefore the speeds for both searches are similar.\n\nEven though our synonym list is quite extensive (see ARCHITECTURE) our\nusers will sometimes use words that are not in the database or the\nsynonym list. In these cases the search software uses a stemming\nalgorithm from the Unix utility ispell to find the stem of the search\nword and the searches for the word stem. The indexing software has\nindexed the stems of all words in the database together with their\noriginal words (see ARCHITECTURE). This word stemming is done as a\nlast resort if no regular match has been found in an attempt to find\nany relevant references.\n\n\\subsubsection{\\label {wildcard} Wildcard Searches}\n\nIn order to be able to search for families of words, a limited\nwildcard capability is available. Two wildcard characters are\ndefined: The question mark `?' is used to specify a single wildcard\ncharacter and the asterisk `*' is used to specify zero or more wildcard\ncharacters. The `?' can be used anywhere in a word. For instance\na search for {\\it M1?} will find all Messier objects between M10 and\nM19. A search for {\\it a?sorb} will find references with {\\it absorb}\nas well as {\\it adsorb}.\n\nThe asterisk can only be used at the beginning or at the end of a\nword. For instance {\\it 3C*} searches for all 3C objects. {\\it\n*sorb} searches for words that end in {\\it sorb} like absorb, desorb,\netc. When synonym replacement is on, all their synonyms\n(e.g. absorption) will be found as well. The `?' and the `*' can be\ncombined in the same search string.\n\n\n\\subsection{Results Combining within a Field}\n\n\\subsubsection{Combining results}\n\nAs mentioned above, the user can select between four types of\ncombination methods: ``OR'', ``AND'', simple logic, and full boolean\nlogic. For the first three cases, the references for all search terms\nare retrieved and sorted first. The reference lists\nare then merged by going through the sorted reference lists\nsequentially and synchronously and selecting references according to\nthe chosen logic.\n\nThe search algorithm for the full boolean logic is different. The\nboolean query is parsed from left to right. For each search term a\nfunction is called that finds the references for this term. A search\nterm is either a search word, a phrase, or an expression enclosed in\nparentheses. If the search term contains other terms (if it is\nenclosed in parentheses), the parsing function is called recursively.\n\nThe next step is to determine the boolean operator that follows the\nsearch term, and then to evaluate the next search term after the\noperator. Once the reference lists for the two terms and the\ncombining operator are determined, the two lists are combined\naccording to the operator. This new list is then used as the first\nterm of the next expression.\n\nIf the boolean operator is `OR', the combining of the lists is\ndeferred, and the next operator and search term are evaluated. This\nensures the correct precedence of `OR' and `AND' operators.\n\nThe `NOT' operator is implemented by getting the reference list for\nthe term, making a copy of all references in the database, and then\nremoving the references from the search term from the complete list.\nThis yields a very large list of references. If the first search term\nin a boolean expression is a `NOT' term, the search will take very\nlong, because this large list has to be propagated through all the\nsubsequent parsing of the boolean expression. Care should therefore\nbe taken to put a `NOT' term to the right of at least one other term,\nsince processing is done left to right.\n\nAs an example, figure~\\ref{pseudocode} shows the processing of the\nboolean expression mentioned in section~\\ref{dataretrieval}:\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF8.eps}}\n\\caption[]{Pseudo code for parsing full boolean search expression. }\n\\label{pseudocode}\n\\end{figure}\n\t\t\n\n\n\\begin{verbatim}\n(pulsar or ``neutron star'') and\n (``red shift'' distance) and\n not 1987A\n\\end{verbatim}\n\n\\subsubsection{Scoring}\n\nIn addition to the information about the references for each word, the\nindex file also contains its frequency in the database. The frequency\nis already pre-calculated as int(10000/(log(frequency))) during\nindexing (see ARCHITECTURE). This saves considerable time during\nexecution of the search engine since all server calculations can be\ndone as integer computations, no floating point operations are\nnecessary. During the first part of the search, this frequency is\nattached to each retrieved reference. In the next step, the retrieved\nreferences are combined according to the selected combination logic\nfor that field.\n\nFor `OR' combination logic, the lists retrieved for each word are\nmerged and uniqued. As described in section~\\ref{optimization}, this is\ndone by going through the sorted reference lists synchronously and\nadding each new reference to the output list. The score for that\nreference is determined by adding up the frequencies from each of the\nlists for weighted scoring, or by setting a score equal to the number\nof matched words for proportional scoring.\n\nFor `AND' combination logic, only references that appear in every one\nof the lists are selected. Each of these references receives a score\nof 1.\n\nFor simple logic and full boolean logic, the score for the returned\nreferences is determined only from the search terms that were combined\nwith `OR'. All words that have mandatory selection criteria (prefixed\nby `+' or `--' in simple logic, and combined with `AND' or `NOT' in\nfull boolean logic) do not affect the final score.\n\n\n\\subsection{Combining Results among Fields}\n\n\\subsubsection{Combining}\n\nAfter the POSIX threads for each search field are started, the main program\nwaits for all threads to complete the search. When all searches are\ncompleted the search engine combines the results of the different\nsearches according to the selected settings. If for instance one\nfield was selected as required for selection in the settings section\nof the query form, only references that were found in the search for\nthat field will be in the final reference list. The combined list is\nthen uniqued and sorted by score. The resulting list of\nreferences is passed back to the user interface software.\n\nIf the user did not specify any search terms, a date range has to be\nselected. The software queries the database for all references in\nthe selected date range and uses this list for further processing,\ne.g. filtering (see section~\\ref{filters}).\n\n\\subsubsection{Scoring}\n\nThe score for each reference in the final results list is determined\nby adding the scores from each list multiplied by the user specified\nweight for each field and then normalizing the score such that a\nreference that matches all search terms from all fields receives a\nscore of 1.\n\n\n\\subsection{\\label{filters} Selection Filters}\n\nAfter the search is completed according to the specified search words\nand the settings that control the combination logic and the scoring\nalgorithms, the resulting list of references can be filtered according\nto several criteria. During the design of the software a decision had\nto be made whether to filter the results while selecting the\nreferences or after completing the search. The first approach has the\nadvantage that the combining of the selected references will be faster\nbecause fewer references need to be combined. The second approach has\nthe advantage that the first selection is faster. We chose the second\napproach because, except for selecting by publication date, only a\nsmall number of queries use filtering (see section~\\ref{accessstats}).\nBecause of that, filtering by publication date is done during\nselection of the references, while the other filtering is done after\nthe search is completed.\n\nReferences can be filtered by five criteria:\n\\begin{verbatim}\n1. Entry date in the data base\n2. Minimum score\n3. Journal\n4. Available links\n5. Group membership\n\\end{verbatim}\n\n1. + 2. Entry date and minimum score. These two filters can be used\nto query the database automatically on a regular basis for new\ninformation that is relevant to a selected topic. The user can build\na query form that returns relevant references, and then save this\nquery form locally. This query form can then be sent to the ADS email\ninterface (see above) on a weekly or monthly basis. By specifying an\nentry day of -7 for instance, the query will retrieve all references\nthat fit the query and that were entered within the last seven days.\nThe minimum score can be used to limit the returned number of\nreferences to only the ones that are really relevant. The references\nare returned via email as described in section~\\ref{email} about the email\ninterface.\n\n3. Journal filter. This filter allows the user to select references\nfrom individual journals or groups of journals. Available options\nfor this filter are:\n\\begin{verbatim}\na. All journals (default)\nb. Refereed journals only\nc. Non-refereed journals only\nd. Selected journals\n\\end{verbatim}\n\nIf the last option is selected, the user can specify one or more\njournal abbreviations (e.g. ApJ, AJ (Astronomical Journal)) that\nshould be selected. More than one abbreviation can be specified by\nseparating them with semicolons or blanks. The filter for journals\ncan also include the volume number (but not the page number). The\njournal abbreviation is compared with the bibliographic codes over the\nlength of the specified abbreviation. For instance if the user\nspecifies {\\it ApJ}, the system selects all articles published in the\nApJ, ApJ Supplement and ApJ Letters. {\\it ApJ..} will select only\narticles from the ApJ and the ApJ Letters. A special abbreviation,\n{\\it ApJL} will select only articles from the ApJ Letters. If a\njournal abbreviation is specified with a prepended `--', all\nreferences that are NOT from that journal are returned. The journal\nabbreviations (or bibstems) used in the ADS are available at:\n\n\\begin{verbatim}\nhttp://adsdoc.harvard.edu/abs_doc/\n journal_abbr.html\n\\end{verbatim}\n\n4. Available links. This filter allows the user to select references\nthat have specific other information available. The returned\nreferences can be filtered for instance to include only references\nthat have data links or scanned articles available. As an example,\na user needs to find on-line data about a particular object. A search\nfor that object in the object field and a filter for references with\non-line data returns all articles about that object that link to\non-line data.\n\n5. Groups. We provide the capability to build a reference collection\nfor a specific subset of references. This can be either articles\nwritten by members of a particular research institute or about a\nparticular subject. Currently there are 5 groups in the ADS. We\nencourage larger institutes or groups to compile a list of their\nreferences and send it to us to be included in the list of groups.\n\n\n\\section{\\label{optimization} Optimizations}\n\nThe search engine is entirely custom-built software. As mentioned in\nthe introduction, the first version of the Abstract Service used\ncommercial database software. Because of too many restrictions and\nserious performance problems, a custom-designed system was\ndeveloped. The main design goal was to make the search engine as fast\nas possible. The most important feature that helped speed up the\nsystem was the use of permanent shared memory segments for the search\nindex tables. In order to make searching fast, these index tables\nneed to be in Random Access Memory. Since they are tens of megabytes\nlong, they cannot be loaded for each search. The use of permanent\nshared memory segments allows the system to have all the index tables\nin memory all the time. They are loaded during system boot. When a\nsearch engine is started, it attaches to the shared segments and has\nthe data available immediately without any loading delays. The shared\nsegments are attached as read-only, so even if the search engine has\nserious bugs, it cannot compromise the integrity of the shared\nsegments. Using shared segments with the custom-built software\nimproved the speed of a search by a factor of 2 -- 20, depending on the\ntype of search.\n\nAccess to the list files (see section~\\ref{searchalgorithm}) was\noptimized too. These files cannot be loaded into memory since they\nare too large (each is over one hundred megabytes in size). To\noptimize access to these files, they are memory mapped when they are\naccessed for the first time. From then on they can be accessed as if\nthey were arrays in memory. The data blocks specified in the index\ntables can be accessed directly. Access is still from file, but it is\nhandled through the paging in the operating system, rather than\nthrough the regular I/O system, which is much more efficient.\n\nOnce the search engine was completed and worked as designed, it was\nfurther optimized by profiling the complete search engine and then\noptimizing the modules that used significant amounts of time. Further\nanalysis of the performance of the search engine revealed instances\nwhere operations were done for each search that could be done during\nindexing of the data and during loading of the shared segments.\nOverall these optimizations resulted in speed improvements of a factor\nof more than 10 over the performance of the first custom-built\nversion. These optimizations were crucial for the acceptance of the\nADS search system by the users.\n\nIn order to further speed up the execution, the search engine uses\nPOSIX threads to exploit the inherent parallel nature of the search\ntask. The search for each field, and in the case of the object field\nfor each database, is handled by a separate POSIX thread. These\nthreads execute in parallel, which can provide speedups in our\nmultiprocessor server. Even for single processor systems this will\nprovide a decrease in search time, since each thread sometimes during\nits execution needs to wait for I/O to complete. During these times\nother threads can execute and therefore decrease the overall execution\ntime of a search.\n\nAnother important part of the optimization was the decision on how to\nstructure the index and list files. The index files contain the\nword frequency information that is used to calculate scores for the\nweighted scoring (see section~\\ref{abstracts}c). The score for a matching\nreference is calculated from the inverse logarithm of the frequency of\nthe word in the database. This requires time consuming floating point\ncalculations. To avoid these calculations during the searches, the\nfloating point arithmetic is done at indexing time. The index file\ncontains the inverse log of the word frequency multiplied by a\nnormalization factor of 10,000. This allows all subsequent\ncalculations to be done in integer arithmetic, which is considerably\nfaster than floating point calculations.\n\nAnother optimization was to pre-compile the translation rules (see\nsection~\\ref{abstracts}). These translation rules are pre-compiled and\nstored in a shared memory segment to which the search process\nattaches. This allows for faster execution of these pattern matching\nroutines.\n\nOverall, these optimizations improved the speed of the searches by two\norders of magnitude between the original design using a commercial\ndatabase and the current software.\n\n\n\\section{\\label {accessstats} Access Statistics}\n\nThe ADS software keeps extensive logs about the use of the search\nand access software. In this section, usage statistics for the search\nsoftware and for access patterns to the Article Service are reported.\nIf not otherwise indicated, the statistics in this section are for the\none-year period from 1 April 1998 through 31 Mar 1999.\n\n\\subsection{Abstract Service}\n\nThe ADS is accessed by users from many different countries. In the\none-year period of this section the ADS was accessed by 127,000\ndifferent users, using 100,000 different hosts from 112 different\ncountries. An individual user is defined as having a unique cookie\n(see section~\\ref{cookies}). Users without cookies are distinguished\nby the hostnames from which the requests came. This may overestimate\nthe number of users, since some users may have more than one cookie,\nfor instance when accessing the ADS from home. The number of\ndifferent hosts is a lower limit of the number of users. Many hosts\nare used by multiple users, so the real number is certainly\nconsiderably higher than that. The development of the number of users\nand queries over the life of the ADS is described in OVERVIEW. This\nsection describes some more detailed investigations of the access\nstatistics.\n\nThe total number of users at first comes as quite a surprise. The\nnumber of working astronomers in the world is probably between 10,000\nand 20,000. The number of ADS users is much larger than that. This\nis probably due to several factors. First, there are certainly many\naccidental users. They somehow find our search page through some\nlink, execute a query to see what they get back, and then never come\nback because it is of no interest to them.\n\nOther possible users are media people. There are certainly many\nreporters occasionally looking up something in astronomy. I have\nspoken with several of them that use the ADS occasionally for that.\n\nAnother group of users are amateur astronomers. The ADS was described\nin Sky \\& Telescope by \\cite{1996S&T....92...81E} a few years ago.\nthis has certainly made amateur astronomers aware of this resource.\nThe number of amateur astronomers world-wide is certainly in the\nmillions, so they comprise a potentially large number of users.\n\nAnother large group of users visits the ADS through links from other\nweb sites. One particularly popular one is NASA's Image of the Day,\nwhich frequently includes links to abstracts or articles in the ADS.\nSince this NASA page is visited by millions of people, a large number\nof them will access the ADS through these links.\n\nThe use of the ADS in different countries depends on several\nfactors. One of these is certainly the population of the country.\nFigure~\\ref{qupop} shows the number of queries per capita as a\nfunction of the population of the country (\\cite{ciafacts}). There\nseems to be an upper limit of about 0.1 -- 0.2 queries per person per\nyear. The one exception is the Vatican with almost 3 queries per\nperson per year. This is understandable since the Vatican has an\nactive Astronomy program, which generates a large number of queries\nfor a small population.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF9.eps}}\n\\caption[]{Number of queries per person per year in each country as a function of the population for the country. }\n\\label{qupop}\n\\end{figure}\n\t\t\n\n\nAnother factor for querying the ADS is the funding available for\nAstronomy in a country, and the available infrastructure to do\nastronomical research. Figure~\\ref{gdprefs} shows the number of\nreferences retrieved per capita as a function of the Gross Domestic\nProduct (GDP, \\cite{ciafacts}) of the country. The symbols are the Internet\ncodes for each country.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF10.eps}}\n\\caption[]{Number of references retrieved per person as a function of the Gross Domestic Product (GDP) per person for each country. }\n\\label{gdprefs}\n\\end{figure}\n\t\t\n\nThe highly industrialized countries cluster in the upper right part of\nthe plot (area 1). A closeup of this region is shown in\nfigure~\\ref{gdprefsclose}. Other clusters are the countries of the\nformer Soviet Union (area 2), and Central and South American countries\n(area 3). The high number of references retrieved per capita combined\nwith the lower GDP per capita of the former Soviet Union is probably\ndue to a recent decline in GDP, but a still existing infrastructure\nfor astronomical research.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF11.eps}}\n\\caption[]{Number of references retrieved per person as a function of\nthe Gross Domestic Product (GDP) per person. This figure is a closeup\nof area 1 in figure~\\ref{gdprefs}. }\n\\label{gdprefsclose}\n\\end{figure}\n\t\t\nThe ADS is used 24 hours per day. The distribution of queries\nthroughout the day is shown in figure~\\ref{24hqu}. This figure shows\nthe number of queries at the two largest mirror sites, as well as the\nqueries at the main ADS site. The usage distribution data are for the\ntime period from 1 November 1998 to 31 March 1999, not the full year,\nto avoid complications due to different periods where daylight savings\ntime is in effect. The queries at the main site are separated into\nUS users and non-US users on the basis of their Internet hostnames.\nAll the individual curves show a distinct two-peaked basic shape, with\nadditional smaller peaks in some cases. This distribution of queries\nover the day shows the usage throughout a workday, with a small\nminimum during lunch hour. The SAO-US distribution does not show a\nreal minimum between the two peaks, presumably because of the\ndistribution of US researchers over three time zones.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF12.eps}}\n\\caption[]{Number of queries per hour as a function of the time of day\nfor the main SAO site and the mirror sites in France and Japan. }\n\\label{24hqu}\n\\end{figure}\n\t\t\n\nThere are three features in this figure that deserve special notice.\nThe first is that the shape of the accesses to the ADS mirror in\nFrance is the same as the shape of the non-US access to the SAO site.\nThis indicates that the large majority of the non-US use on the SAO\nsite is from European users.\n\nThis non-US usage is about 50\\% higher than the total usage of\nthe ADS mirror site at the CDS in France. The reason for this is most\nprobably the fact that the connectivity within Europe is not yet very\ngood. We know that for instance that our users in England and Sweden\nhave better access to the main ADS site in the USA than to our mirror\nsite in France. The same is true for other parts of Europe.\n\nAnother reason for the use of the USA site by European users is the\nfact that our European mirror sites do not yet have the complete set\nof scanned articles on-line. This forces some users to access the\nmain ADS site in order to retrieve scanned articles.\n\nSecond, there is a slight peak in the distribution of queries to the\nNAO mirror in Japan around 21:00 UTC (Universal Time Coordinated,\nformerly Greenwich Mean Time). This is probably due to US west\ncoast users using the Japanese mirror site instead of the US site.\nThe access to Japan is frequently very fast and response times from\nJapan may be better than from SAO during peak traffic times.\n\nThird, there is a distinct peak in the SAO-US usage at 9:00 UTC. This\nfeature was so unusual that we tracked down the reason for it. It\nturns out that one of our users has set up web pages that include\nabout 200 links to ADS abstracts. He had set up a link verifier that\nevery night at 9:00 UTC checked all the links on his pages. This meant\nthat the link verifier executed 200 queries every night at the same\ntime, which showed up in this evaluation of our access statistics.\n\nThe following section shows statistics of how our users use the\ndifferent capabilities of the ADS query system.\nFigure~\\ref{fieldhist} shows a histogram of the relative usage of the\ndifferent search fields (authors, objects, title, text). It shows\nclearly that the majority of queries are queries by author name\n(66\\%). Object names are used in fewer than 5\\% of the queries. The\ntitle field is used in about 21\\% of the queries, and the text field\nin 26\\%. Queries that use more than one field make up about 18\\% of\nthe total. This usage pattern justifies for instance including tables\nof contents (ToCs) in the database that do not have abstracts for searching.\nSince a large part of the usage is through author and title queries,\nsuch ToC entries will still be found.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF13.eps}}\n\\caption[]{A histogram of the relative usage of the different search fields (authors, objects, title, text) and the use of multiple fields. }\n\\label{fieldhist}\n\\end{figure}\n\t\t\n\n\nFigure~\\ref{numsearchitems} shows the number of queries as a function\nof the number of query items in each input field. The query frequency\ngenerally decreases exponentially with increasing number of search\nterms. For title and text queries, the frequency is approximately\nconstant up to 3 query words, before the frequency starts to decrease.\nFor abstract queries there is a significant increase in frequency of\nqueries with more than 20 query words, for title queries there is a\nsimilar increase for queries with more than about 8 query words. This\nis due to queries generated through the query feedback mechanism which\nallows the user to use a given abstract and its title as a new\nquery.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF14.eps}}\n\\caption[]{The number of queries in the period of 1 April 1998 to 31 March 1999 as a function of the number of query items in each input field. }\n\\label{numsearchitems}\n\\end{figure}\n\t\t\n\n\nFigures~\\ref{settingsuse1} and \\ref{settingsuse2} show the usage of\nnon-default query settings (see section~\\ref{searchalgorithm}). The\ndefault settings were chosen to suffice for most queries.\nFigure~\\ref{settingsuse1} shows the percentage of non-default settings\nfor the different settings and query fields available. It shows that\n29\\% of author queries, 78\\% of title queries, and 85\\% of text\nqueries use non-default settings. This was at first disappointing,\nbecause it suggested that the default settings might not be a\nreasonable selection of settings. The two main settings that were\nnon-default were combining words with ``AND'' (see\nsection~\\ref{abstracts}.b.ii), and disabled weighted scoring (see\nsection~\\ref{abstracts}.c). On closer examination of the statistics it\nturns out that the straight weighting settings come from mainly two\nsystems, the NASA Techreports and the International Society for\nOptical Engineering (SPIE).\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF15.eps}}\n\\caption[]{Percentage of non-default settings for the different available settings and query fields. }\n\\label{settingsuse1}\n\\end{figure}\n\t\t\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF16.eps}}\n\\caption[]{Percentage of non-default settings for the different available settings and query fields. This plot excludes the queries from NASA Techreports and SPIE. }\n\\label{settingsuse2}\n\\end{figure}\n\t\t\n\n\nBoth of these systems use our Perl scripts (see\nsection~\\ref{perlaccess}) to access the ADS database. They do not set\nour normal default settings during these queries.\nFigure~\\ref{settingsuse2} shows the non-default settings for all\nqueries that did not come from either of these two servers. There is\nstill a small percentage of queries that use straight weighting,\nprobably mostly due to other systems that use our Perl script\ninterface routines.\n\nThe one remaining non-default setting that is used frequently is the\ncombination of words with ``AND''. We believe that the ``OR''\ncombination as default is more useful since it returns more\ninformation. The beginning of the list of returned references is the\nsame, regardless of whether ``AND'' or ``OR'' combination is selected,\nsince references that match all words are sorted to the beginning of\nthe list. When ``OR'' combination is selected, partial matches will\nbe returned after the ones with perfect matches. This is desirable\nsince there may be relevant references that for some reason do not\nmatch all query words.\n\nThe other selecting mechanism that is available is the filtering of\nreferences according to what other information is available for a\nreference. The usage of the filtering is shown in\ntable~\\ref{filteruse}. About 10\\% of the total queries use the filter\noption. Almost all of these filter by journal or select refereed\njournals only. The sum of the numbers for required data types adds up\nto more than the number for ``Required data'', since more than one\ndata type can be selected.\n\n\\begin{table}\n\\caption[]{Filter requests during the period of 1 April 1998\nto 31 March 1999. }\n\\label{filteruse}\n\\begin{tabular*}{3.4in}{llr}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nFilter Type & Required Data Type & Queries\n\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nTotal queries & ~ & 2754405\\\\\nNon-standard queries & ~ & 286341\\\\\nSelected journal &~ & 158581\\\\\nRefereed journals & ~ & 96270\\\\ \nNon-refereed journals & ~ & 1616\\\\\nData available & ~ & 6381\\\\\nRequired data & ~ & \\\\\n~ & Printable Articles & 2921\\\\\n~ & Scanned Articles & 1951\\\\\n~ & Electronic Articles & 1690\\\\\n~ & Abstracts & 1382\\\\\n~ & Planetary Data System & 834\\\\\n~ & Planetary Nebulae & 667\\\\\n~ & Citations & 615\\\\\n~ & Table of Contents & 506\\\\\n~ & References & 459\\\\\n~ & Author Comments & 393\\\\\n~ & On-line Data & 360\\\\\n~ & SIMBAD Objects & 269\\\\\n~ & NED Objects & 212\\\\\n~ & Library Entries & 204\\\\\n~ & Mail Order & 201\\\\\n~ & Associated Articles & 83\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\end{table}\n\n\n\n\nTable~\\ref{datalinkuse} shows the number of links available and the\nusage pattern of the data links that the ADS provides. The highest\nusage is access to the abstracts, followed by the links to full text articles,\nlinks to citations, and links to on-line electronic\narticles. Reference links and links to SIMBAD objects are next.\n\n\\begin{table}\n\\caption[]{Link types and their accesses during the period of 1 April 1998\nto 31 March 1999. Numbers of links available are as of July 1999.\n}\n\\label{datalinkuse}\n\\begin{tabular*}{3.4in}{lrr}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nLinks & Nr. Links & Nr. Accesses\n\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nAbstracts & 941,293 & 1,608,726\\\\\nScanned Articles & 138,785 & 526,872\\\\\nPrintable Articles & 40,928 & 254,881\\\\\n(Postscript and PDF)\\\\\nElectronic Articles & 125,933 & 186,067\\\\\nCitations & 195,192 & 77,316\\\\\nReferences & 135,474 & 36,969\\\\\nSIMBAD Objects & 110,308 & 23,505\\\\\nOn-line Data & 5,728 & 9,799\\\\\nNED Objects & 31,801 & 6,144\\\\\nMail Order & 247,282 & 3,520\\\\\nLibrary Entries & 18,746 & 1,645\\\\\nTables of Contents & 5,792 & 1,233\\\\\nAuthor Comments & 203 & 313\\\\\nAssociated Articles & 2765 & 169\\\\\nPlanetary Nebulae Data & 281 & 143\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\end{table}\n\n\n\n\\subsection{Article Access Statistics}\n\nThe ADS Article Service provides access to full journal articles. The\nusage statistics should show how astronomy researchers read and use\njournal articles. In this section we describe a few of the statistics\nof the article server. More statistics on the usage of the scanned\narticles are described in OVERVIEW.\n\nFigure~\\ref{nrarticlepages} shows the number of pages of scanned\narticles retrieved over the life of the ADS, figure~\\ref{nrarticles}\nshows the number of articles retrieved. The number of articles\nrepresents the sum of the selected links to on-line electronic\narticles, PDF and Postscript articles at the journals, and scanned\narticles at the ADS.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF17.eps}}\n\\caption[]{Number of pages of scanned articles retrieved through the life of the ADS Article Service. }\n\\label{nrarticlepages}\n\\end{figure}\n\t\t\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_searchF18.eps}}\n\\caption[]{Number of full text articles retrieved by ADS users. These numbers include the scanned articles at the ADS, as well as articles at the sites of the different journals that were requested through ADS links. }\n\\label{nrarticles}\n\\end{figure}\n\t\t\n\n\nBoth the number of pages and the number of articles retrieved is\nsteadily increasing. This is due to both the increased coverage in\nthe ADS of scanned journals and the increase in the number of users\nthat use the system.\n\nTable~\\ref{atclretrieval} shows the number of retrievals in the\nvarious formats. Postscript is a printer control language developed\nby Adobe (see \\cite{postscript}). Postscript Level 1 is the first\nversion of the Postscript language. It generates much larger files\nthan Level 2 Postscript. Some older printers can process only Level 1\nPostscript files. PDF (Portable Document Format) is a newer page\ndescription format, also developed by Adobe. PCL (Printer\nControl Language) is a printer control language developed by Hewlett\nPackard. It is used in low end PC printers. Low\nresolution is 200 dpi for Postscript and PDF, and 150 dpi for PCL.\nHigh resolution is 600 dpi for Postscript and PDF, 300 for PCL.\n\n\\begin{table}\n\\caption[]{Article retrieval by format type for March 1999, March 1998,\nand March 1997. PDF format and GIF Thumbnails were not yet available\nin March 1997. }\n\\label{atclretrieval}\n\\begin{tabular*}{3.4in}{p{0.35\\linewidth}rrr}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nArticle Type & \\multicolumn{3}{c}{Number of Retrievals}\\\\\n& March 99 & March 98 & March 97\n\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nPostscript Level 1 & 476 & 557 & 644\\\\\n(Low Resolution)\\\\\nPostscript Level 2 & 25,664 & 13,031 & 11,189\\\\\n(Low Resolution)\\\\\nPostscript Level 2 & 10,472 & 8,291 & 6,435\\\\\n(High Resolution)\\\\\nPDF & 3,266 & 620 & n/a\\\\\n(Low Resolution)\\\\\nPDF & 7,049 & 1008 & n/a\\\\\n(High Resolution)\\\\\nPCL & 14 & 73 & 72\\\\\n(Low Resolution)\\\\\nPCL & 53 & 111 & 132\\\\\n(High Resolution)\\\\\nGIF Thumbnails & 13,777 & 7,378 & n/a\\\\\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\end{table}\n\n\n\nThe majority of retrievals are of medium resolution\nPostscript files. This is the default setting in the ADS Article\nService. The number of Postscript Level 1 articles (compatible with\nolder printers, but much larger file sizes) retrieved is low compared\nwith Level 2 Postscript articles, and slowly declining. The number of\nPCL articles retrieved is even smaller and also declining. The number\nof PDF articles retrieved was slowly increasing throughout 1998. It\nhas increased much more rapidly in 1999. In early 1998 less than 15\\%\nof the high resolution articles were retrieved as PDF files. This\nfraction increased to 40\\% by March, 1999.\n\n\n\n\\section{\\label {future} Future Plans}\n\nThe ADS Abstract Service is only seven years old, but it is already an\nindispensable part of the astronomical research community. We get\nregular feedback from our users and we implement any reasonable\nsuggestions. In this section we mention some of the plans for\nimprovements that we are currently working on to provide even more\nfunctionality to our users.\n\n\\subsection{Historical Literature}\n\nOne important part of the ADS Digital Library will be the historical\nliterature from the 19th century and earlier. This part of the early\nliterature is especially suited for being on-line in a central digital\nlibrary. It is not available in many libraries, and if available is\noften in dangerously deteriorating condition. The access statistics\nof the ADS show that even old journal articles are accessed regularly\n(see OVERVIEW). The ADS is working on scanning this historical\nliterature through two approaches: Scanning the journals, and scanning\nthe observatory literature.\n\n1. We are in the process of scanning the historical journal\nliterature. We already have most of the larger journals scanned\ncompletely. Table~\\ref{scannedjour} shows how much we have scanned of\neach of the journals and conference proceedings series for which we\nhave permission. The oldest journal we have scanned completely is the\nAstronomical Journal (Vol. 1, 1849). We plan to have the Monthly\nNotices of the Royal Astronomical Society on-line completely by early\nin 2000. After that we plan to scan the oldest astronomical journal,\nAstronomische Nachrichten (Vol. 1, 1821), Icarus, Solar Physics,\nZeitschrift f\\\"ur Astrophysik, Bulletin of the American Astronomical\nSociety, and L'Observateur, and the conference series of IAU Symposia.\nOther journals that we plan to scan are the other precursor journals\nfor Astronomy \\& Astrophysics, if we can obtain permission to do so.\nWe will also scan individual conference proceedings for which we can\nobtain permission.\n\n\\begin{table*}\n\\caption[]{Scanned journals in the ADS database. }\n\\label{scannedjour}\n\\begin{tabular*}{7.0in}{p{0.5\\linewidth}ll}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nJournal & Scanned Volumes & Publication Dates\n\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nActa Astronomica & 42-48 & 1992-1998\\\\\nAnnual Reviews of Astronomy and Astrophysics & 1-33 & 1962-1995\\\\\nAnnual Reviews of Earth and Planetary Sciences & 1-23 & 1973-1995\\\\\nAstronomical Journal & 1-114 & 1849-1997\\\\\nAstronomical Society of the Pacific Conference Series & 1-5, 7-22, 24-63, 65-69& 1988-1994\\\\\nAstronomy and Astrophysics & 1-316 & 1969-1996\\\\\nAstronomy and Astrophysics Supplement Series & 1-120 & 1969-1996\\\\\nAstrophysical Journal & 1-473 & 1895-1996\\\\\nAstrophysical Journal Letters & 148-473 & 1967-1996\\\\\nAstrophysical Journal Supplement Series & 1-107 & 1954-12/1996\\\\\nBaltic Astronomy & 1-5 & 1992-1996\\\\\nBulletin Astronomique de Belgrade & 153-155 & 1996-1997\\\\\nBulletin of the Astronomical Institute of Czechoslovakia & 5-6, 9-42 & 1954-1955, 1958-1991\\\\\nBulletin of the Astronomical Society of India & 8-23 & 1980-1995\\\\\nJournal of the Korean Astronomical Society & 1-29 & 1968-1996\\\\\nJournal of the British Astronomical Association & 92-107 & 1981-1997\\\\\nMeteoritics and Planetary Science & 1-33 & 1953-1998\\\\\nMonthly Notices of the Royal Astronomical Society & 1, 100-301 & 1827, 1950-12/1998\\\\\nAAS Photo Bulletin & 1-43 & 1969-1986\\\\\nPublications of the Astronomical Society of Australia & 1, 3-13 & 1967, 1976-1996\\\\\nPublications of the Astronomical Society of Japan & 1-50 & 1949-1998\\\\\nPublications of the Astronomical Society of the Pacific & 1-109 & 1889-1997\\\\\nReviews in Modern Astronomy & 1-9 & 1988-1996\\\\\nRevista Mexicana de Astronomia y Astrofisica & 1-32 & 1974-1996\\\\\nRevista Mexicana de Astronomia y Astrofisica Ser. de Conf. & 1-6 & 1995-1997\\\\\nSkalnate Pleso, Contributions & 11-14, 16-19, 21-28 & 1983-1986, 1987-1990, 1991-1998\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\end{table*}\n\n\n\n2. One very important part of the astronomical literature in the 19th\ncentury and earlier were the observatory publications. Much of the\nastronomical research before the 20th century was published in such\nreports. We are currently collaborating with the Harvard library in a\nproject to make this part of the astronomical literature available\nthrough the ADS. The Harvard library has a grant from the National\nEndowment of the Humanities to make preservation microfilms of this\n(and other) literature. This project is generating an extra copy of\neach microfilm. We will scan these microfilms and produce electronic\nimages of all the microfilmed volumes. The resolution of the\nmicrofilm and the scanning process is approximately equivalent to our\n600 dpi scans. This project, once completed, will provide access to\nall astronomical observatory literature that is available at the\nHarvard library and the library of the Smithsonian Astrophysical\nObservatory from the 19th century back. For the more recent\nobservatory literature we will have to resolve copyright issues before\nwe can put it on-line.\n\nIn order to complete our data holdings, we still need issues of\nseveral journals for scanning. A list of journals and volumes that we\nneed is on-line at:\n\n\\begin{verbatim}\nhttp://adsabs.harvard.edu/pubs/\n missing_journals.html\n\\end{verbatim}\n\nIn order to feed the pages through a sheet feeder, we need to cut the\nback of the volumes to be scanned. If they have not been bound\nbefore, they can be bound after the scanning. If they have been bound\nbefore, there is not enough margin left to bind them again. If you\nhave any of the journals/volumes that we need, and you are willing to\ndonate them to us, please contact the first author of this article.\nWe would like to have even single volumes of any of the missing journals.\n\n\\subsection{Search Capabilities}\n\nThe capabilities of the search system and user interface have been\ndeveloped in close cooperation with our users. We always welcome\nsuggestions for improvements and usually implement reasonable\nsuggestions very quickly (within days or a few weeks). Because of\nthis rapid implementation of new features we have hardly any backlog\nof improvements that we want to implement. There are currently two\nlarger projects that we are investigating.\n\n1. We plan to convert all our scanned articles into electronic text\nthrough Optical Character Recognition (OCR). In order to be able to\nsearch full text articles we will need to develop new search\nalgorithms. Our current search system depends on the abstracts being\nof fairly uniform length. This caused some problems at one time when\nwe included sets of data with abstracts that were 4-5 times as long as\nour regular abstracts. These long abstracts would be found\ndisproportionally often in searches with many query words (for\ninstance in query feedback searches), since they generally matched\nmore words. We had to reduce the sizes of these abstracts in order to\nmake the searching work consistently with these data sets. OCR'd\nfull text will require new search algorithms to make the search\nwork at all. We currently estimate that the implementation of the\nfull text search capability will take at least 2 years.\n\n2. The scanned articles frequently contain plots of data. For most\nof these plots the numerical data are not available. We plan to\ndevelop an interface that will allow our users to select a plot,\ndisplay it at high resolution, and digitize the points in the plot by\nclicking on them. This will allow our users to convert plots into\ndata tables with as much precision as is available on the printed\npages. At this time we do not know how long it will take us to\nimplement this new capability.\n\n\\subsection{Article Access}\n\nWe are currently investigating several new data compression schemes\nthat would considerably reduce the size of our scanned articles. This\ncould considerably improve the utility of the ADS Article Service,\nespecially on slow links. We plan to be quite conservative in our\napproach to this, since we do not want to be locked into proprietary\ncompression algorithms that could be expensive to utilize. At this\npoint we do not have any time frame in which this might be\naccomplished.\n\n\n\\section{Summary}\n\nThe ADS Abstract Service has been instrumental in changing the way\nastronomers search and access the literature. One of the reasons for\nthe immediate acceptance of the ADS by the astronomical community when\nthe WWW based version became available was the ease of use of the\ninterface. It provided access to many advanced features, while still\nmaking it extremely easy to execute simple queries. Most of the use\nis for simple queries, but a significant number of queries utilize\nthe more sophisticated capabilities.\n\nThe search engine that provides this access was crucial to the success\nof the ADS as well. The most important aspects of a search engine are\nits speed and its flexibility to accommodate special features. The\ncustom-designed software of the ADS search engine proved that at least\nin some instances a custom design has considerable advantage over a\ngeneral purpose system. The search speed that we were able to achieve\nand the flexibility of the custom design that allows us to quickly\nadapt to our users' needs have justified the efforts of developing a\nsystem from scratch that is tailored to the specific data set.\n\nThe ADS had 31,533 users issue 780,711 queries and retrieve 15,238,646\nreferences, 615,181 abstracts, and 1,119,122 scanned pages in\nNovember, 1999. Since the start of the ADS we have served 311,594.261\nreferences and 17,146,370 scanned article pages. These numbers speak\nfor them self about the success of the ADS.\n\n\n\\section{Acknowledgment}\n\nFunding for this project has been provided by NASA under NASA Grant\nNCC5-189.\n\n\n\\begin{thebibliography}{}\n\n\\bibitem[Accomazzi et al. 1996]{1996adass...5..558A} Accomazzi, A.,\n\tGrant, C. S., Eichhorn, G., Kurtz, M. J. \\& Murray, S. S. 1996,\n\tASP Conf. Ser. 101: Astronomical Data Analysis Software and\n\tSystems V, 558\n\n\\bibitem[Accomazzi et al. 2000]{adsarchitecture} Accomazzi, A.,\n\tEichhorn, G., Grant, C. S., Kurtz, M. J., \\& Murray, S. S. 2000,\n\tA\\&AS, this issue\n\n\\bibitem[Adobe, Inc]{acrobat} Adobe Acrobat Reader,\n\thttp://www.adobe.com/prodindex/\\-acrobat/alternate.html\n\n\\bibitem[Adobe Postscript 1990]{postscript} Adobe Systems 1990,\n\t``Postscript Language Reference Manual, Second Edition'',\n\tAddison-Wesley, Reading, MA\n\n\\bibitem[CIA 1999]{ciafacts} CIA World Factbook, 1999, US Government\n\tPublications, http://www.cia.gov/cia/publications/factbook/\n\n\\bibitem[Egret et al. 1991]{simbad} Egret, D, Wenger, M., \\& Dubois,\n P. 1991, The SIMBAD Astronomical Database, ``Databases \\& On-line\n Data in Astronomy'', D. Egret \\& M. Albrecht, Eds, Kluwer\n Acad. Publ., 79\n\n\\bibitem[Eichhorn 1994]{1994ExA.....5..205E} Eichhorn, G. 1994,\n\tExperimental Astronomy, 5, 205\n\n\\bibitem[Eichhorn et al. 1995a]{1995VA.....39..217E} Eichhorn, G.,\n\tAccomazzi, A., Grant, C. S., Kurtz, M. J. \\& Murray, S. S. 1995,\n\tVistas in Astronomy, 39, 217\n\n\\bibitem[Eichhorn et al. 1995b]{1995adass...4...28E} Eichhorn, G.,\n\tMurray, S. S., Kurtz, M. J., Accomazzi, A. \\& Grant, C. S. 1995,\n\tASP Conf. Ser. 77: Astronomical Data Analysis Software and Systems\n\tIV, 28\n\n\\bibitem[Eichhorn 1996a]{1996S&T....92...81E} Eichhorn, G. 1996,\n\tSky \\& Telescope, 92, 81\n\n\\bibitem[Eichhorn et al. 1996b]{1996adass...5..569E} Eichhorn, G.,\n\tAccomazzi, A., Grant, C. S., Kurtz, M. J. \\& Murray, S. S. 1996,\n\tASP Conf. Ser. 101: Astronomical Data Analysis Software and\n\tSystems V, 569\n\n\\bibitem[Eichhorn 1997]{1997Ap&SS.247..189E} Eichhorn, G. 1997,\n\tAstrophys. Space Sci., 247, 189\n\n\\bibitem[Grant et al. 2000]{adsdata} Grant, C. S., Eichhorn, G.,\n\tAccomazzi, A., Kurtz, M. J., \\& Murray, S. S. 2000,\n\tA\\&AS, this issue\n\n\\bibitem[Kristol \\& Montulli 1997]{cookies} Kristol, D.M., Montulli, L.,\n\t``HTTP State Management Mechanism'', RFC 2109, February, 1997\n\n\\bibitem[Kurtz et al. 1993]{1993adass...2..132K} Kurtz, M. J.,\n\tKarakashian, T., Grant, C. S., Eichhorn, G., Murray, S. S.,\n\tWatson, J. M., Ossorio, P. G. \\& Stoner, J. L. 1993, ASP\n\tConf. Ser. 52: Astronomical Data Analysis Software and Systems II,\n\t132\n\n\\bibitem[Kurtz et al. 2000]{adsoverview} Kurtz, M. J., Eichhorn, G.,\n\tAccomazzi, A., Grant, C. S., \\& Murray, S. S. 2000, A\\&AS, this issue\n\n\\bibitem[Lynch 1997]{z3950} Lynch, C. A. 1997, D-lib Magazine, Vol. 3,\n\tNo. 4\n\n\\bibitem[Madore et al. 1992]{1992adass...1...47M} Madore, B. F.,\n Helou, G., Corwin, H. G., Jr., Schmitz, M., Wu, X. \\& Bennett,\n J. 1992, ASP Conf. Ser. 25: Astronomical Data Analysis Software\n and Systems I, 47\n\n\\bibitem[Marsden 1980]{1980CeMec..22...63M} Marsden, B. G. 1980,\n Celestial Mechanics, 22, 63\n\n\\bibitem[Murray et al. 1992]{1992ald2.proc..387M} Murray, S. S.,\n\tBrugel, E. W., Eichhorn, G., Farris, A., Good, J. C., Kurtz, M.\n\tJ., Nousek, J. A. \\& Stoner, J. L. 1992, Astronomy from Large\n\tDatabases II, 387\n\n\\bibitem[Salton \\& McGill 1983]{scoring} Salton, G, \\& McGill,\n\tM. J. 1983, ``Introduction to modern information retrieval'', New\n\tYork, McGraw-Hill\n\n\\bibitem[Schatz \\& Hardin 1994]{mosaic} Schatz, B. R., Hardin, J. B. 1994,\n Science, 265, 895-901\n\n\\bibitem[Schmitz et al. 1995]{1995ioda.book..259S} Schmitz, M., Helou, G., \n\tDubois, P., Lague, C., Madore, B., Corwin, H. G., Jr. \\& Lesteven, S. \n\t1995, ``Information \\& On-line Data in Astronomy'', D. Egret \\& M.A. \n\tAlbrecht, Eds., Kluwer Acad. Publ., 259\n\n\\bibitem[Vaudreuil 1992]{mime} Vaudreuil, G. 1992, ``MIME: Multi-Media,\n Multi-Lingual Extensions for RFC 822 Based Electronic Mail''\n ConneXions, 36-39\n\n\\bibitem[www.w3.org 1999]{www} World Wide Web Consortium 1999,\n\thttp://www.w3.org\n\n\n\\end{thebibliography}\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002102.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Accomazzi et al. 1996]{1996adass...5..558A} Accomazzi, A.,\n\tGrant, C. S., Eichhorn, G., Kurtz, M. J. \\& Murray, S. S. 1996,\n\tASP Conf. Ser. 101: Astronomical Data Analysis Software and\n\tSystems V, 558\n\n\\bibitem[Accomazzi et al. 2000]{adsarchitecture} Accomazzi, A.,\n\tEichhorn, G., Grant, C. S., Kurtz, M. J., \\& Murray, S. S. 2000,\n\tA\\&AS, this issue\n\n\\bibitem[Adobe, Inc]{acrobat} Adobe Acrobat Reader,\n\thttp://www.adobe.com/prodindex/\\-acrobat/alternate.html\n\n\\bibitem[Adobe Postscript 1990]{postscript} Adobe Systems 1990,\n\t``Postscript Language Reference Manual, Second Edition'',\n\tAddison-Wesley, Reading, MA\n\n\\bibitem[CIA 1999]{ciafacts} CIA World Factbook, 1999, US Government\n\tPublications, http://www.cia.gov/cia/publications/factbook/\n\n\\bibitem[Egret et al. 1991]{simbad} Egret, D, Wenger, M., \\& Dubois,\n P. 1991, The SIMBAD Astronomical Database, ``Databases \\& On-line\n Data in Astronomy'', D. Egret \\& M. Albrecht, Eds, Kluwer\n Acad. Publ., 79\n\n\\bibitem[Eichhorn 1994]{1994ExA.....5..205E} Eichhorn, G. 1994,\n\tExperimental Astronomy, 5, 205\n\n\\bibitem[Eichhorn et al. 1995a]{1995VA.....39..217E} Eichhorn, G.,\n\tAccomazzi, A., Grant, C. S., Kurtz, M. J. \\& Murray, S. S. 1995,\n\tVistas in Astronomy, 39, 217\n\n\\bibitem[Eichhorn et al. 1995b]{1995adass...4...28E} Eichhorn, G.,\n\tMurray, S. S., Kurtz, M. J., Accomazzi, A. \\& Grant, C. S. 1995,\n\tASP Conf. Ser. 77: Astronomical Data Analysis Software and Systems\n\tIV, 28\n\n\\bibitem[Eichhorn 1996a]{1996S&T....92...81E} Eichhorn, G. 1996,\n\tSky \\& Telescope, 92, 81\n\n\\bibitem[Eichhorn et al. 1996b]{1996adass...5..569E} Eichhorn, G.,\n\tAccomazzi, A., Grant, C. S., Kurtz, M. J. \\& Murray, S. S. 1996,\n\tASP Conf. Ser. 101: Astronomical Data Analysis Software and\n\tSystems V, 569\n\n\\bibitem[Eichhorn 1997]{1997Ap&SS.247..189E} Eichhorn, G. 1997,\n\tAstrophys. Space Sci., 247, 189\n\n\\bibitem[Grant et al. 2000]{adsdata} Grant, C. S., Eichhorn, G.,\n\tAccomazzi, A., Kurtz, M. J., \\& Murray, S. S. 2000,\n\tA\\&AS, this issue\n\n\\bibitem[Kristol \\& Montulli 1997]{cookies} Kristol, D.M., Montulli, L.,\n\t``HTTP State Management Mechanism'', RFC 2109, February, 1997\n\n\\bibitem[Kurtz et al. 1993]{1993adass...2..132K} Kurtz, M. J.,\n\tKarakashian, T., Grant, C. S., Eichhorn, G., Murray, S. S.,\n\tWatson, J. M., Ossorio, P. G. \\& Stoner, J. L. 1993, ASP\n\tConf. Ser. 52: Astronomical Data Analysis Software and Systems II,\n\t132\n\n\\bibitem[Kurtz et al. 2000]{adsoverview} Kurtz, M. J., Eichhorn, G.,\n\tAccomazzi, A., Grant, C. S., \\& Murray, S. S. 2000, A\\&AS, this issue\n\n\\bibitem[Lynch 1997]{z3950} Lynch, C. A. 1997, D-lib Magazine, Vol. 3,\n\tNo. 4\n\n\\bibitem[Madore et al. 1992]{1992adass...1...47M} Madore, B. F.,\n Helou, G., Corwin, H. G., Jr., Schmitz, M., Wu, X. \\& Bennett,\n J. 1992, ASP Conf. Ser. 25: Astronomical Data Analysis Software\n and Systems I, 47\n\n\\bibitem[Marsden 1980]{1980CeMec..22...63M} Marsden, B. G. 1980,\n Celestial Mechanics, 22, 63\n\n\\bibitem[Murray et al. 1992]{1992ald2.proc..387M} Murray, S. S.,\n\tBrugel, E. W., Eichhorn, G., Farris, A., Good, J. C., Kurtz, M.\n\tJ., Nousek, J. A. \\& Stoner, J. L. 1992, Astronomy from Large\n\tDatabases II, 387\n\n\\bibitem[Salton \\& McGill 1983]{scoring} Salton, G, \\& McGill,\n\tM. J. 1983, ``Introduction to modern information retrieval'', New\n\tYork, McGraw-Hill\n\n\\bibitem[Schatz \\& Hardin 1994]{mosaic} Schatz, B. R., Hardin, J. B. 1994,\n Science, 265, 895-901\n\n\\bibitem[Schmitz et al. 1995]{1995ioda.book..259S} Schmitz, M., Helou, G., \n\tDubois, P., Lague, C., Madore, B., Corwin, H. G., Jr. \\& Lesteven, S. \n\t1995, ``Information \\& On-line Data in Astronomy'', D. Egret \\& M.A. \n\tAlbrecht, Eds., Kluwer Acad. Publ., 259\n\n\\bibitem[Vaudreuil 1992]{mime} Vaudreuil, G. 1992, ``MIME: Multi-Media,\n Multi-Lingual Extensions for RFC 822 Based Electronic Mail''\n ConneXions, 36-39\n\n\\bibitem[www.w3.org 1999]{www} World Wide Web Consortium 1999,\n\thttp://www.w3.org\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002103
|
The NASA Astrophysics Data System: Data Holdings
|
[
{
"author": "C. Grant"
},
{
"author": "A. Accomazzi"
},
{
"author": "G. Eichhorn"
},
{
"author": "M. J. Kurtz"
},
{
"author": "S. S. Murray"
}
] |
Since its inception in 1993, the ADS Abstract Service has become an indispensable research tool for astronomers and astrophysicists worldwide. In those seven years, much effort has been directed toward improving both the quantity and the quality of references in the database. From the original database of approximately 160,000 astronomy abstracts, our dataset has grown almost tenfold to approximately 1.5 million references covering astronomy, astrophysics, planetary sciences, physics, optics, and engineering. We collect and standardize data from approximately 200 journals and present the resulting information in a uniform, coherent manner. With the cooperation of journal publishers worldwide, we have been able to place scans of full journal articles on-line back to the first volumes of many astronomical journals, and we are able to link to current version of articles, abstracts, and datasets for essentially all of the current astronomy literature. The trend toward electronic publishing in the field, the use of electronic submission of abstracts for journal articles and conference proceedings, and the increasingly prominent use of the World Wide Web to disseminate information have enabled the ADS to build a database unparalleled in other disciplines. The ADS can be accessed at http://adswww.harvard.edu \keywords{ methods: data analysis -- astronomical bibliography -- astronomical sociology}
|
[
{
"name": "ADS_data.tex",
"string": "\\documentclass{aa}\n\\usepackage{graphics}\n\\usepackage{supertabular}\n\n\n\n\\begin {document}\n\\title{The NASA Astrophysics Data System: Data Holdings}\n\n\\thesaurus{04(04.01.1)}\n\\author{C. Grant\\and A. Accomazzi\\and G. Eichhorn\\and M. J. Kurtz\n\\and S. S. Murray}\n\\institute{Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138}\n\n\n\\offprints{C. Grant}\n\\mail{C. Grant}\n\n\\date{Received / Accepted}\n\n\\titlerunning{}\n\\authorrunning{C. Grant et al.}\n\n\\maketitle\n\n\\sloppy\n\n\\begin {abstract}\n Since its inception in 1993, the ADS Abstract Service has become an\nindispensable research tool for astronomers and astrophysicists worldwide.\nIn those seven years, much effort has been directed toward improving\nboth the quantity and the quality of references in the database. From the \noriginal database of approximately 160,000 astronomy abstracts, our\ndataset has grown almost tenfold to approximately 1.5 million references\ncovering astronomy, astrophysics, planetary sciences, physics, optics, and\nengineering. We collect and standardize data from \napproximately 200 journals and present the resulting information in a\nuniform, coherent manner. With the cooperation of journal publishers \nworldwide, we have been able to place scans of full journal articles on-line\nback to the first volumes of many astronomical journals, and we are able to \nlink to current version of articles, abstracts, and datasets for \nessentially all of the current astronomy literature. The\ntrend toward electronic publishing in the field, the use of electronic\nsubmission of abstracts for journal articles and conference proceedings, \nand the increasingly prominent use of the World Wide Web to disseminate \ninformation have enabled the ADS to build a database unparalleled in other \ndisciplines.\n\nThe ADS can be accessed at http://adswww.harvard.edu \n\\keywords{ methods: data analysis -- astronomical bibliography --\n astronomical sociology}\n\\end{abstract}\n\n\n\\section {\\label {intro} Introduction}\n\n Astronomers today are more prolific than ever before. Studies in\npublication trends in astronomy (\\cite{1994PASP..106.1015A}, \n\\cite{1995ApJ...455..407A}, \\cite{1997PASP..109.1278S})\nhave hypothesized that the current explosion in published papers in astronomy \nis due to a combination of factors: growth in professional society\nmembership, an increase in papers by multiple authors, the launching of\nnew spacecrafts, and increased competition for jobs and PIs in the field\n(since candidate evaluation is partially based on publication history).\nAs the number of papers in the field grows, so does the need for\ntools which astronomers can use to locate that fraction of papers which\npertain to their specific interests.\n\n The ADS Abstract Service is one of several bibliographic services\nwhich provide this function for astronomy, but due to the broad scope of our coverage and \nthe simplicity of access to our data, astronomers now rely extensively on the\nADS, and other bibliographic services not only link to us, but some have \nbuilt their bibliographic search capabilities on top of the ADS system.\nThe International Society for Optical Engineering (SPIE) and the\nNASA Technical Report Service (NTRS) are two such services.\n\n The evolution of the Astrophysics Data System (ADS) has been largely \ndata-driven. Our search tools and indexing routines have been modified\nto maximize speed and efficiency based on the content of our dataset.\nAs new types of data (such as electronic versions of articles) became\navailable, the Abstract Service quickly incorporated\nthat new feature. The organization and standardization of the database\ncontent is the very core upon which the Abstract Service has been built.\n\n This paper contains a description of the ADS Abstract Service from a \n``data\" point of view, specifically descriptions of our holdings and of the\nprocesses by which we ingest new data into the system. Details are provided \non the organization of the \ndatabases (section \\ref {databases}), the description of the data in the \ndatabases (section \\ref {data}), the creation of bibliographic records\n(section \\ref {creating}), the procedures for updating the database\n(section \\ref {updating}), and on the scanned articles in the Astronomy database \n(section \\ref {articles}). We discuss the interaction between the ADS and\nthe journal publishers (section \\ref {journals}) and analyze some of the numbers \ncorresponding to the datasets (section \\ref {summary}).\nIn conjunction with\nthree other ADS papers in this volume, this paper is intended to offer details on\nthe entire Abstract Service with the hopes that astronomers will have a \nbetter understanding of the reference data upon which they rely for their \nresearch. In addition, we hope that researchers in other disciplines may\nbe able to benefit from some of the details described herein.\n\n As is often the case with descriptions of active Internet resources,\nwhat follows is a description of the present situation with the ADS Abstract\nService. New features are always being added, some of which necessitate\nchanges in our current procedures. Furthermore, with the growth of\nelectronic publishing, some of our core ideas about bibliographic tools\nand requirements must be reconsidered in order to be able to take full\nadvantage of new publishing technologies for a new millennium.\n\n\n\\section {\\label {databases} The Databases}\n\n The ADS Abstract Service was originally conceived of in the mid 1980's\nas a way to provide on-line access to bibliographies of astronomers which \nwere previously available only through expensive librarian search services \nor through the A\\&A Abstracts series (\\cite{1979BICDS..17....2S}, \n\\cite{1982adra.proc..159S}, \\cite{1989lisa.conf...77S}), published by \nthe Astronomisches\nRechen-Institut in Heidelberg. While the ideas behind the Abstract\nService search engine were being developed (see \\cite{kurtz}, hereafter OVERVIEW), \nconcurrent efforts were underway to acquire a reliable data source on which \nto build the server. In order to best develop the logistics of the \nsearch engine it was necessary to have access to real literature data from\nthe past and present, and to set up a mechanism for acquiring data in the\nfuture. \n\n An electronic publishing meeting in the spring of 1991 brought together\na number of organizations whose ultimate cooperation would be necessary to\nmake the system a reality (see OVERVIEW for details). NASA's Scientific and \nTechnical Information Program (STI) offered to provide abstracts to the\nADS. STI's abstracts were a rewritten version of the original abstracts, \ncategorized and keyworded by professional editors. They not only abstracted \nthe astronomical literature, but many other scientific disciplines as well. \nWith STI agreeable to providing the past and present literature, and the \njournals committed to providing the future literature, the data behind the \nsystem fell into place. The termination of the journal abstracting by the \nSTI project several years later was unfortunate, but did not cause the \ncollapse of the ADS Abstract Service because of the commitment of the \njournal publishers to distribute their information freely.\n\n The STI abstracting approximately covered the period from 1975 to 1995.\nWith the STI data alone, we estimated the completeness of the Astronomy database \nto be better than 90\\% for the core astronomical journals. Fortunately, with the additional data supplied by the \njournals, by SIMBAD (Set of Identifications, Measurements, and Bibliographies \nfor Astronomical Data, \\cite{1988alds.proc..323E}) at \nthe CDS (Centre de Donn\\'ees Astronomiques de Strasbourg), and by performing \nOptical Character Recognition (OCR) on the scanned table of contents (see \nsection \\ref{articles} below), we are now closer to \n99\\% complete for that period. In the period since then we are 100\\% complete\nfor those \njournals which provide us with data, and significantly less complete for those \nwhich do not (e.g. many observatory publications and non-U.S. journals). \nThe data prior to 1975 are also \nsignificantly incomplete, although we are currently working to improve the \ncompleteness of the early data, primarily through scanning the table \nof contents for journal volumes as they are placed on-line. We are 100\\%\ncomplete for any journal volume which we have scanned and put on-line,\nsince we verify that we have all bibliographic entries during the procedure of \nputting scans on-line.\n\n Since the STI data were divided into categories, it was easy to create \nadditional databases with non-astronomical data which were still of interest\nto astronomers. The creation of an Instrumentation database has enabled us to\nprovide a database for literature related to astronomical instrumentation, of \nparticular interest to those scientists building astronomical telescopes and\nsatellite instruments. We were fortunate to get the cooperation of the \nSPIE very quickly after \nreleasing the Instrumentation database. SPIE has become our major source of\nabstracts for the Instrumentation database now that STI no longer supplies us \nwith data. \n\n Our Physics and Geophysics database, the third database to go on-line,\nis intended for scientists working in physics-related fields. \nWe add authors and titles from all of the physics journals of the American \nInstitute of Physics (AIP), the Institute of Physics (IOP), and the \nAmerican Physical Society (APS), as well as many physics journals \nfrom publishers such as Elsevier and Academic Press (AP (AP)). \n\n The fourth database in the system, the Preprint database, contains a \nsubset of the Los Alamos National Laboratory's (LANL) Preprint Archive\n(\\cite{lanl}).\nOur database includes the LANL astro-ph preprints which are retrieved from\nLANL and indexed nightly through an automated procedure. That dataset \nincludes preprints from astronomical journals submitted directly by \nauthors.\n\n\n\\section {\\label {data} Description of the Data}\n\n The original set of data from STI contained several basic fields of\ndata (author, title, keywords, and abstracts) to be indexed and made available \nfor searching. All records were keyed on STI's accession number, \na nine-digit code consisting of a letter prefix (A or N) followed \nby a two-digit publication year, followed by \na five-letter identifier (e.g. A95-12345). Data were stored in files\nnamed by accession number. \n\nWith the inclusion of data from other\nsources, primarily the journal publishers and SIMBAD, we extended\nSTI's concept of the accession number to handle other abstracts as well.\nSince the ADS may receive the same abstract from multiple sources, we originally\nadopted a system of using a different prefix letter with the remainder of\nthe accession number being the same to describe abstracts received from\ndifferent sources. Thus, the same abstract for the above accession number\nfrom STI would be listed as J95-12345 from the journal publisher and S95-12345 \nfrom SIMBAD. This allowed the indexing routines to consider only one instance \nof the record when indexing. Recently, limitations in the format of accession\nnumbers and the desire to index data from multiple sources (rather than just\nSTI's version) have prompted us to move to a data storage system based \nentirely on the bibliographic code.\n\n\\subsection{\\label {bibcodes} Bibliographic Codes}\n\n The concept of a unique bibliographic code used to identify an article\nwas originally conceived of by SIMBAD and NED (NASA's Extragalactic Database,\n\\cite{1988alds.proc..335H}). The original specification is detailed in\n\\cite{1995VA.....39R.272S}. In the years since, the ADS has \nadopted and expanded their definition to be able to describe references \noutside of the scope of those projects.\n\n The bibliographic code is a 19-character string comprised of several\nfields which usually enables a user to identify the full reference from\nthat string. It is defined as follows:\n\n\\centerline{\\bf YYYYJJJJJVVVVMPPPPA}\n\n\\noindent\nwhere the fields are defined in Table~\\ref{table1}.\n\n\\begin{table*}\n\\caption[]{Bibliographic Code Definition (e.g. 1996A\\&AS..115....1S)}\n\\label{table1}\n\\begin{tabular*}{7.0in}{lll}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nField & Definition & Example\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nYYYY & Publication Year & 1997 \\\\\nJJJJJ & Journal Abbreviation & ApJ, A\\&A, MNRAS, etc. \\\\\nVVVV & Volume Number & 480 \\\\\nM & Qualifier for Publication & L (for Letter), P (for Pink Page) \\\\\n& & Q, R, S, etc. for unduplicating \\\\\n& & a, b, c, etc. for issue number \\\\\nPPPP & Page Number & 129 \\\\\nA & First Letter of the First Author's Surname & N \\\\\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\end{table*}\n\n\n\nThe journal field is left-justified and the volume and page fields are \nright-justified. Blank spaces and leading zeroes are replaced by periods.\nFor articles with page numbers greater than 9999, the M field contains\nthe first digit of the page number. The A field contains a colon (``:\")\nif there is no author listed.\n\n Creating bibliographic codes for the astronomical journals is \nuncontroversial. Each journal typically has a commonly-used abbreviation,\nand the volume and page are easily assigned (e.g. 1999PASP..111..438F).\nEach volume tends to have individual page numbering,\nand in those cases where more than one article appears on a page (such as\nerrata), a ``Q\",``R\",``S\", etc. is used as the qualifier for publication to \nmake bibliographic codes unique. When page numbering is not continuous across issue\nnumbers (such as Sky \\& Telescope), the issue number is represented by\na lower case letter as the qualifier for publication (e.g. ``a\" for issue 1).\nThis is because there may be multiple articles in a volume starting on the same\npage number.\n\n Creating bibliographic codes for the ``grey\" literature such as\nconference proceedings and technical reports is a more difficult task.\nThe expansion into these additional types of data included in the ADS \nrequired us to modify the original prototype bibliographic code definition in \norder to present identifiers which are easily recognizable to the user. The \nprototype definition of the bibliographic code suggested using a single letter \nin the second place of the volume field to identify non-standard references\n(catalogs, PhD theses, reports, preprints, etc.) and using the third and\nfourth place of that field to unduplicate and report volume numbers (e.g.\n1981CRJS..R.3...14W). Since we felt that this created codes unidentifiable to \nthe typical user and since NED and SIMBAD did not feel that users needed to be \nable to identify books directly from their bibliographic codes, the ADS adopted \ndifferent rules for creating codes to identify the grey literature.\n\n It is straightforward to create bibliographic codes for conference proceedings which are part of \na series. For example, the IAU Symposia Series (IAUS) \ncontains volume numbers and therefore fits the journal model for bibliographic \ncodes. Other conference proceedings, books, colloquia, and reports in the ADS \ntypically contain a four letter word in the volume field such as ``conf\",\n``proc\", ``book\", ``coll\", or ``rept\". When this is the case with a bibliographic \ncode, the journal field typically consists of the first letter from \nimportant words in the title. This can give the user the ability to \nidentify a conference proceeding at a glance (e.g. ``ioda.book\" for \n``Information and On-Line Data in Astronomy\"). We will often leave the \nfifth place of the journal field as a dot for ``readability\" \n(e.g. 1995ioda.book..175M). For most\nproceedings which are also published as part of a series (e.g. ASP Conference \nSeries, IAU Colloquia, AIP Conference Series), we include in the system two\nbibliographic codes, one as described above and one which contains the series \nname and the volume (see section \\ref{masterlist}). We do this so that users can see, for example, \nthat a paper published in one of the ``Astronomical Data Analysis \nSoftware and Systems\" series is clearly labelled as ``adass\" whereas a typical\nuser might not remember which volume of ASPC contained those ADASS papers.\nThis increases the user's readability of bibliographic codes.\n\n With the STI data, the details were often unclear as to whether an\narticle was from a conference proceeding, a meeting, a colloquium, etc.\nWe assigned those codes as best we could, making no significant distinction\nbetween them. For conference abstracts submitted by the editors of \na proceedings prior to publication, we often do not have page numbers. \nIn this case, \nwe use a counter in lieu of a page number and use an ``E\" (for \n``Electronic\") in the fourteenth column, the qualifier for publication. \nIf these conference abstracts are then published, their bibliographic codes \nare replaced by a bibliographic code complete with page number. \nIf the conference abstracts are published only on-line, they retain their \nelectronic bibliographic code with its E and counter number.\n\n There are several other instances of datasets where the bibliographic\ncodes are non-standard. PhD theses in the system use ``PhDT\" as the\njournal abbreviation, contain no volume number, and contain a counter in\nlieu of a page number. Since PhD theses, like all bibliographic codes,\nare unique across all of the databases, the counter makes the bibliographic\ncode an identifier for only one thesis. IAU Circulars also use a\ncounter instead of a page number. Current Circulars are electronic in form,\nand although not technically a new page, the second item of an IAU\nCircular is the electronic equivalent of a second page. Using the page \nnumber as a counter enables us to minimize use of the M identifier in\nthe fourteenth place of a bibliographic code for unduplicating. This is desirable\nsince codes containing those identifiers are essentially impossible to \ncreate a priori, either by the journals or by users.\n\n The last set of data currently included in the ADS which contain non-standard\nbibliographic codes is the ``QB\"\nbook entries from the Library of Congress. QB is the Library of Congress \ncode for astronomy-related books and we have put approximately 17,000 of\nthese references in the system. Because the QB numbers are identifiers by\nthemselves, we have made an exception to the bibliographic code format to use\nthe QB number (complete with any series or part numbers), prepended with\nthe publication year as the bibliographic code. Such an entry is easily \nidentifiable as a book, and these codes enable users to locate the books in \nmost libraries.\n\n It is worth noting that while the bibliographic code makes identification\nsimple for the vast majority of references in the system, we are aware of two\ninstances where the bibliographic definition breaks down. The use of the\nfourteenth column for a qualifier such as ``L\" for {\\it ApJ Letters} makes\nit impossible to use that column for unduplicating. Therefore, if there\nare two errata on the same page with the same author initial, there is\nno way to create unique bibliographic codes for them. We are aware of\nonly one such instance in the 33 years of publication of {\\it ApJ Letters}.\nSecond, with the electronic publishing of an increasing number of journals, \nthe requirement of page numbers to locate articles becomes unnecessary. The\njournal {\\it Physical Review D} is currently using 6-digit article identifiers\nas page numbers. Since the bibliographic code allows for page \nnumbers not longer than 5 digits, we are currently converting these\n6-digit identifiers to their 5-digit hexagesimal equivalent. Both of these\nanomalies indicate that over the next few years we will likely need to\nalter the current bibliographic definition in order to allow consistent\nidentification of articles for all journals.\n\n\\subsection{Data Fields}\n\n The databases are set up such that some data fields are searchable and \nothers are not. The searchable fields (title, author, and text) are the \nbulk of the important data, and these fields are indexed so that a query \nto the database returns the maximum number of meaningful results.\n(see \\cite{aa}, hereafter ARCHITECTURE).\nThe text field is the union of the abstract, title, keywords, and \ncomments. Thus, if a user requests a particular word in the text\nfield, all papers are returned which contain that word in the\nabstract {\\bf OR} in the title {\\bf OR} in the keywords {\\bf OR} in the comments. Appendix A shows version 1.0 of the Extensible Markup Language (XML, see \n\\ref{dataformats}) Document Type Definition (DTD) for text files in the\nADS Abstract Service. The DTD lists fields \ncurrently used or expected to be used in text files in the ADS \n(see section \\ref{textfiles} for details on the text files). We intend to \nreprocess the current journal and affiliation fields in order to extract some \nof these fields.\n \n Since STI ceased abstracting the journal literature, we decided to\nmake the keywords themselves no longer a searchable entity for the time \nbeing -- they are \nsearchable only through the abstract text field. STI used a different \nstandard set of keywords from the AAS journals, who use a different set of \nkeywords from AIP journals (e.g. {\\it AJ} prior to 1998). In addition, keywords from\na single journal such as the {\\it Astrophysical Journal (ApJ)} have evolved over\nthe years so that early {\\it ApJ} volume keywords are not consistent with\nlater volumes. In order to build one coherent \nset of keywords, an equivalence or synonym table for these different keyword \nsets must be created. We are investigating different schemes for \ndoing this, and currently plan to have a searchable keyword field again,\nwhich encompasses all keywords in the system and equates those from different \nkeyword systems which are similar (\\cite{lee}). \n\n The current non-searchable fields in the ADS databases include the \njournal field, author affiliation, category, abstract copyright, \nand abstract origin. Although we may decide to create an index and\nsearch interface for some of these entities (such as category), others \nwill continue to remain unsearchable since searching them is not useful to the \ntypical user. In particular, author affiliations would be useful to search, \nhowever this information is inconsistently formatted so it is virtually \nimpossible to collect all variations of a given institution for indexing \ncoherently. Furthermore, we have the author affiliations for only about \nhalf of the entries in the Astronomy database so we have decided to keep this \nfield non-searchable. For researchers wishing \nto analyze affiliations on a large scale, we can provide this information on \na collaborative basis.\n\n\n\\subsection{Data Sources}\n\n The ADS currently receives abstracts or table of contents (ToC) references\nfrom almost two hundred journal sources. Tables~\\ref{table2}, \\ref{table3},\nand \\ref{table4} list these\njournals, along with their bibliographic code abbreviation, source, frequency\nwith which we receive the data, what data are received, and any links we\ncan create to the data. ToC references typically \ncontain only author and title, although sometimes keywords are included as well.\nThe data are contributed via email, ftp, or retrieved from web sites around the \nworld at a frequency ranging from once a week to approximately once a \nyear. The term ``often\" used in the frequency column implies that we get\nthem more frequently than once a month, but not necessarily on a regular\nbasis. The term ``occasionally\" is used for those journals who submit data\nto us infrequently. \n\n\\begin{table*}\n\\caption[]{The ADS Astronomy Database }\n\\label{table2}\n\\begin{tabular*}{7.5in}{llp{3in}lll}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nJournal & Source & Full Name & How Often & Kind of Data & Links$^{\\mathrm{a}}$\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nSee accompanying text file ADS\\_dataT2.txt for Table 2.\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\begin{list}{}{}\n\\item[$^{\\mathrm{a}}$]Letter codes describing what data are available\n\\item[$^{\\mathrm{b}}$]Astronomische Gesellschaft\n\\item[$^{\\mathrm{c}}$]University of Chicago Press\n\\item[$^{\\mathrm{d}}$]American Institute of Physics\n\\item[$^{\\mathrm{e}}$]Overseas Publishers Association\n\\item[$^{\\mathrm{f}}$]American Geophysical Union\n\\item[$^{\\mathrm{g}}$]Central Bureau for Astronomical Telegrams\n\\item[$^{\\mathrm{h}}$]Academic Press\n\\item[$^{\\mathrm{i}}$]Universitad Nacional Autonoma de Mexico\n\\item[$^{\\mathrm{j}}$]Astronomisches Rechen-Institut\n\\end{list}{}{}\n\\end{table*}\n\n\n\n\\begin{table*}\n\\caption[]{The ADS Instrumentation Database }\n\\label{table3}\n\\begin{tabular*}{7.5in}{llp{3in}lll}\n\n\\hline\n\\noalign{\\smallskip}\nJournal & Source & Full Name & How Often & Kind of Data & Links$^{\\mathrm{a}}$ \\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nSee accompanying text file ADS\\_dataT3.txt for Table 3.\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\begin{list}{}{}\n\\item[$^{\\mathrm{a}}$]Letter codes describing what data are available\n\\item[$^{\\mathrm{b}}$]Optical Society of America\n\\item[$^{\\mathrm{c}}$]The International Society for Optical Engineering (SPIE)\n\\item[$^{\\mathrm{d}}$]Institute of Physics\n\\end{list}{}{}\n\\end{table*}\n\n\n\n\\begin{table*}\n\\caption[]{The ADS Physics Database }\n\\label{table4}\n\\begin{supertabular*}{7.5in}{llp{3in}lll}\n\n\\hline\n\\noalign{\\smallskip}\nJournal & Source & Full Name & How Often & Kind of Data & Links$^{\\mathrm{a}}$\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nSee accompanying text file ADS\\_dataT4.txt for Table 4.\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{supertabular*}\n\\begin{list}{}{}\n\\item[$^{\\mathrm{a}}$]Letter codes describing what data are available\n\\end{list}{}{}\n\\end{table*}\n\n\n\nUpdates to the Astronomy and Instrumentation databases occur approximately \nevery two weeks, or more often if logistically possible, in order to keep \nthe database current. \nRecent enhancements to the indexing software have enabled us to perform \ninstantaneous updates, triggered by an email containing new data (see \nARCHITECTURE). Updates to the Physics database occurs approximately once \nevery two months. As stated earlier, the Preprint database is updated nightly.\n\n\\subsection{\\label {dataformats} Data Formats}\n\n The ADS is able to benefit from certain standards which are adhered to in\nthe writing and submission practices of astronomical literature. The journals\nshare common abbreviations and text formatting routines which are used by\nthe astronomers as well. The use of TeX (\\cite{knuth}) and LaTeX (\\cite{lamport}), and their extension to \nBibTeX (\\cite{lamport}) and AASTeX (\\cite{aas}) results in common formats among \nsome of our data sources. This enables the reuse of parsing routines \nto convert these formats to our standard format. Other variations of TeX \nused by journal publishers also allows us to use common parsing routines\nwhich greatly facilitates data loading.\n\n TeX is a public domain typesetting program designed especially for math and\nscience. It is a markup system, which means that formatting commands are \ninterspersed with the text in the TeX input file. In addition to commands for \nformatting ordinary text, TeX includes many special symbols and commands with \nwhich you can format mathematical formulae with both ease and precision.\nBecause of its extraordinary capabilities, TeX has become the leading \ntypesetting system for science, mathematics, and engineering. It was developed \nby Donald Knuth at Stanford University.\n\n LaTeX is a simplified document preparation system built on TeX. Because \nLaTeX is available for just about any type of computer and because \nLaTeX files are ASCII, scientists are able to send their papers electronically \nto colleagues around the world in the form of LaTeX input. This is also\ntrue for other variants of TeX, although the astronomical publishing community\nhas largely centered their publishing standards on LaTeX or one of the software\npackages based on LaTeX, such as BibTeX or AASTeX. BibTeX is a \nprogram and file format \ndesigned by Oren Patashnik and Leslie Lamport in 1985 for the LaTeX document \npreparation system, and AASTeX is a LaTeX-based package that can be used to \nmark up manuscripts specifically for American Astronomical Society (AAS) journals. \n\n Similar to the widespread acceptance of TeX and its variants, the extensive\nuse of SGML (Standard Generalized Markup Language, \\cite{goldfarb}) by the members of the\npublishing community has given us the ability to standardize many of our\nparsing routines. All data gleaned off the World Wide Web share features \ndue to the use of HTML (HyperText Markup Language, \\cite{powell}), an example of \nSGML. Furthermore, the trend towards using XML (Extensible Markup Language, \n\\cite{harold})\nto describe text documents will enable us to share standard document\nattributes with other members of the astronomical community. \nXML is a subset of SGML which is intended to enable generic SGML to be\nserved, received, and processed on the Web in the way that is now possible\nwith HTML.\nThe ADS parsing routines benefit from these standards in several ways: \nwe can reuse routines designed around these systems; we are able to preserve \noriginal text representations of entities such as embedded accents so these \nentities are displayed correctly in the user's browser; and we are able to capture value-added \nfeatures such as electronic URLs and email addresses for use elsewhere in \nour system.\n\n In order to facilitate data exchange between different parts of the ADS,\nwe make use of a tagged format similar to the ``Refer\" format \n(\\cite{jacobs}).\nRefer is a preprocessor for the word processors nroff and troff which finds and\nformats references. While our tagged formats share some common fields \n(\\%A, \\%T, \\%J, \\%D), the Refer format is not specific enough to be used for\nour purposes. Items such as objects, URLs and copyright notices are beyond\nthe scope of the Refer syntax. Details on our tagged format are provided in \nTable~\\ref{table5}. Reading and writing routines for this format are shared by \nloading and indexing routines, and a number of our data sources \nsubmit abstracts to us in this format.\n\n\\begin{table}\n\\caption[]{Tagged Format Definitions }\n\\label{table5}\n\\begin{tabular*}{3.4in}{lll}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nTag & Name & Comment\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n\\%R&Bibliographic Code &required \\\\\n\\%T&Title &required \\\\\n\\%A&Author List &required \\\\\n\\%D&Publication Date &required \\\\\n\\%B&Abstract Text & \\\\\n\\%C&Abstract Copyright & \\\\\n\\%E&URL for Electronic Data Table & \\\\\n\\%F&Author Affiliation & \\\\\n\\%G&Origin & \\\\\n\\%H&Email & \\\\\n\\%J&Journal Name, Volume, and Page Range & \\\\\n\\%K&Keywords & \\\\\n\\%L&Last Page of Article & \\\\\n\\%O&Object Name & \\\\\n\\%Q&Category & \\\\\n\\%U&URL for Electronic Document & \\\\ \n\\%V&Language & \\\\\n\\%W&Database (AST, PHY, INST) & \\\\\n\\%X&Comment & \\\\\n\\%Y&Identifiers & \\\\\n\\%Z&References & \\\\\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\end{table}\n\n\n\n\\section {\\label {creating} Creating the Bibliographic Records}\n\nOne of the basic principles in the parsing and\nformatting of the bibliographic data incorporated into the ADS database\nover the years has been to preserve as much of the original information as \npossible and delay any syntactic or semantic interpretation of the\ndata until a later stage. From the implementation point of view, this\nmeans that bibliographic records provided to the ADS by publishers or\nother data sources typically are saved as files which are tagged\nwith their origin, entry date, and any other ancillary information\nrelevant to their contents (e.g. if the fields in the record contain\ndata which was transliterated or converted to ASCII).\n\nFor instance, the records provided to the ADS by the University of\nChicago Press (the publisher of several major U.S. astronomical journals)\nare SGML documents which contain a unique manuscript identifier\nassigned to the paper during the electronic publishing process. \nThis identifier is saved in the file created by the ADS system for \nthis bibliographic entry.\n\nBecause data about a particular bibliographic\nentry may be provided to the ADS by different sources and at different\ntimes, we adopted a multi-step procedure in the creation and management\nof bibliographic records:\n\n 1) Tokenization: Parsing input data into a memory-resident data structure using procedures which are format- and source-specific. \n\n 2) Identification: Computing the unique bibliographic record identifier used by the ADS to refer to this record. \n\n 3) Instantiation: Creating a new record for each bibliography formatted according to the ADS ``standard\" format. \n\n 4) Extraction: Selecting the best information from the different records available for the same bibliography and merging them into a single entry, avoiding duplication of redundant information. \n\n\\subsection{Tokenization}\n\nThe activity of parsing a (possibly) loosely-structured bibliographic\nrecord is typically more of an art than a science, given the wide\nrange of possible formats used by people for the representation and \ndisplay of these records.\nThe ADS uses the PERL language (Practical Extraction and Report Language, \\cite{wall91})\nfor implementing most of the routines associated with handling the data. PERL is an\ninterpreted programming language optimized for scanning and \nprocessing textual data. It was chosen over other programming\nlanguages because of its speed and flexibility in handling text strings. \nFeatures such as pattern matching and regular expression substitution \ngreatly facilitate manipulating the data fields.\nTo maximize flexibility in the parsing and formatting operations of\ndifferent fields, we have written a set of PERL library modules and\nscripts capable of performing a few common tasks.\nSome that we consider worth mentioning from the methodological point \nof view are listed below. \n\n\\begin{itemize}\n\\item Character set conversion: electronic data are often delivered\nto us in different character set encodings, requiring translation\nof the data stream in one of the standard character sets expected by\nour input scripts. The default character set that has been\nused by the ADS until recently is ``Latin-1'' encoding\n(ISO-8859-1, \\cite{iso}). We are now in the process of converting to \nthe use of Unicode characters (\\cite{unicode}) encoded in UTF-8 \n(UCS Transformation Format, 8--bit form).\nThe advantage of using Unicode is its universality (all character sets\ncan be mapped to Unicode without loss of information). The advantage\nof adopting UTF-8 over other encodings is mainly the software support\ncurrently available (most of the modern software packages can already \nhandle UTF-8 internally). The adoption of Unicode and UTF-8 also\nworks well with our adoption of XML as the standard format for\nbibliographic data.\n\n\\item Macro and entity expansion: Several of the highly structured document\nformats in use today rely on the strengths of the formatting\nlanguage for the specification of some common formatting tasks or data\ntokens. Typically this means that LaTeX documents that are supplied\nto us make use of one or more macro packages to perform some of the\nformatting tasks. Similarly, SGML documents will conform to some\nDocument Type Definition (DTD) provided to us by the publisher, and will make use of some\nstandard set of SGML entities to encode the document at the required\nlevel of abstraction. What this means for us is that even if most\nof the input data comes to us in one of two basic formats\n(TeX/LaTeX/BibTeX or SGML/HTML/XML), we must be able to parse a large \nnumber of document classes, each one defined by a different\nand ever increasing set of specifications, be it a macro package or\na DTD. \n \n\\item Author name formatting: Special care has been taken in parsing and\nformatting author names from a variety of possible input formats\nto the standard one used by the ADS. The proper handling of author names is \ncrucial to the integrity of the data in the ADS. Without proper author \nhandling, users would be unable to get complete listings on searches by \nauthor names which comprise approximately two-thirds of all searches\n(see \\cite{gei}, hereafter SEARCH).\n\nSince the majority of our data sources do not provide author names\nin our standard format (last name, first name or initial), our loading \nroutines need to be able to invert\nauthor names accurately, handling cases such as multiple word last names \n(Da Costa, van der Bout, Little Marenin) and suffixes (Jr., Sr., III). \nAny titles in an author's name (Dr., Rev.) were previously omitted, but are\nnow being retained in the new XML formatting of text files.\n\n The assessment of what constitutes a multiple word last name as \nopposed to a middle name is non-trivial since some names, such as Davis,\ncan be a first name (Davis Hartman), a middle name (A. G. Davis Philip),\na last name (Robert Davis), or some combination (Davis S. Davis).\nAnother example is how to determine when the name ``Van\" is a first name\n(Van Nguyen), a middle name (W. Van Dyke Dixon), or part of a last\nname (J. van Allen). Handling all of these cases correctly requires not\nonly familiarity with naming conventions worldwide, but an intimate \nfamiliarity with the names of astronomers who publish in the field. We\nare continually amassing the latter as we incorporate increasing amounts\nof data into the system, and as we get feedback from our users.\n\n\\item Spell checking: Since many of the historical records entered in the\nADS have been generated by typesetting tables of contents, typographical\nerrors can often be flagged in an automated way using spell-checking\nsoftware. We have developed a PERL software driver for the international \nispell program, a UNIX utility, which can be used as a spell-checking \nfilter on all input to be considered textual information. A custom dictionary \ncontaining terms specific to astronomy and space sciences is used \nto increase the recognition capabilities of the software module.\nAny corrections suggested by the spell-checker module are\nreviewed by a human before the data are actually updated.\n\n\\item Language recognition: Extending the capability of the spell-checker,\nwe have implemented a software module which attempts to guess the language\nof an input text buffer based on the percentage of words that it can\nrecognize in one of several languages: English, German, French, \nSpanish, or Italian. This module is used to flag records to be\nentered in our database in a language other than English. Knowledge of the\nlanguage of an abstract allows us to create accurate synonyms for those \nwords (see ARCHITECTURE).\n\\end{itemize}\n\n\n\\subsection{Identification}\n\nWe call identification the activity of mapping the tokens extracted from the \nparsing of a bibliographic record into a unique identifier.\nThe ADS adopted the use of bibliographic codes as the identifier for \nbibliographic entries shortly after its inception, in order to facilitate \ncommunication between the ADS and SIMBAD. The advantage of using \nbibliographic codes as unique identifiers is\nthat they can most often be created in a straightforward way from the\ninformation given in the list of references published in the\nastronomical literature, namely the publication year, journal name,\nvolume, and page numbers, and first author's name (see section \\ref{bibcodes} for details).\n\n\\subsection{Instantiation}\n\n``Instantiation\" of a bibliographic entry consists of the creation of a\nrecord for it in the ADS database. \nThe ADS must handle receipt of the same data from multiple sources. We have\ncreated a hierarchy of data sources so that we always know the preferred data\nsource. A reference for which we have received records from STI, the journal publisher, SIMBAD, and NED, for \nexample, must be in the system only once with the best information from each\nsource preserved. When we load a reference into the system, we check whether \na text file already exists for that reference. If there is no text file, it\nis a new reference and a text file is created. If there already is a text file,\nwe append the new information to the current text file, creating a ``merged\" \ntext file. This merged text file lists every instance of every field that we \nhave received. \n\n\\subsection{Extraction}\n\nBy ``extraction\" of a bibliographic entry we mean the procedure\nused to create a unique representation of the bibliography from the\navailable records. This is essentially an activity of data fusion\nand unification, which removes redundancies in the bibliographic\nrecords obtained by the ADS and properly labels fields by their characteristics.\nThe extraction algorithm has been designed with our prior experience as \nto the quality of the data to select the best fields from each data \nsource, to cross-correlate the fields as necessary, and to create a \n``canonical\" text file which contains a unique instance of each field.\nSince the latter is created through software, only one version of the text \nfile must be maintained; when the merged text file is appended, the \ncanonical text file is automatically recreated.\n\n The extraction routine selects the best pieces of information from each\nsource and combines them into one reference which is more complete than\nthe individual references. For example, author lists received\nfrom STI were often truncated after five or ten authors. Whenever we\nhave a longer author list from another source, that author list is used\ninstead. This not only recaptures missing authors, it also provides full\nauthor names instead of author initials whenever possible. In addition,\nour journal sources sometimes omit the last page number of the\nreference, but SIMBAD usually includes it, so we are able to preserve this\ninformation in our canonical text file.\n\n Some fields need to be labelled by their characteristics so that they are\nproperly indexed and displayed. The keywords, for example, need to be \nattributed to a specific keyword system. The system designation allows for\nmultiple keyword sets to be displayed (e.g. NASA/STI Keywords and AAS Keywords)\nand will be used in the keyword synonym table currently under development (\\cite{lee}).\n\n We also attempt to cross-correlate authors with their affiliations\nwherever possible. This is necessary for records where the preferred author\nfield is from one source and the affiliations are from another source.\nWe attempt to assign the proper affiliation based on the last name and do not\nassume that the author order is accurate since we are aware of ordering \ndiscrepancies in some of the STI records.\n\n Through these four steps in the procedure of creating and managing\nbibliographic records, we are able to take advantage of receiving the \nsame reference from multiple sources. We standardize the various\nrecords and present to the user a combination of the \nmost reliable fields from each data source in one succinct text file.\n\n\n\\section {\\label {updating} Updating the Database}\n\nThe software to update bibliographic records in the database consists \nof a series of PERL scripts, typically one \nper data source, which reads in the data, performs any \nspecial processing particular to that data source, and writes out the data\nto text files. The loading routines perform three fundamental tasks: 1) they \nadd new\nbibliographic codes to the current master list of bibliographic codes in \nthe system; 2) they create and organize the text files containing the \nreference data; and 3) they maintain the lists of bibliographic codes \nused to indicate what items are available for a given reference.\n\n\\subsection{\\label {masterlist} The Master List}\n\n The master list is a table containing bibliographic codes together with their\npublication dates (YYYYMM) and entry dates into the system (YYYYMMDD). There is \none master list per database with one line per reference. The most important\naspect of the master list is that it retains information about ``alternative\"\nbibliographic codes and matches them to their corresponding preferred\nbibliographic code. An alternative bibliographic code is usually a \nreference which we receive from another source (primarily SIMBAD or NED) which \nhas been assigned a different bibliographic code from the one used by \nthe ADS. Sometimes this is due to the different rules used to build \nbibliographic codes for non-standard publications (see section \\ref{bibcodes}), but often\nit is just an incorrect year, volume, page, or author initial in one of the\ndatabases (SIMBAD or NED or the ADS). In either case, the ADS must keep \nthe alternative bibliographic code in the system so that it can be found when \nreferenced by the other source (e.g. when SIMBAD sends back a list of their \ncodes related to an object). The ADS matches the alternative bibliographic code \nto our corresponding one and replaces any instances of the alternative code \nwhen referenced by the other data source. Alternative bibliographic codes in \nthe master list are prepended with an identification letter (S for SIMBAD, \nN for NED, J for Journal) so that their origin is retained.\n \n While we make every effort to propagate corrections back to our data \nsources, sometimes there is simply a valid discrepancy. For example, \nalternative bibliographic codes are often different from the ADS bibliographic code due to \nambiguous differences such as which name is the surname of a Chinese author. \nSince Americans tend to invert Chinese names one way (Zheng, Wei) and Europeans \nanother (Wei, Zheng), this results in two different, but equally valid codes.\nSimilarly, discrepancies in journal names such as BAAS (for the published\nabstracts in the {\\it Bulletin of the American Astronomical Society}) and AAS\n(for the equivalent abstract with meeting and session number, but\nno volume or page number) need different codes to refer to the same paper.\nRussian and Chinese translation journals ({\\it Astronomicheskii Zhurnal} vs.\n{\\it Soviet Astronomy} and {\\it Acta Astronomica Sinica} vs. {\\it Chinese Astronomy and\nAstrophysics}) share the same problem. These papers appear once in the\nforeign journal and once in the translation journal (usually with different\npage numbers), but are actually the same paper which should be in the system\nonly once. The ADS must therefore maintain\nmultiple bibliographic codes for the same article since each journal \nhas its own abbreviation, and queries for either one must be able to be\nrecognized. The master list is the source of this correlation\nand enables the indexing procedures and search engine to recognize \nalternative bibliographic codes.\n\n\\subsection{\\label {textfiles} The Text Files}\n\n Text files in the ADS are stored in a directory tree by bibliographic code.\nThe top level of directories is divided into directories with four-digit names \nby publication year (characters 1 through 4 of the bibliographic code). The\nnext level contains directories with five-character names according to \njournal (characters 5 through 9), and the text files are named by full \nbibliographic code under these journal directories. Thus, a sample pathname is \n1998/MNRAS/1998MNRAS.295...75E. Alternative bibliographic codes do not \nhave a text file named by that code, since the translation to the equivalent \npreferred bibliographic code is done prior to accessing the text file.\n\nA sample text file is given in the appendices. Appendix B shows\nthe full bibliographic entry, including all records as received from \nSTI, {\\it MNRAS}, and SIMBAD. It contains XML-tagged fields from each source, \nshowing all instances of every field. Appendix C shows the extracted\ncanonical version of the bibliographic entry which contains only selected \ninformation from the merged text file. This latter version is displayed \nto the user through the user interface (see SEARCH).\n\n\n\\subsection{The Codes Files}\n\n The third basic function of the loading procedures is to modify and\nmaintain the listings for available items. The ADS displays the availability\nof resources or information related to bibliographic entries as letter codes in the\nresults list of queries and as more descriptive hyperlinks in the page\ndisplaying the full information available for a bibliographic entry.\nA full listing of the available item codes and their meaning is\ngiven in SEARCH.\n\nThe loading routines maintain lists of bibliographic codes\nfor each letter code in the system which are converted to URLs \nby the indexing routines (see ARCHITECTURE). Bibliographic codes are\nappended to the lists either\nduring the loading process or as post-processing work depending on\nthe availability of the resource. When electronic availability of data\ncoincides with our receipt of the data, the bibliographic codes can be\nappended to the lists by the loading procedures. When we receive the \ndata prior to electronic availability, post-processing routines must be run \nto update the bibliographic code lists after we are notified that we \nmay activate the links.\n\n\\section {\\label {articles} The Articles}\n\n The ADS is able to scan and provide free access to past issues of the astronomical\njournals because of the willing collaboration of the journal publishers. The \nprimary reason that the journal publishers have agreed to allow the scanning of \ntheir old volumes is that the loss of individual subscriptions does not pose\na threat to their livelihood. Unlike many disciplines, most astronomy \njournals are able\nto pay for their publications through the cost of page charges to astronomers\nwho write the articles and through library subscriptions which are unlikely\nto be cancelled in spite of free access to older volumes through the ADS. \nThe journal publishers continue to charge for access to the current volumes,\nwhich is paid for by most institutional libraries.\nThis arrangement places astronomers in a fortunate position\nfor electronic accessibility of astronomy articles.\n\n The original electronic publishing plans for the astronomical community \ncalled for STELAR (STudy of Electronic Literature for Astronomical Research, \n\\cite{vansteen92}, \\cite{vansteen92al}, \\cite{warnock92}, \n\\cite{1993adass...2..137W})\nto handle the scanning and dissemination of the full journal articles.\nHowever, when the STELAR project was terminated in 1993, the ADS assumed \nresponsibility for providing scanned full journal articles to the astronomical \ncommunity. The first test journal to be scanned was the {\\it ApJ Letters} which was \nscanned in January, 1995 at 300 dots per inch (dpi). It should be noted\nthat those scans were intended to be 600 dpi and we will soon rescan them\nat the higher 600 dpi resolution. Complications in the journal \npublishing format (plates at the end \nof some volumes and in the middle of others) were noted and detailed \ninstructions provided to the scanning company so that the resulting scans \nwould be named properly by page or plate number.\n\n All of the scans since the original test batch have been scanned at 600 dpi \nusing a high speed scanner and generating a 1 bit/pixel monochrome image for \neach page. The files created are then automatically processed in order to \nde-skew and center the text in each page, resize images to a standard U.S. \nLetter size (8.5 x 11 inches), and add a copyright notice at the bottom of \neach page. For each original scanned page, two separate image files of \ndifferent resolutions are generated and stored on disk. The availability of \ndifferent resolutions allows users the flexibility of downloading either high \nor medium quality documents, depending on the speed of their internet \nconnection. The image formats and compression used were \nchosen based on the available compression algorithms and browser capabilities.\nThe high resolution files currently used are 600 dpi, 1 bit/pixel TIFF \n(Tagged Image File Format) files,\ncompressed using the CCITT Group 4 facsimile \nencoding algorithm. The medium resolution files are 200 dpi, 1 bit/pixel \nTIFF files, also with CCITT Group 4 \nfacsimile compression. \n\n Conversion to printing formats (PDF, PCL, and Postscript) is done on demand,\nas requested by the user. Similarly, conversion from the TIFF files to \na low resolution GIF (Graphic Interchange Format) file \n(75, 100, or 150 dpi, depending on user preferences)\nfor viewing on the computer screen is done on demand, then cached so that \nthe most frequently accessed pages do not need to be created every time. \nA procedure run nightly deletes the GIF files with the oldest access time stamp \nso that the total size of the disk cache is kept under a pre-defined limit.\nThe current 10 GBytes of cache size in use at the SAO Article Server causes\nonly files which have not been accessed for about a month to be deleted.\nLike the full-screen GIF images, the ADS also caches thumbnail images of\nthe article pages which provide users with the capability of viewing \nthe entire article at a glance.\n\n The ADS uses Optical Character Recognition (OCR) software to gain\nadditional data from TIFF files of article scans.\nThe OCR software is not yet adequate\nfor accurate reproduction of the scanned pages. Greek symbols, equations, \ncharts, and tables do not translate accurately enough to remain true to the \noriginal printed page. For this reason, we have chosen not to\ndisplay to the user anything rendered by the OCR software in an unsupervised\nfashion. However, we are \nstill able to take advantage of the OCR software for several purposes.\n\n First, we are able to identify and extract the abstract paragraph(s) for\nuse when we do not have the abstract from another source. In these cases, \nthe OCR'd text is indexed so that it is searchable and the extracted image of the \nabstract paragraph is displayed in lieu of an ASCII version of the abstract. \nExtracting the abstract from the scanned pages is somewhat tedious, as it requires establishing different sets \nof parameters for each journal, as well as for different fonts used over the \nyears by the same journal. The OCR software can be taught how to determine \nwhere the abstract ends, but it does not work for every article due \nto oddities such as author lists which extend beyond the first page of an \narticle, and articles which are in a different format from others in the \nsame volume (e.g. no keywords or multiple columns). The ADS currently\ncontains approximately 25,000 of these abstract images and more will be added \nas we continue to scan the historical literature.\n\n We are also currently using the OCR software to render electronic \nversions of the entire scanned articles for indexing purposes. We \nwill not use this for display to the users, but hope to be able to index\nit to provide the possibility of full text searching at some future date.\nWe estimate that the indexing of our almost one million \nscanned pages with our current hardware and software will take \napproximately two years of dedicated CPU time.\n\n The last benefit that we gain from the OCR software is the\nconversion of the reference list at the end of articles. \nWe use parsed reference lists from the scanned articles \nto build citation and reference lists for display through the C and \nR links of the available items. Since reference lists are typically in one of\nseveral standard formats, we parse each reference for author, journal, \nvolume and page number for most journal articles, and conference name, author, and\npage number for many\nconference proceedings. This enables us to build\nbibliographic code lists for references contained in that article (R links)\nand invert these lists to build bibliographic code lists of articles \nwhich cite this paper (C links). We are able to use this process to identify\nand therefore add commonly-cited articles which are currently missing from\nthe ADS. This is usually data prior to 1975 or astronomy-related articles\npublished in non-astronomy journals.\n\nThe Article Service currently contains 250 GBytes of scans, which\nconsists of 1,128,955 article pages comprising 138,789 articles. These\nnumbers increase on a regular basis, both as we add more articles from the\nolder literature and as we scan new journals.\n\n\\section {\\label {journals} ADS/Journal Interaction}\n\nA description of the data in the ADS would be incomplete without a \ndiscussion of the interaction between the ADS and the electronic \njournals. The data available on-line from the journal publishers is an extension\nof the data in the ADS and vice versa. This interaction is greatly\nfacilitated by the acceptance of the bibliographic code by many\njournal publishers as a means for accessing their on-line articles.\n\nAccess to articles currently on-line at the journal sites through the \nADS comprises a significant percent of the on-line journal access (see\nOVERVIEW). The best model for interaction between the ADS and a journal\npublisher is the University of Chicago Press (hereafter UCP), publisher of\n{\\it ApJ, ApJL, ApJS, AJ,} and {\\it PASP}. When a new volume appears on-line at\nUCP, the ADS is notified by email and an SGML header file for each of those\narticles is simultaneously transferred to our site. The data are parsed\nand loaded into the system and appropriate links are created. However,\nprior to this, the UCP has made use of the ADS to build their electronic\nversion through the use of our bibliographic code reference resolver.\n\n Our bibliographic code reference resolver (\\cite{adass8}) was developed to provide\nthe capability to automatically parse, identify, and verify citations\nappearing in astronomical literature. By verifying the existence of a\nreference through the ADS, journals and conference proceedings editors are\nable to publish documents containing hyperlinks pointing to stable, unique\nURLs. Increasingly more journals are linking to the ADS in their\nreference sections, providing users with the ability to read referenced\narticles with the click of a mouse button.\n\nDuring the copy editing phase, UCP editors query the ADS reference\nresolver and determine if each reference exactly matches a bibliographic\ncode in the ADS. If there is a match, a link to the ADS is established for\nthis entry in their reference section. If there is not a match, one of\nseveral scenarios takes place. First, if it is a valid reference not yet\nincluded in the ADS (most often the case for ``fringe\" articles, those \nperipherally associated with astronomy), our reference resolver captures\nthe information necessary to add it to our database during the next update.\nSecond, if it is a valid reference unable to be parsed by the resolver\n(sometimes the case for conference proceedings or PhD theses), no \naction is taken and no link is listed in the reference section. Third,\nif there is an error in the reference as determined by the reference resolver,\nthe UCP editors may ask for a correction or clarification from the authors.\n\nThe last option demonstrates the power of the reference resolver, which has\nbeen taught on a journal-by-journal basis how complete the coverage of\nthat journal is in the ADS. Before the implementation of the reference resolver,\nUCP was able to match 72\\% of references in {\\it ApJ} articles (E. Owens,\nprivate communication). Early results from the use of the reference \nresolver show that we are now able to match conference proceedings, so this\nnumber should become somewhat larger. It is unlikely that we will ever match\nmore than 90\\% of references in an article\ndue to references such as ``private communication\", ``in press\", and preprints,\nas well as author errors (see section \\ref {summary}). Our own reference \nresolving of OCR'd reference lists shows that we can match approximately\n86% of references for the best-case scenario.\n\n The ADS provides multiple ways for authors and journal publishers to link \nto the ADS (see SEARCH). We make every effort to \nfacilitate individuals and organizations linking to us. This is easily \ndone for simple searches such as the verification of a bibliographic code or \nan author search for a single spelling. However, given the complexity of \nthe system, these automated searches can quickly become complicated. \nDetails for conference proceedings editors or journal publishers who are\ninterested in establishing or improving links to the ADS are available upon \nrequest. In particular, those who have individual TeX macros incorporated \nin their references can use our bibliographic code resolver to \nfacilitate linking to the ADS.\n\n\\section {\\label {summary} Discussion and Summary}\n\n As of this writing (12/1999), there are 524,304 references in the \nAstronomy database, 523,498 references in the Instrumentation database, 443,858\nreferences in the Physics database, and 3467 references in the Preprint\ndatabase, for a total of almost 1.5 million references in the system. \nAstronomers currently write approximately 18,000 journal articles annually,\nand possibly that many additional conference proceedings papers per year. \nMore than half of the journal papers appear in peer-reviewed journals. These \nnumbers are more than double what they were in 1975, in spite of an increase\nin the number of words per page in most of the major journals \n(\\cite{1995ApJ...455..407A}),\nand an increase in number of pages per article (\\cite{1997PASP..109.1278S}).\nAt the current rate of publication, astronomers could be writing\n25,000 journal papers per year by 2001 and an additional 20,000 conference proceedings papers.\nFigure \\ref{histogram} shows the total number of papers for each year in the\nAstronomy database since 1975, divided into refereed journal papers,\nnon-refereed journal papers, and conferences (including reports and theses).\nThere are\nthree features worth noting. First, the increase in total references in 1980 \nis due to the inclusion\nof Helen Knudsen's Monthly Astronomy and Astrophysics Index, a rich source\nof data for both journals and conference proceedings which began coverage\nin late 1979 and continued until 1995. Second, the recent\nincrease in conferences included in the Astronomy database (starting\naround 1996) is due to the inclusion of conference proceedings table\nof contents provided by collaborating librarians and typed in by our \ncontractors. Last, the decrease in numbers for 1999 is due to coverage\nfor that year not yet being complete in the ADS. \n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_dataF1.eps}}\n\\caption[]{Histogram showing the number of refereed journal papers, non-refereed journal papers, and conferences (including reports and theses) for each year in the Astronomy database since 1975. }\n\\label{histogram}\n\\end{figure}\n\n\n\nThe growth rate of the Instrumentation and Physics databases is difficult \nto estimate, primarily because we do not have datasets which are as complete\nas astronomy. In any case, the need for the organization and maintenance\nof this large volume of data is clearly important to every research astronomer.\nFortunately, the ADS was designed to be able to handle this large quantity of\ndata and to be able to grow with new kinds of data. New available item links \nhave been added for new types of data as they became available (e.g. the links\nto complete book entries at the Library of Congress)\nand future datasets (e.g. from future space missions) should be able to be \nadded in the same fashion. \n\n As with any dataset of this magnitude, there is some fraction of \nreferences in the system which are incorrect. This is unavoidable given\nthe large number of data sources, errors in indices and tables of\ncontents as originally published, and human error. In addition, many \nauthors do not give full attention to verifying all references in a paper,\nresulting in the introduction of errors in many places. In a \nsystematic study of more than 1000 references contained in a single issue of \nthe {\\it Astrophysical Journal},\nAbt (1992) found that more than 12\\% of those contained errors. This number should be significantly reduced with the integration of the ADS reference\nresolver in the electronic publishing process.\nHowever, any mistakes in the ADS can and will get propagated, so steps are\nbeing taken by us to maximize accuracy of our entries.\n\n Locating and identifying correlations between multiple bibliographic \ncodes which describe the same article is a time-consuming and\nsometimes subjective task as many pairs of bibliographic codes need to\nbe verified by manually looking up papers in the library. We use the\nAbstract Service itself for gross matching of bibliographic codes, submitting\na search with author and title, and considering any resulting matches with \na score of 1.0 as a potential match. These matches are only potential\nmatches which require verification since authors can submit the same paper\nto more than one publication source (e.g. BAAS and a refereed journal), \nand since errata published with the same title and author list will perfectly\nmatch the original paper.\n\nWhen a volume or year is mismatched, it is usually obvious which of a pair\nof matched bibliographic codes is correct, but if a page number is off,\nthe decision as to which code is correct cannot always be automated. We also\nneed to consider matches with very high scores less than 1.0 since these are the\nmatches where an author name may be incorrect. The correction of errors\nof this sort is ongoing work which is carried out as often as time and \nresources permit.\n\n The evolution of the Internet and the World Wide Web, along with the \nexplosion of astronomical services on the Web has enabled the ADS to provide\naccess to our databases in an open and uniform environment. We have been able\nto hyperlink both to our own resources and to other on-line resources such\nas the journal bibliographies (\\cite{1996adass...5..547B}). As part of the \ninternational collaboration Urania (Universal Research Archive of Networked \nInformation in Astronomy, \\cite{1998lisa.conf..107B}), the ADS enables\na fully functioning distributed digital library of astronomical \ninformation which provides power and utility previously unavailable to \nthe researcher. \n\n Perhaps the largest factor which has contributed to the success of the\nADS is the willing cooperation of the AAS, CDS, and all the journal publishers.\nThe ADS has largely become the means for linking together smaller pieces of a \nbigger picture, making an elaborate digital library for astronomers a reality.\nWe currently collaborate with over fifty groups in creating and maintaining\ncross-links among data centers. \nThese additional collaborations with individuals and institutions\nworldwide allow us to provide many value-added features to the system such \nas object information, author email addresses, mail order forms for articles,\ncitations, article scans, and more. A listing of these collaborations is \nprovided in Table~\\ref{table6}. Any omissions from this table are purely\nunintentional, as the ADS values all of our colleagues and the users benefit\nnot only from the major collaborators but the minor ones as well, as these are \noften more difficult for users to learn about independently. Most of the\nabbreviations are listed in Tables 2, 3, and 4.\n\n\\begin{table*}\n\\caption[]{Collaborators }\n\\label{table6}\n\\begin{tabular*}{7.0in}{lp{3.5in}}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nAdditional Collaborations & Nature of the Collaboration\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nA.G. Davis Philip & Scanning of Conference Proceedings \\\\\nAcademic Press (AP) & Scanning of Icarus \\\\\nAmerican Astronomical Society (AAS) & Citations, Scanning of AJ, ApJ, ApJL, ApJS, AASPB$^{\\mathrm{a}}$, BAAS \\\\\nAmerican Institute of Physics & Scanning of SvAL \\\\\nAndre Heck & Star Heads (Author Home Pages) \\\\\nAnnual Reviews, Inc. & Scanning of ARA\\&A \\\\\nAstronomical Data Center (ADC) & D links to data \\\\\nAstronomical Institute of Czechoslovakia & Scanning of BAICz \\\\\nAstronomical Institute of the Slovak Academy of Sciences & Scanning of CoSka \\\\\nAstronomical Society of Australia & Scanning of PASA \\\\\nAstronomical Society of India & Scanning of BASI \\\\\nAstronomical Society of Japan & Scanning of PASJ \\\\\nAstronomical Society of the Pacific (ASP) & Scanning of PASP and Conference Proceedings \\\\\nAstronomische Gesellschaft & Scanning of RvMA \\\\\nAstronomische Nachrichten & Scanning of AN \\\\\nBaltic Astronomy & Scanning of BaltA \\\\\nBritish Astronomical Association & Scanning of JBAA \\\\\nCambridge University Press & M links to order forms, Scanning \\\\\nCentral Bureau for Astronomical Telegrams (CBAT) & Object searches \\\\\nChris Benn & Astropersons.lis (Author Email) \\\\\nEDP Sciences & Scanning of A\\&AS \\\\\nElsevier Publishers & E links to articles \\\\\nGeneral Catalogue of Photometric Data (GCPD) & D links to data \\\\\nInstitute for Scientific Information (ISI) & Citations \\\\\nInternational Society for Optical Engineering (SPIE)& M links to order forms \\\\\nKorean Astronomical Society & Scanning of JKAS \\\\\nKluwer Publishers & M links to order forms, Scanning of SoPh \\\\\nLibrary of Congress (LOC) & Z39.50 interface, L links to data \\\\\nLos Alamos National Laboratory (LANL) & Preprint Archive \\\\\nLunar and Planetary Science Institute (LPI) & Scanning, Object searches \\\\\nMeteoritical Society & Scanning of M\\&PS \\\\\nNED & N links to objects, Object searches \\\\\nThe Observatory & Scanning \\\\\nRoyal Astronomical Society & Scanning of MNRAS \\\\\nSIMBAD & S links to objects, D links to data, Object searches \\\\\nSpringer Verlag & Scanning of A\\&A, ZA$^{\\mathrm{b}}$ \\\\\nUniversitad Nacional Autonoma de Mexico (UNAM) & Scanning of RMxAA, RMxAC \\\\\nUniversity of Chicago Press (UCP) & Reference Resolving \\\\\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\begin{list}{}{}\n\\item[$^{\\mathrm{a}}$]American Astronomical Society Photo Bulletin\n\\item[$^{\\mathrm{b}}$]Zeitschrift f\\\"ur Astrophysik\n\\end{list}{}{}\n\\end{table*}\n\n\n\nThe successful coordination of data exchanges with each of our collaborators\nand the efforts which went into establishing them in the first place have been \nkey to the success of the ADS. Establishing links to and from the journal \npublishers, changing these links due to revisions at publisher websites, and \ntracking and fixing broken links is all considered routine data maintenance\nfor the system. Since it is necessary for us to maintain connectivity \nto external sites, routine checks of sample links are performed on a regular\nbasis to verify that the links are still active.\n\n Usage statistics for the Abstract Service (see OVERVIEW)\nindicate that astronomers and librarians at scientific institutions\nare eager to take advantage of the information that the ADS provides. The \nwidespread acceptance of the ADS by the astronomical community is changing how\nastronomers do research, placing extensive bibliographic information at \ntheir fingertips. This enables researchers to increase their productivity and\nto improve the quality of their work.\n\n A number of improvements to the data in the ADS are planned for the near\nfuture. As always, we will continue our efforts to increase the completeness\nof coverage, particularly for the data prior to 1975. We have collected\nmost of the major journals back to the first issue for scanning and adding\nto the Astronomy database. In addition, we are scanning and OCR'ing table \nof contents for conference proceedings to improve our coverage in that\narea. We are currently OCR'ing full journal articles \nto provide full text searching and to improve the completeness of our \nreference and citation coverage. Finally, as the ADS becomes commonplace for all \nastronomers, valuable feedback from our users to inform us about missing \npapers, errors in the database, and suggested improvements to the system \nserve to guide the future of the ADS and to ensure that the ADS continues to \nevolve into a more valuable research tool for the scientific community.\n\n\\section{\\label{acknowldgements} Acknowledgments}\n\nThe other ADS Team members: Markus Demleitner, Elizabeth Bohlen, and Donna\nThompson contribute much on a daily basis. Funding for this project has been\nprovided by NASA under NASA Grant NCC5-189.\n\n\\begin{thebibliography}{}\n\n\\bibitem[Abt 1994]{1994PASP..106.1015A} Abt, H. A. 1994, PASP, 106, 1015 \n\n\\bibitem[Abt 1995]{1995ApJ...455..407A} Abt, H. A. 1995, ApJ, 455, 407 \n\n\\bibitem [Accomazzi et al. 2000]{aa} Accomazzi, A., Eichhorn, G.,\nGrant, C.S., Kurtz, M.J., \\& Murray, S.S. 2000, (this issue)\n\n\\bibitem [Accomazzi et al. 1999]{adass8} Accomazzi, A., Eichhorn, G.,\nKurtz, M.J., Grant, C.S., \\& Murray, S.S. 1998, ASP Conf. Ser. 172:\nAstronomical Data Analysis Software and Systems VIII, 291\n\n\\bibitem[American Astronomical Society 1999]{aas} American Astronomical\nSociety Manuscript Preparation, 1999, \nhttp://www.journals.uchicago.edu/AAS/AASTeX\n\n\\bibitem[Boyce 1998]{1998lisa.conf..107B} Boyce, Peter B. 1998,\nASP Conf. Ser. 153: Library and Information Services in Astronomy III, 107\n\n\\bibitem[Boyce \\& Biemesderfer 1996]{1996adass...5..547B} Boyce, P.B. \\& \nBiemesderfer, C. 1996, ASP Conf. Ser. 101: Astronomical Data Analysis Software and \nSystems V, 547 \n\n\\bibitem[Egret \\& Wenger 1988]{1988alds.proc..323E} Egret, D. \\&\nWenger, M. 1988, ESO Conf. \\#28: Astronomy from Large Databases, eds F. Murtagh and A. Heck, 323\n\n\\bibitem[Eichhorn et al. 2000]{gei} Eichhorn, G., Kurtz, M.J.,\nAccomazzi, A., Grant, C.S., \\& Murray, S.S. 2000, (this issue)\n\n\\bibitem[Goldfarb \\& Rubinsky 1991]{goldfarb} Goldfarb, Charles F. \\& Rubinsky,\nYuri, 1991, The Sgml Handbook (Clarendon Press)\n\n\\bibitem[Harold 1999]{harold} Harold, Elliotte Rusty, 1998, Xml: Extensible\nMarkup Language (IDG Books Worldwide)\n\n\\bibitem[Helou \\& Madore 1988]{1988alds.proc..335H} Helou, G. \\&\nMadore, B. 1988, ESO Conf. \\#28: Astronomy from Large Databases, eds F. Murtagh and A. Heck, 335\n\n\\bibitem[International Organization for Standardization 1987]{iso} International\nOrganization for Standardization 1987, Information and Processing --- 8--bit Single--byte Coded Graphic Character Sets (Geneva)\n\n\\bibitem[Jacobsen 1996]{jacobs} Jacobsen, Dana, 1996,\nhttp://www.ecst.csuchico.edu/\\-\\~{}jacobsd/bib/formats/refer.html\n\n\\bibitem[Knuth 1984]{knuth} Knuth, Donald E. 1984, The TeXbook (Addison-Wesley\nPublishing Co.)\n\n\\bibitem[Kurtz et al. 2000]{kurtz} Kurtz, M.J., Eichhorn, G., \nAccomazzi, A., Grant, C.S., Murray, S.S., \\& Watson, J.M. 2000, (this issue)\n\n\\bibitem[Lamport 1986]{lamport} Lamport, Leslie 1986,\nLaTex : A Documentation Preparation System (Addison-Wesley Publishing Co.)\n\n\\bibitem[Lee et al. 1999]{lee} Lee, J., Dubin, D.S., Kurtz, M.J. 1999,\nASP Conf. Ser. 172: Astronomical Data Analysis Software and Systems VIII, 287\n\n\\bibitem[Los Alamos National Laboratory 1991]{lanl} Los Alamos National Laboratory 1991,\nhttp://xxx.lanl.gov\n\n\\bibitem[Powell \\& Whitworth 1998]{powell} Powell, Thomas A. \\& Whitworth, Dan,\n1998, Html: Programmer's Reference (Osborne McGraw-Hill)\n\n\\bibitem[Schmadel 1979]{1979BICDS..17....2S} Schmadel, L. D. 1979, \nBulletin d'Information du Centre de Donn\\'ees Stellaires, 17, 2 \n\n\\bibitem[Schmadel 1982]{1982adra.proc..159S} Schmadel, L. D. 1982, \nIAU Colloq. 64: Automated Data Retrieval in Astronomy, 159\n\n\\bibitem[Schmadel 1989]{1989lisa.conf...77S} Schmadel, L. D. 1989, \nASP Conf. Ser. 153: Library and Information Services in Astronomy III, 77 \n\n\\bibitem[Schmitz et al. 1995]{1995VA.....39R.272S} Schmitz, M., Helou, G., \nDubois, P., Lague, C., Madore, B., Corwin, H.G.J., \\& Lesteven, S. 1995, \nVistas in Astronomy, 39, 272 \n\n\\bibitem[Schulman et al. 1997]{1997PASP..109.1278S} Schulman, E., French, \nJ.C., Powell, A.L., Eichhorn, G., Kurtz, M.J., \\& Murray, S.S. 1997, PASP, \n109, 1278 \n\n\\bibitem[Unicode Consortium 1996]{unicode} Unicode Consortium 1996, \nThe Unicode Standard : Version 2.0 (Addison-Wesley Pub Co.)\n\n\\bibitem[van Steenberg 1992]{vansteen92} van Steenberg, M. 1992, \nDesktop Publishing in Astronomy \\& Space Sciences, ed. A. Heck \n(Singapore, World Scientific), 143\n\n\\bibitem[van Steenberg et al. 1992]{vansteen92al} van Steenberg, M., \nGass, J., Brotzman, L.E., Warnock, A., Kovalsky, D., \\& Giovane, F. \n1992, Newsletter of the American Astronomical Society, 62, 11\n\n\\bibitem[Wall \\& Schwartz 1991]{wall91} Wall, Larry \\& Schwartz, Randal L. 1991, Programming PERL (O'Reilly \\& Associates, Inc.)\n\n\\bibitem[Warnock et al. 1992]{warnock92} Warnock, A., Gass, J., \nBrotzman, L.E., van Steenberg, M.E., Kovalsky, D., \\& Giovane, F. \n1992, Newsletter of the American Astronomical Society, 62, 10 \n\n\\bibitem[Warnock et al. 1993]{1993adass...2..137W} Warnock, A., van \nSteenberg, M.E., Brotzman, L.E., Gass, J.E., Kovalsky, D., \\& Giovane, \nF. 1993, ASP Conf. Ser. 52: Astronomical Data Analysis Software and Systems \nII, 137 \n\n\\end{thebibliography} \n\n\\newpage\n\n\\appendix\n\\section {\\label {appendixa}}\n\nVersion 1.0 of the XML DTD describing text files in the ADS Abstract\nService.\n\n\\begin{verbatim}\nDocument Type Definition for the ADS \nbibliographic records\n\nSyntax policy\n=============\n - The element names are in uppercase in order\n to help the reading.\n - The attribute names are preferably in \n lowercase \n - The attribute values are allowed to be of \n type CDATA to allow more flexibility for \n additional values; however, attributes\n typically may only assume one of a well-\n defined set of values\n - Cross-referencing among elements such as \n AU, AF, and EM is accomplished through the \n use of attributes of type IDREFS (for AU) \n and ID (for AF and EM)\n\n<!-- BIBRECORD is the root element of the XML \n document. Attributes are:\n\n origin mnemonic indicating individual(s)\n or institution(s) who submitted \n the record to ADS\n lang language in which the contents of \n this record are expressed the \n possible values are language tags \n as defined in RFC 1766. \n Examples: lang=\"fr\", lang=\"en\"\n-->\n\n<!ELEMENT BIBRECORD ( METADATA?, \n TITLE?, \n AUTHORS?, \n AFFILIATIONS?, \n EMAILS?, \n FOOTNOTES?, \n BIBCODE, \n MSTRING, \n MONOGRAPH?, \n SERIES?, \n PAGE?, \n LPAGE?, \n COPYRIGHT?, \n PUBDATE, \n CATEGORIES*, \n COMMENTS*, \n ANOTE?, \n BIBTYPE?, \n IDENTIFIERS?, \n ORIGINS, \n OBJECTS*, \n KEYWORDS*, \n ABSTRACT* ) >\n\n<!ATTLIST BIBRECORD origin CDATA #REQUIRED\n lang CDATA #IMPLIED >\n\n<!-- Generic metadata about the ADS record \n (rather than the publication) -->\n<!ELEMENT METADATA ( VERSION, \n CREATOR, \n CDATE, \n EDATE ) >\n\n<!-- Versioning is introduced to allow parsers \n to detect and reject any documents not \n complying with the supported DTD -->\n<!ELEMENT VERSION ( #PCDATA ) >\n<!-- CREATOR is purely informative -->\n<!ELEMENT CREATOR ( #PCDATA ) >\n<!-- Creation date for the record -->\n<!ELEMENT CDATE ( YYYY-MM-DD ) >\n<!-- Last modified date -->\n<!ELEMENT EDATE ( YYYY-MM-DD ) >\n\n<!-- Title of the publication -->\n<!ELEMENT TITLE ( #PCDATA ) >\n<!ATTLIST TITLE lang CDATA #IMPLIED >\n\n<!-- AUTHORS contains only AU subelements, each \n one of them corresponding to a single author \n name -->\n<!ELEMENT AUTHORS ( AU+ ) >\n\n<!-- AU contains at least the person's last name \n (LNAME), and possibly the first and middle name(s) \n (or just the initials) which would be stored in \n element FNAME. PREF and SUFF represent the \n salutation and suffix for the name. SUFF \n typically is one of: Jr., Sr., II, III, IV. \n PREF is rarely used but is here for completeness.\n Typically we would store salutations such as \n \"Rev.\" (for \"Reverend\"), or \"Prof.\" (for \n \"Professor\") in this element. \n-->\n<!ELEMENT AU ( PREF?, \n FNAME?, \n LNAME, \n SUFF? ) >\n<!-- The attributes AF and EM are used to cross-\n\t\t reference author affiliations and email \n addresses with the individual author records. \n This is the only exception of attributes in \n upper case. The typical use of this is:\n <AU AF=\"AF_1 AF_2\" EM=\"EM_3\">...</AU>\n-->\n<!ATTLIST AU AF IDREFS #IMPLIED\n EM IDREFS #IMPLIED\n FN IDREFS #IMPLIED >\n<!-- AU subelements -->\n<!ELEMENT PREF ( #PCDATA ) >\n<!ELEMENT FNAME ( #PCDATA ) >\n<!ELEMENT LNAME ( #PCDATA ) >\n<!ELEMENT SUFF ( #PCDATA ) >\n\n<!-- AFFILIATIONS is the wrapper element for \n the individual affiliation records, each \n represented as an AF element -->\n<!ELEMENT AFFILIATIONS ( AF+ ) >\n<!ELEMENT AF ( #PCDATA ) >\n<!-- the value of the ident attribute should \n match one of the values assumed by the AF \n attribute in an AU element -->\n<!ATTLIST AF ident ID #REQUIRED >\n\n<!ELEMENT EMAILS ( EM+ ) >\n<!ELEMENT EM ( #PCDATA ) >\n<!-- the value of the ident attribute should \n match one of the values assumed by the EM \n attribute in an AU element -->\n<!ATTLIST EM ident ID #REQUIRED >\n\n<!-- FOOTNOTES and FN subelements are here for \n future use -->\n<!ELEMENT FOOTNOTES ( FN+ ) >\n<!ELEMENT FN ( #PCDATA ) >\n<!ATTLIST FN ident ID #REQUIRED >\n\n<!-- BIBCODE; for a definition, see:\nhttp://adsdoc.harvard.edu/abs_doc/bib_help.html\nhttp://adsabs.harvard.edu/cgi-bin/\n nph-bib_query?1995ioda.book..259S\nhttp://adsabs.harvard.edu/cgi-bin/\n nph-bib_query?1995VA.....39R.272S\n This identifier logically belongs to the \n IDENTS element, but since it is the \n identifier used internally in the system, \n it is important to have it in a prominent \n and easy to reach place.\n-->\n<!ELEMENT BIBCODE ( #PCDATA ) >\n\n<!-- MSTRING is the unformatted string for the \n monograph (article, book, whatever). Example:\n <MSTRING>The Astrophysical Journal, Vol. 526, \n n. 2, pp. L89-L92</MSTRING>\n-->\n<!ELEMENT MSTRING ( #PCDATA ) >\n<!-- MONOGRAPH is a structured record containing \n the fielded information about the monograph \n where the bibliographic entry appeared. \n Typically this is created by parsing the \n text in the MSTRING element. Example:\n <MTITLE>The Astrophysical Journal</MTITLE>\n <VOLUME>526</VOLUME>\n <ISSUE>2</ISSUE>\n <PUBLISHER>University of Chicago Press\n </PUBLISHER>\n-->\n<!ELEMENT MONOGRAPH ( MTITLE, \n VOLUME?, \n ISSUE?, \n MNOTE?, \n EDITORS?, \n EDITION?, \n PUBLISHER?, \n LOCATION?, \n MID* ) >\n\n<!-- Monograph title (e.g. \"Astrophysical Journal\") -->\n<!ELEMENT MTITLE ( #PCDATA ) >\n<!ELEMENT VOLUME ( #PCDATA ) >\n<!ATTLIST VOLUME type NMTOKEN #IMPLIED >\n<!ELEMENT ISSUE ( #PCDATA ) >\n<!-- A note about the monograph as supplied by the \n publisher or editor -->\n<!ELEMENT MNOTE ( #PCDATA ) >\n<!-- List of editor names as extracted from MSTRING.\n Formatting is as for AUTHORS and AU elements -->\n<!ELEMENT EDITORS ( ED+ ) >\n<!ELEMENT ED ( PREF?, \n FNAME?,\n LNAME,\n SUFF? ) >\n<!-- Edition of publication -->\n<!ELEMENT EDITION ( #PCDATA ) >\n<!-- Name of publisher -->\n<!ELEMENT PUBLISHER ( #PCDATA ) >\n<!-- Place of publication -->\n<!ELEMENT LOCATION ( #PCDATA ) >\n<!-- MID represents the monograph identification as \n supplied by the publisher. This may be useful in \n correlating our record with the publisher's online \n offerings. The \"system\" attribute characterizes \n the system used to express the identifier -->\n<!ELEMENT MID ( #PCDATA ) >\n<!ATTLIST MID type NMTOKEN #IMPLIED >\n\n<!-- If the bibliographic entry appeared in a series, \n then the element SERIES contains information \n about the series itself. Typically this consists \n of data about a conference series (e.g. ASP \n Conference Series). Note that there may be \n several SERIES elements, since some \n publications belong to \"subseries\" within \n a series.\n-->\n<!ELEMENT SERIES ( SERTITLE,\n SERVOL?,\n SEREDITORS?,\n SERBIBCODE? ) >\n<!-- Title, volume, and editors of conference \n series -->\n<!ELEMENT SERTITLE ( #PCDATA ) >\n<!ELEMENT SERVOL ( #PCDATA ) >\n<!ELEMENT SEREDITORS ( ED+ ) >\n<!-- Serial bibcode for publication (may coincide \n with main bibcode) -->\n<!ELEMENT SERBIBCODE ( #PCDATA ) >\n\n<!-- PAGE may have the attribute type set to \n \"s\" for (sequential) the value associated \n to it does not represent a printed volume \n number -->\n<!ELEMENT PAGE ( #PCDATA ) >\n<!ATTLIST PAGE type NMTOKEN #IMPLIED >\n\n<!-- LPAGE gives the last page number (if known).\n Does not make sense if PAGE is type=\"s\" -->\n<!ELEMENT LPAGE ( #PCDATA ) >\n\n<!-- COPYRIGHT is just an unformatted string \n containing copyright information from \n publisher -->\n<!ELEMENT COPYRIGHT ( #PCDATA ) >\n\n<!ELEMENT PUBDATE ( YEAR, MONTH? ) >\n<!ELEMENT MONTH ( #PCDATA ) >\n<!ELEMENT YEAR ( #PCDATA ) >\n\n<!-- CATEGORIES contain subelements indicating in \n which subject categories the publication was \n assigned. STI/RECON has always assigned a \n category for each entry in their system, but \n otherwise there is little else in our \n database. The attributes origin and system \n are used to keep track of the different \n classifications used.\n-->\n<!ELEMENT CATEGORIES ( CA+ ) >\n<!ATTLIST CATEGORIES origin NMTOKEN #IMPLIED\n system NMTOKEN #IMPLIED >\n<!ELEMENT CA ( #PCDATA ) >\n\n<!-- Typically private fields supplied by the \n data source. For instance, SIMBAD and LOC \n provide comments about a bibliographic \n entries -->\n<!ELEMENT COMMENTS ( CO+ ) >\n<!ATTLIST COMMENTS lang CDATA #IMPLIED\n origin NMTOKEN #IMPLIED >\n<!ELEMENT CO ( #PCDATA ) >\n\n<!-- Author note -->\n<!ELEMENT ANOTE ( #PCDATA ) >\n\n<!-- BIBTYPE describes what type of publication \n this entry corresponds to. This is \n currently limited to the following tokens \n (taken straight from the BibTeX \n classification):\n article\n book\n booklet\n inbook\n incollection\n inproceedings\n manual\n masterthesis\n misc\n phdthesis\n proceedings\n techreport\n unpublished\n-->\n<!ELEMENT BIBTYPE ( #PCDATA ) >\n\n<!-- List of all known identifiers for this \n publication -->\n<!ELEMENT IDENTIFIERS ( ID+ ) >\n<!-- Contents of an ID element is the identifier \n used by a particular publisher or institution.\n Examples:\n <ID origin=\"UCP\" system=\"PUBID\">38426</ID>\n <ID origin=\"STI\" system=\"ACCNO\">A90-12345</ID>\n-->\n<!ELEMENT ID ( #PCDATA ) >\n<!ATTLIST ID origin NMTOKEN #IMPLIED\n type NMTOKEN #REQUIRED >\n\n<!-- the collective list of institutions that have given \n us a record about this entry. -->\n<!ELEMENT ORIGINS ( OR+ ) >\n<!ELEMENT OR ( #PCDATA ) >\n\n<!-- The list of objects associated with the \n publication -->\n<!ELEMENT OBJECTS ( OB+ ) >\n<!ELEMENT OB ( #PCDATA ) >\n\n<!-- Keywords assigned to the publication -->\n<!ELEMENT KEYWORDS ( KW+ ) >\n<!ATTLIST KEYWORDS Lang CDATA #IMPLIED\n origin NMTOKEN #IMPLIED\n system NMTOKEN #REQUIRED >\n<!ELEMENT KW ( #PCDATA ) >\n\n<!-- An abstract of the publication. This is \n typically provided to us by the publisher, \n but may in some cases come from other \n sources (E.g. STI, which keyed abstracts \n in most cases). Therefore we allow several \n ABSTRACT elements within each record, each \n with a separate origin or language. \n The attribute type is used to keep track \n of how the abstract data was generated. \n For instance, abstract text generated by \n our OCR software will have: \n origin=\"ADS\" type=\"OCR\" lang=\"en\"\n-->\n<!ELEMENT ABSTRACT ( P+ ) >\n<!ATTLIST ABSTRACT origin NMTOKEN #IMPLIED >\n type NMTOKEN #IMPLIED >\n lang CDATA #IMPLIED >\n\n<!-- Abstracts are composed of separate \n paragraphs which have mixed contents as \n listed below. All the subelements listed \n below have the familiar HTML meaning and \n are used to render the abstract text in a \n decent way -->\n<!ELEMENT P (#PCDATA |A| BR | PRE | SUP | SUB)* >\n<!-- Line breaks (BR) and preformatted text (PRE) \n make it possible to display tables and other \n preformatted text. -->\n<!ELEMENT BR EMPTY >\n<!ELEMENT PRE (#PCDATA | A | BR | SUP | SUB )* >\n<!-- A is the familiar anchor element. -->\n<!ELEMENT A ( #PCDATA | BR | SUP | SUB )* >\n<!ATTLIST A HREF CDATA #REQUIRED >\n<!-- SUP and SUB are superscripts and subscripts. \n In our content model, they are allowed to \n contain additional SUP and SUB elements, \n although we may decide to restrict them to\n PCDATA at some point -->\n<!ELEMENT SUP ( #PCDATA | A | BR | SUP | SUB )* >\n<!ELEMENT SUB ( #PCDATA | A | BR | SUP | SUB )* >\n\\end{verbatim}\n\n\\section {\\label {appendixb}}\n\nA sample text file from the ADS Abstract Service showing \nXML markup for the full bibliographic entry, including records from\nSTI, {\\it MNRAS}, and SIMBAD. Items in bold are those selected to\ncreate the canonical text file shown in Appendix C.\n\n\\noindent\n$<$?xml version=``1.0\"?$>$ \\\\\n$<$!DOCTYPE ADS\\_BIBALL SYSTEM ``ads.dtd\"$>$ \\\\\n$<$ADS\\_BIBALL$>$ \\\\\n\n\\noindent\n$<$BIBRECORD origin=``STI\"$>$ \\\\\n{\\bf $<$TITLE$>$Spectroscopic confirmation of redshifts \npredicted by gravitational lensing$<$/TITLE$>$} \\\\\n$<$AUTHORS$>$ \\\\\n $<$AU AF=``1\"$>$ \\\\\n $<$FNAME$>$Tim$<$/FNAME$>$ \\\\\n $<$LNAME$>$Ebbels$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``1\"$>$ \\\\\n $<$FNAME$>$Richard$<$/FNAME$>$ \\\\\n $<$LNAME$>$Ellis$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``2\"$>$ \\\\\n $<$FNAME$>$Jean-Paul$<$/FNAME$>$ \\\\\n $<$LNAME$>$Kneib$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``2\"$>$ \\\\\n $<$FNAME$>$Jean-Francois$<$/FNAME$>$ \\\\\n $<$LNAME$>$LeBorgne$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``2\"$>$ \\\\\n $<$FNAME$>$Roser$<$/FNAME$>$ \\\\\n $<$LNAME$>$Pello$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``3\"$>$ \\\\\n $<$FNAME$>$Ian$<$/FNAME$>$ \\\\\n $<$LNAME$>$Smail$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``4\"$>$ \\\\\n $<$FNAME$>$Blai$<$/FNAME$>$ \\\\\n $<$LNAME$>$Sanahuja$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n$<$/AUTHORS$>$ \\\\\n$<$AFFILIATIONS$>$ \\\\\n $<$AF ident=``AF\\_1\"$>$Cambridge, Univ.$<$/AF$>$ \\\\\n $<$AF ident=``AF\\_2\"$>$Observatoire Midi-Pyrenees$<$/AF$>$ \\\\\n $<$AF ident=``AF\\_3\"$>$Durham, Univ.$<$/AF$>$ \\\\\n $<$AF ident=``AF\\_4\"$>$Barcelona, Univ.$<$/AF$>$ \\\\\n$<$/AFFILIATIONS$>$ \\\\\n$<$MSTRING$>$Royal Astronomical Society, Monthly Notices, vol. 295, p. 75$<$/MSTRING$>$ \\\\\n$<$MONOGRAPH$>$ \\\\\n $<$MTITLE$>$Royal Astronomical Society, Monthly Notices$<$/MTITLE$>$ \\\\\n $<$VOLUME$>$295$<$/VOLUME$>$ \\\\\n$<$/MONOGRAPH$>$ \\\\\n$<$PAGE$>$75$<$/PAGE$>$ \\\\\n$<$PUBDATE$>$ \\\\\n $<$YEAR$>$1998$<$/YEAR$>$ \\\\\n $<$MONTH$>$03$<$/MONTH$>$ \\\\\n$<$/PUBDATE$>$ \\\\\n{\\bf $<$CATEGORIES$>$ \\\\\n $<$CA$>$Astrophysics$<$/CA$>$ \\\\\n$<$CATEGORIES$>$ \\\\\n$<$BIBCODE$>$1998MNRAS.295...75E$<$/BIBCODE$>$ \\\\\n$<$BIBTYPE$>$article$<$/BIBTYPE$>$ \\\\\n$<$IDENTIFIERS$>$ \\\\\n $<$ID type=``ACCNO\"$>$A98-51106$<$/ID$>$ \\\\\n$<$/IDENTIFIERS$>$} \\\\\n{\\bf $<$KEYWORDS system=``STI\"$>$ \\\\\n$<$KW$>$GRAVITATIONAL LENSES$<$/KW$>$ \\\\\n$<$KW$>$RED SHIFT$<$/KW$>$ \\\\\n$<$KW$>$HUBBLE SPACE TELESCOPE$<$/KW$>$ \\\\\n$<$KW$>$GALACTIC CLUSTERS$<$/KW$>$ \\\\\n$<$KW$>$ASTRONOMICAL SPECTROSCOPY$<$/KW$>$ \\\\\n$<$KW$>$MASS DISTRIBUTION$<$/KW$>$ \\\\\n$<$KW$>$SPECTROGRAPHS$<$/KW$>$ \\\\\n$<$KW$>$PREDICTION ANALYSIS TECHNIQUES$<$/KW$>$ \\\\\n$<$KW$>$ASTRONOMICAL PHOTOMETRY$<$/KW$>$ \\\\\n$<$/KEYWORDS$>$} \\\\\n$<$ABSTRACT$>$ \\\\\nWe present deep spectroscopic measurements of 18 distant field galaxies\nidentified as gravitationally lensed arcs in a Hubble Space Telescope\nimage of the cluster Abell 2218. Redshifts of these objects were\npredicted by Kneib et al. using a lensing analysis constrained by the\nproperties of two bright arcs of known redshift and other multiply\nimaged sources. The new spectroscopic identifications were obtained\nusing long exposures with the LDSS-2 spectrograph on the William\nHerschel Telescope, and demonstrate the capability of that instrument to\nreach new limits, R = 24; the lensing magnification implies true source\nmagnitudes as faint as R = 25. Statistically, our measured redshifts are\nin excellent agreement with those predicted from Kneib et al.'s lensing\nanalysis, and this gives considerable support to the redshift\ndistribution derived by the lensing inversion method for the more\nnumerous and fainter arclets extending to R = 25.5. We explore the\nremaining uncertainties arising from both the mass distribution in the\ncentral regions of Abell 2218 and the inversion method itself, and\nconclude that the mean redshift of the faint field population at R =\n25.5 (B = 26-27) is low, (z = 0.8-1). We discuss this result in the\ncontext of redshift distributions estimated from multicolor photometry.\\\\\n$<$\\/ABSTRACT$>$ \\\\\n$<$/BIBRECORD$>$ \\\\\n\n\\noindent\n$<$BIBRECORD origin=``MNRAS\"$>$ \\\\\n$<$TITLE$>$Spectroscopic confirmation of redshifts \npredicted by gravitational lensing$<$/TITLE$>$ \\\\\n{\\bf $<$AUTHORS$>$ \\\\\n $<$AU AF=``1\"$>$ \\\\\n $<$FNAME$>$Tim$<$/FNAME$>$ \\\\\n $<$LNAME$>$Ebbels$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``1\" EM=``1\"$>$ \\\\\n $<$FNAME$>$Richard$<$/FNAME$>$ \\\\\n $<$LNAME$>$Ellis$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``2\"$>$ \\\\\n $<$FNAME$>$Jean-Paul$<$/FNAME$>$ \\\\\n $<$LNAME$>$Kneib$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``2\"$>$ \\\\\n $<$FNAME$>$Jean-Fran\\çois$<$/FNAME$>$ \\\\\n $<$LNAME$>$LeBorgne$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``2\"$>$ \\\\\n $<$FNAME$>$Roser$<$/FNAME$>$ \\\\\n $<$LNAME$>$Pell\\ó$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``3\"$>$ \\\\\n $<$FNAME$>$Ian$<$/FNAME$>$ \\\\\n $<$LNAME$>$Smail$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``4\"$>$ \\\\\n $<$FNAME$>$Blai$<$/FNAME$>$ \\\\\n $<$LNAME$>$Sanahuja$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n$<$/AUTHORS$>$ \\\\\n$<$AFFILIATIONS$>$ \\\\\n $<$AF ident=``AF\\_1\"$>$Institute of Astronomy, Madingley Road, Cambridge CB3 0HA$<$/AF$>$ \\\\\n $<$AF ident=``AF\\_2\"$>$Observatoire Midi-Pyr\\én\\ées, 14 Avenue E. Belin$<$/AF$>$ \\\\\n $<$AF ident=``AF\\_3\"$>$Department of Physics, University of Durham, South Road, Durham DH1 3LE$<$/AF$>$ \\\\\n $<$AF ident=``AF\\_4\"$>$Departament d\\'Astronomia i Meteorologia, Universitat de Barcelona, Diagonal 648, 08028 Barcelona, Spain$<$/AF$>$ \\\\\n$<$/AFFILIATIONS$>$ \\\\\n$<$EMAILS$>$ \\\\\n $<$EM ident=``EM\\_1\"$>$rse$@$ast.cam.ac.uk$<$/EM$>$ \\\\\n$<$/EMAILS$>$ \\\\\n$<$MSTRING$>$Monthly Notices of the Royal Astronomical Society, Volume 295, Issue 1, pp. 75-91.$<$/MSTRING$>$ \\\\\n$<$MONOGRAPH$>$ \\\\\n $<$MTITLE$>$Monthly Notices of the Royal Astronomical Society$<$/MTITLE$>$ \\\\\n $<$MTITLE$>$Monthly Notices of the Royal Astronomical Society$<$/MTITLE$>$ \\\\\n $<$VOLUME$>$295$<$/VOLUME$>$ \\\\\n $<$ISSUE$>$1$<$/ISSUE$>$ \\\\\n$<$/MONOGRAPH$>$ \\\\\n$<$PAGE$>$75$<$/PAGE$>$ \\\\\n$<$LPAGE$>$91$<$/LPAGE$>$ \\\\\n$<$PUBDATE$>$ \\\\\n $<$YEAR$>$1998$<$/YEAR$>$ \\\\\n $<$MONTH$>$03$<$/MONTH$>$ \\\\\n$<$/PUBDATE$>$ \\\\\n$<$COPYRIGHT$>$1998: The Royal Astronomical Society$<$/COPYRIGHT$>$} \\\\ \n$<$BIBCODE$>$1998MNRAS.295...75E$<$/BIBCODE$>$ \\\\\n$<$KEYWORDS system=``AAS\"$>$ \\\\\n $<$KW$>$GALAXIES: CLUSTERS: INDIVIDUAL: ABELL 2218$<$/KW$>$ \\\\\n $<$KW$>$GALAXIES: EVOLUTION$<$/KW$>$ \\\\\n $<$KW$>$COSMOLOGY: OBSERVATIONS$<$/KW$>$ \\\\\n $<$KW$>$GRAVITATIONAL LENSING$<$/KW$>$ \\\\\n$<$/KEYWORDS$>$ \\\\\n{\\bf $<$ABSTRACT$>$ \\\\\nWe present deep spectroscopic measurements of 18 distant field galaxies\nidentified as gravitationally lensed arcs in a Hubble Space Telescope\nimage of the cluster Abell2218. Redshifts of these objects were\npredicted by Kneib et al. using a lensing analysis constrained by the\nproperties of two bright arcs of known redshift and other multiply\nimaged sources. The new spectroscopic identifications were obtained\nusing long exposures with the LDSS-2 spectrograph on the William\nHerschel Telescope, and demonstrate the capability of that instrument to\nreach new limits, R\\≃24 the lensing magnification implies true source\nmagnitudes as faint as R\\≃25. Statistically, our measured redshifts are\nin excellent agreement with those predicted from Kneib et al.'s lensing\nanalysis, and this gives considerable support to the redshift\ndistribution derived by the lensing inversion method for the more\nnumerous and fainter arclets extending to R\\≃25.5. We explore the\nremaining uncertainties arising from both the mass distribution in the\ncentral regions of Abell2218 and the inversion method itself, and\nconclude that the mean redshift of the faint field population at R\\≃25.5\n(B\\∼26\\–27) is low, \\⟨z\\⟩=0.8\\–1. We discuss this result \nin the context of redshift distributions estimated from multicolour photometry. \nAlthough such comparisons are not straightforward, we suggest that photometric\ntechniques may achieve a reasonable level of agreement, particularly\nwhen they include near-infrared photometry with discriminatory\ncapabilities in the 1\\<z\\<2 range. \\\\\n$<$/ABSTRACT$>$} \\\\\n$<$/BIBRECORD$>$ \\\\\n\n\\noindent\n$<$BIBRECORD origin=``SIMBAD\"$>$ \\\\\n$<$TITLE$>$Spectroscopic confirmation of redshifts \npredicted by gravitational lensing.$<$/TITLE$>$ \\\\\n$<$AUTHORS$>$ \\\\\n $<$AU$>$ \\\\\n $<$FNAME$>$T.$<$/FNAME$>$ \\\\\n $<$LNAME$>$Ebbels$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU$>$ \\\\\n $<$FNAME$>$R.$<$/FNAME$>$ \\\\\n $<$LNAME$>$Ellis$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU$>$ \\\\\n $<$FNAME$>$J.-P.$<$/FNAME$>$ \\\\\n $<$LNAME$>$Kneib$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU$>$ \\\\\n $<$FNAME$>$J.-F.$<$/FNAME$>$ \\\\\n $<$LNAME$>$LeBorgne$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU$>$ \\\\\n $<$FNAME$>$R.$<$/FNAME$>$ \\\\\n $<$LNAME$>$Pell\\ó$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU$>$ \\\\\n $<$FNAME$>$I.$<$/FNAME$>$ \\\\\n $<$LNAME$>$Smail$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU$>$ \\\\\n $<$FNAME$>$B.$<$/FNAME$>$ \\\\\n $<$LNAME$>$Sanahuja$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n$<$/AUTHORS$>$ \\\\\n$<$MSTRING$>$Mon. Not. R. Astron. Soc., 295, 75-91 (1998)$<$/MSTRING$>$ \\\\\n$<$MONOGRAPH$>$ \\\\\n $<$MTITLE$>$Mon. Not. R. Astron. Soc.$<$/MTITLE$>$ \\\\\n $<$VOLUME$>$295$<$/VOLUME$>$ \\\\\n$<$MONOGRAPH$>$ \\\\\n$<$PAGE$>$75$<$/PAGE$>$ \\\\\n$<$LPAGE$>$91$<$/LPAGE$>$ \\\\\n$<$PUBDATE$>$ \\\\\n $<$YEAR$>$1998$<$/YEAR$>$ \\\\\n $<$MONTH$>$03$<$/MONTH$>$ \\\\\n$<$/PUBDATE$>$ \\\\\n$<$BIBCODE$>$1998MNRAS.295...75E$<$/BIBCODE$>$ \\\\\n$<$/BIBRECORD$>$ \\\\\n$<$/ADS\\_BIBALL$>$ \\\\\n\n\\section {\\label {appendixc}}\n\nAn example of an extracted text file from the ADS Abstract Service showing \nonly the preferred instances of each field in XML markup for same bibliographic entry listed in Appendix B.\n\n\\noindent\n$<$?xml version=``1.0\"?$>$ \\\\\n$<$!DOCTYPE ADS\\_ABSTRACT SYSTEM ``ads.dtd\"$>$ \\\\\n$<$ADS\\_ABSTRACT$>$ \\\\\n\n\\noindent\n$<$TITLE$>$Spectroscopic confirmation of redshifts \npredicted by gravitational lensing$<$/TITLE$>$ \\\\\n$<$AUTHORS$>$ \\\\\n $<$AU AF=``1\"$>$ \\\\\n $<$FNAME$>$Tim$<$/FNAME$>$ \\\\\n $<$LNAME$>$Ebbels$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``1\" EM=``1\"$>$ \\\\\n $<$FNAME$>$Richard$<$/FNAME$>$ \\\\\n $<$LNAME$>$Ellis$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``2\"$>$ \\\\\n $<$FNAME$>$Jean-Paul$<$/FNAME$>$ \\\\\n $<$LNAME$>$Kneib$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``2\"$>$ \\\\\n $<$FNAME$>$Jean-Fran\\çois$<$/FNAME$>$ \\\\\n $<$LNAME$>$LeBorgne$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``2\"$>$ \\\\\n $<$FNAME$>$Roser$<$/FNAME$>$ \\\\\n $<$LNAME$>$Pell\\ó$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``3\"$>$ \\\\\n $<$FNAME$>$Ian$<$/FNAME$>$ \\\\\n $<$LNAME$>$Smail$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n $<$AU AF=``4\"$>$ \\\\\n $<$FNAME$>$Blai$<$/FNAME$>$ \\\\\n $<$LNAME$>$Sanahuja$<$/LNAME$>$ \\\\\n $<$/AU$>$ \\\\\n$<$/AUTHORS$>$ \\\\\n$<$AFFILIATIONS$>$ \\\\\n $<$AF ident=``AF\\_1\"$>$Institute of Astronomy, Madingley Road, Cambridge CB3 0HA$<$/AF$>$ \\\\\n $<$AF ident=``AF\\_2\"$>$Observatoire Midi-Pyr\\én\\ées, 14 Avenue E. Belin$<$/AF$>$ \\\\\n $<$AF ident=``AF\\_3\"$>$Department of Physics, University of Durham, South Road, Durham DH1 3LE$<$/AF$>$ \\\\\n $<$AF ident=``AF\\_4\"$>$Departament d\\'Astronomia i Meteorologia, Universitat de Barcelona, Diagonal 648, 08028 Barcelona, Spain$<$/AF$>$ \\\\\n$<$/AFFILIATIONS$>$ \\\\\n$<$EMAILS$>$ \\\\\n $<$EM ident=``EM\\_1\"$>$rse$@$ast.cam.ac.uk$<$/EM$>$ \\\\\n$<$/EMAILS$>$ \\\\\n$<$MSTRING$>$Monthly Notices of the Royal Astronomical Society, Volume 295, Issue 1, pp. 75-91.$<$/MSTRING$>$ \\\\\n$<$MONOGRAPH$>$ \\\\\n $<$MTITLE$>$Monthly Notices of the Royal Astronomical Society$<$/MTITLE$>$ \\\\\n $<$VOLUME$>$295$<$/VOLUME$>$ \\\\\n $<$ISSUE$>$1$<$/ISSUE$>$ \\\\\n$<$/MONOGRAPH$>$ \\\\\n$<$PAGE$>$75$<$/PAGE$>$ \\\\\n$<$LPAGE$>$91$<$/LPAGE$>$ \\\\\n$<$PUBDATE$>$ \\\\\n $<$YEAR$>$1998$<$/YEAR$>$ \\\\\n $<$MONTH$>$03$<$/MONTH$>$ \\\\\n$<$/PUBDATE$>$ \\\\\n$<$CATEGORIES$>$ \\\\\n $<$CA$>$Astrophysics$<$/CA$>$ \\\\\n$<$CATEGORIES$>$ \\\\\n$<$COPYRIGHT$>$1998: The Royal Astronomical Society$<$/COPYRIGHT$>$ \\\\ \n$<$IDENTIFIERS$>$ \\\\\n $<$ID type=``ACCNO\"$>$A98-51106$<$/ID$>$ \\\\\n$<$/IDENTIFIERS$>$ \\\\\n$<$ORIGINS$>$ \\\\\n $<$OR$>$STI$<$/OR$>$ \\\\\n $<$OR$>$MNRAS$<$/OR$>$ \\\\\n $<$OR$>$SIMBAD$<$/OR$>$ \\\\\n$<$/ORIGINS$>$ \\\\\n$<$BIBCODE$>$1998MNRAS.295...75E$<$/BIBCODE$>$ \\\\\n$<$BIBTYPE$>$article$<$/BIBTYPE$>$ \\\\\n$<$KEYWORDS SYSTEM=``STI\"$>$ \\\\\n $<$KW$>$GRAVITATIONAL LENSES$<$/KW$>$ \\\\\n $<$KW$>$RED SHIFT$<$/KW$>$ \\\\\n $<$KW$>$HUBBLE SPACE TELESCOPE$<$/KW$>$ \\\\\n $<$KW$>$GALACTIC CLUSTERS$<$/KW$>$ \\\\\n $<$KW$>$ASTRONOMICAL SPECTROSCOPY$<$/KW$>$ \\\\\n $<$KW$>$MASS DISTRIBUTION$<$/KW$>$ \\\\\n $<$KW$>$SPECTROGRAPHS$<$/KW$>$ \\\\\n $<$KW$>$PREDICTION ANALYSIS TECHNIQUES$<$/KW$>$ \\\\\n $<$KW$>$ASTRONOMICAL PHOTOMETRY$<$/KW$>$ \\\\\n$<$/KEYWORDS$>$ \\\\\n$<$KEYWORDS SYSTEM=``AAS\"$>$ \\\\\n $<$KW$>$GALAXIES: CLUSTERS: INDIVIDUAL: ABELL 2218$<$/KW$>$ \\\\\n $<$KW$>$GALAXIES: EVOLUTION$<$/KW$>$ \\\\\n $<$KW$>$COSMOLOGY: OBSERVATIONS$<$/KW$>$ \\\\\n $<$KW$>$GRAVITATIONAL LENSING$<$/KW$>$ \\\\\n$<$/KEYWORDS$>$ \\\\\n$<$ABSTRACT$>$ \\\\\nWe present deep spectroscopic measurements of 18 distant field galaxies\nidentified as gravitationally lensed arcs in a Hubble Space Telescope\nimage of the cluster Abell2218. Redshifts of these objects were\npredicted by Kneib et al. using a lensing analysis constrained by the\nproperties of two bright arcs of known redshift and other multiply\nimaged sources. The new spectroscopic identifications were obtained\nusing long exposures with the LDSS-2 spectrograph on the William\nHerschel Telescope, and demonstrate the capability of that instrument to\nreach new limits, R\\≃24 the lensing magnification implies true source\nmagnitudes as faint as R\\≃25. Statistically, our measured redshifts are\nin excellent agreement with those predicted from Kneib et al.'s lensing\nanalysis, and this gives considerable support to the redshift\ndistribution derived by the lensing inversion method for the more\nnumerous and fainter arclets extending to R\\≃25.5. We explore the\nremaining uncertainties arising from both the mass distribution in the\ncentral regions of Abell2218 and the inversion method itself, and\nconclude that the mean redshift of the faint field population at R\\≃25.5\n(B\\∼26\\–27) is low, \\⟨z\\⟩=0.8\\–1. We discuss this result \nin the context of redshift distributions estimated from multicolour photometry. \nAlthough such comparisons are not straightforward, we suggest that photometric\ntechniques may achieve a reasonable level of agreement, particularly\nwhen they include near-infrared photometry with discriminatory\ncapabilities in the 1\\<z\\<2 range. \\\\\n$<$/ABSTRACT$>$ \\\\\n$<$/ADS\\_ABSTRACT$>$ \\\\\n\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002103.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Abt 1994]{1994PASP..106.1015A} Abt, H. A. 1994, PASP, 106, 1015 \n\n\\bibitem[Abt 1995]{1995ApJ...455..407A} Abt, H. A. 1995, ApJ, 455, 407 \n\n\\bibitem [Accomazzi et al. 2000]{aa} Accomazzi, A., Eichhorn, G.,\nGrant, C.S., Kurtz, M.J., \\& Murray, S.S. 2000, (this issue)\n\n\\bibitem [Accomazzi et al. 1999]{adass8} Accomazzi, A., Eichhorn, G.,\nKurtz, M.J., Grant, C.S., \\& Murray, S.S. 1998, ASP Conf. Ser. 172:\nAstronomical Data Analysis Software and Systems VIII, 291\n\n\\bibitem[American Astronomical Society 1999]{aas} American Astronomical\nSociety Manuscript Preparation, 1999, \nhttp://www.journals.uchicago.edu/AAS/AASTeX\n\n\\bibitem[Boyce 1998]{1998lisa.conf..107B} Boyce, Peter B. 1998,\nASP Conf. Ser. 153: Library and Information Services in Astronomy III, 107\n\n\\bibitem[Boyce \\& Biemesderfer 1996]{1996adass...5..547B} Boyce, P.B. \\& \nBiemesderfer, C. 1996, ASP Conf. Ser. 101: Astronomical Data Analysis Software and \nSystems V, 547 \n\n\\bibitem[Egret \\& Wenger 1988]{1988alds.proc..323E} Egret, D. \\&\nWenger, M. 1988, ESO Conf. \\#28: Astronomy from Large Databases, eds F. Murtagh and A. Heck, 323\n\n\\bibitem[Eichhorn et al. 2000]{gei} Eichhorn, G., Kurtz, M.J.,\nAccomazzi, A., Grant, C.S., \\& Murray, S.S. 2000, (this issue)\n\n\\bibitem[Goldfarb \\& Rubinsky 1991]{goldfarb} Goldfarb, Charles F. \\& Rubinsky,\nYuri, 1991, The Sgml Handbook (Clarendon Press)\n\n\\bibitem[Harold 1999]{harold} Harold, Elliotte Rusty, 1998, Xml: Extensible\nMarkup Language (IDG Books Worldwide)\n\n\\bibitem[Helou \\& Madore 1988]{1988alds.proc..335H} Helou, G. \\&\nMadore, B. 1988, ESO Conf. \\#28: Astronomy from Large Databases, eds F. Murtagh and A. Heck, 335\n\n\\bibitem[International Organization for Standardization 1987]{iso} International\nOrganization for Standardization 1987, Information and Processing --- 8--bit Single--byte Coded Graphic Character Sets (Geneva)\n\n\\bibitem[Jacobsen 1996]{jacobs} Jacobsen, Dana, 1996,\nhttp://www.ecst.csuchico.edu/\\-\\~{}jacobsd/bib/formats/refer.html\n\n\\bibitem[Knuth 1984]{knuth} Knuth, Donald E. 1984, The TeXbook (Addison-Wesley\nPublishing Co.)\n\n\\bibitem[Kurtz et al. 2000]{kurtz} Kurtz, M.J., Eichhorn, G., \nAccomazzi, A., Grant, C.S., Murray, S.S., \\& Watson, J.M. 2000, (this issue)\n\n\\bibitem[Lamport 1986]{lamport} Lamport, Leslie 1986,\nLaTex : A Documentation Preparation System (Addison-Wesley Publishing Co.)\n\n\\bibitem[Lee et al. 1999]{lee} Lee, J., Dubin, D.S., Kurtz, M.J. 1999,\nASP Conf. Ser. 172: Astronomical Data Analysis Software and Systems VIII, 287\n\n\\bibitem[Los Alamos National Laboratory 1991]{lanl} Los Alamos National Laboratory 1991,\nhttp://xxx.lanl.gov\n\n\\bibitem[Powell \\& Whitworth 1998]{powell} Powell, Thomas A. \\& Whitworth, Dan,\n1998, Html: Programmer's Reference (Osborne McGraw-Hill)\n\n\\bibitem[Schmadel 1979]{1979BICDS..17....2S} Schmadel, L. D. 1979, \nBulletin d'Information du Centre de Donn\\'ees Stellaires, 17, 2 \n\n\\bibitem[Schmadel 1982]{1982adra.proc..159S} Schmadel, L. D. 1982, \nIAU Colloq. 64: Automated Data Retrieval in Astronomy, 159\n\n\\bibitem[Schmadel 1989]{1989lisa.conf...77S} Schmadel, L. D. 1989, \nASP Conf. Ser. 153: Library and Information Services in Astronomy III, 77 \n\n\\bibitem[Schmitz et al. 1995]{1995VA.....39R.272S} Schmitz, M., Helou, G., \nDubois, P., Lague, C., Madore, B., Corwin, H.G.J., \\& Lesteven, S. 1995, \nVistas in Astronomy, 39, 272 \n\n\\bibitem[Schulman et al. 1997]{1997PASP..109.1278S} Schulman, E., French, \nJ.C., Powell, A.L., Eichhorn, G., Kurtz, M.J., \\& Murray, S.S. 1997, PASP, \n109, 1278 \n\n\\bibitem[Unicode Consortium 1996]{unicode} Unicode Consortium 1996, \nThe Unicode Standard : Version 2.0 (Addison-Wesley Pub Co.)\n\n\\bibitem[van Steenberg 1992]{vansteen92} van Steenberg, M. 1992, \nDesktop Publishing in Astronomy \\& Space Sciences, ed. A. Heck \n(Singapore, World Scientific), 143\n\n\\bibitem[van Steenberg et al. 1992]{vansteen92al} van Steenberg, M., \nGass, J., Brotzman, L.E., Warnock, A., Kovalsky, D., \\& Giovane, F. \n1992, Newsletter of the American Astronomical Society, 62, 11\n\n\\bibitem[Wall \\& Schwartz 1991]{wall91} Wall, Larry \\& Schwartz, Randal L. 1991, Programming PERL (O'Reilly \\& Associates, Inc.)\n\n\\bibitem[Warnock et al. 1992]{warnock92} Warnock, A., Gass, J., \nBrotzman, L.E., van Steenberg, M.E., Kovalsky, D., \\& Giovane, F. \n1992, Newsletter of the American Astronomical Society, 62, 10 \n\n\\bibitem[Warnock et al. 1993]{1993adass...2..137W} Warnock, A., van \nSteenberg, M.E., Brotzman, L.E., Gass, J.E., Kovalsky, D., \\& Giovane, \nF. 1993, ASP Conf. Ser. 52: Astronomical Data Analysis Software and Systems \nII, 137 \n\n\\end{thebibliography}"
}
] |
astro-ph0002104
|
The NASA Astrophysics Data System: Overview
|
[
{
"author": "M. J. Kurtz"
},
{
"author": "G. Eichhorn"
},
{
"author": "A. Accomazzi"
},
{
"author": "C. Grant"
},
{
"author": "S. S. Murray"
},
{
"author": "J. M. Watson"
}
] |
The NASA Astrophysics Data System Abstract Service has become a key component of astronomical research. It provides bibliographic information daily, or near daily, to a majority of astronomical researchers worldwide. We describe the history of the development of the system and its current status. Urania (\cite{1996AAS...189.0603B}), and the ADS role in the emerging electronic astronomical data environment are discussed. Astronomy is unique in that it already has a fully functional data resource, where several of the most important data sources exist on-line and inter-operate nearly seamlessly. The ADS and the Strasbourg Data Center (CDS; \cite{1998adass...7..470G}) form the core of this resource. We show several examples of how to use the ADS, and we show how ADS use has increased as a function of time. Currently it is still increasing exponentially, with a doubling time for number of queries of 17 months. Using the ADS logs we make the first detailed model of how scientific journals are read as a function of time since publication. We find four distinct components. We directly compare the readership rate with the citation rate for scientific articles as a function of age. Citations generally follow reads, but there are some differences. The main journals of astronomy have differences in the ways they are read and cited. We discuss these from a number of different aspects. The impact of the ADS on astronomy can be calculated after making some simple assumptions. We find that the ADS increases the efficiency of astronomical research by 333 Full Time Equivalent (2000 hour) research years per year, and that the value of the early development of the ADS for astronomy, compared with waiting for mature technologies to be adopted, is 2332 FTE research years. A full technical description of the ADS is in three companion articles: \cite{gei}, \cite{aa}, and \cite{csg}. The ADS is available at http://adswww.harvard.edu/. \keywords{ methods: data analysis -- databases: misc -- publications: bibliography -- sociology of astronomy}
|
[
{
"name": "ADS_overview.tex",
"string": "\\documentclass[]{aa}\n\\usepackage{graphics}\n\n\\newcommand{\\simless}{\\stackrel{\\scriptstyle <}{\\scriptstyle \\sim}}\n\\newcommand{\\simgreat}{\\stackrel{\\scriptstyle >}{\\scriptstyle \\sim}}\n\n\n\n\n\\begin {document}\n\\title{The NASA Astrophysics Data System: Overview}\n\n\\thesaurus{04(04.01.1)}\n\\author{M. J. Kurtz\\and G. Eichhorn\\and A. Accomazzi\\and C. Grant\n\\and S. S. Murray\\and J. M. Watson}\n\\institute{Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138}\n\n\\offprints{M. J. Kurtz}\n\\mail{M. J. Kurtz}\n\n\\date{Received / Accepted}\n\n\\titlerunning{ADS: Overview}\n\\authorrunning{M. J. Kurtz et al.}\n\n\\maketitle\n\n\\sloppy\n\n\\begin {abstract}\n\nThe NASA Astrophysics Data System Abstract Service has become a key\ncomponent of astronomical research. It provides bibliographic\ninformation daily, or near daily, to a majority of astronomical\nresearchers worldwide.\n\nWe describe the history of the development of the system and its\ncurrent status. Urania (\\cite{1996AAS...189.0603B}), and the ADS role\nin the emerging electronic astronomical data environment are\ndiscussed. Astronomy is unique in that it already has a fully\nfunctional data resource, where several of the most important data\nsources exist on-line and inter-operate nearly seamlessly. The ADS\nand the Strasbourg Data Center (CDS; \\cite{1998adass...7..470G}) form\nthe core of this resource.\n\nWe show several examples of how to use the ADS, and we show how ADS use\nhas increased as a function of time. Currently it is still increasing\nexponentially, with a doubling time for number of queries of 17\nmonths.\n\nUsing the ADS logs we make the first detailed model of how scientific\njournals are read as a function of time since publication. We find\nfour distinct components. We directly compare the readership rate\nwith the citation rate for scientific articles as a function of age.\nCitations generally follow reads, but there are some differences.\n\nThe main journals of astronomy have differences in the ways they are\nread and cited. We discuss these from a number of different aspects.\n\nThe impact of the ADS on astronomy can be calculated after making some\nsimple assumptions. We find that the ADS increases the efficiency of\nastronomical research by 333 Full Time Equivalent (2000 hour) research\nyears per year, and that the value of the early development of the ADS for\nastronomy, compared with waiting for mature technologies to be\nadopted, is 2332 FTE research years.\n\nA full technical description of the ADS is in three companion\narticles: \\cite{gei}, \\cite{aa}, and \\cite{csg}. The ADS is available\nat http://adswww.harvard.edu/.\n\n\n\\keywords{ methods: data analysis -- databases: misc -- publications:\nbibliography -- sociology of astronomy}\n\\end{abstract}\n\n\n\\section {\\label {intro} Introduction}\n\nThe NASA Astrophysics Data System Abstract Service (hereafter ADS,\nexcept in section \\ref {history}) is now a central facility of\nbibliographic research in astronomy. In a typical month (March\n1999) it is used by more than 20,000 individuals, who make $\\sim$\n580,000 queries, retrieve $\\sim$ 10,000,000 bibliographic entries, read\n$\\sim$ 400,000 abstracts and $\\sim$ 110,000 articles, consisting of\n$\\sim$ 1,100,000 pages. The ADS is a key element in the emerging\ndigital information resource for astronomy, which has been dubbed\nUrania (\\cite{1996AAS...189.0603B}). The ADS is tightly\ninterconnected with the major journals of astronomy, and the major\ndata centers.\n\nThe present paper serves as an introduction to the system, a\ndescription of its history, current status, use, capabilities, and\ngoals. Detailed descriptions of the ADS system are in the\ncompanion papers: The design and use of the search engine is in\n\\cite {gei}; hereafter SEARCH. The architecture, indexing system, and\nmirror maintenance is in \\cite {aa}; hereafter ARCHITECTURE. Finally\nthe methods we use to maintain and update the data base, and to\nmaintain communication with our collaborating data centers and\njournals (primarily via bibcodes, \\cite{1995VA.....39R.272S}) is in\n\\cite {csg}; hereafter DATA.\n\nIn section \\ref {history} we discuss the history of the ADS, paying\nparticular note of the persons and events which were most important to\nits development. Section \\ref {status} briefly discusses the current\nstatus of the system, the data it contains, and the hardware,\nsoftware, and organizational methods we use to maintain and distribute\nthese data. Urania, and especially the ADS role in it, is discussed\nin section \\ref {Urania}. The current capabilities and use of the\nsystem are shown in section \\ref {use}; with section \\ref {examples}\nshowing example queries, and section \\ref {stats} showing how ADS use\nhas changed over time. In section \\ref{journals} we show how current\nuse varies as a function of the age of an article and the journal it\nwas published in; in \\ref{read-use} we develop a multi-component model\nwhich accurately describes the whole pattern of article use as a\nfunction of age; in \\ref{cite-use} we compare the similarities and\ndifferences of readership information with citation histories; in\n\\ref{journal-use} we examine several aspects of the readership pattern\nfor the major journals. Finally, in \\ref{impact}, we estimate the\nimpact of the ADS on astronomy.\n\n\\section {\\label {history} Historical Introduction}\n\nThe ADS Abstract Service had its beginnings at the conference\nAstronomy from Large Data-bases, held in Garching in 1987. There\n\\cite {1988alds.proc..143A} discussed the desirability of building a\nnatural language interface to a set of astronomical abstracts\n(Astronomy and Astrophysics Abstracts (A\\&AA) was the model) using\nsoftware from Information Access Systems, Inc. (IAS; E. Busch was the\npresident of IAS). \\cite {1988alds.proc..453W} discussed the existing\nabstract services. At this meeting G. Shaw (who was representing IAS)\nsaw the paper by \\cite {1988alds.proc..113K}, and noticed that the\nvector space classification methods developed by M.\\ J.\\ Kurtz for the\nnumerical classification of stellar spectra were very similar to those\ndeveloped by P.\\ G.\\ \\cite{1966MBR.....1..479O} for the classification\n(and thus natural language indexing) of text. Ossorio's methods were\nthe basis of the proposal by \\cite {1988alds.proc..143A}; Ossorio was\nthe founder of IAS. Shaw suggested Ossorio and Kurtz meet. Also at\nthis conference \\cite{1988alds.proc..489S} presented the NASA plan for\nan astrophysics data system, and Shaw met G.\\ Squibb.\n\nThis meeting of Kurtz and Ossorio took place in January 1988, in\nBoulder, CO. By the end of the meeting it was clear that the\ntechnical difficulties involved in creating an abstract service with a\nnatural language index could be overcome, if the data could become\navailable. A preliminary mathematical solution to the problem was\ndeveloped, under the assumption that A\\&AA would be the source of the\nabstracts. This technique was later called the ``statistical Factor\nSpace'', factor analysis being one of the tools used to create the\nvector space.\n\nOver the next year NASA moved to implement the \\cite\n{1988alds.proc..489S} plan for the establishment of a network based,\ndistributed system for access and management of NASA astrophysics data\nholdings, the Astrophysics Data System. Shaw and Ossorio founded a\nnew company, Ellery Systems, Inc., which obtained the systems\nintegration contract for the ADS. During this time Shaw, Ossorio,\nKurtz, and S.S. Murray all spoke often about the abstract service as\nan integral part of the emerging ADS system, and the abstract service,\nand Factor Space, became nearly synonymous with the ADS project. No\nactual work was done to implement the abstract service during this\ntime, Ossorio and Kurtz worked on applying their vector space\nclassification techniques to galaxy morphologies (\\cite\n{1989daa..conf..121O}, \\cite {1990PaReL..11..507K}), while Murray used\nthe original, non-statistical, Factor Space methods of \\cite\n{1966MBR.....1..479O} to build a small ($\\sim$40 documents) natural\nlanguage indexing system for demonstration purposes.\n\nDuring the next three years the ADS was built\n(\\cite{1992adass...1...35G}), but without a literature retrieval\nservice, which was listed as a future development. No NASA funds were\ndevoted to the abstract service during this time. Independently Kurtz\nand Watson set out to obtain the data necessary to build a prototype\nsystem; keyword data was received from the IAU (International\nAstronomical Union) Thesaurus project (\\cite{1992PASAu..10..134S},\n\\cite{1993asth.book.....S}), and from the NASA Scientific and\nTechnical Information (STI) branch (\\cite{1990GIQ.....7..123P}). A\nbreakthrough occurred in mid 1990 when the Astronomische Rechen\nInstitut graciously provided Watson with magnetic tape copies of the\ntwo 1989 volumes of Astronomy and Astrophysics Abstracts. By the end\nof 1990 Kurtz (1991, 1992) had built a prototype abstract retrieval\nsystem, based on the statistical Factor Space.\n\nIn April, 1991 F. Giovane and C. Pilachowski organized a meeting near\nWashington, D.C. on ``On-Line Literature in Astronomy.'' At this\nmeeting \\cite {boy91} discussed the desire of the American\nAstronomical Society (AAS) to publish on-line journals, \\cite {kur91}\ndiscussed the prototype system, and pointed out the types of queries\nwhich would be made possible if a natural language abstract system\nwere combined with the Strasbourg Data Centers's (CDS) SIMBAD\n(\\cite{1988alds.proc..323E}) database and with the Institute for\nScientific Information's Science Citation Index\n(\\cite{1979cita.book.....G}), and \\cite{van91} discussed the desire of\nthe National Space Science Data Center (NSSDC) to create a database of\nscanned bitmaps of journal articles. Also at this meeting were\nrepresentatives of NASA's STI branch, who indicated that they would be\nwilling to provide the abstracts from the STI (often called NASA\nRECON) abstracts database (\\cite{1990GIQ.....7..149W}).\n\nNear the end of the meeting \\cite{mur91} outlined the possibilities\ninherent in the previous talks. He described a networked data system\nwhere a natural language query system for the STI abstracts would work\njointly with the CDS/SIMBAD object name index to point astronomers to\nrelevant abstracts, article bitmaps, and electronic journal articles.\nSave that the World Wide Web (\\cite{ber94}) has taken the place of the\nproprietary network software created for the ADS project by Ellery\nSystems Inc., and that the ADS has taken over responsibility for the\nbitmaps from the NSSDC, the current system is essentially identical to\nthe one predicted by \\cite {mur91}.\n\nFollowing the meeting the NSSDC group (\\cite{1993adass...2..137W})\norganized the STELAR project, which held a series of meetings where\nmany of the issues involved in electronic journals were discussed, and\na consensus was reached on allowed uses of copyrighted journal article\nbitmaps.\n\nIn the spring of 1992 Murray took over the direct management of\nthe ADS project; G. Eichhorn was hired as project manager. The\ndecision was made to proceed forthwith with the development of an\nabstract service based on the STI abstracts. Because the STI abstract\nsystem is differently structured than the A\\&AA system the statistical\nFactor Space was abandoned in favor of a more traditional entropy\nmatching technique (\\cite{sal83}, see SEARCH).\n\nThe new system was working with a static database by fall, and was\nshown at the Astronomical Data Analysis Software and Systems II\nmeeting in Boston (\\cite{1993adass...2..132K}). The production system\nwas released in February 1993, as part of the package of ADS services,\nstill part of the proprietary ADS network system. Abstract Service\nuse quickly became more than half of all ADS use.\n\nBy summer 1993 a connection had been made between the ADS and SIMBAD,\npermitting users to combine natural language subject matter queries\nwith astronomical object name queries (\\cite{1994AAS...184.2802G}).\nThis connection was enabled by the use of the bibcode (see DATA). We\nbelieve this is the first time an internet connection was made to\npermit the routine, simultaneous, real-time interrogation of\ntransatlanticly separated scientific databases.\n\nBy early 1994 The World Wide Web (\\cite{ber94}) had matured to where\nit was possible to make the ADS Abstract Service available via a web\nforms interface; this was released in February. Within five weeks of\nthe initial WWW release use of the Abstract Service quadrupled (from\n400 to 1600 users per month).\n\nBy the end of 1994 the ADS project had again been restructured,\nleaving primarily the WWW based Abstract Service as its principle\nservice. Also the STELAR project at NSSDC ended, and the ADS took\nover responsibility for creating the database of bitmaps.\n\nThe first full article bitmaps, which were of Astrophysical Journal\nLetters articles, were put on-line in December 1994\n(\\cite{1994AAS...185.4104E}). By the summer of 1995 the bitmaps were\ncurrent and complete going back ten years. At that time the\nElectronic ApJ Letters (\\cite{1995AAS...187.3801B}) went on-line.\n>From the start the ADS indexed the EApJL, and pointed to the\nelectronic version. Also from the beginning the reference section of\nthe EApJL pointed (via WWW hyperlinks) to the ADS abstracts for\narticles referenced in the articles; again this was enabled by the use\nof the bibcode.\n\nAlso during this time the NASA STI branch became unable to provide\nabstracts of the journal articles in astronomy. In order to continue\nthe abstract service cooperative arrangements were made with nearly\nevery astronomical research journal, as well as a number of other\nsources of bibliographic information. DATA describes these\narrangements in detail. \n\nThe next year (1996) saw nearly every astronomy journal which had not\nalready joined into collaboration with ADS join. Also in 1996 the\nAmerican Astronomical Society purchased the right to use a subset of\nthe Science Citation Index, and gave these data to ADS\n(\\cite{1996AAS...189.0607K}).\n\n\n\\section{\\label{status} The Current System}\n\nCurrently the ADS system consists of four semi-autonomous (to the\nuser) abstract services covering Astronomy, Instrumentation, Physics,\nand Astronomy Preprints. Combined there are nearly 1.5 million\nabstracts and bibliographic references in the system. The Astronomy\nService is by far the most advanced, and accounts for $\\sim 85$\\%\\ of\nall ADS use; it ought be noted, however, that the Instrumentation\nService contains more abstracts than Astronomy, and a subset of that\nservice is used by the Society of Photo-Optical Industrial Engineers\nas the basis of the official SPIE publications web site.\n\nAll of what follows will refer only to the Astronomy service.\n\n\\subsection{Data}\n\nHere is a brief overview of the data in the ADS system, a complete\ndescription is in DATA.\n\n\\subsubsection{Abstracts}\n\nThe ADS began with the abstracts from the NASA STI database, in\nprinted form these abstracts were the union of the International\nAerospace Abstracts and the NASA Scientific and Technical Abstracts and\nReports (NASA STAR). While the STI branch has had to substantially\ncut back on their abstracting of the journal literature, we still get\nabstracts of NASA reports and other materials from them.\n\nWe now receive basic bibliographic information (title, author, page\nnumber) from essentially every journal of astronomy. Most also send\nus abstracts, and some cannot send abstracts, but allow us to scan\ntheir journals, and we build abstracts through optical character\nrecognition. Finally we receive some abstracts from the editors of\nconference proceedings, and from individual authors.\n\nThe are $\\sim$500,000 different astronomy articles indexed in the ADS,\nthe database is nearly complete for the major journals articles\nbeginning in 1975.\n\n\\subsubsection{Bitmaps}\n\nThe ADS has obtained permission to scan, and make freely available\non-line, page images of the back issues of nearly all of the major\njournals of astronomy. In most cases the bitmaps of current articles\nare put on-line after a waiting period, to protect the financial\nintegrity of the journal. DATA describes the current status of these\nefforts.\n\nWe plan to provide for each collaborating journal, in perpetuity, a\ndatabase of page images (bitmaps) from volume 1 page 1 to the first\nissue which the journal considers to be fully on-line as published.\nThis will provide (along with the indexing and the more recent\narchives held by the journals) a complete electronic digital library\nof the major literature in astronomy. \n\nOn a longer term we plan to scan old observatory reports, and defunct\njournals, to finally have a full historical collection on-line. This\nwork is beginning with a collaboration with the Harvard Preservation\nProject (\\cite{1997AAS...191.3502E}; \\cite{1995VA.....39..161C}).\n\n\\subsubsection{Links}\n\nADS responds to a query with a list of references and a set of\nhyperlinks showing what data is available for each reference. There\nare $\\sim$1.73 million hyperlinks in the ADS, of which\n$\\sim$ 31\\%\\ are to sources external to the ADS project.\n\nThe largest number of external links are to SIMBAD, NED, and the\nelectronic journals. A rapidly growing number, although still small\nin comparison to the others, are to data tables created by the\njournals and maintained by the CDS and the ADC at Goddard. SEARCH\ndescribes the system of hyperlinks in detail.\n\n\\subsubsection{Citations and References}\n\nThe use of citation histories is a well known and effective tool for\nacademic research (\\cite{1979cita.book.....G}); their inclusion in the\nADS has been planned since the conception of the service. In 1996 the\nAAS purchased a subset of the Science Citation Index from the\nInstitute for Scientific Information, to be used in the ADS; this was\nupdated in 1998. This subset only contains references which were\nalready in the ADS, thus it is seriously incomplete in referring to\narticles in the non-astronomical literature. This citation\ninformation currently spans January 1982-September 1998.\n\nThe electronic journals all have machine readable, web accessible,\nreference pages. The ADS points to these with a hyperlink where\npossible. Several publishers allow us to use these to maintain\ncitation histories; we do this using our reference resolver software\n(see ARCHITECTURE). The same software is also used by some publishers\nto check the validity of their references, pre-publication.\n\nAdditionally we use optical character recognition\nto create reference and citation lists for the historical literature,\nafter it is scanned (\\cite{1999AAS...195.8209D}).\n\n\\subsubsection{Collaboration with CDS/SIMBAD}\n\nThe Strasbourg Data Center (CDS) has long maintained several of the\nmost important data services for astronomy\n(e.g. \\cite{1971BICDS...1....2J}; \\cite{1973BICDS...4...27J};\n\\cite{1998adass...7..470G}); access to parts of the CDS data via ADS\nis a key feature of the ADS.\n\nADS users are able to make joint queries of the ADS bibliographic\ndatabase and the CDS/SIMBAD bibliographic data base. When SIMBAD\ncontains information on a object which is referred to in a paper whose\nreference is returned by ADS then ADS also returns a pointer to the\nSIMBAD data. When a paper has a data table which is kept on-line at\nthe CDS the ADS returns a pointer to it. The CDS-ADS collaboration is\nat the heart of Urania (section \\ref{Urania}). More recently ADS has\nentered into a collaboration with the National Extragalactic Database\n(NED; \\cite{1988alds.proc..335H}, \\cite{1992adass...1...47M}) which is\nsimilar to the SIMBAD portion of the CDS-ADS collaboration.\n\n\\subsection {Search Engine}\n\nThe basic design assumption behind the search engine, and other user\ninterfaces, is that the user is an expert astronomer. This differs\nfrom the majority of information retrieval systems, which assume that\nthe user is a librarian. The default behavior of the system is to\nreturn more relevant information, rather than just the most relevant\ninformation, assuming that the user can easily separate the wheat from\nthe chaff. In the language of information retrieval this is favoring\nrecall over precision. SEARCH describes the user interface in detail.\n\n\\subsection{Hardware and Software Architecture}\n\nThe goals of our hardware and software systems are speed of\ninformation delivery to the user, and ease of maintainability for the\nstaff. We thus pre-compute many things during our long indexing\nprocess for later use by the search engine; we have highly optimized\nall code which is run by user processes; we have developed a worldwide\nnetwork of mirror sites to speed up internet access. ARCHITECTURE\ndescribes these systems.\n\n\\subsection {Data Ingest}\n\nThe basic rule for what books and periodicals the ADS covers is: if it is\nin the Center for Astrophysics library it should be in the ADS. As a goal\nwe are still some ways from realization. We have recently adopted a\nsecond rule for inclusion: if it is referenced by an article in a\nmajor scholarly journal of astronomy it should be in the ADS. DATA\ndescribes the ADS coverage, and ingest procedures.\n\n\n\n\\section{\\label{Urania} Urania}\n\nThe idea that the internet could be used to link sources of\nastronomical information into a unified environment is more than a\ndecade old; it was fully expressed in the planning for the old ADS\n(\\cite{1988alds.proc..489S}) and ESIS (\\cite{1988alds.proc..137A})\nprojects. These early attempts were highly data oriented, their\ninitial goals were the interoperability of different distributed data\narchives, primarily of space mission data.\n\nAstronomical data is highly heterogeneous and complex; essentially\nevery instrument has its quirks, and these must be known and dealt\nwith to reduce and analyze the data. This quirky nature of our data\nessentially prevented the establishment of standardized tools for data\naccess across data archives.\n\nThe new, hyperlink connected network data system for astronomy is\nbased on the highest level of data abstraction, object names and\nbibliographic articles, rather than the lowest, the actual observed\ndata in archives. This change in the level of abstraction has\npermitted the creation of a system of extraordinary power. This new\nsystem, still unique amongst the sciences, has been dubbed Urania\n(\\cite{1996AAS...189.0603B}), for the muse of astronomy.\n\nConceptually the core of Urania is a distributed cross-indexed list\nwhich maintains a concordance of data available at different sites.\nThe ADS maintains a list of sites which provide data organized on an\narticle basis for every bibliographic entry in the ADS database. The\nCDS maintains a list of articles and positions on the sky for every\nobject in the SIMBAD database. The CDS also provides a name to object\nresolver. The possibility for synergy in combining these two data\nsystems is obvious; they have functioned jointly since 1993.\n\nSurrounding this core, and tightly integrated with it, are many of the\nmost important data resources in astronomy, including the ADS Abstract\nService, SIMBAD, the fully electronic journals (currently ApJL, ApJ,\nApJS, A\\&A, A\\&AS, AJ, PASP, MNRAS, New Astronomy, Nature, and\nScience), NED, CDS-Vizier, Goddard-ADC, and the ADS Article Service.\nAll these groups actively exchange information with the Urania core,\nthey point their users to it via hyperlinks, and they are pointed to\nby it.\n\nThe astronomy journals which are not yet fully electronic, in that\nthey do not support hyperlinked access to the Urania core, also\ninteract with the system. Typically they provide access to page\nimages of the journal, either through PDF files, or bitmaps from the\nADS Article Service, or both. Bibliographic information is routinely\nsupplied to the ADS, and the SIMBAD librarians routinely include the\narticles (along with those of the electronic journals) in the SIMBAD\nobject-article concordance.\n\nWhile most data archives are not closely connected to the Urania\nsystem there are some exceptions. For example the National Center for\nSupercomputing Application's Astronomy Digital Image Library\n(\\cite{1996adass...5..581P}) connects with the ADS bibliographical\ndata via links which are papers written about the data in the archive.\nSIMBAD connects with the High Energy Astrophysics Science Archive\nResearch Center (HEASARC) (\\cite{1992adass...1...52W}) archive using\nthe position of an object as a search key, HEASARC has an interface\nwhich permits several archives to be simultaneously queried\n\\cite{1998adass...7..481M}, and a new data mining initiative between\nCDS and the European Southern Observatory (ESO)\n(\\cite{1999adass...8..379O}) will connect the Vizier tables with the\nESO archives. Several archives use the SIMBAD (and in some cases NED)\nname resolver to permit users to use object name as a proxy for\nposition on the sky, the Space Telescope Science Institute (STScI)\nDigital Sky Survey (\\cite{1996stsc.rept.....P}) would be an example.\nThe Space Telescope-European Coordinating Facility archive\n(\\cite{mur95}) allows ADS queries using the observing proposals as\nnatural language queries, and the Principal Investigator names as\nauthors.\n\nThe establishment and maintenance of the Urania core represents a\nsubstantial fraction of the ADS service. SEARCH discusses the user\ninterface to the set of hyperlinks, ARCHITECTURE discusses the methods\nand procedures we use to implement and maintain the links, and DATA\ndiscusses the data sharing arrangements we have with other groups, and\npresents a complete listing of all our data sources.\n\n\n\\section{\\label{use} Capabilities, Usage Patterns, and Statistics}\n\n\\subsection{\\label{examples} Examples}\n\nThe ADS answers about 5,000,000 queries per year, covering a wide\nrange of possible query type, from the simplest (and most popular):\n``give me all the papers written by (some author),'' to complex\ncombinations of natural language described subject matter and\nbibliometric information. Each query is essentially the sum of\nsimultaneous queries (e.g. an author query and a title query), where\nthe evidence is combined to give a final relevance ranking\n(e.g. \\cite{1995InPrM..31..431B}).\n\nThe ADS once supported index term (keyword) queries, but does not\ncurrently. This is due to the incompatibility of the old STI\n(\\cite{1988NASAS7069.....N}) keyword system with the keywords assigned\nby the journals (\\cite {1990ApJ...357....1A};\n\\cite{1992A+A...253..A12.}; \\cite{1992MNRAS.259......}) . Work is\nunderway to build a transformation between the two systems\n(\\cite{1999adass...8..287L}; \\cite{1999sigirconf..198L}).\n\nHere we show four examples of simple, but sophisticated queries, to\ngive an indication of what is possible using the system. A detailed\ndescription of available query options is in SEARCH. We encourage the\nreader to perform these queries now, to see how the passage of time\nhas changed the results.\n\nFigure \\ref{m87.query} shows how to make the query ``what papers are\nabout the metallicity of M87 globular clusters?'' This was the first\njoint query made after the SIMBAD-ADS connection was completed in\n1993. \n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF1.eps}}\n\\caption[]{A query to the ADS Abstract Service requesting a listing of papers on the metallicity of M87 globular clusters. SIMBAD, NED, the ADS phrase index, the ADS word index and the ADS synonym list are all queried, the results are combined and the list shown in figure \\ref{m87.out} is returned. }\n\\label{m87.query}\n\\end{figure}\n\t\t\n\n\n\nThere are 1,765 papers on M87 in SIMBAD, NED, or both; there are 6,425\npapers which contain the phrase ``globular cluster'' in ADS, and there\nare 25,599 papers in ADS containing ``metallicity'' or a synonym\n(abundance is an example of a synonym for metallicity). The result,\nwhich comes in a couple of seconds, is a list of just those 58 papers\ndesired.\n\n\nFive different indices are mixed in this query: the SIMBAD\nobject---bibcode index query on M87 is logically OR'd with the NED\nobject---refcode index query for M87. The ADS phrase index query for\n``globular cluster'' is (following the user's request) logically AND'd\nwith the ADS word index query on metallicity, where metallicity is\nreplaced by its group of synonyms from the ADS astronomy synonym list\n(this replacement is under user control). If the user requires a\nperfect match, then the combination of these simultaneous queries\nyields the list of 58 papers shown in figure \\ref{m87.out}. Before\nthe establishment of the Urania core queries like this were nearly\nimpossible.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF2.eps}}\n\\caption[]{The top of the list ADS returns when the query shown in figure \\ref{m87.query} is made. }\n\\label{m87.out}\n\\end{figure}\n\t\t\n\n\nAnother simple, but very powerful method for making ADS queries is to\nuse the ``Find Similar Abstracts'' feature. Essentially this is an\nextension of the ability to make natural language queries, whereby the\nuser can choose one or more abstracts to become the natural language\nquery. This can be especially useful when one wants to read in depth\non a subject, but only knows one or two authors or papers in the\nfield. This is a typical situation for many researchers, but\nespecially for students.\n\nAs an example, suppose one is interested in Ben Bromley's (1994) PhD\nthesis work. Making an author query on ``Bromley'' gets a list of his\npapers, including his thesis. Next one calls up the abstract of the\nthesis, goes to the bottom of the page, where the ``Find Similar\nAbstracts'' feature is found, and clicks the ``Send'' button. Figure\n\\ref{bromley.list} shows the top of the list returned as a result.\nThese are papers listed in order of similarity to Bromley's (1994)\nthesis; note that the thesis itself is on top, as it matches itself\nperfectly. This list is a detailed subject matter selected custom\nbibliography.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF3.eps}}\n\\caption[]{The top of the list of papers returned when Ben Bromley's (1994) thesis is used as the query. }\n\\label{bromley.list}\n\\end{figure}\n\t\t\n\n\n\n\n\nAs a third example of ADS use figure \\ref{bromley.query} shows an\nintermediate step from the previous example (obtained by clicking on\nthe ``Return Query Form'' button, replacing the default ``Return Query\nResults'' in the ``Find Similar Abstracts'' query. Here we make one\nchange from the default setting: we change ``Items returned'' from the\ndefault ``Abstracts'' to ``References.'' The result, shown in figure\n\\ref{bromley.refs} lists all the papers which are referenced in the 50\npapers most like \\cite{1994PhDT........54B}, sorted by the number of\ntimes they appear in the 50 reference lists. Thus the paper by\n\\cite{1986ApJ...304...15B} appears in 21 reference lists out of 50,\nthe paper by \\cite{1983ApJ...267..465D} appears in 11 lists out of 50,\netc. By this means one has a list of the most cited papers within a\nvery narrowly defined subfield specific to one's personal interest. We\nare not aware of any other system which currently allows this\ncapability.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF4.eps}}\n\\caption[]{A query which returns the papers most cited by the 50 papers most like Ben Bromley's (1994) thesis. }\n\\label{bromley.query}\n\\end{figure}\n\t\t\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF5.eps}}\n\\caption[]{The top of the list of papers returned by the query in Figure \\ref{bromley.query}; these are the most cited papers in a user defined very narrow subfield. }\n\\label{bromley.refs}\n\\end{figure}\n\t\t\n\n\n\n\nFinally we show a somewhat more complex query in figure\n\\ref{bromley.query2}. Here we modify the basic query (Bromley's\n(1994) thesis) by requiring that the papers contain the word ``void.''\nWe do this by changing the logic on the text query to ``simple logic''\nand adding ``+void'' to the query. The returned papers to this query\nwould be very similar to those shown in figure \\ref{bromley.list}, but\nwith all papers which do not contain the word ``void'' removed. In\naddition we change ``Items returned'' to be ``Citations,'' and\nincrease the number of papers to get the citations for to the top 150\nclosest matches to the query. The result, shown in figure\n\\ref{bromley.cites}, are those papers which most cite the 150 papers\nmost like Bromley's (1994) thesis, modified by the requirement that\nthey contain the word ``void.'' Thus the paper by\n\\cite{1997ApJ...491..421E} cited 26 papers out of the 150, the paper\nby \\cite{1988ARA&A..26..245R} cited 19, etc. These are the papers\nwith the most extensive discussions of a user defined very narrow\nsubfield. This feature also is unique to the ADS.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF6.eps}}\n\\caption[]{A query which returns the papers which most cite the 150 papers most like Ben Bromley's (1994) thesis, as modified by the requirement that they contain the word ``void.'' }\n\\label{bromley.query2}\n\\end{figure}\n\t\t\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF7.eps}}\n\\caption[]{The top of the list of papers returned by the query in Figure \\ref{bromley.query2}; these are the papers with the most extensive discussions of a user defined very narrow subfield. }\n\\label{bromley.cites}\n\\end{figure}\n\t\t\n\n\n\n\n\n\\subsection{\\label{stats} Use of the System}\n\nIn September 1998 ADS users made 440,000 queries, and\nreceived 8,000,000 bibliographic references, 75,000 full-text\narticles, and 275,000 abstracts (130,000 were individually selected,\nthe rest were obtained through a bulk retrieval process, which\ntypically retrieves between one and fifty), as well as citation\nhistories, links to data, and links to other data centers. Of the\n75,000 full-text articles accessed through the ADS in September 1998,\nalready 33\\%\\ were via pointers to the electronic journals. This\nnumber increased to 52\\%\\ in March 1999.\n\nADS users access and print (either to the screen, or to paper) more\nactual pages than are printed in the press runs of all but the very\nlargest journals of astronomy. In September 1998, 472,621 page images\nwere downloaded from the ADS archive of scanned bitmaps. About 75\\%\\\nof these were sent directly to a printer, 22\\%\\ were viewed on the\ncomputer screen, and 2\\%\\ were downloaded into files; FAXing and\nviewing thumbnail images make up the rest. If the electronic journals\nprovide ``pages'' of information at the same rate as the ADS archive,\nper article accessed (slightly more than 10 pages/article accessed),\nthen more than 750,000 ``pages'' were ``printed,'' on demand, in\nSeptember 1998 by ADS users. This is about three times the number of\nphysical pages published in September 1998 by the {\\it\nPASP}.\n\nViewed as an electronic library the ADS, five years after its\ninception, provides bibliographic information and services similar to\nthose provided by the sum of all the astronomy libraries in the world,\ncombined. The Center for Astrophysics Library, an amalgamation of the\nlibraries of the Harvard College Observatory and the Smithsonian\nAstrophysical Observatory, is one of the largest, most complete, and\nbest managed astronomy libraries in the world. For several years the\nCfA Library has been keeping records of the number of volumes\nreshelved, as a proxy for the number of papers read (library users are\nrequested not to reshelve anything themselves). This number has\nremained steady in recent years, and was 1117 in September 1998\n(D.J. Coletti \\&\\ E.M. Bashinka 1998, personal communication). If the\nCfA represents 2--3\\%\\ of the use of astronomy libraries, worldwide\n(the CfA has slightly more than 350 PhDs, the AAS has about 6800\nmembers, the IAU about 8500, CfA users made 2.4\\%\\ of ADS queries in\nSeptember 1998, 5.7\\%\\ of articles in the ADS Astronomy database with\n1998 publication dates had at least one CfA author), and if other\nastronomers use their libraries at the same rate as astronomers at the\nCfA, then worldwide there would have been 37,000--56,000 reshelves in\nSeptember 1998. In September 1998 ADS provided access to 75,000 full\ntext articles and 130,000 individually selected abstracts, as well as\nsubstantial other information; current use of ADS is clearly similar\nto the sum of all current traditional astronomy library use.\n\nADS use continues to increase. Figure \\ref{num.queries} shows the\nnumber of queries made each month to the ADS Abstract Service from\nApril 1993 to September 1998, the dotted straight line represents a\nyearly doubling, which represents the five year history reasonably\nwell. Since 1996 use has been increasing at a 17 month doubling rate,\nshown by the dashed line in the figure.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF8.eps}}\n\\caption[]{The number of queries made each month to the ADS Abstract service. The dotted line represents a yearly doubling, while the dashed line represents a doubling period of 17 months, a reasonable match to the recent data. }\n\\label{num.queries}\n\\end{figure}\n\t\t\n\n\n\n\n\nIt is difficult to determine the exact number of ADS users. We track\nusage by the number of unique ``cookies''\\footnote{A cookie is a\nunique identifier which WWW providers (in this case ADS) assign to\neach user, and store on the users computer using the browser.} which\naccess ADS, and by the number of unique IP\\footnote{Each Machine on\nthe internet has a unique IP (Internet Protocol) address.} addresses.\nThere are difficulties with each technique. In addition many\nnon-astronomers find ADS through portal sites like Yahoo, which skews\nthe statistics. In September 1998 10,000 unique cookies accessed the\nfull-text articles, 17,000 made queries, and 30,000 visited the site.\n91\\%\\ of full-text users had cookies, but only 65\\%\\ of site visitors.\n\nFigure \\ref{num.users} shows the number of unique users who made a\nquery using the ADS each month from April 1993 to September 1998.\nBefore early 1994 users had user names and passwords in the old,\nproprietary system, and could be counted exactly; after the ADS became\navailable on the WWW users were defined as unique IP addresses. Note\nthe enormous effect the WWW had on ADS use, a factor of four in the\nfirst five weeks. The straight dashed line represents the 17 month\ndoubling period seen recently in the number of queries; the dotted\nline, which better represents the recent growth, is for a 22 month\ndoubling period. The difference between the two is due to a one third\nincrease in the mean number of queries per month per user (from 19 to\n25) since 1996.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF9.eps}}\n\\caption[]{The number of users who made a query queries made each month to the the ADS Abstract Service. The dashed line represents a doubling every 17 months, the dotted line a doubling every 22 months. }\n\\label{num.users}\n\\end{figure}\n\t\t\n\n\n\n\n>From another perspective, the number of unique IP addresses from a\nsingle typical research site (STScI) which access the full-text data\nin a typical month (September 1998) is 107, the number of unique\ncookies associated with stsci.edu which access the full-text data is\n104, the number of unique IP addresses from STScI which make a query\nto ADS is 148 and the number of cookies is 140. The number of AAS\nmembers listing an STScI address is 145 (J. Johnson, personal\ncommunication), and the number of different people listing an STScI\naddress in the Astropersons e-mail compilation\n(\\cite{1995emdw.book.....B}) is 195. Those who access the full-text\naverage one article per day, those who make queries average two per\nday.\n\nWe believe nearly all active astronomy researchers, as well as\nstudents and affiliated professionals use the ADS on a regular basis.\nMost of the recent exponential growth of use of the ADS is due to an\nincreased number of users; this growth cannot last much longer, the\n17,000 who made queries in September 1998 are probably the majority of\nall those who could conceivably want to make a query of the technical\nastronomy literature.\n\n\n\\section{\\label{journals} How the Astronomical Literature is used}\n\nElectronic libraries, because they provide access to the literature on\nan article basis, can provide direct measures of the use of individual\narticles. Direct bibliometric studies of article use are rare, and\ntend to be based on small samples (e.g. \\cite{1998JASIS..49.1283T});\nmost bibliometric studies use indirect measures, particularly citation\nhistories,(e.g. \\cite{1979cita.book.....G};\n\\cite{1989ARIST..24..119W}; \\cite{1993LibT...49..665L}), as proxies\nfor use.\n\nAstronomy is perhaps unique, in that it already has an integrated\nelectronic information resource (ADS/Urania) which includes electronic\naccess to nearly all the modern journal literature, and which is used\nby a large fraction of practitioners in the field, worldwide. The\ncombined Urania logs, including the electronic journals and the ADS,\nprobably represent a fair sample of total readership in the field,\nperhaps even a majority of the readership as well.\n\nIn this section we will investigate the use of the astronomy\nliterature as shown by the ADS logs; for articles more than a few\nmonths past the publication date they probably represent accurately the\nuse of the astronomy literature. For articles immediately after\npublication the logs of the electronic journals are the definitive\nsource; this usage pattern is substantially different from the pattern\nshown in the ADS logs, for example, the half-life for article reads for\nthe electronic {\\it Astrophysical Journal} is measured in days\n(E. Owens, 1997, personal communication).\n\n\\subsection{\\label{read-use} Readership as a Function of Age}\n\nThe ADS logs provide a direct measure on the readership of individual\narticles. There are several different ADS logs, here we will use the\n``data'' log. Entries in the data log correspond to individual data\nitems selected from a list which is returned following a query, such\nas shown in figure \\ref{m87.out}. Each entry is the result of a user,\nwho can see the authors and title of a paper, choosing to get more\ninformation. 61\\%\\ of these requests are for the abstract, 34\\%\\ are\nfor the whole text, 2\\%\\ are for the citation histories, as well as\nseveral other options; SEARCH lists all the options and their use. In\nwhat follows we will refer to any request for data as a ``read.'' By\n``age'' we refer to the time since publication of an article, NOT the\ntime since birth of the astronomer reading the article!\n\nIn this subsection we restrict the study to the January 1999 log, and\nonly requests for information about articles published in the largest\n(in terms of ADS use) eight journals ({\\it ApJ, ApJL, ApJS, A\\&A,\nA\\&AS, MNRAS, AJ, PASP}; hereafter the Big8). The Big8 represent\n62\\%\\ of the 270,000 entries in the January data log.\n\n\nFigure \\ref{raw-use} shows the number of ADS reads (solid line, left\nabscissa) during January 1999 for articles published in the Big8 from\n1976 to 1998, and the number of Big8 articles for which at least one\ndata item was requested (dotted line, right abscissa), on a log-linear\nplot, binned yearly. The ADS database is 100\\%\\ complete in titles,\nand in links to the full text of articles (either to the ADS scans, or\ndirectly to the electronic journals), and is 99\\%\\ complete in article\nabstracts for the Big8 journal articles published during this 22 year\nperiod.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF10.eps}}\n\\caption[]{The use of journal articles via the ADS as a function of age. The ordinate is the publication year. The solid line (left abscissa) shows the total number of reads, the dotted line (right abscissa) shows the total number of different articles for which data was requested. }\n\\label{raw-use}\n\\end{figure}\n\t\t\n\n\n\n\nThe number of papers published in the Big8 has been increasing at\nabout 4\\%\\ per year during this 22 year period\n(\\cite{1997PASP..109.1278S}; \\cite{1998PASP..110..210A}; figure\n\\ref{num.pub}), figure \\ref{norm-use} shows the information in figure\n\\ref{raw-use} divided by the number of papers published. The top line\nshows the mean number of reads per paper, and the bottom line shows\nthe fraction (maximum 1) of papers published for which information was\nrequested.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF11.eps}}\n\\caption[]{The number of Big8 journal articles published per year. The dotted line represents a 3.7\\%\\ yearly increase. }\n\\label{num.pub}\n\\end{figure}\n\t\t\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF12.eps}}\n\\caption[]{The use of journal articles via ADS as a function of age. The ordinate is the publication year. The upper line shows the mean number of reads per paper, the lower line shows the fraction of different articles for which data was requested. }\n\\label{norm-use}\n\\end{figure}\n\t\t\n\n\n\n\n>From 1976 to about 1994 the two lines are nearly parallel; this\ndemonstrates that the change in readership with age is caused mainly\nby a change in the fraction of papers which are considered interesting\nenough to be read, not by a change in the number of times an\ninteresting paper is read. Extrapolating the relation seen in the\nearliest 16 years of figure \\ref{norm-use} we find that the fraction\nof articles interesting enough to be read is $I = I_0e^{-0.075T}$,\nwhere T is the age of the article in years, and $I_0$ is about 0.7.\nSimilarly readership declines as $\\sim e^{-0.09T}$, so the mean\nnumber of reads per relevant article is $M = M_0e^{-.015T}$, with $M_0$\nequal to 2.5 reads per month. For articles between 4 and 22 years old\nthe readership pattern is well fit by $R = IM$.\n\nFor articles younger than 4 years old the extrapolation of the $R =\nIM$ model substantially underestimates readership. While the fraction\nof read papers is only about 20\\%\\ higher than the extrapolation (it\ncould not be more than 30\\%\\, after which all papers would be read),\nthe mean reads per paper is 350\\%\\ higher.\n\nWe postulate that there is another mode of readership, which dominates\nfor articles between one month and four years old, we will call this\n``papers current enough to be read.'' If we subtract the $R = IM$\nmodel from the data we get the residual of papers current enough to be\nread. This can be well represented by $C = C_0e^{-0.85T}$, where $C_0$\nis equal to 5 reads per month. Now we have a two component model for\nreadership (per article published), valid for papers between one month\nand 22 years old which is $R = IM + C$.\n\n\n\nFigure \\ref{model-diff} shows how well the model fits the actual\nreadership data for January 1999. The solid line shows the difference\nbetween the log of the reads per paper published and the log of the\nmodel; the dotted lines show the $1 \\sigma$ errors, estimated using\n$\\sqrt{N}$. Clearly the model fits the data well.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF13.eps}}\n\\caption[]{Accuracy of the $R = IM + C$ model, versus publication date. The abscissa is the difference between the log of the number of reads per article published using ADS during January 1999 and the log of the readership model described in the text. The dotted lines show $1 \\sigma$ errors using $\\sqrt{N}$. }\n\\label{model-diff}\n\\end{figure}\n\t\t\n\n\nWhile the $R = IM + C$ model accounts for the vast majority of ADS\nuse, there are at least two other modes of readership, which we will\ncall ``historical'', and ``new''. The historical mode describes the\nuse of very old articles, and the new mode describes the readership of\nthe current issue of a journal.\n\nThe ADS in January 1999 had only one journal which is complete to an\nearly enough time to measure the historical mode, the {\\it\nAstronomical Journal}, which is complete from volume 1 in 1849. The\ndata currently available (shown in figure \\ref{AJ.reads}) suggest a\nconstant low level use, independent of time, $H = H_0$, where $H_0$ is\n0.025 reads per month. With the database now being extended to\ninclude much of the literature of the past two centuries this\nparameterization should improve greatly in the next couple of years.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF22.eps}}\n\\caption[]{Readership of the {\\it Astronomical Journal}. Total number of reads of {\\it AJ} articles using ADS during January and February 1999, as a function of publication year. }\n\\label{AJ.reads}\n\\end{figure}\n\t\t\n\n\nThe new mode represents the readership of the latest issue of a\njournal. As soon as a journal is issued, either received in the mail,\nor posted electronically, a large number of astronomers scan the table\nof contents and read the articles of interest. Although ADS has a\nfeature in the Table of Contents page which supports this type of\nreadership, it does not represent a substantial fraction of ADS use.\nWe believe most users do this either with the paper copy, or through\nthe electronic journals directly. We can crudely estimate this mode\nin the ADS use by examining the daily usage logs following the release\nof new issues of the {\\it Astrophysical Journal}, After subtracting\nthe other modes already described we find $N = N_0e^{-16T}$, where\n$N_0$ is about 3.5 reads per month. For an accurate description of\nthis mode one would need to analyze the logs of the electronic\njournals.\n\nFinally we have a four component model for how the astronomical\nliterature is read, as a function of the age of an article, $R = N + C\n+ IM + H$, where the first three terms are exponentials with very\ndifferent time constants, and the fourth is a low level constant. ADS\nuse certainly underestimates the amplitude of the $N$ term, and may\nunderestimate the amplitude of the $C$ term, as there are alternative\nelectronic routes to some of these data.\n\n\\subsection{\\label{cite-use} Comparison of Readership with Citation History}\n\nCitation histories have long been used to study the long-term\nreadership of scientific papers (e.g. \\cite{1960AmDoc..11...18B}) with\nthe basic result that the number of citations that a paper receives\ndeclines exponentially with the age of the article. While it is often\nassumed that the pattern of use is similar to the pattern of citation\nthis has not been conclusively demonstrated. Recently\n\\cite{1998JASIS..49.1283T} has found that the mean use half-life for a\nset of medical journals was 3.4 years, while the mean citation\nhalf-life for the same journals was 6.3 years.\n\nWe will compare the use of some of the Big8 journals with their\ncitation histories using two datasets: the ADS data logs for the\nperiod from 1 May 1998 to 31 July 1998, and the citation information\nprovided to ADS by the Institute for Scientific Information covering\nreferences in articles published during the first nine months of 1998,\nand only covering references from 1981 to date. ISI does not provide\nus with the full citation histories, rather they provide us with pairs\nof citing and cited journal articles where both are in the ADS\ndatabase, so the results will systematically underrepresent the\ncitation histories of articles with substantial influence in areas\noutside astronomy, or where the primary references come from\nconference proceedings.\n\n\n\nFigure \\ref{reads-cites} compares the citation histories of the Big8 \njournals with their readership; the abscissa refers to the citation \ninformation (dotted lines), the readership data (solid lines) have been\narbitrarily shifted for comparison. The lower dotted line represents the \nfraction of Big8 journal articles which were cited during the first nine\nmonths of 1998; the upper dotted line represents the mean number of cites \nper article. The lower solid line shows the mean number of reads per\narticle during the three month period May-July 1998, shifted by a factor\nof 19; the upper solid line shows the fraction of Big8 articles read, times\n1.8.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF14.eps}}\n\\caption[]{The Big8 citation rates as a function of publication date compared with the readership rates. The dotted lines, and the abscissa refer to the citation information. The top dotted line represents the number of citations per article for citations in papers published during the first nine months of 1998. The bottom dotted line represents the fraction of articles which were cited during this period. The bottom solid line shows the number of reads per article for the three month period May-July 1998, and the top solid line shows the fraction of articles read. Both solid lines are arbitrarily shifted to show the similarity of the functional shapes. }\n\\label{reads-cites}\n\\end{figure}\n\t\t\n\n\nThe number of cites has the same functional form as the fraction of\nreads, And the fraction of cites has the same form as the number of\nreads. This result is perhaps surprising.\n\nExcept for the most recent year (1997), where the number of cites\ndeclined from the year before the number of cites per article declines\nwith age as $\\sim e^{-0.09T}$ or proportional to $IM$, the long term\ndeclining readership. The citation half-life for these articles, 7.7\nyears, is longer than the 4.9 years found by \\cite{1990JASIS..41..283G} for\nthe {\\it Physical Review}, but is consistent with results of Abt\n(1981, 1996) of 20-30 year half-lives with no normalization, once one\ntakes the increase in the number of astronomy papers/cites into\naccount (Abt 1981, 1995).\n\nThe fraction of articles cited, on the other hand, appears to follow\nthe same two component form as readership, $R = IM + C$. We postulate\nthe following explanation for this behavior. The degree of citability\nwe define as the degree to which a paper would be cited, were it\npossible. We postulate this is directly proportional to readership:\n$D = D_0R$. The large increase in the fraction of recent papers cited\nis thus due to the large increase in readership. We define the\nability of a paper to be cited to be a steeply increasing function of\nage, simply because for one paper to cite another it must appear\nbefore the second paper is written, refereed, and published: $A = 1 -\ne^{-1.5T}$. Our model for the mean number of citations a paper\nreceives, $Z$, as a function of age is: $Z = Z_0AD$ or $Z = Z_0AD_0R$.\n\nFigure \\ref{cites-fit} shows the the number of citations per paper as\na function of age (thick solid line), the $Z = Z_0AD_0R$ model using\nthe actual number of reads per paper for $R$ (thin solid line), and\nthe $Z = Z_0AD_0R$ model using the $R = IM + C$ model for $R$ (dotted\nline). The product of the constants $Z_0D_0$ is the number of\ncitations per read, currently this is about 0.08.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF15.eps}}\n\\caption[]{The number of citations per article versus the $Z = 0.08R(1 - e^{-1.5T})$ model. The thick solid line represents the number of citations per article from papers published in the first nine months of 1998, as a function of publication date. The thin solid line represents the model, where $R$ is the actual readership data; the dotted line represents the model, where $R$ is the $R = IM + C$ model. }\n\\label{cites-fit}\n\\end{figure}\n\t\t\n\n\n\n\nThe papers which are frequently cited tend also to be frequently read,\nalthough the correlation is not very strong. We rank the papers by\nnumber of cites/reads during the 1998 periods, and perform a Spearman\nrank correlation between the 26988 different Big8 papers cited and the\n53755 papers read (57340 total), we obtain $r_{Spearman} = 0.35$.\nThis underestimates the correlation because it excludes papers which\nwere neither cited nor read.\n\nOf the 66392 Big8 papers published between 1982 and 1997 81\\%\\ were\nread in the 3 month period using ADS, while 41\\%\\ were cited during\nthe 9 month period. The probability that a paper was not read\ndeclined sharply with the number of times it was cited. Figure\n\\ref{frac-unread} shows this; one paper each of the (324, 224, 126)\npapers which were cited (7, 8, 9) times went unread during the period;\nnone of the 430 papers which were cited 10 or more times went unread.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF16.eps}}\n\\caption[]{Fraction of Big8 papers unread during a 3 month period in 1998, as a function of the number of times the papers were cited during a nine month period in 1998. }\n\\label{frac-unread}\n\\end{figure}\n\t\t\n\n\n\n\n\nThe relations between the number of cites or reads of a paper and the\nrank that paper has when ranked by number of cites/reads are\nidentical. If one takes papers published in a single year both cites\nand reads follow a \\cite{1949hbplebook.....Z} power law $n \\sim\nr^{-\\alpha}$ ($n$ is the number of reads or cites, and $r$ is the rank\nof the paper with that many reads/cites), where $\\alpha$ is\n${1}\\over{2}$, this is the same result \\cite{EPhJB...4..131R} found\nfor citation histories for the physics literature. If papers from all\nyears are taken together and ranked the power law index flattens\nidentically for both cites and reads to $\\alpha = {{1}\\over{3}}$.\n\n\\subsection{\\label{journal-use} How the Journals are Used}\n\n\\subsubsection{\\label{main} The main journals}\n\nFigure \\ref{frac.pub} shows the fraction of articles published in the\nBig8 by each of the five main journals, leaving out the letters and\nsupplements. We show the data only for articles published from 1983 to\n1995. Before 1983 the data from ISI are less complete, and after 1995\nthe presence of the electronic journals, and the differing rules for\nthe distribution of the ADS bitmaps, make the meaning of a ``read''\ndiffer from journal to journal. The reads and cites data for figures\n\\ref{frac.pub}, \\ref{norm-reads}, and \\ref{norm-cites} comes from the\nsame 1998 reporting periods described above.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF17.eps}}\n\\caption[]{Fraction of Big8 papers published by five selected journals. The top line (thick. solid) is {\\it ApJ}, below that (dotted) is {\\it A\\&A}, in the middle (dashed) is {\\it MNRAS}, second from the bottom (thin, solid) is {\\it AJ}, and the lowest line (thick, dotted) represents {\\it PASP}. }\n\\label{frac.pub}\n\\end{figure}\n\t\t\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF18.eps}}\n\\caption[]{Readership rates for five journals. Linetypes are as in figure \\ref{frac.pub}. The lines represent the ratio of the fraction of reads of articles in a given journal to the fraction of articles that journal published. Note that the large spike for {\\it PASP} in 1987 is due to a single very well read paper \\cite{1987PASP...99..191S} combined with fluctuations in the number of conference proceeding abstracts published in the journal. }\n\\label{norm-reads}\n\\end{figure}\n\t\t\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF19.eps}}\n\\caption[]{Citation rates for five journals. Linetypes are as in figure \\ref{frac.pub}. The lines represent the ratio of the fraction of cites of articles in a given journal to the fraction of articles read in journal. Note that the large spike for {\\it PASP} in 1987 is again due to a single very well cited paper \\cite{1987PASP...99..191S}. }\n\\label{norm-cites}\n\\end{figure}\n\t\t\n\n\n\nFigure \\ref{norm-reads} shows the relative readership of papers as a\nfunction of journal and publication year. The abscissa is the ratio\nof the fraction of Big8 papers read and the fraction of Big8 papers\npublished. Were all papers read equally frequently, independent on\nthe journal in which they were published, figure \\ref{norm-reads}\nwould show five straight lines at one; it does not. The papers from\nthe {\\it AJ} are read more on a per article basis than the other\njournals; the papers from {\\it A\\&A} are read less. Recent {\\it PASP}\npapers are read substantially more frequently than older ones, when\ncompared with the readership patterns of the other journals.\n\n\nFigure \\ref{norm-cites} shows the ratio of the fraction of citations\nan article received to the fraction of reads, as a function of journal\nand year. Were all articles cited in the same proportion to the\nnumber of times they were read (this is the constant $Z_0D_0$ in\n\\ref{cite-use}) then the figure would be five straight lines at one.\nThe three bi- and tri-monthly journals do not show much deviation from\nstraight lines at one, while the {\\it AJ} appears to be systematically\nless cited than it is read. The {\\it PASP} again shows an increase\nduring the beginning of this decade.\n\n\n\nRecall that the readership and citation information are from hundreds\nof thousands of individual decisions made by more than 10,000\nastronomers during 1998. Taken together figures \\ref{frac.pub},\n\\ref{norm-reads}, and \\ref{norm-cites} show the current opinion of\nastronomers as to the usefulness of articles as a function of journal\nand publication date. The growth of the {\\it AJ} for example, from\n6.5\\%\\ of Big8 articles to 9.5\\%\\ has not greatly affected the\nrelative readership or citation rates for the journal.\n\nThe recent history of the {\\it PASP} is perhaps the most interesting\nfeature on figures \\ref{frac.pub}, \\ref{norm-reads}, and\n\\ref{norm-cites}. From 1983 to 1995 the fraction of Big8 papers\npublished by {\\it PASP} declined from 6\\%\\ to 3\\%\\ . This decline is\noverstated, as {\\it PASP} published some conference proceeding\nabstracts during the late 1980s, a practice which ended in 1991; the\ndecline is nevertheless real: {\\it PASP} published the same number of\npapers in 1995 as 19 years before, during which time the number of\nBig8 journal articles doubled.\n\nFigure \\ref{norm-reads} shows two main features, fluctuations, and a\nslow rise. The large fluctuations during the late 80s and early 90s\nare due to two factors: fluctuations in the number of conference\nproceeding papers and abstracts; and the influence of\n\\cite{1987PASP...99..191S}, which was read at twice the rate of the\nnext most read paper from 1997, and four times the next most read {\\it\nPASP} paper from that year. The rise in the readership measure during\nthe 1990s is not caused by any known systematic; we believe it\nrepresents a real increase in the perceived usefulness of the journal.\n\nFigure \\ref{norm-cites} also shows the influence of\n\\cite{1987PASP...99..191S}, currently the third most cited article in\nthe ADS database, although now without the addition of the\nfluctuations in article counts. It also shows the rise in the\nperceived usefulness per article (this time in the measure of cites\nper read). Noting that the number of cites per article is the product\nof figures \\ref{norm-reads} and \\ref{norm-cites} the rise in the\nnumber of cites per article, compared with the Big8 over the period\n1989 to 1995 is a factor of three, so that now the journal is at full\nparity with the Big8. This demonstrates that the policy during this\nperiod was one of quality rather than quantity, a policy we dub\n``shaken, not stirred.''\n\n\\subsubsection{\\label{currency} Loss of relative currency}\n\nAll Big8 astronomical journals lose currency, the current usefulness\nof an article, at a rate described by the readership and citation\nmodels of \\ref{read-use} and \\ref{cite-use}. Any changes in the loss\nof currency of one journal with respect to the rest of the Big8 should\nbe seen in figure \\ref{norm-reads} in the form of a relative decrease\nin readership, as a function of age. Indeed the changes in the {\\it\nPASP} which we have attributed to changes in editorial policy could\nsimply be a substantial loss of relative currency.\n\n\n\n\nOne of the Big8 journals, the {\\it Astrophysical Journal Letters} is\nintended to lose currency more rapidly than the other journals.\nFigure \\ref{apjl.use} shows the relative fraction of articles\npublished (thin solid), articles read (thick solid), and articles\ncited (dotted) for the {\\it ApJL} from 1981 to 1997. Except for the\nperiod from 1994 to 1997 the curves track each other reasonably well;\nolder {\\it ApJL} papers are not cited or read any more or less than\nthe Big8 average. For the more recent papers the cites and reads\nincrease above the fraction published, implying that the journal is in\nsome sense more current than average.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF20.eps}}\n\\caption[]{Use of the {\\it Astrophysical Journal Letters} from 1981 to 1997. The thin solid line shows the fraction of Big8 papers published in {\\it ApJL}, the thick solid line the fraction of reads, and the dotted line the fraction of cites. }\n\\label{apjl.use}\n\\end{figure}\n\t\t\n\n\nIn terms of readership this effect is strongly affected by a\nsystematic. During the 3 month period in 1998, most of the 1996 and\nall of the 1997 issues of {\\it MNRAS} were not available\nelectronically due to copyright constraints. This dramatically\nlowered the relative readership of that journal, pushing all the\nothers up. Also all five journals which were fully electronic during\n1997 show increases compared with {\\it AJ} and {\\it PASP} which were\nonly available as bitmaps. Thus the increase in readership of the\n{\\it ApJL}, the pioneer electronic journal (\\cite{1995AAS...187.3801B}),\ncould be due to its superior delivery system, rather than its content.\n\n\\subsubsection{\\label{local-diff} Local differences in readership rates}\n\nAstronomers in different parts of the world read different journals at\ndifferent rates than the average. Figure \\ref{uk-fr-us.ratio} shows\nthree typical differences. The three curves show the ratio of\nreadership fractions for a particular subset when compared with the\nrest of the world; a value of 1 means that there is no difference in\nrelative readership. The thin solid line shows the {\\it MNRAS}\nreadership ratio for users who access the US site and have IP\naddresses ending in .uk; it shows that the British read {\\it Monthly\nNotices} about 60\\%\\ more than the world average.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_overviewF21.eps}}\n\\caption[]{Local differences in readership rates for three journals. The thin solid line shows the increased use of {\\it MNRAS} in the UK compared with the rest of the world; the dotted line shows this for {\\it A\\&A} in Europe, and the thick solid line for {\\it AJ} in the US. }\n\\label{uk-fr-us.ratio}\n\\end{figure}\n\t\t\n\n\n\n\n\nThe dotted line shows the {\\it A\\&A} readership ratio for users of the\nStrasbourg mirror, and the thick solid line shows the {\\it AJ}\nreadership ratio for US users with an IP address ending in .edu. They\nshow that Europeans/Americans read {\\it A\\&A}/{\\it AJ} about 20\\%\\\nmore than the rest of the world. The {\\it ApJ} also shows about a\n20\\%\\ increase in the US; the {\\it PASJ} shows a 300\\%\\ increase in\nJapan.\n\n\\subsubsection{\\label{AJhistory} Use of historical literature}\n\nThe ADS is in the process of putting a large fraction of the\nastronomical literature of the past two centuries on-line via\nbitmapped scans. The first nineteenth century journal to be fully\non-line is the {\\it Astronomical Journal}, which was first fully\non-line on 1 January 1999. Figure \\ref{AJ.reads} shows the raw readership\nfigures for the first two months of 1999 (US logs only), this shows\nthe current readership of 150 years of the journal.\n\n\nClearly the back issues are being read; the only year where the\njournal was published, but no paper was read in the two months, was\n1909, where only 12 papers were published. Also there is a break in\nthe exponential falloff with age for articles published between 1950\nand 1960, where approximately twice the expected readership occurred.\nDuring this period 94 different users read 283 articles; the biggest\nuser made 13 reads. We have no explanation for this increased use.\nThe only other period where the use is not predicted by the $C + IM +\nH$ model of \\ref{read-use} is the first decade of the journal's\nexistence, perhaps due to curiosity.\n\n\\section{\\label{impact} The Impact of the ADS on Astronomy}\n\nIt is difficult to judge the impact of scientific work. For\nscientific programs citation histories, personal honors and awards,\nand the success of students can give a measure of impact. For support\ntype programs these measures do not suffice; the impact of the\n200-inch Hale Telescope (\\cite{1948PASP...60..221A},\n\\cite{1948PASP...60..225R}) or the 4-meter Mayall Telescope\n(\\cite{1965S+T....29..268C}) clearly extends beyond the papers and\nhonors of their respective developers. The impact of large software\nprojects is, if anything, even harder to quantify; the large data\nreduction environments, like AIPS (\\cite{1981NRAON...3....3F},\n\\cite{1998aipsm.100....1G}), MIDAS (\\cite{1983Msngr..31...26B}), or\nIRAF (\\cite{1986SPIE..627..733T}) have transformed astronomy, but how\nmuch?\n\nThe ADS is perhaps unique among large support projects in that a\nreasonably accurate quantitative estimate of its impact can be made.\nThis is because many of the services the ADS provides are just more\nefficient methods of doing things astronomers have long done, and\nfound worth the time it took to do them.\n\nWe will assign to each of several ADS functions a time which is our\nestimate of the increase in research time which accrues to the\nresearcher by virtue of using that function. Our fundamental measure\nwill be the time saved in obtaining an article via the ADS, which we\nestimate from the time it takes to go to the library, find the volume,\nphotocopy the article, and return to the office, as 15 minutes. We\nthen estimate that reading an abstract, a reference list, or a\ncitation history saves $1/3$ of the full article time, or 5 minutes,\nand we arbitrarily assign a one minute time savings to each query.\n\nWe can now estimate the impact of ADS, in terms of FTE (Full Time\nEquivalent, 2000 hour) research years, by examining the ADS usage\nlogs. We note that about half of the full text articles currently\nretrieved via the ADS come from the on-line journals, which certainly\ndeserve credit for their work. Also we are ignoring several important\n(but hard to quantify) aspects of the ADS service, such as links from\nother web sites (e.g. the HTML journals), the synergy of joint\nADS/SIMBAD and ADS/NED queries (e.g. that in figure \\ref{m87.query}),\nthe bulk retrieval of abstracts and LATEX formatted references (about\n200,000 per month), and the more than 10,000,000 references returned\neach month. We think that what follows is a reasonable estimate of\nthe impact of the ADS on astronomy, and that the impact of the full\nUrania collaboration is substantially more.\n\nUsing the March 1999 worldwide combined ADS logs there were 113,471\nfull text articles retrieved, 195,026 abstracts (individually\nselected), 10,663 citation histories, and 3,702 reference pages\nretrieved, and 582,836 queries made. Using the estimated time savings\nabove we find that the impact of the ADS on astronomy is 333 FTE\nresearch years per year, approximately the same as the entire\nHarvard-Smithsonian Center for Astrophysics.\n\nIf we crudely estimate that there are 10,000 FTE research years in\nastronomy each year the ADS can be viewed as accounting for 3.33\\%\\ of\nastronomy. Currently the ADS contains 27,712 (11,834) articles\n(refereed articles) in the astronomy database dated 1998, so one way\nof expressing the impact of the ADS would be 923 (394) articles\n(refereed articles) per year.\n\nWhile the efficiencies brought about by the technologies inherent in\nthe ADS and Urania are permanent, and will contribute (compounded) to\nthe accelerating pace of discovery in astronomy, one can ask what was\ngained by being first. Risks were taken in funding the early\ndevelopment and adoption of technologies via the ADS and Urania.\nAlso, had nothing been done, the ``winning'' technologies would\neventually be adopted with very little risk.\n\nTo judge the payoff we adopt a simple model; we assume that the\nincrease in research efficiency due to the ADS has increased linearly\nfrom zero in 1993 to 333 FTE research years in 1999, and that it will\ndecrease linearly to zero over the next six years, after which there\nwill be no difference in the technologies employed.\n\nThis yields a sum impact from the early creation of the ADS of 2,332\nFTE research years, which is 23\\%\\ of the astronomical research done\nin a single year, or 6463 (2760) papers (refereed papers). This is\nsurely equal to the impact of the very largest and most successful\nprojects. Doing this analysis for the entire Urania would yield a\nsubstantially increased amount.\n\n\n\\section{\\label{acknowldgements} Acknowledgments}\n\nPeter Ossorio is a pioneer in the field of automated text retrieval,\nhe gave freely of his ideas in the early phase of the project. Geoff\nShaw provided the enthusiasm to keep the Abstract Service project going\nduring the long period of no funding.\n\nMargaret Geller gave crucial encouragement at the time of the original\nprototype. Frank Giovane long believed in the possibilities of the\nAbstract Service, and acted as a friend in high places.\n\nTodd Karakashian wrote much of the software at the time of the public\nrelease, he left in 1994. Markus Demleitner joined the ADS project in\nApril 1999, he has already produced much of value.\n\nThere are about a dozen individuals at the Strasbourg Observatory, and\nthe Strasbourg Data Center to thank, too many to thank individually.\nThe data services provided by them are at the heart of the new\nastronomy; their collaboration with the ADS has been both very fruitful,\nand a great joy.\n\nPeter Boyce, Evan Owens, and the electronic Astrophysical Journal\nproject staff have had the vision necessary to do things first. Their\ncollaboration has been important to the success of the ADS, and\ncrucial to the success of Urania.\n\nWithout the long term support from NASA, and G\\\"unter Riegler in\nparticular, the ADS would not now exist.\n\nWe are supported by NASA under Grant NCC5-189.\n\n\\begin{thebibliography}{}\n\n\n\\bibitem[Abt 1998]{1998PASP..110..210A} Abt, H. 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MIDAS - \nESO's new image processing system. The Messenger 31, 26-28 \n\n\\bibitem[Bardeen et al. 1986]{1986ApJ...304...15B} Bardeen, J. M., Bond, J. \nR., Kaiser, N., \\& Szalay, A. S. 1986, The statistics of peaks of Gaussian \nrandom fields, ApJ, 304, 15 \n\n\\bibitem[Benn \\& Martin 1995]{1995emdw.book.....B} Benn, C. \\& Martin, R. \n1995, Electronic Mail Directory. World Astronomical Community, Greenwich, \nUK: Royal Greenwich Observatory \n\n\\bibitem[Berners-Lee 1994]{ber94} Berners-Lee, T. 1994, The\nWorld-Wide Web, Communications of the ACM, 37, 76\n\n\\bibitem[Boyce 1991]{boy91} Boyce, P.B. 1991 unpublished talk given\nat the meeting ``On-Line Astronomy Documentation and Literature,''\n20-21 March 1991\n\n\\bibitem[Boyce 1995]{1995AAS...187.3801B} Boyce, P. 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"string": "\\begin{thebibliography}{}\n\n\n\\bibitem[Abt 1998]{1998PASP..110..210A} Abt, H. A. 1998, Is the \nAstronomical Literature Still Expanding Exponentially?, PASP, 110, 210 \n\n\\bibitem[Abt 1996]{1996PASP..108.1059A} Abt, H. A. 1996, How Long Are \nAstronomical Papers Remembered?, PASP, 108, 1059 \n\n\\bibitem[Abt 1995]{1995PASP..107..401A} Abt, H. A. 1995, Changing Sources \nof Published Information, PASP, 107, 401 \n\n\\bibitem[Abt 1990]{1990ApJ...357....1A} Abt, H. A. 1990. Editorial - style \nchanges for most astronomical journals. ApJ, 357, 1 \n\n\\bibitem[Abt 1981]{1981PASP...93..207A} Abt, H. A. 1981, Long-Term Citation \nHistories of Astronomical Papers, PASP, 93, 207 \n\n\\bibitem [Accomazzi, et al.,\\ 1999]{aa} Accomazzi, A., Eichhorn, G.,\nGrant, C.S., Kurtz, M.J., \\& Murray, S.S. 2000, A\\&AS, (this issue)\nARCHITECTURE\n\n\\bibitem[Adorf \\& Busch 1988]{1988alds.proc..143A} Adorf, H.-M. \\&\nBusch, E.K. 1988, Intelligent access to a bibliographic full text\ndatabase, Astronomy from Large Databases, ESO Conf. Proc. 28, eds\nF. Murtagh and A. Heck, p. 143\n\n\\bibitem[Adorf, et al. 1988]{1988alds.proc..137A} Adorf, H.-M.,\nAlbrecht, R., Johnson. M.D., \\& Rampazzo, R. 1988, Towards\nheterogeneous distributed very large Databases, ESO Conf. Proc. 28,\neds F. Murtagh and A. Heck, p. Astronomy from Large Databases, ESO\nConf. Proc. 28, eds F. Murtagh and A. Heck, p. 137\n\n\\bibitem[Anderson 1948]{1948PASP...60..221A} Anderson, J. A. 1948\nOptics of the 200-inch Hale Telescope, PASP, 60, 221\n\n\\bibitem[A\\&A 1992]{1992A+A...253..A12.} A\\&A 1992, List of Keywords\nCommon to A\\&A, ApJ, and MNRAS, A\\&A, 253, A12\n\n\\bibitem[Belkin, et. al 1995]{1995InPrM..31..431B} Belkin, N.J.,\nKantor, P., Fox, E.A., and Shaw, J.A. 1995, Combining the Evidence of\nMultiple Query Representations for Information Retrieval, Information\nProcessing and Management 31, 431.\n\n\\bibitem[Banse et al. 1983]{1983Msngr..31...26B} Banse, K., P. Crane, P. \nGrosbol, F. Middleburg, C. Ounnas, D. Ponz and H. Waldthausen 1983. MIDAS - \nESO's new image processing system. The Messenger 31, 26-28 \n\n\\bibitem[Bardeen et al. 1986]{1986ApJ...304...15B} Bardeen, J. M., Bond, J. \nR., Kaiser, N., \\& Szalay, A. S. 1986, The statistics of peaks of Gaussian \nrandom fields, ApJ, 304, 15 \n\n\\bibitem[Benn \\& Martin 1995]{1995emdw.book.....B} Benn, C. \\& Martin, R. \n1995, Electronic Mail Directory. World Astronomical Community, Greenwich, \nUK: Royal Greenwich Observatory \n\n\\bibitem[Berners-Lee 1994]{ber94} Berners-Lee, T. 1994, The\nWorld-Wide Web, Communications of the ACM, 37, 76\n\n\\bibitem[Boyce 1991]{boy91} Boyce, P.B. 1991 unpublished talk given\nat the meeting ``On-Line Astronomy Documentation and Literature,''\n20-21 March 1991\n\n\\bibitem[Boyce 1995]{1995AAS...187.3801B} Boyce, P. B. 1995, The Electronic \nApJ Letters, American Astronomical Society Meeting, 187, 3801 \n\n\\bibitem[Boyce 1996]{1996AAS...189.0603B} Boyce, P. 1996, Journals, Data \nand Abstracts Make an Integrated Electronic Resource, American Astronomical \nSociety Meeting, 189, 0603 \n\n\\bibitem[Bromley 1994]{1994PhDT........54B} Bromley, B. C. 1994, \nLarge-scale structure of the universe: a clustering analysis, Ph.D. Thesis, \nDartmouth College\n\n\\bibitem[Burton and Kebler 1960]{1960AmDoc..11...18B} Burton, R.E. \\&\nKebler, R.W. 1960, The ``half-life'' of some scientific and technical\nliteratures, American Documentation, 11, 18\n\n\\bibitem[Corbin \\& Coletti 1995]{1995VA.....39..161C} Corbin, B. G.\\& \nColetti, D. J. 1995, Digitization of Historical Astronomical Literature, \nVistas in Astronomy, 39, 161 \n\n\\bibitem[Crawford 1965]{1965S+T....29..268C} Crawford, D.L. 1965 The\nKitt Peak 150-inch Telescope, Sky \\&\\ Telescope, 29, 268\n\n\\bibitem[Davis \\& Peebles 1983]{1983ApJ...267..465D} Davis, M. \\& Peebles, P. \nJ. E. 1983, A survey of galaxy redshifts. V - The two-point position and \nvelocity correlations, ApJ, 267, 465 \n\n\\bibitem[Demleitner, et al. 1999]{1999AAS...195.8209D}\nM. Demleitner, A. Accomazzi, G. Eichhorn, C.S. Grant, M.J. Kurtz,\\&\nS.S. Murray, 1999, Looking at 3,000,000 References Without Growing\nGrey Hair, American Astronomical Society Meeting, 195, 8209\n\n\\bibitem[Egret \\& Wenger 1988]{1988alds.proc..323E} Egret, D. \\&\nWenger, M. 1988, SIMBAD - present status and future, Astronomy from\nLarge Databases, ESO Conf. Proc. 28, eds F. Murtagh and A. Heck, p.\n323\n\n\\bibitem[Eichhorn, et al. 1999]{gei} Eichhorn, G., Kurtz, M.J.,\nAccomazzi, A., Grant, C.S., \\& Murray, S.S. 2000 A\\&AS (this issue)\nSEARCH\n\n\\bibitem[Eichhorn et al. 1997]{1997AAS...191.3502E} Eichhorn, G., Kurtz, M. \nJ., Accomazzi, A.,\\& Grant, C. S. 1997, Historical Literature in the ADS, \nAmerican Astronomical Society Meeting, 191, 3502 \n\n\\bibitem[Eichhorn et al. 1994]{1994AAS...185.4104E} Eichhorn, G., Kurtz, M. \nJ., Accomazzi, A., Grant, C. S.,\\& Murray, S. 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C. 1992, Overview of the \nAstrophysics Data System (ADS), ASP Conf. Ser. 25: Astronomical Data \nAnalysis Software and Systems I, 1, 35 \n\n\\bibitem[Grant, et al. 1999]{csg}Grant, C.S., Accomazzi, A.,\nEichhorn, G., Kurtz, M.J. \\& Murray, S.S. 2000 A\\&AS (this issue) DATA\n\n\\bibitem[Grant, Kurtz \\& Eichhorn 1994]{1994AAS...184.2802G} Grant, C. S., \nKurtz, M. 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J. 1992, Advice from \nthe Oracle: Really Intelligent Information Retrieval, Invited paper in \nAdding Intelligence to Information Retrieval: The Case of Astronomy and \nRelated Space Science, eds. F. Murtagh and A. Heck, Kluwer, p. 21\n\n\\bibitem[Kurtz 1991]{kur91} Kurtz, M.J. 1991 unpublished talk given\nat the meeting ``On-Line Astronomy Documentation and Literature,''\n20-21 March 1991\n\n\\bibitem[Kurtz, Mussio \\& Ossorio 1990]{1990PaReL..11..507K} Kurtz, M. J., \nMussio, P.,\\& Ossorio, P. G. 1990, A cognitive system for astronomical\nimage interpretation, Pattern Recognition Letters, 11, 507\n\n\\bibitem[Kurtz 1988]{1988alds.proc..113K} Kurtz, M. J. 1988, The\nsearch for structure - Object classification in large data sets,\nAstronomy from Large Databases, ESO Conf. Proc. 28, eds F. Murtagh and\nA. Heck, p. 113\n\n\\bibitem[Lee, Dubin \\& Kurtz 1999]{1999adass...8..287L} Lee, J.,\nD. S. Dubin and M. J. Kurtz 1999. Co-occurrence Evidence for Subject\nVocabulary Reconciliation in ADS Databases. Astronomical Data\nAnalysis Software and Systems VIII, ASP Conference Series, Vol. 172.\nEd. David M. Mehringer, Raymond L. Plante, and Douglas\nA. Roberts. p. 287\n\n\\bibitem[Lee \\& Dubin 1999]{1999sigirconf..198L} Lee, J,. \\& Dubin,\nD.S. Context-Sensitive Vocabulary Mapping with a Spreading Activation\nNetwork, in Proceedings of the 1999 ACM SIGIR Conference on Research\nand Development in Information Retrieval, eds. Hearst, M. and Gey,\nF. and Tong, R., Association for Computing Machinery:New York,\npp. 198-205.\n\n\\bibitem[Line 1993]{1993LibT...49..665L} Line, M.B., 1993, Changes in\nthe use of the literature with time - obsolescence revisited, Library\nTrends, 49, 665\n\n\\bibitem[Madore et al. 1992]{1992adass...1...47M} Madore, B. F., Helou, G., \nCorwin, H. G., J.., Schmitz, M., Wu, X.,\\& Bennett, J. 1992, The NASA/IPAC \nextragalactic database, ASP Conf. Ser. 25: Astronomical Data Analysis \nSoftware and Systems I, 40\n\n\\bibitem[McGlynn \\& White 1998]{1998adass...7..481M} McGlynn, T. \\& White, \nN. 1998, Astrobrowse: A Multi-site, Multi-wavelength Service for Locating \nAstronomical Resources on the Web, ASP Conf. Ser. 145: Astronomical Data \nAnalysis Software and Systems VII, 481 \n\n\\bibitem[MNRAS 1992]{1992MNRAS.259......} MNRAS 1992, List of Keywords\nCommon to A\\&A, ApJ, and MNRAS, MNRAS, 259, end note\n\n\\bibitem[Murray 1991]{mur91} Murray, S.S. 1991 unpublished talk\ngiven at the meeting ``On-Line Astronomy Documentation and\nLiterature,'' 20-21 March 1991\n\n\\bibitem[Murtagh 1995]{mur95} Murtagh, F. 1995, \nhttp://www.eso.org/hst-prop-abs-search.html\n\n\\bibitem[NASA-STI 1988]{1988NASAS7069.....N} NASA STI Branch 1988,\nNASA Thsaurus Astronomy Vocabulary, NASA Report SP-7069\n\n\\bibitem[Ossorio \\& Kurtz 1989]{1989daa..conf..121O} Ossorio, P. G.\\& Kurtz, \nM. J. 1989, Automated classification of resolved galaxies, Data Analysis in \nAstronomy, 121 \n\n\\bibitem[Ossorio 1966]{1966MBR.....1..479O} Ossorio, P.G. 1966,\nClassification space: a multivariate procedure for automatic document\nindexing and retrieval, Multivariate Behavioral Research, 1, 479\n\n\\bibitem[Ortiz, et al. 1999]{1999adass...8..379O} Ortiz, P.F.,\nOchsenbein, F., Wicenec, A., \\& Albrecht, M. 1999, ESO/CDS Data-mining\nTool Development Project, ASP Conf. Ser. 172: Astronomical Data\nAnalysis Software and Systems VIII, 379\n\n\\bibitem[Pinelli 1990]{1990GIQ.....7..123P} Pinelli, T.E. 1990,\nNational Aeronautics and Space Administration scientific and technical\ninformation programs, Special Issue of Government Information\nQuarterly, 7, 123\n\n\\bibitem[Plante, Crutcher, \\& Sharpe 1996]{1996adass...5..581P} Plante, R. \nL., Crutcher, R. M., \\& Sharpe, R. K. 1996, The NCSA Astronomy Digital Image \nLibrary, ASP Conf. Ser. 101: Astronomical Data Analysis Software and \nSystems V, 581 \n\n\\bibitem[Postman 1996]{1996stsc.rept.....P} Postman, M. 1996, Distribution \nto the Astronomy Community of the Compressed Digitized Sky Survey, Space \nTelescope Science Inst Report \n\n\\bibitem[Redner 1998]{EPhJB...4..131R} Redner, S. 1998, How Popular is\nyour paper? An empirical study of the citation distribution, European\nPhysics Journal B, 4, 131\n\n\\bibitem[Rood 1988]{1988ARA&A..26..245R} Rood, H. J. 1988, Voids, ARA\\&A, \n26, 245 \n\n\\bibitem[Rule 1948]{1948PASP...60..225R} Rule, B. 1948 Engineering\nAspects of the 200-inch Hale Telescope, PASP, 60, 225\n\n\\bibitem[Salton and McGill 1983]{sal83}Salton, G., \\& McGill,\nM.J. 1983, ``Introduction to modern information retrieval,'' New York:\nMcGraw-Hill\n\n\\bibitem[Schmitz et al. 1995]{1995VA.....39R.272S} Schmitz, M.,\nG. Helou, P. Dubois, C. Lague, B. Madore, H. G. J. Corwin and S.\nLesteven 1995. A Uniform Bibliographic Code. Vistas in Astronomy 39,\n272\n\n\\bibitem[Schulman et al. 1997]{1997PASP..109.1278S} Schulman, E., French, \nJ. C., Powell, A. L., Eichhorn, G., Kurtz, M. J. \\& Murray, S. S. 1997, \nThe Relative Effectiveness of Astronomy Journals, PASP, 109, 1278 \n\n\\bibitem[Shobbrook \\& Shobbrook 1993]{1993asth.book.....S} Shobbrook,\nR. M. \\& Shobbrook, R. R. 1993, The Astronomy Thesaurus, Version 1.1,\nedited by Shobbrook, Robyn M.; Shobbrook, Robert R., Epping:\nAnglo-American Observatory\n\n\\bibitem[Shobbrook \\& Shobbrook 1992]{1992PASAu..10..134S} Shobbrook, R. M. \n\\& Shobbrook, R. R. 1992, The I.A.U. thesaurus for improved on-line access \nto information, Proceedings of the Astronomical Society of Australia, 10, \n134 \n\n\\bibitem[Squibb \\& Cheung 1988]{1988alds.proc..489S} Squibb, G.F., \\&\nCheung, C.Y. 1988, NASA astrophysics data system (ADS) study,\nAstronomy from Large Databases, ESO Conf. Proc. 28, eds F. Murtagh and\nA. Heck, p. 489\n\n\\bibitem[van Steenberg 1991]{van91} Van Steenberg, M. 1991\nunpublished talk given at the meeting ``On-Line Astronomy\nDocumentation and Literature,''20-21 March 1991\n\n\\bibitem[Stetson 1987]{1987PASP...99..191S} Stetson, P. B. 1987, DAOPHOT - \nA computer program for crowded-field stellar photometry, PASP, 99, 191 \n\n\\bibitem[Tody 1986]{1986SPIE..627..733T} Tody, D. 1986, The IRAF Data\nReduction and Analysis System, in Instrumentation in Astronomy VI,\nSPIE Conf. 627, 733\n\n\\bibitem[Tsay 1998]{1998JASIS..49.1283T} Tsay, M.Y. 1998, Library\njournal use and citation half life in medical science, Journal of the\nAmerican Society for Information Science, 49, 1283\n\n\\bibitem[Warnock et al. 1993]{1993adass...2..137W} Warnock, A., Van \nSteenberg, M. E., Brotzman, L. E., Gass, J. E., Kovalsky, D.,\\& Giovane, F. \n1993, STELAR: An Experiment in the Electronic Distribution of Astronomical \nLiterature , ASP Conf. Ser. 52: Astronomical Data Analysis Software and \nSystems II, 137 \n\n\\bibitem[Watson 1988]{1988alds.proc..453W} Watson, J.M.,\n(J.M. Rey-Watson) 1988, Access to astronomical literature through\ncommercial Databases, Astronomy from Large Databases, ESO\nConf. Proc. 28, eds F. Murtagh and A. Heck, p. 453\n\n\\bibitem[Wente 1990]{1990GIQ.....7..149W} Wente, V.A. 1990, Scientific\nand technical information management, Government Information\nQuarterly, 7, 149\n\n\\bibitem[White \\& McCain 1989]{1989ARIST..24..119W} White, H.D. \\&\nMcCain, K.W. 1989, Bibliometrics, Annual Review of Information Science\nand Technology, 24, 119\n\n\\bibitem[White 1992]{1992adass...1...52W} White, N. E. 1992, A Multimission \nDatabase and Analysis Environment, ASP Conf. Ser. 25: Astronomical Data \nAnalysis Software and Systems I, 52 \n\n\\bibitem[Zipf 1949]{1949hbplebook.....Z} Zipf, G.K. 1949, Human\nBehavior and the Principle of Least Effort, Cambridge: Addison-Wesley\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002105
|
The NASA Astrophysics Data System: Architecture
|
[
{
"author": "A. Accomazzi"
},
{
"author": "G. Eichhorn"
},
{
"author": "M. J. Kurtz"
},
{
"author": "C. S. Grant"
},
{
"author": "S. S. Murray"
}
] |
The powerful discovery capabilities available in the ADS bibliographic services are possible thanks to the design of a flexible search and retrieval system based on a relational database model. Bibliographic records are stored as a corpus of structured documents containing fielded data and metadata, while discipline-specific knowledge is segregated in a set of files independent of the bibliographic data itself. This ancillary information is used by the database management software to compile field-specific index files used by the ADS search engine to resolve user queries into lists of relevant documents. The creation and management of links to both internal and external resources associated with each bibliography in the database is made possible by representing them as a set of document properties and their attributes. The resolution of links available from different locations has been generalized to allow its control through a site- and user-specific preference database. To improve global access to the ADS data holdings, a number of mirror sites have been created by cloning the database contents and software on a variety of hardware and software platforms. The procedures used to create and manage the database and its mirrors have been written as a set of scripts that can be run in either an interactive or unsupervised fashion. The modular approach we followed in software development has allowed a high degree of freedom in prototyping and customization, making our system rich of features and yet simple enough to be easily modified on a day-to-day basis. We conclude discussing the impact that new datasets, technologies and collaborations is expected to have on the ADS and its possible role in an integrated environment of networked resources in astronomy. The ADS can be accessed at http://adswww.harvard.edu \keywords{ methods: data analysis -- astronomical data bases: miscellaneous -- publications: bibliography -- sociology of astronomy }
|
[
{
"name": "ADS_architecture.tex",
"string": "\\documentclass{aa}\n\\usepackage{graphics}\n% $Id: main.tex,v 1.5 1999/12/22 15:16:50 alberto Exp alberto $\n%\n% $Log: main.tex,v $\n% Revision 1.5 1999/12/22 15:16:50 alberto\n% Final(?) cleanup, added verbose captions to tables 1. and 2.\n%\n% Revision 1.4 1999/12/22 00:04:55 alberto\n% Last pass before final submission.\n%\n% Revision 1.3 1999/08/31 07:35:30 alberto\n% Finished all figure and captions.\n% Getting ready for submission to A&AS\n%\n% Revision 1.2 1999/08/30 23:42:11 alberto\n% Completed last section, introduction and conclusions.\n% Still needs a complete re-read.\n%\n% Revision 1.1 1999/08/24 19:38:25 alberto\n% Initial revision\n%\n% Revision 1.5 1999/07/22 04:06:55 alberto\n% Mostly completed indexing section (except adding references,\n% possibly making an explanatory diagram for the creation of\n% index and list files); merged comments by gei and most\n% comments by csg.\n%\n% Revision 1.4 1999/07/14 04:18:49 alberto\n% added section about indexing overview, refined section on\n% discipline-specific knowledge as well as section on bibliographic\n% properties. Merged in most of gei's and carolyn's comments (except\n% for section 5 and parts to be developed).\n%\n% Revision 1.2 1999/07/07 06:07:44 alberto\n% added section on creation of links,\n% expanded new synonym file structure with examples,\n% added more details to tokenization section.\n%\n% Revision 1.1 1999/07/01 16:57:31 alberto\n% Initial revision\n\n\n\n\n\\begin {document}\n\\title{The NASA Astrophysics Data System: Architecture}\n\n\\thesaurus{04(04.01.1)}\n\\author{A. Accomazzi\\and G. Eichhorn\\and M. J. Kurtz\\and C. S. Grant\n\\and S. S. Murray}\n\\institute{Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138}\n\n\n\\offprints{A. Accomazzi}\n\\mail{A. Accomazzi}\n\n\\date{Received / Accepted}\n\n\\titlerunning{}\n\\authorrunning{A. Accomazzi et al.}\n\n\\maketitle\n\n\\sloppy\n\n\\begin {abstract}\nThe powerful discovery capabilities available in\nthe ADS bibliographic services are possible thanks to the design\nof a flexible search and retrieval system based on a relational \ndatabase model.\nBibliographic records are stored as a corpus of\nstructured documents containing fielded data and metadata,\nwhile discipline-specific knowledge is segregated in a set of files \nindependent of the bibliographic data itself.\nThis ancillary information is used by the database management software\nto compile field-specific index files used by the ADS search engine \nto resolve user queries into lists of relevant documents.\n\nThe creation and management of links to both internal and external \nresources associated with each bibliography in the database\nis made possible by representing them as a set of \ndocument properties and their attributes. \nThe resolution of links available from different\nlocations has been generalized to allow its control through a site- and\nuser-specific preference database.\nTo improve global access to the ADS data holdings, a number of \nmirror sites have been created by cloning the database contents\nand software on a variety of hardware and software platforms.\n\nThe procedures used to create and manage the database and its mirrors \nhave been written as a set of scripts that can be \nrun in either an interactive or unsupervised fashion.\nThe modular approach we followed in software development has allowed a high\ndegree of freedom in prototyping and customization, making our system\nrich of features and yet simple enough to be easily modified on a\nday-to-day basis.\n\nWe conclude discussing the impact that new datasets, \ntechnologies and collaborations is expected to have on the ADS and\nits possible role in an integrated environment of networked\nresources in astronomy.\n\nThe ADS can be accessed at http://adswww.harvard.edu \n\n\\keywords{ \nmethods: data analysis -- \nastronomical data bases: miscellaneous --\npublications: bibliography -- \nsociology of astronomy\n}\n\\end{abstract}\n\n\n\\section {\\label {intro} Introduction}\n\nThe Astrophysics Data System (ADS) Abstract Service was originally\ndesigned as a search and retrieval system offering astronomers and\nresearch librarians sophisticated bibliographic search capabilities. \nOver time, the system has evolved to include full-text scans of \nthe scholarly astronomical literature and an ever-increasing \nnumber of links to resources available from other information\nproviders, taking full advantage of the\ncapabilities offered by the emerging technology of the \nWorld-Wide Web (WWW).\n\nAs new data and functionality were incorporated in the ADS,\nthe design of its system components evolved as well,\ndriven by the desire to strike a balance between simplicity \nin the operation of the system and richness in its features.\nOver time, we favored design approaches promising long-term \nrewards over short-term gains, within the limits allowed\nby our resources.\nThe approach we followed in software development has always been very\npragmatic and data-driven, in the sense that specialized software\ncomponents were designed to work efficiently with the existing\ndatasets, rather than attempting to use general-purpose,\nmonolithic software packages.\n\nThis paper gives an overview of the architecture of\nthe Astrophysics Data System bibliographic services and discusses\nin detail the design of the underlying data structures \nand the implementation of its key software components.\nIn conjunction with three other ADS papers in this volume,\nit is intended to give a complete description of the \ncurrent state and capabilities of the ADS.\nAn overview of the history and current use of the system is \ngiven in \\cite{OVERVIEW} (OVERVIEW from here on);\ndetails on the datasets in the ADS, their creation and maintenance \nis given in \\cite{DATA} (DATA);\na complete description of the ADS search engine and its\nuser interface is given in \\cite{SEARCH} (SEARCH).\n\nSection \\ref{creation} discusses the methodological approach\nused in the management of bibliographic records,\ntheir representation in the system, and the procedures used\nfor data exchange with our collaborators.\nSection \\ref{indexing} describes the structure of\nthe index files used by the ADS search engine,\nthe implementation of the procedures that create them,\nand the use of discipline-specific knowledge\nto improve search results.\nSection \\ref{properties} details the design and\nimplementation of general procedures for the creation \nand management of properties associated with bibliographic \nrecords, and their use in the creation of links to \ninternal and external resources.\nSection \\ref{mirrors} discusses the set of procedures \nused to clone the ADS bibliographic services\nto the current mirror sites and the \nlevel of system independence necessary for their operation.\nIn section \\ref{discussion} we describe how the recent\ndevelopments in technology and collaborations among \nastronomical data centers may affect the evolution of\nthe ADS.\n\n\n\\section {\\label {creation} Creation of Bibliographic Records}\n\n\nThe bibliographic records maintained by the ADS project consist of a\ncorpus of structured documents describing scientific publications. \nEach record is assigned a unique identifier in the system and all\ndata gathered about the record are stored in a\nsingle text file, named after its identifier. \nThe set of all bibliographic records available to the ADS \nis partitioned into four main\ndata sets: Astronomy, Instrumentation, Physics and Astronomy Preprints\n(DATA). This division of documents into separate groups reflects the\ndiscipline-specific nature of the ADS databases, as discussed in DATA\nand section \\ref{knowledge}.\n\nSince we receive\nbibliographic records from a large number of different sources and in\na variety of formats (DATA), the creation and management of these\nrecords require a system that can parse, identify, and merge\nbibliographic data in a reliable way. In this section we describe the\nframework used to implement such a system and some of its\ndesign principles.\nSection \\ref{methodology} details the methodology behind our\napproach. Section \\ref{xml} describes the file format adopted to\nrepresent the bibliographic records. Section \\ref{harvest}\noutlines the procedures used to automate data exchange between our\nsystem and our collaborators.\nDetails about the pragmatic aspects of creating and managing the\nbibliographic records are described in DATA.\n\n\n\\subsection {\\label{methodology} Methodology}\n\nWhen the ADS abstract service was first introduced to the astronomical\ncommunity (\\cite{1993adass...2..132K}), the system was built on\nbibliographic data obtained from a single source (the NASA STI\nproject, also known as RECON) and in a well-defined format\n(structured ASCII records). \nThe activity of entering these data into the ADS database consisted\nsimply in parsing the individual records, identifying the different\nbibliographic fields in them, and reformatting the contents of these\nfields into the ones used in our system.\nBibliographical records were created as text files named after STI's\naccession numbers (DATA), which the project used to uniquely identify\nrecords in the system.\n\nAs the desire for greater inter-operability with other data services\ngrew (OVERVIEW), the ADS adopted the\nbibliographic code (``bibcode'' from here on) \nas the unique identifier for a bibliographic entry (DATA).\nThis permitted immediate access to the astronomical databases\nmaintained by the Strasbourg Data Center (CDS), and allowed\nintegration of SIMBAD's object name resolution\n(\\cite{1988alds.proc..323E}) within the ADS abstract service\n(OVERVIEW).\n\nAs more journal publishers and data centers became providers of\nbibliographic data to our project,\na unified approach to the creation of bibliographic records became\nnecessary.\nWhat makes the management of these records challenging is the fact\nthat we often receive data about the same bibliographic entry from\ndifferent sources, in some cases with incomplete or conflicting\ninformation (e.g. ordering or truncation of the author list).\nEven when the data received is semantically consistent, there may be\ndifferences in the way the information has been represented in the\ndata file. For instance, while most journal publishers provide us\nwith properly encoded entities for accented characters and\nmathematical symbols, the legacy data currently found in our databases\nand provided to us by some sources only contain plain ASCII\ncharacters.\nIn other, more subtle and yet significant cases, the slightly\ndifferent conventions adopted by different groups in the creation of\nbibcodes (DATA) make it necessary to have ``special case'' provisions\nin our system that take these differences into account when matching\nrecords generated from these sources.\n\nThe paradigm currently followed for the creation of bibliographic\nrecords in our system is illustrated in figure \\ref{ADS_architectureF1}.\nThe different action boxes and tests displayed in the diagram\nrepresent modular procedures, most of which have been implemented as\nPERL (\\cite{PERL}) software modules. \nMore details about each of the\nsoftware components can be found in DATA.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_architectureF1.eps}}\n\\caption[]{Paradigm used for the creation of bibliographic records in the ADS. }\n\\label{ADS_architectureF1}\n\\end{figure}\n\t\t\n\n\nAs the holdings of the ADS databases have grown over time, additional\nmetadata about the literature covered in our databases\nhas been collected and is currently\nbeing used by many of our software modules for a variety of tasks.\nAmong them it is worth mentioning two activities which are significant\nin the context discussed here:\n\n1) Identification of publication sources. \nThis is the activity of associating the\nname of the publication with the standard abbreviation used to compose\nbibliographic codes, and allows us to compute a bibcode for each\nrecord submitted to our system.\n\n2) Data consistency checks. For all major serials and conference\nseries in our databases, we maintain tables correlating the volume,\nissue, and page ranges with publication dates. We also have recently\nstarted to maintain ``completeness'' tables describing in analytical\nform what range of years or volumes are completely abstracted in our\nsystem for each publication. This allows us to flag as errors those\nrecords referring to publications for which the ADS has complete coverage,\nbut which do not match any entry in our system.\nThe availability of this feature is particularly significant for\nreference resolution, as discussed later in this paper.\n\n\n\\subsection {\\label{xml} Data Representation}\n\nFrom the inception of the ADS databases until recently, each\nbibliographic record has been represented as a single entity\nconsisting of a number of different fields (e.g. authors, title,\nkeywords). This information was stored in the database as an ASCII\nfile containing pairs of field names and values. \nWhile this model has allowed us to keep a structured representation of\neach record, over the years its limitations have become apparent.\n\nFirst of all, the issue of dealing with multiple records referring to\nthe same bibliographic entry arose. As previously mentioned, while much of\nthe information present in these records is the same, certain fields\nmay only appear in one of them (for example, keywords assigned by the\npublisher). Therefore the capability of managing\nbibliographic fields supplied by different sources became desirable,\nwhich could not be easily accomplished with the file format being used.\n\nSecondly, the problem of maintaining ancillary information about a\nparticular bibliographic entry or even an individual bibliographic\nfield surfaced. Information such as the time-stamp\nindicating when a bibliographic entry was created or modified, which\ndata provider submitted it, and what is the identifier assigned to the\nrecord by the publisher can be used to decide how this \ndata should be merged into our system or how\nhyperlinks to this resource should be created.\nEven more importantly, it is often necessary to attach semantic\ninformation to individual records. For instance, if keywords are\nassigned to a particular journal article, it is important to know what\nkeyword system or thesaurus was used in order to effectively use this\ninformation for document classification and retrieval (\\cite{DUBIN99}).\n\nThirdly, the issue of properly structuring the bibliographic fields had\nto be considered. Some of these fields contain simply plaintext\nwords, and as such can be easily represented by unformatted\ncharacter strings. Others, however, consist of lists of items\n(e.g. keywords or astronomical objects), or may contain structured\ninformation within their contents (e.g. an abstract containing tables\nor math formulae).\nThe simple tagged format we had adopted did not allow\nus to easily create hierarchical structures containing \nsubfields within a bibliographic field.\n\nFinally, there was the problem of representing relationships among\nbibliographical entries (e.g. an erratum referring the original\npaper), or among bibliographic fields (e.g. an author corresponding \nto an affiliation). \nWhile we had been using ASCII identifiers to cross-correlate authors\nand affiliations in our records, the adopted scheme was very limited\nin its capabilities (e.g. multiple affiliations for an author could\nnot be expressed using the syntax we implemented).\n\nGiven the shortcomings of the bibliographic record representation\ndetailed above, we recently started reformatted all our\nbibliographic records as XML (Extensible Markup Language)\ndocuments. XML is a markup language which is receiving widespread\nendorsement as a standard for data representation and exchange. \nUsing this format, a single XML document was created for each\nbibliographic entry in our system. Each\nbibliographic field is represented as an XML element,\nand may in turn consist of sub-elements (see DATA for an\nexample of such a file).\nAncillary information about the record is stored as metadata elements\nwithin the document. Information about an individual field\nwithin the record is stored as attributes of the element representing\nit. Relationships among fields are expressed as links between the\ncorresponding XML elements.\n\nWhile it is beyond the scope of this paper to describe the\ncharacteristics that make XML a desirable language for representing\nstructured documents, we will point out the main reasons why XML was\nselected over other formats in our environment. The reader should\nnote that most of these remarks not only apply to XML, but also to\nits ``parent'' language, SGML (Standard Generalized Markup Language).\n\nXML can be used to represent precise, possibly non-textual information\norganized in data structures, and as such can be used as a formal\nlanguage for expressing complex data records and their relationships.\nIn our case, this means that bibliographic fields can be described in\nas much detail as necessary. For instance, the publication\ninformation for a conference proceedings volume can be composed of the\nconference title, the conference series name and number, the names of\nthe editors, the name of the publisher, the place of publication, and the\nISBN number for the printed book. While all this information has been\nstored in the past in a single bibliographic field, the obvious\nrepresentation for it is a structured record where items such as\nconference title and editors are clearly indentified and tagged.\nThis allows, among\nother things, to properly identify individual bibliographical items\nwhen formatting the record for a particular application (e.g. when\nciting a work in an article).\n\nA second important feature which XML offers is the possibility of\nrepresenting any amount of ancillary information (the ``metadata'')\nalong with the actual contents of a\ndocument. This permits, among other things, to tag bibliographic\nrecords, or even individual fields, with any relevant piece of information.\nFor instance, an attribute can be assigned \nto the bibliographic field listing a set of keywords\ndescribing what keyword system they belong to.\n\nOther important characteristics of XML are: the adoption of Unicode\n(\\cite{UNICODE}) for character data representation, allowing uniform\ntreatment of all international characters and most scientific symbols;\nand the support for standard mechanisms for managing complex\nrelationships among different documents through hyperlinking.\n\nSome of the practical advantages of adopting XML over other SGML\nvariants simply come from the wide acceptance of the language in the\nscientific community as well as in the software industry.\nThere is currently great interest among the astronomical\ndata centers in creating interfaces capable of seamlessly exchanging\nXML data (\\cite{1999AAS...194.8304S,AML}).\nIt is our hope that as our implementation of an XML-based markup\nlanguage for bibliographic data evolves, it can be integrated in the\nemerging Astronomical Markup Language (\\cite{AML}).\nAs many of the technologies in the field of document management change\nrapidly, it is important for a project of our scope to adopt the ones\nwhich offer the greatest promise of longevity. In this sense, we feel\nthat the level of abstraction and dataset independence that XML\nimposes on programmers and data specialists is justifies the added\ncomplexity.\n\n\n\\subsection {\\label{harvest} Data Harvesting}\n\nOf vital importance to the operation of the ADS is the issue of data\nexchange with collaborators, in particular the capability to\nefficiently retrieve data produced by publishers and data providers.\nThe process of collecting and entering new bibliographic records in\nour databases has benefitted from three main developments: \nthe adoption by all publishers of electronic production systems from\nthe earliest stages of their publication process; \nthe almost exclusive use of SGML and LaTeX as the formats for document\nproduction;\nand the pervasive use of the Internet as the medium for data exchange.\n\nAn overview of the procedures used to collect bibliographic data in\nthe daily interactions between ADS staff and data providers is\npresented in DATA.\nIn this section we discuss how the use of automated procedures has\nbenefitted the activities of data retrieval and entry in the \noperations of the ADS. \nTwo approaches are presented: the ``push''\nparadigm, in which data is sent from the data provider to the ADS, and\nthe ``pull'' paradigm, in which data is retrieved from the data\nprovider.\n\n\\subsubsection {\\label{push} Data Push}\n\nThe ``push'' approach has received much attention since the\nintroduction of web-based broadcasting technologies in 1997\n(\\cite{CDF}), to the point that many people consider both push and\nweb broadcasting to have the same meaning. Here we refer to the\nconcept of data ``push'' in its original meaning, i.e. the activity of\nelectronic data submission to one or more recipients.\nThe primary means used by ADS users and collaborators to send us\nelectronic data are: FTP upload, e-mail, and submission through a web\nbrowser (DATA). \nWhile these three mechanisms are conceptually similar (data is sent\nfrom a user to a computer server using one of several\nwell-established Internet protocols), the one we have found most\namenable to receiving ``pushed'' data is the e-mail approach. \nThis is primarily due to the fact that modern electronic mail \ntransport and delivery agents offer many of the features necessary to\nimplement reliable data delivery, including content encoding, error\nhandling, data retransmission and acknowledgement.\nAdditional features such as strong authentication and encryption can\nbe implemented at a higher level through the use of proper software\nagents after data delivery has been completed.\nIn the rest of the section we describe the implementation of an\nemail-based data submission service used by the ADS, although the\nsystem operation can be easily adapted to work under other delivery\nmechanisms such as FTP or HTTP.\n\nIn an attempt to streamline the management of the increasing amount of\nbibliographic data sent to us, we have put in place procedures to\nautomatically filter and process messages sent to an e-mail address\nwhich has been created as a general-purpose submission mechanism.\nThis activity is implemented by using the procmail filter\npackage.\nProcmail is a very flexible software tool that has been used \nin the past to automatically process\nsubmission of electronic documents by a number of\ninstitutes (\\cite{1999adass...8..257B,1996adass...5..451B}).\nOur procmail filter has been configured to analyze the input message, verify\nits origin, identify which dataset it belongs to, and archive the body\nof the message in the proper dataset-specific directory. Optionally,\nthe filter can be set up so that one or more procedures are executed\nafter archival. \nMost of the submissions received this way are simply archived and\nlater loaded into the databases by the ADS administrators during a\nperiodic update (DATA). \nUsing this paradigm, the email filter allows us to efficiently manage\nsubmissions from different collaborators by enforcing authentication\nof the submitter's email address and by properly filing the message\nbody. \nThis procedure is currently used to archive the IAU Circulars and the\nMinor Planet Electronic Circulars.\n\nBy defining additional actions to be performed after archival of a\nsubmitted e-mail message, automated database updates can be\nimplemented. We currently use this procedure to allow automated\nsubmission and updating of our institution's preprint database, which\nis currently maintained by the ADS project as a local resource for\nscientists working at the Center for Astrophysics.\nThe person responsible for maintaining the database contents simply\nsends a properly formatted email message to the ADS manager account\nand an update operation on the database is automatically triggered;\nwhen the updating is completed, the submitter is notified of the\nsuccess or failure of the procedure.\nWe expect to make increasing use of this capability as the electronic\npublication time-lines have been steadily decreasing.\n\n\n\\subsubsection {\\label{pull} Data Pull}\n\n``Data pull'' is the activity of retrieving data from one or more \nremote network locations. According to this model, the retrieval\nis initiated by the receiving side, which simply downloads the data\nfrom the remote site and stores it in one or more local files.\nWe have been using this approach for a number of years to retrieve\nelectronic records made available online by many of our\ncollaborators. For instance, the ADS LANL astronomy preprint database\n(SEARCH) is updated every night by a procedure that retrieves the\nlatest submissions of astronomy preprints from the Los Alamos\nNational Laboratory (LANL) archive, \ncreates a properly formatted copy of them in the ADS database, and\nthen runs an updating procedure that recreates the index files used by\nthe search engine (section \\ref{indexing}). \nThis nightly procedure has been running in an unsupervised fashion\nsince the beginning of 1997.\n\nThe pull approach is best used to periodically harvest data that\nmay have changed. By using procedures that are capable of\nsaving and comparing the original timestamps generated by web\nservers we can avoid retrieving a network resource unless it has been\nupdated, making efficient use of the bandwidth and resources\navailable. Section \\ref{propsoft} discusses the application of these\ntechniques to the management of distributed bibliographic resources.\n\n\n\\section {\\label {indexing} Indexing of Bibliographic Records}\n\nIn the classic model of information retrieval (\\cite{SALTON83,BC92}), \nthe function of a document indexing engine is: \nthe extraction of relevant items from the collection of text;\nthe translation of such items into words belonging to the so-called\nIndexing Language (\\cite{SALTON83});\nand the arrangement of these words into data structures that\nsupport efficient search and retrieval capabilities.\nSimilarly, the function of a search engine is:\nthe translation of queries into words from the Indexing Language;\nthe comparison of such words with the representations of the documents\nin the Indexing Language; \nand the evaluation and presentation of the results to the user.\n\nThe heterogeneous nature of the bibliographic data entered\ninto our database (DATA), and the need to effectively deal with the\nimprecision in them\nled us to design a system where a large set of discipline-specific\ninterpretations are made. For instance, to cope with the different use of\nabstract keywords by the publishers, and to correct possible spelling errors\nin the text, sets of words have been grouped together as synonyms\nfor the purpose of searching the databases. Also, many astronomical\nobject names cited in the literature are translated in a uniform fashion\nwhen indexing and searching the database to improve recall and\naccuracy.\n\nIn order to achieve a high level of software portability and database\nindependence, the decision was made to write general-purpose indexing and\nsearching engines and incorporate discipline-specific knowledge in a set\nof configuration and ancillary files external to the software itself.\nFor instance, the determination of what parsing algorithm or program\nshould be used to extract tokens indexed in a particular \nbibliographic field was left as a configurable option to the indexing \nprocedure. \nThis allowed us, among other things, to reuse the same code for\nparsing text both at search and index time, guaranteeing consistency\nof results.\n\nThe remainder of this section describes the design and implementation\nof the document indexing system used by the ADS:\nsection \\ref{overview} provides an overview of indexing procedures; \nsection \\ref{knowledge} details the organization of the knowledge base used\nduring indexing;\nsection \\ref{implementation} discusses the implementation of the \nindexing engine.\nDetails on the search engine and user interface can be found in \nSEARCH.\n\n\n\\subsection {\\label {overview} Overview of the Indexing Engine}\n\nThe model we followed for providing search capabilities to the ADS\nbibliographic databases makes use of data structures commonly referred\nto as inverted files or inverted indices (\\cite{KNU73,FB92}). \nTo allow the implementation of fielded queries, \nan inverted file structure is created for each searchable field,\nas described in section\n\\ref{implementation}.\n(In the following we will refer to \n``bibliographic fields'' as the elements composing a\nbibliographic record described in the previous section \n--- e.g. authors, affiliations, abstract ---\nand ``search fields'' as all the possible searchable entities\nimplemented in the query interface and described in detail in \nSEARCH\n--- e.g. author, exact author, and text).\nIn general the mapping between search fields and index files is \none-to-one, while the mapping between inverted files and bibliographic\nfields is one-to-many. \nFor instance, in our current implementation, the ``author'' index\nconsists of the tokens extracted from the authors field, while the\n``text'' index is created by joining the contents of the following\nfields: abstract, title, keywords, comments, and objects.\nThe complete mapping between bibliographic fields and search fields is\ndescribed in section \\ref{implementation}.\n\nDuring the creation of the inverted files, the indexing engine makes\nuse of several techniques commonly used in Natural Language Processing\n(\\cite{EF96}) to improve retrieval accuracy and to implement\nsophisticated search options. These transformations provide the\nmapping between the input data and the words belonging to the Index\nLanguage. Some of them are described below.\n\nNormalization: This procedure converts\ndifferent morphological variants of a term into a single\nformat. The aim of normalization is to reduce redundancy in\nthe input data and to standardize the format of some particular\nexpressions. This step is particularly important when treating data\nfrom heterogeneous sources which may contain textual representations\nof mathematical expressions, chemical formulae, astronomical object\nnames, compound words, etc. A description of how this is implemented\nvia morphological translation rules is provided in section \\ref{morpho}.\n\nTokenization: This procedure \ntakes an input character string and returns an array of elements considered\nwords belonging to the Index Language. While the tokenization of\nwell-structured fields such as author or object names is\nstraightforward, parsing and tokenizing portions of free-text data is\nnot a trivial matter. For instance, the decision on how to split into\nindividual tokens expressions such as ``non-N.A.S.A.'' or \ndesignations for an astronomical object such as ``PSR 1913+16'' is\noften both discipline and context-specific.\nTo ensure consistency of the search interface and index files, the same\nsoftware used to scan text words at search time is used to parse the\nbibliographic records at indexing time. A detailed description of the\ntext tokenizer is presented in SEARCH.\n\nCase folding: Converting the case of words during indexing is a\nstandard procedure in the creation of indices and allows the reduction\nin size of most index files by removing redundancy in the input data.\nFor example, converting all text to uppercase both at indexing and\nsearch time allows us to map the strings ``SuperNova,'' ``Supernova,''\nand ``supernova'' to the canonical uppercase form ``SUPERNOVA.''\nIn our implementation the feature of folding case has been set as an\noption which can be selected \non a field-by-field basis, since case is significant in some\nrare but important circumstances (e.g. the list of planetary objects).\nDetails on the treatment of case in fielded queries are discussed\nin SEARCH.\n\nStop words removal: The process of eliminating high-frequency function\nwords commonly used in the literature also contributes to reduce the\namount of non-discriminating information that is parsed and indexed\n(\\cite{SALTON83}).\nThe use of case-sensitive stop words (described in section \\ref{stop})\nallows us to keep those words in which case alone can discriminate the \nsemantics of the expression.\n\nSynonym expansion: By grouping words in synonym classes we can\nimplement a so-called ``query expansion'' by returning not only the\ndocuments containing one particular search item, but also the ones\ncontaining any of its synonyms. Using a well-defined set of synonyms\nrather than relying on grouping words by stemming algorithms to\nperform query expansion provides much greater control in the\nimplementation of query expansion and can yield a much greater level\nof accuracy in the results. This powerful feature of the ADS indexing\nand search engines is described more fully in section \\ref{synonyms}.\n\n\n\\subsection {\\label {knowledge} Discipline-specific Knowledge Base}\n\nThe operation of the indexing engine is driven by a set of ancillary\nfiles representing a knowledge base (\\cite{HR83}) which is specific to the\ndomain of the data being indexed. This means that in general different\nancillary files are used when indexing data in the different\ndatabases, although in practice much of the metadata used is \nshared among them.\n\nSince the input bibliographies\nconsist of a collection of fielded entries and each field contains \nterms with distinct and well-defined syntax and semantics, the processing \napplied to each field has to be tailored to its contents.\nThe following subsections describe the different components of the\nknowledge base in use.\n\n\n\\subsubsection {\\label{morpho} Morphological Translation Rules}\n\nMorphological translation rules are syntactic operations designed to\nconvert different representations of the same basic literal expression\ninto a common format (\\cite{SALTON83}).\nThis is most commonly done with astronomical object names (e.g. \n``M 31'' vs. ``M31''), as well as some composite words (e.g. ``X RAY'', \n``X-RAY'' and ``XRAY''). The translations are specified as pairs of\nantecedent and consequent patterns, and are applied in a\ncase-insensitive way both at indexing and searching time. \nThe antecedent of the translation is usually a POSIX (\\cite{POSIX})\nregular expression, \nwhich should be matched against the input data being indexed or\nsearched.\nThe consequent is an expression that replaces the\nantecedent if a match occurs, and which may contain \nback-references to substrings matched by the antecedent.\n\nThe table of translation rules used by the indexing and search\nengine uses two sets of replacement expressions for maximum\nflexibility in the specification of the translations, one to be used \nduring indexing and the other one for searching. This allows\nfor instance the contraction of two words into a single expression\nwhile still allowing indexing of the two separate words. For example,\nthe expression ``Be stars'' is translated into ``Bestars'' when\nsearching and ``Bestars stars'' when indexing, so that a search for\n``stars'' would still find the record containing this expression.\nNote that if we had not used the translation rule described above to\ncreate the compound word ``bestars,'' the\nword ``Be'' would have been removed since it is a stop word, and\nthe search would have just returned all documents containing ``stars.''\nThe complete list of translation rules currently in use is displayed in\ntable~\\ref{Tmorpho}.\n\n\\begin{table*}\n\\caption[]{Morphological Translation Rules used by the search and \nindexing engines. The first column contains a sequential rule number.\nThe second column contains the POSIX regular expression used to \nmatch input patterns in a case insensitive way;\nin this context $\\backslash$b represents a word boundary.\nThe third and fourth columns contain replacement strings used \nwhen searching and indexing, respectively; most of these \nstrings contain backreferences to the patterns matched\nby the parenthesized expressions in the antecedent.\nThe class of expressions matching the different sets of rules can be \nsummarized as follows:\n1. spectral types of stars;\n2. $H_{\\alpha}$, $H_{\\beta}$, $H_{I}$, $H_{II}$;\n3-7. Compound terms;\n8. Messier Galaxies;\n9. Abell Clusters;\n10. NGC Catalog;\n11-12. other Catalogs;\n13-14. common abbreviations;\n15. supernova 1987A;\n16. english elisions;\n17. french elisions;\n18-20. all other elisions;\n21-23. chemical symbols and formulae.\n\n}\n\\label{Tmorpho}\n\\begin{tabular*}{7.0in}{llll}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nNr. & Input Pattern & Search replacement & Index replacement\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n1.& $\\backslash$b(BE$\\vert$[OBAFGKMS])(--$\\vert$~+)STAR(S?)$\\backslash$b\t& $\\backslash$1STAR$\\backslash$3\t& $\\backslash$1STAR$\\backslash$3 STAR$\\backslash$3 \\\\\n2.& $\\backslash$bH(--$\\vert$~+)(ALPHA$\\vert$BETA$\\vert$I+)$\\backslash$b\t& H$\\backslash$2\t& H$\\backslash$2 $\\backslash$2 \\\\\n3.& $\\backslash$bINFRA(--$\\vert$~+)RED([A-Z]*)$\\backslash$b\t& INFRARED$\\backslash$2\t& INFRARED$\\backslash$2 RED$\\backslash$2 \\\\\n4.& $\\backslash$bRED(--$\\vert$~+)SHIFT([A-Z]*)$\\backslash$b\t& REDSHIFT$\\backslash$2\t& RED REDSHIFT$\\backslash$2 SHIFT$\\backslash$2 \\\\\n5.& $\\backslash$bT(--$\\vert$~+)TAURI$\\backslash$b & TTAURI & TTAURI TAURI \\\\\n6.& $\\backslash$bX(--$\\vert$~+)RAY(S?)$\\backslash$b\t& XRAY$\\backslash$2\t& XRAY$\\backslash$2 RAY$\\backslash$2 \\\\\n7.& $\\backslash$bGAMMA(--$\\vert$~+)RAY(S?)$\\backslash$b\t& GAMMARAY$\\backslash$2\t& GAMMA GAMMARAY$\\backslash$2 RAY$\\backslash$2 \\\\\n8.& $\\backslash$bMESSIER(--$\\vert$~+)([0-9])\t& M$\\backslash$2\t& MESSIER $\\backslash$2 M$\\backslash$2 \\\\\n9.& $\\backslash$bABELL(--$\\vert$~+)([0-9])\t& A$\\backslash$2\t& ABELL $\\backslash$2 A$\\backslash$2 \\\\\n10.& $\\backslash$bN(--$\\vert$~+)([0-9])\t& NGC$\\backslash$2\t& NGC$\\backslash$2 \\\\\n11.& $\\backslash$b([34]CR?$\\vert$ADS$\\vert$H[DHR]$\\vert$IC$\\vert$[MW])(--$\\vert$~+)([0-9])& $\\backslash$1$\\backslash$3\t& $\\backslash$1$\\backslash$3 $\\backslash$3 \\\\\n12.& $\\backslash$b(MKN$\\vert$NGC$\\vert$PKS$\\vert$PSR[BJ]?$\\vert$SAO$\\vert$UGC)(--$\\vert$~+)([0-9])& $\\backslash$1$\\backslash$3\t& $\\backslash$1$\\backslash$3 $\\backslash$3 \\\\\n13.& $\\backslash$bSHOEMAKER(--$\\vert$~+)LEVY(--$\\vert$~+)([0-9])\t& SL$\\backslash$3\t& SHOEMAKER LEVY $\\backslash$3 SL$\\backslash$3 \\\\\n14.& $\\backslash$bS-Z$\\backslash$b\t& SUNYAEV-ZELDOVICH\t\t& SUNYAEV-ZELDOVICH\t \\\\\n15.& $\\backslash$b1987(--$\\vert$~+)A\t& 1987A\t& 1987A\t\\\\\n16.& ([A-Z])'S$\\backslash$b\t& $\\backslash$1\t& $\\backslash$1\t\\\\\n17.& $\\backslash$b[DL]'([AEIOUY])\t& $\\backslash$1\t& $\\backslash$1\t\\\\\n18.& $\\backslash$b([A-Z]+[A-Z])'([A-RT-Z])$\\backslash$b\t& $\\backslash$1$\\backslash$2\t& $\\backslash$1 $\\backslash$1$\\backslash$2 \\\\\n19.& $\\backslash$b([A-CE-KM-Z])'([A-Z][A-Z]+)$\\backslash$b\t& $\\backslash$1$\\backslash$2\t& $\\backslash$1$\\backslash$2 $\\backslash$2 \\\\\n20.& $\\backslash$b([A-Z]+[A-Z])'([A-Z][A-Z]+)$\\backslash$b\t& $\\backslash$1$\\backslash$2\t& $\\backslash$1 $\\backslash$1$\\backslash$2 $\\backslash$2 \\\\\n21.& ([A-Z0-9]+)([$\\backslash$-$\\backslash$+]+)$\\backslash$B\t& N/A\t& $\\backslash$1$\\backslash$2 $\\backslash$1 \\\\\n22.& ([A-Z0-9]*[A-Z])([$\\backslash$-$\\backslash$+]+)([A-Z0-9]+)\t& N/A\t& $\\backslash$1 $\\backslash$1$\\backslash$2 $\\backslash$1$\\backslash$2$\\backslash$3 $\\backslash$3 \\\\\n23.& ([A-Z0-9]*[0-9])([$\\backslash$-$\\backslash$+]+)([A-Z][A-Z0-9]*) & N/A & $\\backslash$1 $\\backslash$1$\\backslash$2 $\\backslash$1$\\backslash$2$\\backslash$3 $\\backslash$3 \\\\\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\end{table*}\n\n\n\nTo avoid the performance penalties associated with matching large\namounts of literal data against the translation rules,\nthe regular expressions are ``compiled'' into resident RAM\nwhen the ADS services are started,\nmaking the application of regular expressions to the input stream very\nefficient (SEARCH).\n\nDespite the extensive use of synonyms in our databases, \nthere are cases in which\nthe words in an input query cannot be found in the field-specific inverted\nfiles. In order to provide additional search functionality,\ntwo options have been\nimplemented in the ADS databases, one aimed at improving matching of\nEnglish text and a second one aimed at matching of author names.\n\nDuring the creation of the text and title indices, all words found \nin the database are truncated to their stem according to the \nPorter stemmer algorithm (\\cite{HAR91}).\nThose stems that do not already appear in the text\nand title index are added to the index files and point to the \nlist of terms that generated the stem. Upon searching the database\nand not finding a match, the search engine proceeds to apply the same\nstemming rules to the input term(s) and then repeat the search.\nThus word stemming is used as a ``last-resort'' measure in an attempt\nto match the input query to a group of words that may be related to it.\nFor searches that require an exact match, no stemming of the input \nquery takes place. The limited use of stemming techniques during indexing\nand searching text in the ADS system derives from the observation\nthat these algorithms only allow minor improvements in the selection\nand ranking of search results (\\cite{HAR91,XC98}).\n\nTo aid in searches on author names, the option to match \nwords which are phonetically similar was added in 1996 and is\ncurrently available through one of the ADS user interfaces.\nIn this case, a secondary inverted file consisting of the different \nphonetic representations of author last names allows a user to generate\nlists of last names that can be used to query the database.\nTwo phonetic retrieval algorithms have been implemented, based on the\n``soundex'' (\\cite{GADD88}) and ``phonix'' (\\cite{GADD90})\nalgorithms. \n\n\n\\subsubsection {\\label {synonyms} Synonym Expansion}\n\nA variety of techniques have been used in information retrieval\nto increase recall by retrieving documents containing not only\nthe words specified in the query but also their synonyms (\\cite{EF96}).\nBy grouping individual words appearing in a bibliographic database\ninto sets of synonyms, it becomes possible to use this information\neither at indexing or searching time to perform a so-called \n``synonym expansion.''\n\nTypically, this procedure has been used as an alternative to text\nstemming techniques to automatically search for\ndifferent forms of a word (singular vs. plural, name vs. adjective, \ndifferences in spelling and typographical errors). \nHowever, since the specification of the synonyms is database- and \nfield-specific, our paradigm has allowed us to easily extend the use\nof synonyms to other search fields such as authors and planetary\nobjects (SEARCH). \nAdditionally, during the creation of the text synonym groups \nwe were able to incorporate discipline-specific knowledge\nwhich would otherwise be missed. In this sense, the use of synonym\nexpansion in ADS adds a layer of semantic information that can be \nused to improve search results.\nFor instance, the following list of\nwords are listed as being synonyms within the ADS:\n\n\\begin{verbatim}\n\ncircumquasar\t\t\nminiquasar\nnonquasar\nprotoquasars\nqso\nqsos\nqsr\nqsrs\nqsrss\nqss\nquarsars\nquasar\nquasare\nquasaren\nquasargalaxie\nquasargalaxien\nquasarhaufung\nquasarlike\nquasarpaar\nquasars\nquasers\nquasistellar\n\n\\end{verbatim}\n\nDuring indexing and searching, by default \nany words which are part of the same synonym group\nare considered to be ``equivalent'' for the purpose of finding\nmatching documents. Therefore a title search for ``quasar'' will\nalso return papers which contained the word ``quasistellar'' in their\ntitle. Of course, our user interface allows the user to disable \nsynonym expansion on a field-by-field as well as on a word-by-word basis.\n\nIt is the extensive work that has gone into compiling such a list\nthat makes searches in the ADS so powerful. To give\nan idea of the magnitude of the task, it should suffice to say that\ncurrently the synonyms database consists of\nover 55,000 words grouped into 9,266 sets. Over the years, \nthe clustering of terms in synonym groups has incorporated data from\ndifferent sources, including the Multi-Lingual supplement to the \nAstronomy Thesaurus (\\cite{1995VA.....39Q.272S}).\n\nDespite the fact that the implementation of query expansion\nthrough the use of synonyms illustrated above \nhas shown to be an\neffective tool in searching and ranking of results, we are currently\nin the process of reviewing the contents and format of the synonym\ndatabase to improve its functionality. \nFirst of all, as we have added more and\nmore bibliographic references from historical and foreign sources, the\namount of non-English words in our database has been slowly but\nsteadily increasing. As a result, we intend to merge the proper\nforeign language words with each group of English synonyms in a\nsystematic fashion (\\cite{OARD97,GR98}).\n\nSecondly, we intend to review and correct the current foreign words in\nour synonym classes to include, where appropriate, their proper\nrepresentation according to the Unicode standard (\\cite{UNICODE}), \nwhich provides\nthe foundation for internationalization and localization of textual\ndata. By identifying entries in our synonym file that were created\nby transliterating words that require an expanded character\nset into ASCII, \nwe can simply add the Unicode representation of the word to the\nsynonym group, therefore ensuring that both forms will be properly\nindexed and found when either form is used in a search.\n\nFinally, we are implementing a more flexible group structure for the\nsynonyms which allows us to specify hierarchical groupings and\nrelationship among groups rather than simple equivalence among\nwords. This last feature allows us to effectively implement the\nuse of a limited thesaurus for search purposes (\\cite{MILL97}).\nInstead of simply grouping words together in a flat structure as\ndetailed above, we first create separate groups of words, each \nrepresenting a distinct and well-defined concept. \nWords representing \nthe concept are then assigned to one such groups and are considered\n``equivalent'' instantiations of the concept. A word can only belong \nto one group but groups can contain subgroups,\nrepresenting instances of ``sub-concepts.''\nThe following XML fragment shows how grouping of synonyms is\nbeing implemented under this new paradigm:\n\n\\begin{verbatim}\n\n<syngroup id=\"00751\">\n<subgroup rel=\"instanceof\">00752</subgroup>\n<subgroup rel=\"instanceof\">00753</subgroup>\n<subgroup rel=\"instanceof\">00754</subgroup>\n<subgroup rel=\"instanceof\">00755</subgroup>\n<subgroup rel=\"oppositeof\">00756</subgroup>\n<syn>qso</syn>\n<syn>qsos</syn>\n...\n<syn>quasistellar</syn>\n<syn lang=\"de\">quasare</syn>\n<syn lang=\"de\">quasaren</syn>\n<syn lang=\"de\">quasargalaxie</syn>\n<syn lang=\"de\">quasargalaxien</syn>\n</syngroup>\n\n<syngroup id=\"00752\">\n<syn>circumquasar</syn>\n<syn>circumquasars</syn>\n</syngroup>\n\n<syngroup id=\"00753\">\n<syn>miniquasar</syn>\n<syn>miniquasars</syn>\n<syn>microquasar</syn>\n<syn>microquasars</syn>\n</syngroup>\n\n<syngroup id=\"00754\">\n<syn>protoquasar</syn>\n<syn>protoquasars</syn>\n</syngroup>\n\n<syngroup id=\"00755\">\n<syn>quasar cluster</syn>\n<syn>quasar clusters</syn>\n<syn lang=\"de\">quasarhäufung</syn>\n<syn lang=\"de\">quasarhäufungen</syn>\n</syngroup>\n\n<syngroup id=\"00756\">\n<syn>nonquasar</syn>\n<syn>nonquasars</syn>\n</syngroup>\n\n<syngroup id=\"01033\">\n...\n<subgroup rel=\"instanceof\">00755</subgroup>\n...\n<syn>cluster</syn>\n<syn lang=\"de\">häufung</syn>\n...\n</syngroup>\n\n\\end{verbatim}\n\nThe new approach allows a much more sophisticated implementation of \nquery expansion through the use of synonyms. Some of its\nadvantages are:\n\n1) Hierarchical subgrouping of synonyms: every group may contain\n one or more subgroups representing ``sub-concepts'' related\n to the group in question.\n Currently the two relations we make use of are the ones representing\n instantiation and opposition.\n This capability allow us to break down a particular concept at \n any level of detail, grouping synonyms at each level and then\n ``including'' subgroups as appropriate.\n\n2) Multiple group membership: each subgroup may be an instance\n of one or more synonym groups. For instance, the synonyms\n ``quasarh\\\"aufung'' and ``quasar cluster'' are in a subgroup that\n belongs to both the ``qso'' and the ``cluster'' groups.\n\n3) Use of multi-word sequences in synonym groups: in certain cases,\n individual words referring to a concept correspond to a \n sequence of several words in other languages or context.\n Allowing declarations of multi-word synonyms enables us to correctly\n identify most terms.\n\n4) Multilingual grouping: words belonging to a language other than\n English are tagged with the standard international identifier for that\n language. This permits us to use the synonyms in a context \n sensitive way, so that if the same word were to exist in two\n languages with different meanings, the proper synonym group\n would be used when reading documents in each language. \n \n\nThe synonym database described above is used at indexing time to\ncreate common lists of document identifiers for words belonging to the\nsame synonym group or any of its subgroups. \nThe effect of this procedure is that when use of synonyms is enabled,\nsearches specifying a word that belongs to a synonym group\nwill result in the list of records containing that word as\nwell as any other word in the synonym group or its subgroups.\nIn the example given above, a search for ``qso'' would have\nlisted all documents containing ``qso,'' its other synonyms,\nas well as subgroup members such as ``miniquasar'' and\n``protoquasar.'' On the other hand, a search for ``miniquasar''\nwould have only returned the list of documents containing \neither ``miniquasar'' or ``microquasar,'' narrowing significantly\nthe search results.\n\n\n\\subsubsection {\\label {stop} Stop Words}\n\nA number of words considered ``irrelevant'' with respect to the searches\nof the particular field and database at hand are ignored during indexing\nand searching. These words (commonly referred to as ``stop words'') \nconsist primarily of terms used in the English language with great frequency, \nas well as adverbs, prepositions and any other words not carrying a \nsignificant meaning when used in the context under consideration\n(\\cite{SALTON83}).\nSuch words are removed both at indexing and searching time,\ndecreasing the number of irrelevant searches and disregarding search \nterms that would not yield significant results.\n\nThe use of both case-sensitive\nand case-insensitive stop words during indexing allows us to single out \nthose instances of terms that may have different meanings depending on \ntheir case. For instance, the words ``he'' and ``He'' usually represent \ndifferent concepts in the scientific literature (the second one being the \nsymbol for the element Helium). \nBy selectively eliminating all instances of ``he,'' when indexing the\nbibliographies, we stand a good chance that the remaining instances of \nthe word refer to the element Helium.\n\nThe effort currently underway to create a structured synonym database\nwill be used to group and maintain the list of stop words in use.\nBy simply clustering stop words in synonym groups and properly tagging\nthe group as containing stop words, we can use the same software\nthat is currently being developed to create and maintain the list of\nsynonyms in our database. An example of the resulting records is \nshown below:\n\n\\begin{verbatim}\n\n<syngroup id=\"00037\" type=\"stop\">\n<!-- he is used in case-sensitive way to avoid \n removing \"He\" (element helium) from index -->\n<syn case=\"mixed\">he</syn> \n<syn>she</syn>\n<syn lang=\"de\">er</syn>\n<syn lang=\"de\">sie</syn>\n<syn lang=\"fr\">il</syn>\n<syn lang=\"fr\">elle</syn>\n<syn lang=\"es\">él</syn>\n<!-- as above, but without proper accenting -->\n<syn lang=\"es\">el</syn>\n<syn lang=\"es\">ella</syn>\n<syn lang=\"it\">lui</syn>\n<syn lang=\"it\">lei</syn>\n</syngroup>\n\n\\end{verbatim}\n\nThis paradigm allows us to treat stop words as a special case of\nsynonyms (which are identified by the indexing and search engines\nas being of type ``stop'').\n\n\n\\subsection {\\label {implementation} The Indexing Engine}\n\nGeneral-purpose indexing engines and relational\ndatabases were used as part of the abstract service in its first\nimplementation\n(\\cite{1993adass...2..132K}), but they were eventually dropped\nin favor of a custom system as the desire for better performance\nand additional features grew with time (\\cite{1995adass...4...36A}),\nas is often necessary in the creation of discipline-specific\ninformation retrieval systems (\\cite{VR79}).\nThe approach used to implement the data indexing portion of the\ndatabase can be considered ``data-driven'' in the sense that\nparsing, matching and processing of input text data is controlled\nby a single configuration file (described below)\nand by the discipline-specific files described in section \n\\ref{knowledge}.\n\nThe inverted files used by the search engine are the products of a\npipeline of data processing steps that has evolved with time.\nTo allow maximum flexibility in the definition \nof the different processing steps,\nwe have found it useful to break down the indexing\nprocedure into a sequence of smaller and simpler tasks that\nare general enough to be used for the creation of all the files\nrequired by the search engine.\nA key design element which has helped generalize the indexing process is\nthe use of a configuration file which describes all the \nfield-specific processing necessary to create the index files.\nThe configuration file currently in use is displayed in table \n\\ref{Tindexconfig}.\nFor each search field listed in the table, \nan inverted file structure is created by the indexing engine.\n\n\\begin{table*}\n\\caption[]{Configurable parameters used by the indexing engine.\nThe first column lists the searchable fields to be indexed.\nThe second column lists the XML elements whose contents are used to\ncreate each field's occurrence table; \nnote that since the author search field is derived\nfrom the exact author index, no elements are listed for it.\nThe third column shows whether the contents of the field are\nmodified through the use of morphological translation rules.\nThe fourth column lists the name of the procedure used to parse the\nfield contents into individual tokens to be indexed. \nThese procedures currently are: get\\_children, which tokenizes an XML\nfragment by extracting its subelements from it; text\\_parser, which\ntokenizes input text as described in the SEARCH paper;\nand parse\\_authors, which reduces all author names to the canonical\nforms used by ADS.\nThe last three columns show whether stop words, case folding, and\nsynonym grouping is used during indexing of each search field.\nNote that because of the lack of a common set of keywords used\nthroughout the database, keyword searches are currently disabled in\nour standard query interface.\n}\n\\label{Tindexconfig}\n\\begin{tabular*}{7.0in}{lp{2.in}lllll}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nSearch Field & Bibliographic Fields &\nTranslation & Tokenizer & Stop words &\nCase folding & Synonyms\n\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nexact author & $<$AUTHORS$>$\t& \t\tno\t& \tget\\_children\t& no\t& \tyes\t& \tno \\\\\ntitle\t& \t$<$TITLE$>$ \t&\t\tyes\t& \ttext\\_parser\t& yes\t& \tyes\t& \tyes \\\\\ntext\t& $<$TITLE$>$, $<$ABSTRACT$>$, $<$KEYWORDS$>$, $<$OBJECTS$>$, $<$COMMENTS$>$ & yes & text\\_parser\t& yes\t& \tyes\t& \tyes \\\\\nkeyword \t& $<$KEYWORDS$>$\t\t& no \t& \tget\\_children\t& no\t\t& yes\t\t& no \\\\\nobject \t& $<$OBJECTS$>$\t\t& \tyes\t& \tget\\_children\t& no\t\t& no\t\t& yes \\\\\n\nauthor\t& (exact author occurrence table) &\tno\t& \tparse\\_authors\t& no\t\t& yes\t\t& yes \\\\\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\end{table*}\n\n\n\nThe first step performed by the indexing software is the creation of a\nlist containing the document identifiers to be indexed. This usually\nconsists of the entire set of documents included in a particular\ndatabase but may be specified as a subset of it if necessary (for\ninstance when creating an update to the index, see section \\ref{update}).\nThe list of document identifiers is then given as input to an ``indexer''\nprogram, which proceeds to create, for each search field, an inverted file\ncontaining the tokens extracted from the input documents\nand the document identifiers (bibcodes) where such words occur.\n(In the following discussion we will refer to the tokens extracted by\nthe indexer simply \nas ``words,'' although they may not be actual words in the common\nsense of the term. For instance, during the creation of the author\nindex, the ``words'' being indexed are author names.)\nAfter all the inverted files have been created, each one of them is\nprocessed by a second procedure which generates two separate files used by\nthe search engine: an ``index'' file, containing the list of\nwords along with pointers to a list of document identifiers, and a\n``list'' file, containing compact representations of the lists of\ndocument identifiers corresponding to each word.\n\nThe following subsections describe the procedures used during the\ndifferent indexing steps: \nsection \\ref{invfiles} details the creation of the inverted files; \nsection \\ref{indexfiles} describes the creation of the index and list files; \nsection \\ref{update} describes the procedures used to update the index and\nlist files;\nsection \\ref{indexsummary} discusses some of the advantages and\nshortfalls of the implemented indexing scheme.\n\n\n\\subsubsection {\\label {invfiles} Creation of Inverted Files}\n\nAn inverted file (\\cite{VR79,FB92}) is a table consisting of\ntwo columns: the first column contains the instances of words\nbelonging to the indexing language, and the \nsecond column contains the list of document identifiers in which those\nwords were found. \nThe transformation of a document into its indexing language is\nperformed in the following steps:\n\n1) parsing of the document contents and extraction of all the\n\tbibliographic elements needed for the creation of one\n\tor more search fields;\n2) joining of bibliographic elements that should be indexed together\n\tto produce a list of strings;\n3) application of translation rules (if any) to the list of strings;\n4) itemization of the list of strings into an array of words to be\n\tindexed;\n5) removal of stop words from the list of words to be indexed\n\t(either case sensitively or insensitively);\n6) folding of case for each of the words (if requested);\n7) creation or addition of an entry for each word in a hash table\n\tcorrelating the word indexed with the document \n\tidentifiers where it appears.\n\nThe indexer keeps a separate inverted file for each set of indexing\nfields to be created (see table \\ref{Tindexconfig}, column 1).\nEach inverted file is simply implemented as a sorted\nASCII table, with tab separated columns.\nGiven the current size of our databases, the creation of\nthese tables takes place incrementally.\nA pre-set number of documents is\nread and processed by the indexer, \nan occurrence hash table for these documents is\ncomputed in memory, and an ASCII dump of the hash is then written\nto disk file as a set of keys (the words being indexed) \nfollowed by a list of document identifiers containing such words.\nThe global inverted file is then created by simply joining the\npartial inverted files using a variation of the standard UNIX join command.\n\nOnce the occurrence tables for the primary search fields listed in\ntable \\ref{Tindexconfig} have been created,\na set of derived fields are computed if necessary. \nCurrently this step is used to\ncreate the ``authors'' occurrence table from the ``exact authors'' one\nby parsing and formatting entries in it so that all names are reduced\nto the forms ``Lastname, F'' (where ``F'' stands for the first name\ninitial) and ``Lastname.'' This allows efficient searching for the\nstandard author citation format. \n\n\n\\subsubsection {\\label{indexfiles} Creation of the Index and List Files}\n\nAfter all the primary and derived inverted files have been\ngenerated, a separate program is used to produce for each table\ntwo separate files which are used by the search engine:\nan inverted index file (here simply called ``index'' file) \nand a document list file (``list'' file, see \\cite{SALTON89}).\nThe index file is an ASCII table which contains \nthe complete list of words appearing in the inverted file and \ntwo sets of numerical values associated with it, the first set\nis used for exact word searches, the second one for synonym\nsearches. The list file is a binary file containing blocks of\ndocument identifiers in which a particular word was found.\nEach set of numerical values specified in the index file consists of:\nthe relative ``weight'' of the word (or group of synonyms) \nin the database, as defined below;\nthe length of the group of document identifiers in the list file,\nin bytes;\nthe position of the group of document identifiers in the list file,\ndefined as the byte offset from the beginning of the list file.\n\nThe value chosen to express the weight $W(w)$ of a word\n$w$ is a variation of the inverse document frequency\n(\\cite{SALTON88}): \n\n\t$$W(w) = K \\times \\log_{10} {N / df(w)}$$\n\nwhere $K$ is a constant, $N$ is the total number of documents in the\ndatabase, and $df(w)$ is the document frequency of the word $w$,\ni.e. the number of documents in which the word appears (\\cite{SALTON88}).\nThe choice of a suitable value for the constant $K$ (currently set to\n$K = 10^4$) allows the indexing and search engine to perform most of\nthe operations in integer arithmetic.\nTo avoid performing slow log computations during the creation of\nthe index files, the function that maps $df(w)$ to $W(w)$ \nis cached in an associative array so that when repeated \ninteger values of $df(w)$ are encountered, the pre-computed values are\nused.\n\nThe document identifiers which are stored in the list files are 32-bit\nintegers (from here on called sequential identifiers) \ncorresponding to line numbers in the list of bibliographic\ncodes which have been indexed. The search engine resolves all queries\non index files by performing binary searches on the words appearing in\nthe index file, then reading the corresponding list of sequential\nidentifiers in the list files, combining results, and\nfinally resolving the sequential identifiers in bibcodes \n(see figure \\ref{ADS_architectureF2}).\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_architectureF2.eps}}\n\\caption[]{ Implementation of the inverted file structure makes use of\nmultiple lookups for efficiency. This diagram describes the sequence\nof steps performed by the search engine to resolve a fielded query\nwith synonym expansion enabled. First the query word is found in the\nindex file which contains a sorted list of strings, and the address\nand length of sequential identifiers corresponding to the word are\nread. Then the block of sequential identifiers are read from the list\nfile and are individually resolved into their corresponding\nbibcodes. }\n\\label{ADS_architectureF2}\n\\end{figure}\n\nThe procedure for the creation of the index and list files\nreads the inverted file associated with each search field and performs\nthe following steps:\n\n1) read all entries from the list of document identifiers\n (bibcode list) and create a hash table associating each bibcode\n with its corresponding sequential identifier;\n\n2) if synonym grouping is to be used for this field, read the\n synonym file for this field and create a hash table associating each\n entry in the synonym group with the word with the highest frequency in\n the group;\n\n3) for each word in the inverted file translate the list of\n bibcodes associated with it into the corresponding \n list of integer line numbers, and mark word as being processed;\n\n4) if word belongs to a group of synonyms, sequentially find and\n process all other words in the same group, marking them as processed,\n then iteratively process all words in any of the subgroups until \n nesting of subgroups is exhausted; if no synonyms are in use, the\n same procedure is used with the provision that the group of synonyms\n is considered to be composed only of the word itself;\n\n5) join, sort and unique the lists of sequential identifiers \n for all the words in the current group of synonyms;\n\n6) write to the list file the sorted list of sequential\n identifiers for each word\n in the group of synonyms, followed by the\n cumulative list of sequential identifiers for the entire group of\n synonyms;\n\n7) for each word in the group of synonyms, write to the index file an\n entry containing the word itself and the two sets of numerical\n values (weight, length, and offset) for exact word and synonym searches.\n\n\nFigure \\ref{ADS_architectureF3} illustrates the creation of entries for two words in the\n``text'' index and list file from the text inverted file.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_architectureF3.eps}}\n\\caption[]{ Creation of the text index and list file from the inverted\nfile. First the bibliographic codes are translated into sequential\nidentifiers (A). Then the list file is created by concatenating\n``blocks'' of sequential identifiers for each word and each group of\nsynonyms in the inverted file (B), and the index file is created by\nstoring the list of words, weights, and pointers to these blocks of\nsequential identifiers (C). To retrieve the list of documents\ncontaining a word or any of its synonyms, the search engine searches\nthe index file and then reads the block of identifiers for either\nsimple word searches (D) or synonym searches (E). }\n\n\\label{ADS_architectureF3}\n\\end{figure}\n\t\t\n\n\n\n\\subsubsection {\\label {update} Index Updates}\n\nThe separation of the indexing activity into two separate parts offers\ndifferent options when it comes to updating an index. New documents\nwhich are added to the database can be processed by the indexer and\nmerged into the inverted file quickly, and a new set of index\nand list files can then be generated from it. \nSimilarly, since the synonym grouping is performed after the creation\nof the inverted files, a change in the synonym database can be\npropagated to the files used by the search engine by recreating the \nindex and list files, avoiding a complete re-indexing of the database.\n\nDespite the steps that have been taken in optimizing the code used\nin the creation of the index and list files from the occurrence \ntables, this procedure still takes close to two hours to complete\nwhen run on the complete set of bibliographies in the astronomy database\nusing the hardware and software at our disposal.\nIn order to allow rapid and incremental updating of the index and list\nfiles, a separate scheme has been devised requiring only in-place \nmodification of these files rather than their complete re-computation.\n\nDuring a so-called ``quick update'' of an operational set of index\nfiles used by the search engine, a new indexing procedure is run on\nthe documents that have been added to the database since the last full\nindexing has taken place. The indexing\nprocedure produces new sets of incremental index and list files \nas described above,\nwith the obvious difference that these files only contain words that \nappear in the new bibliographic records added to the database.\nA separate procedure is then used to merge the new set of index and list files\ninto the global index and list files used by the operational search \nengine, making the new records immediately available to the user. \nThe procedure is implemented in the following steps (see figure\n\\ref{ADS_architectureF4}):\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_architectureF4.eps}}\n\\caption[]{ Modification of a list file by a ``quick update:'' the\nmain blocks corresponding to a word present in the incremental index\n(M1 and M2) are modified by the insertion of a pointer at their end\nand by extension blocks at the end of the index (x1 and x2). }\n\n\\label{ADS_architectureF4}\n\\end{figure}\n\t\t\n\n\n1) Compute new sequential identifiers for the list of bibcodes in the\n incremental index by adding to each of them the number of entries\n in the operational bibcode list. This guarantees that the mapping\n between bibcodes and sequential identifiers is still unique after\n the new bibcodes have been merged into the operational index.\n\n2) Append the list of sequential identifiers found in the incremental\n list file to the operational list file. In the case of identifiers\n corresponding to a new entry in the index file, their block of \n values is simply appended to the end of the operational list file.\n In the case of identifiers corresponding to an entry already\n present in the operational index file, the original list of \n identifiers (``main block'') needs to be merged with\n the new list of identifiers.\n In order to avoid clobbering\n existing data in the operational list file, the list of identifiers\n from the incremental index is appended to the end of the global\n list file, creating an extension of the main blocks of identifiers\n that we call an ``extension block.''\n To accomplish the linking between main and extension blocks, \n the last sequential identifier in a main block is overwritten\n with a negative value representing the corresponding extension\n block's offset from the beginning of the list file (except the \n change in sign).\n An extension block contains as the first integer value the size of\n the extension block in bytes, followed by the last identifier read\n from the main block in the list file, followed by the sequential\n identifiers from the incremental index (see fig. \\ref{ADS_architectureF4}).\n When the search engine finds a negative\n number as the last document identifier value, it will seek to the \n specified offset, read a single integer entry corresponding to the\n number of bytes composing the extension block, and then proceed to\n read the specified number of identifiers.\n Note that because of the way extension blocks are created, the list\n of sequential identifiers created by concatenating the entries in\n the extension block to the entries in the main block is always sorted.\n\n3) For each entry in each incremental index file, determine if a\n corresponding entry exists in the operational index file.\n If an entry is found, no modification\n of the index file is necessary, otherwise the index file is\n updated by inserting the entry in it. The values of the weights\n and offsets are corrected by taking into account the total number\n of documents in the operational index and the size of the list file.\n\n\n\\subsubsection {\\label{indexsummary} Remarks on the Adopted Indexing Scheme}\n\nOne of the advantages of using separated index and list files is that\nthe size of the files that are accessed most frequently by the\nsearch engine (the list of bibcodes and the index files) is kept small so\nthat their contents can be loaded in random access memory\nand searched efficiently (SEARCH). \nFor instance, the size of the text index file for the astronomy\ndatabase is approximately 16 MB, and once the numerical entries are\nconverted into binary representation when loaded in memory by the search \nengine, the actual amount of memory used is less than 10 MB.\n\nThe use of integer sequential identifiers in the list files\nallows more compact storage of the document identifiers as well as \nimplementation of fast algorithms for merging search results (since\nall the operations are executed in 32-bit integer arithmetic rather\nthan having to operate on 19-character strings).\nFor instance, recent indexing of the ADS astronomy database\nproduces text inverted files which have sizes approaching \n500 MB, while the size of the text list file is about 140 MB.\n\nThe choice of a word weight which is a function of only the \ndocument frequency allows us to store word weights as part of the\nindex files. It has been shown that a better measure for the \nrelevance of a document with respect to a query word is obtained\nby taking into account both the document frequency $df$ and the\nterm frequency $tf$, defined as the frequency of the word in each\ndocument in which it appears (\\cite{SALTON88}), normalized\nto the total number of words in the document. The reasoning\nbehind this is that a word occurring with high relative frequency\nin a document and not as frequently in the rest of the database is\na good discriminant element for that document.\nAlthough we had originally envisioned incorporating document-specific\nweights in the list files to take into account the relative term\nfrequency of each word, we found that little improvement was \ngained in document ranking.\nThis is probably due to the fact that the collection of documents\nin our databases is rather homogeneous as far as document length\nand characteristics are concerned. Eventually the choice was\nmade to adopt the simpler weighting scheme described above.\n\nThe procedures used to create the inverted files can scale well\nwith the size of the database since the global inverted file is\nalways created by joining together partial inverted files.\nThis allows us to limit the number of hash entries used by the indexer\nprogram during the computation of the inverted files. \nAccording to Heap's law (\\cite{HEA78}), and as verified experimentally \nin our databases, a body of $n$ words typically generates a vocabulary of \nsize $V = K n^{\\beta}$ where $K$ is a constant and $\\beta \\approx 0.4 -\n0.6$ for English text (\\cite{NAV98}).\nSince the size of the vocabulary $V$ corresponds to the number of \nentries in a global hash table used by the indexing software, we see\nthat an ever-increasing amount of hardware resources would be \nnecessary to hold the vocabulary in memory; our choice of a partial\nindexing scheme avoids this problem.\nFurthermore, the incremental indexing model is quite suitable to \nbeing used in a distributed computing environment where different \nprocessors can be used in parallel to generate the partial inverted\nfiles, as has been recently shown by \\cite{KITA97}.\n\nThe procedures used to create the list and index files make use of\nmemory sparingly, so that processing of entries from the occurrence\ntables is essentially sequential. \nThe only exception to this is the handling of groups of synonyms.\nIn that case, the data structures used\nto maintain the entries for the words in the current synonym group are\nkept in memory while the cumulative list of sequential identifiers for\nthe entire group is built. The memory is released as soon as\nthe entries for the current synonym group are written to the list and\nindex files.\n\n\n\\section {\\label{properties} Management of Bibliographic Properties}\n\n\nBy combining bibliographic data and metadata available from several sources\nin a single database and by maintaining a list of what properties and\nresources are available for each bibliography, the ADS system allows\nusers to formulate complex queries such as: ``show me all the papers\nthat cite any paper ever written about the object M87 and the subject\n`globular clusters' and which are available online as full-text\ndocuments.'' This query is possible thanks to the\ncollection and fusion of data from several sources:\n\n1) The astronomical object databases, which maintain a collection of\nobject names and bibliographies in which they appear. This search\nis performed through a peer-to-peer network connection with the \nSIMBAD (\\cite{1988alds.proc..323E})\nand NED (\\cite{1988alds.proc..335H}) \ndatabase servers, as described in OVERVIEW and SEARCH. \nThis first step allows us to find the set of bibliographies on M87.\n\n2) The ADS abstract service indices, which allow a search of all\nastronomical papers containing the words ``globular cluster'' or their\nsynonyms. This part of the search is performed by the ADS \nsearch engine and makes use of the local files generated by \nindexing the bibliographic databases as described in section\n\\ref{indexing}.\nThis step allows us to discard any bibliographic\nentry which does not contain the words ``globular cluster'' in its\ntext index.\n\n3) The list of citations in the ADS databases, which maintain updated \nlists of astronomical papers and any paper referenced in them.\nThis allows us to look up the list of papers that have cited \nthe selected bibliographic entries, and then proceed to join the\nresults.\n\n4) The list of papers available electronically from either the \nastronomical journal publishers or the ADS article service,\nboth of which provide access to full-text articles online.\n\n\nThe query given above illustrates how knowing whether a particular\nbibliographic entry possesses a particular property (e.g. whether it\nhas been cited) and what values may be associated with that property\n(e.g. the list of citing papers) can be used as a method for selection\nand ranking of query results. Additionally, the availability\nof remote resources for a particular bibliographic entry can be\ndescribed as being one of its properties, which in turns allows \nan additional filtering of the result lists.\n\nAs new data regarding a bibliographic entry become available, its\nrecord is updated in the ADS database by merging the new information\nwith the existing entry and possibly by updating its relevance within\nthe database and its relation with respect to other internal and\nexternal resources. For instance, when a new paper is published which\nreferences an existing bibliography, the record for the latter paper\nneeds to be updated by establishing a link between the two\npapers; at the same time, the ``citation relevance measure'' for the\npaper, computed as the number of times the paper was cited in the\nliterature, also needs to be updated.\n\nThe procedures used in the creation and management of bibliographic \nproperties (simply called ``properties'' from here on) in the ADS \ndatabases are a result of the need for managing resources \nrelated to bibliographies which may or may not be available locally.\nThe main characteristics of the property sets as defined in our system\ncan be summarized in the following list:\n\n1) Some properties simply denote the fact that an entry belongs to\na certain dataset (e.g. whether a paper is refereed or not), others\nmay have values associated with them (e.g. ``is available online\nelectronically'' will have as its value the URL of the full-text\npaper). In general, the knowledge of whether an entry in the database\nhas a certain property allows the search engine to select it for\nfurther consideration when executing a database query, while the\nvalue(s) assumed by this property do not need to be taken into account\nuntil later.\n\n2) The lists of bibliographic identifiers and their properties may be\ndefined as being either ``static'' or ``dynamic.'' Static properties are\nthose that once defined do not change in time (e.g. whether a paper is\nrefereed), while dynamic properties may change their value with\ntime (e.g. the list of citations for a paper).\n\n3) Some properties may depend on each other (e.g. references and\ncitations), hence the creation and updating order for these properties\nis significant.\n\nCurrently the ADS has defined a set of 21 different properties which\nare applicable to its bibliographies. Some of them are listed in\ntable \\ref{Tcodes}.\n\n\\begin{table*}\n\\caption[]{Examples of bibliographic properties defined in the ADS\nand their possible values.\n}\n\\label{Tcodes}\n\\begin{tabular*}{7.0in}{lp{0.6\\linewidth}p{0.25\\linewidth}}\n\n\\hline\n\\noalign{\\smallskip}\n\n\nName &\nExplanation &\nValue(s)\n\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nassociated & \tone or more associated bibliographic records exist for\n\tthis entry\n\t(e.g. erratum or papers published as part of a series) &\n\tbibcodes of papers associated with bibliographic entry \\\\\ncitation &\tbibliographic entry has been cited by one or more\n\tpapers in the ADS &\n\tbibcodes of papers citing bibliographic entry \\\\\ndata\t&\tbibliographic entry has electronic data tables\n\tpublished with it &\n\tURLs of data tables \\\\\nelectronic &\ta full-text electronic article exist for this\n\tbibliographic entry & \n\tURL of electronic journal article \\\\\nocr\t&\tabstract of bibliographic entry was generated by\n\tOptical Character Recognition programs &\n\tN/A \\\\\nrefereed &\tbibliographic entry is a refereed paper &\n\tN/A \\\\\n\n\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular*}\n\\end{table*}\n\n\n\nIn the rest of this section we will discuss the approach we\nfollowed in implementing the database structures \nallowing query and selection based on properties of bibliographies.\nIn section \\ref{proprep} we describe the implementation used to associate \nproperties and attributes to\nentries in the database and the procedures maintaining relational\nlinks among them. In section \\ref{propsoft} we describe the framework used to\nautomatically update and merge bibliographic data with information\nsubmitted to the ADS.\n\n\n\\subsection {\\label{proprep} Representation of Properties}\n\nThe creation and updating of properties in the ADS system \nis the result of merging entries provided by different data sources\nand individuals at different times and in different formats.\nThe procedures used to maintain the property database are therefore\nstructured to be as general as possible (so that defining a new\nproperty is a simple task) while still allowing as much customization\nas necessary to deal with a variety of sources and formats.\nThe representation of properties allows the search engine to \nefficiently filter results based on whether a bibliographic entry\npossesses a particular property. It also allows fast access \nto the values associated to a particular bibliographic property, \nso that the search interface can quickly access the information\nas required.\n\nInstead of representing these properties as a single relational table\nwhere each bibliographic entry is associated with the ordered set of \nproperty values, a different approach was chosen where each property \nis represented by a separate table. \nThe following definition was adopted: \n\n``A bibliographic entry $b$ possesses property $p$ if the unique identifier\nfor $b$ appears in the property table associated with $p$, $T_p$. \nIf $p$ is a property that can have\none or more values associated with it, the entry for $b$ in table $T_p$ will \ncontain the $n$-tuple of such values next to it.''\n\nAs an example, a possible entry in table $T_{data}$\nfor a bibliographic entry which has a $data$ property associated to it\ncould be:\n\n\\begin{small}\n\\begin{verbatim}\n1999A&A...341..121S\n http://cdsweb.u-strasbg.fr/htbin/myqcat3?\n J/A+A/341/121/\n http://adc.gsfc.nasa.gov/adc-cgi/cat.pl?\n /journal_tables/A+A/341/121/\n\\end{verbatim}\n\\end{small}\n\nThe first column contains the bibliographic identifier for the property,\nwhile the second column contains the values of the $data$ property,\nin this case a list of URLs of electronic data tables published in the\npaper. (Note that this record has been split on several lines for\neditorial reasons.)\n\nThe file structure most amenable to representing these property tables\nis again an inverted file, which allows fast binary searches on the \nbibcode identifiers. As is the case for the inverted files used\nto perform fielded searches on the contents of the bibliographic\nentries in our database (see section \\ref{indexing}), \neach property table is decomposed in two parts, an index file \nand a list file. Since the records in the index file contain only\nbibcodes, which have a fixed length, we can create a\nbinary index file where each record consist of one\nbibcode identifier (which is the sort key in the file), a pointer \ninto the list file, and the number of property values associated with \nthe bibcode.\nEntries in the list file are variable length, newline separated records,\neach record corresponding to a property value.\n\nIn addition to the index and list files, \na database-specific file is generated for each property\ncontaining the list\nof all bibcodes in that particular database which possess that\nproperty. \nWhen the data structures used by the search engine are loaded into\nrandom access memory, these lists of bibcodes are read and \nfor each bibliographic entry a binary array containing the list \nof properties which it possesses is created.\nBy storing this information as part of the memory-resident data \nstructures used by the search engine, selection and filtering of \nbibliographic entries based on their properties becomes a very efficient\noperation.\nThe current implementation uses a 32-bit integer to represent the \nbinary array of properties, where the $n$-th bit is set if and only\nif the bibliographic entry possesses the $n$-th property.\n\n\n\\subsection {\\label{propsoft} Implementation of the Property Database \n\tManagement Software}\n\nTo provide the capability of merging properties and values generated\nfrom separate sources and in different formats, \nwe devised a framework consisting of a\nhierarchical set of files and software utilities which \nare used to implement an efficient processing pipeline \n(see figure \\ref{ADS_architectureF5}). \nThe approach we follow may be regarded as being bottom-up, because\nthe property files are always created from smaller, independently\nupdated datasets. Updating of such datasets is typically event-driven, \nas described below.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_architectureF5.eps}}\n\\caption[]{ Schema used for the creation of bibliographic\nproperties. In this abstract example, four different sources\ncontribute to the creation of bibliographic property files $a.bib,\nb.bib, c.bib, d.bib.$ \nThe input files used to generate the global list of properties may\nconsist of either static lists of bibcodes ($c.bib$), tabular\ndata to be reprocessed to create properly formatted entries ($b.tab$),\nlists of URLs containing information to be retrieved and processed\n($a.uri$), or ``filter'' functions acting on the global list of\nbibliographic entries ($d.flt$). The system allows for the existence\nof ``exception bibcodes,'' here represented as the contents of files\n$x.kill$ and $y.kill$ that are removed from the global list of\nbibcodes before the property inverted file $all.props$ is created. The\nexecution and updating of any of these files is controlled by a system\nof makefiles that trigger updating only if necessary. }\n\n\\label{ADS_architectureF5}\n\\end{figure}\n\t\t\n\nA top-level directory is created which\ncontains one subdirectory for each property in the database. Each of\nthese subdirectories in turn contains files \nrepresenting different datasets which need to be merged together.\nThe nature and content of such files is determined by their \nextension, according to the following conventions:\n\n\n.tab: files containing identifiers and properties as provided by\n\tdifferent data centers and users; these entries will need to\n\tbe translated to the standard format used by scripts \n\tmanaged by the ADS staff\n\n.bib: files containing lists of tab-separated identifier and value pairs;\n\tthese entries are suitable to be merged into a single property\n\tfile used by the ADS search engine\n\n.fmt: executable procedures which generate .bib files from their\n\trespective .tab files; these procedures contain\n\tformat- and domain- specific knowledge about the source of the\n\tparticular dataset and the mapping of entries from the .tab\n\tfile into the .bib file\n\n.uri: file containing the URLs of documents which should be downloaded\n\tfrom the network and merged to create a .tab file; these URLs\n\tmay correspond to static or dynamic documents generated by\n\tother service providers listing the bibliographic properties\n\tavailable on their web site\n\n.flt: executable procedures which generate .bib files by filtering\n\tthe complete list of bibliographic identifiers according to\n\tsome data-specific criteria; one example of such filter is the\n\tone which produces the list of all refereed bibcodes from the\n\tlist of all bibcodes by checking the journal abbreviation\n\n.kill: file containing the list of bibcodes which should $not$ be\n\tlisted as possessing a particular property; these are\n\ttypically used to implement ``exceptions to the rule,'' cases;\n\tfor example, we use a kill file to remove bibcodes\n\tcorresponding to editorial notices from the global list of\n\tpapers appearing in a refereeed journal.\n\nData retrieval and formatting scripts designed after the GNU ``make''\nutility limit the creation and processing of data to what is strictly\nnecessary. \nIn particular, data sources that are specified as URLs are downloaded \nonly if their timestamp is more recent than their local copy.\nThis obviously applies to network protocols that support the notion of\ntime-stamping, e.g. HTTP and FTP.\nSimilarly, scripts that are used to format input tables into lists of\nbibcodes and relative URLs are only executed if the timestamp of the\nrelevant tables indicates that they have been modified more recently\nthan their corresponding target file.\n\n\n\\section {\\label{mirrors} Database Mirroring}\n\nAll of the software development and data processing in the ADS has\nbeen carried out over the last 6 years in a UNIX environment.\nDuring the life of the project, the workgroup-class server used\nto host the ADS services has been upgraded twice to meet the\nincreasing use of the system. The original dual processor Sun 4/690\nused at the inception of the project was replaced by a SparcServer\n1000E with two 85MHz Supersparc CPU modules in 1995 and \nsubsequently an Ultra Enterprise 450 with two 300MHz Ultrasparc CPUs\nwas purchased in 1997. These two last machines are still currently\nused to host the ADS article and abstract services, respectively.\n\nSoon after after the inception of the article service in 1995 it\nbecame clear that for most ADS users the limiting factor when\nretrieving data from our computers was bandwidth rather than raw\nprocessing power.\nWith the creation of the first mirror site hosted by the CDS in late \n1996, users in different parts of the world started being able \nto select the most convenient database server when using the ADS\nservices, making best use of bandwidth available to them. \nAt the time of this writing, there are seven mirror sites located on\nfour different continents, and more institutions have already expressed\ninterest in hosting additional sites.\nThe administration of the increasing number of mirror sites requires a\nscalable set of software tools which can be used by the ADS\nstaff to replicate and update the ADS services both in an\ninteractive and in an unsupervised fashion.\n\nThe cloning of our databases on remote sites has presented new\nchallenges to the ADS project, imposing\nadditional constraints on the organization and operation of our system.\nIn order to make it\npossible to replicate a complex database system elsewhere, the\ndatabase management system and the underlying data sets have to be\nindependent of the local file structure, operating system, \nand hardware architecture.\nAdditionally, networked services which rely on\nlinks with both internal and external web resources (possibly\navailable on different mirror sites) need to be capable\nof deciding how the links should be created, giving users the\noption to review and modify the system's linking strategy. \nFinally, a reliable\nand efficient mechanism should be in place to allow unsupervised\ndatabase updates, especially for those applications involving the\npublication of time-critical data.\n\nIn the next sections we describe the implementation of an efficient\nmodel for the replication of our databases to the ADS mirror sites.\nIn section \\ref{sysindep} we describe how system independence has been\nachieved through the parameterization of site-specific variables and\nthe use of portable software tools. In section \\ref{siteindep} we\ndescribe the approach we followed in abstracting the availability of\nnetwork resources through the implementation of user-selectable\npreferences and the definition of site-specific default values.\nIn section \\ref{mirrorsoft} we describe in more detail the paradigm\nused to implement the synchronization of different parts of the ADS\ndatabases. We conclude with section \\ref{mirrorenh} where we discuss\npossible enhancements to the current design.\n\n\n\\subsection {\\label{sysindep} System Independence}\n\nThe database management software and the search engine used by the\nADS bibliographic services have been written to be independent from\nsystem-specific attributes to provide maximum flexibility in the \nchoice of hardware and software in use on different mirror sites.\nWe are currently supporting the following hardware architectures:\nSparc/Solaris, Alpha/Tru64 (formerly Digital Unix), IBM RS6000/AIX,\nand x86/Linux. Given the current trends in hardware and operating\nsystems, we expect to standardize to GNU/Linux systems in the future.\n\nHardware independence was made possible by writing portable\nsoftware that can be either compiled under a standard compiler and\nenvironment framework (e.g. the GNU programming tools, \\cite{GNU})\nor interpreted by a standard language (e.g. PERL version 5,\n\\cite{PERL}). Under this scheme,\nthe software used by the ADS mirrors is first compiled from a common\nsource tree for the different hardware platforms\non the main ADS server, and then the\nappropriate binary distributions are mirrored to the remote sites.\n\nOne aspect of our databases which is affected by the specific\nserver hardware is the use of binary data in the list files, since\nbinary integer representations depend on the native byte ordering\nsupported by the hardware.\nWith the\nintroduction of a mirror site running Digital UNIX in the summer of\n1999, we were faced with having to decide whether it was better to\nstart maintaining two versions of the binary data files used\nin our indices or if the two integer implementations should be handled\nin software. While we have chosen to perform the integer conversion\nin software for the time being given the adequate speed of the\nhardware in use, we may revisit the issue if the number of mirror\nsites with different byte ordering increases with time.\n\nOperating System independence is achieved by using a standard\nset of public domain tools abiding to well-defined POSIX standards\n(\\cite{POSIX}). Any additional enhancements to the\nstandard software tools provided by the local operating system\nis achieved by cloning more advanced\nsoftware utilities (e.g. the GNU shell-utils package) and using them\nas necessary.\nSpecific operating system settings which control kernel parameters \nare modified when appropriate to increase system performance and/or\ncompatibility among different operating systems \n(e.g. the parameters controlling access to the system's shared memory).\nThis is usually an operation that needs to be done only once\nwhen a new mirror site is configured.\n\nFile-system independence is made possible by organizing the data\nfiles for a specific database under a single directory tree, and\ncreating configuration files with parameters pointing to the location\nof these top-level directories. Similarly, host name\nindependence is achieved by storing the host names of ADS servers in\na set of configuration files.\n\n\n\\subsection {\\label{siteindep} Site Independence}\n\nWhile the creation of the ADS mirror sites makes it virtually \nimpossible for users to notice any difference when accessing the\nbibliographic databases on different\nsites, the network topology of a mirror site and its connectivity\nwith the rest of the Internet play an important role in the way\nexternal resources are linked to and from the ADS services. With the\nproliferation of mirror sites for several networked services in\nthe field of astronomy and electronic publishing, the capability to\ncreate hyperlinks to resources external to the ADS based on the\nindividual user's network connectivity has become an important issue.\n\nThe strategy used to generate links to networked services external to\nthe ADS which are available on more than one site follows a\ntwo-tiered approach. First, a ``default'' mirror can be specified in a\nconfiguration file by the ADS administrator (see figure \\ref{ADS_architectureF6}).\nThe configuration file defines a set of parameters used to compose\nURLs for different classes of resources, lists all the\npossible values that these parameters may assume, and then defines a\ndefault value for each parameter. Since these configuration files are\nsite-specific, the appropriate defaults can be chosen for each of the\nADS mirror sites depending on their location.\nADS users are then allowed to override these defaults by\nusing the ``Preference Settings'' system (SEARCH) to\nselect any of the resources listed under a category as their default\none. Their selection is stored in a site-specific user preference\ndatabase which uses an HTTP cookie as an ID correlating users with\ntheir preferences (SEARCH).\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_architectureF6.eps}}\n\\caption[]{ The configuration file used to define variables and\nrelated sites for resources available from multiple network\nlocations. It should be noted that this approach can be used for\nparameterizing and generalizing URL resolution even in those cases\nwhere the resource is available from a single location. }\n\n\\label{ADS_architectureF6}\n\\end{figure}\n\t\t\n\n\nIn order to create links to external resources which are a function of\na user's preferences, we store the parametrized version of their URLs in\nthe property databases. The search engine expands the\nparameter when the resource is requested by a user\naccording to the user's preferences. \nFor instance, the parametrized URL for the\nelectronic paper associated with the bibliographic entry \n{\\tt 1997ApJ...486...42G} can be expressed as \n{\\tt \\$UCP\\$/cgi-bin/resolve?1997ApJ...486...42G}. Assuming the user has\nselected the first entry as the default server for this resource, the\nsearch engine will expand the URL to the expression:\n\\begin{verbatim}\nhttp://www.journals.uchicago.edu/cgi-bin/resolve?\n 1997ApJ...486...42G\n\\end{verbatim}\nThis effectively allows us to implement simple name resolution for a\nvariety of resources that we link to.\nWhile more sophisticated ways to create dynamic links have been\nproposed and are being used by other institutions \n(\\cite{VDS99,FERNIQUE98}), there is currently no\nreliable way to automatically choose the ``best'' mirror site for a\nparticular user, since this depends on the connectivity between the\nuser and the external resource rather than the connectivity\nbetween the the ADS mirror site and the resource.\nBy saving these settings in a user preference\ndatabase indexed on the user HTTP cookie ID (SEARCH), \nusers only need to define their preferences once and our interface \nwill retrieve and use the appropriate settings as necessary.\n\n \n\n\\subsection {\\label{mirrorsoft} Mirroring software}\n\nThe software used to perform the actual mirroring of the databases\nconsists of a main program running on the ADS master site initiating\nthe mirroring procedure, and a number of scripts, run on the mirror\nsites, which perform the transfer of files and software necessary to\nupdate the database. \nThe paradigm we adopted in creating the tools used to maintain the\nmirror sites in sync is based on a ``push'' approach: updates are\nalways started on the ADS main site. \nThis allows mirroring to be easily controlled by the\nADS administrator and enables us to implement event-triggered updating of\nthe databases.\nThe main mirroring program, which can be run either from\nthe command line or through the Common Gateway Interface (CGI), \nis a script that initiates a remote shell session on the remote sites\nto be updated, sets up the environment by evaluating the mirror sites' and\nmaster site's configuration files, and then runs scripts on the remote\nsites that synchronize the local datasets with the ADS main site.\nAn example of the menu-driven CGI interface and a mirroring\nsession are shown in figure \\ref{ADS_architectureF7}.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_architectureF7.eps}}\n\\caption[]{ The WWW interface used by the ADS administrators to update\ndifferent components of the databases on the different mirror\nsites. The small windows at the bottom of the screen display, for each\nof the ADS databases, the version number currently operational at each\nmirror site. }\n\n\\label{ADS_architectureF7}\n\\end{figure}\n\t\t\n\n\nThe updating procedures are specialized scripts which check and\nupdate different parts of the database and database management\nsoftware (including the procedures themselves). \nFor each component of the database that needs to be updated,\nsynchronization takes place in two steps, namely the remote updating\nof files which have changed to a staging directory, and the action of\nmaking these new files operational. This separation of mirroring\nprocedures has allowed us to enforce the proper checks on integrity\nand consistency of a data set before it is made operational.\n\nThe actual comparison and data transfer for each of the files to be\nupdated is done by using a public domain implementation\nof the rsync algorithm (\\cite{TRIDGELL99}).\nThe advantages of using rsync to update data files rather than\nusing more traditional data replication packages are summarized below.\n\n1) Incremental updates: rsync updates individual files by scanning\n their contents, computing and comparing checksums on blocks of data\n within them, and copying across the network only those blocks that\n differ. Since during our updates only a small part\n of the data files actually changes,\n this has proven to be a great advantage. Recent implementations of the \n rsync algorithms also allow partial transfer of files,\n which we found useful when transferring the large index files \n used by the search engine. In case the network connection is lost\n or times out while a large file is transferred, the partial file\n is kept on the receiving side so that transfer of additional \n chunks of that file can continue where it left off on the next\n invocation of rsync.\n\n2) Data integrity: rsync provides several options that can be used to\n decide whether a file needs updating without having to compare its\n contents byte by byte. The default behavior is to initiate a block\n by block comparison only if there is a difference in the basic file \n attributes (time stamp and file size). The program however can be\n forced to perform a file integrity check by also requesting a match\n on the 128-bit MD4 checksum for the files.\n\n3) Data compression: rsync supports internal compression of the data\n stream sent between the master and mirror hosts by using the zlib\n library (\\cite{ZLIB}). \n\n4) Encryption and authentication: rsync can be used in conjunction with the \n Secure Shell package (\\cite{SSH}) to enforce authentication\n between rsync client and server host and to transfer the data in an\n encrypted way for added security.\n Unfortunately, since all of the ADS mirror sites are outside of the\n U.S., transfer of encrypted data could not be performed at\n this time due to restrictions and regulations on\n the use of encryption technology.\n\n5) Access control: the use of rsync allows\n the remote mirror sites to retrieve data from the master ADS site\n using the so-called anonymous rsync protocol. This allows the\n master site to exercise significant control over which hosts are\n allowed to access the rsync server, what datasets can be \n mirrored, and does not require remote shell access to the main ADS\n site, which has always been the source of great security problems.\n\nDuring a typical weekly update of the ADS astronomy database, as many\nas 1\\% of the text files may be added or updated, while the index files\nare completely recreated. By checking the attributes of the\nindividual files and transferring only the ones for which either \ntimestamp or size has changed, the actual data which gets transferred\nwhen updating the collection of text files\nis of the order of 1.7\\% of the total file size (12MB vs. 700MB).\nBy using the incremental update features of rsync when mirroring a new\nset of index files, the total amount of data being transferred is\nof the order of 38\\% (250MB vs. 650MB).\n\n\n\\subsection {\\label{mirrorenh} Planned Enhancements}\n\n\nWhile the adoption of the rsync protocol has made it possible to\ndramatically decrease the time required to update a remote database,\nthere are several areas where additional improvements could be made to\nthe current scheme in an effort to reduce the amount of redundant\nprocessing and network transfers on the main ADS server. Some of the\nplanned improvements are discussed below.\n\nGiven the CPU-intensive activity of computing lists of file signatures\nand checksums for files selected as potential targets for a transfer,\nthe rsync server running on the main ADS site is often under a heavy\nload when the weekly updates of our bibliographic databases are\nsimultaneously mirrored to the remote sites. \nUnder the current implementation of the rsync server software, each\nrequest from a mirror site is handled by a separate process which\ncreates the list of files and directories being checked.\nTherefore, the load on the server increases linearly with the\nnumber of remote hosts being updated, although much of the processing\nrequested by the separate rsync connections is in common and takes\nplace at the same time.\nBy adding an option to cache the data signatures generated by the\nrsync server and exchanged with each client, most of the processing\ninvolved could be avoided. This option, first suggested by the author\nof the rsync package (\\cite{RCACHE}) but never implemented, would\nsignificantly benefit busy sites such as the ADS main host.\nA similar approach has been used by \\cite{DEMPSEY99} to implement an\nexperimental replication mechanism based on rsync. We hope that a\nstable and general approach to this caching issue can be adopted soon\nand are collaborating with the maintainers of the package on its\ndevelopment. \n\nA second improvement that would significantly reduce the bandwidth\ncurrently used during remote updating of the ADS mirror sites is the\nimplementation of a multicasting or cascading mirroring model (see\nfigure \\ref{ADS_architectureF8}). Internet multicasting is still a\ntechnology under development (\\cite{MILLER98}) and efficient\nimplementations require special software support at the IP (Internet\nProtocol) level, over which we have no control. \nThe cascading model can instead by implemented at the application\nlevel using current software tools. Under this model, the\nadministrator of the main server to be cloned defines a tree in which\nthe nodes represent the mirror sites, with the root of the tree being\nthe main site. Data mirroring is then implemented by having each node\nin the tree ``push'' data to its subordinate nodes.\nThis approach trades off the simplicity of simultaneous updating \nfor all mirror sites from a central host\nin favor of a sequence of cascading updates, which is a sensible\nsolution once the number of mirror sites becomes large.\nWe are currently experimenting with this model on a prototype system and\nplan to make the design operational by the end of 1999 if the design\nproves to be advantageous.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{ADS_architectureF8.eps}}\n\\caption[]{Schematic representation of network mirroring models used \nto replicate a central database available on the ADS master database \nserver to a number of mirror sites (A-H). Traditional model (a): data \nis transferred using parallel, independent data pipes between the master \nand the mirror sites. Multicasting model (b): one single stream of data \nis transferred from the master site to a central router and then \nmultiplexed to the mirror sites using multicast technologies. Cascading \nmodel (c): a hierarchy of mirror nodes is defined based on the relative \nnetwork connectivity; each node updates the local copy of its \ndatabases and then proceeds to mirror them to its subordinate nodes. }\n\n\\label{ADS_architectureF8}\n\\end{figure}\n\t\t\n\n\n\n\\section {\\label{discussion} Future Developments}\n\nBy all accounts, the ADS project has been very successful in providing\nbibliographical services to the astronomer and research librarian.\nMuch of the system's strength has been its role as part \nof a network of services designed to provide advanced search and retrieval\ncapabilities to the scientific community at large.\nGiven the rapid changes in the field of electronic publishing,\nresource linking, digital library research,\nit is of great importance for our project to adapt its operations\nto this ever-changing environment and its underlying technologies.\n\nIn this last section we analyze some of the promises and challenges\nthat we expect to face over the next several years and we discuss\nhow they may affect the evolution of our system.\nIn section \\ref{newdata} we describe the new datasets that are\nbecoming available to our project and the changes necessary for their\nintegration in the existing system architecture.\nSection \\ref{newtech} describes the effect of expected \ntechnological changes on the operations of the ADS.\nFinally, section \\ref{newserv} discussed how increased collaboration\nand inter-operability among data providers can lead to the creation of\na more integrated environment making better use of \ninformation discovery and electronic publishing technologies.\n\n\n\\subsection {\\label{newdata} New Data}\n\nFrom the user prospective, one of the most significant changes will be \nthe completion of our full-text coverage and abstracting for the \nscholarly astronomical literature. \nOver the next year we expect to complete the digitization of all\nastronomical journals back to volume 1 (DATA).\nThe availability of such a large body of scanned publications\nallows us to pursue some important goals through the use \nof Optical Character Recognition (OCR) technology: the creation of\nfull-text documents and the extraction of abstract and citation \ninformation from them.\n\nThe full text of an article produced by OCR programs can be used\nby the indexing and search engine to provide better retrieval\ncapabilities. However, the current indexing model has been\ndeveloped to work well with a homogeneous set of bibliographic\ndata with little variation in document length and content model;\nextending the scope of our databases to include the full-text of\narticles may therefore require a new approach to the entire \narchitecture behind the indexing and search engines.\nFurthermore, since the output generated by OCR packages is known to\ncontain incorrectly recognized characters and words, new strategies\nmay be required to manage this level of uncertainty during indexing\nand searching.\n\nThe extraction and OCRing of important document fragments such as\nabstracts and references is currently an ongoing process which holds\ngreat promise (DATA).\nEssentially, the combination of pattern recognition and OCR \ntechniques allows us to identify areas in a scanned document\ncorresponding to the abstract or reference section of a paper.\nThe text extracted from an abstract section is then reformatted\nand inserted into the bibliographic record for that paper.\nPeriodic analysis of the text index has been \nnecessary to identify and correct misinterpreted characters\nand words produced by the OCR software.\nThe increased amount of human checks on our data set as a quality\nassurance measure has been the price to pay for integrating these\nadditional abstracts in our bibliographic records.\n\nText extracted from a reference section is analyzed by \nprograms making use of natural language processing techniques \nto identify the individual works cited in the article and\nadd them to our citation database.\nThe challenge we are facing in this case is creating a robust system\ncapable of correctly parsing and matching the cited reference\nstrings with bibliographic records in our database\n(\\cite{1999adass...8..291A}), with the additional complication that the\ninput text may contain characters incorrectly recognized by the\nOCR software.\n\n\n\\subsection {\\label{newtech} New Technologies}\n\nThe latest developments in Electronic Data Interchange and User \nInterfaces advocate the adoption of a model of data\nrepresentation where there is clear separation between content,\nmetadata, and style.\nThe widespread endorsement of XML and related proposals such as\nthe XLink language, the Extensible Style Language (XSL), and \nthe Document Object Model (DOM), seems to indicate that we will \nsee pervasive use of XML across platforms and implementations.\nWhile this raises hopes that data exchange among different\nastronomical data centers and institutions can be streamlined, it is not clear \nat this point that a unique framework describing all resources\nin astronomy can be defined, nor that such a system is necessary\nat this point.\nHowever, the adoption of XML as the ``lingua franca'' for data \ninterchange can help remove the initial obstacles preventing more\nwidespread creation of peer-to-peer connections between information\nproviders and can help speed up the creation \nof ``federated'' services (\\cite{AML}).\n\nIn this context, we hope to leverage the wide deployment of XML-based\napplications to generalize and extend the services currently offered \nto our collaborators and users.\nThis involves modifying the implemented APIs (SEARCH) to\nallow output of structured XML documents containing both metadata and \nbibliographic data. \nWe have already started adopting this paradigm while implementing\nnew and experimental services which require the exchange of data and\nmetadata structures between client and server, \nsuch as the ADS reference resolver\n(\\cite{1999adass...8..291A}).\n\nAnother issue related to data interchange which is currently \nreceiving much attention is the definition of persistent identifiers\nfor bibliographic resources available on the Internet. This issue\nis a particular instance of a more general problem, which is \nthe need to define common naming schemes for digital objects \nand distributed locator\nservices allowing their resolution.\nFor a number of years this has been recognized as one of the \nmost important infrastructure components necessary for the \nlarge-scale development of digital library systems (\\cite{DLWR}).\nToday most publishers are providing\nlocation services which are based on the traditional paradigm of\nidentifying a published work by journal, volume and page.\nIt is becoming increasingly clear that a more general mechanism\nwill have to be adopted in the future since this model does not\nextend well into the digital era.\nFor instance, a publication may be available only in electronic\nform (as is already the case for some ``e-journals'' such as\nEPJdirect and ZPhys-e from Springer-Verlag).\nor may correspond to a multimedia object rather than a traditional\ntext document; in these cases, the concept of pagination loses\nits meaning. \nThe Document Object Identifier (DOI, \\cite{DOI}), which has been\nproposed by an international consortium of publishers, holds the \npromise of becoming the universal identifier suitable for \nnaming digital objects. Unfortunately, the required registration\nprocedures and management of DOI space and limited support for its\nlocation services seem to have discouraged\nits widespread adoption so far (\\cite{DAVIDSON98}).\n\nThe ADS has already extended the use \nof the bibcode identifier in different ways to account for the \nexistence of electronic-only publications (DATA), but it is \nbecoming increasingly more difficult to map new document\nidentifiers into a model that was designed to describe printed\nmaterial only.\nIt is likely that over the next few years our project will need\nto adopt new notations for identifying bibliographic records, \nwhile still maintaining backward compatibility with the existing\nbibcodes for printed work.\nIn this sense, it is likely that ADS will be able to help the\nastronomical community in the transition from print-based to\nelectronic publishing by providing resolving services for astronomical\nbibliographies and related resources.\n\n\n\\subsection {\\label{newserv} New Services}\n\nThe adoption of common technologies and protocols by data providers has\nhelped create a low-level of inter-operability among different\ndata services (in the sense that users can simply browse across different\nweb sites by following links between them).\nHowever, with the exponential increase of documents and\nservices available on the web, the problem of providing an \nintegrated tool for locating information of interest to a \nresearcher has remained unsolved. While well-organized \nrepositories and archives with good search interfaces \nexist for a variety of data sets, a scientist who needs to\nconsult several such archives is left with having to\nindividually query each one separately and then organize\nthe results collected from each one of them.\nIt is fortunate that the creation of the ADS and its ongoing\ncollaboration with other data providers has reduced (if not completely\neliminated) this problem for astronomers, but this is not the case for\nscientists in other disciplines or for those researches whose work\nspans across the conventional boundaries of scientific research fields.\n\nThe problem of providing a unified search \nmechanism across datasets is being tackled both within the\nindividual disciplines (\\cite{1999adass...8..221H,FERNIQUE98,AML}) \nand at the architectural level (\\cite{SCHATZ97}).\nA proposed solution to this problem is the creation of federated services\ncomposed by ``clustering'' the combined assets and search capabilities\nof several independent data centers. \nA common set of metadata elements \ndescribing the local search domain and interface can be used to\ntranslate generic queries into site-specific ones, and then\nmerge and present the results to the users.\nWhile this type of approach is known to work within well-restricted\nresearch domains, the broader problem of querying databases belonging\nto different research fields is far more complex and requires\nthe creation of systems capable of implementing semantic\ninter-operability (\\cite{SCHATZ97,DLWR}).\nWhile the ADS has been offering direct access to its search engine\nsince 1996 (SEARCH), \nin order for the ADS to become part of such a federated system, we\nwill need to provide an increased level of abstraction and access to\nthe capabilities of our search interfaces. \nAdditionally, the emerging standards for site- and \ndatabase-specific resource descriptions will require the creation and\nmaintenance of a body of metadata defining both the extent of our\ndatabases and the supported query interfaces.\n\\cite{HANISCH99} has recently proposed the creation of such a\ndistributed system for Astronomy and the Space Sciences.\n\nAnother important aspect of services increasing inter-operability\nbetween data providers is cross-linking of online resources.\nWhile most publishers of scientific journals have been able to \ncreate electronic versions of their journals relatively quickly\nsoon after the explosion in popularity of the web, only a few of them\nhave taken advantage of the new capabilities that the technology\nhas to offer, namely the possibility to create hyperlinks between\nonline documents and related resources.\nIn this respect, electronic publishing in astronomy was ahead of \nits times with the publication by the University of Chicago Press\nin late 1996 of the electronic version of the Astrophysical Journal\nwhich contained hyperlinks from the reference section of\narticles to bibliographic records in the ADS.\nThe early implementation of this feature became possible thanks\nto the close collaboration between the publisher, the ADS staff,\nand the visionary leadership provided by the American Astronomical\nSociety (AAS).\nSimilarly, editors and publishers have now made it their policy to\nsubmit electronic versions of data tables appearing in astronomical\npapers to the CDS and Astronomical Data Center (ADC) archives,\nallowing ADS to easily maintain links to these datasets in its\nbibliographic records. This practice was estabilished back in 1990\nwith an agreement between the CDS and the editors of the journal\nAstronomy \\& Astrophysics. \n\nWhile reference and object linking has today become more commonplace\n(\\cite{HITCHCOCK98}), there are a number of unresolved problems that\nlimit its usefulness.\nThe issue of linking a reference to an instance of the document it\nrefers to can be viewed as a two step process (\\cite{CAPLAN99}):\n(1) resolution of a reference string into a document identifier; \nand (2) resolution of the document identifier into one or more\nURLs.\nIn the current use of the ADS reference resolver, \n(\\cite{1999adass...8..291A}) step (1) is \naccomplished by the publisher during the last stages of the electronic\npublication process, and links are created only if a reference string\nis found to correspond to a valid bibcode in ADS (``static linking'').\nThe step of document resolution (2) is another example of the problem\nof object resolution mentioned in section \\ref{newtech}. In this case,\na bibcode needs to be mapped into the ``best'' URL corresponding to\nit, and is typically implemented as a site-specific resolution\nactivity, so that for example, the CDS mirror of the University of\nChicago journals will link to the CDS mirror of the ADS bibliographic\nservices.\n\nWhile this model has worked well for many astronomical journals,\nit has some shortcomings.\nFirst of all, the computation of static links at publication time\ndoes not allow for the possibility that one of the works cited in\nthe reference section may become available at a later date (e.g.\nif the coverage of the literature has been extended or if a more\naccurate resolution of the reference is later implemented).\nFrom a theoretical point of view, a better approach to the problem\nwould be the use of ``dynamic linking,'' in which links are created\nwhen the document is downloaded (\\cite{VDS99}).\nIt is likely that most publishers will move towards a mixed model \nin which on-line documents are periodically reprocessed for the\npurpose of updating links between them and external resources\nthat may have become available, or to provide options for\nforward-looking citation queries into bibliographical databases.\n\nAs far as the issue of bibcode resolution, it is clear that a better\napproach to having site-specific settings would be to allow real-time\nresolution of bibcode identifiers based on the preference of the\nindividual users and the current availability of relevant resources.\nThe approach we follow when resolving links to external resources\n(SEARCH) does account for user preferences, but does not take into\naccount real-time availability of the possible instances of the\nresource. \nThis is in contrast with the approach followed by \\cite{FERNIQUE98}, where\nthe opposite is true.\nIt is clear that in order to create a reliable system for resolving\nastronomical resources, and integration of both approaches is\nnecessary, so that a global user profile can be used to specify\npreferences while a global resource database can be used to specify\nthe availability and location of these resources on the network.\nThe implementation of such a system is greatly complicated by the\nincreasingly complex organization of networks, with firewalls\nand proxy servers acting as intermediary agents in the activity of\nresource resolution. \nHopefully these issues will be solved over the next few years by the\nadoption of standard practices and software tools.\n\n\n\\section {\\label{conclusions} Conclusions}\n\nThe design and implementation of the ADS bibliographic services has\nbeen driven by the desire to provide flexible search capabilities to\nthe astronomical community. \nThe original decision to create our own suite of software tools for\nindexing and searching the databases has proven to be an important one\nas it has given us the freedom to continuously enhance and tailor the\nsoftware to our users' needs.\nWith freedom, however, also came the responsibility of maintaining a\ncomplex system which has now been ported to a variety of hardware and\nsoftware platforms. Fortunately,\nthe adoption of standard programming languages and coding techniques\nhas greatly facilitated the task.\n\nOver the years, the ADS has evolved from being a user-oriented\nsystem to becoming an open service for the discovery and\nretrieval of bibliographic data, allowing integration of our\ncapabilities in the operation of other information providers.\nAt the same time, our system was expanded from being simply a\nsearchable archive of bibliographic references to being a\nservice offering relational links among records within our system and \nto resources available elsewhere.\nIn this respect, the design of a hierarchical framework for the\nmanagement of bibliographic resources has provided the required\nlevel of flexibility and extensibility.\nWith the recent proliferation of mirror sites for popular resources in\nastronomy, we have adopted a simple yet powerful mechanism for the\nresolution of links to resources available at multiple\nlocations, adding user customization to the\nresolution process. \n\nWith the completion of full-text coverage of the astronomical literature\nover the next few years, the ADS will be able to significantly increase\nthe holdings of its citation database and provide full-text search and\nretrieval capabilities.\nWith the adoption of new technologies and standards in electronic\ndata interchange, the ADS is likely continue to play an important role in the\nintegration of network services in astronomy.\n\n\\acknowledgements\n\nThe usefulness of a bibliographic service is only as good as\nthe quality and quantity of the data it contains. 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Zhou, \n\t745\n\n\\bibitem[Knuth 1973]{KNU73} Knuth, D. 1973, \n\t``The Art of Computer Programming, Vol. 3: Sorting and\n\tSearching,'' Addison-Wesley (New York)\n\n\\bibitem[Kurtz et al. 2000]{OVERVIEW} Kurtz, M. J., Eichhorn, G., \n\tAccomazzi, A., Grant, C. S., Murray, S. S., \\& \n\tWatson, J. M. 2000, \n\t``The NASA Astrophysics Data System: Overview,''\n\tA\\&AS, this issue (OVERVIEW)\n\n\\bibitem[Kurtz et al. 1993]{1993adass...2..132K} Kurtz, M. J., \n\tKarakashian, T., Grant, C. S., Eichhorn, G., Murray, S. S., \n\tWatson, J. M., Ossorio, P. G. \\& Stoner, J. L. 1993, \n\t``Intelligent Text Retrieval in the NASA Astrophysics Data System,''\n\tin ASP Conf. Ser. 52, \n\tAstronomical Data Analysis Software \\& Systems II, \n\ted. R. J. Hanisch, R. J. V. Brissenden, \\& J. Barnes,\n\t(San Francisco: ASP),\n\t132 \n\n\\bibitem[Lee, Dubin \\& Kurtz 1999]{DUBIN99} Lee, J. , Dubin, D. S. \\& \n\tKurtz, M. J. 1999,\n\t``Co-occurrence Evidence for Subject Vocabulary Reconciliation\n\tin ADS Databases,''\n\tin ASP Conf. Ser., 172,\n\tAstronomical Data Analysis Software and Systems VIII, \n\ted. D. M. Mehringer, R. L. Plante, \\& D. A. Roberts,\n\t(San Francisco: ASP),\n\t287\n\n\\bibitem[Loukides \\& Oram 1996]{GNU} Loukides, M., \\& Oram, A. 1996,\n\t``Programming With Gnu Software (Nutshell Handbook),''\n\tO'Reilly \\& Associates, Inc.\n\n\\bibitem[Lynch \\& Molina-Garcia 1996]{DLWR} \n\tLynch, C. \\& Molina-Gracia, H. 1996, \n\t``Interoperability, Scaling, and the Digital Libraries\n\tResearch Agenda,'' \\\\\n\t$<$URL:http://www-diglib.stanford.edu/diglib/pub/\\-reports/iita-dlw/$>$\n\n\\bibitem[Miles 1998]{CDF} Miles, P. 1998,\n\t``Internet World Guide to Webcasting,''\n\tWiley \\& Sons\n\n\\bibitem[Miller et al. 1998]{MILLER98} \n\tMiller, K., Robertson, K., Tweedly, A., \\& White, M. 1998, \n\t``StarBurst Multicast File Transfer Protocol (MFTP) Specification,''\n\tInternet Draft, \n\tInternet Engineering Task Force\n\n\\bibitem[Miller 1997]{MILL97} Miller, U. 1997,\n\t``Thesaurus construction: Problems and their roots,''\n\tInformation Processing \\& Management, 33, 481\n\n\\bibitem[Murtagh \\& Guillaume 1998]{AML} Murtagh, F. \\& \n\tGuillaume, D. 1998, \n\t``Distributed Information Search and Retrieval for \n\tAstronomical Resource Discovery and Data Mining,'' \n\tin ASP Conf. Ser., 153,\n\tLibrary and Information Services in Astronomy III, \n\ted. U. Grothkopf, H. Andernach, S. Stevens-Rayburn, \\& M. Gomez\n\t(San Francisco: ASP),\n\t51\n\n\\bibitem[Navarro 1998]{NAV98} Navarro, G. 1998\n\t``Approximate Text Searching,''\n\tPh. D. Thesis, University of Chile, Santiago, Chile\n\n\\bibitem[Oard \\& Diekema 1997]{OARD97} Oard, D. W., \\& Diekema A. R. 1997,\n\t``Cross-language information retrieval,''\n\tAnn. Rev. of Information Science \\& Technology, 33, 223\n\n\\bibitem[Paskin 1999]{DOI} Paskin, N. 1999,\n\t``DOI: Current Status and Outlook -- May 1999,'' \n\tD-Lib Magazine, 5,\\\\\n $<$URL:http://www.dlib.org/dlib/may99/05paskin.html$>$\n\n\\bibitem[Salton 1989]{SALTON89} Salton, G. 1989,\n\t``Automatic text processing: the transformation, analysis and retrieval\n\tof information by computer,''\n\tAddison-Wesley (Reading, MA)\n\n\\bibitem[Salton \\& Buckley 1988]{SALTON88} Salton, G. \\& Buckley, C. 1988,\n\t``Term weighting approaches in automatic text retrieval,''\n\tInformation Processing \\& Management, 24, 513\n\n\\bibitem[Salton \\& McGill 1983]{SALTON83} Salton, G., \\& McGill, M. J. 1983,\n\t``Introduction to Modern Information Retrieval,''\n\tMcGraw-Hill (New York)\n\n\\bibitem[Schatz 1997]{SCHATZ97} Schatz, B. R. 1997,\n\t``Information Retrieval in Digital Libraries: Bringing Search\n\tto the Net,''\n\tScience, 275, 327\n\n\\bibitem[Schmitz et al. 1995]{1995VA.....39R.272S} Schmitz, M., Helou, G., \n\tDubois, P., Lague, C., Madore, B., Corwin, H. G. J., \n\t\\& Lesteven, S. 1995, \n\t``A Uniform Bibliographic Code,''\n\tVistas in Astronomy, 39, 272 \n\n\\bibitem[Shaya et al. 1999]{1999AAS...194.8304S} Shaya, E., Blackwell, J., \n\tGass, J., Oliversen, N., Schneider, G., Thomas, B., Cheung,\n\tC., \\& White, R. A. 1999, \n\t``XML at the ADC: Steps to a Next Generation Data Archive,'' \n\tAmerican Astronomical Society Meeting, 194, 8304 \n\n\\bibitem[Shobbrook \\& Shobbrook 1992]{1992PASAu..10..134S} \n\tShobbrook, R. M. \\& Shobbrook, R. R. 1992, \n\t``The I.A.U. Thesaurus for Improved On-line Access to Information,''\n\tProc. of the Ast. Soc. of Australia, 10, 134\n\n%\\bibitem[Shobbrook \\& Shobbrook 1993]{1993asth.book.....S} Shobbrook, R. M. \n%\t\\& Shobbrook, R. R. 1993, ``The Astronomy Thesaurus,'' version 1.1,\n%\tEpping: Anglo-American Observatory\n\n\\bibitem[Shobbrook 1995]{1995VA.....39Q.272S} Shobbrook, R. M. 1995, \n\t``The Multi-Lingual Supplement to the Astronomy Thesaurus,''\n\tVistas in Astronomy, 39, 272 \n\n\\bibitem[Tridgell 1999a]{TRIDGELL99} Tridgell, A. 1999a,\n\t``Efficient Algorithms for Sorting and Synchronization,''\n\tPh. D. Thesis, The Australian National University\n\n\\bibitem[Tridgell 1999b]{RCACHE} Tridgell, A. 1999b,\n\tprivate communication\n\n\\bibitem[Unicode Consortium 1996]{UNICODE} Unicode Consortium 1996, \n\t``The Unicode Standard: Version 2.0,'' Addison-Wesley\n\t(Reading, MA)\n\n\\bibitem[Van de Sompel \\& Hochstenbach 1999]{VDS99}\n\tVan de Sompel, H., \\& Hochstenbach, P. 1999,\n\t``Reference Linking in a Hybrid Libary Environment,''\n\tD-Lib Magazine, 5,\\\\\n\t$<$URL:http://www.dlib.org/dlib/april99/van\\_de\\_sompel/\\-04van\\_de\\_sompel-pt1.html$>$\n\n\\bibitem[van Rijsbergen 1979]{VR79} van Rijsbergen, C. J. 1979,\n\t``Information Retrieval,''\n\tButterworths, 2nd ed.\n\n\\bibitem[Wall, Christiansen \\& Schwartz 1996]{PERL} \n\tWall, L., Christiansen, T., \\& Schwartz, R. 1996, \n\t``Programming PERL,'' \n\tO'Reilly \\& Associates, Inc., 2nd ed.\n\n\\bibitem[Wilkins 1998]{1998lisa.conf..317W} Wilkins, G. A. 1998, \n\t``The Revision of UDC 52 and of the Astronomy Thesaurus,''\n\tin ASP Conf. Ser. 153,\n\tLibrary and Information Services in Astronomy III, \n\ted. U. Grothkopf, H. Andernach, S. Stevens-Rayburn, \\& M. Gomez\n\t(San Francisco: ASP),\n\t317\n\n\\bibitem[Xu \\& Croft 1993]{XC98} Xu, J. X., \\& Croft, W. B. 1998, \n\t``Corpus-based stemming using cooccurrence of word variants,''\n\tACM Trans. on Information Systems, 16, 61\n\n\\bibitem[Ylonen et al. 1999]{SSH} \n\tYlonen, T., Kivinen, M., Rinne, T., \\& Lehtinen, S. 1999, \n\t``SSH Protocol Architecture,'' \n\tInternet Draft,\n\tInternet Engineering Task Force\n\n\\end{thebibliography} \n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002105.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Accomazzi et al. 1995]{1995adass...4...36A} Accomazzi, A., \n\tGrant, C. S., Eichhorn, G., Kurtz, M. J., \\& Murray, S. S. 1995, \n\t``ADS Abstract Service Enhancements,''\n\tin ASP Conf. Ser., 77, \n\tAstronomical Data Analysis Software and Systems IV, \n\ted. R. A. Shaw, H. E Payne, \\& J. J. E. Hayes\n\t(San Francisco: ASP),\n\t36 \n\n\\bibitem[Accomazzi et al. 1999]{1999adass...8..291A} Accomazzi, A., \n\tEichhorn, G., Kurtz, M. J., Grant, C. S., \\& Murray, S. S. 1999, \n\t``The ADS Bibliographic Reference Resolver,''\n\tin ASP Conf. Ser., 172,\n\tAstronomical Data Analysis Software and Systems VIII, \n\ted. D. M. Mehringer, R. L. Plante, \\& D. A. Roberts,\n\t(San Francisco: ASP),\n\t291\n\n\\bibitem[Bell et al. 1996]{1996adass...5..451B} \n\tBell, D. J., Biemesderfer, C. D., Barnes, J. \\& Massey, P. 1996, \n\t``An Automated System for Receiving KPNO Proposals by Electronic Mail,'' \n\tin ASP Conf. Ser., 101,\n\tAstronomical Data Analysis Software and Systems V, \n\ted. G. H. Jacoby \\& J. Barnes\n\t(San Francisco: ASP),\n\t451 \n\n\\bibitem[Bell 1999]{1999adass...8..257B} Bell, D. 1999, \n\t``Webmail: An Automated Web Publishing System, '' \n\tin ASP Conf. Ser., 172,\n\tAstronomical Data Analysis Software and Systems VIII, \n\ted. D. M. Mehringer, R. L. Plante, \\& D. A. Roberts,\n\t(San Francisco: ASP),\n\t257\n\n\\bibitem[Belkin \\& Croft 1992]{BC92} Belkin, N. J., \\& Croft, W. B. 1992,\n \t``Information filtering and information retrieval: \n\ttwo sides of the same coin,''\n\tCommunications of the ACM, 35, 29\n\n\\bibitem[Birman 1999]{BIRMAN99} Birman, K. P. 1999,\n\t``A review of experiences with reliable multicast,''\n\tSoftware: Practice \\& Experience, 29, 741\n\n\\bibitem[Caplan \\& Arms 1999]{CAPLAN99} Caplan, P., \\& Arms, W. Y. 1999,\n\t``Reference Linking for Journal Articles,''\n\tD-Lib magazine, 5,\\\\\n\t$<$URL:http://www.dlib.org/dlib/july99/caplan/\\-07caplan.html$>$\n\n%\\bibitem[Cummins 1998]{1998lisa.conf..101C} Cummins, M. 1998, \n%\t``The Astronomy Thesaurus and UDC --- Present and Future \n%\t(Group Discussion for Users and Potential Users),''\n%\tin ASP Conf. Ser., 153,\n%\tLibrary and Information Services in Astronomy III, \n%\ted. U. Grothkopf, H. Andernach, S. Stevens-Rayburn, \\& M. Gomez\n%\t(San Francisco: ASP),\n%\t101\n\n\\bibitem[Davidson \\& Douglas 1998]{DAVIDSON98} \n\tDavidson, L. A., \\& Douglas, K. 1999,\n\t``Digital Object Identifiers: Promise and Problems for\n\tScholarly Publishing,''\n\tJ. of Electronic Publishing, 4, \\\\\n\t$<$URL:http://www.press.umich.edu/jep/04-22/davidson.html$>$\n\n\\bibitem[Dempsey \\& Weiss 1999]{DEMPSEY99} Dempsey, B. J., \\& Weiss, D. 1999,\n \t``Towards An Efficient, Scalable Replication Mechanism \n\tfor the I2-DSI Project,''\n\tTech. Rep. TR-1999-01, \n\tSchool of Information and Library Science,\n University of North Carolina \n\t(Chapel Hill, NC)\n\n\\bibitem[Deutsch \\& Gailly 1996]{ZLIB} Deutsch, L. P. \\& Gailly, J. 1996,\n\t``ZLIB Compressed Data Format Specification, version 3.3,''\n\tRFC 1950, \n\tInternet Engineering Task Force\n\n\\bibitem[Efthimiadis 1996]{EF96} Efthimiadis, E. N. 1996, \n\t``Query expansion,''\n Ann. Rev. of Information Science \\& Technology, 31, 121\n\n\\bibitem[Egret \\& Wenger 1988]{1988alds.proc..323E} \n\tEgret, D. \\& Wenger, M. 1988, \n\t``SIMBAD -- present status and future,''\n\tin ESO Conf. \\#28, \n\tAstronomy from Large Databases: \n\tScientific Objectives and Methodological Approaches, \n\ted. A. Heck \\& F. Murtagh, \n\t323\n\n\\bibitem[Eichhorn et al. 2000]{SEARCH} Eichhorn, G., Kurtz, M. J.,\n\tAccomazzi, A., Grant, C. S., \\& Murray, S. S. 2000, \n\t``The NASA Astrophysics Data System: The Search Engine and its\n\tUser Interface,''\n\tA\\&AS, this issue (SEARCH)\n\n\\bibitem[Frakes \\& Baeza--Yates 1992]{FB92} \n\tFrakes, W., \\& Baeza--Yates, R. 1992,\n\t``Information Retrieval: Data Structures \\& Algorithms,''\n\tPrentice-Hall \n\t(Upper Saddle River, NJ)\n\n\\bibitem[Fernique, Ochsenbein \\& Wenger 1998]{FERNIQUE98} \n\tFernique, P., Ochsenbein, F., \\& Wenger, M. 1998,\n\t``CDS GLU, a Tool for Managing Heterogeneous Distributed Web\n\tServices,''\n\tin ASP Conf. Ser. 145, \n\tAstronomical Data Analysis Software and Systems VII, \n\ted. R. Albrecht, R. N. Hook \\& H. A. Bushouse, \n\t(San Francisco: ASP),\n\t466\n\n\\bibitem[Gadd 1988]{GADD88} Gadd, T. N. 1988, \n\t``Fishing fore Werds: Phonetic Retrieval of written text \n\tin Information Retrieval Systems,'' \n\tProgram-Automated Library and Information Systems, 22, 222\n\n\\bibitem[Gadd 1990]{GADD90} Gadd, T. N. 1990, ``Phonix: the Algorithm,''\n\tProgram-Automated Library and Information Systems, 24, 363\n\n\\bibitem[Grant et al. 2000]{DATA} Grant, C. S., Accomazzi, A., Eichhorn, G.,\n\tKurtz, M. J., \\& Murray, S. S. 2000,\n\t``The NASA Astrophysics Data System: Data Holdings,''\n\tA\\&AS, this issue (DATA)\n\n\\bibitem[Grefenstette 1998]{GR98} Grefenstette, G. 1998,\n\t``Problems and approaches to Cross Language Information Retrieval,''\n Proceedings of the ASIS Annual Meeting, 35, 143\n\n\\bibitem[Hanisch 2000]{HANISCH99} Hanisch, R. 2000,\n\t``Distributed Data Systems and Services in Astronomy and \n\tthe Space Sciences,''\n\tAstronomical Data Analysis Software and Systems IX Proceedings\n\t(in press)\n\n\\bibitem[Harman 1991]{HAR91} Harman, D. 1991, ``How Effective is Suffixing,''\n\tJournal of the American Society for Information Science, 42, 7\n\n\\bibitem[Hayes-Roth, Waterman \\& Lenat 1983]{HR83} \n\tHayes-Roth, F., Waterman, D. A., \\& Lenat, D. B. 1983, \n\t``Building Expert Systems,''\n\tAddison-Wesley (Reading, MA)\n\n\\bibitem[Heap 1978]{HEA78} Heap, J. 1978,\n\t``Information Retrieval -- Computational and Theoretical\n\tAspects,'' Academic Press (New York)\n\n\\bibitem[Helou \\& Madore 1988]{1988alds.proc..335H} Helou, G. \\&\n\tMadore, B. 1988, \n\t``A new extragalactic database,''\n\tin ESO Conf. \\#28, \n\tAstronomy from Large Databases: \n\tScientific Objectives and Methodological Approaches, \n\ted. A. Heck \\& F. Murtagh, \n\t335\n\n\\bibitem[Heikkila, MCGlynn \\& White 1999]{1999adass...8..221H} \n\tHeikkila, C. W., McGlynn, T. A., \\& White, N. E. 1999, \n\t``Astrobrowse: a Web Agent for Querying Astronomical Databases,''\n\tin ASP Conf. Ser., 172, \n\tAstronomical Data Analysis Software and Systems VIII, \n\ted. D. M. Mehringer, R. L. Plante, \\& D. A. Roberts,\n\t(San Francisco: ASP),\n\t221\n\n\\bibitem[Hitchcock et al. 1998]{HITCHCOCK98}\n\tHitchcock, S., Carr, L., Hall, W., Harris, S.,\n\tProbets, S., Evans, D., Brailsford, D. 1998\n\t``Linking Electronic Journals: Lessons from the Open\n Journal Project,''\n\tD-Lib Magazine, December 1998, \\\\\n\t$<$URL:http://www.dlib.org/dlib/december98/\\-12hitchcock.html$>$\n\n\\bibitem[IEEE 1995]{POSIX} IEEE Computer Society 1995,\n\t``1003-1995 IEEE guide to the POSIX Open System Environment,''\n\tThe Institute of Electrical and Electronics Engineers, Inc.\n\n\\bibitem[Kitajima et al. 1997]{KITA97} \n\tKitajima, J. P., Resende, M. D., Ribeiro-Neto, B. Ziviani, N. 1997,\n\t``Distributed parallel generation of indices for very large\n\ttext databases,''\n\tProc. III Int. Conf. on Algorithms and Architectures for\n\tParallel Processing, \n\ted. A. Goscinski, M. Hobbs, W. Zhou, \n\t745\n\n\\bibitem[Knuth 1973]{KNU73} Knuth, D. 1973, \n\t``The Art of Computer Programming, Vol. 3: Sorting and\n\tSearching,'' Addison-Wesley (New York)\n\n\\bibitem[Kurtz et al. 2000]{OVERVIEW} Kurtz, M. J., Eichhorn, G., \n\tAccomazzi, A., Grant, C. S., Murray, S. S., \\& \n\tWatson, J. M. 2000, \n\t``The NASA Astrophysics Data System: Overview,''\n\tA\\&AS, this issue (OVERVIEW)\n\n\\bibitem[Kurtz et al. 1993]{1993adass...2..132K} Kurtz, M. J., \n\tKarakashian, T., Grant, C. S., Eichhorn, G., Murray, S. S., \n\tWatson, J. M., Ossorio, P. G. \\& Stoner, J. L. 1993, \n\t``Intelligent Text Retrieval in the NASA Astrophysics Data System,''\n\tin ASP Conf. Ser. 52, \n\tAstronomical Data Analysis Software \\& Systems II, \n\ted. R. J. Hanisch, R. J. V. Brissenden, \\& J. Barnes,\n\t(San Francisco: ASP),\n\t132 \n\n\\bibitem[Lee, Dubin \\& Kurtz 1999]{DUBIN99} Lee, J. , Dubin, D. S. \\& \n\tKurtz, M. J. 1999,\n\t``Co-occurrence Evidence for Subject Vocabulary Reconciliation\n\tin ADS Databases,''\n\tin ASP Conf. Ser., 172,\n\tAstronomical Data Analysis Software and Systems VIII, \n\ted. D. M. Mehringer, R. L. Plante, \\& D. A. Roberts,\n\t(San Francisco: ASP),\n\t287\n\n\\bibitem[Loukides \\& Oram 1996]{GNU} Loukides, M., \\& Oram, A. 1996,\n\t``Programming With Gnu Software (Nutshell Handbook),''\n\tO'Reilly \\& Associates, Inc.\n\n\\bibitem[Lynch \\& Molina-Garcia 1996]{DLWR} \n\tLynch, C. \\& Molina-Gracia, H. 1996, \n\t``Interoperability, Scaling, and the Digital Libraries\n\tResearch Agenda,'' \\\\\n\t$<$URL:http://www-diglib.stanford.edu/diglib/pub/\\-reports/iita-dlw/$>$\n\n\\bibitem[Miles 1998]{CDF} Miles, P. 1998,\n\t``Internet World Guide to Webcasting,''\n\tWiley \\& Sons\n\n\\bibitem[Miller et al. 1998]{MILLER98} \n\tMiller, K., Robertson, K., Tweedly, A., \\& White, M. 1998, \n\t``StarBurst Multicast File Transfer Protocol (MFTP) Specification,''\n\tInternet Draft, \n\tInternet Engineering Task Force\n\n\\bibitem[Miller 1997]{MILL97} Miller, U. 1997,\n\t``Thesaurus construction: Problems and their roots,''\n\tInformation Processing \\& Management, 33, 481\n\n\\bibitem[Murtagh \\& Guillaume 1998]{AML} Murtagh, F. \\& \n\tGuillaume, D. 1998, \n\t``Distributed Information Search and Retrieval for \n\tAstronomical Resource Discovery and Data Mining,'' \n\tin ASP Conf. Ser., 153,\n\tLibrary and Information Services in Astronomy III, \n\ted. U. Grothkopf, H. Andernach, S. Stevens-Rayburn, \\& M. Gomez\n\t(San Francisco: ASP),\n\t51\n\n\\bibitem[Navarro 1998]{NAV98} Navarro, G. 1998\n\t``Approximate Text Searching,''\n\tPh. D. Thesis, University of Chile, Santiago, Chile\n\n\\bibitem[Oard \\& Diekema 1997]{OARD97} Oard, D. W., \\& Diekema A. R. 1997,\n\t``Cross-language information retrieval,''\n\tAnn. Rev. of Information Science \\& Technology, 33, 223\n\n\\bibitem[Paskin 1999]{DOI} Paskin, N. 1999,\n\t``DOI: Current Status and Outlook -- May 1999,'' \n\tD-Lib Magazine, 5,\\\\\n $<$URL:http://www.dlib.org/dlib/may99/05paskin.html$>$\n\n\\bibitem[Salton 1989]{SALTON89} Salton, G. 1989,\n\t``Automatic text processing: the transformation, analysis and retrieval\n\tof information by computer,''\n\tAddison-Wesley (Reading, MA)\n\n\\bibitem[Salton \\& Buckley 1988]{SALTON88} Salton, G. \\& Buckley, C. 1988,\n\t``Term weighting approaches in automatic text retrieval,''\n\tInformation Processing \\& Management, 24, 513\n\n\\bibitem[Salton \\& McGill 1983]{SALTON83} Salton, G., \\& McGill, M. J. 1983,\n\t``Introduction to Modern Information Retrieval,''\n\tMcGraw-Hill (New York)\n\n\\bibitem[Schatz 1997]{SCHATZ97} Schatz, B. R. 1997,\n\t``Information Retrieval in Digital Libraries: Bringing Search\n\tto the Net,''\n\tScience, 275, 327\n\n\\bibitem[Schmitz et al. 1995]{1995VA.....39R.272S} Schmitz, M., Helou, G., \n\tDubois, P., Lague, C., Madore, B., Corwin, H. G. J., \n\t\\& Lesteven, S. 1995, \n\t``A Uniform Bibliographic Code,''\n\tVistas in Astronomy, 39, 272 \n\n\\bibitem[Shaya et al. 1999]{1999AAS...194.8304S} Shaya, E., Blackwell, J., \n\tGass, J., Oliversen, N., Schneider, G., Thomas, B., Cheung,\n\tC., \\& White, R. A. 1999, \n\t``XML at the ADC: Steps to a Next Generation Data Archive,'' \n\tAmerican Astronomical Society Meeting, 194, 8304 \n\n\\bibitem[Shobbrook \\& Shobbrook 1992]{1992PASAu..10..134S} \n\tShobbrook, R. M. \\& Shobbrook, R. R. 1992, \n\t``The I.A.U. Thesaurus for Improved On-line Access to Information,''\n\tProc. of the Ast. Soc. of Australia, 10, 134\n\n%\\bibitem[Shobbrook \\& Shobbrook 1993]{1993asth.book.....S} Shobbrook, R. M. \n%\t\\& Shobbrook, R. R. 1993, ``The Astronomy Thesaurus,'' version 1.1,\n%\tEpping: Anglo-American Observatory\n\n\\bibitem[Shobbrook 1995]{1995VA.....39Q.272S} Shobbrook, R. M. 1995, \n\t``The Multi-Lingual Supplement to the Astronomy Thesaurus,''\n\tVistas in Astronomy, 39, 272 \n\n\\bibitem[Tridgell 1999a]{TRIDGELL99} Tridgell, A. 1999a,\n\t``Efficient Algorithms for Sorting and Synchronization,''\n\tPh. D. Thesis, The Australian National University\n\n\\bibitem[Tridgell 1999b]{RCACHE} Tridgell, A. 1999b,\n\tprivate communication\n\n\\bibitem[Unicode Consortium 1996]{UNICODE} Unicode Consortium 1996, \n\t``The Unicode Standard: Version 2.0,'' Addison-Wesley\n\t(Reading, MA)\n\n\\bibitem[Van de Sompel \\& Hochstenbach 1999]{VDS99}\n\tVan de Sompel, H., \\& Hochstenbach, P. 1999,\n\t``Reference Linking in a Hybrid Libary Environment,''\n\tD-Lib Magazine, 5,\\\\\n\t$<$URL:http://www.dlib.org/dlib/april99/van\\_de\\_sompel/\\-04van\\_de\\_sompel-pt1.html$>$\n\n\\bibitem[van Rijsbergen 1979]{VR79} van Rijsbergen, C. J. 1979,\n\t``Information Retrieval,''\n\tButterworths, 2nd ed.\n\n\\bibitem[Wall, Christiansen \\& Schwartz 1996]{PERL} \n\tWall, L., Christiansen, T., \\& Schwartz, R. 1996, \n\t``Programming PERL,'' \n\tO'Reilly \\& Associates, Inc., 2nd ed.\n\n\\bibitem[Wilkins 1998]{1998lisa.conf..317W} Wilkins, G. A. 1998, \n\t``The Revision of UDC 52 and of the Astronomy Thesaurus,''\n\tin ASP Conf. Ser. 153,\n\tLibrary and Information Services in Astronomy III, \n\ted. U. Grothkopf, H. Andernach, S. Stevens-Rayburn, \\& M. Gomez\n\t(San Francisco: ASP),\n\t317\n\n\\bibitem[Xu \\& Croft 1993]{XC98} Xu, J. X., \\& Croft, W. B. 1998, \n\t``Corpus-based stemming using cooccurrence of word variants,''\n\tACM Trans. on Information Systems, 16, 61\n\n\\bibitem[Ylonen et al. 1999]{SSH} \n\tYlonen, T., Kivinen, M., Rinne, T., \\& Lehtinen, S. 1999, \n\t``SSH Protocol Architecture,'' \n\tInternet Draft,\n\tInternet Engineering Task Force\n\n\\end{thebibliography}"
}
] |
astro-ph0002106
|
THERMAL INSTABILITY AND THE FORMATION OF CLUMPY GAS CLOUDS
|
[
{
"author": "A. Burkert\\altaffilmark{1} and D. N. C. Lin\\altaffilmark{2}"
}
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The radiative cooling of optically thin gaseous regions and the formation of a two-phase medium and of cold gas clouds with a clumpy substructure is investigated. We demonstrate how clumpiness can emerge as a result of thermal instability. In optically thin clouds, the growth rate of small density perturbations is independent of their length scale as long as the perturbations can adjust to an isobaric state. However, the growth of a perturbation is limited by its transition from isobaric to isochoric cooling when the cooling time scale is reduced below the sound crossing time scale across its length scale. The temperature at which this transition occurs decreases with the length scale of the perturbation. Consequently small scale perturbations have the potential to reach higher amplitudes than large scale perturbations. When the amplitude becomes nonlinear, advection overtakes the pressure gradient in promoting the compression resulting in an accelerated growth of the disturbance. The critical temperature for transition depends on the initial amplitude. The fluctuations which can first reach nonlinearity before their isobaric to isochoric transition will determine the characteristic size and mass of the cold dense clumps which would emerge from the cooling of an initially nearly homogeneous region of gas. Thermal conduction is in general very efficient in erasing isobaric, small-scale fluctuations, suppressing a cooling instability. A weak, tangled magnetic field can however reduce the conductive heat flux enough for low-amplitude fluctuations to grow isobarically and become non-linear if their length scales are of order $10^{-2}$ pc. If the amplitude of the initial perturbations is a decreasing function of the wavelength, the size of the emerging clumps will decrease with increasing magnetic field strength. Finally, we demonstrate how a 2-phase medium, with cold clumps being pressure confined in a diffuse hot residual background component, would be sustained if there is adequate heating to compensate the energy loss.
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"string": "\\documentstyle[aasms4,psfig]{article}\n\n% ---------------------------------------------------\n\\newcommand{\\ins}[2]{\\makebox [#1]{#2}}\n\\newcommand{\\inc}[1]{\\ {\\mbox{#1}}\\ }\n\\newcommand{\\mt}{{{m_1}\\over {m_1 + m_2}}}\n\\newcommand{\\mb}{{m_2}\\over {m_1 + m_2}}\n\\newcommand{\\mtb}{{m_1 m_2}\\over {m_1 + m_2}}\n\\newcommand{\\eq}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\bra}[1]{\\left( #1 \\right)}\n\\newcommand{\\brasq}[1]{\\left[ #1 \\right]}\n\\newcommand{\\pdrv}[2]{{{\\partial #1}\\over {\\partial #2}}}\n\\newcommand{\\pddrv}[2]{{{\\partial^2 #1}\\over {\\partial #2^2}}}\n\\newcommand{\\pderiv}[1]{{{\\partial}\\over {\\partial #1}}}\n\\newcommand{\\pdderiv}[1]{{{\\partial^2}\\over {\\partial #1 ^2}}}\n\\newcommand{\\drv}[2]{{{d #1}\\over {d #2}}}\n\\newcommand{\\deriv}[1]{{d\\over {d #1}}}\n\\newcommand{\\half}{{1\\over 2}}\n\\newcommand{\\thalf}{{3\\over 2}}\n\\newcommand{\\bxi}{\\mbox{\\boldmath$ \\xi $}}\n\\newcommand{\\bgk}[1]{\\mbox{\\boldmath$ #1 $}}\n\n%\\lefthead{BURKERT \\& LIN: THERMAL INSTABILITY}\n\n\\begin{document}\n\n\\title {THERMAL INSTABILITY AND THE FORMATION OF CLUMPY GAS CLOUDS}\n\n\\author {A. Burkert\\altaffilmark{1} and D. N. C. Lin\\altaffilmark{2}}\n\n\\altaffiltext\n{1}{Max-Planck-Institut f\\\"ur Astronomie, K\\\"onigstuhl 17,\nD-69117 Heidelberg, Germany.\nE--mail: burkert@mpia-hd.mpg.de}\n\n\\altaffiltext\n{2} {UCO/Lick Observatory, University of California, Santa Cruz, California, \n95064.\nE--mail: lin@lick.ucolick.org}\n \n\\vspace{3cm}\n\\slugcomment{{\\em Astrophysical Journal, in press}}\n\n\\begin{abstract}\nThe radiative cooling of optically thin gaseous regions and the\nformation of a two-phase medium and of cold gas clouds with a clumpy\nsubstructure is investigated. We demonstrate how clumpiness can\nemerge as a result of thermal instability. In optically thin clouds,\nthe growth rate of small density perturbations is independent of their\nlength scale as long as the perturbations can adjust to an isobaric\nstate. However, the growth of a perturbation is limited by its\ntransition from isobaric to isochoric cooling when the cooling time\nscale is reduced below the sound crossing time scale across its length\nscale. The temperature at which this transition\noccurs decreases with the length scale of the perturbation.\nConsequently small scale perturbations have the potential\nto reach higher amplitudes than large scale perturbations. When\nthe amplitude becomes nonlinear, advection overtakes the pressure gradient\nin promoting the compression resulting in an accelerated growth of the\ndisturbance. The critical temperature for transition depends on\nthe initial amplitude. The fluctuations which can first reach\nnonlinearity before their isobaric to isochoric transition will\ndetermine the characteristic size and mass of the cold dense clumps\nwhich would emerge from the cooling of an initially nearly homogeneous\nregion of gas. Thermal conduction is in general very efficient in erasing\nisobaric, small-scale fluctuations, suppressing a cooling instability.\nA weak, tangled magnetic field can however reduce\nthe conductive heat flux enough for low-amplitude fluctuations to grow\nisobarically and become non-linear if their length scales are of order $10^{-2}$ pc. \nIf the amplitude of the initial perturbations is a decreasing function \nof the wavelength, the size of the emerging clumps will\ndecrease with increasing magnetic field strength.\nFinally, we demonstrate how a 2-phase medium, with cold clumps being pressure confined\nin a diffuse hot residual background component, would be sustained if\nthere is adequate heating to compensate the energy loss.\n\\end{abstract}\n\n\\keywords{globular clusters: general --- instabilities --- ISM: clouds, formation}\n\n\\section{Introduction}\n\nThe interstellar medium and cold gas clouds are characterized by a\nclumpy substructure and a turbulent velocity field (Larson 1981, \nBlitz 1993). As\nmolecular clouds are the sites of star formation, their formation,\ninternal structure and dynamics determines the rate of star formation\nand the properties of young stars, such as their mass function or\nbinarity. The understanding of the origin of cold clouds and\ntheir internal substructure is therefore of fundamental importance for\na consistent theory of star formation and galactic evolution.\n\nIn the nearby clouds, the dispersion velocity inferred from molecular\nline width is often larger than the gas sound speed inferred from\nthe line transition temperatures (Solomon et al 1987). \nMHD turbulence may be responsible for the stirring of these clouds\n(Arons \\& Max 1975). This conjecture is supported by the polarization maps\nand direct measurements of field strength in some star forming regions\n(Myers \\& Goodman 1988, Crutcher et al. 1993). \nRecent simulations of MHD turbulence, however, suggest\nthat it dissipates rapidly (Gammie \\& Ostriker 1996, MacLow et al 1998, MacLow 1999,\nOstriker et al. 1999). One possible\nsource of energy supply is winds and outflows from young stellar objects \n(Franco \\& Cox 1983, McKee 1989). But in regions where star formation is inactive, clumpy\nstructure with velocity dispersion is also observed. Thus,\nthe origin and energy supply of clumpy cloud structure remains an\noutstanding issue.\n\nOn small scales, magnetic field pressure is important in regulating\ninfall and collapse of protostellar clouds and the formation of low-mass\nstars (Mouschovias \\& Spitzer 1976, Nakano 1979, Shu 1993). \nFor clouds with sub-critical masses, \ngravitational contraction is proceeded by ambipolar diffusion which \nfor typical cloud densities operates on a timescale $\\tau_B \\sim 10^{7-8}$ yr\n(Lizano \\& Shu 1989, Mouschovias 1991). \nIn regions with intense star formation activities such as\nthe central region of Orion, $\\tau_B$ for individual dense clumps\nis comparable to the typical age of the young stellar objects. But,\nthe spread in stellar ages ($\\Delta \\tau_\\ast \\sim 10^6$ yrs)\nappears to be considerably shorter than $\\tau_B$ (Carpenter et al. 1997, Hillenbrand, 1997).\nThis coeval star formation history requires either\na coordinated trigger mechanism for star formation\nwithin initially magnetically supported clumps or subcritical \ncollapse, fragmentation and star formation of a larger molecular cloud region\nin which the magnetic field plays a weak role.\n\nA rapid and coordinated episode of star formation can also be inferred\nin globular clusters (Brown et al. 1991, 1995, \nMurray \\& Lin 1992, Lin \\& Murray 1992). In some metal deficient \nclusters such as M92, the total amount of heavy elements corresponds\nto the yield of a few supernovae. If star formation has proceeded\nover a duration $\\Delta \\tau_\\ast$ comparable to the expected life span ($\\sim$ a few \n$10^6$ yrs) of massive stars, a significant metallicity spread \nwould be expected, in contrast to the observations (e.g. Kraft 1979).\nAt least in these systems, $\\Delta \\tau_\\ast <\\tau_B$ and star \nformation may have proceeded through supercritical collapse. The\ndynamical timescale of most clusters at their half mass radius is \n$\\tau_d \\approx 10^6$ yr. Any energy dissipation associated with\nthe episode of star formation would imply an even longer dynamical timescale \nin the proto cluster cloud prior to that event. We infer that \n$\\Delta \\tau_{\\ast}$ was comparable to or shorter than the dynamical \ntimescale of the proto cluster clouds indicating a rapid fragmentation\nand star formation episode.\n\nIn this paper, we focus on the rapid emergence of clumpy structure during\nthe formation and collapse of a thermally unstable supercritical cloud. This process\nis relevant to the formation of stellar clusters as well as galaxies.\nWe assume that the clouds condense out of a diffuse hot medium\nas a result of thermal instability.\nLarge condensations with cooling timescales $\\tau_c > \\tau_d$ are thermally stable\nbecause they can adjust through contraction such that their radiative\nlosses may be compensated by the release of their gravitational energy.\nRunaway cooling of the gas through thermal instability however\noccurs in clouds with $\\tau_c < \\tau_d$. \nIn order to form clumps within an initially almost homogeneous\ncloud, internal density fluctuations must grow rapidly on a timescale\nshort compared to the mean dynamical timescale of the entire cloud.\nSmall scale density fluctuations would begin to dominate if either the\ngrowth timescale or the limiting amplitude is a decreasing function of\nthe perturbations' length scale. One possible fragmentation\nmechanism is gravitational collapse. The reduction in the cloud's\ntemperature reduces its Jeans' mass, leading to the onset of\ngravitational instability and collapse. However, for a non rotating,\ncold, homogeneous gaseous region, gravitational instability alone\ncannot induce fragmentation\nbecause the growth rate is essentially independent of length scale\nsuch that the growth timescale for the density contrast is comparable\nto the dynamical timescale of the whole cloud (Hunter 1962). This has also been\nshown by numerical collapse simulations of initially gravitationally\nunstable perturbed gas clouds (e.g. Burkert \\& Bodenheimer 1993, 1996,\nBurkert, Bate \\& Bodenheimer 1997). If the initial density\nperturbations $\\delta_0$ are linear ($\\delta_0 < 1$), fragmentation is\nsuppressed until the gas cloud has collapsed into either a disk or a\ndense filamentary substructure.\n\nWe propose that clumpyness in clouds arises naturally from their\nformation through a cooling instability which acts on timescales that can\nbe much shorter than the dynamical timescale of the cloud. \nIn a pioneering paper, Field\n(1965) derived a criterion for a cooling gas to be unstable to the\ngrowth of thermal condensations. He showed that thermal instability\ncan lead to the rapid growth of density perturbations from\ninfinitesimal $\\delta_0$ to nonlinear amplitudes on a cooling\ntimescale $\\tau_c$ which for typical conditions in the interstellar\nmedium is short compared to the dynamical timescale. If $\\tau_c$\nincreases with decreasing density any small density difference would\ninduce a temperature difference between the cooler perturbed region\nand the warmer background. Across the interface between the two-phase\nmedium, differential cooling leads to a pressure gradient which\ninduces a gas flow from the lower-density background towards the\nhigher-density perturbed region. The density enhancement in the\ncooler region further reduces its cooling timescale compared to that\nof the background where $\\tau_c$ increases. A more detailed\ninvestigation of the growth of condensations in cooling regions has\nbeen presented by Schwarz et al. (1972) who included also the effects\nof ionization and recombination and by Balbus (1986) who examined the\neffect of magnetic fields. The classical model of the interstellar\nmedium where heating balances cooling was presented by Field et\nal. (1969). A recent progress report on the theory of thermal\ninstability is given by Balbus (1995).\n\nAlthough thermal instability proceeds faster than the collapse of the\ncloud, its growth rate is determined by the local cooling rate.\nDuring the initial linear evolution, variations in the initial over density\n(or under temperature) might lead only to a weak dependence of the growth\ntimescale on the wavelength.\nIn this paper we show however that there \nexist two important transitions which are\nvery sensitively determined by the wavelengths of perturbations. 1) The growth\nof a perturbation is limited by its transition from isobaric to\nisochoric cooling, when the cooling time scale is reduced below the\nsound crossing time scale across the wavelength of the perturbation.\nThis transition occurs at a lower temperature, with correspondingly\nlarger over density, for perturbations with smaller wavelengths.\n2) For those perturbation which can become nonlinear before the isobaric to\nisochoric transition, advection overtakes the pressure gradient in\npromoting the compression and growth of the perturbed region at an\naccelerated rate. The fluctuations which can first reach nonlinearity\nwould dominate the growth of all perturbations with\nlonger wavelengths and homogenize disturbances with smaller\nwavelengths. Thus, they determine the characteristic size and mass of\nthe cold dense clumps which would emerge from the cooling of an\ninitially nearly homogeneous cloud. Thermal conduction could in general\nerase these fluctuations, suppressing the instability. Weak, tangled\nmagnetic fields would however be efficient enough in reducing the\nconductive flux, allowing the medium to break up into cold clumps\non the characteristic length scale.\n\nWe study the cooling\nand fragmentation of gas using simplified power-law cooling functions.\nSince we are primarily interested in supercritical clouds, we neglect\nthe effect of magnetic fields. Note that even a weak magnetic field\ncould have an important destabilizing influence in thermal instability\n(Loewenstein 1990, Balbus 1995). In \\S2, we obtain approximate analytic\nsolutions which describe the evolution of a linear density\nperturbation in the isobaric and nearly isochoric regime. We show\nthat the growth of over density in a thermally unstable fluctuation is\nlimited by a transition from isobaric to isochoric evolution and that\nthe limiting amplitude is a decreasing function of the length scale.\nWe verify our analytic approximations with numerical, hydrodynamical\ncalculations which are also used in \\S3 to study the transition into\nthe non-linear regime. In \\S4 we investigate the cooling of\ninteracting perturbations and determine the critical length scale of\nclumps that emerge through thermal instability. The importance of\nthermal conduction is investigated in \\S5. In \\S6 we discuss the affect of\nheating processes and the formation of a stable 2-phase medium.\nFinally, we summarize our results and discuss\ntheir implications in \\S7.\n\n\\section{The Initial Evolution of Thermal Instability}\n\nThe dynamical evolution of the gas is described by the hydrodynamical\nequations\n\n\\begin{equation}\n\\frac{\\partial \\rho}{\\partial t} + \\sum_{k=1}^3 \n\\frac{\\partial \\rho U_k}{\\partial x_k} = 0\n\\end{equation}\n\\begin{equation}\n\\frac{\\partial U_j}{\\partial t} + \\sum_{k=1}^3U_k \n\\frac{\\partial U_j}{\\partial x_k} + \\frac{R_g}{\\mu \\rho}\n\\frac{\\partial}{\\partial x_j} \\left(\\rho T \\right) = 0\n\\end{equation}\n\\begin{equation}\n\\frac{\\partial T}{\\partial t} + \\sum_{k=1}^3 U_k \n\\frac{\\partial T}{\\partial x_k} + (\\Gamma - 1)T \\sum_{k=1}^3 \n\\frac{\\partial U_k}{\\partial x_k} = -\\frac{\\rho \\Lambda}{C_v}\n\\end{equation}\nwhere j=1,2,3 is the coordinate index, $C_v = R_g/\\mu (\\Gamma -1)$ is\nthe heat capacity, $R_g, \\mu$ and $\\Gamma$ are the gas constant, mean\nmolecular weight and adiabatic index, respectively.\n\nIn the unperturbed state, the gas remains at rest ($U_j=0$) and its\ndensity attains a constant value, $\\rho_0$. The time dependent energy\nequation (3) gives\n\\begin{equation}\nC_v \\frac{\\partial T_0}{\\partial t} = - \\rho_0 \\Lambda\n\\end{equation}\nwhere the cooling rate $\\Lambda= \\Lambda_0 T_0 ^\\beta$. The power\nindex is determined by the detailed atomic processes. Since we are\nprimarily interested in the physical evolution of thermal instability,\nwe adopt a simple constant $\\beta$ prescription. The cooling would be\nthermally unstable (with $\\tau_c = T_0/\\partial T_0/\\partial t$ as an\nincreasing function of $T_0$) in the isochoric region if $\\beta < 1$\nand in the isobaric region if $\\beta < 2$. In the absence of external\nheating, the unperturbed gas temperature $T_0$ can be expressed as a\nfunction of the dimensionless time variable $\\tau \\equiv t /\n\\tau_c(0)$ such that\n\\begin{equation}\nT_0(t)=T_0(0) \\left(1 - (1-\\beta) \\tau \\right)^{\\frac{1}{1-\\beta}}\n\\end{equation}\nwhere $T_0(0)$ and $\\tau_c (0)\\equiv C_v / \\rho_0 \\Lambda_0 T_0(0)\n^{\\beta-1}$ are the initial (at $t=0$) temperature and cooling\ntimescale, respectively.\n\n\\subsection{The Perturbed Quantities}\n\nThe evolution of the perturbed density ($\\rho_1=\\rho-\\rho_0$),\ntemperature ($T_1=T-T_0$), and velocities ($U_j$) are derived from the\nlinearization of the equations (1) to (3):\n \\begin{equation}\n\\frac{\\partial}{\\partial t} \\frac{ \\rho_1}{\\rho_0} \n= -\\sum_{j=1} ^3 \\frac{\\partial U_j}{\\partial x_j},\n\\label{a6}\n\\end{equation}\n\\begin{equation}\n\\frac{\\partial U_j}{\\partial t} = - \\frac{R_g T_0}{\\mu} \\frac{\\partial \n}{\\partial x_j} \\left( \\frac{T_1}{T_0} + \\frac{\\rho_1}{\\rho_0} \\right),\n\\label{a7}\n\\end{equation}\nand\n\\begin{equation}\n\\frac{\\partial}{\\partial t} \\frac{T_1}{T_0} = -(\\Gamma -1) \n\\sum_{j=1} ^3 \\frac{\\partial U_j}{\\partial x_j} -\\frac{1}{\\tau_c}\n\\left( \\frac{\\rho_1}{\\rho_0} + (\\beta-1) \\frac{T_1}{T_0} \\right)\n\\label{a8}\n\\end{equation}\nwhere\n$$\\tau_c (t) \\equiv - \\frac{T_0}{d T_0 / dt} = \\tau_c(0) - \n(1-\\beta)t$$ is the \ncharacteristic cooling timescale at the instant of time t.\n\nSince the perturbation equations are linear in $x_j$, we adopt a local\napproximation in which the positional dependence of all the perturbed \nquantities is proportional to exp(i$k_j x_j$) where $k_j$ is the wave\nnumber in the $j$th direction. Substituting a dimensionless velocity \nvariable $V_j = i k_j \\tau_c(0) U_j$, the perturbed equations reduce to\n\\begin{equation}\n\\frac{\\partial}{\\partial \\tau} \\frac{ \\rho_1}{\\rho_0} = -\\sum_{j=1} ^3 V_j,\n\\label{a10}\n\\end{equation}\n\\begin{equation}\n\\frac{\\partial V_j}{\\partial \\tau} = K_j ^2 \\left( 1 - (1 - \\beta) \\tau\n\\right) ^{1 \\over 1 - \\beta} \\left( \\frac{P_1}{ P_0} \\right),\n\\label{a11}\n\\end{equation}\nwhere $\\frac{P_1}{ P_0} = \\frac{T_1}{T_0} + \\frac{\\rho_1}{\\rho_0}$ is\nthe perturbed pressure, $K_j \\equiv \\tau_c(0) k_j \\sqrt {R_g T_0\n(0)/\\mu}$ is the ratio of the initial cooling to sound crossing\ntimescale over a characteristic wavelength $2 \\pi/ k_j$, and\n\\begin{equation}\n\\frac{\\partial}{\\partial \\tau} \\frac{T_1 }{T_0} = - (\\Gamma -1) \n\\sum_{j=1} ^3 V_j -\\frac{\\tau_c (0)}{ \\tau_c}\n\\left( \\frac{\\rho_1}{\\rho_0} + (\\beta-1) \\frac{T_1}{T_0} \\right).\n\\label{a12}\n\\end{equation}\nFor a perfect gas, the unperturbed pressure $P_0=R_g \\rho_0 T_0/\\mu$\ndecreases at the same rate everywhere. We find from Eqs (\\ref{a10})\nand (\\ref{a12}) that the amplitude of the perturbed pressure is\n\\begin{equation}\n\\frac{\\partial}{\\partial \\tau} \\frac{ P_1}{P_0}= \n\\frac{\\partial}{\\partial \\tau} \\left( \\frac{ \\rho_1}{\\rho_0} \n+ \\frac{T_1}{T_0} \\right) = \n- \\Gamma \\sum_{j=1} ^3 V_j - \\frac{1}{1-(1-\\beta)\\tau} \n\\left((2-\\beta)\\frac{\\rho_1}{\\rho_0} - (1-\\beta)\\frac{P_1}{P_0} \\right).\n\\label{a13}\n\\end{equation}\n\n\\subsection{The initially isochoric regime with K $\\leq$ 1}\n\nFor computational simplicity, we now consider a 1-D limit treatment in\nwhich the initial (at $\\tau=0$) amplitude of $\\rho_1$ equals to a\nfinite value $\\rho_a$ with that of $V_1$ and $P_1$ equal to zero.\nThese conditions correspond to an initially almost homogeneous, hot\nregion of gas in pressure equilibrium. To third order in $\\tau$ the\neqs (\\ref{a10}), (\\ref{a11}), and (\\ref{a13}) give the following\napproximate solution\n\n\\begin{equation}\n\\frac{\\rho_1}{\\rho_0} \\simeq \\frac{\\rho_a}{\\rho_0}\\left(1 \n+ \\frac{K^2}{6}\\left(2-\\beta\\right) \\tau^3\\right)\n\\end{equation}\n\\begin{equation}\nV \\simeq \\frac{(\\beta-2)K^2}{6}\\frac{\\rho_a}{\\rho_0}\n\\left(3\\tau^2 + 2\\beta\\tau^3\\right)\n\\end{equation}\n\\begin{equation}\nP \\simeq (\\beta-2)\\frac{\\rho_a}{\\rho_0}\\left(\\tau^2 \n+ \\left(1-\\beta\\right)\\tau^3 + \\left(\\frac{4}{3} - \n\\frac{7}{3}\\beta + \\beta^2-\\frac{\\Gamma K^2}{6}\\right)\\tau^3\\right)\n\\end{equation}\n\nFigure 1 compares this solution with a numerical integration of the\ncomplete non-linear hydrodynamical equations (1) to (3) for K=1 and\nK=0.5. We use a 1-dimensional version of the second-order Eulerian\nhydro code which is described in Burkert and Bodenheimer (1993). The\nagreement between the numerical results (solid lines) and analytical\nsolution (dots) is excellent, even for large values of $\\tau \\approx \n1$ where the basis of the analytic approximation is no longer valid.\n\nDue to slightly more efficient cooling within the density perturbation\na small pressure gradient builds up. In an attempt to maintain\npressure balance, the slightly warmer gas in the low-density regions\ncontinually compresses the more dense and cooler parts. Consequently\nthe over-density in the perturbed region increases as the gas\ncools. Figure 1 and the equations (13) to (15) show that for small\nvalues of $K \\leq 1$ the growth rate of the density enhancement\ndepends on the size of the perturbation and increases with increasing\nvalues of K or decreasing wavelength. However, due to its long sound\ncrossing timescale, the perturbation cannot be compressed\nsignificantly while cooling; it cools almost isochorically (Parker\n1953). After one cooling timescale the gas temperature has reached its\nminimum value with the density enhancement still in the linear regime.\nNow, the pressure gradient reverses, erasing the fluctuation.\n\n\n\\subsection{The initially isobaric regime: K $\\geq$ 1}\n\nThe solid lines in figure 2 show a numerical calculation of the\nevolution of a density perturbation with K = 200, $\\beta = 0$ and\n$\\Gamma = 5/3$. For $K >> 1$, perturbations can react quickly on any\npressure gradients due to the short sound crossing timescale, relative\nto the cooling timescale. The simulations indicate a solution which\nconsists of a fast oscillatory part and a slowly growing part.\nLinearizing the slowly growing part, we find from the equations (9) to\n(12) the following approximate solution:\n\n\\begin{equation}\n\\frac{\\rho_1}{\\rho_0} \\simeq \\frac{\\rho_a}{\\rho_0}\n\\left(\\frac{i \\omega \\Gamma}{i \\omega \\Gamma -2 + \\beta}\\right)\n\\left( 1 + \\frac{2 - \\beta}{\\Gamma} \\left( \\tau \n+ \\frac{i}{\\omega} e^{i \\omega \\tau} \\right) \\right),\n\\label{a20}\n\\end{equation} \n\\begin{equation}\nV\\simeq \\frac{\\beta-2}{\\Gamma} \\frac{\\rho_a}{\\rho_0} \n\\left(\\frac{i \\omega \\Gamma}{i \\omega \\Gamma -2 + \\beta}\\right)\n\\left( 1 + i \\omega \\tau - e^{i \\omega \\tau} \\right), \n\\label{a21}\n\\end{equation} \nand\n\\begin{equation}\n\\frac{P_1}{P_0} \\simeq \\frac{(2- \\beta) i \\omega }{\\Gamma K^2}\n\\frac{\\rho_a}{\\rho_0} \n\\left(\\frac{i \\omega \\Gamma}{i \\omega \\Gamma -2 + \\beta}\\right)\n\\left( 1 + (1 - \\beta) \\tau - e^{i \\omega \\tau} \\right).\n\\label{a22}\n\\end{equation} \n\nThe characteristic frequency is determined by a cubic dispersion relation\n\\begin{equation}\n\\omega^3 + i (1-\\beta) \\omega^2 - K^2 \\Gamma \\omega -i(2-\\beta) K^2 =0.\n\\label{a23}\n\\end{equation}\n\n\\noindent A similar relation was discussed by Balbus (1995). Note\nthat the linearized solution is also valid for $\\tau > 1/\\omega$ as\nlong as $\\tau << 1$. As $K >> 1$ the two dominant real roots ($\\omega\n\\approx \\pm \\sqrt{\\Gamma} K$) of the dispersion eq(\\ref{a23}) yield\noscillatory parts in $\\rho_1/\\rho_0$, $V$, and $P_1/P_0$. The upper\npanels of figure 2 show that for $\\tau < 0.1$ the analytical\napproximation is in good agreement with the numerical integration of\nthe nonlinear hydrodynamical equations.\n\n\nFor all length scales, the ratio of sound propagation to cooling timescale \n\\begin{equation}\nQ \\equiv \\tau_c (t) k \\sqrt{R_g T_0 (t) /\\mu} \n= K (1-(1 - \\beta)\\tau)^{3-2 \\beta \\over 2- 2 \\beta} \n\\label{a24}\n\\end{equation}\n\n\\noindent decreases during the subsequent evolution. Provided $Q > >\n1$, eq(\\ref{a22}) implies that the magnitude of $P_1/P_0$ is much\nsmaller than both $V$ and $\\rho_1/\\rho_0$. That is, the fluctuation\nreacts isobaric. Adopting $P_1/P_0 \\approx 0$ and neglecting the\noscillatory term, the equations (9) and (12) can be combined to\n\n\\begin{equation}\n-V = \\frac{\\partial}{\\partial \\tau}\\left(\\frac{\\rho_1}{\\rho_0}\\right)\n= \\frac{(2-\\beta)}{\\Gamma(1-(1-\\beta)\\tau)}\\frac{\\rho_1}{\\rho_0}\n\\end{equation}\n\\noindent with the solution \n\\begin{equation}\n\\frac{\\rho_1}{\\rho_0} = \\frac{\\rho_a}{\\rho_0} \\left( 1 - (1 -\\beta)\n\\tau \\right) ^{- \\frac{ 2 - \\beta} {(1 - \\beta) \\Gamma}} \n\\label{a25}\n\\end{equation}\nand \n\\begin{equation}\nV =- \\frac{(2 - \\beta)}{\\Gamma} \\frac{\\rho_a}{\\rho_0} \n(1 - (1-\\beta)\\tau) ^{- \\frac{ 2 - \\beta} {(1 - \\beta) \\Gamma} -1}.\n\\label{a26}\n\\end{equation} \n\nIn contrast to fluctuations with $K < 1$ the evolution of isobaric\nfluctuations is independent of K. For $(1-\\beta)^{-1} > > \\tau >\n\\omega^{-1}$, solutions for $\\rho_1 /\\rho_0$ in Eqs (\\ref{a20}) and\n(\\ref{a25}) are in agreement to first order in $\\tau$. The lower\npanels of figure 2 show that within a cooling time both\n$\\rho_1/\\rho_0$ and $V$ are amplified to very large values. The\nagreement between the numerical calculation and the analytical\nprediction (equation 22 and 23) is excellent. The opposite signs of\n$\\rho_1/\\rho_0$ and V confirm that mass is being pushed into the cool\ndense regions. For $\\tau \\approx 1$, the numerically derived density\nenhancement falls below the predicted values as the fluctuation\nbecomes isochoric and contributions from the perturbed pressure \ncannot be neglected anymore.\n\n\\subsection{Transition to Isochoric Evolution and the Emergence \nof Small Scale Perturbations}\n\nFigure 3 shows the density evolution of initially isobaric\nfluctuations with different ratios of cooling to sound crossing times\nK as determined from the numerical calculations. The initially\nisobaric growth of the density fluctuations is independent of\nwavelength and K and in excellent agreement with equation (22) (dashed\ncurve). The perturbations transform however to the isochoric\nsolution for the epoch after $Q$ has declined below unity.\nThereafter, gas in the perturbed region cools off faster than it\ncan adjust to a pressure equilibrium with the surrounding region.\nSubsequently, the over density of the perturbed region is slowly\nmodified by the inertial motion $V_{trans}$ of the gas at the time of\nthe transition and its growth stalls. In Figure 3 the transition into\nthe isochoric regime is indicated by the overdensity falling below the\nexpected value shown by the dashed thick line.\n\nAlthough the growth of the perturbed quantities does not explicitly\ndepend on the wavelength $k$, the critical transition time when $Q\n\\approx 1$\n\\begin{equation}\n\\tau_{trans} = \\frac{1-K^{\\frac{2 \\beta-2}{3 -2 \\beta}}}{1-\\beta }\n\\label{a32}\n\\end{equation}\nis a function of $K$ (and $k$). At this transition point, the over \ndensity in the perturbed region is\n\n\\begin{equation}\n\\frac{\\rho_{trans}}{\\rho_0} = \\frac{\\rho_a}{\\rho_0} K^{\\frac{(4 - 2\n\\beta)}{(3 - 2 \\beta) \\Gamma}}.\n\\label{a33}\n\\end{equation}\n\n\\noindent and the velocity is\n\n\\begin{equation}\nV_{trans} = - \\frac{2-\\beta}{\\Gamma}\\frac{\\rho_a}{\\rho_0} \nK^{(\\frac{2-2\\beta}{3-2\\beta})(1+\\frac{2-\\beta}{(1 - \\beta) \\Gamma})} .\n\\end{equation}\n\n\\noindent In the isochoric regime the amplitude of the perturbed\ndensity increases as\n\n\\begin{equation}\n\\frac{\\rho_1}{\\rho_0} = \\frac{\\rho_{trans}}{\\rho_0} \n-V_{trans}*(\\tau -\\tau_{trans})\n\\end{equation}\n\n\\noindent which increases much less steeply than the isobaric \nfluctuations (equation 22).\n\nFor thermally unstable clouds, $\\beta < 1$ such that $\\rho_{trans} /\n\\rho_0$ is an increasing function of K or a decreasing function of the\nwavelength ($\\lambda$) of the perturbations. Despite the independence\nof the rate of change of $\\rho_1/\\rho_0$ on $\\lambda$, equation 24\nshows that for $\\beta < 1$ the short length scale disturbances undergo\nisobaric to isochoric transition at a later time and therefore acquire\na greater limiting amplitude than the long length scale disturbances.\nThus, the short length scale disturbances would emerge to dominate the\nstructure of the cloud unless the initial perturbation amplitude\n$\\rho_a/\\rho_0$ increases with $K$ more rapidly than $K ^{(2 \\beta\n-4)/(3 - 2 \\beta) \\Gamma}$. This evolution is physically equivalent\nto the fragmentation process in which the contrast between the\nenhanced density in a disturbance and the average cloud density\nbecomes most pronounced on the smallest scales.\n\n\\section{The Transition into the Nonlinear Regime}\n \nIn Fig. 3 fluctuations with very large values of K show yet another\nevolution: for later times the overdensity rises faster than predicted\nby equation (22). These fluctuations become nonlinear with\n$\\rho_1/\\rho_0 > 1$ before the transition into the isochoric\nregime. The critical value of K for this evolution can be estimated\nfrom equation (25) assuming $\\rho_{trans}/\\rho_0 = 1$:\n\n\\begin{equation}\nK_{crit} = \\left( \\frac{\\rho_a}{\\rho_0} \\right)\n^{\\frac{(2\\beta - 3)\\Gamma }{4-2\\beta}}\n\\label{a28}\n\\end{equation}\n\nFor $K > K_{crit}$ the analytical approximations discussed previously\nare not valid anymore and we have to investigate the evolution\nnumerically, solving the complete non-linear hydrodynamical\nequations. The simulations shown in figure 3 assumed $\\beta = 0$,\n$\\Gamma = 5/3$ and $\\rho_a/\\rho_0=10^{-3}$. For these values the\nsimple approximation (28) predicts $K_{crit}=5600$ which is roughly in\nagreement with the numerical results where the transition into the\nnonlinear regime occurs more smoothly between K=1000 and\nK=5000. Equation (28) somewhat overestimates $K_{crit}$ because\nnonlinear effects actually become important earlier, when the\noverdensity is in the range $0.1 < \\rho_1/\\rho_0 < 1$.\n\nFigure 4 shows the structure and evolution of a non-linear\nfluctuation. During the early isobaric evolution the pressure gradient\n(lower right panel) is negligible. A small pressure gradient builds up\nin the nonlinear regime, where the profiles cannot be approximated\nanymore by sinusoidal functions but instead become strongly peaked\ntowards the center. Non-linear fluctuations grow fast with the density\nand temperature reaching their maximum and minimum values,\nrespectively, at a time $\\tau_{crit} < 1 $ which is shorter than a\ncooling time. Due to the fast growth in the nonlinear regime,\n$\\tau_{crit}$ is roughly given by the time when $\\rho_1/\\rho_0 = 1$.\nFrom Eq (\\ref{a25}), we find \n\\begin{equation}\n\\tau_{crit} = \\frac{1}{1-\\beta} \\left( 1 - \\left( \\frac{\\rho_a}{\\rho_0} \n\\right)^{\\frac{(1-\\beta )\\Gamma}{2-\\beta}} \\right).\n\\end{equation}\nAt $t= \\tau_{crit}$, the dimensionless velocity (see Eq. \n\\ref{a26})\n\\begin{equation}\nV_{crit} = V(\\tau_{crit}) \n= \\frac{\\beta-2}{\\Gamma} \\left( \\frac{\\rho_a}{\\rho_0} \\right)^{\n-\\Gamma \\frac{1-\\beta}{2-\\beta}}\n\\end{equation}\n\\noindent is much larger than unity\nfor perturbations with small initial amplitudes such that\ncontributions due to nonlinear advection (such as $U_j \\partial \\rho /\n\\partial x_j$, $U_j \\partial U_j / \\partial x_j$, and $U_j \\partial T\n/ \\partial x_j$) would exceed the linear contributions contained in\nthe perturbed equations (\\ref{a6}-\\ref{a8}) before the over density\n$\\rho_1$ has become comparable to $\\rho_0$ (see above). Advection\ngenerally enhances the effect of compression and promotes the growth\nof density contrast at an accelerated rate.\n\nAlthough the time of maximum compression for a fluctuation with $K >\nK_{crit}$ does not depend explicitly on the length scale, it is\ndetermined by the initial amplitude $\\rho_a/\\rho_0$ of the\nperturbation which may be a function of the wavelength. For an\ninitial power-law perturbation in which $\\rho_a/\\rho_0 = A_0 (k/k_0)\n^\\eta$, \n\\begin{equation}\n\\tau_{crit} = \\frac{1}{1-\\beta} \\left( 1 - \\left( A_0^{\\frac{1}{\\eta}} \\frac{k}{k_0} \n\\right)^{\\frac{(1-\\beta )\\Gamma \\eta}{2-\\beta}} \\right).\n\\end{equation}\n\nIf the amplitude of the initial perturbation is an increasing function of\nthe wavelength (which corresponds to a negative $\\eta$),\n$\\tau_{crit}$ would be an increasing function of $k$ in the thermally\nunstable region with $\\beta <1$. In this case, nonlinearity would be\nfirst reached on the largest length scale with $K > K_{crit}$. If,\nhowever, the amplitude of the initial perturbation is a decreasing\nfunction of the wavelength ({\\it i.e.} $\\eta >0$), \n$\\tau_{crit}$ would be a decreasing\nfunction of $k$ and nonlinearity would be reached on the smallest\nscale first. Note that for $1 < \\beta < 2$, the dependence of \n$\\tau_{crit}$ on $\\eta$ and $k$ is reversed.\n\nIn Figure 3, a temperature independent cooling function has been\nused. In order to determine the dependence on the specific\nform of the cooling function, additional simulations have been performed,\nadopting a more realistic cooling function (Dalgarno \\& McCray 1972) which assumes\nsolar element abundance and collisional equilibrium ionization.\nNote that for temperatures T $> 10^4$ K the cooling rate is several\norders of magnitudes larger than for T $< 10^4$ K, defining two\ndifferent temperature regimes with very different cooling timescales.\nThe simulations show that the previous results remain\nvalid for each of these temperature regimes. Starting in the low-temperature\nregime, a fluctuation will become non-linear for K $>$ K$_{crit}$ and cool\ndown to the lowest allowed temperature. The same is true for fluctuations\nthat start in the high-temperature regime. Non-linear fluctuations in\nthis regime do however stop cooling efficiently at T $\\approx 10^4$ K,\nleading to high-density clumps with such a temperature.\n\n\\section{Interacting Fluctuations and the Emergence of \nSubstructure with a Critical Wave Length}\n\nUp to now we have investigated the evolution of isolated fluctuations.\nIn reality however a cooling gaseous region consists of a\nsuperposition of fluctuations with different wavelengths and\namplitudes. As we indicated in the previous section, the outcome of\nthe thermal instability may be determined by the wavelength dependence in the\ninitial amplitude of the perturbations.\n\nIn order to illustrate various competing effects such as isobaric to\nisochoric transition and the onset of nonlinear growth, we present in\nFigure 5 a series of models with $\\beta=0$ and $\\Gamma = 5/3$, where\nthe initial density distribution consists of the superposition\nof two fluctuations with ratios of wavelengths $\\lambda_1/ \\lambda_2\n= 20$ and amplitude ratios $\\rho_{a,1}/ \\rho_{a,2}= 2$ which\ncorresponds to $\\eta=-0.23$. Four values of $\\lambda_1$ were\nchosen and they correspond to $K_1$=1,10,100 and 1000, respectively.\nThe $K_2$ values for the smaller perturbation are always a factor 20\nlarger. Since the initial overdensity $\\rho_{a,1}/\\rho_0 =0.01$,\nthe critical value of K for nonlinear evolution is $K_{crit}=316$, according to\nequation (\\ref{a28}). We show the density distribution after 1 $\\tau_c(0)$. In\nthe upper left panels of Fig. 5, the fluctuations have values of $K_1=1$ and\n$K_2=20$ which are small compared to $K_{crit}$. Their growth\ntherefore stalls due to transition into the isochoric regime and the\noverdensity after a cooling time is still linear. The smaller\nfluctuation dominates at the end because its isochoric transition\noccurs later and at a higher overdensity than for the larger\nperturbation. In the upper right panels with $K_1=10$ and $K_2=200$\nthe smaller perturbation is again dominating after $\\tau=1$ although,\nnow, the density distribution is also affected by the underlying\nlarger perturbation. In both cases the density within the density\npeaks does not decrease much with respect to its initial value. The\nsituation is different in the lower left panel with $K_1=100$ and\n$K_2=2000$. Here the smaller perturbation has become nonlinear,\ngenerating small dense clumps which stand out against the larger\nperturbation. Up to now, the smaller perturbation was always\ndominating the density distribution after a cooling time. The\nsituation is however different in the lower right panel where \n$K_1 > K_{crit}$. Now, the larger perturbation becomes nonlinear and\nadvection drives all the gas and its small scale fluctuations into one\nvery dense, cold clump that is embedded in a hot diffuse environment,\nerasing smaller scale fluctuations.\n\nThe dependence of structure formation on the initial power-law perturbation index\n$\\eta$ is illustrated in figure 6 which shows the initial and final density distribution\nof two interacting perturbations with $\\lambda_1/\\lambda_2 = 10$, $K_1 = 2 \\times 10^4$,\n$\\rho_{a,1}/\\rho_{a,2}=10$ ($\\eta=-1$) in the left panels and\n$\\rho_{a,1}/\\rho_{a,2}=0.1$ ($\\eta=1$) in the right panels.\nAs expected, in the case of $\\eta=-1$ the larger perturbation becomes nonlinear first,\nleading to one massive density peak after a cooling time. For $\\eta=1$, the small\nlength scale perturbations begin to dominate after a cooling time, breaking the region up into\ndense clumps on the smallest scale. \nMore specifically, if the amplitude\nof the initial perturbation increases with increasing wavelength ($\\eta < 0$),\nclumps will form with length scales $\\lambda \\approx \\lambda_{crit}$.\nOtherwise, the sizes of the fastest growing perturbations will be\n$\\lambda \\approx \\lambda_{\\kappa}$. In this case, the clump sizes should\ndecrease with increasing magnetic field strength.\n\n\\section{The importance of thermal conduction}\nDuring the growth of linear density perturbations in the isobaric\nregime the resulting temperature gradient will induce conductive\nheating of the fluctuations.\n\n\\subsection{Thermal conduction in the absence of magnetic fields}\n\nSeveral studies (e.g. \nMcKee \\& Begelman 1990, Ferrara \\& Shchekinov 1993) have demonstrated\nthat thermal conduction could stabilize and even erase a density \nperturbation if its scale is smaller than the Field length (Field 1965)\n\n\\begin{equation}\n\\lambda_F = \\left( \\frac{\\kappa T}{n^2 \\Lambda} \\right)^{1/2}\n\\end{equation}\n\n\\noindent where $\\kappa$ is the thermal conduction coefficient.\n\nIn order to include the effect of thermal conduction, the term \n$\\nabla \\left(\\kappa \\nabla T \\right) / \\rho C_v$ has to be added to the\nright-hand side of equation (3). The linearized pressure equation (12) is then\n\n\\begin{equation}\n\\frac{\\partial}{\\partial \\tau} \\frac{ P_1}{P_0}= \n- \\Gamma \\sum_{j=1} ^3 V_j - \\frac{1}{1-(1-\\beta)\\tau} \n\\left((2-\\beta)\\frac{\\rho_1}{\\rho_0} - (1-\\beta)\\frac{P_1}{P_0} \\right)\n- \\frac{\\kappa}{\\rho_0 C_v} \\frac{T_1}{T_0} k^2 \\tau_c(0) .\n\\end{equation}\n\nIn the isobaric regime with $P_1/P_0 \\approx 0$ and $T_1/T_0 \\approx - \\rho_1/\\rho_0$\nthermal conduction will become important if\n\n\\begin{equation}\n\\frac{\\kappa}{\\rho_0 C_v} k^2 \\tau_c(0) \\geq \\frac{2-\\beta}{1-(1-\\beta)\\tau}\n\\end{equation}\n\n\\noindent In the early stages of cooling ($\\tau << 1$) fluctuations will therefore be erased by thermal\nconduction if their wavelenghts are\n\n\\begin{equation}\n\\lambda \\leq \\lambda_{\\kappa} = \\frac{2 \\pi}{(2-\\beta )^{1/2}} \\lambda_F.\n\\end{equation}\n\nFigure 7 shows the evolution of an initially isobaric, 1-dimensional fluctuation\nwith a ratio of cooling- to sound crossing time K=200 and $\\beta = 0$. The 1-dimensional,\nnon-linear hydrodynamical equations (1) - (3) are solved numerically, including thermal \nconduction. The solid line shows the evolution of the density contrast $\\rho_1/\\rho_0$ \nas predicted by the analytical model (equation 22) which is in excellent agreement\nwith the numerical result (filled points) for $\\lambda > \\lambda_{\\kappa}$. For\n$\\lambda = \\lambda_{\\kappa}$ (upper dashed line) conductive heating is non-negligible anymore\nand the fluctuation grows less fast. For $\\lambda < \\lambda_{\\kappa}$ the growth of fluctuations\nis suppressed by thermal conduction.\n\nIn summary, thermal conduction can play a significant role in regulating the\nbreak-up of a radiatively cooling gaseous medium. Small scale substructure can only\nemerge in a limited wavelength regime which is given by \n\n\\begin{equation}\n\\lambda_{\\kappa} \\leq \\lambda \\leq \\lambda_{crit}\n\\end{equation}\n\n\\noindent The growth of perturbations is completely suppressed if\n$\\lambda_{crit} < \\lambda_{\\kappa}$ for all perturbations.\n\nThe dotted lines in figure 8a show $\\lambda_{crit}$ for fluctuations with \ninitial overdensities $\\log (\\rho_a/\\rho_0) = -3,-2,-1$, the solid line shows \n$\\lambda_{\\kappa}$. A cooling function assuming\ncollisional equilibrium ionization (Spitzer 1978, Dalgarno \\& McCray 1972) \nand a realistic conduction coefficient\n(Ferrara \\& Shchekinov 1993) has been adopted. The dashed line shows\nthe mean free path (Cowie \\& McKee 1977)\n\n\\begin{equation}\n\\lambda_e \\approx 10^4 \\left( \\frac{T}{K} \\right)^2 \\left( \\frac{cm^{-3}}{n} \\right) cm\n\\end{equation}\n\n\\noindent for electron energy exchange. Note that for a given temperature the ratios\n$\\lambda_{\\kappa} / \\lambda_{crit} / \\lambda_e$ are independent of pressure.\n\nThe classical thermal conductivity is based on the assumption that $\\lambda_e$ is short\ncompared to the temperature scale height $h_T \\approx \\lambda/(T_1/T_0) > \\lambda_{crit}$.\nOtherwise, the heat flux q is saturated (Cowie \\& McKee 1977) \nand no longer equal to $q = -\\kappa \\nabla T$. Indeed, figure 8a shows that\nlinear fluctuations in astrophysical plasmas will in general lie in the non-saturated regime\n($\\lambda_{crit} > \\lambda_e$) for initial amplitudes $\\rho_a/\\rho_0 \\geq 0.001$.\n\nHowever, we also find that in general\n$\\lambda_{\\kappa} > \\lambda_{crit}$ for perturbations with amplitudes\n$\\log (\\rho_a/\\rho_0) \\leq -2$. This implies that a cooling instability, resulting from\nlinear density perturbations will in general be suppressed by thermal conduction.\n\n\\subsection{Thermal conduction, including magnetic fields}\n\nThe interstellar medium is in general penetrated by magnetic fields. In most situations the\nelectron mean free path $\\lambda_e$ is large compared to the length\nscale at which the resistive destruction of the magnetic field is significant.\nA tangled magnetic field can then develop, concentrated on scales $l_B$ which are\nsmaller than $\\lambda_e$ (Chandran \\& Cowley 1998). When the gyroradius\n\n\\begin{equation}\na = \\frac{v_T m_e c}{e B} \\approx 2.2 \\times 10^8 \\sqrt{\\frac{T}{10^8K}} \n\\left( \\frac{\\mu G}{B} \\right) cm\n\\end{equation}\n\n\\noindent of thermal electrons with typical velocities $v_T = (kT/m_e)^{1/2}$ is much\nsmaller than $l_B$ or $\\lambda_e$ the magnetic field controls the motion of\nindividual electrons. This condition is satisfied in many astrophysical plasmas\neven if the magnetic field is too weak to be hydrodynamically important.\n\nIf $a$ is small compared to the length scale $\\lambda$ of a fluctuation, heat is\nconducted according to the classcal thermal conduction equation (Spitzer 1962), however\nwith a thermal conductivity $\\kappa_B$ which is reduced from the classical\nSpitzer value $\\kappa$ as a result of the tangled magnetic\nfield by (Chandran \\& Cowley 1998)\n\n\\begin{equation}\n\\kappa_B \\approx \\frac{0.1}{\\ln (l_B/a)} \\kappa .\n\\end{equation}\n\n\nIf we normalize B to its value for magnetic-to-thermal energy equipartition\n$B_T = (24 \\pi \\rho R_g T)^{1/2}$ we find\n\n\\begin{equation}\n\\ln \\left(\\frac{l_B}{a} \\right) = -3.1 + \\ln \\left( \\frac{B}{B_T} \\right)\n+ 2 \\ln \\left( \\frac{T}{K} \\right) - 0.5 \\ln \\left( \\frac{n}{cm^{-3}} \\right) + \n\\ln \\left( \\frac{l_B}{\\lambda_e} \\right) .\n\\end{equation}\n\nFor weak magnetic fields ($B \\approx 0.01 B_T$)\nand length scales $\\l_B$ of order the electron mean free path\nequation 40 leads to $\\ln (l_B/a) \\geq 10$, by this reducing $\\kappa_B$ by two\norders of magnitudes and the length scale of thermal conduction\nby one order of magnitude.\nAs an example, the shaded area in figure 8b shows the wavelength regime \n$\\lambda_{\\kappa} \\leq \\lambda \\leq \\lambda_{crit}$ where linear fluctuations\nwith $\\rho_a/\\rho_0 = 10^{-2}$ could grow as a result of cooling,\nassuming a pressure of $P/k_B = 10^3$ K cm$^{-3}$ and $l_B = 0.1 \\lambda_e$.\nThe presence of a weak magnetic field can \nsuppress thermal conduction efficiently, allowing small scale structure\nwith wavelengths $\\lambda \\approx 10^{-2}$ pc to emerge\nas a result of cooling.\n\n\\section{The importance of heating and the emergence of a stable\ntwo-phase medium.}\n\nThe calculations in sections 3 and 4 showed that cooling gas clouds with small\ninitial perturbations break up on a critical wave length\n$\\lambda_{crit}$ below which over density first becomes nonlinear. If\nthe initial amplitude is a decreasing function of $\\lambda$, the\nclouds would break up on the smallest length where the local\nradiative cooling law remains valid and fluctuations are not destroyed by conduction.\nBut, if the initial amplitude\nis an increasing function of the wavelength,\n\\begin{equation}\n\\lambda_{crit} = \\frac{2 \\pi \\tau{_c}(0)}{K_{crit}} \n\\sqrt{\\frac{R_g T_0(0)}{\\mu}}.\n\\label{a30}\n\\end{equation}\n\\noindent small perturbations on scales $\\lambda < \\lambda_{crit}$ are\nerased when the gas accumulates in the center of fluctuations with\n$\\lambda = \\lambda_{crit}$. Perturbations with $\\lambda >\n\\lambda_{crit}$ do not become nonlinear but they break up into\nsubstructures with $\\lambda = \\lambda_{crit}$. \n\nAfter a cooling time the dense, cold, non-linear perturbations are\nembedded in a warmer, diffuse environment (see Fig. 9). However, \nthe example in figure 9 shows that the\ncooling timescale of the inter-clump gas remains short compared to the\ninitial cooling timescale. This gas therefore cools to a\nground state temperature $T_{min}$ shortly after $\\tau =\n1$. Subsequently the reversed pressure gradient would remove the\nfluctuations unless they are gravitationally bound.\n\nIn order to maintain a stable two-phase medium a heating term must be\nincluded (Field et al. 1969). Here we assume a power law\ndependence of the heating rate\n\n\\begin{equation}\n\\Gamma_h = \\Gamma_0 \\rho^{\\gamma}\n\\end{equation}\n\n\\noindent where $\\Gamma_0$ and $\\gamma$ are constants. In general, the\nsize of the whole cooling region is large compared to $\\lambda_{crit}$\nsuch that it cannot establish pressure equilibrium with the\nsurrounding confining medium during a cooling timescale. In this case,\nthe region cools isochorically and breaks up into\nsubstructures on scales of $\\lambda_{crit}$ before establishing\npressure equilibrium with the environment. If the average gas density\n$\\rho_0$ is smaller than a critical value\n\n\\begin{equation} \\rho_{\\Gamma} = \\left( \\frac{\\Gamma_0}{\\Lambda_0}\nT^{-\\beta} \\right)^{\\frac{1}{2-\\gamma}} \\end{equation}\n\n\\noindent heating would dominate everywhere and the region would adjust to\na thermal equilibrium state where heating is balanced against cooling.\nIf $\\rho_0 > \\rho_{\\Gamma}$ cooling dominates and\nthe density fluctuations would grow and become non-linear as discussed\nin the previous sections. Eventually, after a cooling time, the region\nwould break up into cold high-density condensations which are separated\nby warm gas with densities $\\rho_{min} << \\rho_0$. If $\\rho_{min} >\n\\rho_{\\Gamma}$ this interclump medium would cool as shown in figure 9 and\nthe density fluctuations would be erased. Figure 10 shows a situation\nwith $\\rho_{min} < \\rho_{\\Gamma}$. Heating dominates in the interclump\nregion where the gas temperature and gas pressure rise, until pressure\nequilibrium is established. A stable 2-phase medium has formed with\ncold clouds of minimum temperature embedded in a hot interclump medium\nwith a temperature that is determined by the balance of cooling and\nheating.\n\n\n\\section{Discussions}\n\nThe discussions in this paper focussed on the emergence of small scale\nperturbations. We have assumed the pre-existence of small\ninitial perturbations which is a reasonable assumption for\ndynamically evolving systems like the interstellar medium in galaxies\nor in galactic clusters. We have limited our analysis to the\noptically thin regime such that radiation transfer is solely due to\noptically thin local radiative processes. This approximation is\nappropriate for the collapse of supercritical clouds where the effect\nof a magnetic field is dominated by thermal processes. Such a\nsituation may be particularly relevant for the formation of stellar\nclusters and first generation stars in galaxies. Provided that the density\nof the progenitor clouds is relatively small, the local cooling\napproximation is adequate. We also neglected the interaction and merging of\nclumps. These processes become important for the subsequent evolution\nand they will be considered in subsequent papers.\n\nIn the context of our approximations, we have shown that thermal\ninstability can lead to the breakup of large clouds into cold, dense\nclumps with a characteristic length scale which is given by\n$\\lambda_{crit}$ in eq. ({\\ref{a30}) or by the smallest unstable\nwavelength that is not erased by thermal conduction,\ndepending on whether the amplitude of the initial\nperturbation is an increasing or decreasing function of wavelength.\nFor linear perturbations with overdensities $\\rho_a/\\rho_0 \\approx 0.01$\nthe critical wavelength lies in the regime of $10^{-3}$ pc to $10^{-1}$ pc,\ndepending on the initial temperature.\nThe emergence of small scale dense subcondensations is equivalent to\nfragmentation. As in a thermally unstable region the cooling\ntimescale is shorter than the dynamical timescale,\ngravity has no time to play an important role during this fragmentation\nprocess. $\\lambda_{crit}$ may be either\nsmaller or bigger than the Jeans' length. In the latter case\ngravity becomes important eventually. In general however,\nthermally induced fragmentation of clouds with small initial\ndensity fluctuations proceeds the onset of gravitational\ninstability of their individual clumps. \n\nIn our analyses, we adopted an idealized power-law cooling function. In\nreality, the cooling efficiency would terminate when the main cooling\nagents reach their ground state or establish an equilibrium with some\nexternal heating source. The latter is necessary for the clouds to \nattain a two-phase medium. Interaction between these two phases\nmay determine the pressure, density and infall rate of the cloud complex\nas well as the dynamical evolution and size distribution of cloudlets and sub condensations.\nThe analysis of this interaction will be presented elsewhere.\n\n\\newpage\n\n\\acknowledgements\n\nWe would like to thank the referee, Andrea Ferrara, for helpful suggestions\nand for pointing out the importance of thermal conduction.\nA. Burkert thanks the staff of UCO/Lick Observatory for the hospitality\nduring his visits. We thank S.D. Murray for useful conversation.\nThis research was supported by NASA through NAG5-3056, and an astrophysics\ntheory program which supports a joint Center for Star Formation\nStudies at NASA-Ames Research Center, UC Berkeley, and UC Santa Cruz.\n\n\\begin{thebibliography}{DUM}\n\n\\bibitem{ar} Arons, J. \\& Max, C.E. 1975, \\apj, 196, L77\n\\bibitem{ba1} Balbus, S.A. 1986, \\apj, 303, L79\n\\bibitem{ba2} Balbus, S.A. 1995, The Physics of the Interstellar Medium and\nIntergalactic Medium, ASP Conf. Ser. 80, eds. A. Ferrara, C.F. McKee, C. Heiles\n\\& P.R. Shapiro, p. 328\n\\bibitem{bli} Blitz, L. 1993, Protostars and Planets III, eds. E.H. Levy \\& J.I. Lunine, p. 125\n\\bibitem{blu} Blumenthal, G.R., Faber, S.M., Primack, J.R. \\& Rees, M.J. 1984, {\\it Nature},\n311, 517\n\\bibitem{br1} Brown, J.H., Burkert, A., Truran, J.W. 1991, \\apj, 376, 115\n\\bibitem{br2} Brown, J.H., Burkert, A., Truran, J.W. 1995, \\apj, 440, 666\n\\bibitem{bu1} Burkert, A. \\& Bodenheimer, P. 1993, \\mnras, 264, 798\n\\bibitem{bu2} Burkert, A. \\& Bodenheimer, P. 1996, \\mnras, 280, 1190\n\\bibitem{bu3} Burkert, A., Bate, M. \\& Bodenheimer, P. 1997, \\mnras, 289, 497\n\\bibitem{car} Carpenter, J.M., Meyer, M.R., Dougados, C., Strom, S.E.\n\\& Hillenbrand, L.A. 1997, \\aj, 114, 198\n\\bibitem{cow} Chandran, B.D.G. \\& Cowley, S.C. 1998, {\\it Phys. Rev. Lett}., 80, 3077\n\\bibitem{cow} Cowie, L.L. \\& McKee, C.F. 1977, \\apj, 211, 135\n\\bibitem{cru} Crutcher, R.M., Troland, T.H., Goodman, A.A., Heiles, C.,\nKazes, I. \\& Myers, P.C. 1993, \\apj, 407, 175\n\\bibitem{dal} Dalgarno, A. \\& McCray, R.A. 1972, {\\it Ann. Rev. Astron.\nAstroph.}, 10, 375\n\\bibitem{fer} Ferrara, A. \\& Shchekinov, Y. 1993, \\apj, 417, 595\n\\bibitem{fi1} Field, G.B. 1965, \\apj, 142, 531\n\\bibitem{fi2} Field, G.B., Goldsmith, D.W. \\& Habing, H.J. 1969, \\apj, 155, L49\n\\bibitem{fra} Franco, J., \\& Cox, D.P. 1983, \\apj, 273, 24\n\\bibitem{gam} Gammie, C.F. \\& Ostriker, E.C. 1996, \\apj, 466, 814\n\\bibitem{hil} Hillenbrand, L.A. 1997, \\aj, 113, 1733\n\\bibitem{hun} Hunter, C. 1962, \\apj, 136, 594\n\\bibitem{kra} Kraft, R.P. 1979, ARAA, 17, 309\n\\bibitem{lar} Larson, R.B. 1981, \\mnras, 194, 809\n\\bibitem{lin} Lin, D.N.C. \\& Murray, S.D. 1992, \\apj, 394, 523\n\\bibitem{liz} Lizano, S. \\& Shu, F.H. 1989, \\apj, 342, 834\n\\bibitem{loe} Loewenstein, M. 1990, \\apj, 349, 471\n\\bibitem{ma1} MacLow, M.M., Klessen, R.S., Burkert, A., Smith, M.D. \\&\nKessel, O. 1998, {\\it Phys. Rev. Lett.}, 80, 2754\n\\bibitem{ma2} MacLow, M.M. 1999, \\apj, in press\n\\bibitem{mck} McKee, C.F. 1989, \\apj, 345, 782\n\\bibitem{mk2} McKee, C.F. \\& Begelman, M.C. 1990, \\apj, 358, 392\n\\bibitem{mo1} Mouschovias, T.C. \\& Spitzer, L.H. 1976, \\apj, 210, 326\n\\bibitem{mo2} Mouschovias, T.C. 1991, \\apj, 373, 169\n\\bibitem{mur} Murray, S.D. \\& Lin, D.N.C. 1992, \\apj, 400, 265\n\\bibitem{mye} Myers, P.C. \\& Goodman, A.A. 1988, \\apj, 326, L27\n\\bibitem{nak} Nakano, T. 1979, PASJ, 31, 697\n\\bibitem{par} Parker, E.N. 1953, \\apj, 117, 431\n\\bibitem{sch} Schwarz, J., McCray, R. \\& Stein, R. 1972, \\apj, 175, 673\n\\bibitem{shu} Shu, F., Najita, J., Galli, D., Ostriker, E. \\& Lizano, S. 1993,\nProtostars and Planets III, eds. E.H. Levy \\& J.I. Lunine, p.3\n\\bibitem{sol} Solomon, P.M., Rivolo, A.R., Barrett, J. \\& Yahil, A. 1987, \\apj, 319, 730\n\\bibitem{spi62} Spitzer, L. 1962, Physics of Fully Ionized Gases\n(New York: Interscience Publishers).\n\\bibitem{spi78} Spitzer, L. 1978, Physical Processes in the Interstellar Medium\n(New York: Wiley).\ns of Fully Ionized, Solomon, P.M., Rivolo, A.R., Barrett, J. \\& Yahil, A. 1987, \\apj, 319, 730\n\\bibitem{sto} Ostriker, E.C., Gammie, C.F. \\& Stone, J.M. 1999, \\apj, 513, 259\n\\end{thebibliography}\n\n\n\n\\newpage\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig1.ps,height=16cm}}\n\\caption {The solid lines show the numerical results of the\nevolution of the overdensity\n(left panel) and dimensionless velocity (right panel) for almost\nisochoric perturbations with K=1 (upper curves) and K=0.5 (lower curves).\nA cooling law with $\\beta = 0$ is adopted. The dots represent the analytical\nsolution (equations 13 and 14).}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig2.ps,height=16cm}}\n\\caption {The growth of an initially isobaric density perturbation with \nK=200 is shown, adopting $\\beta = 0$ and $\\Gamma = 5/3$. The numerical results (solid lines) are compared\nwith the analytical solutions (dashed curves). The upper two panels show the early\nevolution which is compared with the predictions of the linearized equations\n(16) and (17) assuming $\\omega = \\sqrt{\\Gamma}K$. The lower panels show the\nevolution till $\\tau=1$ which is compared with the results of the\nnonlinear equations (22) and (23).}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig3.ps,height=16cm}}\n\\caption{The growth of initially isobaric fluctuations is shown. The solid curves,\nlabeled by the adopted initial K-values of the fluctuations show the results of numerical\ncalculations for $\\beta = 0$. The thick dashed line shows the evolution of \na linear isobaric perturbation as predicted by equation (22). Fluctuations with small\nvalues of K become isochoric and their density increase stalls. Above a critical value\nof K fluctuations become nonlinear during their isobaric growth. These fluctuations\nevolve faster than predicted by the linear approximation and achieve very\nlarge density contrasts on a timescale which is independent of K and shorter than\na cooling timescale.}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig4.ps,height=16cm}}\n\\caption{The evolution of overdensity $\\rho_1/\\rho_0$, dimensionless velocity V,\ntemperature $T_1/T_0$ and pressure $P_1/P_0$ of a nonlinear fluctuation with K=1000,\nassuming $\\beta=0$. Cooling is assumed to stop after the temperature has decreased\nby 4 orders of magnitude. The evolutionary state of the system is shown\nat the time when the overdensity is 0.1, 0.5, 1 and 5 times the initial density.}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig5.ps,height=16cm}}\n\\caption {The figures show the overdensity and the temperature distribution\nafter a cooling time of regions with two interacting fluctuations with\nwavelength ratios $\\lambda_1/\\lambda_0 = 20$ and amplitude \nratios $\\rho_{a,1}/\\rho_{a,2} = 0.5$, adopting different values of K.\nThe x-coordinate is normalized to the wavelength of a perturbation with K=1.}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig6.ps,height=16cm}}\n\\caption{The left upper and lower panels show, respectively, \nthe initial ($\\tau = 0$) and \nfinal ($\\tau = 1$) density distribution of two nonlinear interacting density perturbations \nwith $\\lambda_1/\\lambda_0 = 10$ and $\\eta=-1$. The initial and final density distributions\nfor interacting nonlinear fluctuations with $\\eta=1$ are shown, respectively, in the\nupper and lower right panels.}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig7.ps,height=16cm}}\n\\caption{The effect of thermal conduction on the growth of a perturbation\nwith $\\rho_a/\\rho_0=0.01$ and $K=200$ is shown, adopting a cooling function with\n$\\beta = 0$. The solid thick line shows the theoretical prediction and the\nfilled points show the numerical result for $\\lambda_{\\kappa}=0$. The lower dashed\nlines show the evolution of fluctuations with \n$\\lambda=\\lambda_{\\kappa}$, $\\lambda=0.75 \\lambda_{\\kappa}$, $\\lambda=0.5 \\lambda_{\\kappa}$,\nand $\\lambda=0.25 \\lambda_{\\kappa}$, respectively.}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig8.ps,height=16cm}}\n\\caption{Fig. 8a shows several interesting lengthscales as function of\ntemperature, adopting a gas pressure of $P/k_B = n T = 10^3 K cm^{-3}$.\nSolid line: $\\lambda_{\\kappa}$. Dashed lines: $\\lambda_{crit}$ for density fluctuations\nwith $\\log(\\rho_a/\\rho_0) = -1, -2, -3$, respectively. Dashed line: $\\lambda_e$. \nThe shaded area in Fig. 8b shows the wavelength regime $\\lambda_{\\kappa} \\leq \\lambda\n\\leq \\lambda_{crit}$ where density perturbations with $\\log (\\rho_a/\\rho_0) = -2$ would\nbe able to grow and become non-linear, adopting a gas pressure of $P/k_B = 10^3 K cm^{-3}$,\na magnetic field of $B = 0.01 B_T$ and a tangled magnetic field length scale of\n$l_B = 0.1 \\lambda_e$.}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig9.ps,height=16cm}}\n\\caption{Evolution of a nonlinear perturbation with K=1000 and $\\beta = 0$.\nThe upper panels show the evolution of the maximum density and temperature (solid line) \nand of the minimum density and temperature (dashed lines)\nfor 2 cooling timescales. Shortly after one cooling timescale the low-density regions\ncool down to the minimum temperature too and the reversed pressure gradient erases the\ndensity contrast. The lower panels show the evolution of the density and temperature \nduring the short epoch at $\\tau \\approx 1$ when a 2-phase medium has formed. }\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig10.ps,height=16cm}}\n\\caption{The evolution of the maximum and minimum density (left panel) and maximum\nand minimum temperature (right panel) of a non-linear \nperturbation, including a cooling term with $\\beta = 0$ and a heating term which\ndominates for $\\rho < \\rho_{\\Gamma}=0.1 \\rho_0$, where $\\rho_0$ is the initial average density. \nThe density perturbation \ngrows and becomes non-linear within a cooling timescale. As gas is pushed into \nthe high-density regions,\nthe density in the inter-clump region decreases below the ciritical value where heating \nbegins to dominate and the inter-clump gas heats up. \nA stable two-phase medium forms.}\n\\end{figure}\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002106.extracted_bib",
"string": "\\begin{thebibliography}{DUM}\n\n\\bibitem{ar} Arons, J. \\& Max, C.E. 1975, \\apj, 196, L77\n\\bibitem{ba1} Balbus, S.A. 1986, \\apj, 303, L79\n\\bibitem{ba2} Balbus, S.A. 1995, The Physics of the Interstellar Medium and\nIntergalactic Medium, ASP Conf. Ser. 80, eds. A. Ferrara, C.F. McKee, C. Heiles\n\\& P.R. Shapiro, p. 328\n\\bibitem{bli} Blitz, L. 1993, Protostars and Planets III, eds. E.H. Levy \\& J.I. Lunine, p. 125\n\\bibitem{blu} Blumenthal, G.R., Faber, S.M., Primack, J.R. \\& Rees, M.J. 1984, {\\it Nature},\n311, 517\n\\bibitem{br1} Brown, J.H., Burkert, A., Truran, J.W. 1991, \\apj, 376, 115\n\\bibitem{br2} Brown, J.H., Burkert, A., Truran, J.W. 1995, \\apj, 440, 666\n\\bibitem{bu1} Burkert, A. \\& Bodenheimer, P. 1993, \\mnras, 264, 798\n\\bibitem{bu2} Burkert, A. \\& Bodenheimer, P. 1996, \\mnras, 280, 1190\n\\bibitem{bu3} Burkert, A., Bate, M. \\& Bodenheimer, P. 1997, \\mnras, 289, 497\n\\bibitem{car} Carpenter, J.M., Meyer, M.R., Dougados, C., Strom, S.E.\n\\& Hillenbrand, L.A. 1997, \\aj, 114, 198\n\\bibitem{cow} Chandran, B.D.G. \\& Cowley, S.C. 1998, {\\it Phys. Rev. Lett}., 80, 3077\n\\bibitem{cow} Cowie, L.L. \\& McKee, C.F. 1977, \\apj, 211, 135\n\\bibitem{cru} Crutcher, R.M., Troland, T.H., Goodman, A.A., Heiles, C.,\nKazes, I. \\& Myers, P.C. 1993, \\apj, 407, 175\n\\bibitem{dal} Dalgarno, A. \\& McCray, R.A. 1972, {\\it Ann. Rev. Astron.\nAstroph.}, 10, 375\n\\bibitem{fer} Ferrara, A. \\& Shchekinov, Y. 1993, \\apj, 417, 595\n\\bibitem{fi1} Field, G.B. 1965, \\apj, 142, 531\n\\bibitem{fi2} Field, G.B., Goldsmith, D.W. \\& Habing, H.J. 1969, \\apj, 155, L49\n\\bibitem{fra} Franco, J., \\& Cox, D.P. 1983, \\apj, 273, 24\n\\bibitem{gam} Gammie, C.F. \\& Ostriker, E.C. 1996, \\apj, 466, 814\n\\bibitem{hil} Hillenbrand, L.A. 1997, \\aj, 113, 1733\n\\bibitem{hun} Hunter, C. 1962, \\apj, 136, 594\n\\bibitem{kra} Kraft, R.P. 1979, ARAA, 17, 309\n\\bibitem{lar} Larson, R.B. 1981, \\mnras, 194, 809\n\\bibitem{lin} Lin, D.N.C. \\& Murray, S.D. 1992, \\apj, 394, 523\n\\bibitem{liz} Lizano, S. \\& Shu, F.H. 1989, \\apj, 342, 834\n\\bibitem{loe} Loewenstein, M. 1990, \\apj, 349, 471\n\\bibitem{ma1} MacLow, M.M., Klessen, R.S., Burkert, A., Smith, M.D. \\&\nKessel, O. 1998, {\\it Phys. Rev. Lett.}, 80, 2754\n\\bibitem{ma2} MacLow, M.M. 1999, \\apj, in press\n\\bibitem{mck} McKee, C.F. 1989, \\apj, 345, 782\n\\bibitem{mk2} McKee, C.F. \\& Begelman, M.C. 1990, \\apj, 358, 392\n\\bibitem{mo1} Mouschovias, T.C. \\& Spitzer, L.H. 1976, \\apj, 210, 326\n\\bibitem{mo2} Mouschovias, T.C. 1991, \\apj, 373, 169\n\\bibitem{mur} Murray, S.D. \\& Lin, D.N.C. 1992, \\apj, 400, 265\n\\bibitem{mye} Myers, P.C. \\& Goodman, A.A. 1988, \\apj, 326, L27\n\\bibitem{nak} Nakano, T. 1979, PASJ, 31, 697\n\\bibitem{par} Parker, E.N. 1953, \\apj, 117, 431\n\\bibitem{sch} Schwarz, J., McCray, R. \\& Stein, R. 1972, \\apj, 175, 673\n\\bibitem{shu} Shu, F., Najita, J., Galli, D., Ostriker, E. \\& Lizano, S. 1993,\nProtostars and Planets III, eds. E.H. Levy \\& J.I. Lunine, p.3\n\\bibitem{sol} Solomon, P.M., Rivolo, A.R., Barrett, J. \\& Yahil, A. 1987, \\apj, 319, 730\n\\bibitem{spi62} Spitzer, L. 1962, Physics of Fully Ionized Gases\n(New York: Interscience Publishers).\n\\bibitem{spi78} Spitzer, L. 1978, Physical Processes in the Interstellar Medium\n(New York: Wiley).\ns of Fully Ionized, Solomon, P.M., Rivolo, A.R., Barrett, J. \\& Yahil, A. 1987, \\apj, 319, 730\n\\bibitem{sto} Ostriker, E.C., Gammie, C.F. \\& Stone, J.M. 1999, \\apj, 513, 259\n\\end{thebibliography}"
}
] |
astro-ph0002107
|
Infrared spectroscopy of NGC~1068:\\ Probing the obscured ionizing AGN continuum
|
[
{
"author": "Tal Alexander\\altaffilmark{1}"
},
{
"author": "Dieter Lutz\\altaffilmark{2}"
},
{
"author": "Eckhard Sturm\\altaffilmark{2}"
},
{
"author": "Reinhard Genzel\\altaffilmark{2}"
},
{
"author": "Amiel Sternberg\\altaffilmark{3}"
},
{
"author": "Hagai Netzer\\altaffilmark{3}"
}
] |
The ISO-SWS\footnote{% Based on observations made with ISO, an ESA project with instruments funded by ESA member states (especially the PI countries: France, Germany, The Netherlands and the United Kingdom) and with the participation of ISAS and NASA. The SWS is a joint project of SRON and MPE. } \( 2.5 \)--\( 45\, \mu \mathrm{m} \) infrared spectroscopic observations of the nucleus of the Seyfert 2 galaxy \( \NGC \) (see companion paper) are combined with a compilation of UV to IR narrow emission line data to determine the spectral energy distribution (SED) of the obscured extreme-UV continuum that photoionizes the narrow line emitting gas in the active galactic nucleus. We search a large grid of gas cloud models and SEDs for the combination that best reproduces the observed line fluxes and NLR geometry. Our best fit model reproduces the observed line fluxes to better than a factor of 2 on average and is in general agreement with the observed NLR geometry. It has two gas components that are consistent with a clumpy distribution of dense outflowing gas in the center and a more extended distribution of less dense and more clumpy gas farther out that has no net outflow. The best fit SED has a deep trough at \( \sim \! 4 \) Ryd, which is consistent with an intrinsic Big Blue Bump that is partially absorbed by \( \sim \! 6\times 10^{19}\, \mathrm{cm}^{-2} \) of neutral hydrogen interior to the NLR.
|
[
{
"name": "ms.tex",
"string": "\\documentstyle[11pt,aaspp4]{article}\n\n\\newcommand{\\noun}[1]{\\textsc{#1}}\n\n\\begin{document}\n\n\\newcommand{\\La}{\\mathrm{Ly}\\alpha }\n\n\\newcommand{\\Lalpha}{\\mathrm{Ly}\\alpha \\, \\lambda 1215}\n\n\\newcommand{\\Ka}{\\mathrm{K}\\alpha }\n\n\\newcommand{\\Lb}{\\mathrm{L}\\beta }\n\n\\newcommand{\\Ha}{\\mathrm{H}\\alpha }\n\n\\newcommand{\\Halpha}{\\mathrm{H}\\alpha \\, \\lambda 6563}\n\n\\newcommand{\\Hb}{\\mathrm{H}\\beta }\n\n\\newcommand{\\Hbeta}{\\mathrm{H}\\beta \\, \\lambda 4861}\n\n\\newcommand{\\Pa}{\\mathrm{P}\\alpha }\n\n\\newcommand{\\HeI}{\\mathrm{He}\\, {\\textsc {i}}\\, \\lambda 5876}\n\n\\newcommand{\\HeII}{\\mathrm{He}\\, {\\textsc {ii}}\\, \\lambda 1640}\n\n\\newcommand{\\CIII}{\\mathrm{C}\\, {\\textsc {iii}}\\, \\lambda 977}\n\n\\newcommand{\\CIIIb}{\\mathrm{C}\\, {\\textsc {iii]}}\\, \\lambda 1909}\n\n\\newcommand{\\CIV}{\\mathrm{C}\\, {\\textsc {iv}}\\, \\lambda 1549}\n\n\\newcommand{\\bOIIIbA}{[\\mathrm{O}\\, {\\textsc {iii]}}\\, \\lambda 4363}\n\n\\newcommand{\\bOIIIbB}{[\\mathrm{O}\\, \\textsc {iii]}\\, \\lambda 5007}\n\n\\newcommand{\\OIIIb}{\\mathrm{O}\\, {\\textsc {iii]}}\\, \\lambda 1663}\n\n\\newcommand{\\OVb}{\\mathrm{O}\\, {\\textsc {v]}}\\, \\lambda 1218}\n\n\\newcommand{\\OVI}{\\mathrm{O}\\, {\\textsc {vi}}\\, \\lambda 1035}\n\n\\newcommand{\\OIVb}{\\mathrm{O}\\, {\\textsc {iv]}}\\, \\lambda 1402}\n\n\\newcommand{\\bOIIb}{[\\mathrm{O}\\, {\\textsc {ii]}}\\, \\lambda 3727}\n\n\\newcommand{\\bOIb}{[\\mathrm{O}\\, {\\textsc {i]}}\\, \\lambda 6300}\n\n\\newcommand{\\NV}{\\mathrm{N}\\, {\\textsc {v}}\\, \\lambda 1240}\n\n\\newcommand{\\NIVb}{\\mathrm{N}\\, {\\textsc {iv]}}\\, \\lambda 1486}\n\n\\newcommand{\\NIIIb}{\\mathrm{N}\\, {\\textsc {iii]}}\\, \\lambda 1750}\n\n\\newcommand{\\MgII}{\\mathrm{Mg}\\, {\\textsc {ii}}\\, \\lambda 2798}\n\n\\newcommand{\\bNeVb}{[\\mathrm{Ne}\\, {\\textsc {v]}}\\, \\lambda 3426}\n\n\\newcommand{\\NeVIII}{\\mathrm{Ne}\\, {\\textsc {viii}}\\, \\lambda 774}\n\n\\newcommand{\\SiIV}{\\mathrm{Si}\\, {\\textsc {iv}}\\, \\lambda 1397}\n\n\\newcommand{\\bFeXb}{[\\mathrm{Fe}\\, {\\textsc {x]}}\\, \\lambda 6734}\n\n\\newcommand{\\bFeXIb}{[\\mathrm{Fe}\\, {\\textsc {xi]}}\\, \\lambda 7892}\n\n\\newcommand{\\FeII}{\\mathrm{Fe}\\, {\\textsc {ii}}\\, }\n\n\\newcommand{\\bSiVIIb}{[\\mathrm{Si}\\, {\\textsc {vii]}\\, \\lambda 2.5\\mu \\mathrm{m}}}\n\n\\newcommand{\\bSiIXbA}{[\\mathrm{Si}\\, {\\textsc {ix]}}\\, \\lambda 2.6\\mu \\mathrm{m}}\n\n\\newcommand{\\bSiIXbB}{[\\mathrm{Si}\\, {\\textsc {ix]}}\\, \\lambda 3.9\\mu \\mathrm{m}}\n\n\\newcommand{\\bMgVIIIb}{[\\mathrm{Mg}\\, {\\textsc {viii]}}\\, \\lambda 3.0\\mu \\mathrm{m}}\n\n\\newcommand{\\bMgIVb}{[\\mathrm{Mg}\\, {\\textsc {iv]}}\\, \\lambda 4.5\\mu \\mathrm{m}}\n \n\\newcommand{\\bMgVIIb}{[\\mathrm{Mg}\\, {\\textsc {vii]}\\, \\lambda 5.5\\mu \\mathrm{m}}}\n\n\\newcommand{\\bNeVIb}{[\\mathrm{Ne}\\, {\\textsc {vi]}}\\, \\lambda 7.6\\mu \\mathrm{m}}\n\n\\newcommand{\\bArIIIb}{}\n \n\\newcommand{\\bArVIb}{[\\mathrm{Ar}\\, {\\textsc {vi]}}\\, \\lambda 4.5\\mu \\mathrm{m}}\n \n\\newcommand{\\bSIVb}{[\\mathrm{S}\\, {\\textsc {iv]}}\\, \\lambda 10.5\\mu \\mathrm{m}}\n\n\\newcommand{\\bNeIIb}{[\\mathrm{Ne}\\, {\\textsc {ii]}}\\, \\lambda 12.8\\mu \\mathrm{m}}\n\n\\newcommand{\\bNeVbA}{[\\mathrm{Ne}\\, {\\textsc {vi]}}\\, \\lambda 14.3\\mu \\mathrm{m}}\n\n\\newcommand{\\bNeIIIbA}{[\\mathrm{Ne}\\, {\\textsc {iii]}}\\, \\lambda 15.6\\mu \\mathrm{m}}\n\n\\newcommand{\\bSIIIbA}{[\\mathrm{S}\\, {\\textsc {iii]}}\\, \\lambda 18.7\\mu \\mathrm{m}}\n\n\\newcommand{\\bNeVbB}{[\\mathrm{Ne}\\, {\\textsc {vi]}}\\, \\lambda 24.3\\mu \\mathrm{m}}\n\n\\newcommand{\\bOIVb}{[\\mathrm{O}\\, {\\textsc {iv]}}\\, \\lambda 25.9\\mu \\mathrm{m}}\n\n\\newcommand{\\bSIIIbB}{[\\mathrm{S}\\, {\\textsc {iii]}}\\, \\lambda 33.5\\mu \\mathrm{m}}\n\n\\newcommand{\\bSiIIb}{[\\mathrm{Si}\\, {\\textsc {ii]}}\\, \\lambda 34.8\\mu \\mathrm{m}}\n\n\\newcommand{\\bNeIIIbB}{[\\mathrm{Ne}\\, {\\textsc {iii]}}\\, \\lambda 36.0\\mu \\mathrm{m}}\n\n\\newcommand{\\EBV}{E_{\\textsc {b-v}}}\n\n\\newcommand{\\Fnlr}{F_{\\textsc {nlr}}}\n\n\\newcommand{\\lgs}{\\log ^{2}S}\n\n\\newcommand{\\qion}{q_{\\mathrm{ion}}}\n\n\\newcommand{\\tion}{\\Delta \\theta _{\\mathrm{ion}}}\n\n\\newcommand{\\ml}{m_{\\ell }}\n\n\\newcommand{\\fl}{f_{\\ell }}\n\n\\newcommand{\\kl}{k_{\\ell }}\n\n\\newcommand{\\Eion}{E_{\\mathrm{ion}}}\n\n\\newcommand{\\maxs}{\\max S_{\\ell }}\n\n\\newcommand{\\Mo}{M_{\\odot }}\n\n\\newcommand{\\Ro}{R_{\\odot }}\n\n\\newcommand{\\Lo}{L_{\\odot }}\n\n\\newcommand{\\NGC}{\\mathrm{NGC}\\, 1068}\n\n%\\maketitle\n\n\\title{Infrared spectroscopy of NGC~1068:\\\\\nProbing the obscured ionizing AGN continuum}\n\n\\author{Tal Alexander\\altaffilmark{1}\\\\\nDieter Lutz\\altaffilmark{2}, Eckhard Sturm\\altaffilmark{2}, Reinhard Genzel\\altaffilmark{2}\\\\\nAmiel Sternberg\\altaffilmark{3}, Hagai Netzer\\altaffilmark{3}}\n\n\\altaffiltext{1}{Institute for Advanced Study, Olden Lane, Princeton, NJ 08540,USA}\n\n\\altaffiltext{2}{Max-Planck-Institut f\\\"{u}r Extraterrestrische Physik, Postfach 1603, D-85740 Garching, Germany}\n\n\\altaffiltext{3}{School of Physics and Astronomy and Wise Observatory, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel}\n\n\\begin{abstract}\nThe \\emph{ISO-SWS}\\footnote{%\nBased on observations made with ISO, an ESA project with instruments funded\nby ESA member states (especially the PI countries: France, Germany, The Netherlands\nand the United Kingdom) and with the participation of ISAS and NASA. The SWS\nis a joint project of SRON and MPE. \n} \\( 2.5 \\)--\\( 45\\, \\mu \\mathrm{m} \\) infrared spectroscopic observations\nof the nucleus of the Seyfert 2 galaxy \\( \\NGC \\) (see companion paper) are\ncombined with a compilation of UV to IR narrow emission line data to determine\nthe spectral energy distribution (SED) of the obscured extreme-UV continuum\nthat photoionizes the narrow line emitting gas in the active galactic nucleus.\nWe search a large grid of gas cloud models and SEDs for the combination that\nbest reproduces the observed line fluxes and NLR geometry. Our best fit model\nreproduces the observed line fluxes to better than a factor of 2 on average\nand is in general agreement with the observed NLR geometry. It has two gas components\nthat are consistent with a clumpy distribution of dense outflowing gas in the\ncenter and a more extended distribution of less dense and more clumpy gas farther\nout that has no net outflow. The best fit SED has a deep trough at \\( \\sim \\! 4 \\)\nRyd, which is consistent with an intrinsic Big Blue Bump that is partially absorbed\nby \\( \\sim \\! 6\\times 10^{19}\\, \\mathrm{cm}^{-2} \\) of neutral hydrogen interior\nto the NLR.\n\\end{abstract}\n\n\\section{Introduction}\n\n%\\label{fig:temp}\\label{fig:mix}\\label{fig:ratios}\\label{fig:abs_sed}\\label{tbl:flux}\\label{tbl:fit}\n\nThe intrinsic spectral energy distribution (SED) of active galactic nuclei (AGN),\nwhich extends from the radio up to \\( \\gamma \\)-rays, cannot be directly observed\nfrom the Lyman limit and up to several hundred eV due to Galactic and intrinsic\nabsorption. However, the extreme-UV (EUV) and soft X-ray continuum can be investigated\nindirectly by the infrared coronal line emission. These lines are emitted by\ncollisionally excited forbidden fine-structure transitions of highly ionized\natoms, whose ionization potentials extend well beyond the Lyman limit up to\nhundreds of eV. Unlike the strong permitted lines of these ions, which are also\nemitted in the obscured EUV, the reddening-insensitive forbidden IR coronal\nlines and semi-forbidden optical coronal lines can be observed. Therefore, when\nphotoionization is the main ionization mechanism, the coronal lines can provide\ninformation on the intrinsic obscured SED and the accretion process that powers\nthe AGN. This information can be extracted by photoionization models of the\nNLR.\n\nThe coronal lines are collisionally suppressed in the dense broad line region\n(BLR) close to the continuum source and are efficiently emitted only from the\nmore rarefied gas in the narrow line region (NLR), hundreds of pc away from\nthe center. It is well established that large quantities of gas attenuate the\ncontinuum emission in many AGN. These gas clouds are detected by narrow UV absorption\nlines (e.g. Kriss et al. \\cite{Kriss92}) or by X-ray absorption features and\nemission lines (e.g. George et al. \\cite{George98}). Although their exact location\nalong the line of sight is unknown, there are reasons to believe that in some\ncases they may be inside the NLR. In particular, the warm absorbers that block\nthe X-ray continuum appear to cover a large fraction of the continuum source\n(George et al. \\cite{George98}). This raises the possibility that in some AGN\nthe ionizing SED, which is traced by the coronal lines, is not the intrinsic\none produced by the accretion process, but rather one that is filtered by intervening\nabsorbers inside the NLR. It has been proposed that such absorbers are common\nin Seyfert galaxies, and are responsible for the observed correlations between\nthe soft X-ray slope and the narrow emission line spectra of Seyfert 1.5 galaxies\n(Kraemer, Ruiz \\& Crenshaw \\cite{KTCG99}).\n\nThis study of the Seyfert 2 galaxy \\( \\NGC \\) is part of the \\emph{ISO-SWS}\nprogram on bright galactic nuclei. Previous studies in this program include\nthe reconstruction of the SED of the Seyfert 2 Circinus galaxy (Moorwood et\nal. \\cite{Moorwood96}; Alexander et al. \\cite{Alexander99}) and of the Seyfert\n1 Galaxy NGC~4151 (Alexander et al. \\cite{Alexander99}). In both cases we found\nevidence of a ``Big Blue Bump'' signature of a thin accretion disk (Shakura\n\\& Sunyaev \\cite{SS73}). However, in the case of NGC~4151 this structure is\nmasked by a deep absorption trough of an absorber situated between the BLR and\nthe NLR, which filters the light that photoionizes the NLR. \n\nIn this paper we apply our SED reconstruction method to \\( \\NGC \\), one of\nthe closest, brightest and most extensively studied Seyfert 2 galaxies, which\nis considered a prototype of this AGN class. The first detection of broad permitted\nemission lines in the polarized light of \\( \\NGC \\) (Antonucci \\& Miller \\cite{AM85})\nprovided a major argument for the Seyfert 1 and 2 unification scheme (Antonucci\n\\cite{Antonucci93}). This scheme postulates that the two Seyfert types have\nboth broad and narrow line regions and an obscuring torus that lies between\nthe two. When the torus is face on and the BLR is directly observed, the AGN\nis classified as a Seyfert 1. When the BLR is obscured by the torus, the AGN\nis classified as a Seyfert 2, and the BLR can be observed only indirectly in\nscattered polarized light. The factors that determine the accretion properties\nand the ionizing SED of AGN are currently unknown. However, the Seyfert unification\npicture implies that all possibly relevant factors being equal, such as luminosity,\nhost galaxy type or redshift, the intrinsic SED of both AGN types should be\nsimilar. It is therefore of interest to complement our previous study of the\nnearby luminous Seyfert 1 galaxy NGC~4151 with a corresponding study of a nearby\nluminous Seyfert 2 galaxy with a similar host galaxy type, such as \\( \\NGC \\).\nThe \\emph{ISO-SWS} observations of \\emph{\\( \\NGC \\)} are presented in a companion\npaper (Lutz et al. \\cite{Lutz00}) and are used there to derive the gas density\nand to place constraints on the structure and dynamics of the NLR.\n\nThis paper is organized as follows. In \\S\\ref{sec:physprop} we summarize the\nphysical properties of the nucleus of \\( \\NGC \\) that are needed for constructing\nthe photoionization models and constraining their results. In \\S\\ref{s:lines} we\npresent the emission line flux compilation that we use in our modeling. In \\S\\ref{s:models}\nwe briefly discuss the construction and fitting of the NLR photoionization models.\nWe present the results in \\S\\ref{s:results} and discuss them in \\S\\ref{s:discuss}.\n\n\n\\section{The physical properties of NGC~1068}\n\n\\label{sec:physprop}\n\n\\label{s:n1068}\\( \\NGC \\) is a barred spiral galaxy at \\( z=0.0036 \\) (distance\n\\( D=16.6\\, \\)Mpc for \\( H_{0}=65\\, \\mathrm{km}\\, \\mathrm{s}^{-1}\\, \\mathrm{Mpc}^{-1} \\))\nwith magnitude \\( m_{B}=9.17 \\) (e.g. Lipovetsky, Neizvestny \\& Neizvestnaya\n\\cite{LNN88}). Observations of the nucleus of \\( \\NGC \\) and models of the\nnuclear line emission indicate that the gas in the nucleus forms a complex system,\nwhich is composed of various spatial and dynamical components. These are excited\nby several physical mechanisms, including photoionization by the nuclear continuum,\nphotoionization by hot stars, and possibly also by shocks and energetic particles\nfrom a radio jet. In order to isolate the effects of the nuclear continuum and\nto construct photoionization models of the NLR it is necessary to understand\nthe morphology and content of the galactic nucleus. We present here a brief\noverview of the properties of the nucleus that are relevant to this work.\n\n\n\\subsection{The galactic nucleus}\n\n\\label{s:n1068-nucleus}\n\nThe most prominent morphological feature in the nucleus of \\( \\NGC \\) is the\nasymmetric bi-polar pattern of both the radio and the optical line emission.\nThe radio emission extends over \\( \\sim \\! 15\\arcsec \\) and has a sharply\ndefined northern lobe and a weaker diffuse southern lobe (Wilson \\& Ulvestad\n\\cite{WU83}; Muxlow et al. \\cite{Muxlow96}). The southern lobe is both smaller\nand redder, which is consistent with the picture that the large northern lobe\nis observed above the galactic disk, generally facing the observer, and the\nsouthern lobe is seen through the galactic disk (Unger et al. \\cite{ULPA92};\nMacchetto et al. \\cite{Macchetto94}). Images of the NLR in low excitation lines\nshow mainly the northern cone (Cecil, Bland \\& Tully \\cite{CBT90}; Unger et\nal. \\cite{ULPA92}; Evans et al. \\cite{Evans91}). The precise value of the\nopening angle associated with the emission maps depends on the way the edge\nof the cone is defined and on the assumed position of the nucleus. The location\nof the nucleus can be determined to within \\( \\sim \\! 0.05\\arcsec \\) by the\ncenter of symmetry of the UV polarization pattern (Capetti et al. \\cite{Capetti95},\nKishimoto \\cite{Kishimoto99}). The position of the nucleus does not appear\nto coincide with the maximum of the continuum emission, which implies that the\nnucleus is heavily obscured even in the infrared. This is consistent with an\nobscuring torus of column density in excess of \\( 10^{24} \\) cm\\( ^{-2} \\),\nas is inferred from X-ray (Marshall et al. \\cite{Marshal93}) and CO observations\n(Tacconi et al. \\cite{Tacconi94}). The positioning of the nucleus makes it\npossible to estimate the opening angle of the radiation cone at \\( \\gtrsim 70\\arcdeg \\)\nup to \\( \\sim \\! 100\\arcdeg \\). The ionization cone appears to be only partially\nfilled.\n\nMarconi et al. (\\cite{MWMO96}) find that the coronal line emission peaks \\( 0.5\\arcsec \\)\nNE of the nucleus and extends up to \\( \\sim \\! 4\\arcsec \\). They note that\nthe blueshift of the emission line profile centroid increases, and the FWHM\nof the profile decreases with \\( \\Eion \\) (the ionization energy required\nto produce the emitting ion from the preceding ionization stage). They interpret\nthis as evidence that the emission lines are emitted from outflowing material.\nThe high ionization lines are emitted in the inner light cone, where the velocity\nfield is relatively coherent, while the lower ionization lines are emitted from\nslower, more extended areas with different velocities. The NLR \\( \\bOIIIbB \\)\nemission extends over the few inner arcseconds (Evans et al. \\cite{Evans91};\nUnger et al. \\cite{ULPA92}; Dietrich \\& Wagner \\cite{DW98}). The extended\nemission line region (EELR) \\( \\bOIIIbB \\) emission extends over more than\n\\( 10\\arcsec \\) (Unger et al. \\cite{ULPA92}). \n\nThe unresolved BLR is seen only in scattered polarized light and has FWHM of\n\\( \\sim \\! 3000 \\) km~s\\( ^{-1} \\) (Miller et al \\cite{MGM91}). As is seen\nin other Seyfert 2 galaxies (Wilson \\cite{Wilson88}; Capetti et al. \\cite{Capetti96}),\nthe morphology of the NLR emission maps is correlated with that of the radio\nstructure (Wilson \\& Ulvestad \\cite{WU83}; Capetti et al. \\cite{CAM97}). In\nparticular, a 3-dimensional reconstruction of the positions of individual clouds\nbased on polarimetric measurements also indicates that the northern NLR cone\nis directed towards the observer, and the southern part away from the observer\n(Kishimoto \\cite{Kishimoto99}). The close correspondence between the NLR and\nthe jet suggests that the jet outflow sweeps and compresses the ambient gas\nand thereby increases the line emissivity. The NLR has a very complex structure\n(Macchetto et al. \\cite{Macchetto94}) and displays large scale clumpiness.\nIt is composed of many line emitting cloud complexes (Alloin et al. \\cite{Alloin83};\nMeaburn \\& Pedlar \\cite{MP1986}; Evans et al. \\cite{Evans91}; Dietrich \\&\nWagner \\cite{DW98}). The individual components have FWHM ranging from \\( \\sim \\! 200 \\)\nkm~s\\( ^{-1} \\) to \\( \\sim \\! 700 \\) km~s\\( ^{-1} \\), and extend over \\( \\sim \\! 2500 \\)\nkm~s\\( ^{-1} \\) in velocity space, resulting in an integrated \\( \\bOIIIbB \\)\nprofile with FWHM of \\( 1150 \\) km~s\\( ^{-1} \\) (Dietrich \\& Wagner \\cite{DW98}).\nThe velocity field of the NLR clouds with the lowest FWHM is consistent with\nrotation around the nucleus. The bulk velocities of intermediate FWHM clouds\nare clearly split relative to the symmetry axis of the radio jet, which suggests\nthat they are associated with the interaction between the radio jet and the\nNLR gas. The highest FWHM clouds are associated with highly polarized emitting\nstructures (Capetti et al \\cite{Capetti95}), and could therefore be a reflected\nimage of an inner obscured region. The EELR appears to follow the galactic rotation\n(Unger et al. \\cite{ULPA92}).\n\nThe large \\emph{ISO} apertures (\\( 14\\arcsec \\times 20\\arcsec \\) to \\( 20\\arcsec \\times 33\\arcsec \\))\nincludes both the outflowing inner NLR and the rotating EELR. \n\n\n\\subsection{The line emitting gas}\n\n\\label{s:n1068-gas}\n\nThere is evidence that at least three different ionization mechanisms are at\nwork in the NLR. The very high ionization states are probably due to the the\ncentral continuum source. Marconi et al. (\\cite{MWMO96}) find that the infrared\ncoronal line ratios point to photoionization as the main excitation mechanism\nof the coronal gas, and that both collisional excitation or photoionization\nby very hot stars can be ruled out. At lower ionization states, the jet / ISM\ninteraction can provide internal sources of excitation in addition to the external\ncentral continuum, for example by fast shocks or cosmic rays. The morphological\nconnection between the radio and line emission suggests that the jet outflow\nshapes the NLR. Estimates of high gas temperatures (Kriss et al. \\cite{KDBFL92})\nand the existence of dense but highly ionized clouds near the nucleus on both\nsides of the jet axis suggest that the jet may also play a role in photoionizing\nthe clouds (Capetti et al \\cite{CAM97}; Axon et al. \\cite{Axon98}; Dietrich\n\\& Wagner \\cite{DW98}). Hot stars are a third ionization mechanism. Unresolved\nUV continuum point sources in the inner \\( 7\\arcsec \\times 7\\arcsec \\), which\nare not observed in \\( \\bOIIIbB \\), could be OB associations (Macchetto et\nal. \\cite{Macchetto94}). Hot stars are certainly a component in the ring-like\nstructure that surrounds the nucleus. An ellipse of H\\,\\textsc{ii} emission\ndelineates the NLR at an average radius of \\( 13\\arcsec \\) (Cecil, Bland \\&\nTully \\cite{CBT90}; Bruhweiler et al. \\cite{BTA91}) and starburst knots and\nCO emission encircle the nucleus and the NLR at an average radius of \\( 18\\arcsec \\)\n(Planesas, Scoville \\& Myers \\cite{Planesas91}). However, the overall similarity\nin the profiles of the mid-infrared high-excitation lines, which cannot be excited\nby hot stars, and the profiles of the intermediate excitation lines (\\( \\Eion >30\\, \\mathrm{eV} \\)),\nwhich could be excited by hot stars, strongly suggests that gas excited by hot\nstars within the large \\emph{ISO} aperture does not contribute more than \\( \\sim \\! 20\\% \\)\nto these NLR line fluxes (Lutz et al. \\cite{Lutz00}). An additional complication\ndue to stars is contamination of the observed emission line spectrum with stellar\nabsorption features. This appears in the difference spectrum of the \\( 30\\arcsec \\oslash \\)\nand \\( 18\\arcsec \\oslash \\) \\emph{HUT} apertures, which shows both a reddened\nearly-type stellar continuum and stellar absorption features (Kriss et al. \\cite{KDBFL92}).\n\nAs is discussed by Lutz et al. (\\cite{Lutz00}), the \\emph{ISO-SWS} line ratios\nindicate that the mid-IR lines are emitted from gas with a hydrogen density\nof \\( \\sim \\! 2000\\, \\mathrm{cm}^{-3} \\). The NLR appears to contain also higher\ndensity gas. The density of individual knots in the high ionization core is\nestimated at \\( 10^{4} \\) to \\( 3\\times 10^{4} \\) cm\\( ^{-3} \\) from \\emph{HST}\nmeasurements of the \\( [\\textrm{S}\\, \\textsc {ii}] \\) doublet, while the overall\ndensity \\( \\sim \\! 1\\arcsec \\) from the nucleus varies between \\( 10^{3} \\)\nto \\( 4\\times 10^{3} \\) cm\\( ^{-3} \\) (Capetti et al. \\cite{CAM97}).\n\nThe ionization parameter\\footnote{%\n\\( U\\equiv Q_{\\mathrm{ion}}/4\\pi r^{2}nc, \\) where \\( Q_{\\mathrm{ion}} \\)\nis the ionizing photon luminosity, \\( n \\) is the hydrogen density at the illuminated\nface of the cloud, \\( r \\) is the distance of the face of the cloud from the\ncontinuum source and \\( c \\) is the speed of light. The local ionization parameter\nin the cloud falls with increasing depth due to absorption and geometrical dilution\nof the radiation field.\n} also appears to vary across the NLR. The \\( \\bOIIIbB /(\\Ha +[\\mathrm{N}\\, {\\textsc {ii]}}\\, \\lambda 6584) \\)\nratio (Capetti et al. \\cite{CAM97}) traces a high excitation core (\\( \\log U\\sim -2.5 \\))\nin the inner \\( 1\\arcsec \\times 2\\arcsec \\) north of the nucleus, followed\nby a lowered ionization halo (\\( \\log U\\sim -3.3 \\)) out to \\( \\sim 4\\arcsec \\)\nfrom the nucleus, and then intermediate ionization filaments (\\( \\log U\\sim -2.8 \\))\nwhich extend out to the EELR. \n\nEstimates of dust reddening in the NLR of \\( \\NGC \\) range from \\( \\EBV =0.07 \\)\nfor the continuum (Kriss et al \\cite{KDBFL92}), to 0.20 (Marconi et al \\cite{MWMO96}),\n0.40 (Shields \\& Oke \\cite{SO75}; Neugebauer et al \\cite{Neugebauer80}; Ward\n\\cite{Ward87}), and \\( \\EBV =0.52 \\) (Koski \\cite{Koski78}) for the NLR.\nThe analysis of Kraemer et al. (\\cite{KRC98}) indicates that there may be some\ndust mixed with gas in varying amounts. The observed line ratios in the NLR\nsuggest that the O/N abundance is less than solar. Netzer (\\cite{Netzer97})\nand Netzer \\& Turner (\\cite{NT97}) interpret this as an indication of under-abundant\noxygen (see also Sternberg, Genzel \\& Tacconi \\cite{SGT94}), and propose that\nthe abundances of He:C:N:O:Ne:Mg:Si:S:Ar:Fe relative to hydrogen are \\( (100:3.7:1.1:2.7:1.1:0.37:0.35:0.16:0.037:0.4)\\times 10^{-4} \\),\nrespectively. Kraemer et al. (\\cite{KRC98}) interpret the line ratios as showing\nan overabundance of nitrogen, as well as hinting at higher than solar iron and\nneon, and propose abundance ratios of \\( (100:3.4:3.6:6.8:2.2:0.33:0.31:0.15:0.037:0.8)\\times 10^{-4} \\).\n\nFinally, Kraemer et al. (\\cite{KRC98}) model the NLR emission with a multi-component\ngas model, and suggest that the low ionization emission lines are emitted by\ngas that is partially screened by a dense, optically thin component. They use\ntheir models to estimate that the filling factor is \\( F\\sim 10^{-4} \\).\n\n\n\\subsection{The ionizing continuum}\n\n\\label{s:n1068-SED}\n\nUnlike the situation in Seyfert 1 galaxies, where it is possible to observe\nthe intrinsic SED outside the obscured range, the intrinsic SED of \\( \\NGC \\)\ncannot be directly observed even in the optical or X-ray bands. Only a small\nfraction of the AGN light is scattered into the line of sight, and can be observed\nagainst the host galaxy in polarized light. Pier et al (\\cite{Pier94}) compiled\nvarious continuum measurements in the optical, UV and X-ray, and carefully took\naccount of aperture differences, star-light contamination, reflection by dust\nand bremsstrahlung emission from the scattering plasma. They conclude that the\nresulting reflected SED is broadly similar to that observed in Seyfert 1 galaxies.\nPier et al (\\cite{Pier94}) also list various estimates of the fraction of light\nreflected by the scatterer. These values range from \\( f_{\\textrm{refl}}=10^{-3} \\)\n(Bland-Hawthorn \\& Voit \\cite{BH93}) to \\( \\sim \\! 0.05 \\) (Bland-Hawthorn,\nSokoloski \\& Cecil \\cite{BSC91}). Pier et al (\\cite{Pier94}) argue that the\nmost reliable estimate is \\( f_{\\textrm{refl}}\\sim 0.01 \\) to within a factor\nof a few. Because the reflectors are more than a hundred light years away from\nthe continuum source (Miller et al. \\cite{MGM91}), short-term continuum variability\nis unlikely to affect the reconstruction of the reflected SED.\n\nWe adopt the Pier et al. nuclear continuum SED in the UV and X-ray as the template\nSED (Fig.~\\ref{fig:temp}), and further extend it from 10~keV to 100~keV with\na slope of \\( F_{\\nu }\\propto \\nu ^{-1} \\). We enumerate on the unobserved\nUV to soft X-ray range to find the best fitting SED.\n\n\n\\section{The observed line flux compilation}\n\n\\label{s:lines}\n\nIn addition to the ISO-SWS mid-IR lines fluxes presented in Lutz et al. (\\cite{Lutz00}),\nwe compiled a list of UV to IR lines from the literature. The compilation initially\nincluded a list of \\( \\sim \\! 120 \\) measured line fluxes, which were obtained\nover the last \\( \\sim \\! 30 \\) years using various instruments with different\napertures, spectral resolutions and reduction techniques. The observed lines\nwere taken from the following references, listed by spectral band with the aperture\nused (where given): UV lines from Kriss et al (\\cite{KDBFL92}) (\\( 18\\arcsec \\oslash \\));\noptical lines from Osterbrock \\& Parker (\\cite{OP65}) (trailing long slit),\nAnderson (\\cite{Anderson70}) (\\( 8\\arcsec \\times 8\\arcsec \\)), Wampler (\\cite{Wampler71})\n(\\( 10\\arcsec \\oslash \\)), Koski (\\cite{Koski78}) (\\( 2.7\\arcsec \\times 3.4\\arcsec \\))\nand Neugebauer et al (\\cite{Neugebauer80}) (\\( \\sim \\! 10\\arcsec \\times 20\\arcsec \\));\noptical to near-IR lines from Shields \\& Oke (\\cite{SO75}) (\\( 10\\arcsec \\times 10\\arcsec \\)),\nnear-IR lines from Oliva \\& Moorwood (\\cite{OM90}) (\\( 6\\arcsec \\times 6\\arcsec \\)),\nMarconi et al (\\cite{MWMO96}) (long slit of width \\( 4.4\\arcsec \\)), Osterbrock\n\\& Fulbright (\\cite{OF96}) (\\( 3\\arcsec \\times 18\\arcsec \\)) and Osterbrock,\nTran \\& Veilleux (\\cite{OTV92}) (long slit of width \\( 1.2\\arcsec \\)); IR\nlines from Thompson (\\cite{Thompson96}) (\\( 2\\arcsec \\times 10\\arcsec \\))\nand the ISO-SWS (\\( 14\\arcsec \\times 20\\arcsec \\) to \\( 20\\arcsec \\times 33\\arcsec \\)).\n\nAs is discussed in detail by Alexander et al. (\\cite{Alexander99}), the result\nof such a compilation is generally not self-consistent, and only a small subset\nof the of the \\( \\sim \\! 120 \\) lines can be used. First, we excluded low and\nmedium excitation lines (\\( \\Eion \\lesssim 100\\, \\)eV) observed through apertures\nwhose smaller dimension is less than \\( 3\\arcsec \\), so as to avoid significant\nloss of light due to incomplete coverage of the line emitting region. The observed\nemission from the high excitation lines is centrally concentrated in the inner\n\\( <4\\arcsec \\) (Marconi et al \\cite{MWMO96}), which are covered even by\nthe smallest apertures used. Second, we excluded lines with \\( \\Eion <30\\, \\)eV\nto avoid using lines that may be photoionized primarily by young hot stars or\nother non-AGN, lower-energy excitation processes. This also reduces the loss\nof light bias. Third, we excluded narrow lines whose measured flux is uncertain,\neither because the flux is very low (flux less than \\( 5\\times 10^{-13}\\, \\)erg\ns\\( ^{-1} \\) cm\\( ^{-2} \\), \\( \\sim \\! 2\\% \\) of the strongest line), or\nbecause it has a significant broad component, such as the \\( \\NV \\) and \\( \\CIV \\)\nlines. Fourth, we excluded the \\( \\bFeXb \\) and \\( \\bFeXIb \\) lines, whose\ncollision strengths are highly uncertain and therefore cannot be modeled reliably.\nThe final, much reduced line list includes 22 lines (Table~\\ref{tbl:flux}),\nwhich we use for obtaining the best-fit SED. Whenever more than one measurement\nof the line exists, we quote the average flux and use the rms scatter as an\nerror estimate. Important IR lines that were not included in the final list\nwere nevertheless compared to the best fit model predictions to verify that\nthere are no gross inconsistencies.\n\n\n\\section{The photoionization models}\n\n\\label{s:models} \n\nThe method of constructing photoionization models for the NLR and, in particular,\nthe ``\\( \\lgs \\) fit procedure'' for obtaining the best fitting SED and\ngas parameters is described in detail in Alexander et al. (\\cite{Alexander99}),\nand is summarized here briefly. We parameterize the SED as a piece-wise broken\npower-law (Fig.~\\ref{fig:temp}), and enumerate on the different possibilities\nof connecting the power-law segments. We test a large number of simplified NLR\ngas models, which consist of optically thick (radiation bounded) clouds whose\nionized surfaces partially cover a spherical shell around the continuum source.\nEach cloud extends in the radial direction as far as it takes to effectively\nabsorb all the ionizing UV photons (specifically, until the hydrogen ionization\nfraction falls below 2\\%). The gas clouds are parameterized by their chemical\ncomposition, the hydrogen density \\( n \\), the ionization parameter \\( U \\)\nat the irradiated face of the cloud, and the filling factor \\( F \\). In addition,\nan asymmetry parameter \\( A \\) expresses the ratio between the ionizing flux\ndirected towards the NLR and that directed towards the observer. This describes\nsituations where the continuum source is not isotropic, or where only a fraction\n\\( f_{\\mathrm{refl}} \\) of the continuum is reflected towards the observer\n(\\( A=1/f_{\\mathrm{refl}} \\)).\n\nFor each NLR gas model, the fit procedure uses the observed line fluxes to derive\nthe best-fit SED for that gas model, and from it to derive in a self-consistent\nway the corresponding covering factor \\( C, \\) the inner NLR angular radius\n\\( \\theta \\), the width of the ionized region \\( \\tion \\) (defined here\nas the radial extent of the Balmer lines emitting gas) and the reddening coefficient\n\\( \\EBV \\). These parameters are constrained by the observations and so can\nbe used to limit the range of acceptable NLR gas models. The \\( \\lgs \\) fit\nprocedure assigns a score \\( S \\) to the best-fit model, which means that the\nmodel line fluxes fit the observed ones up to a factor \\( S \\), on average.\nThe worst-fitting line and the factor by which it deviates from the observed\nvalue are also recorded. Monte-Carlo simulations are used to calculate confidence\nlimits on the best-fit SED. In addition, we calculate the correlation between\nthe model-to-data line ratios and the lines wavelengths, ionization potentials,\ncritical densities and ``deplitivity'' (the tendency of an element to be depleted\ninto dust). These residual correlations test whether the remaining inconsistencies\nin the best-fit model are related to inaccurate modeling of the reddening, the\nspectral hardness / softness of the continuum, the gas density or its dust content.\nThe correct model should not display any such correlations. The final, global\nbest-fit SED is the one with the best \\( S \\)-score among all the NLR gas models\nthat are consistent with the observed NLR geometry and reddening, whose worst-fitting\nline is not too far from the observed value, and which display no significant\nresidual correlations.\n\nWe assume in all models that the gas clouds have constant density and that \\( f_{\\mathrm{refl}}=0.005 \\).\nWe investigate two classes of models. The first consists of models with a single\ntype of cloud. We enumerate on different values for the ionization parameter\n(\\( \\log U=-1,-2 \\) and \\( -3 \\)), gas density (\\( n=2000 \\) and \\( 10^{4}\\, \\mathrm{cm}^{-3} \\))\nand filling factor (\\( \\log F=-2,-3 \\) and \\( -4 \\) at the ionized surface).\nWe test two different sets of non-solar abundances, the low oxygen set and high\nnitrogen set (\\S\\ref{s:n1068-gas}). We test two different possibilities for\nthe radial run of the filling factor. The first is that \\( F \\) is constant,\nwhich corresponds to either a static distribution of clouds, a rotating distribution\nof clouds, a linear constant velocity outflow, a strongly decelerating outflow\nat a constant opening angle, or an outflow where clouds are continuously added\nto the flow (e.g. from the molecular torus). The second is \\( F\\propto r^{-2} \\),\nwhich corresponds to a constant velocity and constant opening angle outflow\nwhere the clouds are formed at the base of the flow. The second class of models\nhave two types of gas clouds, and are constructed by combining all the possible\npairs of one component models. We assume that the clouds do not obscure one\nanother. \n\nThe photoionization calculations were carried out using the numerical photoionization\ncode \\noun{ion9}9, the 1999 version of the code \\noun{ion} described by\nNetzer (\\cite{Netzer96}).\n\n\n\\section{Results}\n\n\\label{s:results}\n\n\n\\subsection{Single component models}\n\nWe find that single component models generally fail to fit the observed line\nratios and the observed constraints on the geometry of the NLR. Low \\( U \\)\nmodels (\\( \\log U=-3 \\)) cannot reproduce the high excitation lines regardless\nof the values of the other model parameters. For the \\( F\\propto r^{-2} \\)\nmodels, the low \\( U \\) models significantly over-estimate the size of the\nNLR, while the high-\\( U \\) models require unphysical covering factors exceeding\nunity. Single component models with a high \\( U \\) and low constant filling\nfactor do somewhat better, although such models are problematic because a constant\nfilling factor is inconsistent with simple scenarios of NLR outflow. The best\nfit single component model has low oxygen abundance with \\( \\log U=-1 \\), \\( \\log n=3.3 \\)\nand \\( \\log F=-3 \\). This model can reproduce the observed lines up to a factor\nof 2 and predicts \\( \\theta =0.8\\arcsec \\), \\( \\tion =4.8\\arcsec \\), \\( C=0.35 \\)\nand \\( \\EBV =0.18. \\) These values are roughly consistent with the observed\nconstraints. However, this model under-predicts the observed \\( \\OVI \\) flux\nby a factor of \\( \\sim \\! 5 \\) and shows a residual negative correlation with\n\\( \\lambda _{0} \\) at the 5\\% confidence level. Like all the models investigated\nhere, the best fit SED displays a deep trough at 4 Ryd (\\( \\log f=-27.4,\\, -29.0,\\, -27.4,\\, -28.2 \\)\nat 2, 4, 8 and 16 Ryd, respectively). A fit of similar quality is obtained with\nthe high nitrogen abundance set.\n\n\n\\subsection{Two component models}\n\nA better fit to the observations is provided by the best-fit two component model\n(Table~\\ref{tbl:fit}). This model fits the 22 observed line fluxes to within\na factor of 1.9 on average (experience shows this is as well as one can expect\nfor AGN photoionization models). The worst fitting line, \\( \\bArVIb \\), is\nunder-predicted by a factor of 4. The model-to-data ratios of individual lines\nare displayed in Fig.~\\ref{fig:ratios}. The low excitation IR lines (\\( \\Eion <30\\, \\mathrm{eV} \\))\nsuch as \\( \\bNeIIb \\), \\( \\bSIIIbA \\) and \\( \\bSIIIbB \\), which were not\nused in the fit, are nevertheless all consistent with the observations to within\na factor of 2. However, the model-to-data line ratios for these lines are not\nmuch smaller than 1, as would be expected if there is a significant contamination\nfrom gas photoionized by starbursts. The high excitation IR lines such as \\( [\\mathrm{S}\\, {\\textsc {ix]}}\\, \\lambda 1.25\\mu \\mathrm{m} \\),\n\\( [\\mathrm{Si}\\, {\\textsc {x]}}\\, \\lambda 1.4\\mu \\mathrm{m} \\) and \\( [\\mathrm{Si}\\, {\\textsc {ix]}}\\, \\lambda 2.6\\mu \\mathrm{m} \\),\nwhich were not used in the fit, are also consistent with the observations to\nwithin a factor of 3. There are no statistically significant residual correlations\nbetween these ratios and \\( \\lambda _{0} \\), \\( \\Eion \\), the deplitivity\nor \\( n_{c} \\). The best fit values of the extinction \\( (\\EBV \\sim 0.2 \\))\nis in agreement with other estimates (\\S\\ref{s:n1068-gas}). The covering factors\nare somewhat larger than is indicated by the observed opening angle of the emission\ncone (\\S\\ref{s:n1068-nucleus}). The dense compact component requires a covering\nfactor of \\( C=0.45 \\), which corresponds to a bi-cone with an opening angle\nof \\( \\sim \\! 115\\arcdeg \\). The less dense, more extended component requires\na covering factor \\( C=0.26 \\), which corresponds to a single cone with an\nopening angle of \\( \\sim \\! 130\\arcdeg \\) or a bi-cone with opening angle\nof \\( \\sim \\! 90\\arcdeg \\). Figure~\\ref{fig:mix} shows the best fit SED for\nthis gas model together with the 99.9\\% confidence limits on it (the lower confidence\nlimits at 2, 4 and 16 Ryd were not calculated as they extend beyond the SED\ngrid). This SED shows the generic trough that is seen in the best-fit SED of\nall the models we investigated. This model has a less than solar oxygen abundance\n(Netzer \\cite{Netzer97}; Netzer \\& Turner \\cite{NT97}). We find only a few\ntwo-component models with high nitrogen abundance that come close to a reasonable\nfit to the observations. Of these, almost all display a negative correlation\nwith deplitivity at the 5\\% to 10\\% significance, which may indicate that the\nline emitting gas is more depleted than is assumed by the high nitrogen abundance\nset.\n\nWe conclude that best-fit two component model provides a better, but not an\noverwhelmingly better fit to the observed line ratios than the single component\nmodel. Its marked advantage over the single component models lies in its consistency\nwith the observed NLR geometry and kinematics. This is further discussed in\nthe next section.\n\n\n\\section{Discussion}\n\n\\label{s:discuss}\n\nAs was discussed in detail by Alexander et al. (\\cite{Alexander99}), there\nare various degeneracies between the parameters that describe the gas model\n(\\( n, \\) \\( A \\), \\( F \\), \\( U \\), \\( C \\), \\( \\theta \\), and \\( \\tion \\)).\nThese degeneracies allow the fit procedure to converge to a robust best-fit\nSED even when the assumed values of \\( n \\), \\( A \\), \\( F \\) or \\( U \\)\nsignificantly differ from their true values, since this can be compensated to\na large degree by a suitable modification of the gas geometry (\\( C \\), \\( \\theta \\),\nand \\( \\tion \\)). This property of the fit procedure is especially important\nin the analysis of \\( \\NGC \\), where observations indicate that the actual\nproperties of the NLR gas are much more complex than can be modeled by our family\nof simplified gas models. For this reason, we place more weight on the fact\nthat all the best-fit SED models, whether one or two-component, display a deep\ntrough at 4 Ryd than on the determination of the exact values of the gas parameters. \n\nThe trough in the SED is required for reproducing the relative line fluxes of\nthe high and low ionization species. To check the robustness of this result,\nwe attempted to re-fit the observed line fluxes with all of our one and two-component\nmodels using an approximate single power-law SED (\\( \\log f=-25.8,\\, -26.6,\\, -27.4,\\, -28.2 \\)\nat 2, 4, 8 and 16 Ryd, respectively), which was held fixed in the fit procedure.\nIn all cases the low excitation lines were over-estimated with respect to the\nhigh excitation lines, regardless of the values of \\( U \\), \\( n \\) or \\( F \\).\nFor example, when the power-law SED is applied to the best-fit two-component\ngas model (Table~\\ref{tbl:fit}), the low excitation lines (\\( \\Eion \\lesssim 50\\, \\mathrm{eV} \\))\nare over-estimated by the model by up to a factor of 13, whereas the high excitation\nlines (\\( \\Eion \\gtrsim 100\\, \\mathrm{eV} \\)) are under-estimated by up to\na factor of 23. The overall mismatch of this SED with the observed line fluxes\nis reflected in both the poor fit score of \\( S=4.1 \\) and in the very strong\nresidual anti-correlation between the line ratios and \\( \\Eion \\), whose random\nprobability is \\( 10^{-4} \\). We caution against generalizing this result to\nmean that every AGN that exhibits a hard emission line spectrum has an absorbed\nionizing SED. The emission line spectrum reflects the gas parameters, such as\n\\( U \\), \\( n \\) and \\( F \\), no less than it does the ionizing SED. It is\nnecessary to have some knowledge of the likely range of values for these parameters\nin order to interpret the hardness of the line spectrum. Alexander et al. (\\cite{Alexander99})\nprovide a counter-example where subtle cancellations between the SED and the\ngas properties lead to a situation where an AGN (NGC4151) with a hard absorbed\nSED has a \\emph{softer} emission line spectrum than another AGN (Circinus) with\na soft unabsorbed Big Blue Bump. \n\nAlthough we do not claim to fix the gas parameters with certainty, the best\nfit model (Table~\\ref{tbl:fit}) is reassuringly consistent with the observations,\nwhich broadly indicate that the integrated NLR emission originates in two components.\nComponent A of the model can be interpreted as a system of dense (\\( n=10^{4} \\)~\\( \\mathrm{cm}^{-3} \\)\n), centrally concentrated (\\( 0.3\\arcsec <\\theta <1.4\\arcsec \\)) outflowing\ngas clouds (\\( F\\propto r^{-2} \\)) with a relatively high filling factor (\\( F\\sim 0.01 \\))\nand high ionization parameter \\( (\\log U=-1 \\)). Component B of the model can\nbe interpreted as a more extended distribution (\\( 1.9\\arcsec <\\theta <4.5\\arcsec \\))\nof lower density gas (\\( n=2\\times 10^{3} \\)~\\( \\mathrm{cm}^{-3} \\)) with\nno net outflow (\\( F=\\mathrm{const}. \\)), with a lower filling factor (\\( F=0.001) \\)\nand a lower ionization parameter (\\( \\log U=-2 \\)). Component A contributes\n58\\% of the total line flux in 22 lines listed in Table~\\ref{tbl:flux}, with\nthe contribution to individual lines ranging from 45\\% of the low excitation\n\\( \\bSIVb \\) (\\( \\Eion =34.8\\, \\mathrm{eV} \\)) to more than 99.9\\% of the\nvery high excitation line \\( \\bSiIXbB \\) (\\( \\Eion =303.2\\, \\mathrm{eV} \\)).\nIts large covering factor indicates that there is probably a significant contribution\nof flux from the inner \\( \\sim \\! 1\\arcsec \\) of the diffuse SW emission cone\nas well as from the bright NE cone. Component B contributes the remaining 42\\%\nof the total line flux, mainly in the lower excitation lines. Its covering factor\nis small enough for it to be concentrated mostly in the NE bright emission cone,\nas is observed. \n\nThe best-fit procedure indicates that models with the low oxygen abundance set\nfit the observed line fluxes somewhat better than models with the high nitrogen\nabundance set. In particular, the \\( \\mathrm{O}\\, {\\textsc {iii]}}\\, \\lambda 1663 \\),\nwhose unusual relative weakness was an important argument for assuming non-solar\nabundances (Netzer \\cite{Netzer97}; Kraemer et al. \\cite{KRC98}), is well\nreproduced by the best-fit low oxygen model with a model-to-data line flux ratio\nof 1.4 (Fig.~\\ref{fig:ratios}), even though it was not included in our fit\nsince it didn't pass the minimal flux criterion. \n\nThe trough in the best fit SED (Fig.~\\ref{fig:mix}) can be interpreted as an\nabsorption trough due to an absorber between the continuum source and the NLR.\nThe energy resolution of the SED template, which is limited by the computational\ncost of enumerating over all the SED combinations, is too low to allow detailed\nmodeling of the absorber. Figure~\\ref{fig:abs_sed} shows an example of how\na quasi-thermal big blue bump that is absorbed by neutral hydrogen would appear\nin our low resolution SED reconstruction. We find that the trough is consistent,\nfor example, with an absorber that shadows the entire NLR (\\( C_{\\mathrm{abs}}=1) \\)\nand has a column density of \\( N_{H^{0}}=6\\times 10^{19}\\, \\mathrm{cm}^{-2} \\)\nin neutral hydrogen, or with an absorber that allows a small leakage of unfiltered\nradiation (\\( C_{\\mathrm{abs}}=0.999 \\)) and a column density of \\( N_{H^{0}}=10^{20}\\, \\mathrm{cm}^{-2} \\).\nA similar trough, consistent with an absorber of \\( C_{\\mathrm{abs}}>0.99 \\)\nand \\( N_{H^{0}}=5\\times 10^{19}\\, \\mathrm{cm}^{-2} \\), was discovered in the\nreconstructed SED of Seyfert 1 galaxy NGC~4151 (Alexander et al. \\cite{Alexander99}).\nThat absorber was also detected in the \\emph{HUT} absorption line spectra of\nthe UV continuum of NGC~4151 (Kriss et al. \\cite{Kriss92}, \\cite{Kriss95})\n. The \\emph{HUT} spectra of \\( \\NGC \\) (Kriss et al \\cite{KDBFL92}) do not\nhave a high enough S/N to allow the detection of absorption lines in the scattered\nUV continuum of this AGN or against the stellar background (G. Kriss, private\ncomm.). We predict that future sensitive absorption line studies should reveal\nthe presence of such an absorber. \n\nThe bias in our results due to the fact that we neglected the line emission\nfrom the absorbing gas is likely to be small if the absorber is similar to the\ndense, high velocity UV absorber that was detected in NGC~4151. Such an absorber\nwill not emit forbidden lines, and its permitted lines will be broader than\ntypical NLR lines. Only 3 of the 22 lines we used in our fit are permitted lines,\nand we did not use lines that are contaminated by broad components. A highly\nionized and optically thin absorber will produce strong \\( \\OVI \\) line emission\nin excess of the typical NLR emission. It is therefore interesting that unlike\nthe two forbidden \\( \\bOIIIbB \\) and \\( \\bOIVb \\) lines and the semi-forbidden\n\\( \\OIIIb \\) line, which are well reproduced by the best fit model, the observed\n\\( \\OVI \\) line is 3.2 stronger than predicted (Fig.~\\ref{fig:ratios}). \n\nWe have, up to now, applied our SED reconstruction method to \\emph{ISO-SWS}\nobservations of IR coronal lines of three AGN: the Seyfert 2 Circinus galaxy\n(Moorwood et al. \\cite{Moorwood96}; Alexander et al. \\cite{Alexander99}),\nthe Seyfert 1 galaxy NGC~4151 (Alexander et al. \\cite{Alexander99}), and the\nSeyfert 2 galaxy \\( \\NGC \\) (this work). In one of these (Circinus), we detect\na Big Blue Bump that peaks at \\( \\gtrsim 50\\, \\mathrm{eV} \\). In the other\ntwo we detect deep troughs, which are consistent (but not exclusively so) with\na Big Blue Bump that is absorbed by neutral gas interior to the NLR. Our findings\nthus far are consistent with the picture that luminous Seyfert galaxies are\npowered by thin accretion disks that produce a quasi-thermal Big Blue Bump,\nand that in a large fraction of them the NLR sees a partially absorbed ionizing\ncontinuum, as suggested by Kraemer et al. (\\cite{KRC98}).\n\n\\acknowledgments\n\nThis work was supported by DARA under grants 50-QI-8610-8 and 50-QI-9492-3,\nand by the German-Israeli Foundation under grant I-0551-186.07/97.\n\n\\begin{thebibliography}{1992a}\n\\bibitem[1999]{Alexander99}Alexander T., Sturm E., Lutz D., Sternberg A., Netzer H., \\& Genzel R., 1999,\n\\apj, 512, 204\n\\bibitem[1983]{Alloin83}Alloin D., Pelat D., Boksenberg A., \\& Sargent W. L. W., 1983, \\apj, 275, 493\n\\bibitem[1970]{Anderson70}Anderson, K. S., 1970, \\apj, 162, 743 \n\\bibitem[1993]{Antonucci93}Antonucci R., 1993, \\araa, 31, 473 \n\\bibitem[1985]{AM85}Antonucci R. R. J., Miller J. S., 1985, \\apj, 297, 621 \n\\bibitem[1998]{Axon98}Axon D. 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SAO.,\n55, 5\n\\bibitem[2000]{Lutz00}Lutz D., et al., 2000, \\apj, in preparation\n\\bibitem[1994]{Macchetto94}Macchetto F., Capetti A., Sparks W. B., Axon D. J., \\& Boksenberg A., 1994,\n\\apj, 435, L15 \n\\bibitem[1996]{MWMO96}Marconi A., van der Werf P. P., Moorwood A. F. M., Oliva E., 1996, \\aap, 315,\n335 \n\\bibitem[1986]{MP1986}Meaburn J., Pedlar A., 1986, \\aap, 159, 336\n\\bibitem[1993]{Marshal93}Marshall et al., 1993, \\apj, 405, 168\n\\bibitem[1990]{MGM91}Miller J. S., Goodrich R. W., \\& Mathews W. G., 1991, \\apj, 378, 47 \n\\bibitem[1996]{Moorwood96}Moorwood A. F. M., et al. 1996, \\aap, 315, L109 \n\\bibitem[1996]{Muxlow96}Muxlow T. W. B., Pedlar A., Holloway A. J., Gallimore J. F., \\& Antonucci R.\nR. J., 1996, \\mnras, 278, 854\n\\bibitem[1996]{Netzer96}Netzer, H., 1996, \\apj, 473, 781 \n\\bibitem[1997]{Netzer97}Netzer, H., 1997, \\apss, 248, 127 \n\\bibitem[1997]{NT97}Netzer H., \\& Turner T. J., 1997, \\apj, 488, 694 \n\\bibitem[1980]{Neugebauer80}Neugebauer G., et al, 1980, \\apj, 283, 502 \n\\bibitem[1990]{OM90}Oliva E., Moorwood A. F. M., \\apj, 1990, 348, L5 \n\\bibitem[1996]{OF96}Osterbrock D. E., Fulbright J. P. , 1996, \\pasp, 108, 183 \n\\bibitem[1965]{OP65}Osterbrock D. E., Parker R., 1965, \\apj, 141, 892 \n\\bibitem[1992]{OTV92}Osterbrock D. E., Tran H. D., Veilleux S., \\apj, 389, 196 \n\\bibitem[1994]{Pier94}Pier E. A., Antonucci R., Hurt T., Kriss G., \\& Krolik J., 1994, \\apj, 428,\n124 \n\\bibitem[1991]{Planesas91}Planesas P., Scoville N. Z. \\& Myers S. T., 1991, \\apj, 369, 364 \n\\bibitem[1975]{SO75}Shields G. A., \\& Oke J. B., 1975, \\apj, 197, 5 \n\\bibitem[1973]{SS73}Shakura N. I., \\& Sunyaev R. A., 1973, \\aap, 24, 337\n\\bibitem[1986]{Snijders86}Snijders M. A. J., Netzer H., \\& Boksenberg A., 1986, \\mnras, 222, 549\n\\bibitem[1994]{SGT94}Sternberg A., Genzel R., \\& Tacconi L., 1994, \\apj, 436, L131\n\\bibitem[1994]{Tacconi94}Tacconi L. J., Genzel R., Blietz M., Cameron M., Harris A. I., \\& Madden S.,\n1994, \\apj, 426, 77 \n\\bibitem[1996]{Thompson96}Thompson R. I., 1996, \\apj, 459, L61 \n\\bibitem[1992]{ULPA92}Unger S. W., Lewis J. R., Pedlar A., \\& Axon D. J., 1992, \\mnras, 258, 371 \n\\bibitem[1971]{Wampler71}Wampler E. J., 1971, \\apj, 164, 1 \n\\bibitem[1987]{Ward87}Ward et al M. J., 1987, \\apj, 316, 138\n\\bibitem[1988]{Wilson88}Wilson A. S., 1988, Advances in Space Research, 8, 27\n\\bibitem[1983]{WU83}Wilson A. S., Ulvestad J, S., 1983, \\apj, 275, 8\n\\end{thebibliography}\n\n\\clearpage\n\n\\figcaption[sed_template.eps]{The template used for enumerating on the SED of\n\\( \\NGC \\). The most and least luminous SEDs are indicated by the lines, together with\nthe relative sense of their spectral hardness between 1 and 150 Ryd. \\label{fig:temp}}\n\n\\figcaption[best_mix.eps]{The best fit SED of the two-component model\n(Table~\\ref{tbl:fit}). \\label{fig:mix}}\n\n\\figcaption[lratios.eps]{The model to data line ratios for the best fit\ntwo-component model (Table~\\ref{tbl:fit}). The $\\OIIIb$ line ratio (white\ncircle), which was not used in the fitting procedure is also\ndisplayed. \\label{fig:ratios}}\n\n\\figcaption[abs_sed.eps]{An example of how \na quasi-thermal Big Blue Bump that is absorbed by neutral hydrogen\nwould appear in the low resolution reconstructed SED. The unabsorbed\nbump (thin line) and the bump after absorption by a $C_{\\rm abs}=1$,\n$N_{H^0}=6\\times10^{19}$\\,cm$^{-2}$ absorber (long dashed line) and a\n$C_{\\rm abs}=0.999$, $N_{H^0}=10^{20}$\\,cm$^{-2}$ absorber (short\ndashed line) are superimposed on the best fit SED\nmodel.\\label{fig:abs_sed}}\n\n\\clearpage\n\n\\begin{deluxetable}{lr@{.}lr@{.}lr@{.}lr@{.}l} \\small\n\\tablecaption{The compiled emission line flux list. \\label{tbl:flux}}\n\\tablewidth{0pt}\n\\tablehead{\n\\colhead{Line} &\n\\multicolumn{2}{c}{\\(\\lambda_{0}\\)}&\n\\multicolumn{2}{c}{\\(E_{\\textrm{ion}}\\)\\tablenotemark{a}}&\n\\multicolumn{2}{c}{\\(f_{\\ell}\\)\\tablenotemark{b}}&\n\\multicolumn{2}{c}{\\(\\Delta f_{\\ell}\\)\\tablenotemark{c}}\\\\ \n\\colhead{}&\n\\multicolumn{2}{c}{\\(\\mu\\)m}&\n\\multicolumn{2}{c}{eV}&\n\\multicolumn{4}{r}{\\(10^{-13}\\,{\\textrm{erg}}\\,{\\textrm{s}}^{-1}{\\textrm{cm}}^{-2}\\)}\n}\n\\tablecolumns{9}\n\\startdata\n\\cutinhead{UV, optical and NIR lines}\nO\\,{\\textsc{vi}}& 0&1032+1038 & 113&9 & 37&4& 3&1\\nl\nN\\,{\\textsc{iv}}]& 0&1487 & 47&4 & 5&1 & 1&1\\nl\n He\\,{\\textsc{ii}}& 0&1640 & 54&4 & 17&7 & 5&2\\nl\n[Ne\\,{\\textsc{v}}]& 0&3426 & 97&1 & 15&7 & 6&7\\nl\n[Ne\\,{\\textsc{iii}}]& 0&3868+3969 & 41&0 & 19&2 & 2&6\\nl\n%[O\\,{\\textsc{iii}}]& 0&4363 & 35&1 & 2&54 & 0&96\\nl\n He\\,{\\textsc{ii}}& 0&4686 & 54&4 & 6&15 & 1&50\\nl\n[O\\,{\\textsc{iii}}]& 0&4959+5007 & 35&1 & 256& & 27&\\nl\n%[Fe\\,{\\textsc{vii}}]& 0&6086 & 99&1 & 3&23 & 0&46\\nl\n[Si\\,{\\textsc{vi}}]& 1&96 & 166&8 & 7&5 & 0&5\\nl\n[Si\\,{\\textsc{vii}}]& 2&48 & 205&1 & 8&3 & 0&9\\nl\n\\cutinhead{ISO-SWS IR lines}\n%[Si\\,{\\textsc{ix}}]& 2&585 & 303&2 & 3&0 & 0&6\\nl\n[Mg\\,{\\textsc{viii}}]& 3&028 & 224&9 & 11& & 1&1\\nl\n[Si\\,{\\textsc{ix}}]& 3&936 & 303&2 & 5&0 & 0&6\\nl\n[Mg\\,{\\textsc{iv}}]& 4&49 & 80&1 & 7&6 & 1&5\\nl\n[Ar\\,{\\textsc{vi}}]& 4&528 & 75&0 & 15& & 3&\\nl\n[Mg\\,{\\textsc{vii}}]& 5&50 & 186&5 & 13& & \\multicolumn{2}{l}{?}\\nl\n[Mg\\,{\\textsc{v}}]& 5&61 & 109&2 & 18& & 2&\\nl\n[Ne\\,{\\textsc{vi}}]& 7&64 & 126&2 & 110& & 11&\\nl\n%[Fe\\,{\\textsc{vii}}]& 7&813 & 99&1 & 3&0 & 0&6\\nl\n[S\\,{\\textsc{iv}}]& 10&51 & 34&8 & 58& & 6&\\nl\n[Ne\\,{\\textsc{v}}]& 14&32 & 97&1 & 97&0 & 9&7\\nl\n[Ne\\,{\\textsc{iii}}]& 15&56 & 41&0 & 160& & 32&\\nl\n[Ne\\,{\\textsc{v}}]& 24&32 & 97&1 & 70& & 7&\\nl\n[O\\,{\\textsc{iv}}]& 25&89 & 54&9 & 190& & 20&\\nl\n[Ne\\,{\\textsc{iii}}]& 36&01 & 41&0 & 17& & 3&\\nl\n\\enddata\n\\tablenotetext{a}{\nThe ionization energy required to produce the emitting ion from the\npreceding ionization stage.}\n\\tablenotetext{b}{\nThe observed flux. For permitted lines, the flux of the decomposed narrow\ncomponent is quoted.}\n\\tablenotetext{c}{\nThe error estimate on the observed flux. The ISO-SWS errors are estimated by\nthe scatter in various methods for defining the underlying continuum and\nmeasuring the line. The errors do not include systematic calibration\nerrors, which are generally smaller than 30\\%. A question mark means that\nerror estimates are unavailable.}\n\\end{deluxetable}\n\n\\clearpage\n\\begin{deluxetable}{llcc}\n\\small\n\\tablecaption{The best-fit two-component model. \\label{tbl:fit}}\n% Mixture of models lowO F0 m12 and lowO F2 m09\n\\tablewidth{5in}\n\\tablehead{\n\\colhead{} & \\colhead{} & \\colhead{Component A} & \\colhead{Component B}\n}\n\\tablecolumns{4}\n\\startdata\n{Input parameters:}&&&\\nl\n&$U$ & 0.1 & 0.01 \\nl\n&$n$ &$10^4$ cm$^{-3}$ &$2\\times10^3$ cm$^{-3}$\\nl \n&Composition & low oxygen & low oxygen \\nl\n&$A$ & $200$ & $200$ \\nl\n&$F$\\tablenotemark{a}&\n $10^{-2}h$ & $10^{-3}h$ \\nl\n&$\\case{{d\\log F}}{{d\\log r}}$\n & $-2$ & $0$ \\nl\n{Best-fit results:\\tablenotemark{b}}&&&\\nl\n&$S$ & \\multicolumn{2}{c}{$1.9$} \\nl\n&$\\max S_\\ell$\\tablenotemark{c}\n & \\multicolumn{2}{c}{4.0$^{-1}$} \\nl\n&worst line\n & \\multicolumn{2}{c}{$\\bArVIb$} \\nl\n&$\\log f_2$\\tablenotemark{d}\n & \\multicolumn{2}{c}{-29.0 (-29.0, -26.6)} \\nl\n&$\\log f_4$ & \\multicolumn{2}{c}{-29.0 (-29.0, -26.6)} \\nl\n&$\\log f_8$ & \\multicolumn{2}{c}{-27.4 (-27.4, -26.6)} \\nl\n&$\\log f_{16}$& \\multicolumn{2}{c}{-29.0 (-29.0, -28.2)} \\nl\n&$C$ & 0.45 & 0.29 \\nl\n&$\\theta$ & $0.26\\arcsec$ & $1.9\\arcsec$ \\nl\n&$\\tion$ & $1.1\\arcsec$ & $2.6\\arcsec$ \\nl\n&$\\EBV$ & \\multicolumn{2}{c}{0.23 (0.18, 0.29)} \\nl\n&$\\qion$ & \\multicolumn{2}{c}{0.24 s$^{-1}$\\,cm$^{-2}$}\\nl\n&$\\log Q_{\\rm ion}$/s$^{-1}$ \\tablenotemark{e}&\n \\multicolumn{2}{c}{54.2} \\nl\n&$\\langle h\\nu \\rangle$\\tablenotemark{f}&\n \\multicolumn{2}{c}{5.1 Ryd} \\nl\n{Residual correlations:}&& Correlation & Random prob. \\nl\n&$\\lambda_0$ & $-0.19$ & $0.23$\\nl\n&$\\Eion$ & $ 0.00$ & $1.00$\\nl\n&depletion & $+0.11$ & $0.70$\\nl\n&$n_c$ & $+0.03$ & $0.86$\\nl\n\\enddata\n\\tablenotetext{a}{Assuming $h=0.65$.}\n\\tablenotetext{b}{Values in parentheses are the 99.9\\% confidence intervals.}\n\\tablenotetext{c}{Model to data ratio, given as the reciprocal when $<1$.}\n\\tablenotetext{d}{Flux in erg\\,s$^{-1}$\\,cm$^{-2}$\\,Hz$^{-1}$.}\n\\tablenotetext{e}{Ionizing photon luminosity assuming isotopic emission.}\n\\tablenotetext{f}{Mean ionizing photon energy between 1 and 16 Ryd.}\n\\end{deluxetable}\n\n%\n% Figures attached at end \n%\n\n%\\setcounter{figure}{0} \n\n%\\clearpage \n%\\plotone{\\texdir/sed_template.eps}\n%\\clearpage\n%\\plotone{\\texdir/best_mix.eps}\n%\\clearpage\n%\\plotone{\\texdir/lratios.eps}\n%\\clearpage\n%\\plotone{\\texdir/abs_sed.eps}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002107.extracted_bib",
"string": "\\begin{thebibliography}{1992a}\n\\bibitem[1999]{Alexander99}Alexander T., Sturm E., Lutz D., Sternberg A., Netzer H., \\& Genzel R., 1999,\n\\apj, 512, 204\n\\bibitem[1983]{Alloin83}Alloin D., Pelat D., Boksenberg A., \\& Sargent W. L. W., 1983, \\apj, 275, 493\n\\bibitem[1970]{Anderson70}Anderson, K. S., 1970, \\apj, 162, 743 \n\\bibitem[1993]{Antonucci93}Antonucci R., 1993, \\araa, 31, 473 \n\\bibitem[1985]{AM85}Antonucci R. R. J., Miller J. S., 1985, \\apj, 297, 621 \n\\bibitem[1998]{Axon98}Axon D. J., Marconi A., Capetti A., Macchetto F. D., Schreier E., \\& Robinson\nA., 1998, \\apj, 496, L75\n\\bibitem[1991]{BSC91}Bland-Hawthorn J., Sokoloski J., \\& Cecil G., 1991, \\apj, 375, 78 \n\\bibitem[1993]{BH93}Bland-Hawthorn J., \\& Voit G. M., 1993, Rev, Mexicana Astron. Af., 27, 73 \n\\bibitem[1991]{BTA91}Bruhweiler F. C., Truong K. Q. \\& Altner B., 1991, \\apj, 379, 596 \n\\bibitem[1995]{Capetti95}Capetti A., Axon D. J., \\& Macchetto F. D. Sparks W. B., Boksenberg A., 1995,\n\\apj, 446, 155 \n\\bibitem[1996]{Capetti96}Capetti A., Axon D. J., \\& Macchetto F. D. Sparks W. B., Boksenberg A., 1996,\n\\apj, 469, 554 \n\\bibitem[1997]{CAM97}Capetti A., Axon D. J., \\& Macchetto F. D., 1997, \\apj, 487, 560 \n\\bibitem[1978]{CBT90}Cecil G., Bland J., Tully R. B., 1990, \\apj, 355, 70 \n\\bibitem[1998]{DW98}Dietrich M., Wagner S. J., 1998, \\aap, 338, 405 \n\\bibitem[1991]{Evans91}Evans I. N., Ford H. C., Kinney A. L., Antonucci R. R. J., Armus L., Caganoff\nS., 1991, \\apj, 369, L27 \n\\bibitem[1998]{George98}George I. M.,Turner, T. J., Netzer H., Nandra K., Mushotzky R. F., \\& Yaqoob\nT., 1998, \\apjs, 114, 73\n\\bibitem[1999]{Kishimoto99}Kishimoto M., 1999, \\apj, 518, 676\n\\bibitem[1978]{Koski78}Koski A. T., 1978, \\apj, 223, 56 \n\\bibitem[1998]{KRC98}Kraemer S. B., Ruiz J. R., \\& Crenshaw D. M., 1998, \\apj, 508, 232 \n\\bibitem[1999]{KTCG99}Kraemer S. B., Turner T. J., Crenshaw D. M., \\& George I. M., 1999, \\apj, in\npress\n\\bibitem[1992a]{Kriss92}Kriss G. A., et al., 1992a, \\apj, 392, 485\n\\bibitem[1992b]{KDBFL92}Kriss G. A., Davidsen A. F., Blair W. P., Ferguson H. C., \\& Long K. S., 1992b,\n\\apj, 394, L37\n\\bibitem[1995]{Kriss95}Kriss G. A., Davidsen A. F., Zheng W., Kruk J. W., \\& Espey B. R., 1995, \\apj,\n454, L7\n\\bibitem[1988]{LNN88}Lipovetsky V. A., Neizvestny S. I., \\& Neizvestnaya O. M., 1988, Soobshch. SAO.,\n55, 5\n\\bibitem[2000]{Lutz00}Lutz D., et al., 2000, \\apj, in preparation\n\\bibitem[1994]{Macchetto94}Macchetto F., Capetti A., Sparks W. B., Axon D. J., \\& Boksenberg A., 1994,\n\\apj, 435, L15 \n\\bibitem[1996]{MWMO96}Marconi A., van der Werf P. P., Moorwood A. F. M., Oliva E., 1996, \\aap, 315,\n335 \n\\bibitem[1986]{MP1986}Meaburn J., Pedlar A., 1986, \\aap, 159, 336\n\\bibitem[1993]{Marshal93}Marshall et al., 1993, \\apj, 405, 168\n\\bibitem[1990]{MGM91}Miller J. S., Goodrich R. W., \\& Mathews W. G., 1991, \\apj, 378, 47 \n\\bibitem[1996]{Moorwood96}Moorwood A. F. M., et al. 1996, \\aap, 315, L109 \n\\bibitem[1996]{Muxlow96}Muxlow T. W. B., Pedlar A., Holloway A. J., Gallimore J. F., \\& Antonucci R.\nR. J., 1996, \\mnras, 278, 854\n\\bibitem[1996]{Netzer96}Netzer, H., 1996, \\apj, 473, 781 \n\\bibitem[1997]{Netzer97}Netzer, H., 1997, \\apss, 248, 127 \n\\bibitem[1997]{NT97}Netzer H., \\& Turner T. J., 1997, \\apj, 488, 694 \n\\bibitem[1980]{Neugebauer80}Neugebauer G., et al, 1980, \\apj, 283, 502 \n\\bibitem[1990]{OM90}Oliva E., Moorwood A. F. M., \\apj, 1990, 348, L5 \n\\bibitem[1996]{OF96}Osterbrock D. E., Fulbright J. P. , 1996, \\pasp, 108, 183 \n\\bibitem[1965]{OP65}Osterbrock D. E., Parker R., 1965, \\apj, 141, 892 \n\\bibitem[1992]{OTV92}Osterbrock D. E., Tran H. D., Veilleux S., \\apj, 389, 196 \n\\bibitem[1994]{Pier94}Pier E. A., Antonucci R., Hurt T., Kriss G., \\& Krolik J., 1994, \\apj, 428,\n124 \n\\bibitem[1991]{Planesas91}Planesas P., Scoville N. Z. \\& Myers S. T., 1991, \\apj, 369, 364 \n\\bibitem[1975]{SO75}Shields G. A., \\& Oke J. B., 1975, \\apj, 197, 5 \n\\bibitem[1973]{SS73}Shakura N. I., \\& Sunyaev R. A., 1973, \\aap, 24, 337\n\\bibitem[1986]{Snijders86}Snijders M. A. J., Netzer H., \\& Boksenberg A., 1986, \\mnras, 222, 549\n\\bibitem[1994]{SGT94}Sternberg A., Genzel R., \\& Tacconi L., 1994, \\apj, 436, L131\n\\bibitem[1994]{Tacconi94}Tacconi L. J., Genzel R., Blietz M., Cameron M., Harris A. I., \\& Madden S.,\n1994, \\apj, 426, 77 \n\\bibitem[1996]{Thompson96}Thompson R. I., 1996, \\apj, 459, L61 \n\\bibitem[1992]{ULPA92}Unger S. W., Lewis J. R., Pedlar A., \\& Axon D. J., 1992, \\mnras, 258, 371 \n\\bibitem[1971]{Wampler71}Wampler E. J., 1971, \\apj, 164, 1 \n\\bibitem[1987]{Ward87}Ward et al M. J., 1987, \\apj, 316, 138\n\\bibitem[1988]{Wilson88}Wilson A. S., 1988, Advances in Space Research, 8, 27\n\\bibitem[1983]{WU83}Wilson A. S., Ulvestad J, S., 1983, \\apj, 275, 8\n\\end{thebibliography}"
}
] |
astro-ph0002108
|
\LargeThe Nature of Associated Absorption and the\\ UV--X-ray Connection in 3C 288.1
|
[
{
"author": "Frederick W. Hamann"
}
] |
%We discuss new {Hubble Space Telescope} spectroscopy of the radio-loud quasar, 3C~288.1. The data cover $\sim$590 \AA\ to $\sim$1610 \AA\ in the quasar rest frame. They reveal a wealth of associated absorption lines (AALs) with no accompanying Lyman-limit absorption. The metallic AALs range in ionization from \ion{C}{3} and \ion{N}{3} to \ion{Ne}{8} and \ion{Mg}{10}. We use these data and photoionization models to derive the following properties of the AAL gas: 1) There are multiple ionization zones within the AAL region, spanning a factor of at least $\sim$50 in ionization parameter. 2) The overall ionization is consistent with the ``warm'' X-ray continuum absorbers measured in Seyfert 1 nuclei and other QSOs. However, 3) the column densities implied by the AALs in 3C~288.1 are too low to produce significant bound-free absorption at any UV--X-ray wavelengths. Substantial X-ray absorption would require yet another zone, having a much higher ionization or a much lower velocity dispersion than the main AAL region. 4) The total hydrogen column density in the AAL gas is $\log N_{H} ({cm}^{-2})\approx 20.2$. 5) The metallicity is roughly half solar. 6) The AALs have deconvolved widths of $\sim$900~\kms\ and their centroids are consistent with no shift from the quasar systemic velocity (conservatively within $\pm$1000 \kms ). 7) There are no direct indicators of the absorber's location in our data, but the high ionization and high metallicity both suggest a close physical relationship to the quasar/host galaxy environment. Finally, the UV continuum shape gives no indication of a ``blue bump'' at higher energies. There is a distinct break of unknown origin at $\sim$1030 \AA , and the decline toward higher energies (with spectral index $\alpha\approx -1.73$, for $f_{\nu}\propto \nu^{\alpha}$) is even steeper than a single power-law interpolation from 1030 \AA\ to soft X-rays.
|
[
{
"name": "3c288.tex",
"string": "%\\documentstyle[11pt,../aastex/saveold/aaspp4]{article}\n\\documentstyle[11pt,aaspp4]{article}\n%\\setlength{\\topmargin}{0.0in}\n%\\setlength{\\oddsidemargin}{0in}\n%\\setlength{\\evensidemargin}{0in}\n%\\setlength{\\parindent}{0.25in}\n%\\setlength{\\hoffset}{-0.5in}\n\\setlength{\\hoffset}{0.25in}\n\\setlength{\\voffset}{0.0in}\n\\setlength{\\textheight}{8.5in}\n\\setlength{\\textwidth}{6.0in}\n\\setlength{\\parskip}{\\smallskipamount}\n%\n\\newcommand \\as {$^{\\prime\\prime}$} %arcsec\n\\newcommand \\cmsq {\\hbox{cm$^{-2}$}}\n%\\newcommand \\deg {\\ifmmode ^{\\circ}\\else $^\\circ$\\fi} \n\\newcommand \\etal {{et~al.} }\n\\newcommand \\flam {\\hbox{ergs s$^{-1}$ cm$^{-2}$ \\AA$^{-1}$}} % flux density\n\\newcommand \\fnu {\\hbox{ergs s$^{-1}$ cm$^{-2}$ Hz$^{-1}$}} % flux density\n\\newcommand \\hst {\\hbox{\\it HST}}\n\\newcommand \\kms {\\rm{\\hbox{km s$^{-1}$}}}\n\\newcommand \\lam {$\\lambda$}\n\\newcommand \\Lya {\\hbox{Ly$\\alpha$}}\n\\newcommand \\Lyb {\\hbox{Ly$\\beta$}}\n\\newcommand \\Lsun {\\hbox{L$_{\\odot}$}}\n\\newcommand \\Msun {\\hbox{M$_{\\odot}$}}\n\\newcommand \\pcc {\\hbox{cm$^{-3}$}}\n\\def \\ul #1{$\\underline{\\smash{\\hbox{#1}}}$}\n\\newcommand \\zaz {{$z_a\\kern -1.5pt \\approx\\kern -1.5pt z_e$}}\n\\newcommand \\zllz {{$z_a\\kern -3pt \\ll\\kern -3pt z_e$}}\n\\newcommand \\Zsun {\\hbox{Z$_{\\odot}$}}\n%\n%\\raggedright\n%\n\\pagestyle{plain}\n%\\thispagestyle{empty}\n%\n\\begin{document}\n\n%\\renewcommand{\\baselinestretch}{1.0}\n\\baselineskip 13.2pt\n\\title\n{\\Large\\bf The Nature of Associated Absorption and the\\\\\nUV--X-ray Connection in 3C 288.1}\n\\bigskip\\medskip\n\n\\author\n{\\large Frederick W. Hamann}\n\\medskip\n\\affil\n{Department of Astronomy, University of Florida, 211 Bryant Space \\\\ Sciences \nCenter, Gainesville, FL 32611-2055 \\ ({\\it hamann@astro.ufl.edu})}\n\\medskip\n\n\\author\n{\\large Hagai Netzer}\n\\medskip\n\\affil\n{Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978 \nIsrael}\n%\\smallskip\n\n%\\bigskip\n\\begin{center}\nand\n\\end{center}\n\\author\n{\\large Joseph C. Shields}\n\\medskip\n\\affil\n{Department of Physics and Astronomy, Clippinger Research Labs 251B,\\\\ \nOhio University, Athens, OH 45701-2979}\n\\bigskip\n%\n\\begin{abstract} \n%\\small\n\nWe discuss new {\\it Hubble Space Telescope} spectroscopy of the \nradio-loud quasar, 3C~288.1. The data cover \n$\\sim$590 \\AA\\ to $\\sim$1610 \\AA\\ in the quasar rest frame. They \nreveal a wealth of associated absorption lines (AALs) with no \naccompanying Lyman-limit absorption. The metallic AALs \nrange in ionization from \\ion{C}{3} and \\ion{N}{3} to \\ion{Ne}{8} \nand \\ion{Mg}{10}. We use these data and photoionization models \nto derive the following properties of the AAL gas: \n1) There are multiple ionization zones within the AAL region, \nspanning a factor of at least $\\sim$50 in ionization \nparameter. 2) The overall ionization is consistent with \nthe ``warm'' X-ray continuum \nabsorbers measured in Seyfert 1 nuclei and other QSOs. \nHowever, 3) the column densities implied by the AALs in 3C~288.1 \nare too low to produce significant bound-free absorption at any \nUV--X-ray wavelengths. Substantial X-ray absorption would \nrequire yet another zone, having a \nmuch higher ionization or a much lower velocity dispersion \nthan the main AAL region. 4) The total hydrogen \ncolumn density in the AAL gas is \n$\\log N_{\\rm H} ({\\rm cm}^{-2})\\approx 20.2$. \n5) The metallicity is roughly half solar. \n6) The AALs have deconvolved widths of $\\sim$900~\\kms\\ and \ntheir centroids are consistent \nwith no shift from the quasar systemic velocity (conservatively \nwithin $\\pm$1000 \\kms ). 7) \nThere are no direct indicators of the absorber's location \nin our data, but \nthe high ionization and high metallicity both suggest a close \nphysical relationship to the quasar/host galaxy environment. \n\nFinally, the UV continuum shape gives no indication of a \n``blue bump'' at higher energies. \nThere is a distinct break of \nunknown origin at $\\sim$1030 \\AA , and the decline toward higher \nenergies (with spectral index $\\alpha\\approx -1.73$, for \n$f_{\\nu}\\propto \\nu^{\\alpha}$) is even steeper than a single \npower-law interpolation from 1030 \\AA\\ to soft X-rays. \n\n\\end{abstract}\n\\smallskip\n\n\\keywords{Galaxies: active; Quasars: absorption lines; Quasars: general; \nQuasars: individual (3C~288.1)}\n\\newpage\n\n%\n\\section{Introduction}\n\nAssociated absorption lines (AALs) in quasar spectra provide \nunique information on the kinematics, physical conditions and \nelemental abundances in the gas near quasars. AALs are defined \nempirically as having 1) relatively narrow \nprofiles (less than a few hundred \\kms ), \nand 2) absorption redshifts, $z_a$, near the emission \nredshift, $z_e$, (generally within 3000--5000~\\kms , see \n\\cite{wey79,fol86,fol88}). The first criterion distinguishes AALs \nfrom the class of broad absorption lines (BALs), which have velocity \nwidths and maximum displacements that often exceed 10,000~\\kms . \nBALs clearly form in high-velocity winds from the central engines \n(see the reviews by \\cite{wey97,wey95,tur95,wey85}). \nAALs (or \\zaz\\ systems) can form potentially in a variety of \nlocations --- from outflows near the black hole/accretion disk, \nperhaps like the BALs, to intervening gas or galaxies at large \n(cosmologically significant) distances. \nA few AAL systems are known to form in quasar ejecta (probably \nwithin a few pc of the energy source, \\cite{h97a,bar97a,gan99}), \nwhile others clearly probe extended regions on host-galaxy scales \n($>$1 kpc distant, \\cite{wil75,sar82,mor86,tri96,bar97b}). \nSurprisingly little else is known about the nature \nof the absorbing regions or their relationship to other quasar \nphenomena. \n\nOne important clue is that both AALs and BALs in the UV appear to \ncorrelate with the presence of continuous absorption in soft X-rays \n(\\cite{gre96,cre99,mat98,mat99,gal99,bra99} and references therein). \nThe X-ray absorbers in AAL sources (both quasars and Seyfert 1 \ngalaxies) tend to have high total hydrogen column densities \n($\\log N_{\\rm H} ({\\rm cm}^{-2})\\sim 21$ to 23) \nand high ionizations (being \ndominated by absorption edges of O~{\\sc vii} and O~{\\sc viii} near \n0.8 keV) (\\cite{rey97,geo98a}). In contrast, the AALs typically \nindicate lower column densities and \nlower levels of ionization (cf. \\cite{h97}). The X-ray absorbers \nthat accompany BALs have even larger total column densities \nof $\\log N_{\\rm H} ({\\rm cm}^{-2})\\ga 23$ \n(\\cite{gre96,gal99}). In those objects, \nthe total column densities derived from X-rays exceed prior estimates \nfrom the BALs by 2 or more orders of magnitude (\\cite{h98a}). \nClearly, we must consider the UV and X-ray data together \nto obtain a complete census and understanding of the \nabsorbing environments. \n\nA key question now is the physical relationship between the \nUV and X-ray absorbers. Mathur \\etal (1998 and refs. therein) \nargue that they could reasonably identify a single absorbing medium, \nwhile other work has shown that multiple regions \n(having different velocities, ionizations and/or column densities) \nare at least sometimes present \n(e.g. \\cite{kri96,h97a,rey97,geo98b,mat99}). High-ionization UV lines, \nsuch as \\ion{Ne}{8} \\lam\\lam 770,780 and \\ion{Mg}{10} \\lam\\lam 610,625, \ncan directly test the UV--X-ray relationship because their \nionization requirements are similar to the \\ion{O}{7} and \n\\ion{O}{8} edges measured in X-rays. The far-UV spectra needed to \nreach the \\ion{Ne}{8} and \\ion{Mg}{10} lines also encompass many \nunder-utilized diagnostics such as the \\ion{H}{1} Lyman limit, \nthe Lyman series lines, and numerous metal lines spanning a \nwide range of ionizations. Unfortunately, these features are \ndifficult or impossible to measure in many sources because of \ntheir short wavelengths. For example, they are obscured by Galactic \nLyman-limit absorption in low-redshift sources (e.g. in all Seyfert \ngalaxies) and contaminated by the dense ``forest'' of \\Lya\\ \nabsorbers at high redshifts. Another problem at high redshifts is \nthat the dominant \\ion{O}{7} and \\ion{O}{8} edges are shifted out of \nthe sensitive energy range of current X-ray telescopes. \n\nIntermediate-redshift quasars ($0.5\\la z\\la 1$) \nprovide a unique opportunity to measure all of the key UV and \nX-ray features in the same object. We have begun a program to \nobtain UV and X-ray spectra of several such objects. \nHere we discuss new UV observations of the radio-loud quasar, \n3C~288.1. This source has both the required moderate redshift, \n$z_e\\approx 0.961$ (\\cite{sch68}), and a strong AAL system \n(\\cite{will95}). It also has a dramatically bipolar (lobe-dominated) \nradio morphology (\\cite{rei95,aku94}). \nThe X-ray absorption properties of 3C~288.1 are not yet known, but it \nwas weakly detected in soft X-rays with the {\\it Einstein} IPC \n(from $\\sim$0.16 to $\\sim$3.5~keV, \\cite{zam81}). Wilkes \\etal (1994) \nestimate its 2-point power-law index between 2500 \\AA\\ and 2~keV to \nbe $\\alpha_{ox} = -1.51$ (where $f_{\\nu}\\propto \\nu^{\\alpha_{ox}}$). \n\n\\section{Observations and Data Reductions}\n\nWe obtained spectra of 3C~288.1 in two observations with the \n{\\it Hubble Space Telescope (HST)}. Both measurements used the \nSpace Telescope Imaging Spectrograph (STIS) with a 0.2\\as\\ $\\times$ \n52\\as\\ slit and the MAMA detectors. \nThe first observation, on 12 January 1999, yielded 8564 s \nof on-source integration time in 3 exposures with the G230L grating. \nThe usable wavelength coverage is $\\sim$1645 \\AA\\ to \n$\\sim$3160 \\AA\\ (observer's frame). The realized spectral resolution \ndepends mostly on the line-spread function of the spectrograph for \nthe quasar point source. We measure this resolution to be roughly \n5.9 \\AA , or 3.7 pixels on the MAMA detector, based on the \nfull widths at half minimum (FWHMs) of Galactic absorption lines. \nThe velocity resolution is thus $\\sim$1080 to \n$\\sim$560 \\kms\\ from the short- to long-wavelength ends of the spectral \ncoverage. The second observation, on 21 January 1999, used the G140L \ngrating for a total of 14778 s in 5 exposures. \nThe spectral coverage in this case is roughly 1155 to 1720 \\AA\\ \nat a measured resolution of $\\sim$2.5 \\AA\\ \n($\\sim$4.2 pixels on the MAMA), corresponding to \n$\\sim$660 to $\\sim$440 \\kms\\ from the short- to long-wavelength ends. \nThe combined spectra provide complete wavelength coverage from \n$\\sim$590 \\AA\\ to $\\sim$1610 \\AA\\ in the quasar rest frame. \n\nWe acquired flux-calibrated spectra for these observations \n(one spectrum for each exposure) \nfrom the Space Telescope Science Institute, based on their \nstandard ``pipeline'' reductions. \nWe then performed additional manipulations and measurements using \nthe IRAF\\footnote{IRAF is distributed by the National Optical Astronomy \nObservatories, which operates under the Association of Universities for \nResearch in Astronomy in cooperative agreement with the National \nScience Foundation.} software package. In particular, \nwe measured Galactic absorption lines to establish that there are \nno significant wavelength shifts between exposures taken with \nthe same grating. \nWe then averaged the 3 G230L spectra and the 5 G140L spectra \nusing weights determined from the integration times. \nTo check the absolute wavelength calibrations with each grating, \nwe measured centroids for several Galactic absorption \nlines in the two averages. Based on those measurements, \nand assuming the Galactic lines are at their laboratory \nwavelengths (\\cite{sch93}), we applied \noffsets of $-$1.25 \\AA\\ and $-$0.2 \\AA\\ to the mean G230L and \nG140L spectra, respectively. \n\n\\section{Results}\n\nFigure 1 shows the final mean spectra. \nThey reveal many new AALs compared to earlier work (\\cite{will95}), \nincluding \\ion{Ne}{8} \\lam\\lam 770,780 and probably \\ion{Mg}{10} \\lam 625. \nThey also show no \\ion{H}{1} Lyman limit absorption related to \nthe AALs (see also Fig. 3 below). \n\n\\subsection{Absorption Lines}\n\nTable 1 lists properties of the detected \nabsorption lines, namely, the vacuum centroid wavelengths \n($\\lambda_{obs}$) and equivalent widths ($W_{\\lambda}$) in the \nobserved frame (both in \\AA ), the line identifications \n(ID), the absorption redshifts ($z_a$) for identified non-Galactic \nfeatures, and the derived column densities as discussed in \\S4.2 \nbelow. The derived quantities use laboratory wavelengths \nand atomic data from Verner \\etal (1994a). \nThe strong AAL system has a nominal redshift of \n$z_a \\approx 0.9627$. Table 1 includes upper limits on \n$W_{\\lambda}$ for several lines \n{\\it not} detected in this system. The last column in the table provides \nadditional notes, including FWHMs for the strongest unblended \nlines at $z_a \\approx 0.9627$.\n\nWe measure the absorption lines by first defining a pseudo-continuum \nbased on smooth polynomial fits to the actual continuum and broad emission \nlines. We then use cursor functions in IRAF's {\\tt splot} program to \nmeasure (by direct integration) significant absorption features \nrelative to the fitted curve.\nFor unblended lines, the uncertainties in $W_{\\lambda}$ are \ndominated by the subjective pseudo-continuum placement. \nWe estimate the 1$\\sigma$ uncertainties for these features to be \n$\\la$0.1 \\AA\\ in the G140L data and $\\la$0.15 \\AA\\ in G230L. \nFor absorption features blended with each other, \nthe uncertainties depend on the severity \nof the blend. If the blending is not severe (i.e. if there are \nstill distinct absorption minima at each transition's wavelength), \nwe again measure/deblend the individual lines ``by eye'' using \ncursor functions in {\\tt splot}. To check our accuracy, \nwe also fit some of these modestly blended lines with \ngaussian profiles (using $\\chi^2$ minimization in the IRAF task \n{\\tt specfit}). Figure 2 shows a blend of 4 such lines, \nincluding \\Lyb\\ and the \\ion{O}{6} doublet in the $z_a\\approx 0.9627$ \nsystem. We fit these features with one gaussian per transition \n(see dotted curves in figure). The redshifts and velocity widths \nof the \\ion{O}{6} pair are forced to be identical. \nThe measurements derived from these fits appear in Table 1. \nThey are within 10\\% of our \nestimates from manual deblending, thus confirming the viability of \nboth procedures. \n\nSome severe blends in the $z_a \\approx 0.9627$ system do not have \ndistinct absorption dips corresponding to each transition. For the \nmultiplets in this category, \\ion{C}{4} \\lam\\lam 1549,1551, \n\\ion{N}{5} \\lam\\lam 1239,1243 and \\ion{N}{3} \\lam\\lam 685,686 (Fig. 1), \nwe make no attempt at deblending and list them as single lines \nin Table 1. For other unresolved blends, we measure $W_{\\lambda}$ for \nthe entire blend and then divide the result among the different \ntransitions. The $W_{\\lambda}$ for both the entire blend and the \nindividual lines are given in Table 1. In particular, \n\\ion{O}{5} \\lam 608 is part of an unresolved blend with \nGalactic \\ion{Si}{2} \\lam\\lam 1190,1193. We estimate \n$W_{\\lambda}$ for \\ion{O}{5} \\lam 608 alone by subtracting a \nprediction for the Galactic \\ion{Si}{2} (1.4 \\AA ), based on the \nrelative strengths of the various \\ion{Si}{2} lines in other quasar \nspectra (\\cite{sch93}). The result is given in Table 1 without \nfurther correction for the possible contribution from \\ion{Mg}{10} \n\\lam 610. Another case involves \\ion{O}{4} \\lam 788 \nand \\ion{S}{5} \\lam 786, which are blended with each other and with \nGalactic \\ion{C}{4} \\lam\\lam 1549,1551 absorption. \nFor this blend, we first subtract a \\ion{C}{4} contribution \n(0.6 \\AA ) derived from the Galactic \\ion{C}{4}/\\ion{Si}{4} ratio \nin other sources (\\cite{sch93}). We then divide the remaining \n$W_{\\lambda}$ between the \\ion{O}{4} and \\ion{S}{5} lines \naccording to the ratio (3.55:1) of their oscillator strengths weighted \nby solar abundances (i.e. their ``strength'' parameters \nin \\cite{ver94a}). \n\nFinally, we note that the measurement \nuncertainties are particularly large for the \\Lya\\ absorption at \n$z_a \\approx 0.9627$ because it lies near a sharp peak in the \n\\Lya\\ emission line (Fig. 1). Our estimate of this \\Lya\\ absorption \nstrength is therefore sensitive to the assumed emission profile. \nIn \\S4.3 we will show that the value of \n$W_{\\lambda}$ given for this line in Table 1 is almost certainly \ntoo small. The 1$\\sigma$ uncertainties in the \\ion{O}{6}, \\ion{N}{5} \nand \\ion{C}{4} AALs, which also sit atop emission lines, should be \n$<$10\\% based on repeated measurements with different assumed \nemission-line profiles. \n\n\\subsection{Emission Lines}\n\nWe measure the emission lines using our fit above \nto the pseudo-continuum (\\S3.1). This fit (for example \nFigure 2) interpolates across the absorption features and \nthus approximates the unabsorbed emission spectrum. We define the \nline emission relative to a subjective estimate of the ``true\" \ncontinuum in this fitted spectrum. Direct integration then \nyields approximate rest-frame equivalent \nwidths of $W_{\\lambda} = 21\\pm 2$ \\AA\\ for \\ion{C}{4} \\lam 1549, \n$W_{\\lambda} = 12\\pm 3$~ \\AA\\ for \n\\ion{O}{6} \\lam 1034, and $W_{\\lambda} = 50\\pm 5$~ \\AA\\ for the \n\\Lya\\ + \\ion{N}{5} \\lam 1240 blend. The 1$\\sigma$ uncertainties \nare estimates based on multiple measurements with different plausible \ncontinuum placements. We estimate a 3$\\sigma$ upper limit on \nthe \\ion{Ne}{8} \\lam 774 equivalent width of very roughly 7 \\AA , \nconsistent with the measured strength of this feature in other \nQSOs (\\cite{h98b}). \n\n\\subsection{Continuum Shape}\n\nFigure 3 shows the combined \\hst -STIS spectra on a log-log scale \nwith frequencies shifted to the quasar rest frame. There is a clear \nchange in the continuum slope near 1030 \\AA\\ \n($\\log\\nu ({\\rm Hz})\\approx 15.46$). \nThis change is illustrated in the figure \nby a broken power-law ($f_{\\nu}\\propto \\nu^{\\alpha}$) with \n$\\alpha\\approx -1.73$ for $\\lambda\\la 1030$ \\AA\\ and \n$\\alpha\\approx -0.83$ for $\\lambda\\ga 1030$ \\AA. A break like \nthis near 1030 \\AA\\ appears to be typical of QSOs \n(\\cite{zhe97,obr88}), although \nthe spectral indices derived here are less negative \n(by 0.2--0.7 dex) than the published averages for other \nradio-loud sources. \n\nIt is interesting to compare the UV continuum fluxes in Figures 1 and 3 \nwith the soft X-ray measurements of 3C~288.1 (\\cite{wilk94}). \nIn particular, the 2-point power-law index between 2 keV and \n1030 \\AA\\ in the rest frame is $\\alpha_{uvx}\\approx -1.51$. \nNote that the X-ray measurement \nis just a $\\sim$3$\\sigma$ detection and that those data were \nobtained $\\sim$19.5 years prior to our \\hst\\ observations. \nAlso note that the value of $\\alpha_{uvx}$ given here is \ncoincidently identical to $\\alpha_{ox}$ (between 2 keV and \n2500 \\AA ) reported by Wills \\etal (1994). They used the same \nX-ray data but a different (ground-based) measurement of the \nrest-frame UV. Evidently, the UV flux varied. The X-rays \nmight have varied also. Nonetheless, the slope we measure at \n$\\lambda\\la 1030$ \\AA\\ appears, like other radio-loud quasars, \nto be significantly steeper than a single power-law \nextrapolation from 1030 \\AA\\ to soft X-rays (\\cite{lao97}). \nThe implications of this continuum shape are discussed in \n\\S5.3 below. \n\n\\subsection{UV Variability Check}\n\nWills \\etal (1995) observed 3C~288.1 with the Faint Object Spectrograph \n(FOS) on board \\hst\\ in April 1993. Those spectra span observed \nwavelengths from 2225 to 3280 \\AA\\ at a resolution slightly higher than \nour STIS data, FWHM $\\approx$ 230 \\kms . Direct comparisons between the \ntwo data sets reveal no significant changes in the continuum (from \n1135 to 1610 \\AA\\ in the rest frame) or the emission or absorption \nlines (\\Lya , \\ion{N}{5} and \\ion{C}{4}) measured in common.\n\n\\section{Properties of the Associated $z_a \\approx 0.9627$ Absorber}\n\n\\subsection{Kinematics}\n\nThe line profiles in the $z_a \\approx 0.9627$ system are marginally \nresolved, with typical measured FWHMs of $\\sim$1100 \\kms\\ \n(Table 1). Simple gaussian deconvolution from the instrumental \nresponse profile therefore suggests that the \nintrinsic line widths are roughly 900 \\kms . \nWe cannot rule out the possibility that these widths \nresult from a blend of many narrower (unresolved) features. However, \nthe higher resolution (230 \\kms ) FOS spectra of Wills et al (1995, \nsee \\S3.4 above) give no indication of narrower features in \\Lya , \n\\ion{C}{4} or \\ion{N}{5}. The $\\sim$900 \\kms\\ line widths should, \nin any case, represent the full line-of-sight velocity \ndispersion through the absorbing region. \n\nWe do not have an accurate estimate of the absorber's velocity \nshift relative to the quasar. The emission redshift quoted in the \nliterature, $z_e \\approx 0.961$, \ncomes from an old photographic measurement \nof \\ion{C}{3}] \\lam 1909 and \\ion{Mg}{2} \\lam 2799 (Schmidt 1968). \nNonetheless, the difference between that $z_e$ and \nour measurement of $z_a \\approx 0.9627$ is consistent with the \napparent small blueshift of the AALs relative to the emission-line \npeaks (e.g. in \\ion{C}{4}, \\Lya , and \\ion{O}{6}, Fig. 1). \nInterpreting this velocity shift, roughly 250 \\kms , \nin terms of a radial flow is problematic, however, because the \nbroad emission lines might be either blue or redshifted with \nrespect to the quasar's true systemic velocity. \nFor example, Marziani \\etal (1996) \nmeasured velocity shifts up to $\\pm$1000 in \\ion{C}{4} relative \nto the narrow emission lines (e.g. [\\ion{O}{3}] \\lam\\lam 4959,5007) in a \nsample of radio-loud quasars. We therefore conclude conservatively \nthat the AALs in 3C~288.1 lie within \n$\\pm$1000 \\kms\\ of the quasar's systemic velocity.\n\n\\subsection{Column Densities}\n\nWe use a curve-of-growth analysis to derive column densities for \neach of the ions detected at $z_a \\approx 0.9627$. \nWith the line equivalent widths from Table 1, \nthe only free parameter in this analysis is the doppler $b$ value \n(where $b$ = FWHM/1.665 for gaussian line profiles). Even though \nthe line profiles are not well resolved, \nthe data provide several independent \nconstraints on $b$ and the inferred column densities. \nIn particular, 1) the deconvolved FWHMs, \nroughly 900 \\kms\\ (\\S4.1), require $b\\la 540$ \\kms . \n2) The absence of an \\ion{H}{1} absorption edge at 912 \\AA\\ \n(see Figs. 1 and 3) places a firm upper limit on the \\ion{H}{1} \ncolumn density and thus a lower limit on the Lyman-line $b$ value. \nWe estimate that the optical depth \nat this edge is no more 10\\%, implying an \\ion{H}{1} column of \n$\\log N_{\\rm HI}({\\rm cm}^{-2}) < 16.2$ \\cmsq\\ and $b\\ga 190$ \\kms\\ \nin the Lyman lines. 3) Comparing different lines of the same ion, \nsuch as the \\ion{H}{1} Lyman series \nand doublets like \\ion{O}{6} and \\ion{Ne}{8}, places firm limits on \ntheir $b$ values and column densities. \nThe fact that these multiplets do not have observed ratios of \n$\\sim$1:1 (Fig. 1 and Table 1) implies immediately that the lines \nare not dominated by very optically thick components (with small $b$). \nFinally, 4) weak lines of low-abundance elements like \n\\ion{P}{5} \\lam\\lam 1118,1128 are not detected. If the metals have \nroughly solar relative abundances, the absence of these weak \ntransitions implies that strong transitions like \n\\ion{C}{4} \\lam 1548 have optical depths $\\la$30 (\\cite{h98a}). \n\nTable 1 lists the column densities derived from each measured line \nin two limiting cases, $b=200$ \\kms\\ and $b=540$ \\kms . \nHigher $b$ values would exceed the deconvolved FWHMs, \nwhile lower $b$ values would violate the upper limit on $N$(\\ion{H}{1}) \nand yield inconsistent results for some multiplets (e.g. \\ion{H}{1} \nand \\ion{O}{6} \\lam\\lam 1032,1038). Comparing these two results in Table \n1 gives an indication of the theoretical uncertainties. \nNote that the results for $b=540$ \\kms\\ are all within 0.2 dex of \nthe optically thin lower limits. \n\nWe adopt an intermediate value of $b=300$ \\kms\\ for \nour ``best guess'' column densities. These columns are listed \nin Table 2 after averaging over all useful lines for each ion. \nEntries marked ``:'' are uncertain by as much as a factor of \n$\\sim$2, while those labeled ``::'' have even larger uncertainties. \n\\ion{C}{3}, \\ion{Mg}{10} and \\ion{S}{5} have these uncertainty \nflags because of blending problems, while \\ion{S}{3} and \\ion{S}{4} \nhave large uncertainties because different lines yield \nsubstantially different column density results (Table 1). \n\\ion{O}{5} is marked as uncertain because the only line measured \nfor that ion, \\lam 630, might be saturated. (The \ncurve-of-growth analysis with $b=300$ \\kms\\ suggests that \n\\ion{O}{5} \\lam 630 has optical depths up $\\sim$7, \nhigher than any other measured line.) \n\nNote that the analysis above assumes the \nabsorber fully covers the background light source(s) along our \nline(s) of sight. Partial coverage is known to occur in some AAL\nsystems, based on measured doublet ratios in high resolution \nspectra (\\cite{wam93,pet94,h97a,bar97b,gan99}, also \\S5.2 below). \nThe only 2 known cases of partial \ncoverage in radio-loud quasars have coverage fractions of \n$>$95\\% (\\cite{bar97a,h99a}). The strongest constraint \non the coverage fraction in 3C~288.1 comes from the measured depth \nof the deepest line, \\ion{O}{5} \\lam 630, which requires $>$75\\% \ncoverage. If the coverage fraction is near 75\\%, then the column \ndensities listed for the deepest lines in Table 2 could be \nunderestimated. On the other hand, if the coverage fraction \nis $>$95\\% like the other radio-loud quasars, all of the \ncolumn densities in Table 2 would be accurate. \n\nClearly, the column densities reported \nhere should be checked with higher resolution spectra. Such data \nwould test for both partial coverage and narrow (presently \nunresolved) line components. Narrow lines (with low $b$ values) \nmight, in principle, harbor large column densities while contributing \nlittle to the total equivalent widths. However, \nthe line multiplet ratios and the lack of a Lyman edge already \nprohibit low $b$ values and large column densities for the \n{\\it dominant} absorber in 3C~288.1 (even if there is incomplete \ncoverage). The column densities in Table 2 should therefore \napply to whatever absorber(s) control the measured equivalent widths. \nWe will adopt these column densities hereafter in our discussion, \nwith the understanding that they apply strictly to the dominant \nAAL absorber. \n\n\\subsection{Ionization, Density and Radial Distance}\n\nThe detected metal lines at $z_a \\approx 0.9627$ range in ionization \nfrom \\ion{C}{3} and \\ion{N}{3} to \\ion{Ne}{8} and \n\\ion{Mg}{10}. There are no strong transitions of higher ions, \nfor example \\ion{Si}{12} \\lam\\lam 499,521, within our wavelength \ncoverage. The upper limit of \nthe ionization is therefore unknown. The lower limit \nis firmly established by the absence of \nsingly-ionized metals such as \\ion{C}{2}, \\ion{N}{2} and \n\\ion{O}{2} (see Table 1). \n\nWe assume the absorber is in photoionization equilibrium with the quasar \nradiation field \nand we use the numerical code CLOUDY (version 90.04, \\cite{fer98}) \nto examine its ionization properties. We note that the column densities \nin Table 2 imply immediately that the absorber is optically \nthin in the Lyman continuum, out to at least $\\sim$0.37 keV (the \nionization threshold of \\ion{Mg}{10}). Figure 4 plots calculated \nionization fractions for \\ion{H}{1} and various metal ions, M$_i$, \nin general optically \nthin clouds that are photoionized by a broken power-law spectrum. \nWe use a spectral index of $\\alpha = -1.7$ in the Lyman continuum \nout to 1~keV, based mainly on our measurement of $\\alpha = -1.73$ \nfor $\\lambda\\la 1030$ \\AA\\ (\\S3.3). At higher energies \nwe adopt the slope $\\alpha_x = -0.9$, based on X-ray \nobservations of similar objects (\\cite{lao97,geo98a}). There is \nconsiderable uncertainty about the true spectral shape of 3C~288.1 \n(and other quasars) in the extreme UV and soft X-rays. \nThe uncertain slope is particularly \nimportant when comparing ions/lines with very different ionization \nenergies. However, these uncertainties are not important to our \nmain conclusions below. \n\nThe ion fractions in Figure 4 are plotted \nfor a range of ionization parameters, \n$U$ --- defined here as the dimensionless ratio of hydrogen-ionizing \nphoton to hydrogen particle densities\\footnote{For comparison, we note \nthat $\\log U_x = \\log U - 1.47$ for this continuum shape, where \n$U_x$ is the ionization parameter defined over the photon energies \n0.1 to 10 keV (\\cite{net96}).} (see \\cite{fer98}). \nThe ionization fractions are not \nsensitve to either the metal abundances or the \nspace density (for a given $U$). They also do not depend on the \ncolumn densities used in the \ncalculations, as long as the gas remains optically thin in the \nionizing continuum (see \\cite{net96,h95,h97} for more \ndiscussion and calculations using other parameters).\n\nWe estimate $U$ in the 3C~288.1 absorber \nby comparing the ion fractions $f$(M$_i$) in Figure 4 to \nvarious column density ratios from Table 2. \nEach column density ratio yields an independent \nestimate. Some of the $U$ values are illustrated in Figure 4 by \nbold vertical lines that connect the $f$(M$_i$) curves used for that \nestimate. For example, the measured \\ion{N}{3}/\\ion{N}{4} column \ndensity ratio is $-$0.6 dex, implying a moderate ionization with \n$\\log U\\approx -1.7$. \nThe \\ion{C}{3}/\\ion{C}{4} and \\ion{O}{3}/\\ion{O}{4} ratios \nsuggest similar $U$. (Although included in Figure 4, \nwe consider the $U$ estimates for sulfur to be \nunreliable because of the uncertainties in their column \ndensities, \\S4.2.) By making the reasonable assumption \nthat O, Ne and Mg have roughly solar relative abundances, we \nuse the \\ion{O}{6}/\\ion{Ne}{8} and \\ion{Mg}{10}/\\ion{Ne}{8} \ncolumn densities to infer much larger values of \n$\\log U\\approx 0.0$ in the region where those lines form. \nThe ratios of intermediate ions like \n\\ion{N}{4}/\\ion{N}{5} and \\ion{O}{5}/\\ion{O}{6} \nindicate intermediate $U$ values\\footnote{Note that these simple \n$U$ estimates do not correct for multiple zones possibly contributing \nto the measured column densities. Such corrections would require \nand explicit (but ad hoc) model.}. \n\nThe differences in these derived $U$ values are well above the \nuncertainties and inconsistent with a single zone absorber. \nFor a given space \ndensity, $n_H$, and distance, $R$, from the ionizing \ncontinuum source, optically thin clouds should have the same level \nof ionization throughout (e.g. there can be no gradient \nin the ionization due to the absorber's own \nopacity). The optically thin clouds in 3C~288.1 must therefore \noccupy a range of densities or distances. From the \ndefinition of $U$ (where $U\\propto n_H^{-1}\\, R^{-2}$), \nand the difference of $\\Delta\\log U \\ga 1.7$ between the ``high'' \nand ``low''-ionization regions, \nwe infer a factor of $\\ga$50 range in the space density, \na factor of $\\ga$7 range in the distance, or some equivalent \ncombination of different $n_H$ and $R$ values. \n\n\\subsection{Elemental Abundances}\n\nThe relative abundance of any two elements $a$ and $b$ can be derived \nfrom the following expression, \n\\begin{equation}\n\\left[{a\\over b}\\right] \\ = \\ \\\n\\log\\left({{N(a_i)}\\over{N(b_j)}}\\right) \\ +\\\n\\log\\left({{f(b_j)}\\over{f(a_i)}}\\right) \\ +\\ \n\\log\\left({{b}\\over{a}}\\right)_{\\odot}\n\\end{equation}\nwhere $(b/a)_{\\odot}$ is the solar abundance ratio (\\cite{gre89}), \nand $N$ and $f$ are respectively the column densities and ionization \nfractions of element $a$ in ion state $i$, etc. With suitable \nionization corrections, $f(b_j)/f(a_i)$ from Figure 4, we can \ntrivially derive abundance ratios from the column densities in Table 2. \nFor example, we estimate average values of [C/O]~$\\approx -0.5$ \nand [N/O]~$\\approx +0.1$ from the ratios \\ion{C}{3}/\\ion{O}{3}, \n\\ion{C}{4}/\\ion{O}{4}, \\ion{N}{3}/\\ion{O}{3} and \n\\ion{N}{4}/\\ion{O}{4}. The theoretical uncertainties \nin these results (e.g. for different continuum shapes) should be \nsmall, $\\la$0.1 dex (at 1$\\sigma$ or $\\sim$60\\% confidence), \nbecause we are comparing similar ions (\\cite{h97}). \nThe observational uncertainties are larger but more \ndifficult to assess; we estimate that they are \n$<$0.2 dex in these averaged ratios (\\S4.2 and Table 2). We derive \nthe overall metallicity by assuming the \\ion{H}{1} absorber resides \nmainly with the doubly- and triply-ionized metals \nat $\\log U\\approx -1.8$ to $-$1.6 (Fig. 4, \\S4.3). \nPlugging the appropriate ion fractions into Equation 1 then \nimplies [C/H]~$\\approx -0.7$, [N/H]~$\\approx -0.1$, \nand [O/H]~$\\approx -0.3$. \nThe theoretical uncertainties in this case are larger, \nperhaps up to 0.3--0.4 dex (\\cite{h97}), because the ions being \ncompared have significantly different ionization energies. \n\nIf we had assumed that most of the \n\\ion{H}{1} coexists with the high ions at $\\log U\\approx 0.0$ \n(Fig. 4, \\S4.3), we would have inferred much lower metallicities \nof [M/H]~$\\approx -1.7$ to $-$1.4 for the metals O, Ne and Mg. \nHowever, these low metallicities would lead \nto a contradiction for the lower ions in Equation 1 (for example, \nby predicting too \nmuch \\ion{H}{1} for the measured amounts of the metal ions). \nThe higher metallicities derived from the lower ions, and \nour original assumption \nthat the \\ion{H}{1} resides mainly in the lower $U$ gas, must \ntherefore be correct. \n\nNonetheless, there are still uncertainties related to \nthe absorber's complexity; the gas does not have a \nsingle $U$ value and we do not know how much of the \n\\ion{H}{1} resides co-spatially with each metal ion. We \ntherefore estimate lower limits on the metal-to-hydrogen \nratios. Hamann (1997) showed that the ionization corrections \n$f$(\\ion{H}{1})/$f$(M$_i$) all have minimum values at some \nparticular $U$ (see also \\cite{ber86}). \nIf the actual absorber has zones with different \n$U$ contributing to the lines, it can only mean \nthat the true ionization corrections are larger. Therefore, the \nminimum ionization corrections yield robust minimum values \nof [M/H]. Hamann \\& Ferland (1999) plot minimum ionization \ncorrections for optically thin clouds photoionized by different \npower-law spectra (their Fig. 11). For the column densities in \nTable 2 and a spectrum similar to that adopted in \n\\S4.3, the Hamann \\& Ferland (1999) calculations imply \nlower limits of [C/H]~$\\ga -0.7$, [N/H]~$\\ga -0.2$, and \n[O/H]~$\\ga -0.5$ for the $z_a\\approx 0.9627$ absorber in 3C~288.1. \n\nWe conclude that the overall metallicity (dominated by O/H) \nis roughly 1/2 \\Zsun , with a firm lower limit near 1/3 \\Zsun . \n\n\\subsection{Total Column Densities and Predicted X-Ray Absorption}\n\nWe just argued that the \\ion{H}{1} column density is contributed \nmostly by a low-ionization region, where $\\log U\\approx -1.8$ to \n$-$1.6 and $f$(\\ion{H}{1})~$\\approx -3.8$ to $-$3.5 (Fig. 4). \nThe measured value of the \\ion{H}{1} column density \n(Table 2) therefore implies a total hydrogen column \nof $\\log N_{\\rm H} ({\\rm cm}^{-2})\\approx 19.5$ in that region. \nIf the metal abundances are approximately 1/2 \\Zsun\\ (\\S4.4), \nwe can estimate $N_{\\rm H}$ in the \nhigh-ionization gas from the column densities (Table 2) \nand ionization fractions (Fig. 4) of \\ion{Ne}{8} and \\ion{Mg}{10}. \nWe find $\\log N_{\\rm H} ({\\rm cm}^{-2})\\approx 20.2$ for that region. \n\nThese results make specific predictions for the X-ray absorption \nthat should accompany the UV AALs. Explicit photoionization \ncalculations, using the column densities, ionizations and abundances \nquoted above, imply that the continuum optical depths should be \n$<$0.016 at 0.2 keV and $<$0.003 at 2.0 keV (in absorber's rest \nframe). The deepest X-ray absorption, due mainly to the combined \n\\ion{O}{7} and \\ion{O}{8} edges near 0.8 keV, should be $\\la$3\\% \nbelow the continuum. We therefore \nexpect no significant X-ray absorption by the AAL gas in 3C~288.1. \nThis prediction is not sensitive to the uncertain continuum shape \nor any other assumptions in the calculations. The only \npossibility for strong X-ray \nabsorption is if that absorber contributes \nnegligibly to the UV lines. Such an absorber would need to have \neither a much lower $b$ value or much higher ionization than \nwe infer from the AALs. \n\n\\section{Discussion}\n\n\\subsection{The UV--X-Ray Absorber Connection}\n\nThe main results of this paper are 1) the detection of the \nhigh-ionization AALs \\ion{Ne}{8} \\lam\\lam 770,780 and \\ion{Mg}{10} \n\\lam 625, and 2) the prediction that the AAL gas will not \nproduce significant bound-free absorption in X-rays (\\S4.5). \nSimple 1-zone models of strong UV line {\\it and} X-ray continuum \nabsorption cannot apply to this object. In fact, the variety of \nUV AALs alone requires multiple absorbing zones with different \nlevels of ionization (\\S4.3). Strong X-ray absorption would require \nyet another zone, having a high-column density of gas with either \nmuch higher ionization or a much lower velocity dispersion \n($b$ value) than the main AAL absorber (\\S4.5). \n\nTo our knowledge, 3C~288.1 is now the fourth quasar for which the \n\\ion{Ne}{8} AALs (and in this case also \n\\ion{Mg}{10}) have been measured. The other \nquasars are UM~675 at redshift $z_e = 2.15$ (\\cite{h95,h97a}), \nHS~1700+6416 at $z_e=2.713$ (\\cite{pet96}), \nand J2233$-$606 at $z_e=2.24$ (\\cite{pet99}). There is another \nobject with well-measured \\ion{Ne}{8}, \\ion{Mg}{10} and even \n\\ion{Si}{12} absorption (SBS~1542+541 at $z_e= 2.36$, \n\\cite{tel98}), but the lines in that case appear \nmore like BALs than AALs (blueshifted by $\\sim$11,500 \\kms\\ \nand having FWHM~$\\approx$~2500 \\kms ). \nIt is not yet clear how common these high-ionization lines \nare in AAL or BAL systems, but we know of\nno cases where high-quality, short-wavelength spectra clearly \nrule out their presence. The AAL column densities measured for \nUM~675 and J2233$-$606 imply that their UV lines also \nform in multi-zone regions with no significant X-ray \nopacity. The total absorbing columns inferred from their AALs \nare similar to 3C~288.1, $\\log N_{\\rm H} ({\\rm cm}^{-2})\\la 20$ for \nsolar abundances. Reliable column densities \nare not available for the UV absorbers in \nHS~1700+6416 and SBS~1542+541, although Telfer \n\\etal (1998) estimate $\\log N_{\\rm H} ({\\rm cm}^{-2})\\ga 21.5$ \nfor the latter BAL-like source. \n\nExisting X-ray data are sparse for these 5 quasars with known \n\\ion{Ne}{8} absorption. The UV--X-ray spectral index of 3C~288.1, \n$\\alpha_{ox}\\approx -1.51$, implies a slightly above \naverage X-ray/UV flux ratio for quasars of similar redshift \nand luminosity (\\cite{wilk94}). \nWhile not a strong constraint on the X-ray absorption, this \nresult is at least consistent with our prediction for negligible \nabsorption based on the AALs alone (\\cite{bra99}). \nBetter data for HS~1700+6416 \n(\\cite{yua98}) indicate a modest X-ray absorbing column of \n$\\log N_{\\rm H} ({\\rm cm}^{-2})\\approx 20.5$. In contrast, the \nBAL-like source SBS~1542+541 appears to be heavily absorbed \nin X-rays, based on its weak X-ray flux (\\cite{tel98,yua98}). \n\nSeveral recent studies describe the correlated appearance of \nUV and X-ray absorbers in quasars and active galaxies (\\S1). \nBrandt \\etal (1999) have gone \na step further by suggesting that the strengths of the \nUV and X-ray features also correlate. Nonetheless, the \nphysical relationship between the absorbers remains unknown. \nAAL regions can clearly have a variety of properties \n(e.g. ionization and column density) that \nare not always conducive to X-ray continuum absorption \n(see also \\cite{kri96,h97,h97a,mat99}). Fundamentally, \nthe column densities needed for strong AALs can be much less \nthan those required for significant bound-free opacity. \nAs a result, even those AAL regions with high, \nwarm absorber-like ionizations (as in 3C~288.1, etc.) \nneed not produce measurable X-ray absorption. Conversely, \nthe high ionizations and high column densities derived for \nX-ray warm absorbers (\\cite{rey97,geo98a}) will not {\\it necessarily} \nproduce strong AALs, especially in the lower ions if the velocity \ndispersion ($b$ value) is small\\footnote{For \nexample, if the X-ray absorber has solar abundances and \n``nominal'' parameters, such as $\\log N_{\\rm H} ({\\rm cm}^{-2})\\approx 22$ \nand $\\log U\\approx 0.5$ (\\cite{geo98a}), then the column density in \nC~IV will be $\\log N ({\\rm cm}^{-2})\\la 14.1$ (using ion \nfractions from Figure 4). \nThe resulting line strengths depend keenly on the velocity dispersion. \nIf the velocities are strictly thermal, then $b\\approx 4.5$ \\kms\\ \nfor carbon in a 15000 K gas and the equivalent width of \nC~IV \\lam 1548 would be just $\\sim$0.08 \\AA\\ in the rest frame. \nAt larger velocity dispersions, say $b=20$ \\kms , this line's strength \nwould be $\\sim$0.24 \\AA , etc., up to $\\sim$0.5 \\AA\\ in the \nhigh $b$ (optically thin) limit.}. \nThe two absorbing regions might be physically related in general, \nbut they need not be identical. \nOne specific possibility, proposed for \nquasar BALs (\\cite{mur95}), is that the X-ray absorption \noccurs at the base of an accretion-disk outflow while the UV \nlines form largely in the accelerated gas farther out. \n\nStudies that encompass both the high-ionization UV lines and \nthe high-ionization X-ray edges (e.g. \\ion{O}{7} and \\ion{O}{8}) \nare needed to test this physical relationship further. \nIntermediate-redshift quasars like 3C288.1 are prime \ntargets for this work (\\S1). However, a special concern with quasar \nAALs is that they can form potentially in a variety of locations. \nThe origin and physical nature of the \nAAL gas, as well as its relationship to the X-ray features, \nare thus intimately tied to the question of the absorber's location. \n\n\\subsection{Where is the Absorber in 3C~288.1?}\n\nRecent studies indicate that AALs have generally high \nmetallicities (near or above the solar value, \ne.g. \\cite{pet94,pet99,h99b}), and strengths that correlate \nwith the quasar's radio properties and perhaps luminosity \n(\\cite{and87,fol88,ald94,will95,bak96,pbar97,ric99,bra99}). \nThese results suggest that AALs are often physically related \nto quasars. Further evidence for a close relationship \nhas come from spectroscopic indicators, such as \n1) time-variable line strengths, 2) well-resolved AAL profiles that \nare smooth and broad compared to thermal line widths, and 3) multiplet \nratios that imply partial coverage of the background light source(s) \n(e.g. \\cite{bar97a,bar97b,h97a,gan99}). The link between these \nproperties and the near-quasar environment is strengthened by the \nfact that they are common among BALs (\\cite{bar93,bar94,h98a,ara99}). \nAALs with these properties are likely to form in outflows from \nthe central engines, at radii of tens of pc or possibly much less \n(e.g. \\cite{h97a}). \nIt should be a high priority to apply these spectroscopic tests of \nan ``intrinsic'' origin to the AALs in 3C~288.1 and other sources. \nThe existing data for 3C~288.1 provide only indirect evidence \nfor intrinsic absorption. In particular: \n\n1) The ionization (\\S4.3) and metallicity (\\S4.4) \nin 3C~288.1 are probably both too high for an \nabsorber at large (cosmologically significant) distances from the \nQSO (\\cite{ver94b,h99b}). The high metallicity suggests that the \nAAL gas resides (or originated) within the \nquasar's host galaxy, while the high ionization suggests a strong \ninfluence of the quasar's intense \nradiation field. If the gas is photoionized by the quasar \nspectrum, the relationship between the gas' \ndensity, ionization parameter and distance from 3C~288.1 is \n$R\\approx 60\\; (1/U)^{1/2}\\,(10^4\\,{\\rm cm}^{-3}/n_H)^{1/2}$ pc \n(based on the measured flux in Fig. 1, the ionizing spectral shape \nused in \\S4.3, and a cosmology with \n$H_o = 65$ km s$^{-1}$ Mpc$^{-1}$ and $q_o = 0.2$). \n\n2) Three of the 5 absorption-line systems with measured \\ion{Ne}{8} \n(UM~675, J2233$-$606 and SBS1542+531 discussed in \\S5.1) are \nknown to have at least one of the spectral indicators of \nan intrinsic origin listed above (\\cite{h95,h97a,tel98,pet99}). \nThese results support the argument in point (1) above, \nthat high-ionization \nlines like \\ion{Ne}{8} and \\ion{Mg}{10} are additional signatures \nof intrinsic absorption. \n\n3) Weaker statistical evidence comes from the \nbipolar radio morphology of 3C~288.1 (\\cite{rei95,aku94}). \nLobe-dominated radio structures are known to correlate \nwith the presence of strong AALs (\\cite{will95,pbar97}). \nThey are also indicative of an edge-on \norientation for the central quasar/accretion disk. \nStrong AALs (as in 3C~288.1) should therefore \ntend to form not only near the quasar, but near the plane \nof its accretion disk or extended torus (\\cite{will95,pbar97}). \nThe situation might be analogous to\nBAL outflows, where disk-like geometries are favored \nby polarization observations (\\cite{goo95,hin95,coh95}) \nand by some theoretical \nmodels of disk-driven outflows (e.g. \\cite{mur95,dek97}). \n\nWe conclude conservatively that the AALs \nin 3C~288.1 are physically related to the quasar, probably forming\nwell within the radius of the quasar's host galaxy. \n\n\\subsection{The Spectral Energy Distribution}\n\nThe shape of the ionizing continuum is a fundamental question in \nstudies of quasars and active galaxies. \nA simple analysis of the broad emission-line equivalent widths \nsuggests that there must be a large ``blue bump,'' peaking around \n2--5 Rydberg and contributing more than 50\\% of the bolometric \nluminosity (e.g. Mathews \\& Ferland 1987, Netzer 1990). \nAGN spectra cannot be measured directly at these energies, \nbut recent far-UV and soft X-ray observations give no evidence for \nthe predicted big blue bump (Zheng et al. 1996 and Laor et al. 1997). \nNetzer (1985) showed that there is a serious \nenergy budget problem in photoionization models of the \nemission-line gas if a strong blue \nbump is not included. In particular, the line strengths are severely \nunderpredicted by the models. This theoretical problem depends \npartly on the global covering factor of the emitting gas. The \nrarity of rest-frame Lyman-limit absorption in quasars implies \nthat we rarely (if ever) view them through the line-emitting \ngas; thus the covering factors are expected to be low --- of order \n10\\% (e.g. Antonnucci \\etal 1989, Koratkar \\etal 1992). \nKorista et al. (1997) recently confirmed that these low covering \nfactors, together with the bump-less ionizing continuum \ninferred from the Zheng et al. and Laor et al. data, \nunderpredict the emission line strengths by factors of several. \nThey estimate, for example, that excessively large covering factors \nof 56\\% --75\\% would be needed to match the typical HeII \\lam \n1640 line strength. One possible solution, proposed by Korista et al., \nis that the broad emission line regions might not ``see'' \nthe same continuum shape we do. \n\nCurrently this theoretical problem is unresolved. The \nspectrum of 3C~288.1 presented here (\\S3.3) is consistent with the \nother observations, providing no evidence for a substantial blue bump \nat higher (unobserved) energies. \n\n\\section{Summary and Conclusions}\n\nComparative \nUV and X-ray studies are beginning to yield new insights into \nthe nature of AGN absorbing environments. However, the \nthe physical relationship of the UV and X-ray absorbers \nremains unclear. \n3C~288.1 provides another counterexample to simple models that \nwould attribute all of the UV and X-ray features to identically the \nsame gas (see \\S1 for references). Realistic models must include \nthe increasing levels of complexity implied by new and better data. \nIntermediate-redshift quasars will be an important source of \nnew data because they allow us to measure a wide range of \nunder-utilized features in the rest-frame far UV --- \nfor example the \\ion{H}{1} Lyman limit and \nhigh-ionization AALs like \\ion{Ne}{8} \\lam\\lam 770,780 \nand \\ion{Mg}{10} \\lam\\lam 610,625. Our analysis of these features \nin 3C~288.1 shows that multiple absorbing regions (spanning a range \nof ionizations, densities and/or distances from the quasar) \ncontribute to the AAL spectrum (\\S4.3). Moreover, the column \ndensities inferred from the AALs are too small to produce significant \nbound-free opacity at any UV through X-ray wavelengths (\\S4.5). \nThere will be no significant X-ray absorption \nin this object unless it occurs in yet another region ---\nhaving a much higher ionization or a \nmuch lower velocity dispersion than the dominant AAL absorber. \nWe are now pursuing X-ray observations of 3C~288.1 to test \nthese predictions. \n\nOne essential ingredient for any model of these regions \nis the location of the absorbing gas. Indirect evidence suggests \nthat the AALs in 3C~288.1 form close to the quasar, \nprobably well within the radius of the quasar's host galaxy \n(\\S5.2). Unfortunately, that weak constraint on the \nlocation allows for a variety of possible absorption sites, \ne.g. interstellar gas in the extended host galaxy, a \ndense torus surrounding the active nucleus, or an outflow from the \ncentral engine/accretion disk. The AAL kinematics indicate that \nthe absorber is clearly {\\it not} part of a high-velocity wind \nlike the BALs; the lines are only $\\sim$900 \\kms\\ wide and \ntheir centroids are within $\\pm$1000 \\kms\\ \nof the quasar rest frame (\\S4.1). \nBetter constraints on the location and kinematics \nwill require higher resolution spectra and, ideally, repeated \nobservations at both UV and X-ray wavelengths (to test \nfor variable absorption, cf. \\cite{h97a,bar97a,geo98b}). \nThose data would also provide more complete and more reliable \nestimates of the ionizations, kinematics, abundances and \ncolumn densities in the different absorbing zones. \n\n\n\\bigskip\n\n\\acknowledgments\nWe are grateful to Gerald Kriss and others \nat the Space Telescope Science Institute for their generous \nhelp with the observations and data processing. We also thank the \nreferee, Smita Mathur, for helpful comments. Financial support for \nthis work was provided by NASA through grant GO-07356-96A \nfrom the Space Telescope Science Institute, which is operated by \nthe Association for Research in Astronomy, Inc., under NASA \ncontract NAS5-26555. 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The upper and lower panels show \nspectra from the G140L and G230L gratings, respectively. \nThe Flux has units $10^{-15}$~\\flam . \nAbsorption lines in the main AAL system ($z_a \\approx 0.9627$) \nare labeled across the top. Galactic lines and a weaker \\Lya\\ system \n(at $z_a \\approx 0.9467$) are marked below. \n\\medskip\n\n\\noindent\\ul{Fig. 2.} --- Observed spectrum of 3C~288.1 (solid histogram) \nand a fit (dotted lines) to the continuum, \\ion{O}{6} emission line, \nand several absorption lines. The \n\\Lyb\\ line at the left has redshift $z_a\\approx 0.9467$, while the \nothers belong to the strong associated system at $z_a \\approx 0.9627$ \n(see Fig. 1 and \\S3.1).\n\\medskip\n\n\\noindent\\ul{Fig. 3.} --- Spectrum of 3C~288.1 on a log-log scale, \nwhere $\\nu$ is the rest-frame frequency in Hz and the flux $F_{\\nu}$ \nhas units \\fnu . The bold solid line is a broken power law with \n$\\alpha = -1.73$ for $\\log\\nu ({\\rm Hz})\\ga 15.46$ and \n$\\alpha\\approx -0.83$ for $\\log\\nu ({\\rm Hz})\\la 15.46$. The dotted \nline is just an extension of the low frequency power law segment. \n``LL'' marks the Lyman limit in the $z_a \\approx 0.9627$ \nabsorption system. \n\\medskip\n\n\\noindent\\ul{Fig. 4.} --- Ionization fractions in optically \nthin clouds that are photoionized at different $U$. The ionizing \nspectrum is a broken power-law with $\\alpha_{uvx} =$~$-$1.7 and \n$\\alpha_x = -0.9$. The HI fraction \nappears across the top. The curves for the metal ions \nare labeled directly above or below their maximum values, except \nfor \\ion{Mg}{2} in the lower left of the bottom panel. The sulfur ions \nin the lower panel, and silicon ions in the upper panel, are represented \nby dash-dot curves for clarity. The \nnotation is HI = H$^o$, CIV = C$^{+3}$, etc. The bold vertical lines \nconnect pairs of $f$(M$_i$) curves at the $U$ value implied by the \nratio of their column densities. Specifically, the bold lines \ncorrespond to the ratios \\ion{C}{3}/\\ion{C}{4}, \\ion{O}{4}/\\ion{O}{5}, \n\\ion{O}{3}/\\ion{O}{4}, \\ion{O}{5}/\\ion{O}{6}, \\ion{O}{6}/\\ion{Ne}{8}, \nand \\ion{Ne}{8}/\\ion{Mg}{10} from left to right in the top panel, \nand \\ion{S}{4}/\\ion{S}{5}, \\ion{S}{3}/\\ion{S}{4}, \n\\ion{N}{3}/\\ion{N}{4}, and \\ion{N}{4}/\\ion{N}{5} in the bottom panel. \nSee \\S4.3.\n\\newpage\n\n\\plotone{figure1.ps}\n\nFIGURE 1.\n\\newpage\n\n\\plotone{figure2.ps}\n\nFIGURE 2.\n\\newpage\n\n\\plotone{figure3.ps}\n\nFIGURE 3.\n\\newpage\n\n\\plotone{figure4.ps}\n\nFIGURE 4.\n\n\\end{document}\n\n\n"
},
{
"name": "tables.tex",
"string": "%\\documentstyle[../aastex/saveold/apjpt4]{article}\n%\n%\\begin{document}\n%\\pagestyle{empty}\n%\n%\\makeatletter\n%\\def\\jnl@aj{AJ}\n%\\ifx\\revtex@jnl\\jnl@aj\\let\\tablebreak=\\nl\\fi\n%\\makeatother\n%\n\\singlespace\n%\\baselineskip 13.5pt\n\\begin{deluxetable}{cclcccl}\n\\tablewidth{0pt}\n\\tablecaption{Absorption Line Data}\n%\\tablecolumns{7}\n\\tablehead{\\colhead{}& \\colhead{}& \\colhead{}& \\colhead{}& \n\\multicolumn{2}{c}{--- log $N$(cm$^{-2}$) ---}\\\\\n\\colhead{\\ \\ $\\lambda_{obs}$\\ \\ }& \\colhead{\\ \\ $W_{\\lambda}$\\ \\ }& \n\\colhead{ID}& \\colhead{$z_a$}& \\colhead{$b=200$}& \\colhead{$b=540$}& \n\\colhead{Notes\\tablenotemark{a}\\ \\ }}\n\\startdata\n1180.0& 0.41& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n1193.5& 3.10& \\nodata & \\nodata & \\nodata & \\nodata & ubl\\nl\n\\nodata & 1.70& \\ion{O}{4} 608& \\nodata & 15.9& 15.7& ubl-i \\nl\n1200.4& 1.06& \\ion{N}{1} 1200& \\nodata & \\nodata & \\nodata & bl,mult,Gal\\nl\n1206.8& 1.07& \\ion{S}{3} 1206& \\nodata & \\nodata & \\nodata & bl,Gal\\nl\n1226.3& 0.27& \\ion{Mg}{10} 625& 0.9622& 15.0& 15.0& bl\\nl\n1236.0& 3.78& \\ion{O}{5} 630& 0.9628& 16.7& 15.2& FWHM=1080\\nl\n1249.1& 0.34& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n1260.2& 1.14& \\ion{Si}{2} 1260& \\nodata & \\nodata & \\nodata & Gal\\nl\n(1265.2)& \\llap{$<$}0.25& \\ion{N}{2} 645& \\nodata & \\llap{$<$}14.2& \\llap{$<$}14.2& up\\nl\n1271.1& 0.19& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n1290.0& 0.51& \\ion{S}{4} 657& 0.9625& 13.8& 13.8& \\nl\n1303.1& 2.04& \\ion{O}{1} 1302& \\nodata & \\nodata & \\nodata & ubl,Gal\\nl\n1330.3& 0.40& \\ion{S}{3} 678& 0.9628& 13.5& 13.5& \\nl\n1335.0& 1.45& \\ion{C}{2} 1335& \\nodata & \\nodata & \\nodata & Gal\\nl\n1344.7& 0.84& \\ion{N}{3} 685& 0.9622& 14.5& 14.4& mult\\nl\n(1348.5)& \\llap{$<$}0.25& \\ion{C}{2} 687& \\nodata & \\llap{$<$}14.0& \\llap{$<$}14.0& up\\nl\n(1374.4)& \\llap{$<$}0.25& \\ion{Ar}{8} 700& \\nodata & \\llap{$<$}13.9& \\llap{$<$}13.9& up\\nl\n1377.7& 0.98& \\ion{O}{3} 702& 0.9615& 15.0& 15.0& \\nl\n1393.9& 0.43& \\ion{Si}{4} 1394& \\nodata & \\nodata & \\nodata & Gal\\nl\n1399.5& 0.71& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n1403.0& 0.95& \\ion{Si}{4} 1403& \\nodata & \\nodata & \\nodata & bl?,Gal\\nl\n1412.2& 0.42& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n1421.9& 0.45& \\ion{S}{3} 724& 0.9631& 14.2& 14.2& \\nl\n1456.9& 0.52& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n1463.3& 0.63& \\ion{S}{4} 745& 0.9645& 14.5& 14.4& bl \\nl\n1468.5& 0.85& \\ion{S}{4} 748& 0.9622& 14.3& 14.3& bl \\nl\n(1481.7)& \\llap{$<$}0.25& \\ion{Ar}{6} 755& \\nodata & \\llap{$<$}14.6& \\llap{$<$}14.6& up\\nl\n1501.5& 3.17& \\ion{N}{4} 765& 0.9624& 15.4& 14.8& FWHM=1140\\nl\n1512.1& 2.21& \\ion{Ne}{8} 770& 0.9629& 15.6& 15.4& FWHM=1060\\nl\n1520.7& 0.31& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n1527.5& 1.10& \\ion{Si}{2} 1527& \\nodata & \\nodata & \\nodata & Gal\\nl\n1532.8& 1.17& \\ion{Ne}{8} 780& 0.9643& 15.5& 15.4& \\nl\n1536.6& 0.31& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n1545.7& 4.31& \\nodata & \\nodata & \\nodata & \\nodata & ubl\\nl\n\\nodata & 0.82& \\ion{S}{5} 786& \\nodata & 13.8& 13.8& ubl-i\\nl\n\\nodata & 2.89& \\ion{O}{4} 788& \\nodata & 15.9& 15.5& ubl-i\\nl\n\\nodata & 0.60& \\ion{C}{4} 1549& \\nodata & \\nodata & \\nodata & ubl-i,Gal\\nl\n(1589.1)& \\llap{$<$}0.30& \\ion{S}{4} 810& \\nodata & \\llap{$<$}14.4& \\llap{$<$}14.4& up\\nl\n1608.1& 0.56& \\ion{Fe}{2} 1608& \\nodata & \\nodata & \\nodata & Gal\\nl\n1635.2& 0.71& \\ion{O}{3} 833& 0.9632& 14.8& 14.8& ID?\\nl\n(1637.8)& \\llap{$<$}0.50& \\ion{O}{2} 834& \\nodata & \\llap{$<$}14.5& \\llap{$<$}14.5& up\\nl\n1663.0& 1.48& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n1671.7& 1.07& \\ion{Al}{2} 1671& \\nodata & \\nodata & \\nodata & Gal\\nl\n1760.0& 1.15& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n1768.6& 0.92& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n(1774.2)& \\llap{$<$}0.50& \\ion{C}{2} 904& \\nodata & \\llap{$<$}14.1& \\llap{$<$}14.0& up\\nl\n(1797.1)& \\llap{$<$}0.50& \\ion{N}{2} 916& \\nodata & \\llap{$<$}14.4& \\llap{$<$}14.3& up\\nl\n1830.3& 0.94& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n(1831.9)& \\llap{$<$}0.50& \\ion{S}{6} 933& \\nodata & \\llap{$<$}13.9& \\llap{$<$}13.9& \\nl\n(1840.6)& \\llap{$<$}0.50& Ly$\\epsilon$ 938& \\nodata & \\llap{$<$}15.7& \\llap{$<$}15.6& up\\nl\n1863.5& 1.49& Ly$\\delta$ 950& 0.9621& 16.0& 15.9& \\nl\n1895.8& 2.00& Ly$\\gamma$ 973& 0.9493& \\nodata & \\nodata & \\nl\n1909.7& 2.35& Ly$\\gamma$ 973& 0.9636& 15.9& 15.8& bl \\nl\n1917.5& 1.87& \\ion{C}{3} 977& 0.9626& 14.3& 14.2& bl \\nl\n1943.1& 0.36& \\ion{N}{3} 990& 0.9631& 14.3& 14.2& \\nl\n1962.0& 0.64& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n1997.0& 1.31& Ly$\\beta$ 1026& 0.9469& \\nodata & \\nl\n2012.8& 4.13& Ly$\\beta$ 1026& 0.9624& 16.1& 15.6& FWHM=1190\\nl\n2025.9& 5.43& \\ion{O}{6} 1032& 0.9632& 16.5& 15.5& FWHM=1140\\nl\n2037.0& 4.49& \\ion{O}{6} 1038& 0.9632& 16.3& 15.7& FWHM=1140\\nl\n2084.2& 0.67& \\ion{S}{4} 1063& 0.9613& 14.9& 14.9& ID?\\nl\n(2127.6)& \\llap{$<$}0.40& \\ion{N}{2} 1084& \\nodata & \\llap{$<$}14.3& \\llap{$<$}14.3& up\\nl\n2144.4& 2.00& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n2166.5& 1.24& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n(2194.3)& \\llap{$<$}0.40& \\ion{P}{5} 1118& \\nodata & \\llap{$<$}13.6& \\llap{$<$}13.6& up\\nl\n2245.8& 1.17& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n2321.1& 1.43& \\nodata & \\nodata & \\nodata & \\nodata & \\nl\n2344.2& 1.90& \\ion{Fe}{2} 2344& \\nodata & \\nodata & \\nodata & Gal\\nl\n2366.5& 4.56& Ly$\\alpha$ 1216& 0.9466& \\nodata & \\nodata & \\nl\n2385.6& 4.40& Ly$\\alpha$ 1216& 0.9627& 15.1& 14.7& \\nl\n2434.7& 7.21& \\ion{N}{5} 1240& 0.9630& 15.4& 15.2& mult \\nl\n(2473.8)& \\llap{$<$}0.40& \\ion{Si}{2} 1260& \\nodata & \\llap{$<$}13.1& \\llap{$<$}13.1& up\\nl\n2586.2& 0.85& \\ion{Fe}{2} 2587& \\nodata & \\nodata & \\nodata & Gal\\nl\n2599.8& 1.24& \\ion{Fe}{2} 2600& \\nodata & \\nodata & \\nodata & Gal\\nl\n(2619.3)& \\llap{$<$}0.40& \\ion{C}{2} 1335& \\nodata & \\llap{$<$}14.0& \\llap{$<$}14.0& up\\nl\n(2735.5)& \\llap{$<$}0.40& \\ion{Si}{4} 1394& \\nodata & \\llap{$<$}13.4& \\llap{$<$}13.4& up\\nl\n2796.1& 1.93& \\ion{Mg}{2} 2796& \\nodata & \\nodata & \\nodata & Gal\\nl\n2803.9& 1.39& \\ion{Mg}{2} 2804& \\nodata & \\nodata & \\nodata & Gal\\nl\n2854.2& 0.50& \\ion{Mg}{1} 2853& \\nodata & \\nodata & \\nodata & Gal\\nl\n3040.1& 7.13& \\ion{C}{4} 1549& 0.9625& 15.0& 14.8& mult \\nl\n\\enddata\n\\tablenotetext{a}{Abbreviations have the following meanings:\nbl = blended line measured separately, ubl = unresolved blend, ubl-i = \nunresolved blend with individual $W_{\\lambda}$ estimated, \nFWHM = full width at half minimum in km s$^{-1}$ , Gal = Galactic line, \nID? = identification uncertain, mult = unresolved multiplet listed as \none line, up = 3$\\sigma$ upper limits at $\\lambda_{obs}$ \ndefined by $z_a = 0.9627$.}\n\\end{deluxetable}\n\n\n\\begin{deluxetable}{lc}\n\\tablewidth{0pt}\n\\tablecaption{Column Densities}\n%\\tablecolumns{2}\n\\tablehead{\\colhead{} & \\colhead{log $N$(cm$^{-2}$)}\\\\\n\\colhead{Ion\\ \\ }& \\colhead{$b=300$}}\n\\startdata\n\\ion{H}{1}& 15.8\\nl\n\\noalign{\\vskip 5pt}\n%\n\\ion{C}{2}& \\llap{$<$}14.0\\nl\n\\ion{C}{3}& 14.3\\rlap{:}\\nl\n\\ion{C}{4}& 14.9\\nl\n\\noalign{\\vskip 5pt}\n%\n\\ion{N}{2}& \\llap{$<$}14.2\\nl\n\\ion{N}{3}& 14.4\\nl\n\\ion{N}{4}& 15.0\\nl\n\\ion{N}{5}& 15.2\\nl\n\\noalign{\\vskip 5pt}\n%\n\\ion{O}{2}& \\llap{$<$}14.5\\nl\n\\ion{O}{3}& 14.9\\nl\n\\ion{O}{4}& 15.7\\nl\n\\ion{O}{5}& 15.6\\rlap{:}\\nl\n\\ion{O}{6}& 15.8\\nl\n\\noalign{\\vskip 5pt}\n%\n\\ion{Ne}{8}& 15.4\\nl\n\\noalign{\\vskip 5pt}\n%\n\\ion{Mg}{10}& 15.0\\rlap{:}\\nl\n\\noalign{\\vskip 5pt}\n%\n\\ion{Si}{2}& \\llap{$<$}13.1\\nl\n\\ion{Si}{4}& \\llap{$<$}13.4\\nl\n\\noalign{\\vskip 5pt}\n%\n\\ion{P}{5}& \\llap{$<$}13.6\\nl\n\\noalign{\\vskip 5pt}\n%\n\\ion{S}{2}& \\llap{$<$}13.5\\nl\n\\ion{S}{3}& 14.0\\rlap{::}\\nl\n\\ion{S}{4}& 14.2\\rlap{::}\\nl\n\\ion{S}{5}& 13.8\\rlap{::}\\nl\n\\ion{S}{6}& \\llap{$<$}13.9\\nl\n%\n\\enddata\n\\end{deluxetable}\n\n%\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002108.extracted_bib",
"string": "\\begin{thebibliography}{}\n%\n\\bibitem[Akujor \\etal 1994]{aku94} Akujor, C.E., L\\\"udke, E., Browne, \nI.W.A., Leahy, J.P., Garrington, S.T., Jackson, N., \\& Thomasson, P. \n1994, \\aaps, 105, 247\n\\bibitem[Aldcroft \\etal 1994]{ald94} Aldcroft, T.L., Bechtold, J., \\& \nElvis, M. 1994, \\apjs, 93, 1\n\\bibitem[Anderson \\etal 1987]{and87} Anderson, S.f., Weymann, R.J., \nFoltz, C.B., \\& Chaffee, F.H. 1987, \\aj, 94, 278\n\\bibitem[Antonucci \\etal 989]{ant89} Antonucci, R.R.J., Kinney, \nA.L., \\& Ford, H.C. 1989, \\apj, 342, 64\n\\bibitem[Arav \\etal 1999]{ara99} Arav, N., Korista, K.T., de Kool, M.,\nJunkkarinen, V.T., \\& Begelman, M.C. 1999, \\apj, 516, 27\n%\\bibitem[Arav 1997]{ara97} Arav, N. 1997, in \n%Mass Ejection From AGN, eds. R. Weymann, I. Shlosman, and N. Arav, \n%ASP Conf. Series, 128, 208\n%\\bibitem[Bahcall \\etal 1993]{bah93} Bahcall, J. N., \\etal 1993, \n%\\apjs, 87, 1\n\\bibitem[Baker \\& Hunstead 1996]{bak96} Baker, J.C., \\& Hunstead, \nR.W. 1996, \\apj, 452, L95\n\\bibitem[Barlow 1993]{bar93} Barlow, T.A. 1993, {\\it Ph.D. Dissertation}, \nUniversity of California, San Diego\n\\bibitem[Barlow \\etal 1997]{bar97b} Barlow, T.A., Hamann, F., \\& \nSargent, W.L.W. 1997, in \nMass Ejection From AGN, eds. R. Weymann, I. Shlosman, and N. Arav, \nASP Conf. Series, 128, 13\n\\bibitem[Barlow \\& Sargent 1997]{bar97a} Barlow, T.A., \\& Sargent, \nW.L.W. 1997, \\aj, 113, 136\n\\bibitem[Barthel 1997]{pbar97} Barthel, P. 1997, in \nMass Ejection From AGN, eds. R. Weymann, I. Shlosman, and N. Arav, \nASP Conf. Series, 128, xxx\n\\bibitem[Bergeron \\& Stasinska 1986]{ber86} Bergeron, J., \\& \nStasinska, G. 1986, \\aap, 169, 1\n\\bibitem[Brandt \\etal 1999]{bra99} Brandt, W.N., Laor, A., \\& \nWills, B.J. 1999, \\apj, in press\n\\bibitem[Cohen \\etal 1995]{coh95} Cohen, M.H., Ogle, P.M., Tran, H.D., \nVermeulen, R.C., Miller, J.S., Goodrich, R.W., \\& Martel, A.R. 1995, \n\\apj, 448, L77\n\\bibitem[Crenshaw \\etal 1999]{cre99} Crenshaw, D.M., Kraemer, S.B., \nBoggess, A., Maran, S.P., Mushoktzky, R.F., \\& Wu, C.-C. 1999, \\apj,\n516, 750\n\\bibitem[de Kool 1997]{dek97} de Kool, M. 1997, in \nMass Ejection From AGN, eds. R. Weymann, I. Shlosman, and N. Arav, \nASP Conf. Series, 128, 233\n%\\bibitem[Della Ceca \\etal 1990]{del90} Della Ceca, R., Palumbo, G., G., \n%C., Persic, M., Boldt, E. A., De Zotti, G., \\& Marshall, E. E. 1990, \n%ApJS, 72, 471\n\\bibitem[Ferland \\etal 1998]{fer98} Ferland, G.J., Korista, K.T., \nVerner, D.A., Ferguson, J.W., \\& Kingdon, J.B. 1998, \\pasp, 110, 761\n\\bibitem[Foltz \\etal 1988]{fol88} Foltz, C.B., Chaffee, F., Weymann, R.J., \n\\& Anderson, S.F. 1988, in QSO Absorption Lines: Probing the \nUniverse, eds. JC Blades, DA Turnshek, CA Norman (Cambridge: \nCambridge Univ Press), p. 53\n\\bibitem[Foltz \\etal 1986]{fol86} Foltz, C.B., Weymann, R.J., Peterson, \nB.M., Sun, L., \\& Malkan, M.A., \\etal 1986, \\apj, 307, 504\n\\bibitem[Gallagher \\etal 1999]{gal99} Gallagher, S.C., Brandt, W.N., \nSambruna, R.M., Mathur, S., \\& Yamasaki, N. 1999, \\apj, in press\n\\bibitem[Ganguly \\etal 1999]{gan99} Ganguly, R., Eracleous, M., \nCharlton, J.C., \\& Churchill, C.W. 1999, \\aj, 117, 2594\n%\\bibitem[Gaskell 1982]{gas82} Gaskell, C.M. 1982, \\apj, 249, 443\n\\bibitem[George \\etal 1998b]{geo98b} George, I.M., Turner, T.J., \nMushotzky, R.F., H., Nandra, \\& Netzer, H. 1998b, \\apj, 503, 174\n\\bibitem[George \\etal 1998a]{geo98a} George, I.M., Turner, T.J., Netzer, \nH., Nandra, K., Mushotzky, R.F., \\& Yaqoob, T. 1998a, \\apjs, 114, 73\n\\bibitem[Goodrich \\& Miller 1995]{goo95} \nGoodrich, R. W., \\& Miller, J. 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Series, 128, 19\n\\bibitem[Hamann \\etal 1997]{h97a} Hamann, F., Barlow, T.A., \nJunkkarinen, V.T., \\& Burbidge, E.M. 1997, \\apj, 478, 80\n\\bibitem[Hamann \\etal 1999]{h99a} Hamann, F., Barlow, T.A., \nWeymann, R.J., Chaffee, F., \\& Foltz, C. 1999, in preparation.\n\\bibitem[Hamann \\etal 1998]{h98b} Hamann, F., Cohen, R.D., Shields, J.C., \nBurbidge, E.M., Junkkarinen, V.T., \\& Crenshaw, D.M. 1998, \\apj, 496, 761\n\\bibitem[Hamann \\& Ferland 1999]{h99b} Hamann, F., \\& Ferland, G.J. \n1999, \\araa, 37, in press\n\\bibitem[Hines \\& Wills 1995]{hin95} Hines, D.C., \\& Wills, B.J. 1995, \n\\apj, 448, L69\n%\\bibitem[Junkkarinen \\etal 1995]{jun95} Junkkarinen, V. T., Beaver, E. A., \n%Burbidge, E. M., Cohen, R. D., Hamann, F., Lyons, R. W., \\& Barlow \n%T. A. 1995, BAAS, 27, 872 \n\\bibitem[Barlow \\& Junkkarinen 1994]{bar94} Barlow, T.A., \\& Junkkarinen, \nV.T. 1994, BAAS, 26, 1339\n%\\bibitem[Kopko \\etal 1994]{kop94} Kopko, M. Jr., Turnshek, D. A., \n%\\& Espey, B. R. 1994, in IAU Symp. \n%159, Multi-Wavelength Continuum Emission of AGN, eds. T. J.-L. Courvoisier \n%\\& A. Blecha (Dordrecht:Kluwar), 450\n\\bibitem[Koratkar \\etal 1992][kora92] Koratkar, A.P., Kinney, A.L., \n\\& Bohlin, R.C. 1992, \\apj, 400, 435\n\\bibitem[Korista \\etal 1997]{kor97} Korista, K. T., Ferland, G., \\& \nBaldwin, J. 1997, \\apj, 487, 555\n%\\bibitem[Korista \\etal 1996]{kor96} Korista, K. T., Hamann, F., Ferguson, \n%J., \\& Ferland, G. J. 1996, \\apj, 461, 641\n%\\bibitem[Korista \\etal 1993]{kor93} Korista, K. T., Voit, G. M., \n%Morris, S. L., \\& Weymann, R. J. 1993, \\apjs, 88, 357\n\\bibitem[Kriss \\etal 1996]{kri96} Kriss, G.A., Espey, B.R., Krolik, J.H., \nTsvetanov, Z., Zheng, W., \\& Davidsen, A.F. 1996, \\apj, 467, 622\n%\\bibitem[Laor \\etal 1994]{lao94} Laor, A., Bahcall, J. N., Jannuzi, B. T., \n%Schneider, D. P., Green, R. F., \\& Hartig, G. F. 1994, \\apj, 420, 110\n%\\bibitem[Laor \\etal 1995]{lao95} Laor, A., Bahcall, J. N., Jannuzi, B. T., \n%Schneider, D. P., Green, R. F., \\& Hartig, G. F. 1995, \\apjs, 99, 1\n\\bibitem[Laor \\etal 1997]{lao97} Laor, A., Fiore, F., Elvis, M., Wilkes, \nB. J., \\& McDowell, J. C. 1997, \\apj, 477, 93\n\\bibitem[Marziani \\etal 1996]{mar96} Marziani, P., Sulentic, J.W., \nDultzin-Hacyan, D., Calvani, M., \\& Moles, M. 1996, \\apjs, 104, 37\n%\\bibitem[Mathur 1994]{mat94b} Mathur, S. 1994, \\apj, 431, L75\n%\\bibitem[Mathur \\etal 1995]{mat95} Mathur, S., Elvis, M., \\& Singh, K. P. \n%1995, \\apj, 455, L9\n\\bibitem[Mathur \\etal 1999]{mat99} Mathur, S., Elvis, M., \\& Wilkes, \nB. 1999, \\apj, 519, 605\n\\bibitem[Mathur \\etal 1998]{mat98} Mathur, S., Wilkes, B., \\& Elvis, M. \n1998, \\apj, 503, L23\n%\\bibitem[Mathur \\etal 1994]{mat94a} Mathur, S., Wilkes, B., \n%Elvis, M., \\& Fiore, F. 1994, \\apj, 434, 493\n\\bibitem[Morris \\etal 1986]{mor86} Morris, S.L., Weymann, R.J., Foltz, \nC.B., Turnshek, D.A., Shectman, S., Price, C., \\& Boroson, T.A. 1986, \n\\apj, 310, 40\n%\\bibitem[Morrison \\& McCammon]{mor83} Morrison, R., \\& McCammon, D. 1995, \n%\\apj, 270, 119\n\\bibitem[Murray \\etal 1995]{mur95} Murray, N., Chiang, J., Grossman, S.A., \n\\& Voit, G.M. 1995, \\apj, 451, 498\n\\bibitem[Netzer 1985]{net85} Netzer, H. 1985, \\apj, 289, 451\n\\bibitem[Netzer 1990]{net90} Netzer, H. 1990, in Active Galactic Nuclei, \neds. R.D. Blandford, H. Netzer, L. Woltjer, (Berlin:Springer), 57\n\\bibitem[Netzer 1996]{net96} Netzer, H. 1996, \\apj, 473, 781\n\\bibitem[O'Brien \\etal 1988]{obr88} O'Brien, P.T., Gondhalekar, P.M., \n\\& Wilson, R. 1988, MNRAS, 233, 801\n\\bibitem[Petitjean \\etal 1994]{pet94} Petitjean, P., Rauch, M., \\& \nCarswell, R. F. 1994, \\aap, 291, 29\n\\bibitem[Petitjean \\etal 1996]{pet96} Petitjean, P., Riediger, R., \\& \nRauch, M. 1996, \\aap, 307, 417\n\\bibitem[Petitjean \\& Srianand 1999]{pet99} Petitjean, P., \\& Srianand, \nR. 1999, \\aap, 345, 73\n\\bibitem[Reid \\etal 1995]{rei95} Reid, A., Shone, D.L., Akujor, C.E., \nBrowne, I.W.A., Murphy, D.W., \\& Walsh, D. 1997, \\aaps, 110. 213\n\\bibitem[Reynolds 1997]{rey97}Reynolds, C. S. 1997, MNRAS, 286, 513\n\\bibitem[Richards \\etal 1999]{ric99} Richards, G.T., York, D.G., \nYanny, B., Kollgaard, R.I., Laurent-Muehleisen, S.A., \\etal 1999, \n\\apj, 513, 576\n\\bibitem[Sargent \\etal 1982]{sar82} Sargent, W.L.W., Boksenberg, A. \n\\& Young, P. 1982, \\apj, 252, 54\n\\bibitem[Shields \\& Hamann 1997]{shi97} Shields, J.C., \\& Hamann, F. 1997, \n\\apj, 481, 752\n\\bibitem[Schmidt 1968]{sch68} Schmidt, M. 1968, \\apj, 151, 393\n\\bibitem[Schneider \\etal 1993]{sch93} Schneider, D.P., \\etal 1993, \\apjs, 87 45\n\\bibitem[Telfer \\etal 1998]{tel98} Telfer, R. C., Kriss, G. A., Zheng, W., \nDavidson, A. F., \\& Green, R. F. 1998, \\apj, 509, 132\n\\bibitem[Tripp \\etal 1996]{tri96} \nTripp, T.M., Lu, L., \\& Savage, B.D. 1996, \\apjs, 102, 239\n%\\bibitem[Turnshek 1984]{tur84} Turnshek, D. A. 1984, \\apj, 280, 51\n%\\bibitem[Turnshek 1988]{tur88} Turnshek, D. A. 1988, in QSO Absorption Lines: \n%Probing the Universe, eds. J. C. Blades, D. A. Turnshek, \\& C. A. \n%Norman (Cambridge: Cambridge Univ. Press), 17\n\\bibitem[Turnshek 1995]{tur95} Turnshek, D. A. 1995, in QSO Absorption \nLines, ed. G. Meylan, (Berlin:Springer-Verlag), 223\n%\\bibitem[Turnshek \\etal 1996]{tur96} Turnshek, D. A., Kopko, M., Monier, E., \n%Noll, D., Espey, B., \\& Weymann, R. J. 1996, \\apj, 463, 110\n%\\bibitem[Tytler \\& Fan 1992]{tyt92} Tytler, D., \\& Fan, X.-M. 1992, \n%\\apjs, 79, 1\n\\bibitem[Verner \\etal 1994a]{ver94a} Verner, D.A., Barthel, \nP.D., \\& Tytler, D., 1994a, \\aaps, 108, 287\n\\bibitem[Verner \\etal 1994b]{ver94b} Verner, D.A., Tytler, D., \\& Barthel, \nP.D. 1994b, \\apj, 430, 186\n%\\bibitem[Verner \\etal 1996]{ver96} Verner, D., Verner, E. M., \n%\\& Ferland, G. J. 1996, Atomic Data and Nuclear Data Tables, 64, 1\n%\\bibitem[Voit \\etal 1993]{voi93} Voit, G. M., Weymann, R. J., \\& \n%Korista, K. T. 1993, \\apj, 413, 95\n\\bibitem[Wampler \\etal 1993]{wam93} Wampler, E. 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}
] |
astro-ph0002109
|
The ALADIN Interactive Sky Atlas
|
[
{
"author": "Fran\\c{c}ois Bonnarel"
},
{
"author": "Pierre Fernique"
},
{
"author": "Olivier Bienaym\\'e"
},
{
"author": "Daniel Egret"
},
{
"author": "Fran\\c{c}oise Genova"
},
{
"author": "Mireille Louys\\thanks{Laboratoire des Sciences de l'Informatique, de l'Image et de la T\\'el\\'ed\\'etection, ENSPS, Universit\\'e Louis Pasteur, F-67000 Strasbourg, France}"
},
{
"author": "Fran\\c{c}ois Ochsenbein"
},
{
"author": "Marc Wenger"
},
{
"author": "James G. Bartlett\\thanks{Present address: Observatoire Midi-Pyr\\'en\\'ees, Toulouse, France} %"
},
{
"author": "% Michel Cr\\'ez\\'e\\thanks{Present address: IUP de Vannes, % Tohannic, rue Yves Mainguy, F-56000 Vannes, France}"
}
] |
The {\sc Aladin} interactive sky atlas, developed at CDS, is a service providing simultaneous access to digitized images of the sky, astronomical catalogues, and databases. The driving motivation is to facilitate direct, visual comparison of observational data at any wavelength with images of the optical sky, and with reference catalogues. The set of available sky images consists of the STScI Digitized Sky Surveys, completed with high resolution images of crowded regions scanned at the MAMA facility in Paris. A Java WWW interface to the system is available at: {http://aladin.u-strasbg.fr/}. \keywords{Astronomical data bases: miscellaneous -- Catalogs -- Atlases --Surveys}
|
[
{
"name": "aladin.tex",
"string": "%\n%\\documentclass[referee]{aa} % for a referee version\n\\documentclass{aa}\n%\n\\usepackage{graphics}\n%\\usepackage{times}\n\n\\begin{document}\n\n \\thesaurus{06 % A&A Section 6: Form. struct. and evolut. of stars\n (04.01.1; % Astronomical data bases: miscellaneous \n 04.01.2; % Atlases\n 04.03.1; % Catalogs\n 04.19.1)} % Surveys.\n\n%\n \\title{The ALADIN Interactive Sky Atlas}\n\n \\subtitle{A Reference Tool for Identification of \n Astronomical Sources}\n\n\\author{Fran\\c{c}ois Bonnarel\n\\and\n Pierre Fernique\n\\and\n Olivier Bienaym\\'e\n\\and\n Daniel Egret\n\\and\n Fran\\c{c}oise Genova\n\\and\n Mireille Louys\\thanks{Laboratoire des Sciences de l'Informatique,\n de l'Image et de la T\\'el\\'ed\\'etection, ENSPS, Universit\\'e\n Louis Pasteur, F-67000 Strasbourg, France}\n\\and\n Fran\\c{c}ois Ochsenbein\n\\and \n Marc Wenger\n\\and\n James G. Bartlett\\thanks{\\emph{Present address:} Observatoire\n Midi-Pyr\\'en\\'ees, Toulouse, France}\n%\\and\n% Michel Cr\\'ez\\'e\\thanks{\\emph{Present address:} IUP de Vannes,\n% Tohannic, rue Yves Mainguy, F-56000 Vannes, France}\n }\n\n \\offprints{Daniel Egret}\n \\mail{question@simbad.u-strasbg.fr}\n\n \\institute{CDS, Observatoire astronomique de Strasbourg, UMR 7550,\n11 rue de l'Universit\\'e, F-67000 Strasbourg, France}\n\n \\date{Received 6 December 1999 / Accepted 16 December 1999}\n\n\\maketitle\n\n \\begin{abstract}\n\n The {\\sc Aladin} interactive sky atlas, developed at CDS, \nis a service providing simultaneous access to digitized\nimages of the sky, astronomical catalogues, and databases.\n The driving motivation is to facilitate direct, \nvisual comparison of observational data at any wavelength with \nimages of the optical sky, and with reference catalogues. \n\n The set of available sky images consists of the STScI Digitized\nSky Surveys, completed with high resolution images of crowded\nregions scanned at the MAMA facility in Paris.\n\n A Java WWW interface to the system is available at:\n\n{http://aladin.u-strasbg.fr/}.\n\n\\keywords{Astronomical data bases: miscellaneous -- Catalogs -- \n Atlases --Surveys}\n\n\\end{abstract}\n\n%\n%________________________________________________________________\n\n\\section{Introduction}\n\n\\subsection{The CDS}\nThe Centre de Donn\\'ees astronomiques de Strasbourg\n(CDS) defines, develops, and maintains services\nto help astronomers find the information\nthey need from the\nvery rapidly increasing wealth of astronomical information, \nparticularly on-line information. \n\nIn modern astronomy, cross-matching data acquired at\ndifferent wavelengths is often the key to the understanding of\nastronomical phenomena, which means that astronomers have to use data\nand information produced in fields in which they are not specialists.\nThe development of tools for cross-identification of objects \nis of particular importance in this context of \nmulti-wavelength astronomy. \n\nA detailed description of the CDS on-line services can be found, e.g., \nin Egret et al.\\ (\\cite{cds-amp2})\nand in Genova et al.\\ (\\cite{cds-hub}, \\cite{cds}, \\cite{cds2000}), \nor at the CDS web site\\footnote{\\emph{Internet address:}\nhttp://cdsweb.u-strasbg.fr/}. \n\n\n\\subsection{The ALADIN Project}\n\n%%%%\nSeveral sites currently provide on-line access \nto digitized sky surveys at different wavelengths:\nthis is, for instance, the case of\nDigitized Sky Survey (DSS) at STScI \n(Morrison \\cite{1995adass...4..179M}),\nand of similar implementations at other sites,\nproviding quick access to cutouts of the \ncompressed DSS images.\n{\\sc SkyView} at HEASARC (McGlynn et al. \\cite{skyview}) \ncan generate images of any portion \nof the sky at wavelengths in all regimes from\nradio to gamma-ray.\n%%%%%\nSome of these services provide\nsimultaneous access to images\nand to catalogue data.\nThe {\\sc SkyCat} tool, recently developed\nat ESO (Albrecht et al.\\ \\cite{skycat}),\naddressed this concern in the context of \nthe European Southern Observatory scientific environment \n(in view of supporting future users of the Very Large Telescope);\n{\\sc SkyCat} uses a standardized syntax to access heterogeneous\nastronomical data sources on the network.\n\n\n{\\sc Aladin} has been developed independently by the CDS\nsince 1993\nas a dedicated tool for identification\nof astronomical sources -- a tool that can fully benefit from the\nwhole environment of CDS databases and services, and that is designed\nin view of being released as a multi-purpose\nservice to the general astronomical community.\n\n{\\sc Aladin} is an interactive sky atlas, \nallowing the user to visualize a part of the sky,\nextracted from a database of images\nfrom digitized surveys and observational\narchives, \nand to overlay objects\nfrom the CDS catalogues and tables, \nand from reference databases ({\\sc Simbad} and NED),\nupon the digitized image of the sky. \n\nIt is intended to become a major cross-identification\ntool, since it allows recognition of astronomical\nsources on the images at optical\nwavelength, and at other wavelengths through the catalogue data. \nExpected usage scenarios include multi-spectral \napproaches such as searching for counterparts of \nsources detected at various wavelengths, and \napplications related to \ncareful identification of astronomical objects.\n%%%%%\n{\\sc Aladin} is also heavily used for the\nCDS needs of catalogue and database quality control. \n\nIn the case of extensive undertakings (such as \nchecking the astrometric\nquality for a whole catalogue), it is expected\nthat {\\sc Aladin} will be useful for understanding the\ncharacteristics of the catalogue or survey, and for setting\nup the parameters to be adjusted while fine tuning the\ncross-matching or classification algorithms, by studying\na sample section of objects or fields.\n\nA discussion of the usage of such a tool for cross-identification \ncan be found in Bartlett \\& Egret (\\cite{xid-179}),\nwhere it is shown how \\emph{training sets} are used to\nbuild likelihood ratio tests. \n\nThe {\\sc Aladin} interactive atlas is available in three modes:\na simple previewer, a Java interface, and an\nX-Window interface. We describe here mostly the Java interface\nwhich is publicly accessible on the World-Wide Web.\n\n%\n%______________________________________________________________\n\n\\section{Access modes}\n\nAfter a long phase of development, \n(see e.g., Paillou et al.\\ \\cite{paillou}),\n{\\sc Aladin} has been first distributed to a\nlimited number of astronomy laboratories in 1997,\nas an X-Window client program, \nto be installed on a Unix machine on the user side.\nThe client program interacts with the servers running\non Unix workstations at CDS (image server, catalogue\nserver, {\\sc Simbad} server) and manages image handling\nand plane overlays.\n\nThe strategy of having a client program on the user side\nis difficult to maintain on the long run.\nThe World-Wide Web offers, with the development of Java\napplications (or \\emph{applets}), a way to solve this difficulty. \nActually, there is still a \\emph{client} program:\nthis is the Java applet itself, \nthat the user receives from the WWW server.\nMost current Internet browsers are able to make it run\nproperly, so that the user does not have to install anything\nspecial other than an Internet browser.\n\nAs a consequence, {\\sc Aladin} is currently available \nin the three following modes:\n\n\\begin{description}\n\\item[{\\sc Aladin} previewer:] a pre-formatted\nimage server provides a compressed image of fixed size\n($14.1\\arcmin \\times 14.1\\arcmin$ for the DSS-I)\naround a given object or position. When an\nobject name is given, its position is resolved\nthrough the {\\sc Simbad} name resolver. Anchors\npointing to the previewer are integral part of \nthe World-Wide Web interfaces\nto the {\\sc Simbad} database\\footnote{\\emph{Internet\naddress}: http://simbad.u-strasbg.fr/Simbad}\nand to the CDS bibliographic service\\footnote{\\emph{Internet\naddress}: http://simbad.u-strasbg.fr/biblio.html}.\n%%%%\nThe result page also gives access to the full resolution\nFITS image for download.\n\n\\item[{\\sc Aladin} Java:] this is the primary\npublic interface, supporting queries to the\nimage database and overlays from any catalogue or table\navailable at CDS, as well as from {\\sc Simbad} and NED databases.\nAccess to personal files is not possible (due to\nsecurity restrictions of the Java language).\nThese restrictions do not apply to the \\emph{stand-alone}\nversion, which can be installed and run on a local \n\\emph{Java virtual machine}. \n\n\\item[{\\sc Aladin~X}:] The X-Window {\\sc Aladin} client\nprovides most of the functionalities of the {\\sc Aladin} Java\ninterface, plus more advanced functions, as described\nbelow (section~\\ref{AladinX}).\n\n\\end{description}\n\n\n%\n%______________________________________________________________\n\n\\section{The image database}\n\n\\subsection{Database summary}\n\nThe {\\sc Aladin} image dataset consists of:\n\n\\begin{itemize}\n\n\\item The whole sky image database from the first Digitized\nSky Survey (DSS-I) digitized from photographic plates\nand distributed by the Space Telescope Science\nInstitute (STScI) as a set of slightly compressed\nFITS images (with a resolution of $1.8\\arcsec$);\nDSS-II is also currently\nbeing integrated into the database (see below);\n\n\\item Images of \\emph{crowded} fields\n(Galactic Plane, Magellanic Clouds) at the full resolution \nof $0.67\\arcsec$, scanned at the {\\em Centre d'Analyse des\nImages} (MAMA machine) in Paris; \n\n\\item Global plate views \n($5\\degr \\times 5\\degr$\nor $6\\degr \\times 6\\degr$ according to the\nsurvey) are also available for all the plates\ncontributing to the image dataset:\nthese are built at CDS by averaging\nblocks of pixels from the original scans;\n\n\\item Other images sets, or user-provided images,\nin FITS format, having suitable World Coordinate System \ninformation in the header (see e.g.\\ Greisen \\& Calabretta \\cite{wcs});\nthis functionality is currently available only for the\nJava stand-alone version.\n\\end{itemize}\n\n\\subsection{Building the database contents}\n\nThe {\\sc Aladin} project has set up collaborations with \nthe major groups providing digitizations of sky surveys.\nThe original surveys are made of photographic Schmidt plates\nobtained at Palomar in the North, \nand ESO/SERC in the South, and\ncovering the whole sky at different epochs and colours\n(see e.g., MacGillivray \\cite{potsdam}). \n\nThe database currently includes the first Digitized Sky \nSurvey (DSS-I) produced by the\nSpace Telescope Institute (Lasker \\cite{dss}), \nfor the needs of the Hubble\nSpace Telescope.\nTo create these images, the\nSTScI team scanned the first epoch (1950/1955) Palomar \n$E$ Red and\nUnited Kingdom Schmidt $J$ Blue plates \n(including the SERC J Equatorial Extension and some\nshort V-band plates at low galactic latitude) \nwith a pixel size of $1.7\\arcsec$ ($25{\\mu}m$).\nThe low resolution and a light data compression\n(factor of 10) permit storage of images covering\nthe full sky on a set of 102 CD-ROMs.\n\n%%%%%%\nDSS-II images in the R-band (from Palomar POSS-II F and\nUK Schmidt SES, AAO-R, and SERC-ER), scanned with\na $1\\arcsec$ ($15{\\mu}m$) sampling interval \n(see Lasker \\cite{dss-ii}) \nare gradually being included into the system,\nand will soon be followed by DSS-II images\nin the B-band (POSS-II J). \n\nIn addition, high resolution digitalization\nof POSS-II, SERC-J, SERC-SR, SERC-I, or ESO-R plates \nfeaturing crowded regions of the sky (Galactic Plane\nand Magellanic Clouds) have been provided by the MAMA\nfacility at the {\\sl Centre d'Analyse des Images} (CAI),\nObservatoire de Paris (Guibert \\cite{MAMA}). \nSampling is $0.67\\arcsec$ per pixel ($10{\\mu}m$).\nCurrently, these high resolution images cover\nabout 15\\% of the sky, and are stored in a juke-box\nof optical disks, with a capacity of 500 Gigabytes.\n\n\n\\subsection{The image server}\n\nThe image server for {\\sc Aladin} had to be able\nto deal with various survey data,\nin heterogeneous formats (uncompressed FITS, compressed\nJPEG or PMT -- see Section \\ref{compression}, etc.).\nFor that, an object-oriented design was chosen,\nallowing an easy manipulation of image calibrations\nand headers, through the use of object classes.\nImage compression or decompression, image reconstruction,\nand in a near future, part of the recalibration, are \nseen as class methods.\n\nImages are currently divided into subimages of\n$500 \\times 500$ pixels (DSS-I),\n$768 \\times 768$ pixels (DSS-II),\nor $1024 \\times 1024$ pixels (MAMA).\n\nThe 1.5 million subimages are described by\nrecords stored in a relational database,\nencapsulated by several classes of the image\nmanagement software.\nWhen an image of the sky is requested,\nthe original subimages containing the\ncorresponding sky area are retrieved\nthrough SQL commands, and \nthe resulting image is built on the fly.\n\n\n\n%\n%______________________________________________________________\n\\section{Usage scenarios}\n\nIn this section we will focus on describing the usage\nof the {\\sc Aladin} Java interface, as it is available now \n(November 1999).\n\n\\subsection{Access}\n\nThe {\\sc Aladin} home page is available through\nthe CDS Web server at the following address: \nhttp://aladin.u-strasbg.fr/\n\nThis site provides access to {\\sc Aladin} documentation,\nincluding scientific reports, recent publications, etc.\n\n\\subsection{Query modes}\n\nThe typical usage scenario starts with a request\nof the digitized image for an area\nof the sky defined by its central position or name of \ncentral object (to be resolved by {\\sc Simbad}).\nThe size of the sky field is determined by the\nphotographic survey used: it is $14.1\\arcmin$ in\nthe case of the DSS-I.\n\nAstrometric information comes from \nthe FITS header of the DSS image, and is generally\naccurate to the arcsecond (with deviations up\nto several arcsec.\\ in exceptional cases, on plate edges).\n\n\\begin{figure}\n%\\vspace{\\hsize}\n\\resizebox{\\hsize}{!}{\\includegraphics{panel.ps}}\n\\caption{Example of Images/Data {\\sc Aladin} query panel.}\n\\label{query-panel}\n\\end{figure}\n\n\\begin{figure*}\n%\\vspace{\\hsize}\n% 18cm if double column\n\\resizebox{\\hsize}{!}{\\includegraphics{ngc7436.ps}}\n\\caption{Example of {\\sc Aladin} window, with an image centered\non NGC 7436, and objects from NED and 2MASS marked by symbols.}\n\\label{sample-image}\n\\end{figure*}\n\nIn a subsequent step, the interface, \nillustrated by Figs.~\\ref{query-panel} and \\ref{sample-image},\nallows the user to stack several information\nplanes related to the same sky field, to superimpose the\ncorresponding data from catalogues and databases, \nand to obtain interactive access to\nthe original data.\n\nThe possible information planes are the following:\n\n\\begin{itemize}\n\n\\item Image pixels from the {\\sc Aladin} database of\ndigitized photographic plates (DSS-I, MAMA, DSS-II);\nfunctionalities include zooming capabilities, inverse\nvideo, modification of the color table;\n\n\\item Information from the {\\sc Simbad} database\n(Wenger et al.\\ \\cite{simbad}); objects\nreferenced in {\\sc Simbad} are\nvisualized by color symbols overlaid on top of the black and\nwhite image; the shape and color of the symbols can be\nmodified on request, and written labels can be added\nfor explicit identification of the objects; these \nfeatures are also available for all\nthe other information planes; \n\n\\item Records from the CDS library of catalogues\n or tables ({\\sc VizieR}\\footnote{\\emph{Internet address:}\n http://vizier.u-strasbg.fr/}, Ochsenbein et al.\\\n \\cite{vizier});\n the user can select the desired catalogue from a\npreselected list including the major reference catalogues\nsuch as the Tycho Reference Catalogue \n(ESA \\cite{tyc}; H{\\o}g et al.\\ \\cite{trc}), \nGSC (Lasker et al.\\ \\cite{gsc}), IRAS Point Source Catalog,\nor USNO A2.0 (Monet \\cite{usno}); the user can alternatively\nselect the catalogues for which entries may be available\nin the corresponding sky field, using the {\\sc VizieR} \nquery mechanism by position\n(see \\ref{catserver}), catalogue name or keyword; \n\n\\item Information from the NED database: objects\nreferenced in the NASA/IPAC Extragalactic \nDatabase\\footnote{\\emph{Internet address:} \nhttp://nedwww.ipac.caltech.edu/}\n(Helou et al. \\cite{ned})\ncan also be visualized through queries submitted to the\nNED server at IPAC;\n\n%%%%%%\n\\item Archive images will gradually become available\nthrough the corresponding mission logs: Hubble Space Telescope\nimages are currently available \n(see Fig.~\\ref{M16} for an example),\nand more archives will follow.\n\n\\begin{figure*}\n%\\vspace{\\hsize}\n% 18cm if double column\n\\resizebox{\\hsize}{!}{\\rotatebox{+90}{\\includegraphics{M16.ps}}}\n\\caption{Example of {\\sc Aladin} display of a famous image\nfrom the HST archive (WFPC2) featuring the Eagle Nebula\n(\\object{M 16}).\nObjects present in Simbad, GSC, and USNO A2.0 are flagged\nwith different symbols. Field size is 2.6 arcmin\n(full image, right) and 1.6 arcmin (left).}\n\\label{M16}\n\\end{figure*}\n\n\n\n\\item Local, user data files can also be overlaid,\nbut, because of current limitations of the Java applications,\nthis feature is only available in the stand-alone\nversion, or in {\\sc Aladin~X}.\n\\end{itemize}\n \nThe stack of images and graphics is made visible\nto the user (under the eye icon, on the\nright of Fig.~2) so that each plane can be \nturned on and off. The status of queries\nis also easily visualized.\n\nFor all information planes ({\\sc Simbad}, {\\sc VizieR}, NED) links are\nprovided to the original data. This is done in the following\nway: when selecting an object on the image,\nwith mouse and cursor, it is\npossible to call for the corresponding information which\nwill appear in a separate window on the Internet browser.\nIt is also possible to select with the mouse and cursor all\nobjects in a rectangular area: the corresponding\nobjects are listed in a panel on the bottom of the {\\sc Aladin}\nwindow; this list includes basic information (name,\nposition and, when applicable, number of bibliographical\nreferences) and anchors pointing to the original catalogue \nor database.\n\nAt any moment the position of the cursor is translated\nin terms of right ascension and declination on the sky\nand visualized in the top panel of the {\\sc Aladin} window.\nAdditional features are available, such as a tool for\ncomputing angular distance between marked objects.\n\n%%%%%\nThe \\emph{standalone} version gives\naccess to additional facilities, \nnot available through the Web, such as printing and\nsaving the images and data.\n\n\\subsection{The catalogue server}\n\\label{catserver}\n\nThe ability to access all {\\sc VizieR} catalogues and tables \ndirectly from {\\sc Aladin} is a unique feature\nwhich makes it an extremely powerful tool for \nany cross-identification or classification work.\n\nThe ``\\emph{Select around target}'' request relies on\na special feature -- the genie of the lamp:\nthis is the ability to decide which catalogues, among\nthe database of (currently) over 2,600 catalogues\nor tables, contain data records for astronomical objects\nlying in the selected sky area.\nIn order to do that, an index map of {\\sc VizieR} catalogues\nis produced (and kept up-to-date), on the basis of about \nten pixels per square degree: for each such `pixel' the\nindex gives the list of all catalogues and tables\nwhich have entries in the field.\n\nWhen a user hits the button ``\\emph{Select around target}'',\nthis index is queried and the list of useful\ncatalogues is returned. It is possible, at this stage,\neither to list all catalogues, or to produce a subset\nselected on the basis of keywords.\nNote that, as the index ``pixels'' generally match\nan area larger than the current sky field,\nthere is simply a good chance, but not 100\\%, \nto actually obtain\nentries in the field when querying one of the selected tables.\n\n\\subsection{Cache}\n\nThe images of the 30,000 most cited objects in {\\sc Simbad} \nare pre-computed\nand available on a cache on magnetic disk. \nFor these objects, the image is served much faster\nthan for other objects\nwhere the image has to be extracted\nfrom the Digitized Sky Survey.\n\n%%%%%%\n\\subsection{Usage statistics}\n\nAs the newest service developed by CDS, {\\sc Aladin} has\nnot yet been widely publicized, and its usage is in\na steeply growing phase. Currently about\n10,000 queries are processed monthly,\ngenerating the extraction of more than 5,000 images.\n\n%______________________________________________________________\n\\section{Image compression}\n\\label{compression}\n\nAstronomical image compression in\nthe context of {\\sc Aladin} has been discussed \nin detail by Louys et al.\\ (\\cite{louys}).\n\nFor the {\\sc Aladin} Java interface and for the {\\sc Aladin}\npreviewer, the current choice has been to deliver to the\nuser an image in JPEG 8-bit format, constructed from the original\nFITS images. JPEG is a general purpose standard\nwhich is supported by all current Internet browsers.\nThe size of such an image does not exceed 30 kBytes, and\nthus the corresponding network load is very small.\n\nIn the near future,\nthe Pyramidal Median Transform (PMT) algorithm,\nimplemented in the MR-1 package\n(Starck et al.\\ \\cite{pmt}), \nwill be used within {\\sc Aladin}\nfor storing or transferring new image datasets,\nsuch as additional high resolution images \n(see again Louys et al.\\ \\cite{louys} for details).\n%%%%%\nThe corresponding decompression package is\nbeing written in Java code, and could be downloaded\non request for use within the Java interface.\n\n\n%______________________________________________________________\n\\section{Aladin~X}\n\\label{AladinX}\n\nThe {\\sc Aladin} X-Window interface is \nthe testbed for further developments.\nIt is currently only distributed for the Unix Solaris\noperating system.\nInterested potential users should contact CDS for details.\n\n\n\\subsection {Source extraction}\n\n{\\sc Aladin~X} includes a procedure for source extraction.\nThe current mechanism will soon be\nreplaced by SExtractor (Bertin \\& Arnouts\n\\cite{1996A&AS..117..393B}).\n\n\n\\subsection{Plate calibrations}\n\nWhile the first level astrometric calibrations are given\nby the digitizing machines, a second level \nis being developed that\nwill allow the user to \\emph{recalibrate} the image with\na new set of standards taken, for example, from the\nTycho Reference Catalogue.\nThe photometric calibrations (surface and\nstellar) will eventually also be performed within {\\sc Aladin}, by using\nthe Guide Star Photometric Catalogs (GSPC I and II;\nFerrari et al.\\ \\cite{gspc2}; Lasker et al.\\ \\cite{gspc1}).\n\nUsers will thus be able to work on the details of local astrometric\nand photometric plate calibrations in order to\nextract the full information from the digitized plates.\n\n%______________________________________________________________\n\\section{Integration of distributed services}\n\nWhile the CDS databases have followed different \ndevelopment paths, the\nneed to build a transparent access \nto the \\emph{whole set} of CDS services has become\nmore and more obvious with the easy\nnavigation permitted by hypertext tools. \n{\\sc Aladin} has become the prototype of such a development,\nby giving comprehensive simultaneous \naccess to {\\sc Simbad}, \nthe {\\sc VizieR} Catalogue service, \nand to external databases such as NED,\nusing a client/server approach and, when possible,\nstandardized query syntax and formats. \n\nIn order to be able to go further, the\nCDS has built a general data\nexchange model, taking into account all types of information available\nat the Data Center, known under the acronym\nof GLU for G\\'en\\'erateur de Liens Uniformes -- Uniform\nLink Generator (Fernique et al.\\ \\cite{glu}). \n\nMore generally, with the development of the Internet, \nand with an increasing\nnumber of on-line astronomical services giving access \nto data or information, it has become critical to develop\nnew tools providing access to distributed services. This\nis, for instance, the concern expressed by NASA through \nthe AstroBrowse project (Heikkila et al.\\ \\cite{astrobrowse}).\nA local implementation of this concept is available at CDS \n(AstroGlu: Egret et al.\\ \\cite{astroglu}). \n\n\n%\n%______________________________________________________________\n\n\\section{Future developments}\n\nAn important direction of development in the near future\nis the\npossibility of providing access to images from other sky surveys\nor deep field observations: obvious candidates are\nthe DENIS (Epchtein \\cite{denis}) and 2MASS\n(Skrutskie \\cite{2mass}) near-infrared surveys.\n%%%%%\nThe first public point source catalogues \nresulting from these surveys\nare already available through {\\sc Aladin},\nsince they are included in the {\\sc VizieR}\nservice. This has already proved useful for validating\nsurvey data in preliminary versions of the DENIS\ncatalogue (Epchtein et al. \\cite{denis-psc}).\n\nThe CDS team will also continue to enrich \nthe system functionality.\nThe users play an important role in\nthat respect, by giving feedback on the desired features\nand user-friendliness of the interfaces.\n\n%%%%\nNew developments are currently considered\nas additional modules which will be incorporated to the\ngeneral release only when needed, possibly\nas optional downloads, in order to keep\nthe default version simple and efficient enough for \nmost of the Web applications.\n\nOn a longer term, the CDS is studying the possibility of\ndesigning \\emph{data mining} tools that will help to make a\nfruitful use of forthcoming very large surveys, and will\nbe used for cross-matching several surveys obtained, \nfor instance, at different wavelengths.\nA first prototype, resulting from a collaboration between\nESO and CDS, in the framework of the VLT scientific\nenvironment is currently being implemented (Ortiz et al.\n\\cite{ortiz}).\n\n\n\n%\n%______________________________________________________________\n\n%\\{Conclusion}\n%\n%The {\\sc Aladin} tool is designed to be an essential tool for\n%multi-wavelength cross-identifications.\n\n\n\\begin{acknowledgements}\nCDS acknowledges the support of INSU-CNRS, the Centre National\nd'Etudes Spatiales (CNES), and Universit\\'e Louis Pasteur.\n\nWe are indebted to Michel Cr\\'ez\\'e who initiated\nthe project while being Director of the CDS, and to \nall the early contributors to the {\\sc Aladin} project:\nPhilippe Paillou, \nJoseph Florsch, \nHouri Ziaeepour, \nEric Divetain,\nVincent Raclot. \n\nCollaboration with STScI, and especially with the\nlate Barry Lasker, and with\nBrian McLean, is gratefully acknowledged.\nWe thank Jean Guibert and Ren\\'e Chesnel from CAI/MAMA\nfor their continuous support to the project.\n\nThe Digitized Sky Survey was produced at the Space Telescope Science \nInstitute under U.S. Government grant NAG W-2166. \nThe images of these surveys are based on photographic data obtained \nusing the Oschin Schmidt\nTelescope on Palomar Mountain and the UK Schmidt Telescope.\n\nJava is a registered trademark of Sun Microsystems.\n\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\n\\bibitem[1997]{skycat} Albrecht, M. A., \nBrighton, A., Herlin, T., et al., 1997, in {\\em Astronomical Data \nAnalysis Software and Systems VI}, ASP Conf. Ser. 125, p. 333 \n% Access to Data Sources and the ESO SkyCat Tool\n\n\\bibitem[1997]{xid-179}\nBartlett, J.G., Egret, D., 1997, in {\\em New Horizons \nfrom Multi-Wavelength Sky Surveys}, IAU Symp. 179, Kluwer Academic Publ.,\np. 437\n% Cross wavelength comparison of images and catalogues\n\n\\bibitem[1996]{1996A&AS..117..393B} Bertin, E., Arnouts, S. 1996, A\\&AS 117, 393\n% SExtractor\n\n\\bibitem[1995]{cds-amp2}\nEgret, D., Cr\\'ez\\'e, M. , Bonnarel, F., et al., 1995,\nin {\\em Information \\& On-line Data in Astronomy}, Egret \\& Albrecht \n(Eds.), Kluwer Academic Publ., p. 163\n% A global perspective on astronomical data and information:\n% the Strasbourg astronomical data centre (CDS)\n\n\\bibitem[1998]{astroglu} \nEgret, D., Fernique, P., Genova, F., 1998, \nin {\\em Astronomical Data\nAnalysis Software and Systems VII}, ASP Conf. Ser. 145, 416\n% AstroGlu: Prototype of a discovery tool \n\n\\bibitem[1998]{denis} Epchtein, N., 1998, in \\emph{The impact of near-infrared\nsurveys on galactic and extragalactic astronomy}, Proc. 3rd.\nEuroconf., Kluwer Academic Publ., ASSL 230, p. 3\n% The Deep Near Infrared Survey of the Southern Sky\n\n\\bibitem[1999]{denis-psc} Epchtein, N., Deul, E., Derriere, S., et al.,\n 1999, A\\&A 349, 236\n\n\\bibitem[1997]{tyc} ESA, 1997, The Hipparcos and Tycho Catalogues, ESA SP--1200\n\n\\bibitem[1998]{glu} Fernique, P., Ochsenbein, F., Wenger, M., 1998, \nin {\\em Astronomical Data\nAnalysis Software and Systems VII}, ASP Conf. Ser. 145, p. 466\n% CDS GLU\n\n\\bibitem[1994]{gspc2} Ferrari, A., Siciliano, E.D., Pizzuti, A.,\net al., 1994, in {\\it Astronomy from Wide-Field Imaging}, \nIAU symposium 161, H.T. MacGillivray \\& E.B. Thomson (Eds.), \nKluwer Academic Publ., p. 301\n% The GSPC-II Program\n\n\\bibitem[1996]{cds-hub} \nGenova, F., Bartlett, J.G., Bienaym\\'e, O., et al., 1996,\nVistas in Astronomy 40, 429\n% CDS as an Astronomical Information Hub \n\n\\bibitem[1998]{cds} Genova, F., Bartlett, J.G., Bonnarel, F., et al., \n1998, in {\\em Astronomical Data\nAnalysis Software and Systems VII}, ASP Conf. Ser. 145, p. 470\n% CDS information hub\n\n\\bibitem[2000]{cds2000} Genova, F., et al., 2000,\nA\\&AS, \\emph{in press}\n(CDS)\n% CDS, in this volume\n\n\\bibitem[1995]{wcs} Greisen, E.W., Calabretta, M., 1995, \nin {\\em Astronomical Data Analysis Software and Systems IV}, \nASP Conf. Ser. 77, p. 233 \n% Representations of Celestial Coordinates in FITS\n\n\\bibitem[1992]{MAMA} Guibert, J. 1992, in {\\it Digitized \nOptical Sky Surveys}, H.T. MacGillivray \\&\n E.B. Thomson (Eds.), Kluwer Academic Publ., p. 103 \n\n\\bibitem[1999]{astrobrowse} Heikkila, C.W., McGlynn, T.A., White, N.E., \n1999, in {\\em Astronomical Data Analysis Software and Systems VIII}, \nASP Conf. Ser. 172, p. 221\n% AstroBrowse {P5.6}\n\n\\bibitem[2000]{ned}\nHelou, G., Madore, B.F., Schmitz, M., et al., 2000,\nA\\&AS, \\emph{in press}\n(NED)\n% The NASA/IPAC Extragalactic Database\n\n\\bibitem[1998]{trc} H{\\o}g, E., Kuzmin, A., Bastian, U., et al., 1998, \nA\\&A 335, 65\n% Tycho Reference Catalogue\n\n\\bibitem[1988]{gspc1} Lasker, B.M., Sturch, C.R., Lopez, C., et al., \n1988, ApJS 68, 1\n% The Guide Star Photometric Catalog\n\n\\bibitem[1990]{gsc} Lasker, B.M., Sturch, C.R., McLean, B.J., et al., \n 1990, AJ 99, 2019\n% The Guide Star Catalog\n\n\\bibitem[1992]{dss} Lasker, B.M., 1992, in {\\it Digitized Optical\n Sky Surveys}, H.T. MacGillivray \\& E.B. Thomson (Eds.),\n Kluwer Academic Publ., p. 87\n% Digitized Sky Surveys at the STScI\n\n\\bibitem[1994]{dss-ii} Lasker, B.M., 1994, in {\\it Astronomy from Wide-Field\n Imaging}, IAU symposium 161, H.T. MacGillivray \\&\n E.B. Thomson (Eds.), Kluwer Academic Publ., p.167\n% DSS-II (Digitization Programs at STScI)\n\n\\bibitem[1999]{louys} Louys, M., Starck, J.-L., Mei, S.,\n Bonnarel, F., Murtagh, F., 1999, A\\&AS 136, 579\n\n\\bibitem[1994]{potsdam} \n MacGillivray, H.T., et al., Editors, 1994, {\\it Astronomy from \nWide-Field Imaging}, Postdam, Germany, Kluwer Academic Publ., pp. 1-760\n\n\\bibitem[1997]{skyview}\nMcGlynn, T., Scollick, K., White, N., 1997, in {\\em New Horizons\nfrom Multi-Wavelength Sky Surveys}, IAU Symp. 179, Kluwer Academic Publ.,\np. 465\n% SkyView: The Multi-Wavelength Sky on the Internet\n\n\\bibitem[1998]{usno} Monet, D., et al., 1998, {\\it The PMM USNO A2.0 Catalogue},\nUS Naval Observatory Flagstaff Station\n% The PMM USNO A2.0 Catalogue\n\n\\bibitem[1995]{1995adass...4..179M} Morrison, J. E., 1995, in\n{\\em Astronomical Data Analysis Software and Systems IV}, ASP \nConf. Ser. 77, p. 179 \n% Accessing the Digitized Sky Survey\n\n\\bibitem[2000]{vizier} Ochsenbein, F., Bauer, P.,\nGenova, F., 2000, A\\&AS, \\emph{in press}\n(VizieR)\n% VizieR\n\n\\bibitem[1999]{ortiz} Ortiz, P., Ochsenbein, F., Wicenec, A.,\nAlbrecht, M., 1999, in {\\em Astronomical Data\nAnalysis Software and Systems VIII}, ASP Conf. Ser., 172, 379\n% ESO/CDS Data-mining Tool Development Project\n\n\\bibitem[1994]{paillou} Paillou, Ph., Bonnarel, F., Ochsenbein, F., \nCr\\'ez\\'e, M., 1994, in {\\it Astronomy from Wide-Field\nImaging}, IAU symposium 161, H.T. MacGillivray and\nE.B. Thomson (Eds.), Kluwer Academic Publ., p. 347\n\n\\bibitem[1998]{2mass} Skrutskie, M., 1998, in ``The impact \nof near-infrared surveys on galactic and extragalactic astronomy'', Proc. 3rd.\nEuroconf., Kluwer Academic Publ., ASSL 230, 11\n% general reference to the 2mass project\n\n\\bibitem[1996]{pmt} Starck, J.-L., Murtagh, F., Pirenne, B.,\nAlbrecht, M., 1996, PASP 108, 446\n% PMT algorithm\n\n\\bibitem[2000]{simbad} Wenger, M., Ochsenbein, F., Egret, D., et al.,\n2000, A\\&AS, \\emph{in press} \n(Simbad)\n% Simbad\n\n\\end{thebibliography}\n\n%\\listofobjects\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002109.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[1997]{skycat} Albrecht, M. A., \nBrighton, A., Herlin, T., et al., 1997, in {\\em Astronomical Data \nAnalysis Software and Systems VI}, ASP Conf. Ser. 125, p. 333 \n% Access to Data Sources and the ESO SkyCat Tool\n\n\\bibitem[1997]{xid-179}\nBartlett, J.G., Egret, D., 1997, in {\\em New Horizons \nfrom Multi-Wavelength Sky Surveys}, IAU Symp. 179, Kluwer Academic Publ.,\np. 437\n% Cross wavelength comparison of images and catalogues\n\n\\bibitem[1996]{1996A&AS..117..393B} Bertin, E., Arnouts, S. 1996, A\\&AS 117, 393\n% SExtractor\n\n\\bibitem[1995]{cds-amp2}\nEgret, D., Cr\\'ez\\'e, M. , Bonnarel, F., et al., 1995,\nin {\\em Information \\& On-line Data in Astronomy}, Egret \\& Albrecht \n(Eds.), Kluwer Academic Publ., p. 163\n% A global perspective on astronomical data and information:\n% the Strasbourg astronomical data centre (CDS)\n\n\\bibitem[1998]{astroglu} \nEgret, D., Fernique, P., Genova, F., 1998, \nin {\\em Astronomical Data\nAnalysis Software and Systems VII}, ASP Conf. Ser. 145, 416\n% AstroGlu: Prototype of a discovery tool \n\n\\bibitem[1998]{denis} Epchtein, N., 1998, in \\emph{The impact of near-infrared\nsurveys on galactic and extragalactic astronomy}, Proc. 3rd.\nEuroconf., Kluwer Academic Publ., ASSL 230, p. 3\n% The Deep Near Infrared Survey of the Southern Sky\n\n\\bibitem[1999]{denis-psc} Epchtein, N., Deul, E., Derriere, S., et al.,\n 1999, A\\&A 349, 236\n\n\\bibitem[1997]{tyc} ESA, 1997, The Hipparcos and Tycho Catalogues, ESA SP--1200\n\n\\bibitem[1998]{glu} Fernique, P., Ochsenbein, F., Wenger, M., 1998, \nin {\\em Astronomical Data\nAnalysis Software and Systems VII}, ASP Conf. Ser. 145, p. 466\n% CDS GLU\n\n\\bibitem[1994]{gspc2} Ferrari, A., Siciliano, E.D., Pizzuti, A.,\net al., 1994, in {\\it Astronomy from Wide-Field Imaging}, \nIAU symposium 161, H.T. MacGillivray \\& E.B. Thomson (Eds.), \nKluwer Academic Publ., p. 301\n% The GSPC-II Program\n\n\\bibitem[1996]{cds-hub} \nGenova, F., Bartlett, J.G., Bienaym\\'e, O., et al., 1996,\nVistas in Astronomy 40, 429\n% CDS as an Astronomical Information Hub \n\n\\bibitem[1998]{cds} Genova, F., Bartlett, J.G., Bonnarel, F., et al., \n1998, in {\\em Astronomical Data\nAnalysis Software and Systems VII}, ASP Conf. Ser. 145, p. 470\n% CDS information hub\n\n\\bibitem[2000]{cds2000} Genova, F., et al., 2000,\nA\\&AS, \\emph{in press}\n(CDS)\n% CDS, in this volume\n\n\\bibitem[1995]{wcs} Greisen, E.W., Calabretta, M., 1995, \nin {\\em Astronomical Data Analysis Software and Systems IV}, \nASP Conf. Ser. 77, p. 233 \n% Representations of Celestial Coordinates in FITS\n\n\\bibitem[1992]{MAMA} Guibert, J. 1992, in {\\it Digitized \nOptical Sky Surveys}, H.T. MacGillivray \\&\n E.B. Thomson (Eds.), Kluwer Academic Publ., p. 103 \n\n\\bibitem[1999]{astrobrowse} Heikkila, C.W., McGlynn, T.A., White, N.E., \n1999, in {\\em Astronomical Data Analysis Software and Systems VIII}, \nASP Conf. Ser. 172, p. 221\n% AstroBrowse {P5.6}\n\n\\bibitem[2000]{ned}\nHelou, G., Madore, B.F., Schmitz, M., et al., 2000,\nA\\&AS, \\emph{in press}\n(NED)\n% The NASA/IPAC Extragalactic Database\n\n\\bibitem[1998]{trc} H{\\o}g, E., Kuzmin, A., Bastian, U., et al., 1998, \nA\\&A 335, 65\n% Tycho Reference Catalogue\n\n\\bibitem[1988]{gspc1} Lasker, B.M., Sturch, C.R., Lopez, C., et al., \n1988, ApJS 68, 1\n% The Guide Star Photometric Catalog\n\n\\bibitem[1990]{gsc} Lasker, B.M., Sturch, C.R., McLean, B.J., et al., \n 1990, AJ 99, 2019\n% The Guide Star Catalog\n\n\\bibitem[1992]{dss} Lasker, B.M., 1992, in {\\it Digitized Optical\n Sky Surveys}, H.T. MacGillivray \\& E.B. Thomson (Eds.),\n Kluwer Academic Publ., p. 87\n% Digitized Sky Surveys at the STScI\n\n\\bibitem[1994]{dss-ii} Lasker, B.M., 1994, in {\\it Astronomy from Wide-Field\n Imaging}, IAU symposium 161, H.T. MacGillivray \\&\n E.B. Thomson (Eds.), Kluwer Academic Publ., p.167\n% DSS-II (Digitization Programs at STScI)\n\n\\bibitem[1999]{louys} Louys, M., Starck, J.-L., Mei, S.,\n Bonnarel, F., Murtagh, F., 1999, A\\&AS 136, 579\n\n\\bibitem[1994]{potsdam} \n MacGillivray, H.T., et al., Editors, 1994, {\\it Astronomy from \nWide-Field Imaging}, Postdam, Germany, Kluwer Academic Publ., pp. 1-760\n\n\\bibitem[1997]{skyview}\nMcGlynn, T., Scollick, K., White, N., 1997, in {\\em New Horizons\nfrom Multi-Wavelength Sky Surveys}, IAU Symp. 179, Kluwer Academic Publ.,\np. 465\n% SkyView: The Multi-Wavelength Sky on the Internet\n\n\\bibitem[1998]{usno} Monet, D., et al., 1998, {\\it The PMM USNO A2.0 Catalogue},\nUS Naval Observatory Flagstaff Station\n% The PMM USNO A2.0 Catalogue\n\n\\bibitem[1995]{1995adass...4..179M} Morrison, J. E., 1995, in\n{\\em Astronomical Data Analysis Software and Systems IV}, ASP \nConf. Ser. 77, p. 179 \n% Accessing the Digitized Sky Survey\n\n\\bibitem[2000]{vizier} Ochsenbein, F., Bauer, P.,\nGenova, F., 2000, A\\&AS, \\emph{in press}\n(VizieR)\n% VizieR\n\n\\bibitem[1999]{ortiz} Ortiz, P., Ochsenbein, F., Wicenec, A.,\nAlbrecht, M., 1999, in {\\em Astronomical Data\nAnalysis Software and Systems VIII}, ASP Conf. Ser., 172, 379\n% ESO/CDS Data-mining Tool Development Project\n\n\\bibitem[1994]{paillou} Paillou, Ph., Bonnarel, F., Ochsenbein, F., \nCr\\'ez\\'e, M., 1994, in {\\it Astronomy from Wide-Field\nImaging}, IAU symposium 161, H.T. MacGillivray and\nE.B. Thomson (Eds.), Kluwer Academic Publ., p. 347\n\n\\bibitem[1998]{2mass} Skrutskie, M., 1998, in ``The impact \nof near-infrared surveys on galactic and extragalactic astronomy'', Proc. 3rd.\nEuroconf., Kluwer Academic Publ., ASSL 230, 11\n% general reference to the 2mass project\n\n\\bibitem[1996]{pmt} Starck, J.-L., Murtagh, F., Pirenne, B.,\nAlbrecht, M., 1996, PASP 108, 446\n% PMT algorithm\n\n\\bibitem[2000]{simbad} Wenger, M., Ochsenbein, F., Egret, D., et al.,\n2000, A\\&AS, \\emph{in press} \n(Simbad)\n% Simbad\n\n\\end{thebibliography}"
}
] |
astro-ph0002110
|
The SIMBAD astronomical database
|
[
{
"author": "Marc Wenger"
},
{
"author": "Fran\\c{c}ois Ochsenbein"
},
{
"author": "Daniel Egret"
},
{
"author": "Pascal Dubois"
},
{
"author": "Fran\\c{c}ois Bonnarel"
},
{
"author": "Suzanne Borde\\thanks{DASGAL, Observatoire de Paris}"
},
{
"author": "Fran\\c{c}oise Genova"
},
{
"author": "G\\'erard Jasniewicz\\thanks{Groupe de Recherche en Astronomie et Astrophysique du Languedoc (GRAAL), Montpellier}"
},
{
"author": "Suzanne Lalo\\\"e"
},
{
"author": "Soizick Lesteven"
},
{
"author": "Richard Monier"
}
] |
{\sc Simbad} is the reference database for identification and bibliography of astronomical objects. It contains identifications, `basic data', bibliography, and selected observational measurements for several million astronomical objects. {\sc Simbad} is developed and maintained by CDS, Strasbourg. Building the database contents is achieved with the help of several contributing institutes. Scanning the bibliography is the result of the collaboration of CDS with bibliographers in Observatoire de Paris (DASGAL), Institut d'Astrophysique de Paris, and Observatoire de Bordeaux. When selecting catalogues and tables for inclusion, priority is given to optimal multi-wavelength coverage of the database, and to support of research developments linked to large projects. In parallel, the systematic scanning of the bibliography reflects the diversity and general trends of astronomical research. A WWW interface to {\sc Simbad} is available at: {http://simbad.u-strasbg.fr/Simbad}. \keywords{Astronomical data bases: miscellaneous -- Catalogs}
|
[
{
"name": "simbad.tex",
"string": "%\n%\\documentclass[referee]{aa} % for a referee version\n\\documentclass{aa}\n%\n\\usepackage{graphics}\n%\\usepackage{times}\n\n\\begin{document}\n\n \\thesaurus{23 % A&A Section 6: Form. struct. and evolut. of stars\n (04.01.1; % Astronomical data bases: miscellaneous \n 04.03.1)} % Catalogs.\n%\n \\title{The SIMBAD astronomical database}\n\n \\subtitle{The CDS Reference Database for Astronomical Objects}\n\n\\author{\n Marc Wenger\n\\and\n Fran\\c{c}ois Ochsenbein\n\\and\n Daniel Egret\n\\and\n Pascal Dubois\n\\and\n Fran\\c{c}ois Bonnarel\n\\and\n Suzanne Borde\\thanks{DASGAL, Observatoire de Paris}\n\\and\n Fran\\c{c}oise Genova\n\\and\n G\\'erard Jasniewicz\\thanks{Groupe de Recherche\n en Astronomie et Astrophysique du Languedoc (GRAAL), Montpellier}\n\\and\n Suzanne Lalo\\\"e\n\\and\n Soizick Lesteven\n\\and\n Richard Monier\n }\n\n \\offprints{Daniel Egret}\n \\mail{question@simbad.u-strasbg.fr}\n\n \\institute{CDS, Observatoire astronomique de Strasbourg, UMR 7550,\n11 rue de l'Universit\\'e, F-67000 Strasbourg, France}\n\n \\date{Received 6 December 1999 / Accepted 16 December 1999}\n\n\\maketitle\n\n \\begin{abstract}\n{\\sc Simbad} is the reference database for identification and\nbibliography of astronomical objects. It contains identifications,\n`basic data', bibliography, and selected observational\nmeasurements for several\nmillion astronomical objects. \n\n{\\sc Simbad} is developed and maintained by CDS, Strasbourg.\nBuilding the database contents is achieved\nwith the help of several contributing institutes. Scanning\nthe bibliography is the\nresult of the collaboration of CDS with bibliographers\nin \nObservatoire de Paris (DASGAL), \nInstitut d'Astrophysique de Paris,\nand Observatoire de Bordeaux.\n\n\nWhen selecting catalogues and tables for inclusion,\npriority is given to optimal\nmulti-wavelength coverage of the database, and to\nsupport of research developments \nlinked to large projects.\nIn parallel, the systematic scanning of the\nbibliography reflects the diversity and general \ntrends of astronomical research.\n\n A WWW interface to {\\sc Simbad} is available at:\n\n{http://simbad.u-strasbg.fr/Simbad}.\n\n\\keywords{Astronomical data bases: miscellaneous -- Catalogs}\n\n\\end{abstract}\n\n%\n%________________________________________________________________\n\n\\section{Introduction}\n\n\\subsection{The CDS}\nThe Centre de Donn\\'ees astronomiques de Strasbourg\n(CDS) defines, develops, and maintains services \nto help the astronomers find the information\nthey need from the\nvery rapidly increasing wealth of astronomical information, and\nparticularly of on-line information. \n\nCDS is operated at the Strasbourg astronomical\nObservatory, under an agreement between French\nInstitut National des Sciences de l'Univers (INSU) and\nUniversit\\'e Louis Pasteur, Strasbourg (ULP). CDS personnel\ncreated and implemented the {\\sc Simbad} data bank and maintain its data\nand software system. \n\nA detailed description of the CDS on-line services can be found, e.g., \nin Egret et al.\\ (\\cite{cds-amp2})\nand in Genova et al.\\ (\\cite{cds-hub}, \\cite{cds}, \\cite{cds2000}), \nor at the CDS web site\\footnote{{\\em Internet address:}\nhttp://cdsweb.u-strasbg.fr/}. \n Questions or comments about the\nCDS services can be sent to the hot line {\\it\nquestion@simbad.u-strasbg.fr}.\n\n\\subsection{SIMBAD}\n \nThe {\\sc Simbad} database contains identifications,\n`basic data', bibliographical references,\nand selected observational measurements for more than\n2.7 million astronomical objects (November 1999).\nData and information published in {\\sc Simbad}\ncome from selected catalogues and tables\nand from the whole astronomical literature.\n\nThe specificity of the {\\sc Simbad} database is to\norganize the information per astronomical object,\nthus offering a unique perspective on astronomical data.\nThis is done through a careful cross-identification \nof objects from catalogues, lists, and journal articles.\nThe ability to gather together any sort of published\nobservational data related to stars or galaxies has \nmade {\\sc Simbad} a key tool used worldwide for all kinds \nof astronomical studies.\n\n\n{\\sc Simbad} is the acronym for {\\sl S}et of\n {\\sl I}dentifications, \n {\\sl M}easurements\n and {\\sl B}ibliography\n for {\\sl A}stronomical\n {\\sl D}ata.\n \nThe main access point to {\\sc Simbad} \nis the WWW home page\\footnote{http://simbad.u-strasbg.fr/Simbad};\nthere is a mirror copy at SAO, \nHarvard\\footnote{http://simbad.harvard.edu/Simbad}.\n\n\\subsection{Historical background}\n\nBuilding a reference database for stars -- and, later, for\nextragalactic objects and all astronomical objects outside\nthe Solar System -- has been the first goal of the CDS: {\\sc Simbad}\nis the result of an on-going effort which started soon after\nthe creation of CDS in 1972.\n{\\sc Simbad} was created by merging the Catalog of Stellar Identifications\n(CSI, Ochsenbein et al.\\ \\cite{csi}) and the Bibliographic Star Index \n(Ochsenbein \\cite{bsi})\nas they existed until 1979. The resulting data base \n(at that time, about 400,000 objects, mainly stars) was then\nexpanded by the addition of source data from the catalogs and\ntables, and by new literature references. \nThe database was extended to galaxies\nand other non-stellar objects in 1983 (Dubois et al. \\cite{dubois83}).\nFor details about the early developments of {\\sc Simbad} see\nEgret (\\cite{story}).\n \nThe first on-line interactive version\nof {\\sc Simbad} was released in 1981, and operated \nat the Strasbourg Cronenbourg computer\ncenter until December 1984, \nwhen it was moved to Universit\\'e Paris-Sud at\nOrsay, and operated there until June 30, 1990. \nThe database is now hosted on a \nUnix server, at the Strasbourg Observatory. \n \nThe original command line interface has been complemented by\nan interactive X-Window interface ({\\sc XSimbad}) in 1994,\nand by a World-Wide Web interface in 1996.\nThere is also a client/server mode, providing quick responses\nto simple queries, essentially for the name resolution in\narchives and information systems (see Section~\\ref{interface}).\n\n%%%%%%\nFor descriptions of earlier stages of the database, \nsee Heck \\& Egret (\\cite{messenger}), and Egret et al.\\\n(\\cite{ampersand}).\n\n\n\\section{SIMBAD main features}\n\n {\\sc Simbad} is, in the first place, a database of identifications,\naliases and names of astronomical objects: in principle any name\nfound in the literature -- provided it is given as a\nsyntactically correct character string -- can be submitted\nto {\\sc Simbad} in order to\nretrieve basic information known for this object,\nas well as pointers to complementary data and bibliography.\nThis implies a continuous careful cross-identification \nof objects from catalogues, lists, and journal articles.\nThis ability to gather together any sort of published\nobservational data related to stars or galaxies is\nthe first key feature of {\\sc Simbad}.\n\nAnother unique feature is the complete and up-to-date\nbibliographic survey of the astronomical literature:\nobjects are associated with the references of all\npapers in which they are mentioned, independently of the\naliases used to name the object.\n\nIn addition, the Dictionary of Nomenclature \n(Section \\ref{Dic}) \nis an essential tool for managing the very complex nomenclature\nof objects found in the literature, and for matching\nnaming variations with those adopted or simply accepted by\n{\\sc Simbad}. It also includes hints for helping to solve ambiguities, \naccording to the type of object, or to the format.\nThis is complemented by the {\\em sesame} module \nwithin {\\sc Simbad},\nfor the management of possible variations in the\nnaming of astronomical objects.\n\n\nThe database management system of {\\sc Simbad}\n(Section \\ref{dbms}) has been developed \nin-house at CDS, using\nthe concepts of object-oriented programming. \n\n{\\sc Simbad} is kept up-to-date (Section \\ref{update})\non a daily basis, as the\nresult of the collaboration of CDS with bibliographers\nin Institut d'Astrophysique de Paris and the\nParis and Bordeaux observatories.\n\n\nThe statistical contents of the database \n(Section~\\ref{stats}) can be summarized \nin a few figures as follows\n(the figures quoted are statistics of November 1999): \n\\begin{itemize}\n\\item \tentries for about 2.7 million astronomical \nobjects (stars, galaxies and all astronomical objects \noutside the solar system);\n\\item \ta cross-index of 7.5 million identifiers\nrelated to 4500 astronomical catalogues and tables,\nlists, and observation logs of space missions;\n\\item \tobservational data from some 25 different \ntypes of data catalogues and compilations;\n\\item a bibliographic survey covering the astronomical \nliterature since 1950 for stars, and since 1983 for \nextragalactic objects: more than 3 million citations from\n110,000 different papers.\n\\end{itemize}\n\n\n\n\n\\section{SIMBAD astronomical contents}\n\\label{stats}\n\n\\subsection{The objects}\n \nThe {\\sc Simbad} data base presently contains information for about:\n \n\\begin{itemize}\n \\item 1,500,000 stars; \n \\item 450,000 galaxies;\n \\item 100,000 other non-stellar objects (planetary nebulae, \n clusters, \\ion{H}{ii} regions, etc.);\n \\item and some 650,000 additional objects observed at various\n wavelengths (Radio, IR, X), and for which \n classification is not yet assigned.\n\\end{itemize}\n \nThe only astronomical objects\nspecifically excluded from {\\sc Simbad} are the Sun and\nSolar System bodies.\n \n\n\nThe {\\sc Simbad} database is primarily organized per astronomical object.\nThe aim is to provide, as much as possible, the user \nwith all published information \n(identifications, observational\ndata, bibliographical references, and pointers towards\nexternal archives) concerning any given object, or list \nof objects.\n\nThe two main channels for feeding the database are the following:\n\\begin{itemize}\n\\item the daily scanning of papers published in the astronomical \nliterature provides new references and new identifiers for existing objects, \nas well as opportunities to create new objects, \nusing the basic data possibly given in the article;\n\\item the complete (or partial) folding of selected catalogues \ninto the database serves as a basis for improving the \ncompleteness and multi-wavelength coverage of the database.\n \\end{itemize}\n\nCatalogues are selected for integration with\npriority given to those which can\nhelp provide an optimal support for \nthe large projects conducted within the astronomical community.\nA large effort was, for instance, devoted in recent years to stellar\ncatalogues (PPM, HIC, CCDM), in the context of the Hipparcos project,\nand to multi-wavelength identifications (IRAS PSC, Einstein 1E and\n2E catalogues, older X--ray catalogues, the IUE Merged Log, etc.). \nThe Hipparcos and Tycho catalogues (ESA \\cite{tyc})\nhave been recently included, and inclusion of the ROSAT All\nSky Survey is planned in the near future.\n\nIn parallel, the systematic scanning of the\nbibliography reflects the diversity and general trends of research\nin astronomy, and takes into account shorter lists. The published lists\nfrom the microlensing surveys, or e.g. the EUVE catalogues, were folded\ninto the database as a result of this scanning.\n\nWhen an object is\nfound in the literature or in a catalogue, its possible\ncross-identification with objects already in {\\sc Simbad} is\nsystematically studied, before entering the reference \nand the new object name in the database. \nAbout 4500 different names of\ncatalogues or object lists from published papers can \ncurrently be found in {\\sc Simbad},\ncovering all the wavelength domains from high energy astrophysics to\nradio. \n\nWhen no proper name is suggested by the authors, or \nwhen the acronym generates an ambiguity with already existing ones, \nthe current practice, shared with the NED database, is to create\nan acronym within brackets using the initials of the last names\nof the first three authors, and the year of publication.\nFor example, [HFE83] 366 is the 366th entry in the main table \nof a paper by Helmer, Fabricius, Einicke and colleagues published in 1983.\nFrom the year 2000 on, the year will be noted with four digits (e.g.,\n[ABC2000]).\n\nMany objects have more than one name, since the database\ncontains more than 7.5 million object names for \n2.7 million objects. \nExamples of objects with more than 50 identifiers,\nare the galaxy \\object{M 87} in Virgo, the bright stars \n\\object{Procyon} and \\object{Capella},\nthe quasar \\object{3C 273}, the \\object{Crab Nebula}.\n\nTo help the users with the complex nomenclature\nof astronomical objects, the CDS now maintains\n and distributes on--line\nthe Dictionary of Nomenclature of Celestial Objects \n(first developed by Lortet et al.\\ \\cite{dic2}; see \nSection~\\ref{Dic}). \n\n\n\n\\subsection{The Data}\n\n In the following, the word {\\em object\\/} will be used\nto designate a star, non stellar object, or collection of\nobjects such as a cluster, which corresponds to an individual\nentry in {\\sc Simbad}. \nFor each object, the following data are included when available:\n \n\\begin{itemize}\n \n\\item Basic data:\n \n \\begin{description}\n \\item[stars]: object type, coordinates, proper motion, \n $B$ and $V$ magnitudes, spectral type, parallax, radial velocity;\n \\item[galaxies]: object type, coordinates, blue and visual \n integrated magnitudes,\n morphological type, dimension, radial velocity or redshift.\n \\item[other]: object type, position, $B$ and $V$ magnitudes.\n\\end{description}\n \n \\item Cross-identifications from some 4500 catalogues \nand tables, either\ncompletely or partially included in the data base. \n \n \\item Observational data (also called {\\em\nmeasurements\\/}), for some 25 data types. \nA list of these types is given in the Table~\\ref{measurements}.\n\n \\item General bibliography,\nincluding references to all published papers since 1983\nciting the object under any of its designations.\nFor stars, the bibliography starts as early as 1950, but\nwith a smaller coverage of the literature. \n{\\sc Simbad} also includes a few hundred references before 1950,\nbut without any systematic trend.\nThe bibliography gives\naccess to abstracts and electronic articles when\navailable (either directly from publishers, or through ADS).\nCurrently about 100 journals\ncovering the complete astronomical literature are \nregularly scanned.\nA complete list is available \non line\\footnote{http://simbad.u-strasbg.fr/guide/chH.htx}.\n \n\\end{itemize}\n\nIn the following, a more detailed description of\nsome of these elements is given.\n\n\\subsubsection{Object type}\n\nThe object type refers to a\nhierarchical classification of the objects in {\\sc Simbad},\nderived by the CDS team on the basis of\nthe catalogue identifiers (as proposed by Ochsenbein\nand Dubois \\cite{type}).\nFrom {\\em Star} to {\\em Maser source}, or {\\em Cluster of Galaxies},\nsome 70 different categories, general, or very specific, are\nproposed (see examples in Table~\\ref{object-type}).\nA complete list is available \non line\\footnote{http://simbad.u-strasbg.fr/guide/chF.htx}.\n\nThis classification is intended to help the user select objects\nout of the database\n(e.g.\\ through the filter procedure, see Section~\\ref{filter}). \nIt is also a powerful tool for data cross--checking\nand quality control.\nIt has been designed to be practical and useful,\nand complements other features also available in {\\sc Simbad} \n(morphological type or spectral type information, catalogues, and\nmeasurements).\n%%%%%\nIt can follow the evolution of astronomy,\nwith the introduction of new categories recently\nappeared in the literature (e.g., in the last years,\nLow-Mass or High-Mass X-Ray binary, Microlensing event, or\nVoid).\n\nEach class has normally a standard designation, a condensed one (used in\n tables) and an extended explanation.\nThe classification uses a hierarchy with four levels, reflecting\nour knowledge of the characteristics of the astronomical object.\nFor instance, an object can be classified as a ``Star'' (this is\nlevel 1). If photometric observations have shown variability\nof the object, it can be classified as a ``Variable star'' (this\nis level 2). Examples of level 3 and 4 are ``Pulsating variable'',\nand ``Cepheid''.\n\nThis hierarchy of object types (and their possible synonyms) \nis managed\nin the database in such a way that selecting variable stars \n({\\tt V*})\nis understood as selecting objects classified\nas {\\tt V*}, and all subdivisions (e.g. {\\tt PulsV*}, {\\tt Mira},\n{\\tt Cepheid}, etc.). \nIf the user is only interested in RR Lyrae type stars, he/she will\nuse the {\\tt RRLyr} type, leaving aside all other variable stars\nfor which the variability mode is different, or not known.\n\nThe classification emphasizes the physical nature of the object\nrather than a peculiar emission in some region of the\nelectromagnetic spectrum or the location in peculiar \nclusters or external galaxies.\nTherefore objects are classified as peculiar emitters \nin a given wavelength (such as UV or IR source)\nonly if nothing more about the nature of the object is known, \ni.e. it cannot be decided on the sole basis\nof the basic data whether the object is a star, \na multiple system, a nebula, or a galaxy. \nFor instance, if an object appears only in the\nIRAS catalogue, it is automatically\nclassified as IR object: it is left\nto the user to decide to go further\nand to derive, e.g. on the basis of the\nIRAS colors, the probability for the source to be stellar\nor extragalactic.\n\n\n\\begin{table}\n\\caption{Object type classification: extracts from the object type table\n illustrating examples of the four levels of the classification scheme}\n\\footnotesize\n\\begin{tabular}{lllp{4cm}}\n\\hline \n Level & Standard & Short & Extended Explanation \\\\\n & name & name & \\\\\n\\hline\n \\dots \\\\\n1 & Star & * & Star \\\\ \n2 & *inCl & *iC & Star in Cluster \\\\\n2 & *inNeb & *iN & Star in Nebula \\\\\n2 & *inAssoc & *iA & Star in Association \\\\\n2 & *in** & *i* & Star in double system \\\\\n2 & V*? & V*? & Star suspected of Variability \\\\\n2 & Pec* & Pe* & Peculiar Star \\\\\n3 & HB* & HB* & Horizontal Branch Star \\\\\n3 & YSO & Y*O & Young Stellar Object \\\\\n3 & Em* & Em* & Emission-line Star \\\\\n4 & Be* & Be* & Be Star \\\\\n \\dots \\\\\n1 & Galaxy & G & Galaxy \\\\\n2 & PartofG & PoG & Part of a Galaxy \\\\\n2 & GinCl & GiC & Galaxy in Cluster of Galaxies \\\\\n2 & GinGroup & GiG & Galaxy in Group of Galaxies \\\\\n2 & GinPair & GiP & Galaxy in Pair of Galaxies \\\\\n2 & High\\_z\\_G & HzG & Galaxy with high redshift \\\\\n \\dots \\\\\n2 & AGN & AGN & Active Galaxy Nucleus \\\\\n3 & LINER & LIN & LINER-type Active Galaxy Nucleus \\\\\n3 & Seyfert & SyG & Seyfert Galaxy \\\\\n4 & Seyfert\\_1 & Sy1 & Seyfert 1 Galaxy \\\\\n4 & Seyfert\\_2 & Sy2 & Seyfert 2 Galaxy \\\\\n3 & Blazar & Bla & Blazar \\\\\n4 & BLLac & BLL & BL Lac - type object \\\\\n4 & OVV & OVV & Optically Violently Variable \\\\\n3 & QSO & QSO & Quasar \\\\\n\\hline\n\\end{tabular}\n\\label{object-type}\n\\end{table}\n\nBecause there is at most one object type per object, this\nclassification should be used with caution when \nextracting samples out of the database.\nThis is typically the case for the wavelength types: using IR\nor X as a criterion cannot generate a sample of all IRAS\nsources, or all X-ray emitting objects, since a number \nof them are in fact classified as stars, galaxies, etc.\n\n\n\\subsubsection{Coordinates, Proper motion, Parallax,\n and Radial Velocity\n or Redshift}\n\nThe coordinates were originally stored in the database\nin the FK4 system for equinox and epoch 1950.0. \n%%%%%%%%%%\nA major change was undergone in 1999, \nwhen they were moved to the \nInternational Celestial Reference System (ICRS, see\nFeissel \\& Mignard \\cite{ICRS}) at epoch 2000.0, after the publication\nof the Hipparcos and Tycho catalogues. \nThe position data frame has become more complex, grouping together all\ndata needed for computing the coordinates into any reference frame, \nat any epoch and equinox: the coordinates themselves, the\nproper motion, the parallax and the radial velocity or\nredshift.\n\nAll these data contain the same subfields: the original data,\ndisplayed with a number of digits consistent with the announced\nprecision of the data; a quality code from 'A' (reference data)\nto 'E' (unreliable origin); an error box (either a standard\nerror, or an ellipse), and the bibliographic reference of the\ndata.\n\nIn earlier versions of {\\sc Simbad}, the determination of the position for\nanother equinox used to take only precession into account.\nIn the current version, a change of equinox takes into account not only \nthe precession but also the proper motion, the reference frame (FK4, FK5, \nICRS), and, when they are known, the parallax and radial\nvelocity. When no epoch is specified, the year of the equinox\nis used by default.\n\nData come from various sources. When astrometric data are \navailable, the most accurate\none has been selected for the 'basic data'. \nOther values may \nbe available as measurements (in the {\\tt pos} type). The Hipparcos and\nTycho catalogues (ESA \\cite{tyc}) constitute the major source of positions for\nstars.\n\nThe coordinates precision may vary from $1\\degr$ to $1/10$ mas. \nThe default display format provides equatorial coordinates in the ICRS\nsystem at epoch 2000.0, and in the FK5 system at equinoxes 2000 and\n1950, as well as galactic coordinates. Coordinates in the FK4 system,\nand ecliptic or super-galactic coordinates can be computed on request.\n\nThe proper motions ($\\mu_\\alpha \\cos\\delta, \\mu_\\delta$) are given in\nmas/year, together with their standard errors (in mas/year).\nThe primary source of proper motions is the Hipparcos and Tycho\ncatalogues (ESA \\cite{tyc}).\n\nThe errors for positions or proper motions \nare expressed as error ellipses, made of three\nnumbers, within brackets: the major axis, the minor axis,\nand the position angle of the major axis\n(measured from North to East).\nMajor and minor axes are expressed in mas for the position,\nand mas/yr for the proper motion;\nthe position angle is expressed in degrees,\nin the range $[0\\degr,180\\degr[$.\n\nWhen available, the stellar parallax is given in mas,\ntogether with the associated error within brackets.\nThe primary source is the Hipparcos\nand Tycho catalogues (ESA \\cite{tyc}).\n\nRadial velocity (in km/s), or redshift (for extragalactic objects)\nare currently available for some 160,000 objects.\nThey are stored in their original type (either redshift,\nor radial velocity in km/sec), associated with the standard error. \nDisplay can be done in the original type or forced to be one of the\ntwo types, using the corresponding translation formula.\n\nStellar radial velocity data\nhave been compiled with the collaboration\nof Observatoire de Marseille.\n\nFor extragalactic objects, up-to-date redshift information has \nrecently been imported from the NASA/IPAC Extragalactic Database\n(NED, Helou et al. \\cite{ned}) as a result\nof the ongoing exchange agreement:\nthe {\\sc Simbad} team is providing NED with bibliographic coverage \nof extragalactic objects for all astronomical journals, \nand is being given access, in return, to extragalactic \ndata collected by NED.\n\nTables from individual articles constitute\nthe other major source of information.\n\n\\subsubsection{Magnitudes}\n\n$B$ and $V$ magnitudes are given, when\npossible, in the Johnson's $UBV$ system. Both magnitudes\nmay be followed by a semicolon meaning they cannot be\nmade homogeneous to the $UBV$ system. \nIn addition the following flags may appear: \n\\begin{itemize} \n\\item a `D' flags a joint magnitude in a double or\nmultiple system; \n\\item a `V' indicates a variable magnitude and is\nfollowed by a coded index giving a rough estimate of the\namplitude:\n\n $$\\begin{tabular}{c l} \\hline\n code & definition \\\\ \\hline\n 1 & 1/100 mag. \\\\\n 2 & 1/10 mag. \\\\\n 3 & 1 mag. \\\\\n 4 & more than 1 mag. \\\\\n ? & suspected variable \\\\ \\hline\n \\end{tabular}$$\n\\end{itemize}\n\nWhen possible the magnitudes have been taken from the\nTycho Reference Catalogue (H{\\o}g et al.\\ \\cite{TRC})\nwhere $B$ and $V$ magnitudes are derived from\nthe original $B_T$ and $V_T$.\nAnother major source is the\n$UBV$ compilation of Mermilliod (\\cite{UBV}). \nOtherwise the data would come from one of the published papers\nassociated to the object.\n\n\n\\subsubsection{Stellar Spectral type}\n\nThe spectral types of stars have been selected \npreferably in the\nMichigan Catalogues of Two-Dimensional Spectral Types for\nthe HD stars (Houk \\cite{mss}, and seq.), or in the\nbibliographical surveys of MK classifications (Jaschek\n\\cite{MK-MJ}).\nIn the absence of a full MK classification, the HD\nspectral type is recorded.\n\n Most of the spectral types need\nless than 5 characters, but this field can be as long as 36\ncharacters. \n\n\n\n\n\\subsubsection{Morphological type and Dimension of galaxy}\n \n\nThe morphological types of galaxies have been \nselected primarily\nfrom the Uppsala General Catalogue of Galaxies (UGC, Nilson \\cite{ugc}), \nthe Morphological Catalogue of Galaxies\n(MCG, Vorontsov-Velyaminov, \\cite{mcg}), and other\ncatalogues (see Dubois et al.\\ \\cite{dubois83}).\n\nIn complement, the following data, primarily from UGC,\nare given, when available, for\ngalaxies:\n\n$$\\begin{tabular}{lp{6cm}}\n$ \\log D_{25}$ & logarithm of the major axis $a$\nexpressed in tenths of arc minutes; \\\\\n$ \\log R_{25}$ & logarithm of the ratio $a/b$\nwhere $a$ and $b$ are the major and minor axis; \\\\\norientation & orientation angle (in degrees) \\\\\n(inclination) & inclination (in units of $15\\degr$\nfrom 0 to 7) \\\\\n\\end{tabular}$$\n\n\n\\subsection{Cross--identifications}\n\n\\subsubsection{Aliases}\n\nCross--identifications of stars and galaxies have been\nsearched for {\\sc Simbad} entries from (currently) about 4500 source\ncatalogues and tables, included, either completely or partially, in\nthe data base.\nThe index of 7.5 million {\\em aliases\\/}, thus constituted, is one of\nthe unique features of the {\\sc Simbad} database.\n\nAliases may serve as entry points for related catalogues\nand tables (e.g. in {\\sc VizieR}). \nCross-fertilization of a given research with\nprevious studies of the same object published in the astronomical\nliterature is made directly possible from the alias list.\n\nThe index of names and aliases constitutes the basis for the\n{\\sc Simbad} name resolver which provides, in response to any\nobject name, the set of coordinates corresponding to the \nobject position on the celestial sphere,\n%%%%%%%%%%%\nor the list of papers citing the object.\nThe name resolving power of {\\sc Simbad} is used by many archives and\ninformation systems (such as \nthe archives of Hubble\nSpace Telescope or European Southern Observatory, \nthe High Energy Astrophysics Science Archive Center, \nthe Astrophysics Data System, \nservers of the Digitized Sky Surveys, etc.).\n\n\nThere is no {\\sc Simbad} preferred name for objects\\footnote{In the early times\nof the \\emph{Catalog of Stellar Identifications} (Ochsenbein et al.\\\n\\cite{csi}), the \\emph{Durchmusterung} number had been used as a preferred\nname for stars.}: all aliases can be equally used. \nA short list of major\ncatalogues is used internally to put at the top of the list \nthe most common name according to the object type\n(e.g., Messier or NGC identifier for galaxies and nebulae). \nAll other identifiers are presented in alphabetical order.\n\nA command of the {\\sc Simbad} native node\n(`{\\tt selectid}'), and an option in\nthe sampling form of the WWW interface, \nallow the user to impose a list of\nidentifiers to be used when displaying object lists.\n\n\n\\subsubsection{Multiple systems}\n\nIt is to be noted that for a double system\nin which the components can be observed separately,\n{\\sc Simbad} frequently includes three entries: A\nand B components, and an additional entry for \nthe joint system (AB), the latter entry\ncarrying the observational data and references related\nto the system as a whole.\nThis has to be taken into account in statistical studies\nsuch as stellar counts.\n\n\\subsection{Observational data}\n\nObservational data are presently given for\nthe measurement types listed in \nTable~\\ref{measurements}.\n\n\\begin{table}\n\\caption{List of measurement types currently included in \n{\\sc Simbad}, together with the number of entries\n(October 1999).}\n\\footnotesize\n\\begin{tabular}{lp{5.5cm}r}\n\\hline \nName & Observational data & \\multicolumn{1}{c}{\\#} \\\\\n\\hline \n{\\tt CEL} &Ultraviolet photometry from {\\em Celescope} & 5230 \\\\\n{\\tt Cl.G} &Clusters of Galaxies (Abell \\& Corwin \\cite{abcg}) & 5345 \\\\\n Einstein &Einstein Observatory Soft X-ray Source List & 5668 \\\\\n{\\tt GEN} &$U B V B_1 B_2 V_1 G$ Geneva photometry & 3650 \\\\ \n{\\tt GJ} &Absolute magnitudes and spatial velocities of nearby stars & 2368 \\\\ \n{\\tt Hbet} &$H_\\beta$ index & 32278 \\\\ \n{\\tt HGAM} &$H_\\gamma$ equivalent width & 723 \\\\\n{\\tt IRAS} &IRAS Point Source Catalog &245784 \\\\\n{\\tt IRC} &$KI$ photometry from {\\em Two Micron Sky Survey} & 4880 \\\\\n{\\tt IUE} &International Ultraviolet Explorer (Merged Observation Log)& 66805 \\\\\n{\\tt JP11} &$UBVRIJKLMNH$ 11-colour Johnson photometry & 5892 \\\\\n{\\tt MK} &Stellar spectral classification in Morgan-Keenan system &190231 \\\\\n{\\tt oRV} &Stellar Radial velocities (also under {\\tt GCRV}) & 68783 \\\\ \n{\\tt PLX} &Trigonometric parallaxes & 16329 \\\\\n{\\tt pm} &Proper motions (from various astrometric catalogues) &243065 \\\\\n{\\tt pos} &Positions (from various astrometric catalogues) &668953 \\\\\n{\\tt ROT} &Rotational velocities ($V \\sin i$) & 7181 \\\\\n{\\tt RVEL} &Radial velocities of extragalactic objects & 36552 \\\\\n{\\tt SAO} &Positions and proper motions from SAO catalogue &252384 \\\\\n{\\tt TD1} &Ultraviolet magnitudes from {\\sl TD1} satellite & 25972 \\\\\n{\\tt UBV} &Johnson $UBV$ photometry &141215 \\\\\n{\\tt uvby} &Str\\\"omgren $uvby$ photometry & 37986 \\\\\n{\\tt V*} &Data related to variable stars & 25764 \\\\\n{\\tt z} &Redshifts (of distant galaxies and quasars)\t & 88888 \\\\\n\\hline \n\\end{tabular}\n\\label{measurements}\n\\end{table}\n\nFor each data type, one can retrieve individual data with\ntheir bibliographical references, and, when available,\nweighted means computed from existing observed values by\nspecialists in the related field.\n\nWhen measurements are listed as a result of a {\\sc Simbad} \nquery, they are\nnormally preceded by a header providing a very short title\nto each listed parameter. \n\nThe important r\\^ole now played by the {\\sc VizieR} database of catalogues\n(Ochsenbein et al.\\ \\cite{vizier}), coming with easier interoperability\nof services, is changing the strategy for inclusion of observational\nmeasurements into {\\sc Simbad}. Let us take the example of\nthe Hipparcos and Tycho catalogues (ESA \\cite{tyc}): once the HIP\nor TYC identifier is available from {\\sc Simbad} it appears convenient \nenough to provide the user with a WWW link to the corresponding data in\nVizieR rather than overloading the {\\sc Simbad} database with the\nfull Hipparcos and Tycho catalogues.\nThis functionality is currently being implemented for important\ncatalogues which have already been cross-identified.\n \nAs a complement, the WWW interface includes pointers to external archives,\ncurrently: the INES database of the IUE project\n(Rodriguez-Pascual et al.\\ \\cite{ines}); the high-energy\nobservational archives at {\\sc heasarc} (HEASARC team \\cite{heasarc}).\n\n\\subsection{Bibliographical references}\n\nOne of the key features of the {\\sc Simbad} astronomical database\nis the unique coverage of bibliographical references to objects.\nThe bibliographic index contains references to stars from\n1950 onwards, and to galaxies and all other objects outside\nthe solar system from 1983 onwards. Presently \n(November 1999) there are\nabout 3 million references taken from 110,000 papers\npublished in the 100 most important astronomical periodical\npublications.\n\n\\subsubsection{Bibliographical data}\n\n Articles are scanned in their entirety, and references\nto all objects mentioned in the title, in the abstract,\nin the text, in the figures, or in the tables \nare included in the bibliography.\nTables larger than 1000 objects are usually considered as\ncatalogues and processed separately.\n\nNo assessment is made of the relevance of the\ncitation in terms of astronomical contents: the paper\ncan be entirely devoted to the object, or simply give a\nside mention of it -- in both cases this gives a reference\nin {\\sc Simbad}. Note that, for instance, the NED team\n(Helou et al.\\ \\cite{ned})\napplies a different strategy when covering bibliography\nof extragalactic objects, and tends to select\nonly those papers that appear most relevant. \nClearly, {\\sc Simbad} approach favours exhaustivity,\nat the cost of increased information noise.\n\nA code (nicknamed {\\em bibcode})\nis assigned to each considered paper: \nthis 19-digit bibcode contains in principle\nenough information to locate the article (including year\nof publication, journal, volume, page, etc.). \n\nWhen one retrieves the bibliography of a {\\sc Simbad} object, a list\nof codes is usually given, and -- according to the options used --\nthese codes are automatically matched against a bibliographic file\nwhich provides the full reference, title \nand list of authors for each citation, \ntogether with an anchor\npointing to the electronic version of the article.\n\nCurrently, in {\\sc Simbad}, about 50\\% of the objects\nhave no bibliographic reference. Among the most cited\nobjects (more than 2000 references) are the\n\\object{Large Magellanic Cloud},\n\\object{M 31},\n\\object{3C 273}, and the supernova\n\\object{SN 1987A}.\n\n\\subsubsection{Bibliographic reference coding convention}\n\\label{bibcode}\n\nThe structure of the 19-digit \\emph{bibcode} \nhas been defined in close collaboration with the\nNED group at NASA/IPAC so that both databases share the same\ncoding system (Schmitz et al.\\ \\cite{bibcode}). \nIt is also used, with some adjustments, by the Abstract Service \nof the Astrophysics\nData System (ADS, Kurtz et al.\\ \\cite{ADS}),\nand by the electronic journals (see e.g., Boyce \\& Dalterio\n\\cite{epub}). Reference codes have the following general structure:\n\n\\begin{center}\nYYYYJJJJJVVVVMPPPPA\n\\end{center}\n\n\\begin{description}\n\\item[YYYY]\nYear of the publication.\n\\item[JJJJJ]\nStandard abbreviation for the periodical.\n\\item[VVVV]\nVolume number (for a journal) or, in the second character\nof this field, one of the following\nabbreviations for another publication:\n B (book),\n C (catalogue),\n P (preprint),\n R (report),\n S (symposium),\n T (thesis),\n U (unpublished).\n\\item[M]\nSpecific qualifier for a paper:\\\\\n\\begin{tabular}{rl}\n L & letter \\\\\n p & pink page (in MNRAS) \\\\\n a-z & issue number within a volume \\\\\n A-K & issue designation used by publisher \\\\\n Q-Z & to distinguish articles on the same page. \\\\\n\\end{tabular}\n\\item[PPPP]\nPage number.\n\\item[A]\nFirst letter of the first author's last name (or `:' if the first\nauthor cannot be identified).\n\\end{description}\n\n\\noindent\nExample: \n {\\tt 1991A\\&A...246L..24M} \\quad for \\quad {\\sl Astron. Astrophys.} 246,\nL24, 1991, a Letter to the Editor of \\emph{Astronomy\n\\& Astrophysics}, by Motch\net al. \n\nFor a complete description see Schmitz et al. (\\cite{bibcode}),\n or the WWW \nserver\\footnote{http://cdsweb.u-strasbg.fr/simbad/refcode.html}.\n\n\n\n\\subsubsection{Comments in the references}\n\nSeveral types of comments are associated with the references\nin {\\sc Simbad} and normally displayed after the reference:\n\n\\begin{itemize}\n%%%%%%%%%%%%%%%\n\\item General comments: they are often comments\n added by the bibliographers,\n about the problems encountered while cross-identifying\n the objects mentioned in the paper, typos in\n object names, etc.\n\\item Notes about the existence of associated electronic\ntables, or abstracts in the CDS server.\nPapers including no object are also flagged.\n\\item Information on how the quoted objects are named in\n{\\sc Simbad} (comments related to the Dictionary of Nomenclature of\nCelestial Objects).\n\\end{itemize}\n\n\\subsection{Statistical aspects of the Data Contents}\n\n\nThe astronomical content of {\\sc Simbad} results from the complex process\nof folding into the database a selection of important\ncatalogues, and of surveying the complete astronomical literature.\n\nThis can be illustrated by the histogram in $V$ magnitudes\nof Figure~\\ref{histo}. The coverage is\nreasonably complete up to beyond magnitude 10 for stars,\nafter the inclusion of the Tycho catalogue. Many objects\nin the range 12 to 26th mag.\\ come from extensive studies of objects\nin selected sky areas: deep fields, external galaxies, etc.\n\nSome well-known very large catalogues are not\npart of {\\sc Simbad}: for instance the Hubble Telescope\nGuide Star Catalogue (GSC, Lasker et al.\\ \\cite{gsc})\nis not systematically included (even if GSC identifiers have been added\nfor all Tycho stars present in {\\sc Simbad}). This\nresults from a compromise aiming to save database load\nas well as manpower for cross-identification and quality\ncontrol. Note that {\\sc VizieR} and {\\sc Aladin} give\naccess to the full GSC catalogue (and to even larger catalogues\nand databases such as USNO-A, DENIS, 2MASS).\n\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\rotatebox{-90}{\\includegraphics{simbad-histo.ps}}}\n% 12cm if double column\n%\\vskip 8cm\n\\caption{Histogram of the number of objects in {\\sc Simbad} per \nmagnitude interval \n(V magnitude; logarithmic scale).}\n\\label{histo}\n\\end{figure}\n\n\nFig.~\\ref{graph1a} illustrates the increase of the\ndata contents of the database in the years 1990 to 1999.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{graph1a.ps}}\n% 18cm if double column\n%\\vskip 8cm\n\\caption{Histograms of different types of database entries for the years\n1990 to 1999: number of objects (top left), number of identifiers\n(top right), number of references (bottom left), number of citations\n(bottom right). The numbers given are the total numbers of entries \npresent in the database at the end of the corresponding year.}\n\\label{graph1a}\n\\end{figure}\n\n\\section{SIMBAD structure and query management}\n\\label{dbms}\n\n\n{\\sc Simbad} query mechanism can be summarized by\nthe following key features:\n\n\\begin{itemize}\n\\item\nDatabase queries can be made mainly through: \n\\begin{itemize}\n\\item identifiers (names of astronomical objects) and lists of identifiers, \n\\item sets of coordinates (retrieving one object by its position\n on the sky, or extracting all objects lying in a given direction), and \n\\item sampling criteria (or {\\em filters\\/}).\n\\end{itemize}\n \\item\nData output is driven by formats. The user may\ndefine his/her own formats or modify existing ones. \nOutput files can be\nsaved and mailed to the user. \n \\item\nThe user interface is adaptable to user\npreferences.\n\\end{itemize}\n\nThe database management system of {\\sc Simbad} has been developed \nby the CDS, using\nthe concepts of object-oriented programming. \n\n\\subsection{Object-oriented concepts}\n\nThe command language is using the concepts of objects (or agents).\nTypical object classes are: astronomical object, object list, database, session,\nreference list, filter, format. Examples of methods are: display, \ndescribe, bye (quit).\n\nThis structure is only visible for the user of the command\nline interface. The WWW interface is rendered quite independent\nof the database structure. \n\n\\subsection{Indexing}\n\n{\\sc Simbad} is organized for optimized access by\nidentifier (through an index table of object names)\nand by position, through an index of small regions. \n\n\\begin{description}\n\\item[Identifiers]:\nA B-tree file contains all identifiers allowing a\nfast access to any of them. For each identifier, a record contains\na pointer to the astronomical object itself in the main database.\n\n\\item[Position]:\nIndexing by coordinates is done in two steps: the coordinates\nare mapped into a set of boxes.\n{\\sc Simbad} uses the spherical-cubic projection\n%%%%%%%%\n-- a technique also used, e.g., for the Cosmic\nBackground Explorer (COBE) data: \nthe celestial sphere is projected\nonto the six faces of a cube, giving six boxes at the first\nlevel. By dividing each face into\nfour parts, one obtains a partition at level two. Further\nlevels are obtained by further divisions of each box into four\nsub-boxes. Through this mechanism one obtains 6144 boxes at the\nlevel 5 with an average size of 6 square degrees and an average\nnumber of objects of 500. Box {\\#}6145 contains all objects\nwithout recorded position.\n\nIn order to optimize access to objects in a coordinate box, \nall objects belonging to a box should be physically grouped\nin a common place in the database. This is done through a clustering \nmechanism placing objects from the same box in data blocks \nlinked together in the database files.\n\\end{description}\n\n\nWhen a set of criteria includes some\nlimitations in coordinates, this generates the definition of\na list of boxes including the requested area:\nall entries from these boxes are read \nand checked against the whole set of criteria.\n\nWhen a set of criteria includes no limits in sky position,\nthe complete database must be scanned -- a long and\nsomewhat expensive operation, which takes typically\n15 minutes in the current hardware configuration.\n\n\\subsection{Query by identifier}\n\nIn principle any name\nfound in the literature -- provided it is given as a\nsyntactically correct character string -- can be submitted\nto the database in order to\nretrieve information known for this object.\n\nThe general syntax of an identifier is \nthe abbreviated catalogue name (or acronym:\ngenerally one to four characters), followed by \na number or a name (character string) within the catalogue. \n\nObject names such as Vega and Altair, but also Barnard's star,\nCrab Nebula, Sgr A, HDFN, or HDFS \nare stored in the database in a specific catalog \ncalled `{\\sc name}', while star names in constellations, \nsuch as $\\alpha$ Lyrae,\nare stored in the catalogue `{\\tt *}', \nand variable stars (such as RR Lyrae)\nin the catalogue `{\\sc var}' (also called `{\\tt V*}'). \n\nThe user can generally type \n{\\tt Vega}, {\\tt Altair}, {\\tt alf Lyrae} (or {\\tt alf Lyr}): \nthe \\emph{sesame} name resolving module \n(Section~\\ref{sesame}) is used for\nguessing the catalogue and making the\ninternal conversion. \nThere are however some\ndifficult cases in which the {\\sc name} keyword remains\nnecessary, such as in {\\sc name sgr 1900+14} where\n{\\sc sgr} stands for Soft Gamma Repeater.\n\nIn addition the following hints can help the user\nunderstand the best way to submit an identifier to {\\sc Simbad}:\n\n\\begin{description}\n\n\\item [Case sensitivity:]\n{\\sc Simbad} is not case-sensitive at this level: {\\tt ALF~AQL} or\n{\\tt alf~Aql} are, for instance, both valid. \nThere are some exceptions to the rule, \nsuch as the cases of the star cluster RMC 136a,\nor the star in a multiple system VdBH 25a A,\nfor which case-sensitivity may be necessary for solving format\nambiguities.\n\n\\item [Greek letters:]\nshould be abbreviated as three letters: {\\tt alf}, {\\tt bet}, for\n$\\alpha$ and $\\beta$, but also {\\tt mu.} {\\tt nu.} and {\\tt\npi.} (with a dot), for $\\mu$, $\\nu$ and $\\pi$. \n\n\\item [Constellations:] \nconstellation names should be\nabbreviated with the usual three letters: {\\tt alf Boo}, {\\tt\ndel Sct}, {\\tt FG Sge}, {\\tt NOVA Her 1991}.\nThe full list is\navailable on-line\\footnote{http://simbad.u-strasbg.fr/guide/chB.htx}. \n\n\\item [Multiple systems:]\nIdentifiers of a multiple system may generate a list of the objects of the\nsystem. For instance, {\\tt ADS 5423} calls for the four components, A to D,\nof the stellar system around Sirius. This is true only for\nsome specific identifiers.\n\n\\item[Stellar clusters:]\nClusters which have no NGC or IC number\nare named under the generic appellation {\\tt Cl}\nfollowed by the cluster name and number: e.g.,\nCl~Blanco~1 is the 1st stellar cluster named by Blanco.\nStars in clusters may belong to a `main' designation\nlist, or to subsequent lists.\nNGC~5272~692 is star 692 in the list by Von Zeipel,\nconsidered as the main list. Subsequent lists have\ndesignations starting with {\\tt Cl*}.\nExamples: \nCl*~NGC~5272 AC~968 (list by Auriere \\& Cordoni);\nCl*~Melotte~25~VA~13 (13th star in the list by Van\nAltena for Melotte 25 -- the Hyades cluster);\nCl* Collinder~110 DI~1101 (list by Dawson \\& Ianna -- there\nis no `main' list for this cluster).\nMore details are available in the on-line \ndescription\\footnote{http://simbad.u-strasbg.fr/guide/chC.htx}.\n\n\\item [Unknown name ?:]\nIf the object name seems unknown to {\\sc Simbad},\nthe user is advised to enter the coordinates of the object:\nthe object may actually exist in the database under a different \ndesignation. Submitting the identifier, or the name of the\nfirst author of the catalogue, to the\nDictionary of Nomenclature may also give useful clues.\n\n\\end{description}\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{m81query.ps}}\n% 12cm if double column\n%\\vskip 8cm\n\\caption{Example of Simbad response page\nfor a query concerning M81 (only the first part of the response\nis visible here).}\n\\label{response}\n\\end{figure}\n\n\nFigure~\\ref{response} illustrates the response received from\nthe database after submitting the identifier `M~81'.\n%%%%%%%%\nIn the identifier list, the\nmeaning of acronyms, such as [VDD93], is explained through\na link to the on-line Dictionary of Nomenclature.\n\n\nThe user interface provides an option for querying\naround objects, with a radius set by default at 10\\arcmin.\nThis is equivalent to a query by position using the\nobject coordinates.\n\nIt is also possible to generate the list of 10 or 25 next\nobjects following a given identifier, or to\nsubmit a list of object names,\nstored in a file with one identifier per line.\n\n\\subsection{Query by coordinates}\n\nQuery by coordinates can be used to retrieve all objects \nin a circular field\ndefined by the coordinates of the center and a radius.\n\nThe coordinates can be replaced by the name of\nan object lying at the center of the field, in which case\nthe coordinates are found through an internal query to {\\sc\nSimbad}. The radius can have any size (default value is\n10\\arcmin). Queries with a radius\nsmaller than 1--$2\\degr$ are answered quite instantaneously.\n\n\n\\subsection{Sampling}\n\\label{filter}\n\nThe sampling mode (also named filter) allows users \nto define criteria for selecting objects in {\\sc Simbad}. \n\nThe user may extract objects which satisfy one\nset of coordinate criteria, several physical criteria \n(using a simple syntax), objects which have specified \nidentifiers or measurements, and, finally, objects having \ncitations within a range of years. \n\nThe WWW interface provides an interactive form \nwhich presents all possible sampling options.\n\nThe resulting list may be ordered\naccording to sort criteria and, furthermore,\nit is possible, through the command line mode,\nto define precisely the output format.\n\nNote that reading the whole database for extracting a\nsample spread on the whole celestial sphere is\npossible, but quite time-consuming (as\nmentioned above). The user is thus encouraged to\ntest the filter on a limited region of the sky, before\napplying it to the whole database.\n\n\n\\subsection{Charts and sky maps}\n\nAfter a sampling by position the user can ask for\nthe corresponding sky plot. This feature is only\navailable through the WWW interface and is generally optimized\nfor a radius range of 10--60 minutes.\n\nThe maps display the objects with different\nsymbols according to object type; symbol size \nfor stars varies with object\nmagnitude (see Figure~\\ref{chart}). The maps are clickable \nand return the object in Simbad corresponding to\ncursor position. \n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{m81chart.ps}}\n% 12cm if double column\n%\\vskip 8cm\n\\caption{Example of finding chart around M81 (radius of the circular field:\n $10\\arcmin$).}\n\\label{chart}\n\\end{figure}\n\nThe WWW interface provides also direct\naccess to the {\\sc Aladin} interactive digitized atlas \n(Bonnarel et al.\\ \\cite{aladin}) as illustrated in Figure~\\ref{figaladin}.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\rotatebox{+90}{\\includegraphics{m81aladin.ps}}}\n% 12cm if double column\n%\\vskip 8cm\n\\caption{Use of {\\sc Aladin} for displaying {\\sc Simbad} entries\n (red diamonds) on top of a DSS-I/STScI image around M81 (width\nof the field: $14.1\\arcmin$).}\n\\label{figaladin}\n\\end{figure}\n\n\n\\subsection{Batch mode}\n\n{\\sc Simbad} can be queried in {\\em batch mode}, by\nsubmitting a mail to the special address\n{\\tt smbmail@simbad.u-strasbg.fr}.\n\nThis is especially useful in case of poor\ninteractive connectivity, or for submitting \ntime-consuming queries or lists.\nA WWW form\\footnote{http://cdsweb.u-strasbg.fr/simbad/batch.html}\nhelps to prepare the submission.\n\n\\subsection{Resolving a bibliographical reference code}\n\nIt is possible to obtain a complete bibliographical\nreference, by entering the corresponding\nreference code (bibcode).\n\nA reference code can be supplied \nwithout indicating all\nthe fields: the first reference corresponding to the\ntruncated code will be displayed. \nAn ampersand ({\\tt \\&}) should be added\nat the end of the truncated bibcode.\n\n\\subsection{Additional tools}\n\nAdditional tools include special commands for querying\nauxiliary databases, on-line help, log files, etc.\nMore details can be found in the {\\sc Simbad} User's Guide\nor on the Web pages.\n\n\n\n\\section{User Interfaces to SIMBAD}\n\\label{xsimbad}\n\\label{interface}\n\nThere are several user interfaces to {\\sc Simbad}.\nNew users are advised to go directly to the WWW interface,\nunless they have very specific needs.\n\n\\begin{itemize}\n\\item The Web interface is currently the easiest\naccess mode to {\\sc Simbad}. This interface takes benefit of the\nWWW features to provide the user with additional links\nto internal documentation, associated services ({\\sc Aladin},\n{\\sc VizieR}), and external archives (currently: \nthe INES database of the IUE project; the high-energy\nobservational archives\nat {\\sc heasarc}). Some features, such as the finding chart,\nhave been specifically designed for the Web and are \nnot available through the other modes.\n\n\\item The command line interface is the basic underlying\ninterface to the database, which serves as a basis for\n the other more user-friendly interfaces. During many years\nit was the sole access mode\nto the database, and many users who are accustomed\nto the commands may find it quicker and more versatile.\nIt implies a {\\em remote login} (through telnet)\non the {\\tt simbad}\nmachine in Strasbourg, and the user needs to have\na user name and password (see Section~\\ref{charge}).\n\n\\item A graphical interactive user interface to {\\sc Simbad},\n{\\sc XSimbad}, \ntaking benefit of the X Window environment has been developed \nin 1993-94 for distribution\nto users working in a Unix environment. \nIt is now obsolete, because all the functionalities,\nand additional ones, are more easily \navailable through the Web. \n\n\\item A client/server package is distributed \non request to data managers\nof archives and information systems, when they need to\norganize the most efficient access to {\\sc Simbad} for\nthe resolution of object names into the corresponding position,\nor the retrieval of other information provided by\nthe database, such as the reference list for a given object. \nWritten currently in C language, it can easily be plugged\ninto any application able to access C routines.\nDistribution is subject to CDS approval.\n\\end{itemize}\n\n\n\\section{SIMBAD usage}\n\n\\subsection{Charging policy}\n\\label{charge}\n\n{\\sc Simbad} is a charged service. The {\\tt telnet}\naccess is protected by userid/password, and the WWW\naccess is protected either by IP address or by\npassword. \n\nUsers have to\nregister, and get a userid/password from the\nCDS staff (or from the U.S. agent for American users).\n\nIn the U.S. there is no invoicing for the end-user\nbecause the charges are covered globally \nby NASA for all U.S. users.\n\nIn Europe, the same situation is also true for\nusers from ESO and ESA member states, thanks to an\nagreement signed with \nEuropean Southern Observatory and \nESA Space Telescope European Coordinating\nFacility (since January 1995).\n\nSpecial arrangements also exist or are currently \nbeing negotiated\nwith other countries, including Canada, Australia, and Japan.\n\n\\subsection{Usage statistics}\n\nThere are currently (November 1999) some 7000 user\naccounts from 64 different countries.\nThe development of the WWW access makes difficult \nto keep precise track of the individual usage statistics, \nbut the global statistics show that the world wide \ninterest for accessing the {\\sc Simbad} database continues \nto increase regularly over the years.\n\nThe number of {\\sc Simbad} queries evolved \nfrom about 30,000 per month in 1997\nto about 100,000 per month in 1999.\nAbout 50\\% of the queries come through\nthe client/server mode.\n\nA mirror copy of {\\sc Simbad} has been established \nat CfA (Harvard) for convenience\nof US users, and about \none third of the queries are currently processed on\nthe mirror site (including name resolving activities for \nthe ADS and major US NASA archives).\nThe mirror copy is managed by CDS and updated\nevery night.\n\n\\section{SIMBAD updates and quality control}\n\\label{update}\n\n\\subsection{Updating SIMBAD}\n\n {\\sc Simbad} is kept up-to-date on a daily basis, as the\nresult of the collaboration of the CDS team, in Strasbourg,\nwith bibliographers\nin \nObservatoire de Paris (DASGAL), \nInstitut d'Astrophysique de Paris, \nand \nObservatoire de Bordeaux \n(Lalo\\\"e et al.\\ \\cite{maj93}; Lalo\\\"e \\cite{maj95})\nwho systematically scan the articles published in some 100\nastronomy journals. \n\nThe references are updated very soon after reception of the\njournal issues, and in some cases directly from the journal\ntable of contents, through agreements with the Editors.\nNew data concerning the objects (identifiers, \nbasic data), and new acronyms for catalogs\nor tables are being entered\nwhen appropriate.\n\nThe inclusion of a large\ncatalogue in the database is often a long-term task which may\nspan over several months or\nyears; the collaboration of specialists in the different fields\nis systematically sought.\n\nThe improvement of the {\\sc Simbad} astronomical contents\nrelies on a network of collaborations: a list of the\nmain current contributors is given in Table~\\ref{collaboration}.\n%%%%%\nMore generally, help of other contributing institutes \nand authors, too numerous to be cited here, \nis gratefully acknowledged.\n \n\\begin{table}\n\\caption{Main institutes associated to the CDS\nfor improving the data contents of {\\sc Simbad}}\n\\begin{tabular}{lp{5.8cm}}\n\\hline \nBibliography & Observatoire de Paris, \n Institut d'Astrophysique de Paris, \n and Observatoire de Bordeaux \\\\\nAstron. contents & GRAAL, Montpellier \\\\\nGalaxies & Observatoire Midi-Pyr\\'en\\'ees and\n NASA/IPAC Extragalactic Database \\\\\nPhotometry & Observatoire de Gen\\`eve\nand Institut d'Astronomie de Lausanne \\\\\nAstrometry & Astronomisches Rechen Institut, Heidelberg \\\\ \nBinary stars & Observatoire de Besan\\c{c}on \\\\\nHigh-energy & Observatoire de Strasbourg \\\\\n\\hline\n\\end{tabular}\n\\label{collaboration}\n\\end{table} \n\n\n\n\\subsection{Quality control}\n\n The data contained in {\\sc Simbad} are also \npermanently updated, as a result of errata, remarks \nfrom the bibliographers (during the scanning of the \nliterature), integration of lists\nand catalogues, quality controls, or special\nefforts initiated by the \nCDS team to better cover some specific domains (e.g., \nmulti-wavelength emitters and complex objects). \n\nRequests for corrections, errata, or suggestions are \nregularly received from {\\sc Simbad} users through a \ndedicated {\\em hot line}, at e-mail address\n{\\tt question@simbad.u-strasbg.fr}.\nA few dozens of messages are usually received every\nweek, and processed on a daily basis by the member of\nthe team who is on duty for that week, or transmitted\nto the key person in case of specialized questions.\nRemarks received from the users by this way are especially\nwelcome, as they help the CDS team to improve the database\ncontents through the scrutiny of specialists' eyes.\n\nDeveloping new tools for quality control\nof the database is a major challenge for the future,\nand CDS is exploring possible solutions.\nMultivariate analysis applied to\nbibliographic information retrieval has\nbeen proven a possible tool for developing quality control\nin a database such as {\\sc Simbad} (Lesteven \\cite{lesteven}).\n\n\n\\subsection{Towards automation of updating procedures}\n\nThe advent of \nelectronic publishing brings new\nperspectives for improvement and automation of the updating\nprocedures. \n\nIn a first place, tables of contents of the major journals are\nnow received electronically through the network, \nthanks to journal Editors and Publishers, \nthus reducing the risk of errors. \nRegularly, a number of electronic lists of objects are also \nfolded into {\\sc Simbad}\nthrough semi-automatic procedures.\n The next step will be the\nautomatic flagging of object names in the text of\nthe articles: this has now become \na very interesting medium-term goal.\n\nTwo ways of achieving this flagging are \ncurrently being considered:\n\\begin{itemize}\n\\item the first one is to ask the authors, with\nthe help of the Editors of electronic journals, to flag\nastronomical object names in their text; this can be done, \nfor instance, by the use of a \\verb+\\object{ }+ command within the {\\TeX} or\n{\\LaTeX} source, which will be eventually used to build\nan anchor pointing towards {\\sc Simbad}, or another\ndatabase, in the on-line version made available\non the network. This approach has been adopted\nby the Editors of {\\em Astronomy \\& Astrophysics}.\n\\item another approach is the use of intelligent\nsearch tools for identifying object names within the electronic\nversion of the paper, using a set of syntactic and semantic\nrules, and the Dictionary of Nomenclature as a reference\ndatabase for already known objects.\n\\end{itemize}\n\nThe first approach seems safer, provided the authors \nunderstand what exactly they are being required,\nand accept this (minor) additional work load.\nThe latter implies a lot of fine tuning from\nthe system developers.\nThe current experience with the handling of publications\n(Lesteven et al.\\ \\cite{lesteven2})\nsuggests that both approaches may be needed, and that a careful\nquality control, including final check by an expert, will\nprobably remain necessary to avoid errors or misinterpretations,\nand to ensure appropriate completeness.\n\n\n\\section{Nomenclature}\n\\label{Dic}\n\n\\subsection{The Dictionary of Nomenclature}\nDesignations of astronomical objects are often confusing.\nA complete list of astronomical designations \nhas been collected and published by Lortet et al.\\\n(\\cite{dic2}) in the\n{\\sl Dictionary of Nomenclature of Celestial Objects \noutside the Solar System}.\n\nThis information is available on-line through the {\\tt info}\ncommand, or on the \nWWW\\footnote{http://vizier.u-strasbg.fr/cgi-bin/Dic-Simbad}.\nThis service is the electronic look-up version of the \n%%%%%%\n{\\sl Dictionary} which is now under the responsibility\nof CDS. It is kept up-to-date on a weekly\nbasis; about 15 new acronyms\nare incorporated every week.\n\nThe {\\sl Dictionary} currently provides full references \nand usages about some 5000 different acronyms. \nIt is used by the International\nAstronomical Union as a reference for its recommendations\nrelated to nomenclature.\n\n\\subsection{The \\emph{sesame} module}\n\\label{sesame}\n\nThe \\emph{sesame} module\nis used inside {\\sc Simbad}\nfor the management of possible variations in the\nnaming of astronomical objects.\nIt is based on a list of rules, written as regular expressions, \nallowing translation of the submitted name\ninto its {\\sc Simbad} canonical form; it is only made visible to\nthe user when a message mentions the submitted syntax\nand its translation.\n\nThere are cases where ambiguities cannot be solved.\nThis is actually specific to the broad context of {\\sc Simbad}.\nLet us give an example: in the context of extragalactic\nobjects `N' is a possible abbreviation for `NGC'\n(accepted by NED); \nbut people studying Novae would frequently use\n`N' as an abbreviation for Nova, people studying\n\\ion{H}{ii} regions would use it for naming\nnebulae in the Magellanic Clouds (LHA 120-N or LHA 115-N),\nand `N' has also been found in the literature for cluster\nstars studied by Nordlund in NGC 2099 (Cl* NGC 2099 N),\nfor stars studied by Neckel ([N78]), or even for `New'\nparts of the galaxy NGC 1275 ([NJS93] in {\\sc Simbad}). \nWhen a name like `N~1992' is submitted\nto {\\sc Simbad} the ambiguity cannot be solved without\nrequesting additional information from the user.\n\n\\section{Integration of SIMBAD into the CDS Hub}\n\nWhile the CDS databases have followed different \ndevelopment paths, the\nneed to build a transparent access \nto the whole set of CDS services has become\nmore and more obvious with the easy\nnavigation permitted by hypertext tools\n(Genova et al.\\ \\cite{cds2000}). \n{\\sc Aladin} has become the prototype of such a development,\nby giving comprehensive simultaneous \naccess to {\\sc Simbad}, \nthe {\\sc VizieR} Catalogue service, \nand to external databases such as NED,\nusing a client/server approach and, when possible,\nstandardized query syntax and formats. \n\nIn order to be able to go further, the\nCDS has built a general data\nexchange model, taking into account all types of information available\nat the Data Center, known under the acronym\nof GLU for G\\'en\\'erateur de Liens Uniformes -- Uniform\nLink Generator (Fernique et al.\\ \\cite{glu}). \n\nIn the current stage of development, the WWW interface\nto {\\sc Simbad} provides access to {\\sc Aladin}\npreviewer (reference image around one object),\nand to the {\\sc Aladin} interactive Java program\n(see Bonnarel et al.\\ \\cite{aladin}).\nThere are also links between {\\sc Simbad} and the\nbibliographic services developed or mirrored\nat CDS, and more generally to the ADS and the\nelectronic journals.\n\nWhile this article is written stronger links between {\\sc Simbad} and\n{\\sc VizieR} are just being created allowing even easier transfers \nof data and information between both services.\n%%%%%%%\nThis will also make easier to build new links pointing to\ndistributed data archives, beyond those already existing\n(currently: IUE/INES and HEASARC).\n\n\n%______________________________________________________________\n\n\\section{Future developments}\n\nIn the near future, the CDS team expects to go on enriching \nthe database contents and system functionality.\nThe users play an important role in\nthat respect, by giving feedback on the desired features,\non the user-friendliness of the interfaces, etc.\n\nIn the context of interoperability of distributed services, \nas currently discussed within the ISAIA project\n(Interoperable Systems for Archival\nInformation Access; Hanisch \\cite{isaia}),\n{\\sc Simbad} is prepared to deliver \nresource profiles and to format the query outputs\nin a standard way, for instance XML\n (Ochsenbein et al. \\cite{adass9}).\n\nAs larger and larger astronomical datasets are being\nproduced, the CDS is studying the concepts of a new\ngeneration database of several billion objects,\ninstead of the current several million objects.\nWe expect {\\sc Simbad} to remain an essential\ntool for astronomical research in the years to come.\n\n\n\\begin{acknowledgements}\nCDS acknowledges the support of INSU-CNRS, the Centre National\nd'Etudes Spatiales (CNES), and Universit\\'e Louis Pasteur (ULP,\nStrasbourg).\nMany of the current developments of {\\sc Simbad} have been\nmade possible by long-term support from NASA, ESA, and ESO.\nWe thank more specifically J.\\ Mead and G.\\ Riegler (NASA),\nP.\\ Benvenuti (ESA/ST-ECF),\nand P.\\ Quinn (ESO) for their help in setting up\nthe current agreements.\n\nDeveloping and maintaining the database is a collective undertaking\nto which many contributors -- too numerous to be listed here --\nare associated. A special mention shall be made of\nM.-J.\\ Wagner, F.\\ Woelfel, J.\\ Marcout (Strasbourg), \nA.\\ Beyneix, G.\\ Chassagnard (IAP, Paris), \nN.\\ Ralite, S.\\ Pasquier (Bordeaux), \nE.\\ Davoust (Toulouse),\nand B.\\ Skiff (Lowell Observatory),\nwho are watching with great care over the {\\sc Simbad}\ncontents.\n\nWe want finally to thank Jean Delhaye, Jean Jung, Carlos Jaschek and\nMichel Cr\\'ez\\'e for their leadership and their vision\nin the consecutive early phases of the {\\sc Simbad} project.\n\n\\end{acknowledgements}\n\n\n\\begin{thebibliography}{}\n\n\\bibitem[1989]{abcg} Abell, G.O., Corwin, H.G., Jr., Olowin, R.P., 1989, ApJS 70, 1\n(ABCG)\n% Abell Cluster of Galaxies\n\n\\bibitem[2000]{aladin} Bonnarel, F., Fernique, P.,\n Bienaym\\'e, O., et al., 2000, A\\&AS, {\\em in press}\n(Aladin)\n% Aladin paper in the same volume\n\n\\bibitem[1996]{epub}\nBoyce, P., Dalterio, H., 1996, \n{\\em Physics Today} 49, 42\n\n\\bibitem[1983]{dubois83} \nDubois, P., Ochsenbein, F., Paturel, G., 1983, Bull. Inform. CDS 24, 125\n% Extension of SIMBAD towards Galaxies\n\n\\bibitem[1983]{story}\nEgret, D., 1983, Bull. Inform. CDS 24, 109\n (SIMBAD Story)\n\n\\bibitem[1995]{cds-amp2}\nEgret, D., Cr\\'ez\\'e, M. , Bonnarel, F., et al., 1995,\nin {\\em Information \\& On-line Data in Astronomy}, Egret \\& Albrecht \n(Eds.), Kluwer Academic Publ., p. 163\n% A global perspective on astronomical data and information:\n% the Strasbourg astronomical data centre (CDS)\n\n\\bibitem[1991]{ampersand}\n Egret, D., Wenger, M., Dubois, P., \n 1991, in \\emph{Databases and On--line Data in Astronomy}, M.A. Albrecht \\&\n D. Egret (Eds.), Kluwer Academic Publishers, p. 79\n% The SIMBAD astronomical database\n\n\\bibitem[1997]{tyc} ESA, 1997, The Hipparcos and Tycho Catalogues, ESA SP--1200\n\n\\bibitem[1998]{ICRS} Feissel, M., Mignard, F., 1998, A\\&A 331, L33 \n(ICRS)\n% ICRS\n\n\\bibitem[1998]{glu} Fernique, P., Ochsenbein, F., Wenger, M., 1998, \nin {\\em Astronomical Data\nAnalysis Software and Systems VII}, ASP Conf. Ser. 145, p. 466\n(GLU)\n% CDS GLU\n\n\\bibitem[1996]{cds-hub} \nGenova, F., Bartlett, J.G., Bienaym\\'e, O., et al., 1996,\nVistas in Astronomy 40, 429\n% CDS as an Astronomical Information Hub \n\n\\bibitem[1998]{cds} Genova, F., Bartlett, J.G., Bonnarel, F., et al., \n1998, in {\\em Astronomical Data\nAnalysis Software and Systems VII}, ASP Conf. Ser. 145, p. 470\n% CDS information hub\n\n\\bibitem[2000]{cds2000} Genova, F., et al., 2000,\nA\\&AS, \\emph{in press}\n(CDS)\n% CDS, in this volume\n\n\\bibitem[2000]{isaia} Hanisch, R., 2000, {\\em Computer\nPhysics Communications}, in press\n\n\\bibitem[1986]{messenger}\n Heck, A., Egret, D., 1987, Messenger, 48, 22-24\n% SIMBAD, the CDS database\n\n\\bibitem[1995]{heasarc} HEASARC team, 1995, \nin {\\em Information \\& On-line Data in Astronomy}, Egret \\& Albrecht \n(Eds.), Kluwer Academic Publ., p. 139\n% The HEASARC facility\n\n\\bibitem[2000]{ned}\nHelou, G., Madore, B.F., Schmitz, M., et al., 2000, A\\&AS,\nin press\n(NED)\n% The NASA/IPAC Extragalactic Database\n\n\n\\bibitem[1998]{TRC} H{\\o}g, E., Kuzmin, A., Bastian, U., et al., 1998, \nA\\&A 335, 65\n(TRC)\n% Tycho Reference Catalogue\n\n\\bibitem[1975]{mss} Houk, N., Cowley, A.P., 1975, Michigan Catalogue of\n Two-Dimensional Spectral Types for the HD Stars, vol. 1\n (MK)\n\n\\bibitem[1978]{MK-MJ} Jaschek, M., 1978,\n Bull. Inf. CDS 15, 121\n% compilation of MK types\n\n\\bibitem[2000]{ADS} Kurtz, M., Eichhorn, G., Accomazzi, A.,\net al., 2000, A\\&AS, in press\n(ADS)\n% The NASA Astrophysics Data System: Overview (this volume)\n\n\\bibitem[1995]{maj95}\n Lalo\\\"e, S. 1995, in {\\em Proceedings of the LISA-II Conference},\nVistas in Astronomy 39, 179\n\n\\bibitem[1993]{maj93} \n Lalo\\\"e, S., Beyneix, A., Borde, S., et al., 1993, CDS Inform. Bull. 43, 57\n\n\\bibitem[1990]{gsc} Lasker, B.M., Sturch, C.R., McLean, B.J., et al., \n 1990, AJ 99, 2019\n(GSC)\n% The Guide Star Catalog\n\n\\bibitem[1995]{lesteven}\n Lesteven, S., 1995, Vistas in Astronomy 39, 187\n% Multivariate data analysis applied to bibliographical\n% information retrieval: SIMBAD quality control\n\n\\bibitem[1998]{lesteven2}\n Lesteven, S., Bonnarel, F., Dubois, P., 1998, in\n {\\sl Proceedings LISA III \n Conference}, U. Grothkpof et al.\\ (Eds.), ASP Conf. Ser. 153, 61\n% Information extraction (finding object names in papers)\n\n\\bibitem[1994]{dic2} Lortet, M.C., Borde, S., Ochsenbein, F., 1994, \nA\\&AS 107, 193\n\n\\bibitem[1987]{UBV} Mermilliod, J.-C., 1987, A{\\&}AS 71, 413 (UBV)\n% UBV Compilation\n\n\\bibitem[1973]{ugc} Nilson, P., 1973, Uppsala General Catalogue of\n Galaxies\n(UGC)\n\n\\bibitem[1982]{bsi}\n Ochsenbein, F., 1982, in {\\em Automated Data\n Retrieval in Astronomy}, ed. C. Jaschek \\& W. D. Heintz, IAU Coll.\n 64, Dordrecht, D. Reidel Publishing Company, p. 171\n(BSI)\n% The Bibliographical Star Index\n\n\\bibitem[2000]{adass9} Ochsenbein, F., Albrecht, M., Brighton, A. \n et al., 2000, in {\\em Astronomical Data Analysis Software and Systems IX}, \n ASP Conf. Ser., in press (XML)\n\n\\bibitem[2000]{vizier} Ochsenbein, Fuer, P., Marcout, J., 2000,\nA\\&AS, \\emph{in press}\n(VizieR)\n% VizieR, in this volume\n\n\\bibitem[1981]{csi}\n Ochsenbein, F., Bischoff, M., Egret, D., 1981, A\\&AS 43, 259\n(CSI)\n% Microfiche edition of CSI (Catalog of Stellar Identifications)\n\n\\bibitem[1992]{type}\n Ochsenbein, F., Dubois, P., 1992, in {\\em Astronomy from\n Large Databases, II}, A. Heck \\& F. Murtagh (Eds.), 405\n% Object type classification \n\n\\bibitem[1999]{ines} Rodriguez-Pascual, P. M.,\nGonz\\'alez-Riestra, R., Schartel, N., Wamsteker, W., 1999, A\\&AS 139, 183\n(INES)\n% INES paper in A&AS, October 1999\n\n\\bibitem[1995]{bibcode}\nSchmitz, M., Helou, G., Dubois, P., LaGue, C., Madore, B.,\nCorwin, H.G. Jr, and Lesteven, S., 1995,\nin {\\em Information \\& On--line Data in Astronomy}, Egret \\& \nAlbrecht (Eds.), Kluwer Acad. Publ., p. 259\n% NED and SIMBAD conventions for bibliographic reference \n% coding\n\n\\bibitem[1962]{mcg} Vorontsov-Velyaminov, B., et al., 1962,\n Morphological Catalogue of Galaxies, in 5 parts, Moscow\n State University, Moscow \n(MCG)\n\n\\end{thebibliography}\n\n%\\listofobjects\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002110.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[1989]{abcg} Abell, G.O., Corwin, H.G., Jr., Olowin, R.P., 1989, ApJS 70, 1\n(ABCG)\n% Abell Cluster of Galaxies\n\n\\bibitem[2000]{aladin} Bonnarel, F., Fernique, P.,\n Bienaym\\'e, O., et al., 2000, A\\&AS, {\\em in press}\n(Aladin)\n% Aladin paper in the same volume\n\n\\bibitem[1996]{epub}\nBoyce, P., Dalterio, H., 1996, \n{\\em Physics Today} 49, 42\n\n\\bibitem[1983]{dubois83} \nDubois, P., Ochsenbein, F., Paturel, G., 1983, Bull. Inform. CDS 24, 125\n% Extension of SIMBAD towards Galaxies\n\n\\bibitem[1983]{story}\nEgret, D., 1983, Bull. Inform. CDS 24, 109\n (SIMBAD Story)\n\n\\bibitem[1995]{cds-amp2}\nEgret, D., Cr\\'ez\\'e, M. , Bonnarel, F., et al., 1995,\nin {\\em Information \\& On-line Data in Astronomy}, Egret \\& Albrecht \n(Eds.), Kluwer Academic Publ., p. 163\n% A global perspective on astronomical data and information:\n% the Strasbourg astronomical data centre (CDS)\n\n\\bibitem[1991]{ampersand}\n Egret, D., Wenger, M., Dubois, P., \n 1991, in \\emph{Databases and On--line Data in Astronomy}, M.A. Albrecht \\&\n D. Egret (Eds.), Kluwer Academic Publishers, p. 79\n% The SIMBAD astronomical database\n\n\\bibitem[1997]{tyc} ESA, 1997, The Hipparcos and Tycho Catalogues, ESA SP--1200\n\n\\bibitem[1998]{ICRS} Feissel, M., Mignard, F., 1998, A\\&A 331, L33 \n(ICRS)\n% ICRS\n\n\\bibitem[1998]{glu} Fernique, P., Ochsenbein, F., Wenger, M., 1998, \nin {\\em Astronomical Data\nAnalysis Software and Systems VII}, ASP Conf. Ser. 145, p. 466\n(GLU)\n% CDS GLU\n\n\\bibitem[1996]{cds-hub} \nGenova, F., Bartlett, J.G., Bienaym\\'e, O., et al., 1996,\nVistas in Astronomy 40, 429\n% CDS as an Astronomical Information Hub \n\n\\bibitem[1998]{cds} Genova, F., Bartlett, J.G., Bonnarel, F., et al., \n1998, in {\\em Astronomical Data\nAnalysis Software and Systems VII}, ASP Conf. Ser. 145, p. 470\n% CDS information hub\n\n\\bibitem[2000]{cds2000} Genova, F., et al., 2000,\nA\\&AS, \\emph{in press}\n(CDS)\n% CDS, in this volume\n\n\\bibitem[2000]{isaia} Hanisch, R., 2000, {\\em Computer\nPhysics Communications}, in press\n\n\\bibitem[1986]{messenger}\n Heck, A., Egret, D., 1987, Messenger, 48, 22-24\n% SIMBAD, the CDS database\n\n\\bibitem[1995]{heasarc} HEASARC team, 1995, \nin {\\em Information \\& On-line Data in Astronomy}, Egret \\& Albrecht \n(Eds.), Kluwer Academic Publ., p. 139\n% The HEASARC facility\n\n\\bibitem[2000]{ned}\nHelou, G., Madore, B.F., Schmitz, M., et al., 2000, A\\&AS,\nin press\n(NED)\n% The NASA/IPAC Extragalactic Database\n\n\n\\bibitem[1998]{TRC} H{\\o}g, E., Kuzmin, A., Bastian, U., et al., 1998, \nA\\&A 335, 65\n(TRC)\n% Tycho Reference Catalogue\n\n\\bibitem[1975]{mss} Houk, N., Cowley, A.P., 1975, Michigan Catalogue of\n Two-Dimensional Spectral Types for the HD Stars, vol. 1\n (MK)\n\n\\bibitem[1978]{MK-MJ} Jaschek, M., 1978,\n Bull. Inf. CDS 15, 121\n% compilation of MK types\n\n\\bibitem[2000]{ADS} Kurtz, M., Eichhorn, G., Accomazzi, A.,\net al., 2000, A\\&AS, in press\n(ADS)\n% The NASA Astrophysics Data System: Overview (this volume)\n\n\\bibitem[1995]{maj95}\n Lalo\\\"e, S. 1995, in {\\em Proceedings of the LISA-II Conference},\nVistas in Astronomy 39, 179\n\n\\bibitem[1993]{maj93} \n Lalo\\\"e, S., Beyneix, A., Borde, S., et al., 1993, CDS Inform. Bull. 43, 57\n\n\\bibitem[1990]{gsc} Lasker, B.M., Sturch, C.R., McLean, B.J., et al., \n 1990, AJ 99, 2019\n(GSC)\n% The Guide Star Catalog\n\n\\bibitem[1995]{lesteven}\n Lesteven, S., 1995, Vistas in Astronomy 39, 187\n% Multivariate data analysis applied to bibliographical\n% information retrieval: SIMBAD quality control\n\n\\bibitem[1998]{lesteven2}\n Lesteven, S., Bonnarel, F., Dubois, P., 1998, in\n {\\sl Proceedings LISA III \n Conference}, U. Grothkpof et al.\\ (Eds.), ASP Conf. Ser. 153, 61\n% Information extraction (finding object names in papers)\n\n\\bibitem[1994]{dic2} Lortet, M.C., Borde, S., Ochsenbein, F., 1994, \nA\\&AS 107, 193\n\n\\bibitem[1987]{UBV} Mermilliod, J.-C., 1987, A{\\&}AS 71, 413 (UBV)\n% UBV Compilation\n\n\\bibitem[1973]{ugc} Nilson, P., 1973, Uppsala General Catalogue of\n Galaxies\n(UGC)\n\n\\bibitem[1982]{bsi}\n Ochsenbein, F., 1982, in {\\em Automated Data\n Retrieval in Astronomy}, ed. C. Jaschek \\& W. D. Heintz, IAU Coll.\n 64, Dordrecht, D. Reidel Publishing Company, p. 171\n(BSI)\n% The Bibliographical Star Index\n\n\\bibitem[2000]{adass9} Ochsenbein, F., Albrecht, M., Brighton, A. \n et al., 2000, in {\\em Astronomical Data Analysis Software and Systems IX}, \n ASP Conf. Ser., in press (XML)\n\n\\bibitem[2000]{vizier} Ochsenbein, Fuer, P., Marcout, J., 2000,\nA\\&AS, \\emph{in press}\n(VizieR)\n% VizieR, in this volume\n\n\\bibitem[1981]{csi}\n Ochsenbein, F., Bischoff, M., Egret, D., 1981, A\\&AS 43, 259\n(CSI)\n% Microfiche edition of CSI (Catalog of Stellar Identifications)\n\n\\bibitem[1992]{type}\n Ochsenbein, F., Dubois, P., 1992, in {\\em Astronomy from\n Large Databases, II}, A. Heck \\& F. Murtagh (Eds.), 405\n% Object type classification \n\n\\bibitem[1999]{ines} Rodriguez-Pascual, P. M.,\nGonz\\'alez-Riestra, R., Schartel, N., Wamsteker, W., 1999, A\\&AS 139, 183\n(INES)\n% INES paper in A&AS, October 1999\n\n\\bibitem[1995]{bibcode}\nSchmitz, M., Helou, G., Dubois, P., LaGue, C., Madore, B.,\nCorwin, H.G. Jr, and Lesteven, S., 1995,\nin {\\em Information \\& On--line Data in Astronomy}, Egret \\& \nAlbrecht (Eds.), Kluwer Acad. Publ., p. 259\n% NED and SIMBAD conventions for bibliographic reference \n% coding\n\n\\bibitem[1962]{mcg} Vorontsov-Velyaminov, B., et al., 1962,\n Morphological Catalogue of Galaxies, in 5 parts, Moscow\n State University, Moscow \n(MCG)\n\n\\end{thebibliography}"
}
] |
astro-ph0002111
|
Comparing Galaxy Morphology at Ultraviolet and Optical Wavelengths
|
[
{
"author": "L. E. Kuchinski\\altaffilmark{1}"
},
{
"author": "W. L. Freedman\\altaffilmark{2}"
},
{
"author": "Barry F. Madore\\altaffilmark{1,2}"
},
{
"author": "M. Trewhella\\altaffilmark{1}"
},
{
"author": "R. C. Bohlin\\altaffilmark{3}"
},
{
"author": "R. H. Cornett\\altaffilmark{4}"
},
{
"author": "M. N. Fanelli\\altaffilmark{4,5}"
},
{
"author": "P. M. Marcum\\altaffilmark{6}"
},
{
"author": "S. G. Neff\\altaffilmark{7}"
},
{
"author": "R. W. O'Connell\\altaffilmark{8}"
},
{
"author": "M. S. Roberts\\altaffilmark{9}"
},
{
"author": "A. M. Smith\\altaffilmark{7}"
},
{
"author": "T. P. Stecher\\altaffilmark{7}"
},
{
"author": "W. H. Waller\\altaffilmark{4,10}"
}
] |
We have undertaken an imaging survey of 34 nearby galaxies in far--ultraviolet (FUV, $\sim 1500 \AA$) and optical ($UBVRI$) passbands to characterize galaxy morphology as a function of wavelength. This sample, which includes a range of classical Hubble types from elliptical to irregular with emphasis on spirals at low inclination angle, provides a valuable database for comparison with images of high--$z$ galaxies whose FUV light is redshifted into the optical and near--infrared bands. Ultraviolet data are from the UIT {Astro--2} mission. We present images and surface brightness profiles for each galaxy, and we discuss the wavelength--dependence of morphology for different Hubble types in the context of understanding high--$z$ objects. In general, the dominance of young stars in the FUV produces the patchy appearance of a morphological type later than that inferred from optical images. Prominent rings and circumnuclear star formation regions are clearly evident in FUV images of spirals, while bulges, bars, and old, red stellar disks are faint to invisible at these short wavelengths. However, the magnitude of the change in apparent morphology ranges from dramatic in early--type spirals with prominent optical bulges to slight in late--type spirals and irregulars, in which young stars dominate both the UV and optical emission. Starburst galaxies with centrally concentrated, symmetric bursts display an apparent ``E/S0'' structure in the FUV, while starbursts associated with rings or mergers produce a peculiar morphology. We briefly discuss the inadequacy of the optically--defined Hubble sequence to describe FUV galaxy images and estimate morphological $k$--corrections, and we suggest some directions for future research with this dataset.
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"string": "\\documentstyle[aas2pp4]{article}\n\\received{}\n\\revised{}\n\\accepted{}\n\\righthead{UV and Optical Galaxy Morphology}\n\\lefthead{Kuchinski et al.}\n\n\\begin{document}\n\n\\title{Comparing Galaxy Morphology at Ultraviolet and Optical Wavelengths}\n\n\\author{L. E. Kuchinski\\altaffilmark{1}, W. L. Freedman\\altaffilmark{2}, Barry F. Madore\\altaffilmark{1,2}, M. Trewhella\\altaffilmark{1}, R. C. Bohlin\\altaffilmark{3}, R. H. Cornett\\altaffilmark{4}, M. N. Fanelli\\altaffilmark{4,5}, P. M. Marcum\\altaffilmark{6}, S. G. Neff\\altaffilmark{7}, R. W. O'Connell\\altaffilmark{8}, M. S. Roberts\\altaffilmark{9}, A. M. Smith\\altaffilmark{7}, T. P. Stecher\\altaffilmark{7}, W. H. Waller\\altaffilmark{4,10}}\n\\altaffiltext{1}{Infrared Processing and Analysis Center, Caltech/JPL, Pasadena, CA 91125}\n\\altaffiltext{2}{Observatories of the Carnegie Institution of Washington, Pasadena, CA 91101}\n\\altaffiltext{3}{Space Telescope Science Institute, Baltimore, MD 21218}\n\\altaffiltext{4}{Raytheon ITSS Corp., NASA Goddard Space Flight Center, Greenbelt, MD 20771}\n\\altaffiltext{5}{Department of Physics, University of North Texas, Denton, TX 76023}\n\\altaffiltext{6}{Department of Physics, Texas Christian University, Fort Worth, TX 76129}\n\\altaffiltext{7}{Laboratory for Astronomy and Solar Physics, NASA Goddard Space Flight Center, Greenbelt, MD 20771}\n\\altaffiltext{8}{Department of Astronomy, University of Virginia, Charlottesville, VA 22903}\n\\altaffiltext{9}{National Radio Astronomy Observatory, Charlottesville, VA 22903}\n\\altaffiltext{10}{Department of Physics and Astronomy, Tufts University, Medford, MA 02155}\n\n\\begin{abstract}\nWe have undertaken an imaging survey of 34 nearby galaxies in\nfar--ultraviolet (FUV, $\\sim 1500 \\AA$)\nand optical ($UBVRI$) passbands to characterize galaxy morphology as a function\nof wavelength.\nThis sample, which includes a range of classical Hubble types from \nelliptical to irregular with emphasis on spirals at low inclination angle,\nprovides a valuable database for comparison \nwith images of high--$z$ galaxies whose FUV light is redshifted into the optical\nand near--infrared bands.\nUltraviolet data are from the UIT {\\it Astro--2} mission.\nWe present images and surface brightness profiles for each galaxy, and we\ndiscuss the wavelength--dependence of morphology for different Hubble types\nin the context of understanding high--$z$ objects.\nIn general, the dominance\nof young stars in the FUV produces the patchy appearance\nof a morphological type later than that inferred from optical images.\nProminent rings and circumnuclear star formation\nregions are clearly evident in FUV images of spirals,\nwhile bulges, bars, and old, red stellar disks\nare faint to invisible at these short wavelengths.\nHowever, the magnitude of the change in apparent morphology ranges from \ndramatic in early--type spirals with prominent optical bulges\nto slight in late--type spirals and irregulars, in which\nyoung stars dominate both the UV and optical emission. \nStarburst galaxies with centrally concentrated, symmetric bursts display\nan apparent ``E/S0'' structure in the FUV, \nwhile starbursts associated with rings or mergers produce a peculiar \nmorphology.\nWe briefly discuss the inadequacy of the optically--defined Hubble sequence to \ndescribe FUV galaxy images and estimate morphological $k$--corrections, and we\nsuggest some directions for future research with this dataset.\n\\end{abstract}\n\n\\section{Introduction}\n \n\\par\nAn understanding of the ultraviolet (UV) properties of local galaxies is\nessential for interpreting images of high--redshift systems and especially \ncritical in searches for\nmorphological evolution in the galaxy population.\nAt redshifts of $ z \\sim 3 - 10$, the rest--frame UV light of \ngalaxies is shifted into the optical (1500$\\AA$ observed in $V$--band\nat $z \\sim 2.7$) and near--infrared (1500$\\AA$ observed in $H$--band at $z \\sim 10$) regions of the \nspectrum that are easily observable from the ground. Although one operational\napproach to overcoming this ``band--shifting'' problem is to observe\nin the infrared\n({\\it e.g.} \\cite{tep98}), \nthe rate of data acquisition for galaxy images is generally highest at optical\nwavelengths where detectors are larger and the sky background is lower \nthan in the infrared. Under these circumstances, the most direct method \nto compare\npresent--day galaxies to those in the early universe is to build a large\nsample of local UV galaxy data.\n\n\\par\nRecent deep surveys suggest that galaxies with peculiar morphology are \nmore prevalent at high redshift ({\\it e.g.} \\cite{bri98}; \\cite{abr96a}).\nHowever, it is difficult to quantify the\ninfluence of band--shifting on observed differences between the optical\ncharacteristics of nearby galaxies and the rest--frame UV appearance of\ndistant ones because UV and optical morphology are not often well--coupled\n(\\cite{oco97a}; Marcum et al. 1997, 2000). Restframe UV images of galaxies\noften suggest a later Hubble type than the\ncorresponding optical appearance: bulges are less prominent, galaxy light\nappears more patchy, and in extreme cases the different star--forming regions\nin a single galaxy may appear as separate systems in the UV (\\cite{oco97a}; \n\\cite{oco96}). On the other hand, recent deep NICMOS imaging of distant\ngalaxies at longer rest wavelengths suggests that some of the morphological\npeculiarities are still visible in the optical and thus are intrinsic in\nthe galaxies' structure ({\\it e.g.} \\cite{bun99}; \\cite{tep98}).\nAlthough methods exist to estimate UV \nmorphology by extrapolation from optical data (\\cite{abr98}; \\cite{afm97}),\nthey rely on\nthe use of global galaxy spectral energy distributions that may not accurately\nrepresent localized conditions, especially in dusty or starbursting regions. \nFor example, Donas, Milliard, \\& Laget (1995) find a variation among UV$-b$\ncolors in galaxies with identical $b-r$.\nThe availability of FUV images for bright, well--resolved galaxies of a \nrange of Hubble types would facilitate a more direct comparison between local\nand distant galaxy populations.\n\n\\par\nThe appearance of galaxies in the UV is determined primarily by emission from\nhot stars and by the distribution of dust, with a contribution in the central\nregions from an AGN if one is present and unobscured.\nLight in the $\\sim$1500$\\AA$ far--ultraviolet (FUV) band of the \nUltraviolet Imaging Telescope (UIT, \\cite{ste97})\noriginates in young objects of spectral types O and B (Fanelli et al. 1997)\nand, if old populations are present, in certain types of low--mass stars \nin late stages of evolution (the ``UVX'' population, see \\cite{oco99} for a review). \nThus this region of the spectrum can probe timescales \nof young stellar populations between that studied via $H\\alpha$ emission\n(only O stars, $\\sim$ 5 Myr) and that evident in the optical colors (which\ntrace the age of a stellar population on timescales of a\nfew Gyr; O'Connell 1997b) .\n\n\\par\nOpacity due to dust in the FUV is a factor of $\\sim$2.5 higher\nthan in the optical $V$ band, assuming a Galactic extinction law \n(\\cite{ccm89}), and even larger for Small Magellanic Cloud--type dust\n (\\cite{gor97}). The young, massive stars that provide the bulk of the\nUV emission also tend to have small scale heights, less than or similar to that\nof the dust, while older stars that dominate at optical wavelengths and \nhave scale heights greater than that of the dust layer (\\cite{mih81}).\nThe degree to which dust extinguishes the UV light of\nhighly inclined disk galaxies is unclear. It likely depends strongly on\nthe relative\ngeometry of star--forming regions and dust concentrations, a phenomenon\nrecently noted in optical/NIR studies of nearby galaxies as well as in\ntheoretical studies of systems with a mixture of stars and dust\n(\\cite{kuc98}; Gordon et al. 1997; \\cite{hui94}). For instance,\nNGC 4631 is quite bright in the FUV and blue in FUV--optical colors, and it \ndoes not show evidence for strong\nattenuation (Smith et al. 1997, 2000; \\cite{oco97a}). \nHowever, NGC 891 is only barely detected \n(Marcum et al 1997, 2000), a phenomenon that Smith et al. suggest is due \nto extinction effects. UV morphology may also be dramatically influenced by \nspecific features such as dust lanes, as noted in Cen~A \nby O'Connell (1997a). \nScattering by dust grains is quite efficient in the FUV (\\cite{wit92})\nand may contribute significantly to the emission near H II regions and\nin spiral arms (\\cite{wal97a}; \\cite{ste82}).\n\\par\nPrior to the Space Shuttle--borne UIT {\\it Astro} missions,\nUV imaging of galaxies was\nlimited to low resolution and/or small fields of view (see \\cite{bro99} for\na detailed review). UIT--prototype \nrocket--borne experiments\nin the 1980's provided images of five nearby galaxies with a resolution\nof $\\sim$15$\\arcsec$ and ten more with a resolution of 100$\\arcsec$\n(\\cite{hil84}; \\cite{boh91}). The FOCA balloon\nexperiment yielded images of similar resolution for six nearby galaxies\n(\\cite{ble90}). Recently, higher resolution UV images of 110 galaxy \nnuclei (\\cite{mao96}) and nine starburst galaxies (\\cite{meu95}) have been\nobtained at 2200$\\AA$ using the Hubble Space Telescope's\nFaint Object Camera with a very small (22\\arcsec) field of view. \nA FUV ($\\sim$1500$\\AA$) survey of galaxies at redshifts of\n$\\sim$~0.1--0.2 is also underway\nusing the Space Telescope Imaging Spectrograph, again with a small (25\\arcsec)\nfield of view (\\cite{gar97}). \nWith a 40$\\arcmin$ field of view and $\\sim$3$\\arcsec$ \nresolution, UIT was optimally suited to \nstudy the morphology of nearby galaxies with good resolution.\nThe usefulness of UV and optical images and radial profiles to study \nmorphology variations with wavelength was demonstrated by \\cite{cor94}\n with UIT {\\it Astro--1}\ndata for M74, by \\cite{hil97} for M51, and by \\cite{rei94} for M81.\n\n\n\\par\nIn this and a companion paper (Marcum et al. 2000), we present\nthe results of an UV--optical imaging survey of \nnearby bright galaxies. The UV images were obtained by the UIT during the \n{\\it Astro--1} and {\\it Astro--2} Spacelab missions in 1990 and 1995 \nrespectively. Ground--based optical CCD images of the sample galaxies \nwere obtained with pixel scales and fields of view approximately comparable\nto those of the UIT images. The {\\it Astro--1} data presented in \nMarcum et al. include both FUV ($\\sim$1500$\\AA$) and NUV($\\sim$2500$\\AA$)\ndata as well as optical images for 43 galaxies. This paper includes FUV\nand optical data for 34 galaxies observed during {\\it Astro--2}\nwith Hubble types specifically chosen to span\nthe range E to Irr, including some interacting/merging systems. \nThere is some emphasis in the sample selection on face--on spirals in \nwhich spiral arm, bar, and ring morphologies are easily observed.\nIn Section 2 we discuss the sample selection, describe the UIT\nand optical observations, and explain the basic data reduction.\nSection 3 contains details of the registration of FUV and optical images and\nthe extraction of surface brightness and color profiles. A qualitative\ncomparison of UV and optical morphology, based on the images and profiles,\nis presented in Section 4. In Section 5 we provide a brief summary and \ndiscuss avenues of future investigation, including studies of the \nmorphological $k$--correction and analysis of the star--formation histories\nof individual galaxies. In a subsequent paper (\\cite{kuc00}), we will\ninvestigate the quantitative concentration and asymmetry indices for these\ngalaxies and consider the implications of these results for the study of \nhigh--redshift galaxies.\n\n\\section{Observations and Data Reduction}\n\n\\subsection{Sample Selection}\n\n\\par\nOur sample consists of 34 galaxies observed with UIT during the\n{\\it Astro--2} mission for which we have also obtained ground--based optical\nimages. Many of the galaxies were selected as part of a UIT Guest Observer\nprogram specifically to investigate the UV morphology in prototypes\nof different Hubble types. Others were observed during UIT studies of \nstarburst galaxies ({\\it e.g.} \\cite{smi96}), early--type galaxies \n(\\cite{ohl98}), AGNs (Fanelli et al. 1997a), or individually for\nselected purposes. It is important to remember that while this sample does\ncontain galaxies with a range of morphologies, it was not chosen to \nstatistically represent the relative distribution of Hubble types \nin the local population. \nThe galaxies have types E to Irr ($T$ = --5.0 -- +10.0), and are located\nat distances of $\\sim 2 - 25$ Mpc ($H_0 = 75$km/s/Mpc).\nLate--type systems in which star\nformation produces prominent morphological features in the FUV are emphasized.\nThree sets of interacting pairs are included: NGC 3226/7, NGC 4038/9, and\nNGC 5194/5. Table~\\ref{galxdat} gives basic properties of the sample galaxies.\n\n\\subsection{Ultraviolet Observations and Data Reduction}\n\n\\par\nThe sample galaxies were observed in the FUV with UIT, a 38cm. \nRitchey--Chretien telescope mounted on the {\\it Astro} payload. The\n{\\it Astro--2} mission during which these data were obtained was flown on\nthe Space Shuttle Endeavour on 2--18 March 1995.\nDetails of the telescope and instrumentation, as\nwell as specific information about pipeline data processing of the UV images, \ncan be found in Stecher et al. (1997) and will be briefly summarized here.\nOnly the FUV ($\\sim $1500\\AA) camera was operational during the \n{\\it Astro--2} mission.\nTwo FUV filters were used: the B1 filter with an effective wavelength of\n1520${\\rm \\AA}$ and width 354${\\rm \\AA}$, and the slightly narrower\nB5 filter with effective wavelength of 1615${\\rm \\AA}$ and width\n225${\\rm \\AA}$, which was used during\ndaylight observations to exclude dayglow emission lines (\\cite{hil98};\n\\cite{wal95}).\nBased on observations of early--type galaxies (\\cite{ohl98}), \nthere is no evidence for a ``red leak'' in the system. The camera consisted\nof a two--stage image intensifier coupled to Kodak IIa--0 film on which\nthe images were recorded. The photographic film was digitized \nwith a 20$\\mu$m square aperture and 10$\\mu$m sample spacing, then binned\nto a 20$\\mu$m spacing (\\cite{ste97}). In the pipeline data reductions,\nbackground ``fog'' from the photographic film was subtracted, and the \nimages were linearized, flatfielded, and calibrated. The final output images\nhave a scale of 1.136\\arcsec/pixel and a typical point spread function of\nFWHM $\\sim$ 3$\\arcsec$ in the central 16$\\arcmin$ of the frame, in which nearly\nall of the galaxies studied here are imaged (\\cite{ste97}).\nUIT images with enough stars to calculate astrometric solutions were corrected\nfor distortion (\\cite{ste97}; \\cite{gre94}); these\ndata products were used where available. However, we note that even on \nuncorrected images, the uncertainty due to distortion\nin the central part of the frame (where most of our galaxy images are located)\nis less than or equal to the PSF FWHM.\n\n\\par\nAfter visual inspection of all available FUV images for each galaxy, we \nselected the ones with the best signal--to--noise and image quality for further \nanalysis. In most cases this is the image with the longest exposure time, \nunless that image is noted in the UIT log to suffer \npointing problems or other defects. In such cases, the longest\nexposure time image of good quality was used. \nThe UV--bright center of NGC 4151 is saturated in the UIT {\\it Astro--2} \nimages; for photometry of this galaxy, see \\cite{fan97a}.\nWe select a long--exposure UIT image of this galaxy to show\nthe faint spiral arms as well as the active nucleus.\nThe UIT exposure time of the image selected for each galaxy\nis given in Table~\\ref{galxd2}.\n\n\\par\nMany of the FUV images required no further processing beyond\nthe UIT pipeline, but some have a noticeable ``stripe'' artifact through\nthe center of the frame (\\cite{ste97}). \nIf the entire galaxy was located within the stripe, no\ncorrection was made and care was taken to determine the sky value within the\nstripe as well. For galaxies located partly within and partly outside the\nstripe, a quadratic surface was fit to the frame after masking out the \ncentral region (where the galaxy lies) and the frame edges.\nThis surface was then subtracted before the sky background and surface\nbrightness profile were measured. The FUV sky background is typically low\n(see \\cite{wal95} for a discussion of the UV background),\nranging from undetectable (with a 1--$\\sigma$ limit of \n$\\sim$25~mag~arcsec$^{-2}$) up to 22~mag~arcsec$^{-2}$ for a few images\nacquired during daylight. \n\n\\subsection{Optical Observations and Data Reduction}\n\n\\par\nBroad--band optical images of the sample galaxies were obtained over\nthe past several years with the Las Campanas Observatory 2.5m du Pont \ntelescope, the CTIO 1.5m telescope, and the Palomar 1.5m and 5m telescopes. \nAll of the galaxies presented here were imaged in at least one of the \n$UBVR_{c}I_{c}$ bands; many have multi--color photometry.\nObservations at Las Campanas were carried out using the 2048$\\times$2048\nTek 5 CCD with a scale of 0.26\\arcsec/pixel. The CTIO observations \nutilized the Tek 2048$\\times$2048 CCD with a scale of 0.43\\arcsec/pixel.\nData from the Palomar 1.5m telescope were taken using the 2048$\\times$2048\nCCD13 or CCD16 with a scale of 0.37\\arcsec/pixel; some of these were \nbinned to 1024$\\times$1024 with a scale of 0.74\\arcsec/pixel. Observations\nwith the Palomar 5m telescope used the COSMIC camera with a 2048$\\times$2048\nCCD and a scale of 0.28\\arcsec/pixel; again some images were binned\nto a scale of 0.55\\arcsec/pixel.\nTable~\\ref{galxd2} shows the telescope, filters, and exposure times\nfor each galaxy.\n\n\\par\nData reduction for the optical images was carried out using the \nIRAF (\\cite{tod86}) and VISTA (\\cite{sto88}) packages.\nThe images were bias--subtracted and flatfielded with twilight or\ndome flats for each filter. An apparent gradient in the background of \nsome of the $V$, $R$, and $I$ frames taken at Palomar remained after these\nsteps. A planar\nsurface was fit to these frames after masking out the galaxy, then subtracted\nbefore further processing. Cosmic rays were identified with the \nIRAF ``cosmicrays'' package and were replaced with an average of surrounding\npixel values. If more than one data frame was available for a galaxy in\na specific filter, the frames were registered using the coordinates of\nseveral bright stars, scaled to the same exposure time, and\na zeropoint offset was applied to match the background levels.\nThe frames were then averaged (for two) or median combined (for \nthree or more). Some of the images are saturated at the galaxy centers; no \ncorrection is applied but the saturated pixels were flagged for future \nconsideration. Sky levels were determined in boxes away from the galaxy. \nIn some cases (flagged in Table~\\ref{galxd2}) the galaxy nearly fills the\nframe and thus the background\nlevel is somewhat uncertain. On images in which several regions of sky away \nfrom the galaxy can be measured, the typical r.m.s. scatter in sky levels\nacross the frame is less than 2\\% of the sky value.\n\n\\subsection{Data Calibration}\n\n\\par\nCalibrations were applied to each image to obtain the approximate\nrelative alignment of the multicolor light profiles presented in Section~3.\nThe UIT data were calibrated using standard stars measured by\nthe International Ultraviolet Explorer ($IUE$). The resulting flux calibration\nis estimated to be accurate to $\\sim~15\\%$ (\\cite{ste97}); this value \nincludes the uncertainty in the final $IUE$ calibration. Magnitudes are\non the monochromatic system:\n\\begin{equation}\n{\\rm mag_{\\lambda}} \\: = \\: -2.5 {\\rm log_{10}} (f_{\\lambda})\\; - \\; 21.1\n\\end{equation}\nwhere the flux is in units of erg cm$^{-2}$s$^{-1}$ $\\AA^{-1}$.\nCalibration data for each image are stored in the image headers of the UIT\ndata products.\n\n\\par\nBecause many of the optical data were obtained under non--photometric \nconditions, the frames were calibrated via comparison to published aperture\nphotometry for each galaxy. We used the catalog of \\cite{pru98}, excluding\nany data whose zeropoint was found by these authors to be systematically \noffset by more than 0.05 mag. from that galaxy's curve of growth.\nWe calculated the difference between a synthetic aperture\nmagnitude measured on our galaxy image and the published value for\neach of the tabulated apertures that fit on our frame. After examining\nthe residuals as a function of ($B-V$) or ($V-I$) color for those galaxies \nwith sufficient\npublished data over a range of colors, we found no strong evidence for \ncolor terms in the calibration. Therefore, we simply used the mean difference\nbetween the measured and published magnitudes as a calibration constant.\nFor images in which the galaxy center was saturated, we compared the\nobserved and published magnitudes in annuli between the smallest published\naperture that enclosed all the saturated pixels and subsequent apertures.\nThe typical scatter around this mean difference ranges from 0.02--0.15 mag.,\nwhich is not unexpected for a mix of photometric and non--photometric data from\nseveral different instruments. The uncertainty in optical aperture magnitudes\ndue to sky and instrument noise is typically $\\leq 3\\%$. If no catalog\ndata were available for a particular galaxy/filter, we substituted an average\nof the calibration constants determined in that filter for other galaxies\nobserved during the same night. As all but one of these cases \ninvolved calibration of $R$ or $I$--band data, airmass differences between \nthe galaxies that were bootstrapped and those for which calibrations were\ndetermined from the literature are likely to contribute only small errors.\nGalaxies for which this procedure was necessary are flagged in \nTable~\\ref{galxd2}; their calibrations are\ncorrespondingly less certain than the others. Overall, combining the \nnoise and calibration errors, we estimate an uncertainty in \nthe optical magnitudes of $\\leq 15\\%$, with the exact value for each\ngalaxy depending on the quality of the observations and the availability\nof published data.\n\n\\subsection{Image Alignment and Stellar Masks}\n\\par\nIn order to facilitate the direct comparison of galaxy morphology at UV and \noptical wavelengths, we transformed the coordinates of the\noptical data onto the system of the UIT data and smoothed all data for a\nparticular galaxy to the same resolution. Because the FUV images contain\nfew or no stars, the coordinates of UV--bright star--forming regions were\nused to determine a linear transformation (rotation, scaling, and\ntranslation) between the shortest wavelength optical image and\nthe UIT data. After the transformation was applied to that optical image, \nthe centroids of several bright stars were used to align additional\noptical data. Finally, we measured the FWHM of the point spread function (PSF)\non each optical image and smoothed the frame\nto the UIT resolution of 3\\arcsec. The PSF FWHM for two galaxies, M51 and \nNGC 925, were slightly larger than the UIT FWHM (4$\\arcsec$ and 4.5$\\arcsec$ \nrespectively); in these cases the \nUIT images were smoothed to the optical resolution.\nThe final images have the UIT scale of 1.136\\arcsec/pixel, implying\nphysical scales ranging from $\\sim 10 - 140$ pc/pixel for our sample galaxies.\n\n\\par\nForeground stars and any remaining artifacts were masked out on the optical\nand FUV data before producing the images and surface brightness \nprofiles presented in Section 3. For the optical data, we identified\nstars on the longest wavelength image and created a mask that\nwas used to interpolate over those pixels on all of the optical images.\nMost of the sample galaxies lie at high Galactic latitude, so few foreground\nbright stars were present. However, in the case of NGC 2403,\nbadly saturated bright \nstars in the $R$ and $I$--bands necessitated masking large areas of those\nimages. For this galaxy, we created a separate mask for the $UBV$ images, \nwhich did not require such extensive corrections.\nIn a few cases it was difficult to determine whether bright spots within\nthe galaxy were foreground stars or HII regions; \nhere we carefully compared the optical and FUV images and masked only those\nspots that were not visible in the FUV. Some galaxies also required \na FUV mask to interpolate over small, bright point--like or streak artifacts\n (mostly due to cosmic rays) that remained after prior data processing. \n\n\\section{Images and Surface Brightness Profiles}\n\n\\par\nIn Figures~\\ref{ims}($a-n$), we present multiwavelength images for the\nsample galaxies. The sky backgrounds have been removed, foreground stars \nhave been masked as described above. For display purposes only, image \npixel values have been converted to ``calibrated'' flux units such that: \n\\begin{equation}\n{\\rm mag \\; arcsec^{-2}} \\: = \\: 26. \\; - \\; 2.5 {\\rm log_{10}(pixel \\; value)}\n\\end{equation}\nThe images for a given galaxy are displayed using the same range of calibrated \nbrightness for each filter, so that pixels with the same brightness\n(flux/$\\AA$) have a constant gray level on each image.\nThis mode of presentation shows the relative limiting surface brightnesses\nof the data at different wavelengths. To conserve space,\nwe do not show every optical \nimage, as those from adjacent optical filters often look nearly identical. \nIt is quite difficult to simultaneously\nshow structure in the bright centers of galaxies and faint outlying\nfeatures, so we present additional images of some galaxies \nwith different scales or normalizations in Figures~\\ref{vfigsf} and\n\\ref{vfigearly}.\nThe four FUV--bright galaxies shown in Figure~\\ref{vfigsf} are displayed with\na much larger scale to show the central regions.\nIn Figure~\\ref{vfigearly}, we show several galaxies with red FUV--optical\ncolors, mainly early--type galaxies or those with a prominent optical bulge.\nHere we show the optical images with a much larger stretch\nthan the FUV data, so that the central structure of the optical image can\nbe compared to the FUV. We also plan to make our images available to the\ncommunity in digital form via the NASA/IPAC Extragalactic Database (NED); \nthey can then be renormalized as appropriate for any application.\n\n\\par\nWe extract surface brightness profiles for each galaxy by azimuthally\naveraging around concentric ellipses. The ellipse center, ellipticity, \nand position angle (P.A.) for each galaxy were determined by running an \nellipse--fitting package in VISTA (based on the method of \\cite{ken83})\non the longest available wavelength image, usually $R$ or $I$. \nThe centroid was determined \nin a small box around the visual center of the galaxy, taking care to use\nan image in which the center was not saturated. The ellipticity and P.A.\n are determined from the outer ellipses, where their values were typically\nstable over a large range in radii. These ellipse parameters were used to\nobtain surface brightness profiles at all wavelengths, in order to avoid \nproblems with determining centroids and fitting ellipses on the\noften asymmetric and irregular FUV images. For one galaxy, NGC 3115, we\nwere unable to align the optical and FUV images due to a lack of bright \nfeatures or foreground stars in the FUV. We determined a separate FUV \nellipticity and P.A. for this galaxy using the ellipse fitting routine. \nThe ellipticity and P.A. for each galaxy, which are given in \nTable~\\ref{galxdat},\nare quite similar to the $RC3$ (\\cite{dev91}) values \n($\\Delta \\epsilon \\sim 0.05$ and $\\Delta {\\rm P.A.} \\leq 15^{\\circ} $).\nThe surface brightness profiles derived for each sample galaxy are shown in \nFigure~\\ref{sbprofs}($a-g$), with data from the various filters denoted\nby different symbols. Images in which the galaxy center was saturated are\nidentifiable by their flat profiles in the central regions; this is the\ncase for several optical images and the inner $\\sim$10$\\arcsec$ of\nthe FUV data for NGC 4151.\nProfiles for a subset of our sample were compared to those extracted\nby Fanelli et al. (1997b) from the same data; no significant differences\nare noted.\nThe profiles have not been corrected for foreground Galactic extinction. \nHowever, the foreground $A_{B}$ values (given in Table~1) are generally small, \nso even FUV extinctions of $\\sim 2\\times A_{B}$ amount to $\\leq 0.5$mag and\nwould have little effect on the plots of Figure~\\ref{sbprofs}.\n\n\\par\nThree systems in our sample are interacting pairs for which it is difficult\nto separate the light profiles of the two galaxies: NGC 4038/9, NGC 3226/7, \nand NGC 5194/5 (M51a,b). (NGC 4647 and NGC 4649 are a close pair that may be\nundergoing a mild interaction, but their FUV isophotes do not overlap in our\nimages.) For NGC 5194/5, the companion galaxy NGC 5195 is \nundetected in the FUV image and thus is not analyzed separately. The \nellipse parameters for NGC 5194 are determined from a region unaffected by\nthe companion on the optical images. Many of the outer ellipses cut through\nthe companion, creating a slight ``bump'' in the outer part of the \noptical surface brightness profiles. The outer ellipses for NGC 3227\nencompass all of the FUV light and a significant fraction of the optical \nlight of its companion NGC 3226. Within the available software packages, \nit is impossible to avoid this situation \nwithout either severely truncating the NGC 3227 profile or changing the\nellipticity so much that it no longer accurately reflects the shape of \nNGC 3227. However, the NGC 3226 profile of the region with\ndetectable FUV emission is relatively unaffected. The merger system\nNGC 4038/9 is treated as one galaxy, as the FUV image does not suggest a\nsimple division into two separate disks. We created an image of\nthis system\nconsisting of only pixels with flux greater than 1.5$\\sigma_{\\rm sky}$ above\nthe background that also have at least 4 adjacent pixels above the threshold.\n(``Adjacent'' pixels are defined as those that share either an edge\nor corner with the pixel in question; thus \neach pixel has 8 adjacent neighbors.) This image is approximately circular, \nso we defined an aperture center at the geometric center of the FUV \nimage and used circular annuli to measure the light profiles.\n\n\\par\nColor profiles are produced by subtracting the surface brightness\nprofiles (in mag~arcsec$^{-2}$) of different filters.\nThe use of a single set of ellipse parameters\nfor all images of a particular galaxy ensures that the light profiles at\neach wavelength sample the same physical region and thus can be \ncompared in this simple manner. Color profiles for many of the sample galaxies\nwill be presented and discussed in the next section.\n\n\\section{Optical and FUV Morphology}\n\nIn this section we present a qualitative discussion of the differences in \napparent morphology between FUV and optical images. The morphological \ntypes included in each subsection below are approximate, stemming in part\nfrom the fact that several galaxies\nhave characteristics associated with more than one ``type''. Rather\nthan discussing each galaxy individually (as is done in Marcum et al. 2000),\nwe summarize the \nchanges in apparent morphology with wavelength for various Hubble types.\n(Interested readers can see the results for each individual galaxy from\nthe data presented in Figure~\\ref{ims}.) Throughout\nthis section, we also consider implications of our analysis for the study\nof high--redshift galaxies that are observed in their rest--frame UV.\nIt is important to remember that this level of discussion assumes\nno evolution of\nthe star--formation rate: we simply consider what galaxies {\\it identical} to \nlocal ellipticals, spirals, and irregulars would look like at high redshift.\nGalaxies undergoing their initial starburst or a subsequent period\nof increased star formation activity due to mergers, etc. would, of course,\nlook different from the quiescent ellipticals and ``normal'' spirals\nin this sample and may more\nclosely resemble star--forming irregular or peculiar systems.\n\n\\subsection{Elliptical and S0 Galaxies}\n\n\\par\nThe elliptical and S0 galaxies in our sample feature smooth, compact FUV\nemission centered on the nuclear regions (see also the detailed analysis\nof UIT data\nfor E/S0 galaxies in Ohl et al. 1998). In galaxies of this type,\nFUV emission is produced not by young stars but by the hot, evolved\npopulation responsible for the spectrosopic UV upturn (\\cite{oco99}).\nThe FUV light profiles of \nthese systems -- NGC 3379, NGC 3384, NGC 4649, NGC 3226, and NGC 3115 -- \ndrop off much more rapidly than the optical light, and the colors throughout\nare quite red (FUV--$R$ $\\sim$ 2--5). FUV half--light radii for these \ngalaxies are $\\sim$20--35\\% of their $B$--band values tabulated in \nthe $RC3$ (we cannot compare directly to our optical data because most\nof the E/SO optical images suffer saturation in the center).\nThe only exception to this pattern is\nNGC 1510, the interacting companion of NGC 1512. The FUV emission in this\ngalaxy is comparable to the optical light in both\nbrightness and physical extent and is likely due to tidally induced star \nformation rather than the evolved population. Although it is classified in the \n$RC3$ as a peculiar S0 galaxy, \\cite{san79} classify NGC 1510 as an\nAmorphous galaxy, and it is also noted to be a star--forming blue compact\ndwarf (BCD) in\n\\cite{kin93} and an HII galaxy in NED.\n(The other S0/Amorphous galaxy in our sample, NGC 5195, is also interacting\nwith companion galaxy NGC 5194 but is not detected in the FUV.)\n\\par\nIt is difficult to predict the appearance of high--redshift E/S0 galaxies in\ntheir rest--frame FUV because the present--day UV emission mechanism, that of \nevolved stars, is likely to be weak to nonexistent at redshifts approaching \n$z \\sim 1$ (Brown et al. 1998, 2000). Indeed, the UV upturn phenomenon is a\npotentially sensitive age indicator for evolved stellar populations, and\nthus its evolution with redshift could help identify the formation epoch of\nearly--type galaxies (\\cite{yi99}). At high redshifts ellipticals may be \nundergoing an initial starburst and/or the UV upturn population will not yet\nhave had time to evolve. In this case, the progenitors of present--day\nelliptical and S0 galaxies may look like local starbursts or mergers\ndepending on their formation mechanism and the timing of the observations.\nHowever, if some high--redshift E/S0's were quiescent and identical to local \nearly--type galaxies ({\\it i.e.} assuming a very high formation redshift),\nthey would still have the smooth and symmetric light distributions associated\nwith early types. Their FUV emission would be much more compact than the\noptical light, which would lead to difficulties in detection and confusion in\nestimating their typical size. \n\n\\subsection{Early--Type Spiral Galaxies}\n\n\\par\nGalaxies of Hubble type Sa--Sbc tend to appear as later--type\nspirals in the FUV than at optical wavelengths, primarily\ndue to fading of the red\nbulge and bar in UV images. A significant fraction of the FUV light in \nthese systems comes from star--forming regions in the spiral arms, which \nare visible in the images of Figure~\\ref{ims} and appear as ``bumps''\nin the FUV surface brightness profiles of Figure~\\ref{sbprofs} (see also \n\\cite{fan97b}).\nSome early--type spirals, such as M63 and NGC 1672, also appear more\npatchy or fragmented in the FUV because old stars in the underlying smooth\ndisk do not produce much light at very short wavelengths. \nThese results are in agreement with earlier work by O'Connell (1997a) and\nO'Connell \\& Marcum (1996) for smaller samples of galaxies.\nThe dramatic fading of \nlight in the central regions (also noted by \\cite{oco97a} and \\cite{wal97b})\nproduces a global pattern in which the central FUV--optical colors are much\nredder than the outer regions, as shown in Figure~\\ref{ecolpr} for M~51, \nNGC~1566, and M~63. \nTwo notable exceptions to this pattern are NGC 4151, in which the Seyfert 1 \nnucleus dominates the central FUV emission and is much brighter than the\nweak spiral arms, and NGC 1068, in which the FUV--bright Seyfert 2 nucleus\nand surrounding star--formation combine to produce a very blue\ncenter. The UV morphologies and luminosities of the AGN and star--forming\ncomponents in these two galaxies are discussed in more detail by \\cite{fan97a}.\n\n\\par\nMany early--type spirals also show evidence of star--forming inner rings or\ncircumnuclear star formation, which often dominate the FUV images and light\nprofiles. Images of these features, which are present in NGC 1097, NGC\n1512, NGC 1672, NGC 3310, NGC 3351, and NGC 4736, are shown in \nFigure~\\ref{sfring}, and the associated color profiles are plotted in \nFigure~\\ref{ringcolpr}. The star--forming rings appear as spikes of FUV\nbrightness or very blue color in the radial profiles of Figures~\\ref{sbprofs}\nand \\ref{ringcolpr}.\nInner and circumnuclear rings are thought to be orchestrated by dynamical \nresonances, which are often associated with central bars \n({\\it e.g.} \\cite{sto96}; \\cite{but96}). The FUV properties of some\nspecific ringed galaxies are discussed by Waller et al. (1997c, 2000)\nfor NGC 4736, Smith et al. (1996) for NGC 3310, and Marcum et al. (2000).\n\n\\par\nGalaxies classified from their optical images as early--type spirals may present\na variety of different appearances when viewed at high redshift, in their\nrest--frame FUV. Optically barred galaxies such as NGC 1097 and NGC 1365 will \nappear unbarred in the ultraviolet. \nIsolated galaxies such as NGC 1672 that appear highly \nfragmented in the FUV may be mistaken for an ongoing merger.\nImages of distant systems may recover only the FUV--bright star--forming\nrings or circumnuclear star formation, yielding little evidence of\nthe underlying regular structure seen in the galaxy's optical light (see\nalso Waller et al. 1997b).\nOn the other hand, galaxies such as NGC 4151 appear to have an earlier\nmorphological type in the FUV due to the prominence of\nhighly symmetric and strongly peaked\nemission from the active nucleus. Finally, the appearance of a galaxy\nundergoing a global starburst,\nsuch as NGC 3310, does not differ a great deal between the FUV and optical\nbecause the light at both wavelengths is dominated by young stars. \nWe have found that all of these effects can vary in magnitude,\nsuch that some galaxies would be assigned nearly the same Hubble type in\nthe optical and FUV, while others would have very different classifications.\nOverall, most optically--classified early--type spirals present the \nappearance of a later type in the FUV, but a small fraction may appear\nto have identical or earlier FUV types in the presence of starburst activity\nor an AGN.\n\n\\subsection{Late--Type Spirals, Irregulars, and Starbursts}\n\n\\par\nGalaxies that are optically classified as late--type spirals generally do\nnot show as dramatic a difference between their FUV and optical morphologies as\ndo early--type spirals. Although they often appear\nsomewhat more patchy in the FUV, there is no prominent optical bulge whose\nabsence at short wavelengths is noticeable. Star formation\noccurs over a large fraction of the galaxy, producing both FUV and optical\nlight in the same physical regions.\nA number of these galaxies, including NGC 4449, NGC 925, NGC 1313, and IC 2574,\nshow color profiles that have no definite trend with radius. These \nprofiles, examples of which are displayed in Figure~\\ref{flatcolpr}, \nare either flat or bumpy depending on the relative prominence of star--forming \nregions against the background disk. \nFigure~\\ref{bluecolpr} shows color profiles for the central starburst galaxies\nM83, NGC 4214, and NGC 5253, which are bluest in their centers. \nNGC 4214 and NGC 5253 have global color gradients in the\nopposite direction of that observed in early--type spirals due to the\npresence of a blue starburst superposed on a more extended old stellar\ndistribution. This ``starburst core'' morphology has been previously\nnoted in FUV--optical image comparisons of NGC 4214 (Fanelli et al. 1997c)\nand NGC 5253 (Kinney et al. 1993). A\ncentral starburst combined with bright star--forming regions in the outer\ndisk can also produce a flat color profile, which is the case for NGC 2903 \n(also shown in Figure~\\ref{bluecolpr}). \n\n\\par\n\nWe find that\nthe morphological $k$--correction for late--type galaxies is expected\nto be highly dependent on whether or not they host starburst activity.\nAs evident from their similar FUV and optical morphology, non--starbursting\nlate--type galaxies (dominated by ongoing disk star formation)\nviewed at high redshift would not generally appear to have a very different\ntype from their local counterparts. Increased patchiness in the FUV (if\nit were still detectable at large distances) might suggest a slightly later\ntype than the optical appearance. However, galaxies with central starbursts\nlike those\nseen in NGC 4214 and NGC 5253 might present compact cores surrounded by \ndiffuse light, similar to some objects seen on deep HST images\n(Giavalisco, Steidel, \\& Duccio Macchetto 1996a). \nThe symmetric central burst in NGC 5253\nmight even appear to be an E or S0 galaxy in the absence of the old stars.\nIf starburst systems are more prevalent at high redshift, their strong\ninfluence on the rest--frame UV morphology must be considered when\nstudying the evolution of the galaxy population.\n\n\\subsection{Interacting Systems}\n\n\\par\nAs might be expected, the morphological $k$--correction for interacting\ngalaxies depends strongly on the details of the interaction itself.\nThree objects in our sample are currently undergoing interactions of various\ndegrees: NGC 4038/9 (the Antennae), NGC 3226/7, and NGC 5194/5 (M51).\nThe merger of two disk galaxies in NGC 4038/9 has produced a significant\namount of massive star formation, concentrated mainly between the two\ndisks and around the edge of the NGC 4038 disk. Thus the FUV image shows\na partial outline of the merger system, and, without the corresponding optical\ndata, suggests the appearance of a single, drastically perturbed galaxy.\nHowever, the old populations visible in long--wavelength optical images\nclearly delineate the inner disks and tidal tails that identify NGC 4038/9\nas an ongoing disk--disk merger. In spite \nof the dramatic difference between its FUV and optical appearances,\nNGC 4038/9 is clearly peculiar at both wavelengths and thus would\nnot be misclassified as any sort of ``normal'' Hubble type galaxy when\nviewed at high redshift.\nBoth galaxies in the NGC 3226/7 interacting pair present FUV morphologies\nconsistent with what would be expected from their Hubble types:\nthe elliptical NGC 3226 appears highly\nconcentrated and the Sa NGC 3227 shows emission from the center\nand a few faint disk star--formation regions. In this case, the influence\nof the interaction in determining the FUV morphology is confined to\nits possible role in driving the Seyfert nucleus and circumnuclear\nstar formation in NGC 3227 (\\cite{kee96}; \\cite{gon97}). \nNGC 5195 is not detected in the\nFUV, likely due to obscuration by dust from a foreground spiral arm in \nNGC 5194 as well as possible internal extinction (see \\cite{san61}.\n\\cite{bar98} also suspect that dust is responsible for their failure to\ndetect NGC 5195 at 2200$\\AA$.) Observed at high redshift in its\nrest--frame UV, the M51 double--galaxy system would appear to be an\nisolated spiral galaxy. Although the examples discussed above demonstrate the \ndifficulty of relating UV and optical morphology for interacting\nsystems, interactions that are significant enough to severely distort\nthe galaxies involved are often associated with enhanced star formation rates\nthat may identify the system as ``abnormal'' in the FUV as well\n(\\cite{ken98} and references therein).\n\n\\subsection{Dust and Morphology}\n\n\\par\nThroughout this section we have discussed FUV morphology mainly in terms\nof the current star formation, but, as suggested by the example of M51,\none cannot neglect the\npossibility that extinction also influences the UV appearance\nof galaxies. It is difficult to ascertain whether the \n``patchiness'' or fragmented appearance of many galaxies in the FUV is due\nto internal extinction or to the pattern of massive star formation.\nTwo of the most highly inclined ($i \\sim 65^\\circ$) galaxies \nin our sample, NGC 2841 and NGC 2903, \nhave asymmetric FUV emission with the bright side corresponding to what\nappears to be the unobscured side of the optical disk. On the other hand, \nNGC 2403 and IC 2574 also have $i \\geq 60^\\circ$ but do not \nappear to suffer heavy extinction on one side of the disk. These results\nprovide further confirmation of the variations in FUV brightness of edge--on\ngalaxies noted by Smith et al. (1997, 2000) for \nNGC~4631 (FUV--bright) and NGC~891 (undetected). An extreme case of\nextinction effects was discussed above for NGC 5195 (M51b), which is completely\nobscured in the FUV by the foreground spiral arm of NGC 5194 (M51a). \nAs noted in the introduction, the role of dust in determining the observed\nFUV morphology depends strongly on the dust--star geometry of individual\ngalaxies and is thus difficult to predict from optical images alone.\n\n\\section{Summary and Discussion}\n\n\\par\nWe have presented FUV and optical images and surface brightness profiles for\n34 galaxies observed with the UIT and compared the apparent morphology at\ndifferent wavelengths in the context of interpreting images of high--redshift\nobjects. The UIT data represent the most detailed set of FUV images obtained\nto date for large, nearby galaxies that are well--resolved. \nPresent--day elliptical and S0 galaxies appear smooth and symmetric in FUV as\nwell as in optical images, but they are much more compact in the FUV and\nmay be faint and/or unresolved at high redshift unless they are \nactively forming stars at that particular look--back time.\nThe majority of spiral galaxies in our sample\nappear to have a later Hubble type in the FUV than at optical wavelengths\ndue to increased patchiness in combination with the fading of light from\nthe bulge and/or bar populations.\nThis effect is particularly dramatic for the early--type spirals, in which\nbulges and often bars are prominent optical features. The optical and FUV\nmorphologies of late--type spirals and irregular galaxies do not differ as much \nas the earlier types because young stars dominate the light in both spectral\nregimes. Some galaxies appear highly fragmented in the FUV images in spite of\na regular optical morphology, making it \nhard to determine from UV data alone whether they are single systems or \nmultiple mergers.\nEven assuming their current rates and patterns of star formation, many spirals\nviewed at high redshift would be assigned later Hubble types than their\nlocal counterparts due to the bandshifting effects.\nCentral or circumnuclear starbursts and star--forming rings, and bright\nspiral arms dominate the FUV light and FUV--optical color profiles of many\ngalaxies. Depending on the relative geometry of dust and young stars, \nextinction can play a varying role (small to dominant) in\ndetermining the apparent\nFUV morphology. From the galaxy sample presented here, it is apparent that\nunderstanding the correlation between FUV and optical morphology depends on\none's knowledge of not only the global optical Hubble type but also \nof smaller scale features, mostly those due to recent star--formation patterns.\n\n\\par\nThe fragmented appearance of many of the FUV images and the prominence of\nyoung stars in structures such as rings or fragments of spiral arms \nproduces FUV morphologies that do not readily fit into the traditional bins\nof the Hubble sequence. In order to characterize\nrest--frame UV galaxy populations at both low and high redshift, it will be\nnecessary to find new ways of describing the morphology that do not by default\ncause the majority of galaxies to fall into the ``peculiar'' or other \ncatch--all bins. It would also be desirable to have an objective \nclassification scheme to express the similarities or differences between \nlocal and distant galaxies in quantitative terms. However, UV data pose\nproblems for many automated classification schemes because galaxy centers\nare often ill--defined and the patchy nature complicates the selection of\nan aperture that encloses a single system. Future work in this area\nwill use UIT data to identify new features or indices that better describe\nthe UV morphology of galaxies. \n\n\\par\nThe dataset presented in this paper will be valuable for studying the\nmorphological $k$--correction that must be taken into account when\ninterpreting deep optical images such as the {\\it Hubble Deep Field} \n(HDF, \\cite{wil96}). The dependence of FUV morphology on features that are\nconsidered minor or secondary details in the optical highlights the\ndifficulty of studying\nevolution in the galaxy population by comparing rest--frame UV observations\nof high--redshift galaxies to the optical properties of local \nsamples. The comparison between local and distant UV galaxy \nimages is much more direct than relying on estimates of the UV morphology \nextrapolated from optical light and colors ({\\it e.g.} Abraham et al. 1997). \nIndeed, a small sample of UIT galaxy images from the {\\it Astro--1} \nmission have\nbeen used to simulate the appearance of high--redshift counterparts of \nnearby bright galaxies (Giavalisco et al. 1996b).\nIn a subsequent paper (\\cite{kuc00}), we simulate the cosmological distance\neffects of surface brightness dimming and loss of spatial resolution on \nthe FUV images of our larger {\\it Astro--2} galaxy sample.\nThese simulations provide examples of how local \ngalaxies would appear in the HDF at redshifts of $\\sim 1 - 4$. In that paper, \nwe also attempt to quantify the effects of bandshifting and distance on \nmorphology using simple parameters such as the central concentration and\nasymmetry of galaxies.\n\n\\par\nOne of the primary goals of studying morphology is to infer the past\nor ongoing physical processes that have shaped galaxies.\nIn combination with current knowledge about the dynamical states\nof nearby galaxies, our multi--wavelength dataset and future UV imaging\ndata from the GALEX sky survey (\\cite{mtin97}) could be used to relate\nUV morphology to physical structures or properties. For example, \nWaller et al. (1997b, 2000) find that UV--bright starburst rings likely\nresult from dynamical resonances with a bar component. Thus ring features\nmay predict the presence of an underlying disk and bar system even in \nUV images that appear to be fragmented or otherwise dynamically disorganized.\nIt would also be of interest to further investigate the suggestion of \nWaller et al. (1997b) that optical Hubble type may be correlated with \nFUV--$V$ color (although rest--frame $V$--band data will not necessarily\nbe available for high--redshift galaxies).\nIf relations between UV morphology and physical properties can be found in \nlocal galaxies {\\it and} shown to extend to large look--back times,\nthey could provide a valuable tool for studying the distant universe\nthrough rest--frame UV imaging.\n\\acknowledgements\nThe authors gratefully acknowledge the help of R. Bernstein, J. Parker, R. Phelps, and N. Silbermann for obtaining some of the optical imaging data presented\nhere. We thank O. Pevunova for assistance with preliminary data reduction.\nWe are also grateful to the anonymous referee for many constructive suggestions.\nFunding for the UIT project was provided through the Spacelab office at NASA \nHeadquarters under Project Number 440-51. WLF and BFM acknowledge support from\nthe Astro--2 Guest Investigator Program through grant number NAG8--1051.\nSome of the data presented here were\nobtained at CTIO, which is operated by AURA as part of NOAO under a cooperative \nagreement with the National Science Foundation. This research has made use of\nthe NASA/IPAC Extragalactic Database (NED), which is operated by the Jet \nPropulsion Laboratory, California Institute of Technology, under contract\nwith NASA.\n\\begin{thebibliography}{}\n\n\\bibitem[Abraham 1998]{abr98} Abraham, R. 1998 in \nThe Ultraviolet Universe at Low and High Redshift, ed. W. H. Waller et al.\n(Woodbury, NY: AIP), 195 \n\\bibitem[Abraham, Freedman, \\& Madore 1997]{afm97} Abraham, R. G., Freedman, W. L., \\& Madore, B. F. 1997, in {\\it HST} and the High Redshift Universe, ed. N. R. Tanvir, A. Aragon--Salamanca, \\& J. V. Wall (Singapore: World Scientific),\n57\n\\bibitem[Abraham et al. 1996]{abr96a} Abraham, R. G., Tanvir, N. R., Santiago, B. 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G. 1993, \\apjs, 86, 5\n\\bibitem[Kuchinski et al. 2000]{kuc00} Kuchinski, L. E., Madore, B. F., Freedman, W. L., \\& Trewhella, M. 2000, in preparation\n\\bibitem[Kuchinski et al. 1998]{kuc98} Kuchinski, L. E., Terndrup, D. M., Gordon, K. D., \\& Witt, A. N. 1998, \\aj, 115, 1438\n\\bibitem[Maoz et al. 1996]{mao96} Maoz, D., Filippenko, A. V., Ho, L. C., Macchetto, F. D., Rix, H.--W., \\& Schneider, D. P. 1996, \\apjs, 107, 215\n\\bibitem[Marcum et al. 1997]{mar97} Marcum, P. M., et al. 1997, in The Ultraviolet Universe at Low and High Redshift, ed. W. H. Waller et al. (Woodbury, NY: AIP), 88\n\\bibitem[, 2000]{mar00} Marcum, P. M., et al. 2000, in preparation\n\\bibitem[Martin et al. 1997]{mtin97} Martin, C., et al. 1997, BAAS, 191, 63.04\n\\bibitem[Martin \\& Roy 1994]{mar94} Martin, P., \\& Roy, J.--R. 1994, \\apj, 424, 599\n\\bibitem[Meurer et al. 1995]{meu95} Meurer, G. R., Heckman, T. M., Leitherer, C., Kinney, A., Robert, C., \\& Garnett, D. R. 1995, \\aj, 110, 2665\n\\bibitem[Mihalas \\& Binney 1981]{mih81} Mihalas, D. \\& Binney, J. 1981, \nGalactic Astronomy (San Francisco: W. H. Freeman)\n\\bibitem[O'Connell 1999]{oco99} O'Connell, R. W. 1999, to appear in \\araa, 1999\n\\bibitem[O'Connell 1997a]{oco97a} O'Connell, R. W. 1997a, in The Ultraviolet Universe at Low and High Redshift, ed. W. H. Waller et al. (Woodbury, NY: AIP), 11\n\\bibitem[O'Connell 1997b]{oco97b} O'Connell, R. W. 1997b, in Star Formation Near and Far, ed. S. S. Holt \\& L. G. Mundy (New York: AIP), 491\n\\bibitem[O'Connell \\& Marcum 1996]{oco96} O'Connell, R. W., \\& Marcum, P. M. 1996, in HST and the High Redshift Universe, ed. N. R. Tanvir, A. Aragon--Salamanca, \\& J. V. Wall (Singapore: World Scientific)\n\\bibitem[Ohl et al. 1998]{ohl98} Ohl, R. G., et al. 1998, \\apj, 505, L11\n\\bibitem[Prugniel \\& Heraudeau (1998)]{pru98} Prugniel, P., \\& Heraudeau, P. 1998, \\aaps, 128,299\n\\bibitem[Reichen et al. (1994)]{rei94} Reichen, M., Kaufman, M., Blecha, A., Golay, M., \\& Huguenin, D. 1994, \\aaps, 106, 523\n\\bibitem[Roberts \\& Haynes 1994]{rob94} Roberts, M. S., \\& Haynes, M. P. 1994, \n\\araa, 32, 115\n\\bibitem[Sandage 1961]{san61} Sandage, A. 1961, The Hubble Atlas of Galaxies (Washington: Carnegie Institution of Washington)\n\\bibitem[Sandage \\& Brucato (1979)]{san79} Sandage, A., \\& Brucato, R. 1979, \\aj, 84, 472\n\\bibitem[Smith et al. 2000]{smi00} Smith, A. M., et al. 2000, \\apj, submitted\n\\bibitem[Smith et al. 1997]{asmi97} Smith, A. M., Collins, N. R., Waller, W. H., Fanelli, M. N., Stecher, T. P., \\& the UIT Team 1997, in The Ultraviolet Universe at Low and High Redshift, ed. W. H. Waller et al. (Woodbury, NY: AIP), 439\n\\bibitem[Smith et al. 1996]{smi96} Smith, D. A., et al. 1996, \\apj, 473, L21\n\\bibitem[Stecher et al. 1982]{ste82} Stecher, T. P., Bohlin, R. C., Hill, J. K., \\& Jura, M. A. 1982, \\apj, 255, L99\n\\bibitem[Stecher et al. 1997]{ste97} Stecher, T. P., et al. 1997, \\pasp, 109, 58, 4\n\\bibitem[Storchi--Bergmann, Wilson, \\& Baldwin 1996]{sto96} Storchi--Bergmann, T., Wilson, A. S., \\& Baldwin, J. A. 1996, \\apj, 472, 83\n\\bibitem[Stover 1988]{sto88} Stover, R. J. 1988, in Instrumentation for Ground--Based Optical Astronomy, ed. L. B. Robinson (New York: Springer), 443\n\\bibitem[Teplitz et al. 1998]{tep98} Teplitz, H. I., Gardner, J. P., Malumuth, E. M., \\& Heap, S. R. 1998, \\apj, 507, L17 \n\\bibitem[Tody 1986]{tod86} Tody, D. 1986, SPIE, 627, 733\n\\bibitem[Tully 1988]{tul88} Tully, R. B. 1988, Catalog of Nearby Galaxies, (Cambridge: Cambridge UP)\n\\bibitem[Waller et al. 2000]{wal00} Waller, W. H., et al. 2000, \\aj, submitted\n\\bibitem[Waller et al. 1997a]{wal97a} Waller, W. H., et al. 1997a, \\apj, 481, 169\n\\bibitem[Waller et al. 1997b]{wal97b} Waller, W. H., Fanelli, M. N., Collins, N. R., Cornett, R. H., Offenberg, J., Marcum, P. M., Stecher, T. P., \\& the UIT Science Team 1997b, in The Ultraviolet Universe at Low and High Redshift, ed. W. H. Waller et al. (Woodbury, NY: AIP), 39\n\\bibitem[Waller et al. (1997c)]{wal97c} Waller, W. H., Stecher, T. P., \\& the UIT Science Team 1997c, in Star Formation Near and Far, ed. S. S. Holt \\& L. G. Mundy (New York: AIP), 287\n\\bibitem[Waller et al. 1995]{wal95} Waller, W. H., et al. 1995, \\aj, 110, 1255 \n\\bibitem[Williams et al. 1996]{wil96} Williams, R. E., et al. 1996, \\aj, 112. 1335\n\\bibitem[Witt et al. 1992]{wit92} Witt, A. N., Petersohn, J. K., Bohlin, R. C., O'Connell, R. W., Roberts, M. S., Smith, A. M., \\& Stecher, T. P. 1992, \\apj, 395, L5\n\\bibitem[Yi et al. 1999]{yi99} Yi, S., Lee, Y.--W., Woo, J.--H., Park, J.--H.,\nDemarque, P., \\& Oemler, A. 1999, \\apj, 513, 128\n\n\\end{thebibliography}\n\n\\figcaption{FUV and optical images of sample galaxies. All images are registered to the FUV coordinate system and oriented with North up and East to the left.\nAs noted in the text, the images are displayed such that pixels of the same\nbrightness (flux) have constant\ngray level for all images of the same galaxy. Scale bars, which are relevant\nto all images of a particular galaxy, are shown on each of the FUV panels. \\label{ims}} \n\\figcaption{FUV and optical images of FUV--bright galaxies rescaled to show\nbright central regions. As in Figure~\\ref{ims}, pixels of the\nsame brightness have constant gray level on all images of a galaxy. \\label{vfigsf}}\n\\figcaption{FUV and optical images of galaxies with red FUV--$V$ colors, \nrenormalized so that optical data are not badly saturated in the display.\nHere, the optical data are displayed with a larger stretch than the FUV images\nin order to compare the central structure in both images. \\label{vfigearly}}\n\\figcaption{FUV and optical surface brightness profiles of sample galaxies. The surface brightnesses are calibrated as described in the text, then offset by a\nconstant to better show the relative shapes. Data from the optical filters are\noffset for ease of viewing; offsets are noted on each panel. Symbols for the \ndifferent filters are as follows: FUV=filled diamonds, $U$=open circles,\n$B$=plus symbols, $V$=open triangles, $R$=open asterisks, \n$I$=open squares. \\label{sbprofs}}\n\\figcaption{FUV--optical color profiles for early--type spiral galaxies. The\ngalaxy name and constant offset (where applicable) are noted next to each profile. \\label{ecolpr}}\n\\figcaption{FUV and optical images of circumnuclear and inner star--forming rings in early--type spirals. The images are aligned, oriented, and scaled as\ndescribed in Figure~\\ref{ims}. \\label{sfring}}\n\\figcaption{Color profiles for early--type spirals with star--forming rings or\ncircumnuclear star--formation. As in Figure~\\ref{ecolpr}, the galaxy name and constant offset are noted next to each profile. Locations of the rings and \ncircumnuclear star--formation (CSF) regions are labeled for each galaxy. \\label{ringcolpr}}\n\\figcaption{Color profiles for late--type galaxies with flat FUV--optical color\ngradients. As in Figure~\\ref{ecolpr}, the galaxy name and constant offset are\nnoted next to each profile. \\label{flatcolpr}}\n\\figcaption{Color profiles for late--type galaxies with central starbursts.\nAs in Figure~\\ref{ecolpr}, the galaxy name and constant offset are\nnoted next to each profile. \\label{bluecolpr}}\n\n\\onecolumn\n\\pagestyle{empty}\n\\small\n\\begin{deluxetable}{lllccrrrr}\n\\tablenum{1}\n\\tablewidth{0pt}\n\\tablecaption{Basic Data for UIT Sample Galaxies \\label{galxdat}}\n\\tablehead{\n\\colhead{Name} \n& \\colhead{$\\alpha $ (2000)\\tablenotemark{a}}\n& \\colhead{$\\delta $ (2000)\\tablenotemark{a}}\n& \\colhead{Type\\tablenotemark{b}}\n& \\colhead{Activity\\tablenotemark{b}}\n& \\colhead{D\\tablenotemark{c}}\n& \\colhead{$A_{B}$\\tablenotemark{c}}\n& \\colhead {$\\epsilon$\\tablenotemark{e}}\n& \\colhead {P. A.\\tablenotemark{f}} \n}\n\\startdata\nNGC 925 & 02 27 16.8 & +33 34 41 & SAB(s)d & \\nodata & 9.4 & 0.25 & 0.40 & 115 \\nl\nNGC 1068 (M 77) & 02 42 40.2 & $-$00 00 48 & RSA(rs)b & Sy 2 & 14.4 & 0.05 & 0.20 & 84 \\nl\nNGC 1097 & 02 46 18.9 & $-$30 16 21 & SB(s)b & Sy 1 & 14.5 & 0.07 & 0.32 & 140 \\nl\nNGC 1313 & 03 18 15.5 & $-$66 29 51 & SB(s)d & \\nodata & 3.7 & 0.03 & 0.20 & 40 \\nl\nNGC 1365 & 03 33 36.6 & $-$36 08 17 & SB(s)b & Sy 1.8 & 16.9 & 0.00 & 0.45 & 32 \\nl \nNGC 1510 & 04 03 32.6 & $-$43 24 01 & S0,pec & H II & 10.3 & 0.00 & 0.12 & 115 \\nl\nNGC 1512 & 04 03 54.6 & $-$43 21 03 & SB(r)a & \\nodata & 9.5 & 0.00 & 0.36 & 56 \\nl\nNGC 1566 & 04 20 00.4 & $-$54 56 18 & SAB(s)bc & Sy 1 & 13.4 & 0.00 & 0.21 & 40 \\nl\nNGC 1672 & 04 45 42.2 & $-$59 14 57 & SB(s)b & Sy 2 & 14.5 & 0.00 & 0.13 & 161 \\nl\nNGC 2403 & 07 36 54.5 & +65 35 58 & SAB(s)cd & \\nodata & 4.2 & 0.16 & 0.44 & 115 \\nl\nNGC 2841 & 09 22 01.8 & +50 58 31 & SA(r)b & LINER, Sy 1 & 12.0 & 0.00 & 0.56 & 147 \\nl\nNGC 2903 & 09 32 09.7 & +21 30 02 & SAB(rs)bc & H II & 6.3 & 0.07 & 0.53 & 24 \\nl\nNGC 3115 & 10 05 14.1 & $-$07 43 07 & S0 & \\nodata & 6.7 & 0.10 & 0.66\\tablenotemark{g} & 43\\tablenotemark{f} \\nl\nNGC 3226 & 10 23 27.4 & +19 53 55 & E2*,pec & LINER & 23.4 & 0.02 & 0.20 & 10 \\nl\nNGC 3227 & 10 23 31.5 & +19 51 48 & SAB(s)a,pec & Sy 1.5 & 20.6 & 0.02 & 0.55 & 157 \\nl\nIC 2574 & 10 28 22.5 & +68 24 39 & SAB(s)m & \\nodata & 2.7 & 0.06 & 0.59 & 62 \\nl\nNGC 3310 & 10 38 46.1 & +53 30 08 & SAB(r)bc,pec & H II & 18.7 & 0.00 & 0.22 & 170 \\nl \nNGC 3351 (M 95) & 10 43 58.0 & +11 42 15 & SB(r)b & H II & 8.1 & 0.04 & 0.32 & 17 \\nl \nNGC 3379 (M 105) & 10 47 49.9 & +12 34 57 & E1 & \\nodata & 8.1 & 0.05 & 0.13 & 65 \\nl\nNGC 3384 & 10 48 17.2 & +12 37 49 & SB0* & \\nodata & 8.1 & 0.05 & 0.50 & 51 \\nl\nNGC 3389 & 10 48 27.9 & +12 32 01 & SA(s)c & \\nodata & 22.5 & 0.06 & 0.55 & 108 \\nl\nNGC 4038 & 12 01 52.9 & $-$18 51 54 & SB(s)m,pec & \\nodata & 25.5 & 0.05 & 0.00\\tablenotemark{h} & \\nodata \\nl\nNGC 4039 & 12 01 53.9 & $-$18 53 06 & SA(s)m,pec & \\nodata & 25.3 & 0.05 & 0.00\\tablenotemark{h} & \\nodata \\nl\nNGC 4151 & 12 10 33.0 & +39 24 28 & SAB(rs)ab*,Pec & Sy 1.5 & 20.3 & 0.00 & 0.36 & 145 \\nl\nNGC 4156 & 12 10 49.7 & +39 28 24 & SB(rs)b & LINER & 90.4\\tablenotemark{i} & 0.00 & 0.20 & 45 \\nl\nNGC 4214 & 12 15 39.5 & +36 19 39 & IAB(s)m & H II & 3.5 & 0.00 & 0.18 & 132 \\nl\nNGC 4449 & 12 28 11.4 & +44 05 40 & IBm & \\nodata & 3.0 & 0.00 & 0.46 & 60 \\nl\nNGC 4647 & 12 43 32.4 & +11 34 56 & SAB(rs)c & \\nodata & 16.8 & 0.04 & 0.20 & 135 \\nl\nNGC 4649 (M 60) & 12 43 40.3 & +11 32 58 & E2 & \\nodata & 16.8 & 0.04 & 0.17 & 130 \\nl\nNGC 4736 (M 94) & 12 50 53.6 & +41 07 10 & (R)SA(r)ab & LINER & 4.3 & 0.00 & 0.22 & 95 \\nl\nNGC 5055 (M 63) & 13 15 49.3 & +42 02 06 & SA(rs)bc & H II, LINER & 7.2 & 0.00 & 0.47 & 102 \\nl\nNGC 5194 (M 51) & 13 29 53.3 & +47 11 48 & SA(s)bc,pec & Sy 2.5 & 7.7 & 0.00 & 0.30 & 30 \\nl\nNGC 5236 (M 83) & 13 37 00.3 & $-$29 52 04 & SAB(s)c & H II & 4.7 & 0.14 & 0.10 & 80 \\nl\nNGC 5253 & 13 39 55.9 & $-$31 38 41 & Pec & H II & 3.2 & 0.19 & 0.57 & 43 \\nl\nNGC 5457 (M 101) & 14 03 12.5 & +54 20 55 & SAB(rs)cd & \\nodata & 5.4 & 0.00 & 0.00 & \\nodata \\nl \n\\vspace*{-0.15in}\n\\tablenotetext{a}{Data from the $RC3$.}\n\\tablenotetext{b}{Nuclear activity classification, from the NASA Extragalactic Database (NED).}\n\\tablenotetext{c}{Distances in Mpc from Tully 1988 ($H_{0} = 75$ km/s/Mpc), except as noted.}\n\\tablenotetext{d}{Foreground Galactic extinction values from Burstein \\& Heiles 1984.}\n\\tablenotetext{e}{Adopted ellipticity for azimuthal averaging in surface brightness profile calculations, defined as $\\epsilon = 1 - \\frac{b}{a}$.}\n\\tablenotetext{f}{Adopted major axis position angle for azimuthal averaging in surface brightness profile calculations.}\n\\tablenotetext{g}{An ellipticity of 0.29 and a P. A. of 118 were used for the\nFUV image of NGC 3115, which was never registered to the optical data (see Section 3).}\n\\tablenotetext{h}{NGC 4038/9 is treated as one galaxy for profile calculation, see Section 3.}\n\\tablenotetext{i}{Distance from V$_{\\rm GSR}$, $H_{0} = 75$ km/s/Mpc.}\n\\enddata\n\\end{deluxetable}\n\n\\begin{deluxetable}{lccrccccccc}\n\\tablenum{2}\n\\tablewidth{0pt}\n\\tablecaption{Observations of Sample Galaxies \\label{galxd2}}\n\\tablehead{\n\\colhead{Name} \n& \\colhead{UV Date}\n& \\colhead{UV(Filter)\\tablenotemark{a}}\n& \\colhead {Optical Date}\n& \\colhead{Telescope\\tablenotemark{b}}\n& \\colhead{$U$\\tablenotemark{a}}\n& \\colhead{$B$\\tablenotemark{a}}\n& \\colhead{$V$\\tablenotemark{a}}\n& \\colhead{$R$\\tablenotemark{a}}\n& \\colhead{$I$\\tablenotemark{a}}\n}\n\\startdata\nNGC 925 & 950314 & 1591 (B5) & 990207 & Pal1.5 & \\nodata & \\nodata & \\nodata& 300\\tablenotemark{c} & \\nodata \\nl\n & & & 990213 & Pal1.5 & 3600\\tablenotemark{c} & 600 & 600 & \\nodata & \\nodata \\nl\nNGC 1068 & 950307 & 753 (B5) & 990214 & Pal1.5 & 3600 & 300 & 300 & 200 & \\nodata \\nl\nNGC 1097\\tablenotemark{d} & 950312 & 1121 (B5) & 951221 & LCO2.5 & 3x400 & 3x200 & 3x200 & \\nodata & 3x200 \\nl\nNGC 1313\\tablenotemark{d} & 950312 & 1071 (B5) & 951224 & LCO2.5 & 2x400 & 2x200 & 2x200 & \\nodata & 2x200 \\nl\nNGC 1365\\tablenotemark{d} & 950315 & 974 (B5) & 951223 & LCO2.5 & 2x400 & 2x200 & 2x200 & \\nodata & 2x200 \\nl\nNGC 1512\\tablenotemark{d}/10\\tablenotemark{e} & 950315 & 949 (B5) & 951220 & LCO2.5 & 3x400 & 3x200 & 3x200 & \\nodata & 3x200 \\nl\nNGC 1566 & 950316 & 1391 (B5) & 951222 & LCO2.5 & 2x400 & 2x200 & 2x200 & \\nodata & 2x200 \\nl\nNGC 1672 & 950307 & 927 (B5) & 951219 & LCO2.5 & 4x400 & 3x200 & 3x200 & \\nodata & 3x200 \\nl\nNGC 2403\\tablenotemark{d} & 950308 & 772 (B1) & 971031& Pal1.5 & 1600 & 600 & 300 & \\nodata & 300 \\nl\n & & & 990208& Pal1.5 & \\nodata & \\nodata & \\nodata & 60& \\nodata \\nl\nNGC 2841 & 950308 & 1021 (B1) & 940214 & Pal5.0 & \\nodata & 300 & \\nodata & \\nodata & 120,2x60 \\nl\n & & & 990213 & Pal1.5 & 3600 & \\nodata & 300 & 200 & \\nodata \\nl\nNGC 2903 & 950307 & 549 (B1) & 951123 & Pal1.5 & \\nodata & 900 & 600 & \\nodata & 600 \\nl\n & & & 990208 & Pal1.5 & \\nodata & \\nodata & \\nodata & 300 & \\nodata \\nl\n & & & 990214 & Pal1.5 & 3600 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\nNGC 3115 & 950307 & 1081 (B1) & 951226 & LCO2.5 & 300 & \\nodata & 300 & \\nodata & 300 \\nl\nNGC 3226/7\\tablenotemark{e} & 950316 & 1271 (B1) & 960218 & Pal1.5 & \\nodata & 450 & \\nodata & \\nodata & \\nodata \\nl\n & & & 990207 & Pal1.5 & \\nodata & \\nodata & \\nodata & 300 & \\nodata \\nl\nIC 2574\\tablenotemark{d} & 950316 & 624 (B1) & 960414 & Pal5.0 & \\nodata & \\nodata & 3x600 & \\nodata & 5x400\\tablenotemark{c} \\nl\n & & & 990208 & Pal1.5 & \\nodata & \\nodata & \\nodata & 300\\tablenotemark{c} & \\nodata \\nl\n & & & 990214 & Pal1.5 & 3600 & 600 & \\nodata & \\nodata & \\nodata \\nl\nNGC 3310 & 950311 & 1131 (B1) & 990207 & Pal1.5 & \\nodata & \\nodata & \\nodata & 300\\tablenotemark{c} & \\nodata \\nl\n & & & 990214 & Pal1.5 & \\nodata & \\nodata & 300 & \\nodata & \\nodata \\nl\nNGC 3351 & 950306 & 881 (B1) & 960118 & Pal1.5 & \\nodata & 600 & 300 & \\nodata & 2x600,300\\nl\n & & & 990208 & Pal1.5 & \\nodata & \\nodata & \\nodata & 300\\tablenotemark{c} & \\nodata \\nl\nNGC 3379/84/89\\tablenotemark{e} & 950306 & 1301 (B1) & 990208 & Pal1.5 & \\nodata & \\nodata & \\nodata & 120 & \\nodata \\nl\nNGC 4038/9\\tablenotemark{d} & 950307 & 881 (B1) & 951222 & LCO2.5 & 1200 & \\nodata & 600 & \\nodata & 600 \\nl\nNGC 4151/6 \\tablenotemark{e} & 950313 & 833 (B1) & 990207 & Pal1.5 & \\nodata & \\nodata & \\nodata & 300 & \\nodata \\nl\nNGC 4214 & 950313 & 1061 (B1) & 960514 & Pal1.5 & \\nodata & 600 & 2x300 & \\nodata & 300\\tablenotemark{c} \\nl\n & & & 990208 & Pal1.5 & \\nodata & \\nodata & \\nodata & 300\\tablenotemark{c} & \\nodata \\nl\nNGC 4449 & 950307 & 987 (B1) & 960515 & Pal1.5 & \\nodata & 600 & 300 & \\nodata & 300 \\nl\n & & & 990207 & Pal1.5 & \\nodata & \\nodata & \\nodata & 300 & \\nodata \\nl\nNGC 4647/9\\tablenotemark{e} & 950311 & 1301 (B1) & 990207 & Pal1.5 & \\nodata & \\nodata & \\nodata & 300 & \\nodata \\nl\nNGC 4736 & 950312 & 1041 (B1) & 990208 & Pal1.5 & \\nodata & 2x600 & \\nodata & 300\\tablenotemark{c} & \\nodata \\nl\n & & & 990213 & Pal1.5 & 3600 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n & & & 990320 & Pal1.5 & \\nodata & \\nodata & 300 & \\nodata & \\nodata \\nl\nNGC 5055\\tablenotemark{d} & 950315 & 1141 (B1) & 990213 & Pal1.5 & 3600 & 600 & 300 & 200 & \\nodata \\nl\nNGC 5194\\tablenotemark{d} & 950312 & 1101 (B1) & 980423 & Pal1.5 & 6x1800 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n & & & 990207 & Pal1.5 & \\nodata & 900 & 600 & 300 & 300 \\nl\nNGC 5236\\tablenotemark{d} & 950306 & 819 (B1) & 960623 & CTIO1.5 & 4x300 & 4x300 & \\nodata & 4x300 & 4x60 \\nl\nNGC 5253 & 950307 & 727 (B5) & 951222 & LCO2.5 & \\nodata & 300 & \\nodata & \\nodata & \\nodata \\nl\n & & & 951223 & LCO2.5 & \\nodata & \\nodata & 3x600 & \\nodata & 2x600 \\nl\nNGC 5457\\tablenotemark{d} & 950311 & 1311 (B1) & 960515 & Pal1.5 & \\nodata & 600 & 300 & \\nodata & 300 \\nl\n\\vspace*{-0.15in}\n\\tablenotetext{a}{Exposure time in seconds. (UV filter in parentheses). }\n\\tablenotetext{b}{LCO2.5 = Las Campanas 2.5m, CTIO1.5 = Cerro Tololo 1.5m, Pal5.0 = Palomar 5m, Pal1.5 = Palomar 1.5m.}\n\\tablenotetext{c}{Calibration estimated from other galaxies observed on the same night (see Section~2.4).}\n\\tablenotetext{d}{Optical sky background uncertain because galaxy fills the frame.}\n\\tablenotetext{e}{Galaxies imaged on same frame.}\n\\enddata\n\\end{deluxetable}\n\\end{document}\n"
}
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{
"name": "astro-ph0002111.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Abraham 1998]{abr98} Abraham, R. 1998 in \nThe Ultraviolet Universe at Low and High Redshift, ed. W. H. Waller et al.\n(Woodbury, NY: AIP), 195 \n\\bibitem[Abraham, Freedman, \\& Madore 1997]{afm97} Abraham, R. G., Freedman, W. L., \\& Madore, B. F. 1997, in {\\it HST} and the High Redshift Universe, ed. N. R. Tanvir, A. Aragon--Salamanca, \\& J. V. Wall (Singapore: World Scientific),\n57\n\\bibitem[Abraham et al. 1996]{abr96a} Abraham, R. G., Tanvir, N. R., Santiago, B. X., Ellis, R. S., Glazebrook, K. G., \\& van den Bergh, S. 1996, \\mnras, 279, L47\n\\bibitem[Barth et al. (1998)]{bar98} Barth, A. J., Ho, L. C., Filippenko, A. V., \\& Sargent, W. L. W. 1998, \\apj, 496, 133\n\\bibitem[Blecha et al. 1990]{ble90} Blecha, A., Golay, M., Huguenin, D., Reichen, D., \\& Bersier, D. 1990, \\aaps, 233, L9\n\\bibitem[Bohlin et al. 1991]{boh91} Bohlin, R. 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}
] |
astro-ph0002112
|
Approximations of the self-similar solution for blastwave \\ in a medium with power-law density variation
|
[
{
"author": "O.~Petruk"
},
{
"author": "NAS of Ukraine"
},
{
"author": "3-b Naukova St."
},
{
"author": "Lviv 79000"
},
{
"author": "Ukraine"
}
] |
% Approximations of the Sedov self-similar solution for a strong point explosion in a medium with the power-law density distribution $\rho^o\propto r^{-m}$ are reviewed and their accuracy are analyzed. Taylor approximation is extended to cases $m\neq 0$. Two approximations of the solution are presented in the Lagrangian coordinates for spherical, cylindrical and plane geometry. These approximations may be used for the investigation of the ionization structure of the adiabatic flow, i.e., inside adiabatic supernova remnants. %
|
[
{
"name": "Approx.tex",
"string": "\\documentstyle{article}\n\\input epsf\n\\setlength{\\topmargin}{-1.2cm} \t\t\n\\setlength{\\headheight}{14pt} \t\t\n\\setlength{\\headsep}{0.5cm}\n\\setlength{\\textheight}{25.1cm}\t\t\n\\setlength{\\oddsidemargin}{0.1cm} \t\n\\setlength{\\evensidemargin}{0.1cm} \t\n\\setlength{\\textwidth}{16.9cm} \t\t\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%========================Title====================================%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{document}\n\\title{Approximations of the self-similar solution for blastwave \\\\\n\tin a medium with power-law density variation}\n\\author{O.~Petruk \\\\\n\tInstitute for Applied Problems in Mechanics and Mathematics \\\\\n \tNAS of Ukraine, 3-b Naukova St., Lviv 79000, Ukraine \\\\\n petruk@astro.franko.lviv.ua}\n\\maketitle \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%=====================Abstract====================================%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{abstract}\n%\nApproximations of the Sedov self-similar solution for a strong point \nexplosion in a medium with the power-law density distribution \n$\\rho^o\\propto r^{-m}$ are reviewed and their accuracy are analyzed. \nTaylor approximation is extended to cases $m\\neq 0$. \nTwo approximations of the solution \nare presented in the Lagrangian coordinates for spherical, cylindrical and \nplane geometry. These approximations may be used for the investigation of \nthe ionization structure of the adiabatic flow, i.e., inside \nadiabatic supernova remnants. \n%\n\\end{abstract}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%======================Intro =====================================%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section {Introduction}\n\nSelf-similar (Sedov \\cite{Sedov-1946b,Sedov}) solutions for the strong \npoint explosion \nin the uniform medium $\\tilde{\\rho}^{o}={\\rm const}$ or in a medium with \npower-law density distribution \n\\begin{equation}\n\\label{rho-power}\n\\tilde{\\rho}^{o}(\\tilde{r})=\\tilde{\\rho}^{o}(0){r}^{-m},\n\\end{equation}\nwhere $\\tilde{r}$ is the distance from the center of explosion, are \nwidely used for modelling the adiabatic supernova remnants, solar flares \nand processes in active galactic nuclei. \\par\n\nSedov (\\cite{Sedov-1946b,Sedov}) has obtained the exact solution \nsolving the system of hydrodynamic differential equation on the base \nof dimensional methods. \nIndependently, Taylor (\\cite{Taylor-50}) has solved the \nsame task in the case of the uniform medium numerically and \nin analitical form approximately. The main Taylor's idea was \nto approximate the fluid velocity variation behind the shock front. \\par\n\nKahn (\\cite{Kahn}) have proposed the approximation of the Sedov \nsolution in the uniform medium. \nHis technic consists in approximation of mass distribution inside the \nshock\\-ed region. \nUsing Kahn methodology, Cox \\& Franco (\\cite{Cox_Fanko-81}) have built the \napproximation of the exact solution in the power-law medium \n(\\ref{rho-power}) for $m<2$. \nWith the same technic, Cox \\& Anderson (\\cite{Cox-And}) have presented the \napproximation for description of the shocked region and blastwave motion \nin uniform medium of finite pressure. \\par\n\nOstriker \\& McKee (\\cite{Ostriker-McKee-88}) basing on the virial \ntheorem have given a number of approximations for \nthe fluid characteristic variation as one- or two-power polinoms. \\par\n\nHnatyk (\\cite{Hn87}) have proposed to approximate firstly the relation between \nthe Eulerian and Lagrangian coordinates of the flow elements. \\par\n\nIn present work, Taylor approximation is written for the medium with \npower-law density variation (\\ref{rho-power}). \nUsing Hnatyk's approach, we develope also two \napproximations of the Sedov solution for power-law medium with $m\\le 2$ in \nLagrangian coordinates \nthat is useful for investigations of the nonequilibrium ionization \nprocesses in a shocked plasma, e.g., inside the adiabatic supernova \nremnants. One of the approximations presented here bases on \nthe approximate hydrodynamic method for description of the \nnonspherical strong point explosion in the medium with arbitrary \nlarge-scale nonuniformity developed by Hnatyk \\& Petruk (\\cite{Hn-Pet-99}). \nTherefore, it may also be considered as additional test on this method. \\par \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%======================Section II=================================%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Sedov solution and its approximations}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Sedov solution}\n\nIf strong ($P_{\\rm s}/P^{o}_{\\rm s}\\rightarrow\\infty$) point \n($R_{o}/R\\rightarrow0$) explosion with finite \nenergy $E_{o}$ becomes in the point with coordinate $\\tilde{r}=0$ \nin time $t=0$, the blastwave creates and propagates with velocity $D$ \nin the ambient medium with density $\\tilde{\\rho}^{o}(\\tilde{r})$ \n($P_{\\rm s}$ and $P^{o}_{\\rm s}$ are pressure of the shocked gas \nand the gas of the ambient medium at the shock \nfront position, $R_{o}$ is the size of the body exploded, $R$ \nis the radius of the blastwave). It is also assumed that \ninjected mass is small and \nno energy lost from the shocked region during the motion. \\par\n\nSuch a task is described by a system of hydrodynamic differential \nequations. \nSedov (\\cite{Sedov}) gives the analytical self-similar \nsolution for description of the motion of shock front and the \ndistribution of fluid parameters inside the shocked region for a \nstrong point explosion in the uniform ambient medium and in the center \nof symmetry of a radially stratified medium (\\ref{rho-power}). \\par\n\nThis solution shows that the strong blastwave in a medium with the \npower-law density distribution (\\ref{rho-power}) moves with \ndeceleration then $m<N+1$ and accelerates then $m>N+1$. \nIf $m\\geq N+1$, both the mass inside any sphere, \nwhich containes the center of the symmetry, and kinetic energy \nequal infinity. We will consider $m<N+1$ cases only. \\par\n\nRadius $R$ and velocity $D$ of the strong blastwave in the medium \n(\\ref{rho-power}) with $m<N+1$ are (Sedov \\cite{Sedov}): \n\\begin{equation} \n\\label{R_s_Sedov-ro^w} \nR=\\left({E_o\\over\\alpha_A\\ \\tilde{\\rho}^o(0)}\\right)^{1/(N+3-m)}\nt^{\\ 2/(N+3-m)}\\ , \n\\end{equation}\n\\begin{equation} \n\\label{D_Sedov-ro^w} \nD(R)={2\\over N+3-m}\\left({E_o\\over\\alpha_A\\ \\tilde{\\rho}^o(0)} \n\\right)^{1/2} R^{-(N+1-m)/2}\\ ,\n\\end{equation} \n\\noindent\nwhere $N=0,1,2$ for plane, cylindrical and spherical wave, respectively, \n$\\alpha_A$ is a self-similar constant. \\par\n\nDistributions of the fluid characteristics behind the shock front \nare self-similar, i.e., for any time $t$ the density $\\tilde{\\rho}$, \npressure $\\tilde{P}$, \nfluid velocity $\\tilde{u}$ variations and coordinate $\\tilde{a}$ are \n\\begin{equation}\n\\label{uni-prof-1}\n\\tilde{\\rho}(\\tilde{r},t)=\\tilde{\\rho}_{\\rm s}(t)\\cdot\\rho(r),\n\\end{equation}\n\\begin{equation}\n\\label{uni-prof-2}\n\\tilde{P}(\\tilde{r},t)=\\tilde{P}_{\\rm s}(t)\\cdot P(r),\n\\end{equation}\n\\begin{equation}\n\\label{uni-prof-3}\n\\tilde{u}(\\tilde{r},t)=\\tilde{u}_{\\rm s}(t)\\cdot u(r),\n\\end{equation}\n\\begin{equation}\n\\label{uni-prof-4}\n\\tilde{a}(\\tilde{r},t)=R(t)\\cdot a(r),\n\\end{equation}\nwhere $r=\\tilde{r}/R(t)$, $\\tilde{a}$ is the original position of the \nfluid mass element and superscript \"s\" corresponds to values of the \nparameters at the shock front (Fig.~\\ref{accuracy_Taylor_Kahn}). \\par\n\nGas occupies whole shocked region ($0\\le \\tilde{r}\\le R$) when $m\\le m_1$, \n\\begin{equation} \nm_1={1+3N+(1-N)\\gamma\\over\\gamma+1}\\ . \n\\end{equation}\nWhen $m\\rightarrow m_1$ central pressure $P(0)\\rightarrow 0$. \nShock waves in media with steep density gradients ($m>m_1$) develop \na cavity around the center of explosion. \nSuch a cavity creates in the uniform medium ($m=0$) when \n$\\gamma>\\gamma_1=(1+3N)/(N-1)$. \nSedov has also presented a solution for hollow blastwaves. \nReview of approximations for these cases is given by Ostriker \\& McKee \n(\\cite{Ostriker-McKee-88}). We do not consider $m>m_1$ in this paper. \\par \n\nFor $m=m_1$ (or $\\gamma=\\gamma^*$ in the uniform medium) solution has very \nsimple form: \n\\begin{equation} \n\\begin{array}{l}\n\\rho(r)=r^{N-1}\\ ,\\qquad P(r)=r^{N+1}\\ , \\\\ \\\\\nu(r)=r\\ ,\\hspace{1.4cm} a(r)=r^{(\\gamma+1)/(\\gamma-1)}\\ . \n\\end{array}\n\\label{solut-m_1}\n\\end{equation}\n\nSingularities in the solution also appear with \n$m_2=(N+1)(2-\\gamma)$ and \n$m_3=(2\\gamma+N-1)/\\gamma$ \nthen some exponents in the solution equal infinity. \nSimilarity solutions for these cases are deduced by \nKorobejnikov \\& Rjazanov (\\cite{Korobejnikov-Rjazanov-59}). \nFor $N=2$ and $\\gamma=5/3$ $m_1=2$, $m_2=1$, $m_3=13/5$. \\par\n\nSelf-similar constant $\\alpha_A=\\alpha_A(N,\\gamma,m)$ in equations \n(\\ref{R_s_Sedov-ro^w})-(\\ref{D_Sedov-ro^w}) \nfor $R$ and $D$ may be found \nfrom the energy balance equation with variations of density $\\tilde{\\rho}$, \npressure $\\tilde{P}$ and mass velocity $\\tilde{u}$ inside the shocked region \n\\begin{equation} \n\\label{enery-bal} \n{E_o\\over \\sigma}=\\int\\limits_0^R {\\tilde{\\rho}(r,t)\n\\tilde{u}(r,t)^2\\over 2} r^Ndr+\n\\int\\limits_0^R {\\tilde{P}(r,t)\\over \\gamma-1} r^Ndr\\ ,\n\\end{equation}\nwhere \n$\\sigma=4\\pi$ for $N=2$, $\\sigma=2\\pi$ for $N=1$ and $\\sigma=2$ for $N=0$ \nor, generally, \n$\\sigma=2\\pi N+(N-1)(N-2)$. \nIf we proceed to normalized parameters using \n(\\ref{uni-prof-1})-(\\ref{uni-prof-3}) and \ngeneral shock front conditions \n\\begin{equation}\n\\tilde{\\rho}_{\\rm s}={\\gamma+1\\over\\gamma-1}\\tilde{\\rho}^o_{\\rm s},\\ \n\\tilde{P}_{\\rm s}={2\\over\\gamma+1}\\tilde{\\rho}^o_{\\rm s}D^2,\\ \n\\tilde{u}_{\\rm s}={2\\over\\gamma+1}D\n\\end{equation}\nwe will obtain that $E_o=\\beta_A\\cdot MD^2/2$ with \n\\begin{equation}\nM=\\sigma\\tilde{\\rho}^o(0)R^{N+1-m}/(N+1-m), \n\\end{equation}\nconstant shape-factor \n\\begin{equation}\n\\beta_A={4(N+1-m)\\over\\gamma^2-1}\\cdot\\left(I_{\\rm K}+I_{\\rm T}\\right)\n\\label{beta_A} \n\\end{equation}\nand constant integrals \n\\begin{equation}\nI_{\\rm K}=\\int\\limits_0^1 \\rho(r)u(r)^2 r^Ndr\\ , \\qquad \nI_{\\rm T}=\\int\\limits_0^1 P(r) r^Ndr\\ . \n\\end{equation}\nAlso we will have a self-similar constant \n\\begin{equation} \n\\label{alpha_A-vs-beta_A} \n\\alpha_A={2\\sigma\\over(N+1-m)(N+3-m)^2}\\cdot\\beta_A\\ .\n\\end{equation}\nSimple formula gives $\\alpha_A(N,\\gamma,m_1)$: \n\\begin{equation}\n\\alpha_A={2\\sigma(\\gamma+1)\\over(N+1)(\\gamma-1)\\big((N+1)\\gamma-N+1\\big)^2}\\ .\n\\end{equation}\n\nThe distributions (\\ref{uni-prof-1})-(\\ref{uni-prof-4}) \nin the exact solution are parametric \nfunctions of an internal parameter. The expressions for the functions are \ncomplicated. These factors stimulate developing the approximations of the \nself-similar solution. \\par\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Taylor approximation}\n\nBasing on own numerical results, Taylor (\\cite{Taylor-50}) propose to \napproximate the velocity variation $u(r)$ behind spherical ($N=2$) shock \nfront moving into the uniform medium ($m=0$) as \n\\begin{equation} \n{\\tilde{u}(r,t)\\over D}={r\\over\\gamma}+\\alpha r^n,\n\\label{app-Taylor-base}\n\\end{equation} \nwhere $\\alpha$ and $n$ are found to give exact values of $\\tilde{u}_{\\rm s}$, \n$\\tilde{P}_{\\rm s}$, $\\tilde{\\rho}_{\\rm s}$ and their first derivatives in \nrespect to $r$. \nSubstituting this approximation into the continuity equation and into the \nequation of state for perfect gas, the approximated distributions of the \ndensity and pressure obtain. \nTaylor do not give the dependence $a(r)$, but it may be taken from the \nadiabaticity condition $P(a)\\rho(a)^{-\\gamma}=P(r)\\rho(r)^{-\\gamma}$ \nand (\\ref{appr_3a})-(\\ref{appr_3b}): \n\\begin{equation} \na^{\\gamma m-(N+1)}=P(r)\\rho(r)^{-\\gamma},\n\\label{a-vs-Prho}\n\\end{equation} \nwith approximations for $P(r)$ and $\\rho(r)$. \\par\n\nSo, Taylor approximation for the variations of density $\\rho$, pressure $P$, \nfluid velocity $u$ and coordinate $a$ are: \n\\begin{equation} \n\\label{Taylor-n} \n\\rho(r)={\\rho(r,t)\\over \\rho_{\\rm s}(t)}=\nr^{\\ 3/(\\gamma-1)}\\ \\left({\\gamma+1\\over\\gamma}-{r^{n-1}\\over\\gamma}\\right)^{-p},\n%r^{\\ 9/2}\\cdot\\left(1+{3\\over5}\\left(1-r^{\\ 5}\\right)\\right)^{-5/2} % <--for \\gamma=5/3\n\\end{equation}\n\\begin{equation} \n\\label{Taylor-T} \nP(r)={P(r,t)\\over P_{\\rm s}(t)}=\n\\left({\\gamma+1\\over\\gamma}-{r^{n-1}\\over\\gamma}\\right)^{-q},\n%\\left(1+{3\\over5}\\left(1-r^{\\ 5}\\right)\\right)^{-8/3} % <--for \\gamma=5/3\n\\end{equation}\n\\begin{equation} \n\\label{Taylor-u} \nu(r)={u(r,t)\\over u_{\\rm s}(t)}=\n{\\gamma+1\\over 2}\\left({r\\over\\gamma}+{\\gamma-1\\over\\gamma+1}{r^{n}\\over\\gamma}\\right),\n%{1\\over 5}\\left(4\\ r+r^{\\ 6}\\right) % <--for \\gamma=5/3\n\\end{equation}\n\\begin{equation} \n\\label{Taylor-a} \na(r)={a_o(r)\\over R(t)}=\nr^{\\ \\gamma/(\\gamma-1)}\\ \\left({\\gamma+1\\over\\gamma}-{r^{n-1}\\over\\gamma}\\right)^{-s},\n%\\left(-{3\\over 5}+{8\\over 5}r^{\\ -5}\\right)^{-1/2} % <--for \\gamma=5/3\n\\end{equation}\nwhere $n=(7\\gamma-1)/(\\gamma^2-1)$, $p=2(\\gamma+5)/(7-\\gamma)$, \n$q=(2\\gamma^2+7\\gamma-3)/(7-\\gamma)$, $s=(\\gamma+1)/(7-\\gamma)$. \nSelf-similar constant $\\alpha_A=\\alpha_A(2,\\gamma,0)$ goes with \n(\\ref{alpha_A-vs-beta_A}) and approximated profiles of $\\rho$, $P$ \nand $u$. %\\par\nFig.~\\ref{accuracy_Taylor_Kahn} and table \\ref{alpha_comp} demonstrate \naccuracy of Taylor approximation in comparison with the exact solution. \\par\n\nThis approximation is extended to cases $m\\neq 0$ in section \n\\ref{Taylor-ext}. \\par\n\n%%%%=== Fig ===%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}%[t]\n\\epsfxsize=8.8truecm\n\\centerline{\\epsfbox{1.eps}}\n\\caption[]{{\\bf a-c.} Sedov solution and the accuracy of Taylor and Kahn \napproximations of the solution in the uniform medium: \n{\\bf a}~exact Sedov solution, \n{\\bf b}~relative differences of Taylor approximation, \n{\\bf c}~relative differences of Kahn approximation. \nLines: 1 -- $\\rho(r)$, 2 -- $P(r)$, 3 -- $u(r)$, 4 -- $a(r)$. $\\gamma=5/3$.\n }\n\\label{accuracy_Taylor_Kahn}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Kahn approximation}\n\nKahn (\\cite{Kahn}) apply his methodology to the strong spherical blastwave \n($N=2$) in uniform medium ($m=0$) with $\\gamma=5/3$. \nIt is proposed to approximate first the mass distribution \n\\begin{equation} \n\\label{mu-def} \n\\mu(r)={M(r,t)\\over M_{\\rm s}(t)}=\n3\\int\\limits^r_0 \\rho(r)r^2dr.\n\\end{equation}\n\nSedov solution shows that $P_r(r)=0$ near the centre \n(subscript \"$r$\" denotes a partial derivative in respect to $r$). \nThis fact allows to find that $\\mu_r/\\mu=15/(2r)$ at $r=0$. \nOn the base of the equation of motion, \n$\\mu_r/\\mu=12$, $\\mu_{rr}=168$ and $(\\mu_r/\\mu)_r=24$ at $r=1$. \nTherefore ratio $\\mu_r/\\mu$ is proposed to be approximated as \n\\begin{equation} \n\\label{Kahn-dmu-appr} \n{\\mu_r\\over\\mu}=\n{15\\over 2r}+{9\\over 2}r^7.\n\\end{equation}\nThis formula satisfies all written boundary conditions at both ends. \\par\n\nThe mass distribution finds as integral from (\\ref{Kahn-dmu-appr}): \n\\begin{equation} \n\\label{Kahn-mu-appr} \n\\mu(r)=r^{15/2}\\ \\exp\\left({9\\over16}\\left(r^8-1\\right)\\right).\n\\end{equation}\nDensity distribution follows from (\\ref{mu-def}) and (\\ref{Kahn-mu-appr}): \n\\begin{equation} \n%\\label{Kahn-rho-appr} \n\\rho(r)=\\mu_r/3r^2.\n\\end{equation}\nAdiabaticity condition gives pressure variation \n\\begin{equation} \n%\\label{Kahn-P-appr} \nP(r)=\\left({2\\over3}\\right)^{5/3}{1\\over 32}\\ {\\mu_r^{5/3}\\over \\mu\\ r^{10/3}}\\ . \n\\end{equation}\nVelocity deduses from the mass conservation equation \n\\begin{equation} \n%\\label{Kahn-u-appr} \nu(r)={4\\over 3}r-{4\\mu\\over\\mu_r}\\ .\n\\end{equation}\nIf present location of mass element $a$ is $r$, then a(r) may be \nfound from the condition of mass conservation \n$\\mu(a)=\\mu(r)$ and relation (\\ref{mu(a)}) $\\mu(a)=a^{3}$: \n\\begin{equation} \n\\label{Kahn-a-appr} \na(r)=\\mu(r)^{1/3}\\ .\n\\end{equation}\n\nThe expressions for Kahn approximation are the same as \n(\\ref{Kahn-n})-(\\ref{Kahn-mu}) with $m=0$. \nThe accuracy of this approximation are shown on the \nFig.~\\ref{accuracy_Taylor_Kahn}. \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Approximation of Cox \\& Franco}\n\nAppling Kahn's approximation technique, Cox \\& Franco \n(\\cite{Cox_Fanko-81}) obtain the approximation of the \nself-similar solution for an ambient medium with the power-law density \ndistribution (\\ref{rho-power}) with $m<2$ for $\\gamma=5/3$ and $N=2$. \nApproximation of Cox \\& Franco are: \n\\begin{equation} \n\\begin{array}{l} \n{\\displaystyle \n\\rho(r)=%{\\rho(r,t)\\over \\rho_{\\rm s}(t)}=\n\\left({5\\over8}+{3\\over8}r^{\\ 8-4m}\\right)\\cdot r^{\\ (9-5m)/2} \n}\\\\ \\\\ \n{\\displaystyle \\qquad\\qquad\\qquad\\!\\!\n\\times\\exp\\left({3\\over8}{(3-m)\\over(2-m)}\\left(r^{\\ 8-4m}-1\\right)\\right)\\ , \n}\n\\end{array} \n\\label{Kahn-n} \n\\end{equation}\n\\begin{equation} \n\\begin{array}{l} \n{\\displaystyle \nP(r)=%{P(r,t)\\over P_{\\rm s}(t)}=\n\\left({5\\over8}+{3\\over8}r^{\\ 8-4m}\\right)^{5/3}\n}\\\\ \\\\ \n{\\displaystyle \\qquad\\qquad\\qquad\\!\\!\n\\times\\exp\\left({3\\over4(2-m)}\\left(r^{\\ 8-4m}-1\\right)\\right)\\ , \n}\n\\end{array} \n\\label{Kahn-T} \n\\end{equation}\n\\begin{equation} \n\\label{Kahn-u} \nu(r)=%{u(r,t)\\over u_{\\rm s}(t)}=\n4\\ r\\ {1+r^{\\ 8-4m}\\over 5+3\\ r^{\\ 8-4m}}\\ ,\n\\end{equation}\n\\begin{equation} \n{\\displaystyle \na(r)=%{a_o\\over R(t)}=\nr^{5/2}\\ \\exp\\left({3\\over8(2-m)}\\left(r^{\\ 8-4m}-1\\right)\\right)\\ ,}\n\\label{Kahn-a} \n\\end{equation}\n\\begin{equation} \n{\\displaystyle \n\\mu(r)=r^{\\ 5(3-m)/2} \n\\ \\exp\\left({3\\over8}{(3-m)\\over(2-m)}\\left(r^{\\ 8-4m}-1\\right)\\right)\\ . }\n\\label{Kahn-mu} \n\\end{equation}\nAuthor's approximation for $\\beta_A$ is \n\\begin{equation} \n\\label{beta-Cox-Fanko} \n\\beta_A=1.125\\cdot(0.22+0.52\\cdot(3-m)/3).\n\\end{equation}\n\nThe accuracy of Cox \\& Franco approximation is shown on \nFig.~\\ref{accuracy_Kahn_N-2} and table \\ref{alpha_comp}. \\par\n\n%%%%=== Fig ===%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}%[t]\n\\epsfxsize=8.8truecm\n\\centerline{\\epsfbox{2.eps}}\n\\caption[]{{\\bf a-c.} Accuracy of Cox \\& Franco approximation of the \nself-similar solution in the power-law medium (\\ref{rho-power}): \n{\\bf a}~relative differences of the approximation for $m=-4$, \n{\\bf b}~relative differences for $m=-2$, \n{\\bf c}~relative differences for $m=1$. \nLines are the same as on Fig.~\\ref{accuracy_Taylor_Kahn}. \nFracture in the curves for $\\rho(r)$ and $a(r)$ \nis due to very strong dependence of the relevant Sedov distributions \non the internal parameter, which changes in these wide intervals \nof $r$ on $10^{-10}$ only. \n }\n\\label{accuracy_Kahn_N-2}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Approximations of Ostriker \\& McKee}\n\\label{Ostr-McKee}\n\nOstriker \\& McKee (\\cite{Ostriker-McKee-88}) in the frame of the virial \ntheorem approach applied to spherical blastwave (N=2) in \nthe power-law ambient medium (\\ref{rho-power}) \nand time-dependent energy injection $E_o(t)\\propto t^{s}$, present a \nnumber of approximations for the self-similar solution. We consider further \n$s=0$. \\par \n\nAuthors introduce the dimensionless moments of coordinate $r$ and velocity \n$u$: \n\\begin{equation} \n\\label{moment-Ostr-McKee} \nK_{ij}=l_\\mu\\int\\limits_0^1 r^iu(r)^j\\rho(r)r^2dr\\ ,\n\\end{equation} \nwhere $l_\\mu=(\\gamma+1)(3-m)/(\\gamma-1)$, \nand consider three types of approximations for $u(r)$ and $\\rho(r)$: \nlinear velocity approximation (LVA)\n\\begin{equation} \n\\label{LVA-Ostr-McKee} \nu(r)=r,\\qquad \\rho(r)=r^{(6-(\\gamma+1)m)/(\\gamma-1)},\n\\end{equation} \none-power aproximation (OPA) \n\\begin{equation} \n\\label{OPA-Ostr-McKee} \nu(r)=r^{l_u},\\qquad \\rho(r)=r^{l_\\rho},\n\\end{equation} \nand two-power aproximation (TPA) \n\\begin{equation} \n\\label{TPA-Ostr-McKee-u} \nu(r)=a_ur^{l_{u,1}}+(1-a_u)r^{l_{u,2}},\\\\ \\\\\n\\end{equation} \n\\begin{equation} \n\\label{TPA-Ostr-McKee-rho} \n\\rho(r)=a_\\rho r^{l_{\\rho,1}}+(1-a_\\rho)r^{l_{\\rho,2}}.\n\\end{equation} \n\nIn such an approach the self-similar constant $\\alpha_A$ as well as \nexponents $l_u$ and $l_\\rho$ may be expressed in terms of moments $K_{02}$ \nand $K_{11}$. \nNamely, under self-similarity $\\alpha_A=2\\pi\\eta^2\\beta_A/(3-m)$, where \n$\\eta=2/(5-m)$ and factor $\\beta_A$ equals \n\\begin{equation} \n\\label{beta_A-Ostr-McKee} \n\\beta_A={2\\over3}\\cdot{2K_{02}(3\\gamma-5)+(5-m)(\\gamma+1)K_{11}\n\\over (\\gamma^2-1)(\\gamma+1)}\\ .\n\\end{equation} \nExponents in OPA are \n\\begin{equation} \nl_u={2K_{20}-K_{11}(1+K_{20})\\over(1-K_{20})K_{11}}\\ , \\quad \nl_{\\rho}={5K_{20}-3\\over1-K_{20}}\\ .\n\\end{equation} \n\nDerivatives at shock front are used to obtain the moments. So, \n\\begin{equation} \nK_{ij}={1\\over 1+s_{ij}/l_\\mu}\\ ,\n\\label{K_Ostr-McKee}\n\\end{equation} \nwhere $s_{ij}=i+j$ in LVA and $s_{ij}=i+j+j(m_1-m)/2$ in OPA. \nUsing (\\ref{K_Ostr-McKee}) $\\alpha_A$ may be written in a simple \nform in LVA: \n\\begin{equation} \n\\label{alpha_A-Ostr-McKee} \n\\alpha_A={16\\pi\\over 3(5-m)^2}\\cdot\n{11\\gamma-5-m(\\gamma+1)\\over \n(\\gamma^2-1)\\big(5\\gamma+1-m(\\gamma+1)\\big)}\\ .\n\\end{equation}\n\nMoments have more complicated form in TPA. \nIn this approach the expression for $u(r)$ coinsides with the approximation \n(\\ref{Taylor-u}) of Taylor with $n=1+\\gamma(m_1-m)/(\\gamma-1)$ that \nequals to Taylor's $n$ at $m=0$. So, TPA is extension of Taylor \napproximation of $u(r)$ to $m\\neq 0$. Contrary to Taylor's approach to find \n$\\rho(r)$ and $P(r)$ from the hydrodynamic equations, Ostriker \\& McKee find \nthe density variation \nindependently as TPA (\\ref{TPA-Ostr-McKee-rho}) with \n\\begin{equation} \n\\begin{array}{l}\n{\\displaystyle a_{\\rho}={\\gamma(m_1-m)\\over 10-\\gamma-(\\gamma+2)m} \\ ,}\\\\ \\\\\n{\\displaystyle l_{\\rho,1}={3-\\gamma m\\over\\gamma-1} \\ ,\n\\quad l_{\\rho,2}={6+(\\gamma+1)(m_1-2m)\\over \\gamma-1} \\ ,}\n\\end{array}\n\\end{equation} \nwhere $\\gamma>1$. \nFor $m=0$ variation $\\rho(r)$ in TPA coinsides with the result of Gaffet \n(\\cite{Gaffet}) for case of uniform medium (Ostriker \\& McKee \n\\cite{Ostriker-McKee-88}). Two-power velocity approximation is used to \nextend Taylor approximation to cases $m\\neq 0$ in section \\ref{Taylor-ext}. \\par\n\nPressure distribution are also restored independently. \nIt may be found in OPA as a linear pressure approximation \n(LPA) and for TPA in the frame of pressure-gradient approximation (PGA). \\par\n\nMost of mass is concentrated near the shock front and distribution \n$u(r)$ is close to a linear function of $r$. Therefore, as noted by \nGaffet (\\cite{Gaffet}), the right side of Euler equation \n\\begin{equation} \n{\\partial\\tilde{P}(\\tilde{r},t)\\over \\partial M(\\tilde{r},t)}=\n-{1\\over4\\pi}{1\\over \\tilde{r}^2}{d\\tilde{u}(\\tilde{r},t)\\over dt}\n\\label{Eul-eq}\n\\end{equation} \nis nearly a constant. LPA (Gaffet \\cite{Gaffet}, Ostriker \\& McKee \n\\cite{Ostriker-McKee-88}) use this feature assuming the \npressure to be a linear function of the mass fraction $\\mu(r)$\n\\begin{equation} \nP(r)=P(0)+(P^*_{\\rm s}/l_{\\mu})\\ \\mu(r).\n\\end{equation} \nLogariphmic derivative of pressure at the shock front is \n$P^*_{\\rm s}=(d\\ln P/d\\ln r)_{\\rm s}=\n(2\\gamma^2+7\\gamma-3-\\gamma m(\\gamma+1))/(\\gamma^2-1)$. \nMass in OPA is $\\mu(r)=3l_\\mu^{-1}r^{l_\\mu}$. \nP(0) in LPA is (Gaffet \\cite{Gaffet}) \n\\begin{equation} \nP(0)=1+{\\overline{u_t^{\\rm s}}\\over\\omega(3-m)}\n\\end{equation} \nwhere $\\overline{u_t^{\\rm s}}=\\tilde{u}_t^{\\rm s}R/D^2=\n\\omega\\big((4-3\\omega)(m-3)+2(1-\\omega)(4-2\\omega-m)\\big)/2$ \n(Hnatyk \\cite{Hn87}), $\\omega=2/(\\gamma+1)$. \\par \n\nSuch an approach (substitution with \n$\\tilde{r}^{-2}_{\\rm s}\\tilde{u}_t^{\\rm s}$ instead of \n$\\tilde{r}^{-2}\\tilde{u}_t$ in (\\ref{Eul-eq})) was also used by Laumbach \n\\& Probstein (\\cite{L-P}) to develop the sector approximation. \\par\n\nIn PGA a power-law form for the pressure gradient \n\\begin{equation} \n{dP(r)\\over dr}=P^*_{\\rm s}r^{l_{p,2}-1}\\ \n\\end{equation} \nis used to give two-power approximation for the pressure \n\\begin{equation} \nP(r)=P(0)+a_pr^{l_{p,2}}\\ , \n\\end{equation} \nwhere $a_p=P^*_{\\rm s}/l_{p,2}$ and \n\\begin{equation} \n\\begin{array}{l}\n{\\displaystyle P(0)={(\\gamma+1)^2(m_1-m)\\over\n3\\gamma^2+20\\gamma+1-(\\gamma+1)(3\\gamma+1)m}\\ ,}\\\\ \\\\\n{\\displaystyle \\hspace{0.4cm} l_{p,2}=\n{3\\gamma^2+20\\gamma+1-(\\gamma+1)(3\\gamma+1)m \n\\over 2(\\gamma^2-1)} \\ .}\n\\end{array}\n\\end{equation} \n%PGA is an extension of an approximation introduced by \n%Gaffet (\\cite{Gaffet-81}). \n\nAccuracy in determination of $\\alpha_A$ and $P(0)$ in approximations of \nOstriker \\& McKee is shown in table \\ref{alpha_comp} and in revealing \nthe flow parameters on Fig.~\\ref{accuracy_Ostr-McKee}. \\par\n\n%%%%=== Fig ===%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}%[t]\n\\epsfxsize=8.6truecm\n\\centerline{\\epsfbox{3.eps}}\n\\caption[]{Relative differences of Ostriker \\& McKee two-power \napproximation of the self-similar solution for the uniform medium. \n$\\gamma=5/3$. \nLines are the same as on Fig.~\\ref{accuracy_Taylor_Kahn}. \n }\n\\label{accuracy_Ostr-McKee}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Cavaliere \\& Messina approximation of $\\alpha_A$} \n\nCavaliere \\& Messina (\\cite{Cavaliere-Messina-76}) with a simple \ntechnique approximate the equations for the radius and velocity \nof shock in the power-law medium (\\ref{rho-power}) and \n$E_o(t)\\propto t^{s}$. \nFor $s=0$ his approximation gives \n\\begin{equation} \n\\label{beta-Cav-Mess} \n\\beta_A={4\\over \\gamma^2-1}\\left({\\gamma-1\\over\\gamma+1}+{1\\over 2}\n{N+1-m\\over N+1}\\right).\n\\end{equation}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Approximate methods for an explosion in medium with \n\tarbitrary large-scale nonuniformity}\n%\\label{App-methods}\n\nIn this subsection we pointed out a number of approximate methods for \ndescription of a point explosion in arbitrary nonuniform medium. \nThese methods may also be \napplicable for a medium with power-law density variation. \nBisnovatyi-Kogan \\& Silich (\\cite{BK-Syl}) and Hnatyk (\\cite{Hn87}) \nhave given the reviews of these methods, their applications and accuracy. \n\n\\subsubsection{Thin-layer approximation}\n\nThin-layer approximation is firstly introduced by Chernyi (\\cite{Chernyi}) \nand used by Kompaneets (\\cite{Komp}) and other authors to find analytical \nsolutions for evolution of the shock front in a number of type of nonuniform \nmedia. It is assumed in this approach that all swept-up mass is concentrated \nin the infinitely thin layer just after shock front and the motion is \nstimulated with the hot gas inside the shocked region with uniform pressure \ndistribution $P(r)=0.5$ (excepting $P_{\\rm s}=1$). \nLayer of the gas moves with velocity $u_{\\rm s}$. This method was developed \nto calculate anly the shock front dynamics and therefore does not allow to \nreveal the distribution of the fluid parameters behind the shock front. \\par\n\nThin-layer approximation gives for spherical blastwave in the uniform medium \n(Andriankin et al. \\cite{Andriankin-et-al}) \n\\begin{equation} \n\\label{alpha_A-TL} \n\\alpha_A={16\\pi(3\\gamma-1)\\over 75(\\gamma-1)(\\gamma+1)^2}\\ .\n\\end{equation}\n\n\\subsubsection{Sector approximation}\n\nIn the sector approximation, the characteristics of an one-dimentional flow \nfind as decompositions into series about the shock front. \\par\n\nLaumbach \\& Probstein (\\cite{L-P}) have proposed the sector approximation \napplying it to \nspherical blastwaves in a plane-stratified exponential medium. Authors \nuse Lagrangian coordinate $a$ and \npropose to approximate pressure variation in the form equivalent to \n$P(a)=1+P_a^{\\rm s}(a-1)$ (Hnatyk \\cite{Hn87}). \nDensity variation is given by the adiabaticity condition and relation \n$r=r(a)$ by continuity equation. Fluid velocity field is not determined. \nFor shock radius and its velocity Laumbach \\& Probstein approximation yeilds \nin the uniform medium limit \n\\begin{equation} \n\\label{alpha_A-SA} \n\\alpha_A={32\\pi(4\\gamma^2-\\gamma+3)\\over 225(\\gamma-1)(\\gamma+1)^3}\\ .\n\\end{equation}\n\nGaffet (\\cite{Gaffet,Gaffet-81}) uses Lagrangian mass coordinates $\\mu$ and \nfinds pressure variation as a linear pressure approximation \n$P(\\mu)=1+P_\\mu^{\\rm s}(\\mu-1)$. \nGaffet (\\cite{Gaffet,Gaffet-81}) also propose to improve accuracy of \nthe approximation, taking into account the second order coefficients \nin the series. \nAuthor calculates such coefficients in terms of Lagrangian mass \ncoordinate $\\mu$. Hnatyk (\\cite{Hn87}), considering different \nmodifications of the sector approximation, presents the coefficients \nup to the second order in terms of $a$. \\par \n\n%%%%=== Fig ===%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}%[t]\n\\epsfxsize=8.6truecm\n\\centerline{\\epsfbox{4.eps}}\n\\caption[]{Accuracy of Hnatyk approximation of Sedov solution for the \nuniform medium. \nLines: 1 -- $\\rho(a)$, 2 -- $P(a)$, 3 -- $u(a)$, 4 -- $r(a)$. $\\gamma=5/3$.\n }\n\\label{accuracy_Hn}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsubsection{Hnatyk approximation}\n\\label{Hn-app}\n\nHnatyk (\\cite{Hn87}) introduces also the idea to aproximate first\\-ly \nthe relation $\\tilde{r}=\\tilde{r}(a,t)$ between the Lagrangian $a$ and \nEulerian $r$ coordinates of the gas element in each sector of shocked \nregion. Density $\\rho$, pressure $P$ and velocity $u$ variation behind \nthe shock front are exactly deduced from this relation. Really, the \ncontinuity equation \n\\begin{equation}\n\\tilde{\\rho}^o(\\tilde{a}) \\tilde{a}^N d\\tilde{a}=\n\\tilde{\\rho}(\\tilde{r}) \\tilde{r}^N d\\tilde{r}\n\\label{cont-eq-rho} \n\\end{equation}\ngives us the density distribution \n\\begin{equation}\n\\label{ro(at)} \n\\rho(a)={\\tilde{\\rho}(a,t)\\over \\tilde{\\rho}^{\\rm s}(t)}= \n{\\tilde{\\rho}^{o}(\\tilde{a})\\over \\tilde{\\rho}(R,t)}\n\t\\left({\\tilde{a}\\over \\tilde{r}(\\tilde{a},t)}\\right)^N\n\t\\left({\\partial \\tilde{r}(\\tilde{a},t)\\over\\partial \\tilde{a}}\n\\right)^{-1}, \n\\end{equation}\nthe equation of adiabaticity \n\\begin{equation} \n\\tilde{P}(\\tilde{a},t)=K\\tilde{\\rho}(\\tilde{a},t)^{\\gamma}\n\\end{equation} \nyields the distribution of pressure\n\\begin{equation} \n\\label{P(at)} \nP(a)=\n{\\tilde{P}(\\tilde{a},t)\\over \\tilde{P}^{\\rm s}(t)}=\n\t\\biggl({\\tilde{\\rho}^{o}(\\tilde{a})\\over\n\t\\tilde{\\rho}^{o}(R)}\\biggr)^{\\!1-\\gamma} \\biggl({D(\\tilde{a})\\over\n\tD(R)}\\biggr)^{\\!2}\\biggl({\\tilde{\\rho}(\\tilde{a},t)\\over \\tilde{\\rho}(R,t)} \n\t\\biggr)^{\\!\\gamma}\n\\end{equation} \nand relation $\\tilde{r}=\\tilde{r}(\\tilde{a},t)$ gives velocity \n\\begin{equation}\n\\label{u(at)}\nu(a)=\n{\\tilde{u}(\\tilde{a},t)\\over \\tilde{u}^{\\rm s}(t)}=\n{\\gamma+1\\over 2}{1\\over D(R)}\n\t{d\\tilde{r}(\\tilde{a},t)\\over dt}\\ .\n\\end{equation}\n\nAuthor propose to approximate $r(a)$ as \n\\begin{equation}\nr(a)=a^\\alpha\\exp\\big(\\beta(a-1)\\big)\\ \n\\label{r(a)-Hn}\n\\end{equation}\nwith \n\\begin{equation}\n\\alpha=(r^{\\rm s}_{a})^2-r^{\\rm s}_{aa} \\quad {\\rm and}\\quad \n\\beta=r^{\\rm s}_{aa}+r^{\\rm s}_{a}-(r^{\\rm s}_{a})^2 \\ .\n\\end{equation}\nSuch an expression ensures the edge condition $r(0)=0$, $r_{\\rm s}=1$ \nand values of the derivatives \n\\begin{equation} \nr^{\\rm s}_a = 1-\\omega,\n\\label{ras}\n\\end{equation} \n\\begin{equation} \nr^{\\rm s}_{aa}=\\omega(1-\\omega) \\bigl[ 3B+N(2-\\omega)-m\\bigr] \n\\label{raas}\n\\end{equation} \nwhere $B=R\\ddot R/\\dot R^2$, $\\dot R=dR/dt$ is the shock velocity, \n$m=-d\\ln\\rho^o(R)/d\\ln R$, \nsubscript \"$a$\" denotes a partial derivative in respect to $a$. \\par\n\nThis approximation is accurate near the shock front, but around \nthe explosion site (for $a<0.1$ or $r<0.4$) characteristics do not \nrestore correctly (Fig.~\\ref{accuracy_Hn}). \nThis approximation does not take into consideration any derivatives of $r(a)$ \nnear the center and the distributions of $\\rho(a)$, $P(a)$, $u(a)$ do not \nbind there, causing such a situation. \nThis approximation is extended to the central region in subsection \n\\ref{app-Hn-imp}. \\par \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%======================Section III================================%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Extension of Taylor approximation to $m\\neq 0$}\n\\label{Taylor-ext}\n\nIn this section Taylor's technic is applied to the case of a medium \nwith the power-law density distribution (\\ref{rho-power}) with $m<m_1$. \nOstriker \\& McKee \n(\\cite{Ostriker-McKee-88}) give the coefficients in the approximation \n(\\ref{app-Taylor-base}) for $u(r)$ in such a case. \nApproximated velocity variation is (\\ref{Taylor-u}) with \n$n=P^*_{\\rm s}-2=(7\\gamma-1-m\\gamma(\\gamma+1))/(\\gamma^2-1)$. \nSubstitution with (\\ref{app-Taylor-base}) into the equations of \ncontinuity and state gives \n\\begin{equation}\n{\\rho_r\\over\\rho}={3+\\alpha\\gamma(n+2)r^{n-1}-m\\gamma\\over (\\gamma-1)r-\\alpha\\gamma r^{n}}\\ , \n\\end{equation}\n\\begin{equation}\n{P_r\\over P}={\\alpha\\gamma^2(n+2)r^{n-1}\\over (\\gamma-1)r-\\alpha\\gamma r^{n}}\\ .\n\\end{equation}\nAfter integration, pressure variation will be expressed \nwith (\\ref{Taylor-T}) where \n\\begin{equation}\nq=%{\\gamma(n+2)\\over(n-1)}=\n{2\\gamma^2+7\\gamma-3-m\\gamma(\\gamma+1)\\over 7-\\gamma-m(\\gamma+1)} \\ .\n\\end{equation}\nDensity is \n\\begin{equation}\n\\rho(r)=\nr^{\\ (3-m\\gamma)/(\\gamma-1)}\\ \\left({\\gamma+1\\over\\gamma}-{r^{n-1}\\over\\gamma}\\right)^{-p},\n\\end{equation}\nwhere \n\\begin{equation}\np=%{3+(n+2)(\\gamma-1)-m\\gamma\\over (n-1)(\\gamma-1)}=\n{2\\big(\\gamma+5-m(\\gamma+1)\\big)\\over 7-\\gamma-m(\\gamma+1)} \\ .\n\\end{equation}\nEq.~(\\ref{Taylor-a}) gives $a(r)$ with \n\\begin{equation}\ns=%{p\\gamma-q\\over 3-m\\gamma}=\n{\\gamma+1\\over 7-\\gamma-m(\\gamma+1)} \\ .\n\\end{equation}\n\nExponents $n=6-5m/2$, $q=(16-5m)/\\big(3(2-m)\\big)$, $p=(5-2m)/(2-m)$ and \n$s=1/(2-m)$ for $\\gamma=5/3$. \nThis extended Taylor approximation is compared with the exact solution on \nFig.~\\ref{accuracy_Taylor-ext_N-2}. \n\n%%%%=== Fig ===%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}%[t]\n%\\resizebox{\\hsize}{!}{\n%\t\\includegraphics{Te(N2).eps}\n%\t\t }\n\\epsfxsize=8.6truecm\n\\centerline{\\epsfbox{5.eps}}\n\\caption[]{{\\bf a-c.} Accuracy of the extended Taylor approximation of the \nself-similar solution in the power-law medium (\\ref{rho-power}): \n{\\bf a}~relative differences of the approximation for $m=-4$, \n{\\bf b}~relative differences for $m=-2$, \n{\\bf c}~relative differences for $m=1$. \nLines are the same as on Fig.~\\ref{accuracy_Taylor_Kahn}. $\\gamma=5/3$.\n }\n\\label{accuracy_Taylor-ext_N-2}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%======================Section IV=================================%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Approximations of the Sedov solution \n\tin Lagrangian coordinates}\n\nIn this section we present two analytical approximations of the self-similar \nsolution for a medium with the power-law density distribution \nexpressed in Lagrangian geometric coordinates $a$. \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Flow characteristic distributions} \n\nExact expressions for normalized density $\\rho$ and pressure $P$ \nvariations behind the shock front moving into the power-law medium \n(\\ref{rho-power}) follow from (\\ref{ro(at)}) and (\\ref{P(at)}): \n\\begin{equation}\n{\\displaystyle \n\\rho(a)=\n{\\gamma-1\\over\\gamma+1}\\cdot a^{N-m}\\cdot \\left(r(a)^N\n\\cdot r_a(a)\\right)^{-1} }\\ , \n\\label{appr_3a}\n\\end{equation}\n\\begin{equation}\n{\\displaystyle \nP(a)=\n\\left({\\gamma-1\\over\\gamma+1}\\right)^{\\gamma}\\cdot \n\ta^{N(\\gamma-1)-1}\\cdot \\left(r(a)^N\n\t\\cdot r_a(a)\\right)^{-\\gamma} }\\ .\n\\label{appr_3b}\n\\end{equation}\n\nDistribution of the fluid velocity $u(a)$ may be found from (\\ref{u(at)}). \nDue to $\\tilde{r}=rR$ time derivative $d\\tilde{r}/dt=Rr_t+Rr_aa_t+rD$ \n(subscript \"$t$\" denotes a partial derivative in respect to $t$). \nWe have also that $a_t=-aD/R$ and, in the self-similar case, $r_t=0$. So, \n\\begin{equation}\nu(a)={\\gamma+1\\over 2}\\Bigl(r(a)-r_a(a)a\\Bigr)\\ .\n\\label{u-distr-r^w}\n\\end{equation}\n\nThe distribution $\\mu(a)$ follows from the definition (\\ref{mu-def}) and \n(\\ref{cont-eq-rho}): \n\\begin{equation} \n\\mu(a)=a^{(N+1)-m}\\ .\n\\label{mu(a)}\n\\end{equation}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Self-similar constant $\\alpha_A$}\n\\label{alpha-A}\n\nSelf-similar constant $\\alpha_A(N,\\gamma,m)$ in equations for $R$ and \n$D$ (\\ref{R_s_Sedov-ro^w})-(\\ref{D_Sedov-ro^w}) obtains from \n(\\ref{alpha_A-vs-beta_A}) and (\\ref{beta_A}): \n\\begin{equation} \n\\label{alpha_A} \n\\alpha_A={8\\over\\gamma^2-1}\\cdot{\\sigma\\over(3+N-m)^2}\\cdot\n\\left(I_{\\rm K}+I_{\\rm T}\\right)\\ ,\n\\end{equation}\nwith\n\\begin{equation}\nI_{\\rm K}%=\\int\\limits_0^1 \\rho(r)u(r)^2 r^Ndr \n={\\gamma^2-1\\over 4}\n\\int\\limits_0^1 \\Bigl(r(a)-r_a(a) a\\Bigr)^2a^{N-m}da\\ , \\quad \n%\\label{I_K(a)}\n%\\end{equation}\n%\\begin{equation}\nI_{\\rm T}%=\\int\\limits_0^1 P(r) r^Ndr \n=\\left({\\gamma-1\\over \\gamma+1}\\right)^\\gamma\n\\int\\limits_0^1 \\Bigl(r(a)^Nr_a(a)\\Bigr)^{1-\\gamma}a^{N(\\gamma-1)-1}da\\ . \n%\\label{I_T(a)}\n\\end{equation}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Factor $C$ and exponent $x$}\n\\label{factor-C}\n\nIn Sedov self-similar solution, if $r\\rightarrow 0$ then the dependence \n$r(a)$ is \n\\begin{equation} \nr=C\\cdot a^x. \n\\label{r_Ca^x}\n\\end{equation} \n\nFor $m<m_1$, if we substitute (\\ref{r_Ca^x}) \ninto (\\ref{appr_3b}) we obtain the connection between the factor $C$ and \nnormalized central pressure $P(0)$: \n\\begin{equation} \n\\label{C-Sedov-2}\nC= \\left({\\gamma\\over\\gamma+1} \\cdot \n P(0)^{-1/\\gamma}\\right)^{1/(N+1)}. \n\\end{equation}\nWe have to put $x=(\\gamma-1)/\\gamma$ during this transformation \nin order to satisfy condition $P(0)\\neq 0$. %\\par\nIn the case $m=m_1$ the exact solution (\\ref{solut-m_1}) gives $x$ and \n$C=1$. %\\par\nGeneral formula for exponent $x$ is \n\\begin{equation} \nx=\\left\\{\\matrix {(\\gamma-1)/\\gamma & {\\rm for}\\ m<m_1 &\\cr\n\t\t (\\gamma-1)/(\\gamma+1) & {\\rm for}\\ m=m_1 &.\\cr}\\right.\n\\label{exponent-x}\n\\end{equation} \n\nAnalytical expressions for $P(0)$ from self-similar solution are presented \nin Appendix \\ref{app-2}. Calculated values of $P(0)$ and $C$ for \na number of $N$, $\\gamma$ and $m$ are shown in table~\\ref{C-value}. \\par \n\n%%%%=== Table ===%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{table}[t]\n\\caption[]{ $P(0)$ calculated according to the self-similar \n\tsolution and $C$ for a strong point explosion \n\tin the power-law medium. \\\\ } \n\\begin{center}\n\\begin{tabular}{cccccccc}\n\\hline \n\\noalign{\\smallskip}\nN&m&&\\multicolumn{2}{c}{$P(0)$}&&\\multicolumn{2}{c}{$C_{\\rm A}$}\\\\\n\\noalign{\\smallskip}\n\\cline{4-5}\\cline{7-8}\n\\noalign{\\smallskip}\n&&&$\\gamma=7/5$&$\\gamma=5/3$&&$\\gamma=7/5$&$\\gamma=5/3$\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n0&0&&0.3900&0.3532&&1.1429&1.1670\\\\\n\\noalign{\\smallskip}\n1&0&&0.3729&0.3215&&1.0863&1.1112\\\\\n\\noalign{\\smallskip}\n2&0&&0.3655&0.3062&&1.0618&1.0833\\\\\n\\noalign{\\smallskip}\n&-4&&0.4268&0.3954&&1.0233&1.0293\\\\\n\\noalign{\\smallskip}\n&-3&&0.4193&0.3848&&1.0276&1.0350\\\\\n\\noalign{\\smallskip}\n&-2&&0.4088&0.3696&&1.0339&1.0433\\\\\n\\noalign{\\smallskip}\n&-1&&0.3928&0.3463&&1.0438&1.0570\\\\\n\\noalign{\\smallskip}\n& 1&&0.3087&0.2217&&1.1054&1.1556\\\\\n\\noalign{\\smallskip}\n& 2&&0.1273&0.0000&&1.3648&1.0000\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{center}\n\\label{C-value}\n\\end{table}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%=== Table ===%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{table}%[b]\n\\caption[]{Derivatives of the relation between Lagrangian and \n\tEulerian coordinates at shock front moving into the power-law \n\tmedium (\\ref{rho-power}).\\\\ } \n\\begin{center}\n\\begin{tabular}{l}\n\\hline\n\\noalign{\\smallskip}\nDerivative \\hfill{$\\gamma$}\\\\\n\\noalign{\\smallskip}\n\\hline\n%\\noalign{\\medskip}\n%\\hfill{$\\gamma=1.3$}\\\\\n%\\noalign{\\medskip}\n%${\\displaystyle r_a^{\\rm s}={3\\over 23}}$\\\\\n%\\noalign{\\medskip}\n%${\\displaystyle r_{aa}^{\\rm s}={30\\over 23^3}\\left(-17N+23m-69\\right)}$\\\\\n%\\noalign{\\medskip}\n%% &${\\displaystyle r_{aaa}^{\\rm s}={30\\over 2^2 23^3}\\left(-{11303143\\over 5329200}N^2+{2170487\\over 297150}Nm+{120404632\\over672815}N-6m^2-240m+590\\right)}$\\\\\n%${\\displaystyle r_{aaa}^{\\rm s}={30\\over 2^2 23^3}\\left(-k_1N^2+k_2Nm+k_3N-6m^2-240m+590\\right)}$\\\\\n%${\\displaystyle \\hspace{2.4cm} k_1=2.1210,\\ k_2=7.3043,\\ k_3=178.9565 }$\\\\\n%\\noalign{\\medskip}\n%\\hline\n\\noalign{\\medskip}\n\\hfill{$\\gamma=7/5$}\\\\\n\\noalign{\\medskip}\n${\\displaystyle r_a^{\\rm s}={1\\over 6}}$\\\\\n\\noalign{\\medskip}\n${\\displaystyle r_{aa}^{\\rm s}={5\\over 2^3 3^3}\\left(-2N+3m-9\\right)}$\\\\\n\\noalign{\\medskip}\n${\\displaystyle r_{aaa}^{\\rm s}={5\\over 2^5 3^5}\\left(-2N^2+9Nm+183N-9m^2-270m+675\\right)}$\\\\\n\\noalign{\\medskip}\n\\hline\n\\noalign{\\medskip}\n\\hfill{$\\gamma=5/3$}\\\\\n\\noalign{\\medskip}\n${\\displaystyle r_a^{\\rm s}={1\\over 4}}$\\\\\n\\noalign{\\medskip}\n${\\displaystyle r_{aa}^{\\rm s}={3\\over 2^6}\\left(-N+2m-6\\right)}$\\\\\n\\noalign{\\medskip}\n${\\displaystyle r_{aaa}^{\\rm s}={3\\over 2^9}\\left(Nm+19N-2m^2-36m+94\\right)}$\\\\\n\\noalign{\\medskip}\n\\hline\n\\end{tabular}\n\\end{center}\n\\label{r^s_deriv}\n\\end{table}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Derivatives at shock front} \n\nExpressions for the derivatives $r_a^{\\rm s}$, $r_{aa}^{\\rm s}$, \n$r_{aaa}^{\\rm s}$ may be obtained \nwith the technic of Gaffet (\\cite{Gaffet}) from the set of \nhydrodynamic equations for perfect gas and conditions on the shock front \n(see Hnatyk \\& Petruk (\\cite{Hn-Pet-99}) for details). \nDerivatives $r_a$, $r_{aa}$ are given with (\\ref{ras})-(\\ref{raas}) and \n\\begin{equation} \n\\begin{array}{l} \nr^{\\rm s}_{aaa}=\\omega\n(1-\\omega)\\Bigl[ 3(7-5\\omega)B^2+ \\\\ \\qquad\\quad +\\bigl[\n(-5\\omega^2+4\\omega +8)N+(4\\omega -11)m\\bigr]B+ \\\\ \\qquad\\quad\n+\\omega(2\\omega ^2-7\\omega+6)N^2+(\\omega^2+\\omega -4)Nm- \\\\ \\qquad\\quad\n-\\omega(2-\\omega)N-(\\omega-2)m^2+(2\\omega-1)m+ \\\\ \\qquad\\quad\n+(2\\omega-1)m'+(6\\omega-4)Q \\Bigr],\n\\label{raaas}\n\\end{array} \n\\end{equation} \nwhere $Q=R^2R^{(3)}/\\dot R^3$ and $m'=-dm/d\\ln R$. \\par\n\nIn the power-law medium (\\ref{rho-power}) $m'=0$. Taking into consideration \nthe equations for the shock radius (\\ref{R_s_Sedov-ro^w}) and shock velocity \n(\\ref{D_Sedov-ro^w}) we may also write \n\\begin{equation}\nB=-{N-m+1\\over2}, \\ \\ Q={(N-m+1)(N-m+2)\\over2}. \n\\end{equation}\nReduced expressions for the derivatives $r_a^s$, $r_{aa}^s$, $r_{aaa}^s$ \nare shown in table~\\ref{r^s_deriv}. \n\n%%%%=== Fig ===%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}[t]\n\\epsfxsize=8.6truecm\n\\centerline{\\epsfbox{6.eps}}\n\\caption[]{{\\bf a-c.} Accuracy of the second order approximation of the \nself-similar solution in the power-law medium (\\ref{rho-power}) for \n$\\gamma=5/3$ and $N=2$: \n{\\bf a}~relative differences for $m=0$, \n{\\bf b}~relative differences for $m=-2$, \n{\\bf c}~relative differences for $m=1$. \nLines are the same as on Fig.~\\ref{accuracy_Hn}.\n }\n\\label{accuracy-Hn-imp}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Second order approximation}\n\\label{app-Hn-imp}\n\nSo, to approximate the self-similar solution, we approximate the relation \n$r=r(a)$ between \nEulerian $r$ and Lagrangian $a$ coordinates of flow elements. \nFollowing to Hna\\-tyk's approach (\\ref{r(a)-Hn}) and like to \nrelation (\\ref{Kahn-a}), $r=r(a)$ may be aproximated in the form \n\\begin{equation}\nr(a)=\na^x\\exp\\Big(\\alpha (a^{\\beta}-1)\\Big)\\ \n\\label{Hn-impruved}\n\\end{equation}\nwith $x$ given by (\\ref{exponent-x}) and \n\\begin{equation}\n\\alpha={(r^{\\rm s}_{a}-x)^2\\over\n\tr^{\\rm s}_{aa}+r^{\\rm s}_{a}-(r^{\\rm s}_{a})^2}\\ ,\\quad \n\\beta={r^{\\rm s}_{aa}+r^{\\rm s}_{a}-(r^{\\rm s}_{a})^2\n\t\\over r^{\\rm s}_{a}-x}\\ ,\n\\end{equation}\nor, after substitution with (\\ref{ras})-(\\ref{raas}), \n\\begin{equation}\n\\begin{array}{l}\n{\\displaystyle \\alpha={2(1-\\omega-x)^2\\over\\omega(1-\\omega)(N+m-1-2N\\omega)}\\ ,}\\\\ \\\\\n{\\displaystyle \\beta=\\alpha^{-1}(1-\\omega-x) .}\n\\end{array}\n\\end{equation}\nSuch a second order approximation, besides $r(0)=0$, $r_{\\rm s}=1$, \n$r^{\\rm s}_{a}$, $r^{\\rm s}_{aa}$, gives \n$(\\partial\\ln r/\\partial\\ln a)^{0}=x$, \nand, contrary to Hnatyk approximation, extends description of a flow to \nthe central region. \\par\n\nVariations of $\\rho(a)$, $P(a)$ and $u(a)$ follow from \n(\\ref{appr_3a})-(\\ref{u-distr-r^w}). For case $N=2$, $\\gamma=5/3$ and $m<2$ \nthese relations give $\\beta=5(2-m)/8$ and \n\\begin{equation} \nr(a)=a^{2/5}\\exp\\left(-{6\\over25(2-m)}(a^{\\beta}-1)\\right)\\!,\n\\label{r(a)-twoa}\n\\end{equation}\n\\begin{equation} \n\\begin{array}{l} \n{\\displaystyle \\rho(a)=\n\\left({8\\over5}-{3\\over5}a^{\\beta}\\right)^{-1}\\cdot a^{(9-5m)/5} }\\\\ \\\\ \n{\\displaystyle \\qquad\\qquad\\qquad\\!\\!\n\\times\n\\exp\\left({18\\over25(2-m)}(a^{\\beta}-1)\\right)\\!, }\n\\end{array} \n\\label{rho(a)-twoa}\n\\end{equation}\n\\begin{equation} \n{\\displaystyle P(a)=\\left({8\\over5}-{3\\over5}a^{\\beta}\\right)^{-5/3} \n\\exp\\left({6\\over5(2-m)}(a^{\\beta}-1)\\right)\\!, }\n\\label{P(a)-twoa}\n\\end{equation}\n\\begin{equation} \nu(a)=a^{2/5}\\left({4\\over5}+{1\\over5}a^{\\beta}\\right)\n\\exp\\left(-{6\\over25(2-m)}(a^{\\beta}-1)\\right)\\!.\n\\label{u(a)-twoa}\n\\end{equation}\nApproximation (\\ref{r(a)-twoa})-(\\ref{u(a)-twoa}) may be considered as an \ninversion of Cox \\& Franko approximation (\\ref{Kahn-n})-(\\ref{Kahn-a}). \nUnfortunately, accuracy of presented formulae is lower \n(Fig.~\\ref{accuracy-Hn-imp}, table \\ref{alpha_comp}). \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Third order approximation}\n\nIn order to improve accuracy, we postulate the approximation $r=r(a)$ \nto give exact values of two additional derivatives: third order \n$r^{\\rm s}_{aaa}$ and \n$(\\partial r/\\partial(a^x))^{0}=C$. Consideration of $r^{\\rm s}_{aaa}$ is \nequivalent to consideration of the second order derivatives \n$\\rho_{aa}^{\\rm s}$, $P_{aa}^{\\rm s}$, $u_{aa}^{\\rm s}$ in expansion of \nrelevant characteristics into the series near the shock front. \nThis approximation is the same as used in the approximate hydrodynamical \nmethod \nfor modelling the asymmetrical strong point explosion in the medium with a \nlarge-scale density nonuniformity (Hnatyk \\& Petruk \\cite{Hn-Pet-99}). \nContrary to the method, we take here that both the self-similar \nconstant $\\alpha_A$ and factor $C$ are different for different $m$. \\par\n\nNamely, if at time $t$ the shock position is $R(t)$, we approximate a \nconnection $r=r(a)$ as follows \n\\begin{equation} \nr(a)=a^x\\cdot \n(1+\\alpha\\cdot \\xi + \\beta \\cdot \\xi^2 + \\varsigma \\cdot \\xi^3 + \\delta \\cdot \n\\xi^4), \n\\label{r(a)_approx}\n\\end{equation} \nwhere $\\xi=1-a$. Coefficients $\\alpha, \\beta, \\varsigma, \\delta$ and exponent \n$x$ are choosen from the condition that the partial derivatives \n$r^{s}_{a}$, $r^{\\rm s}_{aa}$, $r^{\\rm s}_{aaa}$ \nat the shock front ($a=1$) as well as \n$(\\partial\\ln r/\\partial\\ln a)^{0}=x$ and $(\\partial r/\\partial (a^x))^{0}=C$ \nin the place of explosion ($a=0$) equal to their exact values: \n\\begin{equation} \n\\begin{array}{l} \n{\\displaystyle \n\\alpha = -r^{\\rm s}_a +x, }\\\\ [0.2cm]\n{\\displaystyle \n\\beta ={1\\over 2}\\cdot \\bigl( \nr^{\\rm s}_{aa}-2x\\cdot r^{\\rm s}_a + x(x+1)\\bigr), }\\\\ [0.3cm]\n\\varsigma = {\\displaystyle {1\\over 6}\\cdot } \n{\\displaystyle \n\\bigl(- r^{\\rm s}_{aaa} +3x\\cdot r^{\\rm s}_{aa}- }\\\\ [0.3cm]\n\\quad\\qquad -3x(1+x) \\cdot r^{\\rm s}_a+x(x+1)(x+2)\\bigr), \\\\ [0.2cm]\n{\\displaystyle \n \\delta = C - (1 + \\alpha + \\beta + \\varsigma). }\\\\ \\end{array} \n\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\! \n\\end{equation} \nIn terms of $a$ relation (\\ref{r(a)_approx}) and its \nfirst derivative are \n\\begin{equation}\nr(a)=a^x(B_0-B_1 a+B_2 a^2-B_3 a^3+B_4 a^4), \\\\ \\\\\n\\label{appr_2a}\n\\end{equation}\n\\begin{equation}\nr_a(a)=a^{x-1}(A_0-A_1 a+A_2 a^2-A_3 a^3+A_4 a^4), \n\\label{appr_2b}\n\\end{equation}\nwith \\par\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{center}\n\\begin{tabular}{lll}\n\\noalign{\\medskip}\n$B_0=1+\\alpha+\\beta+\\varsigma+\\delta=C,$&&$A_0=xB_0,$ \\\\\n\\noalign{\\smallskip}\n$B_1=\\alpha+2\\beta+3\\varsigma+4\\delta,$ &&$A_1=(1+x)B_1,$\\\\\n\\noalign{\\smallskip}\n$B_2=\\beta+3\\varsigma+6\\delta,$ &&$A_2=(2+x)B_2,$\\\\\n\\noalign{\\smallskip}\n$B_3=\\varsigma+4\\delta,$ &&$A_3=(3+x)B_3,$\\\\\n\\noalign{\\smallskip}\n$B_4=\\delta,$ &&$A_4=(4+x)B_4.$\\\\\n\\noalign{\\medskip}\n\\end{tabular}\n\\end{center}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%=== Table ===%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{table}%[b]\n\\caption[]{Self-similar constant $\\alpha_{\\rm A}(N,\\gamma,m)$ calculated \n\twith third order approximation of $r(a)$ (\\ref{r(a)_approx}). \\\\\n } \n\\begin{center}\n\\begin{tabular}{crcc}\n\\hline \n\\noalign{\\smallskip}\nN&m&\\multicolumn{2}{c}{$\\alpha_{\\rm A}$}\\\\\n\\noalign{\\smallskip}\n\\cline{3-4}\n\\noalign{\\smallskip}\n&&$\\gamma=7/5$&$\\gamma=5/3$\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n0& 0&1.0763&0.6018 \\\\\n\\noalign{\\smallskip}\n1& 0&0.9841&0.5644 \\\\\n\\noalign{\\smallskip}\n2& 0&0.8519&0.4944 \\\\\n\\noalign{\\smallskip}\n&-4&0.2295 &0.1270 \\\\\n\\noalign{\\smallskip}\n&-3&0.2960 &0.1650 \\\\\n\\noalign{\\smallskip}\n&-2&0.3966 &0.2232 \\\\\n\\noalign{\\smallskip}\n&-1&0.5598 &0.3192 \\\\\n\\noalign{\\smallskip}\n& 1&1.4631 &0.8722 \\\\\n\\noalign{\\smallskip}\n& 2&3.3537 &1.8235 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{center}\n\\label{alpha_A-calc}\n\\end{table}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{table}[t]\n\\caption[]{Coefficients in approximation (\\ref{appr_2a}). $\\gamma=5/3$. } \n%{\\footnotesize%\\small\n\\begin{center}\n\\begin{tabular}{rrllllll}\n\\hline\n\\noalign{\\smallskip}\n$N$&$m$&$B_0$&$B_1$&$B_2$&$B_3$&$B_4$\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n0& 0&1.1670 &0.1333 &-0.1127 &-0.1074 &-0.02833 \\\\\n\\noalign{\\smallskip}\n1& 0&1.1112 &-0.01510 &-0.24655 &-0.1530 &-0.03276 \\\\\n\\noalign{\\smallskip}\n2& 0&1.0833 &-0.05189 &-0.2130 &-0.08708 &-0.009294 \\\\\n\\noalign{\\smallskip}\n &-4&1.0293 &0.2837 &0.9302 &0.9766 &0.3008 \\\\\n\\noalign{\\smallskip}\n &-3&1.0350 &0.1744 &0.6152 &0.6971 &0.2213 \\\\\n\\noalign{\\smallskip}\n &-2&1.0433 &0.07170 &0.3041 &0.4162 &0.1406 \\\\\n\\noalign{\\smallskip}\n &-1&1.0570 &-0.01334 &0.01359 &0.1452 &0.06128 \\\\\n\\noalign{\\smallskip}\n & 1&1.1556 &0.08965 &-0.1753 &-0.1471 &-0.03778 \\\\\n\\noalign{\\smallskip}\n & 2&1 &0 &0 &0 &0 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{center}\n%}\n\\label{tabl_appr_1}\n\\end{table}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nDistribution of $\\rho(a)$, $P(a)$ and $u(a)$ obtain from \n(\\ref{appr_3a})-(\\ref{u-distr-r^w}). \nSelf-similar constant $\\alpha_{\\rm A}$ is given with (\\ref{alpha_A}). \nTo simplify the procedure, \nnumerical values of $\\alpha_A(N,\\gamma,m)$ in this appoximation \nare presented in table~\\ref{alpha_A-calc}. \nTable~\\ref{tabl_appr_1} gives ready-calculated values of the coefficients \nin the approximation (\\ref{appr_2a}) for a number of cases. \n\\par\n\nThe accuracy of flow characteristic distributions in this approximation \nis high for uniform medium (Fig.~\\ref{O(m0)}). Approximation coinsides \nwith the exact solution (\\ref{solut-m_1}) for case $m=m_1$. \nFor other $m\\neq0$, differences increase with increasing $|m|$ \nbut maximal errors reveal in the region with low densities (Fig.~\\ref{O(N2)}). \nWe compare also numerical values of $\\alpha_A$ and $P(0)$ in this \napproximation with those from exact Sedov solution in table~\\ref{alpha_comp}. \n$\\alpha_A$ in the approximation is close to the exact values and gives \naccurate shock radius $R$ and velocity $D$. \\par\n\n%%%=== Fig ===%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}%[t]\n\\epsfxsize=8.8truecm\n\\centerline{\\epsfbox{7.eps}} \n\\caption[]{{\\bf a-c.} Accuracy of the third order approximation of the Sedov \nsolution in the uniform medium ($m=0$) for $\\gamma=5/3$: \n{\\bf a}~relative differences of the approximation for $N=0$, \n{\\bf b}~relative differences for $N=1$, \n{\\bf c}~relative differences for $N=2$. \nLines are the same as on Fig.~\\ref{accuracy_Hn}.\n }\n\\label{O(m0)}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%=== Fig ===%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}[t]\n\\epsfxsize=8.8truecm\n\\centerline{\\epsfbox{8.eps}} \n\\caption[]{{\\bf a-c.} Accuracy of the third order approximation \nfor power-law medium, $\\gamma=5/3$ and $N=2$: \n{\\bf a}~relative differences for $m=-4$, \n{\\bf b}~relative differences for $m=-2$, \n{\\bf c}~relative differences for $m=1$. \nLines are the same as on Fig.~\\ref{accuracy_Hn}.\n }\n\\label{O(N2)}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%======================Section IV================================%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Conclusions}\n\nIn this paper, we review approximations of the self-similar \nsolution for a strong point explosion in the power law medium \n$\\rho^o\\propto r^{-m}$ and compare their accuracy with the exact Sedov \nsolution of the problem. Different approaches found on the different basic \napproximations. Namely, Taylor (\\cite{Taylor-50}) and Ostriker \\& McKee \n(\\cite{Ostriker-McKee-88}) approximate first\\-ly the fluid \nvelocity variation behind the shock front. Taylor used approximated \n$u(r)$ substituting it into the hydrodynamic equations to obtain \nfull description of the flow. Contrary to this, Ostriker \\& McKee \napproximate $\\rho(r)$ and $P(r)$ independently. Kahn \n(\\cite{Kahn}) technic, used also by Cox \\& Franco (\\cite{Cox_Fanko-81}), \nconsists in approximation of the fluid mass variation $\\mu(r)$ and further \nusage of the system of hydrodynamic equations. Gaffet (\\cite{Gaffet}), \nLaumbach \\& Probstein (\\cite{L-P}), \nOstriker \\& McKee (\\cite{Ostriker-McKee-88}) base their approaches \non the approximation of $P(\\mu)$ or $P(r)$. Thin layer approximation may also \nbe included into this group. Hnatyk (\\cite{Hn87}) take approximation \nof the connection between Eulerian and Lagran\\-gi\\-an coordinates as basic \nrelation. So, practically all possible approaches are used \nto have approximation for the self-similar solution. \\par\n\nIn this paper we apply Taylor's methodology to discribe a strong point \nexplosion in the power-law medium, extending his approximation written for \nuniform medium, and write also two approximations expressed in Lagran\\-gi\\-an \ngeometric coordinates, approaching $r(a)$ with different accuracy. \\par\n\nErrors of all approximations are caused only by errors in the basic \napproximation. When the first approximation has higher accuracy we \nhave more accurate approximation for parameters of the shock and flow. \\par\n\n%%%%=== Table ===%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{table*}%[b]\n\\caption[]{ Comparision of the self-similar constant \n$\\alpha_{\\rm A}$ and pressure $P(0)$ calculated with: \nS -- Sedov (\\cite{Sedov-1946b}) solution (Kestenboim et al. \\cite{Kestenb}); \nT -- Taylor (\\cite{Taylor-50}) approximation;\nCF -- approximation of Cox \\& Franco (\\cite{Cox_Fanko-81}); \nLVA, OPA and TPA of Ostriker \\& McKee (\\cite{Ostriker-McKee-88}); \nCM -- approximation of Cavaliere \\& Messina (\\cite{Cavaliere-Messina-76}); \nTL -- thin-layer (\\ref{alpha_A-TL}) approximation; \nLP -- approximation (\\ref{alpha_A-SA}) of Laumbach \\& Probstein (\\cite{L-P}); \nSOA -- second order (\\ref{Hn-impruved}) and \nTOA -- third order (\\ref{r(a)_approx}) approximations. \nUniform medium, $\\gamma=5/3$ and $N=2$. \\\\\n } \n\\begin{center}\n\\begin{tabular}{lcccccccccccccc}\n\\hline\n\\noalign{\\smallskip}\n&S&T&CF&LVA&OPA/LPA&TPA/PGA&CM&TL&LP&SOA&TOA\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n$\\alpha_A$&0.4936 &0.4957 &0.4930 &0.5386 &0.5027 &0.4957 &0.5655 &0.5655 &0.4398 &0.4981 &0.4944 \\\\\n\\noalign{\\smallskip}\n$P(0)$\t &0.3062 &0.2855 &0.3140 &-- &0.3333 &0.3333 &-- &0.5000 &0.3333 &0.2507 &0.3062 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{center}\n\\label{alpha_comp}\n\\end{table*}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%=======================Acknowledgements==========================%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\\begin{acknowledgements}\n%We thank to Randall Smith for an assistance during preparation of the paper. \n%\\end{acknowledgements}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%======================Appendix===================================%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\appendix\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section*{Appendix: central pressure $P(0)$}\n\\label{app-2}\n\nIn this appendix, we give exact expression for $P(0)$ in self-similar \nsolution when $m\\leq m_1$ (Sedov \\cite{Sedov}) and when $m=m_2$ \n(Korobejnikov \\& Rjazanov \\cite{Korobejnikov-Rjazanov-59}). \nThese relations complite the full set of formulae to build the third order \napproximation of the Sedov solution for any $\\gamma$, \n$m\\le \\min(N+1,m_1)$ and type of symmetry (plane, cylindrical or spherical \nblastwave). \\par\n\n$P(0)=0$ for $m=m_1$. \\par\n\nIn the case of $m<m_1$ and $m\\neq m_2$ \n\\begin{equation} \nP(0)=\\left(1\\over2\\right)^{\\varepsilon_1}\n\\left(\\gamma+1\\over\\gamma\\right)^{\\varepsilon_2}\n\\left(m-m_3\\over m-m_1\\right)^{\\varepsilon_3\\varepsilon_4}\\ ,\n\\end{equation}\n$$\n\\begin{array}{l}\n\\varepsilon_1=\\displaystyle{ {2(N+1)\\over N+3-m}\\ ,}\\\\ \\\\\n\\varepsilon_2=\\displaystyle{ {2(N+1)\\over N+3-m}-{\\gamma\\big(N+1-m\\big)\\over(N+1)(2-\\gamma)-m}\\ ,}\\\\ \\\\\n\\varepsilon_3=\\displaystyle{ {(N+1-m)(N+3-m)\\over(N+1)(2-\\gamma)-m}+m-2\\ ,}\\\\ \\\\\n\\varepsilon_4=\\displaystyle{ {\\gamma+1\\over(N+1)(\\gamma-1)+2}-{2\\over N+3-m} \\hspace{1.9cm}}\\\\ \\\\\n\\hspace{3.85cm} \\displaystyle{ +{\\gamma-1\\over\\gamma(2-m)+N-1}\\ .}\n\\end{array}\n$$\nIf $m=m_2$ then \n\\begin{equation} \nP(0)=\\left(1\\over2\\right)^{\\varepsilon}\n\\left(\\gamma+1\\over\\gamma\\right)^{\\varepsilon\\gamma N/(N+1)}\n\\exp\\left(-{\\gamma\\over 2}\\ \\varepsilon\\right)\\ ,\n\\end{equation}\n$$\n\\varepsilon=\\displaystyle{ {2(N+1)\\over (N+1)(\\gamma-1)+2}\n\\ .}\\hspace{4.08cm}\n$$\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%======================References=================================%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{thebibliography}{}\n\\bibitem{Andriankin-et-al}\nAndriankin E., Kogan A., Kompaneets A., Krainov P., 1962, Zh. Prikl. \n\tMekh. Tekh. Fiz. 6, 3\n\\bibitem{BK-Syl}\nBisnovatyi-Kogan G., Silich S., 1995, Rev. Mod. Phys. 67, 611\n\\bibitem{Cavaliere-Messina-76}\nCavaliere A., Messina A., 1976, ApJ 209, 424\n\\bibitem{Chernyi} \nChernyi G., 1957, Dokl. Akad. Nauk SSSR 112, 213\n\\bibitem{Cox-And}\nCox D., Anderson P., 1982, ApJ 253, 268\n\\bibitem{Cox_Fanko-81} \nCox D. P., Franco J., 1981, ApJ 251, 687\n\\bibitem{Gaffet}\nGaffet B., 1978, ApJ 225, 442\n\\bibitem{Gaffet-81}\nGaffet B., 1981, ApJ 249, 761 \n\\bibitem{Hn87}\nHnatyk B., 1987, Afz 26, 113 \n\\bibitem{Hn-Pet-99}\nHnatyk B., Petruk O., 1999, A\\&A 344, 295\n\\bibitem{Kahn} \nKahn F., 1975, Proc. 14th International Cosmic Ray Conf., Munich, 11, 3566\n\\bibitem{Kestenb}\nKestenboim Kh., Roslyakov G., Chudov L., 1974, Point Explosion.\nMethods of Calculations. Tables. Nauka, Moskow\n\\bibitem{Komp} \nKompaneets A., 1960, Dokl. Akad. Nauk SSSR 130, 1001\n\\bibitem{Korobejnikov-Rjazanov-59}\nKorobejnikov V., Rjazanov E., 1959, Prikl. Mat. Mekh. 23, 384\n\\bibitem{L-P}\nLaumbach D., Probstein R.F., 1969, Fluid Mech. 35, 53\n\\bibitem{Ostriker-McKee-88}\nOstriker J., McKee C., 1988, Rev. Mod. Phys. 60, 1\n\\bibitem{Sedov-1946b}\nSedov L., 1946, Prikl. Mat. Mekh. 10, 241\n\\bibitem{Sedov}\nSedov L., 1959, Similarity and Dimensional Methods in Mechanics. \nAcademic, New York\n\\bibitem{Taylor-50}\nTaylor G.I., 1950, Proc. R. Soc. London, A201, 159\n\\end{thebibliography}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%======================================================================%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002112.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem{Andriankin-et-al}\nAndriankin E., Kogan A., Kompaneets A., Krainov P., 1962, Zh. Prikl. \n\tMekh. Tekh. Fiz. 6, 3\n\\bibitem{BK-Syl}\nBisnovatyi-Kogan G., Silich S., 1995, Rev. Mod. Phys. 67, 611\n\\bibitem{Cavaliere-Messina-76}\nCavaliere A., Messina A., 1976, ApJ 209, 424\n\\bibitem{Chernyi} \nChernyi G., 1957, Dokl. Akad. Nauk SSSR 112, 213\n\\bibitem{Cox-And}\nCox D., Anderson P., 1982, ApJ 253, 268\n\\bibitem{Cox_Fanko-81} \nCox D. P., Franco J., 1981, ApJ 251, 687\n\\bibitem{Gaffet}\nGaffet B., 1978, ApJ 225, 442\n\\bibitem{Gaffet-81}\nGaffet B., 1981, ApJ 249, 761 \n\\bibitem{Hn87}\nHnatyk B., 1987, Afz 26, 113 \n\\bibitem{Hn-Pet-99}\nHnatyk B., Petruk O., 1999, A\\&A 344, 295\n\\bibitem{Kahn} \nKahn F., 1975, Proc. 14th International Cosmic Ray Conf., Munich, 11, 3566\n\\bibitem{Kestenb}\nKestenboim Kh., Roslyakov G., Chudov L., 1974, Point Explosion.\nMethods of Calculations. Tables. Nauka, Moskow\n\\bibitem{Komp} \nKompaneets A., 1960, Dokl. Akad. Nauk SSSR 130, 1001\n\\bibitem{Korobejnikov-Rjazanov-59}\nKorobejnikov V., Rjazanov E., 1959, Prikl. Mat. Mekh. 23, 384\n\\bibitem{L-P}\nLaumbach D., Probstein R.F., 1969, Fluid Mech. 35, 53\n\\bibitem{Ostriker-McKee-88}\nOstriker J., McKee C., 1988, Rev. Mod. Phys. 60, 1\n\\bibitem{Sedov-1946b}\nSedov L., 1946, Prikl. Mat. Mekh. 10, 241\n\\bibitem{Sedov}\nSedov L., 1959, Similarity and Dimensional Methods in Mechanics. \nAcademic, New York\n\\bibitem{Taylor-50}\nTaylor G.I., 1950, Proc. R. Soc. London, A201, 159\n\\end{thebibliography}"
}
] |
astro-ph0002113
|
Search and Discovery Tools for Astronomical On-line Resources and Services
|
[
{
"author": "Daniel Egret\\inst{1}"
},
{
"author": "Robert J. Hanisch\\inst{2}"
},
{
"author": "Fionn Murtagh\\inst{1,3}"
}
] |
A growing number of astronomical resources and data or information services are made available through the Internet. However valuable information is frequently hidden in a deluge of non-pertinent or non up-to-date documents. % At a first level, compilations of astronomical resources provide help for selecting relevant sites. Combining yellow-page services and meta-databases of active pointers may be an efficient solution to the data retrieval problem. % Responses generated by submission of queries to a set of heterogeneous resources are difficult to merge or cross-match, because different data providers generally use different data formats: new endeavors are under way to tackle this problem. % We review the technical challenges involved in trying to provide general search and discovery tools, and to integrate them through upper level interfaces. \keywords{Astronomical databases: miscellaneous}
|
[
{
"name": "ehm.tex",
"string": "%\\documentclass[referee]{aa} % for a referee version\n\\documentclass{aa}\n%\n\\usepackage{graphics}\n%\\usepackage{times}\n%\\usepackage{epsfig}\n\n\\begin{document}\n\n \\thesaurus{23 % A&A Section 23: Data Processing\n (04.01.1)} % Astronomical databases: miscellaneous \n%\n \\title{Search and Discovery Tools for\n Astronomical On-line Resources and Services}\n\n \\titlerunning{Search and Discovery Tools}\n\n% \\subtitle{From AstroWeb to Astrobrowse and ISAIA}\n\n\\author{\n Daniel Egret\\inst{1}\n\\and\n Robert J. Hanisch\\inst{2}\n\\and\n Fionn Murtagh\\inst{1,3}\n }\n\n% \\offprints{Daniel Egret}\n \\mail{Daniel.Egret@astro.u-strasbg.fr}\n\n \\institute{CDS, Observatoire astronomique de Strasbourg, UMR 7550,\n11 rue de l'Universit\\'e, F-67000 Strasbourg, France\n\\and\n Space Telescope Science Institute, \n 3700 San Martin Drive, Baltimore, MD 21218, USA\n\\and\n School of Computer Science,\n The Queen's University of Belfast, \n Belfast BT7 1NN, Northern Ireland\n}\n\n \\date{Received 5 January 2000 / \\today}\n\n\\maketitle\n\n\\begin{abstract}\n\nA growing number of astronomical resources and data or information\nservices are made available through the Internet. \nHowever valuable information is frequently hidden\nin a deluge of non-pertinent or non up-to-date documents.\n%\nAt a first level, compilations of \nastronomical resources provide\nhelp for selecting relevant sites.\nCombining yellow-page \nservices and meta-databases of active pointers may be\nan efficient solution to the data retrieval problem.\n%\nResponses generated \nby submission of queries\nto a set of heterogeneous resources are\ndifficult to merge or cross-match, because\ndifferent data providers generally\nuse different data formats: new endeavors are under way\nto tackle this problem.\n%\nWe review the technical challenges involved\nin trying to provide general search and discovery\ntools, and to integrate them through upper\nlevel interfaces.\n\n\\keywords{Astronomical databases: miscellaneous}\n\n\\end{abstract}\n\n%\n%________________________________________________________________\n\n\\section{Introduction}\n\nHow to help the users find their way through the jungle of \ninformation services is a question which has been raised since the \nearly development of the WWW (see e.g., Egret \\cite{jungle}), \nwhen it became clear that a\nbig centralized system was not the efficient way to go. \n\nObviously the World Wide Web is a very powerful medium \nfor the development of distributed resources: \non the one hand the WWW provides a \ncommon medium for all information providers -- the language \nis flexible enough \nso that it does not bring unbearable constraints on existing \ndatabases -- on the other hand the distributed hypertextual \napproach opens the way to navigation and links\nbetween services (provided a minimum of coordination can be achieved). \nLet us note that it has been already widely demonstrated that \ncoordinating spirit is not out of reach in a small community such \nas astronomy, largely sheltered from \ncommercial influence.\n\nSearching for a resource (either already visited, or \nunknown but expected),\nor browsing lists of existing services \nin order to discover\nnew tools of interest implies a need for query strategies \nthat cannot generally be managed\nat the level of a single data provider.\n\nThere is a need for road-guides pointing to the \nmost useful resources,\nor to compilations or databases where information\ncan be found about these resources. \nSuch guides have been made in the past, and are of very\npractical help for the novice as well as the trained user,\nfor example:\nAndernach et al.\\ \\cite{AHM94},\nEgret \\& Heck \\cite{waw},\nEgret \\& Albrecht \\cite{amp2},\nHeck \\cite{eppa},\nGrothkopf \\cite{librarians},\nAndernach \\cite{ALDIA}.\n\nIn the present paper our aim is to address the questions\nrelated to the collection, integration and interfacing\nof the wealth of astronomical Internet resources,\nand also to describe some strategies that have to be developed\nfor building cooperative tools which will be essential in the\nresearch environment of the decade to come.\n\n%\n%________________________________________________________\n\\section{Compilations of astronomical Internet resources}\n\nAt a first level, the user looking for new sources of\ninformation can consult compilations\nof existing resources. Examples of such databases,\nor yellow-page services are given in this section.\n\n\n\\subsection{The StarPages}\n\n\\emph{Star*s Family} is the generic name for a collection of \ndirectories, dictionaries and databases which has been \ndescribed in details by Heck (\\cite{starfam})\nwho has been building\nup their contents for more than twenty-five years. \nThese very exhaustive data sets are carefully updated and\nvalidated, thus constituting a gold mine\nfor professional, amateur astronomers, and more generally\nall those who are curious of space-related activities,\nand want to locate existing resources.\n\nThe Star*s Family of products can be \nqueried on-line from the CDS Web site (Strasbourg, France)\nunder the generic name of \nStarPages\\footnote{http://cdsweb.u-strasbg.fr/starpages.html}.\nIt includes the following databases: \n\\begin{description}\n\\item[StarWorlds:] a directory of astronomy, space sciences,\nand related organizations (Heck et al.\\ \\cite{starworlds}); \nit includes URLs of Web sites\nwhen available, as well as e-mail addresses;\nunlike most of the services mentioned in\nthe present paper, it is not restricted to describing\non-line resources, but also lists directory entries\nfor organizations which do not provide any on-line\ninformation.\n\\item[StarHeads:] individual Web pages essentially of\nastronomers and related space scientists\n(Heck \\cite{starheads}).\n\\item[StarBits:] a very\ncomprehensive dictionary of abbreviations,\nacronyms, contractions, and symbols used in astronomy and\nspace sciences (Heck \\cite{starheads}). \n\\end{description}\nAll three databases are associated with a query engine\nbased on character string searches. Filters prevent\nextraction of too large subsets of the database.\n\n\\subsection{AstroWeb} \n\\label{AstroWeb}\n\n\\emph{AstroWeb} (Jackson et al. \\cite{astroweb}) is a \ncollection of pointers to astronomically relevant \ninformation resources available on the Internet.\nThe browse mode of AstroWeb opens a window\non the efforts currently developed -- in some cases, unfortunately,\nin a rather disorganized way -- for\nmaking astronomically related, and hopefully pertinent,\ninformation available on-line through the World Wide Web.\n\nAstroWeb is maintained by a small consortium of individuals\nlocated at CDS, STScI, MSSSO, NRAO, and Vilspa. The master\ndatabase is currently hosted at \nCDS\\footnote{http://cdsweb.u-strasbg.fr/astroweb.html} \n(after having been\nfor a long time at STScI), and all the above-mentioned\nplaces, as well as the Institute of Astronomy, Cambridge,\n host a mirror copy with\ncustomized presentation of the same data.\n\nEach URL is checked by a robot on a daily basis to ensure\naliveness of all referenced resources. The resource descriptions\nare usually submitted by the person or organization responsible\nfor the resource, but are checked and eventually\nmodified by one of the consortium members. \nThe search engine is a {\\sc wais} search index. The index is\nconstructed from the resource descriptions, and also includes \nall the words contained in the referenced home page. This\nlatter feature is quite powerful for bringing new names of\nprojects, topics, research groups, very quickly to the index.\n\nTable \\ref{astroweb} lists the resources present in\nthe AstroWeb database in December 1999.\n\n\n\n\\begin{table}\n\\caption{Resources listed in the AstroWeb database (December 1999).\n The number of resources (Web sites) in each category is given\n between parentheses.\n A number of resources appear in more than one category.}\n\\footnotesize\n\\begin{tabular}{r p{6cm}}\n\\hline \nOrganizations & Astronomy Departments (508) \\\\\n & Professional and Amateur Organizations (159) \\\\\n & Space Agencies and Organizations (46) \\\\\n \\\\\n Observing & Observatories and Telescopes (328) \\\\\n resources & Telescope Observing Schedules (25) \\\\\n & Meteorological Information (10) \\\\\n & Astronomical Survey Projects (65) \\\\\n \\\\ \n Data resources & Data and Archive Centers (145) \\\\\n & Astronomy Information Systems (39) \\\\\n \\\\\n Abstracts, & Bibliographical Services (29) \\\\\n Publications, & Astronomical Journals and Publications (90) \\\\\n Libraries & Astronomy \\& astrophysics preprints (58) \\\\\n & Abstracts of Astronomical Publications (29) \\\\\n & Conference Proceedings (45) \\\\\n & Astronomy-related Libraries (48) \\\\\n & Other Library resources (11) \\\\\n \\\\\nPeople-related & Personal Web pages (800) \\\\\n Resources & People (lists) (14) \\\\\n & Jobs (37) \\\\\n & Conferences and Meetings (45) \\\\\n & Newsgroups (31) \\\\\n & Mailing Lists (16) \\\\\n \\\\\n Software & Astronomy software servers (129) \\\\\n Computer & Document Preparation Tools (9) \\\\\n Science & Overviews \\& technical notes for protocols (11) \\\\\n & Computer Science-related Resources (33) \\\\\n \\\\\n Research areas & Radio Astronomy (109) \\\\\n Astronomy & Optical Astronomy (178) \\\\\n Space Physics & High-Energy Astronomy (77) \\\\\n & Space Astronomy (175) \\\\\n & Solar Astronomy (77) \\\\\n & Planetary Astronomy (64) \\\\\n & History of Astronomy (21) \\\\\n & Earth, Ocean, Atmosphere, Space Sciences (41) \\\\\n & Physics-related Resources (91) \\\\\n \\\\\n Educational & Professional and Amateur Organizations (159) \\\\\n resources & Educational resources (240) \\\\\n & Astronomy Pictures (105) \\\\\n \\\\\nMiscellaneous & Primary Lists of Astronomy Resources (10) \\\\\n & Other lists of astronomy resources (78) \\\\\n & Miscellaneous Resources (137) \\\\\n\\hline\n\\end{tabular}\n\\label{astroweb}\n\\end{table} \n\n\n\n\n\\section{Current status of on-line astronomy resources}\n\nFollowing the classification scheme adopted by AstroWeb,\nwe will outline in this section the current status of\nthe main categories of on-line astronomy resources,\npointing to meta-resources (i.e. organized lists of\nresources) when they are available.\n\n\\subsection{Organizations}\n\nMost of the active astronomical organizations (institutes,\nastronomy departments, etc.) now have\nhome pages on the Internet. \nStarWorlds\\footnote{http://cdsweb.u-strasbg.fr/starworlds.html} \nis currently the most comprehensive searchable directory of \nsuch resources ; it can be queried by names, keywords,\nor character strings. \nFor browsing lists sorted by alphabetical\norder or by country, see AstroWeb (Section~\\ref{AstroWeb}). \nNational or international organizations also maintain\nuseful lists.\n\n\\subsection{Observational projects and missions}\n\nIt is now difficult to envisage an observational project\nwithout a web site. As they are more dynamic and often\ninvolve multiple organizations or institutions,\nthe best way to find\nthem may be to use one of the powerful commercial search\nengines that routinely index millions of web pages on the\nInternet.\n\nThe indexing system of AstroWeb may also be \nhelpful, especially when it is important to\nlimit the investigation domain to astronomy,\nor to keep track of new emerging projects.\n\n\\subsection{Data and information systems}\n\nAstronomy data and information centers are becoming increasingly \ninterconnected, with both explicit links to other relevant resources and \nautomatic cross-links that may be invoked transparently\nto the end-user.\nSection~\\ref{isaia} describes current efforts to provide\ninteroperability within astrophysics (\\emph{Astrobrowse}) and\nacross the space sciences (\\emph{ISAIA}).\n\n\\subsection{Bibliographic resources}\n\nHere also a virtual network is being organized,\nas exemplified by the \n\\emph{Urania}\\footnote{http://www.aas.org/Urania/} \ninitiative, or by the coordinated efforts to\ncreate links between ADS and other services\n(Kurtz et al.\\ \\cite{ADS}).\n%\nNote that many of the bibliographical resources are\nelectronic journals for which a subscription may be\nrequired. \n\n\\subsection{People-related resources}\n\nSome databases \n(RGO E-mail directory\\footnote{http://star-www.rl.ac.uk/astrolist/astrosearch.html},\nStarHeads\\footnote{http://cdsweb.u-strasbg.fr/starheads.hml})\nfollow the development\nof electronic mail addresses and personal Web pages.\nDirectories from national or international societies\n(e.g., AAS, EAS, IAU) are also\ngenerally very carefully kept up to date.\n\nThe database of meetings and conferences maintained\nby CFHT\\footnote{http://cadcwww.dao.nrc.ca/meetings/meetings.html} is very\ncomplete and well organized. Astronomical societies also\nmaintain their own lists.\n\n\\subsection{Astronomical software}\n\nThe Astronomical Software and Documentation Service \n(ASDS\\footnote{http://asds.stsci.edu/}) \nis a network service that allows users to locate existing\nastronomical software, associated technical documentation, and\ninformation about telescopes and astronomical instrumentation\n(Payne et al.\\ \\cite{ASDS96}).\nASDS originated as a service devoted entirely to \nastronomical software packages and their associated \non-line documentation and was originally called the\nAstronomical Software Directory Service. Much code is rewritten these days, \nnot because anyone has found a fundamentally better way \nto solve the problem, but because developers simply don't know \nwho has already done it, whether the code runs on the \nsystem they have available, or where to get it if it does. \nThat is the problem that ASDS was intended to solve. \n\nIn 1998 the scope of ASDS was expanded to include \nastronomical observing sites and their associated \ntelescope and instrument manuals, taken from a listing \nmaintained at CFHT. The service was renamed at this point. \n\n\\subsection{Educational resources}\n\nEducation and public outreach have always been a strong\nconcern in astronomy, but the importance of this\nactivity is growing at a higher rate, with the advent\nof the World Wide Web.\n\nIt is difficult to give general rules for such a\nwide field, going far beyond the limits of\nastronomical institutions. \n%%%%%%%%%%%\nLet us just say that we expect to see in the\nfuture an increasing r\\^ole of educational\ninstitutions (planetariums, or outreach departments\nof big societies or institutions), for conveying \ngeneral astronomy knowledge, or news about recent \ndiscoveries, to the general public.\n\nThe yellow-page services mentioned above do keep\nlists of the most important education services.\n\n\n\\section{Towards a global index of astronomical resources}\n\nIn the following we will focus on Internet resources that\nactually provide data, of any kind, as opposed to those\ndescribing or documenting an institution or a research\nproject, without giving access to any data set or archive.\n\nOne main trend is certainly the increase of interconnections between\ndistributed on-line services, the `Weaving of the Astronomy Web' (which\nwas the title of a Conference organized in Strasbourg \nby Egret \\& Heck \\cite{waw}).\n\nMore generally, with the development of the Internet, and of a large\nnumber of on-line services giving access to data or information, it is\nclear that tools giving \ncoordinated access to distributed services are needed. This\nis, for instance, the concern expressed by NASA through the Astrobrowse\nproject (Heikkila et al.\\ \\cite{astrobrowse-2}). \n\nIn this section we will first describe a tool for managing\na ``metadata'' dictionary of astronomy information services\n(GLU); then we will show how the existence of such a\nmetadatabase can be used for building efficient search\nand discovery tools.\n\n\n\\subsection{The CDS GLU}\n\nThe CDS (Centre de Donn\\'ees astronomiques de Strasbourg) has \nrecently developed a tool for managing remote links in a context of \ndistributed heterogeneous services \n(GLU\\footnote{http://simbad.u-strasbg.fr/glu/glu.htx}, \nG\\'en\\'erateur de Liens \nUniformes, i.e. Uniform Link Generator; \nFernique et al.\n\\cite{glu}). \n\nFirst developed for\nensuring efficient interoperability of the several services existing at CDS \n({\\sc VizieR}, {\\sc Simbad}, {\\sc Aladin}, bibliography, etc.; see\nGenova et al.\\ \\cite{CDS}), \nthis tool has also been \ndesigned for maintaining addresses (URLs) of \ndistributed services \n(ADS, NED, etc.).\n\nA key element of the system is the ``GLU dictionary'' maintained by \nthe data providers contributing to the system, and distributed to all \nsites of a given domain. This dictionary contains knowledge about the \nparticipating services (URLs, syntax and semantics of input fields, \ndescriptions, etc.), so that it is possible to generate automatically a \ncorrect query for submission to a remote database. \n\nThe service provider (data center, archive manager, or \nwebmaster of an astronomical institute) can use GLU for \ncoding a query, taking benefit of the easy update of the system: \nknowing which service to call, and which answer to expect from \nthis service, the programmer does not have to worry about the \nprecise address of the remote service at a given time, nor of the \ndetailed syntax of the query (expected format of the equatorial \ncoordinates, etc.).\n\n\n\n\\subsection{New search and discovery tools}\n\nThe example of GLU demonstrates the usefulness of storing into\na database the knowledge about information\nservices (their address, purpose, domain of coverage,\nquery syntax, etc.). In a second step, such a\ndatabase can be queried when the challenge is to provide\ninformation about whom is providing what, \nfor a given object, region of the sky, or domain of interest.\n\nSeveral projects are working toward providing general solutions.\n\n\\subsubsection{Astrobrowse}\n\n\\emph{Astrobrowse} is a project that began within the United States\nastrophysics community, primarily within NASA data centers, for developing\na user agent which significantly streamlines \nthe process of locating astronomical data on the web. \nSeveral prototype implementations are already \navailable\\footnote{http://heasarc.gsfc.nasa.gov/ab/}.\nWith any of these prototypes, a user can already \nquery thousands\nof resources without having to deal with out-of-date URLs, \nor spend time figuring out how to use each resource's\nunique input formats. \nGiven a user's selection of \nweb-based astronomical databases and an \nobject name or coordinates, Astrobrowse will \nsend queries to all databases identified as containing potentially\nrelevant data. It provides links to these resources and allows the\nuser to browse results from each query. Astrobrowse does not recognize,\nhowever, when a query yields a null result, nor does it integrate\nquery results into a common format to enable intercomparison.\n\n\\subsubsection{AstroGLU}\n\n\nConsider the following scenario: we have a data\nitem $I$ (for example an author's name, the position or name\nof an astronomical object, a bibliographical reference, etc.),\nand we would like to know more about it, but we do not know a\npriori which service $S$ to contact, and what are the\ndifferent data types $D$ which can be requested.\nThis scenario is typical of a scientist\nexploring new domains as part of a research procedure.\n\nThe GLU dictionary can actually be used for helping to solve this \nquestion: the dictionary can be considered as a reference \ndirectory, storing the knowledge about all services accepting data item $I$ as \ninput, for retrieving data $D_1$ or $D_2$. For example, we can \neasily obtain from such a dictionary the list of all services accepting \nan author's name as input; information which can be accessed, in \nreturn, may be an abstract (service ADS), a preprint (LANL/astro-\nph), the author's address (RGO e-mail directory) or personal\nWeb page (StarHeads), etc.\n\nBased on such a system, it becomes possible to create automatically \na simple interface guiding the user towards any of the services \ndescribed in the dictionary.\n\nThis idea has been developed as a prototype tool, under the name of \nAstroGLU\\footnote{http://simbad.u-strasbg.fr/glu/cgi-bin/astroglu.pl}\n(Egret et al.\\ \\cite{astroglu}).\nThe aim of this tool is to help the users find their way among \nseveral dozens (for the moment) of possible actions or services.\nA number of compromises have to be taken between providing the \nuser with the full information (which would be too abundant and \nthus unusable), and preparing digest lists (which implies hiding some\namount of auxiliary information and making somewhat subjective\nselections).\n\nA resulting issue is the fact that the system puts on the same line \nservices which have very different quantitative or qualitative \ncharacteristics. {AstroGLU} has no\nefficient ways yet to provide the user with a hierarchy of\nservices, as a gastronomic guide would do for restaurants.\nThis might come to be a necessity in the future, as more and more \nservices become (and remain) available.\n\n\n%\n%________________________________________________________\n\\section{Towards an integration of distributed data and information\n services}\n\\label{isaia}\n\n To go further, one needs\nto be able to integrate the result of queries \nprovided by heterogeneous services.\nThis is the aim of the ISAIA (Integrated System for Archival \nInformation Access)\nproject\\footnote{http://heasarc.gsfc.nasa.gov/isaia/}\n(Hanisch \\cite{isaia1}, \\cite{isaia2}).\n\nThe key objective of the project is to\ndevelop an interdisciplinary data location and integration \nservice for space sciences. Building upon existing data\nservices and communications protocols, this service will \nallow users to transparently query a large variety of distributed\nheterogeneous Web-based resources (catalogs, data, computational \nresources, bibliographic references, etc.)\nfrom a single interface. The service will collect responses \nfrom various resources and integrate them in a seamless\nfashion for display and manipulation by the user. \n\nBecause the scope of ISAIA is intended to span the space \nsciences -- astrophysics, planetary science, solar physics, and\nspace physics -- it is necessary to find a way to standardize the\ndescriptions of data attributes that are needed in order to formulate\nqueries. The ISAIA approach is based on the concept of \\emph{profiles}.\nProfiles map generic concepts and terms onto mission or dataset specific\nattributes. Users may make general queries across multiple disciplines\nby using the generic terms of the highest level profile, or make more\nspecific queries within subdisciplines using terms from more detailed\nsubprofiles.\n\nThe profiles play three critical and interconnected roles:\n\\begin{enumerate}\n\\item They identify appropriate resources (catalogs, mission datasets,\nbibliographic databases): the \\emph{resource profile}\n\\item They enable generic queries to be mapped unambiguously onto \nresource-specific queries: the \\emph{query profile}\n\\item They enable query responses to be tagged by content type and \nintegrated into a common presentation format: the \\emph{response\nprofile}\n\\end{enumerate}\nThe resource, query, and response profiles are all aspects of a common\ndatabase of resource attributes. Current plans call for these profiles to \nbe expressed using XML (eXtensible Markup Language, an emerging standard\nwhich allows embedding of logical markup tags within a document) and to be \nmaintained as a distributed database using the CDS GLU facility.\n\nThe profile concept is critical to a distributed data service where one\ncannot expect data providers to modify their internal systems or services\nto accommodate some externally imposed standard. The profiles act as a\nthin, lightweight interface between the distributed service and the\nexisting specific services. Ideally the service-specific profile\nimplementations are maintained in a fully distributed fashion, with\neach data or service provider running a GLU daemon in which that site's\nservices are fully described and updated as necessary. Static services \nor services with insufficient staff resources to maintain a local GLU\nimplementation can still be included, however, as long as their profiles\nare included elsewhere in the distributed resource database. The profile\nconcept is not unique to space science, but would apply equally well to \nany distributed data service in which a common user interface is desired\nto locate information in related yet traditionally separate disciplines.\n\n%\n%________________________________________________________\n\\section{Information clustering and advanced user interfaces}\n\n\nA major challenge in current information systems research is to find\nefficient ways for users to be able to visualize the contents and understand\nthe correlations within large databases. The technologies being developed\nare likely to be applicable to astronomical information systems. For\nexample,\ninformation retrieval by means of ``semantic road maps'' was first \ndetailed in Doyle (\\cite{doyle}), using a powerful\nspatial metaphor which \nlends itself quite well to modern distributed computing \nenvironments such as \nthe Web. \nThe Kohonen self-organizing feature map (SOM;\nKohonen \\cite{origk}) method \nis an effective means towards this end of a\nvisual information retrieval user interface. \n\n\\subsection{Interfacing datasets with a Self-organizing Map}\n\nThe Kohonen map is, at heart, $k$-means clustering with the additional \nconstraint that cluster centers be located on a regular grid (or some \nother topographic structure) and furthermore their location on the grid \nbe monotonically related to pairwise proximity (Murtagh \\& \nHern\\'andez-Pajares \\cite{mhp}).\n\nA regular grid is quite convenient for\nan output representation space,\nas it maps conveniently onto a visual user interface.\nIn a web context, it can easily be made interactive and responsive.\n\nFig.\\ \\ref{figmap} shows an example of such\na visual and interactive user interface map,\nin the context of a set of journal articles described\nby their keywords.\nColor is related to density of document clusters located at \nregularly spaced nodes\nof the map, and some of these nodes/clusters are annotated. \nThe map is installed on the Web as a clickable image map, \nwith CGI programs accessing lists of documents\nand -- through further links -- in many\ncases, the full documents. \nIn the example shown, the user has queried a node and\nresults are seen in the right-hand panel. \nSuch maps are maintained for (currently) \n12,000 articles from the {\\em Astrophysical Journal}, 7000 from \n{\\em Astronomy and Astrophysics}, over 2000 astronomical catalogs, and \nother data holdings. More information on the design of this\nvisual interface and \nuser assessment can be found in Poin\\c{c}ot et al.\\ (\\cite{poin1,poin2}).\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{map.ps}}\n%\\epsfysize=10cm \\epsfbox{map.ps} % Was originally 10cm \n\\caption{Visual interactive user interface to a set\nof articles from the journal \n{\\em Astronomy and Astrophysics}. Original in color.} \n\\label{figmap}\n\\end{figure}\n\n\\subsection{Hyperlink clustering}\n\nGuillaume \\& Murtagh (\\cite{guill}) have recently\ndeveloped a Java-based visualization\ntool for hyperlink-based data, in XML,\nconsisting of astronomers, astronomical\nobject names, article titles, and possibly other objects\n(images, tables, etc.). \nThrough weighting, the various types of links could\nbe prioritized. An iterative refinement algorithm was developed to map the\nnodes (objects) to a regular grid of cells, which, as for the Kohonen SOM \nmap, are clickable and provide access to the data represented by the \ncluster. \nFig.\\ \\ref{heyvaerts} shows an example for an astronomer \n(Prof.\\ Jean Heyvaerts, Strasbourg Astronomical Observatory).\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{grid_Heyvaerts_small.ps}}\n%\\epsfysize=8cm \\epsfbox{grid_Heyvaerts_small.ps} % Was originally 10cm \n\\caption{Visual interactive user interfaces, based on graph edges. Vertices\nare author names, article titles and (not shown here) astronomical object\nnames. Map for astronomer Jean Heyvaerts. Original in color.} \n\\label{heyvaerts}\n\\end{figure}\n\nThese new cluster-based visual user interfaces are not computationally \ndemanding. In general they cannot be created in real time, but \nthey are scalable in the sense that many tens of thousands of documents or\nother objects can be easily handled. \nDocument management (see e.g.\\ Cartia\\footnote{http://www.cartia.com/}) \nis less the motivation as is \ninstead the interactive user interface. \n\nFurther information on these visual user interfaces can be found in \nGuillaume (\\cite{guill2}) and Poin\\c{c}ot (\\cite{poin3}). \n\n\\subsection{Future developments for advanced interfaces}\n\nTwo directions of development are planned in the near future. \nFirstly,\nvisual user interfaces need to be coupled together. A comprehensive \n``master'' map is one possibility, but this has the disadvantage of \ncentralized control and/or configuration control. \nAnother possibility is to develop a protocol \nsuch that a map can refer a user to other maps in appropriate circumstances.\nSuch a protocol was developed a number of years ago in a system called\nIngrid\\footnote{http://www.ingrid.org/} \ndeveloped by P.\\ Francis at NTT Software \nLabs in Tokyo (see Guillaume \\cite{guill2}). However this work has been \nreoriented since then. \n\nModern middleware tools may offer the \nfollowing solution.\nThis is to define an information \nsharing bus, which will connect distributed information maps. It\nwill be interesting to\nlook at the advantages of CORBA (Common Object Request Broker Architecture)\nor, more likely, EJB (Enterprise Java Beans), for ensuring this \ninteroperability infrastructure (Lunney \\& McCaughey \\cite{corba}). \n\nA second development path is to note the clustering which is at the core\nof these visual user interfaces and to ask whether this can be further\nenhanced to facilitate construction of query and response agents. It is \nclear to anyone who uses Internet search engines such as AltaVista, \nLycos, etc.\\ that clustering of results\nis very desirable. A good example of such clustering of search results in\npractice is the Ask Jeeves search engine\\footnote{http://www.askjeeves.com/}.\nThe query interface, additionally, is a natural language one, another\nplus.\n\n\n\\section{Conclusion}\n\nThe on-line ``Virtual Observatory'' is currently\nunder construction with on-line archives and services \npotentially giving access to a huge quantity\nof scientific information: its services will allow astronomers to\nselect the information of interest for their research, and to access\noriginal data, observatory archives and results published in\njournals. Search and discovery tools currently in \ndevelopment will be of vital importance to make all the\nobservational data and information\navailable to the widest scientific community.\n\n\\begin{acknowledgements}\n\nCDS acknowledges the support of INSU-CNRS, the Centre National\nd'Etudes Spatiales (CNES), and Universit\\'e Louis Pasteur.\n\\end{acknowledgements}\n\n\n%________________________________________________________\n\n\\begin{thebibliography}{}\n\n\\bibitem[1994]{AHM94}\nAndernach, H., Hanisch, R.J., Murtagh, F., 1994, PASP 106, 1190\n\n\\bibitem[1999]{ALDIA}\nAndernach, H., 1999, in \n\\emph{Astrophysics with Large Databases in the Internet Age},\nProc. IXth Canary Islands Winter School on Astrophysics,\nM. Kidger, I. P\\'erez-Fournon, \\& F. S\\'anchez (Eds.),\nCambridge University Press, p. 1\n\n%\\bibitem[2000]{aladin} Bonnarel, F., Fernique, P.,\n% Bienaym\\'e, O., et al., 2000, A\\&AS, {\\em in press}\n%(Aladin)\n% Aladin paper in the same volume\n\n%\\bibitem[1996]{epub}\n%Boyce, P., Dalterio, H., 1996, \n%{\\em Physics Today} 49, 42\n\n\\bibitem[1961]{doyle}\nDoyle, L.B., 1961, \n{\\em Journal of the ACM}, 8, 553\n\n\\bibitem[1994]{jungle}\n Egret, D., 1994, in {\\em Astronomical Data\nAnalysis Software and Systems III}, ASP Conf. Ser. 61, p. 14 \n\n\\bibitem[1995]{amp2}\nEgret, D., Albrecht, M. (Eds.), 1995,\n{\\em Information \\& On-line Data in Astronomy},\nKluwer Academic Publ., Dordrecht\n\n\\bibitem[1995]{waw}\nEgret, D., Heck, A. (Eds.), 1995,\n\\emph{Weaving the Astronomy Web}, Vistas in Astron. 39, 1--127\n\n%\\bibitem[1995]{cds-amp2}\n%Egret, D., Cr\\'ez\\'e, M. , Bonnarel, F., et al., 1995,\n%in {\\em Information \\& On-line Data in Astronomy}, Egret \\& Albrecht \n%(Eds.), Kluwer Academic Publ., p. 163\n%(CDS Hub)\n%% A global perspective on astronomical data and information:\n%% the Strasbourg astronomical data centre (CDS)\n\n\\bibitem[1998]{astroglu} \nEgret, D., Fernique, P., Genova, F., 1998, \nin {\\em Astronomical Data\nAnalysis Software and Systems VII}, ASP Conf. Ser. 145, p. 416\n(AstroGlu)\n% AstroGlu\n\n\\bibitem[1998]{glu} \nFernique, P., Ochsenbein, F., Wenger, M., 1998, \nin {\\em Astronomical Data\nAnalysis Software and Systems VII}, ASP Conf. Ser. 145, p. 466\n(GLU)\n% CDS GLU\n\n\\bibitem[2000]{CDS} Genova, F., Egret, D., Bienaym\\'e, O.,\net al., 2000, A\\&AS, \\emph{in press}\n(CDS)\n% The CDS Information Hub (this volume)\n\n\\bibitem[1995]{librarians}\nGrothkopf, U., 1995,\nVistas Astron. 38, 401\n% Internet resources for librarians\n\n\\bibitem[2000]{guill}\n Guillaume, D., Murtagh, F., 2000, ``Clustering of XML documents,'' \n{\\em Computer Physics Communications}, in press\n\n\\bibitem[2000]{guill2}\nGuillaume, D., 2000, \n%Distributed Information Retrieval, Search and Processing in Astronomy, \nPhD thesis, Universit\\'e Louis Pasteur, Strasbourg\n\n\\bibitem[2000a]{isaia1} Hanisch, R.J., 2000a, {\\em Computer\nPhysics Communications}, in press\n% Integrated Access to Distributed Data and Information Services\n\n\\bibitem[2000b]{isaia2}\nHanisch, R.J., 2000b, in {\\it ADASS IX}, ASP Conf. Ser. in press\n\n\\bibitem[1995a]{starfam}\n Heck, A., 1995a, \nin {\\em Information \\& On-line Data in Astronomy}, D. Egret \nand M. A. Albrecht, Eds., p. 195\n(Star*s Family)\n% The Star*s Family -- An example of comprehensive yellow-page services\n\n\\bibitem[1995b]{starheads}\n Heck, A., 1995b, A\\&AS 109, 265\n(StarHeads)\n% StarHeads\n\n\\bibitem[1997]{eppa}\n Heck, A., 1997, \\emph{Electronic Publishing for Physics and Astronomy},\n Astrophys. Space Science 247, Kluwer, Dordrecht\n\n\\bibitem[1994]{starworlds}\n Heck, A., Egret, D., Ochsenbein, F., 1994, A\\&AS 108, 447\n(StarWorlds -- StarBits)\n% StarWorlds -- StarBits\n\n\\bibitem[1999]{astrobrowse-2}\nHeikkila, C.W., McGlynn, T.A., White, N.E., 1999,\nin {\\em Astronomical Data\nAnalysis Software and Systems VIII}, ASP Conf. Ser. 172, p. 221\n(Astrobrowse)\n% Astrobrowse: a web agent for querying astronomical databases\n\n\\bibitem[1994]{astroweb} \n Jackson, R., Wells, D., Adorf, H.M., et al., 1994, A\\&AS 108, 235\n(AstroWeb)\n% AstroWeb - A Database of links to astronomy resources \n\n\\bibitem[1982]{origk}\nKohonen, T., 1982, Biological Cybernetics 43, 59\n\n\\bibitem[2000]{ADS} Kurtz, M., Eichhorn, G., Accomazzi, A.,\net al., 2000, A\\&AS, in press\n(ADS)\n% The NASA Astrophysics Data System: Overview (this volume)\n\n\\bibitem[2000]{corba} Lunney, T.F., McCaughey, A.J., 1999,\n Computer Physics Communications, in press\n\n%\\bibitem[1996]{astrobrowse-1}\n%Murray, S.S., Hanisch, R.J. \n%in {\\em Astronomical Data Analysis Software and Systems V}, \n%ASP Conf. Ser. 101\n%(Astrobrowse)\n% Astrobrowse workshop report\n\n\\bibitem[1995]{mhp} Murtagh, F., Hern\\'andez-Pajares, M., 1995,\nJournal of Classification, 12, 165\n\n\\bibitem[1996]{ASDS96} Payne, H. E., Hanisch, R. J., Warnock, A., 1996,\nin {\\em Astronomical Data Analysis Software and Systems V},\nASP Conf. Ser. 101, 577\n\n\\bibitem[1998]{poin1} \nPoin\\c{c}ot, Ph., Lesteven, S., Murtagh, F., 1998, A\\&AS 130, 183\n\n\\bibitem[2000]{poin2} Poin\\c{c}ot, Ph., Lesteven, S., Murtagh, F.,\n2000, \n% ``Maps of information spaces: assessments from astronomy,''\nJournal of the American Society for\nInformation Science, {\\em submitted}\n\n\\bibitem[1999]{poin3}\nPoin\\c{c}ot, Ph., 1999, PhD thesis, Universit\\'e Louis Pasteur,\n Strasbourg\n\n\n\\end{thebibliography}\n\n\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002113.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[1994]{AHM94}\nAndernach, H., Hanisch, R.J., Murtagh, F., 1994, PASP 106, 1190\n\n\\bibitem[1999]{ALDIA}\nAndernach, H., 1999, in \n\\emph{Astrophysics with Large Databases in the Internet Age},\nProc. IXth Canary Islands Winter School on Astrophysics,\nM. Kidger, I. P\\'erez-Fournon, \\& F. S\\'anchez (Eds.),\nCambridge University Press, p. 1\n\n%\\bibitem[2000]{aladin} Bonnarel, F., Fernique, P.,\n% Bienaym\\'e, O., et al., 2000, A\\&AS, {\\em in press}\n%(Aladin)\n% Aladin paper in the same volume\n\n%\\bibitem[1996]{epub}\n%Boyce, P., Dalterio, H., 1996, \n%{\\em Physics Today} 49, 42\n\n\\bibitem[1961]{doyle}\nDoyle, L.B., 1961, \n{\\em Journal of the ACM}, 8, 553\n\n\\bibitem[1994]{jungle}\n Egret, D., 1994, in {\\em Astronomical Data\nAnalysis Software and Systems III}, ASP Conf. Ser. 61, p. 14 \n\n\\bibitem[1995]{amp2}\nEgret, D., Albrecht, M. (Eds.), 1995,\n{\\em Information \\& On-line Data in Astronomy},\nKluwer Academic Publ., Dordrecht\n\n\\bibitem[1995]{waw}\nEgret, D., Heck, A. (Eds.), 1995,\n\\emph{Weaving the Astronomy Web}, Vistas in Astron. 39, 1--127\n\n%\\bibitem[1995]{cds-amp2}\n%Egret, D., Cr\\'ez\\'e, M. , Bonnarel, F., et al., 1995,\n%in {\\em Information \\& On-line Data in Astronomy}, Egret \\& Albrecht \n%(Eds.), Kluwer Academic Publ., p. 163\n%(CDS Hub)\n%% A global perspective on astronomical data and information:\n%% the Strasbourg astronomical data centre (CDS)\n\n\\bibitem[1998]{astroglu} \nEgret, D., Fernique, P., Genova, F., 1998, \nin {\\em Astronomical Data\nAnalysis Software and Systems VII}, ASP Conf. Ser. 145, p. 416\n(AstroGlu)\n% AstroGlu\n\n\\bibitem[1998]{glu} \nFernique, P., Ochsenbein, F., Wenger, M., 1998, \nin {\\em Astronomical Data\nAnalysis Software and Systems VII}, ASP Conf. Ser. 145, p. 466\n(GLU)\n% CDS GLU\n\n\\bibitem[2000]{CDS} Genova, F., Egret, D., Bienaym\\'e, O.,\net al., 2000, A\\&AS, \\emph{in press}\n(CDS)\n% The CDS Information Hub (this volume)\n\n\\bibitem[1995]{librarians}\nGrothkopf, U., 1995,\nVistas Astron. 38, 401\n% Internet resources for librarians\n\n\\bibitem[2000]{guill}\n Guillaume, D., Murtagh, F., 2000, ``Clustering of XML documents,'' \n{\\em Computer Physics Communications}, in press\n\n\\bibitem[2000]{guill2}\nGuillaume, D., 2000, \n%Distributed Information Retrieval, Search and Processing in Astronomy, \nPhD thesis, Universit\\'e Louis Pasteur, Strasbourg\n\n\\bibitem[2000a]{isaia1} Hanisch, R.J., 2000a, {\\em Computer\nPhysics Communications}, in press\n% Integrated Access to Distributed Data and Information Services\n\n\\bibitem[2000b]{isaia2}\nHanisch, R.J., 2000b, in {\\it ADASS IX}, ASP Conf. Ser. in press\n\n\\bibitem[1995a]{starfam}\n Heck, A., 1995a, \nin {\\em Information \\& On-line Data in Astronomy}, D. Egret \nand M. A. Albrecht, Eds., p. 195\n(Star*s Family)\n% The Star*s Family -- An example of comprehensive yellow-page services\n\n\\bibitem[1995b]{starheads}\n Heck, A., 1995b, A\\&AS 109, 265\n(StarHeads)\n% StarHeads\n\n\\bibitem[1997]{eppa}\n Heck, A., 1997, \\emph{Electronic Publishing for Physics and Astronomy},\n Astrophys. Space Science 247, Kluwer, Dordrecht\n\n\\bibitem[1994]{starworlds}\n Heck, A., Egret, D., Ochsenbein, F., 1994, A\\&AS 108, 447\n(StarWorlds -- StarBits)\n% StarWorlds -- StarBits\n\n\\bibitem[1999]{astrobrowse-2}\nHeikkila, C.W., McGlynn, T.A., White, N.E., 1999,\nin {\\em Astronomical Data\nAnalysis Software and Systems VIII}, ASP Conf. Ser. 172, p. 221\n(Astrobrowse)\n% Astrobrowse: a web agent for querying astronomical databases\n\n\\bibitem[1994]{astroweb} \n Jackson, R., Wells, D., Adorf, H.M., et al., 1994, A\\&AS 108, 235\n(AstroWeb)\n% AstroWeb - A Database of links to astronomy resources \n\n\\bibitem[1982]{origk}\nKohonen, T., 1982, Biological Cybernetics 43, 59\n\n\\bibitem[2000]{ADS} Kurtz, M., Eichhorn, G., Accomazzi, A.,\net al., 2000, A\\&AS, in press\n(ADS)\n% The NASA Astrophysics Data System: Overview (this volume)\n\n\\bibitem[2000]{corba} Lunney, T.F., McCaughey, A.J., 1999,\n Computer Physics Communications, in press\n\n%\\bibitem[1996]{astrobrowse-1}\n%Murray, S.S., Hanisch, R.J. \n%in {\\em Astronomical Data Analysis Software and Systems V}, \n%ASP Conf. Ser. 101\n%(Astrobrowse)\n% Astrobrowse workshop report\n\n\\bibitem[1995]{mhp} Murtagh, F., Hern\\'andez-Pajares, M., 1995,\nJournal of Classification, 12, 165\n\n\\bibitem[1996]{ASDS96} Payne, H. E., Hanisch, R. J., Warnock, A., 1996,\nin {\\em Astronomical Data Analysis Software and Systems V},\nASP Conf. Ser. 101, 577\n\n\\bibitem[1998]{poin1} \nPoin\\c{c}ot, Ph., Lesteven, S., Murtagh, F., 1998, A\\&AS 130, 183\n\n\\bibitem[2000]{poin2} Poin\\c{c}ot, Ph., Lesteven, S., Murtagh, F.,\n2000, \n% ``Maps of information spaces: assessments from astronomy,''\nJournal of the American Society for\nInformation Science, {\\em submitted}\n\n\\bibitem[1999]{poin3}\nPoin\\c{c}ot, Ph., 1999, PhD thesis, Universit\\'e Louis Pasteur,\n Strasbourg\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002114
|
R-mode runaway and rapidly rotating neutron stars
|
[
{
"author": "Nils Andersson and David Ian Jones"
}
] |
We present a simple spin evolution model that predicts that rapidly rotating accreting neutron stars will mainly be confined to a narrow range of spin-frequencies; $P= 1.5-5$~ms. This is in agreement with current observations of both neutron stars in the Low-Mass X-ray Binaries and millisecond radio pulsars. The main ingredients in the model are: i) the instability of r-modes above a critical spin rate, ii) thermal runaway due to heat released as viscous damping mechanisms counteract the r-mode growth, and iii) a revised estimate of the strength of dissipation due to the presence of a viscous boundary layer at the base of the crust in an old and relatively cold neutron star. We discuss the gravitational waves that are radiated during the brief r-mode driven spin-down phase. We also briefly touch on how the new estimates affects the predicted initial spin periods of hot young neutron stars.
|
[
{
"name": "astro-ph_rev.tex",
"string": "\\documentclass{article}\n\\usepackage{natbib,epsfig,emulateapj}\n%\\documentclass[preprint,11pt]{aastex}\n\n%\\usepackage{epsf}\n%\\citestyle{aa}\n\n%\\shorttitle{R-mode runaway} \\shortauthors{Andersson et al.}\n\n\\begin{document}\n\n\\lefthead{Andersson et al.}\n\\righthead{R-mode runaway and rapidly rotating neutron stars}\n\n\n\n\\title{R-mode runaway and rapidly rotating neutron stars} \n\n\\author{Nils Andersson and David Ian Jones} \\affil{Department of\n Mathematics, University of Southampton, Southampton SO17 1BJ, United\n Kingdom} \n\\centerline{\\it \\small na@maths.soton.ac.uk, dij@maths.soton.ac.uk}\n\\vspace{0.2cm}\n\n%\\email{na@maths.soton.ac.uk, dij@maths.soton.ac.uk}\n\n\\author{Kostas D. Kokkotas and Nikolaos Stergioulas} \\affil{Department\n of Physics, Aristotle University of Thessaloniki, Thessaloniki\n 54006, Greece} \n\\centerline{\\it \\small kokkotas@astro.auth.gr, niksterg@astro.auth.gr}\n\\vspace{0.2cm}\n\n\\centerline{\\it (Accepted March. 10, 2000)}\n\\vspace{0.2cm}\n\n%\\email{kokkotas@astro.auth.gr, niksterg@astro.auth.gr}\n\n\\begin{abstract} \n We present a simple spin evolution model that predicts that rapidly\n rotating accreting neutron stars will mainly be confined to a narrow\n range of spin-frequencies; $P= 1.5-5$~ms. This is in agreement with\n current observations of both neutron stars in the Low-Mass X-ray\n Binaries and millisecond radio pulsars. The main ingredients in the\n model are: i) the instability of r-modes above a critical spin rate,\n ii) thermal runaway due to heat released as viscous damping\n mechanisms counteract the r-mode growth, and iii) a revised estimate\n of the strength of dissipation due to the presence of a viscous\n boundary layer at the base of the crust in an old and relatively\n cold neutron star. We discuss the gravitational waves that are\n radiated during the brief r-mode driven spin-down phase. We also\n briefly touch on how the new estimates affects the predicted initial\n spin periods of hot young neutron stars.\n\\end{abstract}\n\n\\keywords{dense matter -- gravitation -- stars: neutron -- stars:\n rotation --- stars: oscillations}\n\n\\section{Introduction} \n\nThe launch of the Rossi X-ray Timing Explorer (RXTE) in 1995 heralded\na new era in our understanding of neutron star physics. Detailed\nobservations of quasiperiodic phenomena at kHz frequencies in more\nthan a dozen Low-Mass X-ray Binaries (LMXB) strongly suggest that\nthese systems contain rapidly spinning neutron stars (for a recent\nreview, see \\citet{vanderklis00}), providing support for the standard\nmodel for the formation of millisecond pulsars (MSP) via spin-up due\nto accretion.\n\nDespite these advances several difficult questions remain to be\nanswered by further observations and/or theoretical modeling. For\nexample, we still do not know the reason for the apparent lack of\nradio pulsars at shorter periods than the 1.56~ms of PSR1937+21 (for a\nreview of recent progress in the modelling of rotating neutron stars,\nsee \\citet{stergioulas}). The recent RXTE observations provide a\nfurther challenge for theorists. Various models suggest that the\nneutron stars in LMXB spin rapidly, perhaps in the narrow range\n260-590~Hz \\citep{vanderklis00}. Three different models have been\nproposed to explain this surprising result. The first model (due to\n\\citet{white97}) is based on the standard magnetosphere model for\naccretion induced spin-up, while the remaining two models are rather\ndifferent, both being based on the idea that gravitational radiation\nbalances the accretion torque. In the first such model for the LMXB\n(proposed by \\citet{bildsten98} and recently refined by\n\\citet{ushomirsky00}), the gravitational waves are due to a quadrupole\ndeformation induced in the deep neutron star crust because of\naccretion generated temperature gradients. The second\ngravitational-wave model relies on the recently discovered r-mode\ninstability (see \\citet{akreview} for a review) to dissipate the\naccreted angular momentum from the neutron star.\n\nIn this Letter we reexamine the idea that gravitational waves from\nunstable r-modes provide the agent that balances the accretion torque.\nThis possibility was first analyzed in detail by \\citet{akst99} (but\nsee also \\citet{bildsten98}). Originally, it was thought that an\naccreting star in which the r-modes were excited to a significant\nlevel would reach a spin-equilibrium, very much in the vein of\nsuggestions by \\citet{papaloizou} and \\citet{wagoner}. Should this\nhappen, the neutron stars in LMXB would be prime sources for\ndetectable gravitational waves. However, as was pointed out by\n\\citet{levin99} and \\citet{spruit}, the original idea is not viable\nsince, in addition to generating gravitational waves that dissipate\nangular momentum from the system, the r-modes will heat the star up\n(via the shear viscosity that counteracts the r-mode at the relevant\ntemperatures). Since the shear viscosity gets weaker as the\ntemperature increases, the mode-heating triggers a thermal runaway and\nin a few months the r-mode would spin an accreting neutron star down\nto a rather low rotation rate. Essentially, this conclusion rules out\nthe r-modes in galactic LMXB as a source of detectable gravitational\nwaves, since they will only radiate for a tiny fraction of the systems\nlifetime.\n\nOther recent results would (at first sight) seem to emphasize the\nconclusion that the r-modes are not relevant for the LMXB.\n\\citet{bildsten99} investigated the effect that the presence of a\nsolid crust would have on the r-mode oscillations. They estimated\nthat the dissipation associated with a viscous boundary layer that\narises at the base of the solid crust in a relatively cold neutron\nstar would greatly exceed that of the standard shear viscosity. Thus,\nBildsten and Ushomirsky concluded that the r-mode instability would\nonly be relevant for very high rotation rates, and could therefore not\nplay a role in the LMXB.\n\nWe have reassessed the effect of the viscous boundary layer\n(correcting an erring factor in the estimates of \\citet{bildsten99}).\nOur new estimates show that the presence of the crust is important,\nbut that the instability operates at significantly lower spin rates\nthan suggested by Bildsten and Ushomirsky. Once we combine our\nestimates with the thermal runaway (now due to heating caused mainly\nby the presence of the viscous boundary layer), that results as the\nstar is spun up to the point at which the instability sets in, we\narrive at a model for the spin-evolution of accreting neutron stars.\nRemarkably, this simple model agrees well with existing observations\nof rapidly rotating neutron stars, covering both the LMXB and MSP\npopulations.\n\n\\section{Dissipation due to a viscous boundary layer}\n\nThe r-mode instability follows after a tug of war between (mainly\ncurrent multipole) gravitational radiation that drives the mode and\nvarious dissipation mechanisms that counteract the fluid motion. In\nthe simplest model, the mode is dominated by shear viscosity at low\ntemperatures while bulk viscosity may suppress the mode at high\ntemperatures. At intermediate temperatures, the r-mode sets an upper\nlimit on the neutron star spin rate. In an interesting recent paper,\n\\citet{bildsten99} estimate the strength of dissipation due to the\nsolid crust of an old neutron star, and find that the presence of a\nboundary layer at the base of the crust leads to a very strong damping\nof the r-modes.\n\nWhile we agree with the main idea and the various assumptions made by\nBildsten and Ushomirsky, we would like to point out one important\ndifference between their results and ones used previously in the\nliterature. Their assumed timescale for gravitational radiation\nreaction differs significantly from, for example, the uniform density\nresult derived by \\citet{kokkotas99} (and subsequently used by several\nauthors, see \\citet{akreview}). This is surprising since the uniform\ndensity result, which can be written\n\\begin{equation}\nt_{gw} \\approx -22 \\left( {1.4 M_\\odot\\over M} \\right)\n\\left( {\\mbox{10 km} \\over R} \\right)^4 \\left( {P \\over \\mbox{1 ms}}\n\\right)^6 \\mbox{ s} \\ ,\n\\label{gwapp}\\end{equation}\n(where the negative sign indicates that the mode is unstable) has been\nshown to be close (within a factor of two) to the results for $n=1$\npolytropes. $M$, $R$, and $P$ represent the mass, radius and spin\nperiod of the star, respectively. In contrast, \\citet{bildsten99} use\nthe $n=1$ polytrope result and argue that it corresponds to $t_{gw}\n\\approx -146$~s for a canonical neutron star rotating with a period of\n1~ms, i.e. assume that radiation reaction is almost one order of\nmagnitude weaker than in (\\ref{gwapp}). This difference occurs\nbecause Bildsten and Ushomirsky have only rescaled the fiducial\nrotation frequency $\\Omega_0=\\sqrt{\\pi G\\bar{\\rho}}$ (where\n$\\bar{\\rho}$ represents the average density) in terms of which the\n$n=1$ polytrope results of \\citet{owen98} were expressed\n($t_{gw}\\approx -3.26(\\Omega_0/\\Omega)^6$ for a specific polytropic\nstellar model). Unfortunately, this procedure is not correct. From\nthe fundamental relations, e.g. the formula for the gravitational-wave\nenergy radiated via the current multipoles, one can see that the\ngravitational-wave timescale should scale with $M$, $R$ and $P$ in the\nway manifested in (\\ref{gwapp}). Thus, we believe that Bildsten and\nUshomirsky underestimate the strength of radiation reaction\nsignificantly, which motivates us to reassess the relevance of the\nviscous boundary layer.\n\nWe should, of course, emphasize at this point that our current\nunderstanding of the r-mode instability is based on crude estimates of\nthe various timescales. In order to understand the role of the\ninstability in an astrophysical context we must improve our modelling\nof many aspects of neutron star physics such as the effect of general\nrelativity on the r-modes, cooling rates, viscosity coefficients,\nmagnetic fields, potential superfluidity, the formation of a solid\ncrust etcetera (see \\citet{akreview} for a description of recent\nprogress in these various directions).\n\nIn the following we will mainly consider uniform density stars, i.e.\nuse the gravitational-wave timescale given by (\\ref{gwapp}). In\nestimating the dissipation timescale $t_{vbl}$ due to the presence of\nthe crust, we need to evaluate $t_{vbl} \\approx {-2E / (dE/dt)}$ where\n$E$ is the mode-energy, and $dE/dt$ follows from an integral over the\nsurface area at the crust-core boundary (assumed to be located at\nradius $R_b$), cf. equation (3) of \\citet{bildsten99}. To evaluate\nthis integral we use the standard result for the shear viscosity in a\nnormal fluid. To incorporate our uniform density model, we make the\nreasonable assumption that the density of the star is constant ($\\sim\nM/R^3$) inside radius $R$. Then it falls off rapidly in such a way\nthat the base of the crust is located at a radius only slightly larger\nthan $R$. Hence, it makes sense to use $R_b\\approx R$. If we neglect\nthe small mass located outside radius $R$ we can then immediately\ncompare the result for the viscous boundary layer to the timescales\nused by \\citet{akst99}. In the end, our estimate for the dissipation\ndue to the presence of the viscous boundary layer is\n\\begin{equation}\nt_{vbl} \\approx 200 \n\\left( {M \\over 1.4 M_\\odot } \\right)\n\\left( {\\mbox{10 km} \\over R } \\right)^2 \n\\left( {T \\over 10^8 \\mbox{ K}}\n\\right) \\left( {P \\over \\mbox{1 ms}}\n\\right)^{1/2} \\mbox{ s}\\ .\n\\end{equation}\nwhich is a factor of 2 larger than that of Bildsten and Ushomirsky.\nThis difference arises simply because the mode-energy $E$ is this\nfactor larger for uniform density models. The star is assumed to have\na uniform temperature distribution, with core temperature $T$.\n\nIn Figure~\\ref{fig1} we show the instability window obtained from our\nrevised estimate. As is clear from this Figure, the presence of a\nviscous boundary layer in an old, relatively cold neutron star is,\nindeed, important. However, Bildsten and Ushomirsky's conclusion that\nthe r-mode instability is irrelevant for the LMXB cannot be drawn from\nFigure~\\ref{fig1}. On the contrary, the Figure suggests that the\ninstability may well be limiting the rotation of these systems.\n\n\\section{Thermal runaway in rapidly spinning neutron stars}\n\nThe fact that our revised instability curve for r-modes damped by\ndissipation in a viscous boundary layer agrees well with the fastest\nobserved neutron star spin frequencies, cf. Figure~\\ref{fig1},\nmotivates us to speculate further on the relevance of the instability.\nWe want to model how the potential presence of an unstable r-mode\naffects the spin-evolution of rapidly spinning, accreting neutron\nstars. To do this we use the phenomenological two-parameter model\ndevised by \\citet{owen98}, which is centered on evolution equations\nfor the rotation frequency $\\Omega$ and the (dimensionless) r-mode\namplitude $\\alpha$. Complete details of our particular version of\nthis model will be given elsewhere.\n\n\n\\begin{figure*}[t]\n\\begin{minipage}[t]{3.5in}\n\\epsfysize=6cm\n\\centerline{\\epsfbox{vblfig1b.eps}}\n%\\vskip -0.15in\n\\figcaption{\\label{fig1}\nThe r-mode instability window relevant for\n old neutron stars. We show results for the simplest (crust-free)\n model, where gravitational radiation reaction is balanced by\n standard shear viscosity at low temperatures and bulk viscosity at\n high temperatures (thin solid line). Also shown are Bildsten and\n Ushomirsky's estimate for a star with a crust (dashed line) and our\n improved estimate of this situation (thick solid line). The r-mode\n is potentially unstable in the region above each curve. The\n illustrated results correspond to a canonical neutron star for which\n mass shedding at the equator sets in at the Kepler period\n $P_K\\approx 0.8$~ms. We illustrate two typical r-mode cycles (for\n mode saturation amplitudes $\\alpha_s=0.1$ and 1), resulting from\n thermo-gravitational runaway after the onset of instability. Once\n accretion has spun the star up to the critical period (along the\n indicated spin-up line (thick vertical line)) the r-mode becomes\n unstable and the star evolves along the path A-B-C-D. After a month\n or so, the mode is stable and the star will cool down until it again\n reaches the spin-up line. For comparison with observational data,\n we indicate the possible range of spin-periods inferred from current\n LMXB data (shaded box) as well as the observed periods and estimated\n upper limits of the temperature (cf. \\citet{akst99}) of some of the\n most rapidly spinning MSP (short arrows).}\n\n\\end{minipage}\n\\hfill\n\\begin{minipage}[t]{3.5in}\n\\epsfysize=6cm\n\\centerline{\\epsfbox{vblfig2.eps}}\n\\vskip -0.15in\n\\figcaption{\\label{fig2} We compare the ``r-mode cycle'' predicted\n for accreting neutron stars to the observed rapidly spinning\n pulsars. The observed data is taken from the Princeton pulsar\n database (http://pulsar.princeton.edu/pulsar/catalog.shtml) as well\n as a sample of MSP recently discovered in 47Tuc\n \\citep{Camilo}.}\n\n\\end{minipage}\\end{figure*}\n\nAt the qualitative level, our results are not surprising. Accreting\nstars in the LMXB are expected to have core temperatures in the range\n$1-4\\times10^8$~K \\citep{brown}. For such temperatures the dissipation\ndue to the viscous boundary layer gets weaker as the temperature\nincreases. Consequently, the situation here is essentially identical\nto that considered by \\citet{levin99} (see also \\citet{spruit} and\n\\citet{bildsten99}). After accreting and spinning up for something\nlike $10^7$ years, the star reaches the period at which the r-mode\ninstability sets in. For our particular estimates this corresponds to\na period of 1.5~ms (at a core temperature of $10^8$~K). It is notable\nthat this value is close to the 1.56~ms period of PSR1937+21. Once the\nr-mode becomes unstable (point A in Figure~\\ref{fig1}), viscous\nheating (now mainly due to the energy released in the viscous boundary\nlayer) rapidly heats the star up to a few times $10^9$~K. The r-mode\namplitude increases until it reaches a prescribed saturation level\n(amplitude $\\alpha_s$) at which unspecified nonlinear effects halt\nfurther growth (point B in Figure~\\ref{fig1}). Once the mode has\nsaturated, the neutron star rapidly spins down as excess angular\nmomentum is radiated as gravitational waves. When the star has spun\ndown to the point where the mode again becomes stable (point C in\nFigure~\\ref{fig1}), the amplitude starts to decay and the mode plays\nno further role in the spin evolution of the star (point D in\nFigure~\\ref{fig1}) unless the star is again spun up to the instability\nlimit. Two examples of such r-mode cycles (corresponding to\n$\\alpha_s=0.1$ and 1, respectively) are shown in Figure~\\ref{fig1}.\n\n\n\nThe real surprise here concerns the quantitative predictions of our\nmodel. As already mentioned, the model suggests that an accreting\nstar will not spin up beyond 1.5~ms. This value obviously depends on\nthe chosen stellar model, but it is independent of the r-mode\nsaturation amplitude and only weakly dependent on the accretion rate\n(through a slight change in core temperature). In fact, the accretion\nrate only affects the time it takes the star to complete one full\ncycle. As soon as the mode becomes unstable the spin-evolution is\ndominated by gravitational radiation and viscous heating. Once the\nstar has gone through the brief phase when the r-mode is active it has\nspun down to a period in the range 2.8-4.8~ms (corresponding to\n$0.01\\leq \\alpha_s \\leq 1$). Based on these results we propose the\nfollowing spin-evolution scenario: An accreting neutron star will\nnever spin up beyond (say) 1.5~ms. Once it has reached this level the\nr-mode instability sets in and spins the star down to a several ms\nperiod. At this point the mode is again stable and continued accretion\nmay resume to spin the star up. Since the star must accrete roughly\n$0.1M_\\odot$ to reach the instability point, and the LMXB companions\nhave masses in the range $0.1-0.4M_\\odot$, it can pass through several\n``r-mode cycles'' during its lifetime.\n\nLet us confront this simple model with current observations. To do\nthis we note that our model leads to one main prediction: Once an\naccreting neutron star has been spun up beyond (say) 5~ms it must\nremain in the rather narrow range of periods $1.5-5$~ms until it has\nstopped accreting and magnetic dipole braking eventually slows it\ndown. Since a given star can go through several r-mode cycles before\naccretion is halted one would expect most neutron stars in LMXB and\nthe MSP to be found in the predicted range of rotation rates. As is\nclear from Figure~\\ref{fig1}, this prediction agrees well with the\nrange of rotation periods inferred from observed kHz quasiperiodic\noscillations in LMXB. The observed range shown in Figure~\\ref{fig1}\ncorresponds to rotation frequencies in the range 260-590~Hz (cf.\n\\citet{vanderklis00}). Our model also agrees with the observed data\nfor MSP, which are mainly found in the range $1.56-6$~ms, see\nFigure~\\ref{fig2}. In other words, our proposed model is in agreement\nwith current observed data for rapidly rotating neutron stars.\n \nFinally, it is worthwhile discussing briefly the detectability of the\ngravitational waves that are radiated during the relatively short time\nwhen the r-mode is saturated and the star spins down. As was argued by\n\\citet{levin99}, the fact that the r-mode is active only for a small\nfraction of the lifetime of the system (something like 1 month out of\nthe $10^7$~years it takes to complete one full cycle) means that even\nthough these sources would be supremely detectable from within our\ngalaxy the event rate is far too low to make them relevant. However,\nit is interesting to note that the spin-evolution is rather similar to\nthat of a hot young neutron star once the r-mode has reached its\nsaturation amplitude. This means that we can analyze the\ndetectability of the emerging gravitational waves using the framework\nof \\citet{owen98}. We then find that these events can be observed\nfrom rather distant galaxies. For a source in the Virgo cluster\n(assumed to be at a distance of 15~Mpc) these gravitational waves\ncould be detected with a signal to noise ratio of a few using LIGO~II.\nHowever, even at the distance of the Virgo cluster these events would\nbe quite rare. By combining a birth rate for LMXB of $7\\times\n10^{-6}$ per year per galaxy with the fact that the the volume of\nspace out to the Virgo cluster contains $\\sim 10^3$ galaxies, and the\npossibility that each LMXB passes through (say) four r-mode cycles\nduring its lifetime we deduce that one can only hope to see a few\nevents per century in Virgo. In order to see several events per year\nthe detector must be sensitive enough to detect these gravitational\nwaves from (say) 150~Mpc. This would require a more advanced detector\nconfiguration such as a narrow-banded LIGO~II. We will discuss this\nissue in more detail elsewhere.\n\n \n\\section{Additional remarks}\n\nBefore concluding our discussion, we recall that the initial\nexcitement over the r-mode instability was related to the fact that it\nprovided an explanation for the relatively slow inferred spin rates\nfor young pulsars. In view of this, it is natural to digress somewhat\nand discuss how the picture of the r-mode instability in hot, newly\nborn neutron stars is affected by the possible formation of a solid\ncrust. Hence, we consider the evolution of a neutron star just after\nits birth in a supernova explosion. At a first glance, we might\nexpect to model its r-mode amplitude in the standard way, cf.\n\\citet{owen98}, using the normal (crust-free) fluid viscous damping\ntimes for stellar temperatures above the melting temperature of the\ncrust ($T_m$), and the viscous boundary layer damping time for\ntemperatures below $T_m$. However, the situation is a little more\ncomplicated than this. Recall that the latent heat (i.e. the Coulomb\nbinding energy) of a typical crust is $E_{lat} \\sim 10^{48}$~ergs,\nwhile the r-mode energy is $E_m\\approx 2 \\alpha^2 (\\mbox{1\nms}/P)^2\\times 10^{51}$~ergs. Provided that the time taken for the\nstar to cool to $T_m$ is sufficiently long, the energy in the r-mode\n(which grows exponentially on a timescale $t_{gw} \\sim 20$~s) will\nexceed $E_{lat}$, preventing the formation of the crust, even when $T\n< T_m$. Then the star will spin down in the manner described by, eg.\n\\citet{owen98}. This phase will end either because the star leaves\nthe instability region of the $\\Omega-T$ plot (see, for example,\nFig.~1 of Owen et al.), or because the mode energy in the outer layers\nof the star (where the crust is going to form) has fallen below the\ncrustal binding energy. We can estimate that this would happen at a\nfrequency $\\approx 70\\mbox{ Hz}/\\alpha_s$, by equating $E_{lat}$ to\nroughly 10 \\% of $E_m$). A more accurate treatment would take into\naccount the \\emph{local} kinetic energy of fluid elements and since\nthe latter is smaller near the poles than near the equator, the crust\nmight form earlier at the poles. Clearly the problem of crust\nformation in an oscillating star requires further investigation. The\nfinal spin period will be around 15~ms, if the r-mode grows to an\namplitude of $\\alpha_s \\sim 1$, consistent with the extrapolated\ninitial spin rates of many young pulsars. On the other hand, if the\nmode is not given time to grow very large it will not prevent crust\nformation at $T_m$. Such a scenario was described by\n\\citet{bildsten99}, who noted that the r-mode instability would then\nnot spin the star down beyond a much higher frequency. Using our\nestimated timescales the resultant spin period would be $3-5$~ms in\nthis scenario. Which scenario applies depends sensitively on the\nearly cooling of the star, the crustal formation temperature and\nperhaps most importantly the initial amplitude of the r-mode following\nthe collapse. It is, in fact, possible that both routes are viable and\nthat a bimodal distribution of initial spin periods results. A likely\nkey parameter is whether the supernova collapse leads to a large\ninitial r-mode amplitude $\\sim \\alpha_s$ or not. An initial period of\n$\\sim 15$~ms would fit the long established data for the Crab, while\nthe recently discovered 16~ms pulsar PRS~J0537-6910 \\citep{marshall}\nrequires a considerably shorter initial period of a few ms.\n\nIn conclusion, we have reexamined the effect that the dissipation due\nto a possible viscous boundary layer in a neutron star with a solid\ncrust has on the stability of the r-modes. By combining our new\nestimates with the thermal runaway introduced by \\citet{levin99} and\n\\citet{spruit}, we arrive at a spin-evolution model that agrees with\npresent observations for rapidly spinning neutron stars. In\nparticular, our predictions agree well with observations of both LMXB\nand MSP. Furthermore, the model can potentially explain the\nextrapolated spin periods of the young pulsars. Since it brings out\nthis unified picture, our simple model has many attractive features,\nand we are currently investigating it in more detail.\n\n\n\\acknowledgements We thank L. Bildsten, W. Kluzniak, B. Sathyaprakash,\nH. Spruit and G. Ushomirsky for comments on a draft version of this\npaper. This work was supported by PPARC grant PPA/G/1998/00606 to NA.\n\n\\begin{thebibliography}{23}\n \n\\bibitem[{{Andersson, Kokkotas \\& Stergioulas}(1999)}]{akst99}\nAndersson, N., Kokkotas, K.~D., \\& Stergioulas, N. 1999, \\apj, 516,\n307\n \n\\bibitem[{{Andersson} \\& {Kokkotas}(2000)}]{akreview} Andersson N., \\&\nKokkotas K.D. 2000, to appear in Int. J. Mod. Phys. D\n\n \n\\bibitem[{{Bildsten}(1998)}]{bildsten98} Bildsten, L. 1998, \\apjl,\n501, L89\n \n\\bibitem[{{Bildsten} \\& {Ushomirsky}(2000)}]{bildsten99} Bildsten,\nL. \\& Ushomirsky G. 2000, \\apjl, 529, 33\n \n\\bibitem[{{Brown} \\& {Bildsten}(1998)}]{brown} Brown E.F. and Bildsten\nL. 1998, \\apj, 496, 915\n \n\\bibitem[{Camilo {et~al.}(1999)}]{Camilo} Camilo F., Lorimer D.R.,\nFreire P., Lyne A.G.\\& Manchester R.N., 1999 to appear in \\apj,\n[astro-ph/9911234]\n \n\\bibitem[{{Kokkotas} \\& {Stergioulas}(1999)}]{kokkotas99} Kokkotas,\nK.~D., \\& Stergioulas N. , 1999, Astron. Astrop., 341, 110\n\n\\bibitem[{{Levin}(1999)}]{levin99} Levin, Y. 1999, \\apj, 517, 328\n\n\\bibitem[{Marshall {et~al.}(1998)}]{marshall} Marshall F.E., Gotthelf\nE.V., Zhang W., Middleditch J. and Wang Q.D. 1998, \\apjl 499, 179\n\n\\bibitem[{Owen {et~al.}(1998)Owen, Lindblom, Cutler, Schutz, Vecchio,\n\\& Andersson}]{owen98} Owen, B.~J., Lindblom, L., Cutler, C., Schutz,\nB.~F., Vecchio, A., \\& Andersson, N. 1998, \\prd, 58, 084020\n \n\\bibitem[{{Papaloizou} \\& {Pringle}(1978)}]{papaloizou} Papaloizou\nJ. \\& Pringle J.E. 1978, \\mnras, 184, 501\n\n\\bibitem[{{Spruit}(1998)}]{spruit} Spruit H., 1999, Astron. Astrop.,\n341, L1\n\n\\bibitem[{{Stergioulas}(1998)}]{stergioulas} Stergioulas N. 1998,\nLiving Reviews in Relativity, 1998-8\nhttp://www.livingreviews.org/Articles/Volume1/1998-8stergio/\n \n\\bibitem[{{Ushomirsky, Cutler \\& Bildsten}(2000)}] {ushomirsky00}\nUshomirsky G., Cutler C. \\& Bildsten, L. 2000, {\\em Deformations of\naccreting neutron star crusts and gravitational wave emission}\n[astro-ph/0001136]\n \n\\bibitem[{{van der Klis}(2000)}]{vanderklis00} {van der Klis}, M.\n2000, {\\em Millisecond oscillations in X-ray binaries} to appear in\n{\\em Ann. Rev. Astron. Astrop.} [astro-ph/0001167]\n \n\\bibitem[{{Wagoner}(1984)}]{wagoner} Wagoner R.V. 1984, \\apj, 278, 345\n \n\\bibitem[{{White} \\& {Zhang}(1997)}]{white97} White N.E. and Zhang W.\n1997, \\apjl, 490, L87\n\n\n\\end{thebibliography}\n\n\\end{document}\n\n"
}
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[
{
"name": "astro-ph0002114.extracted_bib",
"string": "\\begin{thebibliography}{23}\n \n\\bibitem[{{Andersson, Kokkotas \\& Stergioulas}(1999)}]{akst99}\nAndersson, N., Kokkotas, K.~D., \\& Stergioulas, N. 1999, \\apj, 516,\n307\n \n\\bibitem[{{Andersson} \\& {Kokkotas}(2000)}]{akreview} Andersson N., \\&\nKokkotas K.D. 2000, to appear in Int. J. Mod. Phys. D\n\n \n\\bibitem[{{Bildsten}(1998)}]{bildsten98} Bildsten, L. 1998, \\apjl,\n501, L89\n \n\\bibitem[{{Bildsten} \\& {Ushomirsky}(2000)}]{bildsten99} Bildsten,\nL. \\& Ushomirsky G. 2000, \\apjl, 529, 33\n \n\\bibitem[{{Brown} \\& {Bildsten}(1998)}]{brown} Brown E.F. and Bildsten\nL. 1998, \\apj, 496, 915\n \n\\bibitem[{Camilo {et~al.}(1999)}]{Camilo} Camilo F., Lorimer D.R.,\nFreire P., Lyne A.G.\\& Manchester R.N., 1999 to appear in \\apj,\n[astro-ph/9911234]\n \n\\bibitem[{{Kokkotas} \\& {Stergioulas}(1999)}]{kokkotas99} Kokkotas,\nK.~D., \\& Stergioulas N. , 1999, Astron. Astrop., 341, 110\n\n\\bibitem[{{Levin}(1999)}]{levin99} Levin, Y. 1999, \\apj, 517, 328\n\n\\bibitem[{Marshall {et~al.}(1998)}]{marshall} Marshall F.E., Gotthelf\nE.V., Zhang W., Middleditch J. and Wang Q.D. 1998, \\apjl 499, 179\n\n\\bibitem[{Owen {et~al.}(1998)Owen, Lindblom, Cutler, Schutz, Vecchio,\n\\& Andersson}]{owen98} Owen, B.~J., Lindblom, L., Cutler, C., Schutz,\nB.~F., Vecchio, A., \\& Andersson, N. 1998, \\prd, 58, 084020\n \n\\bibitem[{{Papaloizou} \\& {Pringle}(1978)}]{papaloizou} Papaloizou\nJ. \\& Pringle J.E. 1978, \\mnras, 184, 501\n\n\\bibitem[{{Spruit}(1998)}]{spruit} Spruit H., 1999, Astron. Astrop.,\n341, L1\n\n\\bibitem[{{Stergioulas}(1998)}]{stergioulas} Stergioulas N. 1998,\nLiving Reviews in Relativity, 1998-8\nhttp://www.livingreviews.org/Articles/Volume1/1998-8stergio/\n \n\\bibitem[{{Ushomirsky, Cutler \\& Bildsten}(2000)}] {ushomirsky00}\nUshomirsky G., Cutler C. \\& Bildsten, L. 2000, {\\em Deformations of\naccreting neutron star crusts and gravitational wave emission}\n[astro-ph/0001136]\n \n\\bibitem[{{van der Klis}(2000)}]{vanderklis00} {van der Klis}, M.\n2000, {\\em Millisecond oscillations in X-ray binaries} to appear in\n{\\em Ann. Rev. Astron. Astrop.} [astro-ph/0001167]\n \n\\bibitem[{{Wagoner}(1984)}]{wagoner} Wagoner R.V. 1984, \\apj, 278, 345\n \n\\bibitem[{{White} \\& {Zhang}(1997)}]{white97} White N.E. and Zhang W.\n1997, \\apjl, 490, L87\n\n\n\\end{thebibliography}"
}
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astro-ph0002115
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Radio Emission Properties of Millisecond Pulsars
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[
{
"author": "Michael Kramer"
}
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We report the most recent progress in understanding the emission properties of millisecond pulsars.
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[
{
"name": "kramer1.tex",
"string": "\\documentstyle[11pt,iau177,twoside,psfig2]{article}\n\n\\pagestyle{myheadings}\n\t\t \\markboth{Kramer and Xilouris}{Radio Emission Properties of Millisecond Pulsars}\n\t\t \\setcounter{page}{229}\n\n\\begin{document}\n\n\n\\keywords{millisecond pulsar, beaming fraction, luminosity, emission region,\npolarization, pulsar spectra, spectrum, multi-frequency observations,\ntiming, EPN}\n\n\\title{Radio Emission Properties of Millisecond Pulsars}\n\n\\author{Michael Kramer}\n\\affil{Max-Planck-Institut f\\\"ur Radioastronomie, Bonn, Germany\\\\\nUniversity of Manchester, Jodrell Bank Observatory, UK}\n\n\\author{Kiriaki M. Xilouris}\n\\affil{Department of Astronomy, University of Virginia, Charlottesville, USA}\n\n\\begin{abstract}\nWe report the most recent progress in understanding the emission properties\nof millisecond pulsars.\n\\end{abstract}\n\n\n\\vspace{-0.7cm}\n\n\\section{Introduction --- {\\it Duo quum faciunt idem, not est idem.$^1$}}\n\\setcounter{footnote}{1}\n\\footnotetext{If two do the same, it is not the same.}\n\n\nThrough intensive research for almost two decades, it has been well\nestablished, both in theory and observation, that millisecond pulsars\n(MSPs) are the end product of mass accretion in binary systems. As\nMSPs emerge in the radio universe having been given a second chance in\nlife, they are surrounded by magnetospheres which are several orders\nof magnitude more compact than those of slower rotating\npulsars. Inferred magnetic fields close to the surface of MSPs are 3\nto 4 orders of magnitude weaker than in normal pulsars while charges\nat these regions experience an accelerating potential similar to that\nof normal pulsars. The impact of the different environment on the\nemission process in MSP magnetospheres has been a question addressed\nalready shortly after the discovery of a first few such sources.\n\nWith the plethora of MSPs detected over the years, a significant\nsample became available to us, enabling a better understanding of not\nonly MSPs (as radio sources and tools) but slower rotating (normal)\npulsars as well. In the following, we will concentrate on {\\em recent}\nprogress, referring to Kramer et al.~(1998, Paper I) on spectra, pulse\nshapes and beaming fraction; Xilouris et al.~(1998, Paper II) on\npolarimetry of 24 MSPs; Sallmen (1998) and Stairs et al.~(1999) on\nmulti-frequency polarimetry; Toscano et al.~(1998) on spectra of\nSouthern MSPs; Kramer et al.~(1999b, Paper III) on multi-frequency\nevolution; and Kramer et al.~(1999a, Paper IV) on profile\ninstabilities of MSPs; but see also the following contributions by\nKuzmin \\& Losovsky and Soglasnov.\n\n\\vspace{-0.3cm}\n\n\\section{Single Pulses vs.~Average Profile Studies}\n\nSingle pulse observations still remain the only tool available to\naddress some fundamental questions listed below. They are, however,\nstill technically challenging and the number of observations described\nin the literature are scarce. In total, data for only three sources\ndescribing 180 min of observations have been presented, i.e.~PSRs\nB1937+21, B1534+12 and J0437--4715 (e.g.~Sallmen 1998, Cognard et\nal.~1996, Jenet et al.~1998 and references therein). The results can\nbe summarized in the statement that based on the single pulses\nstudied, one cannot distinguish between a millisecond or slowly\nrotating pulsar. More observations are required to further investigate\npulse fluctuations (e.g.~stabilization processes), the short-term\nstructure (e.g.~how it relates to microstructure) and in particular\nthe polarization characteristics in detail. For the time being, we\ninvestigate the wealth of information already provided by average\nprofile studies.\n\n\\begin{figure}[h]\n\\vspace{-0.2cm}\n\\centerline{\\psfig{file=kramer1.1.ps,angle=-90,height=5.5cm} }\n%\\plotfiddle{kramer1.1.ps}{6cm}{-90}{45}{45}{-180}{245}\n\\caption{ Pulse profiles for a selected sample of MSPs and normal pulsars\n(Paper I and EPN database). \nNote the similarity and make a guess which is which! See footnote$^2$\nfor the solution.}\n\\end{figure}\n\n\\vspace{-0.8cm}\n\n\\section{Flux Density Spectra and Radio Luminosity}\n\nPrior to the investigations leading to Paper I it was commonly\nbelieved that the spectra of millisecond pulsars were steeper than\nthose of normal pulsars. We demonstrated in Paper I that the\ndistribution of spectral indices for MSPs is in fact not significantly\ndifferent, finding an average index of $-1.76\\pm0.14$ (Paper III). The\ninitial impression was due to a selection effect, since the first MSPs\nwere discovered in previously unidentified steep spectrum sources, as\nit was later pointed out by Toscano et al.~(1998). Consequently, the\nnumber of MSPs to be discovered in high-frequency surveys was\nunderestimated. The predictions for searches at frequencies as high as\n5 GHz appear even more favourable in light of the latest results\npresented in Paper III. These suggest that most spectra can be\nrepresented by a simple power law, i.e.~clear indications for a\nsteepening at a few GHz as known from normal pulsars are not\nseen. Extending the data to lower frequencies (see Paper III; Kuzmin\n\\& Losovsky, next contribution), evidence for spectral turn-overs were\nnot found.\n\n\\setcounter{footnote}{2}\n\\footnotetext{Upper row: MSPs (PSRs J0218+4218, J0621+1001, B1534+12,\nJ1640+2224, J1730$-$2304), lower row: normal pulsars (PSRs B1831$-$04,\nB2045$-$16, B2110+27, B2016+28, B1826$-$17)}\n\nBailes et al.~(1997) pointed out that isolated MSPs are less luminous\nthan those in binary systems, pointing towards a possible relation\nbetween radio luminosity and birth scenarios. We have compared a\ndistance limited sample of normal pulsars and MSPs and came to a\nsimilar result with the MSPs as a whole appearing as weaker sources than\nnormal pulsars.\n\n\n\\begin{figure}\n\\begin{tabular}{@{\\hspace{-0.2cm}}c@{\\hspace{-0.8cm}}c}\n\\psfig{file=kramer1.2.ps,angle=-90,height=5.2cm} &\n\\psfig{file=kramer1.3.ps,angle=-90,height=6cm} \n%\\plotfiddle{kramer1.2.ps}{6cm}{-90}{25}{25}{-400}{150} &\n%\\plotfiddle{kramer1.3.ps}{6cm}{-90}{30}{30}{-640}{170} \n\\end{tabular}\n\\caption{ a) Location of additional pulse features across the pulse period for\n normal pulsars and MSPs. b) The beam radius, $\\rho$, for normal pulsars\n and MSPs. MSPs do not follow the scaling law of normal pulsars (here Gould\n 1994) but their beaming fraction is much smaller. For MSPs with interpulses\nan ``inner'' relationship is indicated.}\n\\end{figure}\n\n\\vspace{-0.3cm}\n\n\n\n\\section{Pulse Profiles -- Complexity, Interpulses and Beaming Fraction}\n\nIt was also believed that MSP profiles are more complex than those of\nnormal pulsars. Using a large uniform sample of profiles for fast and\nslowly rotating pulsars, we showed in Paper I that the apparent larger\ncomplexity is due to the (typically) larger duty cycle of MSPs. As a\nresult we see ``blown-up'' profiles which make it easier to see\ndetailed structure. In fact, blown-up normal pulsar profiles show\nvery similar structure. A quantitative proof is given in Paper I,\nwhile Fig.~1 provides an illustration of this effect.\n\n\n\\begin{figure}\n\\begin{tabular}{cc}\n\\psfig{file=kramer1.4.ps,angle=-90,height=5cm,clip=} &\n \\psfig{file=kramer1.5.ps,angle=-90,height=5.5cm} \n\\end{tabular}\n\\caption{ a) PSR J1640+2224 as an example for a MSP exhibiting a flat PA swing,\nb) distribution of magnetic inclination angles derived from RVM fits.}\n\\end{figure}\n\n\nDespite this apparent similarity, there is a profound difference\nbetweent MSP profiles and those of normal pulsars! Additional pulse\nfeatures like interpulses, pre- or post-cursor are much more common\nfor MSPs. While only $\\sim2$\\% of all normal pulsars are known to show\nsuch features, we detect them for more than 30\\% of all (field)\nMSPs. They also appear at apparently random positions across the pulse\nperiod in contrast to normal pulsars (Fig.~2a). Their frequent\noccurrence and location makes one wonder --- given the similarity of\nthe main pulse shapes otherwise --- whether these components are of\nthe same origin as the main pulse profile or whether other sources of\nemission (e.g.~outer gaps) are responsible (see Paper II). Other\npossibilities involve an interpretation first put forward for some\nyoung pulsars by Manchester (1996), who interpreted some interpulses\nas the results of cuts through a very wide cone. This is an\ninteresting possibility also for MSPs, since their beam width appears\nto be much smaller than predicted from the scaling law derived for\nnormal pulsars. The beam width of normal pulsars, $\\rho$, i.e.~the\npulse width corrected for geometrical effects (see Gil et al.~1984),\nfollows a distinct $\\rho \\propto P^{-0.5}$-law (e.g.~Rankin 1993,\nKramer et al.~1994, Gould 1994). Using polarization information to\ndetermine the viewing geometry and also applying statistical\narguments, we calculated $\\rho$ (at a 10\\% intensity level) for MSPs\nin Paper I. We showed that they are not only much smaller than the\nextrapolation of the known law to small periods, but that -- under the\nassumption of dipolar magnetic fields -- the emission of some MSPs\nseems to come even from within the neutron star --- a really\ndisturbing result! While we discuss the possibility of non-dipolar\nfields and the used polarization information below, one explanation\nwould be that (perhaps below a critical period) the emission beam does\nnot fill the whole open field line region (``unfilled beam''). The\nsituation improves somewhat when we consider the additional pulse\nfeatures as regular parts of the pulse profile (Fig.~2b). In fact,\nthose MSPs with interpulses may indicate an additional inner scaling\nparallel to that known for normal pulsars, which could be a result of\nunfilled beams. We close this section by pointing out that the much\nsmaller beam width has consequences for population studies, which\nusually utilize the $\\rho-P$ scaling as found for normal pulsars. The\nfailure of this law leads to an overestimated beaming fraction and an\nunderestimation of the birth rate of recycled pulsars (see Paper I).\n\n\\begin{figure}\n\\begin{tabular}{c@{\\hspace{-0.8cm}}c}\n\\psfig{file=kramer1.6.ps,height=5cm} &\n\\psfig{file=kramer1.7.ps,height=4.5cm} \n\\end{tabular}\n\\caption{ a) Power law index of profile narrowing with frequency (see Paper III for details), b) degree of polarization for MSPs.}\n\\end{figure}\n\n\n\\vspace{-0.5cm}\n\n\n\\section{Polarization Properties}\n\nThe radio emission of MSPs shows all polarization features known from\nnormal pulsars, i.e.~circular polarization which is usually associated\nwith core components, linear polarization which is usually associated\nwith cone components, and also orthogonal polarization modes (see\nPaper II, Sallmen 1998, Stairs et al.~1999). Despite the qualitative\nsimilarities, the position angle (PA) swing is often strikingly\ndifferent. While normal pulsars show typically a {\\sf S}-like swing,\nwhich is interpreted within the rotating vector model (RVM;\nRadhakrishnan \\& Cooke 1969), the PAs of many MSPs often appear flat\n(see e.g.~Fig.~3a). This could be interpreted in terms of non-dipolar\nfields, but Sallmen (1998) noted that larger beam radii lead to a\nlarger probability for outer cuts of the emission cones, i.e.~flatter\nPA swings according to the RVM. Although one should bear in mind the\nlimitations of the $\\rho$-scaling law and another caveat\ndiscussed later, this interpretation justifies the geometrical\ninterpretation of the data, which is supported by the results of\nHibschman (these proceedings). Magnetic inclination angles derived\nfrom RVM fits are important for binary evolution models and\ndeterminations of the companion mass (Fig.~3b).\n\n\\vspace{-0.3cm}\n\n\\section{Frequency Evolution}\n\nThe radio properties of normal pulsars show a distinct frequency\nevolution, i.e.~with increasing frequency the profile narrows, outer\ncomponents tend to dominate over inner ones, and the emission\ndepolarizes. The emission of MSPs, which at intermediate frequencies\ntends to be more polarized than that of normal pulsars (Paper II),\nalso depolarizes at high frequencies (Fig.~4b; Paper III).\nSimultaneously, the profile width hardly changes or remains constant\n(see Fig.~4a, Paper III; Kuzmin \\& Losovsky, these proceedings). This\nputs under test attempts to link both effects to the same physical\norigin (i.e.~birefringence). In fact, many profiles also exhibit the\nsame shape at all frequencies, while others evolve in an unusual way,\ni.e.~the spectral index of inner components is not necessarily\nsteeper, so that a systematic behaviour as seen for normal pulsars is\nhardly observed. This can be understood in terms of a compact emission\nregion, an assumption further supported by a simultaneous arrival of\nthe profiles at all frequencies. We emphasize that we have not\ndetected any evidence for the existence of non-dipolar fields in\nthe emission region (Paper III).\n\n\\vspace{-0.3cm}\n\n\\section{Profile and Polarization Instabilities}\n\nThe amazing stability with time of MSP profiles has enabled high\nprecision timing over the years. However, in Paper IV we discussed the\nsurprising discovery that a few MSPs do show profile changes caused by\nan unknown origin. The time scales of these profile instabilities are\ninconsistent with the known mode-changing. In particular, PSR\nJ1022+1001 exhibits a narrow-band profile variation never seen before\n(Paper IV), which could, however, be the result of magnetospheric\nscintillation effects described by Lyutikov (these proceedings). With\nthe pulse shape the polarization usually changes as well, and hence\nthis effect is possibly related to phenomena which we discovered in\nPaper II. Some pulsars like PSR J2145--0750 (Paper II) or PSR\nJ1713+0747 (Sallmen 1998) show occasionally a profile which is much\nmore polarized than usual. In the case of PSR J2145--0750, the PA\nalso changes from some distinct (though not {\\sf S}-like) swing to some\nvery flat curve. This is a strong indication that some of the flat PA\nswings discussed above may not be of simple geometrical origin alone.\n\n\\section{Summary -- MSPs in 2000 and Beyond}\n\nWhile we have had to be necessarily brief in reviewing MSP properties,\nwe direct the interested reader to the extensive studies of MSPs\npresented in the quoted literature. We summarize here our point of\nview: MSPs emit their radio emission by the same mechanism as normal\npulsars. Some distinct differences may originate from the way they\nwere formed, but most observed features can be explained by very\ncompact magnetospheres. Our data can be explained without any need to\ninvoke deviations from dipolar field lines, although a large number of\nopen questions remain. We need more polarization information at higher\nfrequencies and, in particular, single pulse studies. These will\nallow us to study the formation of the profile and its stability, to\nsee if the additional pulse features are distinct from the main pulse,\nand how the polarization modes behave under the magnifying glass of\nthe blown-up MSP profiles. There are exciting years to come!\n\n\n\\acknowledgements We are very grateful to all the people involved in the\nstudies of MSPs at Bonn, i.e.~Don Backer, Fernando Camilo, Oleg Doroshenko, \nAlexis von Hoensbroech, Axel Jessner, Christoph Lange, Dunc Lorimer, \nShauna Sallmen, Norbert Wex, Richard Wielebinski and Alex Wolszczan.\n\n\\vspace{-0.5cm}\n\n\\begin{references}\n\\reference Bailes, M., Johnston, S., Bell, J.~F., et al.~1997, \\apj, 481, 386\n\\reference Cognard, I., Shrauner, J., Taylor, J. H., \\& \nThorsett, S. E.~1996, \\apj, 457, 81\n\\reference Gil, J., Gronkowski, P., \\& Rudnicki, W.~1984, A\\&A, 132, 312\n\\reference Gould, D.M.~1994, PhD thesis, University of Manchester\n\\reference Jenet,~F., Anderson, S., Kaspi, V., et al.,~1998, ApJ, 498, 365\n\\reference Kramer~M., Xilouris~K.~M., Lorimer~D.~R., et al.~1998,\nApJ, 501, 270 (Paper I)\n\\reference Kramer~M., Xilouris~K.~M., Camilo~F., et al.~1999a, ApJ, 520, 324\n(Paper IV)\n\\reference Kramer~M., Lange, Ch., Lorimer, D.R., et al.~1999b, ApJ, 526, 975\n(Paper III)\n\\reference Manchester, R.N.~1996, in Proc of IAU Colloq. 177, ASP Conf.\nSeries, p.~193\n\\reference Radhakrishnan, V., \\& Cooke, D.J.,~1969, ARA\\&A, 32, 591\n\\reference Rankin, J.M.~1993, ApJ, 405, 285\n\\reference Sallmen,~S.~1998, {\\rm PhD thesis}, University of California at Berkeley\n\\reference Stairs~,I.~H., Thorsett,~S.~E., \\& Camilo,~F.~1999, ApJS, 123, 627 \n\\reference Toscano,~M., Bailes,~M., Manchester,~R.N., \\& Sandhu,~J.~1998, ApJ, 506, 863\n\\reference Xilouris,~K.~M., Kramer,~M., Jessner,~A., et al.~1998, ApJ, 501, 286\n(Paper II)\n\\end{references}\n\n\\end{document}\n\n\n"
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astro-ph0002116
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Interplanetary Network Localization of GRB991208 and the Discovery of its Afterglow
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"author": "K. Hurley"
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The extremely energetic ($\sim 10^{-4} erg/cm^2$) gamma--ray burst (GRB) of 1999 December 8 was triangulated to a $\sim$ 14 sq. arcmin. error box $\sim$ 1.8 d after its arrival at Earth with the 3rd interplanetary network (IPN), consisting of the Ulysses, Near Earth Asteroid Rendezvous (NEAR), and Wind spacecraft. Radio observations with the Very Large Array $\sim$ 2.7 d after the burst revealed a bright fading counterpart whose position is consistent with that of an optical transient source whose redshift is z=0.707. We present the time history, peak flux, fluence, and refined 1.3 sq. arcmin. error box of this event, and discuss its energetics. This is the first time that a counterpart has been found for a GRB localized only by the IPN.
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"name": "Ms.tex",
"string": "%\\documentstyle[12pt,aasms4]{article}\n\\documentclass{aastex}\n\n\\begin{document}\n\n\\title{Interplanetary Network Localization of GRB991208 and the\nDiscovery of its Afterglow}\n\\author{K. Hurley}\n\\affil{University of California, Berkeley, Space Sciences Laboratory,\nBerkeley, CA 94720-7450}\n\\email{khurley@sunspot.ssl.berkeley.edu}\n\\author{T. Cline}\n\\affil{NASA Goddard Space Flight Center, Code 661, Greenbelt, MD 20771}\n\\author{E. Mazets, R. Aptekar, S. Golenetskii, D. Frederiks}\n\\affil{Ioffe Physico-Technical Institute, St. Petersburg, 194021 Russia}\n\\author{D. Frail}\n\\affil{National Radio Astronomy Observatory, PO Box O, Socorro NM 87801}\n\\author{S. Kulkarni}\n\\affil{Palomar Observatory, 105-24, Caltech, Pasadena, CA 91125}\n\\author{J. Trombka, T. McClanahan}\n\\affil{NASA Goddard Space Flight Center, Code 691, Greenbelt, MD 20771}\n\\author{R. Starr}\n\\affil{The Catholic University of America, Department of Physics, Washington\nDC 20064}\n\\author{J. Goldsten}\n\\affil{The Johns Hopkins University, Applied Physics Laboratory, Laurel, MD 20723}\n\n\n\\begin{abstract}\nThe extremely energetic ($\\rm \\sim 10^{-4} erg/cm^2$) gamma--ray burst (GRB) of \n1999 December 8 was \ntriangulated to a $\\sim$ 14 sq. arcmin.\nerror box $\\sim$ 1.8 d after its arrival at Earth \nwith the 3rd interplanetary network (IPN), consisting of the \\it Ulysses, \nNear Earth Asteroid Rendezvous \\rm (NEAR), \nand \\it Wind \\rm spacecraft. Radio observations with the Very Large Array \n$\\sim$ 2.7 d after the burst revealed a bright fading counterpart whose \nposition is consistent\nwith that of an optical transient source whose redshift is z=0.707.\nWe present\nthe time history, peak flux, fluence, and refined 1.3 sq. arcmin. error box of this event, and discuss\nits energetics. This is the first time that a counterpart has been found\nfor a GRB localized only by the IPN.\n\n\\end{abstract}\n\n\\keywords{gamma rays: bursts}\n\n\\section{Introduction}\n\nMany gamma-ray burst counterparts have\nnow been identified using the rapid, precise localizations available from\nthe BeppoSAX spacecraft ,\nas well as from the \\it Rossi X-Ray Timing Explorer \\rm, starting with\nGRB970228 (Costa et al. 1997; van Paradijs et al. 1997). \nSuch detections occur at a low rate ($\\sim 8 \\, y^{-1}$), and they have been\nlimited to the long--duration events so far, \nbut they have confirmed the\ncosmological origin of at least this class of bursts.\nSince 1977, interplanetary networks of omnidirectional GRB detectors have\nprovided precise triangulations of both short and long bursts at rates up to \n$\\sim$ 1/week, but often\nthe networks have been incomplete, or the data return from the interplanetary\nspacecraft has been slow. The present, 3rd IPN is now complete with \\it Ulysses \\rm\nand NEAR as its distant points (Cline et al. 1999) \nand, in conjunction with numerous near-Earth\nspacecraft, can produce precise GRB error boxes within $\\sim$ 1 d, making\nthem useful for multi-wavelength follow-up observations. Here we present\nthe observations of GRB991208, which was rapidly localized to a small\nerror box, leading to the identification of its radio and optical afterglow, and\neventually to the measurement of its redshift. \n\n\\section{IPN Observations}\n\nGRB 991208 was observed by the \\it Ulysses \\rm GRB (Hurley et al. 1992), KONUS-\\it Wind \\rm \n(Aptekar et al. 1995), and NEAR X-ray/Gamma-ray Spectrometer (XGRS: Goldsten et al.\n1997) experiments. \\it Ulysses \\rm, in heliocentric orbit, NEAR, approaching rendezvous \nwith the asteroid Eros, and \\it Wind \\rm, were 2176, 937, and 1.5 light-seconds\nfrom Earth, respectively. \n\nWe focus here on the \\it Ulysses \\rm and NEAR data; KONUS data\nwill be presented elsewhere.\nThe \\it Ulysses \\rm and XGRS light curves are shown in figure 1. \nAlthough \\it Ulysses \\rm recorded the first 57 s of the burst with\n0.03125 s resolution in the triggered mode, the peak of the event occurred slightly later,\nand we have shown the 0.5 s resolution real-time data in the figure.\nThe XGRS\nBGO anticoincidence shield is employed as the NEAR burst monitor, and the only\ntime history data available from it are 1 s resolution count rates for the 100 - 1000 keV energy\nrange. The burst\ncan be characterized by a T$_{90}$ duration of 68 s, placing\nit firmly in the ``long'' class of bursts (Hurley 1992; Kouveliotou et al.\n1993). The event-integrated \\it Ulysses \\rm spectrum is well fit between 25 and 150 keV\nby a power law, thermal bremsstrahlung, or blackbody spectrum. For the following\nanalysis, we adopt the power law, which has a photon index 1.68 $\\pm$ 0.19,\nand a $\\chi^2$ of 4.3 for 11 degrees of freedom (figure 2).\nThe 25 - 100 keV fluence is $\\rm 4.9 \\times 10^{-5} \\,erg \\,cm^{-2}$, with an\nuncertainty of $\\sim \\rm \\pm 10\\% $ due to count rate statistics and systematics. Since\nthe XGRS shield provides only very low resolution (40 minutes) spectral data, we can\nonly estimate the fluence in the XGRS energy range from its light curve to be about the\nequivalent of that observed by \\it Ulysses \\rm. Thus the total fluence above 25 keV\nis $\\sim \\rm 10^{-4}\\, erg\\, cm^{-2}$. Bursts with this intensity or \ngreater occur at a rate $\\rm \\lesssim 10 \\,y^{-1}$. Since the peak of the event occurs when\nonly the 0.5 s \\it Ulysses \\rm data are available, we can estimate the peak\nflux only over this time interval; it is $\\rm \\sim 5.1 \\times 10^{-6}\\, erg\\, cm^{-2}\\, s^{-1}$,\n25 - 100 keV ($\\sim \\pm \\rm 10\\% $), with a contribution in the 100 - 1000 keV energy range which is\nagain probably equivalent. \n\nA preliminary $\\sim$ 14 \nsq. arcmin. IPN error box was circulated $\\sim$ 44 h after the earth-crossing time\nof the event (04:36:53 UT: Hurley et al. 1999). The final error box\nis shown in figure 3, and nests within the preliminary one; it has an area of \n$\\sim$ 1.3 sq. arcmin. Its coordinates are given in Table 1. \nAlso shown in figure 3 is the position of the radio counterpart to the\nburst detected by Frail (1999). We note that this is the first\ntime that a GRB position determined by the 3rd IPN alone (i.e., no \\it\nCompton Gamma-Ray Observatory \\rm BATSE or \\it BeppoSAX \\rm observations)\nhas been successfully\nused for multiwavelength counterpart searches. \n\n\\section{Observations with NRAO Very Large Array}\n\n\nVery Large Array (VLA)\\footnotemark\\footnotetext{The NRAO is a facility of the National\nScience Foundation operated under cooperative agreement by Associated\nUniversities, Inc.} observations were begun on 1999 December 10.92 UT, 2.73 days\nafter the gamma-ray burst. In order to image the entire 14 sq. arcmin. initial\nIPN error box (Hurley et al. 1999) with the VLA at 8.46 GHz two\npointings were required, each with a field-of-view at half power\nresponse of 5.3\\arcmin. The full 100 MHz bandwidth was used in two\nadjacent 50-MHz bands centered at 8.46 GHz. A single pointing was also\nmade at 4.86 GHz, but the bandwidth was halved in order to image the full\n9\\arcmin \\,field-of-view without distortion. The flux\ndensity scale was tied to the extragalactic sources 3C\\thinspace{48}\n(J0137+331), while the array phase was monitored by switching between\nthe GRB and the phase calibrators J1637+462 (at 8.46 GHz) and J1658+476\n(at 4.86 GHz). \n\nThere were three radio sources inside the initial IPN error box (figure 3). Of these, two\nwere previously known from an earlier survey of this part of the sky\n(Becker, White \\& Helfand 1995). The third source, located at located at\n(epoch J2000) $\\alpha$\\ =\\ $16^h33^m53.50^s$ ($\\pm{0.01^s}$) $\\delta$\\\n=\\ $+46^\\circ27^\\prime20.9^{\\prime\\prime}$ ($\\pm{0.1}^{\\prime\\prime}$)\nwas near the center of the initial IPN error box. On the basis of its position,\ncompactness ($<0.8^{\\prime\\prime}$), and a rising flux density between\n4.86 GHz and 8.46 GHz (327 $\\pm$ 45 $\\mu$J and 707 $\\pm$ 39 $\\mu$J respectively)\n, Frail (1999) proposed that it was the afterglow\nof GRB\\thinspace{991208}. Despite the proximity of this location to the Sun\n($\\rm \\sim 70 \\arcdeg$), numerous optical observations were carried out,\nand this suggestion was quickly confirmed by the\nindependent detection of a coincident optical source, not visible on the\nDigital Sky Survey (Castro-Tirado et al. 1999). \n\nIn the week following the afterglow discovery, it was determined that\nthe optical flux faded as a power-law with a rather steep temporal decay\nindex $\\alpha\\simeq 2.15$ (where $F_\\nu\\propto t^\\alpha$) (Jensen et al.\n1999; Garnavich and Noriega-Crespo 1999; Masetti et al.\n1999). Optical spectroscopy emission lines from a presumed\nhost galaxy, if identified with [OII] and [OIII] features, place\nGRB\\thinspace{991208} at a redshift $z=0.707 \\pm 0.002$ (Dodonov et al\n1999), making this the third closest GRB with a spectroscopically-measured\nredshift. GRB\\thinspace{991208} has been no less interesting at\nradio wavelengths. It has the brightest radio afterglow detected to\ndate and consequently it has been detected and is well-studied between 1\nGHz and 350 GHz (Pooley 1999; Shepherd et al. 1999; Bremer et al. 1999).\n\n\\section{Discussion}\n\nFor a 25 -- 1000 keV fluence of $\\rm 10^{-4}\\, erg\\, cm^{-2}$ and\na redshift z=0.707, the isotropic energy of this burst would have\nbeen $\\rm 1.3 \\times 10^{53} erg$; for a peak flux of $\\rm \\sim 10^{-5}\\, erg\\, cm^{-2}\\, s^{-1}$\nin the same energy range, the isotropic peak luminosity would have been\n$\\rm 1.3 \\times 10^{52} erg\\, s^{-1}$. These estimates assume $\\rm \\Omega=0.2,\n\\Lambda=0, and \\, H_0=65 \\, km\\, s^{-1}\\, Mpc^{-1}$. Rhoads (1997) has\npointed out that one signature of beaming is a steep decay in the\nafterglow light curve, $\\propto t^{-2}$. As the initial optical light\ncurve for GRB991208 indeed appears to decay this steeply, the emission\nmay well be beamed, reducing these estimates.\n\nThe current IPN now consists of \\it Ulysses \\rm and NEAR in interplanetary\nspace, and numerous near-Earth spacecraft such as \\it Wind \\rm, \\it BeppoSAX \\rm, and the\n\\it Compton Gamma-Ray Observatory \\rm. The \\it Mars Surveyor 2001 Orbiter \\rm will\njoin the network in mid-2001. The IPN currently observes $\\sim$ 1 -- 2 GRBs per\nweek and is localizing many of them rapidly to small error boxes. These\nevents tend to be the brighter ones, but apart from this, there is no\nbias towards any particular event duration; indeed, the IPN generally\nobtains its smallest error boxes for the short bursts. Neither is there\nany sun-angle restriction for the event locations, which means that bursts\nwill be detected whose locations are close to the Sun, as this one was,\nmaking prompt radio\nobservations of these positions important. The other advantages of\nradio observations over optical are the longer lifetime of the radio afterglow,\nthe immunity from weather, and the freedom to operate at any part of the\ndiurnal cycle.\nThis should increase the rate of counterpart detections substantially over the next\nseveral years. \n\n\nKH acknowledges support for Ulysses operations under JPL Contract 958056,\nfor IPN operations under NASA LTSA grant NAG5-3500, and for NEAR operations\nunder the NEAR Participating Scientist program. On the\nRussian side, this work was partially supported by RFBR grant \\# 99-02-17031. \nWe are grateful to R. Gold and R. McNutt for their\nassistance with the NEAR spacecraft. RS is supported by NASA grant\nNCC5-380. We are indebted to T. Sheets for her excellent work on NEAR\ndata reduction. Special thanks also go to the NEAR project office for its support of\npost-launch changes to XGRS software that made these measurements possible. In\nparticular, we are grateful to John R. Hayes and Susan E. Schneider for writing\nthe GRB software for the XGRS instrument and to Stanley B. Cooper and David S. Tillman\nfor making it possible to get accurate universal time for the NEAR GRB detections.\n\n\\begin{references}\n\\reference{} Aptekar, R., et al. 1995, Space Sci. Rev. 71, 265\n\\reference{} Becker, R. H., White, R. L., and Helfand, D. J. 1995, \\apj \\, 450, 559 \n\\reference{} Bremer, M., Bertoldi, F., Lisenfeld, U., Castro-Tirado, A., Galama, T.,\nKreysa, E. 1999, GCN Circ. 459\n\\reference{} Castro-Tirado, A. et al. 1999, GCN Circ. 452\n\\reference{} Cline, T. et al. 1999, Astron. Astrophys. Suppl. Ser. 138(3), 557\n\\reference{} Costa, E., et al. 1997, \\nat \\, 387, 783\n\\reference{} Dodonov, S., Afanasiev, V., Sokolov, V., Moiseev, A.,\nand Castro-Tirado, A. 1999, GCN Circ. 475\n\\reference{} Frail, D. 1999, GCN Circ. 451\n\\reference{} Garnavich, P., and Noriega-Crespo, A. 1999, GCN Circ. 456\n\\reference{} Goldsten, J. et al. 1997, Space Sci. Rev. 82(1/2), 169\n\\reference{} Hurley, K., et al. 1992, Astron. Astrophys. Suppl. Ser. 92, 401\n\\reference{} Hurley, K., in Gamma-Ray Bursts, Eds. W. Paciesas and G. Fishman,\nAIP Conf. Proc. 265 (AIP Press, New York), p. 3, 1992\n\\reference{} Hurley, K. et al. 1999, GCN Circ. 450\n\\reference{} Jensen, B., Hjorth, J., Pedersen, H., Kristen, H., Tomassi,\nL., Pian, E., and Hurley, K. 1999, GCN Circ. 454.\n\\reference{} Kouveliotou, C., Meegan, C., Fishman, G., Bhat, N., Briggs, M., Koshut, T., Paciesas, W., and Pendleton, G. 1993, \\apj \\, 413, L101\n\\reference{} Masetti, N., Palazzi, E., Pian, E., Frontera F., Benetti, S.,\nMagazzu, A., Castro-Tirado, A., and Masetti, B. 1999, GCN Circ. 462 \n\\reference{} Pooley, G. 1999, GCN Circ. 457\n\\reference{} Rhoads, J. 1997, \\apj \\, 487, L1\n\\reference{} Shepherd, D., Jogee, S., Kulkarni, S., and Frail, D. 1999, GCN Circ. 455 \n\\reference{} van Paradijs, J., et al. 1997, \\nat \\, 386, 686\n\\end{references}\n\n\\clearpage\n\n\\begin{figure}\n\\figurenum{1}\n\\epsscale{.75}\n\\plotone{figure1.ps}\n\\caption{Time histories of GRB991208 as observed by \\it Ulysses \\rm GRB (22-150 keV, thick line) and\nNEAR XGRS (100-1000 keV, thin line). The \\it Ulysses \\rm data are compressed onboard\nthe spacecraft and decompressed on the ground, leading to discrete count rate levels.}\n\\end{figure}\n\n\\begin{figure}\n\\figurenum{2}\n\\epsscale{.75}\n\\plotone{figure2.eps}\n\\caption{Energy spectrum of GRB991208 as observed by Ulysses GRB (crosses) and\nthe fitted power law spectrum (solid line).}\n\\end{figure}\n\n\\begin{figure}\n\\figurenum{3}\n\\epsscale{}\n\\plotone{figure3.eps}\n\\caption{Original and final IPN error boxes for GRB991208 (3 $\\sigma$ confidence).\nThe original error box (Hurley et al. 1999) is drawn with dashed lines. The final\nerror box is defined by the intersection of the 30 \\arcsec \\it Ulysses \\rm-KONUS annulus\nand the 52 \\arcsec \\it Ulysses \\rm-NEAR annulus, and has an area of 1.3 sq. arcmin.\nThree sources are indicated. Two field sources in the upper right-hand corner are\nmarked VLA 2 and VLA 3; their flux densities are 3.4 and 0.4 mJy respectively. VLA\n1 is the counterpart. It lies at roughly at the 96 \\% confidence contour. }\n\\end{figure}\n\n\\clearpage\n\n\\begin{deluxetable}{ccc}\n\\tablecaption{IPN error box for GRB991208 (3 $\\sigma$ confidence).}\n\\tablehead{\n\\colhead{} & \\colhead{$\\rm \\alpha (2000)$, degrees} & \\colhead{$\\rm \\delta(2000)$, degrees}\n}\n\\startdata\nCenter: & 248.4848 & 46.4413 \\\\\nCorners: & 248.4727 & 46.4487 \\\\\n & 248.5021 & 46.4078 \\\\\n & 248.4674 & 46.4747 \\\\\n & 248.4969 & 46.4338 \\\\\n \n\n\\enddata\n\n\\end{deluxetable}\n\n\\end{document}"
}
] |
[] |
astro-ph0002117
|
The Effelsberg Search for Pulsars in the Galactic Centre
|
[
{
"author": "M.~Kramer"
},
{
"author": "B.~Klein"
},
{
"author": "D.~Lorimer"
},
{
"author": "P.~M\\\"uller"
},
{
"author": "A.~Jessner"
},
{
"author": "R.~Wielebinski"
}
] |
We report the status of a search for pulsars in the Galactic Centre, using a completely revised and improved high-sensitivity double-horn system at 4.85-GHz. We also present calculations about the success rate of periodicity searches for such a survey, showing that in contrast to conclusions in recent literature pulsars can be indeed detected at the chosen search frequency.
|
[
{
"name": "kramer2.tex",
"string": "\\documentstyle[11pt,iau177,twoside,epsf]{article}\n%\n%Search for Pulsars in the Galactic Centre}\n%\n\\pagestyle{myheadings}\n\n\n\\keywords{searching, Galactic Center, Effelsberg, scattering}\n\n\t\t \\markboth{Kramer et al.}{Search for Pulsars in the Galactic Centre}\n\t\t \\setcounter{page}{37}\n\\begin{document}\n%\n\\title{The Effelsberg Search for Pulsars in the Galactic Centre}\n \\author{M.~Kramer, B.~Klein, D.~Lorimer, P.~M\\\"uller, A.~Jessner,\nR.~Wielebinski}\n\\affil{Max-Planck-Institut f\\\"ur Radioastronomie, Bonn, Germany}\n%\\affil{$^1$ Jodrell Bank Observatory, Maccelsfield, Cheshire, SK11 9DL, UK}\n%\\affil{Arecibo Observatory, HC3 Box 53995, Arecibo, PR 00612, USA}\n\n\n\\begin{abstract}\nWe report the status of a search for pulsars in the Galactic Centre,\nusing a completely revised and improved high-sensitivity double-horn\nsystem at 4.85-GHz. We also present calculations about the success\nrate of periodicity searches for such a survey, showing that in\ncontrast to conclusions in recent literature pulsars can be indeed\ndetected at the chosen search frequency.\n\\end{abstract}\n\n\n\\noindent\n The detection of radio pulsars in the near vicinity of the Galactic\nCentre is apparently hampered by the largely increased scattering of\npulsar signals at the inhomogeneities of the interstellar medium.\nThis effect cannot be removed by instrumental means but can only be\nreduced by observations at a high radio frequencies. The steep spectra\nof pulsars require a compromise in the choice of the search frequency\nto be used. As a consequence, we had started to search the Galactic\nCentre at a frequency of 4.85-GHz using the Effelsberg 100-m radiotelescope\n(Kramer et al.~1996, in Proc.~of IAU Colloq.~160, \\pasp, p.~13). \n\nSince recently, we have employed both horns of the high-sensitive double-horn\n6cm-frontend ($T_{sys}\\approx 25$ K) connected to four 8-channel\nfilterbanks with $B=8\\times80=480$ MHz bandwidth. The data are\nrecorded by a new ``48+''-channel backend working under VxWorks with a\nmaximum datarate of $\\sim30$ MB/s (10 MB/s sustained). In combination\nwith new reduction software this results in a greatly improved\nsensitivity of less than 0.1 mJy for a 12 min integration (Fig.~1).\n\n\nRecently, Cordes \\& Lazio (1997, \\apj, 475, 557, hereafter CL97) presented\ncalculations which indicated that periodicity searches in the Galactic\nCentre below 10 GHz would hardly be successful, since scattering will\nreduce the pulsed fraction of the pulsar signal at lower frequencies.\nInstead, they favoured a complementary imaging approach. It has to be\nnoted, however, that their calculations made use of a simplified\nexpression to describe the effect of scattering. A correct treatment\nshows a still significant contribution of power in the higher\nharmonics. As a result, the decrease of pulsed emission towards lower\nfrequencies is much slower than derived by CL97. In fact, we \ndemonstrate that pulsars can still be discovered in periodicity\nsearches at 5 GHz (Fig.~2).\n\n\\begin{figure}\n\\plotfiddle{kramer2.1.ps}{3.1cm}{270}{30}{40}{-240}{180}\n\\plotfiddle{kramer2.2.ps}{3.1cm}{270}{35}{45}{0}{250}\n\\caption{{\\it left)} New search system for the 6cm Galactic\nCentre survey, {\\it right)} improved sensitivity of the new system \nin comparison to that described by Kramer et al.~(1996).}\n\\end{figure}\n\n\\begin{figure}\n\\plotfiddle{kramer2.3.ps}{2.5cm}{270}{30}{35}{-200}{130}\n\\plotfiddle{kramer2.4.ps}{2.5cm}{270}{35}{45}{-10}{253}\n\\caption{{\\it left)} Effects of pulse scattering on time series and\npower spectrum when modeled as by CL97 and when applying the\nactual formulae, {\\it right)} scattered pulsed flux for a model pulsar\nof $P=1$ s and a duty cycle of 5\\% for different spectral indices.\nIn contrast to results by CL97 (thin lines), real scattering (heavy\nlines) still produces detectable pulsed fraction at frequencies around\n5 GHz.}\n\\end{figure}\n\n\n\n\\acknowledgements We thank the receiver group of the MPIfR for\nbuilding the superb 6cm-receiver and the corresponding filterbanks.\nThe digital-group, in particular Thomas Kugelmeier, made significant\ncontributions in the development of the new backend POESY.\n\n%\\begin{references}\n%\\reference Cordes, J.M, Lazio, T.W.L., \n%\\reference Kramer et al., 1996, in IAU Colloq.~160, Pulsars: Problems and Progress, ed.~S.~Johnston, M.A.~Walker, \\& M.~Bailes, \\pasp, p.~13\n%\\end{references}\n\n\\end{document}\n\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002118
|
Near Infrared Photometry of Galactic Globular Clusters $M\,56$ and $M\,15$. Extending the Red Giant Branch vs. Metallicity Calibration Towards Metal Poor Systems. \footnote{Based on data taken at the Steward Observatory 2.3m Bok Telescope equipped with the 256x256 near IR camera.}
|
[
{
"author": "Valentin D. Ivanov"
}
] |
Infrared $JK_{s}$-band photometry of the Galactic globular clusters $M\,15$ and, for the first time, $M\,56$ is presented. We estimated the reddening ($E(B-V)=0.18\pm0.08$ mag) and distance modulus ($({m}-M)_V=15.43\pm0.30$ mag) towards the poorly studied globular cluster $M\,56$. We combined our data with observations of other clusters from the literature (12 in total) to extend the ${[Fe/H]}$ vs. Red Giant Branch (RGB) slope relation towards metal-poor clusters. Our best fit yields to ${[Fe/H]}\,=\,-3.40(\pm0.22)\,-27.74(\pm2.35)\,\times\,(RGB\,Slope)$, with an $r.m.s.\,=\,0.20$. The broader metallicity baseline greatly reduced the uncertainties compared to other existing calibrations. We confirmed a previously obtained calibration of the relation between the RGB color $(J-K_{s})_0(RGB)$ at $M_{K_{s}}=-5.5$ vs. $[ Fe/H]$: ${[Fe/H]}\,=\,-6.90(\pm0.99)\,+6.63(\pm1.05)\,\times\,(J-K_{s})_0(RGB)$ with an $r.m.s.\,=\,0.33$. Finally, using the new RGB slope calibration we estimated the abundance of the super metal-rich cluster Liller 1 ${[Fe/H]}\,=\,0.34\pm0.22$.
|
[
{
"name": "ivanov.tex",
"string": "\\documentstyle[12pt,aaspp4]{article}\n\n\\begin{document}\n\n\\title {Near Infrared Photometry of Galactic Globular Clusters $\\rm M\\,56$ \nand $\\rm M\\,15$. Extending the Red Giant Branch vs. Metallicity Calibration \nTowards Metal Poor Systems.\n\\footnote{Based on data taken at the Steward Observatory 2.3m Bok \nTelescope equipped with the 256x256 near IR camera.}\n}\n\n\\author{Valentin D. Ivanov}\n\\affil{Steward Observatory, The University of Arizona, 933 N. Cherry \nAvenue, Tucson, AZ 85721; vdivanov@as.arizona.edu}\n\n\\author{Jordanka Borissova}\n\\affil{Institute of Astronomy, Bulgarian Academy of Sciences, \n72~Tsarigradsko chauss\\`ee, BG\\,--\\,1784 Sofia, Bulgaria, \njura@haemimont.bg} \n\n\\author{Almudena Alonso-Herrero}\n\\affil{Steward Observatory, The University of Arizona, 933 N. Cherry \nAvenue, Tucson, AZ 85721; aalonso@as.arizona.edu}\n\n\\and\n\n\\author{Tatiana Russeva}\n\\affil{Institute of Astronomy, Bulgarian Academy of Sciences, \n72~Tsarigradsko chauss\\`ee, BG\\,--\\,1784 Sofia, Bulgaria}\n\n\\begin{abstract}\nInfrared $\\rm JK_{\\rm s}$-band photometry of the Galactic globular \nclusters $\\rm M\\,15$ and, for the first time, $\\rm M\\,56$ is presented. \nWe estimated the reddening ($\\rm E(B-V)=0.18\\pm0.08$ mag) and distance \nmodulus ($\\rm ({\\it m}-M)_V=15.43\\pm0.30$ mag) towards the poorly \nstudied globular cluster $\\rm M\\,56$. We combined our data with \nobservations of other clusters from the literature (12 in total) to \nextend the ${\\rm [Fe/H]}$ vs. Red Giant Branch (RGB) slope relation \ntowards metal-poor clusters. Our best fit yields to \n${\\rm [Fe/H]}\\,=\\,-3.40(\\pm0.22)\\,-27.74(\\pm2.35)\\,\\times\\,(RGB\\,Slope)$, \nwith an $\\rm r.m.s.\\,=\\,0.20$. The broader metallicity baseline \ngreatly reduced the uncertainties compared to other existing \ncalibrations. We confirmed a previously obtained calibration of \nthe relation between the RGB color $\\rm (J-K_{\\rm s})_0(RGB)$ at \n$\\rm M_{K_{\\rm s}}=-5.5$ vs. $\\rm[ Fe/H]$: \n${\\rm [Fe/H]}\\,=\\,-6.90(\\pm0.99)\\,+6.63(\\pm1.05)\\,\\times\\,(J-K_{\\rm s})_0(RGB)$\nwith an $\\rm r.m.s.\\,=\\,0.33$. \nFinally, using the new RGB slope calibration we estimated the abundance \nof the super metal-rich cluster Liller 1 ${\\rm [Fe/H]}\\,=\\,0.34\\pm0.22$. \n\\end{abstract}\n\n\n\\keywords{Stars: Population II -- Stars:\n\tHertzsprung-Russell (HR) diagram -- Galaxy: globular\n\tclusters: individual: $\\rm M\\,15$ -- Galaxy: globular\n\tclusters: individual: $\\rm M\\,56$ -- Galaxy: globular\n\tclusters: individual: $\\rm NGC\\,7099$ -- Galaxy: globular\n\tclusters: individual: $\\rm NGC\\,6553$ -- Galaxy: globular\n\tclusters: individual: Liller 1}\n\n\\section{Introduction}\n\nGlobular clusters are a fundamental laboratory for the study and \nunderstanding of stars and their evolution. They offer a unique \nopportunity to study samples of stars with a single age and \nmetallicity, and provide a sequence of parameters which describe \nthe stellar populations as ensembles of stars. Those parameters \ninclude the position of the red giant branch (RGB), the relative \npopulations of the blue and red horizontal branches, and the \nrelative number of RR Lyr variables. \n\nDavidge et al. (1992\\markcite{dav92}) considered for the first time \nthe slope of the RGB on a combined optical-infrared color-magnitude \ndiagram (CMD) as a metallicity indicator. This technique is \nparticularly promising (Kuchinski, Frogel \\& Trendrup \n1995\\markcite{kuc95}; Kuchinski \\& Frogel 1995\\markcite{kuc95b}; \nFerraro et al., 2000\\markcite{fer00}), because it is not affected by \nthe reddening towards the cluster. Bypassing the reddening correction \ncan help to improve significantly the photometric determination of \nthe metallicity of more distant and highly obscured systems. \n\nThe stars on the RGB radiate most of their energy in the infrared, \nwith the added advantage that the reddening is greatly diminished \nin this part of the spectrum. Although both those arguments are not \nrelevant for observations of Galactic globular clusters, they become \ncritical in the studies of distant systems, where the patchy internal \nextinction is added to the foreground extinction in the Milky Way, \nwhich makes the interpretation of the data more difficult. Also, \nmany potential targets of interest (such as nearby dwarf galaxies) \nare expected to have a low metal content. Until recently, the \navailable calibrations did not span all the necessary range of \n$\\rm[Fe/H]$. Indeed, Kuchinski \\& Frogel (1995\\markcite{kuc95b}) \nbased their calibration on a set of Galactic globular clusters with \nmetallicities from $\\rm[Fe/H]$~=~1.01 to -0.25. Ferraro et al. \n(2000\\markcite{fer00}) presented for the first time high quality \nnear infrared CMDs of 10 Galactic globular clusters, and a detailed \nanalysis of the RGB behavior as a function of metallicity. \n\nThe goal of this work is to increase the statistical basis of the \nRGB slope vs. $\\rm[Fe/H]$ calibration, and to test the existing \ncalibrations (Kuchinski, Frogel \\& Trendrup 1995\\markcite{kuc95}; \nKuchinski \\& Frogel 1995\\markcite{kuc95b}; Ferraro et al., \n2000\\markcite{fer00}). Clusters with low metallicities are of \nparticular interest, because they will allow to make this tool \napplicable to metal-poor stellar systems. We will also increase the \nstatistical basis of the RGB slope vs. $\\rm[Fe/H]$ calibration. \n\nWe present here $\\rm JK_s$ photometry of the central area of \n$\\rm M\\,15$ and, for the first time, $\\rm M\\,56$. The basic data for \nthe clusters are given in Table~\\ref{tbl-1} (Harris \n1996\\markcite{har96}; June 22, 1999 version). They are both extremely \nmetal-poor clusters. The table contains data on two more clusters \n($\\rm M\\,30$ and $\\rm NGC\\,6553$) which we collected from the \nliterature. \n\n\\placetable{tbl-1}\n\n$\\rm M\\,15$ is a well studied Galactic globular cluster. It possesses \none of the highest known central densities (Yanny et al. \n1994\\markcite{yan94}). King (1975\\markcite{kin75}) and Bahcall \\& \nOstriker (1975\\markcite{bah75}) speculated that the cluster might have \nundergone a core collapse or might contain a central black hole. Sandage \n(1970\\markcite{san70}) obtained ground-based photometry of the outer \nregion of $\\rm M\\,51$ and detected an extended blue horizontal branch \n(hereafter HB) but no significant population of blue stragglers. \nSubsequent photometric works were presented by Auri\\`{e}re \\& Cordoni \n(1981\\markcite{aur81}), Buonano et al. (1985\\markcite{buo85}), Bailyn et \nal. (1988\\markcite{bai88}), and Cederbloom et al. (1992\\markcite{ced92}). \nMore recently, the cluster was observed in the optical with the {\\it HST} \nby Ferraro \\& Parsce (1993\\markcite{fer93}) and Yanny et al. \n(1994\\markcite{yan94}). Frogel, Persson \\& Cohen (1983\\markcite{fro83}) \npublished $\\rm JHK$ measurements of five bright red giants in \n$\\rm M\\,15$. The most recent variability study of $\\rm M\\,15$ (Buter et \nal., 1998\\markcite{but98}) reported light curves of 30 confirmed \nvariable stars, mostly RR Lyr. \n\nIn contrast, $\\rm M\\,56$ is surprisingly poorly studied, probably because \nis lays close to the Galactic plane $(l=62.66\\arcdeg, b=+8.34\\arcdeg)$. \nRosino (\\markcite{ros51}1951) obtained the first photographic CMD of this \ncluster. Barbon (1965\\markcite{bar65}) built the first CMD in the \nstandard $BV$ colors. Smriglio, Dasgupta \\& Boyle (1995\\markcite{smr95}) \nused the Vilnius photometric system to estimate the extinction towards \n$\\rm M\\,56$, and pointed to a possible reddening variation across the \ncluster area. A number of observations of variable stars in $\\rm M\\,56$ \nhave been undertaken throughout the years (Sawyer 1940\\markcite{saw40}; \nSawyer 1949\\markcite{saw49}; Rosino 1961\\markcite{ros61}; Wehlau \\& \nSawyer Hogg 1985\\markcite{weh85}). The latest CMD for this cluster \n(Grundahl et al. 1999\\markcite{gru99}) is in the Str\\\"{o}mgren $(u,u-y)$ \nsystem and shows very well defined blue and red HBs. \n\n\n\\section{Observations and Data Reduction}\n\nWe obtained $\\rm JK_{\\rm s}$ imaging of $\\rm M\\,56$ and $\\rm M\\,15$ \nusing a $256\\times256$ NICMOS3 array at the 2.3-m Bok Telescope of the \nUniversity of Arizona on Kitt Peak, with a plate scale of $0.6\\,$arcsec \npixel$^{-1}$, under photometric conditions on Nov 5, 1998. The average \nseeing during the observations was 1.0-1.2 arcsec. The observational \nstrategy consisted of taking cluster images interleaved with sky images \n$6\\arcmin-7\\arcmin$ away from the targets. We dithered both object and \nsky images to improve the bad pixel and cosmic ray corrections. \n\nThe data reduction included subtraction of dark current frames, \nflat-fielding with median combined empty sky frames, and sky \nsubtraction using IRAF. \n\\footnote{IRAF is distributed by the National Optical Astronomy \nObservatories, which are operated by the Association of Universities \nfor Research in Astronomy, Inc., under cooperative agreement with \nthe National Science Foundation.}\nThe images were shifted to a common position with cubic spline \ninterpolation, and averaged together to produce the final image. The \nphotometric calibration was performed using observations of standard \nstars from the list of \\markcite{eli82}Elias et al. (1982). Although \nwe used the $\\rm K_{\\rm s}$ filter which has shorter longer wavelength \ntransmission limit than the $\\rm K$ standard filter, the two photometric \nsystem are nearly identical (Persson et al. 1998\\markcite{per98}) \nwithin the observational errors. The photometric calibration errors \nassociated with the standard stars scatter are 0.05, and 0.06 mag in \n$\\rm J$, and $\\rm K_{\\rm s}$ respectively. \n\nThe stellar photometry of the final combined frames was carried out \nusing DAOPHOT II (\\markcite{ste93}Stetson 1993). We found some small \nvariations in the FWHM of the PSF $(\\approx 0.08$ arcsec) between the \ninner and outer frame regions. A variable PSF was constructed using a \nlarge number of moderately bright, isolated stars. We assumed that \nthe PSF varied linearly with the position in the frame. A subset of \nthe photometric data is presented in Table~\\ref{tbl-2} where the \ncoordinates are given in pixels relative to the cluster centers, and \nthe last two columns contain the formal DAOPHOT errors. \n\n\\placetable{tbl-2}\n\nThe formal DAOPHOT errors shown in Figure~\\ref{fig-1} demonstrate the \ninternal accuracy of the photometry. The typical errors down to \n$\\rm J\\leq16$ and $\\rm K_{\\rm s}\\leq16$ are smaller than 0.1 mag. The \nlarger spread of errors in $\\rm M\\,15$ is due to the denser central \ncore of this cluster. To account for the uncertainty of the sky \nsubtraction we added in quadrature 0.01 mag in $\\rm J$, and 0.02 mag \n$\\rm K_{\\rm s}$ to these errors. \nTo estimate independently the internal accuracy of our photometry we \ncarried out an artificial star simulation. This is the most complete \ntechnique for error determination because it includes the sky \nbackground variations, crowding errors, and the PSF variations across \nthe field. We added 100 artificial stars with known brightnesses at \nrandom places on the $\\rm J$ and $\\rm K_{\\rm s}$ images of each cluster. \nWe measured then their magnitudes in the same manner as for the program \nstars. We repeated this simulation ten times and calculated the mean \nstandard deviations for given magnitude bins (Table~\\ref{tbl-3}). We \nsuccessfully recovered the formal DAOPHOT errors (Figure~\\ref{fig-1}). \nThe former errors are small compared with the photometric calibration \nerrors, and thus we used the DAOPHOT errors throughout the paper \ntaking advantage of the individual error estimates for each star. \n\n\\placefigure{fig-1}\n\\placetable{tbl-3}\n\nWe have one star in common with Frogel, Cohen \\& Persson \n(1983\\markcite{fro83}) - I-12 in their notation. It is at the edge of \nour field. They estimated $\\rm K=9.42$, and $\\rm J=10.19$. Our \nmeasurements are $\\rm K_{\\rm s}=9.37\\pm0.06$, and $\\rm J=10.29\\pm0.06$ \nwhere the formal DAOPHOT errors and the photometric calibration errors \nare added in quadrature. The corresponding differences are 0.05 mag and \n0.10 mag, acceptable if compared with the errors. Undoubtedly some of \nthe problem in $\\rm K_{\\rm s}$ may arise from the different photometric \nsystems. Persson et al. (1998\\markcite{per98}; see their Table 3) showed \nthat for red stars $\\rm K_{\\rm s}$ and $\\rm K$ are rarely further apart \nthan 0.02 mag. \n\n\n\\section{Color-Magnitude Diagrams}\n\nThe $\\rm K_{\\rm s}$, $\\rm J-K_{\\rm s}$ CMD for $\\rm M\\,15$ and \n$\\rm M\\,56$ datasets are presented in Figure~\\ref{fig-2}. Only stars \nwith DAOPHOT errors of less than 0.06 for $\\rm K_{\\rm s}\\leq14.0$~mag, \n(filled circles) and stars with errors less than 0.10 for \n$\\rm K_{\\rm s}\\geq14.0$ (open circles) were included. To minimize the \nfield star contamination in $\\rm M\\,56$ for stars with $\\rm K_{\\rm s}$ \nbrighter than $14.0$, only stars within the radius $r\\,=\\,1.16\\arcmin$ \n(\\markcite{har96}Harris 1996) were included. The stars from within 7 \ntimes the core radius of $\\rm M\\,15$ ($r_{core}=0.07\\arcmin$, \n\\markcite{har96}Harris 1996) were excised.\n\n\\placefigure{fig-2}\n\n\\subsection{$\\rm M\\,15$}\n\nThe giant branch of $\\rm M\\,15$ is very well defined up to \n$\\rm K_{\\rm s}=9.5$ mag. The position of the brightest non-variable \nstar suggests that the RGB tip lies at $\\rm (J-K_{\\rm s})=0.92$ mag \nand $\\rm K_{\\rm s}=9.37$ mag. None of the red variables listed in \nClement (\\markcite{cle99}1999) lies in our field. \n\nThe HB can be identified at $\\rm K_{\\rm s}=14.35\\pm0.3$ mag, derived \nas an average of 25 RR Lyr stars (represented by diamonds in \nFigure~\\ref{fig-2}; Clement \\markcite{cle99}1999). Unfortunately our \nobservations do not span long enough time interval to calculate the \naverage K-band magnitude of each RR Lyr star. Instead, the plotted \nRR Lyr magnitudes represent their snapshot brightnesses at the moment \nof the observation. The typical amplitude of RR Lyr in the infrared \nis 0.2-0.3 mag (Carney et al., 1995\\markcite{car95}). Combined with \nthe average photometric error (0.17 mag for K=14-16), it accounts for \nthe HB uncertainty. \n\nThe red HB spans a range from $\\rm (J-K_{\\rm s})=0.46$ to $0.35$ mag. \nOn the $\\rm (V,B-V)$ CMD, $\\rm M\\,15$ shows the typical HB morphology \nof metal-poor clusters, with a high blue-to-red HB star ratio, and \nlarge number of RR Lyr variables (\\markcite{dur93}Durrell \\& Harris \n1993). Our data are not deep enough to detect the blue HB stars. \n\n\n\\subsection {$\\rm M\\,56$}\n\nThe giant branch is well defined up to $\\rm K_{\\rm s}\\approx10$ mag. \nThe RGB tip lies at $\\rm (J-K_{\\rm s})=0.94$ mag and \n$\\rm K_{\\rm s}=9.72$ mag. The horizontal branch can be identified at \n$\\rm K_{\\rm s}=14.45\\pm0.02$ mag. The clump at $\\rm (J-K_{\\rm s})=0.45$ \nmag constitutes the red HB, and the stars with $\\rm (J-K_{\\rm s})$ \nbetween 0.10 and 0.20 mag and $\\rm K_{\\rm s}$ between 14.45 and 15.60 \nmag are the blue HB. Unfortunately our photometry is not complete at \nthis level to determine the blue-to-red HB star ratio. Since the \ncluster is close to the Galactic plane, some background contamination \nwould be present. The stars with $\\rm (J-K_{\\rm s})\\approx0.2$ and \n$\\rm K_{\\rm s}\\leq14.5$ mag are a clear example. Among the fainter \nstars we have a mixture of field and member stars, and we do not \ninclude those in our considerations. \n\nClement (\\markcite{cle99}1999) lists twelve variables in $\\rm M\\,56$. \nOur imaging includes only V2 and V6 (marked in Figure~\\ref{fig-2}). \nTheir membership is confirmed by relative proper motion measurements \n(\\markcite{rus81}Rishel, Sanders, \\& Schroder 1981). Wehlau \\& Sawyer \nHogg (\\markcite{weh85}1985) classified V2 as an irregular red variable \nwith small V amplitude. Its position in our CMD confirms it. V6 has a \nwell determined 90 day period, and was classified as an RV Tau type \n(Sawyer 1940\\markcite{saw40}; Sawyer 1949\\markcite{saw49}; Wehlau \\& \nSawyer Hogg 1985\\markcite{weh85}). \\markcite{rus00}Russeva (2000) \ntentatively identified 7 additional red variable stars, marked in \nFigure~\\ref{fig-2} as open diamonds. They all belong to the RGB, and \nare among the brightest and reddest stars in our sample. There are no \nknown RR Lyr stars in our field. \n\n\\subsection{Reddening and Distance of $\\rm M\\,56$}\n\nOur photometry allows to carry out a new determination of the distance \nand reddening to $\\rm M\\,56$. Since $\\rm M\\,15$ has a similar metal \ncontent to $\\rm M\\,56$, $\\rm M\\,15$ can be used as a template for the \nintrinsic RGB color. In addition, \\markcite{kuc95}Kuchinski \\& Frogel \n(1995) demonstrated that the color of RGB at the level of the HB shows \nlittle or no change with metallicity. \n\nFor $\\rm M\\,15$ we measured a reddening corrected color at the HB \nlevel of $\\rm (J-K_{\\rm s})_{GB,HB,0}=0.58\\pm0.04$ mag. The observed \nRGB color of $\\rm M\\,56$ at the level of HB is \n$\\rm (J-K_{\\rm s})_{GB,HB}=0.62\\pm0.02$ mag. Assuming that the color \ndifference is only due to the reddening, we obtained a relative color \nexcess of $E(J-K_{\\rm s})_{M\\,56,M\\,15}\\,=\\,0.04\\pm0.04$ mag. Using \n\\markcite{rie85}Rieke \\& Lebofsky (1985) extinction law we found \n$E(B-V)_{M\\,56,M\\,15} = 0.08\\pm0.08$ mag, and finally a color excess \nof of $\\rm M\\,56$ is $\\rm E(B-V)_{M\\,56}=0.18\\pm0.08$ mag. The error \nincludes the internal photometric error, errors of fiducial lines fits \nof both globular clusters, and the uncertainty of the HB levels. Note, \nthat even though the HB level in $\\rm M\\,15$ has a large uncertainty \n(0.30 mag), this does not affect seriously our reddening estimate \nbecause of the steep RGB. The calculated reddening of $\\rm M\\,56$ is \nvery close to the value of $\\rm E(B-V)=0.20$ mag given by Harris \n(1996\\markcite{har96}). \n\nThe comparison of the reddening corrected HB levels of $\\rm M\\,56$ \nand $\\rm M\\,15$ can be used to determine the differential distance to \n$\\rm M\\,56$ with respect to $\\rm M\\,15$. We obtained \n$\\rm K_{s,HB,0}=14.32\\pm0.30$ mag, and $\\rm K_{s,HB,0}=14.38\\pm0.04$ \nmag for $\\rm M\\,15$ and $\\rm M\\,56$ respectively, using the reddening \nlaw from Rieke \\& Lebofsky (1985\\markcite{rie85}). We adopted for \n$\\rm M\\,15$ a color excess of $\\rm E(B-V)=0.10$ mag and a distance \nmodulus of $\\rm ({\\it m}-M)_{V}=15.37$ mag from \\markcite{har86}Harris \n(1996). The distance scale was established by adding to his horizontal \nbranch vs. metallicity calibration an empirical evolutionary correction \nto the zero age horizontal branch as determined by Carney et al. (1992\\markcite{car92}). The typical distance modulus uncertainty was \n$\\pm0.1$ mag. Thus, we find a distance modulus to $\\rm M\\,56$ of \n$\\rm ({\\it m}-M)_V=15.43\\pm0.30$ mag. Unfortunately the large \nuncertainty in the HB level prevents us from making a better estimate. \n\\markcite{har96}Harris (1996) gives $\\rm ({\\it m}-M)_V=15.65$ mag. If \ncorrected for the reddening, it becomes $\\rm ({\\it m}-M)_0=15.03$ mag. \nThis estimate is based on RR Lyr observations by Wehlau \\& Sawyer Hogg \n(1985\\markcite{weh85}) who obtained $\\rm ({\\it m}-M)_0=14.81$ mag with \na different extinction value. Previously Harris \\& Racine \n(1979\\markcite{har79}) determined 9.7 kpc or $\\rm ({\\it m}-M)_0=14.81$. \nOur distance estimate is larger than those. We attribute the difference \nto the uncertain HB position in $\\rm M\\,15$. \n\nAccording to Guarnieri et al. (1998\\markcite{gua98}), the $\\rm K_s$-band \nabsolute magnitude of the HB depends on the cluster metallicity: \n$\\rm M_{K}(HB)\\,=\\,-0.2*\\rm[Fe/H]\\,-1.53$. This relation predicts a 0.06 \nmag difference in the HB level of the two clusters, which is smaller \nthan the uncertainties in our observed HB positions. It also predicts \nan absolute $\\rm K_s$-band magnitude for the HB of $\\rm M\\,15$ of \n$\\rm M_{K}(HB)\\,=\\,-1.08$ mag, very close to the average \n$\\rm <M_{K}(HB)>\\,=\\,-1.15\\pm0.10$ mag value measured by Kuchinski \\& \nFrogel (1995b\\markcite{kuc95b}) for their sample of globular clusters. \nOur data yield $\\rm M_{K}(HB)\\,=\\,-0.95\\pm0.30$, where the error is \ndominated by the spread of the RR Lyr apparent brightnesses. \n\n\n\\section{The Red Giant Branch as a Metallicity Indicator}\n\n\\subsection{The Red Giant Branch Slope vs. $\\rm [Fe/H]$}\n\nIt is well known that both intrinsic colors $\\rm (J-K_{\\rm s})_0$ and \n$(V-K_{\\rm s})_0$ are \nsensitive to metallicity (e.g. \\markcite{fro83}Frogel; Cohen \\& Persson \n1983, \\markcite{bra98}Braun et al. 1998). \\markcite{kuc95} Kuchinski et \nal. (1995) and \\markcite{kuc95b}Kuchinski \\& Frogel (1995) demonstrated \nempirically and theoretically that the slope of the upper RGB in the \n$\\rm K_{\\rm s}$ vs. $\\rm (J-K_{\\rm s})$ diagram is sensitive to the \nmetallicity for a sample of metal-rich Galactic globular clusters. \\markcite{tie97}Tiede, Martini \\& Frogel (1997) extended this relation \nto a sample of open clusters and bulge stars. Possible extragalactic \napplications prompted us to extend this calibration towards lower \nmetallicity clusters. \n\nWe added to Kuchinski \\& Frogel (1995\\markcite{kuc95b}) sample our two \nglobular clusters $\\rm M\\,15$, $\\rm M\\,56$, and two more clusters from \nthe literature ($\\rm NGC\\,7099$ and $\\rm NGC\\,6553$). $\\rm NGC\\,7099$ \nis the most metal-poor among the clusters observed in infrared by Cohen \n\\& Sleepers (1995\\markcite{coh95}), and their photometry includes a \nsufficiently large number of RGB stars. $\\rm NGC\\,6553$ was studied by \nGuarnieri et al. (1998\\markcite{gua98}). Although it is not a \nparticularly metal-poor cluster, it will improve the statistical weight \nof our calibration. Gathering data from different sources observed with \ndifferent photometric systems always involves some danger of \nincompatibility. For red stars the average difference between $\\rm K$ \nand $\\rm K_{\\rm s}$ measurements of Persson et al. (1998\\markcite{per98}) \nis 0.01 mag with a standard deviation of 0.02 mag. We increased \ncorrespondingly the uncertainties of the photometry. \n\nFirst, we had to separate the giants belonging to the upper RGB. \nFollowing \\markcite{tie97}Tiede, Martini \\& Frogel (1997), these are \nstars with absolute $\\rm K$ magnitudes spanning the range from $-2$ to \n$-6.5$ mag. However, \\markcite{fro88}Frogel \\& Elias (1988) and \nMontegriffo et al. (\\markcite{mon95}1995) determined that most (if not \nall) of the brightest RGB stars are in fact AGB long-period variables. \nHence, we excluded from our analysis all the known red variable stars. \nFurther, we excluded stars within the central 50 arcsec in both \n$\\rm M\\,15$ and $\\rm M\\,56$ to minimize the errors due to field \ncrowding. \n\nAs in Kuchinski et al. (1995\\markcite{kuc95}) we carried out a \nleast-squares fit to the giants from 0.6 mag to 5.2 mag above the HB \nlevel in $\\rm K_{\\rm s}$, taking into account errors along both axes. \nThis effectively increased the weight of the most accurate measurements, \nwhich are usually the brightest cluster stars. To exclude possible \nrandom errors we rejected stars which deviated more than three times the \nr.m.s. of the first fit. This resulted in a loss of only 5, 1, 2 and 4 \nstars for $\\rm M\\,15$, $\\rm M\\,56$, $\\rm NGC\\,7077$ and $\\rm NGC\\,6553$, \nrespectively, confirming the good quality of the photometry. The best \nfits for the slopes of the RGB of these clusters are shown in \nTable~\\ref{tbl-4}. The errors in this table are purely statistical. The \nfits and the RGB stars used are plotted in Figure~\\ref{fig-3}. Varying \nthe HB level within the errors, produced an additional 0.002 error in \nthe RGB slope, and was added in quadrature to the statistical errors. \nTo verify our fitting technique we carried out simulations by creating \n100 artificial RGBs analogous to the $\\rm M\\,15$ RGB. We started from the \n$\\rm K_{\\rm s}$-band magnitudes of each star, calculated the corresponding \n$\\rm J-K_{\\rm s}$, and added random Gaussian errors with the appropriate \n$\\sigma$ for each star, along both axes. We were able to recover the \noriginal RGB slope to within less than $1\\sigma$.\n\n\\placetable{tbl-4}\n\\placefigure{fig-3}\n\nThe relation of the RGB slope vs. the $\\rm[Fe/H]$ is shown in \nFigure~\\ref{fig-4}. Fitting a straight line to the data taking into \naccount the errors along both axes yields to: \n\\begin{equation}\n{\\rm [Fe/H]}\\,=\\,-3.40(\\pm0.22)\\,-27.74(\\pm2.35)\\,\\times\\,(RGB\\,Slope)\n\\end{equation}\nwith the $\\rm r.m.s.\\,=\\,0.20$. \nTo test for the compatibility of the data collected from various sources, \nwe carried the same fit using only the data from Kuchinski \\& Frogel \n(1995\\markcite{kuc95b}), and our two clusters. We obtained a fit \nstatistically indistinguishable from Equation (1). \n\n\\placefigure{fig-4}\n\nThere are three recent determinations of this relation in the literature. \nKuchinski \\& Frogel (1995\\markcite{kuc95b}) derived for their sample of \nten metal-rich clusters: \n\\begin{equation}\n{\\rm [Fe/H]}\\,=\\,-2.98(\\pm0.70)\\,-23.84(\\pm6.83)\\,\\times\\,(RGB\\,Slope)\n\\end{equation}\n\nLater Tiede, Martini \\& Frogel (1997\\markcite{tie97}) re-derived it. \nFor the sample of twelve globular clusters they obtained: \n\\begin{equation}\n{\\rm [Fe/H]}\\,=\\,-2.78(\\pm0.61)\\,-21.96(\\pm5.92)\\,\\times\\,(GB\\,slope) \n\\end{equation}\nand if the most metal-poor cluster is rejected: \n\\begin{equation}\n{\\rm [Fe/H]}\\,=\\,-2.44(\\pm0.67)\\,-18.84(\\pm6.41)\\,\\times\\,(GB\\,slope)\n\\end{equation}\n\nMost recently Ferraro et al. (2000\\markcite{fer00}) obtained with much \nhigher quality data of 10 clusters: \n\\begin{equation}\n{\\rm [Fe/H]}\\,=\\,-2.99(\\pm0.15)\\,-23.56(\\pm1.84)\\,\\times\\,(GB\\,slope) \n\\end{equation} \nThey used the metallicity scale of Caretta \\& Gratton \n(1997\\markcite{car97}). \n\nOur large range of metallicity improves the fit significantly, although \nthe $1\\sigma$ errors are slightly larger than those of Ferraro et al. \n(2000\\markcite{fer00}). All these derivations are statistically \nindistinguishable from our calibrations. This is particularly important \nwhen one has to extrapolate the RGB slope vs. $\\rm[Fe/H]$ relation \noutside of the explored metallicity range. \n\nWe can now apply our relation to estimate the metallicity of the most \nmetal-rich Galactic globular cluster Liller 1. For this cluster \nArmandroff \\& Zinn (\\markcite{arm88}1988) estimated \n$\\rm [Fe/H]=+0.20\\pm0.3$ based on integrated light spectroscopy. Frogel, \nKuchinski \\& Tiede (1995\\markcite{fro95}) obtained an RGB slope of \n$-0.135\\pm0.009$, and derived $\\rm [Fe/H]=+0.25\\pm0.3$. Using the same \nRGB slope, our fit and that of Ferraro et al. (2000\\markcite{fer00}) \nyield metallicities of $\\rm [Fe/H]=+0.34\\pm0.22$ and \n$\\rm [Fe/H]=+0.19\\pm0.15$, respectively. These estimates have to be \ntaken with caution until more data allow to test whether the RGB slope \nvs. $\\rm[Fe/H]$ relation is indeed linear for super metal-rich stellar \npopulations. \n\n\n\\subsection{The Red Giant Branch Color vs. $\\rm [Fe/H]$}\n\nThe slope of the RGB as described here is difficult to measure in \ndistant stellar systems because it requires deep photometry, reaching \nthe HB level. As somewhat observationally less challenging alternative \nwe considered the RGB color at a given absolute magnitude as a \nmetallicity indicator. Following Frogel, Cohen \\& Persson \n(1983\\markcite{fro83}), we chose to calibrate $\\rm (J-K_{\\rm s})_0(RGB)$ \nat $\\rm M_{K_{\\rm s}}=-5.5$ mag. \n\nA drawback of this method is that unlike the RGB slope, the RGB color \nis reddening sensitive and requires a correction prior to the calibration. \nWe used the reddening and distance estimates from Harris \n(1996\\markcite{har96}). We also assumed that the HB level is always at \n$\\rm M_{K_{\\rm s}}=-1.15$ mag neglecting the HB luminosity dependence on \n$\\rm [Fe/H]$ (Kuchinski \\& Frogel 1995\\markcite{kuc95b}). \n\nWe calculated the RGB colors from the linear fits to the RGBs \n(Table~\\ref{tbl-4}). A test with $\\rm M\\,15$ and $\\rm M\\,56$ showed \nthat it is identical to averaging the colors across the RGB within the \nobservational uncertainties. The small number of stars on the RGB tip \nactually makes the averaging less reliable. In addition, most of the \nRGBs show a high degree of linearity (Kuchinski et al., \n1995\\markcite{kuc95}; Kuchinski \\& Frogel, 1995\\markcite{kuc95b}). \nThe errors associated with the RGB colors were calculated as a \nquadrature sum of the r.m.s. of the fit, the errors from the E(B-V) \n$(\\approx0.02$ mag) and the errors from the uncertain distance moduli \n$(\\approx0.10$ mag). \n\nOur best fit of $\\rm (J-K_{\\rm s})_0(RGB)$ at $\\rm M_{K_{\\rm s}}=-5.5$ vs. \nmetallicity (Figure~\\ref{fig-5}) was derived with errors along both \naxes: \n\\begin{equation}\n{\\rm [Fe/H]}\\,=\\,-6.90(\\pm0.99)\\,+6.63(\\pm1.05)\\,\\times\\,({\\rm J-K_{\\rm s})_0}(RGB)\n\\end{equation}\nwith $\\rm r.m.s.\\,=\\,0.33$. We attribute the large r.m.s. to the \nreddening uncertainties.\n\n\\placefigure{fig-5}\n\nFrogel, Cohen \\& Persson (1983\\markcite{fro83}) found: \n\\begin{equation}\n{\\rm [Fe/H]}\\,=\\,-6.905\\,+6.329\\,\\times\\,({\\rm J-K_{\\rm s})_0}(RGB)\n\\end{equation}\nwith r.m.s. = 0.16. This calibration is identical to ours within the \nuncertainties. It was important to confirm their result, because \nalthough it was based on photometry of a large number of clusters \n(33), it only included 10-20 stars per cluster. \n\nMinitti, Olszewski \\& Rieke (1995\\markcite{min95}) also calibrated \nthe intrinsic RBG color at $\\rm M_{K_{\\rm s}}=-5.5$ mag and obtained: \n\\begin{equation}\n{\\rm [Fe/H]}\\,=\\,-5.0\\,+5.60\\,\\times\\,{\\rm (J-K_{\\rm s})_0}(RGB).\n\\end{equation}\nTheir fit is close to ours but shows a slightly different slope. It \nis based on twenty clusters. Unfortunately the severe field star \ncontamination towards the Galactic bulge prevented them from a \nreliable estimate of the cluster colors in many cases. \n\nFerraro et al. (2000\\markcite{fer00}) also performed a similar \ncalibration: \n\\begin{equation}\n{\\rm [Fe/H]}\\,=\\,-4.76(\\pm0.23)\\,+5.38(\\pm0.27)\\,\\times\\,({\\rm J-K_{\\rm s})_0}(RGB)\n\\end{equation}\nwhere the fit coefficients are within $3\\sigma$ of ours. Obtaining \nbetter reddening estimates would be crucial for resolving this \ndiscrepancy. \n\n\n\\section{Summary} \n\nWe showed that the position of the infrared RGB can be used to reliably \ndetermine the abundance of metal-poor stellar systems with an accuracy \nof $\\approx0.2$ (in $\\rm [Fe/H]$). Our main results include: \n\n(1) We presented infrared photometry of the Galactic globular clusters \n$\\rm M\\,15$ and, for the first time, $\\rm M\\,56$, and studied the \nmorphology of their CMDs. \n\n(2) We estimated the reddening towards $\\rm M\\,56$ by comparing the \nRGB color at the level of HB to that of $\\rm M\\,15$, and obtained \n$\\rm E(B-V)=0.18\\pm0.08$ mag. We used the relative HB levels of \nthe same two clusters to derive a distance modulus to $\\rm M\\,56$ of \n$\\rm ({\\it m}-M)_V=15.43\\pm0.30$ mag if $\\rm ({\\it m}-M)_V=15.37$ mag \nis assumed for $\\rm M\\,15$. \n\n(3) We compiled a sample of 12 Galactic globular clusters with high \nquality infrared photometry. We recalibrated and extended the RGB \nslope vs. $\\rm [Fe/H]$ relation towards low metallicity globular \nclusters. We also reevaluated the RGB color $\\rm (J-K_{\\rm s})_0(RGB)$ \nat $\\rm M_{K_{\\rm s}}=-5.5$ mag vs. $\\rm[ Fe/H]$ relation. These are \npotentially useful tools to study extragalactic metal-poor stellar \nsystems, particularly with high obscuration. Our results independently \nconfirm the previously obtained calibrations. \n\n(3) As an application, we used our newly determined RGB slope vs. \n$\\rm [Fe/H]$ relation to estimate the abundance of the super \nmetal-rich Galactic globular cluster Liller 1, and obtained \n${\\rm [Fe/H]}\\,=\\,0.34\\pm0.22$.\n\n\n\\begin{acknowledgements}\nDuring the course of this work VDI and AA-H were supported by the \nNational Aeronautics and Space Administration on grant NAG 5-3042 \nthrough the University of Arizona. The $256 \\times 256$ camera \nwas supported by NSF Grant AST-9529190. JB and TR were supported by \nthe Bulgarian National Science Foundation grant under contract No. \nF-812/1998 with the Bulgarian Ministry of Education and Sciences. \nWe are thankful to the anonymous referee for the corrections that \nhelped to improve the quality of this paper.\n\\end{acknowledgements}\n\n\\clearpage\n\n\\begin{deluxetable}{crrccrcccc}\n\\tablenum{1}\n\\tablewidth{0pt}\n\\tablecaption{Cluster data.\\label{tbl-1}}\n\\small\n\\tablehead{\n\\multicolumn{1}{c}{Name} & \\multicolumn{1}{c}{$\\rm R_{GC}$} & \n\\multicolumn{1}{c}{$\\rm R_{\\sun}$} & \\multicolumn{1}{c}{$\\rm ({\\it m}-M)_V$} & \n\\multicolumn{1}{c}{$\\rm E(B-V)$} & \\multicolumn{1}{c}{$\\rm S_{RR}$} & \n\\multicolumn{1}{c}{$\\rm HBR$} & \\multicolumn{1}{c}{$\\rm [Fe/H]$} & \n\\multicolumn{1}{c}{$\\rm r_c$} & \\multicolumn{1}{c}{$\\rm r_h$}\\nl}\n\\startdata\n$\\rm M\\,15$/$\\rm NGC\\,7078$&10.4&10.3&15.37&0.10&24.1&0.67&-2.25&0.07&1.06\\nl\n$\\rm M\\,56$/$\\rm NGC\\,6779$& 9.7&10.1&15.65&0.20& 2.2&0.98&-1.94&0.37&1.16\\nl\n$\\rm M\\,30$/$\\rm NGC\\,7099$& 7.1& 8.0&14.62&0.03&10.7&0.89&-2.12&0.06&1.15\\nl\n$\\rm NGC\\,6553$ & 2.5& 5.6&16.05&0.75& 0.6& - &-0.34&0.55&1.55\\nl\n\\tablecomments{Columns: \n(1) name, \n(2) galactocentric distance in kpc, assuming $R_0=8.0$ kpc, \n(3) distance from the Sun in kpc, \n(4) visual distance modulus, not corrected for extinction, \n(5) Galactic reddening, (6) specific frequency of RR Lyr, \n(7) HB ratio HBR = (B-R)/(B+V+R), \n(8) $\\rm[Fe/H]$, \n(9) core radius in arcmin, \n(10) half-mass radius in arcmin}\n\\tablerefs{\\markcite{har96}Harris (1996)}\n\\enddata\n\\end{deluxetable}\n\n\n\\begin{deluxetable}{rrrrrrr}\n\\tablenum{2}\n\\tablewidth{0pt}\n\\tablecaption{Photometry of the Galactic globular clusters $\\rm M\\,15$ \nand $\\rm M\\,56$.\\label{tbl-2}}\n%\\scriptsize\n\\tablehead{\n\\multicolumn{1}{c}{ID\\tablenotemark{a}} & \n\\multicolumn{1}{c}{X} \n& \\multicolumn{1}{c}{Y} & \n\\multicolumn{1}{c}{$\\rm K_{\\rm s}$} & \n\\multicolumn{1}{c}{$\\rm J-K_{\\rm s}$} & \n\\multicolumn{1}{c}{$\\rm \\sigma(K_{\\rm s})$} & \n\\multicolumn{1}{c}{$\\rm \\sigma(J)$}\\nl}\n\\startdata\n%\\cutinhead{$\\rm M\\,15$}\n\\multicolumn{7}{l}{$\\rm M\\,15$}\\nl\n 1 & 11.64 & 2.21 & 17.32 & 0.45 & 0.37 & 0.36\\nl\n 2 & 186.90 & 2.34 & 14.38 & 0.48 & 0.08 & 0.06\\nl\n 3 & 42.45 & 2.72 & 9.37 & 0.92 & 0.03 & 0.01\\nl\n 4 & 117.50 & 3.15 & 16.80 & 0.39 & 0.17 & 0.15\\nl\n 5 & 140.80 & 3.31 & 15.99 & 0.23 & 0.10 & 0.10\\nl\n 6 & 56.02 & 3.50 & 14.53 & 0.60 & 0.05 & 0.04\\nl\n 7 & 228.20 & 3.60 & 13.63 & 0.53 & 0.04 & 0.02\\nl\n\\multicolumn{7}{c}{...}\\nl\n\\multicolumn{7}{l}{$\\rm M\\,56$}\\nl\n%\\cutinhead{$\\rm M\\,56$}\n 1 & 241.90 & 47.89 & 16.28 & 0.81 & 0.08 & 0.12\\nl\n 2 & 254.00 & 47.90 & 18.00 & 0.12 & 0.23 & 0.22\\nl\n 3 & 42.37 & 47.90 & 17.65 & 0.23 & 0.13 & 0.15\\nl\n 4 & 64.44 & 48.20 & 17.33 & 1.10 & 0.23 & 0.26\\nl\n 5 & 233.90 & 48.31 & 11.57 & 0.93 & 0.03 & 0.04\\nl\n 6 & 158.10 & 48.32 & 12.51 & 0.77 & 0.02 & 0.04\\nl\n 7 & 94.04 & 48.67 & 14.70 & 0.59 & 0.01 & 0.04\\nl\n\\multicolumn{7}{c}{...}\\nl\n\\tablenotetext{a}{Numbers larger than 10,000 are composed of \nthe numbers from Clement (\\markcite{cle99}1999) plus 10,000 \nfor cross-identification purposes.}\n\\tablecomments{The complete data set is available in the electronic \nform of the Journal.}\n\\enddata\n\\end{deluxetable}\n\n\n\\begin{deluxetable}{ccccc}\n\\tablenum{3}\n\\tablewidth{0pt}\n\\tablecaption{Mean standard deviations from the artificial star \nsimulations (see Section 2 for details). \n\\label{tbl-3}}\n\\tablehead{\n\\multicolumn{1}{c}{Magnitude} & \n\\multicolumn{2}{c}{$\\rm M\\,56$} & \n\\multicolumn{2}{c}{$\\rm M\\,15$}\\nl\n\\multicolumn{1}{c}{Bin} & \n\\multicolumn{1}{c}{$\\rm J$} & \\multicolumn{1}{c}{$\\rm K_{\\rm s}$} & \n\\multicolumn{1}{c}{$\\rm J$} & \\multicolumn{1}{c}{$\\rm K_{\\rm s}$}\\nl\n}\n\\startdata\n10.0-12.0 & 0.04 & 0.04 & 0.05 & 0.05 \\nl\n12.0-14.0 & 0.05 & 0.06 & 0.07 & 0.08 \\nl\n14.0-16.0 & 0.10 & 0.13 & 0.15 & 0.17 \\nl\n\\enddata\n\\end{deluxetable}\n\n\n\\begin{deluxetable}{lcccc}\n\\tablenum{4}\n\\tablewidth{0pt}\n\\tablecaption{Fits to the RGBs of our clusters. The slopes determined \nby Ferraro et al. (2000) are given in the last column for comparison.\n\\label{tbl-4}}\n\\tablehead{\n\\multicolumn{1}{c}{Cluster} & \n\\multicolumn{1}{c}{r.m.s.} & \n\\multicolumn{1}{c}{b} & \n\\multicolumn{1}{c}{a} & \n\\multicolumn{1}{c}{$\\rm a_{(Ferraro~et~al.,~2000)}$} \n}\n\\startdata\n $\\rm M\\,15$ & $\\pm0.04$ & $1.34\\pm0.08$ & $-0.053\\pm0.007$ & $-0.047\\pm0.001$\\nl\n $\\rm M\\,56$ & $\\pm0.05$ & $1.32\\pm0.06$ & $-0.052\\pm0.005$ & - \\nl\n$\\rm NGC\\,7099$ & $\\pm0.07$ & $1.07\\pm0.06$ & $-0.035\\pm0.004$ & $-0.043\\pm0.003$\\nl\n$\\rm NGC\\,6553$ & $\\pm0.06$ & $2.34\\pm0.09$ & $-0.108\\pm0.008$ & $-0.095\\pm0.002$\\nl\n\\tablecomments{Solutions to $\\rm J-K_{\\rm s}~=a\\times K_{\\rm s}+b$}\n\\enddata\n\\end{deluxetable}\n\n\n\\clearpage\n\\begin{references}\n\\reference{arm88} Armandroff, T.E., \\& Zinn, R., 1988, \\aj, 96, 92\n\\reference{aru81} Auri\\`{e}re, M., \\& Cordoni, J.-P., 1981, \\aaps, 46, 347\n\\reference{bah75} Bahcall, J.N., \\& Ostriker, J.P., 1975, \\nat, 256, 23\n\\reference{bai88} Bailyn, C.D., Grindlay, J.E., Cohn, H., \\& Lugger, P.M., \n\t1988, \\apj, 331, 303\n\\reference{bar65} Barbon, R., 1965, Contr. Oss. Astrof. Padova in Asiago,\n\t175, 63 \n\\reference{bra98} Braun, K., Chiboucas, K., Minske, J., \\& Salgado, J, 1998, \n\t\\pasp, 110, 810\n\\reference{buo85} Buonano, R., Corsi, C.E., \\& Fusi Pecci, F., 1985, \n\t\\aap, 145, 97\n\\reference{but98} Butler, R.F., Shearer, A., Redfern, R.M., Colhoun, M.,\n\tO'Kane, P., Penny, A.J., Morris, P.W., Griffiths, W.K., \\& \n\tCullum, M., 1998, \\mnras, 296, 379\n\\reference{car97} Caretta, E., \\& Gratton, R., 1997, \\aaps, 121, 95\n\\reference{car92} Carney, B.W., Storm, J., \\& Johnes, R.Y., 1992, \\apj, \n\t386, 663\n\\reference{ced92} Cederbloom, S.E., Moss, M.J., Cohn, H.N., Lugger, P.M., \n\tBailyn, C.D., Grindlay, J.E., McClure, R.D., 1992, \\aj, 103, 480\n\\reference{cle99} Clement, C.M., 1999, \"An update to Helen Sawyer Hogg's \n\tthird catalog of variable stars in globular cluster\", in preparation\n\\reference{coh95} Cohen, J.G., \\& Sleepers, C., 1995, \\aj, 109, 242\n\\reference{dur93} Durrell, D., \\& Harris, W., 1993, \\aj, 105, 1420\n\\reference{eli82} Elias, J.H., Frogel, J.A., Matthews, K., \\& Neugebauer, \n\tG. 1982, \\aj, 87, 1029\n\\reference{fer93} Ferraro, F.R., \\& Parsce, F., 1993, \\aj, 106, 154\n\\reference{fer00} Ferraro, F.R., Montegriffo, P., Origlia, L., \\& Fusi Pecci, \n\tF., 2000, preprint (astro-ph/9912265)\n\\reference{fro83} Frogel, J.A., Cohen , J.G., \\& Persson, S.E., 1983, \n\t\\apj, 275, 773\n\\reference{fro88} Frogel, J., \\& Elias, J., 1988, \\apj, 324, 823\n\\reference{gru99} Grundahl, F., Catelan, M., Landsman, W.B., Stetson, \n\tP.B., \\& Andersen, M.I., 1999, \\apj, 524, 242\n\\reference{gua98} Guarnieri, M.D., Ortolani, S., Montegriffo, P., Renzini, \n\tA., Barbuy, B., Bica, E., \\& Moneti, A., 1998, \\aap, 331, 70\n\\reference{har79} Harris, W.E., \\& Racine, R., 1979, \\araa, 17, 241\n\\reference{har96} Harris, W.E., 1996, \\aj, 112, 1487\n\\reference{kin75} King, I.R., 1975, in Dynamics of Stellar Systems, Proc.,\n\tIAU Symposium No. 69, edited by A. Hayli (Reidel, Dordrecht), p.69\n\\reference{kuc95} Kuchinski, L.E., Frogel, J.A., \\& Terndrup D.M., 1995, \n\t\\aj, 109, 1131\n\\reference{kuc95b} Kuchinski, L., \\& Frogel, J., 1995, AJ, 110, 2844\n\\reference{min95} Minitti, D., Olszewski, E.W., \\& Rieke, M., 1995, \\aj, \n\t110, 1686\n\\reference{mon95} Montegriffo, P., Ferraro, F., Fusi Pecci, F., \\&\n\tOriglia, L., 1995, \\mnras, 276, 739\n\\reference{per98} Persson, S.E., Murphy, D.C., Krzeminski, W., Roth, M., \n\t\\& Rieke, M.J., 1998, \\aj, 116, 2475\n\\reference{rie85} Rieke, G.H., \\& Lebofsky, M.J., 1985, \\apj, 288, 618\n\\reference{rus81} Rishel, B., Sanders, W., \\& Schroder, R., 1981, \\aap, \n\t45, 443\n\\reference{ros51} Rosino, L., 1951, Co. Asiago, No. 21, 135\n\\reference{ros61} Rosino, L., 1961, Co. Asiago, No. 117\n\\reference{rus99} Russeva, T., 2000, in preparation \n\\reference{san70} Sandage, A.R., 1970, \\apj, 162, 841\n\\reference{saw40} Sawyer, H.B., 1940, Publ. David Dunlop Obs., 1, No. 5\n\\reference{saw49} Sawyer, H.B., 1949, J.R.A.S.C., 43, 38\n\\reference{smr95} Smriglio, F., Dasgupta, A.K., \\& Boyle, R.P., 1995, \n\tBalt. Astr., 5, 451\n\\reference{ste93} Stetson, P., 1993, User's Manual for DAOPHOT II\n\\reference{tie97} Tiede, G., Martini, P., \\& Frogel, J., 1997, \\aj, 114, 694\n\\reference{weh85} Wehlau, A., \\& Sawyer Hogg, H., 1985, \\aj, 90, 2514\n\\reference{yan94} Yanny, B., Guhathakurta, P., Bahcall, J.N., \\& Schneider,\n\tD.P., 1994, \\aj, 107, 1745\n\n\\end{references}\n\n\\clearpage\n\n\\figcaption[err01.eps]{Formal DAOPHOT errors of the $\\rm M\\,15$ and \n$\\rm M\\,56$ photometry in $\\rm J$ (upper panels) and $\\rm K_{\\rm s}$ \n(lower panels).\n\\label{fig-1}}\n\n\\figcaption[cmd01.eps]{Color-magnitude diagrams $\\rm K_{\\rm s}$ vs. \n$\\rm J-K_{\\rm s}$ for $\\rm M\\,15$ (left) and $\\rm M\\,56$ (right). Only \nstars with DAOPHOT errors less of than 0.06 mag for \n$\\rm K_{\\rm s}\\leq14.0$~mag, (filled circles) and stars with errors \nless than 0.10 mag for $\\rm K_{\\rm s}\\geq14.0$ (open circles) were \nincluded. See Section 3 for details. Open diamonds are variable stars. \nThe typical $1\\sigma$ errors are indicated on the left hand side, for \ndifferent magnitudes. Also the effect of visible extinction of \n$\\rm A_V\\,=\\,1.0$ mag is shown with an arrow. \n\\label{fig-2}}\n\n\\figcaption[cmdf04.eps]{Color-magnitude diagrams $\\rm K_{\\rm s}$ vs. \n$\\rm J-K_{\\rm s}$ for $\\rm M\\,15$, $\\rm M\\,56$, $\\rm NGC\\,6553$ and \n$\\rm NGC\\,7099$ with the RGB linear fits. See Section 4.1 for details.\n\\label{fig-3}}\n\n\\figcaption[p07.eps]{RGB slope vs. $\\rm[Fe/H]$ relation. The filled \ncircles are $\\rm M\\,15$ and $\\rm M\\,56$, the triangles are the data from \nKuchinski \\& Frogel (1995), and the open circles are data added from \nother sources (see Section 4.1 for details). The error bars represent \n$\\pm 1\\sigma$ errors. The thick solid line shows our best fit and the \nthick dashed lines show $\\pm 1\\sigma$ error for the slope. The thin \nsolid line shows the best fit and the thin dashed lines show \n$\\pm 1\\sigma$ error of Ferraro et al., (2000). \n\\label{fig-4}}\n\n\\figcaption[c04.eps]{Relation of $\\rm (J-K_{\\rm s})_0(RGB)$ vs. \n$\\rm[Fe/H]$. The cluster symbols are the same as in Figure 4. The thick \nsolid line shows our best fit and the thick dashed lines show \n$\\pm 1\\sigma$ error for the slope. The thin solid line shows the best \nfit and the thin dashed lines show $1\\sigma$ error of Frogel, Cohen \\& \nPersson (1983). The dotted line is the fit of Minitti, Olszewski \\& \nRieke (1995). \n\\label{fig-5}}\n\n\n\\clearpage\n\\plotone{ivanov.fig1.ps}\n\\clearpage\n\\plotone{ivanov.fig2.ps}\n\\clearpage\n\\plotone{ivanov.fig3_col.ps}\n\\clearpage\n\\plotone{ivanov.fig4_col.ps}\n\\clearpage\n\\plotone{ivanov.fig5_col.ps}\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002119
|
Rotations and Abundances \\ of Blue Horizontal-Branch Stars \\ in Globular Cluster M15\altaffilmark{1}
|
[
{
"author": "Bradford B. Behr\\altaffilmark{2}"
},
{
"author": "Judith G. Cohen\\altaffilmark{2}"
},
{
"author": "\\& James K. McCarthy\\altaffilmark{3}"
}
] |
High-resolution optical spectra of eighteen blue horizontal-branch (BHB) stars in the globular cluster M15 indicate that their stellar rotation rates and photospheric compositions vary strongly as a function of effective temperature. Among the cooler stars in the sample, at $\Teff \sim 8500 \unit{K}$, metal abundances are in rough agreement with the canonical cluster metallicity, and the $\vsini$ rotations appear to have a bimodal distribution, with eight stars at $\vsini < 15 \kms$ and two stars at $\vsini \sim 35 \kms$. Most of the stars at $\Teff \ge 10000 \unit{K}$, however, are slowly rotating, $\vsini < 7 \kms$, and their iron and titanium are enhanced by a factor of 300 to solar abundance levels. Magnesium maintains a nearly constant abundance over the entire range of $\Teff$, and helium is depleted by factors of 10 to 30 in three of the hotter stars. Diffusion effects in the stellar atmospheres are the most likely explanation for these large differences in composition. Our results are qualitatively very similar to those previously reported for M13 and NGC~6752, but with even larger enhancement amplitudes, presumably due to the increased efficiency of radiative levitation at lower intrinsic [Fe/H]. We also see evidence for faster stellar rotation explicitly preventing the onset of the diffusion mechanisms among a subset of the hotter stars.
|
[
{
"name": "m15roteps.tex",
"string": "\\documentstyle[11pt, aaspp4]{article} \n\n\\newcommand{\\Teff} {T_{\\rm eff}}\n\\newcommand{\\logg}{\\log g}\n\\newcommand{\\vsini}{v \\sin i}\n\\newcommand{\\kms}{\\, {\\rm km} \\, {\\rm s}^{-1}}\n\\newcommand{\\Weq}{W_\\lambda}\n\\newcommand{\\etal}{{\\it et al.}}\n\\newcommand{\\e}{$\\pm \\;$}\n\\newcommand{\\mc}[2]{\\multicolumn{#1}{c}{#2}}\n\\newcommand{\\unit}[1]{\\, {\\rm #1}}\n\n\\lefthead{Behr}\n\\righthead{BHB Abundances and Rotations in M15}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{document}\n\n\\title{Rotations and Abundances \\\\ of Blue Horizontal-Branch Stars \\\\ in Globular Cluster M15\\altaffilmark{1}}\n\n\\author{Bradford B. Behr\\altaffilmark{2}, Judith G. Cohen\\altaffilmark{2}, \\& James K. McCarthy\\altaffilmark{3}}\n\n\\altaffiltext{1}{Based in large part on observations obtained at the\n\tW.M. Keck Observatory, which is operated jointly by the California \n\tInstitute of Technology and the University of California}\n\\altaffiltext{2}{Palomar Observatory, Mail Stop 105-24,\n\tCalifornia Institute of Technology, Pasadena, CA, 91125}\n\\altaffiltext{3}{PixelVision, Inc., 4952 Warner Avenue, Suite 300, Huntington Beach, CA, 92649}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\clearpage\n\n\\begin{abstract}\n\nHigh-resolution optical spectra of eighteen blue horizontal-branch (BHB) stars in the globular\ncluster M15 indicate that their stellar rotation rates and photospheric compositions vary strongly\nas a function of effective temperature. Among the cooler stars in the sample, at $\\Teff \\sim 8500\n\\unit{K}$, metal abundances are in rough agreement with the canonical cluster metallicity, and the\n$\\vsini$ rotations appear to have a bimodal distribution, with eight stars at $\\vsini < 15 \\kms$ and\ntwo stars at $\\vsini \\sim 35 \\kms$. Most of the stars at $\\Teff \\ge 10000 \\unit{K}$, however, are\nslowly rotating, $\\vsini < 7 \\kms$, and their iron and titanium are enhanced by a factor of 300 to\nsolar abundance levels. Magnesium maintains a nearly constant abundance over the entire range of\n$\\Teff$, and helium is depleted by factors of 10 to 30 in three of the hotter stars. Diffusion\neffects in the stellar atmospheres are the most likely explanation for these large differences in\ncomposition. Our results are qualitatively very similar to those previously reported for M13 and\nNGC~6752, but with even larger enhancement amplitudes, presumably due to the increased efficiency of\nradiative levitation at lower intrinsic [Fe/H]. We also see evidence for faster stellar rotation\nexplicitly preventing the onset of the diffusion mechanisms among a subset of the hotter stars.\n\n\\end{abstract}\n\n\\keywords{globular clusters: general, globular clusters: individual (NGC 7078), \nstars: horizontal-branch, stars: abundances, stars: rotation} \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\clearpage\n\n\\section{Introduction}\n\nM15 (NGC 7078) is one of the most metal-poor globulars known, with a metallicity ${\\rm [Fe/H]} \\sim\n-2.4$~dex measured from red giant abundances (Cohen 1979, Sneden \\etal\\ 1997). Like many other such clusters, M15's horizontal\nbranch lies predominantly bluewards of the instability strip, and color-magnitude diagrams (Buonanno\n\\etal\\ 1983; Durrell \\& Harris 1993) show an extended ``blue tail'' reaching $\\Teff$ as high as\n$20000 \\unit{K}$, which is separated from the horizontal part of the HB by a ``gap'' in the\ndistribution of stars along the HB (Moehler \\etal\\ 1995). Similar gaps appear in the CMDs of M13,\nM80, NGC~6752, NGC~288, and other clusters, but are difficult to explain via standard models of RGB\nmass loss or HB evolution.\n\nRecently, attention has focused on atmospheric effects as a possible explanation for these\nphotometric features (Caloi 1999; Grundahl \\etal\\ 1998). At $\\Teff \\sim 10000 \\unit{K}$, they\nsuggest, the stellar atmospheres become susceptible to diffusion effects, and thus develop chemical\npeculiarities similar to those that appear in main-sequence CP stars. The resulting changes in\natmospheric opacity alter the emitted flux distributions and thus the measured photometry of the\nhotter stars, giving rise to the gaps. These claims have been bolstered by measurements of large\nphotospheric abundance anomalies among hotter BHB stars in M13 (Behr \\etal\\ 1999) and NGC~6752\n(Moehler \\etal\\ 1999), which show 30 to 50 times the iron abundance expected for these metal-poor\nclusters. In M13, the transition from normal-metallicity cooler stars to metal-enhanced hotter stars\nis remarkably abrupt, and coincides with the location of the gap, further supporting the\nsurface-effect hypothesis.\n\nIt appears, however, that stellar rotation also plays some role in this process. Theoretical\ntreatments of the diffusion mechanisms (Michaud \\etal\\ 1983) suggest that circulation currents\ninduced by higher rotation velocities can easily prevent abundance variations from appearing. This\nprediction is borne out by measurements of $\\vsini$ for the M13 stars (Behr \\etal\\ 2000), which show\nthat although the cooler stars exhibit a range of $\\vsini$, some as high as $40 \\kms$, the hot\nmetal-enhanced stars {\\it all} show very low rotations, $\\vsini < 10 \\kms$. This correlation\nsuggests that slow rotation may be required in order for the metal enhancement and helium depletion\nappear in the photosphere.\n\nAlthough these results from M13 and NGC~6752 imply that we are on the right track towards\nexplaining the photometric peculiarities, BHB stars in many other clusters will have to be analyzed\nin a similar fashion before we can make any firm claims. In particular, since the radiative\nlevitation that causes the observed metal enhancements is thought to depend strongly on the\nintrinsic metallicity of the atmosphere, we should study clusters spanning a range of [Fe/H], to see\nwhether the onset and magnitude of the enhancements vary. To this end, we have observed BHB stars in\nfive clusters in addition to M13. In this Letter, we describe the results for both rotation and\nphotospheric abundances in M15. The data for the other clusters --- M92, M68, NGC~288, and M3 --- are being\nanalyzed currently, and will be presented in a future publication.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Observations and Reduction}\n\nThe eighteen stars in our sample were selected from Buonanno \\etal\\ (1983), and are listed in Table\n1. We acquired supplementary Str\\\"omgren photometry of the target stars using the Palomar 60-inch\ntelescope, in order to better constrain the effective temeratures. The stars generally lie in the\ncluster outskirts, where crowding and confusion are less of a problem than towards the core, and our CCD imaging confirmed\nan absence of faint companions.\n\nThe spectra were collected using the HIRES spectrograph (Vogt \\etal\\ 1994) on the Keck I telescope,\nduring four observing runs on 1997 August 01--03, 1997 August 26--27, 1998 June 27, and 1999 August\n14--17. A 0.86-arcsec slit width yielded $R = 45000$ ($v = 6.7 \\kms$) per 3-pixel resolution\nelement. We limited frame exposure times to 1200 seconds, to minimize susceptibility to cosmic ray\naccumulation, and then coadded four frames per star. $S/N$ ratios were on the order of $30-60$\nper resolution element.\n\nWe used a suite of routines developed by J.K. McCarthy (1988) for the FIGARO data analysis package\n(Shortridge 1988) to reduce the HIRES echellograms to 1-dimensional spectra. Frames were\nbias-subtracted, flat-fielded against exposures of HIRES' internal quartz incandescent lamps\n(thereby removing much of the blaze profile from each order), cleaned of cosmic ray hits, and\ncoadded. A thorium-argon arc lamp provided wavelength calibration. Sky background was negligible,\nand 1-D spectra were extracted via simple pixel summation. A 10th-order polynomial fit to line-free\ncontinuum regions completed the normalization of the spectrum to unity.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Analysis}\n\nThe resulting spectra show a few to over 140 metal absorption lines each, with the hottest stars showing the\nlargest number of lines. Line broadening from\nstellar rotation is evident in a few of the stars, but even in the most extreme cases, the line\nprofiles were close to Gaussian, so line equivalent widths ($\\Weq$) were measured by least-square\nfitting of Gaussian profiles to the data. Equivalent widths as small as 10 m\\AA\\ were measured\nreliably, and errors in $\\Weq$ (estimated from the fit $\\chi^2$) were typically 5 m\\AA\\ or less.\nLines were then matched to the atomic line lists of Kurucz \\& Bell (1995), and those that were\nattributed to a single species ({\\it i.e.} unblended) were used to determine radial velocity $v_r$\nfor each of the stars. On the basis of $v_r$, all of the targets appear to be cluster members.\n\nTo derive photospheric parameters $\\Teff$ and $\\logg$, we compared the published photometry and our\nown Str\\\"omgren indices to synthesized colors from ATLAS9 (Kurucz 1997), adopting a cluster\nreddening of $E(B-V) = 0.09$. Temperatures are well-determined ($\\pm$ a few hundred K) for the\ncooler stars, but are somewhat less firm (as much at $\\pm 1000 \\unit{K}$) for the hotter stars. This\nsituation will improve with a more sophisticated treatment of the various Str\\\"omgren colors, and\nby using transitions with different excitation potentials $\\chi$ to constrain $\\Teff$. We estimated surface\ngravities using the $AB_\\nu$ flux method (Oke \\& Gunn 1984), which relates $\\log g$, stellar mass\n$M_*$, distance $d$, and photospheric Eddington flux $H_\\nu$ at 5480~\\AA. Since $AB_\\nu(5480 \\AA) =\nV$ magnitude, we can derive\n$$\n\\log g = 3.68 + \\log(M_*/M_\\odot) + \\log(H_\\nu) - (M-m)_V + 0.4 V_0 \\: ,\n$$\nwhere unextincted magnitude $V_0 = V + A_V = V + 0.30$ for M15. We assumed $M_* = 0.6 M_\\odot$ as a\nrepresentative BHB star mass, used a distance modulus of 15.26 (Silbermann \\& Smith 1995), and drew the $H_\\nu$ \nvalues from the ATLAS9 model atmospheres (Kurucz 1997), iterating until $\\logg$ converged. The resulting\n$\\logg$ values agree well with model ZAHB tracks (Dorman 1993), except for the hotter stars, which\nare ``overluminous'' as described by Moehler \\etal\\ (1995). Table 1 lists the final photospheric\nparameters used for each of the target stars, as well as the heliocentric radial velocities.\n\nFor the chemical abundance analyses, we use the LINFOR/LINFIT line formation analysis package,\ndeveloped at Kiel, based on earlier codes by Baschek, Traving, and Holweger (1966), with subsequent\nmodifications by M. Lemke. Our spectra of these very metal-poor stars are sufficiently uncrowded\nthat we can simply compute abundances from equivalent widths, instead of performing a full spectral\nsynthesis fit. Only lines attributed to a single chemical species were considered; potentially\nblended lines are ignored in this analysis. Upper bounds on [Ti/H] were determined for two of the\nhotter stars, which did not show any titanium lines, by assigning an equivalent width of 20~m\\AA\\\n(double the strength of the weakest metal lines actually measured in those spectra) to the six strongest Ti II transitions\nand calculating the implied abundance. Microturbulent velocity $\\xi$ was chosen such that the\nabundance derived for a single species (Fe II for most cases) was invariant with $\\Weq$. For those\nstars with an insufficient number of lines to utilize this technique, we adopted a typical value of\n$\\xi = 2 \\kms$. We assumed a cluster metallicity of [Fe/H]~$= -2.4$~dex in computing the initial\nmodel atmospheres, and then adjusted as necessary for those stars that turned out to be considerably\nmore metal-rich, although these adjustments to the atmospheric input were found to have only modest\neffects ($< 0.2$ dex) on the abundances of individual elements.\n\nMeasurement of $\\vsini$ broadening traditionally entails cross-correlation of the target spectrum\nwith a rotational reference star of similar spectral type, but this approach assumes that the\ntemplate star is truly at $\\vsini = 0$, which is rare. Furthermore, given the abundance\npeculiarities that many of these BHB stars exhibit, it is difficult to find an appropriate spectral\nanalog. Since we are able to resolve the line profiles of our stars, we instead chose to measure\n$\\vsini$ by fitting the profiles directly, taking into account other non-rotational broadening\nmechanisms. We used bright unsaturated arc lines to construct an instrumental profile, and then\ncombined it with an estimated thermal Doppler broadening of $3 \\kms$ FWHM and the\npreviously-determined $\\xi$. This profile was convolved with hemicircular rotation profiles for\nvarious $\\vsini$ to create the final theoretical line profiles. Each observed line in a spectrum was\nfit to the theoretical profile using an iterative least-squares algorithm, solving for $\\vsini$ and\nline depth. The values for $\\vsini$ from different spectral lines generally agree quite well, once we \nremoved helium lines and blended lines such as the Mg II 4481 triplet.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Results}\n\nIn Figure 1, abundance determinations for key chemical species are plotted as a function of stellar $\\Teff$.\nThe values [X/H] represent logarithmic offsets from the solar values of Anders \\& Grevesse (1993).\nThe error bars incorporate the scatter among multiple lines of the same species, plus \nthe uncertainties in $\\Teff$, $\\logg$, $\\xi$, $\\Weq$ for each line, and [Fe/H] of the input atmosphere.\n\nIn the cooler stars ($\\Teff < 10000 \\unit{K}$), the compositions are largely as expected. The iron abundance\n[Fe/H] averages $-2.5$, slightly below the value of $-2.4$ expected for this metal-poor cluster. Magnesium and\ntitanium appear at [Mg/H]~$\\sim -2.2$ and [Ti/H]~$\\sim -1.8$, respectively, which are also reasonable\nfor this environment.\n\nAs we move to the hotter stars, however, the iron abundances change radically. Six of the eight stars at\n$\\Teff \\ge 10000 \\unit{K}$ show solar iron abundances, [Fe/H]~$\\sim 0$, an enhancement of a factor of 300\nfrom the cooler stars. (The other two hot stars show the same [Fe/H] as the cool stars, for reasons which will be discussed\nshortly.) Titanium, in a similar fashion, rises to [Ti/H]~$> 0$, although there are hints\nof a monatonic increase with $\\Teff$ rather than an abrupt jump. Magnesium, on the other hand, appears to\nbe unaltered, maintaining a roughly constant metal-poor level across the entire temperature range. The hotter\nstars also start to show helium lines, providing evidence of helium depletion, since [He/H]~$\\sim 0$ at \n$11000 \\unit{K}$ but it then drops by factors of 10 to 30 for $\\Teff = 12000$--$13000 \\unit{K}$.\n\nFigure 1 also charts the values of $\\vsini$ derived for the target stars. Among the cooler stars, we find a range of \nrates, with most of the stars rotating at $15 \\kms$ or less, except for two stars at $29 \\kms$ and $36 \\kms$, respectively.\nThis sort of distribution of $\\vsini$ is not what one would expect given a single intrinsic rotation speed $v$ and\nrandom orientation of the rotation axes, since large $\\sin i$ are more likely than small $\\sin i$.\nInstead, the cool end of the HB appears to contain two rotational populations, one with $v \\sim 35 \\kms$, and another with $v \\sim 15 \\kms$,\nmuch like in M13 (Peterson \\etal\\ 1995).\n\nFor the hotter stars, there also appears to be a bimodal distribution in $v$, although the difference is less pronounced.\nSix of these eight stars show $\\vsini < 7 \\kms$, while the other two have $\\vsini \\sim 12 \\kms$. Interestingly,\nthese two faster-rotating hot stars are the same stars that show ``normal'' (metal-poor) iron abundances.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Discussion}\n\nThese BHB stars in M15 exhibit abundance and rotation characteristics very similar to those reported for\nBHB stars in M13 (Behr \\etal\\ 1999 \\& 2000). The enhancements of metals except for magnesium, the\ndepletion of helium, and the difference in maximum $\\vsini$ between hotter and cooler stars are shared\nby both clusters. The abundance anomalies in M15 are therefore likely to be due to the same diffusion processes \nthat were invoked for the prior study --- radiative levitation of metals, and gravitational settling of helium,\nin the stable non-convective atmospheres of the hotter, higher-gravity stars, as hypothesized by Michaud \\etal\\\nUnfortunately, the stars selected in M15 do not sample the immediate vicinity of the photometric gap as\nwell as those in M13, so the association between the onset of diffusion-driven abundance variations and the\ngap is not as clear-cut, but the general trend still supports this association.\n\nThere are, however, two notable differences between the results for M15 and those for M13. First, the\nmagnitudes of the metal enhancements are somewhat different. Iron and titanium are each enhanced by $\\sim 2.5 \\unit{dex}$ in\nM15, while in M13, iron increases by only $\\sim 2 \\unit{dex}$, and titanium by $\\sim 1.5 \\unit{dex}$.\nDespite this difference, the enhancement mechanism yields the same final metallicities for the hot stars in both clusters: [Fe/H]~$\\sim 0$\nand [Ti/H]~$\\sim 0$. This correspondence suggests that the radiative levitation mechanism reaches equilibrium with gravity\nat or near solar metallicity, independent of the initial metal content of the atmosphere, as the metal lines become saturated \nand are thus unable to support further enhancements.\n\nSecond, there is the issue of the two hotter M15 stars which do not show metal enhancement, denoted by circles in\nFigure 1. Their derived temperatures associate\nthem with the hotter population, as does their photometry, which places them bluewards of the photometric gap. Their\niron abudances, however, are $< -2.5 \\unit{dex}$, like the cooler unenhanced stars in the cluster, and stringent upper\nbounds on their titanium abundances again suggest that they are metal-poor. These two stars\nare also distinguished by having $\\vsini \\sim 12 \\kms$, nearly twice as large as any of the other hot stars. Although\ntheir temperatures and gravities are high enough to support radiative levitation, it appears that their faster rotations\ninduce meridonal circulation, which keeps the atmosphere well-mixed and prevents the metal enhancements\nfrom appearing. Such sensitive dependence upon rotation speed was mentioned by Michaud \\etal, but these\nobservations provide direct evidence that rotationally-driven mixing can and does directly influence the atmospheric composition.\n\nWith these results from M15, we add to the growing body of evidence that element diffusion, regulated by\nstellar rotation, are at least partially responsible for the observed photometric morphology of globular cluster\nHBs. The findings from this cluster corroborate the prior work on M13 and NGC~6752, while adding some\nnew twists which further illuminate the diffusion mechanisms. Analysis of many other clusters, spanning\na range of metallicity and HB morphology, will be necessary before all of the implications of these effects\ncan be known.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\acknowledgments\n\nThese observations would not have been feasible without the HIRES spectrograph and the Keck I telescope. We are indebted\nto Jerry Nelson, Gerry Smith, Steve Vogt, and many others for making such marvelous machines, to the W. M. Keck\nFoundation for making it happen, and to a bevy of Keck observing assistants for making them work. J.G.C. and B.B.B. acknowledge\nsupport from NSF Grant AST-9819614.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\clearpage\n\\begin{references}\n\nAnders E., \\& Grevesse, N. 1991, in Solar interior and atmosphere (Tucson:\nUniversity of Arizona Press), 1227\n\nBaschek, B., Holweger, H., Traving, G. 1966, AAHam, 8, 26\n\nBehr, B. B., Cohen, J. G., McCarthy, J. K., Djorgovski, S. G. 1999, ApJ, 517, L135\n\nBehr, B. B., Djorgovski, S. G., Cohen, J. G., McCarthy, J. K., C\\^ot\\'e, P., Piotto, G., Zoccali, M. 2000, ApJ, in press\n\nBuonanno, R., Buscema,�G., Corsi,�C.�E., Iannicola,�G., Fusi�Pecci,�F. 1983, A\\&AS, 51, 83\n\nCaloi, V. 1999, A\\&A, 343, 904\n\nCohen, J. G. 1979, ApJ, 231, 751\n\nDorman, B., Rood, R. T., O'Connell, W. O. 1993, ApJ, 419, 596\n\nDurrell, P. R., Harris, W. E., 1993, AJ, 105, 1420\n\nGrundahl, F., VandenBerg, D. A., \\& Anderson, M. I. 1998, ApJ, 500, L179\n\nKurucz, R. L. \\& Bell, B. 1995, Atomic Line Data, Kurucz CD-ROM 23\n \nKurucz, R. L. 1997, in The Third Conference on Faint Blue Stars, ed. A. G. D. Philip, J. W. Leibert, \\& R. A. Saffer,\n(Schenectady: L. David Press), 33\n\nMcCarthy, J. K. 1988, PhD thesis, California Institute of Technology\n\nMoehler, S., Heber, U., de Boer, K. 1995, A\\&A, 294, 65\n\nMoehler, S., Sweigart, A. V., Landsman, W. B., Heber, U., Catelan, M. 1999, A\\&A, 346, L1 \n\nMichaud, G., Vauclair, G., \\& Vauclair, S. 1983, ApJ, 267, 256\n\nOke, J. B. \\& Gunn, J. E. 1983, ApJ, 266, 713\n\nPeterson, R. C., Rood, R. T., Crocker D. A. 1995, ApJ, 453, 214\n\nShortridge, K. 1988, ``The Figaro Manual Version 2.4''\n\nSilbermann, N. A. \\& Smith, H. A. 1995, AJ, 110, 704\n\nSneden, C., Kraft, R. P., Shetrone, M. D., Smith, G. H., Langer, G. E., Prosser, C. F. 1997, AJ, 114, 1964\n\nVogt, S. E., Allen, S., Bigelow, B., Bresee, L., Brown, B., Cantrall, T.,\nConrad, A., Couture, M., Delaney, C., Epps, H., Hilyard, D., Hilyard, D.,\nHorn, E., Jern, N., Kanto, D., Keane, M., Kibrick, R., Lewis, J.,\nOsborne, C., Osborne, J., Pardeilhan, G., Pfister, T., Ricketts, T.,\nRobinson, L., Stover, R., Tucker, D., Ward, J. \\& Wei, M.\n1994, SPIE, 2198, 362\n\n\\end{references}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\clearpage\n \n\\figcaption[fig1.eps]{Fe, Ti, Mg, and He abundances, and projected rotation velocity $\\vsini$ for BHB\nstars over a range of $\\Teff$. Abundances are plotted as log offsets from the solar abundances.\nCircles indicate the two hot fast-rotating non-metal-enhanced\nstars discussed in the text, and the open symbols in the [Ti/H] plot are upper bounds on the titianium abundance\nfor these two stars.}\n\n\\epsscale{0.5}\n\\plotone{fig1.eps}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\clearpage \n\n\\begin{deluxetable}{llrcrrccr}\n\\tablenum{1}\n\\tablewidth{0pt}\n\\scriptsize\n\\tablecaption{Parameters for program stars}\n\\label{tab1}\n\\tablehead{\n\t\t\t&\t\t\t&\t\t&\t\t\t\t&$v_r$\\quad ~&$\\Teff$~\\quad ~\t\t&\t\t\t\t&$\\xi$ \t\t&$\\vsini\\;\\;$~\t\\nl\nStar\t\t\t&\\quad $V$\t&$B-V$\t&$N_{\\rm lines}$\t&($\\kms$)\t&(K)~\\quad ~\t\t\t&$\\logg$\t\t\t&($\\kms$)\t&($\\kms$)\n}\n\\startdata\nB124 \t\t&15.91\t\t&0.15~\t\t&47\t\t\t&$-106.0$\t&$7900 \\pm\\;\\: 100$\t&$2.80 \\pm 0.05$\t&2\t\t\t&$6.38 \\pm 0.25$\t\t\\nl\nB558 \t\t&15.93\t\t&0.14~\t\t&18\t\t\t&$-95.3$\t\t&$8100 \\pm\\;\\: 100$\t&$3.00 \\pm 0.10$\t&2\t\t\t&$11.55 \\pm 0.63$\t\t\\nl\nB218 \t\t&15.99\t\t&0.16~\t\t&16\t\t\t&$-96.7$\t\t&$8100 \\pm\\;\\: 200$\t&$2.95 \\pm 0.05$\t&2\t\t\t&$14.88 \\pm 0.69$\t\t\\nl\nB78 \t\t\t&15.99\t\t&0.15~\t\t&34\t\t\t&$-110.8$\t&$8200 \\pm\\;\\: 100$\t&$3.05 \\pm 0.05$\t&2\t\t\t&$9.45 \\pm 0.25$\t\t\\nl\nB153 \t\t&15.95\t\t&0.14~\t\t&7\t\t\t&$-113.8$\t&$8300 \\pm\\;\\: 200$\t&$2.95 \\pm 0.05$\t&2\t\t\t&$29.25 \\pm 1.35$\t\t\\nl\nB244 \t\t&15.96\t\t&0.14~\t\t&23\t\t\t&$-116.0$\t&$8300 \\pm\\;\\: 300$\t&$3.05 \\pm 0.10$\t&1\t\t\t&$9.59 \\pm 0.41$\t\t\\nl\nB331 \t\t&16.04\t\t&0.14~\t\t&12\t\t\t&$-108.4$\t&$8300 \\pm\\;\\: 200$\t&$3.05 \\pm 0.05$\t&2\t\t\t&$7.93 \\pm 0.34$\t\t\\nl\nB177 \t\t&16.03\t\t&0.15~\t\t&25\t\t\t&$-110.6$\t&$8600 \\pm\\;\\: 300$\t&$3.00 \\pm 0.05$\t&2\t\t\t&$10.70 \\pm 0.37$\t\t\\nl\nB424 \t\t&15.89\t\t&0.14~\t\t&6\t\t\t&$-106.5$\t&$8600 \\pm\\;\\: 200$\t&$3.05 \\pm 0.10$\t&2\t\t\t&$35.81 \\pm 3.63$\t\t\\nl\nB130 \t\t&15.96\t\t&0.15~\t\t&22\t\t\t&$-115.2$\t&$9000 \\pm 1000$\t\t&$3.05 \\pm 0.10$\t&2\t\t\t&$5.07 \\pm 0.24$\t\t\\nl\nB267\t\t&16.72\t\t&0.03~\t\t&109\t\t&$-115.2$\t&$10000 \\pm\\;\\: 100$\t&$3.55 \\pm 0.10$\t&0\t\t\t&$7.22 \\pm 0.17$\t\t\\nl\nB334\t\t&16.58\t\t&0.02~\t\t&8\t\t\t&$-109.5$\t&$10800 \\pm 1000$\t&$3.55 \\pm 0.10$\t&2\t\t\t&$11.86 \\pm 1.25$\t\t\\nl\nB348\t\t&16.69\t\t&0.01~\t\t&7\t\t\t&$-107.7$\t&$11600 \\pm\\;\\: 800$\t&$3.60 \\pm 0.10$\t&2\t\t\t&$11.20 \\pm 2.68$\t\t\\nl\nB84\t\t\t&16.56\t\t&0.00~\t\t&49\t\t\t&$-109.0$\t&$11700 \\pm 1000$\t&$3.60 \\pm 0.10$\t&0\t\t\t&$6.12 \\pm 0.20$\t\t\\nl\nB279\t\t&16.56\t\t&0.01~\t\t&144\t\t&$-104.8$\t&$12000 \\pm 1000$\t&$3.60 \\pm 0.10$\t&0\t\t\t&$6.25 \\pm 0.11$\t\t\\nl\nB203\t\t&16.68\t\t&$-0.01$~\t&57\t\t\t&$-95.2$\t\t&$12200 \\pm 1000$\t&$3.60 \\pm 0.10$\t&0\t\t\t&$6.47 \\pm 0.27$ \t\t\\nl\nB315\t\t&16.80\t\t&$-0.02$~\t&48\t\t\t&$-104.6$\t&$12800 \\pm\\;\\: 800$\t&$3.75 \\pm 0.10$\t&0\t\t\t&$4.26 \\pm 0.18$\t\t\\nl\nB374\t\t&16.79\t\t&$-0.02$~\t&91\t\t\t&$-107.2\t$\t&$13000 \\pm 1000$\t&$3.70 \\pm 0.10$\t&0\t\t\t&$5.10 \\pm 0.16$\t\t\\nl\n\\nl\n\\multicolumn{4}{l}{mean and dispersion}\t\t\t\t\t&\\multicolumn{2}{l}{\\quad$-106.6 \\pm 7.0$}\n\\enddata\n\\end{deluxetable}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\end{document}\n"
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astro-ph0002120
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The Magellanic Clouds and the Primordial Helium Abundance
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[
{
"author": "Manuel Peimbert \\& Antonio Peimbert"
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A new determination of the pregalactic helium abundance based on the Magellanic Clouds H~II regions is discussed. This determination amounts to $Y_p = 0.2345 \pm 0.0030$ and is compared with those derived from giant extragalactic H~II regions in systems with extremely low heavy elements content. It is suggested that the higher primordial value derived by other authors from giant H~II region complexes could be due to two systematic effects: the presence of neutral hydrogen inside the helium Str\"omgren sphere and the presence of temperature variations inside the observed volume.
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[
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"name": "peimbert.tex",
"string": "\\documentstyle[11pt,newpasp,twoside]{article}\n\\markboth{M. Peimbert \\& A. Peimbert}{The Magellanic Clouds and the Primordial\nHelium Abundance}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{The Magellanic Clouds and the Primordial Helium Abundance}\n \\author{Manuel Peimbert \\& Antonio Peimbert}\n\\affil{Instituto de Astronom\\'{\\i}a, Universidad Nacional Aut\\'onoma de \nM\\'exico. Apdo. Postal 70--264, M\\'exico, D.F. 04510}\n\n\\begin{abstract}\nA new determination of the pregalactic helium abundance based on the Magellanic\nClouds H~II regions is discussed. This determination amounts to $Y_p = 0.2345\n\\pm 0.0030$ and is compared with those derived from giant extragalactic H~II\nregions in systems with extremely low heavy elements content. It is suggested\nthat the higher primordial value derived by other authors from giant H~II\nregion complexes could be due to two systematic effects: the presence of\nneutral hydrogen inside the helium Str\\\"omgren sphere and the presence of\ntemperature variations inside the observed volume.\n\\end{abstract}\n\n\\section{Introduction}\nThe determination of the pregalactic, or primordial, helium abundance by mass\n$Y_p$ is paramount for the study of cosmology, the physics of elementary\nparticles, and the chemical evolution of galaxies (e. g. Fields \\& Olive 1998,\nIzotov et al. 1999, Peimbert \\& Torres-Peimbert 1999, and references\ntherein). In this review we briefly discuss the method used to derive $Y_p$ and\nits main sources of error as well as a new determination based on observations\nof the SMC. This determination is compared with those carried out earlier based\non extremely metal poor extragalactic H~II regions.\n\nThe Magellanic Clouds determination of $Y_p$ can have at least four significant\nadvantages and one disadvantage with respect to those based on distant H~II\nregion complexes: a) no underlying absorption correction for the helium lines\nis needed because the ionizing stars can be excluded from the observing slit,\nb) the determination of the helium ionization correction factor can be\nestimated by observing different lines of sight of a given H~II region, c) the\naccuracy of the determination can be estimated by comparing the results derived\nfrom different points in a given H~II region, d) the electron temperature is\ngenerally smaller than those of metal poorer H~II regions reducing the effect\nof collisional excitation from the metastable 2$^3$ S level of He~I, and e) the\ndisadvantage is that the correction due to the chemical evolution of the SMC is\nin general larger than for the other systems.\n\n\n\n\\section{He$^+$/H$^+$ Determinations}\n\nTo derive accurate He$^+$/H$^+$ values we need very accurate $N_e$ (He~II),\n$T_e$ (He~II), and $\\tau$(3889, He~I) values. Good approximations to determine\nHe$^+$/H$^+$ for $N_e < 300$ cm$^{-3}$, $13~000$~K~$< T_e < 20~000$~K and\n$\\tau(3889) = 0.0$, have been presented for the main helium lines by Benjamin,\nSkillman and Smits (1999):\n\n\\begin{eqnarray}\n\\frac{N({\\rm He}^+)}{N({\\rm H}^+)} & = & \\frac{I(6678)}{I({\\rm H}\\beta)} \n2.58 T_4^{0.249 - 2.0 \\times 10^{-4} N_e}, \\\\\n& = & \\frac{I(4471)}{I({\\rm H}\\beta)} 2.01 T_4^{0.127 - 4.1 \\times \n10^{-4} N_e}, \\\\\n& = & \\frac{I(5876)}{I({\\rm H}\\beta)} 0.735 T_4^{0.230 - 6.3 \\times \n10^{-4} N_e}.\n\\end{eqnarray}\n\n\nFortunately for giant extragalacic H~II regions $\\tau(3889)$ is very small and\nfrequently close to zero. $\\tau(3889)$ can be estimated together with $N_e$\n(He~II) from the 3889/4471 and the 7065/4471 ratios computed by Robbins (1968).\n\nMost authors assume that $T_e$(O~III) = $T_e$(He~II), there are two reasons for\nthis assumption the He$^+$ and O$^{++}$ emission regions occupy similar volumes\n(but not identical ones) and $T_e$(O~III) is easy to measure. Nevertheless the\nassumption is correct only for isothermal nebulae, and not for real nebulae if\nvery accurate abundances are needed. In the presence of temperature variations\nalong the line of sight the [O~III] lines originate preferentially in the high\ntemperature zones and the helium and hydrogen lines in the low temperature\nzones (e.g. Peimbert 1967, 1995). It can be shown that the temperature derived\nfrom the ratio of the Balmer continuum to a Balmer emission line, $T_e$(Bac),\nis similar to $T_e$(He~II), and that both temperatures are smaller than\n$T_e$(O~III).\n\n{From} models computed with CLOUDY (Ferland 1996) it is found that $T_e$(Bac)\n---labeled $T_e$(Hth) by CLOUDY--- is about 5\\% smaller than\n$T_e$(O~III). Moreover in the model with a homogeneous sphere of I~Zw~18 by\nStasinska and Schaerer (1999) it is found that $\\langle T_e({\\rm Ar~III})\n\\rangle = 16300$~K (for 63\\% of the volume) and $\\langle T_e ({\\rm\nAr~IV})\\rangle = 18300$~K (for 36\\% of the volume) indicating the presence of\ntemperature variations. Notice that the average temperature has to be weighted\nby the emissivities strengthening the effect of the temperature variations.\nMoreover there is additional evidence that indicates that the temperature\nvariations are even higher than those predicted by photoionization models\n(e. g. Peimbert 1995; Luridiana, Peimbert, \\& Leitherer 1999; Stasinska and\nSchaerer 1999). From equations (1--3) it follows that the smaller the adopted\ntemperature the smaller the derived He$^+$/H$^+$ value.\n\nDue to the presence of very strong density variations inside gaseous nebulae\nthe different methods to derive the density yield very different values. The\nroot mean square density, $N_e$(rms), is usually obtained from the observed\nflux in a Balmer line and by assuming a spherical geometry; $N_e$(rms) provides\na minimum value for $N_e$(He~II), the local density needed to derive the helium\nabundance. Forbidden line ratios of lines of similar excitation energy give us\nan average density for cases where the density is similar or smaller than the\ncritical density for collisional deexcitation; available line ratios in the\nvisual region are those of [S~II], [O~II], [Cl~III], and [Ar~IV], unfortunately\ngiant extragalactic H~II regions are close to the low density limit of these\nratios, the line intensities of [Cl~III] are very faint, for most observations\nof the [O~II] lines the resolution is not high enough to separate $\\lambda$3726\nfrom $\\lambda$3729 nor $\\lambda$4711 of [Ar~IV] from $\\lambda$4713 of\nHe~I. Consequently most of the densities in the literature are those derived\nfrom the [S~II] lines, but as rightly mentioned by Izotov, Thuan, \\& Lipovetsky\n(1994, 1997) they are not representative of the regions where the He~I lines\noriginate. The self-consistent method, advocated by Izotov and collaborators,\nis based only on line ratios of helium I and is the best method to derive the\ndensity of the He~II zone: $N_e$(He~II).\n\nThe stellar underlying absorption can affect the derived He~I and H~I emission\nline intensities and has to be taken into account. The best way to reduce this\neffect is to avoid the presence of bright early type stars in the observed\nslit, this can only be done for objects inside the Galaxy and the Magellanic\nClouds. To minimize the effect of the underlying absorption it is recommended\nto use only objects where the line intensities show very large equivalent\nwidths in emission, and to increase the spectral resolution. The best way to\ncorrect for underlying absorption is to use starburst models that predict the\nunderlying stellar spectrum. The correction for underlying absorption can be\ntested by comparing the higher order Balmer lines, that are most affected by\nthis effect, with the brightest Balmer lines that are the least\naffected. Similarly the underlying absorption effect is larger for\n$\\lambda$4471 and smaller for $\\lambda\\lambda$5876, 6678 and 7065; the effect\nfor these three lines is in general negligible due to a combination of causes\n(mainly their large equivalent widths in emission).\n\n\\section{Ionization Structure}\n\nThe total He/H value is given by:\n\n\\begin{eqnarray}\n\\frac{N ({\\rm He})}{N ({\\rm H})} & = & \\frac {N({\\rm He}^0) + N({\\rm He}^+) + \nN({\\rm He}^{++})}{N({\\rm H}^0) + N({\\rm H}^+)},\\\\\n& = & ICF({\\rm He}) \\frac {N({\\rm He}^+) + N({\\rm He}^{++})}\n{N({\\rm H}^+)}. \n\\end{eqnarray}\n \nThe He$^{++}$/H$^+$ ratio can be obtained directly from the 4686/H$\\beta$\nintensity ratio. In objects of low degree of ionization the presence of neutral\nhelium inside the H~II region is important and $ICF$(He) becomes larger than\n1. The $ICF$(He) can be estimated by observing a given nebula at different\nlines of sight since He$^0$ is expected to be located in the outer regions.\nAnother way to deal with this problem is to observe H~II regions of high degree\nof ionization where the He$^0$ amount is expected to be negligible.\nV\\'{\\i}lchez \\& Pagel (1988) (see also Pagel et al. 1992) defined a radiation\nsoftness parameter given by\n\n\\begin{equation}\n\\eta = \\frac {N({\\rm O}^+)N({\\rm S}^{++})}{N({\\rm S}^+)N({\\rm O}^{++})};\n\\end{equation} \n\n\\noindent for large values of $\\eta$ the amount of neutral helium is\nsignificant, while for low values of $\\eta$ it is negligible.\n\nOn the other hand for ionization bounded objects of very high degree of\nionization the amount of H$^0$ inside the He$^+$ Str\\\"omgren sphere becomes\nsignificant and the $ICF$(He) can become smaller than 1. This possibility was\nfirstly mentioned by Shields (1974) and studied extensively by Armour et\nal. (1999) for constant density models. Since H$^0$ will be located in a thin\nshell in the border of the nebula it can be shown that for ionization bounded\nnebulae of homogeneous density the fraction of H$^0$/He$^+$ will be three times\nlarger for an observation of the whole object than for an observation of a line\nof sight that includes the center. Similarly this fraction becomes higher than\na factor of three for models with decreasing density from the center\noutwards. Alternatively for density bounded nebulae this effect can be\nneglected.\n\n\n\n\\section{SMC}\n\n\nPeimbert, Peimbert, \\& Ruiz (2000a) presented long slit observations of the\nmost luminous H~II region in the SMC: NGC~346. They divided the two long slit\npositions into thirteen areas, four including the brightest stars ($m \\sim 14$)\nand 9 without stars brighter than $m = 17$. In the upper part of Figure 1 we\npresent a spectrum that includes all the observed areas (region 346--B); while\nin the lower part of Figure 1 we present a spectrum made by the seven brightest\nareas that do not include the brightest stars (region 346--A).\n\n\\begin{figure}\n\\plotfiddle{peimbert_fig1.eps}{220pt}{0}{80}{80}{-175}{-12}\n\\caption{Spectra of NGC~346 with and without underlying absorption. The \nvertical scale is\nfor the lower spectrum (region 346--A). The flux of the upper spectrum \n(region 346--B) was \nnormalized to the\nH$\\alpha$ emission line flux of the lower spectrum.}\n\\end{figure}\n\n\nAfter correcting region 346--A for extinction, based on the four brightest\nBalmer lines, it is found that the weaker Balmer lines (H9 to H12) are not\naffected by stellar underlying absorption (see Figure 1), therefore the He\nlines are not expected to be affected by underlying absorption. The extinction\nderived from the Balmer lines is in very good agreement with the extinction\nderived from the stellar cluster by Massey, Parker, \\& Garmany (1989), another\nindication that the stellar underlying absorption of the Balmer lines is\nnegligible.\n\n\\begin{table}\n\\begin{center}\n\\caption{$N({\\rm He}^+)/N({\\rm H}^+)^a$ and $\\chi^2$ for NGC~346}\n\\begin{tabular}{ccccccc}\n\\noalign{\\smallskip}\n\\tableline\n\\noalign{\\smallskip}\n$T_e$(K) & \\ & \\multicolumn{5}{c}{$N_e$(cm$^{-3}$)}\\\\\n%\\cline{2-6}\n\\noalign{\\smallskip}\n&& 53 & 100 & 143 & 162 & 247\\\\\n\\noalign{\\smallskip}\n\\tableline\n\\noalign{\\smallskip}\n11200 && 805 & 798 & 793 & 791 & {\\bf 781}$^b$ \\\\\n && (83.2) & (47.7) & (26.4) & (20.0) & {\\it (8.24)}$^c$ \\\\\n\\\\\n11800 && 806 & 799 & 793 & {\\bf 790} & 780 \\\\\n && (38.6) & (15.9) & (7.37) & {\\it (6.59)} & (20.4) \\\\\n\\\\\n11950 && 806 & 799 & {\\bf 793} & 790 & 779 \\\\\n && (30.8) & (11.7) & {\\bf (6.53)}$^d$ & (7.25) & (27.7) \\\\\n\\\\\n12400 && 807 & {\\bf 799} & 793 & 790 & 778 \\\\\n && (15.0) & {\\it (7.17)} & (12.5) & (17.9) & (58.6) \\\\\n\\\\\n13000 && {\\bf 809} & 800 & 793 & 790 & 777 \\\\\n && {\\it (9.72)} & (18.2) & (38.4) & (50.2) & (118) \\\\\n\\noalign{\\smallskip}\n\\tableline\n\\tableline\n\\end{tabular}\n\\begin{list}{}{}\n\\item[$^a$]Given in units of $10^{-4}$, $\\chi^2$ values in\nparenthesis.\n\\item[$^b$]The He$^+$/H$^+$ values in boldface correspond to the minimum\n$\\chi^2$ values at a given temperature.\n\\item[$^c$]The minimum $\\chi^2$ value at a given temperature is presented in\nitalics.\n\\item[$^d$]The smallest $\\chi^2$ value for all temperatures and densities is\npresented in boldface, thus defining $T_e$(He~II) and $N_e$(He~II).\n\\end{list}\n\\end{center}\n\\end{table}\n\nTo derive the He$^+$/H$^+$ value, in addition to the Balmer lines, we made use\nof nine He~I lines, $\\lambda\\lambda$ 3889, 4026, 4387, 4471, 4921, 5876, 6678,\n7065, and 7281 to determine $N_e$(He~II) and $T_e$(He~II) self-consistently. In\nTable~1 we present He$^+$/H$^+$ values for different temperatures and\ndensities; the temperatures were selected to include $T_e$(O~III), $T_e$(Bac),\n$T_e$(He~II), and two representative temperatures; the densities were selected\nto include the minimum $\\chi^2$ at each one of the five temperatures. The\ntemperature with the minimum $\\chi^2$ is the self-consistent $T_e$(He~II) and\namounts to $11950\\pm 560$~K; this temperature is in excellent agreement with\nthe temperature derived from the Balmer continuum that amounts to $11800 \\pm\n500$~K, alternatively $T_e$(O~III) amounts to $13070 \\pm 100$~K. Notice that\nthe $\\chi^2$ test requires a higher density for a lower temperature, increasing\nthe dependence on the temperature of the He$^+$/H$^+$ ratio. The values in\nTable~1 correspond to the case where $\\tau$~(3889) equals zero, for higher\nvalues of $\\tau$~(3889) the $\\chi^2$ values increase. In Table~1 the\nHe$^+$/H$^+$ values in boldface and the $\\chi^2$ values in italics correspond\nto the minimum value of $\\chi^2$ at a given $T_e$, the $\\chi^2$ value in\nboldface is the smallest value for all temperatures and all densities.\n\nFrom Table~1 we obtain that $T_e$(He~II)$ = 11950$~K and $N_e$(He~II)$ =\n143$~cm$^{-3}$, which correspond to He$^+$/H$^+ = 0.0793 \\pm 0.007$. By\ncomparing the He/H values for lines of sight with different ionization degree\nit is found that $ICF$(He) = 1.00. To obtain the total He/H value we have added\nthe contribution of He$^{++}$/H$^+$ that amounts to 2.2 x $10^{-4}$.\n\nIn Table~2 we present the helium abundance by mass $Y$(SMC), derived from\nNGC~346. The $Y$(SMC) values were derived from Table~1, the He$^{++}$/H$^+$\nvalues and the $Z$ value determined by Peimbert et al. (2000a).\n\n\\begin{table}\n\\begin{center}\n\\caption{$Y$(SMC)}\n\\begin{tabular}{ccccccc}\n\\noalign{\\smallskip}\n\\tableline\n\\noalign{\\smallskip}\n$T_e$(K) & \\ & \\multicolumn{5}{c}{$N_e$(cm$^{-3}$)}\\\\\n\\noalign{\\smallskip}\n%\\cline{2-6}\n&& 53 & 100 & 143 & 162 & 247\\\\\n\\noalign{\\smallskip}\n\\tableline\n\\noalign{\\smallskip}\n11200 && 0.2431 & 0.2416 & 0.2404 & 0.2399 & {\\bf 0.2377}$^a$ \\\\\n11800 && 0.2435 & 0.2419 & 0.2405 & {\\bf 0.2399} & 0.2375 \\\\\n11950 && 0.2436 & 0.2420 & {\\bf 0.2405} & 0.2399 & 0.2374 \\\\\n12400 && 0.2439 & {\\bf 0.2421} & 0.2406 & 0.2399 & 0.2372 \\\\\n13000 && {\\bf 0.2443} & 0.2423 & 0.2407 & 0.2400 & 0.2370 \\\\ \n\\noalign{\\smallskip}\n\\tableline\n\\tableline\n\\end{tabular}\n\\begin{list}{}{}\n\\item[$^a$]Boldface values correspond to minimum $\\chi^2$ values, see Table~1.\n\\end{list}\n\\end{center}\n\\end{table}\n\n\\section{$Y_p$}\n\nTo determine the $Y_p$ value from the SMC it is necessary to estimate\nthe fraction of helium present in the interstellar medium produced\nby galactic chemical evolution. We will assume that\n \n\\begin{equation}\nY_p = Y({\\rm SMC}) - Z({\\rm SMC}) \\frac{\\Delta Y}{\\Delta Z}.\n\\end{equation} \n\nPeimbert et al. (2000a) find that for $T_e$(He~II)$ = 11950 \\pm 500$~K,\n$Y$(SMC)$ = 0.2405 \\pm 0.0018 $ and $Z$(SMC)$ = 0.00315 \\pm 0.00063 $. To\nestimate $\\Delta Y/\\Delta Z$ we will consider three observational\ndeterminations and a few determinations predicted by chemical evolution models.\n\nPeimbert, Torres-Peimbert, \\& Ruiz (1992) and Esteban et al. (1999) found that\n$Y = 0.2797 \\pm 0.006$ and $Z = 0.0212 \\pm 0.003$ for the Galactic H~II region\nM17, where we have added 0.10dex and 0.08dex to the carbon and oxygen gaseous\nabundances to take into account the fraction of these elements embedded in dust\ngrains (Esteban et al. 1998). By comparing the $Y$ and $Z$ values of M17 with\nthose of NGC~346 (Peimbert et al. 2000a) we obtain $\\Delta Y/\\Delta Z = 2.17\n\\pm 0.4$. M17 is the best H~II region to determine the helium abundance because\namong the brightest galactic H~II regions it is the one with the highest degree\nof ionization and consequently with the smallest correction for the presence of\nHe$^0$ (i.e. $ICF$(He) is very close to unity). It can be argued that the M17\nvalues are not representative of irregular galaxies, on the other hand they\nprovide the most accurate observational determination. {From} a group of 10\nirregular and blue compact galaxies, that includes the LMC and the SMC, Carigi\net al. (1995) found $\\Delta Y/\\Delta Z = 2.4 \\pm 0.6$, where they added 0.2dex\nto the O/H abundance ratios derived from the nebular data to take into account\nthe temperature structure of the H~II regions and the fraction of O embedded in\ndust, moreover they also estimated that O constitutes 54\\% of the $Z$\nvalue. Izotov \\& Thuan (1998) from a group of 45 supergiant H~II regions of low\nmetallicity derived a $\\Delta Y/\\Delta Z = 2.3 \\pm 1.0$; we find from their\ndata that $\\Delta Y/\\Delta Z = 1.5 \\pm 0.6$ by adding 0.2dex to the O\nabundances to take into account the temperature structure of the H~II regions\nand the fraction of O embedded in dust.\n\nBased on their two-infall model for the chemical evolution of the Galaxy\nChiappini, Matteucci, \\& Gratton (1997) find $\\Delta Y/\\Delta Z = 1.6$ for the\nsolar vicinity. Carigi (2000) computed chemical evolution models for the\nGalactic disk, under an inside-out formation scenario, based on different\ncombinations of seven sets of stellar yields by different authors; the $\\Delta\nY/\\Delta Z$ spread predicted by her models is in the 1.2 to 1.9 range for the\nGalactocentric distance of M17 (5.9 kpc).\n\nCarigi et al. (1995), based on yields by Maeder (1992), computed closed box\nmodels adequate for irregular galaxies, like the SMC, and obtained $\\Delta\nY/\\Delta Z = 1.52$. They also computed models with galactic outflows of well\nmixed material, that yielded $\\Delta Y/\\Delta Z$ values similar to those of the\nclosed box models, and models with galactic outflows of O-rich material that\nyielded values higher than 1.52. The maximum $\\Delta Y/\\Delta Z$ value that can\nbe obtained with models of O-rich outflows, without entering into contradiction\nwith the C/O and $(Z {\\rm -C-O)/O}$ observational constraints, amounts to 1.69.\n\nCarigi, Col\\'{\\i}n, \\& Peimbert, (1999), based on yields by Woosley, Langer, \\&\nWeaver (1993) and Woosley \\& Weaver (1995), computed chemical evolution models\nfor irregular galaxies also, like the SMC, and found very similar values for\nclosed box models with bursting star formation and constant star formation\nrates that amounted to $\\Delta Y/\\Delta Z = 1.71$. The models with O-rich\noutflows can increase the $\\Delta Y/\\Delta Z $, but they predict higher C/O\nratios than observed.\n\nFrom the previous discussion it follows that $\\Delta Y/\\Delta Z = 1.9 \\pm 0.5$\nis a representative value for models and observations of irregular\ngalaxies. Moreover, this value is in good agreement with the models and\nobserved values of the disk of the Galaxy.\n\n\\begin{table}\n\\begin{center}\n\\caption{$Y_p$ Derived from the SMC}\n\\begin{tabular}{ccccccc}\n\\noalign{\\smallskip}\n\\tableline\n\\noalign{\\smallskip}\n$T_e$(K) & \\ & \\multicolumn{5}{c}{$N_e$(cm$^{-3}$)}\\\\\n%\\cline{2-6}\n\\noalign{\\smallskip}\n&& 53 & 100 & 143 & 162 & 247\\\\\n\\noalign{\\smallskip}\n\\tableline\n\\noalign{\\smallskip}\n11200 && 0.2363 & 0.2348 & 0.2336 & 0.2331 & {\\bf 0.2309}$^a$ \\\\\n11800 && 0.2373 & 0.2357 & 0.2343 & {\\bf 0.2337} & 0.2313 \\\\\n11950 && 0.2376 & 0.2360 & {\\bf 0.2345} & 0.2339 & 0.2314 \\\\\n12400 && 0.2384 & {\\bf 0.2366} & 0.2351 & 0.2344 & 0.2317 \\\\\n13000 && {\\bf 0.2395} & 0.2375 & 0.2359 & 0.2352 & 0.2322 \\\\\n\\noalign{\\smallskip}\n\\tableline\n\\tableline\n\\end{tabular}\n\\begin{list}{}{}\n\\item[$^a$]Boldface values correspond to minimum $\\chi^2$ values, see Table~1.\n\\end{list}\n\\end{center}\n\\end{table}\n\nThe $Y_p$ values in Table~3 were computed by adopting $\\Delta Y/\\Delta Z = 1.9\n\\pm 0.5$ . The differences between Tables 2 and 3 depend on $T_e$ because the\nlower the $T_e$ value the higher the $Z$ value for the SMC.\n\n\\section{Discussion}\n\nThe $Y_p$ value derived by us is significantly smaller than the value derived\nby Izotov \\& Thuan (1998) from the $Y$ -- O/H linear regression for a sample of\n45 BCGs, and by Izotov et al. (1999) from the average for the two most metal\ndeficient galaxies known (I~Zw~18 and SBS 0335--052), that amount to $0.2443\n\\pm 0.0015$ and $0.2452 \\pm 0.0015$ respectively.\n\nThe difference could be due to systematic effects in the abundance\ndeterminations. There are two systematic effects not considered by Izotov and\ncollaborators that we did take into account, the presence of H$^0$ inside the\nHe$^+$ region and the use of a lower temperature than that provided by the\n[O~III] lines. We consider the first effect to be a minor one and the second to\nbe a mayor one but both should be estimated for each object.\n\nFrom \\ constant \\ density \\ chemicaly \\ homogeneous \\ models \\ computed with\nCLOUDY we estimate that the maximum temperature that should be used to\ndetermine the helium abundance should be 5\\% smaller than\n$T_e$(O~III). Moreover, if there is additional energy injected to the H~II\nregion $T_e$(He~II) should be even smaller.\n\nLuridiana, Peimbert, \\& Leitherer (1999) produced a detailed photoionized model\nof NGC~2363. For the slit used by Izotov, Thuan, \\& Lipovetsky (1997) they find\nan $ICF$(He) = 0.993; moreover they also find that the $T_e$(O~III) predicted\nby the model is considerably smaller than observed. {From} the data of Izotov\net al. (1997) for NGC~2363, adopting a $T_e$(He~II) 10\\% smaller than\n$T_e$(O~III) and $\\Delta Y/\\Delta Z = 1.9 \\pm 0.5$ we find that $Y_p = 0.234\n\\pm 0.006$.\n\nSimilarly, Stasinska \\& Schaerer (1999) produced a detailed model of I~Zw~18\nand find that the photoionized model predicts a $T_e$(O~III) value 15\\% smaller\nthan observed, on the other hand their model predicts an $ICF$(He) = 1.00.\nFrom the observations of $\\lambda\\lambda$ 5876 and 6678 by Izotov et al.\n(1999) of I~Zw~18, and adopting a $T_e$(He~II) 10\\% smaller than $T_e$(O~III)\nwe obtain $Y_p = 0.237 \\pm 0.007$; for a $T_e$(He~II) 15\\% smaller than\n$T_e$(O~III) we obtain $Y_p = 0.234 \\pm 0.007$, both results in good agreement\nwith our determination based on the SMC. Further discussion of these issues is\npresented elsewhere (Peimbert, Peimbert, \\& Luridiana 2000b).\n\nThe primordial helium abundance by mass of $0.2345 \\pm 0.0030 (1 \\sigma)$ ---\nbased on the SMC --- combined with the computations by Copi, Schramm, \\& Turner\n(1995) for three light neutrino species implies that, at the 95 percent\nconfidence level, $\\Omega_b h^2$ is in the 0.0046 to 0.0103 range. For $h =\n0.65$ the $Y_p$ value corresponds to $0.011 < \\Omega_b < 0.024$, a value\nconsiderably smaller than that derived from the pregalactic deuterium\nabundance, $D_p$, determined by Burles \\& Tytler (1998) that corresponds to\n$0.040 < \\Omega_b < 0.050$ for $h$ = 0.65, but in very good agreement with the\nobservational estimate of the global budget of baryons by Fukugita, Hogan, \\&\nPeebles (1998) who find $0.007 < \\Omega_b < 0.038$ for $h$ = 0.65. The\ndiscrepancy between $Y_p$ and $D_p$ needs to be studied further.\n\nTo increase the accuracy of the $Y_p$ determinations we need observations of\nvery high quality of as many He~I lines as possible to derive $T_e$(He~II),\n$N_e$(He~II), and $\\tau$(3889) self-consistently. We also need observations\nwith high spatial resolution to estimate the $ICF$(He) along different lines of\nsight.\n\n\\bigskip\n\nIt is a pleasure to acknowledge several fruitful discussions on this subject\nwith: L. Carigi, V. Luridiana, B. E. J. Pagel, M. T. Ruiz, E. Skillman,\nG. Steigman, S. Torres-Peimbert, and S. Viegas.\n\n\\begin{references}\n\n\\reference Armour, M. H., Ballantyne, D. R., Ferland, G. F., Karr, J., \\& Martin,\nP.G. 1999, PASP, 111, 1251\n\n\\reference Benjamin, R. A., Skillman, E. D., \\& Smits, D. 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astro-ph0002121
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Observations of Faint, Hard-Band X-ray Sources in the Field of \crsscluster\ with the Chandra X-ray Observatory and the Hobby-Eberly Telescope\footnote{Based on observations obtained with the Hobby-Eberly Telescope, which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximillians-Universit\"at M\"unchen, and Georg-August-Universit\"at G\"ottingen.}
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We present results from a study of 2--8~keV X-ray sources detected by the Advanced CCD Imaging Spectrometer (ACIS) instrument on the \chandra\ X-ray Observatory in the field of the $z=0.516$ cluster \crsscluster. In our 63.5~arcmin$^2$ search area, we detect 10 sources with 2--8~keV fluxes down to $\approx 4\times 10^{-15}$~erg~cm$^{-2}$~s$^{-1}$; our lowest flux sources are $\approx 10$ times fainter than those previously available for study in this band. Our derived source density is about an order of magnitude larger than previous source counts above 2~keV, although this density may be enhanced somewhat due to the presence of the cluster. % We detail our methods for source detection and characterization, and we show that the resulting source list and parameters are robust. % We have used the Marcario Low Resolution Spectrograph on the Hobby-Eberly Telescope to obtain optical spectra for several of our sources; combining these spectra with archival data we find that the sources appear to be active galaxies, often with narrow permitted lines, red optical continua or hard X-ray spectra. Four of the X-ray sources are undetected to $R=21.7$; if they reside in $L^\star$ galaxies they must have $z>$~0.55--0.75 and hard X-ray luminosities of $L_{2-8}\simgt 4\times 10^{42}$~erg~s$^{-1}$. % We detect all but one of our 2--8~keV sources in the 0.2--2~keV band as well. This result extends to significantly lower fluxes the constraints on any large, completely new population of X-ray sources that appears above 2--3~keV.
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{
"name": "brandt.tex",
"string": "\n% SAMPLE2.TEX -- AASTeX macro package tutorial paper.\n\n% The first item in a LaTeX file must be a \\documentstyle command to\n% declare the overall style of the paper. The \\documentstyle lines\n% that are relevant for the AASTeX macros are shown; one is uncommented out\n% so that the file can be processed.\n\n%\\documentstyle[12pt,aasms4]{article}\n\\documentstyle[11pt,aaspp4]{article}\n%\\documentstyle[aas2pp4]{article}\n\n% The eqsecnum style changes the way equations are numbered. Normally,\n% equations are just numbered sequentially through the entire paper.\n% If eqsecnum appears in the \\documentstyle command, equation numbers will\n% be sequential through each section, and will be formatted \"(sec-eqn)\",\n% where sec is the current section number and eqn is the number of the\n% equation within that section. The eqsecnum option can be used with\n% any substyle.\n\n%\\documentstyle[11pt,eqsecnum,aaspp4]{article}\n\n% Authors are permitted to use the fonts provided by the American Mathematical\n% Society, if they are available to them on their local system. These fonts\n% are not part of the AASTeX macro package or the regular TeX distribution.\n\n%\\documentstyle[12pt,amssym,aasms4]{article}\n\n% Here's some slug-line data. The receipt and acceptance dates will be \n% filled in by the editorial staff with the appropriate dates. Rules will \n% appear on the title page of the manuscript until these are uncommented \n% out by the editorial staff.\n\n%\\received{4 August 1988}\n%\\accepted{23 September 1988}\n%\\journalid{337}{15 January 1989}\n%\\articleid{11}{14}\n\n% \\slugcomment{To appear in The Astrophysical Journal Letters}\n\n% Authors may supply running head information, if they wish to do so, although\n% this may be modified by the editorial offices. The left head contains a\n% list of authors, usually three allowed---otherwise use et al. The right\n% head is a modified title of up to roughly 44 characters. Running heads\n% are not printed.\n\n\\lefthead{Brandt et al.}\n\\righthead{X-Ray Background}\n\n%\n\\def\\simgt{\\lower 2pt \\hbox{$\\, \\buildrel {\\scriptstyle >}\\over {\\scriptstyle\n\\sim}\\,$}}\n\\def\\simlt{\\lower 2pt \\hbox{$\\, \\buildrel {\\scriptstyle <}\\over {\\scriptstyle\n\\sim}\\,$}}\n%\n%\n\\def\\sss{\\vskip 0.2truecm}\n\\def\\etal{{\\it et al. }}\n%\n%\n\\def\\apj{{\\it Ap.J.}}\n\\def\\aa{{\\it Astr. Ap.}}\n\\def\\mnras{{\\it M.N.R.A.S.}}\n\\def\\spascirev{{\\it Space Sci. Rev.}}\n\\def\\nature{{\\it Nature}}\n\\def\\araa{{\\it Ann. Rev. Astr. Ap.}}\n\\def\\pasj{{\\it Publ. Astr. Soc. Jap.}}\n%\n%\n\\def\\pn{\\par\\noindent}\n\\def\\ss{\\smallskip\\pn}\n\\def\\ms{\\medskip\\pn}\n\\def\\bs{\\bigskip\\pn}\n%\n%\n\\def\\abrixas{{\\it ABRIXAS\\/}}\n\\def\\ariel{{\\it Ariel-V\\/}}\n\\def\\asca{{\\it ASCA\\/}}\n\\def\\astroe{{\\it Astro-E\\/}}\n\\def\\chandra{{\\it Chandra\\/}}\n\\def\\conx{{\\it Constellation-X\\/}}\n\\def\\euve{{\\it {\\it EUVE}\\/}}\n\\def\\einstein{{\\it Einstein\\/}}\n\\def\\exosat{{\\it EXOSAT\\/}}\n\\def\\ginga{{\\it Ginga\\/}}\n\\def\\heao1{{\\it HEAO-1\\/}}\n\\def\\hst{{\\it {\\it HST}\\/}}\n\\def\\iras{{\\it IRAS\\/}}\n\\def\\iue{{\\it IUE\\/}}\n\\def\\rosat{{\\it ROSAT\\/}}\n\\def\\rxte{{\\it RXTE\\/}}\n\\def\\sax{{\\it BeppoSAX\\/}}\n\\def\\xmm{{\\it XMM\\/}}\n\\def\\vela5b{{\\it Vela-5B\\/}}\n\\def\\xte{{\\it XTE\\/}}\n%\n\\def\\crsscluster{CRSS~J0030.5+2618}\n\\def\\crssqso{CRSS~J0030.6+2620}\n\\def\\crsssy2{CRSS~J0030.7+2616}\n%\n\\def\\todo{{\\Huge $\\bullet$}}\n%\n% This is the end of the \"preamble\". Now we wish to start with the\n% real material for the paper, which we indicate with \\begin{document}.\n% Following the \\begin{document} command is the front matter for the\n% paper, viz., the title, author and address data, the abstract, and\n% any keywords or subject headings that are relevant.\n\n\\begin{document}\n\n\\title{Observations of Faint, Hard-Band X-ray Sources \nin the Field of \\crsscluster\\ with the Chandra X-ray Observatory \nand the Hobby-Eberly Telescope\\footnote{Based on \nobservations obtained with the Hobby-Eberly\nTelescope, which is a joint project of the University of Texas at Austin,\nthe Pennsylvania State University, Stanford University,\nLudwig-Maximillians-Universit\\\"at M\\\"unchen, and Georg-August-Universit\\\"at\nG\\\"ottingen.}\n}\n\n% \\author{REPORT---PLEASE DO NOT DISTRIBUTE}\n\n\\author{\nW.N.~Brandt\\altaffilmark{\\ref{PennState}},\nA.E.~Hornschemeier\\altaffilmark{\\ref{PennState}},\nD.P.~Schneider\\altaffilmark{\\ref{PennState}},\n%\nG.P.~Garmire\\altaffilmark{\\ref{PennState}},\n%\nG.~Chartas\\altaffilmark{\\ref{PennState}},\nGary~J.~Hill\\altaffilmark{\\ref{Texas}},\nP.J.~MacQueen\\altaffilmark{\\ref{Texas}}, \nL.K.~Townsley\\altaffilmark{\\ref{PennState}},\n%\nD.N.~Burrows\\altaffilmark{\\ref{PennState}},\nT.S.~Koch\\altaffilmark{\\ref{PennState}},\nJ.A.~Nousek\\altaffilmark{\\ref{PennState}} and\nL.W.~Ramsey\\altaffilmark{\\ref{PennState}}\n}\n\n% Notice that each of these authors has alternate affiliations, which\n% are identified by the \\altaffilmark after each name. The actual alternate\n% affiliation information is typeset in footnotes at the bottom of the\n% first page, and the text itself is specified in \\altaffiltext commands.\n% There is a separate \\altaffiltext for each alternate affiliation\n% indicated above.\n\n\\newcounter{address}\n\\setcounter{address}{2}\n\\altaffiltext{\\theaddress}{Department of Astronomy and Astrophysics,\nThe Pennsylvania State University, University Park, PA 16802\n\\label{PennState}}\n\\addtocounter{address}{1}\n\\altaffiltext{\\theaddress}{McDonald Observatory,\nUniversity of Texas, Austin, TX 78712\n\\label{Texas}}\n\\addtocounter{address}{1}\n\n% The abstract environment prints out the receipt and acceptance dates\n% if they are relevant for the journal style. For the aasms style, they\n% will print out as horizontal rules for the editorial staff to type\n% on, so long as the author does not include \\received and \\accepted\n% commands. This should not be done, since \\received and \\accepted dates\n% are not known to the author.\n\n\\vbox{\n\\begin{abstract}\nWe present results from a study of 2--8~keV X-ray sources detected by\nthe Advanced CCD Imaging Spectrometer (ACIS) instrument \non the \\chandra\\ X-ray Observatory\nin the field of the $z=0.516$ cluster \\crsscluster. \nIn our 63.5~arcmin$^2$ search area, we detect 10 sources with \n2--8~keV fluxes down to $\\approx 4\\times 10^{-15}$~erg~cm$^{-2}$~s$^{-1}$;\nour lowest flux sources are $\\approx 10$ times fainter than those \npreviously available for study in this band. Our derived source\ndensity is about an order of magnitude larger than previous source \ncounts above 2~keV, although this density may be enhanced somewhat \ndue to the presence of the cluster. \n%\nWe detail our methods for source detection and characterization,\nand we show that the resulting source list and parameters are robust. \n%\nWe have used the Marcario Low Resolution Spectrograph on the Hobby-Eberly \nTelescope to obtain optical spectra for several of our sources; combining \nthese spectra with archival data we find that the sources \nappear to be active galaxies, often with\nnarrow permitted lines, red optical continua or hard X-ray spectra. Four of \nthe X-ray sources are undetected to $R=21.7$; if they reside in \n$L^\\star$ galaxies they must have $z>$~0.55--0.75 and hard X-ray \nluminosities of $L_{2-8}\\simgt 4\\times 10^{42}$~erg~s$^{-1}$. \n%\nWe detect all but one of our 2--8~keV sources in \nthe 0.2--2~keV band as well. This result extends to \nsignificantly lower fluxes the constraints on any large, completely new \npopulation of X-ray sources that appears above 2--3~keV. \n\\end{abstract}\n}\n% The different journals have different requirements for keywords. The\n% keywords.apj file, found on aas.org in the pubs/aastex-misc directory, \n% contains a list of keywords used with the ApJ and Letters. These are \n% usually assigned by the editor, but authors may include them in their \n% manuscripts if they wish. \n\n\\keywords{diffuse radiation --- surveys --- X-rays: galaxies --- X-rays: general}\n\n% That's it for the front matter. On to the main body of the paper.\n% We'll only put in tutorial remarks at the beginning of each section\n% so you can see entire sections together.\n\n% In the first two sections, you should notice the use of the LaTeX \\cite\n% command to identify citations. The citations are tied to the\n% reference list via symbolic KEYs. We have chosen the first three\n% characters of the first author's name plus the last two numeral of the\n% year of publication. The corresponding reference has a \\bibitem\n% command in the reference list below.\n%\n% Please see the AASTeX manual for a more complete discussion on how to make\n% \\cite-\\bibitem work for you. \n\n% -------------------------------------------------------------------------\n\n\\section{Introduction}\n\nAbout 70\\% of the extragalactic \nX-ray background in the soft 0.5--2~keV band has been \nresolved into discrete sources by pencil-beam surveys with the \\rosat\\ \nsatellite (e.g., \\cite{has98}). The 0.5--2~keV \nsource counts have reached a surface \ndensity of $\\approx 1000$~deg$^{-2}$ at a discrete source \ndetection limit of $\\approx 10^{-15}$~erg~cm$^{-2}$~s$^{-1}$,\nand simple extrapolations suggest that all of the 0.5--2~keV \nextragalactic X-ray background will be resolved by a flux limit of \n$\\sim 2\\times 10^{-16}$~erg~cm$^{-2}$~s$^{-1}$\nat which the surface density will be $\\sim 3000$~deg$^{-2}$.\n%\nOptical identification programs (e.g., \\cite{schmidt98})\nhave established that type~1 Active Galactic Nuclei (AGN),\nsuch as Seyfert~1 galaxies and Quasi-Stellar Objects (QSOs), \nare the dominant contributors above a 0.5--2~keV flux of \n$\\approx 5\\times 10^{-15}$~erg~cm$^{-2}$~s$^{-1}$. \nA non-negligible number (about 16\\%) of type~2 AGN are\nseen as well. \n\nLargely due to instrumental limitations, the nature of the sources\nthat produce the $>2$~keV X-ray background is much less certain\nat present. It is important to solve this mystery since \nmost of the energy density in the X-ray background is located above \nthe \\rosat\\ band. The best current constraints on the sources of\nthe 2--10~keV X-ray background have come from the \\asca\\ and \\sax\\\nsatellites. Long observations with these satellites have reached \ndiscrete source detection limits of \n$\\approx$~(3--5)$\\times 10^{-14}$~erg~cm$^{-2}$~s$^{-1}$\nand have resolved $\\approx 30$\\% of the 2--10~keV background\ninto discrete sources (e.g., Ogasaka et~al. 1998;\nGiommi, Fiore \\& Perri 1999). The integrated number of sources, $N$, \nis consistent with the law $N(>S)\\propto S^{-3/2}$ \nexpected for a uniform distribution of sources in Euclidean space.\nThe deepest 2--10~keV source counts to date have\nresolved $\\approx 60$ sources deg$^{-2}$.\nThe faintest 2--10~keV sources appear to have \nflatter spectra (with energy indices of $\\alpha\\approx 0.5\\pm 0.2$) \nthan those of typical unabsorbed AGN (e.g., Ueda et~al. 1998), \nsuggesting that a population of sources with spectra similar to that \nof the integrated X-ray background dominates above 2~keV. The population\nis thought to be at least partially composed of obscured AGN, and some\nof these hard sources have indeed been associated with such \nobjects (e.g., Fiore et~al. 1999; Akiyama et~al. 2000). An\nimportant result, however, is that the majority of the hard sources\nfound thus far appear to have counterparts in the soft X-ray \nband (Giommi, Fiore \\& Perri 1998). Obscured AGN might still\ncreate soft X-ray emission via electron-scattered X-rays or\ndue to non-nuclear X-ray emission (e.g. starburst activity). \n\nThe arcsecond imaging quality and high-energy sensitivity of\nthe \\chandra\\ X-ray Observatory (\\cite{wod96}) promises to \nrevolutionize our understanding of the X-ray background above 2~keV. \nThe source confusion and misidentification problems that have\ndogged earlier hard X-ray surveys will be eliminated. \n%\nIn this paper, we use data from \\chandra, the 8-m class Hobby-Eberly \nTelescope (HET), and public archives to study a small but well-defined \nsample of faint X-ray sources in the 2--8~keV band. Our sample contains \nseveral of the faintest $>2$~keV sources yet detected and identified. \nWe address (1) the number counts at faint hard X-ray fluxes,\n(2) the nature of the faint hard X-ray sources, and (3) the issue of \nwhether most faint hard X-ray sources have soft X-ray counterparts. \n%\nOur X-ray sources\nlie in the PG~0027+260 (an eclipsing cataclysmic variable) field\nof the Cambridge-Cambridge \\rosat\\ Serendipity Survey \n(e.g., Boyle, Wilkes \\& Elvis 1997). This field contains \n\\crsscluster, a $z=0.516$ cluster of galaxies, and it was\nobserved by \\chandra\\ for 44~ks during its first month of \ncalibration-phase operations. \n%\nThe Galactic column density along this line of sight is\n$(3.9\\pm 0.4)\\times 10^{20}$~cm$^{-2}$ (Stark et~al. 1992),\ncorresponding to an optical depth of $\\tau<0.02$ for the\n2--8~keV band of primary interest here. \n%\nIn this paper we assume \n$H_0=70$~km~s$^{-1}$ Mpc$^{-1}$ and $q_0=\\frac{1}{2}$.\n\n% -------------------------------------------------------------------------\n\n\\section{X-ray Observations and Data Analysis}\n\n\\subsection{ACIS Observation Details and Image Creation}\n\nThe field containing \\crsscluster\\ was observed with the \\chandra\\ Advanced \nCCD Imaging Spectrometer (ACIS; \\cite{garnou99a}; Garmire et~al. 2000, in preparation) \nfor a total exposure time of 44~ks on 1999~August~17. \n%\nACIS consists of ten CCDs designed for efficient\nX-ray detection and spectroscopy. Four of the CCDs \n(ACIS-I; CCDs I0--I3) are arranged in a\n$2\\times 2$ array with each CCD tipped slightly to approximate the\ncurved focal surface of the \\chandra\\ High Resolution Mirror Assembly (HRMA). \nThe remaining six CCDs (ACIS-S; CCDs S0--S5) are set in a linear array \nand tipped to approximate the Rowland circle of the objective gratings that \ncan be inserted behind the HRMA. The CCD which lies on-axis in ACIS-S (S3) \nis orthogonal to the HRMA optical axis. It is a back-illuminated \nCCD that is sensitive for imaging soft X-ray objects. \nEach CCD subtends \\hbox{an $8.3^{\\prime}\\times 8.3^{\\prime}$} square on \nthe sky. The individual pixels of the CCDs subtend \n$\\approx 0.5^{\\prime\\prime}\\times 0.5^{\\prime\\prime} $ on the sky.\n%\nThe on-axis image quality of the telescope is approximately~$0.5^{\\prime\\prime}$ \n(FWHM); this quantity increases to~$\\approx 1.0^{\\prime\\prime}$ (critical sampling \non the detector) at an off-axis angle of~$\\approx 2^{\\prime}$. The image size also \nhas a weak energy dependence, with poorer quality at higher energy. \n\nThe observation was performed in two segments (observation ID \nnumbers 1190 and 1226), separated by 1.0~ks. \n%\n\\crsscluster\\ was placed at the aim point for the ACIS-S array \n(on CCD S3) during the observation. The aim point position was \n$\\alpha_{2000}=00^{\\rm h} 30^{\\rm m} 32.5^{\\rm s}$,\n$\\delta_{2000}=+26^\\circ 18^\\prime 13.4^{\\prime\\prime}$. \n%\nThe focal plane temperature was $-99.3^\\circ$C.\nFaint mode was used for the event telemetry format, and \\asca\\ \ngrade~7 events were rejected on orbit to prevent telemetry\nsaturation (see \\S5.7 of the {\\it AXAF Observatory Guide\\/} for\na discussion of grades).\n%\nOnly one 3.3~s frame was `dropped' from the telemetry. \n\nHere we will focus on the data from CCD S3 since it has not \nshown the charge transfer inefficiency (CTI) increase that has affected\nthe front-illuminated CCDs (see \\cite{garnou99b}). \nTo avoid problems associated with the dither of \\chandra\\\n(see \\S4.9.2 of the {\\it AXAF Observatory Guide\\/}), we \nalso neglect data within $20^{\\prime\\prime}$ of the edge of S3. \nOur search area thus comprises 63.5 square arcminutes or\n92\\% of S3. The two observation segments were co-added \nusing the {\\sc event browser} software (\\cite{broos99}). We \nused the CIAO {\\sc datamodel} software, provided by the \\chandra\\ X-ray \nCenter, to create $\\approx 0.5^{\\prime\\prime}$~pixel$^{-1}$ images in the\n`full' (0.2--8~keV), \n`soft' (0.2--2~keV), and\n`hard' (2--8~keV) bands\n(neglecting the 8--10~keV data improves the signal-to-noise \nratio in the hard band; e.g., Baganoff 1999). \nOur 0.2, 2, and 8~keV band boundaries have uncertainties of\n80~eV, 20~eV and 160~eV, respectively. These uncertainties are\nsmaller than or comparable to the S3 spectral resolution, and \nthe 0.2 and 8~keV uncertainties are innocuous due to the small \neffective area of HRMA/ACIS below 0.3~keV and above 8~keV.\nThe 2~keV band boundary is furthermore convenient because it is\nclose to the energy of the HRMA response drop due to the\niridium M-edge. \n\nWe have only used events with ACIS grades of 0, 2, 8, 16 and 64. \nFor the background level during this observation, this \nconservative grade set appears to \nprovide the best overall performance when trying \nto detect faint, hard sources on S3, although we explore other grade \nset choices in \\S2.4. For this 44~ks observation, the average \nbackground in the hard band varies across S3 in the \nrange $\\approx$~0.03--0.05~count~pixel$^{-1}$. \n\nWe corrected the \\chandra\\ astrometry by comparison with \n\\rosat\\ HRI, Palomar Optical Sky Survey (POSS), and \nIsaac Newton Telescope data (see below). The QSO \n\\crssqso\\ ($z=0.493$) and the Seyfert~2 \\crsssy2\\ ($z=0.247$) were \nparticularly useful in this regard (see Boyle et~al. 1995 and\nBoyle et~al. 1997). \n\n\\subsection{Source Searching}\n\nWe used the CIAO {\\sc wavdetect} software (Dobrzycki et~al. 1999;\nFreeman et~al. 2000) to search our \nimages for sources. Our primary interest is in 2--8~keV \npoint sources. We used a significance threshold of $1\\times 10^{-6}$ \nand computed 5 scaled transforms for wavelet scale sizes \nof 1, 2, 4, 6 and 8 pixels. In our hard band image, we have detected \n9 point sources on S3.\\footnote{We also detect a source at\n$\\alpha_{2000}=00^{\\rm h} 30^{\\rm m} 57.8^{\\rm s}$,\n$\\delta_{2000}=+26^\\circ 17^\\prime 44.3^{\\prime\\prime}$, but this\nsource lies $\\approx 19^{\\prime\\prime}$ from the edge of S3\nand is hence excluded from consideration.}\nThese are listed in Table~1 and shown in Figures~\\ref{fig1} \nand \\ref{fig2}. \n%\nWe estimate that our absolute positions in the hard band are good to \nwithin $\\approx 3^{\\prime\\prime}$. They are therefore of \ncomparable quality to those used in the \\rosat\\ High-Resolution Imager \nsurvey of the Lockman Hole (Hasinger et~al. 1998), and they are\n{\\it much\\/} better than earlier positions in the hard X-ray band. \n%\nAll of these sources, except source~5, were also detected in \nthe independent soft-band image (usually with a significantly higher\nnumber of counts), giving us confidence in their reality.\nThe relative positional agreement between hard-band and soft-band sources\nwas typically better than $1^{\\prime\\prime}$. Given this relative\npositional agreement, the probability\nthat any given source is a false match is $\\approx 0.2$\\%. \nWhile the background in the soft band has significant spatial\nstructure due to instrumental effects (e.g., node boundaries) and\nthe presence of the cluster, this does not appear to affect our\nmatching of hard and soft sources. Source~7 lies at a position where\nthe soft-band background is elevated by $\\approx 25$\\% by the \ncentral node boundary. This elevated background arises due to\ncosmic rays interacting with the physically separated frame \nstore regions of the S3 CCD, and it is blurred when the \n\\chandra\\ dither is removed by the pipeline software. \nThe slightly elevated background does not \ncompromise the detection of source~7, but our soft-band \nphotometry may have a small systematic error in addition to the\nstatistical error given in Table~1. In addition, we \nare confident that none of our sources is due to a `hot pixel' because \nthese would show the characteristic Lissajous dither pattern from \nthe spacecraft aspect.\n%\nWe have compared the angular extents of our sources with the 90\\%\nencircled energy radius of the \\chandra\\ PSF\n(see \\S3.8 of the {\\it AXAF Observatory Guide\\/}), and \nalthough the photon statistics are limited\nwe find no clear evidence for anomalous extent. \n\nWe have compared our number counts in the soft band with those of\nHasinger et~al. (1998) as a rough consistency check. Hasinger et~al. (1998) \nfound $940\\pm 170$~sources~deg$^{-2}$ at a 0.5--2~keV flux level\nof $1\\times 10^{-15}$~erg~cm$^{-2}$~s$^{-1}$. Our source density in\nthe soft band is $1500\\pm 300$~sources~deg$^{-2}$ at a 0.2--2~keV \nflux level of $\\approx 6\\times 10^{-16}$~erg~cm$^{-2}$~s$^{-1}$.\nFor plausible bandpass corrections, our number counts are roughly\nconsistent with a simple extrapolation of the Hasinger et~al. (1998) \n$\\log N$--$\\log S$ relation. We note that there is probably an\nenhancement in our number counts due to the presence of the\ncluster \\crsscluster\\ (see \\S4 for further discussion). \n\nThe minimum detectable 2--8~keV flux varies across S3 due to\neffects such as point spread function (PSF) broadening, \nvignetting, and spatially dependent CTI. Within \n$3.5^\\prime$ of the aim point, \nwe estimate our flux limit to be \n(4--5)$\\times 10^{-15}$~erg~cm$^{-2}$~s$^{-1}$ (corresponding to\n$\\approx 6$ counts), while at larger off-axis angles our flux\nlimit increases fairly quickly (e.g., see Figure~6.5 of the\n{\\it AXAF Proposers' Guide\\/}). While this spatially dependent flux\nlimit should be kept in mind, none of our main results below \nis sensitive to the precise details of our flux limit. Even at \nthe locations on S3 furthest from the aim point, the observation is\n$\\simgt 5$ times deeper than previous hard X-ray surveys. \n\n\\subsection{Source Parameterization}\n\n{\\sc wavdetect} performs photometry on detected sources, and \nwe have cross checked the {\\sc wavdetect} results with\nmanual aperture photometry. We find good agreement between \nthe two techniques for all \nsources other than source~2, where the {\\sc wavdetect} photometry\nclearly has failed ({\\sc wavdetect} finds source~2 but claims \nit only has 0.9 counts in the\nhard band). In Table~1 we quote our manual photometry results for \nsource~2 and {\\sc wavdetect} photometry results for all \nother sources. These have not been corrected for vignetting. \n%\nWe also quote the `band ratio' defined as the ratio of hard-band to \nsoft-band counts. The errors for our band ratio values have\nbeen computed following the `numerical method' described in \n\\S1.7.3 of Lyons (1991); in the Poisson limit this method is more \nreliable than the standard approximate variance formula\n(e.g., see \\S3.3 of Bevington \\& Robinson 1992). \nIn Figure~3 we compare our band ratios to power-law models\nwith varying amounts of neutral absorption. Several of our\nsources appear likely to suffer significant internal\nX-ray absorption. \n%\nIn addition, {\\sc wavdetect} reports a significance level for\neach source, defined as the number of source counts divided by\nthe Gehrels (1986) standard deviation of the number of\nbackground counts (see Table~1). For source~2 we\nhave calculated the 2--8~keV significance using \nour manual photometry. We do not report a 0.2--2~keV \nsignificance for source~5 because it is not detected in this \nband. \n\nWe have used {\\sc event browser} to create full-band light curves \nfor our sources. We analyzed these for variability using \na Kolmogorov-Smirnov test. Most of our sources do not show \nsignificant evidence for variability. Source~8 may show\nvariability by a factor of $\\approx 2$ on a timescale of\n$\\approx 10000$~s. The fact that the photon arrival times\nfor our sources are distributed fairly evenly throughout the \nobservation length is a further argument against some brief, \ntransient effect (e.g., a transient `hot pixel' or a cosmic ray) \nproducing spurious sources. We have also examined the energy and \nACIS grade distributions for our sources and find no anomalies \nthat might indicate spurious instrumental effects. \n\nWe have calculated vignetting-corrected\n0.2--2~keV and 2--8~keV fluxes for our sources \nusing the counts from Table~1, and these are given in Table~2.\nWe assume a $\\Gamma=1.9$ power-law model with the Galactic column \ndensity, and our fluxes have not been corrected for Galactic\nor internal absorption. Our 2--8~keV observed fluxes (those of\nprimary scientific interest here) are quite insensitive to the\nassumed column density for $N_{\\rm H}\\simlt 10^{22}$~cm$^{-2}$\n(compare with Figure~3). Our 0.2--2~keV fluxes are somewhat\nmore sensitive to the assumed column density; for our sources\nwith large band ratios the 0.2--2~keV fluxes calculated with \nGalactic absorption are 5--20\\% lower than those calculated using\n$\\Gamma=1.9$ and column densities estimated from Figure~3. \n%\nFor our flux calculations, we have used the calibration-phase ACIS \nredistribution matrix files (rmfs) from the ACIS calibration group\n(S.~Buczkowski \\& N.~Schulz, private communication), and\nwe have also used the calibration-phase ancillary response\nfiles (arfs; N. Schulz, private communication). These spectral\nresponses are for a focal plane temperature of $-100^\\circ$C, and\nthey assume filtering upon \\asca\\ grades 0, 2, 3, 4~and 6. To correct\nfor our more conservative choice of grades, we have multiplied\nour 0.2--2~keV fluxes by a factor of $1.23\\pm 0.12$ and our 2--8~keV \nfluxes by a factor of $1.53\\pm 0.23$ (statistical errors only). \nThese factors have been determined by comparing \nthe numbers of events for our sources obtained\nwith the two different grade filtering methods\n(source~6 is excluded in these comparisons since it would\notherwise dominate the results; we compute separate factors\nfor source~6 of $1.39\\pm 0.06$ and $1.80\\pm 0.16$). We estimate\nthat our fluxes have calibration uncertainties of $\\sim 30$\\%, but it \nis clear that we are detecting 2--8~keV sources {\\it much\\/} fainter\nthan were detected with \\asca\\ and \\sax. \n\nIn addition to the sources described above, we will introduce\ntwo new sources below: \nsource~AG1 (found on S3 when \\asca\\ grade filtering is used; see \\S2.4)\nand\nsource~I3 (found on ACIS CCD I3; see \\S3.2). \n%\nTo compute fluxes for source~AG1, we have followed\nthe method of the previous paragraph but have not made the grade \ncorrection (since we use \\asca\\ grade filtering for this\nsource). \n%\nTo compute fluxes for source~I3, we again\nfollowed the method of the previous paragraph. However, ACIS \nI3 spectral responses are only available at present\nfor a focal plane temperature of $-90^\\circ$C. We have used\nthese but recognize that this may introduce systematic error into\nour flux calculations for source~I3. Therefore, we do not use \nthe fluxes for source~I3 in any of our subsequent analysis. \n\n\\subsection{Additional Safety Checks}\n\nThe background level in the S3 CCD shows significant flaring during\nthe observation due to `space weather' (primarily soft electrons\ninteracting with the CCD). We have repeated the analysis above \nafter editing out the 8.0~ks when the background level was \nhighest. We find the same 2--8~keV sources as those listed in Table~1 \nexcept that source~4 is not detected in the edited data set. Source~4 is\ndetected in the 0.2--2~keV edited data, and we therefore believe that it is \nreliably detected in the hard band in the unedited data set (see Figure~2). \n\nWe have also performed source searches on images where we relax our\ngrade screening so that we accept \\asca\\ grades 0, 2, 3, 4 and 6. \nIn these searches we detect \nmost of the sources discussed in \\S2.2, but we fail to \ndetect sources 2, 4 and 5 in the hard band. We thus infer a generally\nlower source detection efficiency with this grade screening. Our\naverage background across S3 with this grade screening varies from \n$\\approx$~0.07--0.09~count~pixel$^{-1}$, a factor of $\\approx 2$ higher \nthan in \\S2.1 and \\S2.2. However, we \ndo detect one new hard band source, which we will hereafter \nrefer to as `source~AG1' (`AG' is for `\\asca\\ grade'). We consider this \nsource to be reliable since it is also detected in our independent\nsoft band image, and we give its properties in Tables~1 and 2\n(also see Figure~1). This\nsource appears to have been missed by our source searching in \n\\S2.2 because several of its counts were rejected by our conservative\ngrade filtering prescription. This highlights that it is difficult\nto choose a single optimal grade filtering criterion when dealing with\nsources with few counts; chance fluctuations in source\ngrades can be important in this limit. \n\nWe have investigated if our choice of {\\sc wavdetect} wavelet scale\nsizes affects our results, and we find no evidence for this. We have\nrepeated the searching of \\S2.2 using wavelet scale sizes of\n1, 1.414, 2, 2.828, 4, 5.657, 8, 11.314 and 16 pixels \n(a `$\\sqrt 2$ sequence'), and we find the same sources as in \\S2.2. \n\nWe are developing a matched filter code, based on the HRMA PSF, \nwhich we have used to check our {\\sc wavdetect} source detections. \nThis preliminary matched filter code finds the same 9 hard-band sources on S3 \nthat we have discussed in \\S2.1 and \\S2.2, and, \nlike {\\sc wavdetect}, it finds soft-band \ncounterparts for all sources other than source~5 (see \\S2.2). \n\nWe have also examined the spatial distribution of 2--8~keV sources on\nS3 to see if we can detect any spatial non-uniformity. We have used\na two-dimensional `Kolmogorov-Smirnov test' (see \\S14.7 of Press et~al. 1992),\nand we have performed Monte-Carlo simulations to compute significance\nvalues for small numbers of sources. The 9 hard-band sources of \\S2.2 \nare found to be consistent with a uniform distribution. We have also\nperformed the test including source~AG1 (see above), and we found\nthis sample of 10 sources to be consistent with a uniform distribution. \nHowever, we note that the two-dimensional `Kolmogorov-Smirnov test'\nhas limited statistical power for only 9--10 sources. In fact, we might\nhave expected some spatial nonuniformity due to the fact that our\nsensitivity decreases away from the aim point; this may partially \nexplain the absence of sources toward the lower-left part of Figure~1. \n\nWe have searched for spatial correspondences between our hard-band source\npositions and instrumental features, and we find none. In particular, we\nstress that sources 2, 3, 5 and 7 (the four blank-field sources of \\S3)\nare {\\it not\\/} linearly distributed \nalong the dithered central node boundary (see \\S2.2 for a discussion\nof the node boundary). Source~7 is the closest of these four to \nthe node boundary, and it is still $9^{\\prime\\prime}$ from it (much \nlarger than the PSF size at this position). \n\n% -------------------------------------------------------------------------\n\n\\section{Optical Observations and Data Analysis}\n\n\\subsection{Source Matching and Optical Photometry}\n\nWe have compared the positions of our 2--8~keV sources with optical \nsources on the Palomar Optical Sky Survey (POSS) \nplates and an archival 600~s $R$-band image taken \nwith the 2.5-m Isaac Newton Telescope (INT) on 19 October 1995 (see Figure~4 \nand \\S2.5 of Boyle et~al. 1997). The INT image is sensitive down to\n$R\\approx 21.7$. We take an optical source to be positionally \ncoincident with a \\chandra\\ source when its centroid is within\n$3^{\\prime\\prime}$ of the \\chandra\\ position in Table~1. \nFive of our nine sources from \\S2.2 are detected \non the POSS plates. Two of these are AGN that have been previously \nidentified by Boyle et~al. (1997): \nthe QSO \\crssqso\\ at $z=0.493$ (our source~6) and \nthe Seyfert~2 \\crsssy2\\ at $z=0.247$ (our source~8). \nThe other four sources are not detected either \non the POSS plates or in the deeper INT image, and these \nare henceforth referred to as `blank-field sources.'\n%\nThe number of blank-field sources we have obtained appears \nreasonable when compared with an extrapolation to lower hard \nX-ray fluxes of the $R$-magnitude versus 2--10~keV flux \nrelation shown in Figure~3 of Akiyama et~al. (2000); we would\nexpect optical counterparts with $R\\approx$~18--23.5. It is\nalso generally consistent with the results of deep soft X-ray \nsurveys (compare with Figure~3 of Hasinger et~al. 1999). \n%\nWe have used the APM catalog (\\cite{mi92}) and the INT image\nto determine $R$ magnitudes or $R$-magnitude limits for our\nsources; these are given in Table~2. \n\nSource~AG1 from \\S2.4 is not detected on the POSS plates, but it\nis coincident with a faint ($R=21.5$) object seen in the INT image. \n\nUsing the INT image, we find an $R$-band \nsource density of 10.3 per square \narcminute down to $R=21.7$. Given this source density and our \n$3^{\\prime\\prime}$ error circles, the probability that any given \n2--8~keV source has a false optical counterpart is 0.08. \nHowever, we note that most of the counterparts have $R$ magnitudes\nthat are substantially brighter than the detection limit for the\nINT image, and their identifications are correspondingly more\nsecure. The HET spectroscopy below combined with the rarity of AGN \non the sky supports the correctness of our optical matching \n(see \\S4.1 of Schmidt et~al. 1998 for details). \n\nWe have searched for NRAO VLA Sky Survey (NVSS; Condon et~al. 1998) \nsources coincident with our X-ray sources and find none. This area\nof sky has not been covered by the VLA FIRST survey \n(Becker, White \\& Helfand 1995). \n\n\\subsection{Hobby-Eberly Telescope Spectroscopy}\n\nWe used the HET to obtain spectra for the three unidentified 2--8~keV \nsources from \\S2.2 with optical counterparts on the POSS plates. We also \nobtained a spectrum of the $R=19.1$ optical counterpart to a 2--8~keV source \nlocated on ACIS-I CCD I3 (see Table~1 for source details). We have \nnot yet attempted to obtain an optical spectrum for source~AG1. \n\nThe HET, located at McDonald Observatory, is the first optical/infrared 8-m \nclass telescope to employ a fixed-altitude (Arecibo-type) design (\\cite{lwr98}). \nAll spectra were obtained in October~1999 \nwith the Marcario Low Resolution Spectrograph\n(LRS; Hill et~al. 1998; Hill et~al. 2000; \nSchneider et~al. 2000) mounted at the prime focus of the HET. \nA $2.0^{\\prime\\prime}$ slit and 300~line~mm$^{-1}$ grism/GG385 blocking filter \nproduced spectra from 4400~\\AA\\ to 9000~\\AA\\ at 24~\\AA\\ resolution. The exposure\ntime per source ranged from 20--30 minutes. The image quality as delivered\non the detector was typically $2.5^{\\prime\\prime}$ (FWHM). Wavelength calibration \nwas performed with a fourth-order polynomial fit to a set of Cd/Hg/Ne/Zn lines;\nthe rms of the fit was 0.8~\\AA. Observations of the spectrophotometric\nstandards of Oke \\& Gunn (1983) were used to perform the relative flux \ncalibration. Spectra of the four objects are displayed in Figure~5. \n\n{\\bf Source 1:}\n%\nSource~1 has H$\\alpha$ and [O~{\\sc iii}] emission at $z=0.269$, \nwith a derived absolute magnitude of $M_{\\rm B}=-21.9$. \nIt has a large Balmer decrement with \n$H\\alpha/H\\beta\\simgt 10$, and its optical continuum slope is red \n(for an AGN) with \n$\\alpha=-2.5\\pm 0.4$.\\footnote{$F(\\nu)\\propto \\nu^\\alpha$. \nTypical `blue' quasars have $-1.3\\simlt\\alpha\\simlt+0.1$.\nOptical continuum slopes in this paper are for 5500--8800~\\AA\\ in the \nobserved frame.} The H$\\alpha$ line is resolved \nwith a FWHM of 1400~km~s$^{-1}$. \n\n{\\bf Source 4:}\n%\nSource~4 is definitely a $z=0.247$ galaxy (H$\\alpha$, [O~{\\sc iii}], and \n[O~{\\sc ii}] emission, plus a strong Mg~b absorption feature) with\n$M_{\\rm B}=-21.3$. Unfortunately, our spectrum did not permit a search\nfor [Ne~{\\sc v}] emission at 3426~\\AA\\ (compare with \\S4 of\nSchmidt et~al. 1998). Its Balmer decrement is $H\\alpha/H\\beta\\simgt 3$,\nand its optical continuum slope is $\\alpha=-1.8\\pm 0.4$. The optical\ncontinuum emission is dominated by star light. The H$\\alpha$ line\nis unresolved with a FWHM of $<900$~km~s$^{-1}$. \n%\nWith a 2--8~keV flux of $4.1\\times 10^{-15}$~erg~cm$^{-2}$~s$^{-1}$, \nthis is the faintest 2--8~keV source yet identified to our knowledge. \n%\nSomewhat surprisingly, the redshift of this source is the same as that \nof \\crsssy2\\ (our source~8), but we do not have any reason to suspect \nidentification problems. A comparison of our HET spectrum \n(see Figure~5) and the spectrum for \\crsssy2\\ given in Figure~1\nof Boyle et~al. (1995) shows that the equivalent width of \nH$\\alpha$ in \\crsssy2\\ is $\\simgt 2$ times larger than that of \nsource~4. \n\n{\\bf Source 9:}\n%\nSource~9 is difficult to interpret. The brightest optical source in the\nX-ray error circle is clearly extended on the INT image (see Figure~4).\nThe optical counterpart is off the X-ray position by \n$\\approx 3^{\\prime\\prime}$, which is by far the largest discrepancy \nof any of the optical identifications shown in Figure~4. \nThe HET spectrum for this source shows one strong \nnarrow line at 7411~\\AA\\ that is most likely H$\\alpha$ at $z=0.129$. \nThe line is unresolved with a FWHM of $<900$~km~s$^{-1}$, and the\noptical continuum is red with $\\alpha=-2.9\\pm 0.4$. The\nresidual ripple in the continuum below 7000~\\AA\\ is an artifact due to\nincomplete cancellation of fringing from a pellicle by the flat field.\n%\nThe relatively large difference between the optical and X-ray positions\nsuggests that this may not be the correct identification. Another possibility\nis that this galaxy is a member of a small group and that the X-ray emission\narises from the general environment and not an individual galaxy. However,\nthe hard X-ray spectral shape would be difficult to understand in this\ncase. \n\n{\\bf Source~I3:}\n%\nSource~I3 is a strong-lined quasar at $z=1.665$ with\n$M_{\\rm B}=-24.7$. The lines shown in Figure~5 have FWHM of\n$\\approx 5000$~km~s$^{-1}$, and the optical continuum slope\nof $\\alpha=-1.2\\pm 0.4$ is consistent with that of `normal' \nblue quasars. \n\nUsing our HET spectrum, we estimate $(V-R)\\approx +0.3$ \nfor source~I3. For the other sources we estimate \n$(V-R)\\approx +0.5$.\n\n% Gary Hill source 1 = old list of 23 source 5 = this paper `the I3 source'\n% Gary Hill source 7 = this paper source 1\n% Gary Hill source 8 = this paper source 9 \n% Gary Hill source 23 = this paper source 4 \n\n\\subsection{The Blank-Field Sources}\n\nWe have compared the properties of the blank-field sources to those of\nthe other sources to gain clues to their nature.\nExamination of Figure~6 shows that the blank-field sources\nare not the faintest 2--8~keV sources in our sample; we have \nobtained successful HET identifications for sources with comparable \nor smaller 2--8~keV fluxes. This is comforting in that it\nsuggests that our blank-field sources are indeed reliable X-ray\ndetections. \n%\nFigures~6a and 6b also show that the blank-field sources\nhave larger X-ray to $V$-band flux ratios than the other sources, as\nexpected. However, these X-ray to $V$-band flux ratios are still\nconsistent with those expected for AGN (compare with \nFigure~1 of Maccacaro et~al. 1988). Figure~6c suggests \nthat the blank-field sources may be somewhat harder than \nthe other sources, but we do not consider this result to be \nstatistically significant at present. \n\nIf the blank-field X-ray sources are in normal $L^\\star$ galaxies\n(Kirshner et~al. 1983; Efstathiou, Ellis \\& Peterson 1988),\nthey must be at moderately high redshifts to explain their \nnondetections in the INT image (corresponding to $R>21.7$). \nTo avoid detection in the INT image, an $L^\\star$ Scd galaxy \nmust have $z\\simgt 0.75$, and an $L^\\star$ elliptical, \n$z\\simgt 0.55$. Typical $L^\\star$ galaxies \nwould thus need to be at higher redshifts than that of the \ncluster \\crsscluster. \nThe moderately high redshifts required for host galaxies also serve to \nrule out single extragalactic X-ray binaries and other low-luminosity \nX-ray sources associated with galaxies from creating the observed X-ray \nemission (unless the host galaxies have extremely low optical luminosities;\nwe would have detected a host galaxy that is sub-$L^\\star$ by two\nmagnitudes to $z=0.2$). \nLarge hard X-ray luminosities of \n$L_{2-8}\\simgt 5\\times 10^{41}$~erg~s$^{-1}$ are \nrequired for $z\\simgt 0.2$. Such hard \nX-ray luminosities are commonly seen among local AGN. \nThey might also be generated by the most extreme `pure' starburst \ngalaxies, although even the most X-ray luminous starbursts known at\npresent have hard X-ray luminosities \n$\\simlt 3\\times 10^{41}$~erg~s$^{-1}$\n(e.g., Moran, Lehnert \\& Helfand 2000). \nIn addition, the X-ray spectra of the blank-field sources are\nsignificantly harder than those seen for `pure' starbursts\nat low redshift. \n\nIf the blank-field X-ray sources are `bona-fide' quasars, with \n$M_{\\rm B}<-22.3$ for our adopted cosmology, they would need to \nhave $z>1.75$ to avoid detection on the INT image.\nQuasars with $z<3$ and $M_{\\rm B}<-23.2$ would have been seen in the \nINT image, and a quasar as luminous as 3C273 would have been \ndetected at redshifts greater than 4. \n\n% -------------------------------------------------------------------------\n\n\\section{Discussion and Conclusions}\n\nOur results, obtained from a small but well-defined sample of \n2--8~keV sources, extend previous X-ray \nbackground studies in several ways. First, \nwe have detected and securely identified hard X-ray sources about \nan order of magnitude fainter than has previously been possible. \nAt our 2--8~keV flux limit of \n$\\approx$~(4--8)$\\times 10^{-15}$~erg~cm$^{-2}$~s$^{-1}$\n(spatially dependent; see \\S2.2), we find \nten sources (including AG1) in our 63.5~arcmin$^2$ search \narea, corresponding to a 2--8~keV source density of $570\\pm 180$~deg$^{-2}$.\nEven allowing for the possibility of one spurious source detection, \nthis source density is still $\\approx 10$ times larger \nthan previous number counts in this energy band (e.g., Ogasaka et~al. 1998;\nGiommi et~al. 1998), and down to $\\approx 2\\times 10^{-14}$~erg~cm$^{-2}$~s$^{-1}$ \nour number counts appear consistent with the \\asca\\ fluctuation analyses\nof Gendreau et~al. (1998). However, our source counts\nmay be somewhat enhanced due to the presence of the cluster\n\\crsscluster\\ (see below). The fact that we detect sources down to \n$\\approx 4\\times 10^{-15}$~erg~cm$^{-2}$~s$^{-1}$ suggests that the \nnumber counts versus flux relation \ndeparts from the Euclidean form (the X-ray background\nwould be resolved at $\\approx 10^{-14}$~erg~cm$^{-2}$~s$^{-1}$ without\na break in the $\\log N$--$\\log S$ slope), although further data are \nclearly needed to quantify the break parameters. \n\nFour of our five S3 sources with optical spectroscopy have\n$z<0.3$, which clearly exclude them from being associated with the cluster \n\\crsscluster\\ at $z=0.516$. The fifth, \nthe QSO \\crssqso, differs in redshift from the \ncluster by $\\Delta z=0.023$ corresponding to a line-of-sight separation \nof $\\approx 100$~Mpc. While this QSO is certainly not a bound member of the \ncluster, it could be associated with the large-scale cosmic structure producing \nthe cluster. As discussed in \\S3.3, if any of our blank-field sources \n(or AG1) lie in the cluster, they must be sub-$L^\\star$ galaxies \nproducing large hard X-ray luminosities \nof $L_{2-8}\\simgt 4\\times 10^{42}$~erg~s$^{-1}$.\nEven in the most conservative (and unlikely) case, where we allow \nall objects with unknown $z$ to lie in the cluster, our\ncluster-corrected source density is still a factor of $\\approx 4.5$ \ntimes higher than previously attained by \\asca\\ and \\sax. The same\nstatement obtains for possible gravitational lensing effects by the\ncluster. \n\nWe detect nine of our ten 2--8~keV sources in the 0.2--2~keV band. \nWhile our statistics are admittedly limited, this result is consistent \nwith the finding by Giommi, Fiore \\& Perri (1998) that most hard X-ray \nsources have soft X-ray counterparts, and it extends this result downward \nin flux by about an order of magnitude (see \\S1 for discussion). Down to \nour flux limit, we can show with $>90$\\% confidence that hard-band only \nsources comprise $<40$\\% of the total hard-band source population. \nDeeper \\chandra\\ observations are needed to determine if a large \npopulation of hard-band only sources emerges at still fainter flux levels. \n\n% -------------------------------------------------------------------------\n\n\\acknowledgments\n\nWe thank \nC.S.~Crawford and A.C.~Fabian for providing the archival INT image, \nG.M.~Hill and M.~Shetrone for help with the HET data acquisition, \nP.S.~Broos, A.C.~Fabian, E.D.~Feigelson and G.~Hasinger for helpful discussions, and\nD.H.~Saxe for valuable computer support. \n%\nWe thank all the members of the \\chandra\\ team for their enormous efforts. \n%\nWe gratefully acknowledge the financial support of \nNASA grant NAS~8-38252 (GPG, PI), \nNASA LTSA grant NAG5-8107 (WNB),\nNASA GSRP grant NGT5-50247 (AEH), and \nNSF grant AST99-00703~(DPS). \n%\nThe HET is a joint project of \nthe University of Texas at Austin,\nthe Pennsylvania State University, \nStanford University,\nLudwig-Maximillians-Universit\\\"at M\\\"unchen, and \nGeorg-August-Universit\\\"at G\\\"ottingen. \nThe HET is named in honor of its principal benefactors,\nWilliam P. Hobby and Robert E. Eberly. \n%\nThe Marcario LRS is a joint project of \nthe University of Texas at Austin, \nthe Instituto de Astronomia de la Universidad Nacional Autonoma de Mexico, \nLudwig-Maximillians-Universit\\\"at M\\\"unchen, \nGeorg-August-Universit\\\"at G\\\"ottingen,\nStanford University, and \nthe Pennsylvania State University. \n%\nThis research is partially based upon data from the Isaac Newton Group \narchive.\n\n\\clearpage\n \n% -------------------------------------------------------------------------\n \n\\begin{deluxetable}{lcccccccc}\n%\\footnotesize\n\\tablecaption{Basic X-ray Properties of the 2--8~keV Sources. \\label{tbl-1}}\n\\tablewidth{0pt}\n\\scriptsize\n\\tablehead{\n%\n\\colhead{Source} & \n\\colhead{X-ray} & \n\\colhead{X-ray} &\n\\colhead{Aim point} &\n\\colhead{0.2--2~keV} & \n\\colhead{2--8~keV} &\n\\colhead{Hard/Soft} &\n\\colhead{0.2--2~keV} & \n\\colhead{2--8~keV} \\\\\n%\n\\colhead{Name} & \n\\colhead{$\\alpha_{2000}$} & \n\\colhead{$\\delta_{2000}$} &\n\\colhead{distance ($^\\prime$)} & \n\\colhead{counts} & \n\\colhead{counts} &\n\\colhead{ratio} &\n\\colhead{significance} &\n\\colhead{significance} \n}\n\\startdata\n1 & 00$^{\\rm h}$ 30$^{\\rm m}$ 26.0$^{\\rm s}$ & +26$^{\\circ}$ 16$^{\\prime}$ 48.9$^{\\prime\\prime}$ & 2.0 & $128.4\\pm 11.5$ & $9.4\\pm 3.2$ & $0.073\\pm 0.026$ & 41.8 & 4.4 \\nl\n2 & 00$^{\\rm h}$ 30$^{\\rm m}$ 27.8$^{\\rm s}$ & +26$^{\\circ}$ 15$^{\\prime}$ 14.9$^{\\prime\\prime}$ & 3.1 & $36.4\\pm 6.6$ & $9.2\\pm 3.6$ & $0.25\\pm 0.11$ & 6.8 & 3.0 \\nl\n3 & 00$^{\\rm h}$ 30$^{\\rm m}$ 30.8$^{\\rm s}$ & +26$^{\\circ}$ 16$^{\\prime}$ 00.0$^{\\prime\\prime}$ & 2.2 & $30.8\\pm 5.7$ & $12.0\\pm$ 3.6 & $0.39\\pm 0.14$ & 11.3 & 5.2 \\nl\n4 & 00$^{\\rm h}$ 30$^{\\rm m}$ 33.3$^{\\rm s}$ & +26$^{\\circ}$ 14$^{\\prime}$ 50.9$^{\\prime\\prime}$ & 3.3 & $34.9\\pm 6.1$ & $6.2\\pm 2.6$ & $0.18\\pm 0.08$ & 13.1 & 2.8 \\nl\n5 & 00$^{\\rm h}$ 30$^{\\rm m}$ 34.7$^{\\rm s}$ & +26$^{\\circ}$ 16$^{\\prime}$ 29.8$^{\\prime\\prime}$ & 1.8 & $<7.5$ & $8.1\\pm 3.0$ & $>0.68$ & $\\cdots$ & 3.6 \\nl\n6 & 00$^{\\rm h}$ 30$^{\\rm m}$ 39.5$^{\\rm s}$ & +26$^{\\circ}$ 20$^{\\prime}$ 54.9$^{\\prime\\prime}$ & 3.1 & $1830.5\\pm 43.0$ & $413.1\\pm 20.4$ & $0.23\\pm 0.01$ & 355.3 & 122.4 \\nl\n7 & 00$^{\\rm h}$ 30$^{\\rm m}$ 42.6$^{\\rm s}$ & +26$^{\\circ}$ 17$^{\\prime}$ 46.1$^{\\prime\\prime}$ & 2.3 & $21.9\\pm 4.9$ & $11.9\\pm 3.6$ & $0.54\\pm 0.23$ & 8.1 & 5.1 \\nl\n8 & 00$^{\\rm h}$ 30$^{\\rm m}$ 47.8$^{\\rm s}$ & +26$^{\\circ}$ 16$^{\\prime}$ 47.0$^{\\prime\\prime}$ & 3.7 & $141.9\\pm 12.3$ & $27.8\\pm 5.7$ & $0.20\\pm 0.04$ & 34.3 & 8.0 \\nl\n9 & 00$^{\\rm h}$ 30$^{\\rm m}$ 51.3$^{\\rm s}$ & +26$^{\\circ}$ 17$^{\\prime}$ 11.9$^{\\prime\\prime}$ & 4.3 & $99.4\\pm 10.4$ & $42.1\\pm$ 6.9 & $0.42\\pm 0.09$ & 23.5 & 11.8 \\nl\n\\tablevspace{0.2cm}\nAG1 & 00$^{\\rm h}$ 30$^{\\rm m}$ 41.6$^{\\rm s}$ & +26$^{\\circ}$ 17$^{\\prime}$ 40.8$^{\\prime\\prime}$ & 2.1 & $65.9\\pm 8.3$ & $13.1\\pm 4.0$ & $0.20\\pm 0.07$ & 22.4 & 4.5 \\nl\n\\tablevspace{0.2cm}\nI3 & 00$^{\\rm h}$ 31$^{\\rm m}$ 08.4$^{\\rm s}$ & +26$^{\\circ}$ 20$^{\\prime}$ 56.3$^{\\prime\\prime}$ & 8.5 & $136.4\\pm 12.4$ & $36.5\\pm 6.9$ & $0.27\\pm 0.06$ & 26.4 & 8.4 \\nl\n%\n\\enddata\n%\n\\tablenotetext{}{Sources~1--9 are located on the S3 CCD and source~I3 is located on the I3 CCD; properties\nfor these sources have been found using filtering on ACIS grades 0, 2, 8, 16 and 64. \n%\nSource~AG1 is only found when \\asca\\ grade filtering is used (see \\S2.4); properties for this\nsource have been found using filtering on \\asca\\ grades 0, 2, 3, 4 and 6. \n%\n% Ideally should correct band ratio for differential vignetting. \\todo\n%\nNote that we have only listed the sources that are detected in the 2--8~keV band. \n%\n}\n% \n\\end{deluxetable}\n\n% \\clearpage\n\n% FOLLOWING DISCUSSIONS WITH SCHNEIDER I HAVE APPLIED AN \n% ADDITIONAL -2.3 ARCSEC SHIFT IN DECLINATION TO THESE DATA. \n\n% -------------------------------------------------------------------------\n\n\\begin{deluxetable}{lcccccl}\n%\\footnotesize\n\\tablecaption{X-ray Fluxes/Luminosities and Optical Properties of the 2--8~keV Sources. \\label{tbl-2}}\n\\tablewidth{0pt}\n\\scriptsize\n\\tablehead{\n%\n\\colhead{Source} & \n\\colhead{0.2--2~keV flux} & \n\\colhead{2--8~keV flux} &\n\\colhead{2--8~keV $L_{\\rm X}$} &\n\\colhead{} &\n\\colhead{} &\n\\colhead{} \\\\\n%\n\\colhead{Name} & \n\\colhead{(erg cm$^{-2}$ s$^{-1}$)} & \n\\colhead{(erg cm$^{-2}$ s$^{-1}$)} &\n\\colhead{(erg s$^{-1}$)} &\n\\colhead{$R$} &\n\\colhead{$z$} &\n\\colhead{Notes$^{\\rm a}$}\n}\n\\startdata\n1 & $1.0\\times 10^{-14}$ & $6.0\\times 10^{-15}$ & $1.1\\times 10^{42}$ & 18.4 & 0.269 & HET \\nl\n2 & $2.9\\times 10^{-15}$ & $5.9\\times 10^{-15}$ & $\\cdots$ & $>21.7$ & $\\cdots$ & BF \\nl\n3 & $2.5\\times 10^{-15}$ & $7.7\\times 10^{-15}$ & $\\cdots$ & $>21.7$ & $\\cdots$ & BF \\nl\n4 & $2.9\\times 10^{-15}$ & $4.1\\times 10^{-15}$ & $6.1\\times 10^{41}$ & 18.7 & 0.247 & HET \\nl\n5 & $<5.9\\times 10^{-16}$ & $5.2\\times 10^{-15}$ & $\\cdots$ & $>21.7$ & $\\cdots$ & BF \\nl\n6 & $1.6\\times 10^{-13}$ & $3.3\\times 10^{-13}$ & $2.1\\times 10^{44}$ & 16.9 & 0.493 & \\crssqso\\ (QSO) \\nl\n7 & $1.7\\times 10^{-15}$ & $7.7\\times 10^{-15}$ & $\\cdots$ & $>21.7$ & $\\cdots$ & BF \\nl\n8 & $1.1\\times 10^{-14}$ & $1.8\\times 10^{-14}$ & $2.7\\times 10^{42}$ & 18.5 & 0.247 & \\crsssy2 (Seyfert~2) \\nl\n9 & $8.0\\times 10^{-15}$ & $2.9\\times 10^{-14}$ & $1.1\\times 10^{42}$$^{\\rm b}$ & 19.1 & 0.129$^{\\rm b}$ & HET \\nl\n\\tablevspace{0.2cm}\nAG1 & $4.2\\times 10^{-15}$ & $5.5\\times 10^{-15}$ & $\\cdots$ & 21.5 & $\\cdots$ & \\asca\\ grade source \\nl\n\\tablevspace{0.2cm}\nI3 & $1.9\\times 10^{-14}$ & $2.0\\times 10^{-14}$ & $1.9\\times 10^{44}$ & 19.1 & 1.665 & HET \\nl\n%\n\\enddata\n%\n\\tablenotetext{a}{Sources noted as `HET' are those for which we present HET \nspectra, and sources noted as `BF' (for `Blank Field') are those without optical \ncounterparts.}\n% \n\\tablenotetext{b}{We consider this redshift and luminosity to be only \ntentative (see \\S3.2 for details).}\n% \n\\end{deluxetable}\n\n\\clearpage\n\n% -------------------------------------------------------------------------\n\n% Now comes the reference list. In this document, we used \\cite to call\n% out citations, so we must use \\bibitem in the reference list, which\n% means we use the LaTeX thebibliography environment. Please note that\n% \\begin{thebibliography} is followed by a null argument. If you forget\n% this, mayhem ensues, and LaTeX will say \"Perhaps a missing item?\" when\n% you run it. Do not call us, do not send mail when this happens. Put\n% the silly {} after the \\begin{thebibliography}.\n%\n% Each reference has a \\bibitem command to define the citation format\n% to be placed in the text (in []) and the symbolic tag used for \n% cross referencing (in {}).\n%\n% See sample1.tex, or the AASTeX guide, for an alternative to the \\cite-\n% \\bibitem command.\n\n\\begin{thebibliography}{}\n\n\\bibitem[Akiyama et~al. 2000]{aki00}\n Akiyama, M., et~al. \n 2000, ApJ, in press (astro-ph/0001289)\n \n\\bibitem[Baganoff 1999]{baganoff99}\n Baganoff, F. 1999, \n ACIS On-Orbit Background Rates and Spectra from OAC Phase~1.\n Massachusetts Institute of Technology, Cambridge\n\n\\bibitem[Becker et~al. 1995]{becker95}\n Becker, R.H., White, R.L. \\& Helfand, D.J. \n 1995, ApJ, 450, 559\n\n\\bibitem[Becker \\& Robinson 1992]{bevington92}\n Bevington, P.R. \\& Robinson, D.K. 1992, Data Reduction and \n Error Analysis for the Physical Sciences: Second Edition. \n McGraw Hill, New York\n\n\\bibitem[Boyle et~al. 1995]{boyle95}\n Boyle, B.J., McMahon, R.G., Wilkes, B.J. \\& Elvis, M. 1995, \n MNRAS, 276, 315\n\n\\bibitem[Boyle, Wilkes \\& Elvis 1997]{bwe97}\n Boyle, B.J., Wilkes, B.J. \\& Elvis, M. 1997, \n MNRAS, 285, 511\n\n\\bibitem[Broos et~al. 1999]{broos99}\n Broos, P. et~al. 1999, User's Guide for \n the {\\sc tara} Package: Document Revision 5.3.\n Penn State University, University Park\n (available at http://www.astro.psu.edu/xray/docs/) \n\n\\bibitem[Condon et~al. 1998]{condon98}\n Condon, J.J., Cotton, W.D., Greisen, E.W., Yin, Q.F., Perley, R.A., \n Taylor, G.B. \\& Broderick, J.J.\n 1998, AJ, 115, 1693\n \n\\bibitem[Dobrzycki et~al. 1999]{dob99}\n Dobrzycki, A., Ebeling, H., Glotfelty, K., Freeman, P., \n Damiani, F., Elvis, M. \\& Calderwood, T. \n 1999, \\chandra\\ Detect 1.0 User Guide. \n \\chandra\\ X-ray Center, Cambridge\n\n\\bibitem[Efstathiou et~al. 1988]{efstathiou88}\n Efstathiou, G., Ellis, R.S. \\& Peterson, B.A. \n 1988, MNRAS, 232, 431\n\n\\bibitem[Fiore et~al. 1998]{fiore98}\n Fiore, F., La~Franca, F., Giommi, P., Elvis, M., \n Matt, G., Comastri, A., Molendi, S. \\& Gioia I. \n 1999, MNRAS, 306, L55\n\n\\bibitem[Freeman et~al. 2000]{freeman2000}\n Freeman, P.E., Kashyap, V., Rosner, R. \\& Lamb, D.Q.\n 2000, ApJ, submitted\n\n\\bibitem[Garmire \\& Nousek 1999a]{garnou99a}\n Garmire, G.P. \\& Nousek, J.A. 1999a,\n Science Instrument Operations Handbook\n for the Advanced CCD Imaging Spectrometer. \n Penn State University, University Park\n (available at http://www.astro.psu.edu/xray/docs/sop/sop.html)\n\n\\bibitem[Garmire \\& Nousek 1999b]{garnou99b}\n Garmire, G.P. \\& Nousek, J.A. 1999b,\n Preliminary Status Report: ACIS Front-Illuminated\n CCD Detector Anomaly.\n Penn State University, University Park\n (available at http://www.astro.psu.edu/xray/axaf/index.html)\n\n\\bibitem[Gehrels 1986]{gehrels86}\n Gehrels, N. 1986,\n ApJ, 303, 336 \n\n\\bibitem[Gendreau et~al. 1998]{gen98}\n Gendreau, K.C., Barcons, X. \\& Fabian, A.C. \n 1998, MNRAS, 297, 41\n\n\\bibitem[Giommi, Fiore \\& Perri 1999]{gfp99}\n Giommi, P., Fiore, F. \\& Perri, M. \n 1999, \n in Proceedings of the 3rd Integral Workshop, \n (ESA Press, Noorwijk), in press (astro-ph/9812305)\n\n\\bibitem[Hasinger et~al. 1993]{has93}\n Hasinger, G., Burg, R., Giacconi, R., Hartner, G., Schmidt, M.,\n Tr\\\"umper, J. \\& Zamorani, G. 1993, \\aap, 275, 1\n (erratum \\aap, 291, 348)\n\n\\bibitem[Hasinger et~al. 1998]{has98}\n Hasinger, G., Burg, R., Giacconi, R., Schmidt, M., Tr\\\"umper, J. \\&\n Zamorani, G. 1998, \\aap, 329, 482\n\n\\bibitem[Hasinger et~al. 1999]{has99}\n Hasinger, G., Lehmann, I., Giacconi, R., Schmidt, M., \n Tr\\\"umper, J. \\& Zamorani, G. \n 1999, \n in Highlights in X-ray Astronomy, \n (MPE Press, Garching), in press (astro-ph/9901103)\n\n\\bibitem[Hill et~al. 1998]{hill98}\n Hill, G.J., Nicklas, H.E., MacQueen, P.J., Tejada, C., Cobos~Duenas,\n F.J. \\& Mitsch, W. 1998, Proc. 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Figures and figure captions are included within figure \n% environments within the body of the manuscript. In our examples the \n% \\plotone command is placed in the figure environment along with the\n% figure caption. The \\caption command can also include a \\label command.\n% Each figure and its caption are printed on the same page.\n%\n% The \\caption command in the figure environment works like the one in the\n% table environment (it's the same one, actually), except that this one\n% produces identification text that reads \"Figure N.\"\n%\n% If you wish to see this option then you must comment out all of the \n% \\figcaption, \\plotone, and \\end{document} commands above.\n\n% \\newpage\n% \\centerline{\\bf Figure Captions}\n\n\\clearpage\n\n% -------------------------------------------------------------------------\n\n%\\begin{figure}\n\\plotfiddle{brandt.fig1.ps}{6.8in}{0.0}{80.0}{80.0}{-280.0}{-20.0}\n\\vspace{-4cm}\n\\figcaption[]\n{Image of the ACIS S3 CCD from 2--8~keV with the {\\sc wavdetect} sources marked \nand numbered. The box sizes are arbitrary ($\\approx 20^{\\prime\\prime}$ on a \nside); the positional accuracy is much better than the box size. \n%\nThe cross shows the position of the aim point and the \ncluster \\crsscluster\\ ($z=0.516$), and the diamond \nnear source~7 shows the position of source~AG1 (see \\S2.4). \n%\nThe QSO \\crssqso\\ ($z=0.493$) and the Seyfert~2 \\crsssy2\\ ($z=0.247$) \nare labeled as `QSO' and `Sy~2', respectively. \n%\nSources for which we present HET spectra are labeled `HET' and sources\nwithout optical counterparts are labeled `BF' (for `Blank Field'). \n%\nNorth is at the top, and East is to the left. \n%\nFor scale, the CCD is $8.3^{\\prime}$ on a side. \n\\label{fig1}}\n%\\end{figure}\n\n\\clearpage\n\n% -------------------------------------------------------------------------\n\n%\\begin{figure}\n\\plotfiddle{brandt.fig2.ps}{6.8in}{0.0}{80.0}{80.0}{-260.0}{-60.0}\n\\figcaption[]\n{ACIS images of the 2--8~keV sources from the S3 CCD. Each\nimage is centered on the corresponding position from Table~1, \nand each is $30^{\\prime\\prime}$ on a side. Each pixel is\n$0.5^{\\prime\\prime}$ on a side. To further demonstrate the \nreality of sources 1, 2 and 4, we also show their independent \n0.2--2~keV images. The grayscale levels are linear and \nvary from image to image, but white corresponds to zero in \nall images. Most of the non-white pixels away from the sources \nthemselves have one count. \n\\label{fig2}}\n%\\end{figure}\n\n\\clearpage\n\n% -------------------------------------------------------------------------\n\n%\\begin{figure}\n\\plotfiddle{brandt.fig3.ps}{6.8in}{-90}{80.0}{80.0}{-260.0}{+550.0}\n\\vspace{-3 cm}\n\\figcaption[]\n{Plot of the hard-band to soft-band ratio versus column density at \n$z=0$ for power-law models with photon indices of\n$\\Gamma=1.7$ (dashed curve),\n$\\Gamma=1.9$ (solid curve) and\n$\\Gamma=2.1$ (dot-dashed curve).\nThe data points show the band \nratios for sources 3, 5, 7 and 9 (the hardest sources we find). \nThese sources have been arbitrarily placed on the $\\Gamma=1.9$\ncurve; better X-ray spectra would be needed to determine their\nunderlying photon indices. Provided these \nsources have intrinsic X-ray continua that are similar to those\nof Seyferts and QSOs, they appear to have column densities larger than \na few times $10^{21}$~cm$^{-2}$. Source~5 is likely to have a column \ndensity $\\simgt 10^{22}$~cm$^{-2}$. Note that the probable absorption for \nthese sources is presumably intrinsic, and thus correcting for the \neffects of redshift will only increase the inferred column densities. \nThe curves have been calculated assuming only ACIS grade\n0, 2, 8, 16 and 64 events are used. \n\\label{fig3}}\n%\\end{figure}\n\n\\clearpage\n\n% -------------------------------------------------------------------------\n\n%\\begin{figure}\n\\plotfiddle{brandt.fig4.ps}{6.8in}{0.0}{70.0}{70.0}{-220.0}{40.0}\n\\vspace{-1 cm}\n\\figcaption[]\n{INT image of the field of the cluster \\crsscluster. The field\nis $7.5^{\\prime}$ on a side. We have marked our \\chandra\\ sources\nwith circles of $4^{\\prime\\prime}$ radius (note that this is somewhat\nlarger than our positional uncertainty). The cluster is located\nabout $1^\\prime$ North of source~5. \n\\label{fig4}}\n%\\end{figure}\n\n\\clearpage\n\n% -------------------------------------------------------------------------\n\n%\\begin{figure}\n\\plotfiddle{brandt.fig5.ps}{6.8in}{0.0}{90.0}{90.0}{-280.0}{-40.0}\n\\vspace{-4 cm}\n\\figcaption[]\n{HET LRS spectra for the \\chandra\\ sources 1, 4, 9 and I3. The spectral\nresolution is 24~\\AA.\n\\label{fig5}}\n%\\end{figure}\n\n\\clearpage\n\n% -------------------------------------------------------------------------\n\n%\\begin{figure}\n\\plotfiddle{brandt.fig6.ps}{6.8in}{0.0}{80.0}{80.0}{-240.0}{-40.0}\n\\vspace{-2 cm}\n\\figcaption[]\n{X-ray to $V$-band flux ratios and X-ray band ratios for our sources. \nStars indicate sources with HET spectra, squares indicate CRSS\nsources, and solid dots indicate blank-field sources. \nSource~5 is not plotted in panel (a) because it does not have a \nsoft-band detection, and two of the solid dots overlap in panel (b). \nThe fluxes used in panels (a) and (b) are corrected for absorption\nby the Galaxy. Panel (a) is plotted for 0.3--3.5~keV for comparison\nwith the X-ray to $V$-band flux ratios given by Stocke et~al. (1991) \nand Schmidt et~al. (1998). Our X-ray to $V$-band flux ratios are\non average somewhat smaller than those found by these authors, probably a\nselection effect due to our sensitive X-ray data and our relatively\nshallow optical data. \n\\label{fig6}}\n%\\end{figure}\n\n\\clearpage\n\n% -------------------------------------------------------------------------\n\n\n\\end{document}\n\n\n\n"
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{
"name": "astro-ph0002121.extracted_bib",
"string": "\\begin{thebibliography} is followed by a null argument. If you forget\n% this, mayhem ensues, and LaTeX will say \"Perhaps a missing item?\" when\n% you run it. Do not call us, do not send mail when this happens. Put\n% the silly {} after the \\begin{thebibliography}.\n%\n% Each reference has a \\bibitem command to define the citation format\n% to be placed in the text (in []) and the symbolic tag used for \n% cross referencing (in {}).\n%\n% See sample1.tex, or the AASTeX guide, for an alternative to the \\cite-\n% \\bibitem command.\n\n\\begin{thebibliography}{}\n\n\\bibitem[Akiyama et~al. 2000]{aki00}\n Akiyama, M., et~al. \n 2000, ApJ, in press (astro-ph/0001289)\n \n\\bibitem[Baganoff 1999]{baganoff99}\n Baganoff, F. 1999, \n ACIS On-Orbit Background Rates and Spectra from OAC Phase~1.\n Massachusetts Institute of Technology, Cambridge\n\n\\bibitem[Becker et~al. 1995]{becker95}\n Becker, R.H., White, R.L. \\& Helfand, D.J. \n 1995, ApJ, 450, 559\n\n\\bibitem[Becker \\& Robinson 1992]{bevington92}\n Bevington, P.R. \\& Robinson, D.K. 1992, Data Reduction and \n Error Analysis for the Physical Sciences: Second Edition. \n McGraw Hill, New York\n\n\\bibitem[Boyle et~al. 1995]{boyle95}\n Boyle, B.J., McMahon, R.G., Wilkes, B.J. \\& Elvis, M. 1995, \n MNRAS, 276, 315\n\n\\bibitem[Boyle, Wilkes \\& Elvis 1997]{bwe97}\n Boyle, B.J., Wilkes, B.J. \\& Elvis, M. 1997, \n MNRAS, 285, 511\n\n\\bibitem[Broos et~al. 1999]{broos99}\n Broos, P. et~al. 1999, User's Guide for \n the {\\sc tara} Package: Document Revision 5.3.\n Penn State University, University Park\n (available at http://www.astro.psu.edu/xray/docs/) \n\n\\bibitem[Condon et~al. 1998]{condon98}\n Condon, J.J., Cotton, W.D., Greisen, E.W., Yin, Q.F., Perley, R.A., \n Taylor, G.B. \\& Broderick, J.J.\n 1998, AJ, 115, 1693\n \n\\bibitem[Dobrzycki et~al. 1999]{dob99}\n Dobrzycki, A., Ebeling, H., Glotfelty, K., Freeman, P., \n Damiani, F., Elvis, M. \\& Calderwood, T. \n 1999, \\chandra\\ Detect 1.0 User Guide. \n \\chandra\\ X-ray Center, Cambridge\n\n\\bibitem[Efstathiou et~al. 1988]{efstathiou88}\n Efstathiou, G., Ellis, R.S. \\& Peterson, B.A. \n 1988, MNRAS, 232, 431\n\n\\bibitem[Fiore et~al. 1998]{fiore98}\n Fiore, F., La~Franca, F., Giommi, P., Elvis, M., \n Matt, G., Comastri, A., Molendi, S. \\& Gioia I. \n 1999, MNRAS, 306, L55\n\n\\bibitem[Freeman et~al. 2000]{freeman2000}\n Freeman, P.E., Kashyap, V., Rosner, R. \\& Lamb, D.Q.\n 2000, ApJ, submitted\n\n\\bibitem[Garmire \\& Nousek 1999a]{garnou99a}\n Garmire, G.P. \\& Nousek, J.A. 1999a,\n Science Instrument Operations Handbook\n for the Advanced CCD Imaging Spectrometer. \n Penn State University, University Park\n (available at http://www.astro.psu.edu/xray/docs/sop/sop.html)\n\n\\bibitem[Garmire \\& Nousek 1999b]{garnou99b}\n Garmire, G.P. \\& Nousek, J.A. 1999b,\n Preliminary Status Report: ACIS Front-Illuminated\n CCD Detector Anomaly.\n Penn State University, University Park\n (available at http://www.astro.psu.edu/xray/axaf/index.html)\n\n\\bibitem[Gehrels 1986]{gehrels86}\n Gehrels, N. 1986,\n ApJ, 303, 336 \n\n\\bibitem[Gendreau et~al. 1998]{gen98}\n Gendreau, K.C., Barcons, X. \\& Fabian, A.C. \n 1998, MNRAS, 297, 41\n\n\\bibitem[Giommi, Fiore \\& Perri 1999]{gfp99}\n Giommi, P., Fiore, F. \\& Perri, M. \n 1999, \n in Proceedings of the 3rd Integral Workshop, \n (ESA Press, Noorwijk), in press (astro-ph/9812305)\n\n\\bibitem[Hasinger et~al. 1993]{has93}\n Hasinger, G., Burg, R., Giacconi, R., Hartner, G., Schmidt, M.,\n Tr\\\"umper, J. \\& Zamorani, G. 1993, \\aap, 275, 1\n (erratum \\aap, 291, 348)\n\n\\bibitem[Hasinger et~al. 1998]{has98}\n Hasinger, G., Burg, R., Giacconi, R., Schmidt, M., Tr\\\"umper, J. \\&\n Zamorani, G. 1998, \\aap, 329, 482\n\n\\bibitem[Hasinger et~al. 1999]{has99}\n Hasinger, G., Lehmann, I., Giacconi, R., Schmidt, M., \n Tr\\\"umper, J. \\& Zamorani, G. \n 1999, \n in Highlights in X-ray Astronomy, \n (MPE Press, Garching), in press (astro-ph/9901103)\n\n\\bibitem[Hill et~al. 1998]{hill98}\n Hill, G.J., Nicklas, H.E., MacQueen, P.J., Tejada, C., Cobos~Duenas,\n F.J. \\& Mitsch, W. 1998, Proc. SPIE, 3355, 375\n\n\\bibitem[Hill et~al. 2000]{hill2000}\n Hill, G.J., et~al. 2000, PASP, in press\n\n\\bibitem[Kirshner et~al. 1983]{kirshner83}\n Kirshner, R.P., Oemler, A., Schechter, P.L. \\& \n Shectman, S.A. 1983, AJ, 88, 1285\n\n\\bibitem[Lyons 1991]{lyons91}\n Lyons, L. 1991, \n Data Analysis for Physical Science Students.\n Cambridge University Press, Cambridge\n\n\\bibitem[Maccacaro et~al. 1988]{mac88}\n Maccacaro, T., Gioia, I.M., Wolter, A., Zamorani, G. \\& Stocke, J.T.\n 1988, ApJ, 326, 680\n\n\\bibitem [McMahon \\& Irwin 1992]{mi92} \n McMahon, R.G. \\& Irwin, M.J. \n 1992,\n in Digitised Optical Sky Surveys,\n ed. MacGillivray, H. T. \\& Thomson, E. B.\n (Kluwer, Dordrecht), p. 417\n\n\\bibitem[Moran et~al. 2000]{moran2000}\n Moran, E.C., Lehnert, M.D. \\& Helfand, D.J.\n 2000, \n ApJ, in press (astro-ph/9907036)\n\n\\bibitem[Ogasaka et~al. 1998]{oga98}\n Ogasaka, Y., et~al. \n 1998, Astr. 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SPIE, 3352, 34\n\n\\bibitem[Schmidt et~al. 1998]{schmidt98}\n Schmidt, M., Hasinger, G., Gunn, J., Schneider, D., Burg, R.,\n Giacconi, R., Lehmann, I., MacKenty, J., Tr\\\"umper, J. \\& Zamorani,~G.\n 1998, \\aap, 329, 495\n\n\\bibitem[Schneider et~al. 2000]{schneider2000}\n Schneider, D.P., et~al. 2000, PASP, in press (astro-ph/9910306)\n\n\\bibitem[Stark et~al. 1992]{stark92}\n Stark, A.A., Gammie, C.F., Wilson, R.W., Bally, J., \n Linke, R.A., Heiles, C. \\& Hurwitz, M. \n 1992, ApJS, 79, 77 \n\n\\bibitem[Stocke et~al. 1991]{stocke91}\n Stocke, J.T., Morris, S.L., Gioia, I.M., Maccacaro, T., \n Schild, R., Wolter, A., Fleming, T.A. \\& Henry, J.P. \n 1991, ApJS, 76, 813\n\n\\bibitem[Ueda et~al. 1998]{ueda98}\n Ueda, Y., et~al. \n 1998, Nature, 391, 866\n\n\\bibitem[Weisskopf, O'Dell \\& van~Speybroeck~1996]{wod96}\n Weisskopf, M.C., O'Dell, S.L. \\& van~Speybroeck, L. 1996,\n SPIE, 2805, 2\n \n\\end{thebibliography}"
}
] |
astro-ph0002122
|
The VizieR database of Astronomical Catalogues
|
[
{
"author": "Fran\\c cois Ochsenbein"
},
{
"author": "Patricia Bauer"
},
{
"author": "James Marcout %Fran\\c coise Genova\\inst{1}"
}
] |
\VizieR\ is a database grouping in an homogeneous way thousands of astronomical catalogues gathered since dec\-ades by the Centre de Donn\'ees de Strasbourg (CDS) and participating institutes. The history and current status of this large collection is briefly presented, and the way these catalogues are being standardized to fit in the \VizieR\ system is described. The architecture of the database is then presented, with emphasis on the management of links and of accesses to very large catalogues. Several query interfaces are currently available, making use of the {\em ASU} protocol, for browsing purposes or for use by other data processing systems such as visualisation tools. \keywords{ Astronomical data bases: miscellaneous --- Catalogs }
|
[
{
"name": "viz99.tex",
"string": "%\\documentclass[referee]{aa}\n\\documentclass{aa}\n\\usepackage{graphics}\n%\\usepackage{times}\n\\usepackage{psfig}\n\\usepackage{rotate}\n%\\documentstyle[referee]{l-aa}\n%\\renewcommand{\\baselinestretch}{2}\n\\def\\tablab#1{\\label{tab:#1}}\n\\def\\eqnlab#1{\\label{eqn:#1}}\n\\def\\eqnref#1{(\\ref{eqn:#1})}\n\\def\\Tabref#1{Table~\\ref{tab:#1}}\n\\def\\VizieR{{\\sf VizieR}}\n%\\def\\farcs{\\hbox{.\\!\\!^{\\prime\\prime}}}\n\\def\\d{^\\circ}\n\\def\\ie{{\\em i.e.} }\n\\def\\eg{{\\em e.g.} }\n\\def\\ccol#1{\\multicolumn{1}{c}{#1}}\n\\def\\secref#1{section~\\ref{s#1}}\n\\def\\figref#1{Fig.~\\ref{fig:#1}}\n\\def\\tabref#1{Table~\\ref{tab:#1}}\n\\def\\HIP{{\\em Hipparcos}}\n\\def\\TYC{{\\em Tycho}}\n\\def\\colheader#1{\\multicolumn{1}{c}{{\\bf #1}}}\n\\def\\ignore#1{}\n\\hyphenation{data-base}\n\n %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n %%%% Inclusion of PS figures\n %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\iffalse\n\\begin{figure}\n%\\vspace{\\hsize}\n\\resizebox{\\hsize}{!}{\\includegraphics{panel.ps}}\n\\caption{Example of Images/Data {\\sc Aladin} query panel.}\n\\label{query-panel}\n\\end{figure}\n\n%%% Rotated\n\\begin{figure*}\n%\\vspace{\\hsize}\n% 18cm if double column\n\\resizebox{\\hsize}{!}{\\rotatebox{+90}{\\includegraphics{M16.ps}}}\n\\caption{Example of {\\sc Aladin} display of a famous image\nfrom the HST archive (WFPC2) featuring the Eagle Nebula\n(\\object{M 16}).\nObjects present in Simbad, GSC, and USNO A2.0 are flagged\nwith different symbols. Field size is 2.6 arcmin\n(full image, right) and 1.6 arcmin (left).}\n\\label{M16}\n\\end{figure*}\n\n\\fi\n\n%%%% latex-only definitions (for printed paper)\n\\def\\ifhtx{\\iffalse}\t% This redefinition is ignored in HTX context.\n\\begin{document}\n\\ifhtx\n\\def\\bibcode#1{(#1)}\n\\tableofcontents\n\\else\t% Define anchors, etc for a printed edition\n%\\def\\A#1#2{{#2}\\footnote{{\\footnotesize #1}}}\n\\def\\about{$\\sim$}\n%\\def\\A#1#2{{#2}\\footnote{{\\scriptsize\\tt #1}}}\n\\def\\A#1#2{{#2}\\footnote{#1}}\n\\fi\n\n\\def\\Aviz#1#2{\\A{http://vizier.u-strasbg.fr/#1}{#2}}\n\\def\\Section#1#2{\\section{#2}\\label{s#1}}\n\\def\\subSection#1#2{\\subsection{#2}\\label{s#1}}\n\\def\\Avizdup#1#2{ % #2 = 1 to break after parameters\n\t\\Aviz{cgi-bin/VizieR?#1}{a call to \\VizieR\\ with parameters:\n\t\\ifnum#2>0 \\\\ \\fi\n\t{\\tt #1}}}\\def\\bibcode#1{}\n\n \\thesaurus{10 % A&A Section 10: Galaxy Dynamics\n (04.01.1 ;\n 04.03.01) % Stars: fundamental parameters\n %19.63.1)\n }\n\n\\title{The VizieR database of Astronomical Catalogues}\n\n\\author{ Fran\\c cois Ochsenbein,\n Patricia Bauer,\n James Marcout\n %Fran\\c coise Genova\\inst{1}\n }\n\n \\institute{CDS,\n Observatoire Astronomique,\n UMR 7550,\n 11 rue de l'Universit\\'e,\n 67000 Strasbourg, France\n %\\and\n }\n\\offprints{F. Ochsenbein {\\em (francois}@{\\em astro.u-strasbg.fr)}}\n\\date{December 27, 1999}\n\\titlerunning{The \\VizieR\\ database of Astronomical Catalogues}\n\\authorrunning{Ochsenbein et al.}\n\\maketitle\n\n\\begin{abstract}\n\n\\VizieR\\ is a database grouping in an homogeneous\nway thousands of astronomical catalogues gathered since dec\\-ades by\nthe Centre de Donn\\'ees de Strasbourg (CDS) and participating institutes.\nThe history and current status of this large collection is briefly presented,\nand the way these catalogues are being standardized to fit in the \\VizieR\\\nsystem is described.\nThe architecture of the database is then presented, with emphasis\non the management of links and of accesses to very large catalogues.\nSeveral query interfaces are currently available, making use of the\n{\\em ASU} protocol, for browsing purposes or for use by other data\nprocessing systems such as visualisation tools.\n\\keywords{\nAstronomical data bases: miscellaneous --- Catalogs\n}\n\n\\end{abstract}\n\n%\\section{Historical Background}\n\\section{Introduction}\nThe { Centre de Donn\\'ees astronomiques de Strasbourg} (CDS)\nhas a very long experience in acquiring,\ncross-ident\\-ifying, and distributing astronomical data\n(Genova et al. \\cite{CDS}):\na collaboration for the exchange of what was called\n{\\em machine-readable} astronomical data started\nwith the {\\em NASA-GSFC} and the {\\em Astronomisches Rechen-Institut}\naround 1970.\nThis collaboration has been maintained over this 30 year period,\nand collaborations with other institutes for similar exchanges\nhave been developed.\nThe volume of data shared of course increased, at a rate\nwhich has been exploding in the recent years.%, tightly related to the\n%usage of the Internet.\n\n%{\\bf which kind of data}\nCompared to the late 60's, where the bulk of the {\\em machine-readable}\ndata consisted in a set of the basic catalogues carefully keypunched,\nthe situation has changed drastically, now that every instrument or\ndetector is generating megabytes or gigabytes of daily output.\nThese huge data sets are hopefully not stored in data centers,\nbut are processed in the observing center where the expertise\nexists to generate the best high-quality archives and\ncatalogues in a form usable\nby astronomers who are not familiar with the instrument.\nThe Data Centers' role is essentially to collect such\n``final'' catalogues, or more generally high-quality data,\n\\ie data which either were published in the refereed scientific literature,\nor at least a paper describing these data and their context was accepted\nfor publication in a refereed scientific journal.\n\nMaking an efficient usage of the data distributed by the data centers\n--- for instance for the analysis of the statistical properties\nof some interesting population of stars ---\noften requires to {\\em combine} data coming from several\ndata sets;\nthis operation is far from simple, and this is why the first creation\nof CDS was {\\sc SIMBAD},\na data-base resulting from the\ncross-identification of the major catalogues, later\nexpanded to thousands of catalogues and to published literature\n(see Wenger et al. \\cite{simbad}).\n\nThe \\VizieR\\ system results from a different approach: the\nastronomical catalogues are kept in their original form,\nbut homogeneous {\\em descriptions} of all these data sets\nare provided in order to maximize their usability.\nIn other words, \\VizieR\\ relies on an homogenization of the\n{\\em catalogue descriptions} --- what is also called\n{\\em metadata}, or data describing other data ---\nto transform the set of\n{\\em machine-readable} astronomical catalogues\ninto a set of {\\em machine-un\\-der\\-standable} data.\n\\VizieR\\ actually consists in an interface able to\nquery this set of\n{\\em machine-un\\-der\\-standable} astronomical catalogues.\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\Section{2}{Astronomical Catalogues}\n%can now be consulted in \\Aviz{cgi-bin/VizieR?-source=}{\\VizieR}\n% Convert to Copute Means: gawk -f /tmp/a\n%#\n%BEGIN { FS = \"&\" }\n%{ print; p += $2 ; e += $2*$3 }\n%END { printf(\"\\t& %5d\\t\\& %5.1f\\t%% Total\\n\",p,e/p) }\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%�\n\n\\begin{table*}[hbtp]\n%\\begin{center}\n\\begin{tabular}{| l || r r | r r | r r | r r | r r ||r r |} \\hline\n Journal & \\multicolumn{2}{|c|}{1994}\n & \\multicolumn{2}{|c|}{1995}\n & \\multicolumn{2}{|c|}{1996}\n & \\multicolumn{2}{|c|}{1997}\n & \\multicolumn{2}{|c||}{1998}\n & \\multicolumn{2}{|c|}{1994--1998}\n %& \\multicolumn{2}{|c|}{1999}\n \\\\\n & Papers & \\%El. & Papers & \\%El.\n & Papers & \\%El. & Papers & \\%El.\n & Papers & \\%El. & Papers & \\%El.\n \\\\ \\hline\n A\\&A & 1300 & 1.3 % 1994\n & 1223 & 2.9 % 1995\n & 1394 & 5.3 % 1996\n & 1525 & 6.6 % 1997\n & 1569 \t& 4.1 % 1998\n\t%&{\\em 1321} &{\\em 3.3} % 1999: 43\n\t& 5711\t& 4.8\t% Total\n \\\\\n A\\&AS & 236 & 42.8 % 1994\n & 269 & 42.0 % 1995\n & 438 & 28.4 % 1996\n & 298 & 49.0 % 1997\n & 159 & 43.3 % 1998\n\t%&{\\em 403} &{\\em 21.3} % 1999: 86\n\t& 1164\t& 38.9\t% Total\n \\\\\n ApJ(L) & 2064 & 0.3 % 1994\n & 2121 & 0.4 % 1995\n & 2166 & 1.1 % 1996\n & 2255 & 0.8 % 1997\n & 2235 & 0.6 % 1998\n\t%&{\\em 1894} &{\\em 0.1} % 1999: 1\n\t& 10841\t& 0.6\t% Total\n \\\\\n ApJS & 255 & 12.9 % 1994\n & 138 & 25.4 % 1995\n & 116 & 22.4 % 1996\n & 115 & 16.5 % 1997\n & 102 & 11.6 % 1998\n\t%&{\\em 99} &{\\em 2.0} % 1999: 2\n\t& 726\t& 17.2\t% Total\n \\\\\n PASP & 158 & 7.0 % 1994\n & 161 & 4.3 % 1995\n & 153 & 2.0 % 1996\n & 159 & 2.5 % 1997\n & 181 & 2.8 % 1998\n\t%&{\\em 157} &{\\em 157} % 1999: 2\n\t& 812\t& 3.7\t% Total\n \t\\\\\n AJ & 425 & 10.4 % 1994: 44\n & 504 & 14.1 % 1995: 71\n & 477 & 9.2 % 1996: 44\n & 460 & 8.3 % 1997: 38\n & 501 & 9.4 % 1998: 47\n\t%&{\\em 401} &{\\em 0.2} % 1999: 1\n\t& 2367\t& 10.3\t% Total\n \\\\\n MNRAS & 656 & 1.4 % 1994: 9\n & 752 & 2.7 % 1995: 20\n & 775 & 0.8 % 1996: 6\n & 833 & 1.6 % 1997: 13\n & 980 & 1.0 % 1998: 10\n\t%&{\\em 831} &{\\em 0.5} % 1999: 4\n\t& 3996\t& 1.5\t% Total\n \\\\\n\\hline\n\\end{tabular}\n\\caption{\\label{tab:etables}%Existence of electronic tabular data:\nEvolution of the annual number of papers, and the percentage of\npapers with associated electronic data, for some of the main astronomical\nmagazines}\n%\\end{center}\n\\end{table*}\n\n\\begin{table*}[hbtp]\n%\\begin{center}\n%\\footnotesize\n\\scriptsize\n\\begin{tabular}{|rl|rr|rr|rr|rr|rr|rr||r|} \\hline\n\\multicolumn{2}{|l|}{ {\\em Category }}&\n %\\multicolumn{2}{|c|}{May 1993}&\n \\multicolumn{2}{|c|}{June 1994}&\n \\multicolumn{2}{|c|}{June 1995 } &\n %\\multicolumn{3}{|c|}{Dec. 1995 }&\n \\multicolumn{2}{|c|}{June 1996 } &\n \\multicolumn{2}{|c|}{Oct. 1997 } &\n \\multicolumn{2}{|c|}{Oct. 1998} &\n \\multicolumn{3}{|c|}{Oct. 1999} \\\\\n & & % $N$ & Mb &\n $N$ & Mb & %\\mMb &\n $N$ & Mb & %\\mMb&\n $N$ & Mb & %\\mMb&\n $N$&Mb %\\mMb\n & $N$&Mb %http://vizier.u-strasbg.fr/cgi-bin/VizieR %\\mMb\n & $N$&Mb & {\\em Std}\n \\\\ \\hline\nI & Astrometric %& %Catalogues\n & 151 & 1258 %\n & 158 & 1292 %\n & 167 & 1460 %\n & 199 & 2502 %\n & 207 & 2777 %\n & 210 & 2798 & 113%\n \\\\\nII & Photometric %& %Catalogues\n & 144 & 307 %\n & 152 & 320 %\n & 153 & 305 %\n & 187 & 467 %\n & 194 & 525 %\n & 198 & 563 & 110%\n \\\\\nIII & Spectroscopic%& %Catalogues\n & 119 & 162 %\n & 126 & 172 %\n & 125 & 173 %\n & 158 & 233 %\n & 163 & 245 %\n & 170 & 249 & 100%\n \\\\\nIV & Cross-Identification % &\n & 16 & 89 %\n & 16 & 89 %\n & 15 & 83 %\n & 17 & 91 %\n & 17 & 91 %\n & 17 & 91 & 5%\n \\\\\nV & Combined Data % &\n & 63 & 367 %\n & 63 & 372 %\n & 65 & 365 %\n & 76 & 557 %\n & 84 & 728 %\n & 86 & 842 & 53%\n \\\\\nVI & Miscellaneous % & %Catalogues &\n & 43 & 157 %\n & 49 & 188 %\n & 50 & 502 %\n & 70 & 634 %\n & 71 & 634 %\n & 73 & 653 & 46%\n \\\\\nVII & Non-stellar% & %Objects &\n & 115 & 361 %\n & 119 & 280 %\n & 122 & 371 %\n & 157 & 425 %\n & 178 & 453 %\n & 180 & 453 & 121%\n \\\\\nVIII & Radio %& %Catalogues &\n & 24 & 269 %\n & 28 & 269 %\n & 29 & 269 %\n & 39 & 414 %\n & 46 & 615 %\n & 53 & 853 & 51%\n \\\\\nIX & High-Energy %& %Catalogues&\n & --- & --- %--- &\n & --- & ---% ---&\n & --- & --- % --- &\n & 6 & 77 %\n & 8 & 79 %\n & 10 & 200 & 10%\n \\\\\n\\hline \\hline\nJ/A+A & {\\em A\\&A}\n\t& 58 & 2 %\n & 98 & 4 %\n & 158 & 8 %\n & 299 & 16 %\n & 371 & 22 %\n & 424 & 26 & 424%\n\t\\\\\nJ/A+AS & {\\em A\\&A Supp.}\n & 123 & 12 %\n & 235 & 24 %\n & 350 & 33 %\n & 544 & 55 %\n & 698 & 73 %\n & 817 & 83 & 817%\n\t\\\\\nJ/AJ & {\\em Astron. J.}\n & 15 & 1 %\n & 91 & 6 %\n & 126 & 10 %\n & 252 & 21 %\n & 295 & 25 %\n & 345 & 31 & 345%\n\t\\\\\nJ/ApJS & {\\em ApJ Suppl.}\n & 13 & 1 %\n & 36 & 4 %\n & 52 & 7 %\n & 111 & 14 %\n & 147 & 16 %\n & 165 & 18 & 165%\n\t\\\\\nJ/(P)AZh & {\\em Russian Astron. J.}\n & --- & --- %--- &\n & --- & ---% ---&\n & --- & --- % --- &\n\t& 18\t& 0.2\n\t& 26\t& 0.5\n\t& 49\t& 0.9\t& 49\n\t\\\\\n\\hline\nJ & From Journals%&\n & 233 & 17 %\n & 517 & 40 %\n & 766 & 60 %\n & 1404 & 118 %\n & 1771 & 151 %\n & 2087 & 180 & 2087%\n \\\\\n\\hline \\hline\n & {\\em Grand Total} % &\n & 908 & 2986 %\n & 1228 & 3022 %\n & 1492 & 3588 %\n & 2313 & 5517 %\n & 2739 & 6299 %\n & 3084 & 6882 & 2692%\n \\\\\n\\hline\n\\end{tabular}\n\\normalsize\n\\caption{\\label{tab:contents}Summary of the evolution of\naccessible digital catalogues in the\nlast five years (number of catalogues and sizes in Mbytes).\nThe last column gives the number of catalogues with a standardized description\n(see \\secref{std}).}\n%\\end{center}\n\\end{table*}\n\nJaschek (\\cite{cj}) defined a catalogue as\na {\\em long} list of {\\em ordered data} of a specific kind,\ncollected for a {\\em particular purpose}.\n%For the electronic catalogues, the ordering is not really important\n%any more, and\nWhat a {\\em long} list means has evolved dramatically\nin the last decade:\nthe new way of processing data actually resulted in a tremendous increase\nin both the number and the volume of the astronomical catalogues.\n%each satellite mission now issues at least one very large catalogue.\nTo illustrate the evolution in the domain of catalogued {\\em surveys},\none can remember that the largest catalogues in the beginning of this century,\ncalled the {\\em Durchmusterungen} --- the {\\em Bonner},\n{\\em Cordoba} and {\\em Cape} Durchmusterungen ---\nprovided only a position and a visual estimate of the brightness\nfor $\\sim 1.5\\times10^6$ stars,\nand required over 50 years to be completed. Today, a catalogue\ngathering similar parameters\n--- %however\nwith an accuracy one order of magnitude better --- is\nwell represented by the USNO-A2.0 (\\cite{usno}) which contains roughly\n$5\\times10^8$ sources, almost three orders of magnitude larger.\nEven larger catalogues are being built: let us quote the\nGSC-II (Greene et al., 1998)\nwhich should contain all optical sources brighter than $18^{th}$ magnitude,\nwhich can be estimated to about $2\\times10^9$ objects.\n\nThe existence of these new {\\em mega-catalogues} --- which are, in fact,\nrather {\\em giga-catalogues} ---\ndoes however not mean that the\nold catalogues can just be ignored: virtually any astronomical object\ncan be subject to variability, maybe over periods of several centuries,\nand the discrepancies between old and newer results have therefore\nto be analyzed.\n\nAnother important source of %Besides the large catalogues, a large set of\ntabular material\n%(in terms of reusability)\nconsists in tables published in the astronomical literature.\nThese tables are now almost always originally in digital form,\nand contain highly processed data which usage can be precious;\naccess to these electronic data is also essential for maintaining\nthe large databases like {\\sc Simbad} or NED.\n\nThe potential interest of the reusability of these tables led\nthe Editors of the leading astronomical journals to\ndistribute the tabular material in electronic form.\nThe first realisations for {\\em A\\&A} started in 1993\n(see Ochsenbein \\& Lequeux \\cite{aatables}), and \\tabref{etables}\nsummarizes the frequency of the availability of electronic tabular data\namong the publications in some of the main astronomical journals\nin the recent years: not surprisingly, the {\\em Supplement Series},\nwhich were created essentially for the presentation of the observational\nresults, show a high rate of associated electronic data.\n\n%Evolution with the production of the {\\em electronic tables}\n%in A\\&A, an in other journals.\n\n\\Section{2'}{Astronomical Catalogues in the Data Centers}\n\n\\subSection{catcontents}{Current Contents}\nThe growth of the collection of astronomical catalogues\nmanaged by data centers is illustrated\nby \\Tabref{contents}: the current set of available catalogues is now around\n3,000, with an annual increase about 15\\%.\nNote that the entity designated as a ``catalogue''\ncan represent a table of about 100 entries\n(\\eg the list of galactic globular clusters),\nas well as a multimillion source catalogue (\\eg the USNO-A2.0).\n\nIn \\Tabref{contents}, the catalogues are grouped according\nto {\\em categories} which were defined in the 70's,\nwhen the bulk of astronomical\nstudies were dealing with the properties of stars in the optical\nwavelength domain. Rather than defining regularly a new classification scheme\nfollowing the evolution of the discipline, it was decided,\nin agreement with the other data centers,\nto assign designations to electronic tables\naccording to the published paper, and to reserve the assignment\nin the ``traditional'' categories\nto somewhat important catalogues or compilations.\nSimultaneously, it was decided to assign {\\em keywords} to each\ncatalogue, in order to allow easy retrieval of catalogues with similar\ncontents and purposes.\n\nNote that, if most of the catalogues contain data related to the observation of\nastronomical sources,\n%either actual observation or compilationcatalogues,\n%--- like the resulting catalogue of the {\\em Hipparcos} mission --- or from a\n%compilation.\nother types of data are also available, generally grouped in\nthe `Miscellaneous'' (VI) category:\ncatalogues of atomic data like wavelength tables or\nresults of the {\\em Opacity Project}, tabulated results\nof stellar evolution models, ephemeris elements, etc\\dots\n\n\\subSection{catusage}{Usage of astronomical catalogues}\n\n\\begin{table}[htbp]\n%\\begin{tabular}{|l| rr r r|}\n\\begin{tabular}{|l| rr r |}\n\\hline\nPeriod & Files & Gbytes & Nodes \\ignore{& Load }\\\\ \\hline\n1993Jan--1993Dec & 6106 & 1.5 & 458\t\\ignore{& 0.1 Kb/s }\\\\\n1994Jan--1994Dec & 23696& 6.1 & 1599\t\\ignore{& 0.2 Kb/s}\\\\\n1995Jan--1995Dec & 57314 & 11.4 & 4022 \\ignore{& 0.4 Kb/s}\\\\\n%1995Jun--1996May & 70100 & 15.9 & 4928 \\ignore{& 0.5 Kb/s }\\\\\n1996Jan--1996Dec & 71300 & 19.8 & 4953 \\ignore{& 0.6 Kb/s }\\\\\n%1996Jun--1997May & 90000 & 21.4 & 5464 \\\\\n1996Oct--1997Sep & 143000 & 43.5 & 6279 \\ignore{& 1.4 Kb/s}\\\\\n%1997Jan--1997Dec & 134618 & 49.5 & 4959 \\ignore{& 2.4 Kb/s}\\\\\n1997Oct--1998Sep & 308840 & 74.5 & 9780 \\ignore{& 2.4 Kb/s}\\\\\n%1998Jan--1998Dec & 384465 & 69.3 & 10360 \\ignore{& 2.4 Kb/s}\\\\\n1998Oct--1999Sep & 538407 & 77.1 & 10146 \\ignore{& 2.5 Kb/s}\\\\\n\\hline\n\\end{tabular}\n\\caption{\\label{tab:ftp} Yearly traffic on the CDS catalogue ftp server\n{\\em(internal and mirror traffic excluded)}}\n\\end{table}\n\nOne of the main goals of the CDS is to promote the usage of the reliable\nastronomical catalogues to the astronomical community.\nThe ``Catalogue Service'' has been one of the major CDS services since\nthe beginning of the CDS activity, and used to distribute catalogues\non magnetic tapes and floppies; the service has been implemented\non the network as a FTP server in March 1992, generating\nimmediately a large increase in\nthe number of distributed files. The FTP activity is still increasing at a high\nrate, as can be inferred from \\Tabref{ftp}: the current traffic\nis equivalent to a copy of the whole collection every month.\n\nIt is also interesting to quote those catalogues which are the\nmost frequently copied from the CDS archives, %which are\nsummarized in \\Tabref{top} for the last two years: not surprisingly,\n{\\em surveys}, and what Jaschek (\\cite{cj}), in his section 5.2,\ndesignates as {\\em General Compilation Catalogues},\nare among the most popular catalogues.\nIt is also interesting to note the large number of copies\nof the GSC catalogue (about 300 Mbytes): it was copied by over 500 nodes\nin the last 12 months, which is 4 times more than in the previous year;\nthis could indicate that\ncatalogues of this size can be quite easily managed on\nsmall computers nowadays.\n\n\n\\begin{table}[htbp]\n\\scriptsize\n\\begin{tabular}{| r r p{0.34\\textwidth}|} \\hline\n \\multicolumn{2}{|c}{Number of Nodes} & {Catalogue designation and short title} \\\\\n 1999&(1998)& \\\\ \\hline\n 879 &(750)&(I/239) Hipparcos \\& Tycho Catalogues \\\\\n 502 &(123)&(I/220) The HST Guide Star Catalog, V1.1 (Lasker+ 1992) \\\\\n 293&(165)& (VI/87) Planetary Ephemerides (Chapront+ 1996) \\\\\n 284&(241)&(I/131A) SAO Star Catalog J2000 (SAO Staff 1966; USNO, ADC 1990) \\\\\n 248 &(60)&(I/197) Tycho Input Catalogue, Revised version (Egret+ 1992) \\\\\n 203&(221)&(VII/118) NGC 2000.0 \\\\\n 195&(162)&(V/50) Bright Star Catalogue, 5th Revised Ed. (Hoffleit+, 1991)\\\\\n 173&(145)&(VI/80) Opacities from the Opacity Project (Seaton+, 1995)\\\\\n 169&(134)&(I/246) The ACT Reference Catalog (Urban+ 1997) \\\\\n 126& (142)&(V/70A) Nearby Stars, Preliminary 3rd Version (Gliese+ 1991) \\\\\n 124 &(120)&(VI/81) Planetary Solutions VSOP87 (Bretagnon+, 1988) \\\\\n 112 &(73)&(VII/207) Quasars and Active Galactic Nuclei (8th Ed.)\n \t(Veron+ 1998)\\\\\n 102& (134)&(II/214A) Combined General Catalogue of\n\tVariable Stars (Kholopov+ 1998) \\\\\n 101 &(76)& (VII/155) Third Reference Cat. of Bright Galaxies (RC3)\n \t(de Vaucouleurs+ 1991) \\\\\n 100 &(75)& (VI/79) Lunar Solution ELP 2000-82B (Chapront-Touze+, 1988) \\\\\n 99&(153)&(VI/69) Atomic Spectral Line List (Hirata+ 1995)\\\\\n 97&(149)&(V/95) SKY2000 - Master Star Catalog (Myers+ 1997) \\\\\n 90&(118)&(I/196) Hipparcos Input Catalogue, Version 2 (Turon+ 1993) \\\\\n %(98)&(I/146) PPM North Star Catalogue (Roeser+, 1988)\\\\\n %(95)&(V/84) Strasbourg-ESO Catalogue of Galactic Planetary Nebulae\n \t%(Acker+, 1992)\\\\\n % (91)&(I/237) The Washington Visual Double Star Catalog, 1996.0\n \t%(Worley+, 1996)\\\\\n %(85)&(II/183) UBVRI Photometric Standards (Landolt 1992) \\\\\n %(84)&(I/245) Orbital Elements of Minor Planets 1998 (Batrakov+ 1997)\\\\\n\\hline\\end{tabular}\n\\normalsize\n\\caption{\\label{tab:top} Catalogues which have been the most frequently\ncopied}\n\\end{table}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5\n\\Section{std}{Standardized Description of Astronomical Catalogues}\n\n\\begin{figure*}[hbtp]\n\\begin{center}\n\\scriptsize\n\\begin{verbatim}\nI/221 The Magellanic Catalogue of Stars - MACS (Tucholke+ 1996)\n================================================================================\nThe Magellanic Catalogue of Stars - MACS\n Tucholke H.-J., de Boer K.S., Seitter W.C.\n <Astron. Astrophys. Suppl. Ser., 119, 91-98 (1996)>\n <The Messenger 81, 20 (1995)>\n =1996A&AS..119...91T =1995Msngr..81...20D\n================================================================================\nADC_Keywords: Magellanic Clouds ; Positional data\n\nDescription:\n The Magellanic Catalogue of Stars (MACS) is based on scans of ESO\n Schmidt plates and contains about 244,000 stars covering large areas\n around the LMC and the SMC. The limiting magnitude is B<16.5m and the\n positional accuracy is better than 0.5\" for 99% of the stars. The\n stars of this catalogue were screened interactively to ascertain that\n they are undisturbed by close neighbours.\n\n\nFile Summary:\n--------------------------------------------------------------------------------\n FileName Lrecl Records Explanations\n--------------------------------------------------------------------------------\nReadMe 80 . This file\nlmc 52 175779 The Large Magellanic Cloud\nsmc 52 67782 The Small Magellanic Cloud\n--------------------------------------------------------------------------------\n\nByte-by-byte Description of file: lmc smc\n--------------------------------------------------------------------------------\n Bytes Format Units Label Explanations\n--------------------------------------------------------------------------------\n 1- 12 A12 --- MACS Designation\n 14- 15 I2 h RAh Right Ascension J2000 , Epoch 1989.0 (hours)\n 17- 18 I2 min RAm Right Ascension J2000 (minutes)\n 20- 25 F6.3 s RAs Right Ascension J2000 (seconds)\n 27 A1 --- DE- Declination J2000 (sign)\n 28- 29 I2 deg DEd Declination J2000 , Epoch 1989.0 (degrees)\n 31- 32 I2 arcmin DEm Declination J2000 (minutes)\n 34- 38 F5.2 arcsec DEs Declination J2000 (seconds)\n 40 I1 --- Npos Number of positions used\n 42- 46 F5.2 mag Mag []?=99.00 Instrumental Magnitude\n (to be used only in a relative sense)\n 48 I1 --- PosFlag [0/1] Position Flag (0: ok,\n 1: internal error larger than 0.5\")\n 50 I1 --- MagFlag [0/1] Magnitude Flag (0: ok,\n 1: bad photometry or possible variable)\n 52 I1 --- BochumFlag *[0] Bochum Flag\n--------------------------------------------------------------------------------\nNote on BochumFlag: 1 if in Bochum catalog of astrophysical information\n on bright LMC stars (yet empty)\n--------------------------------------------------------------------------------\n\nAuthor's address:\n Hans-Joachim Tucholke <tucholke@astro.uni-bonn.de>\n\n================================================================================\n(End) Hans-Joachim Tucholke [Univ. Bonn] 20-Nov-1995\n\\end{verbatim}\n\\normalsize\n\\caption{\\label{fig:readme}Example of a documentation {\\tt ReadMe} file }\n\\end{center}\n\\end{figure*}\n\nMaking use of the data contained in a set of rapidly evolving catalogues,\nas illustrated by \\Tabref{contents},\nraises the problem of accessing and {\\em understanding} accurately\nthe parameters contained in catalogues which are constantly improved.\n%have nowadays rather short lifetimes.\nTypical questions to be addressed are:\ndoes the catalogue contain colours; if yes what is their reliability;\nare they expressed in a well-known standard system; are they taken from\nother publications or catalogues;\nhow can the associated data file be processed?\nAll these details which describe the data --- the {\\em metadata} ---\nare traditionally\npresented in the introduction of the printed catalogue, or\ndetailed in one or several published papers presenting\nand/or analyzing the catalogued data.\n\nMetadata play therefore a fundamental role: first the\nscientists have to get information about the\n{\\em environment} of the data in order to make\ntheir judgement about the suitability of the data for their project, such as:\ndate and/or method of acquisition, related publications,\nestimation of the internal and external errors, %possible distorsions,\npurpose of the data collection, etc.;\nbut also a minimal knowledge of the metadata is required by\nthe data processing system\n%to understand the data not only as arrays of numbers\nin order to merge or compare data from different origins ---\nfor instance, the comparison of data expressed in different units\nrequires a unit-to-unit conversion which can be performed\nautomatically only if the units are specified unambiguously.\n\nThis need for a description which is readable both by a computer\nand by a scientist led to a standardized way of documenting astronomical\ncatalogues and tables,\npromoted by CDS from 1993\nin the form of a dedicated {\\tt ReadMe} file associated to each catalogue\n(Ochsenbein \\cite{readme}).\nAn example of such a file is presented in \\figref{readme}:\nit is a plain ascii file, quite easy to interpret for a scientist,\nand at the same time structured enough to be interpreted\nby a dedicated software.\nThe {\\tt ReadMe} description file\nstarts with a {\\em header} specifying the basic references\n--- title, authors, references ---\nand contains a few key sections introduced by standard titles like\n{\\tt Description:} or {\\tt Byte-by-byte Description of file:}.\nSuch a file is relatively easy to produce by someone who\nknows the catalogue contents.\nThe example of\n\\figref{readme} represents the documentation of\na very simple catalogue, made of just two data tables, each\nwith a small set of parameters.\nThe \\Aviz{cgi-bin/Cat?I/239}{output catalogue of the \\HIP\\ mission}\nis an example of a much more complex catalogue: it\nis composed of two fundamental large tables (HIP with $10^5$ stars\nand TYC with $10^6$ stars) and includes\na dozen of annex tables, but can still be described by the\nthe same kind of simple standardized documentation.\n\nThe most important part of the {\\tt ReadMe} file\nis the \\\\{\\tt Byte-by-byte Description} which details the table structures\nin terms of {\\em formats}, {\\em units}, column naming or {\\em labels},\n{\\em existence of data}\n(possibility of unspecified or {\\em null} values), and brief explanations.\nAmong the conventions, some fundamental parameters are assigned\nfixed labels like sky coordinates (components of right ascension {\\tt RA}...\nand declination {\\tt DE}... in \\figref{readme}); a {\\em prefix} convention,\ndetailed in \\tabref{prefix}, is also used to specify obvious relations\nbetween a value, its mean error, its origin, etc...\n\n\\begin{table}[hbtp]\n\\begin{center}\n\\scriptsize\n%\\begin{tabular}{lll} \\hline\n\\begin{tabular}{lp{.36\\textwidth}} \\hline\n\\colheader{Symbol} & \\colheader{Explanation} %& \\colheader{Default Limits}\n\t\\\\ \\hline\n%{\\tt 2\\_{\\em label}} & $\\chi^2$ value\n%\t\ton parameter {\\em label} \\ignore{& $\\geq0$} \\\\\n{\\tt a\\_{\\em label}} & {\\em aperture} used for\n\t\tparameter {\\em label} \\ignore{& $\\geq0$} \\\\\n{\\tt E\\_{\\em label}} & mean error (upper limit)\n\t\ton parameter {\\em label} \\ignore{& $\\geq0$} \\\\\n{\\tt e\\_{\\em label}} & mean error ($\\sigma$)\n\t\ton parameter {\\em label} \\ignore{& $\\geq0$} \\\\\n{\\tt f\\_{\\em label}} & {\\em flag}\n\t\ton parameter {\\em label} \\ignore{& } \\\\\n{\\tt l\\_{\\em label}} & {\\em limit flag}\n\t\ton parameter {\\em label} \\ignore{& {\\tt[<>]}} \\\\\n{\\tt m\\_{\\em label}} & {\\em multiplicity index}\n\t\ton parameter {\\em label} to resolve ambiguities \\ignore{& } \\\\\n{\\tt n\\_{\\em label}} & {\\em note} (remark)\n\t\ton parameter {\\em label} \\ignore{& } \\\\\n{\\tt o\\_{\\em label}} & number of {\\em observations}\n\t\ton parameter {\\em label} \\ignore{& $\\geq0$} \\\\\n{\\tt q\\_{\\em label}} & {\\em quality}\n\t\ton parameter {\\em label} \\ignore{& } \\\\\n{\\tt r\\_{\\em label}} & reference (source) for parameter {\\em label}\n\t\t\\ignore{& } \\\\\n{\\tt u\\_{\\em label}} & {\\em uncertainty flag}\n\t\ton parameter {\\em label} \\ignore{& {\\tt[ :]}} \\\\\n{\\tt w\\_{\\em label}} & {\\em weight} of parameter {\\em label}\n\t\t\\ignore{& $\\geq0$} \\\\\n{\\tt x\\_{\\em label}} & unit in which parameter {\\em label} is\n\texpressed \\ignore{& } \\\\\n\\hline\\end{tabular}\n\\normalsize\n\\caption{\\label{tab:prefix}Conventions used for { label} {\\em prefixes} }\n\\end{center}\n\\end{table}\n\nThis standardized way of presenting the metadata\npro\\-ved to be extremely useful, especially for {\\em data checking}\nand {\\em format conversion}:\nmany errors were detected in old catalogues simply because a\ngeneral checking mechanism became available.\nTools have been developed for generating a Fortran source\ncode which loads the data into memory,\nor for converting the data into the FITS format\nwhich is presently the most ``universal'' data format understood by\ndata processing systems in astronomy --- but unfortunately a data\nformat which is not convenient outside this context\n(see \\eg Gr\\o sb\\o l et al. \\cite{fits}).\n\nDuring the six years since this standardized way of describing\nastronomical catalogue has been defined,\nover 2,600 astronomical catalogues have been described\nby means of this {\\tt ReadMe} file, and the same conventions have been adopted\nby the other astronomical data centers and journals for\nthe electronic publication of tables.\nThe present (October 1999) figures of the amount of standardized\ncatalogues are summarized in the rightmost column\nof \\Tabref{contents}; previous figures\nwere presented in an earlier paper (Ochsenbein \\cite{russie}).\n\nIt is expected, in the future,\nthat the authors will supply the documentation of their data\nin this simple form;\nit is already the case for a very significant fraction of\nthe tables mailed to the CDS,\nand in order to help the authors,\ntemplate files as well as a few \\A{http://vizier.u-strasbg.fr/doc/submit.htx}\n{tips on how to create the {\\tt ReadMe} file are accessible on the Web}.\nThe {\\tt ReadMe} files and the data files are then checked by a specialist,\nwho contacts the authors if errors are detected or when changes are\nnecessary to increase the clarity or homogeneity of the description.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\Section{4}{\\VizieR\\ Organisation}\n\n\\A{http://vizier.u-strasbg.fr/}{\\VizieR} is a natural extension\nof the usage of the metadata stored in the\n{\\em ReadMe} files, as an implementation of these metadata\nin terms of tables managed by a relational database management\nsystem (RDBMS).\n\nThe first prototype of \\VizieR\\ was the result of a fruitful collaboration\nbetween {\\em ESIS} (European Space Information System,\na project managed by ESRIN, a department of the European Space Agency)\nand the CDS; \\VizieR\\ has been under full responsibility of CDS since\nJanuary 1996.\nIt was presented at the 1996 AAS meeting (Ochsenbein et al., \\cite{aas96}),\nand became fully operational in February 1996.\nThis prototype has been significantly upgraded in May 1997, just\nin time for the implementation of the final catalogues of the Hipparcos\nmission. %, described in somewhat more\n%details at an ADASS conference (Ochsenbein \\cite{adass97}).\n%The described version of the {\\em META} dictionary was first\n%implemented in 1997 (Ochsenbein \\cite{adass97}).\n%\\VizieR\\ was first presented at the AAS meeting\n%(Ochsenbein et al., \\cite{aas96})\n%in the beginning of 1996, and is described in somewhat more\n%details at an ADASS conference (Ochsenbein \\cite{adass97}).\nThe number of catalogues\naccessible within the \\VizieR\\ system has grown since that time\nto 2,374 catalogues (\\Tabref{vizcounts}).\n\n%\\Section{5}{\\VizieR\\ Metadata}\n\n\nThe core of \\VizieR\\ consists in the organisation\nof the {\\em meta dictionary}, i.e. the set of metadata extracted from the\nstandardized {\\tt ReadMe} descriptions discussed in \\secref{std}.\nThere are however two main problems which had\nto be solved: the access to very large catalogues (larger than a\nfew million rows) for\nwhich RDBMS proved to be inefficient, requiring therefore\ndedicated search methods, % briefly presented in \\secref{L};\nand the generation of {\\em links} allowing to connect two related pieces of\ninformation, like other tables in the same catalog, or\nspectra, images from remote services, etc.%, presented in \\secref{6}.\n\n\\subSection{meta}{META dictionary}\n\n\\begin{table}[htb]\n\\begin{tabular}{|ll|r|r|}\\hline\n\\multicolumn{2}{|l|}{\\VizieR\\ contents}\t& All \t& Dealing with objects \\\\\n\\multicolumn{2}{|l|}{in terms of:}\t& Catalogues\t& having positions\\\\ \t\t\t\t\\hline\n\\multicolumn{2}{|l|}{{\\em Catalogues:}}\t& 2374\t& 1247 \\\\\n\\multicolumn{2}{|l|}{{\\em Tables:}}\t& 6071\t& 1929 \\\\\n\\multicolumn{2}{|l|}{{\\em Columns:}}\t& 77260\t& 30261 \\\\\n\\multicolumn{2}{|l|}{{\\em Rows:}}\t& $1.17\\times10^9$ &$1.16\\times10^9$\\\\\n\t& {\\em(without megacatalogs)} \t& $40.3\\times10^6$ &$31.6\\times10^6$\\\\\n\\hline\\end{tabular}\n\\caption{\\label{tab:vizcounts}Summary of the \\VizieR\\ contents (November 1999)}\n\\end{table}\n\nThe meta-dictionary consists in 3 main tables\ndetailed below, and about 20 annex tables, all stored in a relational\ndatabase:\n\n\\begin{enumerate}\n\\item\t{\\em METAcat} describes the {\\em catalogues}, a\n\t{\\em catalogue} being defined as a set of related tables\n\tpublished together: typically a catalogue\n\tgathers a table of observations,\n\t\ta table of mean values, a table of references,\n\t\ta list of related images, etc\\dots;\n\t{\\em METAcat} details the authors, reference,\n\ttitle, explanations of each stored catalogues.\n\tThis table contains currently 2,374 rows (\\Tabref{vizcounts}).\n\t%of the \\about\\ 2400 stored catalogues.\n\\item\t{\\em METAtab} describes each {\\em data table} stored in \\VizieR:\n table caption, number of rows, how to\n\taccess the actual data, the equinox and epoch of the coordinates,\n\tetc\\dots\n\tThis table contains currently 6,071 rows (\\Tabref{vizcounts}) ---\n\t\\ie the average catalogue is made of 2.6 tables.\n\\item\t{\\em METAcol} details each\n\tof the 77,260 columns (\\Tabref{vizcounts}) currently\n\tstored in \\VizieR: column name or {\\em label},\n\tthe textual {\\em explanation} of the column contents,\n\t{\\em datatypes} (numeric or character) and storage mode\n\twithin the database (integer or floating-point, maximal length of\n\tstrings, etc), {\\em units} in which the data are stored in the\n\tdata-base and {\\em units} in which the data are presented\n\tto the user, edition formats, and a few flags used for searches (e.g.\n\tcolumn used as primary key) or data presentation (e.g. column\n\tto be displayed in the default presentation of the result).\n\tThe average table is therefore made of $\\sim 12.7$ columns ---\n\tin fact $\\sim 11.7$ because each table contains an {\\em identification}\n\tcolumn in addition to the original set of columns.\n\\end{enumerate}\nNote that, since the set of {\\em META} tables is itself described in \\VizieR,\nthe meta-dictionary can be viewed and queried like any\nof the catalogues stored in \\VizieR\\ --- allowing to locate easily \\eg\ntables with a large number of rows, or catalogues having the words\n{\\em mass loss} in the description of one of their columns,\netc\\dots\n\nThe annex tables of the meta-dictionary contain some definitions,\nlike the list of known data-types {\\em(METAtypes)} and\nkeywords {\\em(METAkwdef)};\nor other details like the acronyms\nused to designate well-known catalogues like {\\em HIP}, {\\em GSC}\n\\dots {\\em(METAcro)},\nthe keywords associated to each catalogue {\\em(METAkwd)}, detailed notes\nand remarks {\\em(METAnot)}, or the list of those objects which are\nindividually quoted in the {\\tt ReadMe} files {\\em(METAobj)}.\nA special indexing scheme {\\em(METAcell)}, explained briefly in\n\\secref{cell}, was built to locate the existing objects in all catalogues\nin a single run.\nDetails on how to generate links are stored in the {\\em METAmor} table.\n\n\\subSection{link}{Links in \\VizieR}\nThe interest of having a {\\em link}, or an {\\em anchor} in HTML terms,\nbecomes obvious when a table contains a column representing\na reference to an original paper, % quoting the result detailed in another table,\nas for example in \\Aviz{cgi-bin/VizieR?-source=7207/table1}{V\\'eron\nand V\\'eron's\ncompilation of quasars}: once the rules to transform the contents\nof this column into an actual link to \\eg the\n\\A{http://adswww.harvard.edu/}{ADS bibliographic service} is set up,\ndetails about the authors and references,\nor even the full article, can then be displayed on the screen by a\nsimple mouse click. Another frequent example is the possible expansion\nof some footnote symbol into the\nlengthy note detailed in some other table.\n\nThe links existing in \\VizieR\\ may be classified in the following categories:\n\\begin{enumerate}\n\\item\t{\\em hard-wired links} which are part of the standard description\n\tpresented in \\secref{std}, like the existence of\n\tnotes (stored in the {\\em METAnot} table), or the {\\tt r\\_} prefix\n\t(\\tabref{prefix}) %in a column label\n\twhich indicates a reference\n\twhich may be detailed in a table of references;\n\\item\t{\\em internal links} which connect tables of the same catalogue:\n\tsuch links may be expressed in terms of {\\em keys} in the\n\tRDBMS terminology (definitions of columns as primary and/or foreign keys),\n\tby the existence of {\\em note flags}, or\n\tby more complex relations stored in the {\\em METAmor} table.\n\tAnother type of {\\em internal link} allows one to retrieve\n\tthe spectra or images which are part of the catalogue,\n\tbut which are stored as separate files.\n\\item\t{\\em \\VizieR\\ links} which refer to another catalogue\n\twithin the \\VizieR\\ system;\n\\item\t{\\em external links} which refer to any other service, like\n\tbibliographic services, external databases or archives,\n\timage servers, etc.\n\\end{enumerate}\n\nWhile links of the first 3 categories can easily be maintained,\nthe maintenance of the {\\em external links} depends on modifications\nwhich are completely outside \\VizieR's control.\nThese external links are maintained by the {\\em GLU} system\n(Fernique et al., \\cite{GLU}), a system which %basically\n(i) allows one to use {\\em symbolic names} instead of hard-coded URLs,\nand (ii) translates these symbolic names\nwith the help of a {\\em distributed} dictionary\nin which the service providers keep up the descriptions of their\nown services only\nin terms of URL addresses and actual presentation of the query\nparameters.\n\n\\subSection{pipeline}{\\VizieR\\ feeding pipeline}\nOn the average, about one new catalog -- or 2.6 tables -- is added\n{\\em daily} into VizieR. Such figures imposed the\nfollowing constraints on the addition of new tables into \\VizieR:\n\\begin{enumerate}\n\\item\tno human intervention is required to populate the database\n\t(the meta dictionary and the data tables):\n\tall meta-data related\n\tto a catalogue can be found or computed on the basis of\n\tdocumentation and configuration files which are read by\n\tthe \\VizieR\\ feeding pipe-line ;\n\\item\twe rely as much as possible on the\n\t{\\em standardized description} of the catalogues presented\n\tin \\secref{std}:\n\tthis means that the configuration file associated to\n\teach catalogue should be minimized, i.e.\n\tas few {\\em ad-hoc} details as possible\n\tshould be needed besides the {\\tt ReadMe} files.\n%\\item\tthe system must be {\\em efficient}\n%\tand guarantee that the frequently asked searches\n%\t(typically from a position on the sky, but \\VizieR\\\n%\talso includes frequently used reference tables of atomic\n%\tradiations for which\n%\tthe typical search is based on the wavelength)\n%\tcan be achieved in less than a second,\n%\tregardless of the catalogue size.\n\\end{enumerate}\n\nThe actual delay required to ingest a new catalogue\ninto the system is currently estimated to\nsomething between a few minutes and several days for the preparation of\n\tthe {\\tt ReadMe} description file, depending on the\n\tinitial presentation supplied by the authors and on the\n\tcatalogue complexity --- the delay can\n\tbe occasionally longer when problems are encountered, requiring\n\tinteractions with the authors;\nand\ta few seconds up to an hour for the actual ingestion into \\VizieR\\\n\tfrom the standardized files.\n\n\n%\\Section{L}{Access to Very Large Catalogues}\n\\subSection{L}{Access to Very Large Catalogues}\n\\begin{table}[htb]\n\\begin{tabular}{lrp{0.28\\textwidth}} \\hline\nAcronym & Rows & Catalogue designation \\\\\n & ($\\times10^6$) \\\\ \\hline\nUSNO-A1.0 & 488.0 & The USNO-A1.0 Catalog (Monet 1997) \\\\\nUSNO-A2.0 & 526.3 & The USNO-A2.0 Catalog (Monet 1998),\n\t\t\tcalibrated against Tycho data \\\\\nGSC1.1 & 25.2 & HST Guide Star Catalog, 1992 version \\\\\nGSC1.2 & 25.2 & HST Guide Star Catalog, 1996 version \\\\\nGSC-ACT& 25.2 & HST Guide Star Catalog, calibrated against Tycho data${}^\\dag$\\\\\n2MASS & 20.2 & $2\\mu m$ All Sky Survey, Spring 1999 release\n\t\t(Skrutskie et al., \\cite{2mass}) \\\\\nDENIS & 17.5 & Deep Near-IR Survey first release\n\t\t(Epchtein et al., \\cite{DENIS})\\\\\n\\hline\\end{tabular}\n{\\footnotesize $\\dag$ calibration made by the {\\em Pluto project} \\\\\n\t(http://www.projectpluto.com/gsc\\_act.htm)}\n\\caption{\\label{tab:megacat} Large catalogues currently\nimplemented in \\VizieR}\n\\end{table}\n\nThe second challenge is to open a fast access for querying\nthe {\\em mega-catalogues}\nintroduced in \\secref{2}. This denomination was\nsomewhat arbitrarily assigned to catalogues having $10^7$ or more\nrows. Such large catalogues are essentially surveys used as\n{\\em reference catalogues},\ntypically to find all objects detected in some region of the\nsky under some conditions of wavelength, time, object structure, etc.\nThe set of such catalogues currently implemented is summarized\nin \\Tabref{megacat}, but this set will grow rapidly in the near future\nwith the continuation of the infra-red surveys,\nand the emergence of surveys presently in preparation\n(SLOAN, GSC-II, NVSS, \\dots).\n\nThe limit of $10^7$ rows corresponds to a limit in performance and\ntime required to ingest the tables into\nthe relational data\\-ba\\-ses;\nthe largest table, in terms of number of rows, currently stored in\n\\VizieR\\ is the {\\em AC2000} catalog (Urban et al., \\cite{ac2000}),\nwith $4.62\\times10^6$ rows.\n\nThe method used to access these very large catalogues %basically\nconsists in grouping the objects within carefully designed {groups}\nbased essentially on the location in the sky,\nfollowed by a lossless compression obtained by replacing the\nactual values by offsets within the group;\ndetails about the actual results and performances are\ndescribed in another paper (Derriere \\& Ochsenbein,\n\\cite{adass99-poster}).\nEach very large catalogue has presently its own organisation\nwhich depends on its actual column contents,\nand therefore requires a dedicated program for accessing it.\n\\VizieR\\ stores in its {\\em META} dictionary (see \\secref{meta})\nwhich program has to be called to actually access the catalogue,\nand the description of the columns as they are returned from\nthe dedicated program.\n\n\n\\subSection{cell}{Accessing all catalogues from a position in the sky}\nIn order to allow a fast answer to the question:\n{\\em find out all objects for all available catalogues around\nsome target position}, an indexing mechanism is necessary.\nThe total number of object positions currently stored in \\VizieR,\nexcluding the {\\em megacatalogues}, is\nabout $32\\times10^6$ (\\Tabref{vizcounts}); a classical indexation, in\nterms of relational DMBS, shows very poor performances\nespecially in the updating phase: the addition of a new catalogue\ncan require up to 4.6 millions modifications or additions --\nwhich becomes dramatically slow.\n\nThe method adopted for this indexation consists first in a mapping\nof the celestial coordinates into a set of boxes using a\nhierarchical spherical-cubic projection similar to\nthe techique used by {\\sc Simbad}\n(Wenger et al., \\cite{simbad}), but down to a level 8 which corresponds\nto a granularity of about $20'$, or\n$6\\times4^8$ ($\\simeq 4\\times10^5$) individual boxes.\nThe list of catalogues which exhibit sources in the region of the sky\ncovered by the box is then stored for each of the defined boxes,\nallowing therefore a fast answer to the question:\n``what is the list of catalogues\nwhich have a fair chance of having at least one source close to\na specified target~?'' The final step consists in looking successively\ninto the matching catalogues.\n\nThe method offers the particularity of being {\\em hierarchical}:\n6 boxes are defined at level 0, 24 at level 1, \\dots,\nand going down one step in the\nhierarchy consists in dividing each box into four parts.\nThe indexing mechanism recursively groups contiguous non-empty boxes\nrepresented by a single box\nat the upper level, meaning that a dense survey covering the whole\nsky is just represented by the 6 boxes of level 0 in this index.\nIn practice, the 1247 catalogues with positions are summarized in\nthis index by $3.9\\times10^6$ elements (to be compared to the\n$31.6\\times10^6$ sources in \\Tabref{vizcounts}), \\ie an average of\n3,000 elements per catalogue.\n\n\\subSection{vizcontents}{Current Contents}\n\n\\begin{figure}[htb]\n%\\resizebox{\\hsize}{!}{\\includegraphics{vizh1.ps}}\n\\begin{center}\n\\psfig{figure=vizh1.ps,width=\\hsize}\n\\end{center}\n%\\psfig{figure=viz-histo.eps,width=8cm,angle=90}\n%\\resizebox{\\hsize}{!}{\\rotatebox{+90}{\\includegraphics{viz-histo.eps}}}\n%\\vspace*{-3cm}\n%\\resizebox{\\hsize}{!}{\\rotatebox{-90}{\\includegraphics{viz-histo.eps}}}\n\\caption{\\label{fig:vizhisto}Histogram of the number of rows among\n \\VizieR\\ tables (the darker bars correspond to tables containing celestial coordinates).}\n\\end{figure}\n\nThe status of \\VizieR\\ contents is presented in\n\\Tabref{vizcounts}, where we distinguished those tables representing\ndata about actual {astronomical objects} which can be accessed by\ntheir position in the sky. In terms of number of available records,\nthose containing celestial positions represent over 78\\% even\nwhen the {\\em megacatalogs} are omitted, even though only 32\\% of the\ntables are concerned. In other words, the average table dealing with\nactual astronomical objects contains around 16,000 rows ---\na theoretical mean, as can be seen from the histogram of the table\npopulations in \\VizieR\\ represented in \\figref{vizhisto} which shows\na modal value around tables of 100 objects.\n\n%, represented\n%by 6,071 tables, and a total of 77,260 described columns (November 1999)\n%(\\Tabref{vizcounts}).\n\\Section{U}{\\VizieR\\ Interfaces}\n\n\\begin{figure}[htb]\n\\resizebox{\\hsize}{!}{\\includegraphics{viz1.ps}}\n%\\resizebox{\\hsize}{!}{\\includegraphics{viz-fig1.ps}}\n\\caption{\\label{fig:netscape}Excerpt of the \\VizieR\\ first search page\n }\n\\end{figure}\n\nSeveral interfaces are currently available for an access to the\ndata stored in \\VizieR: directly from a Web browser,\nvia a construction of the query using the {\\em ASU} conventions,\nor the developing {\\em XML } interfaces.\n\n\\subSection{netscape}{Access from a Browser}\nFrom a WWW-browser, a ``standard query'' in \\VizieR\\ consists in a few steps:\n\\begin{enumerate}\n\\item\t\n\tLocate the interesting catalogues in the\n\t\\Aviz{cgi-bin/VizieR}{\\VizieR\\ Service}.\n\tThis can be done in various ways illustrated in \\figref{netscape}:\n\tfrom well-known catalogue\n\tacronyms like {\\em HIP} or {\\em GSC},\n\tfrom a choice in the set of predefined keywords,\n\tfrom authors' names, or from a self-organizing (or\n\tKohonen) map\n\tconstructed on the basis of the keywords attached to\n\tthe catalogues (Poin\\c cot et al. \\cite{kohonen}).\n\tNew possibilities for locating catalogues of interest for the user\n\tare currently under development.% (see \\secref{7}).\n\n\\item\tOnce a catalog table -- or a small set of catalog tables ---\n\tis located (for instance the\n\t\\Aviz{cgi-bin/VizieR?-source=I/239/hip\\_main}{\\HIP\\ Catalog}\n\tresulting from the \\HIP\\ mission),\n\t{\\em constraints} about what to search and how to\n\tpresent the results can be specified, as:\n\t\\begin{itemize}\n\t\\item\tconstraints based on the celestial coordinates, i.e.\n\t\tlocation in the neighbourhood of a target specified\n\t\tby its actual coordinates in the sky, or by\n\t\tone of its name as known in {\\sc Simbad} (see Wenger et al.,\n\t\t\\cite{simbad})\n\t\\item\tany other constraint on any of the columns\n\t\tof the table(s), like a minimal flux value,\n\t\tor the actual existence of some parameter\n\t\t(non-{\\em NULL} value)\n\t\\item\twhich columns are to be displayed, and in which order\n\t\tthe matching rows are to be presented.\n\t\\end{itemize}\n\tBy pushing the appropriate buttons, it is for instance\n\teasy to get the\n\t\\Aviz{cgi-bin/VizieR?-source=I/239/hip\\_main\\&-sort=-\\-Plx\\&Plx=\\%3e=200}\n\t{list of \\HIP\\ stars closer than 5 parsecs to the Sun,\n\tordered by their increasing distance}.\n\n\\item\tObtaining full details about one row is achieved by a %simple\n\tmouse click in the first column of the result: for instance,\n\tthe first row of the search for nearby stars described above\n\tleads to the\n\t\\Aviz{cgi-bin/VizieR-5?-source=I/239/hip\\_main\\&HIP=70890}\n\t {\\VizieR\\ Detailed Page with \\HIP\\ parameters and\n\t their explanations concerning\n\t Proxima Centauri}.\n\n\\item\tFinally, there may be correlated data, like notes or remarks,\n\treferences, etc\\dots. In our example, Proxima Centauri\n\tis related to the $\\alpha$ Cen multiple star system,\n\twhich components can be viewed from the\n\t\\Aviz{cgi-bin/VizieR-6?-source=1239\\&-corr=PK=CCDM\\&CCDM==14396-6050}\n\t{link to the double and multiple stars (CCDM)}\n\tthat appears in the detailed page.\n\\end{enumerate}\n\nThe quantitative monthly usage of \\VizieR\\ is presently\n(October 1999) about 40,000 external requests\nfrom 2700 different nodes;\nmirror copies were installed recently in the\n\\A{http://adc.gsfc.nasa.gov/vizier/}{US} and in\n\\A{http://z13.mtk.nao.ac.jp/vizier/}{Japan}\nin order to overcome the transcontinental network congestions.\n%1,000 different nodes effectively\n%submitted queries to \\VizieR\\\n%during the first\n%3 months of the new installation (June to August 1997);\n%among all queries, about 40\\% of the hits concern the\n%recent results of the \\HIP\\ and \\TYC\\ missions.\n\n%\\begin{figure}\n%\\vbox to 5cm { }\n%\\caption{\\label{fig:ftp}Evolution of the usage of the CDS FTP downloading}\n%\\end{figure}\n\n\\subSection{asu}{The ASU protocol}\n%From the user's point of view,\nThe uniform access to all catalogues is based on the so-called\n\\Aviz{doc/asu.html}{ASU} (Astronomical Standardized URL)\nprotocol resulting from discussions between several institutes\n(CDS, ESO, CADC, Vilspa, OAT).\nThe basic concept of ASU\nis a standardized way of specifying queries to remote catalogues\nin terms of HTTP requests:\nthe target catalogue is specified by a \\quad\n{\\tt-source=}{\\em catalog\\_designation}\nparameter,\nthe target sky position by a \\quad\n{\\tt-c=}{\\em name\\_or\\_position}{\\tt,rm=}{\\em ra\\-dius\\_in\\_arcmin} parameter,\nthe output format by {\\tt-mime=}{\\em type},\nand general constraints on parameters by\n\\quad{\\sl column\\_name}{\\tt=}{\\em constraint}.\nIt should be noticed that the representation of a target by the name of\nan astronomical object (typically a star or galaxy name, \\eg {\\em 3C 273})\nimplies the usage of a {\\em name server} converting a target name\ninto a position in the sky,\nwhich is typically achieved by a call to {\\sc Simbad}.\n\n%All our observations were short direct exposures with\n%\\htmladdnormallinkfoot{CCD's}{http://www.noao.edu/}.\n\n\\subSection{xml}{The XML Interface}\n\nThe output of a query to \\VizieR\\ %for a browsing application\nas presented in \\secref{netscape} can hardly be used\nby an independent application for further data processing,\n%a typical example of a very useful application is represented\nsuch as the \\A{http://aladin.u-strasbg.fr/}{{\\sc Aladin}}\nvisualisation tool (Bonnarel et al., \\cite{Aladin})\nwhich allows to superimpose the catalogued sources on top of\nactual image of the sky:\nthe application requires an accurate interpretation\nof the catalogued output in terms of celestial positions in order\nto find out the exact location of each source. This means that\n{\\sc Aladin} has to figure out not only which are the columns\nrepresenting the celestial coordinates, but also accurate definitions\nof the system used to express the coordinates, their accuracy, etc\\dots ---\nin other words the {\\em metadata} about the celestial coordinates.\n\nXML {\\em(e{\\bf X}tensible {\\bf M}arkup {\\bf L}anguage)} is an emerging\nstandard which allows to embed markup {\\em ``tags''} within a document;\nthe key advantages of this language are that\nthe {\\em same document}\ncan either be parsed by simple-minded programs (XML uses\nhierarchical structuring),\nor can be displayed in the new generation of browsers (via an\nXSL style sheet which maps the markup {\\em ``tags''} into typographical\nspecifications). This language presents other potential interests,\nespecially regarding interoperability issues facilitated by the emergence\nof generic tools able to process XML documents.\n\nThe XML layout of astronomical tables was discussed extensively\nwith interested collaborators, and the agreed definitions were presented\nat a recent ADASS meeting (Ochsenbein et al. \\cite{adass99}).\nThe output of \\VizieR\\ is readily available in this\n\\A{http://vizier.u-strasbg.fr/cgi-bin/asu-xml}{format}, currently used\nby the Aladin image applet; it is\nhoped that it will facilitate the usage of the astronomical\ndata in new contexts.\n\n\\subSection{dm}{Current Developments}\nWith the large set of homogenized catalogues, \\VizieR\\\nplays a central role in a {\\em data-mining project} currently\nin development as a collaboration of ESO and CDS, in two main directions:\n(i) make use of the \\VizieR\\ large set of described columns (over\n70,000 currently) to build up new methods for locating the\ncatalogues which are the best suited to a particular research topic;\nand (ii) develop automatized cross-correlation tools %between data sets\nwhich can take into account the largest possible set of meaningful parameters\n%to make the comparisons\n(Ortiz et al, \\cite{portiz}).\n\n\\Section{conclus}{Conclusions}\n\\VizieR\\ is an illustration of the benefits resulting from\nan homogeneous documentation of the existing astronomical catalogues,\nfacilitating the transformation of a set of heterogeneous data into\na fully interactive database, furthermore able\nto interact with remote services.\n%adressing also remote services.\nThe interoperability issues between the databases,\nin astronomy and problably in connected disciplines,\nwill most likely be among the key developments necessary\nto allow the scientists to make use of the existing high-quality data\nwhithout the prerequisite of being familiar with the data.\n\n\n\\begin{acknowledgements}\n\nThe long-term exchanges of data %especially with NASA,\nhave been fundamental for these developments; more specifically,\nwe wish to thank\nJaylee Mead, Nancy G. Roman, Wayne H. Warren and Gail Schneider at NASA/ADC\nfor decades of collaborative work, and the present director Cynthia Y. Cheung;\nand Olga Dluzhnevskaya at INASAN, the Russian data center.\n%Cynthia Cheung.\n\nThe support of INSU-CNRS and CNES is acknowledged, as well as the\ncontribution of ESA-ESIS for the initial developments of \\VizieR,\nand more specifically Salim Ansari and Isabelle Bourekeb.\nThe development of \\VizieR\\ also resulted from fruitful\ndiscussions with Fran\\c coi\\-se Geno\\-va, Michel Cr\\'{e}z\\'{e} and Daniel Egret;\nthe enthusiasm of James Lequeux and its implication for the\nemergence of electronic tables in the {\\em A\\&A} publication\nhad a large impact on the accessiblity of the astronomical data.\n\nWe are also grateful to those who contributed in the more tedious,\nalthough critical, part of data standardisation:\nSimona Mei, Joseph Florsch and Patricio Ortiz\nat CDS; Gail Schneider and collaborators at NASA/ADC;\nKoichi Nakajima at ADAC/Japan;\nVeta S.Avedisova and collaborators at INASAN;\nand we would like to thank also the authors who %, in their vast majority,\nparticipated in the elaboration of the documentation about their data,\nand answered patiently to all our questions.\n\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n%\\bibitem[1998]{ha98}\n%Andernach H. ``Internet Services for Professional Astronomy'',\n%Kidger M., P\\'erez-Fournon I., and Sanchez F., {\\em Proc. IX$^{th}$\n%Canary Islands Winter School on Astrophysics}, Teneriffe, Spain,\n%Nov. 17-29 (1997)\n\\bibitem[2000]{Aladin}\n Bonnarel F., Fernique P., Bienaym\\'{e} O., et al., 2000, A\\&A, {\\em in press}\n (Aladin)\n%\\bibitem[1991]{simbad}\n% Egret D., Wenger M., Dubois P. in:\n% M.A. Albrecht \\& D. Egret, ed.,\n% {\\em Databases \\& On-line Data in Astronomy}, Kluwer Acad. Publ.,\n% p. 79 (1991)\n%\\bibitem[1997]{astroglu}\n%Egret D., Fernique P., Genova F.,\n%``Prototype of a Discovery Tool for Querying Heteregeneous Services'',\n%in : R. Albrecht, R.N. Hook, and H.A. Bushouse, ed.,\n%{\\em A.S.P. Conf. Ser. {\\bf 145}, 416} (1998)\n\\bibitem[1999]{adass99-poster}\n Derriere S, \\& Ochsenbein F., {\\em ADASS IX Proceedings} (in press)\n\\bibitem[1999]{DENIS}\n Epchtein N., Deul E., Derriere S., et al., 1999,\n A\\&A {\\bf 349}, 236\n\\bibcode{1999A&A...349..236E}\n\\bibitem[1998]{GLU}\n Fernique P., Ochsenbein F., Wenger M.,\n ``CDS GLU, a tool for managing heterogeneous distributed web services'',\n in : R. Albrecht, R.N. Hook, and H.A. Bushouse, ed.,\n {\\em A.S.P. Conf. Ser. {\\bf 145}, 466} (1998)\n\\bibitem[2000]{CDS}\n Genova, F., Egret, D., et al. 2000, A\\&A, {\\em in press}\n% (the CDS Hub)\n\\bibitem[1988]{GSC2}\n Greene G., McLean B., Lasker B., 1998,\n ``Development of the Astronomical Image Archive and Catalog\n Database for Production of GSC-II''\n in\n {\\em Future Generation Computers}\n (in press)\n \\bibcode{http://www-gsss.stsci.edu/branch/papers/Greene_1998_Future_Computing/Greene_1998_Future_Computing.html}\n\\bibitem[1988]{fits}\n Gr\\o sb\\o l P., Harten R.H., Greisen E.W., Wells D.C 1988,\n { A\\&AS {\\bf 73}, 359};\n see also {http://fits.gsfc.nasa.gov/}\n\\bibitem[1989]{cj}\n\tJaschek C. 1989, ``Data in Astronomy'', {\\em Cambridge Univ. Press}\n\\bibitem[Monet 1998]{usno}\n Monet D. 1997, 1998, {\\em The USNO A1.0 and A2.0 catalogues},\n\t\\ignore{see} http://ftp.nofs.navy.mil/projects/pmm\n\\bibitem[1994]{readme}\n Ochsenbein F. 1994, {\\em Bull. Inf. CDS {\\bf 44}, 19};\n see also http://cdsweb.u-strasbg.fr/doc/catstd.htx\n\\bibitem[1997]{russie}\nOchsenbein F. 1997, {\\em Proc. International Cooperation in Dissemination of\n\tAstronomical Data},\n\t{\\em Baltic Astron. {\\bf 6}, 221}\n\\bibitem[1998]{adass97}\n Ochsenbein F. 1998,\n ``The \\VizieR\\ System for Accessing Astronomical Data'',\n in : R. Albrecht, R.N. Hook, and H.A. Bushouse, ed.,\n {\\em A.S.P. Conf. Ser. {\\bf 145}, 387}\n\\bibitem[1999]{adass99}\nOchsenbein, F., Albrecht, M., Brighton, A., Fernique, P.,\n\tGuillaume, D., Hanisch, R., Shaya, E., Wicenec, A\n\t1999, in {\\em Proc. ADASS-IX} (in press);\nsee also http://cdsweb.u-strasbg.fr/doc/astrores.htx\n\\bibitem[1996]{aas96}\nOchsenbein F., Genova F., Egret D., Bourekeb I., Sadat R.,\n\tAnsari S.G., Simonsen E. 1996,\n\t{Bull. American Astron. Soc. {\\bf 187} \\#9103}\n\t\\bibcode{(1995AAS...187.9103O)}\n\\bibitem[1995]{aatables}\n {Ochsenbein F., Lequeux J.} 1995,\n {\\em Vistas in Astron. {\\bf 39}, 227}\n\\bibitem[1999]{portiz}\n Ortiz, P.F., Ochsenbein, F., Wicenec, A., and Albrecht, M. 1999,\n in ASP Conf. Ser., Vol. 172, ADASS VIII,\n eds. D.M. Mehringer, R.L. Plante, \\& D.A. Roberts, 379\n\\bibitem[1998]{kohonen}\n Poin\\c cot P., Lesteven S., Murtagh, F. 1998,\n\t{A\\&AS {\\bf 130}, 183-191}\n\t\\bibcode{1998A\\&AS..130..183P}\n\\bibitem[1997]{2mass}\nSkrutskie, M.F., Schneider, S.E., Stiening, R., et al.\n 1997, in Proc. Workshop {\\em The Impact of Large Scale Near-IR Sky Surveys}\n\\bibitem[1997]{ac2000}\n Urban, S.E., Corbin, T.E., Wycoff, G.L. 1997,\n ``The AC2000: the Astrographic Catalogue on the Hipparcos System''\n CD-ROM, US Naval Observatory.\n%\\bibitem[1995]{bibcode}\n%Schmitz M., Helou G., Dubois P., et al.,\n% \"NED and SIMBAD Conventions for Bibliographic Reference Coding\", in:\n% D. Egret \\& M.A. Albrecht, ed.,\n% {\\em Information \\& On-line Data in Astronomy}, Kluwer Acad. Publ.,\n% p. 259 (1995)\n\\bibitem[2000]{simbad}\n Wenger M., Ochsenbein F., Egret D., et al. 2000, A\\&A , {\\em in press}\n\t(the SIMBAD astronomical database)\n\\end{thebibliography}\n\n\\listofobjects\n\\end{document}\n\n"
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{
"name": "astro-ph0002122.extracted_bib",
"string": "\\begin{thebibliography}{}\n%\\bibitem[1998]{ha98}\n%Andernach H. ``Internet Services for Professional Astronomy'',\n%Kidger M., P\\'erez-Fournon I., and Sanchez F., {\\em Proc. IX$^{th}$\n%Canary Islands Winter School on Astrophysics}, Teneriffe, Spain,\n%Nov. 17-29 (1997)\n\\bibitem[2000]{Aladin}\n Bonnarel F., Fernique P., Bienaym\\'{e} O., et al., 2000, A\\&A, {\\em in press}\n (Aladin)\n%\\bibitem[1991]{simbad}\n% Egret D., Wenger M., Dubois P. in:\n% M.A. Albrecht \\& D. Egret, ed.,\n% {\\em Databases \\& On-line Data in Astronomy}, Kluwer Acad. Publ.,\n% p. 79 (1991)\n%\\bibitem[1997]{astroglu}\n%Egret D., Fernique P., Genova F.,\n%``Prototype of a Discovery Tool for Querying Heteregeneous Services'',\n%in : R. Albrecht, R.N. Hook, and H.A. Bushouse, ed.,\n%{\\em A.S.P. Conf. Ser. {\\bf 145}, 416} (1998)\n\\bibitem[1999]{adass99-poster}\n Derriere S, \\& Ochsenbein F., {\\em ADASS IX Proceedings} (in press)\n\\bibitem[1999]{DENIS}\n Epchtein N., Deul E., Derriere S., et al., 1999,\n A\\&A {\\bf 349}, 236\n\\bibcode{1999A&A...349..236E}\n\\bibitem[1998]{GLU}\n Fernique P., Ochsenbein F., Wenger M.,\n ``CDS GLU, a tool for managing heterogeneous distributed web services'',\n in : R. Albrecht, R.N. Hook, and H.A. Bushouse, ed.,\n {\\em A.S.P. Conf. Ser. {\\bf 145}, 466} (1998)\n\\bibitem[2000]{CDS}\n Genova, F., Egret, D., et al. 2000, A\\&A, {\\em in press}\n% (the CDS Hub)\n\\bibitem[1988]{GSC2}\n Greene G., McLean B., Lasker B., 1998,\n ``Development of the Astronomical Image Archive and Catalog\n Database for Production of GSC-II''\n in\n {\\em Future Generation Computers}\n (in press)\n \\bibcode{http://www-gsss.stsci.edu/branch/papers/Greene_1998_Future_Computing/Greene_1998_Future_Computing.html}\n\\bibitem[1988]{fits}\n Gr\\o sb\\o l P., Harten R.H., Greisen E.W., Wells D.C 1988,\n { A\\&AS {\\bf 73}, 359};\n see also {http://fits.gsfc.nasa.gov/}\n\\bibitem[1989]{cj}\n\tJaschek C. 1989, ``Data in Astronomy'', {\\em Cambridge Univ. Press}\n\\bibitem[Monet 1998]{usno}\n Monet D. 1997, 1998, {\\em The USNO A1.0 and A2.0 catalogues},\n\t\\ignore{see} http://ftp.nofs.navy.mil/projects/pmm\n\\bibitem[1994]{readme}\n Ochsenbein F. 1994, {\\em Bull. Inf. CDS {\\bf 44}, 19};\n see also http://cdsweb.u-strasbg.fr/doc/catstd.htx\n\\bibitem[1997]{russie}\nOchsenbein F. 1997, {\\em Proc. International Cooperation in Dissemination of\n\tAstronomical Data},\n\t{\\em Baltic Astron. {\\bf 6}, 221}\n\\bibitem[1998]{adass97}\n Ochsenbein F. 1998,\n ``The \\VizieR\\ System for Accessing Astronomical Data'',\n in : R. Albrecht, R.N. Hook, and H.A. Bushouse, ed.,\n {\\em A.S.P. Conf. Ser. {\\bf 145}, 387}\n\\bibitem[1999]{adass99}\nOchsenbein, F., Albrecht, M., Brighton, A., Fernique, P.,\n\tGuillaume, D., Hanisch, R., Shaya, E., Wicenec, A\n\t1999, in {\\em Proc. ADASS-IX} (in press);\nsee also http://cdsweb.u-strasbg.fr/doc/astrores.htx\n\\bibitem[1996]{aas96}\nOchsenbein F., Genova F., Egret D., Bourekeb I., Sadat R.,\n\tAnsari S.G., Simonsen E. 1996,\n\t{Bull. American Astron. Soc. {\\bf 187} \\#9103}\n\t\\bibcode{(1995AAS...187.9103O)}\n\\bibitem[1995]{aatables}\n {Ochsenbein F., Lequeux J.} 1995,\n {\\em Vistas in Astron. {\\bf 39}, 227}\n\\bibitem[1999]{portiz}\n Ortiz, P.F., Ochsenbein, F., Wicenec, A., and Albrecht, M. 1999,\n in ASP Conf. Ser., Vol. 172, ADASS VIII,\n eds. D.M. Mehringer, R.L. Plante, \\& D.A. Roberts, 379\n\\bibitem[1998]{kohonen}\n Poin\\c cot P., Lesteven S., Murtagh, F. 1998,\n\t{A\\&AS {\\bf 130}, 183-191}\n\t\\bibcode{1998A\\&AS..130..183P}\n\\bibitem[1997]{2mass}\nSkrutskie, M.F., Schneider, S.E., Stiening, R., et al.\n 1997, in Proc. Workshop {\\em The Impact of Large Scale Near-IR Sky Surveys}\n\\bibitem[1997]{ac2000}\n Urban, S.E., Corbin, T.E., Wycoff, G.L. 1997,\n ``The AC2000: the Astrographic Catalogue on the Hipparcos System''\n CD-ROM, US Naval Observatory.\n%\\bibitem[1995]{bibcode}\n%Schmitz M., Helou G., Dubois P., et al.,\n% \"NED and SIMBAD Conventions for Bibliographic Reference Coding\", in:\n% D. Egret \\& M.A. Albrecht, ed.,\n% {\\em Information \\& On-line Data in Astronomy}, Kluwer Acad. Publ.,\n% p. 259 (1995)\n\\bibitem[2000]{simbad}\n Wenger M., Ochsenbein F., Egret D., et al. 2000, A\\&A , {\\em in press}\n\t(the SIMBAD astronomical database)\n\\end{thebibliography}"
}
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astro-ph0002123
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Age and metallicity gradients in the Galactic Bulge \thanks{B ased on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract No. NAS5-26555}
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[
{
"author": "Sofia Feltzing \\inst{1,2,3}"
},
{
"author": "Gerard Gilmore \\inst{2}"
}
] |
The Galactic Bulge has long been assumed to be a largely old stellar population. However, some recent studies based on observations with the HST WF/PC-1 and WFPC2 of stars in the Galactic Bulge have concluded that the old population may not make up more then 30\% of the total. Other studies using HST/WFPC2 differential studies of `Bulge' globular clusters and field stars have found the bulge to be comparable in age to the Galactic Halo. A complication in all these studies is the presence of a substantial population of stars which mimic a young bulge population, but which may be, and are often assumed to be, foreground disk stars whose reddening and distance distributions happen to mimic a young bulge turnoff. We show, using number counts in HST/WFPC2 colour-magnitude diagrams of both field stars in the Bulge and of two `bulge' and one `disk' globular cluster (NGC6528, NGC6553, and NGC5927) that the stars interpreted as young in fact are foreground disk stars. Thus, we confirm that the bulk of the bulge field stars in Baade's Window are old. The existence of a young {\sl metal-rich} population cannot, however, be ruled out from our data. We also test for age and metallicity gradients in the Galactic Bulge between the two low extinction windows Baade's window ($\ell$=$1\fdg1, b$=$-4\fdg8$) and Sagittarius-I ($\ell$=$1\fdg3, b$=$-2\fdg7$). We use the colour-magnitude diagram of a metal-rich globular cluster as an empirical isochrone to derive a metallicity difference of $\la 0.2$ dex between Baade's window and SGR-I window. This corresponds to a metallicity gradient of $\la 1.3$ dex/kpc, in agreement with recent near-IR CMD studies. Such a steep gradient, if detected, would require the existence of a short scale length inner component to the Bulge, most likely that prominent in the near infra red, which perhaps forms a separate entity superimposed on the larger, optical Bulge as observed in Baade's window. \keywords{Galaxy: abundances, center, general, globular clusters: NGC5927, NGC6528, NGC6553, stellar content}
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[
{
"name": "H0952.tex",
"string": "\\documentstyle[graphics,graphicx,]{l-aa}\n\\begin{document}\n\n \\thesaurus{04(10.01.1; 10.03.1; 10.07.1; 10.07.3; 10.19.2) }\n\n \\title{Age and metallicity gradients in the Galactic Bulge \\thanks{B\nased on observations with the NASA/ESA Hubble Space Telescope,\n obtained at the Space Telescope Science Institute, which is\noperated by\n the Association of Universities for Research in Astronomy,\nInc. under\n NASA contract No. NAS5-26555}}\n\n \\subtitle{A differential study using HST/WFPC2 }\n\n \\author{Sofia Feltzing \\inst{1,2,3} \\and Gerard Gilmore \\inst{2}}\n\n \\offprints{Sofia Feltzing}\n \\institute{Royal Greenwich Observatory\n Madingley Road,\n Cambridge CB3 0EZ,\n U.K.\n \\and Institute of Astronomy,Madingley Road,Cambridge CB3 0HA\n \\and Present address: Lund Observatory, Box 43, S-221 00 Lund, Sweden\n }\n \n% \\authorrunninghead{S. Feltzing \\& \\G. Gilmore}\n% \\titlerunninghead{Age and metallicity gradients in the Galactic\n% Bulge}\n\n \\date{Recieved 06-03-1998; accepted 22-12-1999}\n\n \\maketitle\n\n \\begin{abstract}\n\nThe Galactic Bulge has long been assumed to be a largely old stellar\npopulation. However, some recent studies based on observations with\nthe HST WF/PC-1 and WFPC2 of stars in the Galactic Bulge have\nconcluded that the old population may not make up more then 30\\% of\nthe total. Other studies using HST/WFPC2 differential studies of `Bulge'\nglobular clusters and field stars have found the bulge to be\ncomparable in age to the Galactic Halo. A complication in all these\nstudies is the presence of a substantial population of stars which\nmimic a young bulge population, but which may be, and are often\nassumed to be, foreground disk stars whose reddening and distance\ndistributions happen to mimic a young bulge turnoff. We show, using\nnumber counts in HST/WFPC2 colour-magnitude diagrams of both field\nstars in the Bulge and of two `bulge' and one `disk' globular cluster\n(NGC6528, NGC6553, and NGC5927) that the stars interpreted as young in\nfact are foreground disk stars. Thus, we confirm that the bulk of the\nbulge field stars in Baade's Window are old. The existence of a young {\\sl\nmetal-rich} population cannot, however, be ruled out from our data.\n\nWe also test for age and metallicity gradients in the Galactic Bulge\nbetween the two low extinction windows Baade's window ($\\ell$=$1\\fdg1,\nb$=$-4\\fdg8$) and Sagittarius-I ($\\ell$=$1\\fdg3, b$=$-2\\fdg7$). We use\nthe colour-magnitude diagram of a metal-rich globular cluster as an\nempirical isochrone to derive a metallicity difference of $\\la 0.2$\ndex between Baade's window and SGR-I window. This corresponds to a\nmetallicity gradient of $\\la 1.3$ dex/kpc, in agreement with recent\nnear-IR CMD studies. Such a steep gradient, if detected, would require\nthe existence of a short scale length inner component to the Bulge, most\nlikely that prominent in the near infra red, which perhaps forms a\nseparate entity superimposed on the larger, optical Bulge as observed\nin Baade's window.\n\n\n\\keywords{Galaxy: abundances, center, general, \nglobular clusters: NGC5927, NGC6528, NGC6553, stellar content}\n \n\n\\end{abstract}\n%\n%________________________________________________________________\n\n\n\\section{Introduction}\nThe nature and origin(s) of Galactic Bulges are key aspects of any\ngalaxy formation model, and of the Hubble galaxy classification\nsequence. However, the present-day properties of bulges in\nspiral galaxies are not well known (eg Silk \\& Wyse 1993; Wyse,\net al. 1997). Do bulges form late, early or continuously?\nAre bulges related to halos? To disks? Are they single stellar\npopulations? The existence of smooth and/or discontinuous gradients\nin age and/or metallicity in the stellar population(s) in the Galactic\nBulge can help to discriminate between these different scenarios, and\nis the topic of this paper.\n\nIs there evidence for the widely repeated assumption that the Galactic\nBulge is old? Recently published colour magnitude\ndiagrams from HST/WFPC2 and HST/WFC1 of the Galactic Bulge and the\nbulge globular clusters (Vallenari et al. 1996, Ortolani et al. 1995,\nHoltzman et al 1993) while dominated by fairly old stars, show a\nsubstantial population of stars above the dominant old turnoff.\nAre these foreground disk stars, or is there a minority very young\nbulge population? Since even a minority young bulge population is of\ninterest, we examine here the limits on young stars in the bulge\nwindows. \n\n\nOne common approach to determine the properties of the Bulge is to\nstudy the so called bulge globular clusters (see e.g. Zinn 1996,\nOrtolani et al. 1995, Minniti 1996). While primarily\nmotivated by observational convenience, the rationale behind this\napproach is the assumption that these clusters may be valid tracers of\nthe stellar population(s) of the Bulge (see however Zinn 1996 and\nHarris 1998) Formation scenarios relevant to this approach include the\npossibility that the Bulge has been assembled from numerous such\nclusters and these are the last surviving (Gnedin \\& Ostriker 1997),\nor that the clusters formed a system associated with the Bulge rather\nthan with the rest of the spheroidal component(s) of the Galaxy. Thus\nthe idea is that we may be able to infer the age and/or metallicity of\nthe Bulge stellar population either directly from studies of these\nclusters, or through differential studies of the clusters and field\nstars, under the assumption of similar metallicity. Since there is no\nab initio understanding of the formation of either galactic bulges or\nglobular clusters, and the age range of the globular cluster system\nremains a topic of active debate, such analyses merit close\nscrutiny. The most recent and extensive such analysis is that of\nOrtolani et al. (1995, 1996) who observed two such globular clusters,\nNGC6553 and NGC6528, with HST/WFPC2, and deduced that the Bulge has\nthe same age as the Halo.\n\nAnalysis of suitably-chosen globular clusters introduces\nseveral possible complications. The first is the major problem of\ndefining a proper population of `bulge' globular clusters. Some of\nthe clusters used, e.g. Ter7, have recently been shown to be\nassociated with the satellite dwarf galaxy Sgr dSph, rather than with\nthe Galaxy itself. They may therefore not be representative of the\nGalactic Bulge. The method of comparing ridge-lines of globular\nclusters to infer relative ages requires the clusters in question to have\nsimilar metallicities, and relative chemical abundances of the\nalpha-elements, to avoid an age-metallicity degeneracy\n (Stetson et al. 1996, VandenBerg et al. 1990, 1996). \nNew results by Cohen et al. (1999) show that NGC6553 may be as\nmuch as $\\sim 0.5$ dex more metal-rich than 47 Tuc, illustrating the\npotentially large effects of metallicity range. The impressive recent\nstudy of Rosenberg et al. (1999), indicating a dispersion in ages for\nthe intermediate metallicity globular clusters, and a large systematic age\ndifference between the metal-rich and metal-poor clusters illustrates\nthe complexity. \n\nAnother potential\n uncertainty is that the metallicity distribution function of the\nstars in the galactic Bulge is more similar to that in the\nsolar-neighbourhood (cf. Wyse and Gilmore 1995) than to that for\nclusters within 5 degrees of the Galactic centre (Minniti 1996; Barbuy\net al. 1998). The bulge cluster distribution is both more narrow and\nless metal-rich than the bulge field stars, complicating any direct\ncomparison.\n\nClearly, if one wishes to know the age of the bulge field stars, it is\ndesirable to observe the stars in the Bulge directly. Direct studies\nof the Bulge are difficult due to the severe crowding towards the\ncentral regions of the Galaxy and the large, patchy, reddening along\nthe line of sight. Several detailed studies of the outer Galactic\nBulge exist, providing kinematics and chemical abundance distribution\nfunctions (Ibata and Gilmore 1995a, 1995b; Minniti et al. 1995; see\nalso Wyse et al. 1997). For the inner Bulge several\nanalyses of the low reddening Baade's window are available\n(e.g. Ortolani et al. 1995, Vallenari et al. 1996, Holtzman et\nal. 1993, Terndrup 1988, Ng et al. 1996), with direct studies of the\ninner bulge field stars in the near-IR recently also becoming\navailable (Frogel et al. 1999), and even mid-IR ISO photometry (Omont\net al. 1999, Glass et al. 1999). Additionally, many recent studies have\nemphasized the high continuing rate of star formation in the inner\nbulge/disk. Do these stars diffuse with time the few hundred parsecs\ninto the Sgr and Baade's windows?\n\nThe interpretation of extant data is unclear, with a variety of\ncontradictory results. Vallenari et al. (1996) use a mixture of\nWF/PC-1 and NTT data while Holtzman et al. (1993) rely exclusively\non (the same) WF/PC-1 data. Both groups reached the conclusion that\nthe Bulge is dominated by a significant young stellar\npopulations. Ortolani et al. (1995) using similar NTT data for Baade's\nWindow found the Bulge to be as old as the Halo.\n\nThe confusion among the results from the space based observations\nshould be contrasted with ground based optical observations which find\nlittle evidence for a substantial young stellar population(s) in the\nGalactic Bulge (eg Terndrup 1988), albeit rather far from the centre.\nNote however that these observations do not cover the main-sequence\nturn-off and the results are based on the giant branch. The\nmain-sequence turn-off is more sensitive to detection of a\nsignificantly younger stellar populations. Further complication is\nprovided by studies of OH/IR stars, suspected to be of intermediate\nage, which are common in the inner bulge, or disk (Sevenster et al. 1997).\n\n\nThe distribution function of chemical abundances is a key parameter\ndefining a stellar population. In the outer Galactic Bulge Ibata \\&\nGilmore (1995b) derived the relevant distribution function from\nspectroscopy of K giants. They found a mean abundance of $\\sim -0.2$\ndex, with a very wide dispersion. In Baade's window McWilliam \\& Rich\n(1994) and Sadler et al. (1996) provided similar results. Sadler et\nal. (1996) found for 400 K giants a mean abundance of [Fe/H] $=-0.11\n\\pm0.04$ dex, with more than half the sample in the range $-0.4 < {\\rm\n[Fe/H]} < +0.3 {\\rm dex}$. This is similar to the results from the\ndetailed spectroscopic analysis of McWilliam \\& Rich (1994). A\nmetallicity gradient has been suspected for fields outside Baade's\nWindow, Terndrup (1988) and Minniti et al. (1995). The important\nconclusion from the spectroscopic analyses is that the stellar\npopulations of the inner Galactic Bulge are complex, and that their\nanalysis requires careful consideration of projected disk and other\npopulations.\n\nIn this paper we study colour-magnitude diagrams, derived from\narchival HST/WFPC2 images, for 4 fields and two clusters towards the\nGalactic Bulge and one ``disk'' cluster. We perform a purely\ndifferential study of the properties of the Galactic Bulge\npopulation(s), quantifying any systematic offsets and/or gradients in\nage and/or metallicity in the field population(s).\n\nThe paper is organized as follows; in Sect. 2 we detail the\nobservations used and in Sect. 3 describe how we derive the\nphotometric magnitudes from the images. Sect. 4 discusses reddening\nand distances for the individual fields and clusters, and the utility\nof the cluster data. Sect. 5 discusses the age of the Bulge, while\nSect. 6 asks the question whether a metallicity gradient might be\npresent in the inner Bulge. Sect. 7 includes a summarizing discussion\nwhich puts our results into the context of other studies. A brief\nsummary is found in Sect. 8.\n%\n%________________________________________________________________\n\\section{The data}\n\n\\begin{figure*}\n\\resizebox{12cm}{!}{\\includegraphics[angle=-90]{0952.F01.ps}}\n\\hfill\n\\parbox[t]{55mm}{\n\\caption[]{Positions of fields and clusters. Clusters are denoted by\nopen circles and fields by filled squares. NGC5927 (with\n$l=-34\\degr$) is well outside this map. We also show the positions of\nthe 5 inner-most fields studied by Ibata and Gilmore (1995a,b),\ndenoted by open diamonds. The Sgr dSph has its major axis along\n$l=+5\\degr$, and extends down to $b \\la 4\\degr$}\n\\label{field_positions}}\n\\end{figure*}\n\n\nAll observations analyzed here were obtained from the HST-archive.\nThe observations for the two clusters, NGC6528 and NGC6553, have\npreviously been reported and discussed in Ortolani et al.\\,(1995) and\nthe observation of NGC5927 in Fullton et al.\\,(1996). However, to get\na set of data which is consistently treated we have derived our own\nphotometry from the original images. The images are detailed in Table\n\\ref{fieldlist}, and their positions on the sky are shown in\nFig. \\ref{field_positions}. The results presented here are all, due\nto the crowding in some of the fields, based exclusively on the PC1\nimages.\n\n\n\\subsection{Data reductions} \n\nAll frames have been recalibrated through the STScI pipeline\ncalibration for HST at the Space Telescope - European Coordinating\nFacility, using the most suitable flat field and bias frames\navailable.\n\n\n\\subsection{Combining images}\n\nBecause the WFPC2 images are under-sampled extra care has to be\nexercised so that counts in the centre of stars are not lost when\nimages are combined in order to remove cosmic rays. Sub-pixel shifts\nbetween two images can cause the centre flux in one image (or in both)\nto look like a cosmic ray when the images are compared in the cosmic\nray algorithm. Experiments on several of the image sets, using the\n{\\tt{stsdas.hst\\_calib.wfpc.crrej}} task, showed that up to 10\\% of\nthe counts may be lost unless a term linear in the counts (scalenoise)\nis included in the modeling of $\\sigma$ used in the rejection\nalgorithm (see the help file for {\\sc{crrej}}).\n\n\\begin{table*}\n\\caption[]{Coordinates and passbands of observations for the fields\nand clusters. For the fields we give the coordinates for the centre of\nthe PC1 and for the clusters the coordinates for the cluster\ncentres. the column headed ID give the HST archive identification\nnumber of the original observing program in which the observations\nwere obtained. The last column give the total number of stars\nsimultaneously detected in F814 and F555W or F606W according to the\nselection criteria discussed in Sect.\\ref{sect:cmd}. If the data were\ntruncated the truncation magnitude is indicated in the last column.}\n\\begin{tabular}{lrrllllrllllllllll}\n\\hline\\noalign{\\smallskip}\nField &$l$ & $b$ & Passbands & Total exp.time& ID & Date of obs. &\\multicolumn{2}{l}{ F814W+F555W/F606W} \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nSGR-I & 1\\fdg27 &-2\\fdg66 & F814W, F555W & 3000,3000 &5207 & 28/08/94 & 2940 \\\\\nBW & 1\\fdg14 &-3\\fdg77 & F814W, F555W & 2000,2000 & 5105&12/08/94& 2221& ($V_{\\rm 555}<26$)\\\\\n & & & F814W, F555W & 80,80 & 6185& 2/09/95 & 1150 &($V_{\\rm 555}<23$)\\\\\nMW-12 & -6\\fdg00 & -14\\fdg00 & F814W, F555W & 1000,1200 &6614 & 9/10/96 & 63\\\\\nu811 & 3\\fdg60 & -7\\fdg20 & F814W, F606W & 2600,2600 &5371 & 14,15/09/97& 907\\\\\nDeep & 2\\fdg90 & -7\\fdg95& F814W, F606W & 5800,2900&6254 & 1/05/96 & 463& ($V_{\\rm 606}<27$)\\\\ \nNGC5927 & 326\\fdg6 & 4\\fdg86& F814W, F555W & 3200,2400 &5366 & 8/05/94 & 3289\\\\\n & (-34\\degr)& & F814W, F555W & 210,150 &5366 &8/05/94 & 3587\\\\\nNGC6528 & 1\\fdg14 &-4\\fdg17 & F814W, F555W & 200,100 &5436 & 27/02/94 & 1824\\\\\nNGC6553 & 5\\fdg25 &-3\\fdg02 & F814W, F555W & 200,100 &5436 & 25/02/94 &2795 \\\\\n\\noalign{\\smallskip} \n\\hline\n\\end{tabular}\n\\label{fieldlist}\n\\end{table*}\n\n%____\n%________________________________________________________________\n\n\\section{Stellar Photometry:\nDeriving colour-magnitude diagrams}\n\\label{sect:cmd}\n\nTo derive photometric magnitudes we have used the standard {\\sc{iraf}}\n\\footnote{IRAF is distributed by National Optical Astronomy\nObservatories, operated by the Association of Universities for\nResearch in Astronomy, Inc., under contract with the National Science\nFoundation, USA.} tasks in the {\\sc{daophot}} package. To calibrate\nour data we have used the procedures detailed in Holtzman et\nal.\\,(1995b), as well as empirical determinations of aperture\ncorrections.\n\n\nWe follow the general procedure of first detecting possible stars with\n{\\sc{daofind}}, derive initial photometric magnitudes from aperture\nphotometry using {\\sc{phot}}, derive an analytical\npoint-spread-function ($psf$) for each image (assumed constant over\nthe entire chip) and finally perform $psf$-fitting on the list of\npossible stars to determine stellar magnitudes using\n{\\sc{allstar}}. The initial aperture photometry is done in an aperture\nof 2 pixels. We use the $psf$-fitted magnitudes in our analysis. The\nraw $psf$-fitted magnitudes need to be corrected for a number of\neffects which are peculiar to HST, and calibrated onto the HST\nin-flight system.\n\n\nFor the observations at $(l,b)=(2\\fdg9,-7\\fdg95)$ only one observation\nin the F606W passband was available. We identified the objects on the\ncombined F814W image and used that list to identify the stars on which\nto perform measurements in the F606W image. The colour-magnitude\ndiagram was then searched for anomalous looking stars, which were\ninspected by eye in both passbands and if deemed to be contaminated by\ncosmic rays, excluded.\n\n\nWe first present the steps in our calibration and then discuss and\ndetail each step separately as some of the steps are non-trivial. Our\ncalibration contains the following steps;\n\n\\begin{enumerate}\n\\item apply empirical correction for the difference \nbetween aperture and $psf$-fitted magnitudes,\n\\item add 2 electrons to the flux in each pixel \ninside a radius of 5 pixels,\n\\item correct for the CTE effect,\n\\item correct for the geometric distortion,\n\\item normalize to WF3 and bay 4 (if applicable),\n\\item apply Holtzman's synthetic aperture corrections from 5 pixels out to\n11 pixels (0$\\farcs{5}$),\n\\item add synthetic zero points from Holtzman et al.\n\\end{enumerate}\n\n\n\n\\subsection{Aperture vs $psf$-photometry ($ap/psf$)}\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{0952.F02.ps}}\n\\caption[]{Difference between $psf$-fitted magnitudes and aperture\nmagnitudes measured inside an aperture with radius 5 pixels as a\nfunction of the $psf$-fitted magnitudes. In panel a. we show the data\nfor Baade's window long exposure and in panel b. short exposure. The\nerror bars show the errors as given by {\\sc {phot}} and {\\sc\n{allstar}}. Note the different ranges on the x-axes.}\n\\label{diff_mag}\n\\end{figure}\n\n\n\n\\begin{table}\n\\caption[]{Zero points, aperture corrections from Holtzman et al. (1995a) and\ncorrections for the zero points of the empirical $psf$s.}\n\\begin{tabular}{llllllllllllllllll}\n\\hline\\noalign{\\smallskip}\n Quantity & Field & F555W & F606W & F814W\\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nZero point & & 21.723 & 22.084 & 20.844\\\\\nAp.corr. & & \\underline{0.89} & \\underline{0.88} & \\underline{0.87}\\\\ \n(Holtzman)& & {0.96}& {0.955} & {0.95 } \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\n$Psf$- & SGR-I &0.220 & -- & 0.460 \\\\\n zero-point &BW long & 0.296 & -- & 0.406 \\\\\n corr. &BW short &0.281 & -- & 0.470 \\\\\n &MW-12 & 0.342 & -- & 0.509 \\\\\n &u811 & -- &0.361 & 0.485 \\\\\n\t & Deep & -- &0.363 & 0.434 \\\\\n\t &NGC5927l & 0.303 & -- & 0.493 \\\\\n\t &NGC5927s & 0.240 & -- & 0.469 \\\\\n &NGC6528 &0.270 & -- & 0.444 \\\\\n &NGC6553 &0.460 & -- & 0.310 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\label{ap_corr}\n\\end{table}\n\nThere is usually a zero-point offset (as well as a spread) between\nmagnitudes derived from $psf$-fitting and from aperture measurements.\nSince we construct our own $psf$ from the frame itself this offset is\ndue to the magnitude assigned to the $psf$ by the {\\sc {psf}}\ntask. This magnitude is the magnitude of the first star used in\nconstructing the $psf$, thus it is somewhat arbitrary. This also means\nthat the offset between aperture photometry and $psf$-fitted\nphotometry may not always be the same or even have the same sign in\ntwo frames.\n\nFor the stars that had been used to create the analytic $psf$ we\nmeasured aperture magnitudes inside 5 pixels and subsequently\ncalculated the difference between these magnitudes and the magnitudes\nderived from $psf$-fitting, Fig. \\ref{diff_mag}. The scatter around\nthe mean-value for these corrections is $\\leq 0.03$ magnitudes both in\nF555W and F814W and for both long and short exposures. The difference\nwas used as an empirical aperture correction. The results are listed\nin Table \\ref{ap_corr}. The $psf$-magnitudes were in this way\ncorrected out to $0\\farcs5$.\n\n\\subsection{Long versus short exposures}\n\nFor the field in Baade's window a set of images with exposure times of\n2$\\times$1000s, 4$\\times$200s and 2$\\times$40s is available. This has\nmade it possible to investigate to what extent the magnitudes derived\nfrom long and short exposures of the same stars (and in this case also\nin a crowded and reddened field) give the same magnitudes. There is a\nwell-known ``feature'' of HST photometry that short- and long-exposure\nmagnitudes do not agree in zero-point. An addition of $2 e^-/pixel$ to\nthe flux measured in aperture photometry has been suggested as an\nempirical way of correcting for such a discrepancy. We confirm that\nthis is a practical empirical formula. As we correct out to 5 pixels\nradius for the discrepancy between aperture and $psf$-fitted\nmagnitudes we add 2 electrons to the flux in each pixel inside that\nradius. \\footnote{Since this article was first submitted there has\nbeen significant development in the understanding of the long-vs-short\nexposure problem. Further discussion of this problem and its solution\nmay be found in the WFPC2 Instrument Science Reports 98-02 which can\nbe found at the following URL {\\tt\nhttp://www.stsci.edu/ftp/instrument\\_news/WFPC2\\\\/wfpc2\\_bib.html}}\n\n\\subsection{Aperture corrections, Charge \nTransfer Efficiency ($CTE$) and Effective pixel area ($EPA$)}\n\n Aperture corrections to $0\\farcs5$ apertures, i.e. 11 pixels on the\nPC1, from the 5 pixel apertures used to derive the difference between\n$psf$ and aperture magnitudes are employed from Table 2 of Holtzman et\nal. (1995a).\n\n The $CTE$ has the effect that stellar objects in a given row (more\ncharge transfer) appear fainter then they should have appeared had\nthey been at a lower row number. This is corrected for through a\nsimple formula suggested by Holtzman et al. (1995a,1995b) which means\nthat at the highest row the detected light is 4\\% higher than at the\nfirst row and this correction changes linearly along the column. For\nobservations taken before the cool down of the CCDs in WFPC2, 32 April\n1994, the CTE is higher, $\\sim 10 \\%$.\n\n As discussed in Holtzman et al. (1995a) the WFPC2 cameras have\ngeometric distortions. We correct for these distortions using the\ninformation in the map of effective pixel area given in Fig.16,\nHoltzman et al.\\,(1995a).\n\n\\subsection{Completeness}\n\nIn order to determine the level of completeness, as a function of\nderived apparent magnitude, we have performed the ``{\\sc{addstar}}\nexperiment'', ie we add artificial stars at a given magnitude, thus\ncreating a new image. The new frames were then put through the same\nprocesses as described above and the list of synthetic stars created\nby {\\sc{addstar}} was cross-correlated with the final list of detected\nstars to reveal how many of the synthetic stars had been\nrecovered. For this we required not only that the coordinates should\nbe the same but also that the new magnitude should be within 0.5\nmagnitudes of the magnitude assigned to the synthetic star by\n{\\sc{addstar}}, as illustrated in Fig. \\ref{compl}.\n\nNote that in this study we do not require a detailed knowledge of the\ncompleteness function. This is because we are studying the turn off\nregions and brighter in the colour-magnitude diagrams. Our only\nrequirement here is to show that completeness is not a significant\nproblem near the main-sequence turnoff. In fact, our photometry\nextends several magnitudes fainter than necessary for this experiment.\n\n\\begin{figure}\n\\centerline{\\resizebox{7cm}{!}{\\includegraphics{0952.F03.ps}}}\n\\caption[]{Completeness for the deep exposure of Baade's window.\nSGR-I shows the same level of completeness. This completeness is based\non the stars detected in both $V_{\\rm 555}$ and $I_{\\rm 814}$}\n\\label{compl}\n\\end{figure}\n\n\n\\subsection{Selection of final stellar samples}\n\n\\begin{figure*}\n\\resizebox{\\hsize}{!}{\\includegraphics{0952.F04.ps}}\n\\caption[]{Diagnostics for the SGR-I field. Figures a., b., and\nc. show the error, $\\delta I_{\\rm {814}}$, the sharpness and the\n$\\chi_{\\rm {814}}$ as a function of the $ I_{\\rm {814}}$ magnitude. In\nd. we show the same as in a. but when the cut in $\\chi_{\\rm {814}}$ is\nimposed (as indicated in c.). Finally in Figures e. and f. $\\delta\nV_{\\rm {555}}$ are shown as functions of $V_{\\rm {555}}$\nmagnitudes. In e. without any cuts imposed and in f. when $\\chi_{\\rm\n{555}}$ cut at $2.5$. Figure d. and f. thus show the distribution of\nthe errors in the final sample of stars in SGR-I colour-magnitude\ndiagram as displayed in Fig. \\ref{cmd_deep}.}\n\\label{diagnostics}\n\\end{figure*}\n\nAll images were carefully inspected for saturated stars and spurious\ndetections around saturated stars (mottling) and along the diffraction\npatterns. It was found that once the data for F814W and F555W were\nmatched very few saturated stars remained in the final sample and\nvirtually no detections on diffraction spikes and in the mottling\npattern remained.\n\nThe final selection of stellar samples was based on the diagnostic\ndiagrams produced from the $psf$-fitting photometry of which an\nexample is presented in Fig. \\ref{diagnostics}. As can be seen in this\nfigure a cut at $\\chi_{\\rm {814}} < 2.5$ and $\\chi_{\\rm {555}} < 2.5$\ncleans up the error vs. magnitude diagrams satisfactorily.\n\n\n\\begin{figure*}\n\\resizebox{\\hsize}{!}{\\includegraphics{0952.F05.ps}}\n\\caption[]{Colour magnitude diagrams for the cluster fields and the\nshort exposure of Baade's window. a. NGC5927 short exposure,\nb. NGC6528 c. NGC6553, and d. BW short exposure. The direction of the\nreddening vector, as given in Holtzman et al. (1995b), is indicated by\na solid line in each diagram. The colour-magnitude diagram for Baade's\nwindow was truncated at $V_{\\rm 555} = 23$. }\n\\label{cmd_shallow}\n\\end{figure*}\n\n\\begin{figure*}\n\\resizebox{\\hsize}{!}{\\includegraphics{0952.F06.ps}}\n\\caption[]{Colour magnitude diagrams for the two fields and NGC5927.\na. NGC5927 long exposure, b. MW-12, c. SGR-I, and d. BW long\nexposure. The direction of the reddening vector, as given in Holtzman\net al. (1995b), is indicated by a solid line in each diagram. }\n\\label{cmd_deep}\n\\end{figure*}\n\n\\begin{figure*}\n\\resizebox{\\hsize}{!}{\\includegraphics{0952.F07.ps}}\n\\caption[]{Colour magnitude diagrams for the two fields observed in\nF606W and F814W. a. is the field at (l,b)=(2.9,-7.95) and b. at\n(3.6,-7.2). The colour-magnitude diagram for the field at (2.9,-7.95)\nhas been truncated at $V_{\\rm 606}=26$. The direction of the\nreddening vector, as given in Holtzman et al. (1995b), is indicated by\na solid line in each diagram. }\n\\label{cmd_606}\n\\end{figure*}\n\n\n\\section{Reddening, distances and metallicities.}\n \nAs we are using archive data we do not have control over which\npassbands have been used. This makes it difficult to address the\nquestion of reddening for all fields and clusters in a consistent way.\nWe later consider the sensitivity of our conclusions to the adopted\nreddening. Initially we consider available determinations in\nthe literature.\n\nWe have searched the literature for independent determinations of the\nreddening. For two of the clusters and the SGR-I field observations in\nthe two HST U-passbands exist, which could in principle allow\nderivation of the extinction directly. Unfortunately the clusters were\nobserved in F336W, which has a large red leak. This means that the\nextinction has a non-linear dependence on the reddening which makes it\ndifficult to deredden the stars in the colour-colour diagram.\n\nWe use the extinction for a K5 spectrum as given in Table 12 of\nHoltzman et al.\\,(1995b) to calculate the reddening vector. When\n$E(B-V)$ is not directly available, we use the extinction law given in\nTable 2 of Cardelli et al.\\,(1989) to derive $E(B-V)$ (adopting\n$R_V=3.1$). The extinctions and reddenings from the literature are\ncollected in Table \\ref{reddenings}.\n\n\\begin{table}\n\\caption[]{Reddenings from the literature and extinctions, derived \nfrom Holtzman et al. (1995b)}\n\\begin{tabular}{llllllllllllllllll}\n\\hline\\noalign{\\smallskip}\nField & $E(B-V)$ & $A_{\\rm F555W}$ & $E(V_{\\rm F555W}-I_{\\rm F814W})$\\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nSGR-I & 0.58 & 1.77 & 0.70 \\\\\nBW & 0.49 & 1.49 & 0.59 \\\\\nNGC5927 & 0.46 & 1.41 & 0.56 \\\\\nNGC6528 & 0.6 & 1.83 & 0.73 \\\\\nNGC6553 & 1.0/0.8 & 3.03/2.45 & 1.20/0.50\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\label{reddenings}\n\\end{table}\n\n\\subsection{Comparison with previous studies}\n\n\nThe same observations as we use for NGC6553 and NGC6528 have previously\nbeen reported in Ortolani et al. (1995) and those for NGC5927 in\nFullton et al. (1996). A comparison between our colour-magnitude\ndiagrams and theirs shows excellent agreement where even individual\nstars may be identified. The comparison of both the general structure\nof the colour-magnitude diagrams as well as of magnitudes of\nindividual stars give us confidence in our photometry for the other\nfields, eg. MW, SGR-I. Ortolani et al. (1995) did not\npublish the colour-magnitude diagram for NGC6528 but the ridge-line.\n\n\\subsection{The Bulge fields}\n\n\\subsubsection{SGR-I}\n\\label{sgri_text}\n\nSGR-I is a well known low-extinction area. Glass et al.(1995) adopt\n$A_V=1.87$. They ascribe fairly large and uncertain errors to this\nvalue. The cluster NGC6522 appears to have similar extinction to\nSGR-I. Walker \\& Mack (1986) found $A_V=1.78\\pm0.10$. Using $R_V=3.1$\nthis corresponds to $E(B-V)=0.57$. Frogel et al. (1990) also derive\n0.57 for an A0 star. Terndrup et al.(1990), from M giants, derive a\n$E(B-V)=0.54$. The estimate is, essentially, based on the similarities\nbetween NGC6522 and the SGR-I field. No HST observations in the\nrelevant passbands are available for NGC6522. We adopt $E(B-V)=0.58$.\n\n\\subsubsection{Baade's window at R.A.=18 03 11.7 $\\delta$=--29 51 40.7}\n\\label{bw_text}\n\nThis field is situated in the low extinction area called Baade's\nWindow. Stanek (1996) produced a detailed extinction map of this area\nfrom OGLE data. The uncertainty, which is systematic, in this\ndetermination mainly arises from the zero point. This grid has\n30arcsec spacing, and we are cautioned that there may exist further\nstructure in the reddening below this spatial resolution. For the\nposition of the PC1 his map gives $E(V-I)=0.566$ and $A_V\n=1.452$. Using Cardelli et al.\\,(1989) this corresponds to\n$E(B-V)=0.49$. Using Holtzman et al. (1995b) this translates to\n$E(V_{\\rm F555W}-I_{\\rm F814W}) = 0.59$.\n\n\\subsubsection{Fields at (l,b)=(3\\fdg6,-7\\fdg0) and (2\\fdg9,-7\\fdg95)}\n\nThese fields are part of two parallel programs and we do not have\nfurther information from observations of the extinction. Figure\n\\ref{cmd_606} however suggests that they suffer from similar\nextinctions. Since $V_{\\rm 606}$ is roughly 0.6 magnitudes brighter\nthan $V_{\\rm 555}$ the turn-offs for these two fields appear very\nsimilar in colour to those of SGR-I and Baade's window. We primarily\nuse these observations for number counts in $I_{\\rm 814}$.\n\n\n\\subsection{The globular clusters}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%% tables %%%%%%%%%%%%\n\n\\begin{table*}\n\\caption[]{Data for NGC5927 compiled from the literature.}\n\\begin{tabular}{llllllllllllllllll}\n\\hline\\noalign{\\smallskip}\n & Value & Ref. & Comment\\\\\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nCore radius & $0\\farcm 42$& Harris (1996) &\\\\\n$\\Delta(m-M)$ & 16.10 & Zinn (1980) & 16.6 kpc\\\\\n & 14.52 & Djorgovski (1993) & 8.0 kpc\\\\\n {[Fe/H]}& $-0.16 $ & Zinn (1980) \\\\ \n\t & $-0.30$ &Zinn \\& West (1984) \\\\\n\t & $-0.32/-0.64$ & Rutledge et al. (1997) & Zinn \\& West (1984) scale/Caretta\\& Gratton (1997) scale\\\\\n{[Fe/H]}$_{\\rm 47 Tuc}$& $+0.57$ & Cohen (1983) & relative to 47 Tuc at --0.7 dex\\\\\nAge & $10.9\\pm2.2$ Gyr & Fullton et al. (1996) \\\\\n\t& $15$ Gyr & Samus et al. (1996) \\\\\nE(B-V) & 0.48 & Zinn (1980) \\\\\n & 0.46 & Peterson (1993) \\\\ \n & $(0.44) - 0.46$ & Sarajedini \\& Norris (1994) & For several solutions for \\\\\n & & & reddening and metallicity\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\label{ngc5927_tab}\n\\end{table*}\n\n\\begin{table*}\n\\caption[]{Data for NGC6528 compiled from the literature.}\n\\begin{tabular}{llllllllllllllllll}\n\\hline\\noalign{\\smallskip}\n & Value & Ref. & Comment\\\\\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nCore radius & $0\\farcm 09$& Harris (1996) \\\\\n Distance & 7.5 kpc & Ortolani et al.\\,(1992) \\\\\n$\\Delta(m-M)$ & 16.4 & Zinn (1980) & 19.1 kpc\\\\\n {[Fe/H]} & $+0.01$ & Zinn (1980)\\\\\n & $+0.29$ & Bica \\& Patoriza (1983)\\\\ \n\t & $+0.12$ & Zinn \\& West (1984) \\\\\n\t & $-0.23$ & Armandroff \\& Zinn (1988) & Integrated spectra IR Ca {\\sc ii}\\\\\n\t & high, sim to NGC6553& Ortolani et al.\\,(1992)\\\\\n & $-0.23$ &Origlia et al.\\,(1997) & IR abs. at 1.6 $\\mu$m \\\\\n {[M/H]} & $+0.1/-0.4$ & Richtler et al.\\,(1998)&Trippico isochrone/Bertelli isochrone\\\\\n $Z$ & $Z_{\\odot}$ & Bruzual et al.\\,(1997) & \\\\\n Age & 14 Gyr & Ortolani et al.\\,(1992) & metallicity comparable to solar\\\\\n\t& $12\\pm2$ Gyr & Bruzual et al.\\,(1997) & \\\\\n E(B-V) & 0.55 & Ortolani et al.\\,(1992) & NGC6553 as reference and $\\Delta(m-M)_V= 14.39$\\\\\n\t& 0.62 & Bruzual et al.\\,(1997) & \\\\\n\t& 0.56 & Zinn (1980) \\\\\n E(V-I)& 0.8/0.6 & Richtler et al.\\,(1998)&Trippico isochrone/Bertelli isochrone\\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\n\\end{tabular}\n\\label{ngc6528_tab}\n\\end{table*}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics[angle=-90]{0952.F08.ps}}\n\\resizebox{\\hsize}{!}{\\includegraphics[angle=-90]{0952.F09.ps}}\n\\caption[]{Histogram showing the distribution of integrated $(V-I)_o$\nfor all the clusters in Harris (1996) catalogue for which photometry\nin all passbands are available. We have used the reddening quoted in\nHarris to calculate the intrinsic colours. The catalogue values of\n$V-I$ for NGC6528 and NGC6553 are given. Harris give $E(B-V)_{\\rm\n6528}=0.62$ and $E(B-V)_{\\rm 6553}=0.84$. Note that if we used the\nreddenings quoted in this paper the clusters would in fact become\nintrinsically even less red. The second panel shows the V-I colours as a\nfunction of the [Fe/H] values quoted in Harris. The $\\bullet$ in the\nlower panel indicates the position of NGC6553 with the new iron\nabundance from Cohen et al. (1999).}\n\\label{harris_histogram}\n\\end{figure}\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{0952.F10.ps}}\n\\caption[]{Colour-magnitude diagrams for NGC5927. In panel a\nthe long exposure. The ridge line used in Sect. \\ref{metgrad.sec} \nis over-plotted\nas heavy dots. In panel b and c are the ridge line shown for the\n short exposure with\nisochrones superimposed. Isochrones are for 8, 10, 12, 14, 16,\n18 Gyr, Bertelli et al. (1994) and Guy Worthey (private\ncommunication). The isochrones have been moved to a distance of 8 kpc\nand an extinction of $E(B-V)=0.46$. Reddening vectors are plotted in\nupper right hand corner. Metallicities as indicated}\n\\label{fit_ngc5927}\n\\end{figure}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nTwo of the clusters, NGC6528 and NGC6553, are situated between us and\nthe Galactic Bulge. The third, NGC5927, is also in the disk but well\naway from the Bulge line of sight, hence we will only have\ncontamination from disk stars in this field. All three are thought to\nbe among the more metal-rich globular clusters in the Galaxy (e.g.\nRutledge et al. 1997). The cluster kinematics have been interpreted as\nevidence that the clusters are members of\nwhat is called the bulge population of globular clusters (see Minniti\n1996 and references therein). We noted above that such assignments do\nnot allow any deduction on the relative properties (ages, etc) of\nfield and cluster stars, given the lack of understanding of the\nformation of either population.\n\nWe have searched the literature for data on the clusters. Several\nstudies are available, both in the visual and the IR as well as\nspectroscopic studies of individual stars and of the integrated light\nfrom the cluster, and are summarized in Tables \\ref{ngc5927_tab},\n\\ref{ngc6528_tab} and \\ref{ngc6553_tab}. References\nreporting a result are given in preference to later reviews.\nIt is important for our\nstudy to understand the metallicities of the clusters and the fields,\nat least on a relative scale. Large metallicity differences would\ninfluence the conclusions from the number counts in\nSect. \\ref{sect_age_bulge}.\n\nWe note, using the catalogue data by Harris (1996), that the integrated\ncolours for NGC6528 and NGC6553 show them to be ``normal''\nclusters. This is illustrated in Fig.\\ref{harris_histogram}, where it\nis seen that extreme high metal abundances are unlikely, given their\nintegrated colours.\n\n\\subsubsection{NGC5927}\n%%%%%%%%%%%%%%%%%%%%%%% Figurer %%%%%%%%%%%%%%%%%%%%%%\n\nThis cluster is situated in the disk well away from the Bulge, and is\none of the most metal-rich disk globular clusters known. \nFullton et al.\\,(1996) present colour-magnitude diagrams from the same\nHST/WFPC2 observations as we use. They derive a cluster age of\n$10.9\\pm2.2$ Gyr, using ${\\rm [Fe/H]} = -0.24 \\pm 0.06$ dex. This makes the\ncluster 3-5 Gyr younger than many other disk clusters. The lower\nmetallicity found from Ca{\\sc ii} infrared triplet lines by Rutledge\net al. (1997) would imply a higher age. Samus et al. (1996) presented\nthe first deep ground-based $BVI$ photometry for the cluster from\nwhich they derived an age of 15 Gyr assuming ${\\rm [Fe/H]} =-0.49$ dex.\n\nIn Fig. \\ref{fit_ngc5927} we show the ridge-line of NGC5927 with\ntheoretical isochrones for 8-18 Gyr over-plotted. The isochrones have\nbeen moved to a distance of 8 kpc and an extinction of $E(B-V)=0.46$\n(see Table \\ref{ngc5927_tab}). From this we infer that $[{\\rm\nFe/H}]=-0.64$ dex, as derived by Rutledge et al.\\,(1997), is a good\nfit to the data. Also that a very young age is not likely, but rather\n$12-14$ Gyr.\n\n\n\\subsubsection{NGC6528} \n\\label{sec_ngc6528}\n\nNGC6528 is situated in the line of sight towards Baade's Window. It\nhas been the subject of two separate studies (Ortolani et al.\n1992 and Richtler et al. 1998), as well as figuring in a number of\nstudies of other metal-rich globular clusters (Cohen \\& Sleeper 1995,\nOrtolani et al. 1995, Kuchinski et al.1995, Bruzual et al.1997). To\nour knowledge no spectroscopic abundances have been reported.\n\n\nFrom the similarities in field and cluster colour-magnitude diagrams,\nOrtolani et al.\\,(1992) concluded that not only is NGC6528 projected\nonto the Galactic Bulge but the stellar population is\nindistinguishable from that of the bulge population. They noted a\nstrongly curved red giant branch, interpreted as evidence for high\nmetallicity, and a tilted horizontal branch. Richtler et al. (1998)\ncould not identify the cluster red giant branch directly in their\ncolour-magnitude diagram due to the combination of the Bulge population\nin the observed area and cluster AGB stars. \nThe initial tilt of the horizontal branch was\nsignificantly reduced by carefully selecting bulge stars and\ndiscarding the field stars. By investigating the member-ship of the\nvery red giants, $V-I > 3.5$, they conclude that the cluster is indeed\nsituated in front of the general bulge field population and not embedded in\nit.\n\nOur data do not reach bright enough magnitudes to study the horizontal\nbranch in detail, however, from number counts in\nSect. \\ref{sect_age_bulge} we conclude that our colour-magnitude\ndiagram is significantly contaminated by Bulge stars. Thus, while\nNGC6528 is possibly not a clean fiducial cluster, it is ideal for our\npresent age-test experiment (see also Sect. \\ref{sec_disc}).\n\n\\subsubsection{NGC6553}\n\nNGC6553 is perhaps the best studied cluster of the three. Ortolani et\nal.\\,(1990) published the first detailed study of this cluster, which\nis situated at a projected distance of $\\sim 6\\degr$ from the galactic\ncentre and roughly at a distance of 5 kpc from us. Being some 10-20\nscale lengths from the Galactic centre, this makes it a\nmarginal `bulge' cluster. However it is often included in such studies\n(eg Barbuy et al. 1998). Here we will use its colour-magnitude\ndiagram to constrain the number of young stars in the Galactic Bulge,\nSect. \\ref{sect_age_bulge}. However, the colour-magnitude itself\nmerits a further discussion here. The work of Ortolani et al has been\nfollowed up in the infra red by Davidge \\& Simons (1994), and by\nGuarnieri et al.\\,(1997) who present a study based on both\noptical and infrared observations. The aim with this study is to\nprovide a template for infra red studies of the galactic bulge\npopulation. \n\n\\subsubsection{Differential reddening towards NGC6553?}\n\\label{sec_diff_red}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{figure*}\n\\resizebox{12cm}{!}{\\includegraphics{0952.F11.ps}}\n\\hfill\n\\parbox[b]{55mm}{\n\\caption[]{NGC6553. a. The position on the PC1 chip for the stars on\nthe two giant branches. b. Colour-magnitude diagram for the same\nstars. The direction of the reddening is indicated by a solid\nline. Open circles denote stars with $V_{\\rm 555} < 18.5$ and filled\ncircles stars with $V_{\\rm 555} > 18.5$. Error bars, as given by {\\sc\nallstar}, are over plotted for these stars.}\n\\label{map_sel_ext}}\n\\end{figure*}\t\n\nOur colour-magnitude diagram, in Fig. \\ref{cmd_shallow}, shows some\nintriguing and previously not discussed patterns. At $V \\sim 21.5 $ an\napparent second turn-off is seen and more or less parallel to the red of the\nred giant branch is a second sequence of stars. This sequence is\nactually visible also in the colour-magnitude diagram in Ortolani et\nal.\\,(1995), however the apparent turn-off is not. Additionally, this\ncluster has a well-known `tilted' horizontal branch, with the HB slope\nlying close to that of the reddening vector, and has a broad\nmain-sequence turn-off.\n\nCan the ``extra'' giant branch, and the various other anomalies be due to\ndifferential reddening of cluster stars? Ortolani et al. (1995) found the\nreddening to be variable over the PC1, $\\sim 0.2$ magnitudes across\nthe field. The simplest possible test is to see if the CMD anomalies\nare restricted to one patch of the field that has higher\nreddening. \nIn Fig. \\ref{map_sel_ext} we show the positions of the stars in the\n``extra'' giant branch. It is clear that the stars are evenly\ndistributed over the image and that their positions in the\ncolour-magnitude diagram cannot therefore be due to a simple selective\nextinction effect. Plausible astrophysical explanations all have difficulties:\nthe obvious explanation, that this is the background\nGalactic bulge, with some additional reddening, is very difficult to\nmake consistent with the data. An alternative, though also\nspeculative, explanation is that the second giant branch is part of\nthe Sgr dSph galaxy (Ibata et al. 1995). The absence of any such\nfeatures in Fig.\\ref{cmd_606} for fields closer to the centre of Sgr\nrequires a very non-uniform surface density in the dwarf\ngalaxy. However, even with this explanation, further reddening beyond\nNGC6553 is required to move it to such red colours. \n\nAn explanation of the colour-magnitude data for NGC6553 remains\ndifficult. Reddening which is both patchy and mixed through the\ncluster remains feasible. A detailed HST (WFPC plus NICMOS) study is\nrequired, and is underway. It will be reported elsewhere (Beaulieu et\nal. 1999, in prep.). In the interim, some reserve in deductions from\nthis cluster is advised.\n\n\n\\subsubsection{Spectroscopic abundances}\n\nIn addition to the metallicities based on photometry and spectroscopy\nof the Ca {\\sc ii} infra red triplet, summarized in Table\n\\ref{ngc6553_tab}, two studies have obtained high-resolution abundance\ndata for a handfull of stars in the cluster. Barbuy et al. (1997)\ncompleted the first detailed abundance study and derive Mg, Ti, Si, Ca\nand Eu abundances as well as Fe abundances for 3 very cool\nstars. Preliminary results are ${\\rm [Mg/Fe]} \\simeq +0.15$, ${\\rm\n[Ti/Fe]} \\simeq +0.3$, ${\\rm [Si/Fe]} \\simeq +0.6$, ${\\rm [Ca/Fe]}\n\\simeq 0.0$ and ${\\rm [Eu/Fe]} \\simeq +0.3$. The abundance ratios for\nMg, Ti, Ca and Eu are similar for those found in metal-rich dwarf\nstars in the solar neighbourhood (Feltzing \\& Gustafsson 1998 and\nFeltzing 1999) while the cluster appears overabundant in Si. This\ncould point to a rapid star formation history, but any interpretation\nis contradicted by the low Ca abundance, which is not consistent with\nthe other alpha-elements.\n\n\nCohen et al. (1999) find that five horizontal branch stars have a mean\n[Fe/H] of $-0.16$ dex, which is comparable to the mean abundance in the\nGalactic Bulge as found by McWilliam and Rich (1994). The horizontal\nbranch stars are preferable to use because their spectra are less\ncrowded and abundances are therefore more readily extractable then in\nthe very crowded spectra used by Barbuy et al. We will therefore adopt\nthis new high [Fe/H]. This is also consistent with the early findings\nby Cohen (1983) that an underestimate in $E(B-V)$ of as little as\n$0.^m05$ corresponds to an underestimate in [M/H] of 0.2 dex. \n\n\\begin{table*}\n\\caption[]{Data for NGC6553 from the literature.}\n\\begin{tabular}{llllllllllllllllll}\n\\hline\\noalign{\\smallskip}\n & Value & Ref. & Comment\\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nCore radius & $0\\farcm55$& Harris (1996) & \\\\\n Distance & 4.9 kpc & Ortolani et al.\\,(1990)\\\\\n$\\Delta(m-M)$ & 16.4 & Zinn (1980) & 19.1 kpc\\\\\n & 13.6 $\\pm 0.25$ & Guarnieri et al.\\,(1992) & 5.25 kpc\\\\\n {[Fe/H]} & $+0.26$ & Zinn (1980) \\\\\n & $+0.47$ & Bica \\& Pastoriza (1983)& For a discussion of probable error sources \\\\\n & & & see Barbuy et al.\\,(1992) (CNO excess) \\\\\n & $-0.7$ & Pilachowski (1984) & Spectroscopy of 1 star\\\\\n & $-0.41$ & Webbink (1985) \\\\\n\t& $-0.2^{+0.2}_{-0.4}$& Barbuy et al.\\,(1992) & Spectroscopy of star III-17\\\\\n\t& $\\geq -0.4$ & Davidge \\& Simons (1994) & IR photometry\\\\\n\t& $-0.29$ & Zinn \\& West (1994) \\\\\n & $-0.55$ & Barbuy et al.\\,(1997), Barbuy et al.\\, (1999) & Spectroscopy of 3 giant stars \\\\\n & $-0.33$ & Origlia et al.\\,(1997) & IR abs. at 1.6 $\\mu$m \\\\\n & $-0.60$ & Rutledge et al.\\,(1997) & IR Ca {\\sc ii} triplet \\\\\n & $-0.16$ & Cohen et al. (1999) & from 5 horizontal branch stars \\\\\n{[Fe/H]}$_{\\rm 47 Tuc}$& $+0.24/+0.37$ & Cohen (1983) & Spectroscopy 5 stars/2 most metal-rich stars, \\\\\n & & & relative to 47 Tuc at --0.7 dex\\\\\n\t& $+0.10$ & Cohen \\& Sleeper (1995) & relative to 47 Tuc at --0.71 dex \\\\\n$Z$ & $Z_{\\odot}$ & Bruzual et al.\\,(1997) & \\\\\n Age & & Ortolani et al.\\,(1990)& between 47Tuc and Pal~12\\\\\n\t& $12\\pm2$ Gyr & Bruzual et al.\\,(1997) & \\\\\n E(B-V) & 0.78 & Zinn (1980) \\\\ \n & $\\leq 1.0$ & Ortolani et al.\\,(1990)\\\\\n\t& 0.7 & Guarnieri et al.\\,(1997)\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\label{ngc6553_tab}\n\\end{table*}\n%\n%________________________________________________________________\n\\section{The age of the Galactic Bulge}\n\\label{sect_age_bulge}\n\n\n\\begin{table*}\n\\caption[]{Number of stars in ``boxes''. The first column identifies\nthe fields and clusters, the second the designation, i.e. MS (main sequence), \nTO (turn off), and Disk, for the box, the third gives the range in $V_{\\rm\n555}$ and the fourth gives the range in $V_{\\rm 555}-I_{\\rm 814}$ used for \ndefining the box, then follows the number of stars counted in each box. \nThe last three columns give the relative numbers in the different boxes.}\n\\begin{tabular}{lrrrrrrrrrrrrrrrrrrrrrr}\n\\hline\\noalign{\\smallskip}\nField & &V & V-I & \\# & Disk/MS & Disk/TO & TO/MS \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nSGR-I &Disk & 18-20 & 0-1.6 & 54 &0.13 &0.20 &\\\\\n(d=3deg) &TO & 20-21 & 0-1.6 & 268 & & &0.07\\\\\n &MS & 21-22 & all & 404 & & &\\\\\nBW &Disk & 18-19.7 & 0-1.35 & 34 &0.12 &0.18 &\\\\\n(d=4deg) &TO & 19.7-20.7 & 0-1.4 & 188 & & &0.07\\\\\n1000s &MS & 20.7-21.7 & all & 276 & & &\\\\\nBW &Disk & 16(18)-19.7 & 0-1.35 & 47(39)&0.15(0.13)&0.24(0.20) &\\\\\n40s &TO & 19.7-20.7 & 0-1.4 & 193 & & &0.06\\\\\n &MS & 20.7-21.7 & all & 307 & & &\\\\\nNGC6528 &Disk & 18-20 & 0-1.5 & 50 &0.11 &0.18 &\\\\\n(d=5deg) &TO & 20-21 & 0-1.5 & 278 & & &0.06\\\\\n &MS & 21-22 & all & 473 & & &\\\\\nNGC6553 &Disk & -19.5 & 0-1.44 & 26(31)&0.04(0.05)&0.07(0.08) &\\\\\n(d=6deg) &TO & 19.5-20.5 & 0-1.44 & 397 & & &0.06\\\\\n &MS & 20.5-21.5 & all & 667 & & &\\\\\nNGC5927 &Disk & 18-19.6 & 0-1.3 & 52 &0.06 &0.06 &\\\\\n(d=35deg) &TO & 19.6-20.6 & 0-1.3 & 809 & & &0.09\\\\\n &MS & 20.6-21.6 & all & 889 & & &\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\label{number_counts}\n\\end{table*}\n\n\n\\begin{figure}\n\\centerline{\\resizebox{7cm}{!}{\\includegraphics{0952.F12.ps}}}\n\\caption[]{Definition of windows for NGC6528, Table \\ref{number_counts}.}\n\\label{windows.fig}\n\\end{figure}\n\n\n\nIn our colour-magnitude diagrams in Fig \\ref{cmd_shallow} and\n\\ref{cmd_deep} there appear to be many stars in the ``young stars''\nand ``blue straggler'' region, brighter and bluer than the main\nmain-sequence turn-off. Because the turn-off region is sensitive to\nage (Fig. \\ref{comp_iso}) is this evidence for a young stellar\npopulation? The turn-off region in these diagrams is also sensitive\nto foreground contamination, and to bulge blue stragglers. \nRather than simply assuming the nature\nof the stars around the turn-off in the colour-magnitude diagrams of\nBulge fields, foreground or a substantial young Bulge population, we\ntest the possibility that they are foreground disk contamination. This\nis done by quantifying their spatial distribution, since foreground\ndisk stars will be distributed on the sky differently than are bulge\nstars, of whatever age. The key to this experiment is our\nconsideration of fields in a variety of directions, and in particular\nuse of the cluster NGC5927, which is at longitude $34 \\degr$, \nfar from the bulge.\n\nWe defined three ``windows'' in our colour-magnitude diagrams in which\nwe performed number counts. The location of the windows was decided\nupon by inspecting the colour-magnitude diagrams of SGR-I and\nNGC6528. We defined three windows; one corresponding to stars above\nthe turn-off (young bulge and/or foreground disk and/or blue\nstragglers), one at the turnoff\nof an old population and one on the bulge main sequence, as\nillustrated in Fig. \\ref{windows.fig}. The colour and magnitudes\nlimits were then adjusted for each field and cluster to take distance\nand reddening differences into account, following Table\n\\ref{number_counts}.\n\nWe first compare the counts for the two clusters, NGC6553 and NGC5927,\none near the bulge, one far out in the disk. For these two clusters,\nThe relative number of stars that are either young or are foreground\ndisk stars and stars that are thought to belong to the Bulge, called\n``Disk/MS'' in the table, is constant between the fields, while the\nabsolute number is roughly constant. This is direct evidence that the\ncounts in the disk box are dominated by true disk stars and not true\nbulge stars. \nFurther direct evidence that the ``disk'' stars are disk, is\nthe near constancy of their surface density in the inner bulge fields.\n\nIn this part of the diagram the star numbers do not\nchange with $l,b$ as they would if we were seeing a young Bulge\npopulation. The COBE Bulge has a scale length of $\\sim 1^o$ (Binney,\net al. 1997) and hence the number counts would change\nsignificantly over the area studied.\n\n\nThe ratio of disk to main sequence and turn-off stars for NGC6528 is\ndifferent to that for the other two clusters, suggesting that for this\ncluster the colour-magnitude diagram is significantly affected by\nfield contamination, perhaps explaining some of the apparent anomalies\nnoted in earlier analyses of these HST images (Ortolani et al. 1995).\n\n\n\n\n\n%%%%%%%%%%%%%% Figures %%%%%%%%%%%%%%%%%%%%%\n\n\n\n\\begin{figure}\n\\centerline{\\resizebox{7cm}{!}{\\includegraphics{0952.F13.ps}}}\n\\caption[]{Illustration of the age-metallicity degeneracy around\nthe turn-off. Isochrones are from Bertelli et al. (1994), in the HST\npassbands courtesy of G. Worthey. }\n\\label{comp_iso}\n\\end{figure}\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{0952.F14.ps}}\n\\caption[]{In panel a. we show the colour distribution for stars in\nNGC5927 with $20.2 \\leq V_{\\rm 555} \\leq 21.2$. The histogram has been\nmoved so that its mean colour ($V-I_{\\rm norm}$) is zero. To this\nhistogram a Gaussian is fitted, shown by the dashed line. This Gaussian\ndefines the colour distribution in a single stellar population,\nconvolved with our photometric errors. A colour\ndifference of 0.07 in magnitude corresponds to a change in [Fe/H] of\n0.3 dex (at -0.3 dex and 0.0 dex). Two Gaussians separated in colour\nby the equivalent of a 0.3 dex metallicity difference\nare added to make up a reasonable representation of the colour\ndistribution in Baade's window (see text). This is plotted in b. To\nthe Gaussian representing Baade's window a third population at +0.3\ndex is added in different proportions, to illustrate the effect on the\nobserved colour distribution of a very metal-rich population. The\nthree curves are:\nshort dashed line 50\\% stars added, dotted line 100\\% stars added and long\ndashed line 200\\%.}\n\\label{fe_vs_col}\n\\end{figure}\n\n\\begin{figure*}\n\\resizebox{12cm}{!}{\\includegraphics{0952.F15.ps}}\n\\hfill\n\\parbox[b]{55mm}{\n\\caption[]{Normalized histogram of the colour distribution of \nstars in magnitude slices for NGC5927, SGR-I\nand the deep exposure of Baade's window. The slices are made in\nV$_{\\rm 555}$, with magnitude ranges appropriate for reddening and\ndistance in each line of sight. The magnitude ranges are:\npanels a and c are for 20-21, b for 20.5-21.5,\nd and f for 21-22, and e for 21.5 -22.5. }\n\\label{slices_deep}}\n\\end{figure*}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{table}\n\\caption[]{Number counts in $I_{\\rm 814}$ for the four fields. Their\nrelative numbers are compared with simple predictions using the E2 \nmodel of the Galactic Bulge density distribution from Dwek et al. (1995).}\n\\begin{tabular}{lrrrrrrrrrrrrrrrrrrrrrr}\n\\hline\\noalign{\\smallskip}\nField & $\\Delta I_{\\rm 814}$ & \\# & rel. SGR-I & Model \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nSGR-I & 20.0-21.0 & 536 & -- & --\\\\\nBW & 19.5-20.5 & 372& 0.69 & 0.62\\\\\n & 20.0-21.0 & 328 & 0.61 \\\\\nu811 & 20.0-21.0 & 52 & 0.10 & 0.11\\\\\nDeep & 20.0-21.0 & 44 & 0.08 & 0.09 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\label{number_counts_sim}\n\\end{table}\n\nThe spatial distribution of the number counts in $I_{\\rm 814}$ in the\nfour deep fields are consistent with results from simple simulations\nusing the E2 model of the Galactic Bulge in Dwek et al.\\,(1995)\n(Table \\ref{number_counts_sim}). We present two counts for Baade's\nwindow. This field has the lowest extinction and we would expect the\ncounts between $19.5 \\la I_{\\rm 814} \\la 20.5$ to be comparable with\nthe counts in SGR-I between 20.0 and 21.0. However, for comparison we\nalso give the counts in the same apparent magnitude bin for Baade's\nwindow. As can be seen the difference is small, but consistent with\nBaade's window having an extinction $\\sim$ 0.3 magnitudes less than that\ntowards SGR-I.\n\nWe conclude that the apparent evidence for a significant young Bulge\npopulation in our colour-magnitude diagrams is an artifact of disk\ncontamination. Correcting the observed colour-magnitude diagrams,\nusing the results for NGC5927, removes all the stars above and to the\nblue of the turnoff. That is, there is no evidence in these HST/WFPC2\ndata for a significant age range in the bulge population. \n\nThis tight limit, extending the previous results of Ortolani etal that\nthe bulk of the bulge is old, is somewhat surprising. What happens to\nall the young stars forming in the inner disk?\nWe emphasize however, that available limits still allow an age range of\nseveral Gyr, especially so, as discussed below, if there is an\nage-metallicity relation in the bulge stars.\n\n\\subsection{Can we resolve the metallicity distribution function?}\n\nWe now consider if we are able to use the apparent width of the\nmain-sequences in the colour-magnitude diagrams to constrain the width\nof the stellar metallicity distribution function. Recall, from Fig. \n\\ref{comp_iso} that a younger metal-richer population can hide in the \nturn-off region. It should, however, show up on the main sequence, if \nthe statistics are good enough.\n\nIn Fig.\\ref{fe_vs_col} we show a slice histogram for NGC5927 for all\nstars between $V_{\\rm 555}$ 20.2 and 21.2 and a Gaussian fitted to\nit. We use this Gaussian as a representation of the apparent colour\ndistribution including measurement errors of a single stellar\npopulation in our data. A difference of 0.07 in colour corresponds to\na change in [Fe/H] of 0.3 dex. Two Gaussian separated by 0.3 dex are\nadded to make up the Gaussian drawn with a full line. This should be\na reasonable representation of the colour distribution in Baade's\nwindow (see text). To the Gaussian representing Baade's window we add\na third population at +0.3 dex. As is clear from the figure, to be\nable to resolve a metal-rich extra population, that population has to\nbe large in numbers relative to the metal-poor one, and enough stars have\nto be observed so that the histograms can be constructed with small\nenough bins ($\\sim$ 0.02). This is not the case here.\n\nIn Fig. \\ref{slices_deep} \nthe histograms have been moved so that the mean colour for each slice\nis centred at 0. We have fitted a Gaussian to the two histograms for\nNGC5927. This Gaussian is reproduced in the panels showing the\nhistograms for SGR-I and Baade's window. From this we conclude that\nthere is some evidence for a larger spread in $V-I$ in the fields\nthan in the cluster. In particular, the slice at a fainter $V_{\\rm\n555}$ show a larger spread towards the blue, for the two field\npopulations than for the cluster, consistent with a broad metallicity\ndistribution function with a tail to metal-poor stars. The metal-rich\n(red) sides of the histograms are however too poorly determined for\nuseful conclusions.\n\n\n\\section{Is there a detectable metallicity gradient?}\n\\label{met-grad}\n\nIn order to check a possible metallicity gradient, we compare the\ncolour-magnitude diagrams of the Baade's window and SGR-I field. This\nis a particularly robust method, since we are not sensitive to\nincompleteness at the faint end of the ridge lines, the\ncolour-magnitude diagrams being comparably complete.\n\n\\subsection{The metallicity in Baade's window}\n\\label{metgrad.sec}\n\n%%%%%%%%%%%%%%%%%%%% Figurer %%%%%%%%%%%%%%%%%%%%5\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{0952.F16.ps}}\n\\caption[]{The CMD for Baade's Window is shown, together with its own\nridge line (fainter than $V_{\\rm 555} \\sim 20$, open squares). The\nsolid points ($\\bullet$) are the ridge line constructed from the\ncolour-magnitude diagram of NGC5927, shifted along the reddening line\nappropriately. }\n\n\\label{bw40_ngc5927}\n\n\\end{figure}\n\n\\begin{figure*}\n\\resizebox{12cm}{!}{\\includegraphics{0952.F17.ps}}\n\\hfill\n\\parbox[b]{55mm}{\n\\caption[]{Each of the 4 panels shows the comparison of the ridge\nlines for SGR-I (filled circles) and Baade's window, (open\ncircles). Panel (a) presents the ridge lines as observed, corrected\naccording to the reddenings cited in the literature. This panel also\nshows the ridge line for NGC5927, ($\\times$). In (b) we also over plot\na set of 14 Gyr old isochrones for $[Fe/H] = -0.5, -0.25, 0.0, +0.25 $\ndex, illustrating the apparent large abundance gradient implied by\nthese adopted reddenings. In panel (c) the ridge lines as observed are\nmoved to optimize agreement between the lower part of the two main\nsequences. Isochrones for $[Fe/H] = -0.25 $ dex and 8, 10, 12, 14, 16,\nand 18 Gyr (Bertelli et al. 1994 and Worthey private communication)\nare over-plotted, illustrating the large age gradient implied by this\nmethod. In panel (d) the ridge lines are shifted to optimize an\noverall fit of the morphology. 14 Gyr isochrones for [Fe/H]= -0.5 and\n-0.25 dex are over-plotted to indicate the sensitivity to abundance\ngradients in this case.}\n\\label{comp_ridges}}\n\\end{figure*}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5\n%%%%%%%%%%%%%%%%%%%%%%\nFigure \\ref{bw40_ngc5927} shows the colour-magnitude diagram from the\nshort exposure of Baade's window with its own ridge line, and also the\nridge line derived from the NGC5927 short exposure data. The ridge\nline of the cluster has been moved along the reddening line to account\nfor the differences in reddening for the two fields. We observe that\nthe both the main sequence and the giant branch of the field\npopulation(s) are redder than those of the cluster. From this we\nconclude that the mean metallicity of Baade's window is $\\sim0.3$ dex\nhigher than that of the cluster. This is in good agreement with\nresults from spectroscopic studies.\n\n\\subsection{The Bulge metallicity gradient}\n\nThe most robust way to compare colour-magnitude diagrams is to\nconstruct a ridge line for each field. The ridge lines can then be\nmoved to compensate for differential reddening effects, and compared\nto appropriate isochrones. This is illustrated in\nFig. \\ref{comp_ridges}. We see, in panels (a) and (b), that adopting\nliterature values for the reddening, and attributing all the resulting\ndifference between the ridge lines to metallicity, implies a\ndifference of 0.5 dex in metal abundance, which corresponds to 3.2\ndex/kpc, assuming a distance of 8 kpc to the Galactic Bulge.\n\nHowever, the relative reddening between the fields may well be in\nerror. We thus test two further hypotheses. First, that there is no\nsignificant metallicity gradient, but there is an age gradient. This\nis shown in Fig.\\ref {comp_ridges} panel (c), where one sees that an\nage gradient of $\\sim 6$ Gyr over 0.14 kpc is required, a result we\nconsider implausible.\n\nWe therefore try a further experiment, assuming the reddening is\nunknown, and is a free parameter to be determined. In this case we can\nderive a lower limit to any real age or abundance gradients, if we\nconservatively assign as much as is possible of the differences\nbetween the colour-magnitude diagrams to reddening, while fitting the\ntwo ridge lines using their overall morphology. This is shown in\npanel (d) of Fig. \\ref{comp_ridges}. No significant residual\nsystematic difference between SGR-I and Baade's window remains. \n\nUsing the isochrones by Bertelli et al. (1994) our best estimate of\nany allowed difference is $\\la 0.25$ dex. We conclude that there is no\nstrong evidence for an abundance gradient between Baade's window, at\nprojected distance from the centre of 550 pc, and SGR-I, at projected\ndistance 412 pc, assuming a distance of 8 kpc for the Bulge. The upper\nlimit on the amplitude of any abundance is $\\la 0.2$ dex,\ncorresponding to $\\la 1.3$ dex/kpc. This value may be compared with\nthe recent suggested detection, by Frogel et al. (1999),\nof a gradient of amplitude 0.5dex/kpc.\n\n\\section{Discussion}\n\\label{sec_disc}\n\n\nOur conclusion that the Galactic Bulge is predominately old is in\nconflict with those of Vallenari et al. (1996) and Holtzman et\nal. (1993). Both these studies found evidence for a substantial (up to\n30\\%) young stellar population in Baade's window. Also Kiraga et\nal. (1997), from OGLE data, concluded that the disk stellar population\nin Baade's window is old, while the true Bulge stars have a bluer\nturn-off implying a younger age than 47 Tuc. These results are based\non Baade's window only. The strength of our study is that it utilizes\nfive different line of sight. Our use of data for the cluster NGC5927\nis of considerable value, since this cluster is situated in the disk\nwell away from the sight line towards the Galactic Bulge. Accordingly\nthe contamination present in this colour-magnitude diagram must arise\nfrom foreground disk stars. We show that the relative and absolute\nnumber counts in this cluster show the same pattern as those in the\nBulge fields, showing that the stars previously identified with a\nsubstantial (or exclusively) young stellar population in the Galactic\nBulge are in fact foreground disk stars. Holtzman et al. (1993) note\nthat their interpretation of the data would likely change\nsubstantially if for example the reddening estimates are in error.\nOur results are mainly robust against such errors. Our results are\nalso in accordance with ground-based studies, especially in the IR,\nwhich have found no evidence for a substantial young stellar\npopulation in the Galactic Bulge (e.g. Terndrup 1988, Tiede et\nal. 1995, Frogel et al. 1990).\n\nThe first HST analysis of the stellar populations in Baade's Window\nwhich deduced an old age for the bulk of the bulge stars is that of \nOrtolani et al. (1995). We use the same HST data, and some other\narchive data, to provide a direct test of a critical assumption\nunderlying that study, and to extend the analysis to search for\ngradients in metallicity and/or age. By further removing from the\nanalysis the assumption that the `bulge' globular clusters are a true\ntracer of the age and metallicity of the field stars, we restrict the\nanalysis to the mean bulge star: the metal rich bulge stars, those\nabove about solar abundance, may be substantially younger than the\nbulk of the bulge.\n\nOrtolani et\nal. (1995) observed two `bulge' globular clusters, NGC6553 and\nNGC6528, with HST/WFPC2. By comparing ridge lines of these globular\nclusters with that of the metal-rich globular cluster 47 Tuc they\nconcluded that the `bulge' clusters have ages comparable to the halo\nglobular clusters. They then compared the V-band luminosity function\nof all stars observed in Baade's Window with the V-band luminosity\nfunction observed for NGC6528, concluding that ``the main sequence\nluminosity functions also coincide with extremely high precision in\nthe brighter, age-dependent part that is less affected by\nincompleteness and field contamination (that is, $19.5 \\la {\\rm V} \\la\n20.5$)''. As is illustrated clearly in our colour-magnitude data for\nNGC6528 this part of the apparent magnitude\nrange is indeed heavily contaminated by foreground disk stars, which\nappear as if they are young bulge stars. Why did these stars not\nvitiate the Ortolani etal analysis? The explanation is that analyses\nbased only on luminosity functions are valid if and only if the field\ncontamination is exclusively foreground disk, and that there is no\nsignificant young bulge population. In that case, the cluster\nluminosity function is in error in just the same way as is the field\ndata, and so the two errors compensate. In fact, the luminosity\nfunction method can be justified only {\\sl post hoc}, after an analysis\nof the type reported here. We confirm that Ortolani et al. (1995) were correct\nin that assumption.\n\nThe observational study of the inner bulge is further confused by the\ndistinct possibility that the very centrally-concentrated ``infra-red\nbulge'' seen by IRAS and COBE is not related in a simple way, if at\nall, to the larger ``optical bulge'' studied further from the centre\n(Ibata \\& Gilmore 1995a, 1995b; Wyse et al. 1997, Unavane\n\\& Gilmore 1998, Unavane et al. 1998). Recent studies of external\ngalaxies (Carollo 1999) show that central nuclei are common in bulges,\nand also that bulges have a diversity of properties.\nOptical studies in the Milky Way have been\nrestricted to Baade's window and beyond, $\\geq 4$ COBE scale lengths\nfrom the centre. Here we compare Baade's window with the low\nextinction window called SGR-I, roughly at the limit of optical\nobservations, at $b=2\\fdg6$, testing to see if the inner and outer\nGalactic Bulge have the same stellar population(s).\n\nWe deduce an upper limit to a metallicity gradient of $\\la 1.3$\ndex/kpc. Is such an amplitude surprising? Let us consider two\ndistinct possibilities which show that such a result is plausible.\n\nThe COBE Bulge has a scale height of $\\sim$ 150 pc, and could be\ninterpreted as evidence for a separate component superimposed on top of\nthe optical Bulge. Further evidence that this may indeed be a separate\nentity (the 'nucleus'?) is provided by the fact that both luminosity\nand kinematical models (eg Kent 1992) which describe well the outer\nbulge under-predict the light in the very central part of the Galactic\nBulge. At the position of the SGR-I window, at 3 COBE scale lengths\nfrom the Galactic Centre we are just beginning to pick up the IR\nBulge. It is quite plausible that this centrally condensed structure\nis considerably more metal-rich than the underlying, larger, optical\nBulge which is the main contributor to the stellar population(s) in\nBaade's window, at $<[Fe/H]> = -0.3$ dex.\n\nThese results are supported by recent studies of OH/IR stars\n(Sevenster, et al. 1997). OH/IR stars, which are oxygen-rich, cool giant\nstars in their final stages of evolution, trace basically all stars\nwith a main-sequence mass of $1-6 M_{\\sun}$ and can be reliably\ndetected through their OH maser emission at 1612 MHz. This makes them\nideal tracers of the underlying stellar population. They are\nintermediate age or old, and should therefore be dynamically relaxed\nand trace the global gravitational potential. These stars are\ndistributed in the central Bulge with a scale height $\\la 100$ pc\n(Sevenster et al. 1997).\n\nWe also note the fact that star-forming regions such as Sgr B exist\nshows that star-formation is still going on in the Galactic Bulge on\nscales of 50-100 pc. This is yet further evidence that we could expect\nthe central parts of the Galactic Bulge to be more metal-rich than the\nouter edges of the Galactic Bulge. There remains perhaps no more than\na semantic distinction between continuing formation of the central\nDisk and the central Bulge on such small scale lengths and recent\ntimes.\n\nIn conclusion, both large scale modeling of the dynamics in the Bulge\nand specific tracers show there to be structure in the stellar\npopulations at scales below those of the optical Bulge. The central\nparts are a highly dissipated self-enriching part of the Galaxy which\nis at least partially young.\n\n\\section{Conclusions}\n\nWe demonstrate how deep images with high spatial resolutions, only\navailable since the advent of HST, enable us to determine the\nproperties of the Galactic Bulge stellar population(s). In this we\nhave used three measures;\n\n\\begin{itemize}\n\n\\item number counts - to search for a young stellar population\n\n\\item histograms - to search for a metal-rich population\n\n\n\\item comparison of ridge lines - to derive metallicities and look\nfor internal differences, i.e. gradients in age and metallicity\n\n\\end{itemize}\n\n\\noindent\nIn particular we find that\n\n\\begin{itemize}\n\n\\item our results are consistent with no significant \nyoung stellar population in the Bulge, some 500pc, or 2-5 scale\nlengths, from the centre, \ncontrary to some previous studies;\n\n\\item the Galactic Bulge has a mean metallicity \nequal to that of the old disk;\n\n\\item there is marginal evidence for a central metallicity gradient;\n\n\\item the colour-magnitude diagram of NGC6553 is complex, requiring\ncare in photometric analyses of this cluster.\n\n\n\\end{itemize}\n\n\\begin{acknowledgements}\nThe UK HST support group in Cambridge, Rachel Johnson and Nial Tanvir,\nare thanked for numerous discussions on HST/WFPC2 and the best way to\nextract stellar photometry.\n\nTo produce Fig.\\ref{harris_histogram} we have use the online version\nof the Harris (1996) catalogue.\n\nSF acknowledges financial support from the Swedish Natural Research\nCouncil under their postdoc program.\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\n\n\\bibitem[]{} Armandroff T.E., Zinn R., 1988, AJ 96, 92\n\\bibitem[]{} Barbuy B., Castro S., Ortolani S., Bica E., 1992, A\\&A 259, 607\n\\bibitem[]{} Barbuy B., Ortolani S., Bica E., Renzini A., Guarnieri M.D., 1997, in ``Fundamental Stellar Properties: the Interaction between Observation and Theory'', Bedding, T.R., Booth, A.J., Davies, J. (eds.), page 203\n\\bibitem[]{} Barbuy B., Bica E., Ortolani S., 1998, A.\\&A 333, 117\n\\bibitem[]{} Barbuy, B., Renzini, A., Ortolani, S., Bica, E., Guarnieri, M. D., 1999, A\\&A 341, 539\n\\bibitem[]{} Bertelli G., Bressan A., Chiosi C., Fagotto F., Nasi E. 1994, A\\&AS 106, 275\n\\bibitem[]{} Bica E.L.D., Pastoriza M.G., 1983, Ap\\&SS 91, 99 \n\\bibitem[]{} Binney J., Gerhard O., Spergel D., 1997, MNRAS 288, 365\n\\bibitem[]{} Bruzual G.A., Babruy B., Ortolani S., Bica E., \nCuisinier F., Lejeune T., Schavon R.P., 1997, AJ 114, 1531\n\\bibitem[]{} Cardelli J.A., Clayton G.C., Mathis J.S., 1989, ApJ 345,\n245\n\\bibitem[]{} Carollo, M., 1999 ApJ 523 566\n\\bibitem[]{} Cohen J.G., 1983, ApJ 270, 654\n\\bibitem[]{} Cohen J.G., Sleeper C., 1995, AJ 109, 242\n\\bibitem[]{} Cohen J.G., Gratton R.G., Behr B.B., et al., 1999, astro-ph/9904238\n\\bibitem[]{} Davidge T.J., Simons D.A., 1994, AJ 107, 240\n\\bibitem[]{} Djorgovski, S., 1993, in Structure and Dynamics of Globular Clusters, ASP\nConf. Ser. Vol. 50, Djorgovski. S.G. and Meylan G. (eds.), p. 373\n\\bibitem[]{} Dwek R., G.Arendt, R. G., Hauser, M. G., Kelsall, T., Lisse, C. M., et al., 1995, ApJ 445, 716\n\\bibitem[]{} Feltzing 1998, in Highlights in astronomy 11, J Anderssen (ed.), Kluwer \n\\bibitem[]{} Feltzing S, Gustafsson B, 1998, A\\&AS 129, 237\n\\bibitem[]{} Frogel J.A., Terndrup D.M., Blanco V.M., Whitford A.E., 1990, ApJ 353, 494\n\\bibitem[]{} Frogel, J.A., Tiede, G.P., Kuchinski, L.E., 1999, AJ 117, 2296\n\\bibitem[]{} Fullton L.K., Carney, B. W., Olszewski, E. W., Zinn, R.,\n Demarque, P., et al., 1996, in Formation of the galactic halo... Inside and out, \nASP conf Series, vol 92, H Morris \\& A Sarajedini (eds.), p269\n\\bibitem[]{} Glass I.S., Whitelock P.A., Catchpole R.M., Feast M.W., 1995, MNRAS 273, 383\n\\bibitem[]{} Glass, I., Ganesh, S., Alard, C. et al., 1999 MNRAS 308 127\n\\bibitem[]{} Gnedin, O. Y., Ostriker, J.P., 1997 ApJ 474 223\n\\bibitem[]{} Guarnieri M.D., Montegriffo P., Ortolani S., Moneti A., \nBarbuy B., et al., 1995, ESO Msngr 79, 26\n\\bibitem[]{} Guarnieri, M. D., Ortolani, S., Montegriffo, P., Renzini, A., Barbuy, B., et al., 1998, A\\&A 331, 70\n\\bibitem[]{} Guarnieri M.D., Renzini A., Ortolani S., 1997, ApJL 477, 21\n\\bibitem[]{} Harris W.E. 1996, AJ 112, 1487\n\\bibitem[]{} Harris W.E. 1998, in Galactic Halos: A UC Santa Cruz Workshop, D. Zaritsky\n\\bibitem[]{} Holtzman J.A., Light R.M., Baum W.A., Worthey G., \nFaber S.M. et al. (eds.), 1993, AJ 106, 1826\n\\bibitem[]{} Holtzman J., Hester J.J., Casertano S., Trauger J.T., \nWatson A.M., 1995a PASP 107, 156\n\\bibitem[]{} Holtzman J.A., Burrows J., Casertano S., Hester J.J., \nTrauger J.T., 1995b, PASP 107, 1065\n\\bibitem[]{} Ibata R., Gilmore G., 1995a, MNRAS 275, 591\n\\bibitem[]{} Ibata R., Gilmore G., 1995b, MNRAS 275, 605\n\\bibitem[]{} Ibata R., Gilmore G., Irwin M., 1995, Nature 370, 194\n\\bibitem[]{} Kent S.M., 1992, ApJ 387, 181\n\\bibitem[]{} Kiraga M, Paczynski B, Stanek K, 1997, ApJ 485, 611\n\\bibitem[]{} Kuchinski L.E., Frogel J.A., Terndrup D.M., 1995, AJ 109,1131\n\\bibitem[]{} McWilliam A, Rich R.M., 1994, ApJS 91, 749\n\\bibitem[]{} Minniti D., Olszewski E.W., Liebert J., White S.D.M., \nHill J.M., et al., 1995, MNRAS 277, 1293\n\\bibitem[]{} Minniti D., 1996, ApJ 459, 175\n\\bibitem[]{} Ng. Y.K., Bertelli G., Chiosi C., Bressan A., 1996, A\\&A 310, 771\n\\bibitem[]{} Omont, A., S. Ganesh, C. Alard, et al., \nastro-ph/9906489 and A\\&A in press 1999\n\\bibitem[]{} Origlia L., Ferraro F.R., Fusi Pecci F., Oliva E., 1997 A\\&A 321, 859\n\\bibitem[]{} Ortolani S., Barbuy B., Bica E., 1990, A\\&A 236, 362 \n\\bibitem[]{} Ortolani S., Bica E., Barbuy B., 1992, A\\&AS 92, 441\n\\bibitem[]{} Ortolani S., Renzini A., Gilmozzi R., Marconi G., Barbuy B., et al., 1995, Nature 377, 701\n\\bibitem[]{} Ortolani S, Gilmozzi R., Marconi G., Barbuy B., Bica E., \net al., 1996, in Formation of the galactic halo... Inside and out, \nASP conf Series, vol 92, H Morris \\& A Sarajedini (eds.), p96\n\\bibitem[]{} Peterson, C.J., 1993, in Structure and Dynamics of Globular Clusters, ASP\nConf. Ser. Vol. 50, Djorgovski. S.G. and Meylan G. (eds.), p. 337\n\\bibitem[]{} Pilachowski C.A., 1984, ApJ 281, 614\n\\bibitem[]{} Richtler T., Grebel E.K., Subramaniam A., Sagar R., 1998, A\\&AS 127, 169\n\\bibitem[]{} Rosenberg, A., saviane, I., Piotto, G., \\& Aparicio, A., 1999 AJ 118 2306\n\\bibitem[]{} Rutledge G.A., Hesser J.E., Stetson P.B., 1997, PASP 109, 907\n\\bibitem[]{} Sadler E.M., Rich R.M., Terndrup D.M. 1996, AJ 112, 171\n\\bibitem[]{} Samus N., Kravtsov, V., Ipatov, A., Smirnov, O., Alcaino, G., et al., 1996, A\\&AS 119, 191\n\\bibitem[]{} Sarajedini A., Norris J.E., 1994 ApJS 93, 161\n\\bibitem[]{} Sevenster, M., Dejonghe, H., Habing, H., 1997, A\\&A 299, 689\n\\bibitem[]{} Silk J., Wyse R. 1993, PhR. 231, 293\n\\bibitem[]{} Stanek K.Z., 1996, ApJ 460, L37\n\\bibitem[]{} Stetson P.B., VandenBerg D.A., Bolte M., 1996, PASP 108, 560\n\\bibitem[]{} Terndrup D.M. 1988, AJ 96, 884\n\\bibitem[]{} Terndrup D.M., Frogel, J.A., Whitford, A.E. 1990, ApJ 357, 453\n\\bibitem[]{} Tiede, Glenn P., Frogel, Jay A., Terndrup, D. M., 1995, AJ 110, 2788\n\\bibitem[]{} Unavane M., Gilmore G. 1998, MNRAS 295, 145\n\\bibitem[]{} Unavane M. Gilmore G, Epchtein N., Simon G, Tiphene D., et al. 1998, MNRAS 295, 119\n\\bibitem[]{} Vallenari, A., Chiosi, C., Bertelli, G., Ng, Y.K, 1996, \nin ``The Galactic Centre'' ASP Conf.Ser.102, Gredel, R. (ed.), page 320\n\\bibitem[]{} VandenBerg D.A., Bolte M., Stetson P.B., 1990, AJ 100, 445\n\\bibitem[]{} VandenBerg D.A., Bolte M., Stetson P.B., 1996, ARA\\&A 34, 461\n\\bibitem[]{} Walker A.R., Mack P., 1986, MNRAS 220, 69\n\\bibitem[]{} Webbink R.F., 1985, in Dynamics of Star Clusters, IAU Symp. 113, J Goodman, P Huts (eds.), p541\n\\bibitem[]{} Wyse R.F G., Gilmore G, 1995, AJ 110, 2771\n\\bibitem[]{} Wyse R., Gilmore G., Franx M., 1997 ARA\\&A 35, 637\n\\bibitem[]{} Zinn R., 1980, ApJS 42, 19\n\\bibitem[]{} Zinn R., 1996 in Formation of Galactic Halo ... Inside and Out, ASP Conf. Series, vol. 92, H. Morrison, A. Sarajedini (eds.), p211\n\\bibitem[]{} Zinn R., West M., 1984, ApJS 55, 45\n\n\\end{thebibliography}\n\n\n\\end{document}\n\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002123.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\n\\bibitem[]{} Armandroff T.E., Zinn R., 1988, AJ 96, 92\n\\bibitem[]{} Barbuy B., Castro S., Ortolani S., Bica E., 1992, A\\&A 259, 607\n\\bibitem[]{} Barbuy B., Ortolani S., Bica E., Renzini A., Guarnieri M.D., 1997, in ``Fundamental Stellar Properties: the Interaction between Observation and Theory'', Bedding, T.R., Booth, A.J., Davies, J. (eds.), page 203\n\\bibitem[]{} Barbuy B., Bica E., Ortolani S., 1998, A.\\&A 333, 117\n\\bibitem[]{} Barbuy, B., Renzini, A., Ortolani, S., Bica, E., Guarnieri, M. D., 1999, A\\&A 341, 539\n\\bibitem[]{} Bertelli G., Bressan A., Chiosi C., Fagotto F., Nasi E. 1994, A\\&AS 106, 275\n\\bibitem[]{} Bica E.L.D., Pastoriza M.G., 1983, Ap\\&SS 91, 99 \n\\bibitem[]{} Binney J., Gerhard O., Spergel D., 1997, MNRAS 288, 365\n\\bibitem[]{} Bruzual G.A., Babruy B., Ortolani S., Bica E., \nCuisinier F., Lejeune T., Schavon R.P., 1997, AJ 114, 1531\n\\bibitem[]{} Cardelli J.A., Clayton G.C., Mathis J.S., 1989, ApJ 345,\n245\n\\bibitem[]{} Carollo, M., 1999 ApJ 523 566\n\\bibitem[]{} Cohen J.G., 1983, ApJ 270, 654\n\\bibitem[]{} Cohen J.G., Sleeper C., 1995, AJ 109, 242\n\\bibitem[]{} Cohen J.G., Gratton R.G., Behr B.B., et al., 1999, astro-ph/9904238\n\\bibitem[]{} Davidge T.J., Simons D.A., 1994, AJ 107, 240\n\\bibitem[]{} Djorgovski, S., 1993, in Structure and Dynamics of Globular Clusters, ASP\nConf. Ser. Vol. 50, Djorgovski. S.G. and Meylan G. (eds.), p. 373\n\\bibitem[]{} Dwek R., G.Arendt, R. G., Hauser, M. G., Kelsall, T., Lisse, C. M., et al., 1995, ApJ 445, 716\n\\bibitem[]{} Feltzing 1998, in Highlights in astronomy 11, J Anderssen (ed.), Kluwer \n\\bibitem[]{} Feltzing S, Gustafsson B, 1998, A\\&AS 129, 237\n\\bibitem[]{} Frogel J.A., Terndrup D.M., Blanco V.M., Whitford A.E., 1990, ApJ 353, 494\n\\bibitem[]{} Frogel, J.A., Tiede, G.P., Kuchinski, L.E., 1999, AJ 117, 2296\n\\bibitem[]{} Fullton L.K., Carney, B. W., Olszewski, E. W., Zinn, R.,\n Demarque, P., et al., 1996, in Formation of the galactic halo... Inside and out, \nASP conf Series, vol 92, H Morris \\& A Sarajedini (eds.), p269\n\\bibitem[]{} Glass I.S., Whitelock P.A., Catchpole R.M., Feast M.W., 1995, MNRAS 273, 383\n\\bibitem[]{} Glass, I., Ganesh, S., Alard, C. et al., 1999 MNRAS 308 127\n\\bibitem[]{} Gnedin, O. Y., Ostriker, J.P., 1997 ApJ 474 223\n\\bibitem[]{} Guarnieri M.D., Montegriffo P., Ortolani S., Moneti A., \nBarbuy B., et al., 1995, ESO Msngr 79, 26\n\\bibitem[]{} Guarnieri, M. D., Ortolani, S., Montegriffo, P., Renzini, A., Barbuy, B., et al., 1998, A\\&A 331, 70\n\\bibitem[]{} Guarnieri M.D., Renzini A., Ortolani S., 1997, ApJL 477, 21\n\\bibitem[]{} Harris W.E. 1996, AJ 112, 1487\n\\bibitem[]{} Harris W.E. 1998, in Galactic Halos: A UC Santa Cruz Workshop, D. Zaritsky\n\\bibitem[]{} Holtzman J.A., Light R.M., Baum W.A., Worthey G., \nFaber S.M. et al. (eds.), 1993, AJ 106, 1826\n\\bibitem[]{} Holtzman J., Hester J.J., Casertano S., Trauger J.T., \nWatson A.M., 1995a PASP 107, 156\n\\bibitem[]{} Holtzman J.A., Burrows J., Casertano S., Hester J.J., \nTrauger J.T., 1995b, PASP 107, 1065\n\\bibitem[]{} Ibata R., Gilmore G., 1995a, MNRAS 275, 591\n\\bibitem[]{} Ibata R., Gilmore G., 1995b, MNRAS 275, 605\n\\bibitem[]{} Ibata R., Gilmore G., Irwin M., 1995, Nature 370, 194\n\\bibitem[]{} Kent S.M., 1992, ApJ 387, 181\n\\bibitem[]{} Kiraga M, Paczynski B, Stanek K, 1997, ApJ 485, 611\n\\bibitem[]{} Kuchinski L.E., Frogel J.A., Terndrup D.M., 1995, AJ 109,1131\n\\bibitem[]{} McWilliam A, Rich R.M., 1994, ApJS 91, 749\n\\bibitem[]{} Minniti D., Olszewski E.W., Liebert J., White S.D.M., \nHill J.M., et al., 1995, MNRAS 277, 1293\n\\bibitem[]{} Minniti D., 1996, ApJ 459, 175\n\\bibitem[]{} Ng. Y.K., Bertelli G., Chiosi C., Bressan A., 1996, A\\&A 310, 771\n\\bibitem[]{} Omont, A., S. Ganesh, C. Alard, et al., \nastro-ph/9906489 and A\\&A in press 1999\n\\bibitem[]{} Origlia L., Ferraro F.R., Fusi Pecci F., Oliva E., 1997 A\\&A 321, 859\n\\bibitem[]{} Ortolani S., Barbuy B., Bica E., 1990, A\\&A 236, 362 \n\\bibitem[]{} Ortolani S., Bica E., Barbuy B., 1992, A\\&AS 92, 441\n\\bibitem[]{} Ortolani S., Renzini A., Gilmozzi R., Marconi G., Barbuy B., et al., 1995, Nature 377, 701\n\\bibitem[]{} Ortolani S, Gilmozzi R., Marconi G., Barbuy B., Bica E., \net al., 1996, in Formation of the galactic halo... Inside and out, \nASP conf Series, vol 92, H Morris \\& A Sarajedini (eds.), p96\n\\bibitem[]{} Peterson, C.J., 1993, in Structure and Dynamics of Globular Clusters, ASP\nConf. Ser. Vol. 50, Djorgovski. S.G. and Meylan G. (eds.), p. 337\n\\bibitem[]{} Pilachowski C.A., 1984, ApJ 281, 614\n\\bibitem[]{} Richtler T., Grebel E.K., Subramaniam A., Sagar R., 1998, A\\&AS 127, 169\n\\bibitem[]{} Rosenberg, A., saviane, I., Piotto, G., \\& Aparicio, A., 1999 AJ 118 2306\n\\bibitem[]{} Rutledge G.A., Hesser J.E., Stetson P.B., 1997, PASP 109, 907\n\\bibitem[]{} Sadler E.M., Rich R.M., Terndrup D.M. 1996, AJ 112, 171\n\\bibitem[]{} Samus N., Kravtsov, V., Ipatov, A., Smirnov, O., Alcaino, G., et al., 1996, A\\&AS 119, 191\n\\bibitem[]{} Sarajedini A., Norris J.E., 1994 ApJS 93, 161\n\\bibitem[]{} Sevenster, M., Dejonghe, H., Habing, H., 1997, A\\&A 299, 689\n\\bibitem[]{} Silk J., Wyse R. 1993, PhR. 231, 293\n\\bibitem[]{} Stanek K.Z., 1996, ApJ 460, L37\n\\bibitem[]{} Stetson P.B., VandenBerg D.A., Bolte M., 1996, PASP 108, 560\n\\bibitem[]{} Terndrup D.M. 1988, AJ 96, 884\n\\bibitem[]{} Terndrup D.M., Frogel, J.A., Whitford, A.E. 1990, ApJ 357, 453\n\\bibitem[]{} Tiede, Glenn P., Frogel, Jay A., Terndrup, D. M., 1995, AJ 110, 2788\n\\bibitem[]{} Unavane M., Gilmore G. 1998, MNRAS 295, 145\n\\bibitem[]{} Unavane M. Gilmore G, Epchtein N., Simon G, Tiphene D., et al. 1998, MNRAS 295, 119\n\\bibitem[]{} Vallenari, A., Chiosi, C., Bertelli, G., Ng, Y.K, 1996, \nin ``The Galactic Centre'' ASP Conf.Ser.102, Gredel, R. (ed.), page 320\n\\bibitem[]{} VandenBerg D.A., Bolte M., Stetson P.B., 1990, AJ 100, 445\n\\bibitem[]{} VandenBerg D.A., Bolte M., Stetson P.B., 1996, ARA\\&A 34, 461\n\\bibitem[]{} Walker A.R., Mack P., 1986, MNRAS 220, 69\n\\bibitem[]{} Webbink R.F., 1985, in Dynamics of Star Clusters, IAU Symp. 113, J Goodman, P Huts (eds.), p541\n\\bibitem[]{} Wyse R.F G., Gilmore G, 1995, AJ 110, 2771\n\\bibitem[]{} Wyse R., Gilmore G., Franx M., 1997 ARA\\&A 35, 637\n\\bibitem[]{} Zinn R., 1980, ApJS 42, 19\n\\bibitem[]{} Zinn R., 1996 in Formation of Galactic Halo ... Inside and Out, ASP Conf. Series, vol. 92, H. Morrison, A. Sarajedini (eds.), p211\n\\bibitem[]{} Zinn R., West M., 1984, ApJS 55, 45\n\n\\end{thebibliography}"
}
] |
astro-ph0002124
|
Fractal structures and the large scale distribution of galaxies \footnote{In the proceedings of the 7th Course in astrofundamental physics, Nato Advanced Study Institute, International Euroconference Erice, 5-16 December 1999}
|
[
{
"author": "Luciano Pietronero$^1$ and Francesco Sylos Labini$^{2,1}$"
}
] |
Galaxy structures are certainly fractal up to a certain crossover scale $\lambda_0$. A clear determination of such a scale is still missing. Usually the conceptual and practical implications of this property are neglected and the structures are only discussed in terms of their global amplitude. Here we present a compact summary of these implications. First, we discuss the problem of the identification of the crossover scale $\lambda_0$ and the proper characterization of the scaling. We then consider the implications of these properties with respect to various physical phenomena and to the corresponding characteristic values, i.e. $r_0$, $\sigma_8$, $\Omega$, etc. These implications crucially depend on the value of $\lambda_0$, but they are still important for a relatively small value, say $\lambda_0 \approx 50 \hmp$. Finally we consider the main theoretical consequences of these results.
|
[
{
"name": "erice99.tex",
"string": "%%UNIX --- UPDATED ON 13/8/97 \n%====================================================================%\n% sprocl.tex 27-Feb-1995 %\n% This latex file rewritten from various sources for use in the %\n% preparation of the standard proceedings Volume, latest version %\n% by Susan Hezlet with acknowledgments to Lukas Nellen. %\n% Some changes are due to David Cassel. %\n%====================================================================%\n\n\\documentstyle[sprocl,epsf]{article}\n\n\\font\\eightrm=cmr8\n\n%\\input{psfig}\n\n\\bibliographystyle{unsrt} %for BibTeX - sorted numerical labels by\n %order of first citation.\n\n\\arraycolsep1.5pt\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\etal}{{\\it et al.}}\n\\newcommand{\\hmp}{h^{-1}Mpc}\n\\newcommand{\\bef}{\\begin{figure}}\n\\newcommand{\\eef}{\\end{figure}}\n \n%\\ltapprox and \\gtapprox produce > and < signs with twiddle underneath\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\def\\ltapprox{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}}\n\\def\\gtapprox{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}}\n\\def\\inapprox{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"232$}}}\n \n% A useful Journal macro\n\\def\\Journal#1#2#3#4{{#1} {\\bf #2}, #3 (#4)}\n\n% Some useful journal names\n\\def\\NCA{\\em Nuovo Cimento}\n\\def\\NIM{\\em Nucl. Instrum. Methods}\n\\def\\NIMA{{\\em Nucl. Instrum. Methods} A}\n\\def\\NPB{{\\em Nucl. Phys.} B}\n\\def\\PLB{{\\em Phys. Lett.} B}\n\\def\\PRL{\\em Phys. Rev. Lett.}\n\\def\\PRD{{\\em Phys. Rev.} D}\n\\def\\ZPC{{\\em Z. Phys.} C}\n\n% Some other macros used in the sample text\n\\def\\st{\\scriptstyle}\n\\def\\sst{\\scriptscriptstyle}\n\\def\\mco{\\multicolumn}\n\\def\\epp{\\epsilon^{\\prime}}\n\\def\\vep{\\varepsilon}\n\\def\\ra{\\rightarrow}\n\\def\\ppg{\\pi^+\\pi^-\\gamma}\n\\def\\vp{{\\bf p}}\n\\def\\ko{K^0}\n\\def\\kb{\\bar{K^0}}\n\\def\\al{\\alpha}\n\\def\\ab{\\bar{\\alpha}}\n\\def\\be{\\begin{equation}}\n\\def\\ee{\\end{equation}}\n\\def\\bea{\\begin{eqnarray}}\n\\def\\eea{\\end{eqnarray}}\n\\def\\CPbar{\\hbox{{\\rm CP}\\hskip-1.80em{/}}}%temp replacemt due to no font\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%BEGINNING OF TEXT \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{document}\n\n\\title{Fractal structures and the large scale distribution of galaxies\n\\footnote{In the proceedings of the \n7th Course in astrofundamental physics, Nato Advanced Study Institute, \nInternational \nEuroconference Erice, 5-16 December 1999}}\n\\author{Luciano Pietronero$^1$ and Francesco Sylos Labini$^{2,1}$} \n \n\\address{ \t \n\t\t$^1$INFM Sezione Roma1, \n\t\tDip. di Fisica, Universit\\'a \"La Sapienza\", \n\t\tP.le A. Moro, 2, \n \tI-00185 Roma, Italy. \n \t\\\\ \n \t$^2$D\\'ept.~de Physique Th\\'eorique, \n\t\tUniversit\\'e de Gen\\`eve, \n\t\t24, Quai E. Ansermet, CH-1211 Gen\\`eve, Switzerland. \n\t\t} \n \n \n\\maketitle\n\n\\abstracts{Galaxy structures are certainly fractal\nup to a certain crossover scale $\\lambda_0$.\nA clear determination of such a scale is still missing.\nUsually the conceptual and practical implications of this\nproperty are neglected and the structures are only discussed in \nterms of their global amplitude. \nHere we present a compact summary of these implications.\nFirst, we discuss the problem of the identification of the crossover\nscale $\\lambda_0$ and the proper characterization\nof the scaling. We then consider the implications\nof these properties with respect to various physical phenomena\nand to the corresponding characteristic values,\ni.e. $r_0$, $\\sigma_8$, $\\Omega$, etc. These implications\ncrucially depend on the value of $\\lambda_0$, but they are\nstill important for a relatively small value, say\n$\\lambda_0 \\approx 50 \\hmp$.\nFinally we consider the main theoretical\nconsequences of these results.\n}\n \n\\section{Introduction}\n\nNowadays there is a general agreement about the fact \nthat galactic structures are fractal up to a distance \nscale of $\\sim 50 \\hmp$ \\cite{slmp98,jmsl99} and the \nincreasing interest about the fractal versus \nhomogeneous distribution of galaxy in the last year \n \\cite{coles98,scara98,rees99,cappi98,martinez99,hutton99,chown99,landy99,nl00} \nhas focused, mainly on the determination of the homogeneity \nscale $\\lambda_0$.\\footnote{See the web page {\\it \nhttp://pil.phys.uniroma1.it/debate.html } where \nall these materials have been collected}\nThe main point in this discussion \nis that galaxy structures are fractal no matter what is\nthe crossover scale, and this fact has never been\nproperly appreciated. Clearly, qualitatively different\nimplications are related to different values\nof $\\lambda_0$.\n \n\\begin{itemize} \n \n\\item {\\it Characterization of scaling properties.} \n\nGiven a distribution of points, \nthe first main question concerns the possibility\nof defining a physically meaningful average density.\nIn fractal-like systems such a quantity depends\non the size of the sample, and it does not\nrepresent a reference value, as in the case\nof an homogeneous distribution. \nBasically a system cannot be homogeneous\nbelow the scale of the maximum void\npresent in a given sample. \nHowever the complete statistical characterization\nof highly irregular structures is the objective of\nFractal Geometry\\cite{man77}.\n\n \nThe major problem from the point of view \nof data analysis is to use statistical methods \nwhich are able to properly characterize scale \ninvariant distributions, and hence which are \nalso suitable to characterize an eventual \ncrossover to homogeneity. \nOur main contribution \\cite{pie87,cp92,slmp98}, \nin this respect, has been to clarify that the usual \nstatistical methods (correlation function, \npower spectrum, etc.) are based on the assumption of \nhomogeneity and hence are not appropriate \nto test it. Instead, we have introduced and developed \nvarious statistical tools which are able \nto test whether a distribution is \nhomogeneous or fractal, and to correctly characterize \nthe scale-invariant properties. \nSuch a discussion is clearly relevant also \nfor the interpretation of the properties \nof artificial simulations. The agreement about \nthe methods to be used for the analysis of future \nsurveys such as the Sloan Digital Sky Survey (SDSS) \nand the two degrees Fields (2dF) is clearly a fundamental \nissue. \n\nThen, if and only if the average density is found to be\nnot sample-size dependent, one may study the \nstatistical properties of the fluctuations \nwith respect to the average density itself.\nIn this second case one can study \nbasically two different length scales.\nThe first one is the homogeneity scale ($\\lambda_0$),\nwhich defines\nthe scale beyond which the density fluctuations\nbecome to have a small amplitude with respect to the\naverage density ($\\delta \\rho < \\rho$).\n The second scale is related to the \ntypical length scale of the structures of \nthe density fluctuations, and, according to the terminology\nused in statistical mechanics \\cite{perezmercader}, it is called \ncorrelation length $r_c$. Such a scale has nothing\nto do with the so-called \"correlation length\" \nused in cosmology and corresponding to\nthe scale $\\xi(r_0)=1$\\cite{pee80}, which is instead\nrelated to $\\lambda_0$ if such a scale\nexists.\n \n\\item {\\it Implication of the fractal structure up \nto scale $\\lambda_0$}. \n \n The fact that galactic structures \nare fractal, no matter what is the homogeneity scale $\\lambda_0$, \n has deep implication on the interpretation \nof several phenomena such \nas the luminosity bias, the mismatch \ngalaxy-cluster, the determination of the average \ndensity, the separation of linear and \nnon-linear scales, etc., \nand on the theoretical concepts used \nto study such properties. \nWe discuss in detail some of these points.\n We then review some of the main consequences \nof the power law behavior of the galaxy number\ndensity, by relating various observational\nquantities (e.g. $r_0$, $\\sigma_8$, $\\Omega$, etc.) \nto the length scale $\\lambda_0$. \n\nWe also note that the properties \nof dark matter are inferred from the ones of visible \nmatter, and hence they are closely related. \nIf now one observes different \nstatistical properties for galaxies and clusters, \nthis necessarily implies a change of perspective \non the properties of dark matter. \n\n \n\\item {\\it Determination \nof the homogeneity scale $\\lambda_0$. } \n \nThis is, clearly, a very important point \nwhich is at the basis of the understanding \nof galaxy structures and more generally \nof the cosmological problem. We distinguish \nhere two different approaches: direct tests and \nindirect tests. By direct tests, we mean the determination \nof the conditional average density in three dimensional surveys, \nwhile with indirect tests we refer to other possible analyses, \nsuch as the interpretation of angular surveys, the \nnumber counts as a function of magnitude or of distance or, \nin general, the \nstudy of non-average quantities, i.e. when the fractal\ndimension is estimated without making an average \nover different observes (or volumes).\nWhile in the first case one is able to have a \nclear and unambiguous answer from the data, in the second \none is only able to make some weaker \nclaims about the compatibility of the data \nwith a fractal or a homogeneous distribution. \nFor example the papers of Wu et al\\cite{rees99}\nand Nusser \\& Lahav\\cite{nl00} \nmainly concern with compatibility arguments,\nrather than with direct tests.\nHowever, also in this second case, it is possible to understand \nsome important properties of the data, and to \nclarify the role and the limits of some underlying \nassumptions which are often used without a \ncritical perspective. \nWe do not enter here in the details of the discussion\nabout real data (see e.g. Joyce et al. 1999, Wu et al. 1999),\n however\nin the last section we consider separately the case (i) \n$\\lambda_0 \\approx 50 \\hmp$,\n (ii) \n$\\lambda_0 \\approx 300 \\hmp$ and \n (iii) \n$\\lambda_0 \\approx 1000 \\hmp$, \nbriefly discussing the main theoretical consequences.\n\\end{itemize} \n \n\\section{Characterization of scaling properties}\n\nIn this section we describe in detail the correlation\nproperties of a fractal\ndistribution of points having eventually a\ncrossover towards homogeneity (see Gabrielli \\& Sylos Labini, 2000\nfor a more exhaustive discussion of the subject),\n as the distribution of galaxies is thought\nto be (see Sylos Labini, Montuori \\& Pietronero, 1998 and \nWu, Lahav \\& Rees, 1999 for two opposite views on the matter).\n\nLet \n\\be\n\\label{corr1b}\nn(\\vec{r}) = \\sum_i \\delta(\\vec{r} - \\vec{r}_i)\n\\ee\nbe the number density of points in the system (the index $i$ runs \nover all the points) and let us suppose to have an infinite system.\nIf the presence of an object at the point $\\vec{r}_1$ \ninfluences the probability of finding another object \nat $\\vec{r}_2$, \nthese two points are correlated. Hence there is a correlation\nat the scale distance $r$ if \n\\be\n\\label{corr1}\nG(r) = \\langle n(\\vec{0})n(\\vec{r})\\rangle \\ne \\langle n\\rangle ^2 \n\\ee\nwhere we average over \nall occupied points of the system chosen as origin and on the\ntotal solid angle, supposing statistical isotropy.\nOn the other hand, there is no correlation if\n\\be\n\\label{corr2}\nG(r) = \\langle n\\rangle ^2.\n\\ee\n\n\\subsection{Homogeneity scale and correlation length}\n\nThe proper definition of $\\lambda_0$, the {\\it homogeneity scale},\nis the length scale beyond which the average density\nbecomes to be well-defined, i.e. \nthere is a crossover towards homogeneity with a flattening of $G(r)$.\nThe length-scale $\\lambda_0$ is related to the typical dimension\nof the largest voids in the system.\nOn the other hand, the {\\it correlation length} $r_c$ \nseparates correlated regimes \nof the fluctuations with respect to the average density\nfrom\nuncorrelated ones,\n and it can be defined only if a crossover towards homogeneity is \nshown by the system, i.e. if $\\lambda_0$ exists\\cite{perezmercader}.\nIn other words $r_c$ defines the organization\nin geometrical structures of the fluctuations \nwith respect to the average density. Clearly\n$r_c > \\lambda_0$:\nonly if the average density can be defined \none may study the correlation length of the fluctuations\nfrom it.\nIn the case $\\lambda_0$ is finite \nand then $\\langle n \\rangle >0$, in order \nto study the correlation properties of the fluctuations around the\naverage and then the behaviour of $r_c$, we can introduce the \ncorrelation function\n\\be\n\\label{corr5} \n\\xi(r) = \\frac{ \\langle n(0)n(r)\\rangle - \\langle n\\rangle^2} \n{\\langle n\\rangle^2} \\; .\n\\ee\nIn the case of a fractal distribution, the average\ndensity $\\left<n\\right>$ in the {\\bf infinite system} is zero, then \n$G(r)=0$ and $\\lambda_0 = \\infty$\nand consequently $\\xi(r)$ is not defined.\nIn this case the only well defined quantity characterizing the\ntwo point correlations is the function \n$\\Gamma(r)$ \\cite{pie87,cp92}:\n\\be\n\\label{corr4} \n\\Gamma(r) = \\lim_{R_s\\rightarrow \\infty} \n\\frac{\\langle n(r)n(0) \\rangle_{R_s}}{\\langle n \\rangle_{R_s}}\n\\ee\nwhere $R_s$ is the size of the a generic finite sample of the system, \n$\\left<...\\right>_{R_s}$ indicates the \naverage over all the points of the sample as origins,\nhence $\\langle n \\rangle_{R_s}$ is the average density of the sample.\nThis function measures the average density of points \nat a distance $r$ from another occupied point,\nand this is the reason why it is called\nthe conditional average density \\cite{pie87}.\nObviously in the case of a distribution\nfor which $\\lambda_0$ is finite $\\Gamma(r)$ provides the\nsame information of $G(r)$, i.e. it \ncharacterizes the correlation properties for $r < \\lambda_0$\nand the crossover to homogeneity.\n\nA very important point\nis represented by the kind of information \nabout the correlation properties\nof the {\\bf infinite system}\nwhich can be extracted from the analysis\nof a {\\bf finite sample} of it.\nIn Pietronero (1987) \nit is demonstrated that even \nin the super-correlated \ncase of a fractal the estimate of $\\Gamma(r)$ \nextracted from a finite sample, is \nnot dependent on the sample size $R_s$, \nproviding a good approximation of \nthat of the whole system. Clearly this is true a part from statistical \nfluctuations due to the fact that in a finite sample the average over the all\npossible origins is an average over a finite number of points, while\n in the\nglobal infinite system the average is over an infinite number of points.\n In fact,\n $\\Gamma(r)$ extracted from a sample can be written in the following way:\n\\be\n\\label{and0}\n\\Gamma(r) = \\frac{1}{N} \\sum_{i=1}^{N} \\frac{1}{4 \\pi r^2 \\Delta r}\n\\int_{r}^{r+\\Delta r} n(\\vec{r}_i+\\vec{r}')d^{3}r',\n\\ee\nwhere $N$ is the number of points in the sample,\n$n(\\vec{r}_i+\\vec{r}')$ is the number of\npoints in the volume element $d^3r'$ around the point \n$\\vec{r}_i+\\vec{r}'$ and $\\Delta r$\nis the thickness of the shell at distance $r$ from the point at $\\vec{r}_i$.\n\nTherefore, from an operative point of view,\nhaving a finite sample of points (e.g. galaxy catalogs),\nthe first analysis to be done concerns the determination of \n$\\Gamma(r)$ of the sample itself. Such a measurement\n is necessary to distinguish\nbetween the two cases:\n(1) a crossover towards\n homogeneity in the sample shown by\n a flattening of $\\Gamma(r)$,\nand hence an estimate of $\\lambda_0<R_s$ and $\\langle n \\rangle$;\n(2) a continuation of the fractal behavior.\nObviously only in the case (1), it is \nphysically meaningful to study the correlation function $\\xi(r)$ \n(Eq.\\ref{corr5}), and extract from it the length scale\n$r_0$ ($\\xi(r_0) = 1$), which is related\nto the intrinsic homogeneity scale $\\lambda_0$.\nThe functional behavior of $\\xi(r)$ with distance \ngives instead information on the correlation length of\nthe density fluctuations.\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\n\\subsection{The case of a fractal distribution ($R_s\\ll\\lambda_0$)}\n\n\nHereafter we study the three-dimensional case,\n i.e. $d=3$, and we suppose that \nthe sample is a sphere of radius $R_s$. Obviously, \nthis choice is not a restriction.\n\nLet us analyze the case \n$R_s\\ll\\lambda_0<r_c$. This is the so called ``fractal'' case,\nand it is compatible with both the situation of $\\lambda_0$ finite,\nbut $R_s\\ll\\lambda_0$ (a sample-size which is smaller than \nthe homogeneity scale), or the\nsituation in which $\\lambda_0\\rightarrow \\infty$, i.e. the \ncase of a fractal distribution\nat any scale.\n \nIt is simple to show\\cite{pie87,cp92,slmp98} \nthat in this case (and in a spherical sample),\nEq.\\ref{and0} becomes\n\\be\n\\label{fra4}\n\\Gamma(r) =\\frac{BD}{4 \\pi} r^{D-3}\n\\ee\nwith $B= N/ R_s^D$. Note that $B$ is independent on the sample size:\n in fact, by changing \n$R_s$, $N$ in average scales as $R_s^D$. This shows the \naforementioned assertion\nthat $\\Gamma(r)$ is practically independent on the sample-size. \nOn the other hand, it is possible\nto show that $B$ \nis related approximatively to \nthe average distance between nearest neighbors points \nin the system \\cite{slm98}:\n\\be\n\\label{fra6}\n\\ell \\approx \\left(\\frac{1}{B}\\right)^{\\frac{1}{D}} \\Gamma_e\n\\left(1 + \\frac{1}{D} \\right) \n\\ee\nwhere $\\Gamma_e$ is the Euler's gamma-function.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{The ``standard'' correlation function \nfor a fractal distribution}\n\nAs already mentioned, in the fractal case ($R_s\\ll\\lambda_0$), \nthe sample estimate of the \nhomogeneity scale, through the value of $r$ for which the \nsample-dependent correlation function \n$\\xi(r)$ (given by Eq.\\ref{and0b}) is equal to $1$, is meaningless:\nThis estimate is the so-called ``correlation length''\n$r_0$ \\cite{pee80} in the standard approach of \ncosmology. As we discuss below,\n $r_0$ has nothing to share with the {\\it true} correlation length $r_c$.\n Let us see why $r_0$ is unphysical in the case $R_s\\ll\\lambda_0$.\n$\\xi(r)$ is given operatively by\n\\be\n\\label{and0b} \n\\xi(r)=\\frac{\\langle n(r) n(0) \\rangle_{R_s}}{\\left<n\\right>_{R_s}^2} -1 \n=\n\\frac{\\Gamma(r)}{\\left<n\\right>_{R_s}} -1 \\; .\n\\ee\nThe basic point in the present discussion\\cite{pie87},\nis that the mean density of the sample, $\\langle n \\rangle_{R_s} $,\nused in the normalization of $\\xi(r)$, is not an intrinsic quantity \nof the system,\nbut it is a function of the finite size $R_s$ of the sample.\n\nIn fact, from Eq.\\ref{fra4}, \nthe expression of the $\\:\\xi(r)$ of the sample in the case of\nfractal distributions is \\cite{pie87}\n\\be\n\\label{xi3}\n\\xi(r) = \n\\frac{D}{3} \\left( \\frac{r}{R_s} \\right)^{D-3} -1 \\; .\n\\ee\nFrom Eq.\\ref{xi3} it follows that $\\:r_0$ \n%(defined as $\\:\\xi(r_{0}) = 1$)\nis a linear function of the sample size $\\:R_{s}$\n\\be\n\\label{xi4}\nr_{0} =\\left(\\frac{D}{6}\\right)^{\\frac{1}{3-D}}R_{s}\n\\ee\nand hence it is a spurious quantity without physical meaning but it is\nsimply related to the sample's finite size.\n\nWe note that the amplitude of $\\Gamma(r)$ (Eq.\\ref{fra4})\nis related to the lower\ncut-off of the fractal $\\ell$ by Eq.\\ref{fra6}, while the amplitude of $\\xi(r)$\nis related to the upper cut-off (sample size $R_s$) of the distribution. \nThis crucial difference has never been appreciated appropriately.\n\nFinally we stress that in the standard analysis of galaxy catalogs\nthe fractal dimension is estimated by fitting $\\xi(r)$ with a power law, \nwhich instead, as one can see from\n Eq.\\ref{xi3}, it is power law only for $r \\ll r_0$ (or $\\xi \\gg 1$).\nFor larger distances there is a clear deviation\nfrom the power law behavior due to the definition of $\\xi(r)$.\nAgain this deviation is due to the finite size of the observational \nsample and does not correspond to any real change\nin the correlation properties. It is easy to see that, if \none estimates the exponent \nat distances $r \\ltapprox r_0$, one \nsystematically obtains a higher value \nof the correlation exponent due to the break \nof $\\xi(r)$ in a log-log plot. \nTo illustrate more clearly this we compute\nthe log derivative of Eq.\\ref{xi3} with respect to $\\log(r)$, indicating $D-3$ \nwith $\\gamma$ and its estimate with $\\gamma'$:\n\\be\n\\label{xi6}\n\\gamma'=\\frac{d(\\log(\\xi(r))}{d\\log(r)} =\n\\frac{2 r_0^{\\gamma} r^{-\\gamma}} \n{2 r_0^{\\gamma} r^{-\\gamma} -1} \\, \\gamma \\; ,\n\\ee\nwhere $r_0$ is defined by Eq.\\ref{xi4}.\n The tangent\nto $\\xi(r)$ at $r=r_0$ has a slope $\\gamma'= 2\\gamma$.\nThis explain why it has been found in galaxy and cluster \ncatalogs that $\\gamma \\sim 2$ by the $\\xi(r)$ analysis\n\\cite{dp83,dav97,rees99}\ninstead of $\\gamma \\sim 1$ found with the $\\Gamma(r)$ analysis \n\\cite{slmp98}.\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n \n\\subsection{The case of a fractal\n distribution with a crossover to homogeneity ($R_s\\gg\\lambda_0$)}\n\n\nLet us now analyze the case of a fractal\nwith a crossover to homogeneity.\nIn Coleman \\& Pietronero (1992) \na very simple approximation has been \nused to describe such a situation which we discuss \nin more detail below.\n\nBy defining\n$\\left<n\\right>_{R_s}=N/V$ with $V=4\\pi R_s^3/3$, \nit is simple to see\\cite{cp92} that\nthe behavior of $\\Gamma(r)$ \nin our sample is fractal (i.e. $\\Gamma(r)$ is a power law) \nup to a certain distance $\\lambda_0$,\nand then it flattens, becoming homogeneous at scales\n $R_s > r \\gg \\lambda_0$:\n\\be \n\\left\\{ \n\\begin{array}{l} \n\\label{frao1}\n\\Gamma(r)= \\frac{DB}{4\\pi} r^{D-3} \\; \\; \\mbox{for}\n\\; \\;\\ell \\le r \\ll \\lambda_0\n\\\\\n\\\\\n \\Gamma(r) \n\\simeq \\left<n\\right>_{R_s}\n \\; \\; \\mbox{for}\n \\; \\;\\lambda_0 \\ll r \\le R_s \\,,\n \\end{array} \\right.\n \\ee \nwhere $\\left<n\\right>_{R_s}$ is the estimation of the \naverage density in the sample of size $R_s$. That is,\n$\\left<n\\right>_{R_s}$ does\nnot depend on $r$ if $\\lambda_0 \\ll r \\ltapprox R_s$,\napart small amplitude fluctuations.\nIn Eq.\\ref{frao1} the detailed approach to homogeneity\ndepends on the specific properties of the fluctuations around the average\ndensity, i.e. it is determined by $r_c$.\nHence, the statistical properties of the density fluctuations\ndetermine how good is the estimation of the \naverage density throught $\\left<n\\right>_{R_s}$.\n \nFrom the definition of the function $\\xi(r)$ we can find\\cite{gsl00}\n\\be\n\\label{frao1b}\n\\xi(r) \\approx \n\\left(\\frac{r}{\\lambda_0}\\right)^{D-3}f\\left(\\frac{r}{r_c}\\right) \\; .\n\\ee\nNote that the amplitude of $\\xi(r)$ is determined\n by the homogeneity scale $\\lambda_0$\nwhich has been previously extracted from $\\Gamma(r)$, and that in this\napproximation\n%\\be\n%\\label{frao1c}\n$r_0 \\sim \\lambda_0 \\;$ .\n%\\ee\nThe function $\\xi(r)$ characterizes the correlations among the \nfluctuations of the distribution\nwith respect to the average density.\nIt is important to clarify that these fluctuations must be both \npositive and negative, in fact\nthe integral over the whole sample of Eq.\\ref{and0b} must be $0$.\nHence the function $f\\left(\\frac{r}{r_c}\\right)$ must be oscillating, and \nin the case $\\lambda_0 < r_c , R_s$, it should present\nan exponential cut-off at $r \\approx r_c$. \nWe have that, when \n$\\xi(\\lambda_0) \\simeq 1$, the density fluctuations begin to become \nsmall with respect to the \naverage density $\\langle n \\rangle$, but if $\\lambda_0<r<r_c$\nthey are still well correlated among them. Only for $r\\gg r_c$ \nthe fluctuations are not\ncorrelated.\n\n\nLet us now consider the case $\\lambda_0\\ll R_s<r_c$. \nThis situation is compatible with\nthe following two situations: $r_c$ finite, but larger than $R_s$,\nand the case $r_c\\rightarrow\\infty$.\nIn both cases, $\\xi(r)$ of our sample should be a power law\nmodulated by an oscillating function $g(r)$ which describes\nthe positive and negative fluctuations with respect\nto the average density,\n\\be\n\\label{and4bis}\n\\xi(r) = \\left(\\frac{r}{\\lambda_0}\\right)^{-\\gamma} g(r) \\; .\n\\ee\nIn such a situation the (positive and negative) fluctuations\nfrom the average density are of all sizes and they do not\nhave any intrinsic characteristic scale: this is a critical system \n(see Gaite et al., 1999 for a more detailed discussion). The only \nintrinsic scale of the system is then $\\lambda_0$,\nthe length-scale beyond which $\\Gamma(r)$ flattens and the fluctuations\nare small with respect to the average.\n \n\n\n\nLet us suppose to be in the case in which $\\Gamma(r)$ \nflattens at a certain\n$\\lambda_0\\ll R_s$. We can then evaluate the correlation\nfunction $\\xi(r)$ of the sample via Eq.\\ref{and0b}. \nAt this point we can clarify \nhow to interpret the eventual cut-off shown by $\\xi(r)$.\n\\begin{itemize}\n\\item If the cut-off scale \nis well below $R_s$, we can be sure that it is a good\nestimate of the intrinsic correlation length $r_c$;\n\\item if the cut-off is at a scale $r\\simeq R_s$ we can\n have two cases: it represents \nan ``intrinsic'' cut-off with \n$r_c\\simeq R_s$, or it is only a finite-size effect due to\nthe fact that from Eq.\\ref{and0b} $\\left|\\xi(R_s)\\right|=0$.\nIn order to distinguish between these two possibilities, it\n is necessary to increase \nthe sample size and to look at the behavior of the cut-off scale. \nIf it increases proportionally to $R_s$, then it is a finite size effect.\nOtherwise if it\ndoes not change, it represents the estimate of the intrinsic\n correlation length $r_c$.\n\\end{itemize}\n\nIn Fig.\\ref{gamma} we show two possible\nbehaviours of the flattening of $\\Gamma(r)$,\nwhile in Fig.\\ref{xi} it is shown the corresponding\n$\\xi(r)$ (we neglect for simplicity the oscillating term\nwhich must be present, and we have considered the situation\n$R_s\\rightarrow\\infty$).\n \n\\bef \n\\epsfxsize 10cm\n\\centerline{\\epsfbox{FIG1.PS}}\n\\caption{\\label{gamma} The conditional average density $\\Gamma(r)$\nfor a distribution which\nhas a power law behavior at small scales ($r < \\lambda_0$) , followed \nby a transition to homogeneity at the scale $\\lambda_0 = 10 \\hmp$. \nThe behavior of the flattening\ndepends on the correlation properties\nof the density fluctuations, i.e. on the functional behavior of\n$\\xi(r)$. The dotted line corresponds to a system which has a finite\ncorrelation length $r_c = 30 \\hmp$, while the solid line \ndescribes a system whose density fluctuations present\ncorrelation over all scales. From the $\\Gamma(r)$-analysis alone it is\npossible to compute $\\lambda_0$ but not $r_c$.\n}\n\\eef\n\\bef \n\\epsfxsize 10cm\n\\centerline{\\epsfbox{FIG2.PS}}\n\\caption{\\label{xi} The $\\xi(r)$ correlation function\nfor the distributions shown in the previous figure.\nWith this analysis it is possible to \ncompute the correlation length $r_c$ (finite or infinite) of the density\nfluctuations. The dotted line corresponds to an exponential decay,\nand hence to a finite value of the correlation length ($r_c = 30 \\hmp$)\nwhile the solid line corresponds to an infinite correlation\nlength, and hence to a power law behavior. The length scale\nat which $\\xi(r_0)=1$ gives a reliable estimation of $\\lambda_0$.\n}\n\\eef\n\n\\subsection{About the amplitude of $\\xi(r)$}\n\nWe note that if $\\lambda_0 \\ll R_s$, $\\lambda_0$\nhas nothing to share with questions like ``which is the typical size \nof structures in the system?'' or \n``up to which length-scale the system is clusterised?''.\nThe answer to this question is strictly related to $r_c$ and not to \n$\\lambda_0$. \nThe length scale\n $r_c$ characterizes the distance over which two different points \nare correlated (clusterised)\\cite{perezmercader}. \nIn fact, this property is not related to how large are the \nfluctuations with respect to the average ($\\lambda_0$),\n but to the length extension of their \ncorrelations ($r_c$). \n\nTo be more specific, \nlet us consider a fixed set of density fluctuations.\nThey can be superimposed to\ndifferent values of a uniform density background.\nThe larger is this background the lower $\\lambda_0$, but obviously\nthe length scale \nof the correlations ($r_c$) among these fluctuations is not changed, i.e.\nthey are clusterised independently of the background.\n\nOne can see\\cite{gsl00,gsld00} that a linear amplification of $\\xi(r)$\nsuch that\n\\be\n\\label{and7}\n\\xi'(r)= A \\xi(r)\n\\ee\ndoesn't change $r_c$ (which can be finite or infinite)\nbut only $\\lambda_0$, i.e. if $A>1$\nwe need larger subsamples to have a good \nestimation of $\\langle n \\rangle$,\nbut the characteristic length \n(correlation length) of the structures is not changed.\n\n\\subsection{Homogeneity scale and the size of voids}\n\nBasically $\\lambda_0$ is related to the maximum \nsize of voids: the average density will be constant, \nat least, on scales larger than the maximum \nvoid in a given sample. Several authors have \napproached this problem by looking at \nvoids distribution. For example \nEl-Ad and Piran (1997) have shown that the SSRS2 \nand IRAS 1.2 Jy. redshift surveys are dominated \nby voids: they cover the $\\sim 50 \\%$ of the volume. \nMoreover the two samples show very similar \nproperties even if the IRAS voids \nare $\\sim 33 \\%$ larger than SSRS2 ones because they \nare not bounded by narrow angular limits as the SSRS2 voids. \nThe voids have a scale of at least $\\sim 40 \\div 50 \\hmp$ \nand the largest void in the SSRS2 sample has a \ndiameter of $\\sim 60 \\hmp$, i.e. comparable \nto the Bootes void. The problem is to understand whether \nsuch a scale has been fixed by the samples' volume, \nor whether there is a tendency not to find larger \nvoids: in this case one would have a (weaker evidence) for the \nhomogeneity scale. In any case, we note that \nthe homogeneity scale cannot be smaller \nthan the scale of the largest void found in these samples \nand that one has to be very careful when comparing the size of \nthe voids to the effective depth of catalogs. For example \nin the Las Campanas Redshift Survey, even if \nit is possible to extract sub-samples limited at $\\sim 500 \\hmp$, \n the volume of space investigated is not so \nlarge, as the survey is made by thin slices. In \nsuch a situation a definitive answer to the dimension \nof the of voids, and hence to the existence of the homogeneity \nscale, is rather difficult and uncertain. \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Luminosity Bias} \n \nWe would like to stress again that, even if the \nfractal behavior breaks at a certain scale $\\lambda_0$, \nthe use of $\\xi(r)$ is in anyhow inconsistent at scales \nsmaller than $\\lambda_0$. We illustrate below\nan example of the confusion due to the use \nof $\\xi(r)$ when $r]ll \\lambda_0$.\n\n\nFrom the use of the $\\xi(r)$ analysis, it has been \nfound that $r_0$ is different in different volume (hereafter VL) \nsamples.\nIn particular it has been found \\cite{ben96} that \ndeeper is the VL sample, larger is the value \nof $r_0$. As the deeper VL samples\ncontain brighter galaxies, this fact has been\ninterpreted as a real physical phenomenon,\nleading to the idea that more brighter galaxies\nare more strongly clustered than fainter ones,\nin view of their larger correlation amplitude:\nthis is the so-called luminosity segregation phenomenon\n\\cite{dav88,par94}.\nIn other words, the fact that the giant galaxies are \"more clustered\"\nthan\nthe dwarf ones,\ni.e. that they are located in the peaks of the density field,\nhas given rise to the proposition\nthat larger objects may correlate up to larger\nlength scales and that the amplitude of \n$\\:\\xi(r)$ is larger\nfor giants than for dwarfs one. The deeper VL samples\ncontain galaxies which are in average\nbrighter than those in the VL samples with\nsmaller depths. As the brighter galaxies should have\na larger correlation length the shift of $r_0$ in different samples\ncan be related, at least partially,\nwith the phenomenon of luminosity segregation.\n\nAs previously discussed there are two \nproblems with such a model: \n(i) The amplitude of $\\xi(r)$ in an \nhomogeneous distribution, does not give any\ninformation about the clustering \"strength\".\nIt is instead related to the local\namplitude of the fluctuations with respect to the average density.\n(ii) The amplitude of $\\xi(r)$ has a physical meaning only\nin the case $\\lambda_0$ is found to be finite\nand smaller than the sample's size. This \nis clearly not the case up, at least, to $\\sim 50 \\hmp$.\n\nA natural explanation of the scaling of $r_0$ is\nthen the fractal behavior of galaxy distribution,\nand more specifically the fact that \n$r_0$ is a fraction of the sample's size \nin the fractal case. The fact that\ngiant elliptical galaxies are located \nin the core of rich clusters, and other\nmorphological properties of this kind,\ncan be naturally related to the \nmultifractal properties of matter distribution\\cite{cp92,slp96}.\nIn such a case, bright galaxies are more strongly\nclustered than fainter ones in view of the fact\nthat their fractal dimension is smaller\\cite{gsl00}.\n\n\n\n\\subsection{Power Spectrum of density fluctuations} \n \nThe problems \nwith the standard correlation analysis also show that the \nproperties of fractal correlations have not been really appreciated. These \nproblems are actually far more serious and fundamental than mentioned, \nfor example, by \nLandy \\cite{landy99} \nand the idea that they can be solved by simply taking the Fourier \ntransform is once more a proof of the superficiality of the discussion. \nWe have extensively shown \\cite{sla96,slmp98} that \nthe power spectrum of the density fluctuations \nhas the same kind of problems which $\\xi(r)$ has, \nbecause it is normalized to the average density as well. \nThe density contrast $\\delta(r)=\\delta \\rho(r)/ \\langle \\rho \\rangle$ \nis not a physical quantity unless the average density \nis demonstrated to exist. \nMore specifically, like in the case of $\\xi(r)$, the power spectrum \n(Fourier Transform of the correlation function) \nis affected by finite size effects at large scale: \neven for a fractal distribution the power spectrum \nhas not a power law behavior but it shows \na large scale (small $k$) cut-off which \nis due to the finiteness of the sample \\cite{sla96}. \nHence the eventual detection of the turnover of the power \nspectrum, which is expected in CDM-like models \nto match the galaxy clustering to the anisotropies \nof the CMBR, must be considered a finite size effect, \nunless a clear determination of the average density \nin the {\\it same sample} has been done. \n \n \n \nEssentially all the currently\nelaborated models of galaxy formation \n\\cite{pee93} \n{\\it assume large scale homogeneity} and \npredict that the galaxy\npower spectrum (hereafter PS), \nwhich is {\\it the PS of the density contrast},\ndecreases both toward small scales and toward large\nscales, with a turnaround somewhere in the middle, at a scale $\\lambda_f$\nthat can be taken as separating ``small'' from ``large'' scales. \nBecause of the homogeneity assumption, the PS amplitude\nshould be independent on the survey scale, any residual \nvariation being attributed to luminosity bias (or to the\nfact that the survey scale has not yet reached the homogeneity scale).\nHowever, the crucial clue to this\npicture, the firm determination of the \nscale $\\lambda_f$, is still missing, although\nsome surveys do indeed produce a turnaround\n scale around 100 $\\hmp$\n\\cite{be94,fe94}. \nRecently, the CfA2 survey \nanalyzed by \\cite{par94} \n(hereafter PVGH) \n(and confirmed by SSRS2 \\cite{dac94} \n- hereafter DVGHP), showed a $n=-2$ slope up to $\\sim 30 \\hmp$,\na milder $n\\approx -1$ slope up to 200 $\\hmp$, and some tentative\nindication of flattening on even larger scales. PVGH also find\nthat deeper subsamples have higher power amplitude,\ni.e. that the amplitude scales with the sample depth.\n\n{\\it In the following we argue that both features, bending and scaling,\nare a manifestation of \nthe finiteness of the survey volume, and that they\ncannot be\ninterpreted as the convergence to homogeneity, nor to a PS \nflattening.}\nThe systematic effect of the survey finite size is in fact\nto suppress\npower at large scale, mimicking a real flattening.\nClearly, this effect occurs whenever galaxies have not \na correlation scale much larger than the survey size, and it has\noften been studied in \nthe context of standard scenarios \\cite{it92,col94}.\n We push this argument further, by showing that\neven a fractal distribution of matter, \nwhich never reaches homogeneity, shows a sharp flattening\nand then a turnaround. Such \nfeatures are partially corrected, but not quite eliminated,\n when the correction proposed by \\cite{pn91} is applied to the data.\n We show also\n how the amplitude of the\nPS depends on the survey size as long as \nthe system shows long-range correlations.\n\n\nThe standard PS (SPS) \nmeasures directly the contributions of different scales to the galaxy\ndensity contrast $\\:\\delta\\rho/\\rho$.\nIt is clear that the density contrast, \nand all the quantities based on it, is meaningful only when one can define\na constant density, i.e. reliably identify\nthe sample density with \nthe average density of all the Universe.\nIn other words in {\\it the SPS analysis \none assumes that the survey volume is large enough\nto contain a homogeneous sample.} \nWhen this is not true, and we argue that is \nindeed an incorrect assumption\nin all the cases investigated so far, a false interpretation of the results may\noccur, since both \nthe shape and the amplitude of the PS (or correlation\nfunction) depend on the\nsurvey size.\n\nLet us recall the basic notation of the PS analysis.\nFollowing Peebles \\cite{pee80} we imagine that the Universe is periodic\nin a volume $\\:V_{u}$, with $\\:V_{u}$ much \nlarger than the (presumed) maximum\nhomogeneity scale. The survey volume $V\\in V_u$\ncontains $\\:N$ galaxies at positions $\\:\\vec{r_i}$,\nand the galaxy density contrast is\n\\be\n\\label{eps4}\n\\delta(\\vec{r}) = \\frac{n(\\vec{r})}{\\hat n} -1 \n\\ee\nwhere it is assumed that exists a \nwell defined constant density $\\hat n$, obtained\naveraging over a sufficiently large scale.\nThe density function\n$\\:n(\\vec{r})$ \ncan be described by a sum of delta functions:\n$~n(\\vec{r}) = \\sum_{i=1}^{N} \\delta^{(3)} \n(\\vec{r}-\\vec{r_{i}})\\,.~$\nExpanding the density contrast in its Fourier components we have \n\\be\n\\label{eps7}\n\\delta_{\\vec{k}} = \\frac{1}{N} \\sum_{j \\epsilon V} \ne^{i\\vec{k}\\vec{r_{j}}} - W(\\vec{k})\\,,\n\\ee\nwhere\n\\be\n\\label{eps7b}\n~W(\\vec{k}) = \\frac{1}{V} \\int_V d{\\vec{r}} W(\\vec{r})\n e^{i\\vec{k}\\vec{r}}\\,~\n\\ee\nis the Fourier transform of the survey window $W(\\vec{r})$, \ndefined to be unity inside the survey region, and zero outside.\nIf $\\xi(\\vec{r})$ is the correlation function of the galaxies\n($\\xi(\\vec{r}) = <n(\\vec{r})n(0)>/\\hat n^2 -1$),\nthe true PS $\\:P(\\vec{k})$ is defined as\nthe Fourier conjugate of the \ncorrelation function $\\xi(r)$.\nBecause of isotropy the PS can be simplified to\n\\be\n\\label{eps12}\nP(k) =4\\pi \\int \\xi(r) \\frac{\\sin(kr)}{kr} r^{2}dr\\,.\n\\ee\nThe variance of $\\:\\delta_{\\vec{k}}$ \nis \\cite{pee80,pn91,fis93} \\be\n\\label{eps9}\n<|\\delta_{\\vec{k}}|^{2}> = \\frac{1}{N} + \\frac{1}{V}\\tilde P(\\vec{k})\\,.\n\\ee\nThe first term is the usual additional shot noise term\nwhile the second is the true PS convoluted with a \nwindow function \nwhich describe the geometry of the sample (PVGH)\n\\be\n\\label{eps9b}\n\\tilde P(\\vec{k})= \n{V\\over (2\\pi)^3} \\int\n<|\\delta_{\\vec{k'}}|^{2}>\n|W(\\vec{k}-\\vec{k'})|^2\nd^3 \\vec{k'}\n\\,.\n\\ee\n%\n\\be\n\\label{eps9bb}\n\\tilde P(\\vec{k}) = \\int d\\vec{k'} P(\\vec{k'}) F(\\vec{k}-\\vec{k'}) \\,,\n\\ee\nwith \n\\be\n\\label{eps9c}\nF(\\vec{k}-\\vec{k'}) = \\frac{V}{(2\\pi)^3} |W(\\vec{k}-\\vec{k'})|^2\\,.\n\\ee\nWe apply now this standard analysis to a fractal distribution.\nWe recall the expression \nof $\\:\\xi(r)$ in this case is \n\\be\n\\label{eps16}\n\\xi(r) = [(3-\\gamma)/3](r/R_{s})^{-\\gamma} -1\\,,\n\\ee\n where $\\:\\gamma=3-D$. \n A key point of our discussion is\nthat that\non scales larger that $R_s$ the $\\xi(r)$ cannot be calculated without\nmaking assumptions on the \ndistribution outside the sampling volume.\n\n\nAs we have already mentioned, in a fractal\nquantities like \n$\\xi(r)$ \nare scale dependent: in particular both\nthe amplitude and the shape of $\\xi(r)$ depend \nthe survey size.\nIt is clear that the same kind of \nfinite size effects are also present when computing the SPS, so that \nit is very dangerous to identify real physical features induced\nfrom the SPS analysis without first a firm determination of the\nhomogeneity scale.\n \nThe SPS for a fractal distribution \n model described by\n Eq.\\ref{eps16}\ninside a sphere of radius $R_s$ is\n\\be \n\\label{eps19}\nP(k) = \\int^{R_{s}}_{0} \n 4\\pi \\frac{\\sin(kr)}{kr} \\left[ \\frac{3-\\gamma}{3} \n\\left(\\frac{r}{R_{s}}\\right)^{-\\gamma} -1\\right] r^{2}dr=\n\\frac{a_k(R_s) R_{s}^{3-D}}{k^{D}}-\\frac{b_k(R_s)}{k^{3}}\\,.\n \\ee\nNotice that the integral has to be evaluated inside $R_s$\nbecause we want to compare $P(k)$ with its {\\it estimate}\n in a finite size spherical survey of scale $R_s$. \n In the general case, we must deconvolve the\n window contribution \n from $P(k)$; $R_s$ is then a characteristic window scale. \nEq.\\ref{eps19} shows the two scale-dependent features of the PS. First,\nthe amplitude of the PS \ndepends on the sample depth.\nSecondly,\nthe shape of the PS \nis characterized by two scaling regimes:\nthe first one, at high wavenumbers, \nis related to the fractal dimension of the \ndistribution in real space, \nwhile the second one arises only because of \nthe finiteness of the sample.\nIn the case of $\\:D=2$ in Eq.\\ref{eps19} one has:\n\\be\n\\label{eps22}\n~a_k(R_s) = \\frac{4\\pi}{3} (2+\\cos(kR_{s}))\\,\n\\ee\nand\n\\be\n\\label{eps23}\n~b_k(R_s) = 4\\pi \\sin (kR_{s})\\,.\n\\ee\nThe PS is then a power-law with exponent \n$\\:-2$ at high wavenumbers, \nit flattens at low wavenumbers and reaches a maximum at\n$k\\approx 4.3/R_s$, i.e. at a scale $\\lambda \\approx 1.45 R_s$.\nThe scale at which the transition occurs \nis thus related to the sample depth. \nIn a real survey, things are complicated by the window function,\nso that the flattening (and the turnaround) scale can only be determined\nnumerically.\n\nIn practice one has several complications. First, the survey\nin general is not spherical. This introduces a coupling with\n the survey window\nwhich is not easy to model analytically. \nFor instance, we found that windows of small\nangular opening shift to smaller scales\nthe PS turnaround. \nThis is analogous to what happens with the correlation function\nof a fractal: when it is calculated in small angle surveys, the\ncorrelation length $r_0$ decreases. Second, the observations\nare in redshift space, rather than in real space. \nThe peculiar velocities generally make steeper the PS slope \n\\cite{fis93}\n with respect to the real space. Third, in a fractal\nthe intrinsically high level of fluctuations makes hard\na precise comparison with the theory when the fractal under study\nis composed of a relatively small number of points.\n\n\n\\section{Implications for cosmology}\n\nWe now consider some implications\nfor cosmology of the scaling properties of\ngalaxy distribution, up to a lenght scale $\\lambda_0$.\nFor example,\nwe consider more specifically $\\lambda_0 \\approx 50 \\hmp$.\n\n\n\\subsection{Estimation of the average luminosity and mass density}\n\nFrom the studies of Large Scale Structures (LSS)\nof galaxies and galaxy clusters, one would like to estimate\nthe average density of visible matter and then\nto infer the one of the whole (visible plus dark,\ni.e. all the matter in clusterised objects) \nmatter distribution.\nWhile for the first we have direct estimations,\nfor the second we have only indirect methods, especially at large scales,\nbased on some assumptions, which can be tested by looking at the\ndistribution of what is observable, i.e. visible matter.\n\nWe briefly describe how to do such a measurement\nin galaxy redshift catalogs directly, from the knowledge\nof galaxy positions and luminosity (for a more detailed\ndiscussion see Sylos Labini, 2000). In this\ncase, and by measuring the Mass-to-Luminosity\nratio, one can infer, from the average luminosity\ndensity, the average mass density.\nThe new point we address more specifically is that\ngalaxies are fractally distributed up to a certain\ncrossover scale $\\lambda_0$. As there is still some\ncontroversy about the value \nof $\\lambda_0$ \\cite{slmp98,rees99,chown99,jmsl99,martinez99} we \ngive the estimation as a function\nof $\\lambda_0$.\nWe stress that the way this estimation is performed,\nis substantially different from the usual one \\cite{pee93},\nbecause in such a case the fractal behavior is not considered\nat all, and one assumes a perfect homogeneous \ndistribution at relatively small scale ($\\lambda_0 \\sim 5 \\div 10 \\hmp$).\n This situation\nis clearly not the one corresponding to the more\n\"optimistic\" estimation of the homogeneity scale $\\lambda_0$\n\\cite{slmp98,rees99,jmsl99}.\nThe other assumption usually made is that\ngalaxy positions are independent on their luminosity.\nWe have shown\\cite{syl00}\n that, although such an assumption cannot\ndescribe local morphological properties of \ngalaxy distribution\\cite{slp96}, it works rather well \nin the available galaxy redshift surveys.\n\n\nThe estimation of the the average density we are able\nto make depends hence on two parameters. The first one \nis the \n homogeneity scale $\\lambda_0$ and the second \nis the Mass-to-Luminosity ratio. \nWe can give an \nupper limit to $\\Omega$ by taking the highest \n$({\\cal M}/{\\cal L})_c = 300h$ observed up to now \\cite{bah99}\n(in clusters of galaxies) to be universal across all the scales, \nand by considering\na lower limit for the homogeneity scale $\\lambda_0= 50 \\hmp$. \nWe compute the critical $({\\cal M}/{\\cal L})_{crit} $,\ni.e. the Mass-to-Luminosity ratio needed to have $\\Omega =1$.\nAs the others, also this \nparameter depends on the homogeneity scale $\\lambda_0$.\n\n\n\n\n\n \n\\subsection{Average luminosity density from galaxy catalogs}\nLet\n\\be\n\\label{e1}\n\\langle \\nu(r,L) \\rangle dL d^3r = \n\\phi(L) \\langle \\Gamma(r)\\rangle dL d^3r =\nA r^{D-3} L^{\\alpha} e^{-\\frac{L}{L_*}} d^3r dL\n\\ee\nbe the average number of galaxies in the volume element\n $d^3r$ at distance $r$ from a observer\nlocated on a galaxy, \nand with luminosity in the range $[L,L+dL]$. In Eq.\\ref{e1}\nwe have used the fact that the galaxy luminosity function has \nbeen observed to have the so-called Schechter shape with parameters\n$L_*$ (luminosity cut-off) and $\\alpha$ (power law index)\nwhich can be determined experimentally. The conditional average space density\n $\\langle \\Gamma(r)\\rangle $ has a power \n law behavior corresponding to a fractal\ndimension $D$ (which eventually can be a function of scale, and \nhence can approach to $D=3$ at a scale $\\lambda_0$).\nBoth the fractal dimension $D$ and the overall amplitude \n$A$ can be determined in redshift surveys. \nHence $\\langle \\nu(r,L) \\rangle$ is a function of \nfour parameters: $L_*, \\alpha, D, A$.\nMoreover we note that by writing \n$\\langle \\nu(r,L) \\rangle$ as a product \nof the space density and of the luminosity function\nwe have implicitly assumed that galaxy positions are independent\non galaxy luminosity.\n\n We would like to estimate the average luminosity density\n in a sphere of radius $R$ and volume $V(R)$ placed\n around a galaxy, and defined as \n\\be\n\\label{e2}\n\\langle j(<R) \\rangle = \\frac{1}{V(R)} \n\\int_0^R \\int_{0}^{\\infty} L\\langle \\nu(r,L)\\rangle dL d^3r \n\\equiv j(10) \\left(\\frac{R}{10 \\hmp}\\right)^{D-3}\n\\ee\nwhich is $R$ dependent as long as the space density \nshows power law behavior (i.e. $D<3$).\nBy considering $M_*=19.53$ \n(i.e. $L_*=1.0 \\cdot 10^{10} h^{-2} L_{\\odot}$), $\\alpha=-1.05$ \\cite{lumfun} \nand\nby estimating the prefactor $A$ (Eq.\\ref{e1}) \n and the fractal dimension ($D\\approx 2$) in galaxy redshift samples\nwe obtain\\cite{syl00}\n\\be\n\\label{e7}\nj(10) \\approx 2 \\cdot 10^{8} \\; h L_{\\odot}/Mpc^3 \\; .\n\\ee\n\nWe now estimate the density parameter in terms of the critical density,\n\\be\n\\label{e8}\n\\rho_{c} = 2.78 \\cdot 10^{11} h^2 \\; M_{\\odot}/Mpc^3\n\\ee\nwhere $M_{\\odot}$ is the solar mass.\nBy considering the product of the \nmass-to-luminosity ratio (in solar and $h$ units) and the \naverage luminosity density given by Eqs.\\ref{e2}-\\ref{e7}, we obtain\n\\be\n\\label{e9}\n\\Omega(\\lambda_0) = (6 \\pm 2) \\cdot 10^{-4} \n\\frac{\\frac{{\\cal M}} {{\\cal L}}}{h}\n \\left(\\frac{\\lambda_0}{10h^{-1}}\\right)^{-1} \\; ,\n\\ee\nwhere $\\lambda_0$ is the scale where the crossover to\nhomogeneity occurs (it can also be $\\lambda_0 = \\infty$, and \nin such a case $\\Omega(\\infty)=0$). Note that \nin view of the dependence of ${\\cal M}/{\\cal L}$ on $h$,\n Eq.\\ref{e9}\ndoes not depend on the Hubble's constant.\n\n\nLet us now suppose that ${\\cal M}/{\\cal L} \\approx 10h$ as \nit has been derived by Faber and Gallengher \\cite{fg79}.\nWe obtain\n\\be\n\\label{e11}\n\\Omega(\\lambda_0) \n\\approx 6 \\cdot 10^{-3}\\left(\\frac{\\lambda_0}{10h^{-1}}\\right)^{-1} \\; .\n\\ee\nIf galaxy distribution turns out to be homogeneous at \n$\\lambda_0 \\approx 10 \\hmp$ then $\\Omega \\approx 6 \\cdot 10^{-3}$ as\nit is obtained in the standard treatment \\cite{pee93}.\nIf, instead, the crossover to homogeneity lies at $100 \\hmp$,\nwe obtain $\\Omega \\approx 6 \\cdot 10^{-4}$.\n\n\n\nFrom Eq.\\ref{e9} and if galaxy distribution turns out \nto be homogeneous at $\\lambda_0$,\nwe obtain that the critical Mass-to-Luminosity ratio\n(such that $\\Omega(\\lambda_0)=1$) is given by\n\\be\n\\label{cr1}\n\\left(\\frac{{\\cal M}}{{\\cal L}}\\right)_{crit} \\approx 1600h \n\\left(\\frac{\\lambda_0}{10h^{-1}}\\right) \\;, \n\\ee\nso that if $\\lambda_0=10 \\hmp$ one obtains \n$({\\cal M}/{\\cal L})_{crit} \\approx 1600h$\n(which is again consistent with the usual\n adopted value \\cite{pee93})\nwhile if $\\lambda_0=100 \\hmp$ $({\\cal M}/{\\cal L})_{crit} \\approx 16000h$,\nwhich is about two orders of magnitude larger\nthan the highest $ {\\cal M}/{\\cal L}$ observed in clusterised\nobjects.\nFor an intermediate value of $\\lambda_0= 50 \\hmp$\none obtains $({\\cal M}/{\\cal L})_{crit} \\approx 8000h$.\n\n\n \n\n\n\nFor what concerns the analysis of \ngalaxy clusters it is often used a value $({\\cal M}/{\\cal L})_{c} \\sim 300h$\n\\cite{galclu,bah99}\nwhich, by using Eq.\\ref{e9}, gives \n\\be\n\\label{c1}\n\\Omega(\\lambda_0) \\approx \n2 \\cdot 10^{-1}\\left(\\frac{\\lambda_0}{10h^{-1}}\\right)^{-1} \\; .\n\\ee\nSuch an estimation is based on the fact that\nthe Mass-to-Luminosity ratio found in clusters \nis representative of all the field galaxies. \nThis is a very strong assumption:\nthis means that \n$({\\cal M}/{\\cal L})_{g} = \n({\\cal M}/{\\cal L})_{c}$ which is not supported\nby any observation.\nThe usually adopted value of $\\Omega =0.2$ \\cite{bah99}\ncan be derived from Eq.\\ref{c1} by assuming $\\lambda_0= 10 \\hmp$.\nIn the case the crossover to homogeneity\noccurs at $\\lambda_0=100 \\hmp$ we have that\n$\\Omega(\\lambda_0) = 0.02$ if we consider \n$({\\cal M}/{\\cal L})_{c} \\sim 300h$ to be \"universal\".\n\n\n\nUnder the assumptions:\n\n{\\it (i)} galaxies are homogeneously distributed\nat scales larger than $\\lambda_0 \\approx 5 \\hmp$, \n\n{\\it (ii)} the ${\\cal M}/{\\cal L}$\nof galaxies is the same of clusters,\nthat is galaxies should contain a factor $\\sim 30$ more\ndark matter than what it is observed\nwith the study of the rotation curves \\cite{fg79},\n\n{\\it (iii)} Galaxy positions are independent of galaxy luminosity:\nsuch a assumption is not strictly valid, but it has been \ntested\\cite{syl00} to hold rather well in the available samples,\n\n\nwe get the following upper limit to $\\Omega$.\nIf we assume that ${\\cal M}/{\\cal L} = 300 h$\nacross all the scales, and that \n$\\lambda_0 \\approx 50 \\hmp$,\nwhich we consider to be a lower limit for the homogeneity scale,\nwe get from Eq.\\ref{c1}\n\\be\n\\label{ul1}\n\\Omega(50 Mpc/h, 300 h M_{\\odot}/L_{\\odot}) \\le 0.04 \\;.\n\\ee\n\nThe direct estimation with galaxies (Eqs.\\ref{e9}-\\ref{e11})\ngives lower a value, the reason being \nthe strong assumption of taking ${\\cal M}/{\\cal L} = 300 h$\nas representative of field galaxies (see Fig.\\ref{figomega}).\n\\bef \n\\epsfxsize 8cm \n\\epsfysize 8cm \n\\centerline{\\epsfbox{omega_omega.ps}} \n\\caption{\\label{figomega}\nWe show the behavior of $\\Omega(r,{\\cal M}/{\\cal L})$\nand $\\Omega_c(r)$ (direct estimation from the Mass and number density\nof galaxy clusters),\nin the case $h=1$,\nfor three different values of ${\\cal M}/{\\cal L}=1, 12, 300$.\nIf $\\lambda_0 =50 \\hmp$ we get an upper limit\n$\\Omega =0.04$. In the figure the value of the \nHubble's constant is set $h=1$. (From Sylos Labini, 2000)\n}\n\\eef\n\n\\subsection{Homogeneity scale and primordial nucleosynthesis constraints}\n\nLet us now discuss the previous \nresults in relation with the nucleosynthesis\nconstrain $\\Omega_b^{BBN} = 0.015h^{-2}$, deriving in such a\nway an upper limit for $\\lambda_0$ which is consistent\nwith such a scenario.\nWe may see\\cite{syl00} \n that if $\\lambda_0 \\approx 100 h^2 Mpc$ then\n$\\Omega(\\lambda_0,({\\cal M}/{\\cal L})_c) \\approx \\Omega_b^{BBN}$.\nSuch a fact has two important implications.\n\nFirst of all one does not need the presence \nof {\\it non baryonic dark matter} to reconcile \nlocal observations of matter contained in galaxies\nand galaxy clusters ($\\Omega_{local}$)\nwith the primordial nucleosynthesis\nconstraint. This is an important point as the \nexistence of {\\it non baryonic dark matter}\nhas been inferred also, but not only,\nby the discrepancy $\\Omega_{local}/\\Omega_b^{BBN}$ \\cite{bah99}, \nwhich, we show, is not observed if $\\lambda_0 \\ge 100 h^2 Mpc$.\nThere is still place, in this picture,\nfor a uniform background of {\\it non-baryonic dark matter},\nwhich has completely different clustering properties \nfrom the ones of visible matter.\n \n\nThe second point concerns the baryon fraction in clusters.\nAccording to the usual root, in order to be consistent \nwith $\\Omega_b^{BBN}$,\none has to force $\\Omega =0.1 \\div 0.3$ from clusters \nanalysis\\cite{bah99}. Here we can argue as follows.\nBy assuming a very large ${\\cal M}/{\\cal L} \\sim 300 h$,\nand that it is universal across all scales,\nand by assuming that all dark matter is made\nof baryons, if the crossover to homogeneity occurs at scales larger \nthan $\\sim 150 h^2 Mpc$ then there is not enough baryonic\nmatter to satisfy the nucleosynthesis constraint. \nThe situation gets clearly worst if one takes into account\nthat not all the mass in clusters is baryonic \nor that ${\\cal M}/{\\cal L} < 300 h$, i.e. it is not considered\nto be universal across all scales, or that\n$\\lambda_0 \\gg 100 h^2 Mpc$. \nThere are then two different possibilities:\nthe first is to study the case of a non homogeneous primordial\nnucleosynthesis which could lower the limit\non $\\Omega_b^{BBN}$, given the observed\nabundances of light elements, and the second\nwould be to have a more uniform background of baryonic dark matter.\nThis seems rather unlikely because it would have very different\nclustering properties with respect to visible mass\nand it is very difficult to find a \ndynamical explanations for such a \nsegregation.\n\n\n\n\n\\subsection{ Where does linear approximation hold ?}\nIn the standard picture, \nthe properties of dark matter on \ncosmological relevant scales $r > 5 \\hmp$,\nare inferred from the observed \nproperties of visible matter and radiation.\nNow one studies change in these properties,\ni.e. the presence of fractal correlations, \nand in this respect they will have consequences \non dark matter too\\cite{dsl98,gsl00}.\n For example, the determination of the \nmass density including dark matter has been performed\non the basis of the linear theory \\cite{sw94}.\nHere the problem is: beyond which\nscale can linear theory be considered\nas a useful approximation ?\n\nIn other words, the dynamical estimates use gravitational effects,\nof departure from a strictly homogeneous distribution\non the motion of objects such as galaxies\nconsidered as a test particle.\nA completely different situation occurs if $\\lambda_0$ is larger \nthan the scales at which linear approximation is usually adopted.\nFor example, methods based on the Cosmic Virial Theorem \\cite{pee80},\ndistortions in redshift surveys \\cite{sw94}, local group dynamics \\cite{pee93},\nthe \"reconstructed\" peculiar velocity\nfield from the density field (e.g POTENT-like methods\\cite{sw94}),\nare clearly not useful at scales $r \\ll \\lambda_0$.\nUp to now it is implicitly\n assumed $\\lambda_0 \\approx 5 \\div 10 \\hmp$\nand all these methods are considered to be valid on larger scales. \nIf, for example $\\lambda_0 \\sim 50 \\hmp$\nthen it is not possible to interpret peculiar velocities\nin the range $1 \\div 30 \\hmp$ through the linear \napproximation (as it is usually done\\cite{sw94}),\n unless there is a \nbackground of dark matter which is uniform beyond\na certain small scale. In such a situation however\nthe estimates would be different \\cite{bar98}\n from the usual ones \\cite{sw94}.\n\nLet us review some simple relations between \nthe conditional average density $\\Gamma(r)$ and the usual\ncorrelation function $\\xi(r)$.\nIf $\\Gamma(r)$ has a power law behavior up to a scale $\\lambda_0$\nand then it presents a crossover to homogeneity,\nit is simple to show that (in the case of $D=2$)\nthe length scale at which $\\xi(r_0)=1$ is \nof the order of\n\\be\n\\label{o1}\nr_0 \\approx \\frac{\\lambda_0}{3}\n\\ee\nwhere the exact relation between $r_0$ and $\\lambda_0$\ndepends on the details of the crossover \\cite{gsl00}.\nHowever Eq.\\ref{o1} gives a reasonable order of magnitude\nin the general case.\nIn such a situation it is also simple to\ncompute $\\sigma(r,\\lambda_0) \n= \\langle N(r) - \\langle N \\rangle / \\langle N \\rangle \\rangle$,\ni.e the amplitude of the fluctuation with respect\nto the average at the scale $r \\ll \\lambda_0$ \n\\cite{slmp98}\n\\be\n\\label{o2}\n\\sigma(r,\\lambda_0) \\approx \\frac{\\lambda_0}{2r} \\; .\n\\ee\nIt has been found in various nearby surveys that $\\sigma(8 \\hmp) =1$.\nHowever if the crossover to homogeneity occurs at $\\lambda_0$\nwe have that\n\\be\n\\label{o3}\n\\sigma(8 \\hmp,\\lambda_0) \\approx \\frac{\\lambda_0}{16}\n\\ee\nFor example if $\\lambda_0 \\approx 15 \\hmp$ then $r_0\\approx 5 \\hmp$\nand $\\sigma(8 \\hmp,15 \\hmp) = 1$;\notherwise if $\\lambda_0 \\approx 50 \\hmp$ then $r_0\\approx 16 \\hmp$\nand $\\sigma(8 \\hmp,15 \\hmp) = 3$.\n \nLinear approximation holds in the linear regime,\nwhen the amplitude of the density contrast is small, \ni.e. for $\\sigma \\ll 1$.\nWe have that $\\sigma = 1 $ at a scale $r_{\\sigma=1}(\\lambda_0)$ \n\\be\n\\label{o4}\nr_{\\sigma=1}(\\lambda_0)\\ \\approx \\frac{\\lambda_0}{2}\n\\ee\nFor instance, if the crossover to homogeneity occurs at \n$\\lambda_0 = 50 \\hmp$ one has that $\\sigma(\\lambda_0)=1$\nat $r_{\\sigma=1}= 25 \\hmp$. In such a situation all the\nestimations of the density parameter at smaller scales \nbased on the linear approximation\\cite{sw94}, and hence based\non the untested assumption of linearity, are not correct.\n\nWe have studied in detail\\cite{gslp99} the gravitational force distribution\nin a fractal structure.\nIts behaviour can be \nunderstood as the sum of two parts, a local or `nearest neighbours'\npiece due to the smallest cluster (characterised by the lower\ncut-off $\\Lambda$ in the fractal) and a component coming from the \nmass in other clusters. The latter is bounded above by the\nscalar sum of the forces \n\\begin{equation}\n\\langle |\\vec{F}| \\rangle \\leq \n\\lim_{L\\rightarrow \\infty} \n\\int_{\\Lambda}^L \\frac{G\\rho_m(r)}{r^2} 4\\pi r^2 dr \\sim L^{D-2}\n\\end{equation}\nso that for $D<2$ it is convergent, while for $D>2$\nit may diverge. If there is a divergence, it is due \nto the presence of angular fluctuations at large scales,\ndescribed by the three-point correlation properties of\nthe fractal. For the difference in the force between two points\nthe local contribution will be irrelevant well beyond the scale\n$\\Lambda$, while it is easy to see that the `far-away' contribution\nwill now converge as $L^{D-3}$, and its being non-zero \nis a result of the absence of perfect spherical \nsymmetry. We have then applied such a result to the case\nof an open universe\\cite{jampsl00} in order to compute\nthe expected deviations from a pure linear Hubble flow.\n \n\n\n\\section{Discussion and Conclusions}\n\nWe now present a short discussion about the perspective of our work:\nthe cosmological implications of the fractal behavior of\nvisible matter crucially depend on the crossover scale $\\lambda_0$,\nbut, no matter what is the actual value of such a scale,\nwe have some important consequences from \nthe theoretical point of view. We may identify three\ndifferent scenarios.\n\n\\begin{itemize}\n\n\\item (1) The fractal extends only up to $\\sim 30\\div 100 \\hmp$.\nThis is the minimal concept which begins to be \nabsorbed in the literature\\cite{rees99} but, \nsometimes, without considering its real consequences.\nThe standard approach to galaxy distribution\nhas identified very small \"correlation lengths\",\nnamely $5 \\hmp$ for galaxies and $25 \\hmp$ for clusters.\nThese numbers (which were supposed to know with high \nprecision\\cite{dav97}) are anyhow inconsistent \nwith the fractal extending a factor $2\\div 4$ more.\nWe have shown that this inconsistency is conceptual and not due to \nincomplete data or week statistics. Hence, in this \nhypothesis one has to abandon all the concepts\nrelated to these length scales. These are: \n\n (i) \nThe estimate of the matter density in clusterised objects\n(visible + dark), which has been claimed to be \n$\\Omega \\approx 0.2 \\div 0.3$, decreases \nby one order of magnitude or more. \n\n(ii) The normalization of N-body simulations \nis usually performed to some length-scale\nor amplitude of fluctuations, which are related to\n$5 \\hmp$ and $25 \\hmp$.\n\n(iii) Concepts like the galaxy-cluster mismatch \nand the related luminosity bias, as well as \nthe understanding of the clustering via\nthe bias parameter $b$ (i.e. linear or non-linear - \"stochastic bias\" -\namplification of $\\xi(r)$) loose any physical meaning.\n\n(iv) The interpretation of the velocity field is \nalso based on the linear approximation which\ncannot certainly hold at scales smaller than $30\\div50 \\hmp$.\n\n(v) The reconstruction of the three dimensional properties\n from the angular data suffers of the same untested\n assumption of homogeneity.\n\nIn summary major modifications are necessary \nfor the origin and dynamics of large scale structures\nand for the role of dark matter. However the structures\nmay still formed via gravitational instability,\nin the sense that \nthey are not necessarily primeval\\cite{jampsl00}.\n\n\\item (2) The fractal extends up to $300 \\div 500 \\hmp$.\nIn this case the standard picture of\ngravitationally induced structures after \nthe electromagnetic decoupling is untenable. There\nis no time to create such large scale correlated structures\nvia gravitational instability, starting from Gaussian\ninitial conditions. More string consequences \nare clearly important for what concerns \nthe amount of matter in clusterised objects.\n\n\\item (3) The fractal extends up to $\\gtapprox 1000 \\hmp$,\nand homogeneity does not exist, at least \nfor what concerns galaxies. In this extreme case\na new picture for the global metric\\cite{jampsl00} \nis then necessary.\n\n\\end{itemize}\n\nFor some questions \nthe fractal structure leads to a radically new perspective \nand this is hard to accept. But it is based on the best data and \nanalyses available. It is neither a conjecture nor a model, \nit is a fact. \nThe theoretical problem is that \nthere is no dynamical theory to explain \nhow such a fractal Universe could have arisen from the pretty \nsmooth initial state we know existed in the big bang. \nHowever this is a different \nquestion. The fact that something can be hard to explain theoretically has \nnothing to do with whether it is true or not. Facing a hard problem is far \nmore interesting than hiding it under the rug by an inconsistent procedure.\nFor example some interesting attempts to understand why \ngravitational clustering generates scale-invariant structures have been\nrecently proposed by de Vega et al\\cite{devega1,devega2,devega3}.\nIndeed this will be the key point to understand in the future, \nbut first we should agree on how these new 3d data should be analyzed. \nIn addition, the eventual crossover to homogeneity has also to be found with \nour approach. \nIf for example homogeneity would really be found say at \n$ \\sim100 \\hmp$, then clearly \nall our criticism to the previous methods\nand results still holds fully. In summary the \nstandard method cannot be used neither to disprove homogeneity, nor to \nprove it. One has simply to change methods. \n\n \n\\section*{Acknowledgements} \n \nWe warmly thank \nR. Durrer, A. Gabrielli, \nM. Joyce and M. Montuori \nwith whom various parts of this work have \nbeen done in fruitful collaborations. \nFSL is grateful to Pedro Ferreira for very useful \ncomments and discussions. \nWe thank Prof. N. Sanchez \nfor the organization of this very interesting School. \nThis work has been partially supported by the \nEC TMR Network \"Fractal structures and \nself-organization\" \n\\mbox{ERBFMRXCT980183} and by the Swiss NSF. \n \n\n\n\\section*{References}\n\n\\begin{thebibliography}{99}\n\n\\bibitem{bah99}\nBahcall N., 1999\nIn the Proc. of the Conference \n``Particle Physics and the Universe (astro-ph/9901076)\n\n\\bibitem{bar98} Y. Baryshev, F. Sylos Labini, M. Montuori , \nL. Pietronero, and P. Teerikorpi \n Fractals {\\bf 6}, 231-244 (1998) \n \n\n\\bibitem{be94} Baugh C.M. and Efstathiou G. \nMon.Not.R.Astr.Soc., {\\bf 267}, 323 (1994)\n\n\n\\bibitem{ben96} Benoist C. {\\it et al.}, \n {Astrophys. 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{
"name": "astro-ph0002124.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{bah99}\nBahcall N., 1999\nIn the Proc. of the Conference \n``Particle Physics and the Universe (astro-ph/9901076)\n\n\\bibitem{bar98} Y. Baryshev, F. Sylos Labini, M. Montuori , \nL. Pietronero, and P. Teerikorpi \n Fractals {\\bf 6}, 231-244 (1998) \n \n\n\\bibitem{be94} Baugh C.M. and Efstathiou G. \nMon.Not.R.Astr.Soc., {\\bf 267}, 323 (1994)\n\n\n\\bibitem{ben96} Benoist C. {\\it et al.}, \n {Astrophys. J.} {\\bf 472}, 452 (1996) \n \n\\bibitem{galclu} Carlberg R.G., Yee H.K and Ellingson E.\n {Astrophys. J.} {\\bf 478}, 462-457 (1997) \n\n \n\\bibitem{cappi98} Cappi A. et al., \nAstron.Astrophys {\\bf 335}, 779 (1998) \n \n\\bibitem{chown99} \nChown M. New Scientist, {\\bf 2200}, 22-26 (1999) \n\n\n\\bibitem{cp92} \nColeman, P.H. \\& Pietronero, L., Phys.Rep. {\\bf 231}, \n 311 (1992) \n\n\\bibitem{col94} Colombi S., Bouchet F.R. and Schaeffer R.\nAstron.Astrophys., {\\bf 281}, 301 (1994) \n\n\\bibitem{coles98} Coles P. \nNature {\\bf 391}, 120-121 (1998) \n\n\\bibitem{dac94} Da Costa, L. N. {\\em et al.} \n Astrophys. J. {\\bf 424}, L1 (1994) \n\n\\bibitem{dp83} \n Davis, M., Peebles, P. J. E. \nAstrophys. J., {\\bf 267}, 65 (1983) \n\n\\bibitem{dav88} Davis, M. {\\em et al.} \n Astrophys.J.Lett., {\\bf 333}, L9 (1988)\n\n\\bibitem{dav97} Davis, M. in the Proc of the \nConference \"Critical Dialogues in Cosmology\" p.13 \nN. Turok Ed. World Scientific (1997) \n\n\n\\bibitem{devega1} De Vega H.J., Sanchez N. and Combes F.\nAstrophys.J. {\\bf 500}, 8 (1998)\n\n\\bibitem{devega2} De Vega H.J., Sanchez N. and Combes F.\nNature {\\bf 383}, 56 (1996)\n\n\\bibitem{devega3} De Vega H.J., Sanchez N. and Combes F.\nPhys.Rev.D. {\\bf 54}, 6008 (1996)\n\n\n \\bibitem{dsl98} Durrer R. and Sylos Labini F. \nAstron.Astrophys. {\\bf 339}, L85 (1998) \n \n\n\\bibitem{lumfun} Efstathiou G, Ellis R.S. and Peterson B.,\nMon.Not.R.astr.Soc {\\bf 232}, 431-461, (1988)\n\n\\bibitem{elad97} El-Ad. H. and Piran T. Astrophys.J. \n{\\bf 491}, 421-435 (1997) \n\n\\bibitem{fg79} Faber S.M. \\& Gallagher J.S.\nAstron.Astrophys. Ann.Rev. {\\bf 17}, 135 (1979)\n\n\\bibitem{fe94} Feldman H. Kaiser N. \\& Peacock J.\n \\etal (1994) Ap.J. {\\bf 426}, 23 (1994) \n\n\\bibitem{fis93} Fisher et al. 1993,\nAstrophys.J., {\\bf 402}, 42 (1993)\n\n\\bibitem{gslp99} Gabrielli A., Sylos Labini F. and Pellegrini S.\n Europhys.Lett. {\\bf 46}, 127-133 (1999) \n \n\\bibitem{gsld00} Gabrielli A., Sylos Labini F. \\& Durrer R. \nAstrophys.J. Letters (In the Press) astro-ph/9905183 (2000) \n \n \n\\bibitem{gsl00} Gabrielli A. and Sylos Labini F. \n(2000) Preprint\n\n\\bibitem{perezmercader} Gaite J., Dominuguez A. \nand Perez-Mercader J. \nAstrophys.J.Lett. {\\bf 522} L5 (1999) \n\n\\bibitem{hutton99} Hatton S.J. \n Mon.Not.R. {\\bf 310}, 1128-1136,\n(1999) \n\n\\bibitem{it92} Itho M., Suginohara T. \\& Suto Y., \nPASJ {\\bf 44}, 481\n(1992)\n\n\\bibitem{jmsl99} Joyce M., Montuori M., Sylos Labini F. \n Astrophys. Journal Letters, {\\bf 514}, L5-L8, (1999)\n\n\\bibitem{jampsl00} Joyce M., Anderson P.W., Montuori M., \nPietronero L. and Sylos Labini F. \nPreprint (2000) \n \n\\bibitem{landy99} \n Landy S.D. \nScientific American {\\bf 456}, 30-37, (1999)\n\n\n\\bibitem{man77} Mandelbrot, B.B., 1977 \n{\\it \"Fractals:Form, Chance and Dimension\"}, W.H.Freedman\n\n\\bibitem{martinez99} Martinez V.J. \nScience {\\bf 284}, 445-446 (1999). \n \n\\bibitem{mjsl00} Montuori, M., Joyce, M. and Sylos Labini F. \nPrerpint (2000) \n\n\\bibitem{nl00} Nusser A., Lahav O.\n In Print MNRAS (2000)\n \n\\bibitem{par94}Park C., Vogeley M. and Geller M. \n Astrophys. J. {\\bf 431}, 569-585 (1994) \n\n\\bibitem{pn91} Peacock, J.A., Nicholson, D.\nMon.Not.R.Astr.Soc, {\\bf 235}, 307 (1991)\n\n\n\\bibitem{pee80} Peebles, P.J.E. \nLarge Scale Structure of the Universe , Princeton Univ. Press (1980) \n \n\\bibitem{pee93} Peebles, P.E.J., \nPrinciples of Physical Cosmology, Princeton \n Univ.Press, (1993) \n \n\n\\bibitem{pie87} Pietronero L. Physica A {\\bf 144}, 257 (1987) \n\n\\bibitem{scara98} Scaramella R., et al. \nAstron.Astrophys {\\bf 334}, 404 (1998) \n\n\\bibitem{sw94} \nStrauss M. and Willick J. Physics Reports {\\bf 261 }, 271 \n (1995) \n\n\\bibitem{sla96} Sylos Labini F. \\& Amendola L. \nAstrophys.J.Lett., {\\bf 468}, L1-L4 (1996) \n\n\\bibitem{slp96} Sylos Labini F. and Pietronero L. \nAstrophys. J., {\\bf 469}, 28 (1996) \n \n\\bibitem%[Sylos Labini \\etal, 1998] \n{slmp98} Sylos Labini F., Montuori M., \n Pietronero L., Phys.Rep. {\\bf 293}, 66 (1998) \n\n\\bibitem{slm98} Sylos Labini F. and Montuori M., \nAstron.Astrophys. {\\bf 331}, 809 (1998) \n\n\\bibitem{syl00} Sylos Labini F., Preprint (2000)\n\n\\bibitem{rees99} Wu K.K., Lahav O.and Rees M. \nNature, {\\bf 225} 230 (1999) \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n \n \n\n\\end{thebibliography}"
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astro-ph0002125
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The Lyman Continuum Polarization Rise in the QSO PG~1222+228\footnote {Accepted for publication in Publications of the Astronomical Society of the Pacific, 2000 May}
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"author": "Gregory A. Shields"
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Some QSOs show an abrupt, strong rise in polarization at rest wavelength $\sim750$~\AA. If this arises in the atmosphere of an accretion disk around a supermassive black hole, it may have diagnostic value. In PG 1222+228, the polarization rise occurs at the wavelength of a sharp drop in flux. We examine and reject interpretations of this feature involving a high velocity outflow. The observations agree with a model involving several intervening Lyman limit systems, two of which happen to coincide with the Lyman continuum polarization rise. After correction for the Lyman limit absorption, the continuum shortward of $\lambda 912$ is consistent with a typical power-law slope, $\alpha \approx -1.8.$ This violates the apparent pattern for the Lyman limit polarization rises to occur only in ``candidate Lyman edge QSOs''. The corrected, polarized flux rises strongly at the wavelength of the polarization rise, resembling the case of PG 1630+377. The rise in polarized flux places especially stringent requirements on models.
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"name": "1222pp.tex",
"string": "\\documentstyle[11pt,aaspp4,flushrt]{article}\n%\\documentstyle[12pt,aasms4]{article}\n\n\\def\\hst{{\\em HST}}\n\\def\\hnot{H$_0$}\n\\def\\qnot{q$_0$}\n\\def\\msun{\\ifmmode {\\rm M_\\odot} \\else M$_\\odot$\\fi}\n\n\\def\\msunyr{\\ifmmode {\\rm M_\\odot~yr^{-1}}\\else${\\rm M_\\odot~yr^{-1}}$\\fi}\n\\def\\lam{\\ifmmode {\\lambda} \\else {$\\lambda$} \\fi}\n\\def\\lalpha{L$\\alpha$}\n\\def\\muobs{\\ifmmode {\\mu_{obs}} \\else $\\mu_{obs}$ \\fi}\n\\def\\mdoto{\\ifmmode {\\dot{M}_0} \\else $\\dot{M}_0$ \\fi}\n\\def\\teff{\\ifmmode {T_{eff}} \\else $T_{eff}$ \\fi}\n\\def\\ilam{\\ifmmode {I_\\lambda} \\else $I_\\lambda$ \\fi}\n\\def\\inu{\\ifmmode {I_\\nu} \\else $I_\\nu$ \\fi}\n\\def\\fnu{\\ifmmode {F_\\nu} \\else $F_\\nu$ \\fi}\n\\def\\tauh{\\ifmmode {\\tau_{\\rm H}} \\else $\\tau_{\\rm H}$ \\fi}\n\\def\\cm{\\ifmmode {\\rm cm} \\else cm \\fi}\n\\def\\cmmitwo{\\ifmmode \\rm cm^{-2} \\else $\\rm cm^{-2}$\\fi}\n\\def\\cmmithree{\\ifmmode \\rm cm^{-3} \\else $\\rm cm^{-3}$\\fi}\n\\def\\cmps{\\ifmmode \\rm cm~s^{-1}\\else $\\rm cm~s^{-1}$\\fi}\n\\def\\cmpsps{\\ifmmode \\rm cm~s^{-2}\\else $\\rm cm~s^{-2}$\\fi}\n\\def\\kmps{\\ifmmode \\rm km~s^{-1}\\else $\\rm km~s^{-1}$\\fi}\n\\def\\kmpspmpc{\\ifmmode \\rm km~s^{-1}~Mpc^{-1} \\else\n $\\rm km~s^{-1}~Mpc^{-1}$\\fi}\n\\def\\ergps{\\ifmmode \\rm erg~s^{-1} \\else $\\rm erg~s^{-1}$ \\fi}\n\\def\\ergpspcm{\\ifmmode \\rm erg~s^{-1}~cm^{-2} \n \\else $\\rm erg~s^{-1}~cm^{-2}$ \\fi}\n\\def\\ergpspcmphz{\\ifmmode \\rm erg~s^{-1}~cm^{-2}~Hz^{-1} \\else $\\rm\n erg~s^{-1}~cm^{-2}~Hz^{-1}$ \\fi}\n\\def\\ergpspcmpa{\\ifmmode \\rm erg~s^{-1}~cm^{-2}~\\AA^{-1} \\else $\\rm\nerg~s^{-1}~cm^{-2}~\\AA^{-1}$ \\fi}\n\\def\\ergpsphz{\\ifmmode \\rm erg s^{-1} Hz^{-1} \\else \n $\\rm erg s^{-1} Hz^{-1}$ \\fi}\n\\def\\mdoto{\\ifmmode \\dot M_0 \\else $\\dot M_0$ \\fi}\n\\def\\eg{e.g.}\n\\def\\ie{i.e.}\n\\def\\cf{cf.}\n\\def\\etal{~et al.}\n\n\n\\received{}\n\\accepted{}\n\\journalid{}{}\n\\articleid{}{}\n\n\\slugcomment{}\n\n\n\\begin{document}\n\n\\title{The Lyman Continuum Polarization Rise in the QSO PG~1222+228\\footnote\n{Accepted for publication in Publications of the Astronomical\nSociety of the Pacific, 2000 May}}\n\n\\author{Gregory A. Shields}\n\\affil{Department of Astronomy, University of Texas, Austin, TX 78712}\n\\authoremail{shields@astro.as.utexas.edu}\n\n\\lefthead{G. A. Shields}\n\\righthead{Polarization of PG 1222+228}\n\n\\begin{abstract}\n\nSome QSOs show an abrupt, strong rise in polarization \nat rest wavelength $\\sim750$~\\AA. If this arises\nin the atmosphere of an accretion disk around a supermassive black hole, it may\nhave diagnostic value. In PG 1222+228, the polarization rise occurs at the\nwavelength of a sharp drop in flux. \nWe examine and reject interpretations of this\nfeature involving a high velocity outflow. The observations agree with a model\ninvolving several intervening Lyman limit\nsystems, two of which happen to coincide with the\nLyman continuum polarization rise. After correction for the Lyman limit\nabsorption, the continuum shortward of $\\lambda 912$ is consistent with a\ntypical power-law slope, $\\alpha \\approx -1.8.$ This violates the apparent\npattern for the Lyman limit polarization rises \nto occur only in ``candidate Lyman\nedge QSOs''. The\ncorrected, polarized flux rises strongly at the wavelength of the polarization\nrise, resembling the case of PG 1630+377. The rise in polarized flux places\nespecially stringent requirements on models.\n\n\n\\end{abstract}\n\n\n\\keywords{galaxies: active --- quasars: general --- \naccretion, accretion disks --- polarization --- black hole physics}\n\n\\section{INTRODUCTION}\n\nSpectropolarimetric observations with the \n{\\em Hubble Space Telescope} (\\hst) have\nrevealed an unexpected rise in linear polarization in several QSOs (see review\nby Koratkar \\& Blaes 1999). These are radio quiet ``candidate Lyman edge\nQSOs'', in which the continuum flux drops rather rapidly at rest wavelengths\n$\\lambda < 1000$~\\AA\\ \n(Antonucci, Kinney, \\& Ford 1989; Koratkar, Kinney \\& Bohlin\n1992). Models of accretion disk atmospheres predicted a reduced polarization\nin the Lyman continuum because of a diminished contribution \nof electron scattering\nto the opacity (Laor, Netzer, \\& Piran 1990). With this\nmotivation, Impey\n\\etal\\ (1995) and Koratkar \\etal\\ (1995) used the Faint Object Spectrograph\n(FOS) on \\hst\\ to obtain ultraviolet spectropolarimetry of several QSOs with\nredshifts sufficient to bring the Lyman continuum within the observed\nwavelength band. The surprising result, in several cases, was a rapid {\\em\nrise} in polarization in the Lyman continuum. From values $\\lesssim 1$ percent\nin the optical and near ultraviolet, the observed polarization rises around\nrest wavelength 750~\\AA\\ to values $\\sim5$ percent \nin several objects, and to $\\sim20$\npercent in PG 1630+377. \n\nThis phenomenon has inspired several attemps at\nexplanation. Blaes and Agol (1996) found that, for \neffective temperatures $\\teff \\approx 25,000$~K and low effective gravities, a\npolarization rise of up to\n$\\sim5$~percent at about the observed wavelength could occur naturally in QSO\ndisk atmospheres. This results from the interplay of electron scattering,\nbound-free opacity, and the temperature gradient in the atmosphere. However,\nShields, Wobus, and Husfeld (1998, hereinafter SWH) showed that the effects of\nthe relativistic transfer function destroy the agreement between this model and\nobservation. Beloborodov and Poutanen (1999) suggested a model involving\nCompton scattering in a corona or wind, but this model appears to have trouble\ngiving the rapid rise in polarized flux observed in PG 1630+377 (Blaes \\&\nShields 1999). Lee and Blandford (1997) \ndiscussed the possible role of scattering by\nresonance lines of heavy elements (see Section 5).\n\nSWH showed that, if\nthe polarization is assumed to rise sharply at \n$\\lambda 912$ in the rest frame of\nthe orbiting gas, then relativistic effects would \nnaturally produce the wavelength\ndependence of the observed polarization. This may offer a way of\nmeasuring the black hole spin, but the physical mechanism for the polarization\nrise remains unknown.\n\nPG 1222+228 is a $\\rm B \\approx 15.5$ radio quiet \nQSO (Schmidt \\& Green 1983) whose\npolarization rise at\n$\\lambda \\approx 750$~\\AA\\ coincides with a sharp drop \nin flux (Fig. 1, 2). Impey\n\\etal\\ (1995) noted this and attributed \nit to a coincidental Lyman limit system (LLS),\ncorresponding to an identified absorption line system at \nz = 1.486. However, the\ncoincidence of a broad absorption feature with a polarization rise also is\nobserved for broad absorption line (BAL) QSOs. In these objects, outflowing\ngas at velocities $\\sim10^4~\\kmps$ produces blueshifted absorption troughs,\ntypically seen in the resonance lines of H I, C IV, N V, O VI, Si IV, and\nsometimes Mg II (Weymann \\etal\\ 1991; \nArav, Shlosman, \\& Weymann 1997). Spectropolarimetric\nobservations (\\eg, Ogle 1997; Schmidt \\& Hines 1999; \nOgle \\etal\\ 1999) often show a rise in\npolarization in the troughs, reaching values as \nhigh as $\\sim8$ to 10 percent from $\\sim1$\npercent at unabsorbed wavelengths. This is explained \nin terms of scattering of some of\nthe continuum by an extended region that is \nnot covered by the BAL flow (Hines \\& Wills\n1995; Goodrich \\& Miller 1995; Cohen \\etal\\ 1995). This pattern resembles the\npolarization rise and flux drop in PG 1222+228.\n\nThis paper addresses two questions: (1) Does the polarization rise in PG\n1222+228 result from an intrinsic absorber, analagous to the situation in the\nBAL QSOs? (2) If the \ndrop in flux in PG 1222+228 is an intervening LLS, what are\nthe consequences of correcting the observed, polarized continuum for this\nabsorption?\n\n\n\\section{INTRINSIC ABSORPTION IN PG 1222+228?}\n\nWe first consider the possibility that the flux drop and coincidental\npolarization rise in PG 1222+228 results from some kind of intrinsic\nabsorption. Two possibilities, considered below, are that \nit is a BAL outflow, or that it\nis an unusual, intrinsic LLS. \n\nIn either case, one issue is\nthe behavior of the polarized flux as a function of wavelength. As discussed above, if the\npolarization rise results from the selective absorption of the directly viewed continuum but\nnot the scattered continuum, one might expect a smaller drop (but generally not a rise) in\nthe polarized flux, \n$I_p = p\\ilam$. In order to examine this, we have\nrebinned the data of Impey \\etal\\ (1995), kindly made available in reduced form\nby C. Impey and C. Petri (1999). These data consist of a spectrum with the G190H\ngrating covering $\\lambda\\lambda1575$ to 2320 at 0.37~\\AA\\ per pixel, and\na spectrum with the G270H grating covering the range 2224 to 3295 at 0.52~\\AA\\\nper pixel. The G190H data shortward of $\\lambda1994$ have low signal-to-noise and were\nnot presented by Impey \\etal\\ (1995). We used seven wavelength bins (in \\AA):\n(1)1994--2224, (2) 2224--2287, (3) 2287--2319, (4) 2319--2492, (5)\n2492--2761, (6) 2761--3029, (7) 3029--3295. Bins 2 and 3\ninvolve an average of the two overlapping spectra, and bin 3 is a narrow bin containing\nthe flux drop at $\\lambda 2300$. The resulting values of\n\\ilam, $q \\equiv Q/I$ and $u \\equiv U/I$ are tabulated in Table 1, along with the\npolarization, $ p = \\sqrt{q^2 + u^2}$, and its position angle, $\\theta$. For the\npolarized flux, we use the rotated Stokes flux\n$Q^\\prime$ and polarization\n$q^\\prime \\equiv Q^\\prime/I$ (\\cf\\ Koratkar etal\\ 1995), referred to a position angle of\n168 degrees. \n This is based on the mean polarization position angle of the HST data,\nwhich is in reasonable agreement with optical observations (Stockman \\etal\\ 1984; Webb\n\\etal\\ 1993). (The use of $q^\\prime$ is appropriate if the position angle of the\npolarization is constant with wavelength. Table 1 supports this and also shows that the\npolarization $p$ is reasonably consistent with $q^\\prime$.)\n These quantities are plotted in Figure 2.\nThe shortest wavelength\nbin has larger polarized flux than the longer wavelength bins. At face value, this would\nweigh against an intrinsic absorber model for PG 1222+228; but it involves a single\nwavelength bin with substantial error bars. Therefore, we consider other aspects of the\ntwo outflow models.\n\n\n\\subsection{BAL Absorption}\n\nThe rest wavelength of the onset of the absorption feature in PG 1222+228 is\n$~\\sim750$~\\AA. Some BAL QSOs show absorption by Ne VIII $\\lambda$775 (\\eg,\nArav \\etal\\ 1999; Telfer \\etal\\ 1999). This might be a candidate\nfor the feature in question, in as much as BALs often set in at a wavelength\nsomewhat blueshifted from the emission-line redshift. However, Ne VIII normally\nis accompanied by absorption in O VI\n$\\lambda 1035$, N V $\\lambda 1240$, and C IV $\\lambda 1550$. \nThere is no indication of broad\nC IV or Mg II absorption in the spectrum of PG 1222+228 (Sargent, Steidel, \\& Boksenberg\n1988; Steidel \\& Sargent 1992). The\n\\hst\\ spectrum shows a shallow trough at $\\lambda 3000$ to $\\lambda 3070$ that could be a\nweak O VI feature; but this may simply be a cluster of lines, including several\nstrong\n\\lalpha\\ lines indentified by Impey \\etal\\ (1996). Photoionization models by\nHamann (1997) indicate a range of ionization parameters for which the\nfractional abundance of Ne$^{+7}$ exceeds that of O$^{+5}.$ However, given the normal\nratio of oxygen to neon abundances, the O VI feature would likely be strong in\na situation giving strong Ne VIII. \n\nThe flux drop at\n$\\lambda 750$ does not recover, with decreasing wavelength, in a way\nsuggestive of a BAL (Figure 1). The spectrum has not fully recovered by rest wavelength\n650~\\AA, corresponding to an an\noutflow velocity of more than 40,000 \\kmps\\ if attributed to Ne VIII. Some moderately\nnarrow ``mini-BAL'' features have been observed at such high velocities (Hamann \\etal\\ \n1997), but true BAL troughs rarely reach such velocities. The same can be said in\nconnection with the possibility that the $\\lambda 750$ feature corresponds to a blend of\nfeatures including N III, N IV, O IV, S VI, and Ne VIII seen in BAL QSO spectra at this\nwavelength (\\eg, Arav \\etal\\ 1999). Moreover, given the range of ionization\nstages contributing to this blend, C IV and Si IV absorption \nwould likely accompany it.\n\nRecent work has shown that BAL QSOs systematically have weak soft X-ray\nemission. BAL QSOs have optical to X-ray slopes $\\alpha_{ox} \\lesssim -2.0$, whereas\nnonBAL QSOs tend to have $\\alpha_{ox}$ in the range -1.3 to -1.8 (Brandt, Laor,\nand Wills 1999). Here, $\\alpha_{ox}$ is defined by $F_x/F_o =\n(\\nu_x/\\nu_o)^{\\alpha_{ox}}$, where $F_x$ and $F_o$ are the flux densities ($\\fnu$)\nat 2 keV and 3000~\\AA, respectively. ROSAT pointing observations give a flux of\n$6\\times10^{-14}~\\ergpspcm$ for PG 1222+228 at a significance level of\n$3.3\\sigma$ (Mushotzky 1999). If we assume a ``normal'' power-law slope of\n$\\alpha = -1.6$ over the 0.2 to 2 keV ROSAT band (Brandt \\etal\\ 1999), we find \n$F_x = 1.5\\times10^{-31}~\\ergpspcmphz$ at 2 keV rest energy. Optical\nspectrophotometry (Wampler \\& Ponz 1985; Bechtold \\etal\\ 1984) implies $F_o \\approx\n1.1\\times10^{-26}\\ \\ergpspcmphz$ at rest wavelength 3000~\\AA. (These are\nobserved fluxes at the wavelength corresponding to the indicated rest\nwavelength.) From this, we find $\\alpha_{ox} = -1.8$ for PG 1222+228. This\nresult is uncertain because of the marginal X-ray detection and the\npossibility of variability, but at face value it is more consistent with a\nnon-BAL than a BAL QSO. (Wilkes \\etal\\ 1994 quote an uncertain value \n$\\alpha_{ox}\n\\approx -1.8$ from Einstein data.)\n\nWe conclude that the flux drop at $\\lambda 750$ in PG 1222+228 is unlikely to be a BAL\nfeature.\n\n\n\\subsection{An Instrinsic Lyman Limit System?}\n%\n\nImpey \\etal\\ (1995) suggested that the flux drop at $\\lambda 750$ was an intervening LLS. \nWe show below that Lyman limit absorption does indeed give a good fit to the spectrum. \nThis fit, however, leaves open the question of the location of the absorbing gas. \nBecause of the coincidence with the polarization rise, we consider here the\npossibility that the feature is an {\\em intrinsic} LLS, associated with a high\nvelocity outflow from the QSO. Impey\n\\etal\\ (1996) identify \\lalpha\\ absorption lines at z = 1.4857, 1.5238, 1.5272,\nand 1.5650 that might be associated with the $\\lambda 750$ feature, if it is taken to\nbe a LLS. A redshift of 1.486 corresponds to an outflow velocity $\\sim60,000\\\n\\kmps.$ As noted above, this is not unprecedented for a QSO outflow producing\nabsorption lines. However, the lines associated with the redshift systems in\nquestion in PG 1222+228 are narrow, \nand narrow lines with relative velocities greater than 5000\n\\kmps\\ usually are assumed to be intervening. For a Lyman edge optical depth of\nunity, the measured equivalent widths of the\n\\lalpha\\ lines are consistent with a Doppler parameter\n$b \\lesssim 30~\\kmps$ (see below), normal for\nan intervening LLS. In contrast, the mini-BALs observed at such\nhigh velocities have widths of order $1000~\\kmps$ (Hamann \\etal\\ 1997). \nCould the feature in PG 1222+228 nevertheless be caused by ejected\nmaterial with a high outflow velocity and a small velocity dispersion?\n\n We are not aware of any other case in which a high velocity LLS with narrow lines\nhas been shown to be intrinsic. \nHowever, the existence of many intrinsic, narrow, high velocity absorption systems in\nQSOs has been proposed by Richards \\etal\\ (1999). These authors\ncompare the incidence of absorption-line systems, per unit relative outflow\nvelocity, for highly luminous QSOs with that for less luminous ones. In\nthe velocity range 5000 to 75,000 \\kmps, they find that absorption systems\nhave a substantially larger frequency in luminous systems. Since intervening\nsystems should have no dependence on QSO luminosity (assuming that discovery\nsystematics are accounted for), Richards \\etal\\ conclude that at least\nthe excess number of systems in the high luminosity QSOs are intrinsic.\n\nA peculiar absorption line ratio in the z = 1.94 system in PG 1222+228 has\nbeen noted by Ganguly \\etal\\ (1998). These authors present high resolution\nspectra that show two narrow components, separated by $\\sim17~\\kmps$,\nwith very different strengths of the Al II and Al III absorption\nlines. Photoionization models\nindicate that the component with strong aluminum lines must have an anomalously\nhigh abundance of aluminum. This is reminiscent of claims of\nunusual abundances in BAL QSOs, including an excess of aluminum (\\eg, Turnshek\n\\etal\\ 1996; Junkkarinen \\etal\\ 1997; Shields 1997). The reality of these\nabundance anomalies is in doubt, because of the effects of partial covering of\nthe continuum source (Arav 1997). However, the basic observation of\nanomalously strong Al lines may be a possible parallel between PG 1222+228 and\nthe BAL QSOs, where outflowing gas is clearly present. If this is a hint that\nthe narrow, z = 1.94 system may be intrinsic, perhaps it adds plausibility to\nthe idea that the z = 1.486 system (or its neighbors) may also be intrinsic.\n\nWhat might be the geometry of an intrinsic LLS in PG 1222+228? In order to\nexplain the polarization rise, the absorber would have to intercept the line of\nsight to the continuum source but not the scattering source. The latter is\noften attributed to a wind driven off the inner edge of a ``dust torus'' (Krolik \\&\nBegelman 1986). The location of this may be related to the dust sublimation radius,\n$\\sim0.2 L_{46}^{1/2}$ pc, where $L_{46}$ is the bolometric luminosity of the central\nsource in units $10^{46}~\\ergps$ (Laor \\& Draine 1993). The absorbing material, at a velocity\nof\n$\\sim0.2c,$ would be at a smaller radius in order not to cover the scattering source. Its\nhigh velocity suggests an origin at a small radius where the escape velocity is\nof order the observed outflow velocity. The escape velocity from a central mass of\n$M$ is 0.2$c$ at a radius\n$10^{15.6} M_9$~cm, where $ M_9 \\equiv M/10^9~\\msun$. Let us assume the absorbing\nmaterial is at a radius of $\\lesssim10^{18}$~cm, large enough to obscure the ultraviolet\nemitting part of an accretion disk but not the scattering source. At the observed\nspeed, the crossing time would be a few years or less. Thus, the material should\nchange radius substantially in the seven years between the Sargent \\etal\\ (1988) and\nthe Impey \\etal\\ (1996) observations, and one might expect some change of velocity. These\nauthors, however, quote velocities for the\n$z = 1.486$ and 1.524 systems that agree within $\\Delta z \\approx\n0.001$. This corresponds to a change in outflow velocity of less than\n$\\sim100~\\kmps$. Such precise stability seems difficult to achieve. (Note,\nhowever, the stability of narrow features within the BAL\nprofiles of some QSOs [\\cf, Weymann 1997]). A further problem involves the\nnarrowness of the absorption lines. The radius of the ultraviolet emitting part\nof the disk would be at least\n$\\sim10$ gravitational radii, or about $10^{15.1} M_9$~cm. If the absorber is at a radius\n$\\lesssim 10^{18}$ cm, then the line of sight through the absorber to\ndifferent parts of the continuum source would likely give noticeably different\nprojected flow velocities. The observed linewidths (see below) are\n$\\lesssim30~\\kmps$, less than one thousandth of the outflow velocity. \n\nThese difficulties with the intrinsic absorber model for PG 1222+228 encourage\nus to examine the straightforward idea of an intervening LLS.\n\n\n\\section{INTERVENING ABSORPTION}\n\nImpey \\etal\\ (1995, 1996) attributed the flux drop at observed wavelength $\\lambda 2300$\nto a LLS associated with the $z = 1.4857$ absorption line system. They identify\nabsorption lines of H I, C III, N I, N II, Si II, and Si III. They also\nidentify systems at 1.5238, 1.5272, and 1.5650, which have multiple Lyman\nlines and, for $z = 1.5238$, C III. Sargent, Steidel, \\& Boksenberg (1988)\nmeasure C IV $\\lambda\\lambda 1548$, 1551 in the 1.486 and 1.524 systems with\nequivalent widths $\\sim0.7$~\\AA. However, Steidel\n\\& Sargent (1992) give a spectrum showing no detectable Mg II absorption. \n\nSimple\nestimates suggested that the $\\lambda 2300$ flux drop might be too gradual to be\nattributed to the converging Lyman lines of the $z = 1.486$ system. Therefore, we\ncomputed a model spectrum involving an assumed power-law continuum and absorption by the\nhydrogen lines and bound-free continuum. The column density of H I was\nparameterized by the Lyman edge optical depth, $\\tau_H$, and the lines were assumed to\nhave a Gaussian profile with a Doppler parameter set to a typical value\n$b = 30~\\kmps.$ (A larger line width would give\nan excessive equivalent width for \\lalpha\\ for the required \\tauh. The observed\ndecrement of the Lyman line equivalent widths actually suggests a narrower core\nline width, with some of the\n\\lalpha\\ equivalent width being attributable to a broader component of modest\ncolumn density. These details do not affect our conclusions.) Inclusion of 50\nLyman lines proved more than adequate to trace the convergence to the continuum\noptical depth. The model spectrum was convolved with a single component Gaussian\ninstrumental line profile following the discussion of Impey \\etal\\ (1996), using a\nFWHM of 2.9~\\AA\\ for G190H and 4.2~\\AA\\ for G270H. If only the $z = 1.486$ system\ncontributes to the LLS, then the Lyman line convergence is too close to the Lyman\nlimit ($\\lambda 912$) to fit the observed feature. However, allocation of some H I column\ndensity to both the 1.486 and 1.524 systems gave a good fit. Two additional LLS\nappear to be associated with the\n$z = 1.938$ and 1.174 systems. Figure 3 shows the resulting model spectrum, along\nwith the observed flux, binned in intervals of $\\sim7.3$~\\AA. The model has\n$\\tauh = (1.0, 0.5, 0.8, 0.6)$ for z = (1.174, 1.486, 1.524, 1.938), respectively.\n(The value of \\tauh for z = 1.174 is uncertain because of the poorly determined\namount of scattered light below 2000 \\AA.) \nThe three distinguishable LLS show good agreement with the expected\n$\\nu^{-3}$ behavior of the Lyman continuum optical depth above threshold, for an intrinsic\ncontinuum slope in the range $\\alpha\n\\approx -1.5$ to -2.0. This is consistent with the slope -1.8 found by Zheng\n\\etal\\ (1997) for their composite QSO spectrum in the wavlength range $\\lambda\n600$ to $\\lambda 1050$. A value $\\alpha = -1.8$ is assumed in the fit shown in Figure 3. \nThe gradual descent of the observed flux toward the Lyman limit for the $z = 1.938$ system is\na puzzle, but it may involve the effects of unrelated absorption lines. An\nunderstanding of this is important, as it would play a role in the\nclassification of PG 1222+228 as a candidate Lyman edge QSO.\nObservations at higher spectral resolution would help to clarify the situation.\n\nSargent, Steidel, and Boksenberg (1989) discuss the statistics of LLS in\nQSOs. For the redshift range in question, they give a mean incidence of LLS of $N(z)\n\\approx 1.5$ per unit redshift. Their data show many\n QSOs with multiple LLS,\nalthough the number of LLS in PG 1222+228 may be somewhat higher than typical. However, the\nefforts to measure Lyman continuum polarization in QSOs to some extent targeted the\ncandidate Lyman edge QSOs, and objects with LLS of moderate optical depth may have an\nenhanced probability to be included.\n\nWe conclude that an intrinsic power-law continuum, together with cosmologically\nintervening Lyman limit absorption, provides a straightforward explanation of\nthe ultraviolet spectrum of PG 1222+228. \n\n\\section{THE INTRINSIC POLARIZED CONTINUUM}\n\nThe various LLS in PG 1222+228 substantially attentuate the observed continuum. \nWhat is the behavior\nof the {\\em polarized flux} when corrected for the absorption? In view of the\nuncertainties in the measured polarization, a sufficient procedure is\nto estimate the polarized flux by multiplying the measured polarization in the chosen\nwavelength bins by the assumed intrinsic continuum flux. For this, we use the same\nwavelength bins described earlier, and the $\\inu^{PL}\n\\propto \\nu^{-1.8}$ power-law continuum used in our fit. The resulting rotated\nStokes flux, $Q_{*}^\\prime = q^\\prime \\times \\ilam^{PL}$, is shown in Figure 4. We see that\nthe Stokes flux now rises strongly with decreasing wavelength in the region of the\npolarization rise. This resembles the result found for PG 1630+377 by Koratkar \\etal\\\n(1995). A rising polarized flux is an important constraint on models for the origin of\nthe polarization rise.\n\nSWH showed that the wavelength dependence of the flux and\npolarization in PG 1222+228 and PG 1630+377 could be fit with an ad hoc model\ninvolving an accretion disk. The disk radiates as a black body, but the brightness\ntemperature is depressed below the effective temperature for wavelengths below the Lyman\nlimit, simulating a Lyman edge in the disk atmosphere. The polarization is assumed to\nrise abruptly at $\\lambda 912$ by an arbitrary amount. Relativistic effects give a\nblueshifted, but still fairly abrupt polarization rise in the observed spectrum. The\nmodels are characterized by $a_*,$ the dimensionless angular momentum of the hole;\nthe black hole mass; the accretion rate, $\\mdoto \\equiv {\\dot M}/(1~\\msunyr)$; and the\nviewing angle, $\\mu_{obs} = cos(\\theta_{obs})$. SWH found that\n$a_* = 0.5$ gave approximately the observed wavelength for the polarization rise, for a\nrelatively edge-on viewing angle. Their fits to both objects had a fairly low value of\n$T_{max}$, the maximum disk effective temperature, as required by the dropping flux\nin the Lyman continuum region. The correction for LLS absorption in PG 1222+228 hardens\nthe far ultraviolet spectrum, and a higher value of\n$T_{max}$ is required to fit the energy distribution. Figure 5 shows the\ncontinuum flux and polarization for a model with $a_* = 0.5,$ $M_9 = 8.8$ and $\\mdoto =\n86$. (We have assumed \\hnot = 70 \\kmpspmpc and \\qnot = 0.5.) The model agrees\nreasonably well with the corrected flux in the Lyman continuum and with the longer\nwavelength measurements. Although the corrected flux was assumed to be a\npower law, a disk continuum would also likely fit the observed flux, given some\nfreedom to adjust the LLS optical depths. This model has a step-function rise\nin polarization from negligle polarization at wavelengths longward of\n$\\lambda 912$ to an ad hoc value of 2.1 times the Chandrasekhar (1960) value for\na pure scattering atmosphere. The model predicts an observed\npolarization and polarized flux that rise at a wavelength substantially\nblueshifted from $\\lambda 912$, but the rise is more gradual than observed. This\nunderscores the need for improved polarization measurements of this object.\nIf the relativistic transfer function gives too gradual a polarization rise, even\nfor an instantaneous polarization rise in the rest frame of the orbiting gas, then\naccretion disk models for the polarization rise will face a serious problem.\n\nThe adopted model parameters give a bolometric luminosity $L/L_E = 0.36,$ where $L_E$ is\nthe Eddington limit. Such a high value of $L/L_E$ is barely consistent with a\ngeometrically thin disk. A larger value of $a_*$ would allow a larger mass for the\nrequired\n$T_{max}$, but then the polarization rise would occur at a wavelength shorter than\nobserved (\\cf\\ SWH). Evidently, an accretion disk fit to the corrected continuum of PG\n1222+228, in the manner of SWH, pushes the disk parameters to the limits. Conceivably,\nthe thickening of the disk corresponding to the large value of $L/L_E$ may be related to\nthe origin of the polarization rise.\n\n\n\\section{DISCUSSION}\n\nThe Lyman continuum polarization rises are among the more puzzling recent\nobservational discoveries concerning QSOs. The wavelength dependence, rising rather\nabruptly at nearly the same rest wavelength in the several known cases, suggests a\nconnection with the bound levels of atoms. The proximity of the feature to\n$\\lambda 912$ further suggests an association with the Lyman edge of hydrogen. The ad hoc\nmodel of SWH supports an association with the Lyman edge and raises the possiblity of\nconfirming the presence of a relativistic disk and constraining its parameters.\nHowever, attempts to fit the feature with a physical model have encountered \ndifficulties. This is an important problem for QSO theory.\n\nAre the reported polarization rises real? The\ncoincidence of the polarization rise in PG 1222+228 with a sharp drop in flux might\nraise the question of background problems with the FOS spectropolarimeter. Impey \\etal\\\n(1995) argue that the polarization is unlikely to be less than 2.7\\% around 2000 \\AA\\ under\nany reasonable assumption for the FOS background. However, the degree of polarization in\nthe far ultraviolet is uncertain by at least a factor two because of systematic errors\ninvolving background and scattered light in the FOS. The observed polarization rises in\nseveral QSOs occur at different observed wavelengths but similar rest wavelengths. We are\nnot aware of any polarization rises of this nature in FOS spectropolarimetry of BL Lac\nobjects or stars. There is an urgent need for a renewed capability for ultraviolet\nspectropolarimetry from space to confirm and extend the measurements.\n\nLyman continuum polarization rises have heretofore been associated with the candidate\nLyman edge QSOs (see discussion by Koratkar \\etal\\ 1998). Our results suggest that PG\n1222+228 may not be a true member of this class. \nMeasurements of the Lyman continuum polarization in additional QSOs are needed to\nclarify the frequency of occurence of the phenomenon and to look for correlations with\nfeatures in the continuum flux, in the line intensities and polarization, and other\nproperties. Observations to shorter rest wavelengths are needed to determine whether\nthe polarization falls or continues to rise. Measurements of the time dependence of the\npolarization rises would be most interesting. The emitting\nradius of an accretion disk would be light weeks.\n\nLee and Blandford (1995) considered a model for the far ultraviolet polarization \nrise of QSOs that did not involve the Lyman edge. Noting that a number of resonance\nlines of heavy elements fall in the rest wavelength range where the polarization rises, they\nsuggested that resonance scattering of the QSO continuum might produce the observed\npolarization. Such a model could produce a rising polarized flux, since the polarization\ncould be essentially zero at wavelengths without scattering contributions. As noted above,\nthe polarization rise in PG 1222+228 may be too steep for models involving an accretion\ndisk. In this case, alternative models such as resonance scattering may hold promise. We\nnote that the polarized flux spectrum of PG 1630+377 (Koratkar\n\\etal\\ 1995) shows a strong rise at the wavelength of the N V emission line.\n\nThe claim by Richards \\etal\\ (1999) that luminous QSOs have many\nintrinsic, narrow, high velocity C IV absorption systems has important implications. \nThis would complicate the use of such systems to probe the evolution of galaxies and the\nintergalactic medium. The mechanism for producing the absorbing clouds would add\nanother challenge to the subject of outflows from QSOs. Surveys of QSOs at\ndifferent luminosities, to a uniform standard of signal-to-noise ratio, would allow\nconfirmation of the claimed higher incidence of absorption in more luminous QSOs. \nTests of the intrinsic nature of narrow absorptions have been summarized by Barlow,\nHamann, \\& Sargent (1997). These include time variability of the depth and profile of the\nlines and evidence for saturated but nonblack line profiles. Detection of changes\nin the velocities of the lines would be most revealing. Chemical abundances\nmay be an indicator, given evidence for high abundances in the broad absorption and\nemission-line regions of QSOs (\\eg, Hamann \\& Ferland 1993). If C IV systems in high and\nlow luminosity QSOs have similar, mostly subsolar abundances, this might argue for their\nintervening nature.\n\n\n\n\n\n\n\\acknowledgments\n\nThe author is grateful to C. Impey and C. Petri for providing advice and the\nreduced HST observations and to C. Sneden for the use of a computer subroutine. \nThe work has benefitted from discussions and communications with R. Antonucci, O. Blaes,\nR. Blandford, R. Ganguly, M. Malkan, R. Mushotzky, G. Richards, R. Weymann, and B. Wills.\nThis material is based in part upon work supported by the Space Telescope Science\nInstitute under Grant No. GO-07359.02. This work was carried out in part at the Institute\nfor Theoretical Physics, University of California, Santa Barbara, supported by NSF grant\nPH94-07194.\n\n\n\\begin{thebibliography} {}\n\n\\bibitem {} Antonucci, R. R. J., Kinney, A. L., \\& Ford, H. C. 1989, \\apj, 342, 64\n\n\\bibitem {} Arav, N.\n1997, in ``Mass Ejection from AGN'', ed. N. Arav, I. Shlosman, \\& R. J. Weymann, A.S.P.\nConf. Ser., Vol. 128, p. 208\n\n\\bibitem {} Arav, N., Korista, K. T., de Kool, M., Junkkarinen, V. T., \\& Begelman, M.\n1999, \\apj, 516, 27\n\n\\bibitem {} Arav, N., Shlosman, I., \\& Weymann, R. J. (eds.) 1997, ``Mass Ejection\nfrom AGN'', A.S.P. Conf. Ser., Vol. 128.\n\n\\bibitem {} Barlow, T. A., Hamann, F., \\& Sargent, W. L. W. \n1997, in ``Mass Ejection from AGN'', ed. N. Arav, I. Shlosman, \\& R. J. Weymann, A.S.P.\nConf. Ser., Vol. 128, p. 13\n\n\\bibitem {} Bechtold, J. \\etal\\ 1984, \\apj, 281, 76\n\n\\bibitem {} Beloborodov, A. 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C., \\& Boksenberg, A. 1989,\n \\apjs, 69, 703\n\n\\bibitem {} Schmidt, M., \\& Green, R. F. 1983, \\apj, 269, 352\n\n\\bibitem {} Schmidt, G. D., \\& Hines, D. C. 1999, \\apj, 512, 125\n\n\\bibitem {} Shields, G. A. 1997, in ``Mass Ejection\nfrom AGN'', ed. N. Arav, I. Shlosman, \\& R. J. Weymann, A.S.P. Conf.\nSer., Vol. 128, p. 214\n\n\\bibitem {} Shields, G. A., Wobus, L., \\& Husfeld, D. 1998, \\apj, 496, 743\n\n\\bibitem {} Steidel, C. C., \\& Sargent, W. L. W., 1992, \\apjs, 80, 1\n\n\\bibitem {} Stockman, H. S., Moore, R. L., \\& Angel, J. R. P. 1984,\n\\apj, 279, 485\n\n\\bibitem {} Telfer, R. C., Kriss, G. A., Zheng, W., Davidsen, A. F., \\& \n Green, R. 1999, \\apj, 509, 132\n\n\\bibitem {} Turnshek, D. A., Kopko, M., Jr., Monier, E., Noll, D., \nEspey, B. R., \\& Weymann, R. J. 1996, \\apj, 463, 110\n\n\\bibitem {} Wampler, E. J., \\& Ponz, D. 1985, \\apj, 298, 448.\n\n\\bibitem {} Wardle, J. F. C. \\& Kronberg, P. P. 1974, \\apj, 194, 254\n\n\\bibitem {} Webb, W., Malkan, M., Schmidt, G., \\& Impey, C., 1993, \n\\apj, 419, 494\n\n\\bibitem {} Weymann, R. J. 1997, in ``Mass Ejection\nfrom AGN'', ed. N. Arav, I. Shlosman, \\& R. J. Weymann, A.S.P. Conf.\nSer., Vol. 128, p. 3\n\n\\bibitem {} Weymann, R. J., Morris, S. L., Foltz, C. B., \n\\& Hewett, P. C. 1991, \\apj, 373, 23\n\n\\bibitem {} Wilkes, B. J., Tananbaum, H., Worrall, D. M., Avni, Y., Oey, M. S., \\&\nFlanagan, J. 1994, \\apjs, 92, 53\n\n\\bibitem {} Zheng, W., Kriss, G., Telfer, R. C., Grimes, J. P., Davidsen, \\& A. F. \n1997, \\apj, 475, 469\n\n\\end{thebibliography}\n\n\\clearpage\n\n\\centerline{{\\bf Captions for Figures}}\n\n%\\vskip12pt\n\n\\figcaption[fig1.eps]{Ultraviolet spectrum of PG 1222+228 observed with \\hst\\ by\nImpey \\etal\\ (1995, 1996). Figure gives flux at earth in $10^{-15}~\\ergpspcmpa$\nas a function of observed\nwavelength. Vertical lines give the positions of the Lyman limit (above)\nand \\lalpha\\ (below) for redshifts z = 1.174,\n1.486, 1.524, 1.527, 1.565, and 1.938. Also shown is the \nLyman limit for the emission-line redshift of 2.046. Data plotted here are from the G190H\nspectrum for $\\lambda < 2224$ and G270H for longer wavelengths (see text). \nData is binned by 2 pixels.\nData courtesy of C. Impey and C. Petri (1999). \n\\label{fig1}}\n\n\\figcaption[fig2.eps]{Flux and polarization of PG 1222+228 from \\hst\\ observations\nby Impey \\etal\\ (1995, 1996), binned as described in the text. Abscissa is\nrest wavelength in terms of the emission-line redshift. \n$I$ is the measured flux in units of $10^{-16}~\\ergpspcmpa$. \nRotated Stokes flux $Q$, called\n$Q^\\prime$ in the text, is referred to the mean position angle of 168\ndegrees. The fractional rotated Stokes parameter, $q = Q/I,$ is given as a percentage.\n\\label{fig2}}\n\n\\figcaption[fig3.eps]{Observed flux of PG 1222+228 compared with model involving\npower-law continuum and absorption by H I Lyman lines and continuum at four\nredshifts as described in the text. Observations have been binned into intervals\nof approximately 7.3~\\AA\\ for clarity. Axes are same as in Fig. 1\n\\label{fig3}}\n\n\\figcaption[fig4.eps]{Flux and rotated Stokes flux of PG 1222+228 before \n(filled squares) and after (open squares)\ncorrection for absorption by Lyman limit systems as described in the text. Also\nshown (crosses) are observations of PG 1630+377 by Koratkar \\etal\\ (1995). \nFor PG 1630+377, the Stokes flux has been rotated to the mean position angle of 127\ndegrees, following Koratkar \\etal\\ The plotted values of I and Q have been scaled to\ncorrespond to the peak values in PG 1222+228 in order to emphasize the wavelength\ndependences. The corrected, polarized flux of PG 1222+228 \n($Q_*^\\prime$ in the text) rises strongly below\n$\\lambda 750$, resembling the case of PG 1630+377. Axes are same as in Fig. 2.\n\\label{fig4}}\n\n\\figcaption[fig5.eps]{Accretion disk model compared with \nobservations of PG 1222+228 (see text). \nObservations are from Impey \\etal\\ 1995 (squares), Bechtold \\etal\\\n1984 (open circles), and\nWebb \\etal\\ 1993 (open triangle).\nModel disk with $a_* = 0.5$,\n$M_9$ = 8.8 and \\mdoto = 86 is viewed at angle \\muobs = 0.25. \nAxes are same as in Fig. 2. \\label{fig5}}\n\n\\clearpage\n\n\\evensidemargin -0.20in\n\\oddsidemargin -0.20in\n\n\n\\begin{deluxetable}{crrrrrrrr}\n\n\\tablenum{1}\n\\tablewidth{6.8in}\n\\tablecaption{Continuum Polarization of PG 1222+228$^{a}$}\n\\tablecolumns{9}\n\\tablehead{\n\\colhead{Grating}\n& \\colhead{$\\lambda_{min}$}\n& \\colhead{$\\lambda_{max}$}\n& \\colhead{ $I$}\n& \\colhead{$q(\\%)$ }\n& \\colhead{$u(\\%)$}\n& \\colhead{$p(\\%)$}\n& \\colhead{$\\theta$}\n& \\colhead{$q^\\prime$}\n}\n\n\\startdata\n\n\nG190H &1994 &2224 &4.04$\\pm$0.04 &5.8$\\pm$1.8 \n&-3.4$\\pm$2.6 &6.4$\\pm$2.0 &165$\\pm$16 &6.7$\\pm$1.9\\nl\n\nBoth &2224 &2287 &2.94$\\pm$0.04 &2.4$\\pm$2.0\n&-3.8$\\pm$2.1 &4.0$\\pm$2.0 &151$\\pm$26 &3.7$\\pm$2.0\\nl\n\nBoth &2287 &2319 &4.59$\\pm$0.05 &0.2$\\pm$1.8 \n&-3.4$\\pm$1.9 &2.9$\\pm$1.9 &136$\\pm$31 &1.5$\\pm$1.8 \\nl\n\nG270H &2319 &2492 &9.27$\\pm$0.04 &1.0$\\pm$0.6 \n&-1.0$\\pm$0.6 &1.2$\\pm$0.6 &157$\\pm$26 &1.3$\\pm$0.6 \\nl\n\nG270H &2492 &2761 &9.33$\\pm$0.02 &0.5$\\pm$0.4 \n&-0.0$\\pm$0.4 &0.3$\\pm$0.4 &179$\\pm$48 &0.5$\\pm$0.4 \\nl\n\nG270H &2761 &3029 &14.14$\\pm$0.03 &0.9$\\pm$0.4 \n&-0.8$\\pm$0.4 &1.2$\\pm$0.4 &159$\\pm$17 &1.2$\\pm$0.4 \\nl\n\nG270H &3029 &3295 &16.85$\\pm$0.04 &1.7$\\pm$0.4 \n&0.2$\\pm$0.4 &1.6$\\pm$0.4 &4$\\pm$14 &1.5$\\pm$0.4 \\nl\n\n\n\\enddata\n\n\\tablenotetext{{\\it a}}{Data of Impey et al. (1995, 1996) rebinned with\nrespect to the apparent LLS at $\\lambda$2300.\nWavelength limits (observed) are given in \\AA.\nStokes parameters are given as $I$, the measured flux\n(units 10$^{-16}$ erg\ncm$^{-2}$ s$^{-1}$ \\AA$^{-1}$), $q\\equiv Q/I$, and $u\\equiv U/I$.\nThe quantity \n$q^\\prime$ is $Q/I$ rotated to P.A. 168$^{\\circ}$. Quoted uncertainties\nare 1$\\sigma$, derived from uncertainties in individual pixel\nmeasurements. Polarization $p$ is corrected for bias (Wardle \\&\nKronberg 1974, eq. A3).\n}\n\n\\end{deluxetable}\n\n\\clearpage\n\n\\evensidemargin -0.0in\n\\oddsidemargin -0.0in\n \n\\plotone{fig1.eps}\n\\clearpage\n\\plotone{fig2.eps}\n\\clearpage\n\\plotone{fig3.eps}\n\\clearpage\n\\plotone{fig4.eps}\n\\clearpage\n\\plotone{fig5.eps}\n\\clearpage\n\n\\end{document}\n"
}
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[
{
"name": "astro-ph0002125.extracted_bib",
"string": "\\begin{thebibliography} {}\n\n\\bibitem {} Antonucci, R. R. J., Kinney, A. L., \\& Ford, H. C. 1989, \\apj, 342, 64\n\n\\bibitem {} Arav, N.\n1997, in ``Mass Ejection from AGN'', ed. N. Arav, I. Shlosman, \\& R. J. Weymann, A.S.P.\nConf. Ser., Vol. 128, p. 208\n\n\\bibitem {} Arav, N., Korista, K. T., de Kool, M., Junkkarinen, V. T., \\& Begelman, M.\n1999, \\apj, 516, 27\n\n\\bibitem {} Arav, N., Shlosman, I., \\& Weymann, R. J. (eds.) 1997, ``Mass Ejection\nfrom AGN'', A.S.P. Conf. Ser., Vol. 128.\n\n\\bibitem {} Barlow, T. A., Hamann, F., \\& Sargent, W. L. W. \n1997, in ``Mass Ejection from AGN'', ed. N. Arav, I. Shlosman, \\& R. J. Weymann, A.S.P.\nConf. Ser., Vol. 128, p. 13\n\n\\bibitem {} Bechtold, J. \\etal\\ 1984, \\apj, 281, 76\n\n\\bibitem {} Beloborodov, A. M., \\& Poutanen, J. 1999, \\apjl, 517, L77\n\n\\bibitem {} Blaes, O., \\& Agol, E. 1996, \\apjl, 369, L41\n\n\\bibitem {} Blaes, O., \\& Shields, G. A. 1999, unpublished\n\n\\bibitem {} Brandt, W. N., Laor, A., \\& Wills, B. J. 1999, \\apj, in press\n (astro-ph/9908016)\n\n\\bibitem {} Chandrasekhar, S. 1960, Radiative Transfer (New York: Dover)\n\n\\bibitem {} Cohen, M. L., Ogle, P. M., Tran, H. D., Vermuellen, R. C., Miller, J. S.,\nGoodrich, R. W., \\& Martel, A. R. 1995, \\apjl, 448, L77\n\n\\bibitem {} Ganguly, R., Churchill, C. W., \\& Charlton, J. C. 1998, \\apjl, 498, L103\n\n\\bibitem {} Goodrich, R. R., \\& Miller, J. S. 1995, \\apjl, 448, L73\n\n\\bibitem {} Hamann, F. 1997, \\apjs, 109, 279\n\n\\bibitem {} Hamann, F., Barlow, T., Cohen, R. D., Junkkarinen, V., \\& Burbidge, E. M.\n1997, in ``Mass Ejection from AGN'', ed. N. Arav, I. Shlosman, \\& R. J. Weymann, A.S.P.\nConf. Ser., Vol. 128, p. 19\n\n\\bibitem {} Hamann, F., \\& Ferland, G. 1993, \\apj, 418, 11\n\n\\bibitem {} Hines, D. C., \\& Wills, B. J. 1995, \\apjl, 448, L69\n\n\\bibitem {} Impey, C., Malkan, M., Webb, W., \\& Petry, C. 1995,\n \\apj, 440, 80\n\n\\bibitem {} Impey, C., \\& Petry, C. 1999, personal communication\n\n\\bibitem {} Impey, C., Petry, C., Malkan, M., \\& Webb, W. 1996,\n \\apj, 463, 473\n\n\\bibitem {} Junkkarinen, V., Beaver, E. A., Burbidge, E. M., Cohen,\nR. D., Hamann, F., \\& Lyons, R. W. 1997, in ``Mass Ejection from AGN'', ed. N.\nArav, I. Shlosman, \\& R. J. Weymann, A.S.P. Conf. Ser., Vol. 128, p. 19\n\n\\bibitem {} Koratkar, A., Antonucci, R., Goodrich, R.\n Bushouse, H., \\& Kinney, A. 1995, \\apj, 450, 501.\n\n\\bibitem {} Koratkar, A., Antonucci, R., Goodrich, R., \\& Storrs, A. 1998, \\apj, 503,\n599\n\n\\bibitem {} Koratkar, A., \\& Blaes, O. 1999, \\pasp, 111, 1\n\n\\bibitem {} Koratkar, A., Kinney, A. L., \\& Bohlin, R. C. 1992, \n\\apj, 400, 435\n\n\\bibitem {} Krolik, J. H., \\& Begelman, M. C. 1986, \\apjl, 308, L55\n\n\\bibitem {} Laor, A., \\& Draine, B. T. 1993, \\apj, 402, 441\n\n\\bibitem {} Laor, A., Netzer, H., \\& Piran, T. 1990, \n\\mnras, 242, 560\n\n\\bibitem {} Lee, H.-W., \\& Blandford, R. D. 1997, \\mnras, 288, 19\n\n\\bibitem {} Mushotzky, R. F. 1999, personal communication\n\n\\bibitem {} Ogle, P. 1997, in ``Mass Ejection\nfrom AGN'', ed. N. Arav, I. Shlosman, \\& R. J. Weymann, A.S.P. Conf.\nSer., Vol. 128, p. 78\n\n\\bibitem {} Ogle, D. C., Cohen, M. H., Miller, J. S., Tran, H. D.,\n Goodrich, R. W., Martel, A. R 1999, \\apjs, 125, 1\n\n\\bibitem {} Richards, G. T., York, D. G., Yanny, B., Kollgaard, R. I.,\nLaurent-Muehleisen, S. A., \\& Vanden Berk, D. E. 1999, \\apj, 513, 576\n\n\\bibitem {} Sargent, W. L. W., Steidel, C. C., \\& Boksenberg, A. 1988, \n \\apjs, 68, 539\n\n\\bibitem {} Sargent, W. L. W., Steidel, C. C., \\& Boksenberg, A. 1989,\n \\apjs, 69, 703\n\n\\bibitem {} Schmidt, M., \\& Green, R. F. 1983, \\apj, 269, 352\n\n\\bibitem {} Schmidt, G. D., \\& Hines, D. C. 1999, \\apj, 512, 125\n\n\\bibitem {} Shields, G. A. 1997, in ``Mass Ejection\nfrom AGN'', ed. N. Arav, I. Shlosman, \\& R. J. Weymann, A.S.P. Conf.\nSer., Vol. 128, p. 214\n\n\\bibitem {} Shields, G. A., Wobus, L., \\& Husfeld, D. 1998, \\apj, 496, 743\n\n\\bibitem {} Steidel, C. C., \\& Sargent, W. L. W., 1992, \\apjs, 80, 1\n\n\\bibitem {} Stockman, H. S., Moore, R. L., \\& Angel, J. R. P. 1984,\n\\apj, 279, 485\n\n\\bibitem {} Telfer, R. C., Kriss, G. A., Zheng, W., Davidsen, A. F., \\& \n Green, R. 1999, \\apj, 509, 132\n\n\\bibitem {} Turnshek, D. A., Kopko, M., Jr., Monier, E., Noll, D., \nEspey, B. R., \\& Weymann, R. J. 1996, \\apj, 463, 110\n\n\\bibitem {} Wampler, E. J., \\& Ponz, D. 1985, \\apj, 298, 448.\n\n\\bibitem {} Wardle, J. F. C. \\& Kronberg, P. P. 1974, \\apj, 194, 254\n\n\\bibitem {} Webb, W., Malkan, M., Schmidt, G., \\& Impey, C., 1993, \n\\apj, 419, 494\n\n\\bibitem {} Weymann, R. J. 1997, in ``Mass Ejection\nfrom AGN'', ed. N. Arav, I. Shlosman, \\& R. J. Weymann, A.S.P. Conf.\nSer., Vol. 128, p. 3\n\n\\bibitem {} Weymann, R. J., Morris, S. L., Foltz, C. B., \n\\& Hewett, P. C. 1991, \\apj, 373, 23\n\n\\bibitem {} Wilkes, B. J., Tananbaum, H., Worrall, D. M., Avni, Y., Oey, M. S., \\&\nFlanagan, J. 1994, \\apjs, 92, 53\n\n\\bibitem {} Zheng, W., Kriss, G., Telfer, R. C., Grimes, J. P., Davidsen, \\& A. F. \n1997, \\apj, 475, 469\n\n\\end{thebibliography}"
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astro-ph0002126
|
Quintessence at Galactic Level?
|
[
{
"author": "T. Matos"
}
] |
Recently it has been proposed that the main contributor to the dark energy of the Universe is a dynamical, slow evolving, spatially inhomogeneous scalar field, called the quintessence. We investigate the behavior of this scalar field at galactic level, trying it as the dark matter in the halos of galaxies. Using an exact solution of the Einstein's equations, we find an excellent concordance between our results and observations.\\
|
[
{
"name": "quint_rev.tex",
"string": "\\documentstyle[aps,epsf]{revtex}\n\n\\begin{document}\n\\draft\n\\title{Quintessence at Galactic Level?}\n\n\\author{T. Matos, and F.\\ S.\\ Guzm\\'an\\footnote{E-mail:\nsiddh@fis.cinvestav.mx}}\n\\address\n {Departamento de F\\'{\\i}sica,\\\\\n Centro de Investigaci\\'on y de Estudios\n Avanzados del IPN,\\\\\n AP 14-740, 07000 M\\'exico D.F., MEXICO.\n }\n\n\\maketitle\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n\\begin{abstract}\nRecently it has been proposed that the main contributor to the dark energy\nof the Universe is a dynamical, slow evolving, spatially inhomogeneous\nscalar field, called the quintessence. We investigate the behavior of this\nscalar field at galactic level, trying it as the dark matter in the halos of\ngalaxies. Using an exact solution of the Einstein's equations, we find an\nexcellent concordance between our results and observations.\\\\\n\\end{abstract}\n\nRecent observations\nin type Ia supernovae have suggesteded the value $\\Omega _{0}\\sim 1$\nconsidering \n$\\Omega _{\\Lambda }\\sim 0.6$ \\cite{perlmutter}. \nFrom the theoretic point of view\nsome cosmologists prefer to explain the observed data coming from Ia\nsupernovae using a decaying cosmological constant \\cite{turnerQ}, which\nsimplest realization is a dynamical, slow evolving, spatially inhomogeneous\nscalar field, called the quintessence \\cite{stein1}. Quintessence is the\ningredient the Universe should contain, in order to explain the Cosmic\nBackground Radiation, large scale structure and the cosmic acceleration \nof the Universe \\cite{stein1,stein2}. The quintessence is postulated as a\nslow varying scalar\nfield in order to obtain equations of state $p=\\omega (t)\\rho $, with\n$\\omega (t)<-0.6$ for this substance. \nHere we investigate further consequences of the scalar\nfield hypothesis. A fundamental question arises: how does such scalar\nfield behaves locally? Given that the scalar field varies\nslowly in time, one can study the space variation alone in a certain region\nof the space-time, neglecting the time variation of the scalar field. Let us\nstart from the scalar field action\n\n\\begin{equation}\nS=\\int d^{4}x\\sqrt{-g}[-\\frac{\\cal R}{\\kappa _{0}}+2(\\nabla \\Phi\n)^{2}-V(\\Phi )]\n\\label{1}\n\\end{equation}\n\n\\noindent \nwhere ${\\cal R}$ is the scalar curvature, $\\Phi $ the scalar field,\n$\\kappa _{0}=8\\pi G$ and $V(\\Phi )=\\Lambda e^{-2\\kappa _{0}\\Phi }.$ As\nan example we present a model of a spiral galaxy by\nconsidering the scalar field of action (\\ref{1}) as the dark matter\ncomponent, for which we use an exponential potential, as found convenient\nfor quintessence \\cite{turnerQ}. In order to do so we suppose the analog\nof quintessence but with the scalar field dependence on the spatial\ncoordinates. \n\\newline\n\nWe assume that the space-time of a galaxy has to be axial symmetric and\nstatic; this last condition is reasonable if one considers that dragging\neffects are unappreciable given the small pressure between stars. The most\ngeneral line element having these properties written in the Papapetrou form\nis\n\n\\begin{equation}\nds^{2}=\\frac{1}{f}[e^{2k}(d\\rho^2 + d\\zeta^2)+W^{2}d\\phi ^{2}]-f\\\nc^{2}dt^{2},\n\\label{metric1}\n\\end{equation}\nwith the functions $%\nf,\\ W$ and $k$ depending only on $\\rho $ and $\\zeta $.\nThe general field equations obtained from (\\ref{1}) are the Klein-Gordon and\nthe Einstein's equations\n\n\\begin{equation}\n\\Phi _{;\\mu }^{;\\mu }-\\frac{1}{4}\\frac{dV}{d\\Phi }=0 \\ , \\ \\ \\ \\ \\ \\\n{\\cal R}_{\\mu \\nu } =\\kappa _{0}[2\\Phi _{,\\mu }\\Phi _{,\\nu\n}+\\frac{1}{2}g_{\\mu\n\\nu }V(\\Phi )] \\label{Eins}\n\\end{equation}\n\n\\noindent where a semicolon means covariant derivation. \nIt has been shown that an exact solution for the\nsystem (\\ref{Eins}) is \\cite{us},\n\n\\begin{equation}\nds^{2}=\\frac{r^{2}+b^{2}\\cos ^{2}\\theta }{f_{0}}(\\frac{dr^{2}}{r^{2}+b^{2}}%\n+d\\theta ^{2})+\\frac{r^{2}+b^{2}\\sin ^{2}\\theta }{f_{0}}d\\phi\n^{2}-f_{0}c^{2}(r^{2}+b^{2}\\sin ^{2}\\theta )dt^{2} \\label{metbl}\n\\end{equation}\n\n\\noindent and the effective energy density is\n\n\\begin{equation}\n\\mu _{DM}=V(\\Phi )=\\frac{4f_{0}}{\\kappa _{0}(r^{2}+b^{2}\\sin ^{2}\\theta )}\n\\label{mu}\n\\end{equation}\n\n\\noindent\nbeing $\\rho =\\sqrt{(r^{2}+b^{2})}\\sin \\theta $, $\\zeta =r\\cos \\theta $\nthe Schwarzschild-like coordinates.\nSolution (\\ref{metbl}) is the space-time of a ``scalar field soup'',\ntherefore it is not asymthotically flat, this means that the dark matter\nhere behaves in a completely relativistic manner, there is no Newtonian\nlimit. It is remarkable the coincidence with the profile of an isothermal\nhalo in the equatorial plane \\cite{begeman}. \nThe geodesic equations for test particles (stars) into the equatorial\nplane of our space-time read\n\n\\begin{equation}\n\\label{chr1}\n\\frac{\\partial ^2 R}{\\partial \\tau ^2} - R \\left(\\frac{\\partial\n\\phi}{\\partial \\tau} \\right)^2 + f_{0}^{2} c^2 R \\left(\\frac{\\partial\nt}{\\partial \\tau}\\right)^2 = 0, \\ \\ \\\n\\frac{\\partial \\phi}{\\partial \\tau} = \\frac{B}{R^2 f_0}, \\ \\ \\\n\\frac{\\partial t}{\\partial \\tau} = \\frac{A}{R^2 f_0}\n\\end{equation}\n\n\\noindent\nwhere $\\tau$ is the proper time of the test particle and\n$R=\\int{ds}= \\sqrt{(r^2+b^2)/f_0}$ is the proper distance of the test\nparticle at the equator from the galactic center. Observe that for a\ncircular trajectory, the first of equations (\\ref{chr1}) reduces to\n\n\\begin{equation}\n\\label{chr2}\n\\dot{\\phi} = f_0 c = \\frac{B}{A}\n\\end{equation}\n\n\\noindent\nwhere the dot means derivative with respect to $t$ and we have used the\nother two geodesic equations for the second identity. $A$ and $B$ are two\nconstants of motion of the test particle we are considering. We can\nestimate the constant $A$ using the invariance of the metric. At the\nequator it is obtained\n\n\\begin{equation}\n\\label{chr3}\nds^2 = \n-\\left(f_0(r^2+b^2) - \\frac{v^2}{c^2} \\right)c^2\ndt^2 = -c^2d\\tau^2\n\\end{equation}\n\n\\noindent\nwith $v^{2}=g_{ij}v^{i}v^{j}$, $v^{i}=(\\dot{r},\\dot{\\theta},\\dot{%\n\\phi})$, \nfrom where it arises an expression for $A$ in terms of the metric\nfunctions\n\n\\begin{equation}\n\\label{chr4}\nA = \\frac{r^2+b^2}{\\sqrt{f_0(r^2+b^2)-v^2/c^2}} \\sim\n\\sqrt{\\frac{r^2+b^2}{f_0}} = R\n\\end{equation}\n\n\\noindent\nsince $v^2 \\ll c^2$. Using (\\ref{chr2}) and (\\ref{chr4}) we obtain an\nestimation for the angular momentum $B =\nv_{DM} R$, which implies $B \\sim f_0 cR$, and therefore $v_{DM}\n\\sim f_0 c\n=constant$ in the regions where the scalar matter dominates. This\nremarkable result qualitatively agrees with observations, it means that\nthe circular velocity of a star far away from the center of the galaxy\n$v_{DM}$ does not depend on the distance $R$. \nFurthermore, the angular momentum of test\nparticles is determined by the luminous matter near the center of the\ngalaxy, where $B=f_0 cR \\sim 0$. \nIn the following we use the approximation $B \\sim f_0 cR$\nalong the whole galaxy.\nThe first of equations (\\ref{chr1}) is the second Newton's law for\nparticles travelling into the scalar field background. We can interpret\n\n\\begin{equation}\n\\label{chr5}\n\\frac{\\partial^2 R}{\\partial \\tau^2} = R \\left(\\frac{\\partial\n\\phi}{\\partial \\tau} \\right)^2 - f_{0}^{2}c^2R\\left(\\frac{\\partial\nt}{\\partial \\tau} \\right)^2 = \\frac{B^2}{R^3 f_{0}^{2}} - c^2\n\\frac{A^2}{R^3} = \\frac{c^2}{R} - c^2 \\frac{A^2}{R^3} \n\\end{equation}\n\n\\noindent\nas the force due to the scalar field background, i.e. $F_{\\Phi} =\nc^2/R-c^2 A^2/R^3$. We know that the luminous matter is completely\nNewtonian. At the other hand, the Newtonian force due to the luminous\nmatter is given by $F_{L} = GM(R)/R^2 = v_{L}^{2}/R = B_{L}^{2}/R^3$,\nwhere $v_L$ is the circular velocity of the test particle due to the\ncontribution of the luminous matter \nand $B_L$ is its corresponding angular\nmomentum per unit of mass. The total force acting on the test particle is\nthen $F = F_{\\Phi} + F_{L}$. For circular trajectories $\\partial^2\nR/\\partial \\tau^2 = F = 0$, then\n\n\\begin{equation}\n\\label{chr6}\n\\frac{B_{L}^{2}}{R^2} - c^2 \\frac{A^2}{R^2} = -c^2\n\\end{equation}\n\nThe constants of motion are the total energy per unit of mass of the test\nparticle and its angular momentum per unit of mass\n\n\\begin{equation}\n(E/m)^2 = \\frac{f_0^2 c^4(r^2 + b^2)^2}{f_0(r^2+b^2) - v^2/c^2}\n, \\ \\ \\ \\\n(l/m)^2 = \\frac{v^2(r^2+b^2)}{f_0(f_0(r^2 + b^2) -v^2/c^2)}\n\\end{equation}\n\n\\noindent \ngiven $l/m=B_L$, and $E/l=c^2f_0 A$. Since $v^{2}\\ll c^{2}$\nthe geodesic equation implies the main result of this work \\cite{us}\n\n\\begin{equation}\nv_{DM}=f_{0}l/m \\label{mean}\n\\end{equation}\n\n\\noindent\ni.e. the velocity is independent of the radius as observed at large radii,\nwhere the dark matter dominates. \nThis velocity should be the contribution of our scalar dark matter to the\nvelocity of test particles, and this is why we label it $v_{DM}$.\nIn order to model completely the rotation curves we introduce a typical\nexponential and thin distribution of luminous matter for the disc, for\nwich it is useful to consider the Universal Rotation Curve expression\n\\cite{persic}\n\n\\begin{equation}\nv_{L}^{2} = v^2(R_{opt})\\beta \\frac{1.97 x^{1.22}}{(x^2 + 0.78^2)^{1.43}}\n\\label{vL}\n\\end{equation}\n\n\n\\noindent\nan approximation that works for a sample of 967 spiral galaxies\n\\cite{persic}. In (\\ref{vL}) $x=r/R_{opt}$, the parameter\n$\\beta=v_{L}(R_{opt})/v(R_{opt})$ being $R_{opt}$ the radius into which it\nis contained the 83\\% of the onservable mass of the galaxy and $v$ is the\nobserved circular velocity. Thus we find the\nexpression $l/m=v_{L}\\bar{r}=v_{L}\\int {ds}=v_{L}\\sqrt{(r^{2}+b^{2})/f_0}$\nfor the\nangular momentum per unit of mass into our space-time. Using this result and\nthe assumption of a galaxy being a virilized system, the total circular\nvelocity of a test particle is\n\n\\begin{equation}\nv_{C}^{2}=v_{L}^{2}+v_{DM}^{2}=v_{L}^{2}(f_{0}(r^{2}+b^{2})+1). \\label{vc}\n\\end{equation}\n\n\n%%%%%%%%%%%%%%%%%%%%% FIGURE %%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{figure}[h]\n\\label{fig1}\n\\vspace*{-2cm}\n\\centerline{ \n\\epsfxsize=9cm \\epsfbox{3198.ps} \n\\hspace*{-3cm}\n\\epsfxsize=9cm \\epsfbox{6503.ps}} \n\\vspace*{-6.5cm}\n\\caption\n{The circular velocity profiles of four galaxies. \nContinious lines represent the total circular velocity ($v_C$),\nlong-dashed the contribution of the dark matter to the total velocity\n($v_{DM}$) and the short-dashed curves the contribution of luminous\nmatter ($v_L$); finally the dots represent the observational data. The\nvalue of $r_D$ is the observationally correponding to each of both\ngalaxies $[$7$]$. \nThe units are in (Km/s) in the vertical axis and\nin (Kpc) in the horizontal one.}\n\\end{figure}\n\n\nThe comparison of this model with experimental results of two spiral\ngalaxies is shown in Fig. 1, where it is evident the great coincidence of\nour results with the observed rotation curves. \nObserve that except the relation $v^2 \\ll c^2$, our main result\n(\\ref{mean}) is exact, and that the contribution of luminous matter to the\ncircular velocity (\\ref{vL}) is a very convincing phenomenological model.\nThis result puts the scalar field as a good candidate to be the dark\nmatter in the halos of galaxies. It is remarkable that if this result is\nconfirmed in some way, the scalar field could represent 35\\% of dark\nmatter and 60\\% of dark energy in the Universe, it means that the\nscalar field could be 95\\% of the matter in the whole Universe as\nsuggested in \\cite{luis}.\n\n\\acknowledgements{\nWe want to thank the relativity group in Jena fot its kind hospitality.\nThis work was partly supported by CONACyT M\\'{e}xico, grant 3697-E.}\n\n\\begin{thebibliography}{9}\n\n\\bibitem{perlmutter} Perlmutter {\\it et al. ApJ} {\\bf 517}(1999), 565. \nA. G. Riess {\\it et al., Astron.J.} {\\bf116}(1998), 1009-1038.\n\n\\bibitem{turnerQ} Dragan Hurterer and Michael S. Turner, astro-ph/9808133.\n\n\\bibitem{stein1} R.R.Caldwell, Rahul Dave and Paul J. Steinhardt, {\\it %\nPhys.Rev. Lett.} {\\bf 80, }(1998), 1582.\n\n\\bibitem{stein2} Ivaylo Zlatev, Limin Wang and Paul J. Steinhardt, {\\it %\nPhys.Rev. Lett.} {\\bf 82, }(1998), 896.\n\n\\bibitem{us} \nF. S. Guzm\\'{a}n, T. Matos and H. Villegas-Brena. {\\it Astron. Nachr.}\n{\\bf \n320} (1999) 3, 97-104.\n\n\\bibitem{begeman} K.G. Begeman, A.H. Broeils and R.H. Sanders. 1991, {\\it %\nMNRAS}, {\\bf 249}, 523-537.\n\n\\bibitem{persic} Massimo Persic, Paolo Salucci and Fulvio Stel. 1996, {\\it %\nMNRAS}, {\\bf 281}, 27-47.\n\n\\bibitem{luis} T. Matos, F. S. Guzm\\'an and L. A. Ure\\~na, \n%{\\it Scalar \n%Fields as Dark Matter in the Universe.} \nastro-ph/9908152.\n\n\\end{thebibliography}\n\n\\end{document}\n"
}
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[
{
"name": "astro-ph0002126.extracted_bib",
"string": "\\begin{thebibliography}{9}\n\n\\bibitem{perlmutter} Perlmutter {\\it et al. ApJ} {\\bf 517}(1999), 565. \nA. G. Riess {\\it et al., Astron.J.} {\\bf116}(1998), 1009-1038.\n\n\\bibitem{turnerQ} Dragan Hurterer and Michael S. Turner, astro-ph/9808133.\n\n\\bibitem{stein1} R.R.Caldwell, Rahul Dave and Paul J. Steinhardt, {\\it %\nPhys.Rev. Lett.} {\\bf 80, }(1998), 1582.\n\n\\bibitem{stein2} Ivaylo Zlatev, Limin Wang and Paul J. Steinhardt, {\\it %\nPhys.Rev. Lett.} {\\bf 82, }(1998), 896.\n\n\\bibitem{us} \nF. S. Guzm\\'{a}n, T. Matos and H. Villegas-Brena. {\\it Astron. Nachr.}\n{\\bf \n320} (1999) 3, 97-104.\n\n\\bibitem{begeman} K.G. Begeman, A.H. Broeils and R.H. Sanders. 1991, {\\it %\nMNRAS}, {\\bf 249}, 523-537.\n\n\\bibitem{persic} Massimo Persic, Paolo Salucci and Fulvio Stel. 1996, {\\it %\nMNRAS}, {\\bf 281}, 27-47.\n\n\\bibitem{luis} T. Matos, F. S. Guzm\\'an and L. A. Ure\\~na, \n%{\\it Scalar \n%Fields as Dark Matter in the Universe.} \nastro-ph/9908152.\n\n\\end{thebibliography}"
}
] |
astro-ph0002127
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MeV-scale Reheating Temperature and Thermalization of Neutrino Background
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[
{
"author": "M. Kawasaki and K. Kohri"
}
] |
The late-time entropy production by the massive particle decay induces the various cosmological effects in the early epoch and modify the standard scenario. We investigate the thermalization process of the neutrinos after the entropy production by solving the Boltzmann equations numerically. We find that if the large entropy are produced at $t \sim 1$ sec, the neutrinos are not thermalized very well and do not have the perfect Fermi-Dirac distribution. Then the freeze-out value of the neutron to proton ratio is altered considerably and the produced light elements, especially $\4he$, are drastically changed. Comparing with the observational light element abundances, we find that $T_R \lesssim 0.7$~MeV is excluded at 95 $\%$ C.L. We also study the case in which the massive particle has a decay mode into hadrons. Then we find that $T_R$ should be a little higher, {i.e.} $T_R \gtrsim$ 2.5 MeV - 4 MeV, for the hadronic branching ratio $B_h = 10^{-2}-1$. Possible influence of late-time entropy production on the large scale structure formation and temperature anisotropies of cosmic microwave background is studied. It is expected that the future satellite experiments (MAP and PLANCK) to measure anisotropies of cosmic microwave background radiation temperature can detect the vestige of the late-time entropy production as a modification of the effective number of the neutrino species $N_{\nu}^{eff}$.
|
[
{
"name": "hrt.tex",
"string": "\\documentstyle[prd,aps,preprint,psfig]{revtex}\n%\\documentstyle[prd,aps,twocolumn]{revtex}\n\n\\def\\4he{\\,{{}^4{\\rm He}}}\n\\def\\li7{\\,{{}^7{\\rm Li}}}\n\\def\\D{\\,{\\rm D}}\n\\def\\T{\\,{\\rm T}}\n\\def\\nutau{\\,{\\nu_{\\tau}}}\n\\def\\numu{\\,{\\nu_{\\mu}}}\n\\def\\nue{\\,{\\nu_e}}\n\\def\\mev{\\,{\\rm MeV}}\n\\def\\gev{\\,{\\rm GeV}}\n\\def\\tev{\\,{\\rm TeV}}\n\\def\\sec{\\,{\\rm sec}}\n\\def\\mb{\\, {\\rm mb}}\n\\newcommand{\\order}{{\\cal O}}\n\n\\begin{document}\n%\\twocolumn[\\hsize\\textwidth\\columnwidth\\hsize\\csname\n%@twocolumnfalse\\endcsname\n%%\n%%\n\\tighten\n\\draft\n%%\n\\title{MeV-scale Reheating Temperature and Thermalization of Neutrino\nBackground}\n%%\n%%\n%%\n%%\n\\author{M. Kawasaki and K. Kohri}\n\\address{Research Center for the Early\nUniverse, School of Science, University of Tokyo, Tokyo 113-0033,\nJapan}\n%%\n\\author{Naoshi Sugiyama}\n\\address{Department of Physics, Kyoto University, Kyoto 606-8502, Japan}\n%%\n\\date{\\today}\n%%\n\n\\maketitle\n\\begin{abstract}\n The late-time entropy production by the massive particle decay\n induces the various cosmological effects in the early epoch and\n modify the standard scenario. We investigate the thermalization\n process of the neutrinos after the entropy production by solving\n the Boltzmann equations numerically. We find that if the large\n entropy are produced at $t \\sim 1$ sec, the neutrinos are not\n thermalized very well and do not have the perfect Fermi-Dirac\n distribution. Then the freeze-out value of the neutron to proton\n ratio is altered considerably and the produced light elements,\n especially $\\4he$, are drastically changed. Comparing with the\n observational light element abundances, we find that $T_R\n \\lesssim 0.7$~MeV is excluded at 95 $\\%$ C.L. We also study the\n case in which the massive particle has a decay mode into hadrons.\n Then we find that $T_R$ should be a little higher, {\\it i.e.} \n $T_R \\gtrsim$ 2.5 MeV - 4 MeV, for the hadronic branching ratio\n $B_h = 10^{-2}-1$. Possible influence of late-time entropy\n production on the large scale structure formation and temperature\n anisotropies of cosmic microwave background is studied. It is\n expected that the future satellite experiments (MAP and PLANCK)\n to measure anisotropies of cosmic microwave background radiation\n temperature can detect the vestige of the late-time entropy\n production as a modification of the effective number of the\n neutrino species $N_{\\nu}^{\\rm eff}$.\n\\end{abstract}\n\n\\pacs{98.80.Cq, 98.70.Vc, KUNS-1639}\n\n%]\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Introduction}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nIn the standard big bang cosmology it had been assumed tacitly that\nthe universe was dominated by the thermal radiation at the early\nepoch. Even in the paradigm of the modern cosmology it is commonly\nbelieved that thermal radiation was produced by the reheating process\nafter the primordial inflation and they dominated the energy of the\nuniverse at sufficiently early epoch. Here we ask, ``How early should\nthe universe be dominated by radiation in order to success the\nstandard big bang cosmology?''. We could say that the energy of the\nuniverse should be dominated by the radiation at least before the\nbeginning of the big bang nucleosynthesis (BBN) epoch. In this paper\nwe answer the above question.\n\nThe various models of the modern particle physics beyond the standard\nmodel predicts a number of unstable massive particles which have long\nlifetimes and decays at about BBN epoch. The energy density of the\nnon-relativistic particles or the oscillation energy density of the\nscalar fields (inflaton and so on) decreases as $\\rho_{NR}(t) \\propto\na(t)^{-3}$, where $a(t)$ is a scale factor. On the other hand since\nthe radiation energy density decreases more rapidly $\\rho(t)\\propto\na(t)^{-4}$, if the energy density of the massive non-relativistic\nparticles or the oscillating scalar fields is large enough, it\nimmediately dominates the universe as it expands, and the universe\nnecessarily becomes matter-dominated until the cosmic time reaches to\ntheir lifetime. When the particles decay into standard particles (e.g.\nphoton and electron), they produce the large entropy and the universe\nbecomes radiation-dominated again. It is expected that such\nprocess would change the initial condition for the standard big bang\nscenario. We call the process ``late-time entropy production''.\n\nNow we have some interesting candidates for late-time entropy\nproduction in models based on supersymmetry (SUSY). It is known that\ngravitino and Polonyi field which exist in local SUSY ({\\it i.e.}\nsupergravity ) theories have masses of $\\sim {\\cal O}(100{\\rm\nGeV}-10{\\rm TeV})$~\\cite{Nilles}. In addition they have long lifetimes\nbecause they interact with the other particle only through gravity.\nFor example, since Polonyi field~\\cite{Polonyi} which has a heavy mass\n$\\sim 10$~TeV cannot be diluted by the usual inflation, it immediately\ndominates the universe and decays at the BBN epoch. Moreover it is also\nknown that in the superstring theories there exist many light fields\ncalled dilaton and moduli which have similar properties to the Polonyi\nfield.\n\nRecently Lyth and Stewart~\\cite{Lyth} considered a mini-inflation\ncalled ``thermal inflation'' which dilutes the above dangerous scalar\nfields. In the thermal inflation scenario, however, the flaton field\nwhich is responsible for the thermal inflation decays at late times.\nIn particular, if Polonyi (moduli) mass is less than $\\sim 1$~GeV\nwhich is predicted in the framework of gauge-mediated SUSY breaking\nmodels~\\cite{Giudice}, the sufficient dilution requires that the\nflaton decays just before BBN~\\cite{Asaka}. Thus, in thermal\ninflation models, one should take care of the late-time entropy\nproduction.\n\nTo keep the success of BBN, any long-lived massive particles or the\ncoherent oscillation of any scalar fields which dominate the universe\nat that time must finally decay into the standard particles before the\nbeginning of BBN. Moreover the decay products would have to be quickly\nthermalized through scatterings, annihilations, pair creations and\nfurther decays and make the thermal bath of photon, electron and\nneutrinos. Concerning photons and electrons which electromagnetically \ninteract, the interaction rate is much more rapid than the\nHubble expansion rate at that time. Therefore it is expected that the\nphoton and electron which are produced in the decay and subsequent\nthermalization processes are efficiently thermalized. The problem is\nthat neutrinos can interact only through the weak interaction. In the\nstandard big bang cosmology the neutrinos usually decouple from the\nelectromagnetic thermal bath at about $T \\simeq 2-3$MeV. Therefore it\nis approximately inferred that they can not be sufficiently\nthermalized at the temperature $T \\lesssim $ a few MeV. Namely the\nreheating temperature after the entropy production process should be\nhigh enough to thermalize the neutrinos. Though people had ever used\nthe rough constraints on the reheating temperature between 1MeV -\n10MeV, in the previous paper~\\cite{kks} we pointed out that the\nneutrino thermalization is the most crucial for the successful BBN. In\nthis paper we describe the detail of the method to obtain the neutrino\nspectrum and the formulations to integrate a set of Boltzmann\nequations numerically , and we study the constraint on the reheating\ntemperature using the obtained neutrino spectrum and the full BBN\nnetwork calculations with the revised observational light element\nabundances.\n\nThe above constraint is almost model-independent and hence\nconservative because we only assume that the massive particle decay\nproduces the entropy. However, a more stringent constraint can be\nobtained if we assume a decay mode into quarks or gluons. In this case\nsome modifications are needed for the above description. When the\nhigh energy quark-antiquark pairs or gluons are emitted, they\nimmediately fragment into a lot of hadrons (pions , kaons, protons,\nneutrons, {\\it etc}.). It is expected that they significantly\ninfluence the freeze-out value of neutron to proton ratio at the\nbeginning of BBN through the strong interaction with the ambient\nprotons and neutrons. In the previous paper~\\cite{kks} we did not\nconsider such hadron injection effects on BBN. Therefore we carefully\ntreat the hadron injection effects in the present paper.\n\nFor another constraint, the late-time entropy production may induce\nthe significant effects on the anisotropies of the cosmic microwave\nbackground radiations (CMB). Lopez {\\it et al.}~\\cite{Lopez} pointed\nout that the CMB anisotropies are very sensitive to the equal time of\nmatter and radiation. When the reheating temperature is so low that\nneutrinos do not be sufficiently thermalized, the radiation density\nwhich consists of photon and neutrinos becomes less than that in the\nstandard big bang scenario. It may give distinguishable signals in the\nCMB anisotropies as a modification of the effective number of neutrino\nspecies $N_{\\nu}^{\\rm eff}$. With the present angular resolutions and\nsensitivities of COBE observation~\\cite{COBE} it is impossible to set\na constraint on $N_{\\nu}^{\\rm eff}$ but it is expected that future\nsatellite experiments such as MAP~\\cite{MAP} and PLANCK~\\cite{PLANCK}\nwill gives us a useful information about $N_{\\nu}^{\\rm eff}$. In\naddition the above effect may also induce the signals in the observed\npower spectrum of the density fluctuation for the large scale\nstructure as a modification of the epoch of the matter-radiation\nequality.\n\n\nThe paper is organized as follows. In Sec.~II we introduce the\nformulation of the basic equations and the physical parameters. In\nSec.~III we briefly review the current status of the observational\nlight element abundances. In Sec.~IV we study the spectra of the\nelectron neutrino and the mu(tau)-neutrino by numerically solving the\nBoltzmann equations, and the constraints from BBN are obtained there.\nIn Sec~V we investigate the additional effects in the hadron injection\nby the massive particle decay. In Sec.~VI we consider the another\nconstraints which come from observations for large scale structures\nand anisotropies of CMB. Sec~VII is devoted to conclusions. In\nAppendix we introduce the method of the reduction for the nine\ndimension integrals into one dimension.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Formulation of Neutrino Thermalization}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\label{sec:formulation}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Reheating Temperature}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\label{sec:tr}\n\nIn order to discuss the late-time entropy production process, we\nshould formulate the equations which describe the physical process.\nHere the reheating temperature $T_{R}$ is an appropriate parameter to\ncharacterize the late-time entropy production. We define the\nreheating temperature $T_{R}$ by\n%%\n\\begin{equation}\n \\label{eq:3h}\n \\Gamma \\equiv 3 H(T_{R}),\n\\end{equation}\nwhere $\\Gamma$ is the decay rate (=$\\tau^{-1}$) and $H(T_{R})$ is\nthe Hubble parameter at the decay epoch (t = $\\tau$).~\\footnote{Since the\n actual decay is not instantaneous, the matter-dominated universe\n smoothly changes into radiation-dominated one. Thus it is rather\n difficult to clearly identify the reheating temperature by observing\n the evolution of the cosmic temperature. Instead we ``define'' the\n reheating temperature formally by Eq.~(\\ref{eq:3h})} The Hubble\nparameter is expressed by\n%%\n\\begin{equation}\n H = \\left(\\frac{g_{*}\\pi^2}{90}\\right)^{1/2}\n \\frac{T_{R}^2}{M_{G}},\n\\end{equation}\n%%\nwhere $g_{*}$ is the statistical degrees of freedom for the massless\nparticles and $M_{G}$\nis the reduced Plank mass ($= 2.4\\times 10^{18}$GeV). Then the\nreheating temperature is given by\n%%\n\\begin{equation}\n \\label{eq:rtemp}\n T_{R} = 0.554 \\sqrt{\\Gamma M_{G}}.\n\\end{equation}\n%%\nHere we have used $g_{*} = 43/4$. From Eq.~(\\ref{eq:rtemp}), we can\nsee that the reheating temperature has the one to one correspondence\nwith the lifetime of the parent massive particle.\n\nHere we define the effective number of neutrino species\n$N_{\\nu}^{\\rm eff}$ as a parameter which characterize the time evolution of\nthe energy density of neutrinos. Here $N_{\\nu}^{\\rm eff}$ is defined by\n%%\n\\begin{equation}\n \\label{eq:n-eff}\n N_{\\nu}^{\\rm eff}\n \\equiv\n \\frac{\\rho_{\\nu_e}+\\rho_{\\nu_{\\mu}}+\\rho_{\\nu_{\\tau}}}{\\rho_{\\rm\n std}},\n\\end{equation}\n%%\nwhere $\\rho_{\\rm std}$ is the total neutrino energy density in the\nstandard big bang model ({\\it i.e.} no late-time entropy production and\nthree neutrino species).\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Basic Equations}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\label{sec:fundamental}\n\nWhen a massive particle $\\phi$ which is responsible for the late-time\nentropy production decays, all emitted particles except neutrinos are\nquickly thermalized and make a thermal bath with temperature $\\sim\nT_{R}$. For relatively low reheating temperature $T_{R} \\lesssim\n10$MeV neutrinos are slowly thermalized. Since in realistic situations\nthe decay branching ratio into neutrinos is very small, we assume that\nneutrinos are produced only through annihilations of electrons and\npositrons, {\\it i.e.} $e^{+} + e^{-} \\rightarrow \\nu_{i} +\n\\bar{\\nu}_{i} ( i= e, \\mu, \\tau)$. The evolution of the distribution\nfunction $f_{i}$ of the neutrino $\\nu_{i}$ is described by the\nmomentum dependent Boltzmann equation~\\cite{bernstein}:\n%%\n\\begin{equation}\n \\label{eq:Boltzmann}\n \\frac{\\partial f_{i}(\\mbox{\\boldmath $p$},t)}{\\partial t}\n - H(t) \\mbox{\\boldmath $p$}\\frac{\\partial f_{i}(\\mbox{\\boldmath\n $p$},t)}{\\partial \\mbox{\\boldmath $p$}}\n = C_{i, \\rm coll}\n\\end{equation}\nwhere the right hand side is the total collision term.~\\footnote{\nThe integrated Boltzmann equation~\\cite{BBF} is not adequate in the present\nproblem. As we show in Sec.~\\ref{sec:neu_nu}, the spectral shape of\nthe momentum distribution obtained by our scheme is much different\nfrom the equilibrium one. It should be noticed that the integrated\nBoltzmann equation assumes that the shape of the momentum distribution\nis the same as the equilibrium one. Thus we should solve the momentum\ndependent Boltzmann equation.} When the reaction is two bodies\nscattering $1 + 2 \\rightarrow 3 + 4$, it is given by the expression,\n%%\n\\begin{eqnarray}\n \\label{eq:collision}\n C_{i, \\rm coll} ={ 1\\over 2E_1}\\sum \\int && {d^3 p_2 \\over 2E_2 (2\\pi)^3}\n{d^3 p_3 \\over 2E_3 (2\\pi)^3}{d^3 p_4 \\over 2E_4 (2\\pi)^3}\n\\nonumber \\\\\n && \\times(2\\pi)^4\\delta^{(4)} (p_1+p_2-p_3-p_4)\\Lambda(f_1,f_2,f_3,f_4)\n S\\, |M|^2_{12\\rightarrow 34},\n\\end{eqnarray}\n%%\nwhere $|M|^2$ is the scattering amplitude summed over spins of all\nparticles, $S$ is the symmetrization factor which is 1/2 for identical\nparticles in initial and final states, $\\Lambda = f_3 f_4\n(1-f_1)(1-f_2)-f_1 f_2 (1-f_3)(1-f_4)$ is the phase space factor\nincluding Pauli blocking of the final states. Then the total collision\nterm $C_{i, \\rm coll}$ is expressed by,\n%%\n\\begin{equation}\n \\label{eq:annscat}\n C_{i, \\rm coll} = C_{i, \\rm ann} + C_{i, \\rm scat},\n\\end{equation}\n%%\nwhere $C_{i,\\rm ann}$ is the collision term for annihilation processes\nand $C_{i, \\rm scat}$ is collision term for elastic scattering\nprocesses. Here we consider the following processes:\n%%\n\\begin{eqnarray}\n \\nu_{i} + \\nu_{i}& \\leftrightarrow & e^{+} + e^{-},\n \\nonumber \\\\\n \\nu_{i} + e^{\\pm}& \\leftrightarrow & \\nu_{i} + e^{\\pm}.\n \\nonumber\n\\end{eqnarray}\n%%\nIn this paper we have treated neutrinos as Majorana ones ({\\it i.e.},\n$\\nu = \\bar{\\nu}$). It should be noted that there are no differences\nbetween Majorana neutrinos and Dirac ones as long as they are\nmassless, and since the temperature is $\\order(\\mev)$ at least in this\nsituation, we could have treated them as if they were massless\nparticles. The relevant reactions are presented in\nTable~\\ref{table:Mnue} for $\\nu_e$ and Table~\\ref{table:Mnumu} for\n$\\nu_{\\mu}$ and $\\nu_{\\tau}$.~\\footnote{Here we neglect the neutrino\nself-interactions. It may lead to underestimate the kinetic\nequilibrium rate for high reheating temperatures. However, we think\nthat this effect does not change the results very much. The\ninteractions between electrons and neutrinos are the most important\nbecause they transfer the energy of the thermal bath to neutrinos. The\nself-interactions of the neutrinos cannot increase the energy density\nof neutrinos but mainly change their momentum distribution.\nFurthermore, the neutrino number densities are much smaller than the\nelectron number density at low reheating temperature with which we are\nconcerned. Thus differences caused by the neutrino self interactions\nare expected to be small.}\n\nThe collision terms are quite complicated and expressed by nine\ndimensional integrations over momentum space. However, if we neglect\nelectron mass and assume that electrons obey the Boltzmann\ndistribution $e^{-p/T}$, the collision terms are simplified to one\ndimensional integration form.~\\footnote{The errors due to\nneglecting the electron mass is small and the deviation is just a few\npercent. We show the reasons as follows. The difference between\nFermi-Dirac and Maxwell-Boltzmann distribution ``$df$'' is less than\none at most $df < 1.0$. The week interaction rate is almost expressed\nby $\\langle\\sigma v\\rangle n_e/ H(t)$, where $\\langle\\sigma v\\rangle\n\\sim G_F^2 m_e^2$ and $n_e$ is an electron number density. Then the\nerror is at most estimated by, $\\langle\\sigma_W v\\rangle n_e/\nH(t)\\times df \\lesssim 10^{-2}$ (for $T \\lesssim$ 0.5MeV). Therefore\nthe deviation is a few percent and the neglecting the electron mass\ndoes not change the results. The other methods of the approximation to\nreduce the integral from nine to two dimensions in which the electron\nmass is not neglected are presented in ref.~\\cite{HM,DHS}} Then\n$C_{i,\\rm ann}$ is given by~\\cite{SWO,Kawasaki}\n%%\n\\begin{equation}\n \\label{eq:C-ann}\n C_{i, \\rm ann} = - \\frac{1}{2\\pi^2}\\int p'^2_idp'_i\n (\\sigma v)_i (f_i(p_i) f_i(p'_i)- f_{eq}(p_i)f_{eq}(p'_i)),\n\\end{equation}\n%%\nwhere $f_{eq} (= 1/(e^{p_i/T} +1))$ is the equilibrium distribution and\n$(\\sigma v)_i$ is the differential cross sections given by\n%%\n\\begin{eqnarray}\n \\label{eq:cross}\n (\\sigma v)_{e} & = & \\frac{4G^2_F}{9\\pi}\n (C_V ^2 + C_A ^2)pp',\\\\\n (\\sigma v)_{\\mu,\\tau} & = & \\frac{4G^2_F}{9\\pi}\n (\\tilde{C_V}^2 + \\tilde{C_A}^2)pp',\\\\\n\\end{eqnarray}\n%%\nwhere we take $C_V=\\frac12 + 2\\sin^2\\theta_W$, $C_A= \\frac12 $,\n $\\tilde{C_V}=C_V-1$ ($\\tilde{C_A}=C_A-1$) and $\\theta_W$ is Weinberg\nangle ($\\sin^2\\theta_W \\simeq 0.231$)~\\cite{PDG}.\n\nAs for elastic scattering processes, $C_{i,scat}$ is also simplified to one\ndimensional integration (see Appendix), and it is expressed as\n%%\n\\begin{eqnarray}\n C_{i, scat} & = & \\frac{G_F^2}{2\\pi^3}(C_V^2+C_A^2)\n \\left[ -\\frac{f_i}{p_i^2}\n \\left( \\int_0^{p_i}dp'_i F_1(p_i,p'_i)(1-f_i(p'_i))\n + \\int^{\\infty}_{p_i}dp'_i\n F_2(p_i,p'_i)(1-f_i(p'_i)\\right)\\right.\n \\nonumber \\\\\n \\label{eq:C-scat}\n & & \\left. + \\frac{1-f_i(p_i)}{p_i^2}\n \\left(\\int_0^{p_i}dp'_i B_1(p_i,p'_i)f_i(p'_i)\n + \\int^{\\infty}_{p_i}dp'_i B_2(p_i,p'_i)f_i(p'_i)\\right)\\right],\n\\end{eqnarray}\n%%\nwhere $(C_V^2+C_A^2)$ should be replaced by\n$(\\tilde{C_V}^2+\\tilde{C_A}^2)$ for $i=\\mu, \\tau$, and the functions\n$F_1, F_2, B_1, B_2$ are given by\n\n%%\n\\begin{eqnarray}\n F_1(p, p') & = & D(p, p') + E(p, p')e^{-p'/T},\n \\nonumber\\\\\n F_2(p, p') & = & D(p', p)e^{(p-p')/T} + E(p, p')e^{-p'/T},\n \\nonumber\\\\\n B_1(p,p') & = & F_2(p',p), ~~B_2(p,p') = F_1(p',p),\n\\end{eqnarray}\n%%\nwhere\n%%\n\\begin{eqnarray}\n D(p, p') & = & 2T^4(p^2 + p'^2 + 2T(p-p')+4T^2),\n \\nonumber\\\\\n E(p, p') & = & - T^2[p^2p'^2 + 2pp'(p+p')T\n \\nonumber\\\\\n & & + 2(p+p')^2T^2 + 4(p+p')T^3 + 8T^4].\n\\end{eqnarray}\n%%\n\nTogether with the above Boltzmann equations, we should\nsolve the energy-momentum conservation equation in the expanding universe:\n\n%%\n\\begin{equation}\n \\label{energy_conservation}\n \\frac{d\\rho(t)}{dt} = - 3 H(t) (\\rho(t)+P(t)),\n\\end{equation}\n%%\nwhere $\\rho(t)=\\rho_{\\phi}+\\rho_{\\gamma}+\\rho_{e}+\\rho_{\\nu}$ is the\ntotal energy density of $\\phi$, photon, electron and neutrinos and it\nis given by\n%%\n%\\begin{equation}\n% \\label{rho_tot}\n% \\rho(t) = \\rho_{\\phi}(t) + \\rho_{\\gamma}(t) + \\rho_{e}(t) +\n% \\rho_{\\nu}(t)\n%\\end{equation}\n%%\n\\begin{equation}\n \\label{rho_tot}\n \\rho(t) = \\rho_{\\phi}(t) + {\\pi^2 T^4_\\gamma\\over 15} + {2\\over \\pi^2} \n\\int {dq q^2\n E_e\\over \\exp {(E_e/T_\\gamma)} +1 } + {1\\over \\pi^2}\n \\int dq q^3 f_{\\nu_e}(q) + {2\\over \\pi^2} \\int dq q^3 f_{\\nu_\\mu}(q),\n\\end{equation}\n%%\nwhere $E_e = \\sqrt{q^2 + m^2_e}$ is the electron energy.\n$P(t) \\equiv P_{\\gamma}(t)+P_{e^{\\pm}}(t)+P_{\\nu}(t)$ is the total pressure,\n%%\n\\begin{equation}\n \\label{eq:pressure}\n P(t) = {\\pi^2 T^4_\\gamma\\over 45} + {2\\over \\pi^2} \\int {dq q^4\n \\over 3 E_e [\\exp (E_e/T_\\gamma) +1 ]} + {1\\over\n 3\\pi^2} \\int dq q^3 f_{\\nu_e}(q) + {2\\over 3\\pi^2} \\int dq q^3\n f_{\\nu_\\mu}(q).\n\\end{equation}\n%%\n%\\begin{equation}\n% \\label{tot_pressure}\n% P(t) = P_{\\gamma}(t) + P_{e}(t) + P_{\\nu}(t),\n%\\end{equation}\n$H(t)$ is the Hubble parameter,\n%%\n\\begin{equation}\n \\label{eq:hubble}\n H(t) = \\frac{\\dot{a}(t)}{a(t)} = \\frac{1}{\\sqrt{3}M_G}\\sqrt{\\rho(t)}.\n\\end{equation}\n%%\nThe time evolution equation of $\\rho_{\\phi}$ is given by\n%%\n\\begin{equation}\n \\frac{d\\rho_{\\phi}}{dt} = -\\Gamma\\rho_{\\phi} -3H\\rho_{\\phi}.\n \\label{eq:rho_phi}\n\\end{equation}\n%%\nPractically we solve the time evolution of the photon temperature\ninstead of Eq.~(\\ref{energy_conservation}),\n%%\n\\begin{eqnarray}\n \\label{eq:dTdt}\n \\frac{d T_{\\gamma}}{d t} & = & -\n \\frac{- \\rho_{\\phi}/\\tau_{\\phi} +\n 4H\\rho_{\\gamma}+3H(\\rho_{e^{\\pm}}+P_{e^{\\pm}})+4H\\rho_{\\nu} +\n d\\rho_{\\nu}/dt }{\\partial\\rho_{\\gamma}/\\partial T_{\\gamma}|_{a(t)} +\n \\partial\\rho_{e^{\\pm}}/\\partial T_{\\gamma}|_{a(t)}},\n\\end{eqnarray}\n%%\ntogether with Eqs.~(\\ref{eq:Boltzmann}),~(\\ref{eq:hubble})\nand ~(\\ref{eq:rho_phi}).\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Observational light element abundances}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\label{sec:obs}\nIn this section we briefly show the current status of the\nobservational light element abundances. Concerning the deuterium\nabundance, the primordial D/H is measured in the high redshift QSO\nabsorption systems. For the most reliable D abundance, we adopt the\nfollowing value which is obtained by the clouds at z = 3.572 towards\nQ1937-1009 and at z = 2.504 towards Q1009+2956~\\cite{BurTyt},\n%%\n\\begin{equation}\n \\label{lowd}\n {\\rm D/H} = (3.39 \\pm 0.25) \\times 10^{-5}.\n\\end{equation}\nOn the other hand, recently the high deuterium abundance is reported\nin relatively low redshift absorption systems at z = 0.701 towards\nQ1718+4807~\\cite{webb}, ${\\rm D/H} = (2.0 \\pm 0.5) \\times 10^{-4}$.\nAnother group also observes the clouds independently~\\cite{tyt_high}.\nHowever, because they do not have full spectra of the Lyman series,\nthe analyses would be unreliable. More recently Kirkman {\\it et\nal.}~\\cite{kirkman} observed the quasar absorption systems at z = 2.8\ntowards Q0130-4021 and they obtain the upper bound, D/H $\\lesssim 6.7\n\\times 10^{-5}$. Moreover Molaro {\\it et al.} reported D/H $\\simeq\n1.5 \\times 10^{-5}$ which was observed in the absorber at z = 3.514\ntowards APM 08279+5255 although it has the large systematic errors in\nthe hydrogen column density~\\cite{MBCV}. Considering the current\nsituation, we do not adopt the high deuterium value in this paper.\n%Here, for high D\n%we adopt the following value,\n%%\n%\\begin{equation}\n% \\label{highd}\n% D/H = (2.0 \\pm 0.5) \\times 10^{-4}.\n%\\end{equation}\n%%\n\nThe primordial $^4$He mass fraction $Y_p$ is observed in the low\nmetalicity extragalactic HII regions. Since $^4$He is produced with\nOxygen in the star, the primordial value is obtained to regress to the\nzero metalicity O/H $\\rightarrow 0$ for the observational data. Using\nthe 62 blue compact galaxies (BCG) observations, it was reported that\nthe primordial $Y$ is relatively `` low'', $Y_p \\simeq\n0.234$~\\cite{OliSkiSte}. However, recently it is claimed that HeI\nstellar absorption is an important effect though it was not included\nin the previous analysis~\\cite{Izo} properly. They found the\nrelatively ``high'' primordial value, $Y_p = 0.245 \\pm 0.004$. More\nrecently Fields and Olive~\\cite{FieOLi} also reanalyze the data\nincluding the HeI absorption effect and they obtain\n%%\n\\begin{equation}\n \\label{FieOLi}\n Y_p=0.238 \\pm (0.002)_{stat} \\pm (0.005)_{syst},\n\\end{equation}\nwhere the first error is the statistical uncertainty and the second\nerror is the systematic one. We adopt the above value as the\nobservational $Y_p$.\n\nThe primordial $^7$Li/H is observed in the Pop II old halo stars. In\ngeneral a halo star whose surface effective temperature is low (the\nmass is small), has the deep convective zone. For such a low\ntemperature star, the primordial $^7$Li is considerably depleted in\nthe warm interior of the star. On the other hand for the high\ntemperature stars ($T_{eff} \\gtrsim 5500$K), it is known that the\nprimordial abundance is not changed and they have a ``plateau''of the\n$^7$Li as a function of the effective temperature. In addition, though\nit is also known that $^7$Li/H decreases with decreasing Fe/H, $^7$Li\nstill levels off at lower metalicity, [Fe/H]$\\lesssim -1.5$, in the\nplateau stars. We adopt the recent measurements which are observed by\nBonifacio and Molaro~\\cite{BonMol}. They observed 41 old halo stars\nwhich have the plateau. We take the additional larger systematic\nerror, because there may be underestimates in the stellar depletion\nand the production by the cosmic ray spallation. Then we obtain\n%%\n\\begin{equation}\n \\label{li7}\n {\\rm log_{10}(^7Li/H)} =-9.76 \\pm (0.012)_{stat} \\pm (0.05)_{syst}\n \\pm (0.3)_{add}.\n\\end{equation}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Neutrino Thermalization and BBN}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\label{sec:neu_nu}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Time evolution of Neutrino spectrum}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\label{sec:neutrino}\n{The evolution of the cosmic temperature $T$ is shown in\nFig.~\\ref{fig:temp}~(a) for $T_{R}=10$~MeV, and (b) for $T_{R}=2$~MeV.\nIn Fig.~\\ref{fig:temp}~(a), it is seen that the temperature decreases\nslowly as $t^{-1/4}$, {\\it i.e.} $a^{-3/8}$ before the decay epoch,\n$t \\simeq \\Gamma^{-1}(\\simeq 5\\times10^{-2}\\sec)$ which corresponds to\n$T_{R}=10$~MeV. This is because the actual decay is not instantaneous\nand $\\phi$ decays into radiation continuously at the rate\n$\\Gamma$~\\cite{Kolb-Turner}. Then The universe is still in M.D. After\nthe decay epoch $t \\gg\\Gamma^{-1}$, all $\\phi$-particles decay and the\ntemperature decreases as $a^{-1}$ and $t^{-1/2}$. Then the universe\nbecomes radiation-dominated epoch. Since at the temperature $T\n\\lesssim 0.5$MeV ($t \\gtrsim 3 \\sec$), electrons and positrons\nannihilate into photons $e^+e^- \\rightarrow 2 \\gamma$, the temperature\nis slightly heated. From Fig.~\\ref{fig:temp}~(b) we can see that the\ntemperature decreases as $t^{-1/4}$ until the decay epoch ($t \\lesssim\n0.1 \\sec)$ which corresponds to $T_{R}=2$~MeV. After the decay epoch,\nthe temperature decreases as $t^{-1/2}$ (R.D.). In the actual\ncomputation we take a initial condition that there exists the net\nradiation energy density though the universe is in M.D. This\nrepresents the situation that the massive particle necessarily\ndominated the universe as it expands. On the other hand even if there\nare at first no radiation $\\rho_R \\simeq 0, {\\it i.e.} T \\simeq 0$\nwhich corresponds to the initial condition of the oscillation epoch\nafter the primordial inflation or thermal inflation, the cosmic\ntemperature immediately tracks the same curve $t^{-1/4}$ and then\ntheir decay establish the radiation dominated universe $T \\propto\nt^{-1/2}$. Therefore our treatment is quite a general picture for each\nentropy production scenario and it does not depend on whether the net\ninitial radiation energy exists or not, only if once the unstable\nnon-relativistic particles dominate the energy density of the\nuniverse.\n\nIn Fig.~\\ref{fig:rho-nu} we show the evolutions of $\\rho_{\\nu_e}$ and\n$\\rho_{\\nu_{\\mu}}$ (=$\\rho_{\\nu_{\\tau}}$) (a) for $T_{R} = 10$~MeV and\n(b)$2$~MeV. From Fig.~\\ref{fig:rho-nu}(a) we can see that if $T_{R} =\n10$~MeV, cosmic energy density is as same as the case of standard big\nbang cosmology. As shown in Fig.~\\ref{fig:rho-nu}(b), however, the\nenergy density of each neutrino species for $T_{R} = 2$~MeV is smaller\nthan the case of standard scenario. Since the electron neutrinos\ninteract with electrons and positrons through both charged and neutral\ncurrents, they are more effectively produced from the thermal bath\nthan the other neutrinos which have only neutral current interactions.\nThe final distribution functions $f_e$ and $f_{\\mu} (=f_{\\tau})$ are\nshown in Fig.~\\ref{fig:distribution} (a) for $T_{R} = 10$~MeV and (b)\n$2$~MeV. For $T_{R} = 10$~MeV, each neutrino is thermalized well and\nthe perfect Fermi-Dirac distribution is established. For $T_{R} =\n2$~MeV, however, the distributions are not thermal equilibrium\nforms.~\\footnote{As we noted in Sec.~\\ref{sec:formulation}, we must\nnot use the integrated Boltzmann equation instead of the momentum\ndependent Boltzmann equation in the present problem because the former\nassumes the equilibrium distribution. To see this, let us define the\nratio $R_E$ for a neutrino species by $R_E =\n(\\rho_{\\nu}/n_{\\nu})/(3.151\\tilde{T_{\\nu}})$, where $\\rho_{\\nu}$ is\nthe neutrino energy density, $n_{\\nu}$ is the neutrino number density,\n$\\tilde{T_{\\nu}}$ is the effective neutrino temperature which is\ndefined by the neutrino number density as, $\\tilde{T_{\\nu}} \\equiv\n\\left( 2\\pi^2 /(3 \\zeta(3)) n_{\\nu} \\right)^{1/3}$. Here both\n$\\rho_{\\nu}$ and $n_{\\nu}$ are computed by integrating the neutrino\ndistribution function which is obtained by solving the momentum\ndependent Boltzmann equation. Approximately $R_E$ represents a ratio\nof the mean energy per a neutrino to the thermal equilibrium one. If\nthe neutrino is in thermal equilibrium, $R_E$ is unity. In the case\nof the integrated Boltzmann equation, because it is assumed that the\nshape of the neutrino distribution is the same as the equilibrium one\nat any times, $R_E$ is necessarily unity. On the other hand, in the\ncase of our scheme, i.e. the momentum dependent Boltzmann equation,\n$R_E$ can not be unity. We have computed the ratio $R_E$ in some\nrepresentative reheating temperatures for electron neutrino and have\nfound that they deviated from unity more at the lower reheating\ntemperatures, $R_E$ = 1.00, 1.03 and 1.50 (for $T_R$ = 10 MeV, 3 MeV\nand 1 MeV). Moreover at the lower reheating temperature than 1 MeV,\nthe deviation is much larger. This result tells us that the neutrino\ndistribution deviates from the thermal equilibrium shape considerably\nat the low reheating temperatures and we should solve the momentum\ndependent Boltzmann equation. $R_E$ has a tendency to increase as the\nreheating temperature decreases. This is because neutrinos are\nproduced by the annihilation of electrons-positron pairs whose mean\nenergy per one particle is larger than that of neutrinos.}\n\nIn Fig.~\\ref{fig:tr_nnu} we can see the change of the effective number\nof neutrino species $N_{\\nu}^{\\rm eff}$ as a function of the reheating\ntemperature $T_{R}$. If $T_{R} \\gtrsim 7$ MeV, $N_{\\nu}^{\\rm eff}$ is\nalmost equal to three and neutrinos are thermalized very well. We can\nregard that it corresponds to the initial condition which has ever\nbeen used for the standard big bang cosmology. On the other hand, if\n$T_{R} \\lesssim 7$ MeV, $N_{\\nu}^{\\rm eff}$ becomes smaller than\nthree.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Neutrino thermalization and neutron to proton ratio}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\label{sec:nu_np}\nIf the neutrinos are not thermalized sufficiently and do not have the\nperfect Fermi-Dirac distribution, {\\it i.e.} in this case there is the\ndeficit of the neutrino distribution due to the low reheating\ntemperature, it considerably influences the produced light element\nabundances. In particular, the abundance of the primordial $^4$He is\ndrastically changed. The change of the neutrino distribution function\ninfluences the neutrino energy density and the weak interaction rates\nbetween proton and neutron. At the beginning of BBN (T $\\sim$ 1 MeV -\n0.1 MeV) the competition between the Hubble expansion rate $H$ and the\nweak interaction rates $\\Gamma_{n \\leftrightarrow p}$ determines the\nfreeze-out value of neutron to proton ratio $n/p$. After the\nfreeze-out time, neutrons can change into protons only through the\nfree decay with the life time $\\tau_n $. Since $^4$He is the most\nstable light element and the almost all neutrons are synthesized\ninto $^4$He, the abundance of the primordial $^4$He is sensitive to\nthe freeze-out value of neutron to proton ratio.\n\nIf the neutrino energy density gets smaller than that of the standard\nBBN (SBBN), Hubble expansion rate which is proportional to the square\nof the total energy density is also decreased. Then the freeze out\ntime becomes later and the $\\beta$ equilibrium between neutrons and\nprotons continues for longer time. As a result less neutrons are left.\nIn this case the predicted $^4$He is less than the prediction of SBBN.\nThe effect due to the speed-down expansion is approximately estimated\nby\n%%\n\\begin{equation}\n \\label{speed_down}\n \\Delta Y \\simeq - 0.1 (- \\Delta \\rho_{tot}/\\rho_{tot}),\n\\end{equation}\n%%\nwhere $Y$ is the mass fraction of $^4$He and $\\rho_{tot}$ is the total\nenergy density of the universe.\n\nMoreover, when the electron neutrino is not thermalized, there is\ninteresting effect by which more $^4$He are produced. The weak\nreaction rates are computed by integrating neutrino distribution\nfunctions which are obtained by solving Boltzmann equations\nnumerically. Using the neutrino distribution functions, the six weak\ninteraction rates between neutron and proton are represented by\n%%\n\\begin{eqnarray}\n \\label{eq:beta_reac1}\n \\Gamma_{n \\to p e^- \\bar{\\nu_e}}& = &\n K\\int_0^{Q-m_e}dp_{\\nu_e}\\left[\\sqrt{(p_{\\nu_e}-Q)^2-m_e^2}\n (Q-p_{\\nu_e})\n \\frac{p_{\\nu_e}^2}{1+e^{(p_{\\nu_e}-Q)/T_{\\gamma}}}\n \\left(1-f_{\\nu_e}(p_{\\nu_e})\\right) \\right], \\\\\n \\label{eq:beta_reac2}\n \\Gamma_{ne^+ \\to p \\bar{\\nu_e}} & = &\n K \\int_{Q+m_e}^{\\infty}dp_{\\nu_e}\\left[\\sqrt{(p_{\\nu_e}-Q)^2-m_e^2}\n (p_{\\nu_e}-Q)\n \\frac{p_{\\nu_e}^2}{e^{(p_{\\nu_e - Q})/T_{\\gamma}}+1}\n \\left( 1-f_{\\nu_e}(p_{\\nu_e}) \\right) \\right], \\\\\n \\label{eq:beta_reac3}\n \\Gamma_{n \\nu_e \\to p e^-} & = &\n K \\int_0^{\\infty}dp_{\\nu_e}\\left[\\sqrt{(p_{\\nu_e}+Q)^2-m_e^2}\n (p_{\\nu_e}+Q)\n \\frac{p_{\\nu_e}^2}{1+e^{-(p_{\\nu_e}+Q)/T_{\\gamma}}}\n f_{\\nu_e}(p_{\\nu_e})\\right], \\\\\n \\label{eq:beta_reac4}\n \\Gamma_{pe^-\\bar{\\nu_e} \\to n} & = &\n K \\int_{0}^{Q-m_e}dp_{\\nu_e}\\left[\\sqrt{(p_{\\nu_e}-Q)^2-m_e^2}\n (Q-p_{\\nu_e})\n \\frac{p_{\\nu_e}^2}{e^{-(p_{\\nu_e - Q})/T_{\\gamma}}+1}\n f_{\\nu_e}(p_{\\nu_e}) \\right], \\\\\n \\Gamma_{pe^- \\to n \\nu_e} & = &\n \\label{eq:beta_reac5}\n K \\int_{0}^{\\infty}dp_{\\nu_e}\\left[\\sqrt{(p_{\\nu_e}+Q)^2-m_e^2}\n (Q+p_{\\nu_e})\n \\frac{p_{\\nu_e}^2}{e^{(p_{\\nu_e + Q})/T_{\\gamma}}+1}\n \\left( 1-f_{\\nu_e}(p_{\\nu_e}) \\right)\\right], \\\\\n \\Gamma_{p\\bar{\\nu_e} \\to ne^+} & = &\n \\label{eq:beta_reac6}\n K \\int_{Q+m_e}^{\\infty}dp_{\\nu_e}\\left[\\sqrt{(p_{\\nu_e}-Q)^2-m_e^2}\n (Q-p_{\\nu_e})\n \\frac{p_{\\nu_e}^2}{1+e^{-(p_{\\nu_e - Q})/T_{\\gamma}}}\n f_{\\nu_e}(p_{\\nu_e}) \\right],\n\\end{eqnarray}\n%%\nwhere $Q = m_n - m_p = 1.29$ MeV and $K$ is a normalization factor\nwhich is determined by the neutron life time $\\tau_n $ as $ K \\simeq\n(1.636 \\tau_n)^{-1}$ and $\\tau_n $ is obtained by the\nexperiments~\\cite{PDG}. From the above equations we can see that if\nneutrino and anti-neutrino distribution functions are decreased, both\n$\\beta$ decay rates $\\Gamma_{n \\rightarrow p} = \\Gamma_{n \\to p e^-\n\\bar{\\nu_e}}+\\Gamma_{ne^+ \\to p \\bar{\\nu_e}}+\\Gamma_{n \\nu_e \\to p\ne^-}$ and $\\Gamma_{p \\rightarrow n} = \\Gamma_{pe^-\\bar{\\nu_e} \\to n} +\n\\Gamma_{pe^- \\to n \\nu_e}+ \\Gamma_{p\\bar{\\nu_e} \\to ne^+}$ are\nsimultaneously decreased by the following reasons. The dominant\neffects by the deficit of the distribution functions are to\ndecrease the rates $\\Gamma_{n \\nu_e \\to p e^-}$,\n$\\Gamma_{pe^-\\bar{\\nu_e} \\to n}$ and $\\Gamma_{p\\bar{\\nu_e} \\to ne^+}$\nwhich have the neutrino or anti-neutrino in the initial state. On the\nother hand, though\nthe other rates $\\Gamma_{n \\to p e^- \\bar{\\nu_e}}$, $\\Gamma_{ne^+ \\to\np \\bar{\\nu_e}}$ and $\\Gamma_{pe^- \\to n \\nu_e}$ which have the\nneutrino or anti-neutrino in the final state are slightly increased\ndue to Fermi-blocking factor $(1-f_{\\nu})$, the ratio of the\ndifference $\\Delta f_{\\nu}$ to $(1-f_{\\nu})$ is much smaller than that\nof $\\Delta f_{\\nu}$ to $f_{\\nu}$, {\\it i.e.}\n%%\n\\begin{equation}\n \\label{diff_dist}\n |\\Delta f_{\\nu}/(1-f_{\\nu})| \\ll |\\Delta f_{\\nu}/f_{\\nu}|\n \\qquad {\\rm for } \\ f_{\\nu} \\ll 1.\n\\end{equation}\n%%\nTherefore, the enhancement is small and the latter effect is not\nimportant. In total, both weak interaction rates $\\Gamma_{n\n\\rightarrow p}$ and $\\Gamma_{p \\rightarrow n}$ are decreased and\nbecome smaller than those of SBBN. In Fig.~\\ref{fig:weak_rate} the\nweak interaction rates $\\Gamma_{n \\rightarrow p}$ and $\\Gamma_{p\n\\rightarrow n}$ are plotted. The solid lines denote the case of $T_R =\n10$ MeV which corresponds to the standard big bang scenario. The\ndotted lines denote the case of $T_R = 1$ MeV. In the plot we can see\nthat the insufficient thermalization of the neutrino distributions\nderives the changes of the weak interaction rates.\n\nThe decrease of weak interaction rates gives significant effects on\nthe abundance of $\\4he$. When the weak interaction rate\n$\\Gamma_{n\\leftrightarrow p}$ decreases, Hubble expansion rate becomes\nmore rapid than that of the weak interaction rate earlier. Namely the\nfreeze-out time becomes earlier. Then the freeze-out value of neutron\nto proton ratio becomes larger than in SBBN and it is expected that\nthe predicted $^4$He abundance becomes larger.\n%Second when the\n%interaction rates $\\Gamma_{n \\to p}$ at which neutrons are changed\n%into protons become smaller, less neutrons can turn into protons after\n%the freeze-out time.\nThe above effect is approximately estimated by\n%%\n\\begin{equation}\n \\label{dY_gamma}\n \\Delta Y \\simeq + 0.19 (- \\Delta\\Gamma_{n\\leftrightarrow\n p}/\\Gamma_{n\\leftrightarrow p})\n\\end{equation}\n%%\n\nIn Fig.~\\ref{fig:npratio} we plot the time evolution of the neutron to\nproton ratio. In Fig.~\\ref{fig:npratio}(a) we change only the number\nof neutrino species in SBBN. The dotted line denoted the curve of\n$N_{\\nu}^{\\rm eff}=1.37$ which corresponds to the effective number of\nneutrino species in the case of $T_R = 2$ MeV in the late-time entropy\nproduction scenario. Then we find that the predicted $n/p$ curve is\nlower than that of $N_{\\nu}^{\\rm eff}=3$ due to only the speed down\neffects or the later decoupling. In Fig.~\\ref{fig:npratio}(b) we plot\nthe time evolution of $n/p$ when we change the reheating temperature\nin the late-time entropy production scenario. The dotted line denotes\nthe case of $T_R = 2$ MeV. Comparing to the case of $N_{\\nu}^{\\rm\neff}=1.37$ in Fig.~\\ref{fig:npratio}(a), the $n/p$ ratio becomes\nlarger. It is because the weak interaction rates are decreased by the\ndeficit of the distribution function. Moreover in the case of $T_R =\n1$ MeV the $n/p$ ratio becomes much larger.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Neutrino thermalization and light element abundances}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\label{sec:nu_BBN}\nNext we perform Monte Carlo simulation and the maximum likelihood\nanalysis~\\cite{HKKM} to discuss how the theoretical predictions with\nthe low reheating temperature scenario agree with the observational\nlight element abundances.\n\nIn Fig.~\\ref{fig:pred_he4} we plotted $^4$He mass fraction Y as a\nfunction of $T_R$ at $\\eta = 5 \\times 10^{-10}$ (solid line). The\ndashed line denotes the virtual $^4$He mass fraction computed by\nincluding only the speed down effect due to the change of the\neffective number of neutrino species which is shown in\nFig.~\\ref{fig:tr_nnu}. The dotted line denotes the predicted value of\nY in SBBN at $\\eta = 5 \\times 10^{-10}$. For $T_R \\gtrsim 7$MeV, the\nsolid line and dashed line are quite equal to the value in SBBN. As\n$T_R$ decreases, both the solid and dashed lines gradually decrease\nbecause of the speed down effect due to the change of $N_{\\nu}^{\\rm\neff}$. The dashed line continues to decrease as the reheating\ntemperature decreases.\n\nOn the other hand, for T$_R \\lesssim 2$ MeV the effect that the weak\ninteraction rates are weakened due to the deficit of the neutrino\ndistribution function begins to become important and the predicted\nvalue of $Y$ begins to increase as $T_R$ decreases. For $T_R \\lesssim\n1$ MeV, since it is too late to produce enough electrons whose mass\nis about $m_e$ = 0.511 MeV, the weak interaction rates are still more\nweakened and $Y$ steeply increases as $T_R$ decreases.\n\nIn Fig.~\\ref{fig:eta_tr} we plot the contours of the confidence level\nin the $\\eta$-$T_R$ plane. The solid line denotes 95\n$\\%$ C.L. and the dotted line denotes 68 $\\%$ C.L. The filled square\nis the best fit point between the observation and theoretical\npredictions. The observational data are consistent with the high\nbaryon to photon ratio, $\\eta \\sim (3-6) \\times 10^{-10}$. From\nFig.~\\ref{fig:eta_tr} we find that $T_R \\lesssim 0.7$~MeV is excluded\nat 95 $\\%$ C.L. In other wards $T_R$ as low as $0.7\\rm MeV$ is\nconsistent with BBN. Then $N_{\\nu}^{\\rm\neff}$ can be as small as $0.1$ and it definitely influences the\nformation of the large scale structure and CMB anisotropy as is seen\nin Sec.\\ref{sec:LSS_CMB}.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Hadron injection by massive particle decay}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Hadron Jets and $e^+e^-$ collider experiments}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nIn the previous section we discussed only the case in which the parent\nmassive particle $\\phi$ decays into photons or the other\nelectro-magnetic particles. In this section we consider the entropy\nproduction process along with the hadron injection, {\\it i.e.} the\ncase in which the massive particle has some decay modes into quarks or\ngluons. Then the emitted quark-antiquark pairs or gluons immediately\nfragment into hadron jets and as a result a lot of mesons and baryons,\n{\\it e.g.} pions, kaons, nucleons (protons and neutrons ) are emitted\ninto the electro-magnetic thermal bath which is constituted by photon,\nelectron and nucleons.\n\nFor example, if the gravitino $\\psi_{\\mu}$ is the parent particle\nwhich produces the large entropy, it could have a hadronic decay mode\n({\\it e.g.} $\\psi_{\\mu} \\to \\tilde{\\gamma} q \\bar{q}$ ) with the\nbranching ratio $B_h \\simeq {\\cal O}$($\\alpha$) at least even if the\nmain decay mode is only $\\psi_{\\mu} \\to \\tilde{\\gamma}\n\\gamma$($\\tilde{\\gamma}$ : photino)~\\cite{DDRG}. Then about 0.6 - 3\nhadrons are produced for $m_{\\phi} \\simeq 1 - 100 \\tev$. In addition\nthe emitted high energy photons whose energy is about $m_{\\phi}/2$\nscatter off the background photons and could also produce the\nquark-antiquark pairs through the electromagnetic interaction. For the\ncosmic temperature $\\simeq \\order{(\\mev)}$, the energy in the center\nof mass frame is $\\sqrt{s} \\simeq 2 - 20 \\gev$ for $m_{\\phi} \\simeq 1\n- 100 \\tev$. Then the number of the produced hadrons is about 2 - 7\nwhich effectively corresponds to the hadron branching ratio $B_h \\sim\n10^{-2}$ if we assume that the hadron fragmentation is similar to the\nresults of $e^+e^-$ collider experiments. Thus $B_h$ should not become\nless than about $10^{-2}$ for gravitino decay.~\\footnote{If the decay\nmode $\\psi_{\\mu} \\to \\tilde{g} g$ ($\\tilde{g}$ : gluino) is\nkinematically allowed, the hadronic branching ratio becomes close to\none.} For the other candidate, if the ``flaton'' is the parent\nparticle as in thermal inflation model, it would also have a hadronic\ndecay mode ($\\phi \\to g g$ )~\\cite{Lyth} if the flaton mass is larger\nthan 1 GeV.\n\nIf once such hadrons are emitted to the electro-magnetic thermal bath\nin the beginning of BBN epoch (at $T \\simeq 10 \\mev - 0.1 \\mev)$, they\nquickly transfer all the kinetic energy into the thermal bath through\nthe electro-magnetic interaction or the strong interaction. Through\nsuch thermalization processes the emitted high energy hadrons scatter\noff the background particles, and then they induce some effects on\nBBN. Especially, the emitted hadrons extraordinarily inter-convert the\nambient protons and neutrons each other through the strong interaction\neven after the freeze-out time of the neutron to proton ratio $n/p$.\nFor the relatively short lifetime ($\\tau_{\\phi} \\simeq 10^{-2} \\sec -\n10^2 \\sec$) in which we are interested, the above effect induces the\nsignificant change in the previous discussion. Namely protons which\nare more abundant than neutrons are changed into neutrons by the\nhadron-proton collisions and the ratio $n/p$ increases extremely.\nBecause $\\4he$ is the most sensitive to the freeze out value of $n/p$,\nthe late-time hadron injection scenario tends to increase $Y_p$.\n\nReno and Seckel~\\cite{RS} investigated the influences of the hadron\ninjection on the early stage of BBN. They constrained the lifetime of\nthe parent particle and the number density comparing the theoretical\nprediction of the light element abundances with the observational\ndata. Here we basically follow their treatment and apply it to the\nscenario of late-time entropy production with hadron injections.\n\nThe emitted hadrons do not scatter off the background nucleons\ndirectly. At first hadrons scatter off the background photons and\nelectrons because they are much more abundant than nucleons. For $t\n\\lesssim 200 \\sec$, the emitted high energy hadrons are immediately\nthermalized through the electro-magnetic scattering and they reach to\nthe kinetic equilibrium before they interact with the ambient protons\nand neutrons. Then we use the threshold cross section $\\langle\\sigma\nv\\rangle^{H_i}_{N \\rightarrow N'}$ for the strong interaction process\n$N + H_i \\rightarrow N' + \\cdot \\cdot \\cdot$ between hadron $H_i$ and\nthe ambient nucleon $N$, where $N$ denotes proton $p$ or neutron $n$.\nThe strong interaction rate is estimated by\n%%\n\\begin{eqnarray}\n \\label{eq:gamma^i_nn}\n \\Gamma^{H_i}_{N\\rightarrow N'} &=& n_N \\langle\\sigma v\\rangle^{H_i}_{N\n \\rightarrow N'} \\nonumber \\\\\n &\\simeq& 10^{8} \\sec^{-1} f_N\n \\left(\\frac{\\eta}{10^{-9}}\\right)\n \\left(\\frac{\\langle\\sigma v\\rangle^{H_i}_{N \\rightarrow N'}}{10\n \\mb} \\right)\n \\left(\\frac{T}{2 \\mev}\\right)^3,\n\\end{eqnarray}\n%%\nwhere $n_N$ is the number density of the nucleon species $N$, $\\eta$\nis the baryon to photon ratio ($=n_B/n_{\\gamma}$), $n_B$ denotes the\nbaryon number density ($= n_p + n_n$) and $f_N$ is the nucleon\nfraction ($ \\equiv n_N/n_B$). This\nequation shows that every hadron whose lifetime is longer than ${\\cal\nO}(10^{-8})$ sec contributes to the inter-converting interaction\nbetween neutron and proton at the beginning of BBN. Hereafter we will\nconsider only the following long-lived hadrons, (mesons, $\\pi^{\\pm}$,\n$K^{\\pm}$ and $K_L$, and baryons, $p$, $\\overline{p}$, $n$, and\n$\\overline{n}$). For the relevant process ( $N + \\pi^{\\pm}\n\\to N' \\cdot \\cdot \\cdot$, and $N + K^- \\to N' \\cdot \\cdot \\cdot$,\netc.), we can obtain the cross sections in~\\cite{RS,ky}. Here we\nignore $K^+$ interaction because $n + K^+ \\rightarrow p + K^0$ is the\nendothermic reaction which has $Q = 2.8$ MeV.\n\nWe estimate the average number of emitted hadron species $H_i$ per\none $\\phi$ decay as\n%%\n\\begin{equation}\n \\label{eq:NHi}\n N^{H_i} = B_h N_{jet} f_{H_i} \\frac{\\langle N_{ch}\\rangle}{2},\n\\end{equation}\n%%\nwhere $\\langle N_{ch}\\rangle$ is the averaged charged-particle\nmultiplicity which represents the total number of the charged\nparticles emitted per two hadron jets, $f_{H_i}$ is the number\nfraction of the hadron species $H_i$ to all the emitted charged\nparticles, $B_h$ is the branching ratio of the hadronic decay mode and\n$N_{jet}$ is the number of the produced jets per one $\\phi$ decay.\n\nHere it is reasonable to assume that the averaged charged particle\nmultiplicity $\\langle N_{ch}\\rangle$ is independent of the the source\nbecause the physical mechanism which governs the production of hadron\njets is quite similar and does not depend on the detail of the origin\nonly if the high energy quark-antiquark pairs or gluons are emitted.\nWe adopt the data which are obtained by the $e^+e^-$ collider\nexperiments. LEPII experiments (ALEPH, DELPHI, L3 and OPAL) recently\ngive us the useful data for $\\sqrt{s}$ = 130 $-$ 172 GeV~\\cite{PDG}.\nWe adopt the following fitting function for $\\sqrt{s}$ = 1.4 $-$ 172\nGeV~\\cite{ky},\n%%\n\\begin{equation}\n \\label{eq:nch}\n \\langle N_{ch}\\rangle= 1.73 + 0.268 \\exp\\left(\n 1.42\\sqrt{\\ln(s / \\Lambda^2)}\\right),\n\\end{equation}\n%%\nwhere $\\sqrt{s}$ denotes the center of mass energy, the functional\nshape is motivated by the next-to-leading order perturbative QCD\ncalculations, $\\Lambda$ is the cut-off parameter in the perturbative\ncalculations and we take $\\Lambda = 1$ GeV. In Fig.~\\ref{fig:nch} we\nplot the charged particle multiplicity for $\\sqrt{s} = 1 \\gev -\n100\\tev$. The error of the fitting is about 10$\\%$. Using the\navailable data~\\cite{PDG,ky,biebel}, we obtain the emitted hadron\nfraction $f_{H_i}\\equiv n^{H_i}/\\langle N_{ch}\\rangle$,\n%%\n\\begin{eqnarray}\n \\label{eq:fHi}\n f_{\\pi^+}=0.64,~~ f_{\\pi^-}=0.64,~~\\nonumber \\\\\n f_{K^+}=0.076,~~ f_{K^-}=0.076,~~f_{K_L}=0.054 \\\\\n f_{p}=f_{\\overline{p}}=0.035,~~ f_{n}=f_{\\overline{n}}=0.034,\n ~~\\nonumber\n\\end{eqnarray}\n%%\nwhere $n^{H_i}$ is the number of the emitted hadron species $H_i$\nwhich is defined as the value after both $K_S$ and $\\Lambda^0$ had\ncompletely finished to decay. \\footnote{Although the summation of\n$f_{H_i}$ is obviously more than one, it is because the experimental\nfitting of $\\langle N_{ch}\\rangle$ is defined as a value before $K_S$\nand $\\Lambda^0$ begin to decay~\\cite{biebel}. Here we assume that\n$f_{H_i}$ do not change significantly in the energy range $\\sqrt{s}\n\\simeq $ 10 GeV - 100 TeV. Since we do not have any experimental data\nfor the high energy region more than about 200 GeV, we extrapolate\n$\\langle N_{ch}\\rangle$ to the higher energy regions and we take\n$f_{H_i}$ as a constant.} As we find easily, almost all the emitted\nparticles are pions which are the lightest mesons. To apply the data\nof the $e^+e^-$ collider experiments, we take $\\sqrt{s}= 2 E_{jet}$ in\n$\\langle N_{ch}\\rangle$ where $E_{jet}$ denotes the energy of one\nhadron jet because the $\\langle N_{ch}\\rangle$ is obtained by the\nresult for two hadron jets.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Formulation in Hadron Injection Scenario}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nIn this section we formulate the time evolution equations in the\nlate-time hadron injection scenario. As we mentioned in the previous\nsection, the hadron injection at the beginning of BBN enhances the\ninter-converting interactions between neutron and proton equally and\nthe freeze out value of $n/p$ can be extremely increased. Then the\ntime evolution equations for the number density of a nucleon $N (=p,\nn)$ is represented by\n%%\n\\begin{equation}\n \\label{eq:difeqN}\n \\frac{dn_N}{dt} + 3 H(t) n_N = \\left[\\frac{dn_N}{dt}\\right]_{weak}\n - \\Gamma_{\\phi} n_{\\phi} \\left( K_{N \\rightarrow N'} - K_{N'\n \\rightarrow N} \\right),\n\\end{equation}\n%%\nwhere $H(t)$ is Hubble expansion rate, $[dn_N/dt]_{weak}$ denotes\nthe contribution from the weak interaction rates which are obtained by\nintegrating the neutrino distribution functions as discussed in\nSec.~\\ref{sec:neu_nu}, see\nEqs.(\\ref{eq:beta_reac1} - \\ref{eq:beta_reac6}),\n$n_{\\phi}=\\rho_{\\phi}/m_{\\phi}$ is the number density of $\\phi$, $K_{N\n\\rightarrow N'}$ denotes the average number of the transition $N\n\\rightarrow N'$ per one $\\phi$ decay.\n\nThe average number of the transition $N \\rightarrow N'$ is expressed by\n%%\n\\begin{equation}\n \\label{eq:Knn}\n K_{N \\rightarrow N'} = \\sum_{H_i} N^{H_i}R^{H_i}_{N \\rightarrow N'},\n\\end{equation}\n%%\nwhere $H_i$ runs the hadron species which are relevant to the nucleon\ninter-converting reactions, $N^{H_i}$ denotes the average number of\nthe emitted hadron species $H_i$ per one $\\phi$ decay which is given by\nEq.~(\\ref{eq:NHi}) and $R^{H_i}_{N \\rightarrow N'}$ denotes the\nprobability that a hadron species $H_i$ induces the nucleon transition\n$N \\rightarrow N'$,\n\n%%\n\\begin{equation}\n \\label{eq:trans_prob}\n R^{H_i}_{N \\rightarrow N'} =\n \\frac{\\Gamma^{H_i}_{N \\rightarrow N'}}{\\Gamma^{H_i}_{dec} +\n \\Gamma^{H_i}_{abs}},\n\\end{equation}\n%%\nwhere $\\Gamma^{H_i}_{dec} = \\tau_{H_i}^{-1}$ is the decay rate of the\nhadron $H_i$ and $\\Gamma^{H_i}_{abs} \\equiv \\Gamma^{H_i}_{N \\rightarrow\nN'}+\\Gamma^{H_i}_{N' \\rightarrow N}+\\Gamma^{H_i}_{N \\rightarrow\nN}+\\Gamma^{H_i}_{N' \\rightarrow N'}$ is the total absorption rate of\n$H_i$.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Hadron injection and BBN}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nIn this subsection we compare the theoretical prediction of the light\nelement abundances in the hadron injection scenario to the\nobservational light element abundances. In the computations we assume\nthat the massive particle decays into three bodies\n($E_{jet}=m_{\\phi}/3$) and two jets are produced at the parton level\n($N_{jet}=2$)~\\footnote{The above choice of a set of model parameters\n$E_{jet}$ and $N_{jet}$ is not unique in general and is obviously\nmodel dependent. However, since $\\langle N_{ch}\\rangle$ has the\nlogarithmic dependence of $E_{jet}$, we should not be worried about\nthe modification of $E_{jet}$ by just a factor of two so seriously.\nOn the other hand in Eq.~(\\ref{eq:difeqN}), the second term in the\nright hand side scales as $\\propto N_{jet}/m_{\\phi}$. For the\nmodification of $N_{jet}$, therefore, we only translate the obtained\nresults according to the above scaling rule and push the\nresponsibility off onto $m_{\\phi}$}. In the computing we take the\nbranching ratio of the hadronic decay mode $B_h = \\order(10^{-2}- 1)$.\n\nAs we noted in the previous subsections, it is a remarkable feature\nthat the predicted $Y_p$ tends to increase in the hadron injection\nscenario because $\\4he$ is the most sensitive to the freeze-out value of\nthe neutron to proton ratio. Since protons which are more abundant\nthan neutrons are changed into neutrons through the strong\ninteractions rapidly, the freeze out value of $n/p$ increase extremely\nif once the net hadrons are emitted. In Fig.~\\ref{fig:had_tr_Y} we\nplot the predicted $\\4he$ mass fraction $Y_p$ as a function of $T_R$\nfor (a) $m_{\\phi}$=100 TeV and (b) $m_{\\phi}$ =10 GeV. The solid curve\ndenotes the predicted $Y_p$. Here we take the branching ratio of the\nhadronic decay mode as $B_h$ = 1 (right one) and $B_h$ = 0.01 (left\none). The dot-dashed line denotes $B_h = 0$. The dashed line denotes\nthe virtual value of $Y_p$ computed by including only the speed down\neffect due to the change of the effective number of neutrino species.\nThe dotted line denotes the prediction in SBBN.\n\nAs we mentioned in the previous section, the speed down effect due to\ndeficit of the electron neutrino distribution function are not\nimportant for $T_R \\gtrsim 7$MeV. In addition since it is high enough\nto keep $n/p$ $\\simeq$ 1 for the cosmic temperature $T \\gtrsim 7$MeV,\nthe enhancements of the inter-converting interaction between n and p\ndue to the hadron emission do not induce any changes on the freeze-out\nvalue of $n/p$. As $T_R$ decreases ($T_R \\lesssim 7$MeV), $Y_p$ also\ndecreases gradually because the speed down effect on the freeze-out\nvalue of $n/p$ begins to be important. On the other hand, if a lot of\nhadrons are emitted when the cosmic temperature is $T \\lesssim$ 6 - 7\nMeV and the ratio $n/p$ is less than one, they enhance the\ninter-converting interactions more rapidly. As a result, the ratio\n$n/p$ attempts to get closer to one again although the cosmic\ntemperature is still low. Thus the above effects extremely increase\nthe freeze-out value of $n/p$ and is much more effective than the\nspeed down effects. Namely the produced $Y_p$ becomes larger very\nsensitively only if $T_R$ is just a little lower than 6 - 7 MeV. One\ncan obviously find that this effect becomes more remarkable for the\nlarger $B_h$.\n\nTo understand how it depends on mass, it is convenient to introduce the\nyield variable $Y_{\\phi}$ which is defined by\n%%\n\\begin{equation}\n \\label{eq:yield_phi}\n Y_{\\phi} \\equiv n_{\\phi} / s,\n\\end{equation}\n%%\nwhere $s$ denotes the entropy density in the universe. Because\n$Y_{\\phi}$ is a constant only while the universe expands without any\nentropy production, it represents the net number density of $\\phi$ per\ncomoving volume. For the simplicity let's consider\nthe instantaneous decay of $\\phi$ and assume that the reheating\nprocess has been completed quickly. Because the radiation energy in\nthe thermal bath or entropy $s=2\\pi^2g_{*}/45T_R^3$ is produced only\nfrom the decay products of $\\phi$, $Y_{\\phi}$ is approximately\nestimated using $T_R$ and $m_{\\phi}$ by\n%%\n\\begin{equation}\n \\label{eq:yield2}\n Y_{\\phi} \\simeq 0.28 \\frac{T_R}{m_{\\phi}}.\n\\end{equation}\n%%\n From the above equation, we can see that for the fixed value of $T_R$\nthe net number of $\\phi$, {\\it i.e.} the net number of the emitted\nhadrons, becomes larger for the smaller mass. Comparing\nFig.~\\ref{fig:had_tr_Y} (a) with Fig.~\\ref{fig:had_tr_Y} (b), we find\nthat the theoretical curve of $Y_p$ for the case of $m_{\\phi}$ = 10\nGeV is enhanced more steeply and the starting point to increase $Y_p$\nbecomes higher than for the case of $m_{\\phi}$ = 100 TeV.\n\nSince the other elements (D and $\\li7$) are not so sensitive as\n$\\4he$, it is expected that the observational value of $Y_p$\nconstrains $T_R$ most strongly. In order to discuss how a low\nreheating temperature is allowed by comparing the theoretical\npredictions with observational values (D, $\\4he$ and $\\li7$), we\nperform the Monte Carlo simulation and maximum likelihood analysis as\ndiscussed in Sec.~\\ref{sec:neu_nu}. In addition to the case of\nSec.~\\ref{sec:neu_nu} we take account of the following uncertainties,\nthe error for the fitting of $\\langle N_{ch}\\rangle$ as\n10$\\%$~\\cite{ky} and the experimental error for each cross section of\nthe hadron interaction as 50$\\%$. Because there are not any adequate\nexperimental data for the uncertainties of cross\nsections~\\cite{RS,ky}, here we take the larger values to get a\nconservative constraint.\n\nIn Fig.~\\ref{fig:m100_eta_tr} we plot the contours of the confidence\nlevel for $m_{\\phi}= 100$ TeV in the ($\\eta$-$T_R$) plane for (a)\n$B_h$ = 1 and (b) $B_h = 10^{-2}$. The solid line denotes 95 $\\%$\nC.L., the dotted line denotes 68 $\\%$ C.L. and the filled square is\nthe best fit point between the observation and theoretical prediction\nfor D, $\\4he$ and $\\li7$. The baryon to photon ratio which is\nconsistent with the observational data is restricted in the narrow\nregion, $\\eta \\simeq (4 - 6) \\times 10^{-10}$. From\nFig.~\\ref{fig:m100_eta_tr}(a), we find that $T_R \\lesssim 3.7$~MeV is\nexcluded at 95 $\\%$ C.L. for $B_h$= 1. On the other hand, from\nFig.~\\ref{fig:m100_eta_tr}(b) we obtain the milder constraint that\n$T_R \\lesssim 2.5$~MeV is excluded at 95 $\\%$ C.L. for $B_h =\n10^{-2}$. In Fig.~\\ref{fig:m0.01_eta_tr} we plot the contours of the\nconfidence level for $m_{\\phi}= 10$ GeV in the same way as\nFig.~\\ref{fig:m100_eta_tr}. Compared to Fig.~\\ref{fig:m100_eta_tr}, as\nwe mentioned above, we find that the lower bound on the reheating\ntemperature becomes higher for a smaller mass. From\nFig.~\\ref{fig:m0.01_eta_tr} we get the lower bound on the reheating\ntemperature that $T_R \\gtrsim 5.0$ MeV (4.0 MeV) at 95 $\\%$ C.L. for\n$B_h$= 1 ($B_h = 10^{-2}$)\n\nIn Fig.~\\ref{fig:m_tr} the lower bound on $T_R$ as a function of\n$m_{\\phi}$ are plotted for (a) $B_h$ = 1 and (b) $B_h = 10^{-2}$. The\nsolid line denotes 95 $\\%$ C.L. and the dotted line denotes 68 $\\%$\nC.L. As it is expected, the curve of the lower bound on $T_R$ is a\ngentle monotonic decreasing function of $m_{\\phi}$. In\nFig.~\\ref{fig:m_tr}(a), we can see that $T_R$ should be higher than 4\nMeV at 95 $\\%$ C.L. for $B_h$ = 1 in $m_{\\phi}$ = 10 GeV - $10^2$\nTeV\\footnote{Though we have adopted the experimental error of the each\nhadron interaction cross section as 50$\\%$ in the Monte Carlo\nsimulation because of no data, the lower bound on $T_R$ might become\nabout 10$\\%$ higher than the above values if we adopt the more sever\nexperimental error as 10$\\%$ instead of 50$\\%$.}. On the other hand,\nin Fig.~\\ref{fig:m_tr}(b) we find that the constraint gets milder for\n$B_h = 10^{-2}$. It is shown that $T_R \\lesssim 2.5$ MeV is excluded\nat 95 $\\%$ C.L. for $B_h = 10^{-2}$. In Fig.~\\ref{fig:tr_nnu} we find\nthat $N_{\\nu}^{\\rm eff}$ can be allowed as small as 2.8 for $B_h$ = 1\n( 1.9 for $B_h = 10^{-2}$).\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Summary of hadron injection}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nIn this section we have seen that the BBN constraint on the reheating\ntemperature becomes much more stringent if a massive particle has a\nbranching to hadrons. For successful BBN the reheating temperature\nshould be higher than $2.5 - 4$~MeV for the branching ratio $B_h = 1\n- 10^{-2}$. The hadron injection generally occurs if the late-time\nreheating is caused by the heavy particle with mass larger than $\\sim\n1$~GeV. Many candidates for the late-time reheating such as SUSY\nparticles and flatons have such large masses and hence the constraint\nobtained here is crucial in constructing particle physics models based\non SUSY or thermal inflation models.\n\nFor the lower limit of the reheating temperature, the effective number\nof the neutrino species $N_{\\nu}^{\\rm eff}$ is given by 2.8 and 1.9\nfor $B_h$ = 1 and $10^{-2}$, respectively. Since the limiting\ntemperature is close to the neutrino decoupling temperature, the\ndeviation of $N_{\\nu}^{\\rm eff}$ from the standard value (i.e. 3) is\nsmall and hence the detection may not be easy.\n\nHowever, from more general point of view, it is possible that light\nparticles with mass $\\lesssim 1$~GeV are responsible for the late-time\nreheating. In this case, as seen in the previous section, the\nreheating temperatures as low as $\\sim 0.7$~MeV are allowed. For such\nlow reheating temperature, neutrinos cannot be produced\nsufficiently. Thus the effective number of the neutrino species\n$N_{\\nu}^{\\rm eff}$ becomes much less than $3$. This leads to very\ninteresting effects on the formation of large scale structures and CMB\nanisotropies, which we discuss in the next section.\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Constraints from Large Scale Structure and CMB anisotropy}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\label{sec:LSS_CMB}\n\nIn this section, we discuss possibility to set constraints on the\nlate-time entropy production from the large scale structure and CMB\nanisotropies. Hereafter, we only consider flat universe models with\ncosmological constant which are suggested by recent distant Supernovae\n(SNe) surveys~\\cite{Riess,Perl} and measurements of CMB\nanisotropies~\\cite{CMB}.\n\nThe late-time entropy production influences formation of the large\nscale structure and CMB anisotropies since the matter-radiation \nequality epoch is shifted if the effective number of neutrino species \nchanges. The ratio of neutrino density to black-body photon density \nis $\\rho_\\nu / \\rho_\\gamma = (7/8)(4/11)^{4/3} N_\\nu$. \nTherefore the redshift of matter-radiation equality can be written as \na function of $N_\\nu$: \n\\begin{equation}\n\\label{eq:equality}\n1+z_{\\rm eq} = 4.03 \\times 10^{4} \\Omega_0 h^2 \n\\left( 1+ {7 \\over 8} \\left({4 \\over 11}\\right)^{4/3}N_\\nu \\right)^{-1} ,\n\\end{equation}\nwhere $\\Omega_0$ is the density parameter and $h$ is the non-dimensional \nHubble constant normalized by $100\\rm km/s/Mpc$.\n\n\nLet us now discuss distribution of galaxies on large scales. \nFor a quantitative analysis, we define the matter power spectrum\nin Fourier space as $P(k) \\equiv <\\vert \\delta_k\n\\vert^2>$, where $\\delta_k$ is the Fourier transform of density\nfluctuations and $<>$ denotes the ensemble average. Hereafter, we\nassume the Harrison-Zel'dovich power spectrum, which is motivated by\nthe inflation scenario, as an initial shape of the power spectrum,\ni.e., $P(k) \\propto k$. As fluctuations evolve in the expanding\nuniverse, the shape of the power spectrum is changed. \nOne often introduces the transfer function $T(k)$ to describe \nthis modification of the initial power spectrum as \n$P(k) = A k T(k)^2$, where $A$ is an arbitrary constant. \nIn case of\nstandard cold dark matter (CDM) dominated models, Bardeen et al.~\\cite{Bard}\nfound a fitting formula:\n\\begin{equation}\nT(k)={\\ln (1+2.34q)\\over 2.34q}[1+3.89q+(16.1q)^2 + \n(5.46q)^3 + (6.71q)^4 ]^{-1/4} ,\n\\end{equation}\nwhere $q =k/\\Omega_0 h^2 \\rm Mpc^{-1}$ when the baryon density is\nnegligible small compared to the total density. It is easy to explain\nwhy $q$ is parameterized by $\\Omega_0 h^2$. This is because CDM\ndensity fluctuations cannot evolve and stagnate during a radiation\ndominated era. Only after the matter-radiation equality epoch,\nfluctuations can evolve. Therefore the CDM power spectrum has a peak\nwhich corresponds to the horizon scale of the matter-radiation\nequality epoch. In fact, the wave number of the horizon scale at the\nequality epoch can be written as $k_{\\rm eq} = \\sqrt{2\\Omega_0\n(1+z_{\\rm eq})}H_0$, where $H_0$ is the Hubble constant at present,\nthat is proportional to $\\Omega_0 h^2$. In the actual observations,\ndistances in between galaxies are measured in the units of $h^{-1}\\rm\nMpc$. Therefore to fit the observational data by the CDM type power\nspectrum, we usually introduce so-called {\\it shape parameter}\n$\\Gamma_{\\rm s} = \\Omega_0 h$. It is known that we can fit the galaxy\ndistribution if $\\Gamma_{\\rm s} \\simeq 0.25\\pm 0.05$~\\cite{PD} which\nsuggests a low density universe. If the late-time entropy production\ntakes place, however, we need to take into account $N_\\nu^{\\rm eff}$\ndependence of the matter-radiation equality epoch\n(Eq.~(\\ref{eq:equality})). Therefore $\\Gamma_{\\rm s}$ should be\nwritten as\n\\begin{equation}\n\\Gamma_{\\rm s} = 1.68 \\Omega_0 h/(1+0.227N_\\nu^{\\rm eff}) .\n\\end{equation}\nWe plot contours of $\\Gamma_{\\rm s}$ on $\\Omega_0-N_\\nu^{\\rm eff}$ plane\nin Fig.~\\ref{fig:gamma}. It is shown that \nsmaller $\\Omega_0$ is preferable for $N_\\nu^{\\rm eff} < 3$ \nwith the same value of $\\Gamma_{\\rm s}$.\nWe also plot the power spectra for $\\Omega_0=0.3$ and $h=0.7$ with \ndifferent $N_\\nu^{\\rm eff}$'s in Fig.~\\ref{fig:power}. Here \nwe do not simply employ the fitting formula but \nnumerically solve the evolution \nof density fluctuations~\\cite{SG}. \nIt is shown that the peak location of \na model with smaller $N_\\nu^{\\rm eff}$ shifts to the smaller scale \n(larger in $k$) since \nsmaller $N_\\nu^{\\rm eff}$ makes \nthe equality epoch earlier which means the horizon scale at the equality\nepoch becomes smaller. \nWe have hope that current larege scale structrue surveys such as 2DF and \nSloan Digital Sky Survey (SDSS) may determine the precise value of \n$\\Gamma_{\\rm s}$. \n\n\n\n%Therefore the constraint from the large scale galaxy distribution becomes \n%much tighter with $N_\\nu^{\\rm eff} < 3$ (see Fig. ). \n\nBesides the shape of the power spectrum, the amplitude is another\nimportant observational quantities to test models. \nOn very large scales, the amplitude of the power spectrum is \ndetermined by CMB anisotropies which are measured by COBE/DMR~\\cite{COBE}. \nSince COBE/DMR scales are much larger than the horizon scale \nof the matter-radiation equality epoch, however, \nit is not sensitive to the transfer function $T(k)$ but the \noverall amplitude $A$. \nIn order to compare the expected \namplitude of the power spectrum from each CDM model with \nlarge scale structure observations, \nwe employ the specific mass\nfluctuations within a sphere of a radius of $8h^{-1}\\rm Mpc$, i.e.,\n$\\sigma_8$ which is defined as \n\\begin{eqnarray}\n\\sigma_8^2 & = & <(\\delta M / M(R))^2 >_{R = 8h^{-1}{\\rm Mpc}} \\nonumber\\\\\n& = & {1\\over 2\\pi^2} \\int dk k^2 P(k) W(kR)^2|_{R= 8h^{-1}{\\rm Mpc}} ,\n\\end{eqnarray}\nwhere $W(kR)$ is a window function for which we employ a top hat shape\nas $W(kR) \\equiv 3\\left( \\sin(kR)-kR\\cos(kR)\\right)/(kR)^3$. Eke et\nal.~\\cite{Eke} obtained the observational value of $\\sigma_8$ which is deduced\nfrom the rich cluster abundance at present as \n\\begin{equation}\n\\label{eq:sigma8obs}\n\\sigma_8 = (0.52\\pm\n0.04)\\Omega_0^{-0.52+0.13\\Omega_0} . \n\\end{equation}\nOther estimates of \n$\\sigma_8$~\\cite{sigma8} are agreed with their result. \nFor CDM models with standard thermal history, the value of $\\sigma_8$ \nis a function of $\\Omega_0$ and $h$. With the late-time reheating,\nhowever, $\\sigma_8$ for fixed $\\Omega_0$ and $h$ \nbecomes larger. The reason is following. \nSince we fix $\\Omega_0$ and $h$, the normalization \nfactor $A$ is same regardless of the value of $N_\\nu^{\\rm eff}$.\nAs is shown in Fig.~\\ref{fig:power}, the amplitude of the power spectrum \non $8h^{-1}\\rm Mpc$, i.e., $\\sigma_8$, is larger for smaller \n$N_\\nu^{\\rm eff}$. \nIn Fig.~\\ref{fig:sigma8}, we show the allowed region on the $\\Omega_0-h$ \nplane for $N_\\nu^{\\rm eff} = 0.5, 2$ and $3$ for COBE-normalized \nflat CDM models with the Harrison-Zel'dovich spectrum. \nThe shaded region satisfies the matching \ncondition with the cluster abundance Eq.~(\\ref{eq:sigma8obs}). \nFor fixed $h$, models with smaller $N_\\nu^{\\rm eff}$\nprefer lower $\\Omega_0$. Recently, the HST key project \non the Extragalactic Distance Scale has reported that \n$h=0.71\\pm 0.06$ (1$\\sigma$) by using various \ndistant indicators~\\cite{Mould}.\n From SNe measurements, $\\Omega_0 = 0.28\\pm 0.8$ \nfor flat models (see Fig.~7 of \\cite{Perl}).\nCDM models with $N_\\nu^{\\rm eff} = 0.5 \\sim 3$ are \nstill consistent with above value of $h$ and $\\Omega_0$. \nHowever we expect further precise determination of $\\Omega_0$, $h$ (from \ndistant SNe surveys and measurements of CMB anisotropies) and \n$\\sigma_8$ (from 2DF or SDSS)\nwill set a stringent constraint on $N_\\nu^{\\rm eff}$ and $T_R$ in near future.\n\n\nFinally we discuss the CMB constraint on $T_R$. \n%We expand the CMB temperature anisotropies $\\Delta T/T$ into \n%multipole components as $\\Delta T/T = \\sum_\\ell a_\\ell P_ell(\\mu)$. \nLet us introduce temperature angular power spectrum $C_\\ell$ where \n$\\ell$ is the multipole number of the spherical harmonic \ndecomposition. The rms temperature anisotropy \nof CMB can be written as \n$<\\vert\\Delta T/T\\vert^2> = \\sum_\\ell(2\\ell+1)C_\\ell /4\\pi$.\nUsing $C_\\ell$, we can extract various important information \nof cosmology, such as the curvature of the universe, $\\Omega_0$,\ncosmological constant, $h$ and so on (see, e.g., \\cite{Hu}).\nIn fact, we can measure the matter radiation equality epoch by \nusing the height of peaks of $C_\\ell$. The peaks are boosted during \nthe matter-radiation equality epoch. If the matter-radiation equality \nis earlier, the correspondent horizon scale is smaller. \nTherefore we expect lower heights for first one or two peaks \nsince these peaks are larger than the horizon scale at the \nequality epoch and do not suffer the boost as is shown in \nFig.~\\ref{fig:CMB}.\nWith the present angular\nresolutions and sensitivities of COBE observation~\\cite{COBE} or current\nballoon and ground base experiments, however, it is impossible to set a\nconstraint on $N_{\\nu}^{\\rm eff}$. \nIt is expected that future satellite\nexperiments such as MAP~\\cite{MAP} and PLANCK~\\cite{PLANCK} will give us\na useful information about $N_{\\nu}^{\\rm eff}$. From Lopez et al.'s\nanalysis~\\cite{Lopez}, MAP and PLANCK have sensitivities that $\\delta\nN_{\\nu}^{\\rm eff} \\gtrsim 0.1$ (MAP) and $0.03$ (PLANCK) \nincluding polarization\ndata, even if all cosmological parameters are determined\nsimultaneously (see also Fig.~\\ref{fig:CMB}). \n From such future observations of anisotropies of CMB,\nit is expected that we can precisely determine $T_R$.\n%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Conclusion}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\label{sec:conclude}\nIn this paper we have investigated the various cosmological effects\ninduced by the late-time entropy production due to the massive\nparticle decay. The neutrino distribution functions have been obtained\nby solving the Boltzmann equations numerically. We have found that if\nthe large entropy are produced at about $t \\simeq 1$ sec, the\nneutrinos are not thermalized very well and hence do not have the\nperfect Fermi-Dirac distribution. The deficits of the neutrino\ndistribution functions due to the insufficient thermalization decrease\nthe Hubble expansion rate and weakens the weak interaction rates\nbetween proton and neutron. The above two effects changes the\nfreeze-out value of $n/p$ significantly. Especially the produced\n$\\4he$ mass fraction $Y$ is so sensitive to $n/p$ that the predicted\nvalue of $Y$ is changed drastically. Comparing the theoretical\npredictions of D, $\\4he$ and $\\li7$ to the observational data, we have\nestimated the lower bound on the reheating temperature $T_R$ after the\nentropy production. We have found that $T_R \\lesssim 0.7$~MeV is\nexcluded at 95 $\\%$ C.L. In other wards, $T_R$ can be as low as 0.7\nMeV. Then the effective number of neutrino species $N_{\\nu}^{\\rm eff}$\ncan be as small as $0.1$. It is enough sensitive for \nthe ongoing large scale structure observations such as 2DF and SDSS or future \nsatellite experiments (MAP and PLANCK) of CMB anisotropies \nto detect such modifications on\n$N_{\\nu}^{\\rm eff}$ and we can find out the vestige of the late-time\nentropy production.\n \nFurthermore, we have also studied the case in which the massive\nparticle has some decay modes into quarks or gluons. In this scenario,\na lot of hadrons, {\\it e.g.} pions, kaons, protons and neutrons,\nwhich are originated by the fragmentation of the high energy quarks\nand gluons are injected into thermal bath. The emitted hadrons\nextraordinarily inter-convert the ambient protons and neutrons each\nother through the strong interaction even after the freeze-out time of\nthe neutron to proton ratio $n/p$. Then the predicted value of $Y$\nincrease extremely and we can constrain $T_R$ and the branching ratio\nof the hadronic decay mode $B_h$ comparing to the observational light\nelement abundances. We have found $T_R$ should be higher than 2.5 MeV\n- 4 MeV at 95 $\\%$ C.L. for $B_h$ = $10^{-2}$ - 1. The above results\ntells us that $N_{\\nu}^{\\rm eff}$ can be as small as 1.9 - 2.8 even in\nthe hadron injection scenario for $B_h = 10^{-2}$ - 1. Then it still\nmay be possible to detect the modifications on $N_{\\nu}^{\\rm eff}$ by\nMAP and PLANCK.\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section*{Acknowledgment}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nK.K. wish to thank J. Yokoyama and T. Asaka for useful discussions.\nThis work was partially supported by the Japanese Grant-in-Aid for\nScientific Research from the Monbusho, Nos.\\ 10640250~(MK), 10-04502\n(KK), 9440106~(NS) and ``Priority Area: Supersymmetry and Unified\nTheory of Elementary Particles(\\#707)''(MK) and by the Sumitomo\nFoundation (NS).\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\appendix\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\label{sec:appendix}\n\\section*{Reduction of collision integral}\n\nThis appendix shows how we can reduce the nine dimensional integrals\nin Eq.~(\\ref{eq:collision}) of the collision term $C_{i, \\rm scat}$\nfor the scattering process into one dimensional integrals. Notice\nthat, since we treat the massless neutrino, the norm of the neutrino\nmomentum equals to its energy $|\\mbox{\\boldmath $p_i$}| = E_i$. Here\nwe divide the collision term into two parts:\n%%\n\\begin{equation}\n \\label{dev_coll}\n C_{i, \\rm scat} = - F + B,\n\\end{equation}\n%%\nwhere $F$ represents the forward process and $B$ represents the\nbackward process. They are given by\n%%\n\\begin{equation}\n \\label{forward_rate}\n F = \\frac{g_e}{2E_1}\\int \\frac{dp_2^3}{2E_2(2\\pi)^3}\\int\n \\frac{dp_3^3}{2E_3(2\\pi)^3} \\int \\frac{dp_4^3}{2E_4(2\\pi)^3}\n (2\\pi)^4 \\delta^4(p_1+p_2-p_3-p_4) S|M|^2 \\Lambda_F,\n\\end{equation}\n%%\n\\begin{equation}\n \\label{eq:backward_rate}\n B = \\frac{g_e}{2E_1}\\int \\frac{dp_2^3}{2E_2(2\\pi)^3}\\int\n \\frac{dp_3^3}{2E_3(2\\pi)^3} \\int \\frac{dp_4^3}{2E_4(2\\pi)^3}\n (2\\pi)^4 \\delta^4(p_1+p_2-p_3-p_4) S|M|^2 \\Lambda_B,\n\\end{equation}\n%%\nwhere $g_e$ = 2 and the phase space factors are given by\n%%\n\\begin{eqnarray}\n \\label{eq:Lambda_fb}\n \\Lambda_F &=&\n f_1(E_1)f_2(E_2)\\left(1-f_3(E_3)\\right)\\left(1-f_4(E_4)\\right), \\\\\n \\Lambda_B &=&\n \\left(1-f_1(E_1)\\right)\\left(1-f_2(E_2)\\right)f_1(E_3)f_2(E_4).\n\\end{eqnarray}\n%%\n\nThe integral over $d^3p_4$ is immediately done using\n$\\delta^3(\\mbox{\\boldmath $p_1 + p_2 - p_3- p_4$})$. From the momentum\nconservation, $\\mbox{\\boldmath $|p_4|$}$ is given by\n%%\n\\begin{equation}\n \\label{eq:p4}\n |\\mbox{\\boldmath $p_4$}|^2 = E_4^2 = E_2^2+2E_2R\\cos{\\eta}+R^2,\n\\end{equation}\n%%\nwhere $\\mbox{\\boldmath $R$}$ $\\equiv$ $\\mbox{\\boldmath $p_1 - p_3$}$, $R$\n= $|\\mbox{\\boldmath $R$}|$ and $\\cos{\\eta}$ $\\equiv$ $\\mbox{\\boldmath $R\n\\cdot p_2$}$/($|\\mbox{\\boldmath $p_2$}|$R).\n\nThe remaining delta function $\\delta(E_1+E_2-E_3-E_4)$ shows the\nenergy conservation low which is given by\n%%\n\\begin{equation}\n \\label{eq:energy_cons}\n E_4^2 = E_1^2 + E_2^2 + E_3^2 + 2(E_1E_2-E_1E_3-E_2E_3).\n\\end{equation}\nWe can generally take the momentum axes as\n%%\n\\begin{eqnarray}\n \\label{eq:axes}\n \\mbox{\\boldmath $R$} &=& (0, 0, R) \\\\\n \\mbox{\\boldmath $p_2$} &=& (E_2\\sin{\\eta}\\sin{\\phi},\n E_2\\sin{\\eta}\\cos{\\phi}, E_2\\cos{\\eta}), \\\\\n \\mbox{\\boldmath $p_3$} &=& (E_3\\sin{\\xi}, 0, E_3\\sin{\\xi}),\n\\end{eqnarray}\n%%\nwhere\n%%\n\\begin{equation}\n \\label{eq:cosxi}\n \\cos{\\xi}= \\frac{E_1^2 - E_3^2 - R^2}{2E_3R}.\n\\end{equation}\n%%\nThen $|\\cos{\\xi}| \\le 1$ demands\n%%\n\\begin{equation}\n \\label{eq:int_xi}\n |E_1-E_3| \\le R \\le E_1+E_3.\n\\end{equation}\n%%\nThe volume element of $\\mbox{\\boldmath $p_2$}$ is given by $dp_2^3 =\nE_2^2d\\cos{\\eta}d{\\phi}$ and from Eqs.~(\\ref{eq:p4}) and\n(~\\ref{eq:energy_cons}) the azimuthal angle is obtained by\n%%\n\\begin{eqnarray}\n \\label{eq:angles}\n \\cos{\\eta}=- \\frac{R^2-(E_1-E_3)^2-2E_2(E_1-E_3)}{2E_2R}.\n\\end{eqnarray}\n%%\nThen $|\\cos{\\eta}|\\le 1$ demands\n%%\n\\begin{equation}\n \\label{eq:int_eta}\n |E_1-E_3| \\le R \\le E_1 + 2 E_2 - E_3.\n\\end{equation}\n%%\n From Eqs.~(\\ref{eq:int_xi}) and ~(\\ref{eq:int_eta}), we can obtain the\nallowed region of R,\n%%\n\\begin{equation}\n \\label{eq:R_int}\n |E_1-E_3| \\le R \\le {\\rm Inf}[E_1+E_3, E_1+2E_2-E_3].\n\\end{equation}\n%%\nSince the volume element of $\\mbox{\\boldmath $p_3$}$ is given by\n$dp_3^2 = 2\\pi E_3^2dE_3d\\cos{\\theta}$ where\n$\\cos{\\theta}=\\mbox{\\boldmath{$p_1\\cdot p_3$}}/(E_3E_1)$, the\ndifferential angle element is evaluated by\n%%\n\\begin{equation}\n \\label{eq:dR}\n d\\cos{\\theta}= - \\frac{R}{2 E_1E_3}dR.\n\\end{equation}\n From Eq.~(\\ref{eq:R_int}) we can see that the integration can be performed\nin the four allowed intervals,\n%%\n\\begin{eqnarray}\n \\label{eq:four_int}\n - F + B &=& \\frac1{128E_1^2}\\int_0^{\\infty}dE_3\n \\int_0^{\\infty}dE_2 \\int dR \\int_0^{2\\pi}\\frac{d\\phi}{2\\pi} |M|^2\n (-\\Lambda_F + \\Lambda_B) \\nonumber \\\\\n &=& \\frac1{128E_1^2}\n \\left[\\int_{0}^{E_1}dE_3\\int_{0}^{E_3}dE_2\\int_{E_1-E_3}^{E_1+2E_2-E_3}dR\n +\\int_{0}^{E_1}dE_3\\int_{E_3}^{\\infty}dE_2\\int_{E_1-E_3}^{E_1+E_3}dR\n \\nonumber \\right.\\\\\n & &\\left. \\hspace{1cm} +\\int_{E_1}^{\\infty}dE_3\\int_{-E_1+E_3}^{E_3}dE_2\n \\int_{-E_1+E_3}^{E_1+2E_2-E_3 }dR\n +\\int_{E_1}^{\\infty}dE_3\\int_{E_3}^{\\infty}dE_2\n \\int_{-E_1+E_3}^{E_1+E_3}dR\\right]\n \\nonumber \\\\\n & &\\hspace{1cm} \\times \\int_0^{2\\pi}\\frac{d\\phi}{2\\pi}S|M|^2\n (-\\Lambda_F + \\Lambda_B).\n\\end{eqnarray}\n%%\nEven though we only show the case of of $\\nu_e$ here, we can get the\nsame procedure for $\\nu_{\\mu}$ and $\\nu_{\\tau}$ if $C_V$ and $C_A$ are\nreplaced by $\\tilde{C_V}$ and $\\tilde{C_A}$. As we also noted in\nSec~\\ref{sec:formulation}, we assume that electrons obey the\nBoltzmann distribution function $e^{-E/T}$. In addition, since\nneutrinos are massless, the energy momentum conservation gives $p_1\n\\cdot p_4=p_2 \\cdot p_3$ in the elastic scattering process. The above\nassumptions simplify the integrations still more.\n\nFor the forward reaction, $\\nu(p_1)+e^{\\pm}(p_2) \\rightarrow\n\\nu(p_3)+e^{\\pm}(p_4)$, the phase space factor is given by\n%%\n\\begin{equation}\n \\label{red_lambda_f}\n \\Lambda_F = f_{\\nu}(E_1)\\left(1-f_{\\nu}(E_3)\\right)\\exp{[-\\frac{E_2}{T}]}.\n\\end{equation}\n%%\nThen $F_1$ and $F_2$ in Eq.~(\\ref{eq:C-scat}) are analytically estimated as\n%%\n\\begin{eqnarray}\n \\label{f_1_def}\n F_1 &\\equiv&\n \\left[\\int_{0}^{E_3}dE_2\\int_{E_1-E_3}^{E_1+2E_2-E_3}dR +\n \\int_{E_3}^{\\infty}dE_2\\int_{E_1-E_3}^{E_1+E_3}dR\n \\right]\n \\int_0^{2\\pi}\\frac{d\\phi}{2\\pi} \\cdot\n \\frac{S|M|^2 e^{-\\frac{E_2}{T}}}{256(C_V^2+C_A^2)G_F^2}\n \\nonumber \\\\\n &=& 2T^4 \\left[ E_1^2+E_3^2+2T(E_1-E_3)+4T^4 \\right]\n -T^2\\left[ E_1^2E_3^2+2E_1E_3(E_1+E_3)T \\right.\n \\nonumber \\\\\n & & \\hspace{4cm} \\left. +2(E_1+E_3)^2T^2 +\n 4(E_1+E_3)T^3 + 8T^4 \\right] e^{-\\frac{E_3}{T}},\n\\end{eqnarray}\n%%\n\\begin{eqnarray}\n \\label{f_2_def}\n F_2 &\\equiv&\n \\left[\\int_{-E_1+E_3}^{E_3}dE_2\\int_{-E_1+E_3}^{E_1+2E_2-E_3}dR +\n \\int_{E_3}^{\\infty}dE_2\\int_{-E_1+E_3}^{E_1+E_3}dR\n \\right]\n \\int_0^{2\\pi}\\frac{d\\phi}{2\\pi}\\cdot\n \\frac{S|M|^2 e^{-\\frac{E_2}{T}}}{256(C_V^2+C_A^2)G_F^2}\n \\nonumber \\\\\n &=&\n 2T^4(E_1^2+E_3^2-2T(E_1-E_3)+4T^4) e^{\\frac{E_1-E_3}{T}}\n -T^2 \\left[ E_1^2E_3^2+2E_1E_3(E_1+E_3)T \\right.\n \\nonumber \\\\\n & & \\left. \\hspace{4cm} +2(E_1+E_3)^2T^2 +\n 4(E_1+E_3)T^3 + 8T^4 \\right] e^{-\\frac{E_3}{T}}.\n\\end{eqnarray}\n%%\n\nOn the other hand, for the backward reaction, $\\nu(p_1)+e^{\\pm}(p_2)\n\\leftarrow \\nu(p_3)+e^{\\pm}(p_4)$, the phase space factor is given by,\n%%\n\\begin{equation}\n \\label{red_lambda_B}\n \\Lambda_B =\n \\left(1-f_{\\nu}(E_1)\\right)f_{\\nu}(E_3)\\exp{(-\\frac{E_1+E_2+E_3}{T})}.\n\\end{equation}\n%%\nThen we can analytically obtain $B_1$ and $B_2$ in Eq.~(\\ref{eq:C-scat})\nas\n%%\n\\begin{eqnarray}\n \\label{b_1_def}\n B_1 &\\equiv& \\left[\\int_{0}^{E_3}dE_2\\int_{E_1-E_3}^{E_1+2E_2-E_3}dR +\n \\int_{E_3}^{\\infty}dE_2\\int_{E_1-E_3}^{E_1+E_3}dR\\right]\n \\int_0^{2\\pi}\\frac{d\\phi}{2\\pi}\\cdot\n \\frac{S|M|^2 e^{-\\frac{E_1+E_2+E_3}{T}}}{256(C_V^2+C_A^2)G_F^2},\n \\nonumber \\\\\n &=&\n 2T^4(E_1^2+E_3^2+2T(E_1-E_3)+4T^4)e^{-\\frac{E_1-E_3}{T}}\n -T^2\n \\left[E_1^2E_3^2+2E_1E_3(E_1+E_3)T \\right.\n \\nonumber \\\\\n & & \\hspace{4cm} \\left. +2(E_1+E_3)^2T^2 +\n 4(E_1+E_3)T^3 + 8T^4 \\right] e^{-\\frac{E_1}{T}},\n\\end{eqnarray}\n%%\n\\begin{eqnarray}\n \\label{b_2_def}\n B_2 &\\equiv&\n \\left[\\int_{-E_1+E_3}^{E_3}dE_2\\int_{-E_1+E_3}^{E_1+2E_2-E_3}dR +\n \\int_{E_3}^{\\infty}dE_2\\int_{-E_1+E_3}^{E_1+E_3}dR\n \\right]\n \\int_0^{2\\pi}\\frac{d\\phi}{2\\pi} \\cdot\n \\frac{S|M|^2 e^{-\\frac{E_1+E_2+E_3}{T}}}{256(C_V^2+C_A^2)G_F^2}\n \\nonumber \\\\\n &=&\n 2T^4\\left( E_1^2+E_3^2-2T(E_1-E_3)+4T^4 \\right) -T^2\n \\left[ E_1^2E_3^2+2E_1E_3(E_1+E_3)T \\right.\n \\nonumber \\\\\n & & \\hspace{4cm} \\left. +2(E_1+E_3)^2T^2 +\n 4(E_1+E_3)T^3 + 8T^4 \\right] e^{-\\frac{E_1}{T}}.\n\\end{eqnarray}\n%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{references}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%\n%%\n\\bibitem{Nilles}\n For a review, H.P. 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Letter {\\bf 464}, L1 (1996).\n%%\n\n\\end{references}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%TABLES\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\begin{table}[htbp]\n \\begin{center}\n \\leavevmode\n \\begin{tabular}{ccccc|cc}\n && Process && & S$\\left|M\\right|^2$& \\\\ \\hline\n & $\\nu _{e} + e^{-} $\n & $\\rightarrow$\n & $ \\nu _{e} + e^{-}$\n && $32G_F^2\\left[(C_V + C_A)^2 (p_1 \\cdot p_2)^2 + (C_V -\n C_A)^2 (p_1 \\cdot \n p_4)^2\\right]$\n &\\\\\n & $\\nu _{e} + e^{+} $\n & $\\rightarrow$\n & $ \\nu _{e} + e^{+}$\n && $32G_F^2\\left[(C_V - C_A)^2 (p_1 \\cdot p_2)^2 + (C_V +\n C_A)^2 (p_1 \\cdot \n p_4)^2\\right]$\n &\\\\ & $\\nu _{e} + \\bar{\\nu}_{e} $\n & $\\rightarrow$\n & $ e^{+} + e^{-}$\n && $32G_F^2\\left[(C_V+C_A)^2 (p_1 \\cdot p_4)^2 +\n (C_V-C_A)^2 (p_1 \\cdot p_3)^2\\right]$\n &\\\\\n \\end{tabular}\n \\caption{Matrix elements for electron neutrino\n interactions. $G_F$ is the Fermi coupling constant. Here we take\n $C_V=\\frac12 + 2\\sin^2\\theta_W$, $C_A= \\frac12 $ and the weak\n mixing angle $\\sin^2\\theta_W \\simeq 0.231.$}\n \\label{table:Mnue}\n \\end{center}\n\\end{table}\n\n\\begin{table}[htbp]\n \\begin{center}\n \\leavevmode\n \\begin{tabular}{ccccc|cc}\n && Process && & S$\\left|M\\right|^2$& \\\\ \\hline\n & $\\nu _{\\mu} + e^{-} $\n & $\\rightarrow$\n & $ \\nu _{\\mu} + e^{-}$\n && $32G_F^2\\left[(\\tilde{C_V}+\\tilde{C_A})^2 (p_1 \\cdot\n p_2)^2 + (\\tilde{C_V}-\\tilde{C_A})^2 (p_1 \\cdot\n p_4)^2\\right]$\n &\\\\\n & $\\nu _{\\mu} + e^{+} $\n & $\\rightarrow$\n & $ \\nu _{\\mu} + e^{+}$\n && $32G_F^2\\left[(\\tilde{C_V}-\\tilde{C_A})^2 (p_1 \\cdot\n p_2)^2 + (\\tilde{C_V}+\\tilde{C_A})^2 (p_1 \\cdot\n p_4)^2\\right]$\n &\\\\ & $\\nu _{\\mu} + \\bar{\\nu}_{\\mu} $\n & $\\rightarrow$\n & $ e^{+} + e^{-}$\n && $32G_F^2\\left[(\\tilde{C_V}+\\tilde{C_A})^2 (p_1 \\cdot p_4)^2 +\n (\\tilde{C_V}-\\tilde{C_A})^2 (p_1 \\cdot p_3)^2\\right]$\n &\\\\\n \\end{tabular}\n \\caption{Matrix elements for muon neutrino or tau neutrino\n interactions. $G_F$ is the Fermi coupling constant.\n Here we take $\\tilde{C_V}=C_V-1 = - \\frac12 +\n 2\\sin^2\\theta_W$, $\\tilde{C_A}=C_A-1 = - \\frac12 $ and the weak\n mixing angle $\\sin^2\\theta_W \\simeq 0.231.$}\n \\label{table:Mnumu}\n \\end{center}\n\\end{table}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%FIGURES\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%\n\\begin{figure}\n \\begin{center}\n \\centerline{\\psfig{figure=figure1.ps,width=17cm}}\n \\caption{%%\n Time evolution of the cosmic temperature (a) for $T_{R}=10$~MeV,\n and (b) for $T_{R}=2$~MeV. The dashed line denotes the neutrino\n temperature which can be defined only when they are thermalized\n sufficiently and have the perfect Fermi-Dirac distribution.}\n \\label{fig:temp}\n \\end{center}\n\\end{figure}\n%%\n\\newpage\n%%\n\\begin{figure}\n \\begin{center}\n \\centerline{\\psfig{figure=figure2.ps,width=17cm}}\n \\caption{%%\n Time evolution of the fraction of the energy density of\n $\\nu_{e}$ (solid curve) and $\\nu_{\\mu}$ (dashed curve) to that\n of the standard big bang scenario for (a) $T_{R}= 10$~MeV and\n (b)$T_{R}=2$~MeV. Since the interaction of $\\nu_{\\tau}$ is as\n same as $\\nu_{\\mu}$, the curve of $\\nu_{\\mu}$ also represents\n $\\nu_{\\tau}$.}\n \\label{fig:rho-nu}\n \\end{center}\n\\end{figure}\n%%\n\\newpage\n%%\n\\begin{figure}\n \\begin{center}\n \\centerline{\\psfig{figure=figure3.ps,width=17cm}}\n \\caption{%%\n Distribution function of $\\nu_{e}$ (solid curve) and $\\nu_{\\mu}$\n (dashed curve) (a)for $T_{R}=10$~MeV and (b)for $T_{R}=2$~MeV.\n The dotted curve is the Fermi-Dirac distribution function.\n Since the interaction of $\\nu_{\\tau}$ is as same as $\\nu_{\\mu}$,\n the curve of $\\nu_{\\mu}$ also represents $\\nu_{\\tau}$.}\n \\label{fig:distribution}\n \\end{center}\n\\end{figure}\n%%\n\\newpage\n%%\n\\begin{figure}[htbp]\n \\begin{center}\n \\centerline{\\psfig{figure=tr_nnu3.ps,width=18.0cm}}\n \\caption{%%\n Effective number of neutrino species $N_{\\nu}^{\\rm eff}$ as a\n function of reheating temperature $T_{R}$. The top horizontal\n axis denotes the lifetime which corresponds to $T_{R}$.}\n \\label{fig:tr_nnu}\n \\end{center}\n\\end{figure}\n%%\n\\newpage\n%%\n\\begin{figure}[htbp]\n \\begin{center}\n \\centerline{\\psfig{figure=figure5.ps,width=18.0cm}}\n \\caption{%%\n Weak interaction rates (sec$^{-1}$) between neutron and proton.\n The upper curves are $\\Gamma_{n \\rightarrow p}$. The lower\n curves are $\\Gamma_{p \\rightarrow n}$. The solid lines denote\n the case of $T_R = 10$ MeV which corresponds to the standard big\n bang scenario. The dotted lines denote the case of $T_R = 1$ MeV\n in the late-time entropy production scenario. Notice that $\\Gamma_{n\n \\rightarrow p}^{-1}$ reaches $\\tau_n = 887$ sec in the low\n temperature.}\n \\label{fig:weak_rate}\n \\end{center}\n\\end{figure}\n%%\n\\newpage\n%%\n\\begin{figure}[htbp]\n \\begin{center}\n \\centerline{\\psfig{figure=figure6.ps,width=16cm}}\n \\caption{%%\n Evolution of neutron to proton ratio as a function of the\n temperature, (a)when we change only the number of neutrino\n species in the standard big bang scenario, and (b)when we change\n the reheating temperature in the late-time entropy production\n scenario. The dashed line is the thermal equilibrium curve\n ($= e^{-Q/T}$). }\n \\label{fig:npratio}\n \\end{center}\n\\end{figure}\n%%\n\\newpage\n%%\n\\begin{figure}[htbp]\n \\begin{center}\n \\centerline{\\psfig{figure=figure7.ps,width=18cm}}\n \\caption{%%\n $^4$He mass fraction $Y_p$ as a function of $T_R$ (solid line)\n at $\\eta = 5 \\times 10^{-10}$. The dashed line denotes the\n virtual {}$^4$He mass fraction computed by including only the\n speed down effect due to the change of the effective number of\n neutrino species which is shown in Fig.~\\ref{fig:tr_nnu}. The\n dotted line denotes the value predicted in SBBN at $\\eta = 5\n \\times 10^{-10}$. The long-dashed line denotes the observational\n 2 $\\sigma$ upper bound, $Y^{obs} \\sim 0.252$ which is obtained\n by summing the errors in quadrature. The top horizontal axis\n represents the lifetime which corresponds to $T_R$.}\n \\label{fig:pred_he4}\n \\end{center}\n\\end{figure}\n%%\n\\newpage\n%%\n\\begin{figure}[htbp]\n \\begin{center}\n \\centerline{\\psfig{figure=middle4.ps,width=18cm}}\n \\caption{%%\n Contours of the confidence level in ($\\eta,T_R$) plane. The\n inner (outer) curve is 68$\\%$ (95$\\%$) C.L.. The filled square\n denotes the best fit point. The right vertical\n axis denotes the lifetime which corresponds to\n $T_R$.\n }\n \\label{fig:eta_tr}\n \\end{center}\n\\end{figure}\n%%\n\\newpage\n%%\n\\begin{figure}[htbp]\n \\begin{center}\n \\centerline{\\psfig{figure=nch_100tev.ps,width=18cm}}\n \\caption{%%\n Plot of the charged particle multiplicity\n $\\langle N_{ch}\\rangle$ for the center of mass energy\n $\\protect\\sqrt{s} = 1 \\gev - 100 \\tev$.}\n \\label{fig:nch}\n \\end{center}\n\\end{figure}\n%%\n\\newpage\n%%\n\\begin{figure}[htbp]\n \\begin{center}\n \\centerline{\\psfig{figure=comb_tr_Y.ps,width=18cm}}\n \\caption{%%\n Plot of the predicted $\\4he$ mass fraction $Y_p$ as a function\n of $T_R$ for (a) m$_{\\phi}$=100 TeV and (b) m$_{\\phi}$ =10 GeV\n at $\\eta = 5 \\times 10^{-10}$. The solid curve denotes the\n predicted $Y_p$ where we take the branching ratio of the\n hadronic decay mode as $B_h$ = 1 (right one) and $B_h$ = 0.01\n (left one). The dot-dashed line denotes $B_h = 0$. The dashed\n line denotes the virtual $Y_p$ curve computed by including only\n the speed down effect due to the change of the effective number\n of neutrino species. The dotted line denotes $Y_p$ in SBBN. The\n long-dashed line denotes the rough observational two $\\sigma$\n upper bound that $Y_p$ should be less than about 0.252. The top\n horizontal axis represents the lifetime which corresponds to\n $T_R$.}\n \\label{fig:had_tr_Y}\n \\end{center}\n\\end{figure}\n%%\n\\newpage\n%%\n\\begin{figure}[htbp]\n \\begin{center}\n \\centerline{\\psfig{figure=m100_eta_tr.ps,width=18cm}}\n \\vspace{-5cm}\n \\caption{%%\n Contours of the confidence levels for $m_{\\phi}= 100$ TeV in\n ($\\eta,T_R$) plane for the branching ratio of the hadronic\n decay mode (a) $B_h$ = 1 and (b) $B_h = 10^{-2}$. The solid\n line denotes 95 $\\%$ C.L. and the dotted line denotes 68 $\\%$\n C.L. The filled square is the best fit point between the\n observation and theoretical prediction for D, $\\4he$ and $\\li7$.\n The right vertical axis represents the lifetime which\n corresponds to $T_R$.}\n \\label{fig:m100_eta_tr}\n \\end{center}\n\\end{figure}\n%%\n\\newpage\n%%\n\\begin{figure}[htbp]\n \\begin{center}\n \\centerline{\\psfig{figure=m0.01_eta_tr.ps,width=18cm}}\n \\vspace{-5cm}\n \\caption{%%\n Contours of the confidence levels for $m_{\\phi}= 10$ GeV for the\n same theory parameters as in Fig.~\\ref{fig:m100_eta_tr}. }\n \\label{fig:m0.01_eta_tr}\n \\end{center}\n\\end{figure}\n%%\n\\newpage\n%%\n\\begin{figure}[htbp]\n \\begin{center}\n \\centerline{\\psfig{figure=comb2_m_tr.ps,width=18cm}}\n \\vspace{-3cm}\n \\caption{%%\n Lower bound on $T_R$ as a function of $m_{\\phi}$ for the\n branching ratio of the hadronic decay mode (a) $B_h$ = 1 and (b)\n $B_h = 10^{-2}$. The solid line denotes 95 $\\%$ C.L. and the\n dotted line denotes 68 $\\%$ C.L. The right vertical axis\n represents the lifetime which corresponds to $T_R$. }\n \\label{fig:m_tr}\n \\end{center}\n\\end{figure}\n%%\n\\newpage\n%%\n\\begin{figure}[htbp]\n \\begin{center}\n \\centerline{\\psfig{figure=gamma.ps,width=18cm}}\n% \\vspace{-3cm}\n \\caption{%%\n Contours of $\\Gamma_{\\rm s} = 0.2$ (bold), $0.3, 0.4, 0.5$ and $0.6$ on \n the ($\\Omega_0, N_\\nu^{\\rm eff}$) plane for $h=0.7$.\n }\n \\label{fig:gamma}\n \\end{center}\n\\end{figure}\n%%\n%%\n\\begin{figure}[htbp]\n \\begin{center}\n \\centerline{\\psfig{figure=power.ps,width=18cm}}\n \\caption{%%\n Matter power spectra $P(k)$ of CDM models \n with $N_\\nu^{\\rm eff}=0.5, 2, $ and $3$.\n We take $\\Omega_0=0.3, h=0.7$, and $\\Omega_Bh^2=0.02$ where \n $\\Omega_B$ is the baryon density parameter. \n }\n \\label{fig:power}\n \\end{center}\n\\end{figure}\n%%\n%%\n\\begin{figure}[htbp]\n \\begin{center}\n \\centerline{\\psfig{figure=sigma8.ps,width=18cm}}\n% \\vspace{-3cm}\n \\caption{%%\n Allowed region on $\\Omega_0-h$ plane from observational values of \n $\\sigma_8$ deduced \n from the rich cluster abundance at present for flat CDM models.\n Models with $N_\\nu^{\\rm eff}=0.5, 2,$ and $3$ are plotted. \n }\n \\label{fig:sigma8}\n \\end{center}\n\\end{figure}\n%%\n%%\n\\begin{figure}[htbp]\n \\begin{center}\n \\centerline{\\psfig{figure=cl_new.eps,width=16cm}}\n% \\centerline{\\psfig{figure=cl.ps,width=18cm}}\n \\vspace{0.5cm}\n% \\vspace{-3cm}\n \\caption{%%\n Power spectra of CMB anisotropies (left top panel) and\n polarization (right top panel) of models with \n $N_{\\rm eff}^{\\rm eff}=3, 2$\n and $0.5$. Bottom two panels show $(C_\\ell(N_{\\rm eff})-\n C_\\ell(3))/C_\\ell(3)$ with $N_{\\rm eff}^{\\rm eff}=2.9, 2.5$\n and $2$ for CMB anisotropies (left bottom) and polarization (right \n bottom).\n }\n \\label{fig:CMB}\n \\end{center}\n\\end{figure}\n%%\n\n\n\\end{document}\n\n\n\n\n\n\n"
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"name": "astro-ph0002127.extracted_bib",
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Vladilo,\n astro-ph/9908060.\n%%\n\n\\bibitem{OliSkiSte}\n K.A. Olive, G. Steigman, and E.D. Skillman,\n { Astrophys. J.} {\\bf 483} (1997) 788.\n%%\n\n\\bibitem{Izo}\n Y.I. Izotov, T.X. Thuan, and V.A. Lipovetsky,\n { Astrophys. J. Suppl. Series}, {\\bf 108} (1997) 1;\\\\\n Y.I. Izotov and T.X. Thuan\n { Astrophys. J.}, {\\bf 500} (1998) 188.\n%%\n\n\\bibitem{FieOLi}\n B.D. Fields and K.A. Olive,\n { Astrophys. J.}, {\\bf 506} (1998) 177.\n%%\n\n\\bibitem{BonMol}\n P. Bonifacio and P. Molaro,\n { Mon. Not. R. Astron. Soc.} {\\bf 285} (1997) 847.\n%%\n\n\\bibitem{Kolb-Turner}\n E.W. Kolb and M.S. Turner,\n The Early Universe, Addison-Wesley (1990).\n%%\n\n\\bibitem{PDG}\n C. Caso {\\it et al.}, Particle Data Group,\n { Euro. Phys. J. C} {\\bf 3}, 1 (1998).\n%%\n\n\\bibitem{HKKM}\n E. Holtmann, M. Kawasaki, K. Kohri and T. Moroi,\n { Phys. Rev}. {\\bf D60} {023506} (1999), hep-ph/9805405.\n%%\n\n\\bibitem{DDRG}\n S. Dimopoulos, G. Dvali, R. Rattazzi and G.F. Giudice,\n Nucl. Phys. {\\bf B510} (1998) 12.\n%%\n\n\\bibitem{RS}\n M. H. Reno and D. Seckel,\n Phys. Rev. {\\bf D37}, 3441 (1988).\n%%\n \n\\bibitem{ky}\n K. Kohri and J. Yokoyama,\n Phys. Rev. {\\bf D61} 023501 (2000), astro-ph/9908160.\n%%\n \n\\bibitem{biebel}\n O. Biebel, private communication.\n%%\n \n\\bibitem{Riess} \n A. G. Riess et al., Astron. J. {\\bf 116}, 1009 (1998).\n%%\n \n\\bibitem{Perl} \n S. Perlmutter et al. Astrophys. J. {\\bf 517}, 565 (1999).\n%%\n\n\\bibitem{CMB}\n S. Hancock, G. Rocha, A. N. Lasenby and C. M. Guti\\'errez, Mon. \n Not. R. Astron. Soc. {\\bf 294}, L1 (1998);\n G. Efstathiou et al. Mon. \n Not. R. Astron. Soc. {\\bf 393}, L47 (1999);\n M. Tegmark, Astrophys. J. {\\bf 514}, L69 (1999).\n\n%%\n\n\\bibitem{Bard}\n J. M. Bardeen, J. R. Bond, N. Kaiser and A. S. Szalay, Astrophys. J. \n{\\bf 304}, 15 (1986).\n\n%%\n\n\\bibitem{PD} J.A. Peacock and S.J. Dodds,\n { Mon. Not. R. Astron. Soc.} {\\bf 267}, 1020 (1994).\n%%\n\n\\bibitem{SG}\nN. Sugiyama and N. Gouda, Prog. Theor. Phys. {\\bf 88}, 803 (1992).\n%\n\n\\bibitem{Eke}\n V. R. Eke, S. Cole and C. S. Frenk, Mon. Not. R. Astron. Soc.\n {\\bf 282}, 263 (1996).\n%%\n\n\\bibitem{sigma8}\n N. A. Bahcall and X. Fan, Astrophys. J. {\\bf 504}, 1 (1998); \n P. T. P. Viana and A. R. Liddle, in Proceedings of the Conference\n ``Cosmological Constraints from X-Ray Clusters'' (to be published),\n astro-ph/9902245.\n%%\n\n\\bibitem{Mould}\nJ. R. Mould et al., astro-ph/9909260. \n%%\n\n\\bibitem{Hu}\nW. Hu, N. Sugiyama and J. Silk, Nature {\\bf 386}, 37 (1997).\n%%\n\n\\bibitem{COBE} C.L.~Bennett et al.,\n Astrophys. J. Letter {\\bf 464}, L1 (1996).\n%%\n\n"
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"name": "astro-ph0002128.tex",
"string": "% =============== close_.tex ========================\n%=================== January 2000 ===================\n% ====\n% \n\\textwidth 22cm\n\\textheight 23cm \n\\oddsidemargin -0.5cm\n\\topmargin 0cm\n\\parskip 0.15cm\n\\tolerance = 10000\n\\parindent 10pt\n\\baselineskip= 24pt\n\\def \\yskip{\\penalty-50\\vskip3pt plus 3pt minus 2pt}\n\\def \\reference{\\par \\yskip \\noindent \\hangindent .4in \\hangafter 1}\n\\def \\abc#1#2#3#4 {\\reference#1, {\\sl#2}, {\\bf#3}, #4}\n\\def \\blank {\\lower 5pt\\hbox to 0.75in{\\hrulefill}}\n\\def \\kms{\\rm{km}~\\rm{s}^{-1}}\n\\def \\cc{$\\rm{cm}^{-3}$}\n\\def \\msyr{$M_{\\odot}~yr^{-1}$}\n\\def \\cm{~\\rm{cm}}\n\\def \\s{~\\rm{s}}\n\\def \\km{~\\rm{km}}\n\\def \\gm{\\rm{gm}}\n\\def \\K{~\\rm{K}}\n\\def \\g{~\\rm{g}}\n\\def \\AU{~\\rm{AU}}\n\\def \\yrs{~\\rm{yrs}}\n\\def \\yr{~\\rm{yr}}\n\\def \\pc{~\\rm{pc}}\n\\def \\kpc{~\\rm{kpc}}\n%\n%\\def \\lae{\\mathrel{<\\kern-1.0em\\lower0.9ex\\hbox{$\\sim$}}}\n%\\def \\gae{\\mathrel{>\\kern-1.0em\\lower0.9ex\\hbox{$\\sim$}}}\n\n%\\documentstyle[11pt]{article}\n%\\documentstyle[11pt,aasms]{article}\n%\\documentstyle[11pt,aasms4]{article}\n\\documentstyle[11pt,aasms,tighten,flushrt]{article}\n%Last line makes single line, right side straight, for distribution.\n\n\\begin{document}\n%\\normalsize\n\\small\n\n\\setcounter{page}{1}\n% Starting Date of the Latex File: 14.2.1997\n\\begin{center} \\bf \nECCENTRIC ORBITS OF CLOSE COMPANIONS TO\nASYMPTOTIC GIANT BRANCH STARS\n\\end{center}\n%\\vspace*{2.0cm}\n\n\\begin{center}\nNoam Soker\\\\\nDepartment of Physics, University of Haifa at Oranim\\\\\n%Mathematics-Physics\\\\\nOranim, Tivon 36006, ISRAEL \\\\\nsoker@physics.technion.ac.il \n\\end{center}\n\n%\\vfill \n%\\clearpage \n\n\n\n%\\clearpage \n\\begin{center}\n\\bf ABSTRACT\n\\end{center}\n\n\n I propose that the relatively high eccentricity\n$0.1 \\lesssim e \\lesssim 0.4$ found in some tidally strongly interacting\nbinary systems, where the mass-losing star is an evolved giant star,\ne.g., an asymptotic giant branch star, is caused by an enhanced mass\nloss rate during periastron passages.\n Tidal interaction by itself will circularize the orbits of these\nsystems in a relatively short time, hence a mechanism which increases\nthe eccentricity on a shorter time scale is required.\n The proposed scenario predicts that the nebula formed by the mass\nloss process possesses a prominent departure from axisymmetrical\nstructure.\n Such a departure is observed in the Red Rectangle, which\nhas a central binary system, HD 44179, with an orbital period of\n$T_{\\rm orb} = 318$ days, and an eccentricity of $e=0.38$.\n \n{\\bf Key words:} \nstars: binaries: close\n$-$ stars: AGB and post-AGB\n$-$ stars: mass loss\n$-$ ISM: general \n\n%BIPOLAR.TEX; 20.5.97 ; 63,584 b. \n\n%\\clearpage \n\n% ======================================================================\n\\section{INTRODUCTION}\n% ======================================================================\n \n In recent years it has been found that close binary companions to\nasymptotic giant branch (AGB) stars can influence the \nchemistry of the circumbinary shells (or disks) and of the post-AGB stars \n(e.g., Van Winckel, Waelkens, \\& Waters 1995), and the eccentricities \nof the orbits (e.g., Waelkens {\\it et al.} 1996). \n(In this paper I refer by ``close binary systems'' to \nsystems with orbital periods of $T_{\\rm orb} \\sim 1 \\yr$, i.e., \nthere is a very strong tidal interaction between the AGB star and its \ncompanion. By wide systems I refer to systems where the tidal \ninteraction is very weak.) \n Van Winckel {\\it et al.} (1998) suggest that all post-AGB star with\npeculiar abundances are in close binaries.\n The peculiar abundances, i.e., depletion of Fe peak elements and some other\nelements (e.g., Waters, Trams, \\& Waelkens 1992;\nVan Winckel {\\it et al.} 1999), is explained by accretion back from the\ncircumbinary disk of gas depleted of dust (Waters {\\it et al.} 1992), \nsince the dust is expelled more efficiently from the disk by radiation pressure.\n The disk helps by providing a slow accretion rate and a low density to \nprevent an efficient drag between the gas and dust particles \n(Waters {\\it et al.} 1992).\n It is not clear, though, that a Keplerian circumbinary disk is a necessary\ncondition for the separation of gas from dust.\nIn an earlier paper (Soker 2000) I argued that a dense slowly expanding\nequatorial flow may have the same effect, while having the advantage\nthat it does not require a huge amount of angular momentum as\na Keplerian disk does.\n \n Another peculiar property found among many of these binary systems\nis a high eccentricity (e.g., Van Winckel 1999, and references therein),\ndespite the very strong tidal interaction between the AGB stars and\ntheir companions.\nExamples are:\n {\\bf HD 44179}, which is located at the center of the\nRed Rectangle, a bipolar proto planetary nebula (PN), has an \norbital period of $T_{\\rm orb} = 318$ days, a semimajor axis of \n$a \\sin i = 0.32 \\AU$, and an eccentricity \nof $e=0.38$ (Waelkens {\\it et al.} 1996; Waters {\\it et al.} 1998). \n {\\bf AC Her}, with $T_{\\rm orb} = 1194$ days, $a \\sin i = 1.39 \\AU$, \nand $e=0.12$ (Van Winckel {\\it et al.} 1998). \n {\\bf 89 Herculis}, with $T_{\\rm orb} = 288$ days, \nand $e=0.19$ (Waters {\\it et al.} 1993). \n {\\bf HR 4049}, with $T_{\\rm orb} = 429$ days, \n$a \\sin i = 0.583 \\AU$, and $e=0.31$ (Van Winckel {\\it et al.} 1995).\n\n Van Winckel {\\it et al.} (1995) mention in one sentence in their discussion\nthat ``. . . the large eccentricities suggest that mass loss may have \nstarted at periastron only, thus increasing the eccentricity still.''\n However, they did not carry out any quantitative study, but abandoned\nthis explanation in favor of the ``external disk'' mechanism\n(Waelkens {\\it et al.} 1996; Waters {\\it et al.} 1998). \n What I term ``external disk'' mechanism is the tidal interaction between\nthe binary system and the circumbinary disk, which is the model to\nexplain eccentricities in young stellar binaries \n(Artymowicz {\\it et al.} 1991; Artymowicz \\& Lubow 1994).\n \n In the present paper I claim that higher mass loss rate during\nperiastron passage can indeed explain the high eccentricities observed\nin the systems mentioned above. \n I am motivated by earlier results that variation in the mass loss \nrate and the mass transfer rate with orbital phases in eccentric orbits \ncan explain the formation of multiple shells in PNs\n(Harpaz, Rappaport, \\& Soker 1997; in that paper, though, the orbital \nperiods are $\\sim 100 \\yrs$ rather than $1 \\yr$), and the displacement \nof the the central stars from the centers of PNs \n(Soker, Rappaport, \\& Harpaz 1998).\n In the next section I describe the proposed model and the\ntime scales involved, while in $\\S 3$ the external disk mechanism\nproposed in other studies (e.g., Waelkens {\\it et al.} 1996) is discussed.\nA short summary is in $\\S 4$. \n\n% ======================================================================\n\\section{ECCENTRICITY EVOLUTION DUE TO MASS LOSS} \n% ======================================================================\n \n The eccentricity $e$ is reduced by tidal forces on a time scale called\nthe circularization time and is defined as \n$\\tau_{\\rm circ} \\equiv -e/\\dot e$.\n In the common tidal model in use, the equilibrium tide mechanism\n(Zahn 1977; 1989), the circularization time is given by \n(Verbunt \\& Phinney 1995)\n\\begin{eqnarray}\n\\tau_{\\rm {circ}} = \n1.2 \\times 10^4\n{{1}\\over{f}} \n\\left( {{L} \\over {2000 L_\\odot}} \\right)^ {-1/3}\n\\left( {{R} \\over {200 R_\\odot}} \\right)^ {2/3}\n\\left( {{M_{\\rm {env}}} \\over {0.5M_1}} \\right)^ {-1} \n\\left( {{M_{\\rm {env}}} \\over {0.5M_\\odot}} \\right)^ {1/3} \\nonumber \\\\\n\\times \\left( {{M_2} \\over {M_1}} \\right)^ {-1}\n\\left( 1+ {{M_2} \\over {M_1}} \\right)^ {-1}\n\\left( {{a} \\over {3R}} \\right)^ {8}\n\\yr ,\n\\end{eqnarray}\nwhere $L$, $R$ and $M_1$ are the luminosity, radius, and total mass of the \nprimary AGB star, $M_{\\rm {env}}$ is the primary's envelope mass, \nand $f \\simeq 1$ is a dimensionless parameter. \n The synchronization time is related to the circularization time\nby the expression \n$\\tau_{\\rm {syn}} \\simeq (1+M_2/M_1)(M_2/M_1)^{-1}(I/M_1R^2) \n(R/a)^2 \\tau_{\\rm {cir}} $, where $I$ is the primary's moment of inertia.\nApproximating the envelope density profile of stars on the upper \nRGB and AGB by $\\rho \\propto r^{-2}$, where $r$ is the radial distance\nfrom the star's center, I find $I=(2/9) M_{\\rm env} R^2$. \n Substituting this in the expression for the synchronization time I find\n\\begin{eqnarray}\n\\tau_{\\rm {syn}} = \n150 \n{{1}\\over{f}} \n\\left( {{L} \\over {2000 L_\\odot}} \\right)^ {-1/3}\n\\left( {{R} \\over {200 R_\\odot}} \\right)^ {2/3}\n\\left( {{M_{\\rm {env}}} \\over {0.5M_\\odot}} \\right)^ {1/3}\n% \\nonumber \\\\\n\\left( {{M_2} \\over {M_1}} \\right)^ {-2}\n\\left( {{a} \\over {3R}} \\right)^ {6}\n\\yr.\n\\end{eqnarray}\n The short synchronization time means that the AGB star will spin with an\nangular velocity of $\\omega \\simeq (R/a)^{3/2} \\omega_{\\rm Kep}$,\nwhere $\\omega_{\\rm Kep}$ is the Keplerian velocity on the \nequatorial line of the primary. \n The high angular velocity and close companion will lead to an enhanced\nmass loss rate in the equatorial plane (Mastrodemos \\& Morris 1999).\n\n The change in eccentricity due to an isotropic mass loss \n(the derivation is applicable for an axisymmetric mass loss as well; \nmass transfer will be discussed later) is given by \n(Eggleton 2000) \n\\begin{eqnarray}\n\\delta e = \n{{\\vert \\delta M \\vert} \\over {M}} (e + \\cos \\theta), \n\\end{eqnarray}\nwhere $\\delta M$ is the mass lost from the binary in the stellar wind \nat the orbital phase $\\theta$ (hence $\\delta M < 0$), $M$ is the total\nmass of the binary system, and $\\theta$ is the polar angle, measured\nfrom periastron, of the position vector from the center of mass to\nthe secondary.\n The derivation of equation (3) assumes that\n$\\delta M(\\theta)=\\delta M (-\\theta)$. \n To derive a time scale, I assume that in addition to its constant mass\nloss rate over the orbital motion $\\dot M_w$, the primary AGB star\nloses an extra mass $\\delta M_p$ in a short time during the periastron\npassage, $\\cos \\theta =1$.\n The total mass being lost in one orbital period \n$T_{\\rm orb}$, is $\\Delta M_o = \\dot M_w T_{\\rm orb} + \\delta M_p$. \nI define the fraction of the mass being lost at periastron\n\\begin{eqnarray}\n\\beta \\equiv {{\\delta M_p}\\over{\\Delta M_o}}.\n\\end{eqnarray}\n The constant mass loss rate $\\dot M_w$ does not change the eccentricity.\n Hence, the change in the eccentricity in one orbital period is \n$\\delta e = (1+e) (\\vert \\delta M_p \\vert / M )$.\n Over a time much longer than the orbital period we can write\nfor the rate of change of the eccentricity\n\\begin{eqnarray}\n{{de}\\over{dt}} = - (1+e) \\beta {{\\dot M}\\over{M}} \n\\end{eqnarray}\n where the total mass loss rate is\n$\\dot M = \\Delta M_o/T_{\\rm orb} = \\dot M_w + \\delta M_p/T_{\\rm orb}$.\n I define the time scale for change in eccentricity due to enhanced\nperiastron mass loss as \n\\begin{eqnarray}\n\\tau_p \\equiv {{e}\\over{de/dt}} \n= 4 \\times 10^3 \\beta^{-1}\n\\left[ {{e}\\over{0.2(1+e)}} \\right]\n\\left( {{M_1+M_2} \\over {2M_\\odot}} \\right) \n\\left( {{\\vert \\dot M_o \\vert} \\over {10^{-4} M_\\odot \\yr^{-1}}} \\right)^{-1} \n\\yr.\n\\end{eqnarray}\n\nUnder the assumption that the fraction of mass lost at \nperiastron passage $\\beta$ does not change during the \nevolution, we can integrate equation (5) to yield\n\\begin{eqnarray}\n{{1+e}\\over{1+e_i}} = \n\\left( {{M_i}\\over{M}} \\right)^{\\beta}, \n\\end{eqnarray}\nwhere $e_i$ and $M_i$ are the initial eccentricity and total \nmass, respectively. \n Both the initial over final mass and $\\beta$ can vary continuously\namong different systems.\n It is useful, however, to examine two extreme cases.\n\\newline\n{\\bf Systems with $\\beta \\simeq 1$:}\nWhen most of the mass is being lost during a periastron passage, then\n$\\beta \\simeq 1$.\n Such can be the case for low mass AGB stars and/or stars not yet on\nthe upper AGB, so that the mass loss rate is low, and the secondary,\nvia direct gravitational effects, increases substantially the mass\nloss rate during periastron passages.\n For systems with $\\beta \\simeq 1$, a moderate amount of total mass loss\ncan substantially increase the eccentricity.\n For example, for initial (initial means at the beginning\nof the interaction, not on the main sequence) masses of\n$M_{1i}=1 M_\\odot$ and $M_2 = 0.6 M_\\odot$, and $e_i \\ll 1$, if the\nprimary loses its entire envelope of $0.4 M_\\odot$, the eccentricity\nwill be given by $1+e \\simeq 1.6/1.2 = 1.33$ or $e \\simeq 0.3$.\n For $\\beta =0.5$ we get $e \\simeq 0.15$ for the same mass loss evolution. \nThe circumbinary wind (or nebula) is expected to have two \nprominent properties.\nFirst, since most of the mass, at least in the equatorial plane,\nis lost via a dynamical interaction between\nthe two binary stars, and not by radiation pressure on dust,\nthe wind expansion velocity in the equatorial plane will be very \nlow (Soker 2000). \nSecond, since most of the mass, or a substantial fraction of it, is lost\nduring a periastron passage when the mass-losing star always moves in\nthe same direction, the nebula is expected to possess a large\ndegree of departure from axisymmetry (Soker {\\it et al.} 1998). \n Such a process may explain the departure from axisymmetry observed\nin the Red Rectangle.\n The Red Rectangle has a close eccentric binary system,\nwith $T_{\\rm orb} = 318$ days and $e=0.38$.\nThe general structure of the Red Rectangle is highly axisymmetrical, up\nto $\\sim 1 ^\\prime$ from the central star (e.g., Van Winckel 2000).\nHowever, the 10 $\\mu$m map presented by Waters {\\it et al.}\n(1998; their fig. 3) shows a clear departure from axisymmetry at scales\nof $\\sim 5 ^{\\prime \\prime}$ from the central star. \n Their contour map shows that the equatorial matter is more\nextended in the west side.\n\\newline\n{\\bf Systems with $\\beta \\ll 1$:}\n In these cases the total mass lost by the system should be \nlarger, or only slightly smaller, than the total binary final\nmass in order for the eccentricity to be $e \\gtrsim 0.1$. \n This is expected for systems where the mass-losing star reaches the\nupper AGB, hence has a strong wind.\n The rotation, because of synchronization with the orbital motion (eq. 2),\ncan further increase the mass loss rate.\n Contrary to the previous case, the wind will have an expansion\nvelocity typical for AGB stars, and the departure from axisymmetry \nwill be small.\n Only in the equatorial plane might the flow be slower, since the\nmass lost at periastron via dynamical interaction may not be\naccelerated to high velocities (Soker 2000). \n The departure from axisymmetry might still be large enough to be\ndetected by observations. \n\n The tidal circularization time (eq. 1) and the time scale for\nthe increase of eccentricity due to periastron mass loss\n(eq. 6) have a different dependence on the eccentricity,\nas well as on other parameters.\n We can find the conditions for the eccentricity to grow by requiring\nthat the time scale given by equation (6) be shorter than the\ncircularization time given by equation (1).\n For this purpose, we can neglect the dependence on the luminosity,\nradius, and envelope mass in equation (1).\n Neglecting the dependence on the envelope mass is justified since\nfrom equation (7) it emerges that for the eccentricity to change\nby $e \\gtrsim 0.1$, the envelope mass to be lost should be\n$\\gtrsim 0.2 M_\\odot$. \n Using these approximations and $e \\ll 1$, and taking\n$M_1=M_2 =1 M_\\odot$, we find the condition for the eccentricity to grow\n\\begin{eqnarray}\n\\left( {{a} \\over {3R}} \\right)^ {8}\n\\gtrsim\n\\beta^{-1}\n\\left({{e}\\over{0.2}} \\right)\n\\left( {{\\vert \\dot M_o \\vert} \\over {10^{-4} M_\\odot \\yr^{-1}}} \\right)^{-1}. \n\\end{eqnarray}\n In general, it is expected that $a \\gtrsim 3 R$.\nThis is since for $e\\simeq 0.3$ the periastron distance for $a=3 R$\nis $a_p \\simeq 2 R$, and a Roche lobe over flow is likely to occur\nat these distances.\n The mass loss process increases the orbital separation, increasing further\nthe ratio $a/R$.\nIf the eccentricity does not grow much, and the continuous mass loss\nrate $\\dot M_w$ increases as the AGB star's envelope mass decreases,\nthen the system changes from a $\\beta \\simeq 1$ system into\na $\\beta \\ll 1$ system.\n\n Until now I have considered only mass loss, neglecting mass transfer. \nWhen the primary's radius to orbital separation ratio increases \n(as the primary expands along the AGB) to $(R/a) \\gtrsim 0.5$, \nmass transfer, e.g., due to Roche lobe overflow, becomes important. \n The change in eccentricity due to a mass $\\delta M_{\\rm tran}$\ntransferred from the primary to the secondary is given by (Eggleton 2000)\n\\begin{eqnarray}\n\\delta e = 2 \\delta M_{\\rm tran} \n\\left( {{1}\\over{M_1}} - {{1}\\over{M_2}} \\right) (e+\\cos \\theta).\n\\end{eqnarray}\n Since enhanced mass transfer is expected during periastron passage,\nwe see that the eccentricity will increase if $M_1 < M_2$,\nas is required for stable mass transfer and is found for these systems\n(e.g., HD 44179 in the Red Rectangle; Waelkens {\\it et al.} 1996). \n Because of the extended envelope of AGB stars, the mass transferred \ncan be several times the mass lost in one orbital period. \n Therefore, the change in eccentricity due to mass transfer \nmay become important when the mass-losing star becomes less massive than\nthe accretor. \n The tidal interaction, though, will become stronger as well at\nthese small orbital separations.\n\n A final comment to this section is that because of their close companions,\nthese post-AGB stars did not evolve on a canonical AGB track\n(Van Winckel, H., private communication).\nHowever, it is still expected that they had a high mass loss rate\nin their recent past. \n\n\n% ======================================================================\n\\section{COMPARISON WITH THE EXTERNAL DISK PROCESS} \n% ======================================================================\n\n Waelkens {\\it et al.} (1996) attributed the eccentricity of post-AGB\nclose binaries to the external disk mechanism.\n In the external disk mechanism, which was developed for young binary\nsystems (e.g., Artymowicz \\& Lubow 1994), there is a resonance\ninteraction between the binary system and an external disk,\nmainly with the disk material closer than $\\sim 6 a$ to the \nbinary system (e.g., Artymowicz {\\it et al.} 1991). \n The eccentricity increases at a rate given by \n(e.g., Artymowicz {\\it et al.} 1991) \n\\begin{eqnarray}\n\\dot e \\simeq 1.9 \\times 10^{-3} \n\\left( {{M_{\\rm disk}}\\over{M}}\\right)\n\\left( {{2 \\pi}\\over{T_{\\rm orb}}} \\right),\n\\end{eqnarray}\nwhere $M_{\\rm disk}$ is the mass of the disk inner to $\\sim 6 a$.\n\n The large uncertainty for post-AGB stars, or any post-main sequence\nmass-losing star, is the disk mass within $\\sim 6 a$.\n There is strong evidence for molecular disks in several\nAGB or post-AGB stars, but these disks have typical radii of\nseveral$\\times 100 \\AU$ (Jura \\& Kahane 1999).\n The inner boundaries of the disks can be much closer to the binary system,\ntypically $\\sim 20 \\AU$, or even $5-10 \\AU$ in some cases (Van Winckel,\nprivate communication).\n In the Red Rectangle the inner boundary is modeled to be at\n$\\sim 15 \\AU$ (Waelkens {\\it et al.} 1996), which\nis more than six times the semi-major axis of its central binary system\nHD 44179.\n In 89 Herculis the inner boundary of the circumbinary material,\nwhether a disk or not, is at $r_i \\sim 40 \\AU$\n(Waters {\\it et al.} 1993).\n Waters {\\it et al.} (1993) also estimated the disk mass to\nbe $6 \\times 10^{-4} M_\\odot$.\n The circumbinary material extends to at least several tens of AU\n(Alcolea \\& Bujarrabal 1991), therefore the mass inside a radius of $6 a$\nwill in any case be very small, $< 10^{-4} M_\\odot$, so that\nthe time scale for eccentricity increase will be very long.\n\n The conclusion from this section seems to be that the disk's mass\nclose to the binary systems, i.e., within $\\sim 6 a$, is\ntoo small in these systems to account for the high eccentricity\nvia the external disk mechanism. \n Since these systems are post-AGB stars (or similar objects),\nit is still possible that during their AGB phase the disk mass was\nhigh enough for the external disk mechanism to be efficient.\n This possibility requires further examination. \n\n% ======================================================================\n\\section{SUMMARY} \n% ======================================================================\n\n In the present paper I propose that the relatively high eccentricity\n$e \\lesssim 0.4$, of tidally strongly interacting binary systems\nwhere the mass-losing star is an AGB star, a post-AGB star,\nor a similar object, is caused by an enhanced mass loss rate \nduring periastron passages.\n Tidal interaction by itself will circularize the orbits of these\nsystems in a relatively short time.\n Therefore, a mechanism which increases the eccentricity on a shorter\ntime scale is required.\n Waelkens {\\it et al.} (1996) suggested that the mechanism is an\ninteraction with a circumbinary disk.\n The interaction occurs mainly with the inner regions of the disk,\nwithin $\\sim 6$ times the binary orbital separation\n(e.g., Artymowicz {\\it et al.} 1991). \n In $\\S 3$ above I argued that such disks, if they exist, do not\ncontain enough mass in their inner regions to explain the high\neccentricity.\n Instead, I showed in $\\S 2$ that an increase in the mass loss rate\nat periastron passages can explain these eccentricities.\n\n Both the interaction with a circumbinary disk mechanism \nand the enhanced periastron mass loss rate mechanism predict much \nhigher mass loss rate in the equatorial plane, via the strong binary\ninteraction (Mastrodemos \\& Morris 1999), leading to the\nformation of a bipolar nebula, e.g., the Red Rectangle. \n But each has another strong prediction.\n The external disk mechanism predicts the presence of a relatively\nmassive disk close to the binary system.\n So far there is evidence only for more extended disks.\nIt remains to be shown, theoretically and observationally,\nthat such disks exist (and the material is indeed in a disk and \nnot in an outflow).\n The model proposed in the present paper predicts a prominent departure\nfrom axisymmetry, since the mass-losing star moves in the same direction\nat each enhanced mass loss phase during the periastron passage \n(Soker {\\it et al.} 1998). \n The Red Rectangle possesses a clear departure from axisymmetry.\n This case was discussed in $\\S 2$.\n\n Another interesting object is the binary system AFGL 4106, which has a \nnebula with a clear departure from axisymmetry \n(Van Loon {\\it et al.} 1999; Molster {\\it et al.} 1999). \n However, this binary system is not a post-AGB system, but\nis composed of two massive stars (Molster {\\it et al.} 1999),\nwith an orbital period of less than 4500 days.\nIts eccentricity has not been determined yet, and according to\nthe model presented here, it is very likely that the eccentricity \nof the binary system AFGL 4106 is $e>0.1$. \n\n\n%====================================================================\n\n\\bigskip\n\n{\\bf ACKNOWLEDGMENTS:} \nI thank Hans Van Winckel for many helpful discussions and comments.\n This research was supported in part by a grant from the University\nof Haifa and a grant from the Israel Science Foundation. \n\n% ===================================================================\n\\begin{references} \n% ===================================================================\n\n\\reference{} Alcolea, J., \\& Bujarrabal V. 1991, A\\&A, 245, 499.\n\n\\reference{} Artymowicz, P., Clarke, C. J., Lubow, S. H., Pringle, J. E.\n1991, ApJ, 370, L35. \n\n\\reference{} Artymowicz, P., \\& Lubow, S. H. 1994, ApJ, 421, 651. \n\n\\reference{} Eggleton, P. 2000, Evolutionary Processes in Binary and\nMultiple Stars (Cambridge: Cambridge Univ. Press), in preparation.\n\n\\reference{} Harpaz, A., Rappaport, S., \\& Soker, N. 1997, ApJ, 487, 809.\n\n\\reference{} Jura, M. \\& Kahane, C. 1999, ApJ, 521, 302. \n\n\\reference{} Kahane, C., Barnbaum, C., Uchida, K., Balm, S. P., \n\\& Jura, M. 1998, ApJ, 500, 466. \n\n\\reference{} Mastrodemos, N., \\& Morris, M. 1999, ApJ, 523, 357.\n\n\\reference{} Molster, F. J., {\\it et al.} 1999, A\\&A, 350, 163. % 11 authors\n\n\\reference{} Soker, N. 2000, MNRAS, in press (astro-ph/9908320) % ring2\n\n\\reference{} Soker, N., Rappaport, S. A., \\& Harpaz, A. 1998, ApJ, 496, 842.\n\n\\reference{} Van Loon, J. Th., Molster, F. J., Van Winckel, H., \n\\& Waters, L. B. F. M. 1999, A\\&A, 350, 120. \n\n\\reference{} Van Winckel, H. 1999, Asymptotic Giant Branch Stars,\nIAU Sym. 191, eds. T. Le Bertre, A. Lebre, and C. Waelkens,\n(ASP; printed by BookCrafters, Inc., Chelsea, Michigan), p. 465.\n\n\\reference{} Van Winckel, H. 2000, Ap\\&SS, in press. \n\n\\reference{} Van Winckel, H., Waelkens, C., Fernie, J. D.,\n\\& Waters, L. B. F. M. 1999, A\\&A, 343, 202.\n\n\\reference{} Van Winckel, H., Waelkens, C., \\& Waters, L. B. F. M. 1995,\nA\\&A, 293, L25. \n\n\\reference{} Van Winckel, H., Waelkens, C., Waters, L. B. F. M., \nMolster, F. J., Undry, S., \\& Bakker, E. J. 1998, A\\&A, 336, L17. \n\n\\reference{} Verbunt, F., \\& Phinney, E. S. 1995, A\\&A, 296, 709. \n\n\\reference{} Waelkens, C., Van Winckel, H., Waters, L. B. F. M.,\n\\& Bakker, E. J. 1996, A\\&A, 314, L17.\n\n\\reference{} Waters, L. B. F. M., Trams, N. R., \\& Waelkens, C. 1992, \nA\\&A, 262, L37. \n\n\\reference{} Waters, L. B. F. M., Waelkens, C., Mayor, M., \\& Trams, N. R. \n1993, A\\&A, 269, 242. \n\n\\reference{} Waters, L. B. F. M. {\\it et al.} 1998, Nature, 391, 868. \n\n\\reference{} Zahn, J-P. 1977, A\\&A, 57, 383; erratum 67, 162. \n\n\\reference{} Zahn, J-P. 1989, A\\&A, 220, 112. \n\n\\end{references}\n\n\\end{document}\n\n\n\n\n\n"
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astro-ph0002129
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Multifrequency VLBI observations of faint gigahertz peaked spectrum sources
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[
{
"author": "I.A.G. Snellen$^{1,2}$"
},
{
"author": "R.T. Schilizzi$^{2,3}$"
},
{
"author": "H.J van Langevelde$^{3}$"
},
{
"author": "Madingley Road"
},
{
"author": "Cambridge CB3 0HA"
},
{
"author": "United Kingdom"
},
{
"author": "$^{2}$Leiden Observatory"
},
{
"author": "P.O. Box 9513"
},
{
"author": "2300 RA"
},
{
"author": "Leiden"
},
{
"author": "The Netherlands"
},
{
"author": "Postbus 2"
},
{
"author": "7990 AA"
},
{
"author": "Dwingeloo"
}
] |
We present the data and analysis of VLBI observations at 1.6, 5 and 15 GHz of a sample of faint Gigahertz Peaked Spectrum (GPS) sources selected from the Westerbork Northern Sky Survey (WENSS). The 5 GHz observations involved a global array of 16 stations and yielded data on the total sample of 47 sources. A subsample of 26 GPS sources with peak frequencies $\nu_p > 5$ GHz and/or peak flux densities $S_p > 125 $ mJy was observed with the VLBA at 15 GHz. A second subsample of 29 sources, with $\nu_p <5$ GHz, was observed at 1.6 GHz using a 14 station global VLBI array. In this way, 44 of the 47 sources (94\%) in the sample were observed above and at or below their spectral peak. Spectral decomposition allowed us to identify 3, 11, 7, and 2 objects as compact symmetric objects, compact doubles, core-jet and complex sources respectively. However, many of the sources classified as compact double or core-jet sources show only two components making their classification rather tentative. This may explain why the strong morphological dichotomy of GPS quasars and galaxies found for radio-bright GPS sources, is not as clear in this faint sample.
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[
{
"name": "mn_vlbi.tex",
"string": "\\documentstyle[psfig]{mn}\n%\\renewcommand{\\baselinestretch}{2}\n%%% http://nedwww.ipac.caltech.edu/cgi-bin/nph-datasearch?search_type=Photo_id&objid=56183&objname=CGCG%20502-027\n\n\\title[VLBI Observations of faint GPS sources]{Multifrequency VLBI observations of faint gigahertz peaked spectrum sources}\n\n\n\\author[I. Snellen et al.]{I.A.G. Snellen$^{1,2}$, R.T. Schilizzi$^{2,3}$,\nH.J van Langevelde$^{3}$, \\\\ \n$^{1}$Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, United \nKingdom\\\\\n$^{2}$Leiden Observatory, P.O. Box 9513, 2300 RA, Leiden, The Netherlands \\\\\n$^{3}$Joint Institute for VLBI in Europe, Postbus 2, 7990 AA, Dwingeloo, \nThe Netherlands}\n\n\n\\date{}\n\\begin{document}\n\\maketitle\n\\begin{abstract}\nWe present the data and analysis of VLBI observations at 1.6, 5 and 15\nGHz of a sample of faint Gigahertz Peaked Spectrum (GPS) sources\nselected from the Westerbork Northern Sky Survey (WENSS). The 5 GHz\nobservations involved a global array of 16 stations and yielded data\non the total sample of 47 sources. A subsample of 26 GPS sources with\npeak frequencies $\\nu_p > 5$ GHz and/or peak flux densities $S_p > 125\n$ mJy was observed with the VLBA at 15 GHz. A second subsample of 29 sources,\nwith $\\nu_p <5$ GHz, was\nobserved at 1.6 GHz using a 14 station global VLBI array.\nIn this way, 44 of the 47 sources (94\\%) in the sample were observed \nabove and at or below their spectral peak.\nSpectral decomposition allowed us to identify 3, 11, 7, and 2\nobjects as compact symmetric objects, compact doubles, core-jet and \ncomplex sources respectively. \n However, many of the sources classified \nas compact double or core-jet sources show only two components making \ntheir classification rather tentative. This may explain why\nthe strong morphological dichotomy of GPS quasars and galaxies found for \nradio-bright GPS sources, is not as clear in this faint sample.\n\\end{abstract}\n\n\\section{Introduction}\n\nGigahertz Peaked Spectrum (GPS, e.g. O'Dea 1998) are\na class of extragalactic radio source, characterised by a convex shaped\nradio spectrum peaking at about 1 GHz in frequency, and sub-galactic sizes.\nTheir small sizes make observations using\nVery Long Baseline Interferometry (VLBI) necessary to reveal their \nradio morphologies. Early VLBI observations showed that some GPS sources \nidentified with galaxies have Compact Double (CD) morphologies (Philips\nand Mutel, 1982), and it was suggested that \nthese were the mini-lobes of very young or alternatively old, frustrated \nobjects (Philips\nand Mutel, 1982; Wilkinson et al. 1984, van Breugel, Miley and Heckman, 1984).\nLater, when reliable VLBI observations at higher frequencies became possible, \nit was found that some of the CD-sources had a compact flat spectrum \ncomponent in their centres (Conway et al. 1992, Wilkinson et al. 1994).\nThese flat spectrum components were interpreted as the central cores,\nand many CD-sources were renamed compact triples or \nCompact Symmetric Objects (CSO, Conway et al. 1992, Wilkinson et al. 1994). \nHigh dynamic range VLBI observations by\nDallacasa et al (1995) and Stanghellini et al.\n(1997) have shown that most GPS galaxies indeed have jets leading from\nthe central compact core to the outer hotspots or lobes.\nThis is in contrast to the GPS sources identified with quasars, which tend\nto have core-jet morphologies with no outer lobes (Stanghellini et al. 1997). \nSnellen et al. (1999) have shown that the redshift distributions of the \nGPS galaxies and quasars are very different, and that it is therefore\nunlikely that they form a single class of object unified by orientation.\nThey suggest that they are separate classes of object, which just happen to \nhave the same radio-spectral morphologies.\n\nThe separation velocities of the hotspots have now\nbeen measured for a small number of GPS galaxies to be $0.2h^{-1}$c \n(Owsianik and Conway, 1998; Owsianik, Conway and Polatidis, 1998; Tschager et\nal. 1999).\nThis makes it very likely that these are young objects of \nages typically $\\sim 10^3$ yr (assuming a constant separation velocity),\nrather than old objects constrained in their growth by a dense ISM. \nThese are therefore the objects of choice to study the early evolution\nof extragalactic radio sources.\n\nIn the past, work has been concentrated on samples of \nthe radio brightest GPS sources (eg. O'Dea et al 1991).\nIn order to disentangle radio power and redshift effects on the properties\nof GPS sources, we constructed a sample of faint GPS sources \nfrom the Westerbork Northern Sky Survey (WENSS, Rengelink et al. 1997),\nwhich in combination with other samples allows, for the first time,\nthe study of these objects over a large range of flux density and radio \nspectral peak frequency.\nThe construction of the faint sample is described in Snellen et al. (1998a); \nthe optical and near-infrared imaging is described in \nSnellen et al. (1998b); and the optical spectroscopy in Snellen et al. (1999a).\nThis paper describes multi-frequency VLBI observations of the sample, and\nthe radio-morphologies of the individual sources.\nWhat can be learned from the faint GPS sample about radio source\nevolution is discussed in the accompanying paper (Snellen et al. 2000).\n\n\\section{The Sample}\n\nThe selection of the sample has been described in detail \nin Snellen et al. (1998a), and is summarised here.\nCandidate GPS sources were selected from the Westerbork Northern Sky survey, \nby means of \n an inverted spectrum between 325 MHz and higher frequencies.\nThe sources are located in two regions of the survey; one with $15^h < \\alpha \n< 20^h$\nand $58^\\circ< \\delta < 75^\\circ$, which is called the {\\it mini-survey} region\n(Rengelink et al. 1997), and the other with $4^h00^m < \\alpha < 8^h30^m$ and\n$58^\\circ< \\delta < 75^\\circ$. Additional observations at 1.4, 5, 8.4 and 15\nGHz were carried out with the WSRT and the VLA, yielding a sample of 47\ngenuine GPS sources with peak frequencies ranging from 500 MHz to more than 15\nGHz, and peak flux densities ranging from $\\sim30$ to $\\sim900$ mJy.\nThis sample has been imaged in the optical and near-infrared, resulting in\nan identification fraction of $\\sim$ 87 \\% (Snellen et al. 1998b).\nRedshifts have been obtained for 40\\% of the sample (Snellen et al., 1999).\n\n\n\n\\section{Observations}\n\nSnapshot VLBI observations were made of the entire sample of \nfaint GPS sources \nat 5 GHz, and of sub-samples at 15 GHz and 1.6 GHz frequency.\nIn order to observe the large number of sources required in a reasonable\namount of time, we observed in ``snapshot'' mode (eg. Polatidis et al. 1995, \nHenstock et al. 1995).\nThis entails observing a source for short periods of time at several different\nhour angles. Using a VLBI array of typically more than 10 telescopes, this\nprovides sufficient $u,v$ coverage for reliable mapping of \ncomplex sources (Polatidis et al. 1995).\nTo maximize the $u,v$ coverage for each source we attempted to schedule three \nto four scans as widely spaced as possible within the visibility window \nduring which the source could be seen by all antennas. \nFortunately, the majority of the sources are located at a sufficiently high \ndeclination ($>57^{\\circ}$) that they are\ncircumpolar for most EVN and VLBA antennas, and therefore could be scheduled for\nobservation at optimal hour angles.\n\n\\begin{figure}\n\\psfig{figure=fig1a.ps,width=6cm}\n\\psfig{figure=fig1b.ps,width=6cm}\n\\psfig{figure=fig1c.ps,width=6cm}\n\\caption{\\label{UV} Typical $u,v$ coverages for a source observed at 1.6 GHz \n(upper), 5 GHz (middle), 15 GHz (lower).}\n\\end{figure}\n\n\n\\begin{table*}\n\\centerline{\n\\begin{tabular}{llcccc} \n & & & &\\\\ \nTelescope&Location&Diam. &SEFD$_{1.6GHz}$ & SEFD$_{5GHz}$&SEFD$_{15 GHz}$ \\\\\n & &(m)&(Jy) & (Jy) & (Jy)\\\\ \nCambridge &EVN, U.K. &32 & &136&\\\\\nEffelsberg &EVN, Germany &100 &19&20&\\\\\nJB, Lovell&EVN, U.K. &76 &44&&\\\\\nJB, MK2 &EVN, U.K. &25 & &320&\\\\\nMedicina &EVN, Italy &32 & &296&\\\\\nNoto &EVN, Italy &32 & &260&\\\\\nTorun&EVN, Poland &32 &230& &\\\\\nWesterbork &EVN, Netherlands&$12\\times25$&450$^*$&90&\\\\\nVLBA\\_BR& Brewster, WA, USA&25&300&300&525\\\\\nVLBA\\_FD& Fort Davis, TX, USA&25&300&300&525\\\\\nVLBA\\_HN& Hancock, NH, USA&25&300&300&525\\\\\nVLBA\\_KP& Kitt Peak, AZ, USA&25&300&300&525\\\\\nVLBA\\_LA& Los Alamos, NM, USA&25&300&300&525\\\\\nVLBA\\_MK& Mauna Kea, HI, USA&25&300&300&525\\\\\nVLBA\\_NL&North Liberty, IA, USA&25&300&300&525\\\\\nVLBA\\_OV& Owens Valley, CA, USA&25&300&300&525\\\\\nVLBA\\_PT& Pie Town, NM, USA&25&300&300&525\\\\\nVLBA\\_SC& Saint Croix, VI, USA&25&300&300&525\\\\ \n\\end{tabular}}\n$^*$ Westerbork only observed with a single antenna at 1.6 GHz.\n\\caption{\\label{tel} The telescopes used for the VLBI observations}\n\\end{table*}\n\n\\subsection{The 5 GHz Observations, Correlation and Reduction}\n\nThe 5 GHz data were obtained during a 48 hour observing session on 15 and\n16 May 1995. All telescopes of the VLBA, and six\ntelescopes of the EVN were scheduled to participate\nin this global VLBI experiment (see table \\ref{tel}). \nThe data were recorded using the Mark III recording system in mode B, \nwith an effective bandwidth of 28 MHz centred at 4973 MHz.\nLeft circular polarization was recorded. \nSince the motion of some of the antennas is limited in hour angle,\nwe inevitably had to schedule a few scans \nwhen the source could not be observed at one or two telescopes. \nAll sources were observed for three \nscans of 13 minutes (13$^m$ corresponds to a single pass on a tape).\n\nThe data were correlated using the VLBA correlator in Socorro, New Mexico,\nfour months after the observations took place. \nThe output of the correlator provides a measure of the complex\nfringe visibility sampled at intervals of 2 seconds on each baseline, \nat $7\\times16$ frequencies within the 28 MHz band, with the phase\nreferenced to an {\\it a priori} model of the source position, antenna \nlocations, and atmosphere. The residual phase gradients in time and frequency\ndue to delay and rate errors in the {\\it a priori} model are estimated and removed, during the process of ``fringe fitting''. Fringe fitting was performed \nusing the AIPS task FRING, an implementation of the Schwab \\& Cotton (1983) \nalgorithm.\nA solution interval of 3 minutes and a point source model were used, and\nEffelsberg was taken as the ``reference telescope'' whenever possible.\nNo fringes were found for the Cambridge telescope.\nThe amplitude calibration was performed with the AIPS tasks ANTAB and\nAPCAL, using system temperature and antenna gain information. \nThe visibility data were averaged across the observing band and then \nwritten in one single $u,v$-file per object.\nThe typical $u,v$ coverage obtained for a source is shown in figure \\ref{UV}.\n\nThe final images were produced after several cycles of imaging and \nself-calibration \nusing the AIPS tasks IMAGR and CALIB. Solution intervals were decreased in\neach step, starting with a few minutes, until no increase of the image \nquality \n(using noise-level and the presence of negative structure as criteria) was \ndetected. If a source was sufficiently strong, \nantenna amplitude solutions were also determined for each scan.\nFor each source a ``natural'' weighted image was produced.\nIf the $u,v$-data were of sufficient quality, a ``uniform'' weighted image \nwas also produced.\n\n\\subsection{The 15 GHz Observations, Correlation and Reduction}\n\n\\begin{figure*}\n\\psfig{figure=fig2.ps,width=17cm}\n\\caption{\\label{rmspeak} The rms noise levels as function of peak brightness\nfor the 1.6, 5 and 15 GHz images.}\n\\end{figure*}\n\nThe 15 GHz data were obtained during a 24 hour observing session on \n29 June 1996, using the ten telescopes of the VLBA. \nThe data were recorded in $128-8-1$ mode (128 Mbits/sec, 8 IF channels,\n1 bit/sample), with an effective bandwidth of 32 MHz centred at 15360 MHz.\nAll 27 sources in the sample with peak frequencies higher than 5 GHz and/or \npeak flux densities greater than 125 mJy were observed.\nThe expected maximum brightness in each of the images at 15 GHz was estimated \nfrom the overall radio spectra of the sources and their 5 GHz VLBI morphology.\nIn order to use the conventional fringe-fitting methods of VLBI imaging,\n the signal to noise ratio on each baseline within the coherence time has to \nbe sufficiently high.\nSources with an expected maximum brightness at 15 GHz of $>60$ mJy/beam \nare sufficiently strong and were \nobserved for 3 scans of 11 minutes each. However, sources with expected \nmaximum brightnesses of $<60$ mJy/beam, were observed using a\n``phase-referencing'' method to increase the signal to noise ratio.\nThis involves observations of the target source \ninterspersed with observations of a nearby ($<2.5^{\\circ}$) \ncompact calibrator source. Measurements of residual delay and rate are made \ntowards this bright source and transferred to the target source data.\nWe used cycles of 3 minutes on the target source and 1.5 minutes on the \ncalibrator source. The total integration time on a target was 45 minutes \ndivided over three scans. The sources for which the phase referencing technique\nwas required and the calibration sources used (in brackets) were \nB0400+6042 (B0354+599), B0436+6152 (B0444+634), B0513+7129 (B0518+705),\nB0531+6121 (B0539+6200), B0538+7131 (B0535+6743), B0755+6354 (B0752+6355),\\\\\nB1525+6801 (B1526+670), B1538+5920 (B1550+5815), B1600+7131 (B1531+722), \nB1819+6707 (B1842+681),\\\\ and B1841+6715 (B1842+681). \nData reduction of the phase referenced observations is similar to\nthat for the 5 GHz data. The typical $u,v$ coverage obtained for a source at \n15 GHz is shown in figure \\ref{UV}.\n\n\\subsection{The 1.6 GHz Observations, Correlation and Reduction}\n\nThe 1.6 GHz data were obtained during two \nobserving sessions, both involving the ten telescopes of the VLBA and 4 \nantennas of the EVN (see table \\ref{tel}). The Westerbork data in the \nsecond session was lost due to technical failure.\nThe data were recorded in $128-4-2$ mode (128 Mbits/sec, 4 IF channels,\n2 bit/sample), with an effective bandwidth of 32 MHz centred at 1663 MHz and\n1655 during the first and second session respectively.\nIn the first session, a subsample of 23 objects was observed for\n$2\\times12$ hours on 14 and 16 September 1997. This subsample contained\nall sources with peak frequencies $<5$ GHz, which were found to be extended in\nthe 5 GHz observations. In the second session, all 9 remaining sources \nwith peak frequencies $<3$ GHz, which had not been imaged before at this \nfrequency, were observed. The sources were typically observed for $4\\times11$ \nminutes each, and an example of a $u,v$ coverage is shown in figure \\ref{UV}.\nThe data were correlated in Socorro. No fringes were found for\nB0513+7129, B0537+6444, and B0544+5847. \nSeveral sources in the second session were observed using phase referencing.\nThese sources, with their calibrators in brackets, are \nB0537+6444 (B0535+677), B0830+5813 (B0806+573), B1557+6220 (B1558+595), \nB1639+6711 (B1700+685), and B1808+6813 (B1749+701).\nThe data were reduced in a similar way as the data at 5 GHz.\n\n\n\\section{Results}\n\nThe parameters of the resulting 102 images (29 at 1.6 GHz, 47 at 5 GHz, and \n26 at 15 GHz) are given in table \\ref{mappar}. \nFigure \\ref{rmspeak} shows the rms noise as function of the peak brightness\nin the images at the three observing frequencies. \nThe dynamic ranges (defined as the ratio of the maximum brightness in the image\nto the rms noise in an area of blank sky) are between 125 and 2500 at 1.6 GHz,\nbetween 25 and 1700 at 5 GHz, and between 30 and 500 at 15 GHz.\nAt 1.6 GHz, two of the bright sources have higher rms-noise levels than\nexpected, which may indicate that the dynamic range is not limited by \nthe thermal noise. To be able to compare the VLBI observations of this faint\nsample with those on bright GPS samples, it is important to determine\nwhether components have been missed due to the limited dynamic range\nfor this faint sample. We therefore plotted the distribution of dynamic range\nfor the observations closest in frequency to the spectral peak \n(Fig. \\ref{dynrange}).\nOnly 2 objects (B0755+6354 and B0544+5847) turn out not to have an image \nwith a dynamic range $>100$.\n\n\n\\begin{figure}\n\\psfig{figure=fig3.ps,width=7cm}\n\\caption{\\label{dynrange} The dynamic ranges for all sources in the sample at\nthe observed frequency closest to their spectral peak.}\n\\end{figure}\n\nIn Figure \\ref{totvlbi} the ratio of total VLBI flux density in the images\nto the flux density in the NVSS at 1.6 GHz, to the MERLIN observations at \n5 GHz, and to the VLA 15 GHz flux densities (from Snellen et al. 1998a), are \nplotted.\nThis enables us to judge whether substantial structure has been\nresolved out in the VLBI observations. At 1.6 GHz, typically 90\\% of the NVSS \nflux density is recovered in the VLBI observations, while at 5 GHz the \ndistribution peaks at 100\\%. Only at 15 GHz is the distribution much broader\nand peaks at about 80\\% of the flux density in the VLA observations, and\nhence provides some evidence that at this frequency some extended structure\nmay be missed. The broadness of the peak is probably also influenced\nby variability.\n\n\\begin{figure*}\n\\psfig{figure=fig4.ps,width=17cm}\n\\caption{\\label{totvlbi} The ratio of total VLBI flux density in the maps\nto the flux density in the NVSS at 1.6 GHz (left), \nto the MERLIN observations at \n5 GHz (middle), and to the VLA 15 GHz flux densities (right). }\n\\end{figure*}\n\n\nFigures \\ref{fig3}, \\ref{fig2}, \\ref{fig1} give the maps of \nthe individual sources with observations at three, two and one \nfrequency respectively. For each source, the images have the same size at \neach frequency, and are centred in such a way that identical components at \ndifferent frequencies match in relative position.\n\n\n\\subsection{Model Fitting \\label{modelfit}}\n\nQuantitative parameters of the source brightness distributions were \nestimated by fitting elliptical Gaussian functions to the maps, using the \nAIPS-task JMFIT. \nFor some of the complex sources it was necessary to restrict the\nfit to a number of point sources (e.g. 0513+7129 at 5 GHz). \nIn a few cases, the positions of some of the fitted components were\nkept fixed to correspond to their positions at higher frequency \n(e.g. 0752+6355 at 5 GHz). We checked whether \nthe model was a good representation of the source structure, by\ncomparing the total flux density in the image to that in the model, and \nby ensuring that the residual image did not \nshow any significant negative structure.\nA spectral decomposition was performed by matching the components believed\nto correspond to each other at the different frequencies. \nDue to the increase in resolution with frequency, some components at the\nhigher frequencies were combined to match a single component at \nthe lower frequency. The decomposed spectra are shown along with the images \nin \nfigures \\ref{fig3} and \\ref{fig2}.\nThe results of the fits are given in table \\ref{sourcepar}.\n\nColumn 1 gives the source name, column 2 the figure in which the maps are \nshown, column 3 the classification (as discussed in the next section), \nand in column 4 the component name used for the spectral decomposition.\nColumns 5 to 9 give for each component observed at 1.6 GHz the flux \ndensity, relative position in R.A. and Dec., and the fitted angular size \n(major and minor axis, and position angle). Columns 10 to 14, and \ncolumns 15 to 19 give the same for the components observed at\n5 GHz and 15 GHz respectively.\n\n\\subsection{Classification of the Radio Morphologies}\n\nWe classify the radio morphologies in four ways:\n\\begin{itemize}\n\\item[1)] {\\bf Compact Symmetric Objects (CSO)}. Sources with a compact flat \nspectrum component with extended components with steeper \nspectra on either side.\n\\item[2)] {\\bf Core-Jet sources (CJ)}. Sources with compact flat spectrum \ncomponent with one or more components with steeper spectra on one side only.\n\\item[3)] {\\bf Compact Double (CD)}. Sources showing two dominant \ncomponents with comparable spectra, but no evidence of a central flat spectrum\ncomponent.\n\\item[4)] {\\bf Complex sources (CX)}. Sources with a complex morphology, not\nfalling in one of the above categories.\n\\end{itemize}\n\nFrom the 47 sources in the sample, 3 could be classified as CSO,\n11 as CD, 7 as CJ, and 2 as CX. Of the 25 remaining sources, 2 were \nresolved at only one frequency, 2 were only observed at one frequency, \nand 20 show a single component at 2 frequencies, and therefore could\nnot be classified. For one source\n(1642+6701) it was not clear how to overlay the 1.6 and 5 GHz maps.\nThe individual sources are briefly discussed below.\n\n\\subsubsection{Discussion of Individual Sources}\n\n\\noindent {\\bf B0400+6042: CD}\nSeveral components are visible with the two outer components having \ncomparable spectra and the central component \nhaving a marginally flatter spectrum. This source is tentatively classified as \na CD, but it could also be a CSO.\n\n\\noindent {\\bf B0436+6152: CSO}\nThe brightest component at 15 GHz in the centre is interpreted as \nthe core, with extended steeper spectrum components to the north-east\nand south-west. This source is classified as a CSO. \n\n\\noindent {\\bf B0513+7129: CX}\nThis object shows two dominant components with a jet-like feature pointed\nto the north-west. Although the component with the flattest \nspectrum is located in the center, this source is classified as \na complex source due to the strangely bent structure.\n\n\n\\noindent {\\bf B0539+6200: CJ}\nThe south-western component has a flatter spectral index than the \nnorth-eastern component. Only two components are visible, hence this object \nis tentatively classified as a CJ. \n\n\\noindent {\\bf B0752+6355: CX}\nThe ``C'' shaped morphology of this compact source showing components \nwith a large range of spectral indices, leads us\nto classify this object as one with a complex morphology. \n\n\n\\noindent {\\bf B1620+6406: CD}\nThe steep spectrum of the northern component is similar to the \nspectrum of the southern component (using the upper-limit for the flux\ndensity at 5 GHz). We therefore tentatively classify this object as a CD.\n \n\n\\noindent {\\bf B1642+6701: -}\nIt was not possible to reliably overlay the two maps at 1.6 and 5 GHz, \nbut the most likely match is shown in figure \\ref{fig2}.\nDue to this uncertainty, it was not possible to reliably classify this \nsource.\n\n\\noindent {\\bf B1647+6225: CD}\nThe two components have similar spectra, with a possible jet leading\nto the northern component. This object is tentatively classified as a CD.\n\n\\noindent {\\bf B1655+6446: CD}\nOnly the southern component is detected at 5 GHz. However its steep spectral \nindex, and the upper-limit to the spectral index of the northern component\nmakes us tentatively classify this source as a CD. \n\n\\noindent {\\bf B1657+5826: CD}\nOnly the western component is detected at 5 GHz. However its steep spectral \nindex, and the upper-limit to the spectral index of the eastern component\nmakes us classify this source as a CD. \n\n\\noindent {\\bf B1819+6707: CSO}\nTwo dominant components are visible in this source at 1.6, 5, and 15 GHz \nwith comparable spectra. A faint compact component is visible in between\nin the 5 GHz map. This object is therefore classified as a CSO.\n\n\\noindent {\\bf B1942+7214: CJ}\nThis object shows faint extended structure to the south-west in its \n1.6 and 5 GHz images. The bright northern component appears to\nhave a flatter spectrum than the faint extended emission. \nWe tentatively classify this object as a core-jet.\n\n\\noindent {\\bf B1946+7048: CSO}\nThis source is the archetype compact symmetric object (CSO), and has\nbeen discussed in detail by Taylor and Vermeulen (1997).\nThe core is only visible at 15 GHz.\n\n\\noindent {\\bf B1954+6146: CJ}\nOnly the flat spectrum compact component in the south is detected at \n15 GHz. The limit to the spectral index of the northern component makes\nus tentatively classify this source as a core-jet.\n\n\\include{table.map}\n\\include{table_vlbi}\n\n\n\n\\section{Discussion}\n\nIn radio bright samples, GPS quasars are found to have\n core-jet or complex structure, while GPS galaxies are found\nto have larger sizes with jets and lobes on both sides of a\nputative center of activity (Stanghellini et al. 1997). Although observations\nat another frequency are needed to confirm their classification, allmost all\nradio-bright GPS galaxies from Stanghellini et al (1997) can be \nclassified as CSOs. The morphological dichotomy of GPS\ngalaxies and quasars, and their very different redshift distributions \nmake it likely that GPS galaxies and quasars are not related to each\nother and just happen to have similar radio spectra. \nIt has been speculated that GPS quasars are a \nsubset of flat spectrum quasars in general (eg. Snellen et al. 1999a). \nIn addition, if galaxies and quasars were to be unified by orientation, \ndue to changes in its observed radio spectrum (Snellen et al. 1998c),\nit is not expected that a GPS galaxy observed at a small viewing angle would \nbe seen as a GPS quasar. \n \nNot all CSOs are GPS sources. The contribution of the (possibly\nvariable) flat spectrum core can be significant and outshine the\nconvex spectral shape produced by the mini-lobes. This can be due to a\nsmall viewing angle towards the object, causing the Doppler boosted\ncore and fast moving jet, which feeds the approaching mini-lobe, to be\nimportant (Snellen et al. 1998c). \nAn example of such a CSO, possibly observed at a small viewing\nangle, is 1413+135 (Perlman et al. 1994). In\naddition, the jets feeding the mini-lobes can be significantly curved,\nfor example in 2352+495 by precession (Readhead et al. 1996).\nThis can cause parts of the jet to move at an angle close to the line\nof sight, with significant Doppler boosting as a result. In both\ncases the large contrast between the approaching \nand receding parts of the radio source makes it also \nincreasingly difficult to identify the object as a CSO.\n\n Figure \\ref{class} shows the number of galaxies and quasars, in our faint \nGPS sample, classified as CJ, CSO, CX and those not possible to classify. All\nthree objects classified as CSOs are optically identified with\ngalaxies. Although this is in agreement with the findings of\nStanghellini et al (1997) for the radio-bright sample, it should be\nnoted that for only 4 quasars was it possible to make a\nclassification. This is mainly due to the fact that the angular \nsizes of the quasars are significantly smaller than the angular sizes\nof the galaxies.\n Six out of 18 classifiable GPS galaxies are found to\nhave CJ or CX structures, and 9 of the classifiable GPS galaxies are\nfound to have CD structures. We conclude that the strong \n morphological dichotomy between\nGPS galaxies and quasars found by Stanghellini (1997) in the bright\nGPS sample, is not as strong in this faint sample. Note,\nhowever, that the classification for the majority of the CJ and CD\nsources is based on two components and their relative spectral indices\nonly. This makes their classification rather tentative. \nFirstly, a CD source could be erroneously\nclassified as a CJ source due to a difference in the observed age\nbetween the approaching and receding lobe, causing a difference in\nobserved radio spectrum of the two lobes. For a separation velocity\nof 0.4c, as observed for radio bright GPS galaxies (Owsianik and\nConway 1998; Owsianik, Conway and Polatidis 1998), such an age difference can \nbe as large as 30\\%.\nSecondly, differences in the local environments of the two lobes can\nalso influence the spectra of the two lobes, resulting in an\nerroneous classification as core-jet. For example, \nif only the two lobes had been visible, B1819+6707 (fig \\ref{fig2})\ncould\nhave been mistaken for a core-jet source, since the spectral index of\nthe eastern lobe is flatter than that of the western lobe.\n\n\n\\section{Conclusions}\n\nMulti-frequency VLBI observations have been presented of a faint\nsample of GPS sources. All 47 sources in the sample were successfully\nobserved at 5 GHz, 26 sources were observed at 15 GHz, and 20 sources\nwere observed at 1.6 GHz. In this way 94\\% of the sources have been\nmapped above and below their spectral peak. The spectral\ndecomposition allowed us to classify 3 GPS galaxies as compact\nsymmetric objects (CSO), 1 galaxy and 1 quasar as complex (CX)\nsources, 2 quasars and 5 galaxies as core-jet (CJ) sources, and 9\ngalaxies and 2 quasars as compact doubles (CD). \nTwenty-five of the sources could not be classified, 20 because they \nwere too compact. The strong\nmorphological dichotomy of GPS galaxies and quasars found by\nStanghellini et al. (1997) in their radio bright GPS sample is not so\nclear in this sample. However, many of the sources classified as CD and CJ \nhave a two-component structure, making their classification only tentative.\n\n\\section*{Acknowledgements}\n\nThe authors are greatful to the staff of the EVN and VLBA for support of the \nobserving projects. \nThe VLBA is an instrument of the National Radio Astronomy Observatory,\nwhich is operated by Associated Universities,\nInc. under a Cooperative Agreement with the National Science Foundation.\nThis research was supported by the European Commission, \nTMR Access to Large-scale Facilities programme under contract No. \nERBFMGECT950012, and TMR Programme, Research Network Contract \nERBFMRXCT96-0034 ``CERES''.\n\n\n\n\\begin{thebibliography}{}\n\n\\bibitem{} Conway J.E., Pearson T.J., Readhead A.C.S., Unwin S.C., Xu W., \n Mutel R.L. 1992, {\\sl Ap. J.}, {\\bf 396}, 62\n\n\\bibitem{} Dallacasa D., Fanti C., Fanti R., Schilizzi R.T., Spencer R.E., 1995\n {\\it Astron. 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J.}, {\\bf 88}, 688 \n\n\\bibitem{} Snellen, I.A.G., Schilizzi R.T., de Bruyn A.G., Miley G.K.,\n Rengelink R.B., R\\\"ottgering H.J.A., Bremer M.N., 1998a, {\\it A\\&AS.}, \n {\\bf 131}, 435\n\n\\bibitem{} Snellen I.A.G., Schilizzi R.T., Bremer M.N., de Bruyn A.G., \n Miley G.K., R\\\"ottgering H.J.A., McMahon R.G., P\\'erez Fournon I., 1998b, \n {\\it M.N.R.A.S.}, {\\bf 301},985\n\n\\bibitem{} Snellen, I.A.G., Schilizzi R.T., de Bruyn A.G., Miley G.K.,\n1998c, A\\&A, 333, 70\n\n\\bibitem{} Snellen I.A.G., Schilizzi R.T., Bremer M.N., Miley G.K., de Bruyn\n A.G., R\\\"ottgering H.J.A., 1999, {\\it M.N.R.A.S}, {\\bf 307}, 149\n\n\\bibitem{} Snellen I.A.G., Schilizzi R.T., Miley G.K., de Bruyn A.G., Bremer M.N., R\\\"ottgering H.J.A., {\\it M.N.R.A.S}, submitted (companion paper)\n\n\\bibitem{} Staghellini C., O'Dea C.P., Baum S.A., Dallacasa D., Fanti R.,\n Fanti C., {\\it Astron. \\& Astrophys.}, 1997, {\\bf 325}, 943\n\n\\bibitem{} Taylor G.B. and Vermeulen R.C., 1997, {\\it Astrophys. J.}, \n {\\bf 485}, L9\n\n\\bibitem{} van Breugel, W., Miley, G., and Heckman, T.,{\\it Astron. J.}, \n {\\bf 89}, 5\n\n\\bibitem{} Wilkinson, P. N., Booth, R. S., Cornwell, T. J., Clark, R. R. \n 1984, {\\it Nature}, {\\bf 308}, 619\n\n\\bibitem{} Wilkinson, P. N., Polatidis, A. G., Readhead, A. C. S., Xu, W., \n Pearson, T. J. 1994, {\\it Astrophys. J.}, {\\bf 432}, L87\n\n\\vfill\n\\end{thebibliography}{}\n\\begin{figure*}\n\\centerline{\\psfig{figure=fig5a.ps,width=16cm}}\n\\caption{\\label{fig3} The VLBI maps and spectral decomposition for sources observed at 3 frequencies. The noise level, $\\sigma$ is given in the top right \ncorner of each map. The contour levels are at $\\sigma \\times (-3, 3, 6, 12, 24, 48...)$. The solid line in the spectrum indicates the best fit to \nthe overall radio spectrum, as derived in Snellen et al. (1998a).}\n\\end{figure*}\n\\addtocounter{figure}{-1}\n\\begin{figure*}\n\\centerline{\\psfig{figure=fig5b.ps,width=16cm}}\n\\caption{\\label{fig3} Continued...}\n\\end{figure*}\n\\addtocounter{figure}{-1}\n\\begin{figure*}\n\\centerline{\\psfig{figure=fig5c.ps,width=16cm,angle=90}}\n\\caption{\\label{fig3} Continued...}\n\\end{figure*}\n\n\\begin{figure*}\n\\psfig{figure=fig6a.ps,width=17cm,angle=180}\n\\caption{\\label{fig2} The VLBI maps and spectral decomposition for sources observed at 2 frequencies. See table 2 for the beam sizes.\nThe noise level, $\\sigma$ is given in the top right \ncorner of each map. The contour levels are at $\\sigma \\times (-3, 3, 6, 12, 24, 48...)$. The solid line in the spectrum indicates the best fit to \nthe overall radio spectrum, as derived in Snellen et al. (1998a).}\n\\end{figure*}\n\\addtocounter{figure}{-1}\n\\begin{figure*}\n\\psfig{figure=fig6b.ps,width=17cm,angle=180}\n\\caption{Continued...}\n\\end{figure*}\n\\addtocounter{figure}{-1}\n\\begin{figure*}\n\\psfig{figure=fig6c.ps,width=17cm,angle=180}\n\\caption{Continued...}\n\\end{figure*}\n\\addtocounter{figure}{-1}\n\\begin{figure*}\n\\centerline{\\psfig{figure=fig6d.ps,width=10cm,angle=90}}\n\\caption{Continued...}\n\\end{figure*}\n\\begin{figure*}\n\\centerline{\\psfig{figure=fig7.ps,width=14cm,angle=90}}\n\\caption{\\label{fig1} The VLBI maps for the sources observed only at 5 GHz.\nThe noise level, $\\sigma$ is given in the top right \ncorner of each map. The contour levels are at $\\sigma \\times (-3, 3, 6, 12, 24, 48...)$.}\n\\end{figure*}\n\n\\begin{figure}\n\\psfig{figure=fig8.ps,width=7cm}\n\\caption{\\label{class}. The number of galaxies and quasars classified as\ncompact symmetric objects (CS0), Compact Doubles (CD), Core-jets (CJ), \nComplex sources (CX), and sources for which no classification was possible.}\n\\end{figure}\n\\end{document}\n\n\n\n\n\n\n\n\n\n"
},
{
"name": "table.map.tex",
"string": "\\begin{table}\n\\begin{tabular}{crrrrrrrrrrrr}\nName&\\multicolumn{4}{c}{1.6 GHz Map Parameters}&\\multicolumn{4}{c}{5 GHz Map Parameters}&\\multicolumn{4}{c}{15 GHz Map Parameters}\\\\\n&\\multicolumn{2}{c}{Beam}&rms&$S_{peak}$&\\multicolumn{2}{c}{Beam}&rms&$S_{peak}$&\\multicolumn{2}{c}{Beam}&rms&$S_{peak}$\\\\\n&(mas)&$^{\\circ}$&$\\frac{\\mu Jy}{beam}$&$\\frac{mJy}{beam}$&(mas)&$^{\\circ}$&$\\frac{\\mu Jy}{beam}$&$\\frac{mJy}{beam}$&(mas)&$^{\\circ}$&$\\frac{\\mu Jy}{beam}$&$\\frac{mJy}{beam}$\\\\\n0400+6042&&&&&$1.2\\times1.1$&65.8&180&38&$1.1\\times0.6$&-22.4&280&34\\\\\n0436+6152&$5.6\\times2.5$&-26.3&120&110&$3.4\\times1.2$&68.5&230&42&$1.3\\times1.1$&-35.3&200&25\\\\\n0441+5757&&&&&$2.3\\times1.3$&70.5&200&96&$1.6\\times1.2$&-70.2&230&73\\\\\n0513+7129&&&&&$1.4\\times0.9$&14.2&190&51&$0.8\\times0.7$&41.0&170&52\\\\\n0531+6121&&&&&$2.0\\times1.0$&24.0&130&19&$1.2\\times1.0$&-46.4&270&30\\\\\n0535+6743&$9.7\\times 3.7$&-5.8&416&89&$1.6\\times1.0$&10.3&230&148&$1.4\\times1.2$&45.9&200&71\\\\\n0537+6444&$9.3\\times 3.7$&-10.6&85&29&$2.2\\times1.0$&12.8 &190&13&&&\\\\\n0538+7131&&&&&$1.5\\times1.1$&13.4&170&73&$1.9\\times1.6$&-51.5&310&30\\\\\n0539+6200&$4.4\\times2.9$&-2.6&550&83&$1.9\\times1.0$&22.4&170&91&$0.8\\times0.5$&56.9&290&95\\\\\n0543+6523&$3.8\\times3.0$&-11.6&240&50&$1.7\\times1.1$&23.1 &170&32&&&&\\\\\n0544+5847&&&&&$1.9\\times1.0$&-7.1 &210&19&&&\\\\\n0552+6017&$4.3\\times2.9$&-7.4&120&40&$2.1\\times0.9$&3.4 &350&8&&&&\\\\\n0557+5717&$4.7\\times3.0$&3.7&90&39&$1.4\\times0.9$&-11.7 &150&10&&&&\\\\\n0601+5753&&&&&$1.5\\times1.0$&-1.5&210&147&$1.5\\times0.9$&-44.7&380&73\\\\\n0748+6343&&&&&$1.5\\times1.0$&15.1 &270&124&&&\\\\\n0752+6355&&&&&$1.0\\times0.9$&19.1&150&152&$0.7\\times0.5$&-18.4&330&104\\\\\n0755+6354&&&&&$2.8\\times1.9$&12.8&340&14&$0.7\\times0.5$&11.8&280&20\\\\\n0756+6647&&&&&$2.2\\times1.1$&46.3&130&94&$0.7\\times0.5$&-33.5&270&63\\\\\n0758+5929&$4.6\\times 2.6$&-18.2&149&144&$2.5\\times1.2$&20.1&170&116&$1.3\\times0.5$&13.5&200&62\\\\\n0759+6557&$4.1\\times2.9$&-4.7&140&24&$1.9\\times1.1$&-27.1 &220&10&&&&\\\\\n0826+7045&&&&&$1.3\\times1.2$&15.1 &190&85&&&\\\\\n0830+5813&$4.3\\times 2.5$&-15.7&107&44&$1.6\\times1.1$&9.0 &180&29&&&\\\\\n1525+6801&$4.3\\times3.2$&-72.0&170&109&$1.1\\times1.0$&7.0&120&48&$1.4\\times1.4$&-29.8&230&23\\\\\n1538+5920&&&&&$2.7\\times1.2$&0.4&140&42&$0.5\\times0.5$&0.0&350&11\\\\\n1550+5815&&&&&$2.6\\times1.2$&-0.4&170&198&$1.2\\times0.4$&15.8&360&120\\\\\n1551+6822&$4.4\\times3.2$&-65.4&130&46&$3.3\\times1.3$&6.2 &160&20&&&&\\\\\n1557+6220&$4.4\\times 2.8$&6.6&76&34&$2.7\\times1.1$&-2.8 &240&15&&&\\\\\n1600+7131&$3.9\\times3.1$&64.3&110&161&$2.3\\times1.5$&68.6&170&45&$0.6\\times0.5$&-40.0&190&26\\\\\n1620+6406&$3.9\\times3.3$&63.3&110&27&$3.6\\times3.3$&-33.4 &370&12&&&&\\\\\n1622+6630&&&&&$2.9\\times1.2$&-28.7&150&198&$0.8\\times0.5$&16.6&290&138\\\\\n1639+6711&$4.1\\times 2.7$&13.3&72&57&$2.1\\times1.1$&0.1 &140&28&&&\\\\\n1642+6701&$3.9\\times3.2$&72.2&120&62&$1.4\\times0.9$&13.9 &110&19&&&&\\\\\n1647+6225&$4.0\\times3.3$&36.5&130&25&$3.6\\times3.1$&-33.2 &190&15&&&&\\\\\n1655+6446&$3.7\\times3.2$&1.6&140&31&$3.1\\times2.0$&-28.5 &310&14&&&&\\\\\n1657+5826&$3.9\\times3.2$&1.0&110&30&$3.8\\times2.1$&38.0 &260&14&&&&\\\\\n1746+6921&$5.3\\times 3.0$&20.6&75&91&$1.5\\times1.0$&2.1&180&86&$1.0\\times0.7$&-76.8&350&63\\\\\n1807+5959&$4.1\\times3.4$&-89.8&110&14&$2.5\\times1.0$&3.2 &170&26&&&&\\\\\n1807+6742&$3.9\\times3.2$&80.4&120&25&$4.8\\times3.6$&50.1 &310&14&&&&\\\\\n1808+6813&$4.1\\times 2.8$&19.9&59&18&$2.6\\times0.8$&-4.1 &200&17&&&\\\\\n1819+6707&$3.9\\times3.2$&57.3&150&67&$2.5\\times1.1$&46.1&180&22&$0.9\\times0.7$&-21.7&260&27\\\\\n1841+6715&$3.9\\times3.2$&84.4&170&120&$2.8\\times1.1$&35.0&180&104&$1.3\\times1.0$&15.1&300&57\\\\\n1843+6305&$4.0\\times3.3$&83.3&150&46&$3.0\\times0.9$&9.7 &200&20&&&&\\\\\n1942+7214&$3.9\\times 2.8$&33.5&65&161&$3.3\\times1.6$&15.2&250&172&$0.7\\times0.5$&23.2&310&84\\\\\n1945+6024&&&&&$2.7\\times1.1$&-3.7&170&73&$0.9\\times0.5$&22.8&310&78\\\\\n1946+7048&$3.9\\times3.3$&-79.7&250&305&$1.0\\times0.9$&-28.6&180&84&$1.6\\times1.1$&28.6&240&70\\\\\n1954+6146&&&&&$2.5\\times1.2$&-1.6&210&142&$0.8\\times0.5$&2.9&360&89\\\\\n1958+6158&&&&&$2.5\\times1.1$&0.0&240&111&$1.2\\times0.6$&-13.4&380&60\\\\ \n\\end{tabular}\n\\caption{ \\label{mappar} Relevant parameters of the presented maps.}\n\\end{table}\n\n\n\n\n\n\n\n"
},
{
"name": "table_vlbi.tex",
"string": "\\begin{table*}\n\\setlength{\\tabcolsep}{1mm}\n\\begin{tabular}{ccrc|rrrcr|rrrcr|rrrcr}\nName&Fg&Cls&Cp&\\multicolumn{5}{c}{1.6 GHz Data}&\\multicolumn{5}{c}{5.0 GHz Data}&\\multicolumn{5}{c}{14.9 GHz Data}\\\\\n&&&&Flx&$\\Delta$X &$\\Delta$Y&Size&PA&Flx&$\\Delta$X&$\\Delta$Y&Size&PA&Flx&$\\Delta$X&$\\Delta$Y&Size&PA\\\\\n&&&&mJy&mas&mas&mas&$^\\circ$&mJy&mas&mas&mas&$^\\circ$&mJy&mas&mas&mas&$^\\circ$\\\\\n0400+6042&2&CD&\nE&\n&&&&&\n$ 62.7$$\\pm$$3.1$& 0.0& 0.0&$1.8$$\\times$$1.2$&$140$&\n$ 58.5$$\\pm$$2.9$& 0.0& 0.0&$1.3$$\\times$$0.2$&$153$\n\\\\\n&&&\nW&\n&&&&&\n$ 11.0$$\\pm$$0.6$& 4.1& 1.7&$2.2$$\\times$$1.7$&$ 71$&\n$ 1.9$$\\pm$$0.2$& 4.1& 1.7&$ -$&$ 0$\n\\\\\n&&&\nW&\n&&&&&\n$ 2.8$$\\pm$$0.2$& 1.2& 1.2&$ <0.2$&$ 0$&\n$ 6.1$$\\pm$$0.4$& 1.2& 1.2&$ -$&$ 0$\n\\\\\n&&&\nW&\n&&&&&\n$ 3.3$$\\pm$$0.3$& 2.0& 1.2&$ <0.1$&$ 0$&\n$ 2.3$$\\pm$$0.2$& 2.0& 1.2&$ -$&$ 0$\n\\\\\n0436+6152&1&CSO&\nS&\n$169$$\\pm$$ 8$& 0.0& 0.0&$3.1$$\\times$$0.9$&$ 41$&\n$ 84.7$$\\pm$$4.2$& 0.0& 0.0&$2.9$$\\times$$0.9$&$ 38$&\n$ 7.2$$\\pm$$0.4$& 0.0& 0.0&$2.7$$\\times$$0.8$&$ 41$\n\\\\\n&&&\nC&\n$ 36.8$$\\pm$$1.9$& -2.8& 4.8&$1.5$$\\times$$0.6$&$ 67$&\n$ 37.3$$\\pm$$1.9$& -3.2& 5.0&$1.4$$\\times$$0.8$&$ 64$&\n$ 25.5$$\\pm$$1.3$& -3.0& 4.8&$0.2$$\\times$$0.1$&$ 50$\n\\\\\n&&&\nC&\n&&&&&\n&&&&&\n$ 2.2$$\\pm$$0.2$& -3.7& 6.4&$1.5$$\\times$$0.5$&$ 43$\n\\\\\n&&&\nC&\n&&&&&\n&&&&&\n$ 2.8$$\\pm$$0.2$& -1.8& 3.2&$1.2$$\\times$$0.8$&$ 66$\n\\\\\n&&&\nN&\n$ 3.1$$\\pm$$0.3$& -5.2& 10.5&$ <1.2$&$ 0$&\n$ 2.2$$\\pm$$0.2$& -5.9& 11.4&$1.8$$\\times$$0.8$&$ 50$&\n$ 4.4$$\\pm$$0.3$& -5.7& 9.5&$2.0$$\\times$$0.5$&$ 32$\n\\\\\n&&&\nN&\n$ 4.3$$\\pm$$0.3$& -8.4& 14.9&$9.3$$\\times$$2.9$&$ 21$&\n&&&&&\n&&&&\n\\\\\n0441+5757&2&$-$&\nC&\n&&&&&\n$111$$\\pm$$ 5$& 0.0& 0.0&$1.0$$\\times$$0.5$&$ 45$&\n$ 73.9$$\\pm$$3.7$& 0.0& 0.0&$ <0.1$&$ 0$\n\\\\\n0513+7129&2&CX&\nN&\n&&&&&\n$ 64.7$$\\pm$$3.2$& 0.0& 0.0&$0.8$$\\times$$0.5$&$ 34$&\n$ 54.7$$\\pm$$2.7$& 0.0& 0.0&$ <0.1$&$ 0$\n\\\\\n&&&\nS&\n&&&&&\n$ 60.4$$\\pm$$3.0$& -0.7& -3.5&$1.2$$\\times$$0.6$&$ 33$&\n$ 18.6$$\\pm$$1.0$& -0.6& -3.6&$ <0.1$&$ 0$\n\\\\\n&&&\nW&\n&&&&&\n$ 4.2$$\\pm$$0.3$& 2.0& 1.1&$ -$&$ 0$&\n&&&&\n\\\\\n&&&\nW&\n&&&&&\n$ 2.0$$\\pm$$0.2$& 2.9& 1.4&$ -$&$ 0$&\n&&&&\n\\\\\n&&&\nW&\n&&&&&\n$ 3.7$$\\pm$$0.3$& 4.8& 2.3&$ -$&$ 0$&\n$ 2.5$$\\pm$$0.2$& 5.1& 1.8&$1.5$$\\times$$0.6$&$ 65$\n\\\\\n&&&\nW&\n&&&&&\n$ 2.6$$\\pm$$0.2$& 6.4& 3.4&$ -$&$ 0$&\n&&&&\n\\\\\n0531+6121&2&$-$&\nC&\n&&&&&\n$ 18.7$$\\pm$$1.0$& 0.0& 0.0&$ <0.2$&$ 0$&\n$ 30.1$$\\pm$$1.5$& 0.0& 0.0&$0.2$$\\times$$0.1$&$142$\n\\\\\n0535+6743&1&$-$&\nC&\n$ 94.5$$\\pm$$4.7$& 0.0& 0.0&$4.0$$\\times$$1.9$&$165$&\n$166$$\\pm$$ 8$& 0.0& 0.0&$0.5$$\\times$$0.4$&$174$&\n$ 78.8$$\\pm$$3.9$& 0.0& 0.0&$0.5$$\\times$$0.4$&$ 94$\n\\\\\n0537+6444&2&$-$&\nC&\n$ 31.9$$\\pm$$1.6$& 0.0& 0.0&$1.8$$\\times$$0.9$&$ 9$&\n$ 15.3$$\\pm$$0.8$& 0.0& 0.0&$1.3$$\\times$$0.2$&$ 12$&\n&&&&\n\\\\\n&&&\nC&\n&&&&&\n$ 1.3$$\\pm$$0.2$& 1.1& -4.7&$ -$&$ 0$&\n&&&&\n\\\\\n0538+7131&2&$-$&\nC&\n&&&&&\n$ 78.0$$\\pm$$3.9$& 0.0& 0.0&$0.5$$\\times$$0.3$&$152$&\n$ 29.6$$\\pm$$1.5$& 0.0& 0.0&$ <0.2$&$ 0$\n\\\\\n0539+6200&1&CJ&\nW&\n$ 96.8$$\\pm$$4.8$& 0.0& 0.0&$1.7$$\\times$$1.2$&$126$&\n$101$$\\pm$$ 5$& 0.0& 0.0&$0.6$$\\times$$0.4$&$163$&\n$ 95.0$$\\pm$$4.8$& 0.0& 0.0&$ <0.2$&$ 0$\n\\\\\n&&&\nE&\n$ 10.3$$\\pm$$0.6$& -4.6& 4.0&$2.7$$\\times$$0.8$&$121$&\n$ 4.3$$\\pm$$0.3$& -4.8& 2.8&$3.3$$\\times$$1.8$&$ 36$&\n&&&&\n\\\\\n0543+6523&2&$-$&\nC&\n$ 62.7$$\\pm$$3.1$& 0.0& 0.0&$2.1$$\\times$$1.3$&$ 90$&\n$ 36.8$$\\pm$$1.9$& 0.0& 0.0&$0.7$$\\times$$0.5$&$ 36$&\n&&&&\n\\\\\n&&&\nC&\n&&&&&\n$ 5.2$$\\pm$$0.3$& 2.5& -0.6&$1.2$$\\times$$0.5$&$ 36$&\n&&&&\n\\\\\n0544+5847&3&$-$&\nC&\n&&&&&\n$ 18.6$$\\pm$$1.0$& 0.0& 0.0&$0.4$$\\times$$0.1$&$175$&\n&&&&\n\\\\\n&&&\nC&\n&&&&&\n$ 7.9$$\\pm$$0.4$& 0.6& 1.6&$0.7$$\\times$$0.4$&$ 21$&\n&&&&\n\\\\\n&&&\nC&\n&&&&&\n$ 1.4$$\\pm$$0.2$& 1.3& 4.7&$ <1.1$&$ 0$&\n&&&&\n\\\\\n&&&\nC&\n&&&&&\n$ 3.0$$\\pm$$0.2$& 1.6& 8.0&$1.8$$\\times$$0.7$&$173$&\n&&&&\n\\\\\n0552+6017&2&$-$&\nC&\n$ 41.8$$\\pm$$2.1$& 0.0& 0.0&$0.9$$\\times$$0.2$&$ 71$&\n$ 13.6$$\\pm$$0.7$& 0.0& 0.0&$1.5$$\\times$$0.3$&$114$&\n&&&&\n\\\\\n&&&\nC&\n$ 1.2$$\\pm$$0.2$&-12.2& -3.3&$ <1.7$&$ 0$&\n&&&&&\n&&&&\n\\\\\n0557+5717&2&CJ&\nN&\n$ 49.2$$\\pm$$2.5$& 0.0& 0.0&$2.5$$\\times$$1.2$&$ 44$&\n$ 12.5$$\\pm$$0.7$& 0.0& 0.0&$3.1$$\\times$$1.5$&$ 42$&\n&&&&\n\\\\\n&&&\nS&\n$ 10.9$$\\pm$$0.6$& 3.0& -5.8&$2.3$$\\times$$1.5$&$124$&\n$ 16.3$$\\pm$$0.8$& 2.2& -8.9&$3.4$$\\times$$1.8$&$ 18$&\n&&&&\n\\\\\n0601+5753&2&$-$&\nC&\n&&&&&\n$188$$\\pm$$ 9$& 0.0& 0.0&$0.8$$\\times$$0.3$&$106$&\n$ 94.9$$\\pm$$4.7$& 0.0& 0.0&$0.9$$\\times$$0.3$&$ 98$\n\\\\\n0748+6343&3&$-$&\nC&\n&&&&&\n$126$$\\pm$$ 6$& 0.0& 0.0&$0.2$$\\times$$0.1$&$ 65$&\n&&&&\n\\\\\n0752+6355&2&CX&\nC&\n&&&&&\n$182$$\\pm$$ 9$& 0.0& 0.0&$1.2$$\\times$$0.2$&$167$&\n$ 31.6$$\\pm$$1.6$& 0.0& 0.0&$0.4$$\\times$$0.1$&$144$\n\\\\\n&&&\nS&\n&&&&&\n$105$$\\pm$$ 5$& 0.3& -0.5&$1.9$$\\times$$0.5$&$ 24$&\n$ 62.3$$\\pm$$3.1$& 0.3& -0.5&$0.8$$\\times$$0.3$&$ 24$\n\\\\\n&&&\nN&\n&&&&&\n$ 17.4$$\\pm$$0.9$& 0.3& 0.7&$ <0.8$&$ 0$&\n$108$$\\pm$$ 5$& 0.3& 0.7&$0.2$$\\times$$0.1$&$142$\n\\\\\n&&&\nW&\n&&&&&\n$ 2.4$$\\pm$$0.2$& 1.8& 1.5&$ -$&$ 0$&\n&&&&\n\\\\\n&&&\nW&\n&&&&&\n$ 4.6$$\\pm$$0.3$& 4.2& 1.8&$ -$&$ 0$&\n&&&&\n\\\\\n0755+6354&2&$-$&\nC&\n&&&&&\n$ 19.9$$\\pm$$1.0$& 0.0& 0.0&$0.7$$\\times$$0.2$&$132$&\n$ 19.9$$\\pm$$1.0$& 0.0& 0.0&$ <0.1$&$ 0$\n\\\\\n0756+6647&2&$-$&\nC&\n&&&&&\n$ 98.1$$\\pm$$4.9$& 0.0& 0.0&$0.4$$\\times$$0.3$&$ 34$&\n$ 72.6$$\\pm$$3.6$& 0.0& 0.0&$0.3$$\\times$$0.2$&$ 29$\n\\\\\n0758+5929&1&CD&\nW&\n$122$$\\pm$$ 6$& 0.0& 0.0&$ -$&$ 0$&\n$121$$\\pm$$ 6$& 0.0& 0.0&$0.8$$\\times$$0.2$&$ 36$&\n$ 76.4$$\\pm$$3.8$& 0.0& 0.0&$0.7$$\\times$$0.2$&$ 31$\n\\\\\n&&&\nE&\n$ 71.4$$\\pm$$3.6$& -1.7& 1.0&$ -$&$ 0$&\n$ 34.1$$\\pm$$1.7$& -1.8& 0.9&$0.6$$\\times$$0.5$&$ 41$&\n$ 10.4$$\\pm$$0.6$& -1.9& 0.8&$0.6$$\\times$$0.3$&$ 12$\n\\\\\n0759+6557&2&CD&\nW&\n$ 25.5$$\\pm$$1.3$& 0.0& 0.0&$0.9$$\\times$$0.6$&$ 3$&\n$ 12.6$$\\pm$$0.7$& 0.0& 0.0&$0.9$$\\times$$0.6$&$154$&\n&&&&\n\\\\\n&&&\nE&\n$ 17.8$$\\pm$$0.9$& -4.8& -5.6&$1.7$$\\times$$1.4$&$ 62$&\n$ 4.1$$\\pm$$0.3$& -5.5& -5.8&$1.3$$\\times$$1.0$&$ 23$&\n&&&&\n\\\\\n&&&\nE&\n&&&&&\n$ 1.8$$\\pm$$0.2$& -3.0& -5.3&$1.7$$\\times$$1.4$&$142$&\n&&&&\n\\\\\n0826+7045&3&$-$&\nC&\n&&&&&\n$ 90.5$$\\pm$$4.5$& 0.0& 0.0&$0.4$$\\times$$0.2$&$162$&\n&&&&\n\\\\\n0830+5813&2&$-$&\nC&\n$ 50.8$$\\pm$$2.5$& 0.0& 0.0&$1.9$$\\times$$1.0$&$ 0$&\n$ 39.6$$\\pm$$2.0$& 0.0& 0.0&$0.6$$\\times$$0.5$&$ 66$&\n&&&&\n\\\\\n1525+6801&1&CD&\nS&\n$137$$\\pm$$ 6$& 0.0& 0.0&$2.5$$\\times$$1.1$&$170$&\n$ 80.9$$\\pm$$4.0$& 0.0& 0.0&$1.1$$\\times$$0.6$&$151$&\n$ 24.4$$\\pm$$1.2$& 0.0& 0.0&$0.4$$\\times$$0.2$&$171$\n\\\\\n&&&\nN&\n$ 14.5$$\\pm$$0.8$& 13.1& 17.8&$2.1$$\\times$$1.2$&$166$&\n$ 8.5$$\\pm$$0.5$& 13.2& 18.1&$1.5$$\\times$$0.8$&$170$&\n$ 3.9$$\\pm$$0.3$& 12.7& 18.4&$2.9$$\\times$$0.9$&$ 22$\n\\\\\n&&&\nN&\n$ 15.6$$\\pm$$0.8$& 10.2& 13.7&$5.4$$\\times$$3.4$&$135$&\n$ 5.8$$\\pm$$0.4$& 11.5& 16.3&$2.4$$\\times$$1.9$&$112$&\n&&&&\n\\\\\n&&&\nN&\n&&&&&\n$ 2.3$$\\pm$$0.2$& 10.4& 13.4&$1.6$$\\times$$0.3$&$ 36$&\n&&&&\n\\\\\n1538+5920&2&$-$&\nC&\n&&&&&\n$ 45.9$$\\pm$$2.3$& 0.0& 0.0&$0.7$$\\times$$0.3$&$ 27$&\n$ 20.1$$\\pm$$1.0$& 0.0& 0.0&$0.7$$\\times$$0.3$&$ 20$\n\\\\\n1550+5815&2&$-$&\nC&\n&&&&&\n$233$$\\pm$$11$& 0.0& 0.0&$1.4$$\\times$$0.2$&$158$&\n$174$$\\pm$$ 8$& 0.0& 0.0&$0.7$$\\times$$0.2$&$164$\n\\\\\n1551+6822&2&$-$&\nC&\n$ 49.6$$\\pm$$2.5$& 0.0& 0.0&$1.7$$\\times$$0.5$&$105$&\n$ 21.1$$\\pm$$1.1$& 0.0& 0.0&$ <0.3$&$ 0$&\n&&&&\n\\\\\n&&&\nC&\n&&&&&\n$ 5.1$$\\pm$$0.3$& -2.3& -0.9&$ <1.0$&$ 0$&\n&&&&\n\\\\\n1557+6220&2&$-$&\nC&\n$ 39.3$$\\pm$$2.0$& 0.0& 0.0&$1.5$$\\times$$0.8$&$ 89$&\n$ 17.9$$\\pm$$0.9$& 0.0& 0.0&$1.2$$\\times$$0.4$&$156$&\n&&&&\n\\\\\n\\end{tabular}\n\\caption{\\label{sourcepar} The fitted parameters of the observed components.}\n\\end{table*}\n\\addtocounter{table}{-1}\n\\begin{table*}\n\\setlength{\\tabcolsep}{1mm}\n\\begin{tabular}{ccrc|rrrcr|rrrcr|rrrcr}\nName&Fg&Cls&Cp&\\multicolumn{5}{c}{1.6 GHz Data}&\\multicolumn{5}{c}{5.0 GHz Data}&\\multicolumn{5}{c}{14.9 GHz Data}\\\\\n&&&&Flx&$\\Delta$X&$\\Delta$Y&Size&PA&Flx&$\\Delta$X&$\\Delta$Y&Size&PA&Flx&$\\Delta$X&$\\Delta$Y&Size&PA\\\\\n&&&&mJy&mas&mas&mas&$^\\circ$&mJy&mas&mas&mas&$^\\circ$&mJy&mas&mas&mas&$^\\circ$\\\\\n1557+6220&2&$-$&\nC&\n$ 39.3$$\\pm$$2.0$& 0.0& 0.0&$1.5$$\\times$$0.8$&$ 89$&\n$ 17.9$$\\pm$$0.9$& 0.0& 0.0&$1.2$$\\times$$0.4$&$156$&\n&&&&\n\\\\\n1600+7131&1&CD&\nN&\n$261$$\\pm$$13$& 0.0& 0.0&$3.1$$\\times$$2.2$&$124$&\n$ 54.4$$\\pm$$2.7$& 0.0& 0.0&$1.0$$\\times$$0.7$&$ 47$&\n$ 26.3$$\\pm$$1.3$& 0.0& 0.0&$ <0.1$&$ 0$\n\\\\\n&&&\nN&\n&&&&&\n$ 19.8$$\\pm$$1.0$& -1.4& -1.7&$2.4$$\\times$$1.4$&$110$&\n&&&&\n\\\\\n&&&\nN&\n&&&&&\n$ 4.0$$\\pm$$0.3$& 2.6& -3.6&$ <1.4$&$ 0$&\n&&&&\n\\\\\n&&&\nS&\n$ 8.3$$\\pm$$0.5$& 4.7&-22.2&$2.2$$\\times$$1.2$&$115$&\n$ 6.7$$\\pm$$0.4$& 7.7&-20.9&$1.5$$\\times$$1.2$&$141$&\n&&&&\n\\\\\n&&&\nS&\n$ 15.9$$\\pm$$0.8$& 8.2&-19.3&$1.9$$\\times$$1.4$&$165$&\n&&&&&\n&&&&\n\\\\\n1620+6406&2&CD&\nN&\n$ 29.0$$\\pm$$1.5$& 0.0& 0.0&$1.1$$\\times$$0.8$&$142$&\n$ 12.9$$\\pm$$0.7$& 0.0& 0.0&$1.0$$\\times$$0.8$&$170$&\n&&&&\n\\\\\n&&&\nS&\n$ 5.2$$\\pm$$0.3$& 0.3&-14.2&$ <1.2$&$ 0$&\n&&&&&\n&&&&\n\\\\\n1622+6630&2&$-$&\nC&\n&&&&&\n$218$$\\pm$$10$& 0.0& 0.0&$0.6$$\\times$$0.2$&$ 60$&\n$169$$\\pm$$ 8$& 0.0& 0.0&$0.3$$\\times$$0.2$&$122$\n\\\\\n1639+6711&2&$-$&\nC&\n$ 68.5$$\\pm$$3.4$& 0.0& 0.0&$1.8$$\\times$$0.9$&$ 92$&\n$ 38.6$$\\pm$$1.9$& 0.0& 0.0&$1.0$$\\times$$0.7$&$ 69$&\n&&&&\n\\\\\n1642+6701&2&$-$&\nW&\n$ 83.4$$\\pm$$4.2$& 0.0& 0.0&$3.5$$\\times$$0.5$&$ 86$&\n$ 14.8$$\\pm$$0.8$& 0.0& 0.0&$1.3$$\\times$$0.3$&$ 76$&\n&&&&\n\\\\\n&&&\nC&\n$ 8.7$$\\pm$$0.5$& -4.9& 0.0&$ <0.8$&$ 0$&\n$ 36.8$$\\pm$$1.9$& -2.7& 0.3&$1.5$$\\times$$0.4$&$ 87$&\n&&&&\n\\\\\n&&&\nE&\n$ 7.8$$\\pm$$0.4$& -9.6& 0.1&$5.1$$\\times$$0.9$&$ 99$&\n$ 9.8$$\\pm$$0.5$& -5.8& 0.5&$2.1$$\\times$$0.6$&$ 79$&\n&&&&\n\\\\\n1647+6225&2&CD&\nN&\n$ 24.2$$\\pm$$1.2$& 0.0& 0.0&$ <0.4$&$ 0$&\n$ 15.8$$\\pm$$0.8$& 0.0& 0.0&$0.7$$\\times$$0.5$&$ 65$&\n&&&&\n\\\\\n&&&\nN&\n$ 7.0$$\\pm$$0.4$& 4.1& -2.0&$2.9$$\\times$$1.0$&$ 81$&\n&&&&&\n&&&&\n\\\\\n&&&\nS&\n$ 16.1$$\\pm$$0.8$& 10.0&-12.0&$1.9$$\\times$$0.7$&$ 76$&\n$ 2.7$$\\pm$$0.2$& 10.5&-12.3&$0.8$$\\times$$0.3$&$ 19$&\n&&&&\n\\\\\n1655+6446&2&CD&\nS&\n$ 38.5$$\\pm$$1.9$& 0.0& 0.0&$2.2$$\\times$$1.1$&$ 76$&\n$ 18.2$$\\pm$$0.9$& 0.0& 0.0&$2.0$$\\times$$1.0$&$108$&\n&&&&\n\\\\\n&&&\nN2&\n$ 10.2$$\\pm$$0.5$& -4.7& 5.1&$ <2.1$&$ 0$&\n&&&&&\n&&&&\n\\\\\n&&&\nN&\n$ 2.6$$\\pm$$0.2$&-19.8& 15.0&$2.1$$\\times$$1.3$&$ 0$&\n&&&&&\n&&&&\n\\\\\n1657+5826&2&CD&\nS&\n$ 34.6$$\\pm$$1.7$& 0.0& 0.0&$1.4$$\\times$$1.4$&$ 90$&\n$ 20.2$$\\pm$$1.0$& 0.0& 0.0&$1.9$$\\times$$1.6$&$ 31$&\n&&&&\n\\\\\n&&&\nN&\n$ 4.2$$\\pm$$0.3$&-27.0& 6.8&$ <2.8$&$ 0$&\n&&&&&\n&&&&\n\\\\\n1746+6921&1&CJ&\nW&\n$ 67.7$$\\pm$$3.4$& 0.0& 0.0&$2.7$$\\times$$0.9$&$116$&\n$102$$\\pm$$ 5$& 0.0& 0.0&$ -$&$ 0$&\n$ 70.8$$\\pm$$3.5$& 0.0& 0.0&$0.5$$\\times$$0.1$&$105$\n\\\\\n&&&\nC&\n$ 67.7$$\\pm$$3.4$&-64.0&-65.0&$ -$&$ 0$&\n$ 50.3$$\\pm$$2.5$& -1.1& -0.5&$ -$&$ 0$&\n$ 12.5$$\\pm$$0.7$& -1.2& -0.4&$1.4$$\\times$$0.2$&$129$\n\\\\\n&&&\nE&\n$ 2.5$$\\pm$$0.2$& -7.4& -4.3&$7.6$$\\times$$2.1$&$149$&\n&&&&&\n&&&&\n\\\\\n1807+5959&2&CJ&\nS&\n$ 27.2$$\\pm$$1.4$& 0.0& 0.0&$1.1$$\\times$$0.4$&$173$&\n$ 29.3$$\\pm$$1.5$& 0.0& 0.0&$1.1$$\\times$$0.1$&$ 8$&\n&&&&\n\\\\\n&&&\nC&\n$ 6.0$$\\pm$$0.4$& 0.1& 4.8&$2.1$$\\times$$1.9$&$ 39$&\n$ 1.5$$\\pm$$0.2$& -0.2& 6.3&$ <0.8$&$ 0$&\n&&&&\n\\\\\n&&&\nN&\n$ 12.5$$\\pm$$0.7$& -0.6& 12.4&$4.7$$\\times$$1.4$&$ 6$&\n$ 4.0$$\\pm$$0.3$& -0.6& 13.0&$3.8$$\\times$$0.8$&$ 9$&\n&&&&\n\\\\\n1807+6742&2&CJ&\nS&\n$ 26.5$$\\pm$$1.3$& 0.0& 0.0&$1.1$$\\times$$0.7$&$104$&\n$ 5.0$$\\pm$$0.3$& 0.0& 0.0&$2.9$$\\times$$2.2$&$165$&\n&&&&\n\\\\\n&&&\nN&\n$ 11.5$$\\pm$$0.6$& 1.1& 5.9&$2.6$$\\times$$0.4$&$178$&\n$ 14.8$$\\pm$$0.8$& 1.1& 6.8&$ <0.7$&$ 0$&\n&&&&\n\\\\\n1808+6813&2&$-$&\nC&\n$ 26.9$$\\pm$$1.4$& 0.0& 0.0&$3.5$$\\times$$1.2$&$167$&\n$ 19.0$$\\pm$$1.0$& 0.0& 0.0&$ <0.7$&$ 0$&\n&&&&\n\\\\\n1819+6707&1&CSO&\nE&\n$123$$\\pm$$ 6$& 0.0& 0.0&$4.6$$\\times$$2.2$&$ 58$&\n$ 70.2$$\\pm$$3.5$& 0.0& 0.0&$3.7$$\\times$$1.6$&$ 51$&\n$ 56.2$$\\pm$$2.8$& 0.0& 0.0&$1.2$$\\times$$0.6$&$ 90$\n\\\\\n&&&\nE&\n&&&&&\n&&&&&\n$ 9.1$$\\pm$$0.5$& -2.6& 2.1&$ <0.2$&$ 0$\n\\\\\n&&&\nE&\n&&&&&\n$ 4.7$$\\pm$$0.3$& 3.2& 1.6&$3.5$$\\times$$1.5$&$ 32$&\n&&&&\n\\\\\n&&&\nC&\n$ 4.7$$\\pm$$0.3$& 7.0& 1.8&$ -$&$ 0$&\n$ 5.7$$\\pm$$0.3$& 8.6& 2.0&$2.6$$\\times$$2.0$&$ 96$&\n&&&&\n\\\\\n&&&\nW&\n$ 66.5$$\\pm$$3.3$& 16.0& 4.8&$6.4$$\\times$$4.3$&$112$&\n$ 14.6$$\\pm$$0.8$& 15.0& 3.3&$4.4$$\\times$$2.3$&$ 58$&\n&&&&\n\\\\\n&&&\nW&\n$ 52.9$$\\pm$$2.7$& 18.6& 4.8&$4.2$$\\times$$2.1$&$ 33$&\n$ 41.4$$\\pm$$2.1$& 18.0& 5.2&$4.2$$\\times$$1.9$&$ 38$&\n$ 7.9$$\\pm$$0.4$& 25.5& 8.3&$ <0.1$&$ 0$\n\\\\\n&&&\nW&\n&&&&&\n&&&&&\n$ 4.4$$\\pm$$0.3$& 27.2& 7.3&$ <0.2$&$ 0$\n\\\\\n&&&\nW&\n&&&&&\n&&&&&\n$ 2.6$$\\pm$$0.2$& 28.1& 6.5&$ <0.2$&$ 0$\n\\\\\n1841+6715&1&CD&\nS&\n$127$$\\pm$$ 6$& 0.0& 0.0&$1.0$$\\times$$0.8$&$126$&\n$123$$\\pm$$ 6$& 0.0& 0.0&$0.8$$\\times$$0.5$&$169$&\n$ 67.3$$\\pm$$3.4$& 0.0& 0.0&$0.5$$\\times$$0.4$&$142$\n\\\\\n&&&\nN&\n$ 17.8$$\\pm$$0.9$& 1.4& 5.2&$2.5$$\\times$$1.9$&$132$&\n$ 5.2$$\\pm$$0.3$& 1.7& 5.9&$1.0$$\\times$$0.9$&$ 71$&\n$ 2.6$$\\pm$$0.2$& 2.3& 6.9&$ <0.4$&$ 0$\n\\\\\n1843+6305&2&CD&\nS&\n$ 50.1$$\\pm$$2.5$& 0.0& 0.0&$1.4$$\\times$$0.7$&$156$&\n$ 26.7$$\\pm$$1.3$& 0.0& 0.0&$1.1$$\\times$$0.7$&$177$&\n&&&&\n\\\\\n&&&\nN&\n$ 17.8$$\\pm$$0.9$& 2.6& 8.9&$2.3$$\\times$$0.6$&$ 59$&\n$ 7.0$$\\pm$$0.4$& 2.6& 9.1&$1.6$$\\times$$1.0$&$ 17$&\n&&&&\n\\\\\n1942+7214&1&CJ&\nN&\n$176$$\\pm$$ 8$& 0.0& 0.0&$1.4$$\\times$$0.8$&$ 58$&\n$173$$\\pm$$ 8$& 0.0& 0.0&$0.5$$\\times$$0.4$&$ 3$&\n$101$$\\pm$$ 5$& 0.0& 0.0&$0.4$$\\times$$0.3$&$ 14$\n\\\\\n&&&\nC&\n$ 3.5$$\\pm$$0.3$& 6.1&-11.0&$ -$&$ 36$&\n$ 1.5$$\\pm$$0.2$& 4.4&-10.8&$0.8$$\\times$$0.8$&$ 0$&\n$ 2.5$$\\pm$$0.2$& 4.0&-11.8&$2.4$$\\times$$0.7$&$ 55$\n\\\\\n&&&\nS&\n$ 2.0$$\\pm$$0.2$& 6.5&-17.4&$ -$&$171$&\n&&&&&\n&&&&\n\\\\\n&&&\nS&\n$ 3.5$$\\pm$$0.3$& 11.7&-29.3&$ -$&$ 6$&\n&&&&&\n&&&&\n\\\\\n1945+6024&2&$-$&\nC&\n&&&&&\n$ 81.3$$\\pm$$4.1$& 0.0& 0.0&$0.6$$\\times$$0.3$&$105$&\n$ 79.7$$\\pm$$4.0$& 0.0& 0.0&$ <0.1$&$ 0$\n\\\\\n1946+7048&1&CSO&\nN&\n$292$$\\pm$$14$& 0.0& 0.0&$1.6$$\\times$$0.9$&$ 61$&\n$215$$\\pm$$10$& 0.0& 0.0&$1.6$$\\times$$1.0$&$ 86$&\n$106$$\\pm$$ 5$& 0.0& 0.0&$1.1$$\\times$$0.6$&$ 96$\n\\\\\n&&&\nN&\n$196$$\\pm$$ 9$& -3.4& -0.1&$7.9$$\\times$$3.0$&$ 83$&\n$ 53.0$$\\pm$$2.7$& -5.9& -0.5&$3.0$$\\times$$1.5$&$ 95$&\n$ 16.2$$\\pm$$0.8$& -2.3& -0.6&$1.8$$\\times$$1.0$&$ 73$\n\\\\\n&&&\nN2&\n$150$$\\pm$$ 7$& 1.2& -6.6&$3.2$$\\times$$1.2$&$ 9$&\n$ 81.0$$\\pm$$4.1$& 1.2& -7.0&$2.9$$\\times$$0.6$&$ 13$&\n$ 40.7$$\\pm$$2.0$& 1.2& -7.1&$2.1$$\\times$$0.6$&$ 11$\n\\\\\n&&&\nC&\n$ 66.0$$\\pm$$3.3$& 5.4&-13.3&$4.2$$\\times$$1.4$&$ 47$&\n$ 33.6$$\\pm$$1.7$& 5.6&-13.5&$1.3$$\\times$$0.2$&$ 45$&\n$ 17.8$$\\pm$$0.9$& 5.5&-13.2&$ <1.0$&$ 0$\n\\\\\n&&&\nC&\n&&&&&\n$ 27.6$$\\pm$$1.4$& 7.4&-15.2&$0.9$$\\times$$0.3$&$ 47$&\n$ 66.5$$\\pm$$3.3$& 6.5&-14.5&$1.2$$\\times$$0.4$&$ 44$\n\\\\\n&&&\nS2&\n$ 76.4$$\\pm$$3.8$& 10.3&-20.4&$3.0$$\\times$$1.2$&$ 14$&\n$ 41.4$$\\pm$$2.1$& 10.2&-20.2&$1.5$$\\times$$0.5$&$ 12$&\n$ 18.2$$\\pm$$0.9$& 9.9&-19.9&$1.0$$\\times$$0.5$&$ 29$\n\\\\\n&&&\nS&\n$ 89.8$$\\pm$$4.5$& 13.6&-28.9&$5.0$$\\times$$2.6$&$ 51$&\n$ 19.9$$\\pm$$1.0$& 13.1&-29.0&$3.0$$\\times$$1.1$&$ 44$&\n&&&&\n\\\\\n1954+6146&2&CJ&\nS&\n&&&&&\n$146$$\\pm$$ 7$& 0.0& 0.0&$0.5$$\\times$$0.2$&$153$&\n$ 99.6$$\\pm$$5.0$& 0.0& 0.0&$0.4$$\\times$$0.1$&$141$\n\\\\\n&&&\nN&\n&&&&&\n$ 5.7$$\\pm$$0.3$& 2.2& 3.8&$2.4$$\\times$$1.5$&$159$&\n&&&&\n\\\\\n1958+6158&2&$-$&\nC&\n&&&&&\n$134$$\\pm$$ 6$& 0.0& 0.0&$0.8$$\\times$$0.4$&$ 60$&\n$ 93.3$$\\pm$$4.7$& 0.0& 0.0&$0.7$$\\times$$0.4$&$ 87$\n\\\\\n\\end{tabular}\n\\end{table*}\n"
}
] |
[
{
"name": "astro-ph0002129.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem{} Conway J.E., Pearson T.J., Readhead A.C.S., Unwin S.C., Xu W., \n Mutel R.L. 1992, {\\sl Ap. J.}, {\\bf 396}, 62\n\n\\bibitem{} Dallacasa D., Fanti C., Fanti R., Schilizzi R.T., Spencer R.E., 1995\n {\\it Astron. Astrophys.}, {\\bf 295}, 27\n\n\\bibitem{} Henstock D.R., Browne I.W.A., Wilkinson P.N.,\n Taylor G.B., Vermeulen R.C., Pearson T.J., Readhead A.C.S, 1995\n{\\it Astrophys. J. Suppl.}, {\\bf 100}, 1\n\n\\bibitem{} O'Dea C.P., Baum S.A., Stanghellini C., 1991, \n {\\it Astrophys. J.}, {\\bf 380}, 66\n\n\\bibitem{} O'Dea C.P., 1998, P.A.S.P., {bf 110}, 493\n\n\\bibitem{} Owsianik I. and Conway J.E., 1998, \n {\\it Astron. \\& Astrophys.}, {\\bf 337}, 69\n\n\\bibitem{} Owsianik I., Conway J.E., and Polatidis A.G., 1998,\n {\\it Astron. \\& Astrophys.}, {\\bf 336}, L37\n\n\\bibitem{} Perlman E.S., Stocke J.T., Shaffer D.B., Carilli C.L., Ma C., 1994,\n ApJ, 424, 69\n\n\\bibitem{} Philips R.B. and Mutel R.L., 1982, {\\it Astrophys. J.}, {\\bf 236}, \n 89\n\n\\bibitem{} Polatidis A.G. Wilkinson P.N., Readhead A.C.S, Pearson T.J.,\nTaylor G.B., Vermeulen R.C., 1995, {\\it Astrophys. J. Suppl.}, {\\bf 98}, 1\n\n\\bibitem{} Rengelink R.B., Tang Y., de Bruyn A.G., Miley G.K., Bremer M.N., \n R\\\"ottgering H.J.A., Bremer M.A.R., 1997, \n {\\it Astr. \\& Astrophys.}, in press\n\\bibitem{} Schwab F.R. and Cotton W.D., 1983, {\\it Astron. J.}, {\\bf 88}, 688 \n\n\\bibitem{} Snellen, I.A.G., Schilizzi R.T., de Bruyn A.G., Miley G.K.,\n Rengelink R.B., R\\\"ottgering H.J.A., Bremer M.N., 1998a, {\\it A\\&AS.}, \n {\\bf 131}, 435\n\n\\bibitem{} Snellen I.A.G., Schilizzi R.T., Bremer M.N., de Bruyn A.G., \n Miley G.K., R\\\"ottgering H.J.A., McMahon R.G., P\\'erez Fournon I., 1998b, \n {\\it M.N.R.A.S.}, {\\bf 301},985\n\n\\bibitem{} Snellen, I.A.G., Schilizzi R.T., de Bruyn A.G., Miley G.K.,\n1998c, A\\&A, 333, 70\n\n\\bibitem{} Snellen I.A.G., Schilizzi R.T., Bremer M.N., Miley G.K., de Bruyn\n A.G., R\\\"ottgering H.J.A., 1999, {\\it M.N.R.A.S}, {\\bf 307}, 149\n\n\\bibitem{} Snellen I.A.G., Schilizzi R.T., Miley G.K., de Bruyn A.G., Bremer M.N., R\\\"ottgering H.J.A., {\\it M.N.R.A.S}, submitted (companion paper)\n\n\\bibitem{} Staghellini C., O'Dea C.P., Baum S.A., Dallacasa D., Fanti R.,\n Fanti C., {\\it Astron. \\& Astrophys.}, 1997, {\\bf 325}, 943\n\n\\bibitem{} Taylor G.B. and Vermeulen R.C., 1997, {\\it Astrophys. J.}, \n {\\bf 485}, L9\n\n\\bibitem{} van Breugel, W., Miley, G., and Heckman, T.,{\\it Astron. J.}, \n {\\bf 89}, 5\n\n\\bibitem{} Wilkinson, P. N., Booth, R. S., Cornwell, T. J., Clark, R. R. \n 1984, {\\it Nature}, {\\bf 308}, 619\n\n\\bibitem{} Wilkinson, P. N., Polatidis, A. G., Readhead, A. C. S., Xu, W., \n Pearson, T. J. 1994, {\\it Astrophys. J.}, {\\bf 432}, L87\n\n\\vfill\n\\end{thebibliography}"
}
] |
astro-ph0002130
|
On the evolution of young radio-loud AGN
|
[
{
"author": "I.A.G. Snellen$^{1,2}$"
},
{
"author": "R.T. Schilizzi$^{2,3}$"
},
{
"author": "G.K. Miley$^{2}$"
},
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"author": "A.G. de Bruyn$^{4,5}$"
},
{
"author": "\\cr M.N. Bremer$^{2,6,7}$"
},
{
"author": "H.J.A. R\\\"ottgering$^{2}$"
},
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"author": "Madingley Road"
},
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"author": "Cambridge CB3 0HA"
},
{
"author": "United Kingdom"
},
{
"author": "$^{2}$Leiden Observatory"
},
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"author": "P.O. Box 9513"
},
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"author": "2300 RA"
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"author": "Leiden"
},
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"author": "The Netherlands"
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"author": "Postbus 2"
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"author": "7990 AA"
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"author": "Dwingeloo"
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"author": "$^{4}$Netherlands Foundation for Research in Astronomy"
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"author": "Postbus 800"
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"author": "9700 AV"
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"author": "Groningen"
},
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"author": "$^{6}$Institut d'Astrophysique de Paris"
},
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"author": "98bis Boulevard Arago"
},
{
"author": "75014 Paris"
},
{
"author": "France"
},
{
"author": "$^{7}$ Department of Physics"
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"author": "H H Wills Physics Laboratory"
},
{
"author": "Tyndall Avenue"
},
{
"author": "Bristol"
},
{
"author": "BS8 1TL"
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] |
This paper describes an investigation of the early evolution of extra-galactic radio sources using samples of faint and bright Gigahertz Peaked Spectrum (GPS) and Compact Steep Spectrum (CSS) radio galaxies. Correlations found between their peak frequency, peak flux density and angular size provide strong evidence that synchrotron self absorption is the cause of the spectral turnovers, and indicate that young radio sources evolve in a self-similar way. In addition, the data seem to suggest that the sources are in equipartition while they evolve. If GPS sources evolve to large size radio sources, their redshift dependent birth-functions should be the same. Therefore, since the lifetimes of radio sources are thought to be short compared to the Hubble time, the observed difference in redshift distribution between GPS and large size sources must be due to a difference in slope of their luminosity functions. We argue that this slope is strongly affected by the luminosity evolution of the individual sources. A scenario for the luminosity evolution is proposed in which GPS sources increase in luminosity and large scale radio sources decrease in luminosity with time. This evolution scenario is expected for a ram-pressure confined radio source in a surrounding medium with a King profile density. In the inner parts of the King profile, the density of the medium is constant and the radio source builds up its luminosity, but after it grows large enough the density of the surrounding medium declines and the luminosity of the radio source decreases. A comparison of the local luminosity function (LLF) of GPS galaxies with that of extended sources is a good test for this evolution scenario. Unfortunately, only a handful of GPS sources are known at low redshift, and an LLF can only be derived, assuming that their cosmological number density evolution is similar to that of steep spectrum sources. The LLF derived in this way is shown to be in good agreement with the proposed evolution scenario. However, the uncertainties are large, and larger, homogeneously selected samples of GPS sources are needed.
|
[
{
"name": "mn_evolution.tex",
"string": "\\documentstyle[psfig,amsmath]{mn}\n%\\renewcommand{\\baselinestretch}{2}\n\n\\title[On the evolution of young radio-loud AGN]\n{On the evolution of young radio-loud AGN}\n\n\n\\author[I. Snellen et al.]{I.A.G. Snellen$^{1,2}$, R.T. Schilizzi$^{2,3}$, G.K. Miley$^{2}$, A.G. de Bruyn$^{4,5}$,\\cr M.N. Bremer$^{2,6,7}$, H.J.A. R\\\"ottgering$^{2}$\\\\ \n$^{1}$Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, United \nKingdom\\\\\n$^{2}$Leiden Observatory, P.O. Box 9513, 2300 RA, Leiden, The Netherlands \\\\\n$^{3}$Joint Institute for VLBI in Europe, Postbus 2, 7990 AA, Dwingeloo, \nThe Netherlands\\\\\n$^{4}$Netherlands Foundation for Research in Astronomy, Postbus 2, 7990 AA, \nDwingeloo, The Netherlands\\\\\n$^{5}$Kapteyn Institute, Postbus 800, 9700 AV, Groningen, The Netherlands\\\\\n$^{6}$Institut d'Astrophysique de Paris, 98bis Boulevard Arago, 75014 \n Paris, France\\\\\n$^{7}$ Department of Physics, Bristol University, H H Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom}\n\n\n\\date{}\n\\begin{document}\n\\maketitle\n\\begin{abstract}\nThis paper describes an investigation of the early evolution of extra-galactic \nradio sources using samples of faint and bright Gigahertz Peaked Spectrum\n(GPS) and Compact Steep Spectrum (CSS) radio galaxies.\nCorrelations found between their peak frequency, peak flux density and \nangular size provide strong evidence that synchrotron self absorption is the \ncause of the spectral turnovers, and indicate that young radio sources \nevolve in a self-similar way. In addition, the data seem to suggest that \nthe sources are in equipartition while they evolve.\nIf GPS sources evolve to large size radio sources, their redshift dependent \nbirth-functions should be the same. Therefore, since the\nlifetimes of radio sources are thought to be short compared to the Hubble \ntime, the observed difference in redshift distribution between GPS and \nlarge size sources must be due to a difference in slope of their luminosity \nfunctions.\nWe argue that this slope is strongly affected by the luminosity evolution of \nthe individual sources. A scenario for the luminosity evolution \nis proposed in which \nGPS sources increase in luminosity and large scale radio sources decrease\nin luminosity with time. \nThis evolution scenario is expected for a ram-pressure confined \nradio source in a surrounding medium with a King profile density.\nIn the inner parts of the King profile, the density of the medium is constant\nand the radio source builds up its\nluminosity, but after it grows large enough the density of the surrounding \nmedium declines and the luminosity of the radio source decreases.\nA comparison of the local luminosity function (LLF) of GPS galaxies with that\nof extended sources is a good test for this evolution scenario.\nUnfortunately, only a handful of GPS sources are known at low redshift, \nand an LLF can only be derived, assuming that their \ncosmological number density evolution is similar to that \nof steep spectrum sources. The LLF derived in this way is shown to be\nin good agreement with the proposed evolution scenario. However, the\nuncertainties are large, and larger, homogeneously selected samples of \nGPS sources are needed.\n\n\\end{abstract}\n\n\\section{Introduction}\n\\subsection{Gigahertz Peaked Spectrum and Compact Symmetric Objects.}\n\nAn important element in the investigation of the evolution of\nextra-galactic radio sources is the study of young counterparts of\n`old' FRI/FRII extended objects. Two classes of compact radio source\ncan be found in the literature as most likely representatives of this\nearly evolutionary stage: I) Gigahertz Peaked Spectrum (GPS) sources,\nwhich are characterised by a convex-shaped radio spectrum peaking at\nabout 1 GHz in frequency (O'Dea 1998), and II) Compact Symmetric \nObjects (CSO) which are characterised by their small size ($<500$ pc) and \ntwo-sided radio structure, e.g. having jets and lobes on both sides of a \ncentral core (Wilkinson et al. 1994). \nClearly, samples of GPS sources and CSOs are \nselected in very\ndifferent ways. GPS sources are selected on their broadband radio\nspectra, while CSOs are selected on their multi-frequency\nmilli-arcsecond morphology. Therefore studies of these objects have\nmostly been presented separately. However, a significant overlap\nbetween the two classes of sources exists. GPS sources optically\nidentified with galaxies are most likely to possess compact symmetric\nradio morphologies (Stanghellini et al. 1997a, 1999), \nand the large majority of CSOs exhibit a gigahertz-peaked spectrum. \nThe large but not complete overlap between\nthese two classes of source is most likely caused by the synchrotron\nself-absorbed mini-lobes, located at the extremities of most CSOs,\nbeing the main contributors to the overall radio spectrum, and\nproducing the peak at about 1 GHz in frequency.\n\n\\subsection{Evidence for the young nature of GPS sources and CSOs.}\n\nSince the early discovery of GPS sources, it has been speculated\nthat these were young objects (Shklovsky 1965, Blake 1970). \nHowever, a commonly \ndiscussed alternative to them being young was that they are small \ndue to confinement by a particularly dense and clumpy interstellar\nmedium that impedes the outward propagation of the jets \n(van Breugel, Miley \\& Heckman 1984; O'Dea, Baum \\& Stanghellini 1991).\nThis latter hypothesis now looks less likely since recent observations show \nthat the surrounding media of peaked spectrum sources are not significantly\ndifferent from large scale radio sources, and insufficiently dense to \nconfine these sources.\nThe most compelling evidence for youth is found in observations of the \npropagation velocities of the hot spots of several GPS/CSOs\n(Owsianik \\& Conway 1998; Owsianik, Conway \\& Polatidis 1998;\nTschager et al. 1999). They all appear to have separation velocities\nof typically $\\sim 0.2h^{-1}c$, indicating a\ndynamical age of $\\sim 10^3$ year and clearly showing that these are\nindeed young objects. Recent measurements of the\nhigh frequency breaks in Compact Steep Spectrum (CSS)\nsources, indicate that these somewhat larger objects have radiative ages\nin the range of $10^3$ to $10^5$ years (Murgia et al. 1999).\n\n\n\\subsection{Current views on Radio Source Evolution}\n\nObservational constraints on the luminosity evolution of radio sources\nmainly come from the source density in the power - linear size $(P-D)$ \ndiagram (Shklovsky 1963). It was found that sources with large sizes\n($D>1$ Mpc, eg. Schoenmakers 1999) and high radio luminosities ($P>10^{26}$ W/Hz at 178 MHz) \nare rare, suggesting that the luminosities of sources should decrease quickly\nwith linear sizes approaching 1 Mpc. Several authors have compared the \nnumber densities of GPS and CSS sources with those of large radio \nsources to investigate the luminosity evolution of young radio sources\n(Fanti et al. 1995; Readhead et al. 1996; O'Dea \\& Baum 1997).\nFanti et al. (1995) argue that the luminosities of CSS sources decrease by\na factor of $\\sim 10$ as they evolve to extended objects. Readhead et al. \n(1996) find a factor of 8 decrease in luminosity as a source expands from \n500 pc to 200 kpc in overall size. Taking into account their CSO statistics,\nthey find that the luminosity evolution in the phases CSO-MSO-LSO\n(MSO = Medium Symmetric Object; LSO = Large Symmetric Object), i.e. \nfrom 10 pc to 150 kpc, is consistent with a single power-law luminosity\nevolution. This conclusion is not supported by O'Dea \\& Baum (1997), \nwho found that GPS and CSS sources must decrease in luminosity at a \nfaster rate than the classical 3CR doubles. \nBlundell, Rawlings \\& Willott (1999) showed that any radio source evolution\ninvolving a decrease in luminosity with time would, at the highest redshifts,\nresult in a bias towards young sources in flux density limited samples.\nSince this effect is only important at $z>2-3$, it is not relevant\nto the analysis presented in this paper.\n\nSeveral GPS and CSOs (eg. 0108+388; Baum et al. 1990) exhibit low\nlevel, steep spectrum, extended emission on arcsecond scales, which seem to\nbe relics of much older radio-activity. These objects are often classified\nas being intermittent or re-occurent, and therefore not as young objects.\nHowever, the components related to their gigahertz-peaked spectra and\nCSO morphologies are certainly young. \nThe presence of faint relic emission\nonly indicates that the active nucleus has been active before, and may\nconstrain the typical timescale and frequency of such events. \nBased on the current knowledge of the formation of massive \nblack-holes in the centers of galaxies, \nit is unlikely that the central engine itself is young, but just the \nradio source (Richstone et al. 1998).\n\nIt is unclear whether all young sources actually evolve to large extended \nobjects. Some, or even the majority, may be short-lived phenomena \ndue to a lack of significant fuel (Readhead 1994). The possible existence\nof these objects can have a large influence on the source statistics of young \nradio sources.\n\n\n\\section{Samples of GPS and CSS sources}\n\nIn this paper, we present a study of the evolution of young \nradio sources from the analysis of three samples of faint and bright\nGPS and CSS radio sources:\nThe faint GPS sample from WENSS (Snellen et al. 1998a), the \nbright (Stanghellini et al. 1998) GPS sample, and the Fanti et al. (1990)\nCSS sample. As discussed in the companion paper (Snellen, Schilizzi \\& van\nLangevelde, 2000), we do not regard GPS quasars to be related to their\ngalaxy counterparts; in the following\nwe choose not to use the quasars for\nfurther analysis and only concentrate on the GPS and CSS galaxies.\nUnless stated otherwise, we will assume that {\\it all} GPS galaxies\nevolve to large scale radio galaxies, and that {\\it all} large scale radio \ngalaxies were once GPS galaxies. \n\n\\subsection{The faint GPS sample from WENSS}\n\nThe selection of this sample has been described in detail \nin Snellen et al. (1998a). Candidate GPS sources were selected in two ways;\ni) with inverted spectra between 325 MHz and 625 MHz in WENSS\n(Rengelink et al. 1997), and ii) with inverted \nspectra between WENSS 625 MHz and Greenbank 5 GHz (Gregory \\& Condon 1991). \nThe sources are located in two regions of the survey; one at $15^h < \\alpha < \n20^h$\nand $58^\\circ< \\delta < 75^\\circ$, which is called the {\\it mini-survey} region\n(Rengelink et al. 1997), and the other at $4^h00^m < \\alpha < 8^h30^m$ and\n$58^\\circ< \\delta < 75^\\circ$. Additional observations at 1.4, 5, 8.4 and 15\nGHz were carried out with the WSRT and the VLA, yielding a sample of 47\ngenuine GPS sources with peak frequencies ranging from 500 MHz to more than 15\nGHz, and peak flux densities ranging from $\\sim30$ to $\\sim900$ mJy.\nThis sample has been imaged in the optical and near-infrared, resulting in\nan identification fraction of $\\sim$ 87 \\% (Snellen et al. 1998b, 1999).\nAll the galaxies in the sample were used for the morphological evolution \nstudy. The redshifts of the majority of the objects \nhad to be estimated from their optical magnitudes, using\nthe well determined Hubble diagram for GPS galaxies \n(Snellen et al. 1996, O'Dea et al.1996). \nSome, assumed to be galaxies, have only faint lower limits to their \nmagnitudes. For these a redshift of z=1.5 was assumed.\n\nThe overall angular sizes were \nmeasured from the VLBI observations as the maximum angular \nseparation of components or the angular size for single component source\n(see companion paper)\nTheir 5 GHz radio power was determined, assuming $H_o=50$ km sec$^{-1}$ Mpc$^{-1}$\nand $\\Omega_o=1$. For a few sources, the rest-frame peak frequency was above 5 GHz.\nThe radio power of these galaxies was corrected for the spectral turnover\nby extrapolating their optically thin spectrum to rest-frame 5 GHz.\nIn the most extreme case (B0752+6355), this correction is $<20\\%$.\nB0531+6121 was omitted from the sample since it does not\nhave a genuine GPS spectrum.\n\nFor the luminosity evolution study to be discussed in section 4, \nit is crucial to have a good understanding of the selection effects. \nWe therefore applied \nmore strict constraints than in the original sample. Only the GPS sources \nwhich have inverted spectra between 325 MHz and 5 GHz, and with \nflux densities of $>20$ mJy at 325 MHz, 14 in total, were selected.\n\nAll the 26 galaxies in the sample are given in table \\ref{WENSS}.\nColumn 1 gives the B1950 name, column 2 indicates whether the \nsource is in the complete sub-sample or not, column 3 gives the \n(estimated) redshift, column 4 gives the observed peak frequency, \ncolumn 5 the observed peak flux density,\ncolumn 6 the rest-frame 5 GHz radio power, and column 7 the overall\nangular size. \n\n\\begin{table}\n\\setlength{\\tabcolsep}{1mm}\n\\centerline{\n\\begin{tabular}{ccrcrcr}\\hline\nName&C&z&$\\nu_{peak}$&$S_{peak}$&$P_{5GHz}$&$\\theta$\\\\\n & & & (GHz) & (mJy) & (Log$\\frac{W}{Hz}$) & (mas)\\\\ \\hline\nB0400+6042&+&1.5$^2$&1.0& 184& 26.8 & 4.4\\\\\nB0436+6152&+&1.5$^2$&1.0& 237& 26.9 &17.1\\\\\nB0535+6743&+&1.5$^1$&5.7& 192& 27.2 & 4.0\\\\\nB0539+6200&+&1.4$^1$&1.9& 129& 26.6 & 6.1\\\\\nB0552+6017&-&1.5$^2$&1.0& 50& 26.2 &12.6\\\\\nB0557+5717&-&1.2$^1$&1.1& 69& 26.2 & 6.5\\\\\nB0752+6355&-&0.9$^1$&6.4& 314& 26.7 & 4.6\\\\\nB0759+6557&-&1.5$^1$&1.7& 46& 26.2 & 8.0\\\\\nB0830+5813&+&0.093 &1.6& 65& 24.1 &$<4.3$\\\\\nB1525+6801&+&1.1$^1$&1.8& 163& 26.5 &22.4\\\\\nB1551+6822&+&1.3$^1$&1.5& 52& 26.1 & 2.5\\\\\nB1557+6220&+&0.9$^1$&2.3& 49& 25.8 &$<4.4$\\\\\nB1600+7131&+&1.5$^2$&1.7& 346& 27.0 &22.7\\\\\nB1620+6406&-&1.2$^1$&2.2& 47& 25.9 &14.2\\\\\nB1622+6630&+&0.201 &4.0& 363& 25.5 &$<2.9$\\\\\nB1639+6711&-&1.5$^2$&1.0& 68& 26.4 &$<4.1$\\\\\nB1655+6446&+&1.5$^2$&1.0& 69& 26.3 &24.8\\\\\nB1657+5826&-&1.1$^1$&0.5& 64& 26.0 &27.8\\\\\nB1807+5959&-&1.0$^1$&1.0& 47& 25.9 &13.0\\\\\nB1807+6742&-&1.5$^2$&0.8& 54& 26.2 & 6.9\\\\\nB1808+6813&-&1.1$^1$&1.3& 42& 25.9 & 3.5\\\\\nB1819+6707&-&0.220 &0.8& 338& 25.5 &19.2\\\\\nB1841+6715&+&0.486 &2.1& 178& 26.0 & 6.1\\\\\nB1843+6305&-&1.5$^2$&1.9& 75& 26.4 & 9.5\\\\\nB1942+7214&+&1.1$^1$&1.4& 233& 26.7 &31.5\\\\\nB1946+7048&+&0.101 &1.8& 929& 25.4 &31.9\\\\ \\hline\n\\end{tabular}}\n\\centerline{\n\\begin{tabular}{l}\n$^1$ estimate from optical magnitude\\\\\n$^2$ assumed at z=1.5\\\\\n\\end{tabular}}\n\\caption{\\label{WENSS} The GPS galaxies from the faint WENSS sample.\nThe second column (+/$-$) indicates whether a source is part of the \ncomplete sub-sample or not.}\n\\end{table}\n\n\\subsection{The bright Stanghellini et al. GPS sample}\n\nA sample of radio bright GPS sources has been constructed by\nStanghellini et al. (1998) from GPS candidates selected from the K\\\"uhr \net al. (1981)\n 1 Jy catalogue, with declination \n$>-25^{\\circ}$ and galactic latitude $|b|>10^\\circ$.\nStanghellini et al. supplemented this data set with multi-frequency \nobservations from the VLA, WSRT and data from the literature, and\nselected sources with a turnover frequency between 0.4 and 6 GHz, and \nan optical thin spectral index $\\alpha_{thin}<-0.5$ at high frequency.\nThe final complete sample consists of 33 GPS sources, of which 19 are\noptically identified with galaxies. \nFour galaxies do not have a spectroscopic redshift. Their redshifts were\nestimated from their optical magnitudes, in the same way as for \ngalaxies in the WENSS-sample. Their rest-frame radio power at 5 GHz has\nalso been calculated in the same way as for the objects in the WENSS sample.\n\nAll the galaxies in the sample are given in table \\ref{BRIGHT}.\nColumn 1 gives the B1950 name, column 2 the \nredshift, column 3 the observed peak frequency, \ncolumn 4 the observed peak flux density,\ncolumn 5 the rest-frame 5 GHz radio power, and column 6 the overall\nangular size. Column 7 gives the reference for the angular size.\n\n\\begin{table}\n\\caption{\\label{BRIGHT}The complete sample of Bright GPS galaxies\nfrom Stanghellini et al. (1998)}\n\\setlength{\\tabcolsep}{1mm}\n\\centerline{\n\\begin{tabular}{crcrcrr}\\hline\nName&z&$\\nu_{peak}$&$S_{peak}$&$P_{5GHz}$&$\\theta$&Refs.\\\\\n & & (GHz) & (Jy) & (Log$\\frac{W}{Hz}$) & (mas)\\\\ \\hline\n0019$-$000&0.305&0.8&3.5&26.7& 70&5\\\\\n0108+388 &0.669&3.9&1.3&27.3& 6&6\\\\\n0316+161 &1.2 &0.8&9.6&28.2&300&3\\\\\n0428+205 &0.219&1.0&4.0&26.6&250&3\\\\\n0500+019 &0.583&2.0&2.5&27.3& 15&1\\\\\n0710+439 &0.518&1.9&2.1&27.1& 25&7\\\\\n0941$-$080&0.228&0.5&3.4&26.4& 48&8\\\\\n1031+567 &0.459&1.3&1.9&26.9& 33&9\\\\\n1117+146 &0.362&0.5&3.9&26.8& 90&10\\\\\n1323+321 &0.369&0.5&7.0&27.1& 60&3\\\\\n1345+125 &0.122&0.6&8.9&26.3& 85&1\\\\\n1358+624 &0.431&0.5&6.6&27.1& 80&3\\\\\n1404+286 &0.077&4.9&2.8&25.8& 8&4\\\\\n1600+335 &1.1 &2.6&3.1&27.9& 60&3\\\\\n1607+268 &0.473&1.0&5.4&27.2& 49&8\\\\\n2008+068 &0.7 &1.3&2.6&27.3& 30&2\\\\\n2128+048 &0.990&0.8&4.9&27.8& 35&1\\\\\n2210+016 &1.0 &0.4&4.5&27.7& 80&1\\\\\n2352+495 &0.237&0.7&2.9&26.5& 70&7\\\\ \\hline\n\\end{tabular}}\n\\centerline{\n\\begin{tabular}{ll}\nRefs for angular sizes:\\\\\n1) Stanghellini et al. (1997a)& 2) Stanghellini et al. (1999)\\\\\n3) Dallacasa et al. (1995)& 4) Stanghellini et al. (1997b)\\\\\n5) Hodges, Mutel \\& Phillips (1984)& 6) Owsianik et al. (1998)\\\\\n7) Wilkinson et al. (1994)& 8) Dallacasa et al. (1998)\\\\\n9) Taylor, Readhead \\& Pearson (1996)& 10) Bondi et al. (1998).\\\\\n\\end{tabular}}\n\\end{table}\n\n\\subsection{The Fanti et al. CSS sample}\n\nThe sample of CSS sources used in this paper is \nfrom Fanti et al. (1990). They constructed a sample without spectral bias \nby integrating the 3CR sample with sources from the Peacock and Wall\nsample (1982) which would be stronger than 10 Jy at 178 MHz, if\ncorrected for low frequency absorption by extrapolation of the straight \nhigh-frequency part of the spectrum. All sources were included\nwith projected linear size $<15$ kpc, (corrected) flux density at\n178 MHz $>$10 Jy, and with Log $P_{178}>$ 26.5, in a well defined\narea of sky ($|b|>10^\\circ$, $\\delta>10^\\circ$). A number of sources, \nwhich are included in the Stanghellini et al. sample are\nomitted from the Fanti et al. sample to avoid duplication.\nThe remaining CSS galaxies are listed in table \\ref{CSS}.\n \n\\begin{table}\n\\caption{\\label{CSS} The complete sample of CSS galaxies \nfrom Fanti et al. (1990).}\n\\setlength{\\tabcolsep}{1mm}\n\\centerline{\n\\begin{tabular}{lrcrcrr}\\hline\nName&z&$\\nu_{peak}$&$S_{peak}$&$P_{5GHz}$&$\\theta$&Refs.\\\\\n & & (GHz) & (Jy) & (Log$\\frac{W}{Hz}$) & ($''$)\\\\ \\hline\n3C49 &0.62&0.12 & 11 &27.2 & 1.0 &1\\\\\n3C67 &0.31&0.05 & 10 &26.6 & 2.5 &1\\\\\n3C93.1 &0.24&0.06 & 10 &26.3 & 0.6 &2\\\\\n0404+76 &0.59&0.60 & 6 &27.6 & 0.1 &2\\\\\n3C237 &0.88&0.05 & 40 &27.9 & 1.2 &1\\\\\n3C241 &1.62&0.04 & 17 &27.8 & 0.8 &1\\\\\n3C268.3 &0.37&0.08 & 11 &26.9 & 1.3 &1\\\\\n3C299 &0.37&0.08 & 13 &26.8 &11.5 &1\\\\\n3C303.1 &0.27&0.10 & 10 &26.4 & 2.0 &1\\\\\n3C305.1 &1.13&0.09 & 10 &27.5 & 2.8 &1\\\\\n3C318 &0.75&$<0.04$& 20 &27.3 & 0.8 &1\\\\\n3C343.1 &0.75&0.25 & 13 &27.6 & 0.3 &1\\\\\n3C346 &0.16&$<0.04$& 10 &26.2 & 2.3 &1\\\\\n1819+39 &0.80&0.10 & 7 &27.6 & 0.5 &2\\\\\n3C454.1 &1.84&$<0.04$& 10 &27.8 & 1.6 &1\\\\\n\\end{tabular}}\n\\centerline{\n\\begin{tabular}{l}\nRefs for angular sizes:\\\\\n1) Spencer et al. 1989\\\\\n2) Dallacasa et al 1995\\\\\n\\end{tabular}}\n\\end{table}\n\n\n\\section{The spectral turnovers and the morphological evolution of young \nradio sources}\n\n\n\\begin{figure*}\n\\psfig{figure=fig1.ps,width=16cm}\n\\caption{\\label{morph} Correlations found between the spectral turnover and \nthe overal size in samples of GPS and CSS sources. Squares, open\nand filled diamonds indicate objects from the CSS, bright and faint GPS\nsample respectively.\n(top left) The maximum angular size versus peak frequency.\n(top right) The maximum angular size versus peak flux density for\nsources with $0.8<\\nu_p<3$.\n(bottom left) The maximum angular size versus $S_p^{1/2} \\nu_p^{-5/4}$.\nThe line indicates a linear correlation between the two parameters.\n(bottom right) The overall linear size versus the equipartition component\nsize. The distance of the data-points to the dotted line indicates\nthe component to overall size ratio.}\n\\end{figure*}\n\nEarly measurements of the angular sizes of GPS and CSS sources using VLBI\nstrongly suggested that their spectral turnovers are caused by\nsynchrotron self absorption (SSA, Jones, O'Dell \\& Stein 1974; Hodges, Mutel\n\\& Phillips 1984; Mutel, Hodges \\& Phillips 1985)\nIt was realised by Jones, O'Dell \\& Stein (1974) that if the optical depth\ndue to SSA was less than unity at the spectral peak-frequency of these \nsources, \nlower magnetic fields, far from equipartition, would be present \nwhich should result in detectable self-compton radiation.\nFanti et al. (1990) showed that there is a strong anti-correlation between \nthe linear size and the turnover frequencies of CSS sources, as expected\nfor SSA. However, more recently it was suggested by Bicknell, Dopita \\&\nO'Dea (1997) that such a correlation can also be explained by a particular\nmodel in which these sources undergo free-free absorption by ionised gas\nsurrounding the lobes. \nIn addition, Kuncic, Bicknell \\& Dopita (1998) argued that in addition to\nfree-free absorption, induced Compton scattering will also have an important \neffect in forming the spectral peak. As a result, \nit opened up the debate again \nabout the cause of the spectral turnovers in CSS and GPS sources.\n\nThe combination of bright and faint GPS and CSS samples as presented here,\ngives us a unique opportunity to carefully investigate the correlation between\nsize and spectral peak. \nNot surprisingly, we confirm the anti-correlation between peak frequency \n$\\nu_p$ and maximum angular size $\\theta_{max}$ (see figure \\ref{morph}, top\nleft panel).\nHowever, in addition we find a correlation between peak flux density $S_p$ and \n$\\theta_{max}$. This is shown in the top right panel of figure \\ref{morph}.\nNote that only sources from the bright and faint GPS samples are\nwith $0.8<\\nu_p<3$ GHz are plotted here. This is necessary, since the \npeak flux densities are correlated with the\n peak frequencies, which would erroneously result in a correlation between\npeak flux density and angular size. \n\n\nFrom SSA theory, it is expected that the angular size $\\theta$ of a radio \nsource is proportional to (Kellerman \\& Pauliny-Toth,1981):\n\\begin{equation}\\label{eq1}\n \\theta \\propto B^{1/4} S_p^{1/2} (1+z)^{1/4} \\nu_p^{-5/4}\n\\end{equation}\nwhere $B$ is the magnetic field strength and $z$ the redshift. \nNote that $\\theta$ is\nonly weakly dependent on both $B$ and $z$. Most remarkably, the strength\nand signs of the correlations between $v_p$, $S_p$ and $\\theta_{max}$ as \nshown in figure \\ref{morph} are exactly as expected from equation \\ref{eq1}.\n\nThe overall angular size, $\\theta_{max}$\n(eg. the distance between the two mini-lobes), is used in the analysis above, \nbut $\\theta$ in equation \\ref{eq1} corresponds to the size of the radio \n{\\it components} which are dominant at the peak-frequency (the mini-lobes).\nTherefore, these correlations have implications for the \nmorphological evolution of these radio sources. \nThe lower left panel of figure \\ref{morph} shows the maximum angular size\nas function of $S_p^{1/2}\\nu_p^{-5/4}$. The solid line indicates the \nbest linear fit. The dependence of this relation on redshift is \nproportional to $(1+z)^{1/4}$, which in any case is smaller than \n$<20\\%$ and negligible for our z-range. \nTherefore the same relation is expected in the rest-frame of \nthe objects. In the rest-frame, we can solve for the magnetic field \n$B$ by assuming equipartition. For this we use the equation derived by \nScott \\& Readhead (1977) assuming an optically thin spectral index \n$\\alpha=-1$,\n\\begin{equation}\nL = 3.5\\times (1-(1+z)^{-1/2})^{-1/17}(1+z)^{1/2}S_p^{8/17}\\nu_p^{33/34}\n\\end{equation} \nwhere $L$ is the equipartition component size. The projected linear size\nis shown as function of the equipartition component size in the lower right \npanel of figure \\ref{morph}. The dashed line indicates the dependence for which\nboth quantities are the same. The solid line is the best linear least-squares \nfit, indicating a ratio of overall size to component size of $5-6$, throughout\nthe samples of faint and bright GPS and CSS galaxies.\nThis means that if GPS sources evolve into CSS sources, their ratio of \ncomponent size to overall linear size remains constant, implying a \nself-similar evolution.\n\nNote that the main difference between the lower left and right panels\nof figure \\ref{morph} is that in the first a constant magnetic field is \nassumed, and in the second an equipartition magnetic field. It appears\nthat the first correlation is slightly flatter than expected for self-similar\nevolution. Indeed the ratio of the component to overall angular size \nis on average a factor 2 smaller for the CSS sample than for the GPS samples,\nwhile these ratios are virtually the same assuming an equipartition magnetic \nfield. This may indicate that young radio sources stay in equipartition \nwhile evolving in a self-similar way. This would require that the \nmagnetic fields in CSS sources are typically a factor $\\sim20$ lower than\nin GPS sources. The linear correlation itself only indicates a constant\nratio between the magnetic field and particle energies.\nThis constant does not have to be equal to \nunity, as required for equipartition.\nHowever, for a ratio of unity in energies, the bottom right panel of \nFigure \\ref{morph} requires a ratio of overall to component size \nof typically $5-6$, which is close to the result seen in VLBI \nobservations. This means that the energy ratio is not only constant, \nbut also close to unity, which indicates that equipartition probably holds.\n\nFigure \\ref{morph} demonstrates that the data is consistent with\na combination of SSA, equipartition, and self-similar growth. \nIt is not obvious that the same correlation\nshould apply for free-free absorption. Although other more complicated \ncombinations of mechanisms such as free-free absorption with\ninduced Compton scattering (Kuncic, Bicknell \\& Dopita, 1998)\nmay also fit the data, the simplest explanation by far is to assume \nthat SSA, equipartition and self-similar source growth all individually \nhold. We therefore believe that SSA is indeed the cause of the spectral \nturnovers in GPS and CSS sources.\n\nIt may not be surprising that young radio sources evolve in a self-similar \nway. Leahy and Williams (1984) showed that the cocoons of FRII sources of\nvery different physical size had similar axial ratios. More recently, \nSubrahmanyan, Saripalli \\& Hunstead (1996) found very similar ratios for \nsources of linear sizes above 900 Kpc, also suggesting that radio sources \nevolve in a self-similar way. An analytical model for radio sources with \npressure confined jets developed by Kaiser \\& Alexander (1997) \nshows that the properties of the bow shock and of the surrounding gas \n{\\it force} the sources to grow in a self-similar way, provided that the \ndensity of the surrounding gas falls off less steeply than $1/r^2$.\n\n\\section{The luminosity evolution of young radio sources}\n\nThe number count statistics and linear size distributions \nused in studies to constrain the luminosity evolution of radio sources, have\nall been averaged over a wide redshift range and only include the brightest \nobjects in the sky (Fanti et al. 1995, Readhead et al. 1996, O'Dea \\& Baum 1997). However, in flux density limited\nsamples, the redshift distribution of GPS galaxies is significantly different\nfrom that of large size radio galaxies (see figure \\ref{reddis}). \nThis suggests that the interpretation of the number count statistics is not \nstraightforward.\nNote that given the expected luminosity evolution as sources evolve in size,\nmany of the present day GPS sources will have FRI luminosities. \nIt is therefore assumed that GPS galaxies evolve into both FRI and FRII \nsources.\n\n\\begin{figure}\n\\psfig{figure=fig2.ps,width=8cm}\n\\caption{ \\label{reddis} The cumulative redshift distribution for 3C galaxies\nand GPS galaxies from the Stanghellini et al. sample.}\n\\end{figure}\n\nThe bias of GPS galaxies towards higher redshifts than large size radio \ngalaxies itself provides an important clue about the luminosity evolution of \nradio sources. \nIt implies that GPS galaxies are more likely to have higher\nradio power than extended objects in flux density limited\nsamples. If GPS and large size radio sources are identical objects, \nobserved at different ages, their cosmological density evolution, for \nexample \ntheir birth rate as function of redshift, should be the same. Since their \nlifetimes are short compared to the Hubble time, the redshift distributions \nof the GPS galaxies, and the objects they evolve to, should \nalso be the same. The bias of GPS sources towards higher redshifts and \nradio powers \ntherefore implies that their luminosity function must be flatter than\nthat of large size radio sources. We argue that the luminosity evolution\nof the individual objects strongly influences their collective luminosity \nfunction, and propose an evolution scenario in which GPS sources \nincrease in luminosity and large size sources decrease in luminosity with time\n(see section 4.1).\nIn the simplified case, in which source to source variations in\nthe surrounding medium can be ignored,\nthe luminosity of a radio source depends only on its age and jet power.\nConsider first the luminosity function\n of large size sources. It is expected that \nlarge size sources decrease in luminosity with age (see section 4.1). \nTherefore high luminosity sources will tend to be biased towards objects \nwith both small ages and high jet powers. The intrinsic space density for \nhigh power jet sources will of course tend to be small.\nFurthermore, for a given jet power there are fewer young sources than\nold sources, simply because sources spend only a small fraction of their time \nbeing young. The result is a very low space density of large size sources\nof high power. In contrast, large size sources of low power are biased to \nbe both old and with low jet power, both common conditions, hence the space \ndensity of large size sources with low power is much higher than that for \nthose with high power, and the luminosity function for large size sources \nis steep. In contrast, the luminosity of GPS sources is expected to \nincrease with sources age (see section 4.1). High luminosity GPS sources\nare therefore biased to be old and of high jet power, while low luminosity\nobjects are biased to be young and of low jet power. Instead of \nreinforcing each other as in the case for large size sources, for GPS sources\nthe age and jet power space density biases partly counteract.\nThe result is a much less difference in the space density of \nlow and high power GPS sources and hence a much flatter luminosity \nfunction for GPS sources.\n\nIn the next section we will show that \nthe luminosity evolution as proposed is expected for a ram-pressure confined,\nself similarly evolving\nradio source in a surrounding medium with a King-profile density. \nIn the inner parts of the King profile, the density of the medium is \nconstant and the radio source builds up its luminosity (eg. Baldwin 1982), \nbut after it grows\nlarge enough the density of the medium declines and the luminosity of the radio\nsource decreases. \n\nIn section \\ref{liflaf} we will show how the luminosity evolution \nof the individual sources modifies the luminosity function, and in section\n\\ref{loclumfun}, the local luminosity function of GPS sources is constructed\nand compared with that of large size radio sources.\n\n\\subsection{A self-similar evolution model}\n\nAn important parameter in evolution models of radio sources is the \ndensity profile of the surrounding medium. In general, X-ray \nobservations of nearby ellipticals have shown that their \nISM are well fitted by a King profile distribution (Trinchieri et al. 1986):\n\\begin{equation}\n\\rho(r) = \\rho_0 \\biggl[ 1+\\biggl(\\frac{r}{r_c}\\biggr)^2\\biggr]^{-\\beta/2}\n\\end{equation}\nwhere $\\rho$ is the density of the medium as function of distance to \nthe centre of the host galaxy $r$, $r_c$ is the core radius, \nand $\\beta$ the slope parameter.\nTypical core radii in giant ellipticals\nare observed to be $r_c=500-1000$ pc (Trinchieri et al. 1986), \nFor simplicity, we treat the two regimes separately: 1) The GPS phase \nat $r<r_c$ where the density of the medium, $\\rho_{ism}$, \nis assumed to be constant. 2) The large size (LS) phase at $r>r_c$ where\n$\\rho_{ism} \\propto r^{-\\beta}$.\n\nIf the thrust of the radio jet is balanced by the ram-pressure\nof the surrounding medium, the growth of the radio source is equal to\n\\begin{equation}\\label{Meq1}\ndr/dt \\propto \\biggl(\\frac{P_J}{\\rho_{ism}(r) A}\\biggr)^{1/2}\n\\end{equation}\nwhere $dr/dt$ is the propagation \nvelocity of the hot-spots, $P_J$ is the jet power, \nand $A$ is the cross-sectional area (Begelman 1996).\nIn the previous section we showed that young radio sources\nseem to evolve in a self-similar way. Since it is in close \nagreement with the theoretical work of Kaiser \\& Alexander (1997), we will \nassume self-similar evolution, with $A \\propto r^2$.\nNote however, that in the work by Kaiser \\& Alexander (1997), the \ncross-sectional area of the jet grows slightly more slowly with size,\nwhich is therefore not completely self-similar, but \nallowing the expansion of the bow-shock and cocoon to be fully self-similar\n(Kaiser 2000, private communications). \nHere, by assuming $A\\propto r^2$, this will not be the case, \nbut differences are small and for simplicity's sake we use this anyway.\n\nFrom integrating eq. \\ref{Meq1} it follows that in the GPS phase a source grows\nin linear size with time as $t^{1/2}$, assuming that the jet-power is \nconstant with time. The average internal density of the radio source, \n$\\rho_i$, is proportional to $P_Jt/V$, where $V$ is the volume\nof the radio source which is proportional to $r^3$. \nHence,\n$\\rho_i\\propto r^{-1}$, indicating that the radio emitting \nplasma expands proportionally to its linear size, $r$, and that \nexpansion losses have to be taken into account. If the energy\nspectrum of the electrons is $n(E)=n_oE^{-\\gamma}$, $n_o$ varies \nproportionally to $r^{-4/3}$ for $\\gamma=2$ ($\\alpha=-0.5$, Moffet, 1977).\nWe will assume that the radio source is in equipartition, so\nthat $n_o \\propto B^2$, where $B$ is the magnetic field.\nThe radio power $L_\\nu$\nat a particular frequency in the optically thin part of the spectrum\nscales as\n\\begin{equation}\nL_\\nu \\propto n_o^{7/4} V \\propto P_J^{7/8}r^{2/3} \n\\end{equation}\nfor $\\gamma=2$. Hence radio sources increase in luminosity in the \nGPS phase.\n\nIn the LS phase, radio sources grow as $t^{2/(4-\\beta)}$, and the\ndensity of the radio emitting plasma varies as $\\rho_i\\propto r^{-\\frac{\\beta+2}{2}}$,\nTaking into account expansion losses in a similar way\nas for the GPS phase, this means that\n$n_o \\propto r^{-4\\frac{\\beta+2}{6}}$, and under equipartition conditions,\n\\begin{equation}\nL_\\nu \\propto P_J^{7/8}r^{\\frac{2}{3}-\\frac{7}{6}\\beta}\n\\end{equation}\nHence radio sources in the LS phase decrease in radio luminosity.\nNote that we do not take synchrotron losses and losses due to scattering \nof the CMB into account, \nwhich may influence the LS phase and cause sources to decrease faster\nin luminosity with time.\nThe schematic evolution in radio power of a radio source according to this \nmodel is shown in figure \\ref{lumevol}. \n\n\\begin{figure}\n\\psfig{figure=fig3.ps,width=8cm,angle=-90}\n\\caption{\\label{lumevol} The evolution in radio power as function of \nlinear size for a self-similar evolving, ram-pressure confined radio source\nin a surrounding medium with a King-profile density. }\n\\end{figure}\n\nIt is interesting to determine what the expected evolution in peak frequency\nand peak flux density is for a radio source in the GPS phase and the LS phase.\nA source will become optically thick at a frequency where $\\kappa_\\nu l \\approx\n1$, where $\\kappa_\\nu$ is the absorption coefficient and $l$ the pathlength \nthrough the radio plasma. For synchrotron self absorption, assuming \nequipartition and self-similar evolution, this means that,\n\\begin{equation}\n\\kappa_\\nu l \\ \\propto \\ n_o B^{2} \\nu_p^{-3} r \\ \\propto \\ n_o^2 \\nu_p^{-3} \nr=1\n\\end{equation}\nfor $\\gamma = 2$ (Moffet, 1977). \nThe optically thin radio power, as determined above,\nwill be frequency dependent and proportional to \n$P_\\nu \\propto S_p\\nu_p^{1/2}$. Therefore in the GPS phase,\n\\begin{equation}\n\\nu_p \\propto r^{-5/9}, \\ \\ S_p \\propto r^{17/18}, \\ \\\nS_p \\propto \\nu_p^{-17/10}\n\\end{equation}\nIn the LS phase,\nassuming $\\beta=1.5$, which is a typical value based on \nobservations of X-ray halos (Trinchieri et al. 1986),\n\\begin{equation}\n\\nu_p \\propto r^{-11/9}, \\ \\ S_p \\propto \\nu_p^{17/44}\n\\end{equation}\nFrom figure \\ref{morph} we can estimate the transition between the two\nphases (500-1000 pc) to occur at $\\nu_p \\approx 100-500$ MHz \nThe evolutionary tracks are shown in figure \\ref{evoltracks}.\n\n\\begin{figure}\n\\psfig{figure=fig4.ps,width=8cm,angle=-90}\n\\caption{\\label{evoltracks} An evolutionary track \nfor a self-similar evolving, ram-pressure confined radio source\nin a surrounding medium with a King-profile density}\n\\end{figure}\n\n\\subsection{Luminosity evolution and the luminosity function.\\label{liflaf}}\n\nIn this section the influence of the luminosity evolution of \nthe individual objects on the slope of their collective luminosity \nfunction is derived. \nWe will ignore source to source variations in the surrounding\nmedium and use the radio-size dependent luminosity evolution \nas derived in the previous section.\n\\begin{figure}\n\\psfig{figure=fig5.ps,width=8cm,angle=-90}\n\\caption{\\label{integral} Schematic representation of the source density\nas function of age and jet power. The lines indicate sources with identical\nluminosities. The greyscales indicate the source density for a particular jet \npower and age. The dashed line indicates the border between the GPS phase and \nthe LS phase.}\n\\end{figure}\n\nSuppose that the comoving number density of sources with a jet \npower $N(P_J)$ is a power-law distribution\n\\begin{equation}\nN(P_J) \\propto P_J^\\delta\n\\end{equation}\nbetween $P_-$ and $P_+$, \nand the sources have a flat distribution of ages below a certain maximum \nage, then the source density as function of age and jet power is \nrepresented by the grey scales in figure \\ref{integral}.\nThe radio power of a source, $L_\\nu$, can be parameterised as \n\\begin{equation}\nL_\\nu \\propto P_J^\\kappa r^\\epsilon\n\\end{equation}\nwhere $\\epsilon=2/3$ and $\\epsilon=-13/12$ in the GPS phase and LS phase\nrespectively, and $\\kappa=7/8$, as derived in the previous section.\nA line-integral over a solid line in figure \\ref{integral} gives\nthe total number of sources in the volume with a particular \nluminosity. It can be seen that in the GPS phase, these lines \nare approximately perpendicular to the \ndensity gradient, indicating that a change in luminosity results\nin only a small change in the number of sources. \nIn the LS phase, they \nare parallel to the density gradient, and \na change in luminosity results in a large change in the number of objects.\nThe luminosity function $ N(L)$ can be derived \nfrom,\n\\begin{equation}\nN(L_\\nu) = \\frac{\\delta}{\\delta L_{*}} \\iint\\limits_{L_\\nu(p,r)<L_{*}}\n N(p,r) \ndp dr\n\\end{equation}\nwhere $p$ is the jet power and $r$ is the size of the radio source.\nAs can be seen in figure \\ref{integral}, the integration limits of this \nequation are a different function of age and jet power, depending \non the luminosity . The equation should be\nsolved separately for a high and low luminosity regime, in both the \nLS and the GPS phase. Since the border between the GPS and LS phase\nis at a constant source size, $r_{*}$, it is better to integrate over\nthe source size $r$ than over the source age $t$.\n For the low luminosity regime in the GPS phase, \n\n\\begin{equation}\nN(L_\\nu<L_*)=\\int\\limits_{P_{-}}^{P_{+}}\\int\\limits_0^{\\frac{L_*^{1/\\epsilon}}{p^{\\kappa/\\epsilon}}} \np^{\\delta-\\frac{1}{2}}r dr dp = L_*^{\\frac{2}{\\epsilon}}\\int\\limits_{P_{-}}^{P_{+}}\np^{\\delta-\\frac{1}{2}-\\frac{2\\kappa}{\\epsilon}}\ndp\n\\end{equation}\n\nwhere $N(L_\\nu<L_*)$ are the total number of sources below a \nparticular luminosity $L_*$, and therefore integrating over jet power $p$\nand age $t$ gives,\n\\begin{equation}\nN(L_\\nu) \\propto L_\\nu^{2/\\epsilon-1}\n\\end{equation}\nFor the high radio power regime in the GPS phase,\n\\begin{equation}\\label{16}\nN(L_\\nu\\!\\! > \\!\\! L_*)=\\!\\!\\int\\limits_{\\left(\\frac{L_*}{P_+^\\kappa}\\right)^{\\frac{1}{\\epsilon}}}^{r_*}r \\int\\limits_{\\left(\\frac{L_*}{r^\\epsilon}\\right)^{\\frac{1}{\\kappa}}}^{P_{+}} \np^{\\delta-\\frac{1}{2}} dp dr \\propto L_*^{(\\delta+\\frac{1}{2})\\frac{1}{\\kappa}}\n\\end{equation}\nwith a sharp cut-off near $L_\\nu = P_+^\\kappa r_*^{\\epsilon}$. \nIn this regime of radio power,\n\\begin{equation}\nN(L_\\nu) \\propto L_\\nu^{(\\delta+\\frac{1}{2})\\frac{1}{\\kappa}-1}\n\\end{equation}\nFor the low luminosity regime in the LS phase, \n\\begin{equation}\nN(L_\\nu<L_*)=\\int\\limits_{p_{-}}^{\\left(\\frac{L_*}{r_+^\\epsilon}\\right)^\\frac{1}{\\kappa}} p^{\\delta-\\frac{1}{2}}\n\\int\\limits_{\\left( \\frac{L_*}{p^\\kappa} \\right)^{\\frac{1}{\\epsilon}}}\n^{r_+} r^\\frac{1}{2} dr dp \\propto L_*^{(\\delta+\\frac{1}{2})\\frac{1}{\\kappa}}\n\\end{equation}\nwith a sharp cut-off near $L_\\nu=P_-^\\kappa r_+^\\epsilon$. In this regime of radio power,\n\\begin{equation}\\label{18}\nN(L_\\nu) \\propto L_\\nu^{(\\delta+\\frac{1}{2})\\frac{1}{\\kappa}-1}\n\\end{equation}\nFor the high radio power regime in the LS phase,\n\\begin{equation}\nN(L_\\nu>L_*)=\\int\\limits^{\\left(\\frac{L_*}{P_+^\\kappa}\\right)^{\\frac{1}{\\epsilon}}}_{r_*} r^\\frac{1}{2}\n\\int\\limits^{P_+}_{\\left(\\frac{L_*}{r^\\epsilon}\\right)^\\frac{1}{\\kappa}}\n p^{\\delta-\\frac{1}{2}} dp dr \\propto L_*^{3/2\\epsilon}\n\\end{equation}\nwith a cut-off near $L_\\nu=P_+^\\kappa r_*^\\epsilon$. In this radio power regime,\n\\begin{equation}\nN(L_\\nu) \\propto L_\\nu^{3/2\\epsilon-1}\n\\end{equation}\n\nAs can be seen from equations \\ref{16} and \\ref{18}, the slope of \nthe luminosity function is expected to be the same in the \nhigh luminosity and low luminosity regimes for the GPS and \nLS phases respectively, since $\\delta$ and $\\kappa$ are independent of the \nage of the radio source. The low luminosity regime and the high\nluminosity regime of the GPS phase and the LS phase are expected\nto have a slope of $+2$ and $-2.4$ respectively for the proposed evolution\nmodel.\n\n\\subsection{The Local Luminosity Function of GPS sources.\\label{loclumfun}}\n\nAs is shown in the previous section, the comparison of the local luminosity \nfunction (LLF) of young and \nold radio sources can put strong constraints on the rise and \ndecay of their radio luminosity. \nOne would like to compare the LLF of GPS sources with the model derived in \nsection 4.1 \\& 4.2 directly. This is not possible due to the lack\nof local GPS sources in present samples (the low local number density of \nGPS sources catalysed this discussion in the first place).\n For example, only 2 GPS \ngalaxies in the Stanghellini et al. sample are at $z<0.2$.\nHowever, since we assume that GPS sources evolve into \nlarge size sources and their lifetimes are short compared to \ncosmological timescales, their birth rate as function of redshift\n should be the same. Therefore\nthe cosmological evolution as determined for large scale radio sources can\nbe used to describe the cosmological evolution for GPS sources.\nIn this way, the GPS LLF can be estimated using the GPS galaxies at\nall redshifts, which will be attempted in this section.\nThis estimated GPS LLF will then be compared with what is expected\nfrom the model, as derived in section 4.2.\n\n\nThe LLF for powerful radio sources and its cosmological evolution, has \nbeen studied by Dunlop \\& Peacock (1990). We will use the pure luminosity\nevolution model, since it fits the available redshift and source-count data \nwell, and it is relatively straightforward to implement.\nIn this particular model, the overall shape of the \nluminosity function does not change with \ncosmological epoch, only the normalisation in luminosity (see fig. \\ref{lfevolve}).\nDunlop and Peacock (1990) parameterise an evolving two-power-law luminosity\nfunction as\n\\begin{equation}\n\\rho(P_\\nu,z)=\\rho_o \\left\\{ \\left( \\frac{P}{P_c(z)}\\right)^a + \n\\left( \\frac{P}{P_c(z)}\\right)^b \\right\\}^{-1}\n\\end{equation}\nwhere $a$ and $b$ are the two power-law slopes, $P_c(z)$ is the \nevolving `break' luminosity, and $\\rho_o$ is determined by normalisation\nat z=0. The redshift dependence, $P_c(z)$, was parameterised by \nDunlop \\& Peacock as \n\\begin{equation}\\label{eqcor}\n\\log P_c(z) = a_0 +a_1z+a_2z^2\n\\end{equation}\nThe best-fit model parameters for pure luminosity evolution ($\\Omega_0=1$)\nare, $\\rho_o=-6.91$, $a=0.69$, $b=2.17$, $a_0=25.99$ (in W/Hz), \n$a_1=1.26$, $a_2=-0.26$.\nSince Dunlop \\& Peacock (1990) did their analysis at 2.7 GHz, their radio\npowers have to be transformed to 5 GHz. Assuming a mean spectral index of \n$-0.75$, we use a conversion factor of $-0.20$ in the logarithm.\nThis luminosity evolution parameterisation, as shown in figure \\ref{lfevolve},\n is used to derive the LLF of GPS sources.\nFirst the radio powers, as given in table 1 and \n2, are corrected for the cosmological evolution of the luminosity \nfunction. This correction factor as function of redshift is equation \\ref{eqcor}.\nFor example, at z=1, the luminosity function has shifted a factor 10\ntowards higher luminosities, and therefore 2128+048 with a radio power of \n$10^{27.8}$ W/Hz will contribute to the LLF at $10^{26.8}$ W/Hz.\nNote that this correction is independent of luminosity, and therefore \nthe difference in radio luminosity of young and old sources does not \nhave to be accounted for. Note however, that the increase in number density\n{\\it is} dependent on radio luminosity due to a change in the slope of the \nluminosity function. The number densities increase from z=0 to z=1 by a \nfactor of 5 and 150 for low and high luminosity sources respectively.\n\n\\begin{figure}\n\\psfig{figure=fig6.ps,width=8cm}\n\\caption{\\label{lfevolve} The evolution of the luminosity function of \nsteep spectrum sources as determined by Dunlop and Peacock (1990).}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{figure=fig7.ps,width=8cm}\n\\caption{\\label{lumcor} The radio power for a source of 10 mJy, 100 mJy, and \n1 Jy as function of redshift, and its radio power corrected for the evolution\nof the luminosity function, assuming $H_0$=50 km sec$^{-1}$Mpc$^{-1}$, and \n$\\Omega_0$=1.}\n\\end{figure}\n\nFigure \\ref{lumcor} shows the corrected and uncorrected radio powers\nfor a source with flux densities of 10 mJy, 100 mJy and 1 Jy (assuming \na spectral index of $-0.5$ at about 5 GHz).\nInterestingly, the corrected radio power for a source with an certain observed\nflux density, does not significantly change at $0.6<z<2.0$. Hence, although for\nmany GPS galaxies no spectroscopic redshift has been measured, this is \nnot likely to influence the result, since they will probably all be \nin this redshift range.\n\nThe next step is to correct the number of sources observed for the volume \nof space over which they can be observed. As can be seen from figure \n\\ref{lumcor}, a flux density limit in the sample of 1 Jy means that all\nsources with corrected luminosities greater than 25.4 $W Hz^{-1}Sr^{-1}$\ncan be detected out to z=2, and that only source with lower radio power,\nand consequently at $z<0.6$, have to be corrected for the fact that they\nonly could have been seen out to a certain redshift. However, \na possible additional redshift limit results from the lower limit in peak \nfrequency at 0.4 GHz in the bright Stangellini et al. sample, and \nin the faint sample due to the limit in 325-5000 MHz spectral index.\nFor these sources a weight-factor is used equal to the volume of the survey \n(assuming a redshift limit of 2.0) divided by the maximum volume over which \nthey could have been in the sample, which is dependent on the maximum \nobservable redshift. \nThe corrections above are relatively straight-forward. However, some\nadditional, more complicated corrections have to be made for the \nfaint GPS sample. Firstly, this sample is originally selected at \n325 MHz frequency, eg. on the optically thick part of their spectrum. \nFurthermore, only sources with positive spectral indices between\nthis frequency and 5 GHz were initially selected. Therefore the faint \nWENSS sample is more biased towards GPS sources with higher \npeak frequencies than the bright Stanghellini et al. sample. To correct\nfor this we assumed that the parent distribution of peak frequencies is \nindependent of flux density and radio power, and determined what fraction\nof the Stangellini et al sample would have been included in the sample\nif it would have been selected as for the faint WENSS sample. \nIt turns out that 26 \\% of the galaxies in the bright sample have 325 MHz \nflux densities $>$ 1 Jy and positive spectral indices between 325 MHz and \n5 GHz. In addition, the bright GPS sample has a limit in optically thin\nspectral index of $-0.5$, while several sources in the faint sample have \na flatter optically thin spectral index. Taking into account these two \neffects, the number densities for the faint sample are multiplied by a factor \n3.2. \n\\begin{figure}\n\\psfig{figure=fig8.ps,width=8cm}\n\\caption{\\label{llf} The local luminosity function of GPS radio sources,\nas derived from the bright sample of Stanghellini et al. (diamonds) and \nour faint GPS sample (squares). The dashed and solid lines give the \nsimulated LLFs for GPS and large size radio sources respectively.\nThe model-parameters are chosen in such way that the simulated LLF of \nlarge size radio sources matches that of steep spectrum sources\nas derived by Dunlop \\& Peacock (1990).}\n\n\n\n\\end{figure}\n\nThe resulting local luminosity function of GPS sources is shown in \nfigure \\ref{llf}. Note that a luminosity bin (centred at 23.75 Watt/Hz) \ncontaining only a single source (B0830+5813) is omitted due to its \nlarge uncertainty.\n\nWe compared the resulting LLF with an LLF of a simulated radio source \npopulation of $10^6$ objects, with random ages, and a jet-power \ndistribution defined as in equation 10.\nThe `observed' luminosity of a source was calculated assuming that it had evolved over its lifetime according to the \nluminosity evolution derived in section 4.1, out to a maximum size, $r_+$.\nAt $r<r_*$, the size of the source evolves as $r=t^{1/2}P_J^{1/4}$.\nTo avoid a discontinuity in propagation velocity \nat $r_*$, the source evolves from $r_*$ as,\n\\begin{equation}\nr(P_J,t)=\\frac{\\gamma}{2}\\gamma^{-\\frac{1}{\\gamma}}(\\gamma P_J^\\frac{1}{2}t)\n^\\frac{1}{\\gamma}+(1-\\frac{\\gamma}{2})\n\\end{equation}\nwith $\\gamma=(4-\\beta)/2$. The luminosity of a source increases at $r<r_*$\nas $L=P_J^{7/8}(r/r_*)^{2/3}$, and as $L=P_J^{7/8}(r/r_*)^{\\frac{2}{3}-\\frac{7}{6}\\beta}$ at $r>r_*$. This results in a similar evolution for \nlarge size radio sources as derived in section 4.1, with the luminosity\nat $r=r_*$ only dependent on $P_J$.\nIt was not our aim to determine absolute\nvalues for number densities and radio powers with these simulations.\nThe results of the simulation were\nscaled in such way, that the LLF obtained for large size radio sources,\nmatched the LLF of steep spectrum sources as derived by Dunlop \\& peacock \n(1990). \n\n\\begin{table}\n\\caption{\\label{param} Dependence of LLF characteristics on \n the model parameters}\n\\begin{tabular}{ccr}\nCharacteristic of LLF & Dependence& Value used \\\\\n \\\\\nLS-LLF slope at high $L$&$\\frac{5+7\\beta}{4-7\\beta}$& $-$3.17$^a$\\\\\n\\\\\nLS-LLF slope at low $L$&$(\\delta+\\frac{1}{2})\\frac{1}{\\kappa}-1$&$-$1.69$^a$\\\\\n\\\\\n$L_{max}$ & $ P_+^{\\kappa}$ & $10^{27.1}$ \\\\\n\\\\\n$L_{ls*}$ & $P_+^{\\kappa}\\left(\\frac{r_{+}}{r_{*}}\\right)^\n{\\frac{2}{3}-\\frac{7}{6}\\beta}$ & $10^{25.8^a}$ \\\\\n\\\\\n$L_{gps*}$ & $P_{-}^{\\kappa}$ & $10^{25.0}$ \\\\\n\\\\\n\\end{tabular}\n\\begin{tabular}{l}\n$^a$ Value chosen to match the LLF of Dunlop \\& Peacock (1990).\n\\end{tabular}\n\\end{table}\n\nTable \\ref{param} lists the important characteristics of the \nsimulated LLF of large size and GPS sources, and their dependence on\nthe free model parameters. \nThe parameters $\\delta$ and $\\beta$, as defined in equations 10 and 3, \ndetermine the slope of the low and high luminosity part of the \nLLF of large size radio sources. These were chosen to be similar \nto the parameters $a-1$ and $b-1$ as derived by Dunlop \\& Peacock (1990),\nwith $\\delta=-1.10$ and $\\beta=1.16$.\nThis value of $\\beta$ is slightly lower than derived from \nX-ray observations of nearby ellipticals ($\\beta=1.5-2$, \nTrinchieri et al. 1986). \nNote however, that the radio source population is dominated by \nobjects with size $>20$ kpc, for which the surrounding medium is \ndominated by intra-cluster gas, which is expected to have a flatter\ndensity gradient.\nWith the parameters $\\delta$ and $\\beta$ and the slopes \nof the LLF of large size radio sources fixed, the relative positions of \nthe break luminosities could be determined. A sharp cut-off will occur\nnear the highest luminosity, $L_{max}$.\nThe number of GPS galaxies in the highest luminosity bin, as \nshown in figure \\ref{llf}, is lower than expected from the extrapolation \nof the LLF at lower luminosities. This can be explained if this luminosity\nbin is near the cut-off luminosity $L_{max}$. We therefore chose log $L_{max}$ to be 27.1 (W Hz$^-1$). The break luminosity of large size \nradio sources, is also determined by Dunlop \\& Peacock (1990)\nto be log $L_{LS*}$ = 25.79 (corrected to 5 GHz).\nAs can be seen from table \\ref{param}, the luminosity ratio\n$L_{max}/L_{ls*}$ determines the value of $r_{+}/r_{*}$. \n This corresponds to \na maximum size for a radio source of 100 kpc, assuming $r_*=1$ kpc. \nThis value is quite near the turnover seen in the linear size\ndistribution of 3CR galaxies, as shown by O'Dea \\& Baum (1997).\nThe break luminosity of GPS sources, $L_{gps*}$, relative to $L_{max}$,\nis dependent on the range of jet-powers $(P_+/P_-)$.\nTo let $L_{gps*}$ coincide with the peak in the observed GPS LLF, \na value of $(P_+/P_-)$=200 was used.\n\nAlthough the uncertainties on the datapoints are large and several free\nparameters enter the simulation, \nfigure \\ref{llf} shows that the shape of the LLF of GPS \nsources is as expected. Note that most free parameters are determined\nby fitting the LLF of large size radio sources to that of Dunlop \\&\nPeacock (1990), except $r_{+}$ and $(P_+/P_-)$.\nThis analysis should be\nregarded as an example of how future large and homogeneously\ndefined samples of GPS sources can constrain the luminosity\nevolution of extragalactic radio sources.\n\nThe proposed increase in luminosity for young radio sources seems to \nbe in contradiction to the high number counts of GPS sources with respect\nto large size radio sources suggesting that they should decrease in \nradio luminosity by a factor $~10$ during their lifetime (Fanti et al. 1995,\nReadhead et al. 1996, O'Dea \\& Baum 1997). However, this is not the case.\nFlux density limited samples, as used for these analyses, only \nprobe the most luminous objects at any redshift. As can be seen\nfrom figure \\ref{llf}, at high luminosities, the two luminosity function\napproach each other, due to the flatter slope of the \nluminosity function of GPS sources.\nThis results in a relatively high number density of GPS sources in\nflux density limited samples. \n\n\\subsection{Summary and Conclusions}\n\nIn this paper we show that in addition to the well known correlation\nbetween spectral peak frequency and angular size (eg. Fanti et al. 1990),\na correlation exists between the peak flux density and angular size\nof GPS \\& CSS sources. The strength and sign of these correlations \nare exactly as expected from SSA theory, assuming equipartition, and are \ntherefore a strong indication that SSA is indeed the cause of the spectral\nturnovers in these objects. Furthermore, these correlations are consistent\nwith GPS \\& CSS sources evolving in a self-similar way.\nInterestingly, the self-similar evolution scenario is \nbetter fitted by assuming an equipartition than a constant magnetic field.\n\nIn flux density limited samples, GPS galaxies are found at higher \nredshifts than large size radio sources. Since \nthe lifetimes of radio sources are short compared to cosmological timescales,\nthis can only mean that the slope of their luminosity functions\nare different, if GPS sources are to evolve into large size radio sources.\nIt is shown that that the slope of a luminosity function is strongly\ndependent on the evolution of radio power of the individual sources. \nA new method is introduced to constrain the luminosity evolution \nof radio sources using the luminosity functions of `young' and `old' \nobjects. It is shown that if GPS sources are increasing in radio power \nwith time, it would result in a relatively flatter slope of their luminosity\nfunction compared to that of large size radio sources which decrease in \nradio power.\n\nA simple model was developed in which a radio source, embedded in \na King profile medium, evolves in a self similar way under the \nequipartition energy assumption.\n This model indeed results in \nthe suggested increase in luminosity for young radio sources, \nand decrease in luminosity for old, extended objects.\nThe calculated luminosity function for large size radio sources shows \na break and slopes at low and high luminosity comparable to that derived by\nDunlop \\& Peacock (1990) for steep spectrum sources. \nThe local luminosity function (LLF) of GPS sources can not be\nmeasured directly since so few GPS sources are found at low redshift.\nTherefore, the knowledge of the cosmological evolution of the luminosity\nfunction of steep spectrum sources, as derived by Dunlop \\& Peacock (1990),\nis used, so that the LLF can be derived from the complete samples\nof bright and faint GPS sources. 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"string": "\\begin{thebibliography}{}\n\n\\bibitem{} Baldwin J., 1982, In: Extragalactic radio sources,\n NM, D. Reidel Publishing Co., 1982, p. 21\n\\bibitem{} Baum S.A., O'Dea C.P., Murphy D.W., de Bruyn A.G., 1990, A\\&A, 232,\n 19\n\n\\bibitem{} Begelman M.C., 1996, in proceedings of ``Cygnus A: A study of a \n radio galaxy'', eds. C. Carilli \\& D. Harris (Cambridge, Cambridge\n University Press), p.209\n\n\\bibitem{} Bicknell, G.V., Dopita M.A., O'Dea C.P., 1997, ApJ, 485, 112\n\n\\bibitem{} Blake G.M., 1970, ApJ, 6, L201\n\n\\bibitem{} Blundell K.M., Rawlings S., Willott C.J., 1999\n Astronomical Journal, 117, 677\n\n\\bibitem{} van Breugel, W., Miley, G.K., Heckman T., 1984, AJ, 89, 5\n\n\\bibitem{} Bondi M., Garrett M.A., Gurvits L.I., 1998, MNRAS, 297, 559\n\n\\bibitem{} Dallacasa D., Fanti C., Fanti R., Schilizzi R.T., Spencer R.E., 1995\n A\\&A, 295, 27\n\n\\bibitem{} Dallacasa D., Bondi M., Alef W., Mantovani F., 1998, A\\&AS, 129, 219\n\n\\bibitem{} Dunlop J.S., Peacock J.A., 1990, MNRAS, 247, 19\n\n\\bibitem{} Fanti R., Fanti C., Schilizzi R.T., Spencer R.E., Nan Rendong, \n Parma P., Van Breugel W.J.M., Venturi T., 1990, A\\&A, 231, 333\n\n\\bibitem{} Fanti C., Fanti R., Dallacasa D., Schilizzi R.T., Spencer R.E.,\n Stanghellini C., 1995, A\\&A, 302, 317\n\n\\bibitem{} Gregory P.C., Condon J.J., 1991, ApJS, 75 1011\n\n\\bibitem{} Hodges M.W., Mutel R.L., Phillips R.B., 1984, AJ, 89, 1327\n\n\n\\bibitem{} Jones T.W., O'Dell S.L., Stein W.A., 1974, ApJ, 192, 261\n\n\\bibitem{} Kaiser C.R., Alexander P., 1997, MNRAS, 286, 215\n\n\\bibitem{} Kellerman K.I., Pauliny-Toth I.I.K, 1981, ARA\\&A, 19, 373\n\n\\bibitem{} K\\\"uhr H., Witzel A., Pauliny-toth I.I.K., Nauber U., 1981, A\\&AS, 45,\n 367\n\\bibitem{} Kuncic Z., Bicknell G.V., Dopita M.A., 1998, ApJ, 495, L35\n\\bibitem{} Leahy J.P., Williams A.G., 1984, MNRAS, 210, 929\n\n\\bibitem{} Murgia M., Fanti C., Fanti R., Gregorini L., Klein U., \n Mack K-H., Vigotti M., 1999, A\\&A, 345, 769\n\n\\bibitem{} Mutel R.L., Hodges M.W., Phillips R.B., 1985, ApJ, 290, 86\n\n\\bibitem{} O'Dea C.P., Baum S.A., Stanghellini C., 1991, ApJ, 380, 66\n\n\\bibitem{} O'Dea C.P., Stanghellini C., Baum S.A., Charlot S., ApJ, 470, 806\n\n\\bibitem{} O'Dea C.P., Baum S.A., 1997, AJ, 113, 148\n\n\\bibitem{} O'Dea C.P., 1998, PASP, 110, 493\n\n\\bibitem{} Owsianik I., Conway J.E., 1998, A\\&A, 337, 69\n\n\\bibitem{} Owsianik I., Conway, J.E., Polatidis, A.G., 1998, A\\&A, 336, L37\n\n\\bibitem{} Peacock J.A., Wall J.V., 1982, MNRAS, 198, 843\n\n\\bibitem{} Readhead A.C.S, Xu W., Pearson T.J., 1994, in Compact\n Extragalactic Radio Sources, eds Zensus \\& Kellerman, p19 \n\n\\bibitem{} Readhead A.C.S., Taylor G.B., Xu W., \n Pearson T.J., Wilkinson P.N., 1996, ApJ, 460, 634\n\n\\bibitem{} Rengelink R.B., Tang Y., de Bruyn A.G., Miley G.K., Bremer M.N., \n R\\\"ottgering H.J.A., Bremer M.A.R., 1997, A\\&AS, 124, 259 \n\n\\bibitem{} Richstone D., Ajhar E.A., Bender R., Bower G., Dressler A.,\n Faber S.M., Filippenko A.V., Gebhardt K., \n Green R., Ho L.C., Kormendy J., Lauer T.R., \n Magorrian J., Tremaine S., 1998, Nature, 395, 14\n\n\\bibitem{} Schoenmakers, A., 1999, PhD thesis, Leiden University\n\n\\bibitem{} Scott M.A., readhead A.C.S., 1977, MNRAS, 180, 539\n\n\\bibitem{} Shklovsky, I. 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}
] |
astro-ph0002131
|
Jet directions in Seyfert galaxies
|
[
{
"author": "A. L. Kinney\\altaffilmark{1,2,5}"
},
{
"author": "H.R.Schmitt\\altaffilmark{1}"
},
{
"author": "C.J.Clarke\\altaffilmark{2}"
},
{
"author": "J.E. Pringle\\altaffilmark{2,1}"
},
{
"author": "J.S. Ulvestad\\altaffilmark{3} and R.R.J. Antonucci\\altaffilmark{4}"
}
] |
Here we present the study of the relative angle between the accretion disk (or radio jet) and the galaxy disk for a sample of Seyfert galaxies selected from a mostly isotropic property, the 60$\mu$m flux, and warm infrared colors. We used VLA A-array 3.6cm continuum data and ground based optical imaging, homogeneously observed and reduced to minimize selection effects. For parts of the analysis we enlarged the sample by including galaxies serendipitously selected from the literature. For each galaxy we have a pair of points ($i$,$\delta$), which are the inclination of the galaxy relative to the line of sight and the angle between the jet projected into the plane of the sky and the host galaxy major axis, respectively. For some galaxies we also had information about which side of the minor axis is closer to Earth. This data is combined with a statistical technique, developed by us, to determine the distribution of $\beta$ angles {in 3 dimensions}, the angle between the jet and the host galaxy plane axis. We found from an initial analysis of the data of the 60$\mu$m sample, where Seyfert 1's and 2's were not differentiated, that the observed distribution of $i$ and $\delta$ values can be well represented either by a homogeneous $\sin\beta$ distribution in the range $0^{\circ}\leq\beta\leq90^{\circ}$, or $0^{\circ}\leq\beta\leq65^{\circ}$, but not by an equatorial ring. A more general model, which tested $\beta-$distributions in the range $\beta_1\leq\beta\leq\beta_2$, for different ranges of $\beta_1$ and $\beta_2$ values, required $\beta_2$ to be larger than 65$^{\circ}$ and gave preference for $\beta_1$ smaller than 40$^{\circ}$ - 50$^{\circ}$. An important result from our analysis was obtained when we distinguished if the jet was projected against the near or the far side of the galaxy, and differentiated between Seyfert 1's and Seyfert 2's, which showed that the model could not represent Seyfert 1's adequately. We found that the inclusion of viewing angle restrictions for Seyfert 1's, namely, that a galaxy can only be recognized as a Seyfert 1 if the angle between the jet and the line of sight ($|\phi|$) is smaller than a given angle $\phi_c$ and that the galaxy inclination $i$ is smaller than an angle $i_c$, gave rise to statistically acceptable models. This indication that there is a difference in viewing angle to the central engine between Seyfert 1's and Seyfert 2's is a direct and independent confirmation of the underlying concepts of the Unified Model. We discuss possible explanations for the misalignment between the accretion disk and the host galaxy disk, which are: warping of the accretion disk by self-irradiation instability, by the Bardeen-Petterson effect, or by a misaligned gravitational potential of a nuclear star cluster surrounding the black hole, as well as feeding of the accretion disk by a misaligned inflow of gas from minor mergers, capture of individual stars or gas from the nuclear star cluster, or the capture of individual molecular clouds from the host galaxy.
|
[
{
"name": "paper.tex",
"string": "%\\documentstyle[12pt,aasms4]{article}\n\\documentstyle[11pt,aaspp4]{article}\n%\\documentstyle[art8,emulateapj]{article}\n%\\documentstyle[aas2pp4]{article}\n\\input psfig\n\n% The eqsecnum style changes the way equations are numbered. Normally,\n% equations are just numbered sequentially through the entire paper.\n% If eqsecnum appears in the \\documentstyle command, equation numbers will\n% be sequential through each section, and will be formatted \"(sec-eqn)\",\n% where sec is the current section number and eqn is the number of the\n% equation within that section. The eqsecnum option can be used with\n% any substyle.\n\n%\\documentstyle[12pt,eqsecnum,aaspp4]{article}\n\n% Authors are permitted to use the fonts provided by the American Mathematical\n% Society, if they are available to them on their local system. These fonts\n% are not part of the AASTeX macro package or the regular TeX distribution.\n\n%\\documentstyle[12pt,amssym,aasms4]{article}\n\n% Here's some slug-line data. The receipt and acceptance dates will be \n% filled in by the editorial staff with the appropriate dates. Rules will \n% appear on the title page of the manuscript until these are uncommented \n% out by the editorial staff.\n\n\\received{\\today}\n%\\accepted{23 September 1988}\n%\\journalid{337}{15 January 1989}\n%\\articleid{11}{14}\n\n\\slugcomment{Submitted to ApJ}\n\n% Authors may supply running head information, if they wish to do so, although\n% this may be modified by the editorial offices. The left head contains a\n% list of authors, usually three allowed---otherwise use et al. The right\n% head is a modified title of up to roughly 44 characters. Running heads\n% are not printed.\n\n\\lefthead{Kinney et al.}\n\\righthead{Jets in Seyferts}\n\n% This is the end of the \"preamble\". Now we wish to start with the\n% real material for the paper, which we indicate with \\begin{document}.\n% Following the \\begin{document} command is the front matter for the\n% paper, viz., the title, author and address data, the abstract, and\n% any keywords or subject headings that are relevant.\n\n\\begin{document}\n\n\\title{Jet directions in Seyfert galaxies}\n\n\\author{A. L. Kinney\\altaffilmark{1,2,5}, H.R.Schmitt\\altaffilmark{1}, \nC.J.Clarke\\altaffilmark{2}, J.E. Pringle\\altaffilmark{2,1},\nJ.S. Ulvestad\\altaffilmark{3} and R.R.J. Antonucci\\altaffilmark{4}}\n\n\n% Notice that each of these authors has alternate affiliations, which\n% are identified by the \\altaffilmark after each name. The actual alternate\n% affiliation information is typeset in footnotes at the bottom of the\n% first page, and the text itself is specified in \\altaffiltext commands.\n% There is a separate \\altaffiltext for each alternate affiliation\n% indicated above.\n\n\\altaffiltext{1}{Space Telescope Science Institute, 3700, San Martin Drive,\nBaltimore, MD 21818, USA}\n\\altaffiltext{2}{Institute of Astronomy, The Observatories, Madingley\nRoad, Cambridge CB3 0HA, England.}\n\\altaffiltext{3}{National Radio Astronomy Observatory, P.I. Box O,\n1003 Lopezville Road, Socorro, NM, 87801, USA}\n\\altaffiltext{4}{University of California, Santa Barbara, Physics Department,\nSanta Barbara, CA 93106, USA}\n\\altaffiltext{5}{Present address: NASA Headquarters, 300 E St., Washington,\nDC20546}\n\n% The abstract environment prints out the receipt and acceptance dates\n% if they are relevant for the journal style. For the aasms style, they\n% will print out as horizontal rules for the editorial staff to type\n% on, so long as the author does not include \\received and \\accepted\n% commands. This should not be done, since \\received and \\accepted dates\n% are not known to the author.\n\n\\begin{abstract}\n\nHere we present the study of the relative angle between the accretion\ndisk (or radio jet) and the galaxy disk for a sample of Seyfert\ngalaxies selected from a mostly isotropic property, the 60$\\mu$m flux,\nand warm infrared colors. We used VLA A-array 3.6cm continuum data and\nground based optical imaging, homogeneously observed and reduced to\nminimize selection effects. For parts of the analysis we enlarged the\nsample by including galaxies serendipitously selected from the\nliterature. For each galaxy we have a pair of points ($i$,$\\delta$),\nwhich are the inclination of the galaxy relative to the line of sight\nand the angle between the jet projected into the plane of the sky and\nthe host galaxy major axis, respectively. For some galaxies we also\nhad information about which side of the minor axis is closer to Earth.\nThis data is combined with a statistical technique, developed by us, to\ndetermine the distribution of $\\beta$ angles {\\it in 3 dimensions}, the\nangle between the jet and the host galaxy plane axis.\n\nWe found from an initial analysis of the data of the 60$\\mu$m sample,\nwhere Seyfert 1's and 2's were not differentiated, that the observed\ndistribution of $i$ and $\\delta$ values can be well represented either\nby a homogeneous $\\sin\\beta$ distribution in the range\n$0^{\\circ}\\leq\\beta\\leq90^{\\circ}$, or\n$0^{\\circ}\\leq\\beta\\leq65^{\\circ}$, but not by an equatorial ring. A\nmore general model, which tested $\\beta-$distributions in the range\n$\\beta_1\\leq\\beta\\leq\\beta_2$, for different ranges of $\\beta_1$ and\n$\\beta_2$ values, required $\\beta_2$ to be larger than 65$^{\\circ}$ and\ngave preference for $\\beta_1$ smaller than 40$^{\\circ}$ -\n50$^{\\circ}$. An important result from our analysis was obtained when\nwe distinguished if the jet was projected against the near or the far\nside of the galaxy, and differentiated between Seyfert 1's and Seyfert\n2's, which showed that the model could not represent Seyfert 1's\nadequately. We found that the inclusion of viewing angle restrictions\nfor Seyfert 1's, namely, that a galaxy can only be recognized as a\nSeyfert 1 if the angle between the jet and the line of sight ($|\\phi|$)\nis smaller than a given angle $\\phi_c$ and that the galaxy inclination\n$i$ is smaller than an angle $i_c$, gave rise to statistically\nacceptable models. This indication that there is a difference in\nviewing angle to the central engine between Seyfert 1's and Seyfert 2's\nis a direct and independent confirmation of the underlying concepts of\nthe Unified Model.\n\nWe discuss possible explanations for the misalignment between the\naccretion disk and the host galaxy disk, which are: warping of the\naccretion disk by self-irradiation instability, by the\nBardeen-Petterson effect, or by a misaligned gravitational potential of\na nuclear star cluster surrounding the black hole, as well as feeding\nof the accretion disk by a misaligned inflow of gas from minor\nmergers, capture of individual stars or gas from the nuclear star\ncluster, or the capture of individual molecular clouds from the host\ngalaxy.\n\n\n\\end{abstract}\n\n% The different journals have different requirements for keywords. The\n% keywords.apj file, found on aas.org in the pubs/aastex-misc directory, \n% contains a list of keywords used with the ApJ and Letters. These are \n% usually assigned by the editor, but authors may include them in their \n% manuscripts if they wish. \n\n\n\\keywords{galaxies:active -- galaxies:jets -- galaxies:Seyfert -- galaxies:structure}\n%\\keywords{globular clusters,peanut clusters,bosons,bozos}\n\n% That's it for the front matter. On to the main body of the paper.\n% We'll only put in tutorial remarks at the beginning of each section\n% so you can see entire sections together.\n\n% In the first two sections, you should notice the use of the LaTeX Figure~\\ref\n% command to identify citations. The citations are tied to the\n% reference list via symbolic KEYs. We have chosen the first three\n% characters of the first author's name plus the last two numeral of the\n% year of publication. The corresponding reference has a \\bibitem\n% command in the reference list below.\n%\n% Please see the AASTeX manual for a more complete discussion on how to make\n% Figure~\\ref-\\bibitem work for you. \n\n\\section{Introduction}\n\nWe would expect, based on grounds of symmetry and simplicity, that the\njets emanating from a Seyfert nucleus would emerge at right angles to\nthe disk of the host spiral galaxy. The processes for bringing material\nclose to the core (within the innermost 10pc) of a galaxy, either for\nthe initial formation of the black hole or to provide fuel to the black\nhole, are of two sorts -- those that feed the nucleus from the visible\ngas reservoir in the galaxy disk, and those that feed the nucleus by\nintroducing material from outside the galaxy. In the simplest pictures,\nfueling by both internal gas and by external gas favors co-alignment\nbetween accretion disk and galaxy disk, since most of the gas is in the\ngalaxy disk and any gas added to it may rapidly end up there, either by\nshocks or by settling in the galaxy potential. Since the jets are\nlaunched perpendicular to the accretion disk, the simplest assumption\nwould be to see them aligned to the host galaxy minor axis.\n\nHowever, the above scenario is flatly contradicted by the\nobservations. Investigations of the observed distribution of the angle\n$\\delta$, the difference between the position angle of the major axis\nof the galaxy and the position angle of the radio jet projected on the\nplane of the sky, shows that Seyfert galaxies can have jets along any\ndirection, from aligned along the minor axis to aligned along the major\naxis (Ulvestad \\& Wilson 1984; Brindle et al. 1990; Baum et al. 1993;\nSchmitt et al. 1997; Nagar \\& Wilson 1999). It was shown by Clarke,\nKinney \\& Pringle (1998), using data for a sample of Seyfert galaxies\nselected from the literature, that it is possible to obtain a reliable\nestimate of the distribution of the angle $\\beta$ {\\it in 3-dimensions}\nbetween the jet axis and the normal to the galaxy plane, by considering\nfor each galaxy in the sample, the pair of values of $i$ and $\\delta$\n($i$ is the inclination of the galaxy to the line of sight). They\nconclude that the directions of the radio jets are consistent with\nbeing completely uncorrelated with the planes of the host galaxies (see\nalso Nagar \\& Wilson 1999).\n\nThe observed random alignment between accretion disks and galaxy disks\nis intriguing, and the study of this effect is important for the\nunderstanding of the inner workings of Seyfert galaxies. This result\nmay imply, for example, that recently suggested ideas about radiation\ninduced warping of accretion disks (Pringle 1996, 1997, and Maloney,\nBegelman \\& Pringle 1996) come into play both to determine the\ndirectionality of the accretion disk and to produce the ionization\ncones, or that the warping is caused by the rapid spinning of the\ncentral black hole with spin misaligned with the spin of the\ngalaxy (Bardeen-Petterson effect). Alternatively, this misalignment may\nresult by the feeding of the accretion disk from gas outside the\ngalaxy, by mergers, for example.\n\nHere we study the distribution of angles $\\beta$ in a well defined\nsample of Seyfert galaxies, selected from a mostly isotropic property,\nthe flux at 60$\\mu$m, and warm infrared colors (de Grijp et al. 1987,\n1992). Most of the previous works in this subject used samples selected\nfrom the literature and were likely to suffer from selection effects.\nThe example of one problem possibly caused by selection effects was the\n``zone of avoidance'' found by Schmitt et al. (1997), a region of\n20$^{\\circ}$ around the host galaxy minor axis where no jets were\ndetected, but which was shown later by Nagar \\& Wilson (1999) to be\ndue to the sample. Another problem of previous papers was the use of\ndata collected from the literature, measured by different authors, using\ndifferent methods, which resulted in uncertainties that cannot be\nquantified. We have addressed this problem by using radio and optical\ndata observed, reduced and measured in a homogeneous way.\n\n\nThis paper is organized in the following way. In Section 2 we discuss\nthe details about the data and the samples. In Section 3 we present the\ngeometry of the problem and the statistical technique used to determine\nthe distribution of $\\beta$ angles. In Section 4 we compare the data\nwith the models, determine which $\\beta$-distribution and what kind of\nrestrictions are required to better represent the observed data. In\nSection 5 we discuss a series of possible explanations for the observed\nmisalignment between the accretion disk and the host galaxy disk,\nand finally in Section 6 we give a summary of the work.\n\n\\section{The data}\n\n\\subsection{The 60$\\mu$m sample}\n\nThe previous studies on relative angle in different types of Seyfert\ngalaxies (Ulvestad \\& Wilson 1984; Brindle et al. 1990; Baum et al.\n1993; Schmitt et al. 1997; Nagar \\& Wilson 1999) were not based on well\ndefined samples. Most of these papers used data selected from the\nliterature, and were most likely biased with respect to orientation.\nOne possible bias would be the preferential selection of galaxies which\nhave jets shining into the plane of the galaxy, resulting in brighter\nradio emission and narrow line regions, which would be easier to\ndetect. Another possible selection effect happens in the case of\nSeyferts selected by ultraviolet excess. According to the Unified\nModel, we see $\\approx$1\\% of the nuclear continuum by reflection in\nSeyfert 2's, and the whole continuum in Seyfert 1's, which means that\nSeyfert 2's selected in this way are on the higher luminosity end of\nthe luminosity function and are likely to have stronger and more\nextended radio emission. In an attempt to alleviate this problem we\nare using a sample chosen from a mostly isotropic property, the flux at\n60$\\mu$m. According to the torus models of Pier \\& Krolik (1992),\nwhich are the most anisotropic and hence the most conservative models,\nthe circumnuclear torus radiates nearly isotropically at 60$\\mu$m.\n\nOur sample includes 88 Seyfert galaxies (29 Seyfert 1's and 59 Seyfert\n2's), which correspond to all galaxies from the de Grijp et al. (1987,\n1992) sample of warm IRAS galaxies with redshift z$\\leq0.031$. The\ngalaxies in this sample were selected based on the quality of the\n60$\\mu$m flux, Galactic latitude $|b|>20^{\\circ}$, and\n25$\\mu$m$-60\\mu$m color in the range $-1.5<\\alpha(25/60)<0$, chosen as\nto exclude starburst galaxies as much as possible. The candidate AGN\ngalaxies were all observed spectroscopically (de Grijp et al. 1992) to\nconfirm their activity class as being Seyfert 1 or Seyfert 2 and {\\it\nnot} a lower level of activity such as starburst or LINER. The distance\nlimit of z$\\leq0.031$ allows us to study a statistically significant\nnumber of objects which are nearer, and thus more likely to be resolved\nin the radio.\n\nWe note that although the use of the $60 \\mu$m sample provides an initial\nobject selection that is expected to be more or less isotropic, the\noptical follow up required to classify the galaxies spectroscopically\ninevitably re-introduces a degree of orientation bias. We find however\nthat the objects in the 60$\\mu$m sample contain a higher proportion of\nmore nearly edge-on galaxies than do objects selected serendipitously\nfrom the literature. This provides some {\\it a posteriori}\njustification for the notion that the orientation bias is {\\it\nweakened} (though not removed) by use of this sample (see a further\ndiscussion in 4.4.4). In any case, a major benefit of the $60 \\mu$m\nsample is that its use considerably speeds up the process of weeding\nout the (very many) galaxies without Seyfert or starburst activity, and\nassures that Seyfert 1's and Seyfert 2's are matched in luminosity.\n\nIn Figure 1 we show the histogram of the 60$\\mu$m luminosity\ndistribution for the Seyfert 1's and Seyfert 2's in our sample. This\ndemonstrates that the sample has no significant difference in\nluminosities between the two types, with a KS test showing that there\nis a 45.3\\% chance that two samples drawn from the same parent\npopulation would differ this much, or more. Similarly, Keel et al.\n(1994) shows that both the [OIII] and the IR luminosities for the\n60$\\mu$m sample have very similar distributions, demonstrating that\nselection according to the $60 \\mu$m flux is unlikely to bias the survey\ntowards either Seyfert 1s or Seyfert 2s. In particular, this histogram\nshows that we are selecting the subtypes from the same part of the\nluminosity function.\n\nOf the 88 galaxies in our sample, 77 have $\\delta>-47^{\\circ}$ and can\nbe observed from VLA in a reasonable amount of time. Of these 77\ngalaxies, 38 were previously observed with the A-array in X-band\n(3.6cm) and are available in the archive. We carried out a snapshot\nsurvey to observe 36 of the remaining 39 galaxies, using the same\nfrequency and configuration (Schmitt et al. 2000). As a result, we have\nA-array X-band (3.6cm) data, which gives a spatial resolution of\n$\\approx0.24^{\\prime\\prime}$, for 74 galaxies. One of these galaxies,\nTOL1238-3364, was not detected, while for one of the galaxies in the\nsouthern hemisphere, PKS2048-57, which cannot be observed from VLA, we\ngot literature data from Morganti et al. (1999), who observed it with\nATCA also at 3.6cm.\n\nWe reduced the data for the 36 galaxies in our sample, as well as for\n21 of the 38 galaxies available in the archive, for which there was no\ndata previously published, or for which we could find better data in\nthe archive. Details about the reduction of the radio data and a\ndiscussion on individual objects can be seen in Schmitt et al. (2000).\nThe 17 remaining objects were obtained from the literature, only using\ndata that were reduced and analyzed in a way similar to ours. The\nsample is presented in Table 1 where we show the de Grijp et al. (1987)\nnumber of the galaxies, their names, activity class, radial velocity,\n60$\\mu$m luminosity, radio 3.6cm flux, 3.6cm luminosity and the extent\nof the radio emission at 3.6cm.\n\nWhile 74 out of 75 galaxies observed at 3.6cm were detected, 36 of\nthese objects, $\\approx$50\\% of the sample, show extended emission. For those\nobjects with linear extent (based on the Ulvestad and Wilson 1984\ndefinition), the radio emission was decomposed into individual\ncomponents by fitting Gaussians to them. The radio position angle\n(PA$_{RAD}$) is measured between the central position of these\nGaussians. We estimate that the error in the measurements is of the\norder of 3$^{\\circ}-5^{\\circ}$ for linear extended radio sources and\n5$^{\\circ}-10^{\\circ}$ for slighly resolved radio sources. For\nMCG-03-34-064 we measured PA$_{RAD}$ using only the inner\n0.5$^{\\prime\\prime}$ of the jet, because outside this region the jet\nchanges direction, bending to the south. For MRK348, NGC1068 and\nNGC5506, instead of using the VLA data we used higher resolution VLBA\ndata from Ulvestad et al. (1999), MERLIN data from Gallimore, Baum \\&\nO'Dea (1996) and VLBA data from Roy et al. (2000), respectively. This\ndata gives the orientation of the jet closer to the nucleus, which in\nsome cases is different from the orientation seen on VLA scales.\nWe note that in the case of NGC1068 we used PA$_{RAD}=0^{\\circ}$,\nsince the inner E-W radio structure is related to the torus (Gallimore\net al. 1996).\n\nWe estimate that the influence of galaxy disk emission is not important\nin the determination of the position angle of extended radio emission\nin the more distant galaxies of our sample. The emission from the\ngalaxy disk is usually diffuse and weak, and largely resolved out in\nour high resolution observations: most of our galaxies just show small\nlinear extended emission in the nucleus. There is the possibility that\npart of the extended emission in slightly extended sources could be due\nto circumnuclear star formation. However, since the extended emission\nwas usually detected on scales smaller than\n1$^{\\prime\\prime}-2^{\\prime\\prime}$, and the spectra used to classify\nthese galaxies were obtained with a similar aperture, these galaxies\nwould probably have been classified as Starbursts.\n\n\nAnother limitation of previous papers on the orientation of radio jets\nrelative to the host galaxy in Seyferts was the use of inhomogeneous\ninformation about the position angle of the major axis, and inclination\nof the galaxy (PA$_{MA}$ and $i$ hereafter). Most of these studies used\ndata from the literature, or measured the values from the Digitized Sky\nSurvey I, which does not have good enough resolution for sources\nsmaller than $\\approx1^{\\prime}$. To solve this problem we obtained\nhigh signal to noise ratio ground based B and I images for almost all\nthe galaxies in the sample (for a small number of galaxies it was\npossible to observe only one of the bands). The data were taken at\nCTIO, KPNO and Lick Observatory. The reduction and analysis are\nreported in detail by Schmitt \\& Kinney (2000).\n\nThe values of PA$_{MA}$ and the inclination were obtained by fitting\nellipses to the images of the galaxies. The values of PA$_{MA}$ were\nmeasured directly from the ellipses fitted to the isophotes\ncorresponding to the surface brightness level 24-25\nB~mag~arcsec$^{-2}$. We point out that this level is usually deep enough\nto avoid the problem of bars and oval distortions, besides the fact\nthat we have also checked the images of the galaxies for these\neffects. Assuming that the galaxies are circular when seen face-on, we\ncan use the ellipticity of the outer isophotes to determine their\ninclinations $i$. To do this we used the relation $\\cos i = b/a$. We\ncompared the values obtained using this method with the values obtained\nusing the empirical formula $\\sin^2 i = [1-(b/a)^2]/0.96$ from Hubble\n(1926), which takes into account the thickness of the galaxy disk.\nSince the difference between the two measurements was always smaller\nthan 1$^{\\circ}$ to 2$^{\\circ}$, which is less than or approximately of\nthe order of the measurement errors, we decided to use the values\nobtained using the first relation. We estimate that the error in the\ndetermination of the host galaxy inclination and PA$_{MA}$ is of the\norder of 2$^{\\circ}-4^{\\circ}$ for the more inclined galaxies, and\nlarger for the face-on galaxies, where it can be as much as\n6$^{\\circ}$. For a small number of galaxies it was possible to find\nvalues of PA$_{MA}$ and $i$ obtained from kinematical data in the\nliterature. Since this is the most precise way to determine these quantities,\nwhenever it was possible we used these measurements instead of ours.\n\n\nIn this paper we introduce an important improvement relative to\nprevious studies, which is the use of information about which side of\nthe minor axis of the galaxy is closer to Earth. As pointed out by\nClarke et al. (1998), this information can improve the statistics of\nthe sample by a factor of two, because we constrain the jet to lie\nalong a particular segment of the great circle. One way we used to\nobtain this information was the inspection of dust lanes in the\nimages of the galaxies. We expect to see dust lanes only in the closer\nside of the galaxy, since they are highlighted against background bulge\nlight. A considerable number of objects show dust lanes,\neither in our B and I images, or higher resolution HST V band images.\n\nFor galaxies where it was not possible to detect dust lanes, we\nobtained the information about the galaxy orientation from the rotation\ncurve of the galaxy and the direction of the spiral arms. Assuming\nthat the spiral arms are trailing and knowing which side of the galaxy\nis approaching Earth, we can determine which side of the minor axis is\ncloser. To do this we used rotation curves from the literature and also\nobtained, for several galaxies in the sample, long-slit spectra aligned\nclose to the major axis. Our spectra were obtained at CTIO and La Palma\nobservatory and will be published elsewhere. We were\nable to obtain the information about the closer side of the minor axis\nfor approximately two thirds of the sample with extended radio\nemission. Most of the objects for which we were not able to obtain\nthis information were S0 galaxies, for which we could not see the\nspiral arms and also do not show dust lanes, or galaxies very close to\nface-on, where it is difficult to obtain a reliable rotation curve.\n\nIn Table 2 we show the 36 galaxies with extended radio emission, their\nactivity classes, PA$_{MA}$, $i$, PA$_{RAD}$, the side of the galaxy\ncloser to Earth and the morphology of the extended radio emission,\naccording to the Ulvestad \\& Wilson (1984) method. Notice that\nNGC5548, MRK176 and NGC7212 are being shown in this Table just for\ncompleteness, because they are interacting galaxies and will not be\nused in the analysis.\n\n\n\\subsection{Serendipitous sample}\n\nIn some sections of the paper we will also use a larger sample,\nconsisting of 69 galaxies, all Seyferts known to have extended radio\nemission. This sample is composed of 33 galaxies from the 60$\\mu$m\nsample, plus 36 additional galaxies serendipitously obtained from the\nliterature (e.g. Schmitt et al. 1997, Nagar \\& Wilson 1999). We point\nout that, for most of the 36 serendipitous galaxies, the values of\nPA$_{RAD}$, PA$_{MA}$ and $i$ were obtained from the literature. For\nsome of these galaxies, PA$_{RAD}$ was obtained from Nagar et al.\n(1999), so they were measured in a way similar to that of the 60$\\mu$m\nsample. Also, we were able to obtain B and I images for some of these\ngalaxies (Schmitt et al. 2000), which insures homogeneous measurements\nof PA$_{MA}$ and $i$. However, most of the measurements for these 36\ngalaxies come from inhomogeneous datasets, done using different\nmethods. In Table 3 we show the 36 galaxies from the serendipitous\nsample, their activity classes, PA$_{MA}$, $i$, PA$_{RAD}$, the side of\nthe galaxy closer to Earth and the morphology of the extended radio\nemission.\n\n\n\\section{Statistical Analysis}\n\n\\subsection{Geometry}\n\\label{geometry}\n\nThe geometry of our analysis has been described by Clarke, Kinney \\&\nPringle (1998), but is repeated here for completeness. For each galaxy\nwe can determine two observational parameters, $i$ and $\\delta$. The\nangle $i$ is the inclination of the plane of the galaxy to the plane of\nthe sky, or equivalently the angle between the line of sight and the\nvector normal to the galaxy plane. The angle $i$ lies in the range\n$0^{\\circ} < i <90^{\\circ}$. We use a Cartesian coordinate system OXYZ\n(see Figure~\\ref{figNN}) so that OX lies along the apparent major axis\nof the galaxy disk, OY lies along the apparent minor axis, and thus OZ\nis the vector normal to the galaxy plane. In these coordinates the unit\nvector in the direction of the line of sight is\n%\n\\begin{equation}\n{\\bf k}_s = ( 0, -\\sin i, \\cos i). \n\\end{equation}\n%\n\nThe angle $\\delta$ corresponds to the difference between the position\nangle of the apparent major axis of the galaxy and the position angle\nof the radio jet projected onto the plane of the sky. By convention\n$\\delta$ is taken to lie in the range $0^{\\circ} < \\delta <90^{\\circ}$.\nThe definition of all the angles involved in the geometry of the\nproblem, the angles used in the models, and their allowed values is\ngiven in Table~4.\n\nFor a given value of $\\delta$ and $i$, the direction of the jet,\nwhich we denote by a unit vector ${\\bf k}_j$ is determined to lie on a\ngreat circle drawn on a unit sphere centered at the origin of\nour coordinate system. In the OXYZ coordinates described above\nthe great circle is the set of points:\n%\n\\begin{equation}\n\\label{kjet}\n{\\bf k}_j = ( k_{jx}, k_{jy}, k_{jz}) \n= ( \\cos \\delta \\sin \\phi, \n\\sin \\delta \\cos i \\sin \\phi - \\sin i \\cos \\phi, \n\\sin \\delta \\sin i \\sin \\phi + \\cos i \\cos \\phi), \n\\end{equation}\n%\nwhere $\\phi$ is the angle between the vectors ${\\bf k}_s$\nand ${\\bf k}_j$ between the jet and the line of sight,\nand formally lies in the range $-180^{\\circ} < \\phi <\n180^{\\circ}$. We should also note that there is a mirror symmetry to the\nproblem about the apparent minor axis of the galaxy, that is about the\nOYZ plane. In terms of our coordinates this translates into the\nstatement that reversing the direction of the OX axis leaves the\nproblem unchanged. Thus, formally, the sign of $k_{jx}$ is not an\nobservationally meaningful quantity, or in other words the jet vector\nin fact lies on one of two great circles which are reflections of each\nother in the OYZ plane. We have therefore simplified the discussion by\nconsidering just one of these great circles.\n\nIf we define\n$\\beta$ as the angle the jet vector ${\\bf k}_j$ makes with the disk\nnormal OZ, then we see from Equation~\\ref{kjet} that\n%\n\\begin{equation}\n \\cos \\beta = k_{jz}\n= \\sin \\delta \\sin i \\sin \\phi + \\cos i \\cos \\phi.\n\\end{equation}\n%\nThen the only relevant values of $\\phi$ are those which give\n$0^{\\circ} < \\beta < 90^{\\circ}$, or $\\cos \\beta > 0$. In terms of $\\phi$, this\nmeans that $\\phi$ lies in the range $\\phi_1 < \\phi < \\phi_1 +180^{\\circ}$,\nwhere $\\phi_1 \\, (<0)$ is the value of\n%\n\\begin{equation}\n\\label{phi1}\n\\phi_1 = \\tan^{-1} ( - \\cot i/ \\sin \\delta ),\n\\end{equation}\n%\nwhich lies in the range $-90^{\\circ} < \\phi_1 <0^{\\circ}$. We note that\nphysically, if $\\phi < 0$, then the jet vector is projected against\nthe half of the galaxy disk which is nearest to us, whereas $\\phi > 0$\ncorresponds to the jet being projected against the half of the galaxy\ndisk which is furthest from us. \n\nWhat we are trying to determine is the distribution of the directions\nof the jets, relative to their host galaxies ($\\beta$). Relative to the host\ngalaxy we will assume that the jet direction is given by the unit\nvector ${\\bf k}_j$ where,\n%\n\\begin{equation}\n{\\bf k}_j = (\\sin \\beta \\cos \\theta, \\sin \\beta \\sin \\theta, \\cos\n\\beta).\n\\end{equation}\n%\n\nThus the jet direction is determined by the two angles $\\beta$ and\n$\\theta$, where $\\beta$ is the angle the jet axis makes with the\nsymmetry axis of the galaxy, and $\\theta$ is the azimuthal angle about\nthat axis.\n\n\\subsection{Estimation of the $P(\\beta)$ distribution}\n\n\nThe value of the azimuthal angle $\\theta$ for a particular galaxy is not an\nintrinsic property of the galaxy but just depends on the orientation\nof the galaxy relative to the line of sight. In contrast the angle\n$\\beta$ is an intrinsic property of the galaxy and is the angle we\nwould like to be able to determine. In fact what we would like to\ndetermine is the distribution of angles $\\beta$ the jet vectors in our\nsample make with the galaxy normal. We denote this distribution in\nterms of a probability distribution $P(\\beta)$, which is defined so\nthat\n%\n\\begin{equation}\n\\int_{0}^{\\pi/2} P(\\beta) \\, d\\beta = 1.\n\\end{equation}\n%\nThus, for example, if the jet axes were randomly oriented in space,\nand thus were independent of the galaxy disc, then we would find that\n$P(\\beta)=\\sin \\beta$.\n\nIn order to proceed with our analysis, we shall initially make two\nassumptions. First, we assume that all values of $\\theta$ are equally\nlikely to occur in nature. This is reasonable, since otherwise we\nwould have some special place in the Universe. Second, we assume that\nthe inclusion of a galaxy in our sample is independent of the value of\n$\\theta$. This is a more problematic assumption, and we return to it\nbelow in our discussion of selection effects (Section~\\ref{selfx}). \n\nSince, as will become apparent, we do not have enough data points to\n determine $P(\\beta)$ directly (even if our sample were not subject to\n selection effects), we shall adopt the procedure of taking model\n distributions of $P(\\beta)$ and asking if, in a statistical sense,\n they are consistent with the data. The trial distributions we shall\n consider correspond to the jet directions, as seen from the nucleus\n of the host galaxy, being randomly distributed over a band on the sky\n given by $\\beta_1 \\leq \\beta \\leq \\beta_2$, and we shall denote these\n distributions as $P(\\beta \\mid \\beta_1, \\beta_2)$. As we shall see in\n Section~\\ref{results} these model distributions are sufficiently\n general, given the data we are dealing with.\n\n\n\n\\subsubsection{Estimation of $P(\\beta)$ at a fixed value of $i$}\n\\label{fixedi}\n\nIt is simplest to understand the procedure for estimating $P(\\beta)$\nfrom the observed distribution of $\\delta$, if we initially consider\nthe procedure at a fixed value of the galaxy inclination $i$. We shall\nsuppose therefore that we have a set of $N$ galaxies, each observed at\nthe same value of $i$, and that for each galaxy $k$, for $1 \\leq k\n\\leq N$, there is an observed value of $\\delta$, $\\delta_k$, such that\n$0^{\\circ} \\leq \\delta_k \\leq 90^{\\circ}$. As discussed above, for a galaxy at a\ngiven value of $i$, the observation of the value of $\\delta$ implies\nthat the unit vector ${\\bf k}_j$ lies along a great circle given by\nEquation~\\ref{kjet}. Thus at a given value of $i$, the probability\ndistribution $P(\\beta)$ for $\\beta$ implies a corresponding\nprobability distribution $P(\\delta \\mid i)$ for $\\delta$. For example,\nif $\\beta_1 = 0^{\\circ}$, and $\\beta_2 = 90^{\\circ}$, so that the jet directions are\nrandomly oriented over the whole sky, then $P(\\delta)$ would be a\nconstant, independent of $\\delta$, because then all great circles\nwould be equally likely. Thus if we had a large sample of galaxies all\nat the same inclination $i$, we could test the hypothesis that the jet\ndirections were uniformly distributed over the sky, simply by testing\nthe observed $\\delta$ distribution to see if it was uniformly\ndistributed in the allowed range $0^{\\circ} \\leq \\delta \\leq 90^{\\circ}$.\n\nMore generally, if the jet directions are uniformly distributed over\nthe band on the sky $\\beta_1 \\leq \\beta \\leq \\beta_2$, then the distribution\nfor $\\delta$, at given $i$ is given by $P(\\delta \\mid i, \\beta_1, \\beta_2)$,\nwhere $\\delta$ is distributed over the range $\\delta_{\\rm min} \\leq\n\\delta \\leq 90^{\\circ}$, and\n%\n\\begin{equation}\n\\int_{\\delta_{\\rm min}}^{\\pi/2} P(\\delta \\mid i, \\beta_1,\\beta_2)\n\\, d\\delta = 1.\n\\end{equation}\n%\nThe expressions for $P(\\delta \\mid i,\\beta_1,\\beta_2)$ are given in\nAppendix~\\ref{formulae}. \n\nWe note that the lower end of the possible range for $\\delta$ is not\nnecessarily zero. This is because the circle $\\beta = i$ and the great\ncircle defined by $\\delta = 0 $ touch at the line of sight vector\n${\\bf k}_s$. Thus if $\\beta_2 < i$, there is a range of values of\n$\\delta$, $0 \\leq \\delta \\leq \\delta_{\\rm min}$ such that the great\ncircles do not intersect the polar region $\\beta \\leq \\beta_2$.\n\n\nAll points on a\ngiven great circle, defined by $(i, \\delta)$, lie at values of $\\beta\n\\geq \\beta_{\\rm min}(i, \\delta)$, where \n%\n\\begin{eqnarray}\n\\label{bmin}\n\\beta_{\\rm min}(i, \\delta)& =& \\cos^{-1} (\\sin^2 \\delta \\sin^2 i +\n\\cos^2 i )^{1/2},\\cr\n&=& \\sin^{-1} (\\sin i \\cos \\delta)\n\\end{eqnarray}\n%\n(Clarke, Kinney \\& Pringle, 1998). Thus if $\\beta_2 < i$, then the minimum\nvalue $\\beta$ can take is such that $\\beta_{\\rm min}=\\beta_2$. Thus, using\nequation 8 we find that:\n%\n\\begin{eqnarray}\n\\delta_{\\rm min} &= 0 & (\\beta_2 > i)\\cr\n&= \\cos^{-1} (\\sin \\beta_2/\\sin i) & (\\beta_2 < i).\n\\end{eqnarray}\n%\n\nThus, if we had a sample of $N$ galaxies, all observed at the same\ninclination $i$, to check the consistency of the data with the model\ndistribution $P(\\beta \\mid \\beta_1, \\beta_2)$, the procedure to follow\nwould be to compare the observed distribution of values of $\\delta$\nwith the distribution predicted by the model, by means of some\nsuitable statistical test. The test we shall use is one which is\nstraightforwardly generalizable to more complicated datasets, and the\nprocedure is as follows. In general, the distribution $P(\\delta \\mid\ni, \\beta_1,\\beta_2)$, which we derived from our model distribution\n$P(\\beta \\mid \\beta_1, \\beta_2)$ is not uniform. For each datapoint\n$\\delta_k$, for $1 \\leq k \\leq N$, the centile point $c_k$, $0 \\leq\nc_k \\leq 1$ is defined such that:\n%\n\\begin{equation}\nc_k = \\int_{\\delta_{\\rm min}}^{\\delta_k} P(\\delta \\mid i,\n\\beta_1,\\beta_2) \\, d\\delta.\n\\end{equation}\n%\nThen, of course, the values, $c_k$, $1 \\leq k \\leq N$ should be\nuniformly distributed on the interval $[0,1]$. We then use the KS test\nto see with what degree of confidence the $c_k$ distribution is\nconsistent with being drawn from a uniform distribution.\n\n\n\\subsubsection{Estimation of $P(\\beta)$ for a general dataset}\n\nIn general, of course, for the actual dataset of $N$ galaxies in the\nsample, each galaxy is not observed at the same inclination $i$. Thus\nfor each galaxy, $k$, in the sample, for $1 \\leq k \\leq N$, we have\nthe observed pair of values $(i_k, \\delta_k)$. Thus for each\ndatapoint, for a given assumed model for the $\\beta$-distribution,\n$P(\\beta \\mid \\beta_1, \\beta_2)$, there is a corresponding\n$\\delta$-distribution, $P(\\delta \\mid i_k, \\beta_1, \\beta_2)$. It is\nnow, however, straightforward to generalize the statistical procedure\ndiscussed above. For each datapoint $k$, we define the centile, $c_k$,\nsuch that\n%\n\\begin{equation}\nc_k = \\int_{\\delta_{\\rm min}}^{\\delta_k} P(\\delta \\mid i_k, \\beta_1,\n\\beta_2) \\, d\\delta.\n\\end{equation}\n%\nThen it is still true, even for this more general dataset, that if the\ngalaxy sample is indeed chosen from a set of galaxies with\ndistribution $P(\\beta \\mid \\beta_1, \\beta_2)$, then the values $c_k$,\nfor $1 \\leq k \\leq N$ should be uniformly distributed in the interval\n$[0,1]$. As before, we may use the KS test to ascertain the likelihood\nof this hypothesis.\n\n\n\\subsubsection{Introduction of additional constraints}\n\\label{addcon}\n\nThe utility of the statistical procedure we have adopted becomes\napparent as soon as we need to add additional information to the\ndata, and/or additional constraints to the models. For example, for\nsome of the galaxies in our sample we have the additional information\nas to whether the jet is seen in projection against the near side or\nfar side of the galaxy. If we are prepared to make the additional\nassumption that the observed jet (or the stronger of the two in the\ncase of a two-sided jet) is the one that lies above the host galaxy\nplane (as seen from Earth), then for a given pair of values of $(i,\n\\delta)$, the arc of the great circle on which the end of the jet can\nlie, is further constrained (Section~\\ref{geometry}). In addition we\nmay wish to add to our set of models, against which the data is being\ntested, some aspects of the unified model, such as restrictions on\n$\\phi$ the angle between the jet axis and the line of sight, depending\non whether the AGN is a Seyfert 1 or a Seyfert 2.\n\nWhatever additional assumptions we wish to impose on interpretation of\nthe data and/or on the models to be tested, it is evident that for\neach galaxy, $k$, in the sample at its given value of $i_k$ we can\ncalculate, given the additional assumptions/constraints, a\ndistribution in $\\delta$. From that distribution in $\\delta$, and the\nvalue of $\\delta_k$ for that galaxy, we can calculate the centile,\n$c_k$. Note that since the centiles, $c_k$ are computed on a galaxy by\ngalaxy basis, we do not need to have the same type of information\navailable for each galaxy. If the data are consistent with the model,\nthen the values $c_k$ should still be distributed uniformly in the\ninterval [0,1], and as before we may use the KS test to ascertain the\nlikelihood of our hypotheses. \n\n\n\n\n\\section{Results}\n\\label{results}\n\nIn Figure~\\ref{figAA} we plot the data in the $(i,\\delta)$ plane. In\nFigure~\\ref{figAA}a we plot the total sample (i.e the 60$\\mu$m sample\nplus the serendipitous sources) which comprises 69 objects, and in\nFigure~\\ref{figAA}b we plot the 60$\\mu$m sample alone (33 objects). In\neach Figure we distinguish between the Seyfert 1s and the Seyfert 2s.\n\nAs can be seen from the Figures, the distribution of galaxies with\ninclination shows an apparent dearth of galaxies at low inclinations\n(face-on) and at high inclinations (edge-on). The dearth at low\ninclinations could be a problem for our analysis, since we measure the\ninclinations by assuming that the outer parts of the galaxies are\nintrinsically circular. If this were not so, then there would be a\nsystematic upward bias in our inclination determinations. However, if\ngalaxies are oriented randomly in space, then the number density of\ngalaxies is proportional to $\\sin i \\, di$. If this is taken into\naccount the apparent dearth of low inclination galaxies is consistent\nwith random galaxy orientations (Schmitt et al. 2000). In fact, as\nfar as the analysis of jet orientations is concerned, we learn least\nfrom face-on galaxies -- the most informative data points are those\nfor galaxies with high inclination (Section~\\ref{basic}). The dearth\nof galaxies with high inclination may be due to detectability problems\nfor active nuclei in very edge-on galaxies, but in any case it turns\nout that the inclination distribution is consistent with those\nnormally found for galaxies in the field (Schmitt et al. 2000). We\nnote that one major advantage of the galaxies from the 60$\\mu$m sample\nfor our present purposes is that the detection criteria have\napparently enabled the identification of a number of AGN with high\ngalaxy inclinations.\n\nIn Figure~\\ref{figAA}a and Figure~\\ref{figAA}b we also plot contours of\nconstant $\\beta_{\\rm min}$ (Equation~\\ref{bmin}) in the $(i,\n\\delta)$-plane. The value of $\\beta_{\\rm min}$ for each object, derived\nusing Equation~\\ref{bmin} from the object's pair of values\n$(i,\\delta)$, is the smallest angle $\\beta$ which the jet in that\nobject can make with the normal to the galaxy plane. In both the total\nand the 60$\\mu$m samples, it is evident that the data are incompatible\nwith the jets tending to be closely aligned with the galactic normal.\nIn both samples, at least 40 per cent of the galaxies must have jets\nlying at greater than $\\beta = 30^{\\circ}$ to the normal, and at least\n10 per cent must lie at an angle $\\beta \\geq 50^{\\circ}$ (c.f. Clarke,\nKinney \\& Pringle, 1998). The largest value of $\\beta_{\\rm min}$ lies\nin the range $60^{\\circ}$ -- $70^{\\circ}$, so that any model which\nrestricts jets to a circumpolar cap of angular radius less than this is\nimmediately ruled out.\n\n\nThe basic assumptions which underlie all of our analysis of the data\nare that (i) the set of galaxies in the sky have their jet directions\ndistributed uniformly in azimuth about the normal to the galaxy disk\nplane {\\em and} (ii) the galaxies in our sample have been randomly\nselected from that set. While the first of these assumptions is based\non the reasonable expectation that galaxies are oriented randomly in\nspace, the second may be more problematic, and we return to it below\n(Section~\\ref{selfx}). In the meantime we continue with our analysis of\nthe data, gradually introducing more assumptions about the data as we\nproceed. \n\n\n\n\\subsection{No extra assumptions}\n\\label{basic}\n\nWe proceed initially without making any extra assumptions. In\nparticular, we shall ignore our knowledge about whether an object is a\nSeyfert 1 or a Seyfert 2, or equivalently, we shall assume that, in\ncontradiction of the unified model (or related current wisdom), the\nproperty of being a Seyfert 1 or a Seyfert 2 is intrinsic to the\ngalaxy, and is independent of the angle from which the nuclear region\nof that galaxy is viewed.\n\nIn order to illustrate how we make use of the distribution of galaxies\nin $(i,\\delta)$, we consider three simple models for the\n$\\beta$-distributions, before proceeding to more general models.\n\n\n\n\\subsubsection{Uniform $\\sin\\beta$ distribution: $\\beta_1 = 0^{\\circ}, \\beta_2 = 90^{\\circ}$}\n\nIf the jets are oriented completely randomly relative to the host\ngalaxies, then, as discussed in Section~\\ref{fixedi} we expect the\ngalaxies to be distributed uniformly in $\\delta$ independent of galaxy\ninclination $i$. A visual inspection of Figure~\\ref{figAA2}a and\nFigure~\\ref{figAA2}b confirms that the distribution of galaxies in\n$\\delta$ is not strikingly non-uniform in either the 60$\\mu$m sample,\nor in the data as a whole. We show the quartiles as lines in\nFigure~\\ref{figAA2}. Under this uniform $\\sin\\beta$ model there should be\nequal numbers of data points in each quartile marked in the diagram. By\ninspection it can be seen that this is approximately the case. A more\nformal analysis, using the KS test, shows that the hypothesis that the\ndata are drawn from a set of galaxies with uniform distribution in\n$\\sin\\beta$ is consistent at the 81\\% level for the total sample. To be\nprecise, this means that the data, if drawn from the assumed model set\nof galaxies, would on average differ from the model by the amount\nobserved (or more) 81\\% of the time. Consistency is at the 67\\% level\nfor the 60$\\mu$m sample. Thus in each case, we confirm our visual\nimpression that the distribution of data is consistent with the\nhypothesis that the jets point randomly with respect to their host\ngalaxies (c.f. Clarke, Kinney, \\& Pringle, 1998).\n\n\n\\subsubsection{Uniform polecap: $\\beta_1 = 0^{\\circ}, \\beta_2 = 65^{\\circ}$}\n\n\nWe now consider a model for the $\\beta$-distribution of the 60$\\mu$m\ndata in which the jets are uniformly distributed over a polecap of\nhalf angle $65^{\\circ}$ centered on the normal to the galaxy plane (i.e $0^{\\circ}\n\\leq \\beta \\leq 65^{\\circ}$). The value of $65^{\\circ}$ is chosen as being just\nlarger than the largest value of $\\beta_{\\rm min}$ for galaies in the\n60$\\mu$m sample. It therefore represents the smallest polecap\ncompatible with the 60$\\mu$m data. As discussed in\nSection~\\ref{fixedi}, at each value of $i$, an assumed distribution of\n$\\beta$ gives rise to a corresponding distribution in $\\delta$. At\neach $i$ we may therefore compute the quartiles of the expected\n$\\delta$-distribution, and by joining together the quartile points at\ndifferent values of $i$ we may plot quartile lines in the\n($i,\\delta$)-plane. In Figure~\\ref{figB} we plot the quartile lines for the\n$0^{\\circ} \\leq \\beta \\leq 65^{\\circ}$ polecap model, as well as the 60$\\mu$m\ndata. If the data are a true sample from the model then we would\nexpect (on average) an equal number of data points to fall within each\nquartile on the diagram. A KS test indicates that the data are\nconsistent with the model at the 69\\% level. Thus this mildly aligned\nmodel is not ruled out by the data.\n\nWe draw attention briefly to the shape of the quartile contours in the\n($i,\\delta$)-plane. At low values of $i$, the quartiles tend to those\nfor the randomly oriented jet model. This must be so, because, when\nthe galaxy is viewed face-on, a random distribution of jets in azimuth\n(assumption (i) above) translates into a uniform distribution in\n$\\delta$. For larger values of $i$, the quartiles differ significantly\nfrom the random jet orientation model, and for this assumed\n$\\beta$-distribution they bend towards higher values of $\\delta$. For\ninclinations $i > 65^{\\circ}$ there is an excluded area (the zeroth\ncentile), since a galaxy with a value of $(i,\\delta)$ in this area\nwould imply a jet with $\\beta_{\\rm min} > 65^{\\circ}$, and therefore a jet\nlying outside the assumed polecap distribution.\n\n\n\\subsubsection{Equatorial ring: $\\beta_1 = \\beta_2 = 90^{\\circ}$}\n\nAs a contrast, we now consider a model in which all jets lie in the\nplane of the host galaxy. We plot the quartiles for this model, as\nwell as the 60$\\mu$m data, in Figure~\\ref{figC}. At high values of inclination\n$i$, the quartiles now tend in the direction of decreasing\n$\\delta$. This has to be the case, because if the jets all lie in the\nhost galaxy planes, then as $i \\rightarrow 90^{\\circ}$, we must have that\n$\\delta \\rightarrow 0^{\\circ}$. From inspection of Figure~\\ref{figC}, it is apparent\nthat the data are not uniformly distributed across the quartiles. A KS\ntest indicates that the data are consistent with the model at only the\n0.8\\% level. Thus a model in which all the jets are assumed to lie in\nthe planes of the host galaxies is not compatible with the data.\n\n\n\\subsubsection{More general models}\n\\label{genmod}\n\n\nWe now discuss the more general set of model $\\beta$-distributions\nconsidered above (Section~\\ref{fixedi}). In these models the jet\ndirections are uniformly distributed over the band on the sky,\n$\\beta_1 \\leq \\beta \\leq \\beta_2$, where, of course, $\\beta_1 \\leq\n\\beta_2$. Each individual model, in this general set of models, is\nrepresented by a point in the $(\\beta_2, \\beta_1)$-plane, and\nassociated with each model (and hence with each point) is a percentage\nvalue from the KS test indicating the level of consistency with the\nassumed model. In Figure~\\ref{figD}a and Figure~\\ref{figD}b we plot the KS contours in the\n($\\beta_2,\\beta_1)$-plane for the whole dataset, and for the 60$\\mu$m\nsample, respectively. Note that the permitted areas of the diagrams\nare bounded by the line $\\beta_2 = \\beta_1$ and by the line $\\beta_2 =\n(\\sup \\beta_{\\rm min})$, where $ \\sup (\\beta_{\\rm min}) $ is the largest\nvalue of $\\beta_{\\rm min}$ in the sample and is equal to $75^{\\circ}$ for\nthe whole dataset, and to $65^{\\circ}$ for the 60$\\mu$m sample. \n\nWe find that a broad range of models is permitted by the datasets, and\nnote that as commented earlier, although use of the serendipitous\ndata, in addition to the 60$\\mu$m sample, doubles the number of data\npoints, it does not result in correspondingly (or even, significantly)\ngreater constraints on the permitted models. It is evident that\npermitted models are insensitive to the value of $\\beta_2$ (within the\npermitted set of values) but favor values of $\\beta_1$ which are less\nthan around $50^{\\circ}$ -- $60^{\\circ}$. Thus large zones of avoidance are not\nfavored by the data, but otherwise, as long as $\\beta_2$ is big\nenough (that is, as long as jets are not excluded from lying in\nregions too close to the host galaxy planes) all models are reasonably\nconsistent with the data.\n\n\n\\subsection{Using near side/far side information}\n\nUp until now, we have made no assumptions about the orientation of the\njet, other than it is a quasi-linear structure that can be described by\na position angle. (It has not, for example, been necessary to know at\nwhich end of the jet the nucleus lies). In most cases, however, it is\npossible to locate the nucleus and to see that the jet is either\none-sided or highly asymmetric in brightness. It is unlikely that this\nasymmetry results from relativistic boosting (e.g. Ulvestad et al 1999)\nand so one is left with the possibility that the jets are intrinsically\nasymmetric (or even one-sided), or that the radio emission can be seen\nonly if the jet interacts with interstellar gas, or else, that the\ncounter-jet is somehow partially concealed by intervening material. The\nlatter possibility appears to be the case for jets on parsec scales\n(Ulvestad et al 1999), where the density of ionized material required\nfor significant free-free attenuation is consistent with measured X-ray\nabsorption columns. In the few cases where larger scale jets have been\nsimultaneously imaged in the radio continuum and in HI 21 cm\nabsorption, it is found that absorption peaks on the side of the\nfainter (or less coherent) jet (Gallimore et al 1999 and references\ntherein). In these cases at least, it would appear that obscuration\n(possibly by free-free absorption) may play a role in rendering the\ncounter-jet less visible. Given that there are no working models for\nthe generation of intrinsically one-sided jets, we now adopt as a\ntentative working hypothesis the notion that the brighter jet is the\none that lies above the host galaxy plane (as seen from the Earth).\nIf, {\\it and only if}, we make this hypothesis, we can utilize the\ninformation (which we have for some galaxies) as to whether the\ndominant jet is projected against the near/farside of the galaxy. The\ncombination of this hypothesis and the near/farside information\nprovides a much finer discriminant between jet models than has been\npossible thus far. It allows us, for example, to shed some light on the\ntopical issue of Unified Models for Seyfert 1s and Seyfert 2s. We here\nlay out the method and results of such an analysis and urge future\ncampaigns of HI absorption mapping in Seyfert nuclei in order to\nsubject the hypothesis to direct observational scrutiny. We stress that\nnone of the results discussed thus far (i.e. in Section 4.1) rely upon\nthis hypothesis.\n\n\nUsing the additional information as to whether the observed jet is seen\nin projection against the near or the far side of the host galaxy\nplane, and making the additional assumption that the observed jet is\nthe one that lies above the host galaxy plane (as seen from Earth),\nimposes further constraints on the $\\delta$-distributions of the\ngalaxies involved (Section~\\ref{addcon}). We now use the data of the\n60$\\mu$m sample, including this additional assumption, and compare it\n(using the KS test) with the models described in Section~\\ref{genmod}.\nThe resulting KS contours in the $(\\beta_2, \\beta_1)$-plane are shown\nin Figure~\\ref{figH}. In comparison with Figure~\\ref{figD}b, the\npermitted area is now more restricted by the addition of the extra\ninformation and we now require $\\beta_2 \\geq 75^{\\circ}$. In comparison\nwith Figure~\\ref{figD}a and Figure~\\ref{figD}b, although the level of\nacceptability of the models is reduced somewhat, it is evident that at\nthe 5\\%-level (corresponding to 2-$\\sigma$ on a normal distribution)\nthe favored region has not changed to any great extent, especially as\nfar as $\\beta_1$ is concerned.\n\n\n\\subsubsection{Distinguishing Seyfert 1s and Seyfert 2s}\n\n\nSince, by adding the additional information about whether the jet is\nseen in projection against the near or far side of the galaxy, the\nformal acceptability of the models has been reduced (although the\nmodels are still acceptable), we now investigate which feature of the\ndata is causing the additional problem. In particular, we wish to test\nthe assumption we have used so far, which is that the property of being\na Seyfert 1 or a Seyfert 2 is intrinsic to the galaxy, and does not\ndepend on viewing angle. If this hypothesis is correct, then we should\nbe able to obtain estimates of the $\\beta$-distributions for the\nSeyfert 1s and Seyfert 2 separately. In Figure~\\ref{figI}a we plot the\nKS acceptability contours using the data from the 60$\\mu$m sample for\nthe Seyfert 2s alone. Apart from the constraints that $\\beta_2 \\geq\n\\beta_1$ and that $\\beta_2 > \\beta_{\\rm min}$ almost all of the\npermitted region of parameter space is acceptable, although, as found\nfor the Seyfert 1s and 2s combined (Figure~\\ref{figH}), smaller values\nof $\\beta_1$ (that is smaller excluded polecaps) are preferred.\n\nWhen we plot the contours for the Seyfert 1 60$\\mu$m data alone,\nhowever, (Figure~\\ref{figI}b) it is clear that there is a problem. Here\nthe maximum acceptability level is only 7\\%. Most of the permitted\nregion of parameter space has acceptability levels less than 5\\%\n(equivalent to 2-$\\sigma$ on a normal distribution), and the model in\nwhich the jets are oriented randomly with respect to the host galaxy is\nacceptable only at the 3\\% level. In technical terms, the low level of\nacceptability has come about because all of the eight Seyfert 1s in\nthis sample have $\\delta > 35^{\\circ}$, and because three of them have\nthe jet seen in projection against the near side of the galaxy. If a\njet is seen in projection against the near side of a galaxy, then for\nthat galaxy low values of $\\delta$ are much more probable than high\nvalues. This is because, for near side jets, the arc lengths,\n$|\\phi_1|$, of the great circles along which the jet axis is restricted\nto lie (by the combination of $i$ and $\\delta$) are shorter if $\\delta$\nis larger. Thus the models predict low values of $\\delta$, and the\ndata contain a preponderance of high values of $\\delta$.\n\n\\subsection{Viewing restrictions for Seyfert 1s and 2s}\n\n\nThus, we have found that our assumption that a Seyfert 1 is seen as a\nSeyfert 1, no matter from which direction it is viewed, has led us into\nan inconsistency (albeit a fairly mild one). In the light of current\nwisdom, the fact that a Seyfert 1 might not be seen as Seyfert 1 from\nall viewing angles does not come as a surprise, but this is, to our\nknowledge, the first time that such an inconsistency has been\ndemonstrated directly in a general way, from the data on a large\nstatistical sample of galaxies. In addition it is evident from our\ndata where the problem lies, and that is with the long great circle\narcs (and corresponding high probabilities) associated with low values\nof $\\delta$. There is a straightforward way of rectifying this problem,\nand this is to truncate the arcs in some way. Taking current wisdom\ninto account, we can do this by adding the hypothesis that an AGN only\nappears as a Seyfert 1 if the angle $\\phi$ between the jet axis and the\nline of sight is less than some value $\\phi_c$. We do not have enough\ndata to determine the value of $\\phi_c$ with any accuracy, and so we\nadopt a value of $\\phi_c = 40^{\\circ}$ as being consistent with the\nratio of Seyfert 1s to Seyfert 2s in our own data, as well as being\nconsistent with previous estimates (e.g. Osterbrock \\& Shaw 1988;\nOsterbrock \\& Martel 1993). This is also consistent with the fact that,\nin the 60$\\mu$m sample, there is a much larger proportion of unresolved\nradio sources in Seyfert 1's compared to Seyfert 2's, and that their\naverage radio extent is smaller.\n\nIf we make this additional assumption, then the acceptability contours,\nusing the KS test, for the Seyfert 1s alone is shown in\nFigure~\\ref{figK}. The region of permitted values is now bounded as\nbefore by requiring $\\beta_2 > \\beta_{\\rm min}$, but now also by\nrequiring $\\beta_1 < \\beta_{\\rm max}$. The value of $\\beta_{\\rm max}$\ncomes about because the additional restriction $|\\phi| < \\phi_c$, means\nthat for each galaxy, with given $(\\delta, i)$, there is a largest\nvalue that $\\beta$ can take. In order for all the galaxies in the\nsample to be able to have jet axes such that $\\beta_1 \\leq \\beta \\leq\n\\beta_2$, we therefore require that $\\beta_1$ be less than some\nquantity $\\beta_{\\rm max}$. We see from Figure~\\ref{figK}, that most of\nthe permitted region of parameter space is now acceptable. For example,\nthe model with randomly oriented jets is acceptable at the 18\\% level.\n\n\nHowever, if we make the stronger assumption that all AGN with $|\\phi| <\n\\phi_c$ are Seyfert 1s, we have an immediate conflict with the data.\nThis comes about because of the properties of one object, NGC4388. This\nobject has $i = 70^{\\circ}$, $\\delta = 70^{\\circ}$, and therefore\n$|\\phi_1| = 21^{\\circ}$. In addition, the jet in this system is\nprojected against the near side of the galaxy. Therefore, we must have\n(given our assumptions) $|\\phi| \\leq 21^{\\circ}$. Thus, by our\nassumptions so far, this object should be a Seyfert 1. In fact, it is a\nSeyfert 2. We are therefore drawn to the conclusion that the simple\nhypothesis that all AGN with $|\\phi| < \\phi_c$, for some value of\n$\\phi_c$ are Seyfert 1s, and the rest are Seyfert 2s, cannot be\nsustained.\n\nWe note, however, that the problem came about for a galaxy which had a\nlarge value of inclination $i$. Indeed, returning to\nFigure~\\ref{figAA}b, we can see that all the galaxies with large values\nof $i$ are Seyfert 2s. Again, drawing on current wisdom (Keel 1980;\nLawrence \\& Elvis 1982; Maiolino \\& Rieke 1995; see the discussion in\nAntonucci 1999), this leads us to introduce the additional hypothesis\nthat an active nucleus seen in a galaxy with high inclination, $i >\ni_c$, for some value $i_c$, is always identified as a Seyfert 2,\nindependent of the jet orientation relative to the line of sight. We\ncannot measure the value of $i_c$ from the data, but the data do\nrequire that $i_c \\gtrsim 60^{\\circ}$.\n\nAn observation that corroborates this proposition is the detection of\nseveral highly inclined Seyfert 2 galaxies in our sample, without\nextended radio emission (MRK607, IRAS04385-0828, UGC12348,\nIRAS13059-2407, and NGC3281). From the point of view of the Unified\nModel, we would expect to see Seyfert 1's with unresolved, or smaller\nextended radio emission than Seyfert 2's, because they are seen\npole-on. As discussed in Section 2.1, 50\\% of the galaxies in the\n60$\\mu$m sample do not show extended radio emission, and $\\approx2/3$\nof these galaxies are Seyfert 1's, which is consistent with the predictions.\nIn this way, the observation of highly inclined, unresolved Seyfert 2's\nis consistent with the proposition that galaxies will always be\nclassified as Seyfert 2's if they have high inclination, irrespective\nof the angle between the jet and the line of sight.\n\nCombining all these ideas, we construct the following model. We assume\nthat an AGN is seen as a Seyfert 1 only (i) if it is seen with jet axis\nclose enough to the line of sight ($|\\phi| < \\phi_c$; we adopt $\\phi_c\n= 40^{\\circ}$), {\\em and} (ii) if it is seen from sufficiently far out\nof the plane of the host galaxy ($i < i_c$; we adopt $i_c =\n60^{\\circ}$). Otherwise, the AGN is seen as a Seyfert 2. Adopting this\nhypothesis, we can now construct models for the $\\beta$-distributions\nand compare them with the data. In Figure~\\ref{figG}, we plot the\nconsistency levels for the 60$\\mu$m sample. (Note that this combined\nhypothesis enables us to combine all the data, using both Seyfert 1s\nand Seyfert 2s.) We find that all of the permitted region is\nacceptable, and the preference still is for low values of $\\beta_1$ and\nhigh values of $\\beta_2$. The model with randomly oriented jets is\nacceptable at the 76\\% level. We note here that a similar model was\nfavored by the analyzes of Nagar \\& Wilson (1998).\n\n\n\\subsection{Selection Effects}\n\\label{selfx}\n\nUntil now, as we mentioned earlier, we have made the assumption that\nthe objects in our sample are representative of the set of Seyfert\ngalaxies as a whole. Because of selection effects, however, this may\nnot be the case. Here we consider briefly what these selection effects\nmight be, and to what extent they might effect the conclusions of our\npaper. We consider in turn the possibilities of, and implications\nfor, selection effects in $i, \\delta, \\beta$, and $\\phi$. \n\n\\subsubsection{Selection effects in $i$}\n\nAs we noted above, (see Figure~\\ref{figAA}a and Figure~\\ref{figAA}b)\nthe sample is apparently deficient in objects at large values of the\ninclination, $i$. For example, for randomly oriented galaxies one\nexpects half of the sample to lie at $i > 60^{\\circ}$, whereas for the\n60$\\mu$m sample only 13/33 lie in that range. However, as we emphasized\nabove, the method we have adopted for estimating the distribution of\njets in $\\beta$ does not rely on completeness of the sample in $i$. The\nmethod is still valid even if all the galaxies in the sample had the\nsame value of $i$. However, as we have seen, galaxies with larger\ninclinations provide much better discriminants between the various\npossible model distributions in $\\beta$. Thus a sample, such as the\n60$\\mu$m sample, which contains a relatively high fraction of galaxies\nat high inclination, is particularly valuable for our current\npurposes.\n\n\n\\subsubsection{Selection effects in $\\delta$}\n\n\nThe radio position angle and the position angle of the host galaxy's\nmajor axis are determined by different methods and at different\nwavelengths. Thus it is difficult to envisage any selection effect\nwhich might preferentially populate, or exclude, any particular range in\n$\\delta$. Thus any selection effects here are really physical.\n\n\n\\subsubsection{Selection effects in $\\beta$}\n\n\nWhat we address here is whether a particular value of $\\beta$ for a\nhost galaxy might render that galaxy to be more, or less, likely to be\nincluded in our sample. For example, what we require for inclusion is\nthat we are able to detect a radio jet. Thus we require the radio\nsource to be bright enough and to display sufficient extension. It is\npossible that these qualities do depend on the direction in which the\njet emerges from the nucleus. For example, if the jet emerges close to\nthe galaxy plane (large $\\beta$) it might be that it impinges upon\nmore material and so appears brighter, thus increasing the probability\nof inclusion in the sample. Conversely, such a jet, because it meets\nmore material might be unable to propagate so far, and thus fail to be\ndetected as an elongated source, and so fail to qualify for inclusion\nin the sample. Since it is not evident whether this effect works for,\nor against, inclusion, it is not obvious what remedial action might be\ntaken.\n\n\n\n\\subsubsection{Selection effects in $\\phi$}\n\n\nThe angle $|\\phi|$ is the angle between the jet axis and the line of\nsight. Given current ideas about the AGN environment, towards which we\nhave been drawn by the present dataset, it is evident that objects with\nlow values of $|\\phi|$ (and low values of inclination $i$) are ones in\nwhich the nucleus is directly observable, and are therefore more\nlikely to be detected. In contrast, for a given set of intrinsic jet\nsizes, it is those jets which are nearly at right angles to the line\nof sight ($\\phi \\simeq 90^{\\circ}$) which would be preferentially included\nin the sample. Thus we can identify two selection effects which\noperate in different directions as far as values of $\\phi$ are\nconcerned.\n\nThe 60$\\mu$m sample is chosen using a\nbrightness limit at 60$\\mu$m, and an additional color criterion\nusing the ratio of 25$\\mu$m to 60$\\mu$m fluxes; de Grijp et al\n(1987). Because the hypothetical molecular torus is believed to\nemit more isotropically at longer wavelengths (Pier \\& Krolik 1992;\nEfstathiou \\& Rowan-Robinson 1995), it is hoped\nthat such selection criteria would help to minimize the effect of\ninclusion in the sample depending on the viewing angle of the\nobject. A secondary consequence of this selection criterion has been\nthat by using far infrared discriminants we have been able to include\nin the sample a relatively large number of galaxies at high\ninclination.\n\nThus the main selection effect of which we are aware is the problem of\nresolution of the nuclear radio source into an elongated structure\n(jet), and the fact that an intrinsically elongated source is more\neasily resolved if $\\phi \\simeq 90^{\\circ}$. In order to examine this effect\nmore closely we separated the 60$\\mu$m sample (which of course only\nincludes those objects which are resolved at radio wavelengths) into\ntwo equal sample of 17 objects, sorted according to distance\n(redshift). In Schmitt et al (2000) we have shown that there is no\nstrong dependence of intrinsic length of jet on 60$\\mu$m\nluminosity. Under these circumstances, we might expect the further set\nof objects to be closer to the resolution limit (that is to have\nvalues of $\\phi$ closer to $90^{\\circ}$) than the nearer set. If true, then\nwe might expect that the $(i, \\delta)$-distributions of the two sets\nmight differ in some systematic way. As far as we can tell this is not\nthe case.\n\nAlternatively, if it happened that this selection effect (the hypothetical\nincreased radio resolvability for high $\\phi$) was so\ndominant that it overrode all other considerations (so that for each\ngalaxy included in the sample we know that $\\phi = 90^{\\circ}$), then we\nwould be able to determine $\\beta$ for each galaxy, and thus determine\nthe $\\beta$-distribution directly. We plot the resultant distribution\nin Figure~\\ref{figZ}. We see from the Figure that the distribution is\nconsistent with being uniform in $\\cos \\beta$, which corresponds to\njet orientations being independent of the host galaxy. We stress that\nthis is not a sensible method for deriving the $\\beta$-distribution of\nSeyfert jets, since $\\phi = 90^{\\circ}$ is not a good assumption for nearby\ngalaxies, nor for those galaxies with intrinsically long, and so\neasily resolved, jets. Nevertheless, this exercise does demonstrate\nthat the extreme assumption that all jets lie in the plane of the sky\n($\\phi = 90^{\\circ}$), does not lead to results that are radically different\nfrom those we have obtained above.\n\n\n\n\\subsection{Summary of findings}\n\nIn this Section, for convenience, we summarize our results.\n\nWe have analyzed the data under the assumption that the galaxies in\nour sample have been randomly selected from a set of galaxies whose\njet directions are distributed uniformly in azimuth about the normal\nto the galaxy disk plane. We have then also assumed that the\nunderlying set of galaxies from which our sample has been selected has\na particular distribution in $\\beta$, the angle between the jet and\nthe galaxy normal. We find that an adequately general set of model\ndistributions is given by assuming that galaxy jets are uniformly\ndistributed over the galactic sphere in an azimuthal band $\\beta_1 <\n\\beta < \\beta_2 $. We then apply a KS test to give (loosely speaking)\nthe probability that the hypothesis that our sample is drawn from\nthe assumed model distribution is valid.\n\n\n\\subsubsection{Analysis with no extra assumptions}\n\\label{noextra}\n\nFirst we consider the whole dataset, displayed in Figure~\\ref{figAA}a and\nFigure~\\ref{figAA}b,\nand make no use of additional information such as whether an AGN is a\nSeyfert 1 or 2, or whether we have information about the jet being\nprojected against the near or far side of the galactic plane. Thus we\nare making the assumption here that, in contradiction to the unified\nmodel, classification of an object as a Seyfert 1 or Seyfert 2 is\nindependent of the angle $\\phi$ between the jet and the line of sight.\n\nUnder these assumptions we find, using the data from the 60$\\mu$m\nsample, and taking the data for both Seyfert 1s and 2s together\n(Figure~\\ref{figD}b), that the data are compatible with the jets being randomly\noriented relative to the host galaxy $(\\beta_1 = 0^{\\circ}, \\, \\beta_2 =\n90^{\\circ})$ at the 67\\% level. The data are also consistent with the jets\nbeing distributed in uniform polecaps as long as the cap is large\nenough to encompass the galaxy with the largest value of $\\beta_{\\rm\nmin}$. Thus models with $\\beta_1 = 0, \\, \\beta_2 > \\beta_{\\rm min}$\nare equally acceptable. In addition models with excluded regions\naround the pole $(\\beta_1 > 0)$ are also acceptable, as long as the\nregion of exclusion, i.e. $\\beta_1$, is not too large. For example the\nprobability that the data is drawn from a model with $\\beta_1 = 60^{\\circ},\n\\, \\beta_2 = 90^{\\circ}$ is less than 5\\%. These conclusions are essentially\nunchanged (Figure~\\ref{figD}a) if we use the whole dataset, adding the\nserendipitous sources to the 60$\\mu$m sample.\n\n\\subsubsection{Using near side/far side information}\n\\label{nearfar} \n\nIn addition to the assumptions of Section~\\ref{noextra}, we now add\nthe premise that the observed jet (or the dominant jet, in the case of\na two-sided jet) is the one which lies above the disk plane of the\nhost galaxy (as seen from Earth). We then make use of the\nobservational data which enables us to ascertain (for a number of\ngalaxies) whether the jet is seen in projection against the near side\nor the far side of the galaxy plane. We then use this knowledge as a\nfurther constraint on the jet direction.\n\nUsing, again, just the 60$\\mu$ sample, we find:\n\n(i) If we use all the data (combining Seyfert 1s and 2s) then only\nmodels with $\\beta_1 \\gtrsim 45^{\\circ}$ are inconsistent with the data at\nthe 5\\% level, as long as we choose $\\beta_2 > \\beta_{\\rm min} = 75^{\\circ}$\n(Figure~\\ref{figH}). Thus, for example, the data are consistent with randomly\noriented jets. The conclusions are similar, if we use just the data\nfor the Seyfert 2s alone (Figure~\\ref{figI}a).\n\n(ii) However, if we consider the Seyfert 1s alone, then there is a\nproblem finding compatibility with the simple models we have used so\nfar (Figure~\\ref{figI}b). The problem arises because all 8 of the Seyfert 1\ngalaxies have $\\delta > 35^{\\circ}$, and because of these 8, at least 3 have\nthe jet projected against the nearside of the galaxy. For these 3\ngalaxies, the jet axis must (according to our assumption) lie on the\nshort arc of the great circle between the line of sight and the\ngalactic plane. For such galaxies, the predicted distribution of\n$\\delta$ for any $\\beta$-distribution, is heavily weighted towards\nsmall values of $\\delta$, because the arc length, $|\\phi_1|$ is\nlargest for small values of $\\delta$. This contrasts with the finding\nthat $\\delta > 35^{\\circ}$ for the data set as a whole, and $\\delta > 43^{\\circ}$\nfor the 3 nearside galaxies. We find that the optimal model is for\njets oriented in a narrow band along the galactic equators, and that\neven this model is inconsistent with the data at the 7\\% level. Most\nof the permitted parameter space is excluded at the 5\\% (2-$\\sigma$)\nlevel. \n\n\n\\subsubsection{Need for further restrictions - a generalized unified model}\n\nThe problem with the Seyfert 1 galaxies, discussed in\nSection~\\ref{nearfar}, comes about because, for galaxies whose jets\nare projected against the near side of the galaxy plane, great circles\nwith low values of $\\delta$ have the longest arcs. The inconsistency\ncan, therefore, be circumvented if the arc lengths can be\ntruncated. One way of doing this is to invoke the unified model for\nSeyfert 1s and 2s, which makes the additional assumption that any\nSeyfert viewed with angle, $\\phi$, between jet axis and line of sight\nsmall enough, i.e. $|\\phi| < \\phi_c$, is a Seyfert 1. As an example,\nwhich is consistent with other aspects of our and other datasets, we\ntake $\\phi_c = 40^{\\circ}$. Then adding the restriction that all Seyfert 1s\nhave $|\\phi| < 40^{\\circ}$ we find that a wide range of models, including the\nrandomly oriented model, are consistent with the data (Figure~\\ref{figK}). \n\nHowever, the converse of this assumption, that all Seyfert 2s have\n$|\\phi| > 40^{\\circ}$ is then not consistent with the data. The problem arises\nbecause of NGC4388, which has the jet projected against the near side of\nthe galaxy plane, and for which $|\\phi_1| = 21^{\\circ}$. This implies that\nfor this galaxy $|\\phi| < 21^{\\circ}$, and therefore, according to our\nhypothesis, this galaxy should be a Seyfert 1, however, it is a\nSeyfert 2. Thus the application of the simple unified model, just in\nterms of $\\phi_c$ leads to a contradiction with the data. \n\nIf we are prepared to make one more assumption , then there is a way\nout of this dilemma. We note from Figure~\\ref{figAA}b that all Seyfert 1 galaxies\nhave $i < 60^{\\circ}$. In addition, the galaxy NGC4388, which gives rise to the\ncontradiction has $i = 70^{\\circ}$. We therefore arrive at the following\nhypothesis: \n\nIf a galaxy has $|\\phi| < \\phi_c$ (where we adopt $\\phi_c = 40^{\\circ}$),\nand has $i < i_c$ (where from the data we conclude $i_c \\geq 60^{\\circ}$,\nand we adopt $i_c = 60^{\\circ}$), then it is seen as a Seyfert 1; if either\nof these conditions is not met, then the galaxy is seen as a Seyfert\n2.\n\nUnder this hypothesis, the data is consistent with a large\nrange of models, and, in particular, the most general models of random\njet orientations is fully acceptable (Figure~\\ref{figG}).\n\n\n\n\\section{Implications for feeding the nucleus}\n\nMost of the gas in a spiral galaxy is in the plane of the galaxy. Any\ngas added to a spiral galaxy is likely to rapidly end up in the galaxy\ndisk -- either by direct collision with gas already there, or by\nsettling in the galaxy potential to the extent that it is axisymmetric\nand disky, rather than spherical. Thus the simplest expectation for\ngas flow into the nucleus of a spiral galaxy would be that gas\narriving at the central black hole would do so with angular momentum\nvector perpendicular to the disk of the galaxy. Since jets are\nexpected to be launched perpendicular to the central disc, the simple\nhypothesis and expectation is that all jets in spirals should be\nperpendicular to the disk plane. This expectation is flatly\ncontradicted by observations. Indeed we have shown above that a\ncompletely random orientation of the jets with respect to their host\ngalaxies is consistent with all the data. In the light of this, we now\ndiscuss the implications of our findings for the means by which the\ncentral black hole is fed in Seyfert nuclei, and in other active\ngalactic nuclei.\n\n\nThere seem to be two general approaches to explaining the mismatch\nbetween the angular momentum vectors of the galaxy disk and the\ncentral accretion disk.\n\n\\subsection{Aligned gas inflow from the galaxy disk}\n\n\nFirst, one can assume that the matter is indeed fed to the nucleus\nfrom the visible gas reservoir in the galaxy disk. The mechanisms by\nwhich this might be accomplished have been discussed by a number of\nauthors, and possibilities include tidal interactions (Byrd et al.,\n1986; Hernquist \\& Mihos, 1996) and bar driven inflow (Shlosman et\nal., 1989; Thronson et al., 1989; Mulchaey \\& Regan, 1997). Recent\nwork on the environments of Seyfert galaxies seem to imply that minor\nmergers (that is, the merging with the Seyfert host galaxy of a much\nless massive, but gas-rich, companion) might play a prominent r\\^ole\nin triggering Seyfert activity (De Robertis et al, 1998a,b;\nDultzin-Hacyan et al 1999). We should note, however, that doubts have\nbeen raised as to whether such mechanisms can actually deliver gas to\nthe nucleus of the galaxy and so excite activity, because the presence\nof an inner Lindblad resonance can act to choke off inward gas flow\n(Sellwood and Moore, 1999). But, however the delivery of gas to the\nnucleus is achieved, it is evident that in this case the gas reaching\nthe nucleus should have angular momentum vector parallel to that of\nthe bulk of the gaseous disk of the galaxy. In this case, therefore,\nsome means must be found to warp the disk between where matter is\nadded at the outside and where the jet is produced at the inside. The\nobvious possibilities here are:\n\n\\subsubsection{Warping due to self-irradiation instability}\n\nPringle (1996, 1997) has shown that an accretion disk around a compact\nobject such as a black hole in unstable to warping, caused by photon\nback-pressure from the unevenness of the disk's self-illumination. For\nan AGN disk he estimates that the warping might occur at radii as\nsmall as 0.02 pc and on a timescale of around $10^6$ years. He found\nthat the disk plane in the inner regions of such a disk might in\ngeneral bear little relation to the outer disk plane, and also that\nthe disk shapes could be such that photons from the center might only\nemerge in a pair of narrow cones and that the cones might in general\nnot be necessarily simply aligned with either the inner or the outer\ndisk. Thus the naive conclusions from these simple calculations are\nthat a) there is likely to be little relationship between the plane of\nthe outer disk and the direction if the jets, and b) ionization cones\nwhich emerge from these disks need not be centered on the jet\ndirections. However, Pringle also stressed that these simple\ncalculations underestimate the strength of the effect by only taking\nphoton momentum (rather than wind momentum) into account, and that\nthey also neglect various other effects such as: the effect of\nself-irradiation on the structure of the disk, self-gravity in the\ndisk, the effect of the central jet striking the disk when the warp\nexceeds 90 degrees, and the major uncertainties about the\ntime-dependent behavior of a warped accretion disk, including\nuncertainties about the viscous processes themselves (Ogilvie 1999).\n\n\n\\subsubsection{Warping by the Bardeen-Petterson effect}\n\nThe dragging of inertial frames by a rapidly rotating black hole leads\nto the inner regions of the disk being forced to precess\ndifferentially about a vector parallel to the spin axis of the black\nhole. Then viscous dissipation of the disk twist so caused leads to\nthe inner disk regions being aligned with the spin of the black hole\n(Bardeen \\& Petterson, 1975). Then the jet/galaxy\ndisk misalignment could be explained if the black hole spin is\nmisaligned with that of the galaxy disk. For this to be a plausible\nexplanation we need to be able to answer the two questions: Why should\nthe black hole be rapidly rotating and why should its spin be\nmisaligned? If the self-irradiation instability discussed above is\noperative, it is no longer clear that accretion from a disk will\nnecessarily lead to spin-up of the hole, because the incoming disc at\nthe center wanders in orientation. Thus the simplest way for the\ncentral black hole to be spun-up {\\it and} misaligned is for it to\naccrete a black hole from the nucleus of a captured galaxy (Wilson and\nColbert, 1995, and see below). Note that the accreted black hole need\nonly be, say, 0.1 - -0.2 of the original host mass for spin-up and\nmisalignment to take place because, in the final stages of the black\nhole merger, the orbital angular momentum of the merging black holes\ngets subsumed into the spin of the remnant. However, the long term\neffect of feeding a misaligned black hole from the steadily oriented\ndisk is to align the black hole with the disk, and the timescale for\ndoing so is faster than the mass growth timescale of the hole by about\ntwo orders of magnitude, and may be even faster. This is because\nangular momentum transfer between the hole and the disk takes place at\na large radius in the disk (Scheuer \\& Feiler 1996), and because warp\nis propagated through an accretion disk much faster than mass or\n(aligned) angular momentum (Papaloizou \\& Pringle, 1983; Kumar \\&\nPringle, 1985; Natarajan \\& Pringle 1998).\n\n\\subsubsection{Warping by a misaligned gravitational potential}\n\n\nThe central black hole appears to be surrounded by a nuclear star\ncluster both in early-type galaxies (Gebhardt et al., 1996; Faber et\nal., 1997; van der Marel, 1999) and in spiral galaxies (Carollo \\&\nStiavelli, 1998; Carollo, 1999), where the mass of the cluster begins\nto dominate the mass of the hole at a radius of a few tens of parsecs.\nIf the star cluster is axi-symmetric (rather than spherically\nsymmetric, see the discussion by Merritt \\& Quinlan, 1998) and has its\nsymmetry axis misaligned with the galaxy disk, and if the degree of\nnon-sphericity is sufficiently great, then it would be possible for\ntidal potential of the cluster to induce differential precession in\nthe disk. This, coupled with viscous dissipation of the disk twist so\ninduced, would act to align the disk with the symmetry axis of the\ncluster.\n\nThe cause of such a misalignment might be some form of minor merger,\ndiscussed in more detail below (Section~\\ref{mmergers}). There are two\nreasons, however, why a misaligned central star cluster may not be\nthe answer. First, the work by Carollo (Carollo et al, 1997; Carollo\n\\& Stiavelli, 1998, Carollo, 1999) on the structure of the centers of\nspiral galaxies indicates that there is a tendency for late-type\nspirals to contain exponential disk-related bulges around the central\nstar cluster. This supports scenarios in which bulge formation occurs\nrelatively late, in dissipative accretion events driven by the\ndisk. If so, it seems likely that the central star cluster, formed as\npart of the same process, would be aligned with the disk. Second, if\nit does appear that the stellar kinematics of the nuclear region does\nprovide the explanation of the jet/galaxy misalignment found in\nSeyferts, it would be in stark contrast to the finding (Van Dokkum \\&\nFranx, 1995; Section~\\ref{misgas}) that in early-type galaxies the jet\ndirection is determined by the angular momentum of the incoming\nmaterial, and not by the stellar rotation axis.\n\n\n\\subsection{Misaligned gas inflow}\n\\label{misgas}\n\n\nSecond, one can assume that the disk is not fed from the obvious gas\nreservoir of the disk of the spiral galaxy, in which case the problem\nof alignment does not (necessarily) arise. In this context it is worth\nnoting the survey of dust in the cores of early type galaxies by Van\nDokkum \\& Franx (1995). They find that dust disks are present in a\nhigh fraction of these galaxies, indicating (perhaps) that minor\nmergers occur quite frequently, and also find that the detection rate\nis higher in radio galaxies, indicating (perhaps) a connection between\nthe presence of dust and nuclear activity. The overall finding is that\nthe dust plane is not in general relaxed to any symmetry plane of the\ngalaxy, but that the dust plane is in general perpendicular to the\nradio axis, if there is one. This finding is consistent with the\nresults of surveys of 3CR radio-galaxies by de Koff et al. (1999), and\nby Martel et al. (1999). The simplest interpretation of this is that\nthe dust plane is the debris trail of a small merger incident, and\nthat the direction of the radio jet is determined by the orbital plane\nof the incoming mergee. This result has implications for the foregoing\ndiscussion. First, the jet axis in these early-type radio galaxies\nseems to be determined by outside influences, and not by the intrinsic\nspin of the black hole (unless, either each minor mergee brings in a\nsmall nuclear black hole of its own and tweaks the central black hole\ninto line, or the disk accretion is very efficient at aligning the\nblack hole with the disk itself, Natarajan \\& Pringle, 1998). Second,\nthe self-irradiation instability (Pringle 1996,1997) appears not to be\noperative in these systems. And, third, jet direction does not appear\nto be determined by asymmetries in the potential of the host galaxy.\n\nWe now consider various processes which might give rise to misaligned\ngas flow to the central regions. \n\n\n\\subsubsection{Misaligned minor mergers}\n\\label{mmergers}\n\nMisaligned gas in the center of a spiral galaxy, could be provided as\nthe result of small scale cannibalism, whereby a small, gas-rich\ngalaxy is accreted on a trajectory which goes more or less straight to\nthe nucleus (if the trajectory of the small mergee intersects the\nsymmetry plane of the spiral, it seems likely that the gas in the\nmergee would be stripped by interaction with the spiral's gaseous\ndisk). The misaligned accreting gas needs to be provided by the small\ngalaxy participating in this minor merger event. This cannot be a\nlarge scale merger of two comparable mass systems, such as for example\nArp 220 where counter-rotating gas disks are seen around the two\noriginal nuclei which have yet to merge (Sakamoto et al., 1999),\nbecause the resulting galaxy is then elliptical rather than spiral\n(Barnes and Hernquist, 1992,1996), and because Seyferts are simply not\nin rich enough environments (De Robertis et al 1998b). \n\n\n\nThere is increasing evidence that the kinematics in the nuclei of\nspiral galaxies is not simple -- for example, the evidence for\ncounter-rotation in the core of the Galaxy (Genzel et al 1996), the\nmultiple nuclei in M31 (Stark \\& Binney, 1994; Tremaine, 1995;\nSil'chenko, Burenkov, \\& Vlasyuk, 1998), and the results of a HST high\nresolution imaging surveys of nearby Seyferts (Malkan et al., 1996),\nand of nearby spiral galaxies (Carollo, 1999). In addition there is an\nincreasing number of instances of complex gaseous and stellar\nkinematics in the nuclei of S0 and spiral galaxies, including\nmisaligned and counter-rotating discs of gas and stars (Rubin, 1994;\nGalletta, 1996; Kuijken, Fisher and Merrifield, 1996; Sil'chenko et\nal., 1997; Zasov \\& Sil'chenko, 1997; Garcia-Burillo et al.,1998; and\nSil'chenko, 1999). However, even though (Carollo, 1999) the brightest\nnuclei embedded in spiral galaxies with an active (AGN or HII-type)\nground-based central spectrum are surrounded typically at HST\nresolution by complex circum-nuclear structure (e.g. spiral arms,\nstar-forming rings, spiral-like dust lanes), there is little evidence\nthat this structure is severely misaligned with the main galaxy disk.\n\n\n\n\nFrom a theoretical point of view, an interesting calculation which\nneeds to be carried out in this context is to calculate where the\nlarge/small merger border lies. The main problem here is to calculate\nhow accurate the initial trajectory needs to be for the gas associated\nwith the incoming small galaxy to reach the nucleus of the Seyfert\nhost with its orbital angular momentum intact. Calculations of small\nscale cannibalism have yet to be carried out for incoming gas-rich\ngalaxies on arbitrary orbits. Calculations have been carried out for\nincoming galaxies on coplanar orbits in both the aligned and\ncounter-aligned cases (Thakar \\& Ryden, 1998), who find, for example\nthat the accretion of massive counter-rotating disks drives spiral galaxies\ntowards earlier (S0/Sa) Hubble types. In addition, N-body calculations\nof minor mergers with disk galaxies (neglecting the hydrodynamics)\nhave been carried out by Vel\\'azquez and White (1999). One simple\nexpectation would be that for each direct hit, there are many more\nmisses whose orbits intersect the disk of the galaxy. This would be\nlikely to merge the gas in the small mergee with the gas already in\nthe spiral disk. This might result in feeding the nucleus but the gas\nreaching the nucleus would in this case be essentially aligned with\nthe spiral disk. We also note that there may be a relationship between\nthe formation of a nuclear ring and the capture of a small\ncounter-rotating satellite galaxy (Thakar et al., 1997). In addition,\none expects capture cross-sections for small scale capture to be\nstrongly dependent on the initial orbit (prograde aligned capture is\nstrongly preferred) and one also expects the ability of the mergee to\npenetrate to depend strongly on its initial central\nconcentration/structure (Vel\\'azquez \\& White, 1999). Moreover it\nseems that the distribution of satellite galaxies tends to be\nanisotropic in that their angular momenta tend to align with the\ncentral disk (Zaritsky et al., 1997). Also of interest in this case is\nwhat happens to the central black hole (nucleus) of the intruder, if\nit has one. If this can be captured by the host nucleus before its\norbit aligns with the spiral then it might be able to lead to a\nrapidly spinning and misaligned central black hole (see above).\n\n\n\nIf this is the predominant mechanism by which activity is initiated in\nSeyfert galaxies, then, unless each Seyfert we detect has just\nswallowed its last companion, we would expect to find a strong\ncorrelation between Seyfert activity and environment, in that active\ngalaxies should have far more small companions, and should show\nenhanced evidence of disturbance. Current evidence appears to indicate\nthat Seyfert 1s have a similar number of small companions as the\ncontrol samples, but that Seyfert 2s do display an enhanced number of\nsmall companions (De Robertis et al 1998a,b; Dultzin-Hacyan et al\n1999). In addition, Malkan et al (1996) find that the rates for\noccurrences of bars in Seyfert 1s, Seyfert 2s and non-Seyferts is the\nsame (see also Mulchaey \\& Regan 1997; Ho, Filippenko \\& Sargent 1997),\nbut that Seyfert 2s are significantly more likely to show\nnuclear dust absorption than Seyfert 1s, and tend to reside in\ngalaxies of later type. This is consistent with the tendency for\nSeyfert 2s at HST resolution to show a disturbed, clumpy morphology\n(Capetti et al, 1996; Colina et al, 1997; Simpson,et al, 1997).\n\nIf the minor merger hypothesis is to be made to work, it may therefore\nbe necessary to argue (c.f. Chatzichristou 1999; Taniguchi 1999) that\nat an early stage in the merger, the nucleus is more likely to be\nobserved as a Seyfert 2 (with disturbed central regions, large regions\nof out-of-plane gas, and hence larger extents of NLRs (Schmitt \\&\nKinney, 1996). Later on, the disturbed gas settles more into the galaxy\nplane, and the nucleus is more likely to be observed as a Seyfert 1. If\nso, because in a volume limited sample there are about equal numbers of\nSeyfert 1s and Seyfert 2s, this would mean that the time taken for\ndynamic evolution of the gas must be about equal to the length of time\nthe Seyfert is active (typically estimated at about $10^8$ years). In\naddition, if there is (on average) a time-sequence of Seyfert 1\n$\\rightarrow$ Seyfert 2, and if the jet/galaxy misalignment is caused\nby the misalignment of the merger, then one might expect the amount of\nmisalignment to be (on average) less for Seyfert 1s than for Seyfert\n2s.\n\n\n\\subsubsection{Capture of individual stars or gas from the nuclear\nstellar cluster}\n\nCapture and consumption of individual stars from the central star\ncluster by the central black hole has been put forward as a mechanism\nfor feeding the central nucleus (Frank \\& Rees, 1976; Shlosman et al.,\n1990). Shlosman et al. (1990) make the case that standard thin\naccretion disks are not a viable means of delivering fuel to AGN on\nscales much larger than a parsec because of the long inflow\ntimescales. If activity proceeds on a star by star basis then the\norientations of the central disks might be expected to be fairly\nrandom. However, if an accretion rate of about a star per year is\nrequired, and if the central disk contains tens or hundreds (or more)\nsolar masses then the effects of individual star orbits are going to\nbe averaged out. Even so, if the central stellar cluster has an\nanisotropic velocity distribution in the form of a net rotation, then\non average we might expect the nuclear accretion disk to be aligned\nwith the central nuclear cluster. As mentioned above, it might well be\nthat the direction of spin of the central stellar cluster is\nmisaligned with the galaxy as a whole.\n\nAn alternative possibility is if the source of accreted material is\nmass loss from the stars making up the nuclear cluster. If matter is\nlost from the stars in such a way that it can cool and be accreted by\nthe central black hole, and if the nuclear cluster has a net rotation\nabout some axis misaligned with the spin of the galaxy disk, then once\nagain the rotation axis of the central accretion disk need not be\ncorrelated with the rotation axis of the galaxy as a whole.\n\nIn both these cases, however, there is a question as to whether a\nsufficient mass accretion rate can be provided to power the observed\nSeyfert nuclei (Shlosman et al, 1990). Recent calculations of the\nrates of disruption of stars by massive central black holes (applied\nto early-type galaxies) indicate that the highest disruption rates are\naround one star every $10^4$ years (Magorrian \\& Tremaine, 1999; Syer\n\\& Ulmer, 1999). As a time-averaged rate, this is about two orders of\nmagnitude too low to power standard Seyfert nuclei. However, since the\nSeyfert phenomenon may well have a duty cycle of only about a per\ncent, if the stellar disruption rate can be made to be intermittent\n(for example brought about by dynamical phenomena associated with\nminor mergers), then this mechanism for feeding the black hole might\nmerit further investigation. Similarly, even if some means can be\nfound for stellar mass loss to be channeled efficiently towards the\ncentral black hole, Shlosman et al (1990) argue that time-averaged\ngas production rate from Population II (aged stars) is $\\sim 10^{-5}\nM_{\\odot}$ per year per $10^6{\\rm M}_\\odot$ of stars. Once again this\nwould give an inadequate mass accretion rate to power Seyfert\nnuclei. However, there is increasing evidence in terms of the nuclei\nbeing chemically distinct stellar sub-systems (Sil'chenko, 1999;\nSil'chenko et al., 1999) and in terms of recent star formation (Genzel\net al., 1996; Ozernoy et al., 1997; Davidge et al 1997a,b) that the\npossibility of sporadic enhanced mass loss form stars in the nuclear\ncluster might be worth further investigation as a source of fuel for\nSeyfert nuclei.\n\n\n\\subsubsection{Capture of individual molecular clouds from the host\ngalaxy}\n\n\nAn alternative possibility is if the gas flow onto the nucleus comes\nfrom the capture and consumption of individual molecular clouds from\nthe host galaxy. Evidence from the center of our Galaxy in the form of\nyoung stars showing a rotation axis misaligned with the galactic\nplane(Genzel et al., 1996), demonstrates the possibility of gas\narriving in the neighborhood of a nucleus with misaligned angular\nmomentum. In this case the amount of star formation produced is about\nwhat one might expect from the arrival of a single molecular cloud. If\nthe ensemble of molecular clouds in a galaxy has a positional and\nvelocity distribution such that the scale-height of the cloud layer is\nlarger than the tidal radius of the clouds (typically about 100pc for\na black hole mass of $10^8 M_\\odot$) then just as in the case of stars\naccreting individually from a central star cluster (see above) the\nangular momenta of accreted clouds could point in fairly random\ndirections. Even so, it seems unlikely that the molecular cloud\ndistribution is completely unrelated to the galactic plane, and so in\nthis case too one might expect to see some relationship between disk\ndirection and galactic plane.\n\n\n\n\\section{Summary}\n\nIn this paper we presented the study of the relative angle between the\naccretion disk and the galaxy disk for active galaxies hosted by\nspirals (Seyferts), using a sample selected by a mostly isotropic\nproperty, the flux at 60$\\mu$m, and warm infrared colors.\nThis sample consists of 88 galaxies\n(29 Seyfert 1's and 59 Seyfert 2's), 33 of which show extended radio\nemission and are not in interacting systems (8 Seyfert 1's and 26\nSeyfert 2's). Our study used VLA 3.6cm data taken by us, archival VLA\ndata, ground based B and I images of the galaxy disks, as well as long\nslit spectroscopy. All the data were observed, reduced and analyzed in\na similar way, to ensure a homogeneous dataset and minimize, as much as\npossible, selection effects. For parts of the analysis we also used an\nenlarged sample, which includes the 33 galaxies from the 60$\\mu$m\nsample, plus 36 serendipitous Seyfert galaxies selected from the\nliterature, giving a total of 69 galaxies (20 Seyfert 1's and 50\nSeyfert 2's). Most of the data for the serendipitous sample was\nobtained from the literature and not measured homogeneously as for the\n60$\\mu$m sample.\n\nFor each galaxy we had a pair of measurements ($i$,$\\delta$), where $i$\nis the galaxy inclination relative to the line of sight and $\\delta$ is\nthe angle between the jet projected into the plane of the sky and the\nhost galaxy major axis. For some of the objects, we also had the\ninformation about which side of the galaxy is closer to Earth, obtained\nthrough the inspection of dust lanes or from the rotation curve,\nassuming that the spiral arms are trailing. This information was used\ntogether with a statistical technique developed by us, to determine the\ndistribution of angles $\\beta$, the angle between the jet and the host\ngalaxy rotation axis. This technique tests different\n$\\beta-$distributions in the range $\\beta_1\\leq\\beta\\leq\\beta_2$, to\ndetermine which range of parameters $\\beta_1$ and $\\beta_2$ produces\nthe most acceptable models.\n\nFrom the assumption that the of a homogeneous $\\sin\\beta$ distribution\nin the range $0^{\\circ}\\leq\\beta\\leq90^{\\circ}$ and not differentiating\nbetween Seyfert 1's and 2's, we showed that the observed data and the\nmodels agree at the 67\\% level for the 60$\\mu$m sample and 81\\% level\nfor the total sample (60$\\mu$m plus serendipitous sources). Using only\na polecap ($0^{\\circ}\\leq\\beta\\leq65^{\\circ}$) we showed that the model\nand 60$\\mu$m data agree at the 69\\% level, while for an equatorial ring\n($\\beta_1=\\beta_2=90^{\\circ}$) there is a bad agreement, only at the\n0.8\\% level. Using a more general model, we tested which range of\nvalues $\\beta_1$ and $\\beta_2$ (where $\\beta_1\\leq\\beta_2$) are\nacceptable. This showed that, independent of the sample (60$\\mu$m or\ntotal), $\\beta_2$ has to be larger than 65$^{\\circ}$-75$^{\\circ}$, and\nthe acceptability of the models does not depend strongly on this value,\nbut for $\\beta_1$ the agreement is better for values smaller than\n40$^{\\circ}$-50$^{\\circ}$. The addition of the information about which\nside of the galaxy is closer to Earth, and if the jet is projected\nagainst the near or the far side of the galaxy, shows that the\nacceptable parameter range does not change considerably, but the\nmaximum acceptability of the models was reduced. As discussed in\nSection 4.2, this result depends on the assumption that the dominant\njet lies above the galaxy plane (as seen from Earth). We plan to test\nthis hypothesis observing HI and free-free absorption against the weaker\nside of the radio jets.\n\nAn important result from our analysis appeared when we distinguished\nbetween Seyfert 1's and Seyfert 2's. The Seyfert 2's still have a good\nagreement with the models, and all the permitted $\\beta_1-\\beta_2$\nparameter space is accepted at the 2$\\sigma$ level or higher. However,\nwhen we consider only the Seyfert 1's, the agreement is poor, with the\nmaximum acceptability being only 7\\%. In order to solve this problem,\nwe introduced a viewing angle restriction to the models, which is, a\ngalaxy can only be recognized as a Seyfert 1 if the angle between the\njet and the line of sight $|\\phi|$ is smaller than a given angle\n$\\phi_c$. We chose $\\phi_c=40^{\\circ}$ based on information from the\nliterature, and show that this assumption increases the\nacceptability of the models. This is, to our knowledge, the first time\nit is shown in a general way, using a statistically significantsample,\nthat there is a difference in the viewing angle to the\ncentral engine of Seyfert 1's and Seyfert 2's, and is an independent\nconfirmation of the Unified Model.\n\n\nHowever, if we assume that all the Seyfert 2's have $|\\phi|>40^{\\circ}$\nwe find that NGC4388 would contradict this model, since the analysis of\nits data requires $|\\phi|\\leq21^{\\circ}$. We assumed, based on this and\nthe analysis of the $i-$distribution of the Seyfert 1's in our sample,\nthat a galaxy is only recognized as a Seyfert 1 if the jet is seen at\nan angle $|\\phi|\\leq\\phi_c$ and the host galaxy inclination is smaller\nthan $i\\leq i_c$, otherwise it is a Seyfert 2. Comparing the models\nconstructed assuming $\\phi_c=40^{\\circ}$ and $i_c=60^{\\circ}$ with the\nobserved data for the 60$\\mu$m sample, we see that all permitted regions\nof the parameter space is acceptable, with a preference for small\nvalues of $\\beta_1$ and large values of $\\beta_2$.\n\n\nAs we discussed in the introduction, the simplest assumption suggests\nthat the accretion disk is fed from gas in the galaxy disk, so we would\nexpect that both disks have the same angular momentum vector. Since\njets are supposed to be launched perpendicular to the accretion disk,\nthe expectation would be to see all the jets aligned with the minor\naxis. However, as shown above, this expectation is contradicted by our\nresults, which clearly shows that the observed distribution of $\\delta$\nand $i$ values can be represented by a homogeneous $\\beta-$distribution\nin the $0^{\\circ}\\leq\\beta\\leq90^{\\circ}$ range. We explored two main\nlines to explain the misalignment between the accretion disk axis and\nthe host galaxy disk axis: i) feeding of the accretion disk by aligned\ninflow from the galaxy disk, with the misalignment of the\naccretion disk; ii) feeding of the accretion disk by misaligned gas\ninflow. In the case of aligned inflow, the randomness of the\naccretion disks could be due to warping of the accretion disk by\nself-irradiation instability, warping by the Bardeen-Petterson effect,\nor warping by a misaligned gravitational potential of a nuclear star\ncluster surrounding the black hole. In the case of misaligned inflow,\nthe randomness of the jets could be due to misaligned minor mergers,\ncapture of individual stars or gas from the nuclear star cluster, or\nthe capture of individual molecular clouds from the host galaxy.\n\n\n\\acknowledgements\nJEP is grateful for continued support from the STScI visitor program.\nALK would like to thank IoA for support under its visitor program.\nALK, HRS and JEP would like to acknowledge the Isaac Newton Institute\nfor Mathematical Sciences for support during the programme ``The\nDynamics of Astrophysical Discs'', where this work started. HRS and ALK\nwould like to acknowledge the hospitality and help from the staff at\nCTIO, KPNO, VLA and Lick Observatory. We thank La Palma observatory for\nthe service observing of several galaxies in our sample. Alastair\nYoung, Marcella Carollo, Stefi Baum, Paul Hewett, Gerry Gilmore, Blaise\nCanzian and the referee, Andrew Wilson are gratefully acknowledged for\nuseful comments and discussions during the development of this paper.\nThis work was supported by NASA grants NAGW-3757, AR-5810.01-94A,\nAR-6389.01-94A and the HST Director Discretionary fund D0001.82223.\nThis research made use of the NASA/IPAC Extragalactic Database (NED),\nwhich is operated by the Jep Propulsion Laboratory, Caltech, under\ncontract with NASA. We also used the Digitized Sky Survey, which was\nproduced at the Space telescope Science Institute under U.S. Government\ngrant NAGW-2166. The National Radio Astronomy Observatory is a\nfacility of the National Science Foundation operated under cooperative\nagreement by Associated Universities, Inc.\n\n\\appendix\n\n\n\\section{Formulae for $P(\\delta \\mid \\beta_1, \\beta_2, i)$}\n\\label{formulae}\n\nWe consider a line of sight at an angle $i$ to the galactic pole and a\nmodel in which jets are uniformly distributed over the galactic hemisphere at galactic latitudes satisfying \n$\\beta_1 \\leq \\beta \\leq \\beta_2$. We wish to calculate for given values of $i$, $\\beta_1$, $\\beta_2$ the probability density function (p.d.f.) as a function\nof $\\delta$: we denote the fraction of jets with angles in the plane of the sky in the range $\\delta$ to $\\delta + d \\delta$ by \n$p(\\delta | i, \\beta_1, \\beta_2)d \\delta$. From this we can readily calculate the corresponding cumulative distribution function (c.d.f.):\n$$c (\\delta | i, \\beta_1,\\beta_2) = \\int^\\delta_0 \np(\\delta ' | i, \\beta_1,\\beta_2) d\\delta '\\ .\\eqno(A1)$$\nNote that any jet (viewed at given $i$) for which $\\delta$ is in the\nrange $\\delta$ to $\\delta + d\\delta$ is constrained to lie between a\npair of great circles (angular separation $d\\delta$) with pole at\n$\\beta = i$ (see Figure~\\ref{figNN}).\n\nWe here introduce the variable $\\Phi$ which, for a given great circle\n(defined by ($i,\\delta )$), measures the angular distance along the\ngreat circle from its pole. $\\Phi$ is related to $i,\\beta, \\delta$ via \n$$\\sin \\Phi = {\\cos \\beta \\sin \\delta \\sin i - \\left(\\sin^2 \\beta -\n\\sin^2 i \\cos^2 \\delta \\right) ^{1 \\over 2} \\cos i \\over\n1- \\sin^2 i \\cos^2 \\delta}\\eqno(A2)$$\n\nEach great circle has two intersections (at $\\Phi = \\Phi^a_1$ and $\\Phi\n= \\Phi^b_1$) with the line of latitude $\\beta = \\beta_1$, and\ncorrespondingly two intersections (at $\\Phi = \\Phi^a_2$ and $\\Phi =\n\\Phi^b_2$) with the line of latitude $\\beta = \\beta_2$. $\\Phi^a_1$,\n$\\Phi^b_1$, $\\Phi^a_2$ and $\\Phi^b_2$ are readily obtained from A2\nwith $\\beta$ set equal to $\\beta_1$ and $\\beta_2$ respectively.\n\nNote that, depending on the values of $i, \\beta_1, \\beta_2$ there may be a range\nof angles, $\\delta$, for which $p=0$. This means that jets\nwith such angles lie on great circles which do not intersect\nthe band of latitudes that are populated with jets in the model. In\ngeneral, for a line of latitude at $\\beta = b$, all great circles\nintersect this line if $i < b$, but if $i> b$ intersection occurs only\nfor\n$$\\delta > \\delta_b = \\cos^{-1} \n\\left({\\sin b \\over \\sin i}\\right)\\eqno(A3)$$\nWe denote the probability density of sources per unit solid angle on\nthe galactic sphere by $\\Sigma (\\beta , \\theta )$. Since a complete set\nof great circles (with $\\delta$ in the range 0 to ${\\pi \\over 2}$)\ncovers an area equal to half the galactic hemisphere, we normalize\n$\\Sigma$ such that $\\Sigma (\\beta,\\theta )d\\Omega$ is the fraction of sources\nin half of the galactic hemisphere that are contained in a solid angle\n$d\\Omega$ centered on $[\\beta, \\theta ]$. For a uniform band of jet\norientations between $\\beta = \\beta_1$ and $\\beta = \\beta_2$ we have\n\n\\begin{eqnarray*}\n\\Sigma ={1 \\over \\pi (\\cos \\beta_1 - \\cos \\beta_2)} & \\qquad(\\beta_1 < \\beta < \\beta_2)&\\cr\n= 0\\quad\\quad\\quad\\quad\\quad\\quad\\qquad&\\qquad{\\rm otherwise}&(A4)\\cr\n\\end{eqnarray*}\n\nThe fraction of jets, therefore, to be found in a small surface element\nlying between $\\Phi$ and $\\Phi+d\\Phi$, between the pair of great\ncircles with angles $\\delta$ and $\\delta + d\\delta$ is thus\n$\\Sigma \\sin \\Phi d \\Phi d\\delta$.\n\nTherefore the fraction of jets lying anywhere between this pair of\ngreat circles is $\\int \\Sigma \\sin \\Phi d \\Phi d \\delta$ so that\n$$p(\\delta | i, \\beta_1, \\beta_2) = \\int \\Sigma \\sin \\Phi d \\Phi\\eqno(A5)$$\n\nIn order to derive explicit forms for $p$, we distinguish 3 regimes:\n\ni) $i > \\beta_2$\n\nHere great circles fall in 3 categories: a) those that never intercept\nthe band of latitudes populated by jets; b) those that intercept the\npopulated band but not the empty polecap region; and c) those that\ntraverse both the populated band and the empty polecap. In these\ncases, $p$ is given respectively by:\n\\begin{eqnarray*}\np= 0\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad&\\left( {\\rm for}\\ \\delta < \\delta_{b_2}\\right)&(A6a)\\cr\np= \\Sigma \\left(\\cos \\Phi^a_2 - \\cos \\Phi^b_2\\right)\\qquad\\qquad\\qquad\\qquad&\\left({\\rm for}\\ \\delta_{b_2} < \\delta < \\delta_{b_1}\\right)&(A6b)\\cr\np= \\Sigma \\left(\\cos \\Phi^a_2 - \\cos \\Phi^b_2 - \\cos \\Phi^a_1 + \\cos \\Phi^b_1\\right)&\\left({\\rm for}\\ \\delta > \\delta_{b_1}\\right).&(A6c)\\cr\n\\end{eqnarray*}\nwhere $\\delta_{b_1}$ and $\\delta_{b_2}$ are the values of $\\delta_b$ (A3) for $b= \\beta_1$ and $b =\\beta_2$ respectively.\n\nSubstituting for $\\Phi^a_1, \\ \\Phi^b_1,\\ \\Phi^a_2,\\ \n\\Phi^b_2$ from (A2) we obtain\n\\begin{eqnarray*}\np=0\\quad\\quad\\quad\\quad\\quad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad&\\left(\\delta < \\delta_{b_2}\\right)&(A7a)\\cr\np= {2 \\sin \\delta \\sin i \\left(\\sin^2 \\beta_2 - \\sin^2 i \\cos^2 \\delta\\right)^{1 \\over 2} \\over\n\\pi \\left(\\cos \\beta_1 - \\cos \\beta_2\\right) \\left(1 - \\sin^2 i \\cos^2 \\delta \\right)}.\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad&\n\\left(\\delta_{b_2} < \\delta < \\delta_{b_1}\\right)&(A7b)\\cr\np= {2 \\sin \\delta \\sin i \\left(\\left(\\sin^2 \\beta_2 - \\sin^2 i \\cos^2 \\delta\\right)^{1 \\over 2} \n- \\left(\\sin^2 \\beta_1 - \\sin^2 i \\cos^2 \\delta\\right)^{1 \\over 2}\\right)\n\\over \\pi \\left(\\cos \\beta_1 - \\cos \\beta_2 \\right) \\left(1 - \\sin^2 i \\cos^2 \\delta \\right)}&\n\\left(\\delta > \\delta_{b_1}\\right)&(A7c)\\cr\n\\end{eqnarray*}\nThe corresponding cumulative distribution functions (A1) are then\n\\begin{eqnarray*}\nc=0\\quad\\quad\\quad\\quad\\quad\\quad\\quad\\quad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\n&\\left(\\delta < \\delta_{b_2} \\right)&(A8a)\\cr\nc={2 \\over \\pi (\\cos \\beta_1 - \\cos \\beta_2)}\n\\left[{\\pi \\over 2} - \\sin^{-1} \\left({\\cos \\delta \\over \\cos \\delta_{b_2}}\\right) - {1 \\over 2} \\cos \\beta_2 \\sin^{-1}\\Psi_2\\right]&\n\\left(\\delta_{b_2}< \\delta < \\delta_{b_1}\\right)&(A8b)\\cr\nc={2 \\over \\pi (\\cos \\beta_1 - \\cos \\beta_2)} \n\\left[\\sin^{-1} \n\\left({\\cos \\delta \\over \\cos \\delta_{b_1}}\\right) + {1 \\over 2} \n\\cos \\beta_1 \\sin^{-1} \\Psi_1\\right.\\qquad&&\\cr\n- \\sin^{-1} \n\\left.\\left({\\cos \\delta \\over \\cos \\delta_{b_2}}\\right) - {1 \\over 2}\n\\cos \\beta_2 \\sin^{-1} \\Psi_2\\right]\n&\\left(\\delta > \\delta_{b_1}\\right)&(A8c)\\cr\n\\end{eqnarray*}\n\nwhere\n$$\\Psi_2 = {2 \\cos \\beta_2 \\left({\\cos \\delta \\over \\cos \\delta_{b_2}}\\right) \n\\sqrt{1 -\\left({\\cos \\delta \\over \\cos \\delta_{b_2}}\\right)^2} \\over\n1- \\sin^2 i \\cos^2 \\delta}.\\eqno(A9a)$$\nand\n$$\\Psi_1 = {2 \\cos \\beta_1 \\left({\\cos \\delta \\over \\cos \\delta_{b_1}}\\right)\n\\sqrt{1 -\\left({\\cos \\delta \\over \\cos \\delta_{b_1}}\\right)^2} \\over\n1- \\sin^2 i \\cos^2 \\delta}.\\eqno(A9b)$$\nNote that $\\sin^{-1} \\Psi_1, \\\n\\sin^{-1} \\Psi_2$ are defined as monotonically increasing functions of\n$\\delta$ in the range 0 to $\\pi$.\n\nii) $\\beta_1 < \\beta < \\beta_2$\n\nHere the line of sight passes through the populated band of\nlatitudes. Recalling that all great circles intersect the line of\nlongitude $\\beta = \\beta_2$, but that only those with $\\delta >\n\\delta_{b_1}$ intersect the line $\\beta = \\beta_1$, we have\n\\begin{eqnarray*}\np=\\Sigma \\left(2 - \\left(\\cos \\Phi^a_2 + \\cos \\Phi^b_2\\right)\\right)\n\\quad\\qquad\\qquad\\qquad\\qquad&\\left(\\delta < \\delta_{b_1}\\right)&(A10a)\\cr\np= \\Sigma \\left(2-\\left(\\cos\\Phi^a_2 + \\cos \\Phi^b_2\\right) -\n\\left(\\cos \\Phi^a_1 - \\cos \\Phi^b_1 \\right)\\right)&\\left(\\delta > \\delta_{b_1}\\right)&(A10b)\\cr\n\\end{eqnarray*}\nwhich can be written\n$$p={2 \\over \\pi(\\cos \\beta_1 - \\cos \\beta_2)} \\left(1-{\\cos \\beta_2 \\cos i \\over\n\\left(1- \\sin^2 i \\cos^2 \\delta\\right)}\\right) \\quad\\left(\\delta < \\delta_{b_1}\\right)\\eqno(A11a)$$\n\n$$p = {2 \\over \\pi (\\cos \\beta_1 - \\cos \\beta_2)} \n\\left(1 - {\\left(\\cos \\beta_2 \\cos i + \\sin \\delta \\sin i \\left(\\sin^2 \\beta_1 -\n\\sin^2 i \\cos ^2 \\delta\\right)^{1 \\over 2}\\right)\\over\n1-\\sin^2 i \\cos^2 \\delta}\\right)\n\\quad \\left(\\delta > \\delta_{b_1}\\right)\\eqno(A11b)$$\nThe corresponding cumulative distributions are:\n$$c={2 \\over \\pi(\\cos \\beta_1 - \\cos \\beta_2)} \n\\left(\\delta - {1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi\\right) \n\\left(\\delta < \\delta_{b_1}\\right) \\eqno\n(A12a)$$\n$$c = {2 \\over \\pi (\\cos \\beta_1 - \\cos \\beta_2)}\n\\left(\\delta - {1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi - {\\pi \\over 2}\n+ \\sin^{-1} \\left({\\cos \\delta \\over \\cos \\delta_{b_1}}\\right)\n+ {1 \\over 2} \\cos \\beta_1 \\sin^{-1} \\Psi_1\\right)\n\\left(\\delta > \\delta_{b_1}\\right)\n\\eqno(A12b)$$\nwhere $\\Psi_1$ is given by (A9b) and \n$$\\Psi =\n{2 \\cos i \\sin \\delta \\cos \\delta \\over 1 - \\cos^2 \\delta \\sin^2 i}\n\\eqno(A13)$$\nAgain, both $\\sin^{-1} \\Psi_1$ and $\\sin^{-1} \\Psi$ are monotonically\nincreasing functions of $\\delta$ in the range $0$ to $\\pi$.\n\niii) $i < \\beta_1$\n\nIn this case, all great circles intercept both the lines\n$\\beta = \\beta_1$ and $\\beta = \\beta_2$. Here\n$$p = \\Sigma \\left(\\left(\\cos \\Phi_1^a + \\cos \\Phi^b_1\\right)\n-\\left(\\cos \\Phi^a_2 + \\cos \\Phi^b_2\\right)\\right)\n\\eqno(A14)\n$$\nwhich becomes\n$$p = {2 \\cos i \\over \\pi \\left(1-\\sin^2 i \\cos^2 \\delta\\right)}\n\\eqno(A15)\n$$\nso that\n$$c = {1 \\over \\pi} \\sin^{-1} \n\\left[{2 \\cos i \\cos \\delta \\sin \\delta \\over 1- \\sin^2 i \\cos^2 \\delta}\\right].\n\\eqno(A16)\n$$\nNote that in this regime (where the line of sight passes through the\nexcluded polecap), the probability density function is independent of\n$\\beta_1$ and $\\beta_2$.\n\n\\section{Formulae for $P(\\delta \\mid \\beta_1, \\beta_2, i)$ in the case\nwhen there is information about frontside and backside of the galaxy}\n\n We now derive corresponding expressions (see Appendix A for definitions)\nin the case that we know whether a galaxy is a `frontside' or `backside'\nsource (i.e. whether the jet lies on the short arc of the great circle,\nlength $|\\Phi_1|$, or the long arc, length $180 - |\\Phi_1|$).\nAs before, we distinguish three regimes:\n\ni) $i > \\beta_2$\n\nIn this case the `frontside' arc does not intercept the region populated \nby jets, so all such galaxies must be `backside' sources. The p.d.f. ($p$)\nand c.d.f. ($c$) for these `backside' sources are given by equations\n(A6) to (A9).\n\nii) $\\beta_1 < \\beta < \\beta_2$ \n\n We now denote the surface density of jets by\n$\\Sigma_f$ and $\\Sigma_b$ for regions of the galactic sphere intercepted\nby `frontside' and `backside' arcs respectively. We fix $\\Sigma_f$ and \n$\\Sigma_b$ by appropriate normalization below.\n\n For frontside sources:\n$$p=\\Sigma_f \\left(1 - \\cos \\Phi^a_2 \\right)$$\n\nwhich can be written\n\n$$p = \\Sigma_f \n\\left(1 - {\\left(\\cos \\beta_2 \\cos i + \\sin \\delta \\sin i \\left(\\sin^2 \\beta_2 -\n\\sin^2 i \\cos ^2 \\delta\\right)^{1 \\over 2}\\right)\\over\n1-\\sin^2 i \\cos^2 \\delta}\\right)\n\\eqno(B1)$$\n\nThe corresponding c.d.f. is given by:\n\n$$c = \\Sigma_f \n\\left(\\delta - {1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi \n+ \\sin^{-1} \\left({\\cos \\delta \\sin i \\over \\sin \\beta_2}\\right)\n+ {1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi_2\n- \\sin^{-1} \\left({ \\sin i \\over \\sin \\beta_2}\\right)\n- {1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi_2|_0 \\right)\n\\eqno(B2)$$\n\nwhere $\\Psi_2$ and $\\Psi$ are given by equations (A9) and (A13) and\n$\\Psi_2|_0$ is equal to $\\Psi_2$ evaluated at $\\delta = 0$. Note that\nas before, both $\\sin^{-1} \\Psi_2$ and $\\sin^{-1} \\Psi$ are equal to\n$\\pi$ when $\\delta=\\pi/2$, and are monotonically increasing functions\nof $\\delta$ for $\\delta$ in the range $0$ to $\\pi/2$. Normalising so that\n$c=1$ when $\\delta = \\pi/2$ we have\n\n$$ \\Sigma_f = {1 \\over {\\pi \\over 2} - \\sin^{-1} \\left({ \\sin i \\over \\sin \\beta_2}\\right)\n-{1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi_2|_0}\n\\eqno (B3)$$ \n\nFor `backside' sources, we need to distinguish between those great\ncircles (with $\\delta <$ and $> \\delta_{b_1}$) that do not and do\nrespectively cross the excluded polecap region: \n \n\\begin{eqnarray*}\np=\\Sigma_b \\left(1 - \\cos \\Phi^b_2\\right)\\quad\\qquad\\qquad\\qquad\\qquad&\n\\left(\\delta < \\delta_{b_1}\\right)&(B4a)\\cr\np= \\Sigma_b \\left(1- \\cos \\Phi^b_2 -\n\\left(\\cos \\Phi^a_1 - \\cos \\Phi^b_1 \\right)\\right)&\\left(\\delta > \\delta_{b_1}\\right)&(B4b)\\cr\n\\end{eqnarray*}\n\n which can be written\n \n$$p=\\Sigma_b\n\\left(1 - {\\left(\\cos \\beta_2 \\cos i - \\sin \\delta \\sin i \\left(\\sin^2 \\beta_2 -\n\\sin^2 i \\cos ^2 \\delta\\right)^{1 \\over 2}\\right)\\over\n1-\\sin^2 i \\cos^2 \\delta}\\right)\n\\quad \\left(\\delta < \\delta_{b_1}\\right)\n\\eqno(B5a)$$\n\n$$p = \\Sigma_b\n\\left(1 - {\\left(\\cos \\beta_2 \\cos i - \\sin \\delta \\sin i \\left(\\left(\\sin^2 \\beta_2 -\n\\sin^2 i \\cos ^2 \\delta\\right)^{1 \\over 2}-\n\\left(\\sin^2 \\beta_1 -\n\\sin^2 i \\cos ^2 \\delta\\right)^{1 \\over 2}\\right)\\right)\\over\n1-\\sin^2 i \\cos^2 \\delta}\\right)\n\\quad \\left(\\delta > \\delta_{b_1}\\right)\\eqno(B5b)$$\n\nThe corresponding c.d.f. are given by:\n\n\\begin{eqnarray*}\nc= &\\Sigma_b\n\\left[\\delta - {1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi\n- \\sin^{-1} \\left({\\cos \\delta \\sin i \\over \\sin \\beta_2}\\right)\\right.\\qquad\\qquad\\qquad\\quad&\\cr\n&- {1 \\over 2} \\left.\\cos \\beta_2 \\sin^{-1} \\Psi_2\n+ \\sin^{-1} \\left({ \\sin i \\over \\sin \\beta_2}\\right)\n+ {1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi_2|_0 \\right]&\n\\left(\\delta < \\delta_{b_1}\\right) ~~(B6a)\\cr\n\\end{eqnarray*}\n\n\\begin{eqnarray*}\nc = \\Sigma_b\n\\left[\\delta - \\pi - {1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi\n- \\sin^{-1} \\left({\\cos \\delta \\sin i \\over \\sin \\beta_2}\\right)\n- {1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi_2\n+ \\sin^{-1} \\left({ \\sin i \\over \\sin \\beta_2}\\right)\\right.&&\\cr\n+ {1 \\over 2} \\left.\\cos \\beta_2 \\sin^{-1} \\Psi_2|_0 \n+2 \\sin^{-1} \\left({\\cos \\delta \\sin i \\over \\sin \\beta_1}\\right)\n+\\cos \\beta_1 \\sin^{-1} \\Psi_1 \\right ]&\n\\quad \\left(\\delta > \\delta_{b_1}\\right)&\\cr\n&&(B6b)\\cr\n\\end{eqnarray*}\n\n Normalising so that $c=1$ for $\\delta = \\pi/2$ we have \n\n$$ \\Sigma_b = {1 \\over \\pi \\left(\\cos \\beta_1 - \\cos \\beta_2 \\right) -\n{\\pi \\over 2} + \\sin^{-1} \\left({ \\sin i \\over \\sin \\beta\n_2}\\right)\n+{1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi_2|_0}\n\\eqno (B7)$$\n\niii) $i < \\beta_1$\n\n For frontside galaxies:\n\n\n\n$$p=\\Sigma_f \\left(\\cos \\Phi^a_1 - \\cos \\Phi^a_2 \\right)$$\n\nwhich may be written:\n\n$$p = \\Sigma_f\n\\left({\\left(\\cos \\beta_1-\\cos \\beta_2\\right) \\cos i - \n\\sin \\delta \\sin i \\left(\\left(\\sin^2 \\beta_2\n-\\sin^2 i \\cos ^2 \\delta\\right)^{1 \\over 2}-\n\\left(\\sin^2 \\beta_1 -\n\\sin^2 i \\cos ^2 \\delta\\right)^{1 \\over 2}\\right)\\over\n1-\\sin^2 i \\cos^2 \\delta}\\right)\n\\eqno(B8)$$\n\nwith a corresponding cumulative distribution\n\n\\begin{eqnarray*}\nc = \\Sigma_f\n&\\left[{1 \\over 2} \\left(\\cos \\beta_1 - \\cos \\beta_2\\right) \\sin^{-1} \\Psi\n+ \\sin^{-1} \\left({\\cos \\delta \\sin i \\over \\sin \\beta_2}\\right)\n+ {1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi_2\n- \\sin^{-1} \\left({ \\sin i \\over \\sin \\beta_2}\\right)\\right.&\\cr\n&- {1 \\over 2} \\left.\\cos \\beta_2 \\sin^{-1} \\Psi_2|_0\n- \\sin^{-1} \\left({\\cos \\delta \\sin i \\over \\sin \\beta_1}\\right)\n- {1 \\over 2} \\cos \\beta_1 \\sin^{-1} \\Psi_1\n+ \\sin^{-1} \\left({ \\sin i \\over \\sin \\beta_1}\\right)\\right.&\\cr\n&+ {1 \\over 2} \\left.\\cos \\beta_1 \\sin^{-1} \\Psi_1|_0\n\\right ]&(B9)\\cr\n\\end{eqnarray*}\n\nAs before $\\sin^{-1} \\Psi$,$\\sin^{-1} \\Psi_2$ and $\\sin^{-1} \\Psi_1$\nare each equal to $\\pi$ for $\\delta={\\pi \\over 2}$ and are monotonocially\nincreasing functions of $\\delta$. $\\Psi_1|0$ is equal to $\\Psi_1$\nevaluated at $\\delta = 0$. Normalising so that $c=1$ for\n$\\delta={\\pi \\over 2}$:\n\n$$ \\Sigma_f = {1 \\over \n\\sin^{-1} \\left({ \\sin i \\over \\sin \\beta\n_1}\\right)\n-\\sin^{-1} \\left({ \\sin i \\over \\sin \\beta\n_2}\\right)\n+{1 \\over 2} \\cos \\beta_1 \\sin^{-1} \\Psi_1|_0\n-{1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi_2|_0}\n\\eqno (B10)$$\n\n \n\n For backside galaxies:\n\n\n\n$$p=\\Sigma_b \\left(\\cos \\Phi^b_1 - \\cos \\Phi^b_2 \\right)$$\n\nwhich may be written:\n\n$$p = \\Sigma_b\n\\left({\\left(\\cos \\beta_1-\\cos \\beta_2\\right) \\cos i +\n\\sin \\delta \\sin i \\left(\\left(\\sin^2 \\beta_2\n-\\sin^2 i \\cos ^2 \\delta\\right)^{1 \\over 2}-\n\\left(\\sin^2 \\beta_1 -\n\\sin^2 i \\cos ^2 \\delta\\right)^{1 \\over 2}\\right)\\over\n1-\\sin^2 i \\cos^2 \\delta}\\right)\n\\eqno(B11)$$\n\nwith a corresponding cumulative distribution\n\n\\begin{eqnarray*}\nc = \\Sigma_b\n&\\left[{1 \\over 2} \\left(\\cos \\beta_1 - \\cos \\beta_2\\right) \\sin^{-1} \\Psi\n- \\sin^{-1} \\left({\\cos \\delta \\sin i \\over \\sin \\beta_2}\\right)\n- {1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi_2\n+ \\sin^{-1} \\left({ \\sin i \\over \\sin \\beta_2}\\right)\\right.&\\cr\n&+ {1 \\over 2} \\left.\\cos \\beta_2 \\sin^{-1} \\Psi_2|_0\n+ \\sin^{-1} \\left({\\cos \\delta \\sin i \\over \\sin \\beta_1}\\right)\n+ {1 \\over 2} \\cos \\beta_1 \\sin^{-1} \\Psi_1\n- \\sin^{-1} \\left({ \\sin i \\over \\sin \\beta_1}\\right)\\right.&\\cr\n&- {1 \\over 2} \\left.\\cos \\beta_1 \\sin^{-1} \\Psi_1|_0\n\\right ]&(B12)\\cr\n\\end{eqnarray*}\n\nNormalisation ($c=1$ for $\\delta = {\\pi \\over 2}$) then yields:\n\n$$ \\Sigma_b = {1 \\over\n\\pi \\left(\\cos \\beta_1 - \\cos \\beta_2 \\right) -\\sin^{-1} \\left({ \\sin i \\over \\sin \\beta\n_1}\\right)\n+\\sin^{-1} \\left({ \\sin i \\over \\sin \\beta\n_2}\\right)\n-{1 \\over 2} \\cos \\beta_1 \\sin^{-1} \\Psi_1|_0\n+{1 \\over 2} \\cos \\beta_2 \\sin^{-1} \\Psi_2|_0}\n\\eqno (B13)$$\n\n\n\n\n\\begin{references}\n\nAntonucci, R. 1999, in High Energy Processes in Accreting Black Holes, ASP\nConference Series 161, ed. 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K. 1997, AR, 41, 734\n\n\\end{references}\n\n\\clearpage\n\n\\begin{figure}\n\\psfig{figure=f1.ps,width=12cm,height=12cm}\n\\caption{Histogram of 60$\\mu$m luminosities for the 60$\\mu$m sample.\nSeyfert 1's are represented by the solid line and Seyfert 2's by the dotted\nline.}\n\\label{fig1}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{figure=f2.ps,width=11cm,height=11cm}\n\\caption{The galaxy lies in the XY plane, with coordinates placed so\nthat the apparent major axis is the X axis and the galaxy axis is Z.\nThe line of sight Z$^{\\prime}$, designed by the vector ${\\bf k}_s$, is\nin the plane of the paper. The angle of inclination is $i$. The PA\nbetween the apparent major axis of the galaxy and the radio jet\nprojected onto the sky plane is $\\delta$. The radio jet, whose vector\nis given as ${\\bf k}_j$, is designated by an arrow. The angle between\nthe radio jet and the galaxy axis is $\\beta$. The angle between the\nline of sight and the radio axis, commonly referred to as the opening\nangle of the active galaxy, is $\\phi$. For an accretion disk\nperpendicular to the jet, $\\phi = \\pm i_{\\rm disk}$.}\n\\label{figNN}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{figure=f3a.ps,width=10cm,height=10cm}\n\\psfig{figure=f3b.ps,width=10cm,height=10cm}\n\\caption{a-top) Distribution of observed $\\delta$ and $i$ values for the\ntotal sample (serendipitous + 60$\\mu$m sources); b-bottom) 60$\\mu$m\nsample only. Seyfert 1's are represented by open squares and Seyfert 2's by\nfilled circles. The solid lines represent the contours of constant\n$\\beta_{min} = 10^{\\circ}, 30^{\\circ}, 50^{\\circ}$ and 70$^{\\circ}$,\nfrom bottom to top, respectively, calculated using\nEquation~\\ref{bmin}.}\n\\label{figAA}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{figure=f4a.ps,width=10cm,height=10cm}\n\\psfig{figure=f4b.ps,width=10cm,height=10cm}\n\\caption{Same as Figure~\\ref{figAA} for; a-top) the total sample; b-bottom) the\n60$\\mu$m sample. The solid lines represent the quartiles\n(indicated beside the lines) calculated assuming a uniform\n$\\beta-$distribution from $\\beta_1=0^{\\circ}$ to $\\beta_2=90^{\\circ}$\nand not differentiating between Seyfert 1's and Seyfert 2's. The KS test\nshows that the total sample is consistent with the homogeneous distribution\nmodel at the 81\\% level, while the agreement is at the 67\\% level for the\n60$\\mu$m sample.}\n\\label{figAA2}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{figure=f5.ps,width=10cm,height=10cm}\n\\caption{The observed $\\delta$ and $i$ values of the 60$\\mu$m sample\ncompared with the quartiles (solid lines) calculated assuming a uniform\npolecap $\\beta-$distribution, from $\\beta_1=0^{\\circ}$ to\n$\\beta_2=65^{\\circ}$ and not differentiating between Seyfert 1'a and\nSeyfert 2's. The hatched area corresponds to the parameter space\nexcluded by the models. Symbols as in Figure~\\ref{figAA}. The KS test\nindicates that the data are consistent with the model at the 69\\%\nlevel.}\n\\label{figB}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{figure=f6.ps,width=10cm,height=10cm}\n\\caption{The observed $\\delta$ and $i$ values of the 60$\\mu$m sample\ncompared with the quartiles (solid lines) calculated assuming the jets\nare in an equatorial ring, $\\beta_1=\\beta_2=90^{\\circ}$, and not \ndifferentiating between Seyfert 1's and Seyfert 2's. The KS test shows that\nthe data are consistent with the model only at the 0.8\\% level.\nSymbols as in Figure~\\ref{figAA}.}\n\\label{figC}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{figure=f7a.ps,width=10cm,height=10cm}\n\\psfig{figure=f7b.ps,width=10cm,height=10cm}\n\\caption{Probability contours obtained applying the KS test to the\nmodels of uniformly distributed jets over the band\n$\\beta_1\\leq\\beta\\leq\\beta_2$, where $\\beta_1\\leq\\beta_2$, and not\ndistinguishing between Seyfert 1's and 2's. a-top) total sample, and\nb-bottom) the 60$\\mu$m sample in the.}\n\\label{figD}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{figure=f8.ps,width=10cm,height=10cm}\n\\caption{Same as Figure~\\ref{figD} for the 60$\\mu$m sample only, but using\nthe information about near and far side of the galaxy. The acceptability\nlevel of the models is reduced in comparison to Figure~\\ref{figD}b.}\n\\label{figH}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{figure=f9a.ps,width=10cm,height=10cm}\n\\psfig{figure=f9b.ps,width=10cm,height=10cm}\n\\caption{Same as Figure~\\ref{figH} but: a-top) distinguishing between\nSeyfert 2's, and b-bottom) Seyfert 1's. Almost all the permitted parameter\nspace region is accepted for Seyfert 2's, but the maximum acceptability\nis only 7\\% for Seyfert 1's.}\n\\label{figI}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{figure=f10.ps,width=10cm,height=10cm}\n\\caption{Same as Figure~\\ref{figI}b, only the Seyfert 1's, but imposing\na viewing restriction. That is, a galaxy is only recognized as a\nSeyfert 1 if the angle between the jet and the line of sight ($\\phi$)\nis smaller than a given value $\\phi_c$, which we assumed to be equal to\n40$^{\\circ}$.}\n\\label{figK}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{figure=f11.ps,width=10cm,height=10cm}\n\\caption{Same as Figure~\\ref{figH}, using both Seyfert 1's and 2's.\nHere we impose that the galaxy is only recognized as a Seyfert 1 if\n$|\\phi|<\\phi_c$ and if the host galaxy has a smal inclination $i<i_c$,\notherwise the galaxy is classified as a Seyfert 2. We used\n$\\phi_c=40^{\\circ}$ and $i_c=60^{\\circ}$.}\n\\label{figG}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{figure=f12.ps,width=10cm,height=10cm}\n\\caption{The $\\beta-$distribution obtained making the extreme assumption\nthat all galaxies in the 60$\\mu$m sample have phi=90.}\n\\label{figZ}\n\\end{figure}\n\n\\end{document}\n\n\n\n"
},
{
"name": "tables.tex",
"string": "\\makeatletter\n\\def\\jnl@ap{AJ}\n\\ifx\\revtex@jnl@aj\\let\\tablebreak=\\fi\n\\makeatother\n\\documentstyle[art8,aj_pt4]{article}\n\\hsize=25cm\n\\hoffset=-3.0cm\n%\\nlines 70 \n \n\\begin{document}\n \n%\\ptlandscape\n \n\\small\n \n\\begin{deluxetable}{rlrrrrrrl}\n\\tablewidth{0pc}\n\\tablecaption{60$\\mu$m Sample Properties}\n\\tablehead{\\colhead{Number}&\\colhead{Name}&\\colhead{Type}&\\colhead{V$_{rad}$}&\n\\colhead{L$_{60\\mu m}$}&\\colhead{F$_{3.6cm}$}&\\colhead{L$_{3.6cm}$}&\n\\colhead{Radio Extent}&\\colhead{Comments}\\cr\n& & &(km~s$^{-1}$)&(erg s$^{-1}$)&(mJy)&(W~Hz$^{-1}$)&at 3.6cm (pc)&}\n\\startdata\n16&MRK\\,348 \t&2&\t4540&\t43.52& 345.6& 23.18&\t33&\t\\cr\n24&TOL\\,0109-38 \t&2&\t3496&\t43.38& 13.1& 21.53&\t330&\t\\cr\t\n26&MRK\\,1 \t \t&2&\t4780&\t43.81& 11.1& 21.73&\t31&\tu\\cr\n27&MRK\\,359 \t&1&\t5012&\t43.37& 0.5 & 20.43&\t170&\t\\cr\n33&MRK\\,573 \t&2&\t5174&\t43.56& 1.8 & 21.01&\t1003&\t\\cr\t\n37&IRAS\\,01475-0740 \t&2&\t5306&\t43.54& 135.4& 22.91&\t34&\tu\\cr\n41&ESO\\,153-G20\t \t&2&\t5917&\t43.52& --- & ---&\t---&\t\\cr\n47&MRK\\,1040 \t \t&1&\t4927&\t43.88& 1.1 & 20.76&\t32&\tu\\cr\n52&ESO\\,355-G25 \t&2&\t5039&\t43.59& --- & ---&\t---&\t\\cr\n53&UGC\\,2024 \t \t&2&\t6714&\t44.12& 0.7 & 20.83&\t43&\tu\\cr\n57&NGC\\,1068 \t&2&\t1136& \t44.41& 762.4& 22.32&\t745&\t\\cr\t\n67&MCG\\,-02-08-039 \t&2&\t8874&\t43.69& 2.0 & 21.53&\t57&\tu\\cr\n68&UGC\\,2514 \t&1&\t3957&\t43.11& 0.6 & 20.30&\t69&\t\\cr\n75&IRAS\\,03106-0254 \t&2&\t8154&\t43.89& 10.8 & 22.18&\t854&\t\\cr\n78&IRAS\\,03125+0119 \t&2&\t7200&\t43.67& 8.8 & 21.99&\t47&\tu\\cr\n83&MRK\\,607 \t \t&2&\t2716&\t43.27& 1.3 & 20.31&\t20&\tu\\cr\n85&ESO\\,116-G18 \t&2&\t5546&\t43.64& --- & ---&\t---&\t\\cr\n141&IRAS\\,04385-0828 \t&2&\t4527&\t43.81& 7.5 & 21.52&\t29&\tu\\cr\n154&IRAS\\,04502-0254 \t&2&\t4737&\t43.34& 0.4 & 20.28&\t107&\t\\cr\n156&IRAS\\,04507+0358 \t&2&\t8811&\t43.74& 0.8 & 21.12&\t205&\t\\cr\n157&ESO\\,33-G02 \t&2&\t5426&\t43.34& --- & ---&\t---&\t\\cr\n174&MCG\\,-05-13-017 \t&1&\t3790&\t43.31& 2.5 & 20.88&\t24&\tu\\cr\n196&MRK\\,3 \t&2&\t4050&\t43.85& 79.0& 22.44&\t375&\t\\cr\n203&UGC\\,3478 \t&1&\t3828&\t43.38& 1.4 & 20.64&\t25&\tu\\cr\n209&MRK\\,6 \t&1&\t5537&\t43.63& 30.0& 22.29&\t437&\t\\cr\n213&FAIRALL\\,265 \t&1&\t8844&\t43.81& --- & ---&\t---&\t\\cr\n225&MRK\\,79 \t&1&\t6652&\t43.85& 2.9 & 21.44&\t1255&\t\\cr\t\n227&MRK\\,10\t \t&1&\t8785&\t43.85& 0.3 & 20.69&\t57&\tu\\cr\n233&UGC\\,4155\t \t&1&\t7645&\t43.83& 2.4 & 21.48&\t49&\tu\\cr\n236&MRK\\,622 \t&2&\t6964&\t43.85& 1.7 & 21.24&\t110&\t\\cr\t\n244&ESO\\,18-G09\t \t&2&\t5341&\t43.60& --- & ---&\t---&\t\\cr\n253&MCG\\,-01-24-012 \t&2&\t5892&\t43.41& 8.9 & 21.82&\t133&\t\\cr\n260&MRK\\,1239 \t \t&1&\t5974&\t43.73& 7.9 & 21.78&\t53&\tu\\cr\n272&NGC\\,3393 \t&2&\t4107&\t43.50& 10.7& 21.59&\t683&\t\\cr\n278&NGC\\,3516 \t&1&\t2649&\t43.15& 4.1 & 20.79&\t18&\t\\cr\n281&IRAS\\,11215-2806 \t&2&\t4047&\t43.01& 10.8& 21.58&\t403&\t\\cr\n282&MCG\\,-05-27-013 \t&2&\t7162&\t43.53& 4.7 & 21.71&\t1530&\t\\cr\n283&MRK\\,176 \t&2&\t8346&\t43.69& 6.3 & 21.97&\t135& interacting \\cr\n286&NGC\\,3783\t \t&1&\t2550&\t43.42& 7.7 & 21.03&\t17&\tu\\cr\n292&MRK\\,766 \t&1&\t3876&\t43.79& 8.6 & 21.44&\t67&\t\\cr\n293&NGC\\,4388 \t&2&\t2524& \t43.84& 9.4 & 21.11&\t2940&\t\\cr\n299&NGC\\,4507\t \t&2&\t3538&\t43.73& --- & ---&\t---&\t\\cr\n301&NGC\\,4593 \t&1&\t2698&\t43.23& 2.1 & 20.51&\t17&\tu\\cr\n302&TOL\\,1238-364 \t&2&\t3285&\t43.87& --- & ---&\t---&\t\\cr\n306&NGC\\,4704 \t&2&\t8134&\t44.09& 0.8 & 21.05&\t53&\tu\\cr\n309&MCG\\,-02-33-034 \t&1&\t4386&\t43.35& 1.2 & 20.69& \t28&u interacting\\cr\n310&ESO\\,323-G32 \t&2&\t4796&\t43.34& --- & ---&\t---&\t\\cr\n313&MCG\\,-04-31-030 \t&2&\t2957&\t43.34& 6.5 & 21.08&\t478&\t\\cr\n314&IRAS\\,13059-2407 \t&2&\t4175&\t43.42& 10.4& 21.59&\t27&\tu\\cr\n317&MCG\\,-03-34-064 \t&2&\t5152&\t44.16& 54.1& 22.49&\t278&\t\\cr\n322&ESO\\,383-G18 \t&2&\t3837&\t43.01& 1.7 & 20.73&\t107&\t\\cr\n324&MCG\\,-6-30-15 \t&1&\t2323&\t42.77& 0.9 & 20.01&\t110&\tu\\cr\n329&NGC\\,5347\t \t&2&\t2335&\t42.96& 1.6 & 20.27&\t15&\tu\\cr\n340&IRAS\\,14082+1347 \t&2&\t4836&\t43.96& 3.2 & 21.2&\t53&\t\\cr\n341&NGC\\,5506 \t&2&\t1753&\t43.47& 95.0& 21.79&\t302&\t\\cr\n344&NGC\\,5548 \t&1&\t5149&\t43.48& 3.1 & 21.24&\t44&interacting\\cr\n349&IRAS\\,14317-3237 \t&2&\t7615&\t43.76& 1.9 & 21.37&\t286&\t\\cr\n354&IRAS\\,14434+2714 \t&2&\t8814&\t43.81& 8.8 & 22.16&\t120&\tu\\cr\n369&UGC\\,9826 \t \t&1&\t8754&\t43.59& 0.2 & 20.51&\t57&\tu\\cr\n377&UGC\\,9944 \t&2&\t7354&\t43.91& 5.9 & 21.83&\t3430&\t\\cr\n383&IRAS\\,15480-0344 \t&2&\t9084&\t44.02& 11.2& 22.29&\t59&\tu\\cr\n409&IRAS\\,16288+3929 \t&2&\t9091&\t43.78& 4.8 & 21.93&\t59&\tu\\cr\n418&IRAS\\,16382-0613 \t&2&\t8317&\t43.81& 2.1 & 21.49&\t54&\tu\\cr\n445&UGC\\,10889\t \t&2&\t8424&\t43.72& 1.1 & 21.22&\t54&\tu\\cr\n447&MCG\\,+03-45-003 \t&2&\t7292&\t43.60& 0.3 & 20.53&\t47&\tu\\cr\n471&FAIRALL\\,49\t \t&2&\t6065&\t44.09& --- & ---&\t---&\t\\cr\n473&FAIRALL\\,51\t \t&1&\t4255&\t43.56& --- & ---&\t---&\t\\cr\n497&ESO\\,143-G09\t&1&\t4462&\t43.33& --- & ---&\t---&\t\\cr\n501&FAIRALL\\,341\t&2&\t4887&\t43.32& --- & ---&\t---&\t\\cr\n510&UGC\\,11630\t \t&2&\t3657&\t43.25& 0.4 & 20.06&\t24&\tu\\tablebreak\n512&PKS\\,2048-57 \t&2&\t3402&\t43.84& 229.1& 22.75&\t924&\t\\cr\n530&NGC\\,7213\t \t&1&\t1792&\t42.93& 187.9& 22.11&\t12&\tu\\cr\n537&MRK\\,915\t \t&1&\t7230&\t43.48& 14.7 & 22.21&\t47&\tu\\cr\n538&UGC\\,12138\t \t&1&\t7375&\t43.72& 1.9 & 21.34&\t81&\tu\\cr\n540&AKN\\,564 \t&1&\t7195&\t43.67& 7.0 & 21.89&\t316&\t\\cr\n549&UGC\\,12348\t \t&2&\t7585&\t43.97& 1.1 & 21.13&\t118&\tu\\cr\n555&NGC\\,7674 \t&2&\t8713&\t44.64& 39.8 & 22.81&\t422&\t\\cr\n590&MRK\\,590\t \t&1&\t7910&\t43.49& 3.2 & 21.63&\t51&\tu\\cr\n594&MRK\\,1058\t \t&2&\t5138&\t43.19& 0.2 & 20.05&\t33&\tu\\cr\n602&NGC\\,1386 \t&2&\t868&\t42.61& 10.8 & 20.24&\t20&\t\\cr\n615&MCG\\,+8-11-11 \t&1&\t6141&\t44.06& 24.4 & 22.29&\t1230&\t\\cr\n627&MRK\\,705\t \t&1&\t8658&\t43.65& 2.0 & 21.50&\t56&\tu\\cr\n634&NGC\\,3281\t \t&2&\t3200&\t43.85& 17.0 & 21.57&\t60&\t\\cr\n638&UGC\\,6100\t \t&2&\t8778&\t43.65& 0.8 & 21.12&\t57&\tu\\cr\n665&NGC\\,4941 \t&2&\t1108&\t42.26& 4.0 & 20.02&\t15&\t\\cr\n703&UGC\\,10683B \t&1&\t9234&\t43.61& 0.6 & 21.04& \t60&u interacting\\cr\n708&ESO\\,103-G35\t&2&\t3983&\t43.57& --- & ---&\t---&\t\\cr\n721&NGC\\,7212 \t&2&\t7984&\t44.27& 18.1 & 22.39& \t361&interacting\\cr\n\\tablenotetext{}{In the cases where the radio emission was not extended\nwe assumed an upper limit of 0.1$^{\\prime\\prime}$. These cases are indicated by\na letter ``u'' in the last column.}\n\\enddata\n\\end{deluxetable}\n \n\\clearpage\n\\newpage\n\n\n\\begin{deluxetable}{lcrrrlllc}\n\\tablewidth{0pc}\n\\tablecaption{Measurements for galaxies with extended radio emission\nin the 60$\\mu$m sample}\n\\tablehead{\\colhead{Name}&\\colhead{Type}&\\colhead{PA$_{MA}$}&\n\\colhead{i}&\\colhead{PA$_{RAD}$}&\\colhead{closer}&\n\\colhead{source}&\\colhead{Radio}&\\colhead{references/}\\cr\n&&&&&side&side&Morphology&comments}\n\\startdata\nMRK\\,348 &2 & 170 & 16 & -15 & e & rot & L &1, 9 \\cr\nTOL\\,0109-38 &2 & 61 & 64 & 96 & s & dust & S &2, 5 \\cr\nMRK\\,359 &1 & 8 & 34 & 75 & - & - & S &2, 5 \\cr\nMRK\\,573 &2 & 5 & 30 & 125 & n & rot & L &3, 5 \\cr\nNGC\\,1068 &2 & 115 & 28 & 0 & s & rot & L &4, 10 \\cr \nUGC\\,2514 &1 & -40 & 55 & 56 & sw & dust & L &5, 5 \\cr\nIRAS\\,03106-0254&2 & -14 & 71 & 37 & - & - & L &5, 5 \\cr \nIRAS\\,04502-0317&2 & 15 & 59 & 22 & e & dust & L &5, 5 \\cr \nIRAS\\,04507+0358&2 & 46 & 36 & 153 & - & - & S &5, 5 \\cr\nMRK\\,3 &2 & 28 & 33 & 86 & - & - & L &3, 5 \\cr\nMRK\\,6 &1 & -46 & 54 & -3 & ne & dust & L &5, 5 \\cr\nMRK\\,79 &1 & -47 & 36 & 11 & e & rot & L &5, 5 \\cr\nMRK\\,622 &2 & -35 & 26 & 0 & - & - & S &2, 5 \\cr\nMGC\\,-01-24-012 &2 & 42 & 54 & 89 & nw & rot & L &5, 5 \\cr\nNGC\\,3393 &2 & 41 & 30 & 56 & nw & rot & L &5, 5 \\cr\nNGC\\,3516 &1 & 56 & 36 & 10 & n & dust & L &2, 5 \\cr\nIRAS\\,11215-2806&2 & -34 & 70 & 75 & - & - & L &5, 5 \\cr\nMGC\\,-05-27-013 &2 & -82 & 69 & 2 & s & dust & L &5, 5 \\cr\nMRK\\,766 &1 & 67 & 31 & 32 & - & - & S &2, 5\\cr\nNGC\\,4388 &2 & -89 & 70 & 21 & n & dust & L &2, 5 \\cr\nMGC\\,-04-31-030 &2 & 58 & 62 & 84 & n & dust & L &5, 5 \\cr\nMGC\\,-03-34-064 &2 & 48 & 46 & 39 & - & - & L &5, 5 \\cr\nESO\\,383-g18 &2 & 88 & 63 & 178 & - & - & S &5, 5\\cr\nIRAS\\,14082+1347&2 & -85 & 47 & 99 & n & dust & S &5, 5 \\cr\nNGC\\,5506 &2 & -89 & 76 & 70 & s & dust & L &5, 5 \\cr\nIRAS\\,14317-3237&2 & 3 & 41 & 169 & - & - & L &5, 5\\cr\nUGC\\,9944 &2 & -7 & 71 & 67 & w & rot & L &5, 5 \\cr\nPKS\\,2048-57 &2 & -60 & 32 & -65 & sw & dust & L &6, 5 \\cr\nAKN\\,564 &1 & -73 & 37 & 6 & - & - & L &5, 5 \\cr\nNGC\\,7674 &2 & -26 & 43 & 117 & sw & rot & L &7, 5 \\cr\nNGC\\,1386 &2 & 25 & 68 & 170 & nw & dust & S &2, 5 \\cr\nMGC\\,+8-11-11 &1 & 33 & 16 & 128 & - & - & L &5, 11 \\cr\nNGC\\,4941 &2 & 17 & 61 & -25 & e & rot & L &5, 5\\cr\nMRK\\,176 &2 & 59 & 70 & 92 & - & - & S &5, 5 interact\\cr\nNGC\\,5548 &1 & -80 & 33 & 168 & - & - & L &2, 5 interact\\cr\nNGC\\,7212 &2 & -- & -- & -7 & -- & -- & L &8, - interact\\cr\n\\tablenotetext{}{Column 7 indicates the kind of measurement used to\ndetermine the closer side of the galaxy: dust lane (dust) or rotation\ncurve (rot). Column 8 shows the morphology of the extended radio emission,\nL (linear), S (slightly resolved), D(difuse).\nColumn 9 shows the references from which we obtained the\nvalues of PA$_{RAD}$ and PA$_{MA}$, respectively. The galaxies\nMRK\\,176, NGC\\,5548 and NGC\\,7212 are show in this table because they\nhave extended radio emission, but they are not used in the analysis,\nbecause they are interacting systems. Sources of radio data (PA$_{RAD}$):\n(1) Ulvestad et al. (1999);\n(2) Nagar et al. (1999);\n(3) Ulvestad \\& Wilson (1984)b;\n(4) Gallimore, Baum \\& O'Dea (1996);\n(5) our measurements;\n(6) Morganti et al. (1999);\n(7) Kukula et al. (1995);\n(8) Falcke, Wilson \\& Sipmson (1998);\nSources of optical data (PA$_{MA}$, i):\n(9) Simkin et al. (1987);\n(10) Brinks \\& Mundell (1996);\n(11) Canzian (1998).\n}\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\\newpage\n\n\\begin{deluxetable}{lcrrrllcl}\n\\tablewidth{0pc}\n\\tablecaption{Measurements for galaxies in the serendipitous sample}\n\\tablehead{\\colhead{Name}&\\colhead{Type}&\\colhead{PA$_{MA}$}&\n\\colhead{ellipticity}&\\colhead{PA$_{RAD}$}&\\colhead{closer}&\n\\colhead{source}&\\colhead{Radio}&\\colhead{references}\\cr\n&&&&&side&side&Morphology&}\n\\startdata\nngc513 & 2 & 69 & 55 & 167 & - & - & S+D &1,13\\cr\nngc591 & 2 & 5 & 33 & -28 & - & - & S &2,13\\cr\nmrk1066 & 2 & 90 & 54 & 134 & sw & dust& L &2,15\\cr\nngc1365 & 1 & 42 & 45 & 125 & nw & rot & S &3,16\\cr\nmrk618 & 1 & 80 & 39 & 146 & s & rot & S &4,13\\cr\neso362-g8 & 2 & -15 & 63 & 165 & - & - & L &1,14\\cr\nngc2110 & 2 & 161 & 42 & 10 & w & rot & L &1,17\\cr\nngc2273 & 2 & 62 & 50 & 96 & - & - & L &1,14\\cr\neso428-g14& 2 & -44 & 49 & 129 & ne & rot & L &2,14\\cr\nmrk78 & 2 & 84 & 56 & 90 & - & - & L &5,14\\cr\nngc2622 & 2 & 52 & 48 & 155 & - & - & S &6,14\\cr\nngc2639 & 2 & -43 & 53 & 100 & ne & dust& L &7,14\\cr\nngc3227 & 1 & 158 & 54 & 173 & e & rot & S &8,18\\cr\nmrk34 & 2 & 65 & 30 & 158 & - & - & L &5,14\\cr\nngc4051 & 1 & 132 & 39 & 81 & sw & rot & L+D &5,19\\cr\nngc4117 & 2 & 18 & 60 & 177 & e & dust& L &1,15\\cr\nngc4151 & 1 & 26 & 21 & 77 & e & rot & L &8,20\\cr\neso323-g77& 1 & 155 & 60 & 35 & ne & dust& L &1,15\\cr\nngc5135 & 2 & 15 & 34 & 25 & w & rot & A &7,14\\cr\nngc5252 & 2 & 15 & 59 & -10 & - & - & L &8,14\\cr\nmrk268 & 2 & -67 & 54 & 70 & - & - & S &5,14\\cr\nmrk270 & 2 & -60 & 30 & 48 & s & dust& L &5,14\\cr\nngc5273 & 1 & 11 & 32 & 5 & w & dust& S &1,14\\cr\nic4329a & 1 & 44 & 58 & 97 & se & dust& L &1,14\\cr\nmrk279 & 1 & 33 & 57 & 90 & - & - & S &4,14\\cr\nngc5643 & 2 & 136 & 23 & 87 & sw & rot & L &9,9\\cr\nngc5728 & 2 & 2 & 51 & 127 & e & rot & L &10,10\\cr\nmrk509 & 1 & 75 & 35 & 110 & - & - & S &4,13\\cr\nngc7172 & 2 & 100 & 56 & 90 & n & dust& S &11,15\\cr\nic5169 & 2 & 24 & 72 & 16 & - & - & L &1,13\\cr\nngc7450 & 1 & 25 & 47 & 100 & - & - & L &5,14\\cr\nngc7465 & 2 & -19 & 44 & 32 & - & - & S &1,13\\cr\nmrk926 & 1 & -88 & 38 & 90 & - & - & S &4,13\\cr\nngc7672 & 2 & 28 & 39 & 95 & - & - & L &7,14\\cr\nngc7743 & 2 & 86 & 38 & 21 & - & - & S &1,13\\cr\neso137-g34& 2 & -48 & 40 & -60 & - & - & S &12,13\\cr\n\\tablenotetext{}{Column 7 indicates the kind of measurement used to\ndetermine the closer side of the galaxy: dust lane (dust) or rotation\ncurve (rot). Column 8 shows the morphology of the\nextended radio emission, L (linear), S (slightly resolved), D (difuse)\nand A (amorphous). Column 9 gives the references\nfrom which we obtained PA$_{RAD}$ and PA$_{MA}$, respectively.\nSources of PA$_{RAD}$:\n(1) Nagar et al. 1999;\n(2) Bower et al. 1995;\n(3) Sandqvist, Joersaeter \\& Lindblad 1995;\n(4) Ulvestad \\& Wilson 1984a;\n(5) Ulvestad \\& Wilson 1984b;\n(6) Ulvestad 1986;\n(7) Ulvestad \\& Wilson 1989;\n(8) Kukula et al. 1995;\n(9) Morris et al. 1985;\n(10) Schommer et al. 1988;\n(11) Unger et al. 1987;\n(12) Morganti et al. 1999;\nSources of PA$_{MA}$:\n(13) Our measurements on DSS images;\n(14) Our measurements on our images;\n(15) RC3;\n(16) Ondrechen \\&van der Hulst 1989;\n(17) Wilson \\& Baldwin 1985;\n(18) Mundell et al. 1995;\n(19) Lizst \\& Dickey 1995;\n(20) Simkin 1975.}\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\\newpage\n\n\\begin{deluxetable}{lll}\n\\tablewidth{0pc}\n\\tablecaption{Definition of the angles used in the models}\n\\tablehead{\\colhead{Angle}&\\colhead{Definition}&\\colhead{Allowed Range}}\n\\startdata\n$\\beta$&angle between the radio jet and the galaxy disk axis& 0$^{\\circ} - 90^{\\circ}$\\cr\n$\\phi$ &angle between the radio jet and line of sight& $-180^{\\circ} - 180^{\\circ}$\\cr\n$\\delta$&difference between the PA of the radio jet and the PA of the galaxy major axis& 0$^{\\circ} - 90^{\\circ}$\\cr\n$i$ & inclination of the galaxy relative to the line of sight& 0$^{\\circ} - 90^{\\circ}$\\cr\n$\\theta$& azimuthal angle of the radio jet& 0$^{\\circ} - 360^{\\circ}$\\cr\n$\\beta_{min}$& minimum value $\\beta$ can have, for a given pair ($i$,$\\delta$)&---\\cr\n$\\beta_1$& minimum value $\\beta$ can have in the models &$<\\beta_2$\\cr\n$\\beta_2$& maximum value $\\beta$ can have in the models &$>$sup$\\beta_{min}$$^a$\\cr\n$\\phi_c$ & maximum value of $\\phi$ for a galaxy to be recognized as a Seyfert 1&---\\cr\n$i_c$ & maximum value of $i$ for a galaxy to be recognized as a Seyfert 1&---\\cr\n\\tablenotetext{a}{sup$\\beta_{min}$ is the largest value of $\\beta_{min}$ among the galaxies\nin the sample.}\n\\enddata\n\\end{deluxetable}\n\n\n\\end{document}\n\\end\n"
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"name": "astro-ph0002131.extracted_bib",
"string": "\\bibitem\n% command in the reference list below.\n%\n% Please see the AASTeX manual for a more complete discussion on how to make\n% Figure~\\ref-\n\\bibitem work for you. \n\n\\section{Introduction}\n\nWe would expect, based on grounds of symmetry and simplicity, that the\njets emanating from a Seyfert nucleus would emerge at right angles to\nthe disk of the host spiral galaxy. The processes for bringing material\nclose to the core (within the innermost 10pc) of a galaxy, either for\nthe initial formation of the black hole or to provide fuel to the black\nhole, are of two sorts -- those that feed the nucleus from the visible\ngas reservoir in the galaxy disk, and those that feed the nucleus by\nintroducing material from outside the galaxy. In the simplest pictures,\nfueling by both internal gas and by external gas favors co-alignment\nbetween accretion disk and galaxy disk, since most of the gas is in the\ngalaxy disk and any gas added to it may rapidly end up there, either by\nshocks or by settling in the galaxy potential. Since the jets are\nlaunched perpendicular to the accretion disk, the simplest assumption\nwould be to see them aligned to the host galaxy minor axis.\n\nHowever, the above scenario is flatly contradicted by the\nobservations. Investigations of the observed distribution of the angle\n$\\delta$, the difference between the position angle of the major axis\nof the galaxy and the position angle of the radio jet projected on the\nplane of the sky, shows that Seyfert galaxies can have jets along any\ndirection, from aligned along the minor axis to aligned along the major\naxis (Ulvestad \\& Wilson 1984; Brindle et al. 1990; Baum et al. 1993;\nSchmitt et al. 1997; Nagar \\& Wilson 1999). It was shown by Clarke,\nKinney \\& Pringle (1998), using data for a sample of Seyfert galaxies\nselected from the literature, that it is possible to obtain a reliable\nestimate of the distribution of the angle $\\beta$ {\\it in 3-dimensions}\nbetween the jet axis and the normal to the galaxy plane, by considering\nfor each galaxy in the sample, the pair of values of $i$ and $\\delta$\n($i$ is the inclination of the galaxy to the line of sight). They\nconclude that the directions of the radio jets are consistent with\nbeing completely uncorrelated with the planes of the host galaxies (see\nalso Nagar \\& Wilson 1999).\n\nThe observed random alignment between accretion disks and galaxy disks\nis intriguing, and the study of this effect is important for the\nunderstanding of the inner workings of Seyfert galaxies. This result\nmay imply, for example, that recently suggested ideas about radiation\ninduced warping of accretion disks (Pringle 1996, 1997, and Maloney,\nBegelman \\& Pringle 1996) come into play both to determine the\ndirectionality of the accretion disk and to produce the ionization\ncones, or that the warping is caused by the rapid spinning of the\ncentral black hole with spin misaligned with the spin of the\ngalaxy (Bardeen-Petterson effect). Alternatively, this misalignment may\nresult by the feeding of the accretion disk from gas outside the\ngalaxy, by mergers, for example.\n\nHere we study the distribution of angles $\\beta$ in a well defined\nsample of Seyfert galaxies, selected from a mostly isotropic property,\nthe flux at 60$\\mu$m, and warm infrared colors (de Grijp et al. 1987,\n1992). Most of the previous works in this subject used samples selected\nfrom the literature and were likely to suffer from selection effects.\nThe example of one problem possibly caused by selection effects was the\n``zone of avoidance'' found by Schmitt et al. (1997), a region of\n20$^{\\circ}$ around the host galaxy minor axis where no jets were\ndetected, but which was shown later by Nagar \\& Wilson (1999) to be\ndue to the sample. Another problem of previous papers was the use of\ndata collected from the literature, measured by different authors, using\ndifferent methods, which resulted in uncertainties that cannot be\nquantified. We have addressed this problem by using radio and optical\ndata observed, reduced and measured in a homogeneous way.\n\n\nThis paper is organized in the following way. In Section 2 we discuss\nthe details about the data and the samples. In Section 3 we present the\ngeometry of the problem and the statistical technique used to determine\nthe distribution of $\\beta$ angles. In Section 4 we compare the data\nwith the models, determine which $\\beta$-distribution and what kind of\nrestrictions are required to better represent the observed data. In\nSection 5 we discuss a series of possible explanations for the observed\nmisalignment between the accretion disk and the host galaxy disk,\nand finally in Section 6 we give a summary of the work.\n\n\\section{The data}\n\n\\subsection{The 60$\\mu$m sample}\n\nThe previous studies on relative angle in different types of Seyfert\ngalaxies (Ulvestad \\& Wilson 1984; Brindle et al. 1990; Baum et al.\n1993; Schmitt et al. 1997; Nagar \\& Wilson 1999) were not based on well\ndefined samples. Most of these papers used data selected from the\nliterature, and were most likely biased with respect to orientation.\nOne possible bias would be the preferential selection of galaxies which\nhave jets shining into the plane of the galaxy, resulting in brighter\nradio emission and narrow line regions, which would be easier to\ndetect. Another possible selection effect happens in the case of\nSeyferts selected by ultraviolet excess. According to the Unified\nModel, we see $\\approx$1\\% of the nuclear continuum by reflection in\nSeyfert 2's, and the whole continuum in Seyfert 1's, which means that\nSeyfert 2's selected in this way are on the higher luminosity end of\nthe luminosity function and are likely to have stronger and more\nextended radio emission. In an attempt to alleviate this problem we\nare using a sample chosen from a mostly isotropic property, the flux at\n60$\\mu$m. According to the torus models of Pier \\& Krolik (1992),\nwhich are the most anisotropic and hence the most conservative models,\nthe circumnuclear torus radiates nearly isotropically at 60$\\mu$m.\n\nOur sample includes 88 Seyfert galaxies (29 Seyfert 1's and 59 Seyfert\n2's), which correspond to all galaxies from the de Grijp et al. (1987,\n1992) sample of warm IRAS galaxies with redshift z$\\leq0.031$. The\ngalaxies in this sample were selected based on the quality of the\n60$\\mu$m flux, Galactic latitude $|b|>20^{\\circ}$, and\n25$\\mu$m$-60\\mu$m color in the range $-1.5<\\alpha(25/60)<0$, chosen as\nto exclude starburst galaxies as much as possible. The candidate AGN\ngalaxies were all observed spectroscopically (de Grijp et al. 1992) to\nconfirm their activity class as being Seyfert 1 or Seyfert 2 and {\\it\nnot} a lower level of activity such as starburst or LINER. The distance\nlimit of z$\\leq0.031$ allows us to study a statistically significant\nnumber of objects which are nearer, and thus more likely to be resolved\nin the radio.\n\nWe note that although the use of the $60 \\mu$m sample provides an initial\nobject selection that is expected to be more or less isotropic, the\noptical follow up required to classify the galaxies spectroscopically\ninevitably re-introduces a degree of orientation bias. We find however\nthat the objects in the 60$\\mu$m sample contain a higher proportion of\nmore nearly edge-on galaxies than do objects selected serendipitously\nfrom the literature. This provides some {\\it a posteriori}\njustification for the notion that the orientation bias is {\\it\nweakened} (though not removed) by use of this sample (see a further\ndiscussion in 4.4.4). In any case, a major benefit of the $60 \\mu$m\nsample is that its use considerably speeds up the process of weeding\nout the (very many) galaxies without Seyfert or starburst activity, and\nassures that Seyfert 1's and Seyfert 2's are matched in luminosity.\n\nIn Figure 1 we show the histogram of the 60$\\mu$m luminosity\ndistribution for the Seyfert 1's and Seyfert 2's in our sample. This\ndemonstrates that the sample has no significant difference in\nluminosities between the two types, with a KS test showing that there\nis a 45.3\\% chance that two samples drawn from the same parent\npopulation would differ this much, or more. Similarly, Keel et al.\n(1994) shows that both the [OIII] and the IR luminosities for the\n60$\\mu$m sample have very similar distributions, demonstrating that\nselection according to the $60 \\mu$m flux is unlikely to bias the survey\ntowards either Seyfert 1s or Seyfert 2s. In particular, this histogram\nshows that we are selecting the subtypes from the same part of the\nluminosity function.\n\nOf the 88 galaxies in our sample, 77 have $\\delta>-47^{\\circ}$ and can\nbe observed from VLA in a reasonable amount of time. Of these 77\ngalaxies, 38 were previously observed with the A-array in X-band\n(3.6cm) and are available in the archive. We carried out a snapshot\nsurvey to observe 36 of the remaining 39 galaxies, using the same\nfrequency and configuration (Schmitt et al. 2000). As a result, we have\nA-array X-band (3.6cm) data, which gives a spatial resolution of\n$\\approx0.24^{\\prime\\prime}$, for 74 galaxies. One of these galaxies,\nTOL1238-3364, was not detected, while for one of the galaxies in the\nsouthern hemisphere, PKS2048-57, which cannot be observed from VLA, we\ngot literature data from Morganti et al. (1999), who observed it with\nATCA also at 3.6cm.\n\nWe reduced the data for the 36 galaxies in our sample, as well as for\n21 of the 38 galaxies available in the archive, for which there was no\ndata previously published, or for which we could find better data in\nthe archive. Details about the reduction of the radio data and a\ndiscussion on individual objects can be seen in Schmitt et al. (2000).\nThe 17 remaining objects were obtained from the literature, only using\ndata that were reduced and analyzed in a way similar to ours. The\nsample is presented in Table 1 where we show the de Grijp et al. (1987)\nnumber of the galaxies, their names, activity class, radial velocity,\n60$\\mu$m luminosity, radio 3.6cm flux, 3.6cm luminosity and the extent\nof the radio emission at 3.6cm.\n\nWhile 74 out of 75 galaxies observed at 3.6cm were detected, 36 of\nthese objects, $\\approx$50\\% of the sample, show extended emission. For those\nobjects with linear extent (based on the Ulvestad and Wilson 1984\ndefinition), the radio emission was decomposed into individual\ncomponents by fitting Gaussians to them. The radio position angle\n(PA$_{RAD}$) is measured between the central position of these\nGaussians. We estimate that the error in the measurements is of the\norder of 3$^{\\circ}-5^{\\circ}$ for linear extended radio sources and\n5$^{\\circ}-10^{\\circ}$ for slighly resolved radio sources. For\nMCG-03-34-064 we measured PA$_{RAD}$ using only the inner\n0.5$^{\\prime\\prime}$ of the jet, because outside this region the jet\nchanges direction, bending to the south. For MRK348, NGC1068 and\nNGC5506, instead of using the VLA data we used higher resolution VLBA\ndata from Ulvestad et al. (1999), MERLIN data from Gallimore, Baum \\&\nO'Dea (1996) and VLBA data from Roy et al. (2000), respectively. This\ndata gives the orientation of the jet closer to the nucleus, which in\nsome cases is different from the orientation seen on VLA scales.\nWe note that in the case of NGC1068 we used PA$_{RAD}=0^{\\circ}$,\nsince the inner E-W radio structure is related to the torus (Gallimore\net al. 1996).\n\nWe estimate that the influence of galaxy disk emission is not important\nin the determination of the position angle of extended radio emission\nin the more distant galaxies of our sample. The emission from the\ngalaxy disk is usually diffuse and weak, and largely resolved out in\nour high resolution observations: most of our galaxies just show small\nlinear extended emission in the nucleus. There is the possibility that\npart of the extended emission in slightly extended sources could be due\nto circumnuclear star formation. However, since the extended emission\nwas usually detected on scales smaller than\n1$^{\\prime\\prime}-2^{\\prime\\prime}$, and the spectra used to classify\nthese galaxies were obtained with a similar aperture, these galaxies\nwould probably have been classified as Starbursts.\n\n\nAnother limitation of previous papers on the orientation of radio jets\nrelative to the host galaxy in Seyferts was the use of inhomogeneous\ninformation about the position angle of the major axis, and inclination\nof the galaxy (PA$_{MA}$ and $i$ hereafter). Most of these studies used\ndata from the literature, or measured the values from the Digitized Sky\nSurvey I, which does not have good enough resolution for sources\nsmaller than $\\approx1^{\\prime}$. To solve this problem we obtained\nhigh signal to noise ratio ground based B and I images for almost all\nthe galaxies in the sample (for a small number of galaxies it was\npossible to observe only one of the bands). The data were taken at\nCTIO, KPNO and Lick Observatory. The reduction and analysis are\nreported in detail by Schmitt \\& Kinney (2000).\n\nThe values of PA$_{MA}$ and the inclination were obtained by fitting\nellipses to the images of the galaxies. The values of PA$_{MA}$ were\nmeasured directly from the ellipses fitted to the isophotes\ncorresponding to the surface brightness level 24-25\nB~mag~arcsec$^{-2}$. We point out that this level is usually deep enough\nto avoid the problem of bars and oval distortions, besides the fact\nthat we have also checked the images of the galaxies for these\neffects. Assuming that the galaxies are circular when seen face-on, we\ncan use the ellipticity of the outer isophotes to determine their\ninclinations $i$. To do this we used the relation $\\cos i = b/a$. We\ncompared the values obtained using this method with the values obtained\nusing the empirical formula $\\sin^2 i = [1-(b/a)^2]/0.96$ from Hubble\n(1926), which takes into account the thickness of the galaxy disk.\nSince the difference between the two measurements was always smaller\nthan 1$^{\\circ}$ to 2$^{\\circ}$, which is less than or approximately of\nthe order of the measurement errors, we decided to use the values\nobtained using the first relation. We estimate that the error in the\ndetermination of the host galaxy inclination and PA$_{MA}$ is of the\norder of 2$^{\\circ}-4^{\\circ}$ for the more inclined galaxies, and\nlarger for the face-on galaxies, where it can be as much as\n6$^{\\circ}$. For a small number of galaxies it was possible to find\nvalues of PA$_{MA}$ and $i$ obtained from kinematical data in the\nliterature. Since this is the most precise way to determine these quantities,\nwhenever it was possible we used these measurements instead of ours.\n\n\nIn this paper we introduce an important improvement relative to\nprevious studies, which is the use of information about which side of\nthe minor axis of the galaxy is closer to Earth. As pointed out by\nClarke et al. (1998), this information can improve the statistics of\nthe sample by a factor of two, because we constrain the jet to lie\nalong a particular segment of the great circle. One way we used to\nobtain this information was the inspection of dust lanes in the\nimages of the galaxies. We expect to see dust lanes only in the closer\nside of the galaxy, since they are highlighted against background bulge\nlight. A considerable number of objects show dust lanes,\neither in our B and I images, or higher resolution HST V band images.\n\nFor galaxies where it was not possible to detect dust lanes, we\nobtained the information about the galaxy orientation from the rotation\ncurve of the galaxy and the direction of the spiral arms. Assuming\nthat the spiral arms are trailing and knowing which side of the galaxy\nis approaching Earth, we can determine which side of the minor axis is\ncloser. To do this we used rotation curves from the literature and also\nobtained, for several galaxies in the sample, long-slit spectra aligned\nclose to the major axis. Our spectra were obtained at CTIO and La Palma\nobservatory and will be published elsewhere. We were\nable to obtain the information about the closer side of the minor axis\nfor approximately two thirds of the sample with extended radio\nemission. Most of the objects for which we were not able to obtain\nthis information were S0 galaxies, for which we could not see the\nspiral arms and also do not show dust lanes, or galaxies very close to\nface-on, where it is difficult to obtain a reliable rotation curve.\n\nIn Table 2 we show the 36 galaxies with extended radio emission, their\nactivity classes, PA$_{MA}$, $i$, PA$_{RAD}$, the side of the galaxy\ncloser to Earth and the morphology of the extended radio emission,\naccording to the Ulvestad \\& Wilson (1984) method. Notice that\nNGC5548, MRK176 and NGC7212 are being shown in this Table just for\ncompleteness, because they are interacting galaxies and will not be\nused in the analysis.\n\n\n\\subsection{Serendipitous sample}\n\nIn some sections of the paper we will also use a larger sample,\nconsisting of 69 galaxies, all Seyferts known to have extended radio\nemission. This sample is composed of 33 galaxies from the 60$\\mu$m\nsample, plus 36 additional galaxies serendipitously obtained from the\nliterature (e.g. Schmitt et al. 1997, Nagar \\& Wilson 1999). We point\nout that, for most of the 36 serendipitous galaxies, the values of\nPA$_{RAD}$, PA$_{MA}$ and $i$ were obtained from the literature. For\nsome of these galaxies, PA$_{RAD}$ was obtained from Nagar et al.\n(1999), so they were measured in a way similar to that of the 60$\\mu$m\nsample. Also, we were able to obtain B and I images for some of these\ngalaxies (Schmitt et al. 2000), which insures homogeneous measurements\nof PA$_{MA}$ and $i$. However, most of the measurements for these 36\ngalaxies come from inhomogeneous datasets, done using different\nmethods. In Table 3 we show the 36 galaxies from the serendipitous\nsample, their activity classes, PA$_{MA}$, $i$, PA$_{RAD}$, the side of\nthe galaxy closer to Earth and the morphology of the extended radio\nemission.\n\n\n\\section{Statistical Analysis}\n\n\\subsection{Geometry}\n\\label{geometry}\n\nThe geometry of our analysis has been described by Clarke, Kinney \\&\nPringle (1998), but is repeated here for completeness. For each galaxy\nwe can determine two observational parameters, $i$ and $\\delta$. The\nangle $i$ is the inclination of the plane of the galaxy to the plane of\nthe sky, or equivalently the angle between the line of sight and the\nvector normal to the galaxy plane. The angle $i$ lies in the range\n$0^{\\circ} < i <90^{\\circ}$. We use a Cartesian coordinate system OXYZ\n(see Figure~\\ref{figNN}) so that OX lies along the apparent major axis\nof the galaxy disk, OY lies along the apparent minor axis, and thus OZ\nis the vector normal to the galaxy plane. In these coordinates the unit\nvector in the direction of the line of sight is\n%\n\\begin{equation}\n{\\bf k}_s = ( 0, -\\sin i, \\cos i). \n"
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astro-ph0002132
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Jet directions in Seyfert galaxies: B and I imaging data
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[
{
"author": "H. R. Schmitt\\altaffilmark{1,2,3,4,6}"
},
{
"author": "A. L. Kinney\\altaffilmark{1,2,3,5}"
}
] |
We present the results of broad-band B and I imaging observations for a sample of 88 Seyfert galaxies (29 Seyfert 1's and 59 Seyfert 2's), selected from a mostly isotropic property, the flux at 60$\mu$m. We also present the B and I imaging results for an additional sample of 20 Seyfert galaxies (7 Seyfert 1's and 13 Seyfert 2's), selected from the literature and known to have extended radio emission. The I band images are fitted with ellipses to determine the position angle and ellipticity of the host galaxy major axis. This information will be used in a future paper, combined with information from radio observations, to study the orientation of radio jets relative to the plane of their host galaxies (Kinney et al. 2000). Here we present surface brightness profiles and magnitudes in the B and I bands, as well as mean ellipticities and major axis position angles.
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"name": "paper.tex",
"string": "\\documentstyle[11pt,aaspp4]{article}\n%\\documentstyle[12pt,aasms4]{article}\n\\input psfig\n\n\n\\begin{document}\n\n\n\\title{Jet directions in Seyfert galaxies: B and I imaging data}\n\n\\author\n {H. R. Schmitt\\altaffilmark{1,2,3,4,6}, A. L. Kinney\\altaffilmark{1,2,3,5}}\n\\altaffiltext{1}{Space Telescope Science Institute, 3700 San Martin Drive, \nBaltimore, MD 21218, USA}\n\\altaffiltext{2}{Visiting Astronomer Cerro Tololo Interamerican Observatory,\nNational Optical Astronomy Observatories, which is operated by AURA, Inc.\nunder a cooperative agreement with the National Science Foundation}\n\\altaffiltext{3}{Visiting Astronomer Kitt Peak National Observatory\nNational Optical Astronomy Observatories, which is operated by AURA, Inc.\nunder a cooperative agreement with the National Science Foundation}\n\\altaffiltext{4}{Visiting Astronomer Lick Observatory, operated by the\nUniversity of California Observatories}\n\\altaffiltext{5}{Present address: NASA Headquarters, 300 E St., Washington, DC20546}\n\\altaffiltext{6}{email:schmitt@stsci.edu}\n\n\\date{\\today}\n\n\\begin{abstract}\n\nWe present the results of broad-band B and I imaging observations for a\nsample of 88 Seyfert galaxies (29 Seyfert 1's and 59 Seyfert 2's),\nselected from a mostly isotropic property, the flux at 60$\\mu$m. We\nalso present the B and I imaging results for an additional sample of 20\nSeyfert galaxies (7 Seyfert 1's and 13 Seyfert 2's),\nselected from the literature and known to have extended radio\nemission. The I band images are fitted with ellipses to determine the\nposition angle and ellipticity of the host galaxy major axis. This\ninformation will be used in a future paper, combined with information\nfrom radio observations, to study the orientation of radio jets\nrelative to the plane of their host galaxies (Kinney et al. 2000). Here we\npresent surface brightness profiles and magnitudes in the B and I bands,\nas well as mean ellipticities and major axis position angles.\n\n\n\\end{abstract}\n\n\\keywords{galaxies:active -- galaxies:structure -- galaxies:Seyfert -- \ngalaxies:photometry}\n\n\\section {Introduction}\n\nWe have recently shown (Schmitt et al. 1997; Clarke, Kinney \\& Pringle\n1998; see also Nagar \\& Wilson 1999) that there is no correlation\nbetween the position angle of radio jets and disk major axes\nin Seyfert galaxies, confirming previous results based on smaller\nsamples (Ulvestad \\& Wilson 1984; Brindle et al. 1990; Baum et al.\n1993). Clarke et al. (1998) and Nagar \\& Wilson (1999) showed, using a\nstatistical inversion technique, that the observed values of $\\delta$ (the\ndifference between the position angle of the jet and the host galaxy\ndisk major axis) and $i$ (inclination of the galaxy disk relative to\nthe line of sight) can be reproduced by a homogeneous distribution\nof angles $\\beta$ between the jet and the galaxy disk axis.\n\nThese results contradict the expectation that the jets should be\naligned perpendicular to the galaxy disk. The simplest assumption\nabout the feeding of the accretion disk and the black hole\nsuggests that the gas comes from the host galaxy disk, so it is\nnatural to expect both disks to be aligned and have the same angular\nmomentum vector. Since jets are emitted perpendicular to the accretion\ndisk, we would expect them to be aligned with the host galaxy\nminor axis, which is not observed. These studies give us information\nabout the inner workings of Seyferts and may shed some light on the\nprocesses involved in the feeding of the AGN.\n\nAlthough the results from Clarke et al. (1998) and Nagar \\& Wilson\n(1999) were statistically significant, they had two major limitations,\ntheir samples and most of their measurements were obtained from the\nliterature. This indicates that their results could be biased by\nselection effects, like the preferential selection of galaxies which\nhave jets shining into the plane of the galaxy, resulting in brighter\nradio emission and narrow line regions, which would be easier to\ndetect. From the point of view of the data, using measurements\ncollected from the literature can also influence the results, since\ndifferent authors are likely to measure the position angle of radio jets,\nthe disk inclination and the position angle of the host galaxy\nmajor axis using different techniques and data of different quality.\n\nIn order to improve the data relative to previous studies, we obtained radio\ncontinuum maps at 3.6cm, optical broad band images and spectroscopy for\na sample of Seyfert galaxies selected from a mostly isotropic property,\nthe flux at 60$\\mu$m. In this way we avoid selection effects and create\na homogeneous database, with measurements done using a consistent\ntechnique.\n\nAnother possible improvement which will be used in the analysis paper\n(Kinney et al. 2000), is the distinction between which side of the\ngalaxy minor axis is closer to Earth. According to Clarke et al.\n(1998), this information can improve the statistical determination of\nthe $\\beta$-distribution by a factor of 2. One way to obtain this\ninformation is from the inspection of dust lanes in the galaxies'\nimages. Dust lanes can be seen in the near side of the galaxy, because\nthey are highlighted against the background bulge light. Due to this\nfact, we decided to obtain images in the B and I bands, with a large\nwavelength separation, which will allow us to search for dust lanes.\nAnother way to obtain this information is from the rotation curve of\nthe galaxy. Knowing which side of the galaxy is approaching us and\nassuming that the spiral arms are trailing, we can determine which side\nof the minor axis is closer to Earth. In order to do this, we obtained\nlong-slit spectra, with the slit aligned close to the host galaxy major\naxis, for several objects in our sample.\n\nIn this paper we present the broad-band B and I imaging data. The radio\ncontinuum observations and optical spectroscopic data will be presented\nelsewhere. In Section 2 we present the samples used in our study. The\ndescription of the observations and reductions is given in Section 3,\nand the measurements are presented in Section 4. A summary is given in\nSection 5.\n\n\\section{Sample}\n\\label{sample}\n\n\\subsection{60$\\mu$m sample}\n\nIn order to avoid selection effects as much as possible, we have chosen a\nsample from a mostly isotropic property, the flux at 60$\\mu$m.\nAccording to the torus models of Pier \\& Krolik (1992), which are the\nmost anisotropic and hence the most conservative models, the\ncircumnuclear torus radiates nearly isotropically at 60$\\mu$m.\n\nOur sample includes 88 Seyfert galaxies (29 Seyfert 1's and 59 Seyfert\n2's), which correspond to all galaxies from the de Grijp et al. (1987,\n1992) sample of warm IRAS galaxies with redshift z$\\leq0.031$. The\ngalaxies in this sample were selected based on the quality of the\n60$\\mu$m flux, Galactic latitude $|b|>20^{\\circ}$, and\n25$\\mu$m$-60\\mu$m color in the range $-1.5<\\alpha(25/60)<0$, chosen to\nexclude starburst galaxies as much as possible. The candidate AGN\ngalaxies were all observed spectroscopically (de Grijp et al. 1992) to\nconfirm their activity class as being Seyfert 1 or Seyfert 2 and {\\it\nnot} a lower level of activity such as starburst or LINER. The distance\nlimit of z$\\leq0.031$ is large enough to encompass a statistically\nsignificant number of objects yet close enough to ensure that radio\nfeatures can be resolved.\n\nTable 1 presents the galaxies in the de Grijp et al. (1987) catalog,\nselected for our study. We list their catalog numbers, names,\ncoordinates, the total exposure times in the B and I bands, and the\nobserving runs in which the galaxies were observed.\n\n\\subsection{Additional sample}\n\nParts of the study presented by Kinney et al. (2000) will also use an\nadditional sample of 53 Seyfert galaxies selected from the literature.\nThis sample comprises Seyferts known to have extended radio emission,\nused in previous studies (such as Schmitt et al. 1997; or Nagar et al.\n1999) but which are not in the 60$\\mu$m sample. For 20 of these\ngalaxies (7 Seyfert 1's and 13 Seyfert 2's) we were able to obtain B\nand/or I images during our observing runs. Table 2 gives the names of\nthe galaxies, their coordinates, total exposure times in B and I bands\nand the observing run in which they were observed.\n\nSome of the galaxies in the additional sample were used in previous\npapers, but we now consider that they should not be included in this\nanalysis. The reasons to exclude them are the fact that they are in\ninteracting systems, mergers, or the radio emission is not extended\nenough to allow a reliable measurement of the position angle of the\njet. For these galaxies, Column 8 (Comments) of Table 2 gives the\nreasons why they are excluded.\n\n\n\n\\section{Observations and reductions}\n\\label{obs}\n\nThe data presented in this paper were obtained in 5 different observing\nruns, using 3 different observatories. The dates of these observing\nruns, corresponding telescopes and instruments are shown in Table 3.\n\nThe CTIO observations were done in the 0.9m telescope with\nfocal ratio f/13.5, using the detector T2K6 for run $a$ and\ndetector T2K3 for run $d$. Both CCD's have the same plate scale,\nwhich gives a pixel size of 0.384$^{\\prime\\prime} pixel^{-1}$. The\nimages in run $a$ were obtained using the whole CCD area of\n2048$\\times$2048 pixels, reading it out using 4 different amplifiers,\nwhich gives a field of view of $\\approx13^{\\prime}\\times13^{\\prime}$.\nFor run $d$ we used only a 1024$\\times$1024 section of the CCD, reading\nit out using one amplifier, which gives a field of view of\n$\\approx7.5^{\\prime}\\times7.5^{\\prime}$.\n\nThe observations at Lick Observatory were done in the 1.0m Nickel\ntelescope with focal ratio f/17, using Dewar \\#5 in both runs ($b$ and\n$c$), which gives a pixel size of 0.248$^{\\prime\\prime} pixel^{-1}$.\nWe used the whole CCD area (1024$\\times$1024 pixels) for these\nobservations, which gives a field of view of\n$\\approx4.8^{\\prime}\\times4.8^{\\prime}$. The KPNO observations were\ndone in the 0.9m telescope with focal ratio f/7.5, using the detector\nT2KA, which gives a pixel size of 0.688$^{\\prime\\prime} pixel^{-1}$. We\nused only a 1024$\\times$1024 section of the CCD, which gives a field of\nview of $\\approx11.7^{\\prime}\\times11.7^{\\prime}$.\n\nWe followed the same observing procedure for each one of the runs. For\neach night we obtained a series of bias images (between 20 and 50\nexposures), dome flats (between 15 and 30 exposures per filter) and sky\nflats (between 5 and 10 exposures per filter). We did not obtain dark\nimages, because our exposure times were short enough that the\ncontribution of dark current was negligible.\n\nThe reductions were done following standard IRAF procedures. The\nindividual images were overscanned, bias subtracted and divided by the\nnormalized flat field. Tests showed that, for each observing run, there\nwas no significant differences between calibration frames from\nindividual nights. Therefore, all frames were combined and we used the\nresulting images, which had a higher S/N, for the data reduction. The\nimages were flat-fielded using only the sky flats, since tests showed\nthat the dome flats had inhomogeneous illumination. \n\n\nTo calibrate the images in the Cousins system, each night we observed\nseveral standard star fields from Graham (1982) and Landolt (1992). We\nestimate that the photometric accuracy of our observations is of the\norder of 0.05 mag. To avoid the saturation of the nuclear region and to\neliminate cosmetic defects and cosmic rays, the images were dithered\nusing 3 or more exposures of 400s or less. For three of the galaxies\nin the 60$\\mu$m sample it was possible to obtain images in only one of\nthe bands (I for MRK1040 and B for IRAS16382-0613 and UGC10683B).\nFurthermore, runs $a$ and $e$ took place close to full moon,\nresulting in shallower B images.\n\nSince our images will be used to compare the position angles in the\nradio and optical, it is important to determine the orientation of the\nCCD's relative to the equatorial plane. This was done using stars in\nthe images, which showed that the fields are not rotated. The final\norientation of the images is N up and E to the left, with an\nuncertainty of $\\approx1^{\\circ}$.\n\n\n\\section{Measurements}\n\nIn Figure 1 we present the I band images of the galaxies, organized\nfollowing the same order of Tables 1 and 2. In the case of UGC10683B\nand IRAS16382-0613, for which we were not able to obtain I band images,\nthe B band images are shown instead.\n\nMeasurements of disk ellipticities and major axis position angles\n(defined as the angle measured from N to E) were\nobtained fitting ellipses to the isophotes of the galaxies, using the\nroutine ``ellipse'' in the STSDAS package of IRAF. We have chosen to\nfit the ellipses over the I band images because they were deeper, and\nalso because this band is more sensitive to old stars, so the outer\nisophotes are not disturbed by HII regions like they can be in the B\nimages.\n\nThe ellipses were fitted from the inner $\\approx0.7^{\\prime\\prime}$ of\nthe I images, out to the level where the surface brightness reached the\n3$\\sigma$ level above the background (this limiting value is listed in\nTables 4 and 5). The background level and its standard deviation\n($\\sigma$) were determined from several blank regions around the\ngalaxy. For some galaxies, with bright stars close to the low surface\nbrightness isophotes (e.g. NGC3783), the ellipse fitting procedure was\ntruncated before it reached the 3$\\sigma$ level, to avoid the\ndisturbance of the fit by these stars. Ellipses centers were hold fixed\nat the nuclear position, and were fitted using a constant increment of\nthe semi-major axis, 2 pixels for runs {\\it a, b, c} and $d$ and 1\npixel for run $e$, which corresponds to $\\approx0.77^{\\prime\\prime}$\nfor runs $a$ and $d$, $\\approx0.5^{\\prime\\prime}$ for runs $b$ and $c$\nand $\\approx0.69^{\\prime\\prime}$ for run $e$. The surface brightness\nof the 3$\\sigma$ level in I was typically 21-22.5 mag~arcsec$^{-2}$,\nwhich corresponds to 23-24.5 mag~arcsec$^{-2}$ in the B band, assuming\nthat the mean color of spiral disks is (B-I)$\\approx2$ (H\\'eraudeau,\nSimien \\& Mamon 1996; see also our own measurements in Figure 2).\n\nThe ellipse parameters obtained from the fit of the I band images were\nused to measure the surface brightness profile of the B images, thus\nallowing a direct comparison between the two measurements. In Figure 2\nwe show the surface brightness profiles, major axis position angle\n(PA$_{MA}$) and disk ellipticity (e), defined as e=1-b/a, where b/a is\nthe ratio between the minor and major axis. Notice that the ellipse\nparameters in the inner 1$^{\\prime\\prime}-2^{\\prime\\prime}$ are\nunreliable, because they were made on scales smaller or comparable to\nthe seeing.\n\nIn Tables 4 and 5, for the 60$\\mu$m and additional samples,\nrespectively, we present the size of the ellipse major axis at the\n3$\\sigma$ level above the background, the surface brightness of this\nlevel, the integrated magnitude inside this region and the seeing\nduring the observations, for both B and I bands. The integrated\nmagnitudes were calculated by integrating the flux inside the ellipses\ncorresponding to the 3$\\sigma$ isophote, using the major axis lengths\ngiven in Tables 4 and 5, the ellipticities and PA$_{MA}$'s given in Tables\n6 and 7 for the 60$\\mu$m and additional samples, respectively. Notice\nthat, since there is a difference between the 3$\\sigma$ level of the B\nand I band images, the B images are usually shallower and not as\nextended as the I images, the ellipse parameters used to measure\nthe integrated magnitudes of these two bands are slightly different.\nThis is the reason why Tables 6 and 7 give different values of\nellipticity and PA$_{MA}$ for B and I bands.\n\n\nThe I band ellipticities and PA$_{MA}$'s were obtained by averaging the\nresults from the ellipses fitted between the isophotes 3$\\sigma$ and\n4$\\sigma$ above the background (4 to 10 points, depending on the\ngalaxy). We adopted this procedure to eliminate large spurious\nvariations, since these values will be combined with radio measurements\nto study the orientation of radio jets relative to the host galaxy disk\naxis in these galaxies (Kinney et al. 2000). An inspection of the\nradial profiles in Figure 2 shows that there is not too much variation\nin the ellipticities and PA$_{MA}$'s of the outer isophotes, with the\nexception usually being the galaxies close to face-on and interacting\nsystems.\n\n\n\n\\section{Summary}\n\nWe presented B and I band images for a sample of 88 Seyfert galaxies\nselected from a mostly isotropic property, the flux at 60$\\mu$m, as\nwell as for an additional 20 Seyfert galaxies with extended radio\nemission. The isophotes of the I band images were fitted with ellipses\nto determine the surface brightness profiles, the\nellipticities and position angles of the host galaxy major axis. The\nparameters obtained with these fits were used to measure the surface\nbrightness profiles in the B band. These images were also used to\nmeasure the integrated B and I magnitudes of the galaxies. These\nmeasurements will be combined with information from radio observations\nto study the orientation of radio jets relative to the host galaxy disk\n(Kinney et al. 2000).\n\n\\acknowledgements \n\nWe would like to acknowledge the hospitality and help from the staff at\nCTIO, KPNO and Lick Observatories during the observations. We also\nwould like to thank Blaise Canzian for useful comments on the\nmeasurement of ellipticities and position angles in spiral galaxies,\nas well as the anonymous referee for helpful comments.\nThis work was supported by NASA grants NAGW-3757, AR-5810.01-94A,\nAR-6389.01-94A and the HST Director Discretionary fund D0001.82223.\nThis research made use of the NASA/IPAC Extragalactic Database (NED),\nwhich is operated by the Jep Propulsion Laboratory, Caltech, under\ncontract with NASA. We also used the Digitized Sky Survey, which was\nproduced at the Space telescope Science Institute under U.S. Government\ngrant NAGW-2166.\n\n\\begin{references}\n\nBaum, S.A., O'Dea, C.P., de Bruyn, A.G., \\& Pedlar, A. 1993, ApJ, 419,\n553\n\nBrindle, C., Hough. J.H., Bailey, J.A., Axon, D.J., Ward, M.J.,\nSparks, W.B., \\& McLean, I.S. 1990, MNRAS, 244, 577\n\nClarke, C.J., Kinney, A.L., \\& Pringle, J.E. 1998, ApJ, 495, 189\n\nDe Grijp, M.H.K., Keel, W. C., Miley, G.K., Goudfrooij, P. \\& Lub, J. 1992,\nA\\&AS, 96, 389\n\nDe Grijp, M.H.K., Miley, G.K., \\& Lub, J. 1987, A\\&AS, 70, 95\n\nGraham, J. A. 1982, PASP, 94, 244\n\nH\\'eraudeau, P., Simien, F. \\& Mamon, G. A. 1996, A\\&AS, 117, 417\n\nKinney, A.L., Schmitt, H.R., Clarke C.J., Pringle, J.E., Ulvestad, J.S.,\n\\& Antonucci, R.R.J. 2000, ApJ, submitted\n\nLandolt, A. U. 1992, AJ, 104, 340\n\nNagar, N.M., \\& Wilson, A.S. 1999, ApJ, 516, 97\n\nSchmitt, H.R., Kinney, A.L., Storchi-Bergman, T., \\& Antonucci,\nR. 1997, ApJ, 477, 623\n\nUlvestad, J.S., \\& Wilson, A.S. 1984, ApJ, 285, 439\n\n\\end{references}\n\n\\begin{figure}\n\\caption{I band images of the 60$\\mu$m sample and additional\nsample. In the case of UGC10683B and IRAS16382-0613, we present the B\nband images, because we were not able to observe them in the I band.\nThe orientation of the images is N to the top and E to the left. The\nnames of the galaxies are shown on the top left corner of the image\nwhich are organized following their order of appearence in Tables 1 and\n2. The grayscale is a liner stretch from 0 counts (the background level) to\nthe 19 mag~arcsec$^{-2}$ surface brightness level. The contours start\nat 3$\\sigma$ above the background level, presented in Tables 4 and 5,\nand increase in powers of 2, times 3$\\sigma$ (3$\\sigma\\times2^n$).}\n\\end{figure}\n\n\\begin{figure}\n\\caption{B (open triangles) and I (filled squares) surface brightness\n(in units of mag~arcsec$^{-2}$), position angle of the major axis\n(PA$_{MA}$) and ellipticity (e) as a function of the semi-major axis.\nThe position angles and ellipticities were obtained fitting ellipses to\nthe I band images. The B surface brightness were measured using the\nellipse parameters obtained from the I band images, which allow a\ndirect comparison between the measurements in the two bands. The errorbars\nrepresent $\\pm 1\\sigma$ (the standard deviation).}\n\\end{figure}\n\n\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n\n\n"
},
{
"name": "tables.tex",
"string": "\\makeatletter\n\\def\\jnl@ap{AJ}\n\\ifx\\revtex@jnl@aj\\let\\tablebreak=\\fi\n\\makeatother\n\\documentstyle[apjpt4]{article}\n\n\\textheight 25cm\n\\begin{document}\n\n\\begin{small}\n\\begin{deluxetable}{rlcccrrl}\n\\tablewidth{0pc}\n\\tablecaption{The Data for the 60$\\mu$m Sample}\n\\tablehead{\\colhead{Number}&\\colhead{Name}&\\colhead{Type}&\\colhead{RA(2000)}&\n\\colhead{Dec(2000)}&\\colhead{B}& \\colhead{I}&\\colhead{Run}\\cr\n&&&&&(s)&(s)&}\n\\startdata\n16 &MRK\\,348\t\t&2& 00 48 47.1& $+$31 57 25& 1200 & 1200 & b\\cr\n24 &TOL\\,0109$-$38\t&2& 01 11 27.5& $-$38 05 01& 720 & 720 & a\\cr\n26 &MRK\\,1 \t\t&2& 01 16 07.2& $+$33 05 22& 1800 & 1200 & c,b\\cr\n27 &MRK\\,359 \t\t&1& 01 27 32.5& $+$19 10 44& 960 & 960 & a\\cr\n33 &MRK\\,573 \t\t&2& 01 43 57.8& $+$02 21 00& 720 & 720 & a\\cr\n37 &IRAS\\,01475$-$0740 \t&2& 01 50 02.7& $-$07 25 48& 1600 & 2000 & a\\cr\n41 &ESO\\,153$-$G20 \t&2& 02 06 03.6& $-$55 11 35& 900 & 1200 & a\\cr\n47 &MRK\\,1040\t\t&1& 02 28 14.5& $+$31 18 42& -- & 1200 & b\\cr\n52 &ESO\\,355$-$G25 \t&2& 02 31 51.0& $-$36 40 16& 1200 & 1200 & a\\cr\n53 &UGC\\,2024 \t\t&2& 02 33 01.2& $+$00 25 15& 900 & 900 & a\\cr\n57 &NGC\\,1068 \t\t&2& 02 42 40.7& $-$00 00 48& 720 & 720 & a\\cr\n67 &MCG$-$02$-$08$-$039 &2& 03 00 29.8& $-$11 24 59& 900 & 900 & a\\cr\n68 &UGC\\,2514 \t&1& 03 03 48.5& $-$01 06 13& 1200 & 1200 & a\\cr\n75 &IRAS\\,03106$-$0254 \t&2& 03 13 08.3& $-$02 43 19& 1200 & 1200 & a\\cr\n78 &IRAS\\,03125$+$0119 \t&2& 03 15 05.3& $+$01 30 30& 1200 & 1200 & a\\cr\n83 &MRK\\,607 \t\t&2& 03 24 48.7& $-$03 02 33& 1600 & 1600 & a\\cr\n85 &ESO\\,116$-$G18\t&2& 03 24 53.1& $-$60 44 20& 1600 & 1200 & a\\cr\n141&IRAS\\, 04385$-$0828\t&2& 04 40 54.9& $-$08 22 22& 1600 & 1200 & a\\cr\n154&IRAS\\, 04502$-$0317\t&2& 04 52 44.0& $-$03 13 01& 1600 & 1600 & a\\cr\n156&IRAS\\, 04507$+$0358\t&2& 04 53 24.9& $+$04 03 39& 900 & 1600 & d,a\\cr\n157&ESO\\,33$-$G02 \t&2& 04 55 59.6& $-$75 32 27& 1600 & 1600 & a\\cr\n174&MCG$-$05$-$13$-$017 &1& 05 19 35.5& $-$32 39 30& 1600 & 1200 & a\\cr\n196&MRK\\,3\t \t&2& 06 15 36.3& $+$71 02 15& 900 & 1200 & e\\cr\n203&UGC\\,3478 \t&1& 06 32 47.3& $+$63 40 25& 900 & 1200 & e\\cr\n209&MRK\\,6\t \t&1& 06 52 12.3& $+$74 25 37& 1200 & 1200 & e\\cr\n213&FAIRALL\\,265\t&1& 06 56 29.7& $-$65 33 43& 1600 & 1600 & a\\cr\n225&MRK\\,79\t \t&1& 07 42 32.8& $+$49 48 35& 1200 & 1600 & b\\cr\n227&MRK\\,10\t \t&1& 07 47 29.1& $+$60 56 01& 900 & 1200 & b-e,e\\cr\n233&UGC\\,4155\t \t&1& 08 00 20.4& $+$26 36 56& 1200 & 1200 & e\\cr\n236&MRK\\,622\t \t&2& 08 07 41.0& $+$39 00 15& 1200 & 1200 & e\\cr\n244&ESO\\,18$-$G09\t&2& 08 24 07.4& $-$77 46 53& 900 & 900 & d\\cr\n253&MCG$-$01$-$24$-$012\t&2& 09 20 51.7& $-$08 04 47& 900 & 900 & d\\cr\n260&MRK\\,1239 \t\t&1& 09 52 19.1& $-$01 36 43& 900 & 900 & d\\cr\n272&NGC\\,3393\t\t&2& 10 48 24.0& $-$25 09 40& 900 & 900 & d\\cr\n278&NGC\\,3516 \t\t&1& 11 06 47.5& $+$72 34 07& 1200 & 1200 & e\\cr\n281&IRAS\\,11215$-$2806 \t&2& 11 24 02.6& $-$28 23 15& 900 & 900 & d\\cr\n282&MCG$-$05$-$27$-$013\t&2& 11 27 23.3& $-$29 15 31& 900 & 1200 & d\\cr\n283&MRK\\,176 \t&2& 11 32 35.3& $+$52 56 50& 1200 & 1200 & e\\cr\n286&NGC\\,3783 \t&1& 11 39 01.8& $-$37 44 20& 900 & 900 & d\\cr\n292&MRK\\,766 \t&1& 12 18 26.5& $+$29 48 46& 1200 & 1200 & e\\cr\n293&NGC\\,4388 \t&2& 12 25 46.7& $+$12 39 41& 1200 & 1200 & e\\cr\n299&NGC\\,4507\t \t&2& 12 35 37.0& $-$39 54 31& 900 & 900 & d\\cr\n301&NGC\\,4593\t \t&1& 12 39 39.4& $-$05 20 39& 900 & 900 & d\\cr\n302&TOL\\,1238$-$364 \t&2& 12 40 52.9& $-$36 45 22& 900 & 900 & d\\cr\n306&NGC\\,4704\t \t&2& 12 48 46.4& $+$41 55 16& 1200 & 1200 & e\\cr\n309&MCG$-$02$-$33$-$034\t&1& 12 52 12.4& $-$13 24 54& 900 & 900 & d\\cr\n310&ESO\\,323$-$G32 \t&2& 12 53 19.8& $-$41 38 14& 900 & 900 & d\\cr\n313&MCG$-$04$-$31$-$030\t&2& 13 07 06.0& $-$23 40 43& 900 & 900 & d\\cr\n314&IRAS\\,13059$-$2407 \t&2& 13 08 42.1& $-$24 23 00& 900 & 900 & d\\cr\n317&MCG$-$03$-$34$-$064\t&2& 13 22 24.4& $-$16 43 43& 900 & 900 & d\\cr\n322&ESO\\,383$-$G18\t&2& 13 33 26.3& $-$34 00 59& 900 & 900 & d\\cr\n324&MCG$-$6$-$30$-$15\t&1& 13 35 53.7& $-$34 17 45& 900 & 900 & d\\cr\n329&NGC\\,5347\t \t&2& 13 53 17.8& $+$33 29 27& 900 & 1200 & e\\cr\n340&IRAS\\,14082$+$1347\t&2& 14 10 41.4& $+$13 33 29& 1200 & 1200 & e\\cr\n341&NGC\\,5506\t \t&2& 14 13 14.8& $-$03 12 27& 900 & 1200 & e\\cr\n344&NGC\\,5548\t \t&1& 14 17 59.5& $+$25 08 12& 900 & 1200 & e\\cr\n349&IRAS\\,14317$-$3237\t&2& 14 34 44.9& $-$32 50 28& 900 & 900 & d\\cr\n354&IRAS\\,14434$+$2714\t&2& 14 45 36.8& $+$27 02 05& 1200 & 1200 & e\\cr\n369&UGC\\,9826\t \t&1& 15 21 33.0& $+$39 12 01& 900 & 1200 & e\\cr\n377&UGC\\,9944\t \t&2& 15 35 47.8& $+$73 27 02& 1200 & 1200 & e\\cr\n383&IRAS\\,15480$-$0344\t&2& 15 50 41.5& $-$03 53 18& 1200 & 1200 & e\\cr\n409&IRAS\\,16288$+$3929\t&2& 16 30 32.6& $+$39 23 03& 1200 & 1200 & e\\cr\n418&IRAS\\,16382$-$0613\t&2& 16 40 52.3& $-$06 18 52& 1200 & -- & a-e\\cr\n445&UGC\\,10889 \t \t&2& 17 30 20.7& $+$59 38 20& 1200 & 900 & e\\cr\n447&MCG$+$03$-$45$-$003\t&2& 17 35 32.7& $+$20 47 48& 1200 & 1200 & e\\cr\n471&FAIRALL\\,49\t \t&2& 18 36 58.1& $-$59 24 09& 1200 & 720 & a\\cr\n473&FAIRALL\\,51\t \t&1& 18 44 54.3& $-$62 21 49& 1200 & 1500 & a\\cr\n497&ESO\\,143$-$G09\t&1& 20 08 46.1& $-$61 05 56& 900 & 900 & a\\tablebreak\n501&FAIRALL\\,341\t&2& 20 19 59.0& $-$52 37 20& 1600 & 1200 & a\\cr\n510&UGC\\,11630\t \t&2& 20 47 33.5& $+$00 24 42& 720 & 720 & a\\cr\n512&PKS\\,2048$-$57\t&2& 20 52 02.0& $-$57 04 09& 900 & 900 & a\\cr\n530&NGC\\,7213\t \t&1& 22 09 16.2& $-$47 10 00& 900 & 900 & a\\cr\n537&MRK\\,915\t \t&1& 22 36 46.5& $-$12 32 43& 1200 & 1200 & a\\cr\n538&UGC\\,12138\t \t&1& 22 40 17.0& $+$08 03 14& 1600 & 1600 & a\\cr\n540&AKN\\,564\t \t&1& 22 42 39.3& $+$29 43 31& 1200 & 1200 & b\\cr\n549&UGC\\,12348\t \t&2& 23 05 19.4& $+$00 11 28& 1200 & 1600 & a\\cr\n555&NGC\\,7674\t \t&2& 23 27 56.7& $+$08 46 45& 1200 & 1200 & a\\cr\n590&MRK\\,590\t\t&1& 02 14 33.6& $-$00 46 00& 1600 & 1600 & a\\cr\n594&MRK\\,1058\t\t&2& 02 49 51.8& $+$34 59 17& 1800 & 1200 & c,b\\cr\n602&NGC\\,1386\t\t&2& 03 36 45.4& $-$35 59 57& 1200 & 1200 & a\\cr\n615&MCG\\,+8-11-11\t&1& 05 54 53.6& $+$46 26 22& 1200 & 1200 & b\\cr\n627&MRK\\,705\t\t&1& 09 26 03.3& $+$12 44 04& 1200 & 1200 & e\\cr\n634&NGC\\,3281\t\t&2& 10 31 52.1& $-$32 51 13& 900 & 900 & d\\cr\n638&UGC\\,6100\t\t&2& 11 01 34.0& $+$45 39 14& 1200 & 1200 & e\\cr\n665&NGC\\,4941\t\t&2& 13 04 13.1& $-$05 33 06& 900 & 900 & d\\cr\n703&UGC\\,10683B\t\t&1& 17 05 00.4& $-$01 32 29& 1200 & -- & e\\cr\n708&ESO\\,103-G35\t&2& 18 38 20.3& $-$65 25 42& 720 & 720 & a\\cr\n721&NGC\\,7212\t\t&2& 22 07 02.0& $+$10 14 00& 1200 & 1200 & a\\cr\n\\tablenotetext{}{Column 1 shows the galaxy number in the de Grijp et\nal. (1987) catalogue, Column 2 shows their names and Column 3 the\nSeyfert type. Columns 4 and 5 give the Right Ascention and\nDeclination, respectively. Columns 6 and 7 give the total exposure time\nof the B and I images, respectively. Column 8 shows the observing run\nwhen the galaxies were imaged, according to the code given in Table 1.}\n\\enddata\n\\end{deluxetable}\n\\end{small}\n\n\\clearpage\n\\newpage\n\n\\begin{small}\n\\begin{deluxetable}{lcccrrll}\n\\tablewidth{0pc}\n\\tablecaption{The Additional Sample}\n\\tablehead{\\colhead{Name}&\\colhead{Type}&\\colhead{RA(2000)}&\n\\colhead{Dec(2000)}&\\colhead{B}& \\colhead{I}&\\colhead{Run}&\\colhead{Comments}\\cr\n&&&&(s)&(s)&&}\n\\startdata\nNGC\\,235A\t\t&1& 00 42 52.8& $-$23 32 29& -- & -- & --&interacting\\cr\nNGC\\,513\t\t&2& 01 24 26.9& $+$33 47 58& -- & -- & --&\\cr\nNGC\\,526A\t\t&1& 01 23 54.2& $-$35 03 55& -- & -- & --&interacting\\cr\nNGC\\,591\t\t&2& 01 33 31.3& $+$35 40 05& -- & -- & --&\\cr\nNGC\\,788\t\t&2& 02 01 06.4& $-$06 48 56& -- & -- & --¬ extended in radio\\cr\nNGC\\,1144\t\t&2& 02 55 12.2& $-$00 11 01& -- & -- & --&merger\\cr\nESO\\,417-G6\t\t&2& 02 56 21.5& $-$32 11 06& -- & -- & --¬ extended in radio\\cr\nMRK\\,1066\t\t&2& 02 59 58.6& $+$36 49 14& -- & -- & --&\\cr\nNGC\\,1365\t\t&1& 03 33 36.4& $-$36 08 25& -- & -- & --&\\cr\nMRK\\,618\t\t&1& 04 36 22.2& $-$10 22 34& -- & -- & --&\\cr\nESO\\,362-G8\t\t&2& 05 11 09.0& $-$34 23 36& 900 & 900 & d &\\cr\nNGC\\,2110\t\t&2& 05 52 11.4& $-$07 27 22& -- & -- & --&\\cr\nNGC\\,2273\t\t&2& 06 50 08.7& $+$60 50 45& 800 & 1200 & e &\\cr\nESO\\,428-G14\t\t&2& 07 14 32.9& $-$29 14 04& 900 & 900 & d &\\cr\nMRK\\,78\t\t\t&2& 07 42 41.7& $+$65 10 37& 1200 & 1200 & e &\\cr\nNGC\\,2622\t\t&1& 08 38 10.9& $+$24 53 43& 1200 & 1200 & e &\\cr\nNGC\\,2639\t\t&1& 08 43 38.0& $+$50 12 20& 1200 & 1200 & e &\\cr\nMRK\\,110\t\t&1& 09 25 12.9& $+$52 17 11& -- & -- & --&merger\\cr\nUGC\\,5101\t\t&1& 09 35 51.6& $+$61 21 11& 1200 & 800 & e &merger\\cr\nNGC\\,2992\t\t&2& 09 45 42.0& $-$14 19 35& -- & 900 & d &interacting\\cr\nNGC\\,3081\t\t&2& 09 59 29.5& $-$22 49 35& -- & -- & --¬ extended in radio\\cr\nNGC\\,3227\t\t&1& 10 23 30.6& $+$19 51 54& -- & 1600 & e &\\cr\nMRK\\,34\t\t\t&2& 10 34 08.6& $+$60 01 52& -- & 900 & e &\\cr\nNGC\\,3362\t\t&2& 10 44 51.7& $+$06 35 48& -- & 900 & e &interacting\\cr\nMRK\\,423\t\t&2& 11 26 48.5& $+$35 15 03& -- & 900 & e &merger\\cr\nNGC\\,4051\t\t&1& 12 03 09.6& $+$44 31 53& -- & -- & --&\\cr\nNGC\\,4074\t\t&2& 12 04 29.7& $+$20 18 59& -- & -- & --¬ extended in radio\\cr\nNGC\\,4117\t\t&2& 12 07 46.1& $+$43 07 35& -- & -- & --&\\cr\nNGC\\,4151\t\t&1& 12 10 32.6& $+$39 24 21& -- & -- & --&\\cr\nMRK\\,231\t\t&1& 12 56 14.2& $+$56 52 25& -- & -- & --&merger\\cr\nESO\\,323-G77\t\t&1& 13 06 26.6& $-$40 24 50& -- & -- & --&\\cr\nNGC\\,5135\t\t&2& 13 25 44.0& $-$29 50 02& -- & -- & --&\\cr\nNGC\\,5252\t\t&2& 13 38 16.0& $+$04 32 33& -- & 1200 & e &\\cr\nMRK\\,266\t\t&2& 13 38 17.7& $+$48 16 34& -- & -- & --&merger\\cr\nMRK\\,268\t\t&2& 13 41 11.1& $+$30 22 41& -- & 1200 & e &\\cr\nMRK\\,270\t\t&2& 13 41 05.8& $+$67 40 20& 1200 & 1200 & e &\\cr\nNGC\\,5273\t\t&1& 13 42 08.3& $+$35 39 15& 1200 & 1200 & e &\\cr\nMRK\\,273\t\t&2& 13 44 42.1& $+$55 53 13& -- & -- & --&merger\\cr\nIC\\,4329A\t\t&1& 13 49 19.3& $-$30 18 34& -- & 720 & d &\\cr\nMRK\\,279\t\t&1& 13 53 03.4& $+$69 18 30& -- & -- & --&\\cr\nMRK\\,463E\t\t&2& 13 56 02.9& $+$18 22 19& -- & -- & --&merger\\cr\nNGC\\,5643\t\t&2& 14 32 40.7& $-$44 10 29& -- & -- & --&\\cr\nNGC\\,5728\t\t&2& 14 42 23.9& $-$17 15 11& -- & -- & --&\\cr\nNGC\\,5929\t\t&2& 15 26 06.2& $+$41 40 14& 1200 & 1200 & e &interacting\\cr\nESO\\,137-G34\t\t&2& 16 35 14.2& $-$58 04 41& -- & -- & --&\\cr\nMRK\\,509\t\t&1& 20 44 09.7& $-$10 43 25& -- & -- & --&\\cr\nNGC\\,7172\t\t&2& 22 02 01.7& $-$31 52 18& -- & -- & --&\\cr\nIC\\,5169\t\t&2& 22 10 10.0& $-$36 05 18& -- & -- & --&\\cr\nNGC\\,7450\t\t&1& 23 00 47.8& $-$12 55 07& -- & 1200 & b &\\cr\nNGC\\,7465\t\t&2& 23 02 00.9& $+$15 57 53& -- & -- & --&\\cr\nMRK\\,926\t\t&1& 23 04 43.5& $-$08 41 08& -- & -- & --&\\cr\nNGC\\,7672\t\t&2& 23 27 31.4& $+$12 23 06& -- & 900 & b &\\cr\nNGC\\,7743\t\t&2& 23 44 21.5& $+$09 56 05& -- & -- & --&\\cr\n\\tablenotetext{}{Column 1 gives the galaxy name and Column 2 the Seyfert type.\nColumns 3 and 4 give the Right Ascention and Declination, respectively.\nColumns 5 and 6 give the total exposure time of the B and I images,\nrespectively. Column 7 shows the observing run when the galaxies were\nimaged, according to the code given in Table 1. For those galaxies which will\nnot be used in future analysis, we give in Column 8 the reason to exclude them.}\n\\enddata\n\\end{deluxetable}\n\\end{small}\n\n\\clearpage\n\\newpage\n\n\\begin{small}\n\\begin{deluxetable}{llrlrrl}\n\\tablewidth{0pc}\n\\tablecaption{Observing Runs}\n\\tablehead{\\colhead{Date}&\\colhead{Telescope}&\\colhead{f-ratio}&\n\\colhead{Instrument}&\\colhead{FOV}&\\colhead{Scale}&\\colhead{Code}\\cr\n&&&&$^{\\prime}$&$^{\\prime\\prime}/pixel$}\n\\startdata\nOctober 03-09/10 1998 &CTIO 0.9m&13.5 &CCD Direct T2K6 &13.0&0.384 &a\\cr\nNovember 13-18/19 1998 &Lick 1.0m&17.0 &CCD Direct CCD \\#5 & 4.8&0.248 &b\\cr\nDecember 17-21/22 1998 &Lick 1.0m&17.0 &CCD Direct CCD \\#5 & 4.8&0.248 &c\\cr\nFebruary 10-12/13 1999 &CTIO 0.9m&13.5 &CCD Direct T2K3 & 7.5&0.384 &d\\cr\nApril 23-29/30 1999 &KPNO 0.9m& 7.5 &CCD Direct T2KA &11.7&0.688 &e\\cr\n\\enddata\n\\end{deluxetable}\n\\end{small}\n\n\\clearpage\n\\newpage\n\n\\begin{small}\n\\begin{deluxetable}{lrrrrrrrr}\n\\tablewidth{0pc}\n\\tablecaption{Magnitudes of the 60$\\mu$m Sample}\n\\tablehead{\\colhead{Name}&\\colhead{Aperture B}&\n\\colhead{3$\\sigma$B}&\\colhead{B}&\\colhead{(seeing B)}&\\colhead{Aperture I}& \n\\colhead{3$\\sigma$I}&\\colhead{I}&\\colhead{(seeing I)}\\cr\n&(arcsec)&(mag arcsec$^{-2}$)&(mag)&(arcsec)&\n(arcsec)&(mag arcsec$^{-2}$)&(mag)&(arcsec)}\n\\startdata\nMRK\\,348\t\t&39.7 &23.80 &14.96 &0.9 &42.7 &22.56 &12.87 & 0.9\\cr\nTOL\\,0109$-$38\t\t&46.1 &22.18 &13.84 &1.2 &84.5 &22.13 &11.67 & 1.0\\cr\nMRK\\,1 \t\t&27.8 &24.04 &15.62 &2.6 &31.7 &22.69 &13.52 & 1.1\\cr\nMRK\\,359 \t\t&23.0 &22.67 &14.44 &1.4 &32.3 &21.65 &12.57 & 1.2\\cr\nMRK\\,573 \t\t&24.6 &23.08 &14.66 &1.2 &36.9 &21.92 &12.43 & 1.0\\cr\nIRAS\\,01475$-$0740 \t&16.9 &24.52 &16.58 &2.7 &20.0 &23.03 &14.46 & 1.2\\cr\nESO\\,153$-$G20 \t\t&30.7 &22.40 &15.09 &1.3 &76.8 &22.35 &12.10 & 1.1\\cr\nMRK\\,1040\t\t&--- &--- &--- &--- &123.0 &22.56 &11.73 & 1.5\\cr\nESO\\,355$-$G25 \t\t&49.2 &23.60 &14.00 &2.6 &49.2 &21.65 &12.02 & 1.0\\cr\nUGC\\,2024 \t\t&26.1 &23.19 &15.26 &1.3 &43.0 &22.26 &13.02 & 1.2\\cr\nNGC\\,1068 \t\t&192.0 &22.84 &9.93 &1.5 &318.7 &21.86 &7.73 & 1.3\\cr\nMCG$-$02$-$08$-$039 \t&33.8 &23.07 &15.57 &1.2 &56.8 &21.99 &12.80 & 1.3\\cr\nUGC\\,2514 \t\t&32.3 &22.79 &14.96 &1.5 &92.2 &22.14 &11.74 & 1.2\\cr\nIRAS\\,03106$-$0254 \t&20.0 &22.61 &16.37 &1.5 &58.4 &22.45 &12.86 & 1.2\\cr\nIRAS\\,03125$+$0119 \t&15.4 &22.90 &15.87 &1.4 &32.3 &22.16 &13.46 & 1.4\\cr\nMRK\\,607 \t\t&81.4 &23.60 &13.79 &2.7 &101.4 &22.45 &11.41 & 1.5\\cr\nESO\\,116$-$G18\t\t&36.9 &23.36 &15.36 &2.5 &33.8 &20.54 &12.85 & 1.3\\cr\nIRAS\\, 04385$-$0828\t&18.4 &22.57 &16.19 &1.0 &35.3 &22.15 &13.52 & 1.0\\cr\nIRAS\\, 04502$-$0317\t&20.0 &23.16 &15.92 &2.5 &30.7 &22.64 &13.65 & 1.2\\cr\nIRAS\\, 04507$+$0358\t&36.9 &24.18 &15.25 &1.6 &27.7 &21.79 &13.02 & 1.2\\cr\nESO\\,33$-$G02 \t\t&30.7 &23.58 &15.13 &2.5 &43.0 &21.83 &12.58 & 1.2\\cr\nMCG$-$05$-$13$-$017 \t&43.0 &23.59 &13.60 &1.7 &44.5 &22.08 &11.94 & 1.2\\cr\nMRK\\,3\t \t\t&53.7 &23.99 &13.94 &1.7 &82.6 &22.29 &11.28 & 1.3\\cr\nUGC\\,3478 \t\t&62.8 &23.43 &14.11 &1.6 &111.5 &22.98 &11.83 & 1.9\\cr\nMRK\\,6\t \t\t&111.5 &22.98 &11.83 &1.8 &67.4 &22.77 &12.22 & 1.3\\cr\nFAIRALL\\,265\t\t&29.2 &23.48 &14.99 &2.0 &46.1 &22.29 &13.11 & 1.1\\cr\nMRK\\,79\t \t\t&47.6 &23.91 &14.39 &1.1 &77.4 &22.76 &12.10 & 1.0\\cr\nMRK\\,10\t \t\t&64.7 &23.67 &14.45 &1.8 &92.2 &23.15 &12.43 & 1.3\\cr\nUGC\\,4155\t \t&30.3 &23.41 &14.92 &2.4 &45.4 &21.87 &12.60 & 1.9\\cr\nMRK\\,622\t \t&27.5 &23.10 &14.96 &1.8 &30.3 &22.45 &13.40 & 2.1\\cr\nESO\\,18$-$G09\t\t&49.2 &24.17 &14.45 &1.3 &45.3 &22.07 &12.88 & 1.3\\cr\nMCG$-$01$-$24$-$012\t&66.1 &24.38 &15.00 &1.3 &61.4 &22.60 &13.16 & 1.1\\cr\nMRK\\,1239 \t\t&21.5 &24.41 &15.19 &1.3 &23.8 &22.75 &13.21 & 1.4\\cr\nNGC\\,3393\t\t&92.2 &24.16 &13.19 &1.3 &90.6 &22.11 &11.04 & 0.9\\cr\nNGC\\,3516 \t\t&83.9 &23.83 &12.78 &1.9 &103.2 &22.13 &10.68 & 1.9\\cr\nIRAS\\,11215$-$2806 \t&30.7 &23.85 &15.58 &1.1 &30.7 &21.53 &13.43 & 1.1\\cr\nMCG$-$05$-$27$-$013\t&79.9 &24.50 &14.96 &1.1 &92.2 &23.01 &12.27 & 1.0\\cr\nMRK\\,176 \t\t&31.7 &23.50 &15.18 &1.8 &41.3 &22.28 &13.21 & 1.6\\cr\nNGC\\,3783 \t \t&106.0 &24.31 &12.62 &1.3 &86.8 &22.08 &10.77 & 1.0\\cr\nMRK\\,766 \t\t&46.8 &23.60 &13.96 &1.7 &55.0 &22.15 &12.08 & 1.7\\cr\nNGC\\,4388 \t\t&227.0 &23.66 &12.11 &1.8 &192.6 &21.90 &10.38 & 1.7\\cr\nNGC\\,4507\t \t&76.8 &24.02 &13.11 &1.1 &69.1 &21.83 &11.12 & 0.9\\cr\nNGC\\,4593\t \t&179.7 &24.25 &12.12 &1.3 &216.6 &22.88 &9.97 & 1.3\\cr\nTOL\\,1238$-$364 \t&61.4 &23.94 &13.03 &1.3 &61.4 &22.46 &11.52 & 1.7\\cr\nNGC\\,4704\t \t&45.4 &23.91 &14.73 &1.9 &56.4 &22.76 &12.68 & 1.6\\cr\nMCG$-$02$-$33$-$034\t&96.0 &23.90 &13.71 &1.1 &96.0 &22.39 &11.73 & 1.3\\cr\nESO\\,323$-$G32 \t\t&58.4 &24.15 &13.85 &1.3 &73.7 &22.56 &11.53 & 1.1\\cr\nMCG$-$04$-$31$-$030\t&87.6 &24.23 &14.24 &1.3 &115.2 &22.81 &11.70 & 1.0\\cr\nIRAS\\,13059$-$2407 \t&32.3 &24.27 &16.55 &1.1 &41.5 &23.20 &14.01 & 0.9\\cr\nMCG$-$03$-$34$-$064\t&46.9 &24.13 &14.44 &0.9 &73.7 &22.73 &11.83 & 1.1\\cr\nESO\\,383$-$G18\t\t&27.7 &23.26 &15.63 &1.4 &30.7 &22.08 &13.92 & 1.5\\cr\nMCG$-$6$-$30$-$15\t&44.5 &23.95 &14.11 &1.1 &50.7 &22.41 &11.87 & 1.1\\cr\nNGC\\,5347\t \t&79.8 &23.90 &13.61 &1.7 &100.4 &22.99 &11.58 & 1.4\\cr\nIRAS\\,14082$+$1347\t&26.1 &23.19 &15.64 &1.4 &38.5 &22.25 &13.42 & 1.3\\cr\nNGC\\,5506\t \t&148.6 &23.62 &13.14 &1.7 &166.5 &22.33 &10.94 & 1.5\\cr\nNGC\\,5548\t \t&99.1 &24.79 &13.04 &1.7 &112.8 &23.47 &11.43 & 1.5\\cr\nIRAS\\,14317$-$3237\t&23.0 &24.05 &16.33 &1.0 &30.7 &22.69 &13.91 & 1.2\\cr\nIRAS\\,14434$+$2714\t&27.5 &24.30 &15.73 &1.6 &26.1 &22.38 &14.02 & 1.5\\cr\nUGC\\,9826\t \t&55.0 &24.39 &15.11 &1.6 &66.1 &23.00 &13.02 & 1.1\\cr\nUGC\\,9944\t \t&63.3 &23.65 &14.99 &1.5 &78.4 &22.74 &12.77 & 1.2\\cr\nIRAS\\,15480$-$0344\t&20.6 &24.32 &16.32 &1.3 &37.2 &22.98 &13.45 & 1.4\\cr\nIRAS\\,16288$+$3929\t&30.3 &23.93 &15.62 &1.2 &39.9 &22.80 &13.55 & 1.6\\cr\nIRAS\\,16382$-$0613\t&19.3 &23.32 &16.60 &1.3 &--- &--- &--- &--- \\cr\nUGC\\,10889 \t \t&74.3 &25.54 &14.97 &1.2 &71.6 &22.95 &12.88 & 2.3\\cr\nMCG$+$03$-$45$-$003\t&35.8 &24.20 &15.71 &1.2 &41.3 &21.44 &13.30 & 2.0\\cr\nFAIRALL\\,49\t \t&15.4 &22.77 &15.61 &1.5 &27.7 &22.01 &12.85 & 1.3\\cr\nFAIRALL\\,51\t \t&33.8 &22.88 &14.74 &1.7 &79.9 &22.29 &12.14 & 1.2\\cr\nESO\\,143$-$G09\t\t&39.9 &22.42 &13.89 &1.8 &61.4 &22.35 &11.66 & 1.3\\tablebreak\nFAIRALL\\,341\t\t&58.4 &24.60 &14.41 &2.3 &61.4 &22.65 &12.17 & 1.0\\cr\nUGC\\,11630\t \t&29.2 &22.10 &14.60 &1.1 &78.3 &21.91 &11.79 & 1.0\\cr\nPKS\\,2048$-$57\t\t&47.7 &22.81 &13.75 &1.5 &93.7 &21.68 &10.80 & 1.5\\cr\nNGC\\,7213\t \t&69.1 &22.25 &11.75 &1.5 &190.5 &21.84 & 8.86 & 1.3\\cr\nMRK\\,915\t \t&24.6 &22.57 &15.21 &1.1 &53.8 &22.76 &12.41 & 1.0\\cr\nUGC\\,12138\t \t&38.4 &24.38 &14.78 &2.2 &36.9 &22.21 &12.91 & 1.0\\cr\nAKN\\,564\t \t&32.7 &23.79 &14.82 &1.1 &39.7 &22.57 &13.16 & 0.9\\cr\nUGC\\,12348\t \t&30.7 &22.34 &15.78 &1.2 &38.4 &20.32 &13.25 & 1.2\\cr\nNGC\\,7674\t \t&27.7 &22.33 &14.62 &1.6 &49.2 &21.57 &12.25 & 1.2\\cr\nMRK\\,590\t\t&61.4 &24.23 &13.80 &2.5 &58.4 &21.91 &11.78 & 1.2\\cr\nMRK\\,1058\t\t&35.7 &23.94 &15.52 &2.1 &37.7 &22.19 &13.21 & 1.2\\cr\nNGC\\,1386\t\t&155.1 &23.67 &12.22 &2.1 &184.3 &22.49 &9.95 & 1.2\\cr\nMCG\\,+8-11-11\t\t&81.3 &24.10 &14.17 &1.0 &99.2 &22.21 &11.52 & 0.9\\cr\nMRK\\,705\t\t&34.4 &24.30 &14.89 &1.6 &44.0 &23.03 &12.99 & 1.6\\cr\nNGC\\,3281\t\t&178.2 &24.45 &12.82 &1.1 &184.3 &22.36 &10.44 & 1.2\\cr\nUGC\\,6100\t\t&48.2 &23.77 &14.66 &1.8 &60.5 &22.37 &12.70 & 1.9\\cr\nNGC\\,4941\t\t&190.5 &24.18 &12.30 &1.0 &192.0 &22.17 &10.16 & 1.1\\cr\nUGC\\,10683B\t\t&27.5 &23.31 &16.13 &1.3 &--- &--- &--- & ---\\cr\nESO\\,103-G35\t\t&30.7 &22.48 &15.22 &1.4 &63.0 &22.29 &12.43 & 1.3\\cr\nNGC\\,7212\t\t&30.7 &22.60 &15.60 &1.5 &27.7 &20.14 &13.34 & 1.3\\cr\n\\tablenotetext{}{Column 1 shows the galaxies names. Column 2 (6) presents the diameter of\nthe ellipse major axis used to measure the galaxy flux in B (I); Column 3 (7) presents\nthe surface brightness of the 3 $\\sigma$ level above the background in B (I); Column 4 (8)\npresents the integrated B (I) magnitude; and Column 5 (9) presents the seeing during\nthe observation.}\n\\enddata\n\\end{deluxetable}\n\\end{small}\n\n\\clearpage\n\\newpage\n\n\\begin{small}\n\\begin{deluxetable}{lrrrrrrrr}\n\\tablewidth{0pc}\n\\tablecaption{Magnitudes of the Additional Sample}\n\\tablehead{\\colhead{Name}&\\colhead{Aperture B}&\n\\colhead{3$\\sigma$B}&\\colhead{B}&\\colhead{(seeing B)}&\\colhead{Aperture I}& \n\\colhead{3$\\sigma$I}&\\colhead{I}&\\colhead{(seeing I)}\\cr\n&(arcsec)&(mag arcsec$^{-2}$)&(mag)&(arcsec)&\n(arcsec)&(mag arcsec$^{-2}$)&(mag)&(arcsec)}\n\\startdata\nESO\\,362-G8\t\t&63.0 &24.34 &13.36 &1.4 &70.7 &22.67 &11.45 & 1.0\\cr\nNGC\\,2273\t\t&88.1 &23.54 &13.05 &1.9 &144.5 &22.53 &10.60 & 2.0\\cr\nESO\\,428-G14\t\t&89.1 &24.32 &13.47 &1.2 &107.5 &21.84 &10.83 & 1.0\\cr\nMRK\\,78\t\t\t&24.8 &23.83 &15.56 &2.2 &33.0 &23.41 &13.51 & 1.4\\cr\nNGC\\,2622\t\t&30.3 &22.67 &15.17 &1.8 &37.2 &21.55 &12.86 & 1.7\\cr\nNGC\\,2639\t\t&77.1 &23.23 &12.92 &1.7 &114.2 &22.46 &10.55 & 2.2\\cr\nUGC\\,5101\t\t& --- & --- & --- &--- &48.2 &23.03 &13.36 & 1.7\\cr\nNGC\\,2992\t\t& --- & --- & --- &--- &115.2 &22.25 &10.96 & 1.1\\cr\nNGC\\,3227\t\t& --- & --- & --- &--- &242.2 &22.12 &9.61 & 1.7\\cr\nMRK\\,34\t\t\t& --- & --- & --- &--- &27.5 &21.81 &13.67 & 1.9\\cr\nNGC\\,3362\t\t& --- & --- & --- &--- &59.2 &22.42 &12.32 & 1.8\\cr\nMRK\\,423\t\t& --- & --- & --- &--- &34.4 &21.09 &13.18 & 2.1\\cr\nNGC\\,5252\t\t& --- & --- & --- &--- &74.3 &22.58 &12.03 & 1.5\\cr\nMRK\\,268\t\t& --- & --- & --- &--- &48.2 &23.11 &13.04 & 1.3\\cr\nMRK\\,270\t\t&46.8 &23.95 &14.38 &1.4 &74.3 &23.12 &12.00 & 1.2\\cr\nNGC\\,5273\t\t&114.2 &23.86 &12.70 &1.3 &151.4 &22.88 &10.52 & 1.7\\cr\nIC\\,4329A\t\t& --- & --- & --- &--- &84.5 &22.64 &11.45 & 1.6\\cr\nNGC\\,5929\t\t&55.0 &22.74 &14.02 &1.3 &41.3 &20.54 &12.23 & 1.2\\cr\nNGC\\,7450\t\t& --- & --- & --- &--- &45.6 &21.93 &12.99 & 1.4\\cr\nNGC\\,7672\t\t& --- & --- & --- &--- &48.6 &22.52 &13.00 & 1.6\\cr\n\\tablenotetext{}{Column 1 gives the galaxies names. Column 2 (6)\npresents the diameter of the ellipse major axis used to measure the\ngalaxy flux in B (I); Column 3 (7) presents the surface brightness of\nthe 3 $\\sigma$ level above the background in B (I); Column 4 (8)\npresents the integrated B (I) magnitude; and Column 5 (9) presents the\nseeing during the observation.}\n\\enddata\n\\end{deluxetable}\n\\end{small}\n\n\\clearpage\n\\newpage\n\n\\begin{small}\n\\begin{deluxetable}{lrrrr}\n\\tablewidth{0pc}\n\\tablecaption{PA's and Ellipticities of the 60$\\mu$m Sample}\n\\tablehead{\\colhead{Name}&\\colhead{PA$_{MA}$-I}&\\colhead{e-I}&\\colhead{PA$_{MA}$-B}&\\colhead{e-B}\\cr\n&(degrees)&&(degrees)&}\n\\startdata\nMRK\\,348\t\t&-45 &0.061 &-60 &0.066 \\cr\nTOL\\,0109$-$38\t\t&61 &0.555 &61 &0.507 \\cr\nMRK\\,1 \t\t&70 &0.361 &67 &0.347 \\cr\nMRK\\,359 \t\t&8 &0.167 &-21 &0.119 \\cr\nMRK\\,573 \t\t&58 &0.137 &4 &0.137 \\cr\nIRAS\\,01475$-$0740 \t&-28 &0.186 &-35 &0.161 \\cr\nESO\\,153$-$G20 \t\t&8 &0.298 &-50 &0.465 \\cr\nMRK\\,1040\t\t&75 &0.702 &--- &--- \\cr\nESO\\,355$-$G25 \t\t&-41 &0.086 &-29 &0.076 \\cr\nUGC\\,2024 \t\t&-30 &0.373 &-29 &0.342 \\cr\nNGC\\,1068 \t\t&-67 &0.106 &-5 &0.196 \\cr\nMCG$-$02$-$08$-$039 \t&12 &0.434 &17 &0.451 \\cr\nUGC\\,2514 \t\t&-40 &0.428 &-38 &0.309 \\cr\nIRAS\\,03106$-$0254 \t&-14 &0.681 &-17 &0.585 \\cr\nIRAS\\,03125$+$0119 \t&-32 &0.439 &-29 &0.440 \\cr\nMRK\\,607 \t\t&-42 &0.616 &-42 &0.630 \\cr\nESO\\,116$-$G18\t\t&--- &--- &-87 &0.567 \\cr\nIRAS\\, 04385$-$0828\t&44 &0.517 &44 &0.493 \\cr\nIRAS\\, 04502$-$0317\t&15 &0.489 &13 &0.510 \\cr\nIRAS\\, 04507$+$0358\t&46 &0.192 &52 &0.310 \\cr\nESO\\,33$-$G02 \t\t&-88 &0.086 &-74 &0.069 \\cr\nMCG$-$05$-$13$-$017 \t&-41 &0.193 &-40 &0.199 \\cr\nMRK\\,3\t \t\t&28 &0.159 &26 &0.223 \\cr\nUGC\\,3478 \t\t&44 &0.623 &43 &0.518 \\cr\nMRK\\,6\t \t\t&-46 &0.411 &-48 &0.379 \\cr\nFAIRALL\\,265\t\t&2 &0.435 &2 &0.460 \\cr\nMRK\\,79\t \t\t&-47 &0.186 &69 &0.393 \\cr\nMRK\\,10\t \t\t&-53 &0.494 &-44 &0.513 \\cr\nUGC\\,4155\t \t&-40 &0.231 &-75 &0.312 \\cr\nMRK\\,622\t \t&-35 &0.098 &-46 &0.089 \\cr\nESO\\,18$-$G09\t\t&-3 &0.138 &-22 &0.140 \\cr\nMCG$-$01$-$24$-$012\t&42 &0.414 &38 &0.527 \\cr\nMRK\\,1239 \t\t&-25 &0.188 &-24 &0.193 \\cr\nNGC\\,3393\t\t&41 &0.131 &48 &0.128 \\cr\nNGC\\,3516 \t\t&56 &0.191 &56 &0.187 \\cr\nIRAS\\,11215$-$2806 \t&-34 &0.659 &-34 &0.649 \\cr\nMCG$-$05$-$27$-$013\t&-82 &0.640 &-82 &0.663 \\cr\nMRK\\,176 \t\t&59 &0.609 &59 &0.612 \\cr\nNGC\\,3783 \t \t&-46 &0.074 &-44 &0.155 \\cr\nMRK\\,766 \t\t&67 &0.152 &70 &0.144 \\cr\nNGC\\,4388 \t\t&-89 &0.665 &-88 &0.722 \\cr\nNGC\\,4507\t \t&60 &0.164 &65 &0.122 \\cr\nNGC\\,4593\t \t&-72 &0.295 &66 &0.328 \\cr\nTOL\\,1238$-$364 \t&72 &0.104 &81 &0.078 \\cr\nNGC\\,4704\t \t&-61 &0.083 &-84 &0.037 \\cr\nMCG$-$02$-$33$-$034\t&--- &--- &--- &--- \\cr\nESO\\,323$-$G32 \t\t&-89 &0.097 &-70 &0.091 \\cr\nMCG$-$04$-$31$-$030\t&58 &0.531 &58 &0.529 \\cr\nIRAS\\,13059$-$2407 \t&-59 &0.669 &-59 &0.688 \\cr\nMCG$-$03$-$34$-$064\t&48 &0.318 &47 &0.231 \\cr\nESO\\,383$-$G18\t\t&88 &0.546 &88 &0.552 \\cr\nMCG$-$6$-$30$-$15\t&-76 &0.352 &-74 &0.359 \\cr\nNGC\\,5347\t \t&-60 &0.211 &-62 &0.223 \\cr\nIRAS\\,14082$+$1347\t&-85 &0.317 &-83 &0.305 \\cr\nNGC\\,5506\t \t&-89 &0.755 &-89 &0.758 \\cr\nNGC\\,5548\t \t&-80 &0.143 &-87 &0.198 \\cr\nIRAS\\,14317$-$3237\t&3 &0.245 &-1 &0.249 \\cr\nIRAS\\,14434$+$2714\t&88 &0.120 &77 &0.081 \\cr\nUGC\\,9826\t \t&-9 &0.327 &7 &0.300 \\cr\nUGC\\,9944\t \t&-7 &0.669 &-7 &0.676 \\cr\nIRAS\\,15480$-$0344\t&49 &0.113 &48 &0.066 \\cr\nIRAS\\,16288$+$3929\t&-77 &0.572 &-77 &0.568 \\cr\nIRAS\\,16382$-$0613\t&--- &--- &89 &0.253 \\cr\nUGC\\,10889 \t \t&43 &0.580 &45 &0.598 \\cr\nMCG$+$03$-$45$-$003\t&-33 &0.428 &11 &0.302 \\cr\nFAIRALL\\,49\t \t&-59 &0.111 &-28 &0.186 \\cr\nFAIRALL\\,51\t \t&-22 &0.447 &2 &0.576 \\cr\nESO\\,143$-$G09\t\t&35 &0.332 &34 &0.351 \\tablebreak\nFAIRALL\\,341\t\t&-23 &0.235 &-26 &0.228 \\cr\nUGC\\,11630\t \t&-81 &0.530 &-79 &0.436 \\cr\nPKS\\,2048$-$57\t\t&-60 &0.156 &-62 &0.167 \\cr\nNGC\\,7213\t \t&48 &0.033 &75 &0.026 \\cr\nMRK\\,915\t \t&-7 &0.507 &-18 &0.579 \\cr\nUGC\\,12138\t \t&-2 &0.077 &69 &0.024 \\cr\nAKN\\,564\t \t&-73 &0.198 &-72 &0.175 \\cr\nUGC\\,12348\t \t&-46 &0.715 &-46 &0.708 \\cr\nNGC\\,7674\t \t&-26 &0.266 &76 &0.228 \\cr\nMRK\\,590\t\t&-55 &0.087 &-73 &0.068 \\cr\nMRK\\,1058\t\t&-68 &0.418 &-68 &0.422 \\cr\nNGC\\,1386\t\t&25 &0.628 &25 &0.638 \\cr\nMCG\\,+8-11-11\t\t&54 &0.190 &1 &0.514 \\cr\nMRK\\,705\t\t&77 &0.226 &80 &0.225 \\cr\nNGC\\,3281\t\t&-39 &0.589 &-37 &0.599 \\cr\nUGC\\,6100\t\t&17 &0.336 &21 &0.360 \\cr\nNGC\\,4941\t\t&17 &0.518 &16 &0.529 \\cr\nUGC\\,10683B\t\t&--- &--- &--- &--- \\cr\nESO\\,103-G35\t\t&39 &0.597 &40 &0.610 \\cr\nNGC\\,7212\t\t&43 &0.638 &42 &0.621 \\cr\n\\tablenotetext{}{Column 1 gives the galaxy name; Columns 2 and 3 give\nthe position angle (PA$_{MA}$) and the ellipticity of the major axis\n(e=1-b/a), and are also the values used to measure the I magnitudes;\nColumns 4 and 5 give the position angle and ellipticity of the ellipse\nused to measure the B magnitude, presented in Table 4.}\n\\enddata\n\\end{deluxetable}\n\\end{small}\n\n\\clearpage\n\\newpage\n\n\\begin{small}\n\\begin{deluxetable}{lrrrr}\n\\tablewidth{0pc}\n\\tablecaption{PA's and Ellipticities of the Additional Sample}\n\\tablehead{\\colhead{Name}&\\colhead{PA$_{MA}$-I}&\\colhead{e-I}&\\colhead{PA$_{MA}$-B}&\\colhead{e-B}\\cr\n&(degrees)&&(degrees)&}\n\\startdata\nESO\\,362-G8\t\t&-15 &0.543 &-16 &0.537 \\cr\nNGC\\,2273\t\t&62 &0.362 &-87 &0.356 \\cr\nESO\\,428-G14\t\t&-44 &0.343 &-39 &0.313 \\cr\nMRK\\,78\t\t\t&84 &0.435 &84 &0.430 \\cr\nNGC\\,2622\t\t&52 &0.332 &52 &0.329 \\cr\nNGC\\,2639\t\t&-43 &0.398 &-43 &0.455 \\cr\nUGC\\,5101\t\t&79 &0.417 &--- &--- \\cr\nNGC\\,2992\t\t&13 &0.556 &--- &--- \\cr\nNGC\\,3227\t\t&-31 &0.459 &--- &--- \\cr\nMRK\\,34\t\t\t&65 &0.130 &--- &--- \\cr\nNGC\\,3362\t\t&0 &0.062 &--- &--- \\cr\nMRK\\,423\t\t&--- &--- &--- &--- \\cr\nNGC\\,5252\t\t&15 &0.480 &--- &--- \\cr\nMRK\\,268\t\t&-67 &0.415 &--- &--- \\cr\nMRK\\,270\t\t&-60 &0.137 &-61 &0.156 \\cr\nNGC\\,5273\t\t&11 &0.156 &10 &0.170 \\cr\nIC\\,4329A\t\t&44 &0.464 &--- &--- \\cr\nNGC\\,5929\t\t&49 &0.423 &48 &0.437 \\cr\nNGC\\,7450\t\t&25 &0.321 &--- &--- \\cr\nNGC\\,7672\t\t&28 &0.281 &--- &--- \\cr\n\\tablenotetext{}{Column 1 gives the galaxy name; Columns 2 and 3 give\nthe position angle (PA$_{MA}$) and the ellipticity of the major axis\n(e=1-b/a), and are also the values used to measure the I magnitudes;\nColumns 4 and 5 give the position angle and ellipticity of the ellipse\nused to measure the B magnitude, presented in Table 5.}\n\\enddata\n\\end{deluxetable}\n\\end{small}\n\n\\end{document}\n\\end\n\n"
}
] |
[] |
astro-ph0002133
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Models of Disk Evolution: Confrontation with Observations
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[
{
"author": "Rychard Bouwens"
}
] |
We present simple models for disk evolution based on two different approaches: a forward approach based on predictions generic to hierarchical models for structure formation (e.g., Mo, Mao, \& White 1998) and a backwards approach based on detailed modeling of the Milky Way galaxy (e.g., Bouwens, Cay\'on, \& Silk 1997). We normalize these models to local observations and predict high-redshift luminosities, sizes, circular velocities, and surface brightnesses. Both approaches yield somewhat similar predictions for size, surface brightness, and luminosity evolution though they clearly differ in the amount of number evolution. These predictions seem to be broadly consistent with the high-redshift observations of Simard et al.\ (1999), suggesting that the $B$-band surface brightness of disks has indeed evolved by $\sim1.5^m$ from $z\sim0$ to $z\sim1$ similar to the models and is not an artifact of selection effects as previously claimed. We also find a lack of low surface brightness galaxies in several high redshift samples relative to model predictions based on local samples (de Jong \& van der Kruit 1994; Mathewson, Ford, \& Buchhorn 1992).
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[
{
"name": "ms.tex",
"string": "\\documentstyle[aaspp4,12pt,epsfig,color]{article}\n\n\\begin{document}\n\n\\title{Models of Disk Evolution: Confrontation with Observations}\n\n\\author{Rychard Bouwens}\n\\affil{Physics Department,\n University of California,\n Berkeley, CA 94720; bouwens@astro.berkeley.edu}\n\\centerline \\&\n\\author {Joseph Silk}\n\\affil{Astrophysics, Department of Physics, University of Oxford, Oxford OX1 3RH UK and Astronomy and Physics Departments, and Center for Particle\n Astrophysics, University of California,\n Berkeley, CA 94720; silk@astro.berkeley.edu}\n\n\\begin{abstract}\n\nWe present simple models for disk evolution based on two different\napproaches: a forward approach based on predictions generic to\nhierarchical models for structure formation (e.g., Mo, Mao, \\& White\n1998) and a backwards approach based on detailed modeling of the\nMilky Way galaxy (e.g., Bouwens, Cay\\'on, \\& Silk 1997). We normalize\nthese models to local observations and predict high-redshift\nluminosities, sizes, circular velocities, and surface brightnesses.\nBoth approaches yield somewhat similar predictions for size, surface\nbrightness, and luminosity evolution though they clearly differ in the\namount of number evolution. These predictions seem to be broadly\nconsistent with the high-redshift observations of Simard et al.\\\n(1999), suggesting that the $B$-band surface brightness of disks has\nindeed evolved by $\\sim1.5^m$ from $z\\sim0$ to $z\\sim1$ similar to the\nmodels and is not an artifact of selection effects as previously\nclaimed. We also find a lack of low surface brightness galaxies in\nseveral high redshift samples relative to model predictions based on\nlocal samples (de Jong \\& van der Kruit 1994; Mathewson, Ford, \\&\nBuchhorn 1992).\n\n\\end{abstract}\n\n\\keywords{galaxies: evolution}\n\n\\section{Introduction}\n\nOver the last several years, there has been a steady increase in the\nnumber and quality of observations available for disk galaxies from\n$z=0$ and $z=1$. Schade et al.\\ (1995,1996), using early ground and\nspace based images of galaxies from the Canada-France Redshift Survey\n(CFRS), found a net increase in the surface brightness of galaxies to\n$z\\sim1$. Along the same lines, Roche et al.\\ (1998), compiling 347\ngalaxies from the Medium Deep Survey and other surveys, concluded that\ndisk galaxies had undergone a net evolution in surface brightness and\na net devolution in size. Lilly et al.\\ (1998), using structural\nparameters extracted from HST images of the combined CFRS and LDSS2\nsample, concluded that there has been essentially no evolution in\nlarge disks out to $z\\sim1$. As a preliminary effort as part of the\nDEEP survey, Vogt et al.\\ (1996,1997) found little evolution in the\nTully-Fisher relationship ($<0.3^m$) out to $z\\sim1$. More recently,\nthese observations have been augmented by the DEEP sample with 197\ngalaxies from the Groth strip to $I<23.5$, 1.5 magnitudes deeper than\nthe LDSS2-CFRS sample. In a first paper, Simard et al.\\ (1998)\nconcluded that there had been little evolution in the disk surface\nbrightness distribution to $z\\sim1$ contrary to previous claims.\n\nA number of different approaches have been proposed for making\nspecific predictions about disk evolution. Mo, Mao, \\& White (1998a)\nshowed how the standard paradigm for hierarchical growth of structure\ncombined with simple assumptions about angular momentum conservation\nled to simple scaling relationships for the change in disk properties\nas a function of redshift. Other authors (Ferrini et al.\\ 1994;\nPrantzos \\& Aubert 1995; Prantzos \\& Silk 1998; Boissier \\& Prantzos\n1999; Chiappini, Matteucci \\& Gratton 1997), taking more of a\nbackwards approach to the problem, used detailed studies of the\nprofiles of the Milky Way and other nearby galaxies to propose\nradially dependent models of star formation in disk galaxies, models\nwhich could be used to make detailed predictions about high-redshift\ndisk evolution.\n\nAlready there have been a number of elegant studies in which both the\nbackwards approach (Cay\\'on, Silk, \\& Charlot 1996; Bouwens, Cay\\'on,\n\\& Silk 1997; Roche et al.\\ 1998) and the forwards approach (Mao, Mo,\n\\& White 1998; Steinmetz \\& Navarro 1999; Contardo, Steinmetz, \\&\nFritze-von Alvensleben 1998; van den Bosch 1998; Mo, Mao, \\& White\n1998b) have been used to interpret the observations available for disk\ngalaxies, mostly to $z\\sim1$.\n\nUnfortunately, none of these studies considered the important effect\nthat a large spread in surface brightness could have on the\ninterpretation of these observations, particularly the potentially\nlarge fraction of low surface brightness galaxies. In some studies,\nthe surface brightness selection effects at low and high redshift were\nsimply ignored, and in others, e.g., Roche et al.\\ (1998), the spread\nwas limited to $0.3\\,\\textrm{mag/arcsec}^2$ about Freeman's law\n(Freeman 1970). Clearly, given the apparent large numbers of low\nsurface brightness galaxies seen locally, it is quite logical to\nwonder if these galaxies are detectable in current high redshift\nsurveys. Indeed, one might wonder whether these galaxies or the\nobserved correlation between luminosity and surface brightness may\nhave already affected the interpretation of high redshift\nobservations. In light of the recent claim by Simard et al.\\ (1999)\nthat the apparent surface brightness evolution thus far inferred to\n$z\\sim1$ is completely due to surface brightness selection effects,\nsuch a study would seem to be especially timely. Secondly, none of\nthese studies directly compared the predictions of the forward and\nbackward approaches using the same observations. Simple comparisons\nof the scaling expected in surface brightness, size, luminosity, and\nnumber are useful for interpreting the high redshift observations.\n\nTo address these shortcomings, we shall therefore consider\nimplementations of both approaches, normalize them to the observed\n$z\\sim0$ size-luminosity relationship, compare their predictions, and\nconsider how each of them fares at explaining the observed disk\nevolution out to $z\\sim1$ incorporating all the selection effects as\nthey are best understood. We commence by presenting our models (\\S2)\nand the observational samples with which we compare (\\S3). We present\nthe results (\\S4), discuss them (\\S5), and then summarize our\nconclusions (\\S6). Throughout this study, we use $H_0 =\n50\\,\\textrm{km/s/Mpc}$ unless otherwise noted.\n\n\\section{Models}\n\nWe begin by sketching the base $z=0$ model to be used for both the\nmodels which follow. We use a set of gaussian LFs based on those\npresented in Binggeli, Sandage, and Tammann (1988):\n\\begin{equation}\n\\phi(M) dM = \\frac{\\phi_0}{2\\pi \\sigma_M}\n\\exp(-(\\frac{M-M_{*}}{\\sigma_M})^2) dM\n\\end{equation}\nWe adjusted the bulge-to-total ($B/T$) distributions of these galaxy\ntypes to obtain fair agreement with the de Jong \\& van der Kruit\n(1994) sample. Finally, we adjusted the luminosity function so there\nwas rough agreement with the combined Sabc and Sdm luminosity\nfunctions presented in Pozzetti, Bruzual, \\& Zamorani (1996). We\npresent our parameterized populations in Table 1. \n\n\\begin{deluxetable}{cccccccc}\n\\tablewidth{0pt}\n\\tablecaption{Model parameters for disk population.\\label{lowl}}\n\\tablehead{\n\\colhead{$\\phi_o$} & \\colhead{$\\sigma_M$} & \\colhead{$M_{b_j}^*$} &\n\\colhead{$B/T$} &\n\\colhead{$\\sigma_{B/T}$}}\n\\startdata\n2.0 & 1.1 & -19.4 & 0.25 & 1.8\\\\\n2.5 & 1.1 & -19.6 & 0.08 & 0.5\\\\\n8.0 & 1.3 & -18.4 & 0.04 & 0.25\\\\\n24.0 & 1.3 & -16.0 & 0.01 & 0.25\n\\enddata\n\\end{deluxetable}\n\nFor the above luminosity functions, we convert $z=0$ $B$-band\nluminosity to mass using a constant mass-to-light ratio, where the\nmass of a $M_{b_J} = -21.1$ galaxy is $1.1 \\cdot 10^{12} M_{\\odot}$.\nWe assume a log-normal scatter of 0.3 dex to reproduce the observed\nTully-Fisher scatter though variation in the formation times (van den\nBosch 1998) and concentration indexes (Avila-Reese, Firmani, \\&\nHernandez 1998) certainly play a role.\n\nTo translate this mass into a circular velocity and size, we calculate\nthe time at which the ambient halo formed. Since halos are always\naccreting more mass and merging with larger halos, there is some\nambiguity in defining this, so for simplicity we take it to equal the\nredshift at which half of the mass in a halo has been assembled. We\ndetermine the distribution of formation times using the procedure\noutlined in Section 2.5.2 of Lacey \\& Cole (1993). We take the\ncircular velocity of the halo to be that corresponding to the halo at\nits formation time using Eq. (14).\n\nThen, given the mass, circular velocity, and luminosity of the $z=0$\ndisk, we randomly draw the sizes $r_e$ from the following\ndistribution:\n\\begin{equation}\n\\phi (r_e) d \\log r_e = \\frac{1}{\\sigma_{\\lambda}\\sqrt{2\\pi}} \n\\exp(-\\frac{1}{2} [\\frac{\\log r_e/r_e ^{*} - 0.4(M-M_{*,s})(1/3)}\n{\\sigma_{\\lambda}/\\ln(10)}]^2) d \\log r_e\n\\end{equation}\nwhere $r_e^* = 6.9 \\textrm{kpc}$, $\\sigma_{\\lambda} = 0.37$, and $M_{*,s}\n= -21.1$. We provide a basic observational and theoretical motivation\nfor this scaling in \\S2.1. Note that here the surface brightness is\nproportional to $L^{1/3}$, that the spread in the size distribution is\nproportional to the spread in the distribution of $\\lambda$, and that\nthe scale length (surface brightness) of the average $L_{*}$ galaxy is\nexactly equal to that predicted by Freeman's law.\n\nWe assume that the SED of disks and bulges is identical to that of a\n10 Gyr-old stellar population with an e-folding time of 4.5 Gyr and a\n$\\tau_{B} = 0.3$ foreground dust screen, the extinction curve being\nthat of Calzetti (1997). For simplicity, we assume this SED is\nconstant independent of time. We use the Bruzual \\& Charlot tables\nfrom the Leitherer et al.\\ (1996) compilation for this calculation.\nIn the following models, we evolve the size, number, and luminosity of\nall galaxy types using simple single-valued functions of redshift:\n\\begin{equation}\nR(z) = R(0) E_R (z)\n\\end{equation}\n\\begin{equation}\nN(z) = N(0) E_N (z)\n\\end{equation}\n\\begin{equation}\nL(z) = L(0) E_L (z)\n\\end{equation}\nFor simplicity, we assume similar scalings in the properties of bulges\nas a function of time.\n\nSince the color and luminosity of disks has been shown to be\ncorrelated with inclination, it is reasonable to suppose that disks\nare not transparent. Unfortunately, there is much controversy\nconcerning the degree to which disks are or are not transparent. For\nbetter or worse, we will side-step this controversy and simply adopt\nthe Tully \\& Fouqu\\'e (1985) prescription for extinction in the $B$\nband:\n\\begin{equation}\nA_B = -2.5 \\log(f(1-\\exp(-\\tau \\sec i)) + (1 - 2f)\n(\\frac{1-\\exp(-\\tau \\sec i)}{\\tau \\sec i}))\n\\end{equation}\nwhere $\\tau = 0.55$, $f = 0.25$, and $i$ is the inclination of the\ndisk, 0 corresponding to a face-on disk. We shall assume our model\ngalaxies are always observed at an inclination of $70\\deg$ and\ntherefore always correct the observations to this inclination for\ncomparison with the models. In the $B$ band, this corresponds to an\nextinction correction of $0.67^m$.\n\n\\subsection{Hierarchical Model (Forwards Approach)}\n\nThe use of simple scaling relationships between the properties of\ndisks and the halos in which they live has provided a relatively\nsuccessful way of explaining both the internal correlations between\ndisk properties and their evolution to high redshift. In this picture\ndeveloped by Fall \\& Estathiou (1980) and revived more recently by\nDalcanton et al.\\ (1997) and Mo et al.\\ (1998) among others, the\nbivariate mass and angular momentum distribution nicely translates\ninto a luminosity and surface brightness relationship for disk\ngalaxies, mass translating directly into luminosity and the\ndimensionless angular momentum translating directly into surface\nbrightness.\n\nThis picture has had much success in explaining the internal\ncorrelations between size, circular velocity, and mass. For example,\nDe Jong \\& Lacey (1999) recently showed that the observed local\nbivariate luminosity-size distribution is nicely fit by this picture,\nalbeit with a slightly smaller scatter in surface brightness than\nmight otherwise be expected. For constant mass-to-light ratios, the\nrough $M \\propto V_c^3$ relationship for halos provides a relatively\nnatural explanation for the luminosity-circular velocity\n(Tully-Fisher) relationship (Dalcanton, Spergel, \\& Summers 1997a; Mo\net al.\\ 1998a; Steinmetz \\& Navarro 1999; Contardo et al.\\ 1998).\nFinally, the $R \\propto V_c$ relationship found in galaxy halos is\nsimilarly observed in the disk population (Courteau 1997).\n\nOn the other hand, this picture says little, if anything, about how\nthe gas disk evolved over time and therefore what its local properties\n(i.e., spatial variations in the metallicity, color, stellar ages, gas\ndensity, etc.) or global properties (total gas mass) are, and\ntherefore comparisons of this sort will depend upon the model adopted,\nwhether it be one of the popular semi-analytic approaches (Cole et\nal.\\ 1999, Somerville \\& Primack 1998) or a full N-body hydrodynamical\nsimulation (e.g., Contardo et al.\\ 1998). Moreover, it is now\napparent that the simple scaling model is fundamentally flawed with\nregard to the implementation of galaxy formation theory as revealed by\nhigh resolution numerical simulations (Moore et al. 1999; Navarro \\&\nSteinmetz 1999; Steinmetz \\& Navarro 1999). Since it however is the\nonly detailed model available, it is imperative to fully explore\ncomparisons with data, properly incorporating observational selection\neffects, in order to establish the correct basis for ultimately\nrefining the model.\n\nFor a detailed discussion of this picture, i.e., the idea that simple\nscalings in the properties of halos lead to simple scalings in the\nproperties of disks, the reader is referred to Mo et al.\\ (1998a) and\nlater papers by the same authors. For the sake of clarity, we shall\nreview some of this material. In the standard spherical collapse\nmodel for an Einstein-de Sitter universe, the density of the collapsed\nhalo is $18 \\pi^2 \\approx 178$ times the critical density of the\nuniverse at collapse time (see also Gunn \\& Gott 1972; Bertschinger\n1985; Cole \\& Lacey 1996), but depends on the density of universe\nthrough the parameter $x = 1 - \\Omega(z)$. Expressing the result in\nterms of the super critical density parameter $\\Delta_c$\n\\begin{equation}\n\\frac{M}{\\frac{4}{3}\\pi r_{vir}^3} = \\Delta_c \\rho_c\n\\end{equation}\nBryan \\& Norman (1998) found that for $\\Omega + \\Omega_{\\Lambda} = 1$,\n\\begin{equation}\n\\Delta_c \\approx 18 \\pi^2 + 82 x - 39 x^2 \n\\end{equation}\nfor $\\Omega_{\\Lambda} = 0$,\n\\begin{equation}\n\\Delta_c \\approx 18 \\pi^2 + 60 x - 32 x^2\n\\end{equation}\nwhere $x = \\Omega (z) - 1$. \n\nUsing the virial theorem, it is possible to write equations to relate\nthe mass, radius, and circular velocity of each halo. As in\nSomerville \\& Primack (1998), it can be shown that\n\\begin{equation}\nV_{vir} ^2 = \\frac{GM}{r_{vir}} - \\frac{\\Omega_{\\Lambda}}{3} H(z) ^2\nr_{vir} ^2\n\\end{equation}\nwhere $r_{vir}$ is the halo size, $V_{vir}$ is the circular velocity\nof the halo at $r_{vir}$, $G$ is Newton's constant, and\n\\begin{equation}\nH(z_f) = H_0 \\sqrt{\\Omega_{\\Lambda,0} + (1 - \\Omega_0 - \\Omega_{\\Lambda,0}) \n\t(1 + z_f)^2 + \\Omega_0 (1+z_f)^3}.\n\\end{equation}\nUsing the fact that $M = \\Delta_c \\rho_c \\frac{4}{3}\\pi r_{vir}^3 =\n\\Delta_c H(z) ^2 \\frac{1}{2G} r_{vir}^3$, we can rewrite this as\n\\begin{equation}\nV_{vir} ^2 = \\frac{1}{2}(\\Delta_c - \\Omega_{\\Lambda}) H(z) ^2 r_{vir} ^2\n\\end{equation}\nor\n\\begin{equation}\nr_{vir} = \\frac{V_{vir}}{\\sqrt{\\frac{1}{2}(\\Delta_c - \\Omega_{\\Lambda})}H(z)}\n\\end{equation}\nSimilarly, we can now rewrite the halo mass as\n\\begin{equation}\nM = \\frac{V_{vir} ^2 r_{vir}}{G} = \\frac{V_{vir} ^3}\n{G H(z) \\sqrt{\\frac{1}{2}(\\Delta_c - \\Omega_{\\Lambda})}},\n\\end{equation}\nAssuming the matter which settles in the disk to be some fraction\n$m_d$ of the halo mass and the angular momentum of this settling\nmatter to be some fraction $j_d$ of the halo's angular momentum, a\nstraightforward derivation (e.g., Mo et al.\\ 1998a) allows one to\nobtain\n\\begin{equation}\nM_d = \\frac{m_d V_{vir} ^3}\n{G H(z_f) \\sqrt{\\frac{1}{2}(\\Delta_c - \\Omega_{\\Lambda})}}\n\\end{equation}\nfor the mass of the disk and\n\\begin{equation}\nR_d = \\frac{1}{\\sqrt{2}} \\left( \\frac{j_d}{m_d} \\right ) \\lambda r_{vir}\n\\end{equation}\nfor the radius of the disk. The dimensionless angular momentum parameter\n$\\lambda$ is defined as\n\\begin{equation}\n\\lambda = J |E|^{1/2} G^{-1} M^{-5/2}\n\\end{equation}\nwhere $J$ is angular momentum, $M$ is the mass, and $E$ is the total\nenergy of the bound system.\n\nThere are three relatively simple reasons to go beyond this simple\napproach. First, the adiabatic contraction of the halo due to\ndissipation of baryons towards the halo center will modify the halo\nprofile. Second, numerical simulations show that model halos actually\nhave a Navarro, Frenk, \\& White (1997) profile for the the dark halo\nrather than the isothermal profile used above. Finally, in order to\nmake comparisons back to the observations, it is important to consider\nthe observationally-measured rotational velocities of the disk rather\nthan the rotational velocities of the halo proper. Mo et al.\\ (1998a)\nhave found approximate fitting formulas for the consequent corrections\nmade to the disk radius $R_d$ and the circular velocity at $3R_d$:\n\\begin{equation}\nR_d = \\frac{1}{\\sqrt{2}} \\left( \\frac{j_d}{m_d} \\right ) \\lambda r_{vir}\nf_c ^ {-1/2} f_R\n\\end{equation}\n\\begin{equation}\nV_c (3R_d) = V_{vir} f_V\n\\end{equation}\nwhere approximate fitting functions for $f_c$, $f_R$, and $f_V$ are\ngiven by\n\\begin{equation}\nf_c \\approx \\frac{2}{3} + \\left( \\frac{c}{21.5} \\right) ^{0.7}\n\\end{equation}\n\\begin{equation}\nf_R \\approx \\left( \\frac{\\lambda}{0.1} \\right) \n^{-0.06+2.71 m_d + 0.0047/\\lambda}\n(1 - 3 m_d + 5.2 m_d^2) (1 - 0.019c + 0.00025c^2 + 0.52/c)\n\\end{equation}\n\\begin{equation}\nf_V \\approx \\left( \\frac{\\lambda}{0.1} \\right) \n^{-2.67 m_d - 0.0038/\\lambda + 0.2 \\lambda}\n(1 + 4.35 m_d - 3.76 m_d^2) \\frac{1 + 0.057c - 0.00034 c^2 - 1.54/c}\n{\\left[ -c/(1+c) + \\ln(1+c) \\right]^{1/2}}\n\\end{equation}\nwhere $c$ is the standard halo concentration parameter for the Navarro\net al.\\ (1997) profile. For simplicity, we use $m_d = 0.05$ and\n$c=10$ to convert $V_{vir}$ to $V_c$ in order to compare with the\nobservations. We do not use Eqs. (15)-(16) for these comparisons. Note\nthat larger values of $m_d$ render disks unstable at relatively faint\nsurface brightnesses and thus have difficulty accounting for Freeman\nLaw-type surface brightnesses (Freeman 1970).\n\nOn the basis of these simple halo scaling relations, the size and mass\nof disks at any redshift simply scales as\n$1/H(z_f)\\sqrt{\\frac{1}{2}\\Delta_c(z_f)-\\Lambda(z_f)}$, $z_f$ being\nthe redshift at which these high-redshift disks \\textit{formed}.\nConsequently, the size and luminosity scale as\n\\begin{equation}\nr(z) = \\frac{V_{vir}}\n{\\sqrt{\\frac{1}{2}(\\Delta_c(z_f(z)) - \\Omega_{\\Lambda}(z_f(z)))}H(z_f(z))}\n\\end{equation}\n\\begin{equation}\nL(z) = \\frac{L}{M}(z) M(z) = \\frac{L}{M}(z) \\frac{V_{vir} ^3}\n{G H(z_f(z)) \\sqrt{\\frac{1}{2}(\\Delta_c(z_f(z)) - \\Omega_{\\Lambda}(z_f(z))}} f_V\n\\end{equation}\nUsing Eq. (3) and (4), we now have our functions $E_R(z)$ and $E_L(z)$:\n\\begin{equation}\nE_R(z) = \\frac{H(z_f(0))\\sqrt{\\frac{1}{2}(\\Delta_c(z_f(0)) -\n\\Omega_{\\Lambda}(z_f(0)))}}{H(z_f(z))\n\\sqrt{\\frac{1}{2}(\\Delta_c(z_f(z)) - \\Omega_{\\Lambda}(z_f(z)))}}\n\\end{equation}\n\\begin{equation}\nE_L(z) = \\frac{\\gamma(0) H(z_f(0))\\sqrt{\\frac{1}{2}(\\Delta_c(z_f(0)) -\n\\Omega_{\\Lambda}(z_f(0)))}}{\\gamma(z) H(z_f(z))\n\\sqrt{\\frac{1}{2}(\\Delta_c(z_f(z)) - \\Omega_{\\Lambda}(z_f(z)))}}\n\\end{equation}\nwhere $\\gamma(z)$ is the mass-to-light ratio at redshift $z$. Note\nthat this is quite different from scaling these disks simply in terms\nof the redshift at which these disks were \\textit{observed},\nparticularly in the case of low $\\Omega$ where little evolution in the\nsize or baryonic mass of the disk population is expected.\n\nWe assume that the $z=0$ luminosity function scales in number as a\nfunction of $z$ in an analogous way to how the $10^{12} M_{\\odot}$\nhalos scale in number. Using the Press-Schechter (Press \\& Schechter\n1974) mass function\n\\begin{equation}\nN(M,z) dM = -\\sqrt{\\frac{2}{\\pi}} \\frac{\\rho_0}{M}\n\\frac{\\delta_c}{\\sigma(M) D(z)} \n\\exp \\left(\n-\\frac{\\delta_c^2}{2 \\sigma^2(M) D(z)^2}\n\\right) \\frac{d\\sigma(M)}{dM} dM\n\\end{equation}\nwe see that the halo number density scales as\n\\begin{equation}\nn \\propto [D(z)]^{-1}\n\\end{equation}\nsince the exponential factor remains approximately unity for the\n$10^{12} M_{\\odot}$ mass scale. In terms of the formalism of\nEqs. (3-5),\n\\begin{equation}\nE_N(z) = \\frac{D(0)}{D(z)}\n\\end{equation}\nHere, $D(z)$, the growth factor, was computed using the formula\ntabulated in Carroll, Press, \\& Turner (1992).\n\nWe now provide a theoretical and observational justification for our\nsize-luminosity distribution. Theoretically, in the Fall \\& Estathiou\n(1980) picture, the spread in surface brightnesses derives from the\nspread in dimensionless angular momenta for halos. An approximate\nparameterization of the dimensionless angular momentum distribution is\n\\begin{equation}\np(\\lambda) = \\frac{1}{\\sqrt{2\\pi \\sigma_{\\lambda}}} \\exp \n\\left[ - \\frac{\\ln(\\lambda / \\bar{\\lambda})^2}{2 \\sigma_{\\lambda} ^2} \\right ]\n\\frac{d\\lambda}{\\lambda}\n\\end{equation}\nFor $\\bar{\\lambda}=0.05$ and $\\sigma_{\\lambda}=0.5$, the above\nexpression closely approximates the distribution obtained from N-body\nsimulations (Warren et al.\\ 1992; Cole \\& Lacey 1996; Catelan \\&\nTheuns 1996) and analytical treatments (Steinmetz \\& Bartelmann 1995).\nThe above spread in dimensionless angular momentum directly translates\ninto the following distribution of sizes:\n\\begin{equation}\n\\phi(r) dr = \\frac{1}{\\sqrt{2\\pi \\sigma_{\\lambda}}} \\exp \n\\left[ - \\frac{\\ln(r / \\bar{r_e})^2}{2 \\sigma_{\\lambda} ^2} \\right ]\nd \\log r\n\\end{equation}\nFor disks with a constant mass-to-light ratio, it follows from\nEqs. (13-16) that $r_d \\propto r_{vir} \\propto V_{vir} H(z_f)^{-1}\n\\propto M_d^{1/3} H(z_f)^{-2/3} \\propto L_d^{1/3} H(z_f)^{-2/3}$.\nIgnoring the dependence of $H(z_f)^{-2/3}$ on the luminosity, it\nfollows that the surface brightness ($L_d / r_d^2$) scales as\n$L_d^{1/3}$.\n\nIn fact, de Jong \\& Lacey (1998) found that the Mathewson, Ford, \\&\nBuchhorn (1992) data set gave a good fit to the following bivariate\nsize-luminosity distribution with similar properties to those\npredicted above:\n\\begin{eqnarray}\n\\lefteqn{\n\\Phi (r_e,M) d \\log r_e dM = \\frac{\\Phi_0}{\\sigma_{\\lambda}\n\\sqrt{2\\pi}} \n\\exp(-\\frac{1}{2} [\\frac{\\log r_e/r_e ^{*} - 0.4(M-M_*)(2/\\beta-1)}\n{\\sigma_{\\lambda}/\\ln(10)}]^2)}\\nonumber\\\\\n& & 10^{-0.4*(M-M_{*})(\\alpha+1)} \\exp(-10^{-0.4*(M-M_*)}) d \\log r_e dM\n\\end{eqnarray}\nwhere $\\Phi_0 = 0.0033 \\textrm{Mpc}^{-3}$, $\\alpha = -1.04$, $\\beta =\n3$, $M_{*} = -22.8$, $r_e ^{*} = 7.9 \\textrm{kpc}$, and\n$\\sigma_{\\lambda} = 0.37$ (converting their sizes and luminosities\nfrom $h_0 = 0.65$ to the $h_0 = 0.50$ used here). Implicit in the\nabove bivariate distribution is a distribution in sizes analogous to\nEq. (31), a Schechter distribution in luminosity, and a\n$SB \\propto L^{1/3}$ correlation between luminosity and surface\nbrightness. Similar scalings are apparent in the McGaugh \\& de Blok\n(1997) sample.\n\nNow let us compare a typical $L_{*}$ galaxy in this model with the\nobservations. Using our stated assumption, a $L_{*}$ galaxy has a\nmass of $1.1 \\cdot 10^{12} M_{\\odot}$. A typical formation time\noccurs at $z = 0.3$. Using Eqs. (13-14), the circular velocity and\nsize of the halo is 132 km/s and 272 kpc (compared to the 140 km/s and\n241 kpc predicted assuming a constant $200\\rho_c$ for the collapse\ndensity as in Mo et al.\\ 1998). Then, using Eq. (18), the size of the\ndisk is $\\sim6.0$ kpc.\n\nThis is smaller than the empirical findings of de Jong \\& Lacey (1998)\n(7.9 kpc), our own comparisons to local observations (\\S4.4) (6.9\nkpc), and Freeman's Law, which gives 6.9 kpc. Supposing this to be\ndue to a slight cut-off at low values of the dimensionless angular\nmomentum due to disk instabilities (Efstathiou, Lake \\& Negroponte\n1982; Dalcanton et al.\\ 1997; Mo et al.\\ 1998a; van den Bosch 1998),\nwe scale up the size of a typical $L_{*}$ disk galaxy to 6.9 kpc and\nreduce the spread in dimensionless angular momenta to\n$\\sigma_{\\lambda} = 0.37$, as found by de Jong \\& Lacey (1999) in the\nanalysis of the Mathewson et al.\\ (1992) sample.\n\nThroughout our analysis, we shall take the $\\Omega=0.3$,\n$\\Omega_{\\Lambda}=0.7$ model as our preferred fiducial hierarchical\nmodel because of its better correspondence with the evolution in the\nnumber of small disks observed up to $z\\sim1$ (Mao et al.\\ 1998). We\nevolve the mass-to-light ratio $\\gamma(z)$ as $(1+z)^{-0.5}$ to\nreproduce the observed evolution in the Tully-Fisher relationship (see\n\\S4.2).\n\n\\subsection{Infall Model (Backwards Approach)}\n\nInstead of trying to determine how the global structural properties of\ndisks evolve based on the corresponding properties of their ambient\nhalos, it is also possible to examine a number of local disk galaxies\nin great detail and to use detailed models of their observed\nproperties (gas profiles, stellar profiles, metallicity profiles,\ncurrent SFR profiles, age-metallicity relationships) to determine how\ngalaxies might have evolved to high redshift.\n\nThere is no consideration of how individual halos might evolve\nbackwards in time in these models, both for simplicity and because of\nlarge uncertainties in the local distribution of dark matter.\nConsequently, while for the forwards approach, the entire evolution of\ndisk properties derives from an evolution of the halo properties, the\ninfall models considered here completely ignore these effects.\nConversely, while the forwards approach presented here ignores issues\nrelated to the manner in which halo gas is converted into stars, for\nthe infall model, such issues are important.\n\nNaturally, given that one always adopts the observed local universe in\nthis approach as known, this approach does not explain in and of\nitself why the local disk population is as it is. Indeed, it cannot\nsince there is no link to the initial conditions. In this view, for\nthe hierarchical approach, we adopted the local universe we did\nbecause it was a natural prediction of the model, and for the infall\napproach, we adopted it because it agrees with the observations.\n\nWe examine such a model for the evolution of local galaxies based upon\nthe Prantzos \\& Aubert (1995) model for the star formation rates,\nmetallicites, stars, and gas content for the Milky Way disk. We\npreviously presented this infall model elsewhere (Bouwens et al.\\\n1997; Cay\\'on et al.\\ 1996), and we shall revisit it here. This model\nignores radial inflows for simplicity and takes the star formation\nrate to be proportional to both the gas surface density ($\\Sigma_g$)\nand the reciprocal of the radius $r$, which for a flat rotation curve\nis proportional to the epicyclic frequency:\n\\begin{equation}\n\\frac{d\\Sigma_{*}(r,t)}{dt} = \\frac{\\Sigma_g (r,t)}{\\tau_g (r)}\n\\end{equation}\nwhere $\\tau_g (r) = [0.3 (r/r_{\\odot})^{-1}\\,\\textrm{Gyr}]^{-1}$.\nPhysically, such a star formation rate results if the star formation\nrate is proportional to the rate at which molecular clouds collide\n(Wang \\& Silk 1994) or the periodic compression rate (Wyse \\& Silk\n1989).\n\nFor simplicity, the accretion time scale $\\tau_{ff}$ was taken to be\nindependent of radius since a variation in this time scale is not\nstrongly constrained by the observations (Prantzos \\& Aubert 1995).\nThe spread in Hubble types was then naturally taken to arise from a\nspread in this time scale (Cay\\'on et al.\\ 1996). The equation for the\nevolution of the gas density is then\n\\begin{equation}\n\\frac{d\\Sigma_g (r)}{dt} = \\frac{\\Sigma_g (r,T) + \\Sigma_{*} (r,T)}{1\n - e^{-T/\\tau_{ff}}} \\frac{e^{-t/\\tau_{ff}}}{\\tau_{ff}} -\n \\frac{\\Sigma_g (r)}{\\tau_g}\n\\end{equation}\nwhere $T$ is the time from the formation of the disk to the present.\nIntegrating these equations yields the result\n\\begin{equation}\n\\Sigma_g (r,t) = \\frac{\\Sigma_g (r,T) + \\Sigma_{*} (r,T)}{1 -\ne^{-T/\\tau_{ff}}} \\frac{e^{-t/\\tau_{ff}} - e^{-t/\\tau_g}}{\\tau_{ff} -\n\\tau_g} \\tau_g\n\\end{equation}\n\nGiven the fact that this model derived from only one galaxy, it is\ndifficult to know how to extend its evolutionary predictions to\ngalaxies with different luminosities and surface brightnesses. One\npossible means of extending this model to galaxies beyond the Milky\nWay involves simply scaling the star formation rates by the\ndifferential rotation rate. The change in the star formation rate\nwould then be proportional to $V_c/R$ or the typical dynamical time\nfor the disk. Since $R$ is roughly proportional to $V_c$, there would\nbe no large change in the time scales as a function of disk mass or\nrotational velocity. Accordingly, Bouwens et al.\\ (1997) simply\nelected to scale everything in size to reproduce all luminosities\nwhile conserving surface brightness, which is precisely what we have\ndone here.\n\nTo determine the scaling relations for galaxies using the infall\napproach, we performed the calculation for each galaxy on a series of\n30 different rings varying logarithmically in size, where the smallest\nis a circle with radius 0.2 kpc and the largest is a ring of radius 60\nkpc with width 12 kpc as done in Bouwens et al.\\ (1997) and Roche et\nal.\\ (1998). We calculate the evolution in rest-frame $B$ band\nmagnitudes by evolving each ring separately to keep track of its gas\nmass, stellar composition, and metallicity, and we output its colors\nusing the Bruzual \\& Charlot instantaneous-burst metallicity-dependent\nspectral synthesis tables compiled in Leitherer et al.\\ (1996).\n\nIn the rest-frame $B$ band, we found the following scaling\nrelationships:\n\\begin{equation}\nE_L (z) = 10^{-0.4(-0.6z)}\n\\end{equation}\n\\begin{equation}\nE_R (z) = 1 - 0.27z\n\\end{equation}\nClearly, without number evolution, we take $E_N(z) = 1$.\n\nFor the sake of clarity, we note that the present model differs from\nthe one presented in Bouwens et al.\\ (1997) in terms of both the\nluminosity functions used and the bulge-to-total distribution assumed.\nFurthermore, in the Bouwens et al.\\ (1997) study, the preferred values\nof the age $T$ and gas-infall time scale $\\tau_{ff}$ used in the\nPrantzos \\& Aubert (1995) study were scaled to reproduce the number\ncounts. No such scaling was attempted in the present model and we\nsimply use the same $\\tau_{ff}$ for all disk types.\n\nThis model is similar in spirit to the size-luminosity evolution model\npresented by Roche et al.\\ (1998) based on the infall models of\nChiappini et al.\\ (1997), which models the infall, star formation, and\nchemical evolution of both the thin and thick disk components. For\nthe purposes of illustration, we shall compare the Chiappini et al.\\\n(1997) infall model to the one just described in \\S4.1, after which we\nwill restrict our consideration to the redshift scalings given by the\nPrantzos \\& Aubert prescription. In this model, the star formation\ntime scale is equal to\n\\begin{equation}\n\\tau = \\left\\{\n\\begin{array}{ll}\n1\\, \\textrm{Gyr},&r<2\\, \\textrm{kpc}\\\\\n(0.875r - 0.75)\\,\\textrm{Gyr},&r\\geq2\\, \\textrm{kpc}\\\\\n\\end{array}\n\\right.\n\\end{equation}\nThe star formation commences at $t_{form} = (16\\,\\textrm{Gyr} - 0.35\n\\tau)$. Note that the time scale for star formation here depends on\nthe radius to the first power as in our model, the preferred Prantzos\n\\& Aubert (1995) model, and the recent work by Boissier \\& Prantzos\n(1999).\n\n\\section{Observations}\n\n\\subsection{Low-Redshift Samples}\n\nWe make comparisons against local samples with information on the\nsize, luminosity, and circular velocity of local galaxies. Though in\nprinciple we could have just used the Courteau (1997) sample, we\nfollow Mao et al.\\ (1998) in using a compilation of three\ndifferent samples for the comparisons which follow to examine the\nthree two-dimensional relationships.\n\n\\textit{de Jong \\& van der Kruit Sample:}\n\nThe de Jong \\& van der Kruit (1994) sample provides a nice sample for\nexamining the local size/magnitude relationship. It is selected from\nthe Uppsala Catalogue of Galaxies (Nilson 1973, hereinafter UGC), over\nonly $\\sim12.5\\%$ of the sky and uses only relatively face-on ($b >\n0.625$) galaxies (37.5\\% of all orientations). Following de Jong\n(1996), we also take it to be diameter-limited in $R$ to galaxies\nlarger than $2'$ at 24.7 $R$-band $\\textrm{mag/arcsec}^2$. Whereas de\nJong \\& van der Kruit (1994) in their treatment of their sample assume\ntransparent disks, we correct observed magnitudes to an inclination of\n$70\\deg$ using the Tully \\& Fouqu\\'e (1985) inclination corrections.\n\n\\textit{Courteau (1997) Sample:}\n\nWe use the Courteau (1997) sample to calibrate the local $z=0$\n$V_c-\\textrm{size}$ relationship. The Courteau (1997) sample contains\n304 Sb-Sc galaxies from the UGC with Zwicky magnitudes $m_B < 14.5$,\n$R$-band angular diameters larger than $1'$, and $B$-band major axis\n$< 4'$. We take their $v_{opt} = V_c (3.2 R_d)$ as the circular\nvelocity and the $25\\,r\\,\\textrm{mag/arcsec}^2$ isophote as the\nradius.\n\n\\textit{Pierce \\& Tully (1988) Sample:}\n\nWe use the Pierce \\& Tully (1988) sample to calibrate the local $z=0$\n$V_c-\\textrm{luminosity}$ relationship. The Pierce \\& Tully sample\nwas taken from galaxies in the area of the Ursa Major cluster and is\ncomplete up to $B_T < 13.3$. It includes all galaxies which are not\nelliptical or S0, not more face on than $30\\deg$, and not possessing\nconfused H I profiles. Note that in this study and in the Vogt et\nal.\\ (1996,1997) studies to be discussed, the observed absolute\n$B$-band magnitudes were corrected to intrinsic (unextincted) values\nusing the Tully \\& Fouqu\\'e (1985) inclination corrections.\n\n\\subsection{High-Redshift Samples}\n\n\\textit{Simard et al.\\ (1999) Sample:}\n\nFor the magnitude-radius relationship, we use the data presented by\nSimard et al.\\ (1999). This data set contains structural information\nfor $\\sim200$ galaxies to $I<23.5$ from 6 different WFPC2 pointings in\nthe Groth strip ($\\sim 30\\,\\textrm{arcmin}^2$). Spectra were obtained\nfor only a fraction of the faint galaxies, but for galaxies with\nspectra, there was nearly 100\\% redshift identification. Following\nSimard et al.\\ (1999), we can quantify the selection effects of this\nsample. The probability that a galaxy with apparent magnitude\n$I_{814}$ and radius $r_d$ would fall in the photometric sample is\n$S_{UP} (I_{814},r_d)$. From Figure 4 of Simard et al.\\ (1999), we\nhave approximated this as\n\\begin{displaymath}\n\\left\\{\n\\begin{array}{ll} 1,& I_{814} + 5 \\log r_d(\\prime\\prime) < 21,\\\\\n1 - \\frac{2}{3}(I_{814} + 5 \\log r_d(\\prime\\prime)), & 21 < I_{814} +\n5 \\log r_d(\\prime\\prime) < 22.5,\\\\ 0, & 22.5 < I_{814} + 5 \\log\nr_d(\\prime\\prime).\n\\end{array}\n\\right.\n\\end{displaymath}\n(Actually, this provides a steeper surface brightness cut-off than the\nselection function given in Simard et al.\\ 1999.) The probability\nthat a galaxy with apparent magnitude $I_{814}$ and radius $r_d$ would\nbe selected from the photometric sample for spectroscopic follow-up is\ngiven by $S_{PS} (I_{814},r_d)$, which we have approximated as\n\\begin{displaymath}\n\\left\\{\n\\begin{array}{ll} 1,& I_{814} < 19.3,\\\\\n1 - \\frac{0.8}{4}(I_{814} - 19.3),& 19.3<I_{814}<23.5,\\\\\n0,&23.5<I_{814}\n\\end{array}\n\\right.\n\\end{displaymath}\n(again by eyeballing Figure 4 of Simard et al.\\ 1999). Putting these\ntwo selection effects together, the probability of selecting a galaxy\nwith apparent magnitude $I_{814}$ and radius $r_d$ is simply the\nproduct of these quantities, namely, $S_{UP} (I_{814},r_d) S_{PS}\n(I_{814},r_d)$. Given our ignorance about the inclinations used in\nthe Simard et al.\\ (1999) study, we assume an average inclination of\n$60\\deg$ in transforming the absolute magnitudes to an inclination of\n$70\\deg$ using the Tully \\& Fouqu\\'e (1985) law, which yields a\ncorrection of $0.27^m$ here.\n\n\\textit{Lilly et al.\\ (1998) Sample:}\n\nWe also use the data from the LDSS2-CFRS sample with HST WFPC2\nfollow-up to look at the magnitude-radius relationship. From Table 3\nof Brinchmann et al.\\ (1998), the effective area of the CFRS portion\nof this sample is $0.01377\\,\\textrm{deg}^2$ ($49\\,\\textrm{arcmin}^2$).\nThe survey is magnitude limited to $17.5 < I < 22.5$, where the\nmagnitudes are isophotal to $28.0\\,I_{AB}\\,\\textrm{mag/arcsec}^2$.\nThough the surface brightness limit is quoted as\n$24.5\\,I_{AB}\\,\\textrm{mag/arcsec}^2$, we have used the more\nconservative surface brightness limit\n$23.5\\,I_{AB}\\,\\textrm{mag/arcsec}^2$. In principle, then, for any\ngalaxy detected the isophotal magnitude should be approximately equal\nto the total magnitude. Lilly et al.\\ (1998) chose to examine that\nsubset of galaxies from this data-set which were disk-dominated and\nhad disk scale lengths $>4$ kpc, a sample we shall henceforth refer to\nas the Lilly et al.\\ (1998) large disk sample. Given that the central\nsurface brightness is not strongly correlated with inclination angle,\nLilly et al.\\ (1998) concludes that disks are consistent with being\nopaque. We use the Tully \\& Fouqu\\'e (1985) to transform the listed\nabsolute magnitudes to an inclination of $70\\deg$.\n\n\\textit{Vogt et al.\\ (1997) Sample:}\n\nIn contrast to high-redshift samples with both magnitude and radial\ninformation, high-redshift samples with circular velocity measurements\nare considerably smaller and possess less well-defined selection\ncriteria. In fact, the Vogt et al.\\ (1996,1997) sample with 16\ngalaxies is the largest such published sample. The selection criteria\nfor this sample is still somewhat qualitative and patchy in nature.\nIt considers galaxies with an inclination greater than $30\\deg$,\ndetectable line emission, undistorted disk morphology, and an extended\nprofile. We assume an $I_{814} < 22.5$ magnitude limit as used in the\nVogt et al.\\ (1997) sample.\n\n\\section{Results}\n\n\\subsection{Basic Scalings}\n\nBefore getting into a detailed comparison of the models with the\nobservations, we begin by illustrating the manner in which the sizes\nof $L_{*}$ ($M \\sim 1.2 \\cdot 10^{12} M_{\\odot}$) galaxies typically\nevolve as a function of redshift for the different models in Figure 1.\nWe present this evolution in terms of the rest-frame $B$ half-light\nradius, the specification of a band and a measure being necessary to\nthe intrinsic band and profile dependence of evolution in the infall\nmodel.\n\nThe hierarchical models predict more size evolution than expected from\nboth infall models considered here. Of course, the $\\Omega = 1$ model\npossesses more size evolution than the $\\Omega=0.3$;\n$\\Omega_{\\Lambda}=0.7$ model, and the $\\Omega=0.3$;\n$\\Omega_{\\Lambda}=0.7$ model more size evolution than the $\\Omega=0.1$\nmodel because of the steeper dependence of $1/H(z)$ at the typical\n\\textit{formation} redshifts of disks to $z\\sim1$. The predictions of\nboth the Prantzos \\& Aubert (1995) and Chiappini et al.\\ (1997) models\nare quite similar, encouragingly enough given that Prantzos \\& Aubert\n(1995) and Chiappini et al.\\ (1997) models represent completely\nindependent efforts to model the evolution of the Milky Way galaxy.\n\nTaking $R/V_c$ as the measure of size for a given mass halo, we plot\nboth the Courteau sample at $z=0$ and the higher-redshift data of Vogt\net al.\\ (1996,1997) scaled appropriately so that the Courteau data is\ncentered on unevolved scale size of a galaxy at $z=0$. At face value,\na comparison of the Vogt data with the Courteau data indicates that\nthere has been size evolution from $z=0$ to $z=1$ as any of the models\nhere would predict (Mao et al.\\ 1998). Nevertheless, the lack of a\nstrong trend in redshift across the Vogt data-set makes one suspicious\nthat there may be selection effects at work or even systematic errors\nin the measurements of parameters which may produce the observed\ndifferences. In any case, strong conclusions must await the\ncompilation of a larger high-redshift dataset, where the selection\neffects have been more carefully quantified.\n\nWe also present model scalings of the number, luminosity, and surface\nbrightness expected for $L_{*}$ galaxies in Figure 1. By\nconstruction, the hierarchical models produce more number evolution\nthan the infall models, which involve no evolution in number. Except\nfor the infall model based upon the Chiappini et al.\\ (1997)\nprescription, our ``Infall'' model produces similar evolution in\nluminosity as the hierarchical models to $z\\sim1$. The infall models\nalso produce less surface brightness evolution than the hierarchical\nmodels.\n\n\\subsection{Tully-Fisher Relationship}\n\nTo assess hierarchical and infall models, we compare their predicted\nTully-Fisher relationships with both low and high-redshift\nobservations in the left panels of Figures 2-3. For the Monte-Carlo\nsimulations, we use the same selection effects as already specified\nfor the low (Pierce \\& Tully 1988) and high-redshift (Vogt et al.\\\n1996, 1997) samples. We have added the Pierce \\& Tully (1992) fit to\nthese plots for comparison. Naturally, for both our hierarchical and\ninfall models, we obtained good agreement with the Pierce \\& Tully\n(1988) sample since we used that sample to adjust the mass-to-light\nratio (we assumed that a $M_{b_J} = -21$ galaxy had a mass $1.2\\cdot\n10^{12} M_{\\odot}$) and its assumed log-normal scatter (one sigma\nscatter of 0.3 dex). At higher redshift, we again obtain basic\nagreement with the Vogt et al.\\ (1996,1997) sample for both our infall\nand hierarchical models.\n\n\\subsection{Size-$V_c$ Relationship}\n\nWe also compare our model predictions with the low and high-redshift\nobservations for the size-$V_c$ relationship in the right panels of\nFigures 2-3. Again, we apply the selection criteria given in \\S3 to\nthe low (Courteau 1997) and high-redshift (Vogt et al.\\ 1996,1997)\nmodel results. At low redshift, we obtain basic agreement with the\nobservations of Courteau (1997) though there seems to be a slight\nshift in our models toward larger sizes. No adjustment of our models\nwas made to obtain agreement with the Courteau (1997) sample, and so\nthis comparison can be considered a self-consistency check on our\n$z=0$ models.\n\nAt high redshift, sizes for both models are consistent, if not a\nlittle larger than the sizes in the Vogt et al.\\ (1996,1997) sample.\nOne of the most surprising thing about a comparison of the models with\nthe observations is the significant size evolution observed in the\nlowest redshift bin ($z<0.6$) relative to the models. In fact, as\ndiscussed in relation to Figure 1, the low redshift ($z<0.6$) points\nseem to have undergone more size evolution than the high redshift\n($z>0.6$) points. As the low redshift points are primarily low\nluminosity galaxies and the high redshift high luminosity galaxies,\nthis could point to some luminosity-dependent evolutionary trend\nthough the numbers are still too small to make any claims toward this\nend.\n\n\\subsection{Size-Magnitude Relationship}\n\nAs so often in making low-to-high redshift comparisons, freedom in the\nchoice of the $z=0$ no-evolution model can be very important in\ninterpreting the high-redshift results. In particular, due to the\nfact that each redshift bin in the Simard et al.\\ (1999) sample\ncontains galaxies of a particular luminosity, significant evolution in\ndisk surface brightness would appear to be present, simply as a result\nof correlations between luminosity and surface brightness at $z=0$.\nThere are also important surface brightness selection effects in\nconstructing the Simard et al.\\ (1999) sample. We illustrate the\nimportance of these considerations in Figure 4 by presenting a\nno-evolution model, hereafter referred to as our fiducial no-evolution\nmodel, identical to our $z=0$ hierarchical and infall models except\nthere is no-evolution in the disk size, number, surface brightness, or\nluminosity, i.e., $E_L(z) = E_N(z) = E_R(z) = 1$. We also present the\nsurface brightness distributions recovered from a similar no-evolution\nmodel differing only in its use of the $M_{b_J} = -21$ surface\nbrightness distribution for all luminosities. We also present the\nsurface brightness distributions recovered both by including a less\nconservative surface brightness selection\n\\begin{equation}\nS_{UP} (I_{814},r_d (\\prime\\prime)) =\n\\left\\{\n\\begin{array}{ll} 1,& I_{814} + 5 \\log r_d(\\prime\\prime) < 21,\\\\\n1 - \\frac{1}{3}(I_{814} + 5 \\log r_d(\\prime\\prime)), & 21 < I_{814} +\n5 \\log r_d(\\prime\\prime) < 24,\\\\ 0, & 24 < I_{814} + 5 \\log\nr_d(\\prime\\prime)\n\\end{array}\n\\right.\n\\end{equation}\n(more resembling the one used by Simard et al.\\ (1999)) and without\nincluding surface brightness ($S_{UP}$) selection at all. Notice the\napparent increase in surface brightness for our fiducial model, where\n$SB\\propto L^{1/3}$, as a function of z relative to our constant\nsurface brightness model. It is interesting to note that there is an\nabsence of galaxies at surface brightnesses close to the threshold for\ndetection in the Simard et al.\\ (1999) sample.\n\nWith these caveats in mind, we compare our model $B$-band surface\nbrightness distributions with both the low and high redshift\nobservations in Figure 5. The models seem to be in rough agreement\nwith the surface brightness distribution of the observations. Given\nthat model populations increase in $B$-band surface brightness by\n$\\sim1.5^m$ to $z\\sim1$ (see Figure 1), this suggests a similar\nincrease in the surface brightness of disks to $z\\sim1$. The models\nthemselves show no large differences. As so often, the uncertainties\nin the $z=0$ modeling are large enough to preclude detailed\ndiscrimination among models, especially given the limited high\nredshift data sets.\n\nIn Figures 6-7, we plot the observed luminosity-size distributions at\nlow (de Jong \\& van der Kruit 1994) and high (Simard et al.\\ 1999)\nredshift and compare them with those obtained for the\n$\\Omega=0.3/\\Omega_{\\Lambda}=0.7$ hierarchical and infall models. We\nshow a similar comparison of the hierarchical model with the high\nredshift Lilly et al.\\ (1998) large disk data-set in Figure 8. We\nalso plot the cumulative size and luminosity distributions along the\nvertical and horizontal axes, respectively, for both the observations\n(histogram) and the models (lines).\n\nAs in Figures 4-5, the models predict too many low surface brightness\ngalaxies relative to the observations. This also results in too many\nlarge model galaxies and too many low luminosity model galaxies\nrelative to the observed size and luminosity distributions at\nintermediate to low luminosities, especially for the Lilly et al.\\\n(1998) large disk sample even with our more conservative surface\nbrightness limit. For large, luminous galaxies, there is no obvious\nchange in numbers to high redshift.\n\nIn Figures 6-7, there are also relatively large differences in\nnormalization between the observations and models. This is apparently\nthe result of large-scale structure (there are small groups/clusters\nat $z\\sim0.8$ and $z\\sim1.0$ in the Groth Strip). It is therefore\ndifficult to make extremely quantitative statements about the\nevolution in the number density of galaxies with specific surface\nbrightnesses, sizes, and luminosities across the redshift intervals\nsurveyed.\n\nNevertheless, the abundance of high surface brightness disk galaxies\nat high redshifts relative to the model predictions is surely\nconspicuous and suggests that there has been a significant increase in\nthe number of high surface brightness disk galaxies to $z\\sim1$ as we\nhave already argued in comparing the model and observed surface\nbrightness distributions. Again, shifting the surface brightness\ndistribution toward these high surface brightnesses (here by the\n$\\sim1.5^m$ predicted by the models) is an obvious way of\naccommodating this increase. Of course, any argument based on the\nnormalization of specific galaxy populations is subject to\nconsiderable uncertainties important when such small contiguous areas\nare being probed.\n\nTo provide a visual comparison between our no-evolution and\nevolutionary models, we include a simulation of a patch of the HDF\n($I_{F814W}$, $B_{F450W}$, and $V_{F606W}$) in Figure 9 using our\nfiducial no-evolution model (panel a), the $\\Omega=1$ hierarchical\nmodel (panel b), and the $\\Omega=0.3$,$\\Omega_{\\Lambda} = 0.7$ infall\nmodel (panel c) for comparison with the actual HDF North and South\n(panel d). Clearly, the lack of high surface brightness galaxies is\napparent in the no-evolution model relative to the HDF and even\nsomewhat in the apparent in the $\\Omega=1$ hierarchical model relative\nto the HDF. Of course, our simulations do not include ellipticals or\npeculiars, so the actual HDF will include more bright objects than the\nsimulations.\n\n\\section{Discussion}\n\nThere is a real question about a lack of low surface brightness\ngalaxies relative to our predictions, especially as compared to the\nno-evolution model predictions. This conclusion is somewhat dependent\non the assumed correlation between surface brightness and luminosity\nas is evident in Figure 4. This conclusion is also dependent on the\nselection biases against low surface brightness galaxies not being\nstronger than those considered here.\n\nThere is an extensive literature discussing surface brightness\nselection biases (Disney 1976; Allen \\& Shu 1979) and various attempts\nto derive the bivariate luminosity-surface brightness distribution of\ngalaxies (McGaugh 1996; Dalcanton et al.\\ 1997b; Sprayberry et al.\\\n1997). Surface brightness has a particularly strong effect on\nisophotal magnitude determinations, especially for low surface\nbrightness galaxies; and this can introduce significant errors in the\nmagnitude determinations, so the effective volume probed for these\ngalaxies is significantly smaller than it is for equivalent luminosity\nhigh surface brightness galaxies (McGaugh 1996).\n\nSimard et al.\\ (1999) in a detailed quantification of the selection\neffects of the DEEP sample do not consider the effect of surface\nbrightness on the magnitudes and sizes recovered since typical errors\nwere found to be $0.2^m$ (Simard 1999, private communication).\nDespite the relatively small size of this error, it is not entirely\nclear to the present authors that the errors would not become quite\nsignificant for the lowest surface brightness galaxies in the sample,\nparticularly those just marginally detectable given the chosen object\nidentification and photometric parameters. Secondly, Simard et al.\\\n(1999) considers disk galaxies to be optically thin whereas the\nobservations of Lilly et al.\\ (1998) are more consistent with disks\nbeing optically thick. Highly-inclined optically thin disks would be\nmuch more detectable than face-on or optically-thick disks. The\nupshot is that at many apparent magnitudes and radii, Simard et al.\\\n(1998) would suppose that at least some highly inclined galaxies would\nbe detectable and therefore the selection function $S_{UP}$ there\nwould be non-zero when in reality if disks were optically thick it\nwould be zero. For these reasons, we used a slightly more\nconservative selection function in surface brightness than that given\nin Figure 4 of Simard et al.\\ (1999) (see \\S3.2).\n\nAnother possibility, not considered here, is that low surface\nbrightness galaxies might form relatively late, meaning that their\nmass-to-light ratios remain relatively large until relatively recent\nepochs. Of course, prima facie, this would seem unlikely given the\napparently constant slope in the Tully-Fisher relationship to faint\nmagnitudes.\n\nIn their own analysis of their sample of $\\sim200$ galaxies, Simard et\nal.\\ (1999) concluded that there had been little evolution in the\nsurface brightness distribution of disk galaxies when all selection\neffects had been carefully considered, quite in contrast to our\nestimated $\\sim1.5^m$ of $B$-band surface brightness evolution.\nLittle consideration, however, was paid to the evolution in the total\n\\textit{numbers} of high surface brightness galaxies. Here, we find\nthat the number of high surface brightness galaxies dramatically\nexceeds that predicted by the evolutionary models considered here, and\nwe have argued that this provides evidence for an evolution in the\nsurface brightness distribution of disk galaxies.\n\nOur interpretation seems to be furthermore supported by the lack of\nlow surface brightness galaxies relative to our models. For\nno-evolution in the disk surface brightness distribution really to be\npresent as Simard et al.\\ (1999) claims, high-redshift intervals\nshould have similar numbers of low surface brightness galaxies to\nthose found in local samples, and these galaxies seem to be deficient,\neven with respect to our models which show significant evolution in\nsurface brightness.\n\nWhile the conclusions of Simard et al.\\ (1999) appear to have been\ncarefully drawn, we would like to suggest that there are significant\nuncertainties in their determination of the mean surface brightnesses\nin the lowest redshift intervals and therefore the inferred evolution\nin surface brightness due to the small size of the low redshift\nsamples considered. By applying the selection effects from the\nhigh-redshift bin identically to all redshift intervals, Simard et\nal.\\ (1999) restricted their analysis to that fraction of disk\ngalaxies exceeding the high-redshift surface brightness detection\nlimit. Applying these selection criteria uniformly to all low\nredshift intervals severely pares down the low-redshift samples and\nsignificantly increases the uncertainty of their average surface\nbrightness measure. Given the observed range in observed surface\nbrightness ($\\sim 2\\, \\textrm{mag/arcsec}^2$) and typical numbers ($\\sim\n5-6$) for the lowest redshift bins, there is a non-negligible\nuncertainty in the average surface brightness at low redshift, $\\sim\n0.6^m$.\n\nOur estimates of $\\sim1.5^m$ of $B$-band surface brightness evolution\nare somewhat larger than that inferred by most authors. Roche et al.\\\n(1998) found $0.9^m$ of surface brightness evolution from $z\\sim0.2$\nto $z\\sim0.9$, Lilly et al.\\ (1998) found $0.8^m$ of surface\nbrightness evolution in their large disk sample, and Schade et al.\\\n(1995,1996a) inferred $1.2^m$ and $1.5^m$ respectively to $z\\sim0.8$.\nDespite different differential measures of surface brightness\nevolution, most of these samples give similar values for the mean disk\nsurface brightness near $z\\sim1$: $20.79 \\pm 0.17$ for the Roche et\nal.\\ (1998) sample ($0.65<z$), $19.9 \\pm 0.2$ for the Simard et al.\\\n(1999) sample ($0.9<z<1.1$), $20.7 \\pm 0.25$ for the Lilly et al.\\\n(1998) large disk sample ($0.5<z<0.75$), $20.2 \\pm 0.25$ for the\nSchade et al.\\ (1995) sample ($0.5<z$), and $19.8 \\pm 0.1$ for the\nSchade et al.\\ (1996) sample ($0.5<z<1.1$). Consequently, differences\nin the surface brightness evolution inferred derive from differences\nin the $z=0$ surface brightness distributions assumed. We assume a\ndistribution consistent with the local data of de Jong \\& van der\nKruit (1994) and Mathewson et al.\\ (1992) as a baseline for measuring\nevolution with a surface brightness peaking faintward of Freeman's Law\n($\\sim 21.7 B\\,\\textrm{mag/arcsec}^2$; Freeman 1970) while Schade et\nal.\\ (1995,1996) simply makes reference to Freeman's Law ($\\sim\n21.65\\,b_j\\,\\textrm{mag/arcsec}^2$). Simard et al.\\ (1999), Lilly et\nal.\\ (1998), and Roche et al.\\ (1998) measure surface brightness\nevolution differentially across their samples. Possible problems here\nare surface brightness selection effects and limited low-redshift\nsamples.\n\n\\section{Summary}\n\nIn the present paper, we presented models based on two different\napproaches for predicting the evolution in disk properties: a\nhierarchical forwards approach, where the evolution in disk properties\nfollows from corresponding changes in halo properties, and a backwards\napproach, where the evolution in disk properties follows from an\ninfall model providing a close fit to numerous observables for the\nMilky Way. We normalized the models to the local $z=0$ observations,\nwe made high-redshift predictions for the models, and we compared\nthese predictions with high-redshift observations.\n\nOur findings are as follows:\n\\begin{itemize}\n\\item{The hierarchical and infall models predict relatively similar\namounts of evolution in global properties (size, surface brightness,\nand luminosity) for disk galaxies to $z\\sim1$. Clearly,\ndiscriminating between the models will require a careful look at\nevolution in number (and therefore surveys over a much larger area)\nand/or measurements of certain internal properties, like color, star\nformation, or metallicity gradients of high redshift disks.}\n\\item{There is an apparent lack of low surface brightness galaxies in\nthe high-redshift observations of Simard et al.\\ (1999) and Lilly et\nal.\\ (1998) as compared to model predictions based on local\nobservations (Mathewson et al.\\ 1992; de Jong \\& van der Kruit 1994).}\n\\item{Our model surface brightness distributions produce relatively\ngood agreement with the observations, suggesting that the $B$-band\nsurface brightness has evolved by $\\sim1.5^m$ from $z=0$ to $z\\sim1$\nsimilar to that found in the models. This finding is supported by the\nfact that there is a significantly larger number of high surface\nbrightness galaxies than in our model predictions, suggesting that\nthere has been a significant evolution in number, most easily\naccommodated by shifting the mean surface brightness of the disk\npopulation to higher surface brightnesses. This is contrary to the\nconclusion reached by Simard et al.\\ (1999) based on the same data.}\n\\end{itemize}\n\nHere the hierarchical and infall models were presented as competing\nmodels to describe the evolution in the properties of disk galaxies.\nIf the hierarchical structural paradigm is roughly correct as is\ngenerally supposed, the infall model simply provides a modification of\nthe basic hierarchical scalings to account for the fact that the gas\ninfall rate or star formation efficiency is not the same at all radii.\nIn this sort of scenario, if there is an appreciable formation of\nstructure at low redshift, a consideration of hierarchical scalings is\nprobably more appropriate and if there is not, a consideration of\nscalings following from infall models is probably more appropriate.\nObviously, at the present time, a complete incorporation of radially\ndependent gas infall and star formation scenarios into a hierarchical\nparadigm is not merited given the lack of high-redshift data needed to\nconstrain such hybrid models.\n\nWe acknowledge helpful discussions with David Schade and Luc Simard.\nWe are especially grateful to Laura Cay\\'on for helping compile some\nof the samples used here, for some useful discussions, and for\nproviding a critical read of this document. We thank Stephane\nCourteau and Nicole Vogt for sending us their data in electronic form.\nThis research has been supported in part by grants from NASA and the\nNSF. RJB would like to thank the Oxford astrophysics department for\nits hospitality while this work was being carried out.\n\n\\begin{thebibliography}{}\n\\bibitem[Allen \\& Shu 1979]{1979ApJ...227...67A} Allen, R. J. \\& Shu,\nF. H. 1979, \\apj, 227, 67.\n\\bibitem[Firmani et al.\\ 1998]{lei96} Avila-Reese, V., Firmani, C., \\&\nHernandez, X. 1998, \\apj, 505, 37.\n\\bibitem[Bertschinger 1985]{ber85} Bertschinger, E. 1985, \\apjs, 58, 39.\n\\bibitem[Bingelli et al.\\ 1988]{bin88} Binggeli, B., Sandage, A., \\&\nTammann, G.A. 1988, \\araa, 26, 509.\n\\bibitem[Boissier \\& Prantzos 1999]{1999MNRAS.307..857B} Boissier, S. \\& \nPrantzos, N. 1999, \\mnras, 307, 857.\n\\bibitem[Bouwens, Cayon, \\& Silk 1997]{bou97} Bouwens, R.J., Cay\\'on,\nL., \\& Silk, J. 1997, \\apj, 489, L21.\n\\bibitem[Bouwens, Cayon, \\& Silk 1999]{bou99} Bouwens, R.J., Cay\\'on, L., \\& \nSilk, J. 1999, \\apj, in press.\n\\bibitem[Brinchmann et al.\\ 1998]{bri98} Brinchmann, J., et al.\\ 1998,\n\\apj, 499, 112.\n\\bibitem[Bryan \\& Norman 1998]{bry98} Bryan, G.L. \\& Norman, M.L.\n1998, \\apj, 495, 80.\n\\bibitem[Calzetti 1997]{cal97} Calzetti, D. 1997, to appear in the\nProceedings of the Conference ``The Ultraviolet Universe at Low and\nHigh Redshift'' preprint: astro-ph/9706121.\n\\bibitem[Carroll, Press, \\& Turner 1992]{car92} Carroll, S.M., Press,\nW.H., \\& Turner, E.L. 1992, \\araa, 30, 499.\n\\bibitem[Catelan \\& Theuns 1996]{cat96} Catelan, P. \\& Theuns, T. 1996, \n\\mnras, 282, 436.\n\\bibitem[Cayon, Silk, \\& Charlot 1996]{cay96} Cay\\'on, L., Silk, J., \\& \nCharlot, S. 1996, \\apj, 467, L53.\n\\bibitem[Chiappini, Matteucci, \\& Gratton 1997]{chi97} Chiappini, C., \nMatteucci, F., Gratton, R. 1997, \\apj, 477, 765.\n\\bibitem[Cole \\& Lacey 1996]{col96} Cole, S. \\& Lacey, C. 1996,\n\\mnras, 281, 1176.\n\\bibitem[Cole et al.\\ 1999]{col99} Cole, S., Lacey, C.G., Baugh, C.M.,\nFrenk, C.S. 1999 (in preparation).\n\\bibitem[Contardo, Steinmetz, \\& Fritze-Von Alvensleben\n1998]{1998ApJ...507..497C} Contardo, G., Steinmetz, M., \\& Fritze-von\nAlvensleben, U. 1998, \\apj, 507, 497.\n\\bibitem[Courteau 1997]{cou97} Courteau, S. 1997, \\apjs, 103, 363.\n\\bibitem[Dalcanton et al.\\ 1997]{dal97a} Dalcanton, J.J., Spergel,\nD.N., James, J.E., Schmidt, M.,\\& Schneider, D.P. 1997, \\aj, 114, 635.\n\\bibitem[Dalcanton, Spergel, \\& Summers 1997]{dal97} Dalcanton, J.J.,\nSpergel, D.N., \\& Summers, F.J. 1997, \\apj, 482, 659.\n\\bibitem[de Jong \\& van der Kruit 1994]{dej94} de Jong, R.S. \\& van\nder Kruit, P.C. 1994, \\aaps, 106, 451.\n\\bibitem[de Jong 1996]{dej96} de Jong, R.S. 1996, \\aap, 313, 45.\n\\bibitem[de Jong \\& Lacey 1999]{dej99} de Jong, R.S. \\& Lacey,\nC. 1999, preprint.\n\\bibitem[Disney 1976]{dis76} Disney, M.J. 1976, \\nat, 263, 573.\n\\bibitem[Efstathiou, Lake \\& Negroponte 1982]{efs82} Efstathiou, G.,\nLake, G., Negroponte, J. 1982, \\mnras, 199, 1069.\n\\bibitem[Ferrini et al.\\ 1994]{fer94} Ferrini, F., Molla, M., Pardi,\nM.C., \\& Diaz, A.I. 1994, \\apj, 427, 745.\n\\bibitem[Freeman 1970]{1970ApJ...160..811F} Freeman, K. C. 1970, \\apj, \n160, 811.\n\\bibitem[Gunn \\& Gott 1972]{gun72} Gunn, J. \\& Gott, R. 1972, \\apj,\n176, 1.\n\\bibitem[Lacey \\& Cole 1993]{lac93} Lacey, C. \\& Cole, S. 1993,\n\\mnras, 262, 627.\n\\bibitem[Lacey \\& Cole 1994]{lac94} Lacey, C., Cole, S. 1994, \\mnras, \n271, 676.\n\\bibitem[Leitherer et al.\\ 1996]{lei96} Leitherer et al.\\ 1996, \\pasp,\n 108, 996.\n\\bibitem[Lilly et al.\\ 1998]{lil98} Lilly, S., et al.\\ 1998, \\apj,\n500, 75.\n\\bibitem[Mathewson, Ford, \\& Buchhorn 1992]{mat92} Matthewson, D.S.,\nFord, V.L., \\& Buchhorn, M. 1992, \\apjs, 81, 413.\n\\bibitem[Mo, Mao, \\& White 1998]{mo98} Mao, S., Mo, H.J., \\& White,\nS.D.M. 1998a, \\mnras, 295, 319.\n\\bibitem[Mo, Mao, \\& White 1998]{mao98a} Mao, S., Mo, H.J., \\& White,\nS.D.M. 1998b, preprint, astro-ph/9807341.\n\\bibitem[Mao, Mo, \\& White 1998]{mao98b} Mao, S., Mo, H.J., \\& White,\nS.D.M. 1998, \\mnras, 297, L71.\n\\bibitem[McGaugh 1996]{mcg96} McGaugh, S.S. 1996, \\mnras, 280, 337.\n\\bibitem[McGaugh \\& de Blok 1997]{mcg97} McGaugh, S.S., \\& de Blok,\nW.J.G. 1997, \\apj, 481, 689.\n\\bibitem[Moore et al. 1999]{Moore99} Moore, B. et al. 1999, ApJ, 524, 19.\n\\bibitem[Navarro, Frenk, \\& White 1997]{nav97} Navarro, J., Frenk, C.,\n\\& White, S.D.M. 1997, \\apj, 487, 73.\n\\bibitem[Navarro \\& Steinmetz 1999]{Navarro99} Navarro, J. and\nSteinmetz, M. 1999, ApJ, in press.\n\\bibitem[Nilson 1973]{nil73} Nilson, P. 1973, Uppsala General\nCatalogue of Galaxies (Uppsala: Uppsala Obs. Ann.)\n\\bibitem[Pozzetti et al.\\ 1996]{poz96} Pozzetti, L., Bruzual, G.,\n \\& Zamorani, G. 1996, \\mnras, 274, 832.\n\\bibitem[Prantzos \\& Aubert 1995]{pra95} Prantzos, N. \\& Aubert,\nO. 1995, \\aap, 302, 69.\n\\bibitem[Prantzos \\& Silk 1998]{pra98} Prantzos, N. \\& Silk, J. 1998,\n\\apj, 507, 229.\n\\bibitem[Press \\& Schechter]{pre74} Press, W. H., \\& Schechter,\nP. L. 1974, \\apj, 187, 425.\n\\bibitem[Pierce \\& Tully 1988]{pie88} Pierce, M.J. \\& Tully, B.R. 1988,\n\\apj, 330, 57\n\\bibitem[Pierce \\& Tully 1992]{pie92} Pierce, M.J. \\& Tully, B.R. 1992,\n\\apj, 387, 47\n\\bibitem[Roche 1998]{roc98} Roche, N., Ratnatunga, K., Griffiths,\nR.E., Im, M., \\& Naim, A. 1998, \\mnras, 293, 157.\n\\bibitem[Schade 1995]{sch95} Schade, D., Lilly, S.J., Crampton, D.,\nHammer, F., Le Fevre, O., \\& Tresse, L. 1995, \\apj, 451, L1.\n\\bibitem[Schade 1996]{sch96} Schade, D., Lilly, S.J., Le Fevre, O.,\nHammer, F., \\& Crampton, D. 1996, \\apj, 464, 79.\n\\bibitem[Simard et al.\\ 1999]{sim99} Simard, L., et al.\\ 1999,\nsubmitted, astro-ph/9902147.\n\\bibitem[Somerville \\& Primack 1998]{som98} Somerville, R., Primack,\nJ. 1998, \\mnras, in press, astro-ph/9807277.\n\\bibitem[Sprayberry et al.\\ 1997]{spr97} Sprayberry, D., Impey, C.,\nIrwin, M.J., \\& Bothun, G.D. 1997, \\apj, 481.\n\\bibitem[Steinmetz \\& Bartelmann 1995]{1995MNRAS.272..570S} Steinmetz, M. \n\\& Bartelmann, M. 1995, \\mnras, 272, 570 \n\\bibitem[Steinmetz \\& Navarro 1999]{stei99}Steinmetz, M. and Navarro,\nJ. 1999, ApJ, 513, 550.\n\\bibitem[Tully \\& Fouque 1985]{tul85} Tully, B. \\& Fouqu\\'e, P. 1985,\n\\apjs, 58, 67.\n\\bibitem[van den Bosch 1998]{van98} van den Bosch, F. 1998, \\apj, 507, 601.\n\\bibitem[Vogt et al.\\ 1996]{vog96} Vogt, N.P., Forbes, D.A., Phillips,\nA.C., Gronwall, C., Faber, S.M., Illingworth, G.D., \\& Koo, D.C.\n1996, \\apj, 465, L15.\n\\bibitem[Vogt et al.\\ 1997]{vog97} Vogt, N.P., et al.\\ 1997, \\apj, 479, L121.\n\\bibitem[Wang \\& Silk 1994]{wan94} Wang, B. \\& Silk, J. 1994, \\apj, 427, 759.\n\\bibitem[Warren Quinn Salmon \\& Zurek 1992]{1992ApJ...399..405W} Warren, M. \nS., Quinn, P. J., Salmon, J. K. \\& Zurek, W. H. 1992, \\apj, 399, 405.\n\\bibitem[Wyse \\& Silk 1989]{wys89} Wyse, R. \\& Silk, J. 1989, \\apj, 339, 700.\n\n \n\n\\end{thebibliography}{}\n\n\\newpage\n\n\\begin{figure}\n\\epsscale{0.95}\n\\plotone{sizeplot.ps}\n\\caption{Evolution of size, rest-frame $B$ luminosity, number, and\nsurface brightness for a fiducial $L_{*}$ ($M\\sim 1.2 \\cdot 10^{12}\nM_{\\odot}$) galaxy in our $\\Omega = 0.3/ \\Omega_{\\Lambda} = 0.7$\nhierarchical model, our $\\Omega = 0.1$ hierarchical model (long dashed\nline), our $\\Omega=1$ hierarchical model (dotted line), our infall\nmodel (dashed line), and the Chiappini et al.\\ (1997) infall model\n(dotted-dashed line). Using the $R_d/V_c$ as a measure of size for a\ngiven mass halo, we have added the $z=0$ Courteau (1997) sample and\nhigher-redshift Vogt et al.\\ (1996, 1997) sample to this plot, our\nscaling the $R_d/V_c$ values so that the Courteau sample had a\nfiducial scale length of unity at $z=0$. Both the data and models are\npresented using $\\Omega=0.3$, $\\Omega_{\\Lambda}=0.7$, $H_0 =\n70\\,\\textrm{km/s/Mpc}$, and corrected to unattenuated magnitudes\n(Tully \\& Fouqu\\'{e} 1985).}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\epsscale{0.95}\n\\plotone{rmv.ps}\n\\caption{Comparison of the observed Tully-Fisher and size-circular\nvelocity relationships as a function of redshifts against the\npresented $\\Omega=0.3, \\Omega_{\\Lambda}=0.7$ hierarchical model at low\nand high redshift. The low-redshift Tully-Fisher data is from Pierce\n\\& Tully (1988), the high-redshift data is from Vogt et al.\\ (1996,\n1997), the superimposed line is the Pierce \\& Tully (1992)\nTully-Fisher relationship, and the low-redshift $V_c$-size data is\nfrom Courteau (1997).}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\epsscale{0.95}\n\\plotone{rmvi.ps}\n\\caption{Comparison of the observed Tully-Fisher and radius-circular\nvelocity relationships against the presented $\\Omega = 0.3,\n\\Omega_{\\Lambda} = 0.7$ infall model at low and high redshift. The\ndata is as in Figure 2.}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\epsscale{0.95}\n\\plotone{SBNE.ps}\n\\caption{Comparison of the observed rest-frame $B$ surface brightness\ndistributions (histogram) with those from our fiducial no-evolution\nmodel (solid line), our fiducial no-evolution model with constant\n$M_{b_J} = -21$ surface brightness distribution (dotted line), our\nfiducial no-evolution model without surface brightness selection\n(dashed line), and our fiducial no-evolution model with the less\nconservative selection function of Simard et al.\\ (1999) (long dashed\nline). This illustrates the possible importance of surface brightness\nselection and an assumed luminosity-surface brightness correlation on\nthe conclusions derived. The local $(z<0.1)$ data is from de Jong \\&\nvan der Kruit (1994) and the high-redshift $(z>0.1)$ data is from\nSimard et al.\\ (1999).}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\epsscale{0.95}\n\\plotone{SB.ps}\n\\caption{Comparison of the observed rest-frame $B$-band surface\nbrightness distributions (histogram) with those from our hierarchical\nmodels ($\\Omega=0.3$, $\\Omega_{\\Lambda}=0.7$/solid line; $\\Omega =\n0.1$/dashed line; $\\Omega = 1$/dotted line), our infall models (thick\ndotted line), and our fiducial no-evolution model (thick solid line)\npresented here. The local $(z<0.1)$ data is from de Jong \\& van der\nKruit (1994) and the high-redshift $(z>0.1)$ data is from Simard\net al.\\ (1999).}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\epsscale{0.95}\n\\plotone{rm.ps}\n\\caption{Comparison of the observed magnitude-radius (rest-frame $B$)\ndistributions with the hierarchical models presented here. The\nlow-redshift data (filled circles) is from de Jong \\& van der Kruit\n(1994) and the high-redshift data (filled circles) is from Simard et\nal.\\ (1999), and the small dots are the results for the $\\Omega=0.3$,\n$\\Omega_{\\Lambda}=0.7$ hierarchical model. Cumulative size and\nluminosity distributions are presented on the vertical and horizontal\naxes, respectively, for our $\\Omega=0.1$ hierarchical model (dashed\nline), our $\\Omega = 1$ hierarchical model (dotted line), our $\\Omega\n= 0.3$,$\\Omega_{\\Lambda}=0.7$ hierarchical model (solid line), and our\nfiducial no-evolution model (thick solid line) for comparison with the\nobservations (histogram). Both the data and models are presented\nusing $\\Omega=0.3$, $\\Omega_{\\Lambda}=0.7$, $H_0 =\n70\\,\\textrm{km/s/Mpc}$, and assuming an inclination of 70 deg (Tully\n\\& Fouqu\\'{e} 1985).}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\epsscale{0.95}\n\\plotone{rmi.ps}\n\\caption{Comparison of the observed magnitude-radius (rest-frame $B$)\ndistributions with the $\\Omega = 0.3, \\Omega_{\\Lambda} = 0.7$ infall\nmodel presented here (\\S2.2). The data is as on Fig 5, and the small\ndots trace out the model distribution. Cumulative size and luminosity\ndistributions are presented for the infall model (solid lines), the\nno-evolution models (thick line), and the observations (histogram).}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\epsscale{0.95}\n\\plotone{rmc.ps}\n\\caption{Comparison of the observed magnitude-radius (rest-frame $B$)\ndistributions from the Lilly et al.\\ (1998) large disk sample with the\nhierarchical models presented here. The models and data are as in\nFigure 6. Both the data and models are presented using $\\Omega=0.3$,\n$\\Omega_{\\Lambda}=0.7$, $H_0 = 70\\,\\textrm{km/s/Mpc}$, and assuming an\ninclination of 70 deg (Tully \\& Fouqu\\'{e} 1985). There are an excess\nof model galaxies at low magnitudes and large sizes relative to the\nobservations.}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\epsscale{0.8}\n\\begin{center}\n\\plotone{diskcompl.ps}\n\\end{center}\n\\caption{Panels (a), (b), (c), and (d) show 60'' x 80'' color images\n($I_{F814W}$, $B_{F450W}$, and $V_{F606W}$) for an HDF-depth\nsimulation using our fiducial no-evolution model, an HDF-depth\nsimulation using our $\\Omega=1$ hierarchical model, an HDF-depth\nsimulation using our $\\Omega=0.3$,$\\Omega_{\\Lambda}=0.7$ infall model,\nand a portion of the actual HDF North and South. Clearly, our\nno-evolution model has fewer high surface brightness galaxies than the\nHDF. Our $\\Omega=1$ hierarchical model also appears to lack high\nsurface brightness galaxies though the fact that we did not include\npeculiars and bright ellipticals in our simulations would tend to bias\nthe eye.}\n\\end{figure}\n\n\\end{document}"
}
] |
[
{
"name": "astro-ph0002133.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[Allen \\& Shu 1979]{1979ApJ...227...67A} Allen, R. J. \\& Shu,\nF. H. 1979, \\apj, 227, 67.\n\\bibitem[Firmani et al.\\ 1998]{lei96} Avila-Reese, V., Firmani, C., \\&\nHernandez, X. 1998, \\apj, 505, 37.\n\\bibitem[Bertschinger 1985]{ber85} Bertschinger, E. 1985, \\apjs, 58, 39.\n\\bibitem[Bingelli et al.\\ 1988]{bin88} Binggeli, B., Sandage, A., \\&\nTammann, G.A. 1988, \\araa, 26, 509.\n\\bibitem[Boissier \\& Prantzos 1999]{1999MNRAS.307..857B} Boissier, S. \\& \nPrantzos, N. 1999, \\mnras, 307, 857.\n\\bibitem[Bouwens, Cayon, \\& Silk 1997]{bou97} Bouwens, R.J., Cay\\'on,\nL., \\& Silk, J. 1997, \\apj, 489, L21.\n\\bibitem[Bouwens, Cayon, \\& Silk 1999]{bou99} Bouwens, R.J., Cay\\'on, L., \\& \nSilk, J. 1999, \\apj, in press.\n\\bibitem[Brinchmann et al.\\ 1998]{bri98} Brinchmann, J., et al.\\ 1998,\n\\apj, 499, 112.\n\\bibitem[Bryan \\& Norman 1998]{bry98} Bryan, G.L. \\& Norman, M.L.\n1998, \\apj, 495, 80.\n\\bibitem[Calzetti 1997]{cal97} Calzetti, D. 1997, to appear in the\nProceedings of the Conference ``The Ultraviolet Universe at Low and\nHigh Redshift'' preprint: astro-ph/9706121.\n\\bibitem[Carroll, Press, \\& Turner 1992]{car92} Carroll, S.M., Press,\nW.H., \\& Turner, E.L. 1992, \\araa, 30, 499.\n\\bibitem[Catelan \\& Theuns 1996]{cat96} Catelan, P. \\& Theuns, T. 1996, \n\\mnras, 282, 436.\n\\bibitem[Cayon, Silk, \\& Charlot 1996]{cay96} Cay\\'on, L., Silk, J., \\& \nCharlot, S. 1996, \\apj, 467, L53.\n\\bibitem[Chiappini, Matteucci, \\& Gratton 1997]{chi97} Chiappini, C., \nMatteucci, F., Gratton, R. 1997, \\apj, 477, 765.\n\\bibitem[Cole \\& Lacey 1996]{col96} Cole, S. \\& Lacey, C. 1996,\n\\mnras, 281, 1176.\n\\bibitem[Cole et al.\\ 1999]{col99} Cole, S., Lacey, C.G., Baugh, C.M.,\nFrenk, C.S. 1999 (in preparation).\n\\bibitem[Contardo, Steinmetz, \\& Fritze-Von Alvensleben\n1998]{1998ApJ...507..497C} Contardo, G., Steinmetz, M., \\& Fritze-von\nAlvensleben, U. 1998, \\apj, 507, 497.\n\\bibitem[Courteau 1997]{cou97} Courteau, S. 1997, \\apjs, 103, 363.\n\\bibitem[Dalcanton et al.\\ 1997]{dal97a} Dalcanton, J.J., Spergel,\nD.N., James, J.E., Schmidt, M.,\\& Schneider, D.P. 1997, \\aj, 114, 635.\n\\bibitem[Dalcanton, Spergel, \\& Summers 1997]{dal97} Dalcanton, J.J.,\nSpergel, D.N., \\& Summers, F.J. 1997, \\apj, 482, 659.\n\\bibitem[de Jong \\& van der Kruit 1994]{dej94} de Jong, R.S. \\& van\nder Kruit, P.C. 1994, \\aaps, 106, 451.\n\\bibitem[de Jong 1996]{dej96} de Jong, R.S. 1996, \\aap, 313, 45.\n\\bibitem[de Jong \\& Lacey 1999]{dej99} de Jong, R.S. \\& Lacey,\nC. 1999, preprint.\n\\bibitem[Disney 1976]{dis76} Disney, M.J. 1976, \\nat, 263, 573.\n\\bibitem[Efstathiou, Lake \\& Negroponte 1982]{efs82} Efstathiou, G.,\nLake, G., Negroponte, J. 1982, \\mnras, 199, 1069.\n\\bibitem[Ferrini et al.\\ 1994]{fer94} Ferrini, F., Molla, M., Pardi,\nM.C., \\& Diaz, A.I. 1994, \\apj, 427, 745.\n\\bibitem[Freeman 1970]{1970ApJ...160..811F} Freeman, K. C. 1970, \\apj, \n160, 811.\n\\bibitem[Gunn \\& Gott 1972]{gun72} Gunn, J. \\& Gott, R. 1972, \\apj,\n176, 1.\n\\bibitem[Lacey \\& Cole 1993]{lac93} Lacey, C. \\& Cole, S. 1993,\n\\mnras, 262, 627.\n\\bibitem[Lacey \\& Cole 1994]{lac94} Lacey, C., Cole, S. 1994, \\mnras, \n271, 676.\n\\bibitem[Leitherer et al.\\ 1996]{lei96} Leitherer et al.\\ 1996, \\pasp,\n 108, 996.\n\\bibitem[Lilly et al.\\ 1998]{lil98} Lilly, S., et al.\\ 1998, \\apj,\n500, 75.\n\\bibitem[Mathewson, Ford, \\& Buchhorn 1992]{mat92} Matthewson, D.S.,\nFord, V.L., \\& Buchhorn, M. 1992, \\apjs, 81, 413.\n\\bibitem[Mo, Mao, \\& White 1998]{mo98} Mao, S., Mo, H.J., \\& White,\nS.D.M. 1998a, \\mnras, 295, 319.\n\\bibitem[Mo, Mao, \\& White 1998]{mao98a} Mao, S., Mo, H.J., \\& White,\nS.D.M. 1998b, preprint, astro-ph/9807341.\n\\bibitem[Mao, Mo, \\& White 1998]{mao98b} Mao, S., Mo, H.J., \\& White,\nS.D.M. 1998, \\mnras, 297, L71.\n\\bibitem[McGaugh 1996]{mcg96} McGaugh, S.S. 1996, \\mnras, 280, 337.\n\\bibitem[McGaugh \\& de Blok 1997]{mcg97} McGaugh, S.S., \\& de Blok,\nW.J.G. 1997, \\apj, 481, 689.\n\\bibitem[Moore et al. 1999]{Moore99} Moore, B. et al. 1999, ApJ, 524, 19.\n\\bibitem[Navarro, Frenk, \\& White 1997]{nav97} Navarro, J., Frenk, C.,\n\\& White, S.D.M. 1997, \\apj, 487, 73.\n\\bibitem[Navarro \\& Steinmetz 1999]{Navarro99} Navarro, J. and\nSteinmetz, M. 1999, ApJ, in press.\n\\bibitem[Nilson 1973]{nil73} Nilson, P. 1973, Uppsala General\nCatalogue of Galaxies (Uppsala: Uppsala Obs. Ann.)\n\\bibitem[Pozzetti et al.\\ 1996]{poz96} Pozzetti, L., Bruzual, G.,\n \\& Zamorani, G. 1996, \\mnras, 274, 832.\n\\bibitem[Prantzos \\& Aubert 1995]{pra95} Prantzos, N. \\& Aubert,\nO. 1995, \\aap, 302, 69.\n\\bibitem[Prantzos \\& Silk 1998]{pra98} Prantzos, N. \\& Silk, J. 1998,\n\\apj, 507, 229.\n\\bibitem[Press \\& Schechter]{pre74} Press, W. H., \\& Schechter,\nP. L. 1974, \\apj, 187, 425.\n\\bibitem[Pierce \\& Tully 1988]{pie88} Pierce, M.J. \\& Tully, B.R. 1988,\n\\apj, 330, 57\n\\bibitem[Pierce \\& Tully 1992]{pie92} Pierce, M.J. \\& Tully, B.R. 1992,\n\\apj, 387, 47\n\\bibitem[Roche 1998]{roc98} Roche, N., Ratnatunga, K., Griffiths,\nR.E., Im, M., \\& Naim, A. 1998, \\mnras, 293, 157.\n\\bibitem[Schade 1995]{sch95} Schade, D., Lilly, S.J., Crampton, D.,\nHammer, F., Le Fevre, O., \\& Tresse, L. 1995, \\apj, 451, L1.\n\\bibitem[Schade 1996]{sch96} Schade, D., Lilly, S.J., Le Fevre, O.,\nHammer, F., \\& Crampton, D. 1996, \\apj, 464, 79.\n\\bibitem[Simard et al.\\ 1999]{sim99} Simard, L., et al.\\ 1999,\nsubmitted, astro-ph/9902147.\n\\bibitem[Somerville \\& Primack 1998]{som98} Somerville, R., Primack,\nJ. 1998, \\mnras, in press, astro-ph/9807277.\n\\bibitem[Sprayberry et al.\\ 1997]{spr97} Sprayberry, D., Impey, C.,\nIrwin, M.J., \\& Bothun, G.D. 1997, \\apj, 481.\n\\bibitem[Steinmetz \\& Bartelmann 1995]{1995MNRAS.272..570S} Steinmetz, M. \n\\& Bartelmann, M. 1995, \\mnras, 272, 570 \n\\bibitem[Steinmetz \\& Navarro 1999]{stei99}Steinmetz, M. and Navarro,\nJ. 1999, ApJ, 513, 550.\n\\bibitem[Tully \\& Fouque 1985]{tul85} Tully, B. \\& Fouqu\\'e, P. 1985,\n\\apjs, 58, 67.\n\\bibitem[van den Bosch 1998]{van98} van den Bosch, F. 1998, \\apj, 507, 601.\n\\bibitem[Vogt et al.\\ 1996]{vog96} Vogt, N.P., Forbes, D.A., Phillips,\nA.C., Gronwall, C., Faber, S.M., Illingworth, G.D., \\& Koo, D.C.\n1996, \\apj, 465, L15.\n\\bibitem[Vogt et al.\\ 1997]{vog97} Vogt, N.P., et al.\\ 1997, \\apj, 479, L121.\n\\bibitem[Wang \\& Silk 1994]{wan94} Wang, B. \\& Silk, J. 1994, \\apj, 427, 759.\n\\bibitem[Warren Quinn Salmon \\& Zurek 1992]{1992ApJ...399..405W} Warren, M. \nS., Quinn, P. 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astro-ph0002134
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Temporal and Spectral Variabilities of High Energy Emission from Blazars Using Synchrotron Self-Compton Models
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"author": "Hui Li\\altaffilmark{1} and Masaaki Kusunose\\altaffilmark{2}"
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Multiwavelength observations of blazars such as Mrk 421 and Mrk 501 show that they exhibit strong short time variabilities in flare-like phenomena. Based on the homogeneous synchrotron self-Compton (SSC) model and assuming that time variability of the emission is initiated by changes in the injection of nonthermal electrons, we perform detailed temporal and spectral studies of a purely cooling plasma system, using parameters appropriate to blazars. One important parameter is the total injected energy ${\cal E}$ and we show how the synchrotron and Compton components respond as ${\cal E}$ varies. When the synchrotron and SSC components have comparable peak fluxes, we find that the SSC process contributes strongly to the electron cooling and the whole system is nonlinear, thus simultaneously solving electron and photon kinetic equations is necessary. In the limit of the injection-dominated situation when the cooling timescale is long, we find a unique set of model parameters that are fully constrained by observable quantities. In the limit of cooling-dominated situation, TeV emissions arise mostly from a cooled electron distribution and Compton scattering process is always in the Klein-Nishina regime, which makes the TeV spectrum having a large curvature. Furthermore, even in a single injection event, the multiwavelength light-curves do not necessarily track each other because the electrons that are responsible for those emissions might have quite different lifetimes. We discuss in detail how one could infer important physical parameters using the observed spectra. In particular, we could infer the size of the emission region by looking for exponential decay in the light curves. We could also test the basic assumption of SSC by measuring the difference in the rate of peak energy changes of synchrotron and SSC peaks. We also show that the trajectory in the photon-index--flux plane evolves clockwise or counter-clockwise depending on the value of ${\cal E}$ and observed energy bands.
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"name": "paper.tex",
"string": "\\documentstyle[11pt,aaspp4,epsfig]{article}\n%\\documentstyle[12pt,aasms4,epsfig]{article}\n%\\documentstyle[emulapj,epsfig]{article}\n\n%\n\n%\\received{4 August 1988}\n%\\accepted{23 September 1988}\n%\\journalid{337}{15 January 1989}\n%\\articleid{11}{14}\n\n%\\slugcomment{}\n\n%\\lefthead{}\n%\\righthead{}\n\n\\begin{document}\n\\title{Temporal and Spectral Variabilities of \nHigh Energy Emission from Blazars\nUsing Synchrotron Self-Compton Models}\n\n\\author{Hui Li\\altaffilmark{1} and\nMasaaki Kusunose\\altaffilmark{2}} \n\n\\altaffiltext{1}{Theoretical Astrophysics (T-6, MS B288), \nLos Alamos National Laboratory, Los Alamos, NM 87545;\nhli@lanl.gov}\n\n\\altaffiltext{2}{Department of Physics, School of Science,\nKwansei Gakuin University, Nishinomiya 662-8501, Japan; \nkusunose@kwansei.ac.jp}\n\n\\begin{abstract}\nMultiwavelength observations of blazars such as Mrk 421 and \nMrk 501 show that they exhibit strong short time variabilities\nin flare-like phenomena. Based on the homogeneous \nsynchrotron self-Compton (SSC)\nmodel and assuming that time variability of the emission is\ninitiated by changes in the injection of nonthermal electrons, \nwe perform detailed temporal and spectral studies of a purely\ncooling plasma system, using \nparameters appropriate to blazars. \nOne important parameter is the total injected energy ${\\cal E}$ and \nwe show how the synchrotron and Compton components respond \nas ${\\cal E}$ varies.\nWhen the synchrotron and SSC components have comparable peak fluxes,\nwe find that the SSC process contributes strongly to the electron\ncooling and the whole system is nonlinear, thus simultaneously\nsolving electron and photon kinetic equations is necessary.\nIn the limit of the injection-dominated situation when the cooling\ntimescale is long, \nwe find a unique set of model parameters that are fully constrained \nby observable quantities. \nIn the limit of cooling-dominated situation, \nTeV emissions arise mostly from a cooled electron distribution and \nCompton scattering process is always in the Klein-Nishina regime,\nwhich makes the TeV spectrum having a large curvature.\nFurthermore, even in a single injection event, the multiwavelength\nlight-curves do not necessarily track each other because the electrons\nthat are responsible for those emissions might have quite different\nlifetimes. \nWe discuss in detail how one could infer important physical\nparameters using the observed spectra. \nIn particular, we could\ninfer the size of the emission region by looking for exponential\ndecay in the light curves. We could also test the basic assumption\nof SSC by measuring the difference in the rate of peak energy changes\nof synchrotron and SSC peaks.\nWe also show that the trajectory in the photon-index--flux plane\nevolves clockwise or counter-clockwise depending on the value of\n${\\cal E}$ and observed energy bands.\n\n\\end{abstract}\n\n\n\\keywords{BL Lacertae objects: general -- gamma rays: theory --\nradiation mechanisms: nonthermal}\n\n\n\\section{INTRODUCTION}\n\nBlazars are a class of flat radio spectrum, core-dominated active\ngalactic nuclei (AGNs).\nThe overall radiation spectra of blazars show two broad\npeaks in the $\\nu F_{\\nu}$ space; one is between IR and X-rays,\nand the other in the $\\gamma$-ray regime (e.g., \\cite{vm95}).\nFlares also have been observed at X- and gamma-ray bands by\nmultiwavelength observations of \nMrk 421 (e.g., Macomb et al. 1995; Macomb et al. 1996\nfor erratum; Buckley et al. 1996)\nand Mrk 501 (Catanese et al. 1997; Pian et al. 1998).\nThe tremendous luminosity and fast time variabilities from blazars\nhave led to the usual arguments that relativistic motion is occurring\nin the emitting plasma. Moreover, the favored scenario to explain\nthese sources is that we are viewing nearly along the axis of a \nrelativistically outflowing plasma jet that has been ejected\nfrom an accreting super massive black hole (e.g., \\cite{br78}). \n\nAlthough the origin of these multiwavelength spectra is still\nunder debate, several models on the radiative processes have\nbeen put forth, in particular, models of Compton scattering of \nsynchrotron photons or\nexternal photons have been developed in recent years\n(e.g., Bloom \\& Marscher 1996;\nInoue \\& Takahara 1996;\nGhisellini \\& Madau 1996;\nDermer, Sturner, \\& Schlickeiser 1997;\nMastichiadis \\& Kirk 1997;\nSikora et al. 1997; \nB\\\"{o}ttcher, Mause, \\& Schlickeiser 1997;\nGeorganopoulos \\& Marscher 1998;\nGhisellini et al. 1998). \nMost of these calculations are either semi-analytic, or\nfor steady state situations, or not including the Compton\nscattering process self-consistently. The main purpose of\nthis paper is to improve upon this situation. \nThe physics of how energy is dissipated into relativistic\nparticles is, unfortunately, not well understood (see, however,\n\\cite{rl97}) and will not be treated fully in this paper.\n\nAmong various blazar models, synchrotron self-Compton (SSC) \nmodels have received a fair amount of attention,\nby virtue of its simplicity and its possible predictive power. \nIn these models, it is proposed that the nonthermal\nsynchrotron emission forms the radio-through-X-ray continuum, and\nthat the Compton scattering of these (soft) synchrotron photons by the\nsame nonthermal electrons produces the gamma rays ($\\sim$ GeV -- TeVs).\nIn this paper, we focus on the so-called homogeneous SSC model\nwhere a spherical blob of uniform relativistic plasma is postulated.\nEven with such a greatly simplified picture, a number of parameters\nhave to be invoked, whose interplay gives rise to a rich dynamic \nbehavior of the observed radiation. Of particular interest is\nthe correlated variabilities in X-ray and $\\gamma$-ray fluxes,\nsince they represent the tail of nonthermal electrons which have\nthe shortest cooling timescale.\nAlthough the generic multiwavelength spectra from radio to TeV \ncan be fitted by a steady state model with fixed parameters \n(e.g, Kataoka et al. 1999), time-dependent calculations almost\nalways offer stronger constraints. \nFurthermore, when the self-Compton component contains a comparable\nor even larger fraction of the radiative energy than the synchrotron\ncomponent, the whole problem becomes inherently nonlinear and\nboth components need to be calculated simultaneously and \nself-consistently. This naturally leads to the need of solving\ncoupled, time-dependent, nonlinear particle and photon \nkinetic-equations. \nMoreover, by examining the energy-dependence of flare data\nat gamma-ray energies, one could potentially discriminate \nbetween SSC and external Compton-scattering\norigins of the seed photons (Dermer 1998).\n\nThe simplest model for time variability of blazars \n(Mastichiadis \\& Kirk 1997; hereafter MK97)\nassumes that electrons obeying \na power-law distribution are injected uniformly throughout\na relativistically moving blob over an extended period of time,\nand that electrons cool by both synchrotron radiation \nand Compton scattering.\nThe blob is assumed not to accelerate or decelerate,\nand the energy loss by Compton scattering of photons\nimpinging from outside the blob is assumed to be small \nin comparison with the synchrotron self-Compton loss.\nMK97 reproduced the qualitative behavior of the energy-dependent\nlags and the hysteresis diagrams (Takahashi et al. 1996).\nMuch of the work presented here follows closely to the previous\nstudy by MK97, but we are using a completely different \nkinetic code which will be\ndiscussed in later sections. \nKirk, Rieger, \\& Mastichiadis (1998) further modeled \nthe evolution of synchrotron emission, \ncalculating acceleration and cooling regions separately,\nthough Compton scattering was not included.\n\n\nIn this paper we present a detailed study of the time-evolution\nof an electron-photon plasma (the positive particles could be either\nprotons or positrons) by solving the kinetic equations numerically. \nWe briefly describe our model in \\S \\ref{sec:codes} and\nshow numerical results in \\S \\ref{sec:results}.\nSummary is given in \\S \\ref{sec:sum}.\n\n\n\\section{MODEL}\n\\label{sec:codes}\n\n%\\subsection{Kinetic Equations}\n\nWe assume that observed photons are emitted from\na blob moving relativistically towards us\nwith a Doppler factor ${\\cal D} = [\\Gamma (1-\\beta_{\\Gamma} \n\\cos\\theta)]^{-1}$,\nwhere $\\Gamma$ is the Lorentz factor of the blob,\n$\\beta_{\\Gamma} c$ is the velocity with $c$ being the light speed,\nand $\\theta$ is the angle between the direction of blob motion \nand the line of sight. \nThe blob is a spherical and uniform cloud with radius $R$.\nRelativistic electrons \nare injected into the blob and produce high energy emission.\nElectrons and photons are uniformly distributed\nthroughout the blob.\nThe most important physical processes for electrons include \nsynchrotron radiation and Compton scattering.\nThe spectra of electrons and photons in the blob are\ncalculated by solving the kinetic equations described below\n(see also \\cite{cb90}).\n\nThe kinetic equation describing the time-evolution of electron\ndistribution $n(\\gamma)$\nis given by\n\\begin{equation}\n\\label{eq:elkinetic}\n\\frac{\\partial n}{\\partial t} \n= - \\frac{\\partial}{\\partial \\gamma}\n\\left[ \\left( \\frac{d\\gamma}{dt} \\right)_{\\rm loss} n \\right]\n+ \\frac{1}{2} \\, \\frac{\\partial^2}{\\partial \\gamma^2} \n( D_e \\, n ) \n - \\frac{n}{t_{e, {\\rm esc}}} + Q(\\gamma) \\, ,\n\\end{equation}\nwhere $n$ is the electron number density per $\\gamma$,\n$\\gamma$ is the electron Lorentz factor, and $t_{e, {\\rm esc}}$\nis the time for electrons to escape from the blob.\nThe term $(d\\gamma/dt)_{\\rm loss}$ represents various\nelectron energy loss processes, such as synchrotron \nand Compton scattering; their corresponding energy diffusion\nis given as $D_e$. \nWe also include the synchrotron ``boiler'' effect (Ghisellini et al. 1988)\nand other processes such as Coulomb collisions, \nthough they are not important in the present \nstudy. Pair-production and annihilation are not treated in\nthe present code, though they tend to be less important too.\nIn our code, the particle equation is actually discretized in \nthe momentum space so that thermal particles and their processes can be \nhandled accurately. This is less important for AGN jet\nparameters but will be very useful for modeling the emissions from \nstellar-mass black hole systems.\nNote that equation (\\ref{eq:elkinetic}) assumes a continuous \nelectron energy loss (i.e., Fokker-Planck type). \nThis assumption does not account for the situation when there is\na significant energy loss in a single\nCompton scattering which is important in the Klein-Nishina regime.\nThis discrete nature of the Compton energy loss is, however, \nincluded in the photon kinetic equation, i.e., \nequations (\\ref{eq:phkinetic}) and (\\ref{eq:comp}). \nWe have checked the accuracy of the continuous\napproximation of the Compton energy loss in equation (1) in view of\nenergy conservation. Our numerical tests show that the total energy\nis conserved with the accuracy better than 5 per cent after 10 $R/c$,\nwhen the SSC component is dominant and the scatterings occur frequently\nin the Klein-Nishina regime.\n\nThe relevant kinetic equation for the time-evolution of\nphotons is given by\n\\begin{equation}\n\\label{eq:phkinetic}\n\\frac{\\partial n_{\\rm ph}(\\epsilon)}{\\partial t} \n= \\dot{n}_{\\rm C}(\\epsilon) \n+ \\dot{n}_{\\rm em}(\\epsilon) - \\dot{n}_{\\rm abs}(\\epsilon) \n- \\frac{n_{\\rm ph}(\\epsilon)}{t_{\\rm ph, esc}} \\, ,\n\\end{equation}\nwhere $n_{\\rm ph}(\\epsilon)$ is the photon number\nspectrum per unit volume per unit energy $\\epsilon$.\nCompton scattering is calculated as\n\\begin{equation}\n\\label{eq:comp}\n\\dot{n}_{\\rm C}(\\epsilon) \n= - n_{\\rm ph}(\\epsilon) \\, \\int d\\gamma \\, n(\\gamma) \\, \nR_{\\rm C}(\\epsilon, \\gamma) + \\int\\int d\\epsilon^{\\prime} \\, d\\gamma \\, \nP(\\epsilon; \\epsilon^{\\prime}, \\gamma) \\, \nR_{\\rm C}(\\epsilon^{\\prime}, \\gamma) \\,\nn_{\\rm ph}(\\epsilon^{\\prime}) n(\\gamma) \\, .\n\\end{equation}\nFirst term of the right hand side of equation (\\ref{eq:comp}) denotes \nthe rate that photons with energy $\\epsilon$\nare scattered by electrons with number spectrum $n(\\gamma)$ \nper unit volume per unit $\\gamma$;\n$R_{\\rm C}$ is the angle-averaged scattering rate.\nSecond term of equation (\\ref{eq:comp}) denotes \nthe spectrum of scattered photons:\n$P(\\epsilon; \\epsilon^{\\prime}, \\gamma)$ is the probability \nthat a photon with energy $\\epsilon^\\prime$ is scattered off \nby an electron with $\\gamma$ to have energy $\\epsilon$.\nThe probability $P$ is normalized such that\n$\\int P(\\epsilon; \\epsilon^{\\prime}, \\gamma) \\, d\\epsilon = 1$.\nThe details of $R_{\\rm C}$ and $P$ are given in \\cite{jones68}\nand the appendix A of Coppi \\& Blandford (1990).\nWe use the exact Klein-Nishina cross section \nin the calculations of Compton scattering.\nPhoton production and self-absorption by synchrotron radiation\nare included in\n$\\dot{n}_{\\rm em}(\\epsilon)$ and $\\dot{n}_{\\rm abs}(\\epsilon)$,\nrespectively.\nThe synchrotron emissivity and the absorption coefficient are calculated \nusing the approximations given in Robinson and Melrose (1984) \nfor transrelativistic electrons and Crusius and Schlickeiser (1986) \nfor relativistic electrons.\nExternal photon sources such as disk photons can be included, \nthough they are not considered here.\nThe rate of photon escape is estimated as \n$n_{\\rm ph}(\\epsilon)/t_{\\rm ph, esc}$.\nSince we are in the optically thin limit, \nwe set $t_{\\rm ph, esc} = R/c$,\nwhich is a good approximation.\nThe photon spectra from \nsolving equation (\\ref{eq:phkinetic}) has been extensively \ncompared with those from Monte-Carlo simulations and we have\nfound very good agreement between them (Kusunose, Coppi, \\& Li 1999).\n\n\nThe comoving quantities are transformed back \ninto the observer's frame using\n$\\epsilon_{\\rm obs} = \\epsilon \\, {\\cal D}/(1+z)$\nand $dt_{\\rm obs} = dt \\, (1+z)/{\\cal D}$, where\n$z$ is the redshift of the source.\n\nWe assume that electrons are injected obeying a power law in energy:\n$$Q(\\gamma, t) = Q_0(t) \\, \\gamma^{-p} $$ \nwith $\\gamma_{\\rm min} \\leq \\gamma \\leq \\gamma_{\\rm max}$.\nThe total energetics of the electrons can be represented\nby a compactness parameter which is proportional to $L/R$,\nwhere $L$ is the source luminosity. We do not consider specific\nacceleration mechanisms in this paper. Thus particles are just\nbeing injected into the blob over a finite time. We emphasize\nthat in order to be consistent with the basic assumption of\nspatial homogeneity, we require the injection time $t_{\\rm inj}$\nto be longer than $t_{\\rm dyn} = R/c$. In effect, we can not\nprobe variabilities shorter than $t_{\\rm dyn}$ in the comoving frame.\nOther physical effects such as adiabatic loss via expansion\nmight play an important role but is not considered here.\nIt is unfortunate that we need such a large number of parameters\nto proceed with the calculations, and this is the main reason\nwe opt not to add further complications such as acceleration.\n\n\n\\section{RESULTS}\n\\label{sec:results}\n\nThe dynamic behavior of the emission spectra is controlled by\nseveral timescales, namely, the cooling time $t_{\\rm cool}$,\nthe dynamic time $t_{\\rm dyn}$, the injection duration $t_{\\rm inj}$,\nand the escape time $t_{\\rm esc}$. The causality argument requires\nthat $t_{\\rm dyn} \\leq t_{\\rm inj}, t_{\\rm esc}$, whereas $t_{\\rm cool}$\ncan be smaller than $t_{\\rm dyn}$. For SSC models, both\nsynchrotron and Compton processes contribute to the electron cooling,\nso $1/t_{\\rm cool} = 1/t_{\\rm syn} + 1/t_{\\rm ssc}$, where\n$t_{\\rm syn} = \\gamma/|{\\dot \\gamma}_{\\rm syn}|$ and\n$t_{\\rm ssc} = \\gamma/|{\\dot \\gamma}_{\\rm ssc}|$.\n\nIn the following analyses, we will divide our results into two \nmajor parts, based on whether $t_{\\rm cool}$ is longer or shorter\nthan $t_{\\rm inj}$. In the limit of $t_{\\rm cool}\n\\geq t_{\\rm inj} \\geq t_{\\rm dyn}$, where $t_{\\rm cool}$ is evaluated\nusing the highest particle energy, the injected particle distribution\ndoes not change appreciably during the injection process. We call this\nthe injection-dominated limit. On the\nother hand, if $t_{\\rm inj} \\geq t_{\\rm dyn} \\geq t_{\\rm cool}$,\nthen particles will be sufficiently cooled while the injection still\noccurs, and emissions are from a cooled particle distribution\nrather than from the injected one. We call this the \ncooling-dominated limit. Consequently, we expect rapid variations\nin both fluxes and spectra in the latter case and relatively slow\nspectral variations in the former case.\n\nThe primary purpose of this paper is to understand the dynamics of\nSSC model. We thus have chosen a broad range of parameters rather than\ntry to fit any specific source spectrum, but we certainly use \nparameters thought to be applicable to those\nsources (Mrk 421 in particular) to guide our calculations. \n\n\n\\subsection{Long Cooling Time Limit}\n\nWe show that, in this limit, a set of SSC model \nparameters can be uniquely determined from the observable quantities.\nWe use observations of Mrk 421 as an example and \nfurther discuss their implications for\nmultiwavelength observations.\n\n\\subsubsection{A Unique Solution}\n\\label{sec:us}\n\nLet $\\cal E$ represent the energy (in ergs) injected in nonthermal electrons,\nwhich we assume can be described as $N_e(\\gamma) = N_0 \\, \\gamma^{-p}$\nand $\\gamma_{\\rm min} \\leq \\gamma \\leq \\gamma_{\\rm max}$.\nThen $N_0 = (2-p) {\\cal E} / [m_e c^2 (\\gamma_{\\rm max}^{2-p}\n- \\gamma_{\\rm min}^{2-p})]$ (for $p\\ne 2$).\nIn the limit of long cooling time, we can use the injected\nelectron distribution to calculate the synchrotron and SSC fluxes.\nThus, for the peak energies of synchrotron and SSC, we have\n\\begin{equation}\n\\label{eq:nusyn}\n{\\cal D} \\gamma_{\\rm max}^2 B \\approx \\nu_{\\rm syn}/2.8\\times 10^6\n= {\\tilde \\nu}_{\\rm syn}~~,\n\\end{equation}\n\\begin{equation}\n\\label{eq:nussc}\n{\\cal D} \\gamma_{\\rm max} \\approx \\nu_{\\rm ssc}/1.236\\times 10^{20}\n= {\\tilde \\nu}_{\\rm ssc}~~,\n\\end{equation}\nwhere $\\nu_{\\rm syn}$ and $\\nu_{\\rm ssc}$ are the\nsynchrotron and $\\gamma$-ray peaks in Hz, respectively, and\n$B$ is magnetic fields in Gauss. The numerical normalization factors\nare easily obtainable using the standard expressions for the peak\nsynchrotron energy and inverse Compton peak energy in the KN limit.\nFor Mrk 421, we have ${\\tilde \\nu}_{\\rm syn} \\approx 1.72\\times 10^{11}$\n($\\sim 2$ keV) and ${\\tilde \\nu}_{\\rm ssc} \\approx 10^7$\n($\\sim 5$ TeV). From equations (\\ref{eq:nusyn}) and (\\ref{eq:nussc}),\nwe get\n\\begin{equation}\n\\label{eq:mag}\nB = {\\cal D} {\\tilde \\nu}_{\\rm syn}/{\\tilde \\nu}^2_{\\rm ssc}~~.\n\\end{equation}\n\nThe relative ratio $\\eta$ of SSC to synchrotron fluxes for Mrk 421\nis close to 1. This ratio can be approximately represented by\nthe ratio of the comoving-frame synchrotron photon energy-density,\n$U_{\\rm syn} = L_{\\rm syn}/(4\\pi R^2 c {\\cal D}^4)$, \nto the magnetic field energy-density, $U_B = B^2/(8 \\pi)$. \nBut the exact value of $\\eta$ could be quite different from this\nestimate owing to several factors: the end point effect\nat the peak of both synchrotron and SSC fluxes,\n\\footnote{For $p < 3$, the peak of $\\nu L_{\\nu}$\nis at $\\nu_{\\rm syn} \\propto \\gamma^2_{\\rm max}B$, but its flux \nis {\\em smaller} than that obtained using the $\\delta-$function\napproximation to the scattering cross section. To be consistent with\nour numerical code results which have used the {\\em exact} \nsynchrotron emissivity formulations, we have\nintroduced a reduction factor of $f_{\\rm syn} (< 1)$ in our simplified\nanalytic estimates for the peak synchrotron flux (see also\nequation (\\ref{eq:lsyn}). \nNote that this reduction only\napplies to the end points of emissivity. For energies much smaller\nthan $\\nu_{\\rm syn}$, the $\\delta-$function approximation is quite\naccurate.}\nthe KN effect of Compton scattering for producing TeV emission, \nand the fact that\nthe electron distribution will be slightly cooled even though\nthe cooling timescale is long. It is very difficult to get an exact\nanalytic value to account for all these effects, so we introduce\na correction factor $f_c$ in calculating $\\eta$.\nThus, we have\n\\begin{equation}\n\\label{eq:eta}\n\\eta = f_c~\\frac{U_{\\rm syn}}{U_B} ~~{\\rm or}~~\nL_{\\rm syn} \\approx {\\cal D}^4 4\\pi R^2 c ~ U_B~(\\eta / f_c) \\, .\n\\end{equation}\nFurthermore, since all blazar sources are observed to be highly variable,\nan additional constraint has usually been proposed that\n\\begin{equation}\nR \\approx {\\cal D} ~c t_{\\rm var}~~,\n\\end{equation}\nwhere $t_{\\rm var}$ is defined as a variability timescale\nin the observer's frame. \n\nCombining all the equations given above, we have 4 equations for\n4 independent variables (i.e., ${\\cal D}, B, \\gamma_{\\rm max},$ and\n$R$). The supplemental information include\n${\\tilde \\nu}_{\\rm syn}, {\\tilde \\nu}_{\\rm ssc}, L_{\\rm syn}$, $\\eta$,\nand $t_{\\rm var}$, with a somewhat variable factor $f_c$. \nThus we can {\\em uniquely} determine a solution set for all the\nparameters. The Doppler factor from this solution (denoted\nby a subscript `$s$') can be expressed as\n\\begin{equation}\n\\label{eq:solution}\n{\\cal D}_s \\approx 22.2 \n\\left(\\frac{L_{\\rm syn}}{6\\times 10^{44}}\\right)^{\\frac{1}{8}}\n\\left(\\frac{{\\tilde \\nu}_{\\rm ssc}}{10^7}\\right)^{\\frac{1}{2}}\n\\left(\\frac{{\\tilde \\nu}_{\\rm syn}}{1.7\\times 10^{11}}\\right)^{-\\frac{1}{4}}\n\\left(\\frac{t_{\\rm var}}{10^4}\\right)^{-\\frac{1}{4}}\n\\left(\\frac{f_c}{0.4}\\right)^{\\frac{1}{8}}\n\\left(\\frac{\\eta}{1.0}\\right)^{-\\frac{1}{8}}~~.\n\\end{equation}\n\nThe peak luminosity ($L_{\\rm syn}$) of the synchrotron component \nin the observer's frame can be estimated using $\\nu L_{\\nu}$ at\n$\\nu_{\\rm syn}$ (again taking into account the end-point effects), \n\\begin{equation}\n\\label{eq:lsyn}\nL_{\\rm syn} \\approx {\\cal D}^4~ f_{\\rm syn}\n\\frac{2(2-p)}{3} \\sigma_{\\rm T} c U_B\n\\frac{{\\cal E}}{m_e c^2}~\\gamma_{\\rm max}~~,\n\\end{equation}\nwhere $\\sigma_{\\rm T}$ is the Thomson cross section,\n$f_{\\rm syn} (< 1)$ represents the reduction of synchrotron\nflux at the end point, ${\\cal D}^4$ is due to the Doppler boosting.\nObservationally,\n$L_{\\rm syn}$ at $\\sim 2$ keV is $\\geq 6\\times 10^{44}$ ergs s$^{-1}$\nwith a luminosity distance of $3.8 \\times 10^{26}$ cm ($z = 0.0308$)\nfor a $q_0 = 1/2$ and $\\Lambda = 0$ cosmology. Here, \n$H_0 = 75$ km s$^{-1}$ Mpc$^{-1}$ is assumed. Also, \nfitting of Mrk 421's synchrotron spectrum suggests $p \\approx 1.65$\n(MK97). From this, we can determine the rest of the parameters for\nthis unique solution (again denoted by a subscript `s')\n\\begin{eqnarray}\nB_s & = & {\\cal D}_s {\\tilde \\nu}_{\\rm syn}/ \n{\\tilde \\nu}_{\\rm ssc}^2 \n\\approx 0.038~~ {\\rm G}~~,\\label{eq:b-d}\\\\\n\\gamma_{{\\rm max}, s} & = &{\\tilde \\nu}_{\\rm ssc} / {\\cal D}_s\n\\approx 4.5\\times 10^5~~,\\\\\nR_s & =& c \\, t_{\\rm var} {\\cal D}_s \\approx 6.5\\times 10^{15} \n~~{\\rm cm}~~,\\\\\n{\\cal E}_s &=& \\frac{1.55\\times 10^9}{(2-p) f_{\\rm syn}}~\n\\frac{L_{\\rm syn}}{\\gamma_{{\\rm max}, s} B^2_s {\\cal D}^4_s}\n\\approx 4.1 \\times 10^{46} ~~{\\rm ergs} ~~,\\label{eq:e-d}\n\\end{eqnarray}\nwhere we have used $p = 1.65$ and $f_{\\rm syn} = 0.4$. \n\\footnote{The fact that $f_c$ and $f_{\\rm syn}$ are both chosen as\n$0.4$ is a coincidence. The evaluation of $f_c$ involves end-point\neffects from both synchrotron and Compton scattering, whereas \n$f_{\\rm syn}$ is only concerned with synchrotron. The value\n$0.4$ is obtained by comparing the analytic estimates with\nthe exact numerical calculations.}\nMore importantly, we can check our original assumption that\ncooling time is long compared to $t_{\\rm dyn} = R/c$.\nThis is obviously satisfied since \n$t_{\\rm syn} \\approx (6\\pi m_e c/\\sigma_{\\rm T})/(\\gamma_{\\rm max} B^2)\n\\approx 1.2\\times 10^6$ sec, which is much longer than \n$t_{\\rm dyn}\\approx 2.2 \\times 10^5$ sec. \n\nUsing the above derived parameters, we solve \nequations (\\ref{eq:elkinetic}) and (\\ref{eq:phkinetic})\nsimultaneously and follow the evolution until \n$20 t_{\\rm dyn}$. A total energy of ${\\cal E}$ is injected\nin nonthermal electrons over a comoving timescale of\n$t_{\\rm inj} = 2 t_{\\rm dyn}$.\nIn these calculations electrons are not allowed to escape.\nFigure \\ref{fig:parpht-us} shows the time evolution of electron and\nphoton distributions as the system evolves.\nNote that the time for synchrotron and SSC components to\nreach their peak fluxes is different, and that it happens\nafter the electron injection has stopped.\nTo qualitatively understand this, we can write the photon \nkinetic equation symbolically as\n\\begin{equation}\n\\label{eq:dndt}\n\\frac{\\partial n_{\\rm ph}(\\epsilon)}{\\partial t} \n = {\\rm Production}(\\epsilon) - {\\rm Escape}(\\epsilon)~~.\n\\end{equation}\nThus, the photon flux at energy $\\epsilon$ will increase\nif the production rate is larger than the escape and decrease\nif escape is quicker. This determines when the peak of photon\nflux at certain energy is reached. Using photon flux at keV\nas an example, the production of these photons still continues\neven when the electron injection stops because the cooling timescale\nis much longer than $R/c$. Eventually as electrons cool, they\ncan no longer produce keV synchrotron emissions, the flux\nat keV starts to decline.\n\nFigure \\ref{fig:ltcv-us} shows the light curves at different energy bands\nexpected from this injection event. Since the cooling time\nis rather long, only the energy bands corresponding to the tail\nof electron distributions show short time variabilities\ndue to that electron injection is turned on and off;\nwhereas other energy bands show a long plateau, representing\na balance between the photon production and escape.\nA clear prediction from this is that there should be very \nlittle spectral evolution except at the peaks of synchrotron \nand SSC. All these are commensurate with the dynamics \nof electron cooling.\n\nIn order to further differentiate the role of synchrotron\nversus Compton cooling on electrons, we plot the ratio\nof $|\\dot\\gamma_{\\rm ssc}/\\dot\\gamma_{\\rm syn}|$ as a\nfunction of electron energies at different times in Figure \n\\ref{fig:syn-ssc-ratio}.\nIt is clear that SSC cooling becomes more important than\nsynchrotron cooling when the photon energy density builds up \nwithin the system as time proceeds. After reaching the peak,\nthe SSC cooling starts to decrease as the photon energy density\ndecreases. The dependence of this ratio on the electron energy\nis partly due to the KN effect. This figure clearly indicates that\none can not ignore SSC cooling in estimating certain parameters\nand that the evolution is very nonlinear, thus a self-consistent\nnumerical calculation is required for fitting\nthe data more accurately.\n\n\nNote that the spectra given in Figure \\ref{fig:parpht-us} is not intended to\nbe an accurate fit to the observed spectra from Mrk 421.\nIn fact, the TeV spectrum of Mrk 421 is known to be roughly\na power law (\\cite{ketal99}), but the generic spectrum in TeV obtained here\nhas a clear curvature, due to the fact that the Compton scattering\nis in the KN regime. Nevertheless, this exercise allows us to\nestablish a parameter space where a reasonable fit to the\nactual spectrum might be obtainable, and it has the nice feature\nthat the electron energy distribution retains the injected form\nwithout much softening, which greatly simplifies the analysis.\n\n\n\\subsubsection{Parameter Variations on the Unique Solution}\n\nIn this subsection, we explore how sensitive the above results\nare to parameter variations. The parameter we want to emphasize\nis the ratio $\\eta$ of the SSC component to \nthe synchrotron component. From equations (\\ref{eq:mag})\nand (\\ref{eq:solution}),\nand holding other parameters unchanged, we can see that \n\\begin{equation}\n\\label{eq:eta-b}\n\\eta \\propto {\\cal D}^{-8} \\propto B^{-8}~~,\n\\end{equation}\nwhich implies that a small change in magnetic field and/or Doppler\nfactor could result in a large variation in $\\eta$. \nFigure \\ref{fig:varyb} shows this effect when $B$ is being varied.\nThe general trend from equation (\\ref{eq:eta-b}) is indeed\nconfirmed, i.e., smaller/larger $B$ (versus $B_s$) gives \nmuch larger/smaller $\\eta$. For $B < B_s$, the variation amplitude\nin $\\eta$ does not exactly follow equation (\\ref{eq:eta-b}).\nWe attribute this discrepancy mostly to variation in \n$f_c$ because both $\\gamma_{\\rm max}$ and synchrotron\nphoton energy in comoving frame are varying for different $B$.\nAdditionally, when $\\eta > 1$ (SSC cooling is more important\nthan synchrotron cooling), electron distribution is subject\nto stronger cooling. This is evident in its rapid spectral\nvariation in the middle panel of Figure \\ref{fig:varyb}. \nFor larger $B$ which results in $\\eta < 1$,\nequation (\\ref{eq:eta-b}) is mostly confirmed. Note that\nthe Doppler factor ${\\cal D}$,\nusing equation (\\ref{eq:mag}), is now getting uncomfortably large.\n\n\nTo conclude, in the limit that the cooling time of the highest \nenergy electrons\nis longer than the dynamic timescale on which injection occurs,\nwe can most likely find a {\\em unique} set of parameters that \nroughly satisfy\nthe observational constraints. The most important prediction is\nthat even though the fluxes of the synchrotron and SSC peaks\ncan vary by a large factor ($> 10$) in a short time whose time\nhistories look like ``pulses'', the duration of emission at other wave bands \n(such as GeV, MeV, eV) can be considerably longer by at least\na factor of $4$, which is commensurate with long electron cooling\ntime at those energies. \n\nThis parameter space has some interesting implications\nfor interpreting multiwavelength data from blazar monitoring campaigns.\nUsing keV and eV bands as an example (similar arguments can be\nmade for TeV and GeV bands too),\nsince the lifetimes for keV-producing and eV-producing electrons are \ndifferent, there is really no reason to expect their light curves\nto track each other and to have the same rise and fall patterns\nor timescales. Furthermore, when there are multiple injections\noccurring over a timescale shorter than the lifetime of\nkeV-producing electrons but longer than the lifetime of \neV-producing electrons, fluxes at keV could vary rapidly to\nreflect the multiple injections. \nFluxes at eV, however, might only show a \ncontinuous increase with no obvious decline because of \nthe accumulation of eV-producing electrons from multiple injections \n(see also \\S \\ref{sec:multi}).\n\n\n\\subsection{Short Cooling Time Limit}\n\n\nIn this subsection we explore the limit where\n$t_{\\rm cool}(\\gamma_{\\rm max})\n< t_{\\rm dyn}$, i.e., electrons are efficiently being cooled \nwhile they are injected into the system. \nAll the runs in this section have\nsize $R = 1.5 \\times 10^{16}$ cm which gives a comoving\ndynamic timescale $R/c = 5\\times 10^5$ sec,\nparticle's $\\gamma_{\\rm min} = 10$, $\\gamma_{\\rm max} = 10^{6}$,\nand index $p=2$. The Doppler factor is chosen as 10 and magnetic\nfield $B = 0.1$ G, though most of the conclusions depend\nweakly on ${\\cal D}$ and $B$ in this section. \nThe particularly\nattractive feature of this limit is that it is possible to\nachieve short time variabilities for many wave bands, contrary\nto the case shown in Figure \\ref{fig:ltcv-us} from the previous section.\n\nOne serious problem in comparing the theoretical results with\nthe actual observations is that most observations need to \naccumulate over certain time interval\n(to collect enough photons) and different\nintegration times are needed for different energy bands. \nSo, in order to make a direct comparison with the observations,\nproperly averaged fluxes are needed,\nrather than the prompt flux we have presented above.\nThis inevitably introduces many more additional parameters\nin determining how photons at different energy bands are sampled.\nTo avoid these complications, as before, \nwe will continue to present the prompt\nflux results, leaving the problem of integrated fluxes\nto future studies on detailed spectral fitting of \nparticular sources.\n\nTo quantify the relative importance of SSC versus synchrotron,\nthe previous expression for $\\eta$ has to be modified.\nTo recapitulate, the comoving synchrotron photon energy-density is\n$U_{\\rm syn} \\simeq [ m_e c^2 / ( 4 \\pi R^2 c)] \n\\int_{\\gamma_{\\rm min}}^{\\gamma_{\\rm max}} N_e(\\gamma) | \\dot{\\gamma} |\n\\, d \\gamma$,\nwhere the electron energy loss-rate through synchrotron radiation\nis given by $\\dot{\\gamma} = - [ 4 \\sigma_{\\rm T} / (3 m_e c) ]\nU_B \\gamma^2$. Thus, we get\n\\begin{equation}\n\\label{eq:ussc1}\n\\eta = f_c~\\frac{U_{\\rm syn}}{U_B} \n= f_c~\\frac{\\sigma_{\\rm T}}{3\\pi R^2} \\, \\frac{{\\cal E}}{m_e c^2}\n\\frac{2-p}{3-p} \\,\n\\frac{\\gamma_{\\rm max}^{3-p} - \\gamma_{\\rm min}^{3-p}}\n{\\gamma_{\\rm max}^{2-p} - \\gamma_{\\rm min}^{2-p}}\n\\approx f_c~ \\frac{\\sigma_{\\rm T}}{3\\pi R^2} \\,\n\\frac{{\\cal E}}{m_e c^2} \\frac{\\gamma_{\\rm max}}\n{\\ln (\\gamma_{\\rm max} / \\gamma_{\\rm min})} \\, ,\n\\end{equation}\nwhere the last expression applies to the case $p = 2$.\nOn the other hand, if $t_{\\rm dyn} > t_{\\rm cool}$, a cooled\nelectron distribution has to be used when calculating the\nsynchrotron photon energy-density. A very rough estimate of\nthe electron break energy $\\gamma_{\\rm br}$,\nbeyond which cooling dominates can be given as \n$$\\frac{6\\pi m_e c}{\\sigma_{\\rm T}}~\\frac{1}{\\gamma_{\\rm br} B^2} \\approx \n{\\rm max}(t_{\\rm inj}, t_{\\rm dyn})~~.$$\nThe cooled electron distribution has the original index $-p$ between\n$\\gamma_{\\rm min}$ and $\\gamma_{\\rm br}$, and roughly $-p-1$ between \n$\\gamma_{\\rm br}$ and $\\gamma_{\\rm max}$. Since the number density\nof electron at high energy end is very small for $p > 1$, the\nprevious expression for $N_0$ (\\S\\ref{sec:us}) still applies. \nThen we can derive another expression for $\\eta$ as\n\\begin{equation}\n\\label{eq:ussc2}\n\\eta_c = f_c~\\frac{\\sigma_{\\rm T}}{3\\pi R^2} \\frac{\\cal E}{m_e c^2}\\,\n \\left[\\left(\\frac{2-p}{3-p}\\right)\n\\frac{\\gamma^{3-p}_{\\rm br}}{\\gamma^{2-p}_{\\rm max}}\n~ +~ 1 \\right]\\,\n\\approx f_c~\\frac{\\sigma_{\\rm T}}{3\\pi R^2} \\frac{\\cal E}{m_e c^2}\\,\n\\left[\\frac{\\gamma_{\\rm br}~+~\\ln (\\gamma_{\\rm max} / \\gamma_{\\rm br})}\n{\\ln (\\gamma_{\\rm max} / \\gamma_{\\rm min})}\\right] \\, ,\n\\end{equation}\nwhere again, the last expression applies to the case $p = 2$.\nNote that this ratio $\\eta_c$ depends on $B$ through $\\gamma_{\\rm br}$.\nUsing the same parameters given previously, we find that\nequations (\\ref{eq:ussc1}) and (\\ref{eq:ussc2}) give\n$\\eta_c \\simeq (\\gamma_{\\rm br}/\\gamma_{\\rm max}) \\eta$.\nIn other words, in order to reach the same relative ratio\nbetween synchrotron and SSC,\nmore energy is needed (by a factor of \n$\\gamma_{\\rm max}/\\gamma_{\\rm br}$ for $p=2$) \nif electrons are cooled efficiently during injection.\n\n\n\n\\subsubsection{Dynamics of a Single Injection}\n\nIn this subsection we concentrate on the dynamics of a single injection\nevent lasting $t_{\\rm inj}$ and its corresponding\nevolution of electron and photon distributions.\nThe idea is to mimic individual flaring events in blazars\nand gain some basic knowledge of how synchrotron and SSC\ncomponents are dynamically linked.\nTo simplify the calculations and analysis,\nwe choose 6 total injection energies\nwith a factor of 10 increase from $10^{44}$ ergs to $10^{49}$ ergs.\nThese energies in nonthermal electrons are injected \nover a comoving timescale of $t_{\\rm inj} = 2 t_{\\rm dyn}$.\nWe solve equations (\\ref{eq:elkinetic}) and (\\ref{eq:phkinetic})\nsimultaneously and follow the evolution until \n$10 t_{\\rm dyn}$. Electrons are not allowed to escape.\nWith these parameters, $t_{\\rm cool}(\\gamma_{\\rm max})$ is\nmuch smaller than $t_{\\rm dyn}$, so electrons are appreciably\ncooled during injection. \n\nFigure \\ref{fig:6curves} shows the $\\nu F_\\nu$ spectra of these\n6 injections taken at $t = t_{\\rm inj}$ and with fluxes \ndivided by ${\\cal E}/10^{44}$.\nIt is evident that synchrotron is the dominant cooling process\nfor ${\\cal E} \\leq 10^{47}$ cases, whereas SSC becomes the dominant \ncooling process as the photon energy density builds up in the\n$10^{48}$ and $10^{49}$ cases. In fact, electron cooling is so\nsignificant in the $10^{49}$ case that the maximum synchrotron flux\nis reduced by almost a factor of 10 compared to other lower \ninjection energy cases, and its SSC peak energy is also much \nsofter than others.\n\nAs given in equation (\\ref{eq:ussc2}), the ratio of SSC to\nsynchrotron is roughly proportional to ${\\cal E}$. Thus as ${\\cal E}$ \nincreases, so is this ratio. This is shown as the (almost) linear\nincrease in the SSC peaks of Figure \\ref{fig:6curves}. So we\nconclude that so long as the peak in SSC is less than synchrotron,\nthe magnitude of increase in SSC peak will be the {\\em square} of\nthe magnitude of increase in synchrotron peak. When the \nSSC component becomes comparable to synchrotron component, the \nsystem becomes highly nonlinear, the estimate of $\\gamma_{\\rm br}$\nbased on pure synchrotron cooling is no longer valid, even though\nequation (\\ref{eq:ussc2}) probably still applies as long as a\ncooled electron distribution is used. \n\nA further point regarding the relative ratio of SSC versus synchrotron\ncomponents is that the initial $\\sim 10$ GeV -- TeV production via SSC\nis in the KN regime, which reduces the SSC flux. \nThis implies that an even larger ${\\cal E}$ is needed than those \ngiven in equation (\\ref{eq:ussc2}). \nObservations of Mrk 421 and 501 seem to indicate roughly the same\nheights of synchrotron and SSC peaks. Thus, in modeling the \ntime-dependent (or even steady state) emissions from these objects,\na full KN cross section has to be used, as was done here in our code.\n\n\n\\subsubsection{Dynamics and Light Curves}\n\nWe now study in detail the full time evolution of three injection\ncases: ${\\cal E} = 10^{44}, 5\\times 10^{47},$ and $10^{49}$ ergs.\nThey are shown in \nFigures \\ref{fig:pp-e44}, \\ref{fig:pp-5e47}, and \\ref{fig:pp-e49},\nwhere the time-evolution of \nelectron distributions and photon spectra are presented.\nFigures \\ref{fig:ltcv-e44}, \\ref{fig:ltcv-5e47}, and \n\\ref{fig:ltcv-e49} show the corresponding light curves of different\nphoton energies for the above three injection cases. \nTo qualitatively understand the light curves, \nwe refer to equation (\\ref{eq:dndt}) again. The peak\nof the light curves is reached when the production and escape\nare balanced, which depends on whether particle distribution\nhas softened enough. Furthermore, once the production at certain \nphoton energy has\nstopped, the pure escape process will produce an exponential decay.\nSince the photon escape timescale is $t_{\\rm dyn} = R/c$, \none could get an \nestimate of the size by fitting the decline portion of the\nlight curves. This can be done using Figures \\ref{fig:ltcv-e44}, \n\\ref{fig:ltcv-5e47}, and \\ref{fig:ltcv-e49} where fluxes have been\nplotted in logarithm. The straight \nlines give a clear representation of photon escape, especially when it \nshows up in several energy bands, thus this might be a useful\nmethod in analyzing the real blazar data.\n\n\n\\subsubsection{Spectral Variations}\n\nThe flux changes depicted in the above subsection are\naccompanied by large spectral variations too as shown\nin Figures \\ref{fig:pp-e44}, \\ref{fig:pp-5e47}, and \\ref{fig:pp-e49}. \nThese curves contain a wealth\nof information, some of which are rather parameter dependent.\nNevertheless, we can draw some general conclusions:\n\n(1) Since the cooling time at $\\gamma_{\\rm max}$ is the shortest\ntimescale in our system, the electron distribution at high energy\nend is always substantially softened.\nFurthermore, the production of photons $>$ tens of GeV is always\nin the KN regime using SSC model. Both effects make the TeV spectrum very\nsoft, with a large curvature. [Additional effects such\nas intrinsic absorption at the source or intergalactic \nabsorption by infrared background can cause further curvature\n(e.g., Coppi \\& Aharonian 1999).]\nThis curvature is not consistent with the TeV spectra we have seen \nfrom Mrk 421 (\\cite{ketal99}), but it is perhaps consistent with the\nobservations of Mrk 501 where a curvature in the Compton component is\nclearly seen (\\cite{cat99}). \n\n(2) The ``hysteresis'' in the relation of\nphoton energy flux and spectral index was first pointed\nout by Takahashi et al. (1996) at the keV band.\nIn Figures \\ref{fig:flxinx-e44}, \\ref{fig:flxinx-5e47}, and\n\\ref{fig:flxinx-e49}, we show \nthe evolution of photon index as a function of energy flux \nin the observer's frame.\nClockwise rotation is always seen at 1 GeV, regardless\nof whether synchrotron or SSC cooling dominates.\nClockwise rotation is found at 2 keV for\nthe case where synchrotron losses dominate the electron\ncooling (${\\cal E} = 10^{44}$ ergs). \nWe find that this clockwise rotation at 2 keV is true for\nall cases with injection energy less than $10^{48}$ ergs\n(with the above injection form). \nThis is mostly related to the fact that if we can associate\n2 keV with the synchrotron peak, the spectrum always softens when its\nflux is decreasing because the electrons that can produce 2 keV photons\nhave diminished. When the injection energy is large, the\nSSC loss is dominant (${\\cal E} = 10^{49}$ ergs),\nthe hysteresis diagrams rotate in the opposite sense at 2 keV.\nThe hardening at later time is actually due to the fact that\n2 keV flux is now from the first generation of SSC, not synchrotron\nanymore. Different behaviors of the hysteresis, however, are found at \n100 keV: counter-clockwise for ${\\cal E} = 10^{44}$ ergs\nand clockwise for ${\\cal E} = 10^{49}$ ergs.\nGiven these large variations and their sensitivity\nof various parameters, it is difficult to use these \n``hysteresis'' diagrams to draw firm conclusions.\n\n(3) If observations show a synchrotron peak in 1 -- 10 keV band,\none should be very careful with fitting the spectrum in the 100 keV\nenergy band (such as OSSE and BeppoSAX), \nsince it is right in the region where synchrotron and SSC meet. \nThere is a very large and rapid spectral evolution during the flare\n(e.g., Figure \\ref{fig:flxinx-5e47}). \n\n(4) In the rising part of the $\\nu F_\\nu$ spectra, such as\n1 -- 10 eV and MeV -- GeV, the spectral index variation is much\nslower than the keV and TeV energy bands even though their fluxes vary \nby a large factor (e.g., Figures \n\\ref{fig:flxinx-e44}, \\ref{fig:flxinx-5e47}, and\n\\ref{fig:flxinx-e49}).\n\n\n(5) To further quantify the spectral evolution, we\nplot the peak energies of synchrotron and SSC components in \n$\\nu F_\\nu$ as a function of time in Figure \\ref{fig:epkt}\nfor the case with ${\\cal E} = 5\\times 10^{47}$ ergs. An important\npart is the early softening stage, where the synchrotron peak energy\ndecreases as $\\gamma^2$ whereas the SSC peak energy goes down first\nas $\\gamma$ because the scattering is in the KN regime. \nThis effect might be observable with the current keV and TeV\nobservational capabilities. Such a ``correlated'' evolution\nin peak energies might provide a definitive test of SSC. \n\n(6) As shown in Figure \\ref{fig:6curves}, when the SSC cooling\nbecomes comparable to or dominant over the synchrotron cooling,\nthe synchrotron peak becomes broader than those dominated\nby synchrotron cooling only.\n\nSome of the above conclusions might be testable using the\ncurrent data collected on blazars, and some might require \nmuch higher quality data. \n\n\n\\subsubsection{Time-Dependent Injection}\n\nIn this subsection we show how different injection profiles\nchange the light curves in a single injection event.\nDifferent from the previous subsection where a constant\ninjection is used (box-shaped injection), \nwe calculate another case with \na linearly increasing injection rate (triangle-shaped injection),\ni.e., $Q(\\gamma) = Q_0 \\gamma^{-2} t/t_{\\rm dyn}$ for\n$0 \\leq t \\leq 2 t_{\\rm dyn}$, and $Q(\\gamma) = 0$ for\n$t > 2 t_{\\rm dyn}$. \nThe time evolution is followed until $t = 10 t_{\\rm dyn}$\nand electrons are allowed to escape with \n$t_{e, {\\rm esc}} = 5 t_{\\rm dyn}$.\nWe use the same number of particles and same amount of\ntotal injected energy in both box- and triangle-shaped injections;\nthe injected energy is $5 \\times 10^{47}$ ergs per $2 t_{\\rm dyn}$\nin the blob frame.\nIn Figure \\ref{fig:light-triangle-box}, we compare \ntheir light curves at 1 keV.\nThe light curve for the box-shaped injection is asymmetric,\nbecause more electrons are injected at an early stage\nthan in the triangle injection.\nOn the other hand, the light curve from triangle injection\nshape is almost symmetric.\nIn both cases, light curves decay exponentially\nafter the end of the injection.\n\n\n\\subsubsection{Multiple Injections}\n\\label{sec:multi}\n\nWe now move to study other injection profiles, \nwhich are done by artificially turning \nthe electron source term on and off. \nThis is admittedly quite artificial.\nThe purpose is to understand whether there are any generic \nfeatures associated with these multiple injections, which might aid us on \nmodeling the multiple flares often observed from blazars.\nIn all the following runs, we allow electrons to escape with \n$t_{e, {\\rm esc}} = 5 t_{\\rm dyn}$.\nOther parameters are the same as the single injection case.\n\nSuccessive flares can be produced by repeated injections\nof nonthermal electrons. \nAs an example of this picture, \nwe present light curves for two repeated injection cases\nof nonthermal electrons.\nThe top panels of Figures \\ref{fig:multi-light-long} and\n\\ref{fig:multi-light-short} show the injection profiles,\nwhich consist of two triangle injections separated by a\nlong ($8 t_{\\rm dyn}$) and a short ($2 t_{\\rm dyn}$) intervals\n(in the comoving frame), respectively.\nIn both cases $5 \\times 10^{47}$ ergs are injected in each ``flare''\nwith a triangle-shaped time profile.\nThe lower panels of Figures \\ref{fig:multi-light-long}\nand \\ref{fig:multi-light-short} show the expected\nlight curves calculated by our code.\nThe shape of the light curves from each injection is very\nsimilar to that in Figure \\ref{fig:light-triangle-box}\nwhere a single injection is involved (i.e., quasi-symmetric).\nThe peak fluxes of light curves in multiple injections are, however,\naffected by the separation time of two flares.\nWhen the separation interval is longer than the electron escape time\n($5 t_{\\rm dyn}$), the light curves can almost be regarded as a simple\nsequence of two separate single injections. But when the\nseparation interval is shorter than the electron escape time,\nmultiwavelength light curves become rather complicated.\nThe main physical reason behind this complication is the\ndynamic accumulation of both photons and relativistic \nelectrons. First of all, 1 eV and 1 keV emissions are from synchrotron\nand others are from SSC. All the SSC emissions have second peak\nhigher than the first one, this is due to the increase both\nin soft photon energy density and in the number of electrons which\nare not completely cooled yet when the second injection occurs.\nThis accumulation of electrons also accounts for the increase in\n1 eV synchrotron flux. The 1 keV emissions, however, show a lower flux\nin the second peak, this is because the relativistic\nelectrons from the second injection are subject to a much\nstronger cooling due to the enhanced photon energy density from\nthe first injection. In addition to the flux differences,\nthere are obvious delays in reaching the peak fluxes\nfor different wavelengths with respect to the synchrotron and SSC\npeaks, though 1 keV and 1 TeV fluxes track each other rather well.\n\nAs demonstrated in these figures, the slow response and relatively\nsmall amplitude variations at the photon energies other than the\nsynchrotron and SSC peaks argue against the usual belief of closely \ncorrelated variations in multiwavelength observations. \nOnly the emissions from the tail of\nthe electron energy distribution can be reliably used as diagnostics\nfor separate injections. Still, extra caution is obviously needed \nwhen relating the energy contained in nonthermal particles versus\nthe observed fluxes.\n\n\n\\section{SUMMARY AND DISCUSSIONS}\n\\label{sec:sum}\n\nUsing a homogeneous synchrotron self-Compton model, \nwe have calculated the time evolution of emission spectra\nand electron energy distributions when nonthermal electrons\nare uniformly injected into a relativistically moving plasma blob with\nconstant velocity. \nWe have found that:\n\n(1) When the luminosities of the synchrotron and SSC peaks\nare comparable, the electron cooling by inverse Compton scattering\nis not negligible and the system is inherently nonlinear\nand dynamic. One has to solve the time-dependent,\ncoupled electron and photon kinetic-equations self-consistently.\nFurthermore, since observations\nare most sensitive to the peak fluxes of synchrotron and \nSSC components, accurate treatments of synchrotron emissivity\ndue to the end point effects and inverse\nCompton scattering in the KN regime are quite essential.\n \n(2) When the cooling time at the maximum particle energy is\nlonger than the injection\ntimescale ($\\ge R/c$), the light curve of emissions\ncorresponding to the tail of the electron distribution can\nhave short, large amplitude variations but emissions\nat other wavelengths show considerably longer and \nsmaller amplitude changes. Additionally, spectral\nevolution is also rather slow. All these features are \nsimply caused by the long cooling time of electrons.\n\n(3) When cooling time at the maximum particle energy is\nshorter than the dynamic timescale, strong spectral\nevolutions are observed for both synchrotron and SSC \ncomponents and short duration flares are obtained in\nmost energy bands.\n\n(4) Generally, the prompt TeV spectrum is curved due to the\nKN effect and the fact that TeV-production electrons\nare usually in a cooled distribution. This consideration\ndoes not take into account the possible infrared background\nattenuation of the TeVs, which might cause further curvature\nin the TeV spectrum. On the other hand, most current TeV\nobservations require an accumulation time probably much\nlonger than the dynamic timescale of the blob, so that it\nmight still be possible to obtain a quasi power-law TeV\nspectrum by averaging over an evolving spectrum. Further\nstudy is needed to address this issue.\n\n(5) We recommend plotting the light curves in a fashion\nthat is logarithmic flux versus linear time. The goal\nis to look for exponential decays at specific energy\nbands, which might give direct measurements of the size\nof the system, as indicated in Figures\n\\ref{fig:ltcv-e44} -- \\ref{fig:ltcv-e49}.\n\n(6) One has to be cautious about the common belief that \nlight curves in different energy bands should track each other.\nThe electrons responsible for producing specific energy photons\nmight have quite different lifetimes, especially when\nmultiple and closely spaced injections are involved. \nThis complication also applies to the leading/lagging\nanalysis for different photon energy bands.\n\n(7) When high time-resolution spectroscopy is available\nboth in keV and TeV bands, one should be able to prove\nwhether TeV production is via SSC process by comparing\nthe rates of spectral softening as done in Figure \\ref{fig:epkt}.\n\nThe primary purpose of this paper is to investigate \nthe radiative signatures in a purely cooling and dynamic system,\nthus providing a bridge between observations and the detailed\nbut largely unknown physics of particle energization processes.\nSince we did not address the particle acceleration problem here,\nin this sense, some of the conclusions drawn above are certainly\nsubject to revisions as our understanding of energy flow in\nAGNs improves.\n\n\nIn conclusion, we have found that solving time-dependent, coupled \nelectron and photon kinetic-equations provides an easy\nand efficient way of comparing multiwavelength, time-dependent\nobservations with some simplified SSC models. It has the\nadvantage of naturally combining the spectral and temporal\nevolutions in a dynamic system, which is very useful when more\nand more high quality data become available.\n\n\n\\acknowledgements\n\nWe thank C. Dermer for useful discussions and \nthe anonymous referee for the helpful comments.\nH.L. gratefully acknowledges the support of an Oppenheimer Fellowship, \nand his research is supported by the Department of Energy, \nunder contract W-7405-ENG-36.\nM.K. thanks F. Takahara for stimulating discussions and\nhis research was partially supported by Scientific Research Grants\n(09223219, 10117215) from the Ministry of Education, \nScience, Sports and Culture of Japan. \n\n\n\n\\begin{thebibliography}{}\n\n\\bibitem[Blandford \\& Rees 1978]{br78}\nBlandford, R.D., \\& Rees, M.J. 1978, in Pittsburgh Conf. on BL Lac\nObjects, ed. A.M. Wolfe (Pittsburgh: Univ. Pittsburgh Press), 328\n\n\\bibitem[Bloom \\& Marscher (1996)]{bm96}\nBloom, S. D., \\& Marscher, A. P. 1996, \\apj, 461, 657\n\n\\bibitem[]{}\nB$\\ddot{o}$ttcher, M., Mause, H., \\& Schlickeiser, R. 1997,\nA\\&A, 324, 395\n\n\\bibitem[Buckley et al. (1996)]{buck96}\n Buckley, J. H. et al. 1996, \\apjl, 472, L9\n\\bibitem[Catanese et al. (1997)]{cat97}\n Catanese, M. et al. 1997, \\apjl, 487, L143\n\n\\bibitem[Coppi \\& Aharonian 1999]{ca99}\n Coppi, P. S., \\& Aharonian, F. A. 1999, \\apjl, 521, L33\n\n\\bibitem[Coppi \\& Blandford 1990]{cb90}\n Coppi, P. S., \\& Blandford, R. D. 1990, \\mnras, 245, 453\n\n\\bibitem[Crusius \\& Schlickeiser (1986)]{cs86}\n Crusius, A., \\& Schlickeiser, R. 1986, A\\&A, 164, L16\n\n\\bibitem[Dermer (1998)]{dermer98}\n Dermer, C. D. 1998, \\apjl, 501, L157\n\n\\bibitem[Dermer, Sturner, \\& Schilickeiser (1997)]{dss97}\n Dermer, C. D., Sturner, S. J., \\& Schlickeriser, R. 1997,\n \\apjs, 109, 103\n\n\\bibitem[Djannati-Atai et al. 1999]{cat99}\n Djannati-Atai, A. et al. 1999, A\\&A, submitted\n\n\\bibitem[Georganopoulos, \\& Marcher (1998)]{gm98}\n Georganopoulos, M., \\& Marcher, A. P.1998, \\apjl, 501, L11\n\n\\bibitem[Ghisellini et al. (1988)]{ghi88}\n Ghisellini, G., Guilbert, P. W., \\& Svensson, R. 1988\n \\apjl, 334, L5\n\n\\bibitem[ghisellini \\& Madau (1996)]{gm96}\n Ghisellini, G., \\& Madau, P. 1996, \\mnras, 280, 67\n\n\\bibitem[Ghisellini et al. (1998)]{gcfmc98}\n Ghisellini, G., Celotti, A., Fossati, G.,\n Maraschi, L., \\& Comastri, A. 1998, \\mnras, 301, 451\n\n\\bibitem[Inoue \\& Takahara 1996]{it96}\n Inoue, S., \\& Takahara, F. 1996, \\apj, 463, 555\n\n\\bibitem[Jones (1968)]{jones68}\n Jones, F. C. 1968, Physical Review, 167, 1159\n\n\\bibitem[Kataoka et al. (1999)]{kat99}\n Kataoka, J. et al. 1999, \\apj, 514, 318\n\n\\bibitem[Kirk et al. (1998)]{kirketal98}\n Kirk, J. G., Rieger, F. M., \\& Mastichiadis, A. 1998, \\aap, 333, 452\n\n\\bibitem[Krennrich et al. 1999]{ketal99}\n Krennrich, F. et al. 1999, \\apj, 511, 149\n\n\\bibitem[Kusunose, Coppi, \\& Li 1999]{kcl99}\n Kusunose, M., Coppi, P.S., \\& Li, H. 1999, unpublished,\navailable upon request\n\n\\bibitem[Macomb et al. (1995)]{macomb95}\n Macomb, D. J., et al. 1995, \\apjl, 449, L99\n\n\\bibitem[Macomb et al. (1996)]{macomb96}\n Macomb, D. J., et al. 1996, \\apjl, 459, L111 (erratum)\n\n\\bibitem[Mastichiadis \\& Kirk (1997)]{mk97}\n Mastichiadis, A., \\& Kirk, J. G. 1997, \\aap, 320,19\n\n\\bibitem[Pian et al. (1998)]{pian98}\n Pian, E. et al. 1998, \\apjl, 492, L17\n\n\\bibitem[Robinson \\& Melrose (1984)]{rm84}\n Robinson, P. A., \\& Melrose, D. B. 1984, Australian J. Physics, 37, 675\n\n\\bibitem[Romanova \\& Lovelace 1997]{rl97}\n Romanova, M.M. \\& Lovelace, R.V.E. 1997, \\apj, 475, 97\n\n\\bibitem[Sikora et al. (1997)]{smmp97}\n Sikora, M., Madejski, G., Moderski, R., Poutanen, J. 1997,\n \\apj, 484, 108\n\n\\bibitem[Takahashi et al. (1996)]{taka96}\n Takahashi, T., Tashiro, M., Madejski, G., Kubo, H.,\n Kamae, T., Kataoka, J., Kii, T., Makino, F.,\n Makishima, K., \\& Yamasaki, N. 1996, \\apjl, 470, L89\n\n\\bibitem[Vermeulen \\& Cohen 1994]{vc94}\n Vermeulen, R.C. \\& Cohen, M.H. 1994, \\apj, 430, 467\n\n\\bibitem[von Montigny et al. 1995]{vm95}\n von Montigny, C. et al. 1995, \\apj, 440, 525\n\n\\end{thebibliography}\n\n\n\\clearpage\n\n\\begin{figure}\n\\epsfig{file=fig1.ps,height=5in,width=4in,angle=-90}\n\\caption{Time evolution of electron energy distribution (upper panel)\nand the corresponding photon spectra (lower panel) \nusing parameters from the unique solution discussed in \\S \\ref{sec:us}.\nElectrons are injected at a constant\nrate lasting $2 t_{\\rm dyn}$ in the comoving frame.\nThere are 20 curves in each panel, which start at $t = 0.5 t_{\\rm dyn}$\nand end at $t = 10 t_{\\rm dyn}$ with a time interval of \n$0.5 t_{\\rm dyn}$ between them. The injection process is shown by\nthe dashed curves moving up in $n(E)$, \nalong with the increasing photon fluxes.\nAfter the injection stops, electrons are continuously cooled and\nthe photon spectrum softens. These parameters give a comparable\npeak fluxes for synchrotron and SSC components.\n}\n\\label{fig:parpht-us}\n\\end{figure}\n\n\\begin{figure}\n\\epsfig{file=fig2.ps,height=5in,width=4in,angle=0}\n\\caption{Multiwavelength light curves in observer's frame\n(${\\cal D}$ is assumed to be 10) using parameters from\nthe unique solution (cf. Figure \\ref{fig:parpht-us}).\nFluxes at the synchrotron and SSC peaks show fast time variability\nwith large amplitudes, but fluxes at other wavelengths have\na very long plateau with very small amplitude variation.\n}\n\\label{fig:ltcv-us}\n\\end{figure}\n\n\\begin{figure}\n\\epsfig{file=fig3.ps,height=5in,width=4in,angle=0}\n\\caption{Shown is $|\\dot\\gamma_{\\rm ssc}/\\dot\\gamma_{\\rm syn}|$\nas a function of electron energy at different times \n(from $0.5 - 10 t_{\\rm dyn}$)\nusing parameters from the unique solution \n(cf. Figure \\ref{fig:parpht-us}). The horizontal solid line at \nthe ratio being $1$ is plotted to guide the comparison.\nThe SSC process becomes important as soon as the photon energy\nis built up and, in fact, is more important than synchrotron cooling\nfor most of the electron energies.\n}\n\\label{fig:syn-ssc-ratio}\n\\end{figure}\n\n\\begin{figure}\n\\epsfig{file=fig4.ps,height=5in,width=4in,angle=-90}\n\\caption{Shown is the photon spectral evolution from $0 - 4 t_{\\rm dyn}$\nas the magnetic field is varied from the unique solution value $B_s$.\nThe ratio $\\eta$ is unity when $B = B_s$ (cf. Figure \\ref{fig:parpht-us})\nbut varies nearly as $(B_s/B)^8$ as shown in the middle and lower\npanels here.\n}\n\\label{fig:varyb}\n\\end{figure}\n\n\\begin{figure}\n\\epsfig{file=fig5.ps,height=5in,width=4in,angle=-90}\n\\caption{The photon spectra $\\nu F_\\nu$ for 6 different \ntotal-injection-energy ${\\cal E}$, ranging from $10^{44}$ ergs to\n$10^{49}$ ergs with a factor of 10 increment in each case.\nAll 6 spectra are taken at the end of electron injection \n($t = 2 t_{\\rm dyn}$) and their fluxes are divided by \n${\\cal E}/10^{44}$ so that if the synchrotron flux was \nexactly proportional to ${\\cal E}$, they would have had the \nsame heights. As ${\\cal E}$ increases, the electron cooling\nchanges from synchrotron dominated (when ${\\cal E} \\leq 10^{47}$)\nto synchrotron self-Compton (SSC) dominated. Note that the\nincrease in SSC component is proportional to ${\\cal E}^2$ \nfor ${\\cal E} \\leq 10^{47}$. When SSC cooling is very strong,\nelectrons cool so quickly that the synchrotron flux at\n$2 t_{\\rm dyn}$ is no longer scaled as ${\\cal E}$ anymore\nas shown in the $10^{48}$ ({\\it dashed}) \nand $10^{49}$ ({\\it dotted}) cases. Also in these\nlarge ${\\cal E}$ cases, the efficient cooling makes the \nsynchrotron peak rather broad.\n}\n\\label{fig:6curves}\n\\end{figure}\n\n\n\\begin{figure}\n\\epsfig{file=fig6.ps,height=5in,width=4in,angle=-90}\n\\caption{Time evolution of electron energy distribution (upper panel)\nand the corresponding photon spectra (lower panel) for\n${\\cal E} = 10^{44}$ ergs. Electrons are injected at a constant\nrate lasting $2 t_{\\rm dyn}$ in the comoving frame, with \n$\\gamma_{\\rm min} = 10$, $\\gamma_{\\rm max} = 10^6$, and index $p = 2$.\nThere are 20 curves in each panel, which start at $t = 0.5 t_{\\rm dyn}$\nand end at $t = 10 t_{\\rm dyn}$ with a time interval of \n$0.5 t_{\\rm dyn}$ between them. The injection process is shown by\nthe dashed curves moving up in $n(E)$, \nalong with the increasing photon fluxes.\nAfter the injection stops, electrons are continuously cooled and\nphoton spectrum softens (solid curves). With this injection energy,\nthe SSC peak is considerably lower than the synchrotron peak.}\n\\label{fig:pp-e44}\n\\end{figure}\n\n\\begin{figure}\n\\epsfig{file=fig7.ps,height=5in,width=4in,angle=-90}\n\\caption{Same as Figure \\ref{fig:pp-e44}, except that\n${\\cal E} = 5\\times 10^{47}$ ergs. Now the SSC component has become\ncomparable to the synchrotron component, and the whole system\nunderstandably evolves on a faster timescale.}\n\\label{fig:pp-5e47}\n\\end{figure}\n\n\\begin{figure}\n\\epsfig{file=fig8.ps,height=5in,width=4in,angle=-90}\n\\caption{Same as Figure \\ref{fig:pp-e44}, except that\n${\\cal E} = 10^{49}$ ergs. The SSC component dominates over\nthe synchrotron component, and the buildup of synchrotron photon\nenergy-density is so quick that electron cooling is very efficient.\nTowards the end of simulation ($\\sim 10 t_{\\rm dyn}$), multiple\nCompton scattering features are evident.}\n\\label{fig:pp-e49}\n\\end{figure}\n\n\\begin{figure}\n\\epsfig{file=fig9.ps,height=5in,width=4in,angle=-90}\n\\caption{Multiwavelength light curves in observer's frame\n(${\\cal D}$ is assumed to be 10) with ${\\cal E} = 10^{44}$ ergs\n(cf. Figure \\ref{fig:pp-e44}).\nSolid and dashed curves are for synchrotron and SSC components,\nrespectively. The exponential decay depicted by the keV and TeV\nfluxes allows a direct estimate of the size of the emission cloud.\n}\n\\label{fig:ltcv-e44}\n\\end{figure}\n\n\\begin{figure}\n\\epsfig{file=fig10.ps,height=5in,width=4in,angle=-90}\n\\caption{Same as Figure \\ref{fig:ltcv-e44}\nexcept that ${\\cal E} = 5\\times 10^{47}$ ergs. \n(Also cf. Figure \\ref{fig:pp-5e47})}\n\\label{fig:ltcv-5e47}\n\\end{figure}\n\n\\begin{figure}\n\\epsfig{file=fig11.ps,height=5in,width=4in,angle=-90}\n\\caption{Same as Figure \\ref{fig:ltcv-e44}\nexcept that ${\\cal E} = 10^{49}$ ergs. \n(Also cf. Figure \\ref{fig:pp-e49})}\n\\label{fig:ltcv-e49}\n\\end{figure}\n\n\\begin{figure}\n\\epsfig{file=fig12.ps,height=5in,width=4in,angle=-90}\n\\caption{The time evolution of the correlation between \nthe photon index and the flux (ergs cm$^{-2}$ s$^{-1}$) at 2 keV, 100 keV, \nand 1 GeV, respectively.\nArrows indicate the direction of the time evolution.\nThe total injected energy is ${\\cal E}=10^{44}$ ergs.\nA large spectral evolution is seen at 100 keV, where\nsynchrotron and SSC components mix.\nSpectral evolution at keV and GeV bands are relatively\nmoderate and clockwise.\n}\n\\label{fig:flxinx-e44}\n\\end{figure}\n\n\\begin{figure}\n\\epsfig{file=fig13.ps,height=5in,width=4in,angle=-90}\n\\caption{Same as Figure \\ref{fig:flxinx-e44}\nexcept that ${\\cal E} = 5\\times 10^{47}$ ergs.\nThe evolution is qualitatively the same as in Figure \\ref{fig:flxinx-e44}.\n}\n\\label{fig:flxinx-5e47}\n\\end{figure}\n\n\\begin{figure}\n\\epsfig{file=fig14.ps,height=5in,width=4in,angle=-90}\n\\caption{Same as Figure \\ref{fig:flxinx-e44}\nexcept that ${\\cal E} = 10^{49}$ ergs.\nStrong evolution at 2 keV is evident, mostly\ndue to the efficient cooling of electrons by\nSSC process.\n}\n\\label{fig:flxinx-e49}\n\\end{figure}\n\n\\begin{figure}\n\\epsfig{file=fig15.ps,height=5in,width=4in,angle=0}\n\\caption{Evolution of peak photon energies of both synchrotron and SSC\ncomponents. The total injected energy is ${\\cal E}=5\\times 10^{47}$ ergs\n(cf. Figure \\ref{fig:pp-5e47}). \nThe upper panel shows their actual values and the lower panel\nshows the normalized values after dividing each peak energy by the\nvalue at $t = 0.5 t_{\\rm dyn}$ for synchrotron and SSC components,\nrespectively. The synchrotron peak energy ($\\propto \\gamma^2$)\ndecreases faster than SSC peak energy ($\\propto \\gamma$) {\\em initially}, \nbecause SSC process is still in the Klein-Nishina regime. \n}\n\\label{fig:epkt}\n\\end{figure}\n\n\\begin{figure}\n\\epsfig{file=fig16.ps,height=5in,width=4in,angle=0}\n\\caption{\nLight curves of observed spectra at 1 keV when power-law electrons\nare injected.\nSolid curve is calculated when\n$Q(\\gamma) = Q_0 \\gamma^{-2} $ for\n$0 \\leq t \\leq 2 t_{\\rm dyn}$, and $Q(\\gamma) = 0$ for\n$t > 2 t_{\\rm dyn}$.\nDotted curve is obtained \nwhen $Q(\\gamma) = Q_0 \\gamma^{-2} t/t_{\\rm dyn}$ for\n$0 \\leq t \\leq 2 t_{\\rm dyn}$, and $Q(\\gamma) = 0$ for\n$t > 2 t_{\\rm dyn}$.\nThe upper panel shows the time profile of \nthe injection $Q$ in arbitrary units.\n}\n \\label{fig:light-triangle-box}\n\\end{figure}\n\n% Double flare --- long space\n\\begin{figure}\n\\epsfig{file=fig17.ps,height=5in,width=4in,angle=0}\n\\caption{Expected light curves at different wavelengths (lower panel)\nwhen power-law electrons are injected according to the\nprofile in the upper panel. The time is measured in the observer's\nframe. In the comoving frame, two injections are separated by \n$8 t_{\\rm dyn}$, longer than the electron escape timescale, \nwhich is chosen as $5 t_{\\rm dyn}$. The same amount of energy,\n$5 \\times 10^{47}$ ergs, is injected in each flare.\nThe dotted, dashed, dash-dotted, dash-dot-dot-dotted, and\nsolid represent fluxes at 1 eV, 1 keV, 1 MeV, 1 GeV, and 1 TeV,\nrespectively. The two flares can be regarded as a simple sequence of\ntwo unrelated injections.\n}\n \\label{fig:multi-light-long}\n\\end{figure}\n\n\n\n% Double flare --- short space\n\\begin{figure}\n\\epsfig{file=fig18.ps,height=5in,width=4in,angle=0}\n\\caption{Same as Figure \\ref{fig:multi-light-long},\nexcept that the separation of two flares is shorter ($2 t_{\\rm dyn}$)\nthan the electron escape timescale. The second flare is now strongly\naffected by the residual effects from the first electron injection. \n}\n \\label{fig:multi-light-short}\n\\end{figure}\n\n\n\\end{document}\n"
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{
"name": "astro-ph0002134.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Blandford \\& Rees 1978]{br78}\nBlandford, R.D., \\& Rees, M.J. 1978, in Pittsburgh Conf. on BL Lac\nObjects, ed. A.M. Wolfe (Pittsburgh: Univ. Pittsburgh Press), 328\n\n\\bibitem[Bloom \\& Marscher (1996)]{bm96}\nBloom, S. D., \\& Marscher, A. P. 1996, \\apj, 461, 657\n\n\\bibitem[]{}\nB$\\ddot{o}$ttcher, M., Mause, H., \\& Schlickeiser, R. 1997,\nA\\&A, 324, 395\n\n\\bibitem[Buckley et al. (1996)]{buck96}\n Buckley, J. H. et al. 1996, \\apjl, 472, L9\n\\bibitem[Catanese et al. (1997)]{cat97}\n Catanese, M. et al. 1997, \\apjl, 487, L143\n\n\\bibitem[Coppi \\& Aharonian 1999]{ca99}\n Coppi, P. S., \\& Aharonian, F. A. 1999, \\apjl, 521, L33\n\n\\bibitem[Coppi \\& Blandford 1990]{cb90}\n Coppi, P. S., \\& Blandford, R. D. 1990, \\mnras, 245, 453\n\n\\bibitem[Crusius \\& Schlickeiser (1986)]{cs86}\n Crusius, A., \\& Schlickeiser, R. 1986, A\\&A, 164, L16\n\n\\bibitem[Dermer (1998)]{dermer98}\n Dermer, C. D. 1998, \\apjl, 501, L157\n\n\\bibitem[Dermer, Sturner, \\& Schilickeiser (1997)]{dss97}\n Dermer, C. D., Sturner, S. J., \\& Schlickeriser, R. 1997,\n \\apjs, 109, 103\n\n\\bibitem[Djannati-Atai et al. 1999]{cat99}\n Djannati-Atai, A. et al. 1999, A\\&A, submitted\n\n\\bibitem[Georganopoulos, \\& Marcher (1998)]{gm98}\n Georganopoulos, M., \\& Marcher, A. P.1998, \\apjl, 501, L11\n\n\\bibitem[Ghisellini et al. (1988)]{ghi88}\n Ghisellini, G., Guilbert, P. W., \\& Svensson, R. 1988\n \\apjl, 334, L5\n\n\\bibitem[ghisellini \\& Madau (1996)]{gm96}\n Ghisellini, G., \\& Madau, P. 1996, \\mnras, 280, 67\n\n\\bibitem[Ghisellini et al. (1998)]{gcfmc98}\n Ghisellini, G., Celotti, A., Fossati, G.,\n Maraschi, L., \\& Comastri, A. 1998, \\mnras, 301, 451\n\n\\bibitem[Inoue \\& Takahara 1996]{it96}\n Inoue, S., \\& Takahara, F. 1996, \\apj, 463, 555\n\n\\bibitem[Jones (1968)]{jones68}\n Jones, F. C. 1968, Physical Review, 167, 1159\n\n\\bibitem[Kataoka et al. (1999)]{kat99}\n Kataoka, J. et al. 1999, \\apj, 514, 318\n\n\\bibitem[Kirk et al. (1998)]{kirketal98}\n Kirk, J. G., Rieger, F. M., \\& Mastichiadis, A. 1998, \\aap, 333, 452\n\n\\bibitem[Krennrich et al. 1999]{ketal99}\n Krennrich, F. et al. 1999, \\apj, 511, 149\n\n\\bibitem[Kusunose, Coppi, \\& Li 1999]{kcl99}\n Kusunose, M., Coppi, P.S., \\& Li, H. 1999, unpublished,\navailable upon request\n\n\\bibitem[Macomb et al. (1995)]{macomb95}\n Macomb, D. J., et al. 1995, \\apjl, 449, L99\n\n\\bibitem[Macomb et al. (1996)]{macomb96}\n Macomb, D. J., et al. 1996, \\apjl, 459, L111 (erratum)\n\n\\bibitem[Mastichiadis \\& Kirk (1997)]{mk97}\n Mastichiadis, A., \\& Kirk, J. G. 1997, \\aap, 320,19\n\n\\bibitem[Pian et al. (1998)]{pian98}\n Pian, E. et al. 1998, \\apjl, 492, L17\n\n\\bibitem[Robinson \\& Melrose (1984)]{rm84}\n Robinson, P. A., \\& Melrose, D. B. 1984, Australian J. Physics, 37, 675\n\n\\bibitem[Romanova \\& Lovelace 1997]{rl97}\n Romanova, M.M. \\& Lovelace, R.V.E. 1997, \\apj, 475, 97\n\n\\bibitem[Sikora et al. (1997)]{smmp97}\n Sikora, M., Madejski, G., Moderski, R., Poutanen, J. 1997,\n \\apj, 484, 108\n\n\\bibitem[Takahashi et al. (1996)]{taka96}\n Takahashi, T., Tashiro, M., Madejski, G., Kubo, H.,\n Kamae, T., Kataoka, J., Kii, T., Makino, F.,\n Makishima, K., \\& Yamasaki, N. 1996, \\apjl, 470, L89\n\n\\bibitem[Vermeulen \\& Cohen 1994]{vc94}\n Vermeulen, R.C. \\& Cohen, M.H. 1994, \\apj, 430, 467\n\n\\bibitem[von Montigny et al. 1995]{vm95}\n von Montigny, C. et al. 1995, \\apj, 440, 525\n\n\\end{thebibliography}"
}
] |
astro-ph0002135
|
The Formation and Fragmentation of Primordial Molecular Clouds
|
[
{
"author": "Tom Abel$^{1}$"
},
{
"author": "Greg L. Bryan$^{2,3}$ and Michael L. Norman$^{4,5}$"
},
{
"author": "{$^1$Harvard Smithsonian Center for Astrophysics, MA, US--02138 Cambridge}"
},
{
"author": "{$^3$Hubble Fellow}"
}
] |
Many questions in physical cosmology regarding the thermal history of the intergalactic medium, chemical enrichment, reionization, etc. are thought to be intimately related to the nature and evolution of pregalactic structure. In particular the efficiency of primordial star formation and the primordial IMF are of special interest. We present results from high resolution three--dimensional adaptive mesh refinement simulations that follow the collapse of primordial molecular clouds and their subsequent fragmentation within a cosmologically representative volume. Comoving scales from 128 kpc down to 1 pc are followed accurately. Dark matter dynamics, hydrodynamics and all relevant chemical and radiative processes (cooling) are followed self-consistently for a cluster normalized CDM structure formation model. Primordial molecular clouds with $\sim 10^5$ solar masses are assembled by mergers of multiple objects that have formed hydrogen molecules in the gas phase with a fractional abundance of $\lsim 10^{-4}$. As the subclumps merge cooling lowers the temperature to $\sim200$ K in a ``cold pocket'' at the center of the halo. Within this cold pocket, a quasi--hydrostatically contracting core with mass $\sim 200\Ms$ and number densities $\gsim 10^5 \cm^{-3}$ is found. We find that less than 1\% of the primordial gas in such small scale structures cools and collapses to sufficiently high densities to be available for primordial star formation. %Our results constrain various scenarios % discussed in the literature. We conclude that very massive objects, % or massive black holes are unlikely to be formed within the very % first cosmological objects. Also, fragmentation of a large fraction % of baryons into brown dwarfs or Jupiter size fragments within the % smallest first structures, seems very unlikely. Furthermore, it is worthwhile to note that this study achieved the highest dynamic range covered by structured adaptive mesh techniques in cosmological hydrodynamics to date. \vspace{0.3cm}
|
[
{
"name": "first.tex",
"string": "%\\documentstyle[epsfig, emulateapj]{article}\n\\documentclass[preprint2]{aastex}\n\\input{english.sty}\n%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% %%%%\n%%%% PLACE YOUR OWN MACROS HERE %%%%\n%% Some examples follow. %% \n\\def\\etal{{\\it et\\thinspace al.\\/~}}\n\\def\\adhoc{{\\it ad hoc\\/}}\n\\def\\ie{{i.e}}\n\\def\\eg{{e.g}}\n\\def\\etc{{etc}}\n\\def\\viz{{\\sl viz\\/}}\n\\def\\cf{{cf}}\n\\def\\kms{\\mbox{km s$^{-1}$}}\n\\def\\mpc{\\mbox{Mpc}}\n%%%% equation STUFF: %%%%\n\\def\\dex{\\rm dex}\n\\def\\beq#1{\\begin{equation}\\label{#1}}\n\\def\\eeq{\\end{equation}}\n\\def\\beqa#1{\\begin{eqnarray}\\label{#1}}\n\\def\\eeqa{\\end{eqnarray}}\n\\def\\eq#1{equation~(\\ref{#1})}\n\\def\\Eq#1{Equation~(\\ref{#1})}\n\\def\\eqnum#1{~(\\ref{#1})}\n\\def\\tento#1{\\times 10^{#1}}\n\n% UNITS:\n\\def\\Ms{\\ M_{\\odot}} \n\\def\\Ls{\\ L_{\\odot}}\n\\def\\K{{\\rm \\ K}}\n\\def\\s{{\\rm \\ s}}\n\\def\\sr{{\\rm \\ sr}}\n\\def\\ergs{{\\rm \\ erg}}\n\\def\\erg{{\\rm \\ erg}}\n\\def\\cm{{\\rm \\ cm}}\n\\def\\eV{{\\rm \\ eV}}\n\\def\\Mpc{{\\rm \\ Mpc}}\n\\def\\kpc{{\\rm \\ kpc}}\n\\def\\pc{{\\rm \\ pc}}\n\\def\\years{{\\rm \\ years}}\n\\def\\yrs{{\\rm \\ years}}\n\\def\\angstrom{\\stackrel{o}{\\rm A}}\n\\def\\Hz{{\\rm \\ Hz}}\n\\def\\nd#1{n_{ \\rm #1}}\n\\def\\k#1{k_{{\\rm #1}}}\n\n\\def\\nhi{N_{\\rm HI}}\n\\def\\HH{H$_2$ }\n\\def\\H2p{H$_2^+$ }\n\\def\\Hp{H$^+$ }\n\\def\\Hm{H$^-$ }\n\\def\\Hep{He$^+$ }\n\\def\\Hepp{He$^{++}$ }\n\n\\def\\HH{H$_2$ }\n\\def\\H2p{H$_2^+$ }\n\\def\\HHp{H$_2^+$ }\n\\def\\Hp{H$^+$ }\n\\def\\Hm{H$^-$ }\n\\def\\Hep{He$^+$ }\n\\def\\Hepp{He$^{++}$ }\n\\def\\mHH{H_2}\n\\def\\mH2p{H_2^+}\n\\def\\mHp{H^+}\n\\def\\mHm{H^-}\n\\def\\mHep{He^+}\n\\def\\mHepp{He^{++}}\n\n\\def\\gtsima{$\\; \\buildrel > \\over \\sim \\;$}\n\\def\\ltsima{$\\; \\buildrel < \\over \\sim \\;$}\n\\def\\prosima{$\\; \\buildrel \\propto \\over \\sim \\;$}\n\\def\\gsim{\\lower.7ex\\hbox{\\gtsima}}\n\\def\\lsim{\\lower.7ex\\hbox{\\ltsima}}\n\\def\\simgt{\\lower.7ex\\hbox{\\gtsima}}\n\\def\\simlt{\\lower.7ex\\hbox{\\ltsima}}\n\\def\\simpr{\\lower.7ex\\hbox{\\prosima}}\n\\def\\la{\\lsim}\n\\def\\ga{\\gsim}\n\n%% %%\n%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% %%%%\n\\makeatletter\n\\newenvironment{tablehere}\n {\\def\\@captype{table}}\n {}\n\\newenvironment{figurehere}\n {\\def\\@captype{figure}}\n {}\n\\makeatother\n\\begin{document}\n\\title{The Formation and Fragmentation of Primordial Molecular Clouds}\n\\author{Tom Abel$^{1}$, Greg L. Bryan$^{2,3}$ and Michael L. Norman$^{4,5}$\\\\\n{\\it $^1$Harvard Smithsonian Center for Astrophysics, MA, US--02138 Cambridge}\\\\\n{\\it $^2$Massachusetts Institute of Technology, MA, US--02139 Cambridge}\\\\\n{\\it $^3$Hubble Fellow}\\\\\n{\\it $^4$LCA, NCSA, University of Illinois, US--61801 Urbana/Champaign}\\\\\n{\\it $^5$Astronomy Department, University of Illinois, Urbana/Champaign} }\n\\begin{abstract} Many questions in physical cosmology regarding the thermal\n history of the intergalactic medium, chemical enrichment,\n reionization, etc. are thought to be intimately related to the\n nature and evolution of pregalactic structure. In particular the\n efficiency of primordial star formation and the primordial IMF are\n of special interest. We present results from high resolution\n three--dimensional adaptive mesh refinement simulations that follow\n the collapse of primordial molecular clouds and their subsequent\n fragmentation within a cosmologically representative volume.\n Comoving scales from 128 kpc down to 1 pc are followed accurately.\n Dark matter dynamics, hydrodynamics and all relevant chemical and\n radiative processes (cooling) are followed self-consistently for a\n cluster normalized CDM structure formation model. Primordial\n molecular clouds with $\\sim 10^5$ solar masses are assembled by\n mergers of multiple objects that have formed hydrogen molecules in\n the gas phase with a fractional abundance of $\\lsim 10^{-4}$. As\n the subclumps merge cooling lowers the temperature to $\\sim200$ K\n in a ``cold pocket'' at the center of the halo. Within this cold pocket, a\n quasi--hydrostatically contracting core with mass $\\sim 200\\Ms$ and\n number densities $\\gsim 10^5 \\cm^{-3}$ is found. We find that less\n than 1\\% of the primordial gas in such small scale structures cools\n and collapses to sufficiently high densities to be available for\n primordial star formation. \n%Our results constrain various scenarios\n% discussed in the literature. We conclude that very massive objects,\n% or massive black holes are unlikely to be formed within the very\n% first cosmological objects. Also, fragmentation of a large fraction\n% of baryons into brown dwarfs or Jupiter size fragments within the\n% smallest first structures, seems very unlikely.\n Furthermore, it is worthwhile to note that this study achieved the\n highest dynamic range covered by structured adaptive mesh techniques\n in cosmological hydrodynamics to date. \\vspace{0.3cm}\n\\end{abstract}\n\n\\thispagestyle{empty}\n\\section{Introduction}\n\nSaslaw and Zipoy (1967) realized the importance of gas phase \\HH\nmolecule formation in primordial gas for the formation of\nproto--galactic objects. Employing this mechanism in Jeans unstable\nclouds, Peebles and Dicke (1968) formulated their model for the\nformation of primordial globular clusters. Further pioneering studies\nin this subject were carried out by Takeda \\etal (1969), Matsuda \\etal\n(1969), and Hirasawa \\etal (1969) who followed in detail the gas\nkinetics in collapsing objects and studied the possible formation of\nvery massive objects (VMO's). In the 1980's the possible cosmological\nconsequences of population III star formation were assessed (Rees and\nKashlinsky 1983; Carr \\etal 1984; Couchman and Rees 1986). In\nparticular Couchman and Rees (1986) discussed first structure\nformation within the standard cold dark matter model. Their\nmain conclusions were that the first objects might reheat and reionize\nthe universe, raise the Jeans mass and thereby influence subsequent\nstructure formation.\n\nEarly studies focused on the chemical evolution and cooling of\nprimordial clouds by solving a chemical reaction network within highly\nidealized collapse models (cf. Hirasawa 1969; Hutchins 1976; Palla\n\\etal 1983; MacLow and Shull 1986; Puy \\etal 1996; Tegmark \\etal\n1997). Some hydrodynamic aspects of the problem were studied in\nspherical symmetry by Bodenheimer (1986) and Haiman, Thoul and Loeb\n(1996). Recently multi--dimensional studies of first structure\nformation have become computationally feasible (Abel 1995; Anninos \\&\nNorman 1996; Zhang \\etal1997; Gnedin\n\\& Ostriker 1997; Abel \\etal 1998a,1998b; Bromm \\etal~1999). These\ninvestigations have provided new insights into the inherently\nmultidimensional, nonlinear, nonequilibrium physics which determine\nthe collapse and fragmentation of gravitationally and thermally\nunstable primordial gas clouds.\n\nIn Abel, Anninos, Norman \\& Zhang 1998a (hereafter AANZ) we presented\nthe first self-consistent 3D cosmological hydrodynamical simulations\nof first structure formation in a standard cold dark matter--dominated\n(SCDM) universe. These simulations included a careful treatment of the\nformation and destruction of \\HH---the dominant coolant in low mass\nhalos ($M_{tot}=10^5-10^8 M_{\\odot}$) which collapse at high redshifts\n($z \\sim 30-50$). Among the principal findings of that study were:\n(1) appreciable cooling only occurs in the cores of the high density\nspherical knots located at the intersection of filaments; (2) good\nagreement was found with semi-analytic predictions (Abel 1995; Tegmark\n\\etal 1997) of the minimum halo mass able to cool and collapse to\nhigher densities; (3) only a small fraction ($< 10\\%$) of the bound\nbaryons are able to cool promptly, implying that primordial Pop III\nstar clusters may have very low mass. Due to the limited spatial\nresolution of the those simulations ($\\sim 1$ kpc {\\em comoving}), we\nwere unable to study the collapse to stellar densities and address the\nnature of the first objects formed.\n\nIn this paper we present new, higher- resolution results using the\npowerful numerical technique of adaptive mesh refinement (AMR, Bryan\n\\& Norman 1997; Norman \\& Bryan 1999) which has shed some light on how\nthe cooling gas fragments. With an effective dynamic range of\n$262,144$ the numerical simulations presented here are the highest\nresolution simulations in cosmological hydrodynamics to date. Although\nwe are not yet able to form individual protostars, we are able to\nresolve the collapsing protostellar cloud cores which must inevitably\nform them. We find the cores have typical masses $\\sim 200 M_{\\odot}$,\nsizes $\\sim 0.3$ pc, and number densities $n \\geq 10^5$\ncm$^{-3}$--similar to dense molecular cloud cores in the Milky Way\nwith one vital difference: the molecular hydrodgen fraction is $\\sim 5\n\\times 10^{-4}$, meaning the cores evolves very differently from\nGalactic cores.\n\nThe plan of this paper is as follows. The simulations are briefly\ndescribed in Sec. 2. Results are presented in Sec. 3. The properties\nand fate of the primordial protostellar cloud are discussed in\nSec. 4. Conclusions follow in Sec. 5. Results of a broader survey of\nsimulations will be reported in Abel, Bryan \\& Norman (1999).\n\n\\section{Simulations}\n\nThe three dimensional adaptive mesh refinement calculations presented\nhere use for the hydrodynamic portion an algorithm very similar to the\none described by Berger and Collela (1989). The code utilizes an\nadaptive hierarchy of grid patches at various levels of resolution.\nEach rectangular grid patch covers some region of space in its parent\ngrid needing higher resolution, and may itself become the parent grid\nto an even higher resolution child grid. Our general implementation of\nAMR places no restriction on the number of grids at a given level of\nrefinement, or the number of levels of refinement. However, we do\nrestrict the refinement factor -- the ratio of parent to child mesh\nspacing -- to be an integer (chosen to be 2 in this work). The dark\nmatter is followed with methods similar to the ones presented by\nCouchman (1991). Furthermore, the algorithm of Anninos \\etal (1997) is\nused to solve the time--dependent chemistry and cooling equations for\nprimordial gas given in Abel \\etal (1997). More detailed descriptions\nof the code are given in Bryan \\& Norman (1997, 1999), and Norman \\&\nBryan (1999).\n\nThe simulations are initialized at redshift 100 with density\nperturbations of a SCDM model with $\\Omega_B = 0.06$, $h=0.5$, and\n$\\sigma_8=0.7$. The abundances of the 9 chemical species (H, \\Hp, \\Hm,\nHe, \\Hep, \\Hepp, \\HH, \\HHp, e$^-$) and the temperature are initialized\nas discussed in Anninos and Norman (1996). After a collapsing\nhigh--$\\sigma$ peaks has been identified in a low resolution run, the\nsimulation is reinitialized with multiple refinement levels covering\nthe Langrangian volume of the collapsing structure. The mass\nresolution in the initial conditions within this region are $0.53\n(8.96) \\Ms$ in the gas (dark matter). The refinement criteria ensure\nthat: (1) the local Jeans length is resolved by at least 4 grid zones,\nand (2) that no cell contains more than 4 times the initial mass\nelement ($0.53\\Ms$). We limit the refinement to 12 levels within a\n$64^3$ top grid which translates to a maximum dynamic range of\n$64\\times 2^{12}=262,144$.\n\n\\section{Results}\n\nWe find that primordial molecular clouds are only formed at the\nintersection of filaments, in agreement with the results of AANZ.\nThe evolution of these primordial molecular clouds is marked by\nfrequent mergers yielding highly complex velocity and density fields\nwithin the ``virial'' radius. In the following three sections, we\nfirst describe the evolution of these objects and then their morphology\nand structure.\n%The chemo--thermal instability caused by\n%the gas--phase production of \\HH yields multiple cold pockets on\n%scales of roughly a tenth of the virial radius. These pockets are\n%approximately isothermal at temperatures at $\\sim 200\\K$ and a few\n%thousand times the mean density of the universe at that redshift.\n\n\n\\subsection{Formation of the First Objects}\n\nTo illustrate the physical mechanisms at work during the formation of\nthe first cosmological object in our simulation, we show the evolution\nof various quantities in Figure~\\ref{evolution}. The top panel of\nthis plot shows the virial mass of the largest object in the\nsimulation volume. We divide the evolution up into four intervals.\nIn the first, before a redshift of about 35, the Jeans mass in the\nbaryonic component is larger than the mass of any non-linear\nperturbation. Therefore, the only collapsed objects are dark-matter\ndominanted, and the baryonic field is quite smooth. (We remind the\nreader that a change in the adopted cosmological model would modify\nthe timing, but not the nature, of the collapse.)\n\n% FIGURE 1 GOES HERE !!\n\\begin{figure*}\\vspace{0.4cm}\n\\epsscale{2}\n\\plotone{evolution.eps}\\vspace{-0.4cm}\n\\caption{ The top panel shows the evolution of the virial\nmass of the most massive clump as a function of redshift. The remaining\npanels show the density (both dark and baryonic), the temperature, and\nthe molecular hydrogen mass fraction at the central point of that clump. The\ncentral point is defined as the point with the highest baryon density.\nClearly the finite gas pressure prevents baryons from clumping as\nmuch as the dark matter at redshifts $\\gsim 23$. The vertical line at $z=19.1$\nindicates where our numerical model breaks down.} \\vspace{.2cm}\n\\label{evolution}\n\\end{figure*}\n\n\nIn the second epoch, $23 < z < 35$, as the non-linear mass increases, the\nfirst baryonic objects collapse. However, these cannot efficiently\ncool and the primordial entropy of the gas prevents dense cores from\nforming. This is shown in the second frame of figure~\\ref{evolution}\nby a large gap between the central baryonic and dark matter densities\n(note that while the dark matter density is limited by resolution, the\nbaryonic is not, so the true difference is even larger). As mergers\ncontinue and the mass of the largest clump increases, its temperature\nalso grows, as shown in the third panel of this figure. The \\HH\nfraction also increases (bottom panel).\n\nBy $z \\sim 23$, enough \\HH has formed (a few $\\times 10^{-4}$), and the\ntemperature has grown sufficiently high that cooling begins to be\nimportant. During this third phase, the central temperature decreases\nand the gas density increases. However, the collapse is somewhat\nprotracted because around this point in the evolution, the central\ndensity reaches $n \\sim 10^4$ cm$^{-2}$, and the excited states of \\HH\nare in LTE. This results in a cooling time which is nearly\nindependent of density rather than in the low--density limit where\n$t_{cool} \\sim \\rho^{-1}$ (e.g. Lepp \\& Shull 1983).\n\nFinally, at $z \\sim 19$, a very small dense core forms and reaches the\nhighest resolution that we allowed the code to produce. It is\nimportant to note that at this point, the maximum gas density in the\nsimulations exceeds $10^8\\cm^{-3}$, and at these densities, 3--body\nformation of molecular hydrogen will become dominant (see Palla\n\\etal~1983). Also, the assumption of optical thin cooling begins to\nbreak down and radiative transfer effects become important.\nTherefore, only simulation results at and above this redshift will be\ndiscussed. It is worthwhile to note that the simulations presented\nhere are physics rather than resolution limited.\n\n\\subsection{Morphology}\n\nThe increase in dynamic range by $\\sim 1000$ in the simulations\npresented here as compared to AANZ allow us to investigate the\ndetails of the fragmentation process in detail. Visualizations of the\ngas density and temperature on two different scales at $z=19.1$ are\nshown in the color plate~\\ref{color_p}. In the upper left panel the\nvelocity field is shown superimposed on the density. The\n$5\\tento{5}\\Ms$ structure forms at the intersection of two filaments\nwith overdensities of $\\sim 10$. Most of the mass accretion occurs\nalong these filaments. The complexity of the velocity field is\nevident; the accretion shock is highly aspherical and of varying\nstrength. Within the virial radius ($r = 106$ pc), there are a\nnumber of other cooling regions.\n%Multiple shocks are evident within the accretion shock. \nThe right-hand panels zooms in on the collapsing fragment.\n%At a 10 times smaller scale (right\n%panels) far within the virialized structure one fragment becomes\n%visible\n(note that the smallest resolution element ($0.02\\pc$) in the\nsimulations is still 1600 times smaller than the slice shown in the\nright panels). The small fragment in the center of this image has a\ntypical overdensity of $\\gsim 10^{6}$ and a mass of $\\sim 200\\Ms$.\n%with a mass of $\\sim 200\\Ms$ is formed due the Bonnor--Ebert\n%instability of the surrounding close to isothermal cool ``pocket'' of\n%gas at $T\\sim 200\\K$.\n\n\\subsection{Profiles}\n\nDespite the complex structure of the primordial molecular clouds much\nof their structure can be understood from spherical profiles of the\nphysical quantities, particularly for the dense central core which is\nnearly spherical. Figure~\\ref{profile} shows mass-weighted, spherical\naverages of various quantities around the densest cell found in the\nsimulation at redshift 19.1. Panel a) plots the baryon number density,\nenclosed baryon mass, and local Bonnor-Ebert mass\\footnote{{\\sl\nBonnor-Ebert mass} is the analog of the Jeans Mass but assuming an\nisothermal ($\\rho\\propto r^{-2}$) instead of a uniform density\ndistribution.} $\\approx 27\\Ms T_K^{1.5}/\\sqrt{n}$ versus radius.\nPanel b) plots the abundances of \\HH and free electrons. Panel c)\ncompares three timescales defined locally: the \\HH cooling time\n$t_{H_2}$, the freefall time $t_{ff}=[3\\pi/(32G\\rho)] ^{1/2}$, and the\nsound crossing time $t_{cross}=r/c_s=7.6\\tento{6} r_{pc}/\\sqrt{T_K}$\nyrs. In panel d) we identify two distinct regions---labeled I and\nII---as defined by the temperture profile. Region I ranges from\noutside the virial radius to $r_{T_{min}}\\sim 5\\pc$, the radius at\nwhich the infalling material has cooled down to $T_{min} \\sim\n200\\K$--near the minimum temperature allowed by \\HH cooling. Within\nregion I, the temperature profile reflects, in order of decreasing\nradius, cosmic infall, shock virialization, adiabatic heating in a\nsettling zone, and an \\HH cooling flow. In region II, the temperature\nslowly rises from $T_{min}$ to $\\sim 400 K$ due to adiabatic heating.\n\nFor most of region I the \\HH cooling time $t_{H_2}$ is comparable to\nthe free--fall time, as is illustrated in panel c) of\nFigure~\\ref{profile}. The \\HH number fraction rises from $7\\tento{-6}$\nto $2\\tento{-4}$ as the free electron fraction drops from\n$2\\tento{-4}$ to $2\\tento{-5}$.\n%At $r_{cool}$ the\n%free--fall time becomes smaller than the cooling time. \nAt $r_{T_{min}}$, the sound crossing time becomes substantially\nshorter than the cooling time. This suggests that region II is\ncontracting quasi--hydrostatically on the cooling time scale, which\napproaches its constant high--density value at small radii.\n%\\footnote{This effect is due to the transition from non-LTE to\n% LTE populations of the \\HH rotational/vibrational states (e.g. Leep\n% and Shull~1983).}. \nThis constant cooling time of $\\sim 10^5\\yrs$ sets the time scale of\nthe evolution of the fragment until it can turn fully molecular via\nthree body associations.\n% z = 19.075, time dump 0058 of rerun\nInside $r \\sim 0.3$ pc, the enclosed baryonic mass of $\\sim 200\nM_{\\odot}$ exceeds the local Bonnor-Ebert mass, implying this material\nis gravitationally unstable. However, due to the inefficient cooling,\nits collapse is subsonic (panel e). The radius where $M > M_{BE}$\ndefines our protostellar cloud core.\n\n\\begin{figure*}\n\\vspace{0.3cm}\n\\epsscale{1.5}\n\\plotone{pro_all.eps}\\vspace{+0.2cm}\\label{profile}\n\\caption{ Spherically averaged mass weighted profiles around the\n baryon density peak shortly before a well defined fragment forms\n (z=19.1). Panel a) shows the baryonic number density, enclosed gas\n mass in solar mass, and the local Bonnor--Ebert mass ($\\approx\n 27\\Ms T_K^{1.5}/\\sqrt{n}$). Panel b) plots the molecular hydrogen\n number fraction $f_{H_2}$ and the free electron number fraction $x$.\n The \\HH cooling time $t_{H_2}$, the time it takes a sound wave to\n travel to the center, $t_{cross}$, and the free--fall time\n $t_{ff}=[3\\pi/(32G\\rho)]^{1/2}$ are given in panel c). Panel d)\n gives the temperature in Kelvin as a function of radius. The bottom\n panel gives the local sound speed, $c_s$ (solid line with circles),\n the rms radial velocities of the dark matter (dashed line) and the\n gas (dashed line with asterisks) as well as the rms gas velocity\n (solid line with square symbols).\n The vertical dotted line indicates the radius at which the gas has\n reached its minimum temperature allowed by \\HH cooling ($\\sim 5pc$).\n The virial radius of the $5.6\\tento{6}\\Ms$ halo is $106\\pc$. The\n cell size on the finest grid corresponds to $0.024\\pc$. Note that\n the simulation box size corresponds to 6.4 proper kpc.}\n\\end{figure*}\n\n\n%From the time scales one would conclude that below $r_{cool}$ the gas\n%should evolve quasi--hydrostatically on the cooling time scale. This\n%is, however, not strictly true. It turns out that centrifugal forces\n%play an important role in the collapse. As can be directly seen from\n%the radial gas velocity (dashed line with asterisks) in panel e) of\n%Figure~\\ref{profile}.\n\n\\section{Discussion}\n\nMany interesting features of the collapsing and fragmenting\n``primordial molecular cloud'' are identified. Most notable is the\nformation of an initially quasi--hydrostatically contracting core of\n$\\sim 200\\Ms$ which becomes gravitationally unstable. We argue that\nthis is a characteristic mass scale for core formation mediated by \\HH\ncooling. Substituting into the formula for the Bonnor-Ebert mass\n$T_{min}$ and $n_{LTE}$ we get $240 M_{\\odot}$.\n \nWhat will be the fate of the collapsing core? Within the core the\nnumber densities increase from $10^{5}$ to $10^8\\cm^{-3}$. For\ndensities $\\gsim 10^8\\cm^{-3}$, however, three--body formation of \\HH\nwill become the dominant formation mechanism, transforming all\nhydrogen into its molecular form (Palla \\etal1983). Our chemical\nreaction network does not include this reaction and the solution\ncannot be correct at $r\\lsim 0.1\\pc$. The most interesting effect of\nthe three--body reaction is that it will increase the cooling rate by\na factor $\\sim 10^3$, leading to a further dramatic density\nenhancement within the core. This will decrease the dynamical\ntimescales to $\\ll 100\\yrs$, effectively decoupling the evolution of\nthe fragment from the evolution of its host primordial molecular\ncloud. Therefore, it is a firm conclusion that only the gas within\nthese cores can participate in population III star formation.\n\nOmukai \\& Nishi (1998) have simulated the evolution of a collapsing,\nspherically symmetric primordial cloud to stellar density including\nall relevant physical processes. Coincidentally, their initial\nconditions are very close to our final state. Based on their results,\nwe can say that if the cloud does not break up, a massive star will be\nformed. Adding a small amount of angular momentum to the core does\nnot change this conclusion (Bate 1998). A third possibility is that\nthe cloud breaks up into low mass stars via thermal instability in the\nquasi-hydrostatic phase. Silk (1983) has argued that, due to the\nenhanced cooling from the 3--body produced \\HH, fragmentation of this\ncore might continue until individual fragments are opacity limited\n(i.e. they become opaque to their cooling radiation). Exploring which\nof these scenarios is correct will have to await yet higher resolution\nsimulations including the effects of radiative transfer. It will also\nbe interesting to examine the possible effects of molecular HD which,\nalthough much less abundant, is a much more efficient coolant at low\ntemperatures.\n\nHow many cores are formed in our halo? Because our timestep contracts\nrapidly once the first core forms, we are not yet able to answer this\nquestion definitively. An earlier, less well resolved simulation\nyielded $5-6$ cores by $z=16.5$, suggesting that multiple cores do\nform. We speculate that the total number of cores to eventually form\nwill be proportional to the total amount of cooled gas. However, the\nfirst star in a given halo will most likely always be formed close to\nits center where the dynamical timescale is shortest. The cooling\ntimescale at $r_{T_{min}}$ in Figure 2. of $\\gsim 10^6 \\yrs$ should\nroughly correspond to the typical formation time of fragments. During\nthis time the product of the first collapsed fragment might already be\nan important source of feedback. Hence, even for the question of the\nefficiency of fragmentation it seems that feedback physics have to be\nincluded. \n\nLet us assume the first $\\sim 200\\Ms$ cores fragment to form stars\nwith 100\\% efficiency. If the ratio of produced UV photons per solar\nmass is the same as in present day star clusters than about\n$6\\tento{63}$ UV photons would be liberated during the average life\ntime of massive star ($\\sim 5\\tento{7}\\yrs$). This is about hundred\ntimes more than the $\\sim 4\\tento{61}$ hydrogen atoms within the\nvirial radius. However, the average recombination time\n$(nk_{rec})^{-1}\\sim 5\\tento{5}\\yrs$ within the virial radius is a\nfactor 100 less than the average lifetime of a massive star. Hence,\nvery small or zero UV escape fractions for these objects are\nplausible. However, the first supernovae and winds from massive stars\nwill substantially change the subsequent hydrodynamic and chemical\nevolution as well as the star formation history of these objects. A\nmore detailed understanding of the role of such local feedback will\nhave to await yet more detailed simulations that include the poorly\nunderstood physics of stellar feedback mechanisms.\n%Although, one might ask whether all the\n%non--linear physics of star formation and feedback within these\n%objects could ever be modeled in sufficient detail to make reliable\n%predictions on their star formation history, metal production, etc.\n\nSince the collapsing core evolves on much faster timescales than the\nrest of the halo it seems plausible that the first star (or star\ncluster) will have a mass of less or the order of the core mass. It\nseems also quite clear that the radiative feedback from this star\n(these stars) will eventually halt further accretion. As a consequence\nthis might suggest that the formation of very massive objects or\nsupermassive black holes is unlikely. This later speculation will be\ntested by yet higher resolution simulations we are currently working\non.\n\nRecently Bromm, Coppi, and Larson (1999) have studied the\nfragmentation of the first objects in the universe. The results of\ntheir simulations using a smooth particle hydrodynamics technique with\nisolated boundary conditions disagree with the results presented here.\nTheir objects collapse to a disk which then fragments quickly to form\nmany fragments throughout the rotationally supported disk. The\nefficiently fragmenting disk in those simulations originates from the\nassumed idealized intial conditions. These authors simulated top-hat\nspheres that intially rotate as solid bodies on which smaller density\nfluctuations were imposed. Naturally they find a disk. Also it is\nclear that for a top-hat if the disk breaks up it will do so\neverywhere almost simultaneously. Our results with realistic initial\nconditions do not lead to a disk and form the first fragment close to\nthe center of the halo.\n\n\n\n\n\\section{Conclusions}\n\nWe have reported first results from an ongoing project that studies\nthe physics of fragmentation and primordial star formation in a\ncosmological context. The results clearly illustrate the advantages\nand power of structured adaptive mesh refinement cosmological\nhydrodynamic methods to cover a wide range of mass, length and\ntimescales. All findings of AANZ are confirmed in this study. Among\nother things, these are that 1) a significant number fraction of\nhydrogen molecules is only formed in virialized halos at the\nintersection of filaments, and 2) only a few percent of the halo gas\nhas cooled to $T\\ll T_{vir}$.\n\nThe improvement of a factor $\\sim 1000$ in resolution over AANZ has\ngiven new insights into the details of the fragmentation process and\nconstraints on the possible nature of the first structures:\n1) Only $\\lsim 1\\%$ of the baryons within a virialized object can\n participate in population III star formation.\n2) The formation of super massive black holes or very massive\n objects in small halos seem very unlikely.\n3) Fragmentation via Bonnor--Ebert instability yields a $\\sim\n200\\Ms$ core within one virialized object.\n4) If the gas were able to fragment further through 3--body \\HH\n association and/or opacity limited fragmentation, only a small\n fraction of all baryons in the universe will be converted into small\n mass objects. \n5) The escape fraction of UV photons above the Lyman limit should\ninitially be small due to the high column densities of HI ($N_{HI}\\sim\n10^{23}\\cm^{-2}$) of the parent primordial molecular cloud.\n6) The first star in the universe is most likely born close to the\ncenter of its parent halo of $\\gsim 10^5\\Ms$.\n\n\\acknowledgments \n\nThis work is supported in part by NSF grant AST-9803137 under the\nauspices of the Grand Challenge Cosmology Consortium (GC$^3$). NASA\nalso supported this work through Hubble Fellowship grant\nHF-0110401-98A from the Space Telescope Science Institute, which is\noperated by the Association of Universities for Research in Astronomy,\nInc under NASA contract NAS5-26555. Tom Abel acknowledges support\nfrom NASA grant NAG5-3923 and useful discussions with Karsten\nJedamzik, Martin Rees, Zoltan Haiman, and Simon White.\n\n\n\\begin{references}\n\\small\n\\reference{Abel95} Abel, T. 1995, Thesis, University of Regensburg, Germany\n\\reference{o} Abel, T., Anninos, P., Zhang, Y., Norman, M.L. 1997,\n NewA, 2, 181\n\\reference{o} Abel, T., Anninos, P., Norman, M.L., Zhang, Y. 1998a (AANZ),\n ApJ, 508, 518.\n\\reference{o} Abel, T., Bryan, G.L., Norman, M.L. 2000, in preparation.\n\\reference{o} Abel, T., Stebbins, A., Anninos, P., Norman,\n M.L. 1998b, ApJ, 508, 530.\n\\reference{o} Anninos, P., Norman, M.L. 1996, ApJ, 460, 556\n\\reference{o} Anninos, P., Zhang, Y., Abel, T., Norman,\n M.L. 1997, NewA, 2, 209\n\\reference{o} Bate, M. 1998. ApJL, 508, 95\n\\reference{o} Berger, M.J., Collela, P. 1989, J. Comp. Phys., 82, 64\n\\reference{o} Bertoldi, F., Draine, B. T. 1996, ApJ, 458, 222\n\\reference{o} Bodenheimer, P.H. 1986, {\\sl Final Technical\n Report, California Univ., Santa Cruz.}\n\\reference{o} Bromm, V., Coppi, P., Larson, R.B. 1999, ApJL, 527, L5\n\\reference{o} Bryan, G.L., Norman, M.L. 1997, in {\\it\n Computational Astrophysics}, eds. D.A. Clarke and M. Fall, ASP\n Conference \\#123\n%\\reference{o} Bryan, G.L., Norman, M.L. 1999, {\\it in preparation}\n\\reference{o} Bryan, G.L., Norman, M.L. 1999, in {\\it Workshop on\n Structured Adaptive Mesh Refinement Grid Methods}, IMA Volumes\n in Mathematics No. 117, ed. N. Chrisochoides, p. 165\n\\reference{o} Carr, B.J., Bond, J.R., Arnett,\n W.D. 1984, ApJ, 277, 445\n\\reference{o} Couchman, H. 1991, ApJL, 368, L23\n\\reference{o} Gnedin, N.Y., Ostriker, J.P. 1997, ApJ, 486, 581\n\\reference{o} Haiman, Z., Thoul, A.A., Loeb, A. 1996, ApJ, 464, 523\n\\reference{o} Hirasawa, T. 1969, Progr. Theoret. Phys. , 42, 523\n\\reference{o} Hoyle, F. 1953, ApJ, 118, 513\n\\reference{o} Hutchins, J.B. 1976, ApJ, 205, 103\n\\reference{o} Kashlinsky, A., Rees, M.J. 1983, MNRAS, 205, 955\n\\reference{o} Lepp, S., \\& Shull, J.M. 1983, \\apj, 270, 578\n\\reference{o} Mac Low, M.-M. \\& Shull, J.M. 1986, ApJ, 302, 585\n\\reference{o} Matsuda, T., Sato, H., Takeda, H.1969,\n Progr. Theoret. Phys., 41, 840\n\\reference{o} Norman, M.L., Bryan, G.L. 1998, in {\\it Numerical\n Astrophysics 1998}, eds. S. Miyama \\& K. Tomisaka\n\\reference{o} Omukai, K. \\& Nishi, R. 1998. ApJ, 508, 1410.\n\\reference{o} Palla, F., Salpeter, E.E., Stahler, S.W. 1983, ApJ, 271, 632\n\\reference{o} Padmanabhan, T. 1993, {\\it Structure formation in the\n universe}, Cambridge University Press\n\\reference{o} Peebles, P.J.E., Dicke, R.H. 1968, ApJ, 154, 891\n\\reference{o} Puy, D., Signore, M. 1996, A\\&A, 305, 371\n\\reference{o} Saslaw, W.C., \\& Zipoy, D. 1967, Nature, 216, 976\n\\reference{o} Silk, J. 1983, MNRAS, 205, 705\n\\reference{o} Takeda, H., Sato, H., Matsuda, T. 1969,\n Progr. Theoret. Phys., 41, 840\n\\reference{o} Tegmark, M., Silk, J., Rees, M.J., Blanchard, A., Abel, T.,\n Palla, F. 1997, ApJ, 474, 1\n\\reference{o} Zhang, Y., Norman, M.L., Anninos, P., \\& Abel,\n T. 1997, in S.S. Holt and L.G. Mundy, eds., {\\it Star\n formation, near and far}, AIP Press, New York, 329\n\\end{references}\n\n\n\\begin{figure*}\n%\\epsscale{.9}\n\\plotone{color_plate.ps}\n\\caption{Gas density and temperature in the first cosmological objects\n expected to form in hierarchical structure formation scenarios. The\n upper panels show the log of the baryonic overdensity in a slice\n through the point of highest gas density at a scale of $320\\pc$\n (left) and $32\\pc$ (right). The lower panels give the corresponding\n plots of the log of the gas temperature. Additionally the velocity\n field is also visualized in the upper left panel. Note that the\n computational volume simulated is 20$^3$ times larger than the left\npanels. }\\label{color_p} \n\\end{figure*}\n\n\\end{document}"
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astro-ph0002136
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Cosmic Star Formation History Required from Infrared Galaxy Number Count : Future Prospect for {\sl Infrared Imaging Surveyor} ({\sl IRIS})
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[
{
"author": "T.\\"
},
{
"author": "T. Ishii\\inst{1,2}"
},
{
"author": "T. Takeuchi\\inst{1}"
},
{
"author": "H. Hirashita\\inst{1}"
},
{
"author": "K. Yoshikawa\\inst{1}"
}
] |
We constructed a model of infrared and sub-mm (hereafter IR) galaxy number count and estimated history of the IR luminosity density. We treat the evolutionary change of galaxy luminosities as a stepwise nonparametric form, in order to explore the most suitable evolutionary history which reproduces the present observational results. We found the evolutionary patterns which satisfy both constraints required from Cosmic Infrared Background (CIRB) and IR galaxy number counts. One order of magnitude increase of luminosity at redshift $z=0.75 - 1.0$ was found in IR $60\; \mu$m luminosity density evolution. We also found that a large number of galaxies ( $\sim 10^7$ in the whole sky) will be detected in all-sky survey at far-infrared by {\sl Infrared Imaging Surveyor} ({\sl IRIS}); Japanese infrared satellite project Astro-F. \keywords{ galaxies: evolution -- galaxies: formation -- galaxies: starburst -- infrared radiation}
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{
"name": "ishiit.tex",
"string": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\n% sample.tex -- ESLAB Conference Proceedings tutorial paper\n% ----------------------------------------------------------\n% Lines starting with \"%\" are comments; they will be ignored by LaTeX.\n%\n% NB! Use the LaTeX2e style packages!\n% You need the file EslabStyle.cls. Please, download by ftp at\n% ftp://astro.estec.esa.nl/pub/ESLAB/proceedings\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\documentclass[a4paper]{EslabStyle}\n\\usepackage{graphics}\n\n\\begin{document}\n\n\n\\title{Cosmic Star Formation History Required from \nInfrared Galaxy Number Count : \nFuture Prospect for {\\sl Infrared Imaging Surveyor} ({\\sl IRIS})\n}\n\n\\author{T.\\,T. Ishii\\inst{1,2} \\and T.\\,T. Takeuchi\\inst{1} \\and \nH. Hirashita\\inst{1} \\and K. Yoshikawa\\inst{1}}\n\n\\institute{Department of Astronomy, Faculty of Science, Kyoto University, \nJAPAN, 606-8502\n\\and \nKwasan and Hida Observatories, Kyoto University, JAPAN, 607-8471\n}\n\n\\maketitle \n\n\n\\begin{abstract}\nWe constructed a model of infrared and sub-mm (hereafter IR) \ngalaxy number count and estimated \nhistory of the IR luminosity density. \nWe treat the evolutionary change of galaxy luminosities \nas a stepwise nonparametric form, in order to explore the most suitable\nevolutionary history which reproduces the present observational results.\nWe found the evolutionary patterns which satisfy \nboth constraints required from Cosmic Infrared Background (CIRB) \nand IR galaxy number counts.\nOne order of magnitude increase of luminosity \nat redshift $z=0.75 - 1.0$ was found in IR $60\\; \\mu$m \nluminosity density evolution.\nWe also found that a large number of galaxies \n( $\\sim 10^7$ in the whole sky) will be \ndetected in all-sky survey at far-infrared by \n{\\sl Infrared Imaging Surveyor} ({\\sl IRIS}); \nJapanese infrared satellite project Astro-F.\n\\keywords{\ngalaxies: evolution -- galaxies: formation -- galaxies: starburst \n-- infrared radiation}\n\\end{abstract}\n\n\\section{Introduction}\n\nRecent infrared and sub-mm surveys revealed a very steep\nslope of galaxy number count compared with that expected\nfrom no evolution model, and provided a new \nimpetus to the related field.\nSuch excess of galaxy number count is generally understood \nas a consequence of strong galaxy evolution, i.e. rapid \nchange of the star formation rate in galaxies.\nNow \nJapanese infrared satellite project Astro-F \n({\\sl Infrared Imaging Surveyor}: {\\sl IRIS}) is in \nprogress, and we calculated the expected number count by\na simple empirical method (Takeuchi et al. 1999; Hirashita \net al. 1999).\nThe applied model was based on the {\\sl IRAS} surveys, \nand we need more realistic one to study the detailed \nobservational plans and follow-up strategies.\nIn order to construct the advanced model, we first compiled the \ninfrared/sub-mm SEDs of galaxies \nobtained by {\\sl ISO}, SCUBA, and other facilities, and \nderived average SEDs for various classes of galaxies.\nThen, \nusing the local luminosity function, we studied the \nrequired galaxy evolutionary history statistically.\n\n\n\\begin{figure}[ht]\n\\resizebox{\\hsize}{!}{\\includegraphics{ishiit1.ps}}\n\\caption{Assumed galaxy spectral energy distribution (SED) \nin the near infrared to radio wavelengths. \\label{fig1}}\n\\end{figure}\n\n\n\\begin{figure}[ht]\n\\resizebox{\\hsize}{!}{\\includegraphics{ishiit2.ps}}\n\\caption{The double power-law form (Soifer et al. 1987) for the local \nluminosity function. \nWe assumed pure luminosity evolution in this study. \\label{fig2}}\n\\end{figure}\n\n\\begin{figure}[ht]\n\\resizebox{\\hsize}{!}{\\includegraphics{ishiit3.ps}}\n\\caption{Stepwise nonparametric form of \nthe evolutionary change of galaxy luminosities.\n \\label{fig3}}\n\\end{figure}\n\n\\begin{figure}[ht]\n\\resizebox{\\hsize}{!}{\\includegraphics{ishiit4.ps}}\n\\caption{The expected cosmic infrared background (CIRB)\nspectra with Evolution $1-3$ and No evolution.\nThe observational constraints on CIRB obtained by \nCOBE measurement (Fixsen et al. 1998, \nHauser et al. 1998 and references therein) \nare also plotted. \\label{fig4}}\n\\end{figure}\n\n\\begin{figure}[ht]\n\\resizebox{\\hsize}{!}{\\includegraphics{ishiit5.ps}}\n\\caption{{\\it The FIR $60\\; \\mu$m luminosity density evolution.} \\label{fig5}}\n\\end{figure}\n\n\n\\begin{figure}[ht]\n\\resizebox{\\hsize}{!}{\\includegraphics{ishiit6.ps}}\n\\caption{{\\it The multiband galaxy at the infrared\nwavelengths.} \\label{fig6}}\n\\end{figure}\n\n\n\n\\begin{figure}[ht]\n\\resizebox{\\hsize}{!}{\\includegraphics{ishiit7.ps}}\n\\caption{The multiband galaxy at the sub-mm -- radio\nwavelengths. \\label{fig7}}\n\\end{figure}\n\n\\begin{figure}[ht]\n\\resizebox{\\hsize}{!}{\\includegraphics{ishiit8.ps}}\n\\caption{The galaxy number count predictions at assumed \nIRIS two bandpasses (N60 and N170).\nThe dot-dashed lines denote the IRIS \nFar-infrared Scanner (FIS) flux detection \nlimit at each waveband.\n \\label{fig8}}\n\\end{figure}\n\n\\section{Model Description}\n\n\nWe construct the SEDs of galaxies based on the {\\sl IRAS}~color--luminosity \nrelation (Smith et al. 1987; Soifer \\& Neugebauer 1991).\nFor the infrared -- sub-mm component, we consider PAH (polycyclic aromatic \nhydrocarbon), graphite and silicate dust spectra (Dwek et al. 1996).\nDetailed PAH band emission parameters are taken from Allamandola et al. \n(1989).\nFor the longer wavelength regime, power-law continuum produced by \nsynchrotron radiation ($\\propto \\nu^{-\\alpha}$) dominates.\nWe set $\\alpha = 0.7$ according to Condon (1992).\nThe SEDs are presented in Fig. 1.\n\n\n\nWe applied the double power-law form (Soifer et al. 1987) for the local \nluminosity function, and assumed pure luminosity evolution in this study.\nThis is depicted in Fig. 2.\nThe faint-end slope does not affect the result, because the number \ncount is an integrated value along with redshift and volume, and its\ncontribution is small.\n\n\\section{Results and Discussions}\n\n\\subsection{Evolutionary history}\n\n\nWe treat the evolutionary change of galaxy luminosities \nas a stepwise nonparametric form, in order to explore the most suitable\nevolutionary history which reproduces the present observational results.\nFurthermore the constraint from Cosmic Infrared Background (CIRB) \nshould be considered as another observational constraint to the \nmodels of evolutionary history.\n\n\n\n\\subsubsection{CIRB}\n\nFirst, we searched the evolutionary pattern which satisfy \nthe constraint required from CIRB and \nwe found three patterns (Evolution $1 - 3$) shown in Fig. 3.\nThese three evolutionary patterns satisfy the constraint \nfrom CIRB (Fig. 4).\nIn order to satisfy the high background intensity \nat $\\sim 150\\; \\mu$m, \nthe high evolutionary factor at $z \\sim 0.8$ is a mandatory.\nWe note that too large \nevolutionary factor at high $z$ would produce the excess \naround $1000\\; \\mu$m.\n\n\nWe obtain IR $60\\; \\mu$m luminosity density\nalong with redshift (Fig. 5) from Fig. 3.\nFigure 5 show the rapid evolution in $\\rho_{\\rm L} (60\\; \\mu{\\rm m})$.\nThe increase is well described by $(1 + z)^5$~!\nWe need such a sudden rise of $\\rho_{\\rm L} (60\\; \\mu{\\rm m})$ \nto reproduce the very high CIRB intensity at \n$\\sim 150\\; \\mu$m mentioned before. \nThe peak of the IR luminosity density is \nlocated at $z \\sim 1$.\n\n\n\n\\subsubsection{number count}\n\n\nRecently, new observational results of the galaxy number counts at the \nmid-infrared and far-infrared (mainly by {\\sl ISO}), and submillimeter \n(SCUBA and others).\nWe are able to compile these data as well as previously obtained \n{\\sl IRAS} data and radio data.\nIt is obviously important to calculate multiband number count predictions \nand compare the multiband observations, because the response of the results \nto the galaxy evolutionary form varies with different wavelengths.\nIn principle, the galaxy number count is an integrated value along with \nredshift $z$, and the information of the redshift is not available.\nBut the redshift degeneracy can be solved to some extent, \nby treating the multiband\nobservational results at the same time.\n\nWe check whether the three evolutionary patterns found \nin the previous section also satisfy the constraints from \nobservations of number counts.\nWe compare our number counts with observations in Fig. 6\n(infrared), and Fig. 7 (sub-mm -- radio).\nEvery pattern satisfys the constraints.\nWhen we especially focus on the sub-mm number counts, \nthe evolution 3 is the most desirable.\n\n\n\n\\subsection{Infrared Imaging Surveyor ({\\sl IRIS})}\n\nInfrared Imaging Surveyor ({\\sl IRIS}) is a satellite \nwhich will be launched in 2003, by the M-V rocket of the \n{\\sl ISAS} (the Institute of Space and Astronautical Science \nin Japan).\nOne of the main purposes of the {\\sl IRIS} mission is \nan all-sky survey at far-infrared (FIR) with a flux limit \nmuch deeper than that of {\\sl IRAS}.\nDetailed information of {\\sl IRIS} is available \nat http://koala.astro.isas.ac.jp/Astro-F/index-e.html.\n\nIn order to examine the performance of the survey,\nwe estimated the FIR galaxy counts in two narrow bands \n(i.e. N60 and N170) based on models described \nin the previous section.\nWe found that a large number of galaxies \n( $\\sim 10^7$ in the whole sky) will be \ndetected in this survey (Fig. 8).\n\n\n\n\n\n\\begin{acknowledgements}\n\nWe wish to thank Dr. Hiroshi Shibai, Dr. Izumi Murakami and \nDr. Hideo Matsuhara for helpful discussions.\nDr. Kimiaki Kawara also deserves our thanks for providing us their \nnumber count in the Lockman Hole for reference.\nTTI is grateful to Dr. Hiroki Kurokawa for continuous encouragement.\nTTT, HH, and KY acknowledge the Research Fellowships\nof the Japan Society for the Promotion of Science for Young\nScientists.\nWe are grateful to all the participants who gave us \nuseful suggestions and comments at the Symposium.\n\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\n\\item\nAllamandola L. J., et al. 1989, ApJS, 71, 733\n\n\\item\nAltieri, B., et al. 1999, A\\&A, 343, L65\n\n\\item\nAussel, H., et al. 1999, A\\&A, 342, 313\n\n\\item\nBarger, A. J., et al. 1998, Nature, 394, 248\n\n\\item\nBarger, A. J., et al. 1999, astro-ph/9904126\n\n\\item\nBlain, A. W., et al. 1999, ApJ, 512, L87\n\n\\item\nClements, D. L., et al. 1999, A\\&A, 346, 383\n\n\\item\nCondon J. J., 1992, ARA\\&A, 30, 575\n\n\\item\nDole, H., et al. 1999, astro-ph/9902122\n\n\\item\nDwek, E., et al. 1996, ApJ, 457, 244\n\n\\item\nEales, S., et al. 1999, ApJ, 515, 518\n\n\\item \nFixsen, D., J., et al. 1998 ApJ, 508, 123\n\n\\item\nFlores, H., et al. 1999, A\\&A, 343, 389\n\n\\item\nFlores, H., et al. 1999, ApJ, 517, 148\n\n\\item\nFomalont, E. B., et al. 1991, AJ, 102, 125\n\n\\item\nHauser, M. G., et al. 1998, ApJ, 508, 25\n\n\\item\nHughes, D., et al. 1998, Nature, 394, 241\n\n\\item\nHirashita H., et al. 1999, PASJ, 51, 81\n\n\\item\nHolland, W. S., et al. 1999, MNRAS, 303, 659\n\n\\item\nKawara, K., et al. 1999, in prep.\n\n\\item\nPuget, J.-L., et al. 1999, astro-ph/9812039\n\n\\item\nRowan-Robinson, M., et al. 1991, MNRAS, 253, 485\n\n\\item\nRush, B., et al. 1993, ApJS, 89, 1\n\n\\item\nSmail, I., et al. 1997, ApJ, 490, L5\n\n\\item\nSmith B. J., et al. 1987, ApJ, 318, 161\n\n\\item\nSoifer B. T., et al. 1987, ApJ, 320, 238\n\n\\item\nSoifer B. T., \\& Neugebauer, G. 1991, AJ, 101, 354\n\n\\item\nStickel, M., et al. 1998, A\\&A, 336, 116\n\n\\item\nTakeuchi T. T., et al. 1999, PASP, 111, 288\n\n\\item\nWilner, D. J., \\& Wright, M. C. H. 1997, ApJ, 488, L67\n\n\\end{thebibliography}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002136.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\item\nAllamandola L. J., et al. 1989, ApJS, 71, 733\n\n\\item\nAltieri, B., et al. 1999, A\\&A, 343, L65\n\n\\item\nAussel, H., et al. 1999, A\\&A, 342, 313\n\n\\item\nBarger, A. J., et al. 1998, Nature, 394, 248\n\n\\item\nBarger, A. J., et al. 1999, astro-ph/9904126\n\n\\item\nBlain, A. W., et al. 1999, ApJ, 512, L87\n\n\\item\nClements, D. L., et al. 1999, A\\&A, 346, 383\n\n\\item\nCondon J. J., 1992, ARA\\&A, 30, 575\n\n\\item\nDole, H., et al. 1999, astro-ph/9902122\n\n\\item\nDwek, E., et al. 1996, ApJ, 457, 244\n\n\\item\nEales, S., et al. 1999, ApJ, 515, 518\n\n\\item \nFixsen, D., J., et al. 1998 ApJ, 508, 123\n\n\\item\nFlores, H., et al. 1999, A\\&A, 343, 389\n\n\\item\nFlores, H., et al. 1999, ApJ, 517, 148\n\n\\item\nFomalont, E. B., et al. 1991, AJ, 102, 125\n\n\\item\nHauser, M. G., et al. 1998, ApJ, 508, 25\n\n\\item\nHughes, D., et al. 1998, Nature, 394, 241\n\n\\item\nHirashita H., et al. 1999, PASJ, 51, 81\n\n\\item\nHolland, W. S., et al. 1999, MNRAS, 303, 659\n\n\\item\nKawara, K., et al. 1999, in prep.\n\n\\item\nPuget, J.-L., et al. 1999, astro-ph/9812039\n\n\\item\nRowan-Robinson, M., et al. 1991, MNRAS, 253, 485\n\n\\item\nRush, B., et al. 1993, ApJS, 89, 1\n\n\\item\nSmail, I., et al. 1997, ApJ, 490, L5\n\n\\item\nSmith B. J., et al. 1987, ApJ, 318, 161\n\n\\item\nSoifer B. T., et al. 1987, ApJ, 320, 238\n\n\\item\nSoifer B. T., \\& Neugebauer, G. 1991, AJ, 101, 354\n\n\\item\nStickel, M., et al. 1998, A\\&A, 336, 116\n\n\\item\nTakeuchi T. T., et al. 1999, PASP, 111, 288\n\n\\item\nWilner, D. J., \\& Wright, M. C. H. 1997, ApJ, 488, L67\n\n\\end{thebibliography}"
}
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astro-ph0002137
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Electron Acceleration and Time Variability \\ of High Energy Emission from Blazars
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[
{
"author": "Masaaki Kusunose"
}
] |
Blazars are known to emit a broad band emission from radio to gamma-rays with rapid time variations, particularly, in X- and gamma-rays. Synchrotron radiation and inverse Compton scattering are thought to play an important role in emission and the time variations are likely related to the acceleration of nonthermal electrons. As simultaneous multiwavelength observations with continuous time spans are recently available, some characteristics of electron acceleration are possibly inferred from the spectral changes of high energy emission. In order to make such inferences, we solve the time-dependent kinetic equations of electrons and photons simultaneously using a simple model for electron acceleration. We then show how the time variations of emission are dependent on electron acceleration. We also present a simple model for a flare in X-rays and TeV gamma-rays by temporarily changing the acceleration timescale. Our model will be used, in future, to analyze observed data in detail to obtain information on electron acceleration in blazars.
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[
{
"name": "paper.tex",
"string": "\\documentclass[preprint]{aastex} %one-column, single-spaced \n%\\documentclass{aastex}\n%\\documentclass[preprint2]{aastex} %two-column, single-spaced \n%\\usepackage{epsfig}\n\n%\\slugcomment{ver. 1, 10-20-99}\n\n\\shorttitle{Electron Acceleration and Time Variability} \n\\shortauthors{Kusunose et al.}\n\n\\begin{document}\n\\title{Electron Acceleration and Time Variability \\\\\nof High Energy Emission from Blazars}\n\n\\author{Masaaki Kusunose}\n\\affil{Department of Physics, School of Science, \nKwansei Gakuin University, \\\\ \nNishinomiya 662-8501, Japan}\n\\email{kusunose@kwansei.ac.jp}\n\n\\author{Fumio Takahara}\n\\affil{Department of Earth and Space Science, Graduate School of Science,\nOsaka University, Toyonaka, Osaka 560-0043, Japan} \n%\\email{takahara@vega.ess.sci.osaka-u.ac.jp} \n\n\\and\n\n\\author{Hui Li}\n\\affil{Theoretical Astrophysics (T-6, MS B288), Los Alamos National \nLaboratory, \\\\ \nLos Alamos, NM 87545}\n%\\email{hli@lanl.gov}\n\n\n\\begin{abstract}\nBlazars are known to emit a broad band emission from radio to \ngamma-rays with rapid time variations, particularly, in X- and \ngamma-rays. Synchrotron radiation and inverse Compton scattering\nare thought to play an important role in emission \nand the time variations are likely related to the acceleration \nof nonthermal electrons. \nAs simultaneous multiwavelength observations with continuous \ntime spans are recently available, some characteristics\nof electron acceleration are possibly inferred from the spectral \nchanges of high energy emission. \nIn order to make such inferences, we solve the time-dependent kinetic \nequations of electrons and photons simultaneously using a simple model \nfor electron acceleration. \nWe then show how the time variations of emission are dependent \non electron acceleration. \nWe also present a simple model for a flare in X-rays and TeV \ngamma-rays by temporarily changing the acceleration timescale.\nOur model will be used, in future, to analyze observed data in detail to \nobtain information on electron acceleration in blazars.\n\\end{abstract}\n\n\n\\keywords{BL Lacertae objects: general -- gamma rays: \ntheory -- radiation mechanisms: nonthermal}\n\n\n\\section{INTRODUCTION}\n\nHigh energy emission from blazars is usually thought to be produced by \nrelativistically moving jets or blobs from the nucleus of galaxies\n\\citep[e.g.,][]{br78,bk79,mgc92,sbr94,it96}.\nThe physical properties of such jets have been probed mostly based on \nthe steady state models of synchrotron radiation and inverse Compton \nscattering by a nonthermal electron population (SSC model).\nHowever, blazars are also characterized by rapid \nand strong time variability.\nRecent observations have revealed that the emission exhibits short time \nvariations in X- and gamma-ray bands on timescales from weeks down to \nhalf an hour \n\\citep[e.g.,][for review]{muk97,umu97},\nas fast time variations of Mrk 421 were\nobserved by X-rays and TeV gamma-rays \\citep{gaid96,taka96};\nsimilar time variations of Mrk 501 were also found by multiwavelength \nobservations \\citep{kat99}.\nThese observations should provide important clues on physical processes \nin relativistic jets, in particular, on electron acceleration. \n\nTo make theoretical inferences, we need to calculate time-dependent \nemission spectra from a time-dependent electron population. \nAn example of such theoretical models was recently presented by \n\\cite{mk97}. They solved the kinetic equations of \nelectrons and photons simultaneously, by injecting power-law electrons \nwith an exponential cutoff. They showed various possibilities to \nexplain the time variations observed from Mrk 421, such as the changes\nin the magnetic field or the maximum Lorentz \nfactor of nonthermal electrons. Although the correlation between \nX-rays and TeV gamma-rays are important to discuss the SSC model, \ntheir estimate of Compton scattering in the Klein-Nishina regime \ndoes not necessarily correctly account for the energy change in\nscatterings, because of a simplified treatment of Compton scattering\nin the Klein-Nishina regime\n[see \\cite{mk95} for the details of their calculation method].\n\\cite{kirketal98}, on the other hand, extended the above model, \nassuming that an acceleration region and a cooling region \nare spatially separated; \ni.e., electrons accelerated in a shock region are transferred to \na cooling region where they emit synchrotron photons\n(they did not include Compton scattering).\nTheir model was intended to explain the time variability of X-rays, \nby changing acceleration timescale. \n\nBesides the time variations of flare activities explained \nby \\cite{mk97} and \\cite{kirketal98}, the early stages of \nacceleration are of great importance. \nBy examining the properties of the time evolutions of photon spectra during \nacceleration, we may obtain the diagnoses of acceleration mechanisms. \nThe recent development of observations in X-rays (ASCA and Beppo-SAX) to \nTeV gamma-rays (e.g., Whipple and HEGRA) and future experiments \nmight be used to confirm the diagnoses.\n\nIn this paper, we use a formulation similar to \\cite{mk97}, \nbut with the full Klein-Nishina cross section \nin the Compton scattering kernel,\nso that the emission in the TeV range is calculated correctly. \nWe also include a particle acceleration process \nby considering spatially separated acceleration and cooling regions \nas in \\cite{kirketal98}, although we do not consider the spatial transfer\nof electrons.\nWe particularly emphasize the detailed study of the properties of \nelectron and photon spectra in the early stage of acceleration.\n\nWe describe our model in \\S \\ref{sec:model} and present numerical results\nin \\S \\ref{sec:results}. Summary of our results is given in \n\\S \\ref{sec:summary}. \n\n\n\n\\section{MODEL}\n\\label{sec:model}\n\n\\subsection{Acceleration and Cooling Regions} \n\nWe assume that observed photons are emitted from a blob moving \nrelativistically towards us with Doppler factor \n${\\cal D} = [ \\Gamma ( 1- \\beta_\\Gamma \\mu )]^{-1}$,\nwhere $\\Gamma$ is the Lorentz factor of the blob,\n$\\beta_\\Gamma$ is the speed of the blob in units of \nlight speed $c$, and $\\mu$ is the cosine of the angle\nbetween the line of sight and the direction of motion of the blob.\nThe blob is a spherical and uniform cloud with radius $R$, \nexcept that the blob includes an acceleration region \nwhich is presumably a shock front. \nIt is assumed that the spatial volume of the acceleration region \nis small, and that\nthe acceleration region is a slab with thickness \n$R_{\\rm acc}$ defined below.\nThe spectra of electrons and photons in the blob are calculated for \nthe acceleration and cooling regions separately \nby solving equations described in \\S \\ref{sec:kinetic}.\n\nWe assume that the acceleration region (hereafter AR)\nand the cooling region (hereafter CR) are spatially separated;\nshocks in the blob are expected to be the site of electron acceleration \nand electrons cool mainly outside the shock regions. \nIn the AR, electrons are mainly accelerated and \ncooling is unimportant except for the highest value of $\\gamma$, \nwhile, in the CR, electrons with a nonthermal spectrum \nare injected from the AR;\nthe escape rate of electrons from the AR is equal to \nthe injection rate of electrons in the CR because of the number conservation. \nWe further assume that acceleration time, $t_{\\rm acc}$,\nand escape time, $t_{e, \\mathrm{esc}}$, in the AR are energy independent \nas given in equation (\\ref{eq:tacc}) below.\nWith these assumptions, the number spectrum of electrons \nin the AR is a power law with a power-law index $-2$, \ni.e., $N(\\gamma) \\propto \\gamma^{-2}$, \nwhich is confirmed analytically \\citep[e.g.,][]{kirketal98}. \nThus the maximum energy of electrons is \ndetermined by the balance of cooling and acceleration. \nSince we consider $t_{\\rm acc} \\ll R/c$ (see \\S \\ref{sec:results-1}), \nthe size of the AR\nis much smaller than the size of the blob itself. \n\nWe use this formulation because $N(\\gamma) \\propto \\gamma^{-2}$\nis expected from the theory of shock acceleration \n\\citep[e.g.,][]{druly,be87}.\nWe, however, do not solve the spatial transfer of electrons \nas was done by \\cite{kirketal98}.\nInstead, we simply calculate escaping electrons from the AR\nand put them into the CR. \nAlthough this may be an oversimplified model for realistic situations,\nthe actual geometrical situation of shocks is not well known, either. \nStrictly speaking, our formulation is valid\nwhen ARs and CRs are more or less uniformly distributed in a cloud, \nbut it is expected to be a fair approximation to the case \nwhere a single shock propagates in a jet as was studied by \\cite{kirketal98}. \nAs for the calculation of photon spectra, photons originating from one \nregion penetrate into the other region but most of the photons originate \nfrom the CR since the size of the AR is small. \nThus, the electron cooling in the blob is governed either \nby its own magnetic field or by synchrotron photons \nstemming from the CR. \nWe treat appropriately this situation in numerical calculations. \n\n\n\\subsection{Kinetic Equations}\n\\label{sec:kinetic}\n\nThe equation describing the time-evolution of the electron number \nspectrum in the AR is given by \n\\begin{equation}\n\\label{eq:elkinetic}\n\\frac{\\partial N(\\gamma)}{\\partial t}\n= - \\frac{\\partial}{\\partial \\gamma}\n\\left\\{ \\left[ \\left( \\frac{d\\gamma}{dt} \\right)_{\\rm acc} \n-\\left( \\frac{d\\gamma}{dt} \\right)_{\\rm loss} \\right] N(\\gamma) \\right\\} \n- \\frac{N(\\gamma)}{t_{e, {\\rm esc}}} + Q(\\gamma) \\, , \n\\end{equation}\nwhere $\\gamma$ is the Lorentz factor of electrons and $N(\\gamma)$ is \nthe number density of electrons per unit $\\gamma$. \nWe assume that monochromatic electrons with Lorentz factor $\\gamma_0$ \nare injected in the AR, i.e., \n$Q(\\gamma) = Q_0 \\, \\delta(\\gamma-\\gamma_0)$. \nElectrons are then accelerated\nand lose energy by synchrotron radiation and Compton scattering;\nthe energy loss rate is denoted by $(d \\gamma / dt)_{\\rm loss}$. \nThe acceleration term is approximated by \n\\begin{equation}\n\\left( \\frac{d\\gamma}{dt} \\right)_{\\rm acc} \n= \\frac{\\gamma} {t_{\\rm acc}} \\, .\n\\end{equation}\nIn the framework of diffusive shock acceleration \n\\citep[e.g.,][]{druly,be87},\n$t_{\\rm acc}$ can be approximated as \n\\begin{equation}\nt_{\\rm acc} = \\frac{20 \\lambda(\\gamma) c}{3 v_s^2} \n\\sim 3.79 \\times 10^{-6} \\left( \\frac{0.1 {\\rm G}}{B} \\right) \\xi \\, \n\\gamma \\quad {\\rm sec},\n\\end{equation}\nwhere $v_s \\approx c$ is the shock speed, $B$ is the magnetic field, \nand $\\lambda(\\gamma) = \\gamma m_e c^2 \\xi / (e B)$ is the mean free path \nassumed to be proportional to the electron Larmor radius with $\\xi$ \nbeing a parameter, $m_e$ the electron mass,\nand $e$ the electron charge. Although this expression is \nvalid only for test particle approximation in non-relativistic shocks, \nwe rely on this since the basic dependences are not much changed in \ngeneral cases. \n\n\nFor the convenience of numerical calculations, \nwe assume $t_{\\rm acc}$ does not depend on $\\gamma$: \n\\begin{equation}\nt_{\\rm acc} = 3.79 \\times 10 \\left( \\frac{0.1 {\\rm G}}{B} \\right) \n\\left( \\frac{\\gamma_f}{10^7} \\right) \\xi \\quad {\\rm sec}, \n\\label{eq:tacc}\n\\end{equation}\nwhere $\\gamma_f$ is assumed to be a characteristic Lorentz factor\nof relativistic electrons and used as a parameter;\nwe set $\\gamma_f = 10^7$ throughout this paper. \nAlthough realistic acceleration time for the smaller values of\n$\\gamma$ should be correspondingly shorter, we make this choice because \nwe mainly concern about the electrons with the large values of $\\gamma$.\nOne worry about this choice is the effect on the spectrum of accelerated \nelectrons. We make sure that the resultant spectrum is that expected \nin diffusive shock acceleration by choosing \n$t_{e, \\mathrm{esc}} = t_\\mathrm{acc}$ in the AR;\nthis assumption of $t_{e, \\mathrm{esc}} = t_\\mathrm{acc}$ \nis the same as used by \\cite{mk95}\nin their proton acceleration model.\n\nThe electron spectrum in the CR is calculated by equation \n(\\ref{eq:elkinetic}), with $(d \\gamma / dt )_{\\rm acc}$ dropped.\nAlso $Q(\\gamma)$ is replaced by the escaping electrons from\nthe AR and $t_{e, {\\rm esc}}$ is set to be $2 R/c$.\nThe assumption of $2 R/c$ in estimating $t_{e, {\\rm esc}}$ \nis merely based on that electrons escaping from the blob \ntake longer time than photons, and this point needs further work.\n\nThe relevant equation for the time evolution of photons is given by\n\\begin{equation}\n\\label{eq:phkinetic}\n\\frac{\\partial n_{\\rm ph}(\\epsilon)}{\\partial t} = \\dot{n}_{\\rm C}(\\epsilon)\n+ \\dot{n}_{\\rm em}(\\epsilon) - \\dot{n}_{\\rm abs}(\\epsilon) \n- \\frac{n_{\\rm ph}(\\epsilon)}{t_{\\gamma, {\\rm esc}}} \\, , \n\\end{equation}\nwhere $n_{\\rm ph}(\\epsilon)$ is the photon number density per \nunit energy $\\epsilon$. Compton scattering is calculated as\n\\begin{equation}\n\\label{eq:comp}\n\\dot{n}_{\\rm C}(\\epsilon)\n= - n_{\\rm ph}(\\epsilon) \\, \\int d\\gamma\t\\, N(\\gamma) \\,\nR_{\\rm C}(\\epsilon, \\gamma) + \\int\\int d\\epsilon^{\\prime} \\, d\\gamma \\, \nP(\\epsilon; \\epsilon^{\\prime}, \\gamma) \\,\nR_{\\rm C}(\\epsilon^{\\prime}, \\gamma) \\,\nn_{\\rm ph}(\\epsilon^{\\prime}) N(\\gamma) \\, , \n\\end{equation}\nusing the exact Klein-Nishina cross section. First term of equation \n(\\ref{eq:comp}) denotes the rate that photons with energy $\\epsilon$ \nare scattered by electrons with the number spectrum $N(\\gamma)$;\n$R_{\\rm C}$ is the angle-averaged scattering rate. \nSecond term of equation (\\ref{eq:comp}) denotes the spectrum of \nscattered photons:\n$P(\\epsilon; \\epsilon^{\\prime}, \\gamma)$ is the probability that a photon \nwith energy $\\epsilon^\\prime$ is scattered by an electron with energy \n$\\gamma$ to have energy $\\epsilon$. The probability $P$ is normalized \nsuch that $\\int P(\\epsilon; \\epsilon^{\\prime}, \\gamma) \\, d\\epsilon = 1$. \nThe details of $R_{\\rm C}$ and $P$ are given in \n\\cite{jones68} and \\cite{bc90}.\n\nPhoton production and self-absorption by synchrotron radiation \nare included in\n$\\dot{n}_{\\rm em}(\\epsilon)$ and $\\dot{n}_{\\rm abs}(\\epsilon)$, respectively.\nThe synchrotron emissivity and absorption coefficient are calculated \nbased on the approximations given in \\cite{rm84} for mildly\nrelativistic electrons\nand \\cite{cs86} for relativistic electrons.\nExternal photon sources are not included. \nThe rate of photon escape is estimated as \n$n_{\\rm ph}(\\epsilon)/t_{\\gamma, {\\rm esc}}$. \nWe set $t_{\\gamma, {\\rm esc}} = R_{\\rm acc}/c$ and\n$R/c$ in the AR and CR, respectively,\nbecause the scattering depth of the blob is much smaller than unity.\n\nThe comoving quantities are transformed back into the observer's frame\ndepending on the Doppler factor and the redshift $z$; \n$\\epsilon_{\\rm obs} = \\epsilon \\, {\\cal D}/(1+z)$, \nand $dt_{\\rm obs} = dt \\, (1+z)/{\\cal D}$ \n\n\n\n\\section{RESULTS}\n\\label{sec:results}\n\n\nWe first examine the case where the cloud is initially empty and \nthe injection of electrons starts at $t = 0$.\nThe distribution function of the injected electrons is mono-energetic:\nHere $\\gamma_0 = 2$ is assumed.\nThe strength of magnetic fields is assumed to have the same value \nboth in ARs and in CRs,\nwhich is 0.1 G except in \\S \\ref{sec:mag}.\nOther parameters are redshift $z = 0.05$, Hubble constant \n$H_0 = 75$ km sec$^{-1}$ Mpc$^{-1}$, \nand Doppler factor ${\\cal D} = 10$.\nWe also assume that the size of a cloud is measured \nby the timescale of variability,\nwhich is assumed to be $R/(c {\\cal D}) = 5 \\times 10^4$ sec \nin the observer's frame.\n\n\n\\subsection{Time Evolution in Early Phase} \n\\label{sec:results-1}\n\nFirst we simulate the time evolution from $t = 0$ to $R/c$ to study \nthe evolution in an early stage.\nWe assume $\\xi = 5 \\times 10^2$\n(i.e., $t_{\\rm acc} \\approx 1.9 \\times 10^4$ sec in the blob frame), \nand injection duration $t = 0$ -- $R/c$. \nIn the CR, the escape time of electrons is assumed to be $2 R/c$.\nThe size of the AR is assumed to be $R_{\\rm acc} = c t_{\\rm acc} / 2$.\n(Note that, in sections below, when we change the value of $t_{\\rm acc}$, \n$R_{\\rm acc}$ is also changed accordingly.) \nThe injection rate of electrons in the AR is \n$0.1$ electrons cm$^{-3}$ sec$^{-1}$. \nThe volume of the AR is $\\sim 2.1 \\times 10^{47}$ cm$^3$\nand the total injection rate is \n$\\sim 2.1 \\times 10^{46}$ electrons sec$^{-1}$,\nassuming that the AR is approximated by a disk with\nradius $R$ and thickness $R_\\mathrm{acc}$.\nThe total power of electrons amounts \nto $\\sim 5 \\times 10^{41}$ ergs sec$^{-1}$ by acceleration,\nif the power-law spectrum with an index of 2 is realized between \n$\\gamma_{\\rm min}$ and $\\gamma_{\\rm max}$; \nthe minimum and maximum Lorentz factors \n$\\gamma_{\\rm min}$ and $\\gamma_{\\rm max}$ are tentatively taken to be \n$2$ and $3\\times 10^6$, respectively.\n\nIn Figure \\ref{fig:el-e3-a}, the evolution of the electron number\nspectrum is shown both for an AR and a CR.\nIt is seen that electrons injected with the Lorentz factor 2 are gradually \naccelerated and the value of $\\gamma_{\\rm max}$ increases with time, \nwhere we take the value of $\\gamma_{\\rm max}$ such that \n$N(\\gamma) = 0$ for $\\gamma > \\gamma_{\\rm max}$. \nThe value of $\\gamma_{\\rm max}$ in a steady state is determined by \nthe balance among $t_{\\rm acc}$, $t_{e, {\\rm esc}}$,\nand cooling time $t_{\\rm cool}$ in the AR.\nBecause we assume $t_{\\rm acc} = t_{e, {\\rm esc}}$ \nin the AR, $\\gamma_{\\rm max}$ is simply \ndetermined by $t_{\\rm acc}$ and $t_{\\rm cool}$. \nThe value of $\\gamma_{\\rm max}$ in Figure \\ref{fig:el-e3-a}\nis $\\sim 4 \\times 10^6$.\nThe spectrum reaches almost a steady state within $R/c$, \nwhich is a power law, $N(\\gamma) \\propto \\gamma^{-2}$;\nnote that $t_{\\rm acc} \\sim 2 \\times 10^4$ sec\nand $R/c = 5 \\times 10^5$ sec \nin the comoving frame of the blob for the present model.\n\nIn the CR, the effect of electron escape is negligible in \nthe time interval shown in Figure \\ref{fig:el-e3-a}, because \nthe simulation is terminated \nat $t = R/c$ while $t_{e, {\\rm esc}} = 2 R/c$.\nBecause of radiative cooling, \na break $\\gamma_{\\rm br}$ appears at around $3 \\times 10^5$.\nThis break moves to lower energy when the evolution is continued \nuntil a steady state is attained; \n$\\gamma_{\\rm br} \\sim 10^4$ at $t = 10 R/c$. \nThere is also a slight deceleration of electrons by cooling, \nwhich is shown by curves below $\\gamma = 2$.\n\nThe spectral energy distribution (SED) of emission from the CR\nis shown in Figure \\ref{fig:ph-e3-a};\nthe flux and the photon energy are plotted in the observer's frame.\nCurves in the figure show the time evolution, \nwith equally spaced time interval for $t = 0 - R/c$ by solid curves. \nThey evolve from lower to upper curves.\nIn this stage, the synchrotron radiation dominates, because \nCompton scattering needs a timescale $\\sim R/c$ to be effective. \nSED at $t = 2 R/c$ (dotted curve) and $10 R/c$ (dashed curve) are also \nshown in the figure; here electrons are continuously injected\nuntil $t = 10 R/c$.\nAs shown by those curves, when the evolution is continued after $R/c$, \nthe Compton component continues to increase before reaching\na steady state.\nThe peak energy of synchrotron emission initially increases \nbut begins to decrease after about $0.8R/c$ \nbecause electrons with $\\gamma < \\gamma_{\\rm br}$ \ncontinue to accumulate and the value of $\\gamma_{\\rm br}$\ndecreases while those with $\\gamma > \\gamma_{\\rm br}$ \nare saturated because of radiative cooling.\nAfter $t = 2R/c$ the effects of electron escape begin to further\nmodify the synchrotron spectrum; the intensity \nat the high energy part decreases \nwhile that at low energy still continues to increase slightly. \n\nFor $t = 0 \\sim R/c$, light curves in the X-ray range are\nshown in Figure \\ref{fig:lightcv-e3-a}.\nHard X-rays become dominant after $t \\sim 15 t_\\mathrm{acc}$,\nwhere $t_\\mathrm{acc}/{\\cal D} \\sim 2 \\times 10^3$ sec \nin the observer's frame.\n\nThe time evolution of the energy densities of electrons and photons \nin the CR are shown in Figure \\ref{fig:ene-e3}:\nThe energy densities in the AR are comparable with those \nin the CR for the parameters we used.\nIn the CR, $t_{e, {\\rm esc}} = 2 R/c$ and \n$t_{\\gamma, {\\rm esc}} = R/c$ are assumed, \nso that the energy density of electrons is larger than that of photons. \nAs was mentioned above, first the synchrotron photon energy-density \nrapidly increases and later the Compton photon \nenergy-density (indicated by SSC in the figure) increases.\nIt should be noted that the ratio of the energy densities \nof the Compton component to the synchrotron component\nis about 0.7 in the final stage, \nwhile the ratio of energy densities of synchrotron photons to \nmagnetic fields is about 9. \nThis is because the energy range of the target photons of Compton scattering \nis only a part of the synchrotron spectrum due to the Klein-Nishina limit. \nThis result implies that we should be cautious about the estimate of \nthe magnetic field strength from observations; \nif we simply estimate the magnetic field by multiplying \nthe energy density of synchrotron photons \nby the ratio of synchrotron luminosity to Compton luminosity, \nit results in a large overestimation of magnetic field. \n\nThe energy injected through the electron acceleration is finally\ncarried away by electrons and photons from the blob.\nThe ratio of the amounts of the energies\ncarried by electrons and photons is about $1.8 : 1$\nin a steady state (i.e., $t \\sim 10 R/c$).\nThat is, electrons carry more jet power than radiation\nin this specific model.\n\nThe trajectories in the energy-flux {\\it vs.} photon-index plane are \nshown for $t = 0$ -- $10 R/c$ in Figure \\ref{fig:alpha-e3} \nfor various energy bands.\nBecause the value of $\\gamma_{\\rm max}$ decreases due to\nradiative cooling, \nthe flux of X-rays decreases when $t$ $>$ a few $R/c$.\nThe flux of gamma-rays, on the other hand, continues to increase\nbecause of Compton scattering (see Figure \\ref{fig:ph-e3-a}).\n\n\n\\subsection{Dependence on Acceleration Timescale} \n\nBy changing the value of $\\xi$,\nwe compare the electron spectrum for different values of the \nacceleration time,\nwhere we keep $t_{\\rm acc} = t_{e, {\\rm esc}}$ in the AR.\nIn Figure \\ref{fig:el-e3-8-9},\nsteady-state distributions of electrons\nfor different values of $\\xi$ are compared. \nWhen the acceleration time scale is longer, \nthe value of $\\gamma_{\\rm max}$ is reduced because of \nradiative cooling in the AR. \nConsequently, the emission spectrum becomes softer \n(Figure \\ref{fig:ph-e3-8-9}).\nIt should be noted that because a smaller value of $\\xi$\nleads to a smaller value of $R_\\mathrm{acc}$ in out model,\nthe luminosity from a blob becomes smaller when $\\xi$ is smaller.\nThe extreme limit of $\\xi=1$ corresponding to the B\\\"ohm limit \nresults in the most efficient Compton luminosity and the highest \ngamma-ray energy. \nIn this limit, $\\gamma_{\\rm max}$ is about $2 \\times 10^9$ \nand the inverse Compton SED shows a steep cut off at $\\sim 10^4$ TeV\nfor ${\\cal D} = 10$ if electron-positron pair production is neglected.\nNote that $t_{\\rm acc}$ in reality depends on $\\gamma$,\nwhile we assume $t_{\\rm acc}$ does not depend on $\\gamma$\nand the above values were calculated assuming $\\gamma_f = 10^7$ in\nequation (\\ref{eq:tacc}).\n\nThe shape of SED has a significant curvature in the TeV region\nin our calculations.\nThis curvature is in contrast to the observations of \nTeV gamma-rays from Mrk 421,\nwhich are fitted by a power law \\citep{kretal99}.\nMrk 501, on the other hand, show a curvature in TeV emission\n\\citep{cat97}, and there are models which explain the curvature\nby intergalactic absorption \\citep[e.g.,][]{ko99,kretal99}.\nWe, however, do not address these issues in this paper,\nsince we are mainly interested in the temporal behavior of\nelectrons and photons due to electron acceleration in the source.\n\n\n\n\n\\subsection{Dependence on the Injection Rate}\n\nThe spectral energy distributions of electrons and photons\ndepend on the value of the injection rate \n$Q(\\gamma)$ in the AR as well.\nIf the value of $Q(\\gamma)$ is larger\nwith the fixed values of $\\gamma_0$, $t_{e, {\\rm esc}}$, and $t_{\\rm acc}$,\nthe accumulation of electrons in the CR increases, \nresulting in the dominance of the Compton component. \nAn example of SED is shown \\ref{fig:ph-e4-e3},\nwhere the electron injection rate in the acceleration \nsmaller by a factor 10 than in the model shown in Figure \\ref{fig:ph-e3-a},\ni.e., electrons are injected at the rate of $0.01$ electrons\ncm$^{-3}$ sec$^{-1}$. \nThe peak of the synchrotron component decreases by a factor 10\nand that of the Compton component decreases by a factor 100.\n\n\n\n\\subsection{Dependence on Magnetic Field}\n\\label{sec:mag}\n\n\nWhen the size of a cloud and the number density of electrons are\nfixed, the value of $\\gamma_{\\rm max}$ is larger for smaller values of $B$,\nbecause the synchrotron cooling rate is proportional to $B^{2}$.\nHowever, this is not the case in our model,\nbecause not only the cooling rate but also $t_{\\rm acc}$ depends on B.\nWhen $B$ is smaller, $t_{\\rm acc}$ is larger,\nwhich results in the larger size of the AR.\nBecause we fix the particle injection rate per unit volume in the AR, \nthe total number of electrons injected\ninto the CR per unit time is larger by\nthe electron number conservation.\nAs a result, the Compton cooling in the CR\nbecomes stronger and the value of $\\gamma_{\\rm max}$ becomes smaller.\nHowever, the increase or decrease of $\\gamma_{\\rm max}$\nactually depends on the combination of synchrotron cooling\nand Compton cooling.\nSuch dependence on $B$ in the CR is shown in Figure \\ref{fig:light-b05-g2};\nSEDs at $t = 10 R/c$ are compared for $B = 0.05$, $0.1$, and\n$0.5$ G with the same values of other parameters as\nin Figure \\ref{fig:ph-e3-a}. \nIn the CR, the values of $\\gamma_{\\rm max}$ are $8 \\times 10^6$,\n$4 \\times 10^6$, and $8 \\times 10^5$ for \n$B = 0.05$, $0.1$, and $0.5$ G, respectively.\n\n\n\n\\subsection{Termination of Acceleration} \n\nIt is conceivable that acceleration is terminated \nby the end of electron injection in the AR\ndue to the change of shock structure, etc., so that \nplasmas cease to emit hard photons. \nTo exemplify such a situation, \nwe continue the injection and acceleration up to $t = 4 R/c$ with the \nparameters used in Figure \\ref{fig:el-e3-a} and terminate the injection \nand the acceleration abruptly at $t = 4 R/c$, \nwhile the simulation is continued until $t = 7 R/c$. \nA break of the power-law spectrum of electrons \nin the AR appears after acceleration is terminated,\nand the break moves to lower energy with time. \nThe response of the emission spectrum to the termination of \nacceleration is almost simultaneous\nin different energy bands as shown by light curves \nin Figure \\ref{fig:light-e3-c}. \nIt is observed that the decay at 0.5 -- 2 keV band lags \nthat at 2 -- 40 keV,\nwhich is characteristic to the models that assume\nthe injection of power-law electrons and a sudden termination\nof injection.\nThe decay in the keV range and 1 -- 10 TeV bands is exponential,\nbecause the supply of the electrons producing those photons \nis turned off.\nOn the other hand, electrons producing GeV photons are still supplied for\na while by the cooling of the highest energy electrons \nwhich produced 1 -- 10 TeV photons.\n\n\n\n\\subsection{Flare}\n\nUp to now, we have assumed that at the initial stage \nthe cloud is empty and there are no high energy electrons or photons. \nThis is certainly an over simplification. \nMany flare events have been observed in X- and gamma-ray ranges \nby ASCA, Whipple, etc. They are overlaid on a steady emission component. \nAs an example of applications of our code, a flare is simulated, \ni.e., we simply change the value of \n$t_{\\rm acc}$ for a period of time. \nMore specifically, at $t = 0$ the distributions of electrons \nand photons are in the steady state which is obtained\nfor the parameters used in \\S \\ref{sec:results-1};\nsee the dashed curve in Figure \\ref{fig:ph-e3-a} \nfor the steady photon energy distribution.\nThe steady state is still continued for $R/c$.\nWe then replace $t_{\\rm acc}$ by\n$t_{\\rm acc}/1.2$ for $t = R/c - 2 R/c$\n(about 14 hours in the observer's frame); \nafter $t = 2 R/c$, the original value of $t_{\\rm acc}$ is used. \nThe electron escape time in the AR is \nalso changed keeping $t_{e, {\\rm esc}} = t_{\\rm acc}$. \nIn Figure \\ref{fig:light-flare}, light curves are shown for\nsuch a flare.\nThe response of the light curves to the change of \n$t_{\\rm acc}$ (on/off of a flare) is slightly delayed, \nbecause of photon production and Compton scattering time. \nIt is also noticed that the change of the light curve \nat $1 - 10$ GeV band delays behind X-rays and TeV gamma-rays. \nThis is a result of an interplay of the time evolution of \nelectron and synchrotron photon spectra. \nIt is shown that the light curves of 2 -- 10 and 10 -- 40 keV\nproceed that of 0.5 -- 2 keV.\nThis behavior is different from that shown \nin Figure \\ref{fig:lightcv-e3-a},\nwhere the initial condition was an empty blob.\n\nThe trajectories in the energy flux and photon index are shown \nin Figure \\ref{fig:alpha-flare} for $t = 0 $ -- $10 R/c$. \nThis behavior is qualitatively similar to observed one for Mrk 421 by \nASCA \\citep{taka96}.\nThough the amplitudes of the change in the photon index of 2 -- 10 keV \nand its energy flux are different from those of the observation,\nthese values are dependent on parameters such as $t_{\\rm acc}$ \nand the duration of the flare, etc.\n\n\n\n\\section{SUMMARY}\n\\label{sec:summary}\n\nSimulations of the time evolution of electron and photon energy \ndistributions were presented as a model of time variations observed \nby X- and gamma-rays from blazars. \nBy assuming that acceleration and cooling regions in a blob are \nspatially separated,\nwe calculated the energy spectra of electrons in each regions. \nElectrons in the acceleration region are accelerated with a characteristic \ntimescale $t_{\\rm acc}$ and escape on a timescale $t_{e, {\\rm esc}}$; \nhere we assumed $t_{\\rm acc} = t_{e, {\\rm esc}}$, so that the electron \nspectrum in a steady state obeys a power law,\n$N(\\gamma) \\propto \\gamma^{-2}$, as realized in the standard model \nof shock acceleration \\citep[e.g.,][]{druly,be87}.\nElectrons escaping from the acceleration region are injected into \nthe cooling region\nwhere they lose energy by radiation and finally escape from the blob \non a timescale assumed to be $2R/c$.\nWith these assumptions, we performed the simulations\nof the time evolutions of electrons and photons for various \nvalues of parameters.\nAlthough we did not include a specific acceleration mechanism, \nwe took into account the salient features of diffusive shock\nacceleration, so that we could study the properties of time variation\naccompanying shock acceleration.\n\nWe first presented the results of\nthe time evolution of the spectral energy distribution of radiation\nassociated with the evolution of the electron number spectrum.\nIn the early stage of the evolution, i.e., \n$t = 0$ -- $R/c$, the synchrotron component dominates the spectrum.\nThe energy flux of soft X-rays starts to rise earlier than that\nof hard X-rays.\nLater ($t > R/c$), the Compton luminosity gradually increases.\nAt the same time, the peak energy of the synchrotron component\ndecreases because of radiative cooling.\nIt was found that in a steady state, \nescaping electrons carry more energy than radiation:\nThis result, of course, depends on the values of the parameters used.\nWe also showed the dependence of time evolution on \nthe acceleration timescale,\nthe electron injection rate, and the strength of magnetic fields.\nThe value of $\\gamma_{\\rm max}$ and the ratio of the synchrotron\nluminosity to the Compton luminosity depend on such parameters.\n\nWe next simulated a flare by simply changing the value of \n$t_{\\rm acc}$ for a certain time span.\nWith a shorter acceleration timescale,\nmore energetic electrons are produced and consequently \nmore hard photons are produced. \nThe relation between the energy flux and the photon index during a flare\nwas obtained, which is similar to the one \nobserved from Mrk 421 \\citep{taka96}.\n\nOur formulation provides a method to treat high energy flares \nincluding particle acceleration processes, which is beyond \nusual analyses where nonthermal electron spectra are arbitrarily assumed \nand only cooling processes are included.\nAlthough we have not applied our model to any specific case of \nflares, it is straightforward to do this using our code. \nThe examples presented here seem to cover a wide range of \nobserved flares. \nThese applications are deferred to future work. \nOn the theoretical side, as proposed by \\cite{kirketal98},\nelectrons accelerated at a shock are transferred outside of\nthe shock and cool radiatively. \nTo include such spatial transfer of electrons,\nwe, in future, need to solve for the structure \naround acceleration regions.\n\nRecently \\cite{cg99} showed observational consequences\nassociated with time variations with timescales shorter than $R/c$.\nWhen such short timescale variations occur,\nobserved emission is a superposition from various parts of a cloud.\nThen the time profile of each time variation is not necessarily\nobserved clearly.\nThe model presented in this paper contains the acceleration timescale\nshorter than $R/c$.\nThus our model may not directly reflect observed spectra.\nHowever, to understand the relation between electron acceleration\nand time variation of emission, such a study should be useful.\n\n\n\n\\acknowledgements\n\nM.K. and F.T. have been partially supported by Scientific Research Grants \n(M.K.: Nos. 09223219 and 10117215; F.T.: Nos. 09640323, 10117210, and \n11640236) from the Ministry of Education, Science, Sports and Culture \nof Japan.\n\n\n%\\clearpage\n\n\\begin{thebibliography}{}\n\\bibitem[Blandford \\& Coppi (1990)]{bc90} \nBlandford, R. D., \\& Coppi, P. S. 1990, \\mnras, 245, 453 \n\n\\bibitem[Blandford \\& Eichler (1987)]{be87} \nBlandford, R.., \\& Eichler, D. 1987, Phys. Rep., 154, 1 \n\n\\bibitem[Blandford \\& K\\\"{o}nigl (1979)]{bk79} \nBlandford, R. D., \\& K\\\"{o}nigle, A. 1979, \\apj, 232,34 \n\n\\bibitem[Blandford \\& Rees (1978)]{br78} \nBlandford, R. D., \\& Rees, M. J. 1978, \nin Pittsburgh Conf. on BL Lac Objects, ed. A. M. Wolfe \n(Pittsburgh: Univ. Pittsburgh Press), 328\n\n\\bibitem[Catanese et al. (1997)]{cat97}\nCatanese, M. et al. 1997, \\apjl, 487, 143 \n\n\\bibitem[Chiaberge \\& Ghisellini (1999)]{cg99}\nChiaberge, M., \\& Ghisellini, G. 1999, \\mnras, 306, 551\n\n\\bibitem[Crusius \\& Schlickeiser (1986)]{cs86}\nCrusius, A., \\& Schlickeiser, R. 1986, A\\&A, 164, L16\n\n\\bibitem[Druly (1983)]{druly}\nDruly, L. O.' C. 1983, Rep. Prog. Phys., 46, 973 \n\n\\bibitem[Gaidos et al. (1996)]{gaid96}\nGaidos, J. A. et al. 1996, \\nat, 383, 319 \n\n\\bibitem[Inoue \\& Takahara (1996)]{it96} \nInoue, S., \\& Takahara, F. 1996, \\apj, 463, 555 \n\n\\bibitem[Jones (1968)]{jones68}\nJones, F. C. 1968, Physical Review, 167, 1159 \n\n\\bibitem[Kataoka et al. (1999)]{kat99}\nKataoka, J. et al. 1999, \\apj, 514, 138 \n\n\\bibitem[Kirk et al. (1998)]{kirketal98} \nKirk, J. G., Rieger, F. M., \\& Mastichiadis, A. 1998, \\aap, 333, 452 \n\n\\bibitem[Konopelko et al. (1999)]{ko99}\nKonopelko, A. K., Kirk, J. G., Stecker, F. W., \\& Mastichiadis, A. \n1999, \\apjl, 518, L13\n\n\\bibitem[Krennrich et al. (1999)]{kretal99}\nKrennrich, F. et al. 1999, \\apj, 511, 149\n\n\\bibitem[Maraschi, Ghisellini, \\& Celotti (1992)]{mgc92}\nMaraschi, L., Ghisellini, G., \\& Celotti, A. 1992, \\apjl, 397, L5 \n\n\\bibitem[Mastichiadis \\& Kirk (1995)]{mk95} \nMastichiadis, A., \\& Kirk, J. G. 1995, \\aap, 295, 613\n\n\\bibitem[Mastichiadis \\& Kirk (1997)]{mk97} \nMastichiadis, A., \\& Kirk, J. G. 1997, \\aap, 320, 19 \n\n\\bibitem[Mukherjee et al. (1997)]{muk97} \nMukherjee, R. et al. 1997, \\apj, 490, 116 \n\n\\bibitem[Robinson \\& Melrose (1984)]{rm84}\nRobinson, P. A., \\& Melrose, D. B. 1984, Australian J. Physics, 37, 675\n\n\\bibitem[Sikora, Begelman, \\& Rees (1994)]{sbr94}\nSikora, M., Begelman, M. C., \\& Rees, M. J. 1994, \\apj, 421, 153 \n\n\\bibitem[Takahashi et al. (1996)]{taka96} \nTakahashi, T., Tashiro, M., Madejski, G., Kubo, H., Kamae, T., \nKataoka, J., Kii, T., Makino, F., Makishima, K., \\& Yamasaki, N. 1996,\n\\apjl, 470, L89 \n\n\\bibitem[Ulrich, et al. (1997)]{umu97}\nUlrich, M.-H., Maraschi, L., \\& Urry, C. M. 1997, \\araa, 35, 445 \n\\end{thebibliography}\n\n\n\n\\clearpage\n \n% Figure 1\n%\\epsfig{file=fig1.ps,height=16cm,width=15cm} \n\\scalebox{0.9}[0.9]{\\includegraphics{fig1.ps}}\n\n\\figcaption{\nTime evolution of electron number spectra \nin the acceleration (upper panel) and cooling (lower panel)\nregions for $t = 0$ -- $R/c$ \nwith the equally spaced time span of $0.05 R/c$.\nThe spectra evolve from lower to upper curves in each panel.\n\\label{fig:el-e3-a}\n}\n\n\n% Figure 2\n% \\clearpage\n%\\epsfig{file=fig2.ps,height=15cm,width=15cm} \n\\scalebox{0.9}[0.9]{\\includegraphics{fig2.ps}}\n\n\\figcaption{\nTime evolution of the spectral energy distribution (SED) \nof photons emitted by electrons in the cooling region shown \nin Figure \\ref{fig:el-e3-a};\nSED is shown in the observer's frame.\nThe solid curves are for $t = 0$ -- $R/c$ (lower to upper curves)\nwith the equally spaced time span of $0.05 R/c$.\nSEDs when the simulation is continued after $R/c$ \nwith continuous injection and acceleration are also shown; \nthe dotted curve shows SED at $t = 2R/c$ \nand the dashed curve is SED at $t = 10R/c$, \nat which the radiation is already in a steady state. \n\\label{fig:ph-e3-a}\n}\n% wip .. Work-osaka3/Fig-e3-a/photon.wip %\n\n\n% Figure 3\n% \\clearpage\n%\\epsfig{file=fig3.ps,height=15cm,width=15cm} \n\\scalebox{0.9}[0.9]{\\includegraphics{fig3.ps}}\n\n\\figcaption{Light curves for 0.5 -- 2, 2 -- 10, and 10 -- 40 keV\nbands. The energy flux of soft X-rays is larger than\nthat of hard X-rays for $t \\lesssim 15 t_{\\rm acc}$.\n\\label{fig:lightcv-e3-a}\n}\n\n\n% Figure 4\n% \\clearpage\n%\\epsfig{file=fig4.ps,height=15cm,width=15cm} \n\\scalebox{0.8}[0.8]{\\includegraphics{fig4.ps}}\n\n\\figcaption{\nTime evolution of the energy densities of electrons and photons\nin the cooling region.\nHere the strength of magnetic field is fixed, $B = 0.1$ G.\nCurves are plotted for $t = 0$ -- $10 R/c$,\nwhere $R/(c {\\cal D}) = 5 \\times 10^4$ sec \nand $t_{\\rm acc}/{\\cal D} \\approx 2 \\times 10^3$ sec in the observer's frame.\nSolid curve: electrons, long-dashed: photons (synchrotron plus SSC),\ndotted: synchrotron photons, dash-dot-dot-dotted: SSC photons,\nand dash-dotted: magnetic field.\n\\label{fig:ene-e3}\n}\n\n\n% Figure 5\n% \\clearpage\n%\\epsfig{file=fig5.ps,height=15cm,width=15cm} \n\\scalebox{0.9}[0.9]{\\includegraphics{fig5.ps}}\n\n\\figcaption{\nTrajectory in the energy-flux and photon-index plane for\nvarious energy bands.\nThe evolution is calculated for $t = 0$ -- $10 R/c$.\nSymbols on the curves indicate the time from $t = 0$; \n$t = 0.5 R/c$ (squares), $R/c$ (asterisks), \n$2 R/c$ (circles), and $3 R/c$ (triangles).\n\\label{fig:alpha-e3}\n}\n\n\n% Figure 6\n% \\clearpage\n%\\epsfig{file=fig6.ps,height=18cm,width=15cm} \n\\scalebox{0.9}[0.9]{\\includegraphics{fig6.ps}}\n\n\\figcaption{\nElectron distribution in the cooling region at $t = 10 R/c$ for \nvarious values of the acceleration timescale.\nThe solid curve is for $\\xi = 5 \\times 10^2$,\nthe dashed curve for $\\xi = 10^3$,\nand the dotted curve for $\\xi = 2.5 \\times 10^2$. \n\\label{fig:el-e3-8-9}\n}\n\n\n\n% Figure 7\n% \\clearpage\n%\\epsfig{file=fig7.ps,height=18cm,width=15cm} \n\\scalebox{0.9}[0.9]{\\includegraphics{fig7.ps}}\n\n\\figcaption{\nSDEs at $t = 10 R/c$, corresponding \nto Figure \\ref{fig:el-e3-8-9}, for various values of \nthe acceleration timescale. The solid curve is for $\\xi = 5 \\times 10^2$,\nthe dashed curve for $\\xi = 10^3$,\nand the dotted curve for $\\xi = 2.5 \\times 10^2$. \n\\label{fig:ph-e3-8-9}\n}\n\n\n% Figure 8\n% \\clearpage\n%\\epsfig{file=fig8.ps,height=16cm,width=15cm} \n\\scalebox{0.9}[0.9]{\\includegraphics{fig8.ps}}\n\n\\figcaption{\nEvolution of SEDs for different values of $Q(\\gamma)$.\nThe solid curves are the evolution of SED with $Q(\\gamma)$ smaller\nby a factor 10 than that of Figure \\ref{fig:ph-e3-a} \nshown here by the dashed curves. \nThe curves are plotted for $t = 0$ -- $10 R/c$ with\nthe time interval $0.5 R/c$ and evolve from lower to upper.\n\\label{fig:ph-e4-e3}\n}\n\n\n% Figure 9\n% \\clearpage\n%\\epsfig{file=fig9.ps,height=16cm,width=15cm} \n\\scalebox{0.9}[0.9]{\\includegraphics{fig9.ps}}\n\n\\figcaption{\nSED at $t = 10 R/c$ for different values of $B$.\nThe solid curve is SED for $B = 0.1$ G (the same curve as shown\nin Figure \\ref{fig:ph-e3-a}),\nthe dotted curve is SED for $B = 0.05$ G,\nand the dashed curve is for $B = 0.5$ G.\n\\label{fig:light-b05-g2}\n}\n\n% Figure 10\n% \\clearpage\n%\\epsfig{file=fig10.ps,height=18cm,width=14cm} \n\\scalebox{0.8}[0.8]{\\includegraphics{fig10.ps}}\n\n\\figcaption{\nThe response of light curves to the termination of acceleration. \nAcceleration and injection are terminated at $4 R/c$ \nor $2 \\times 10^5$ sec in the observer's frame,\nshown by the vertical dash-dotted line.\nParameters are the same as in Figure \\ref{fig:el-e3-a}. \n\\label{fig:light-e3-c}\n}\n\n\n% Figure 11\n% \\clearpage\n%\\epsfig{file=fig11.ps,height=18cm,width=15cm} \n\\scalebox{0.8}[0.8]{\\includegraphics{fig11.ps}}\n\n\\figcaption{\nLight curves for $t = 0 $ -- $5 R/c$ including a flare which occurs\nduring $t = R/c$ and $2 R/c$, indicated by the vertical dash-dotted lines. \nThe fluxes are in units of ergs cm$^{-2}$ sec$^{-1}$.\n\\label{fig:light-flare}\n}\n\n\n\n% Figure 12\n% \\clearpage\n%\\epsfig{file=fig12.ps,height=15cm,width=15cm} \n\\scalebox{0.8}[0.8]{\\includegraphics{fig12.ps}}\n\n\\figcaption{\nTime evolution of the energy flux and the photon index associated with \nthe flare shown in Figure \\ref{fig:light-flare}; \nthe trajectories start from a steady state (shown by open circles)\nand rotate clockwise. The evolution is calculated until $t = 10 R/c$.\n\\label{fig:alpha-flare}\n}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002137.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[Blandford \\& Coppi (1990)]{bc90} \nBlandford, R. D., \\& Coppi, P. S. 1990, \\mnras, 245, 453 \n\n\\bibitem[Blandford \\& Eichler (1987)]{be87} \nBlandford, R.., \\& Eichler, D. 1987, Phys. Rep., 154, 1 \n\n\\bibitem[Blandford \\& K\\\"{o}nigl (1979)]{bk79} \nBlandford, R. D., \\& K\\\"{o}nigle, A. 1979, \\apj, 232,34 \n\n\\bibitem[Blandford \\& Rees (1978)]{br78} \nBlandford, R. D., \\& Rees, M. J. 1978, \nin Pittsburgh Conf. on BL Lac Objects, ed. A. M. Wolfe \n(Pittsburgh: Univ. Pittsburgh Press), 328\n\n\\bibitem[Catanese et al. (1997)]{cat97}\nCatanese, M. et al. 1997, \\apjl, 487, 143 \n\n\\bibitem[Chiaberge \\& Ghisellini (1999)]{cg99}\nChiaberge, M., \\& Ghisellini, G. 1999, \\mnras, 306, 551\n\n\\bibitem[Crusius \\& Schlickeiser (1986)]{cs86}\nCrusius, A., \\& Schlickeiser, R. 1986, A\\&A, 164, L16\n\n\\bibitem[Druly (1983)]{druly}\nDruly, L. O.' C. 1983, Rep. Prog. Phys., 46, 973 \n\n\\bibitem[Gaidos et al. (1996)]{gaid96}\nGaidos, J. A. et al. 1996, \\nat, 383, 319 \n\n\\bibitem[Inoue \\& Takahara (1996)]{it96} \nInoue, S., \\& Takahara, F. 1996, \\apj, 463, 555 \n\n\\bibitem[Jones (1968)]{jones68}\nJones, F. C. 1968, Physical Review, 167, 1159 \n\n\\bibitem[Kataoka et al. (1999)]{kat99}\nKataoka, J. et al. 1999, \\apj, 514, 138 \n\n\\bibitem[Kirk et al. (1998)]{kirketal98} \nKirk, J. G., Rieger, F. M., \\& Mastichiadis, A. 1998, \\aap, 333, 452 \n\n\\bibitem[Konopelko et al. (1999)]{ko99}\nKonopelko, A. K., Kirk, J. G., Stecker, F. W., \\& Mastichiadis, A. \n1999, \\apjl, 518, L13\n\n\\bibitem[Krennrich et al. (1999)]{kretal99}\nKrennrich, F. et al. 1999, \\apj, 511, 149\n\n\\bibitem[Maraschi, Ghisellini, \\& Celotti (1992)]{mgc92}\nMaraschi, L., Ghisellini, G., \\& Celotti, A. 1992, \\apjl, 397, L5 \n\n\\bibitem[Mastichiadis \\& Kirk (1995)]{mk95} \nMastichiadis, A., \\& Kirk, J. G. 1995, \\aap, 295, 613\n\n\\bibitem[Mastichiadis \\& Kirk (1997)]{mk97} \nMastichiadis, A., \\& Kirk, J. G. 1997, \\aap, 320, 19 \n\n\\bibitem[Mukherjee et al. (1997)]{muk97} \nMukherjee, R. et al. 1997, \\apj, 490, 116 \n\n\\bibitem[Robinson \\& Melrose (1984)]{rm84}\nRobinson, P. A., \\& Melrose, D. B. 1984, Australian J. Physics, 37, 675\n\n\\bibitem[Sikora, Begelman, \\& Rees (1994)]{sbr94}\nSikora, M., Begelman, M. C., \\& Rees, M. J. 1994, \\apj, 421, 153 \n\n\\bibitem[Takahashi et al. (1996)]{taka96} \nTakahashi, T., Tashiro, M., Madejski, G., Kubo, H., Kamae, T., \nKataoka, J., Kii, T., Makino, F., Makishima, K., \\& Yamasaki, N. 1996,\n\\apjl, 470, L89 \n\n\\bibitem[Ulrich, et al. (1997)]{umu97}\nUlrich, M.-H., Maraschi, L., \\& Urry, C. M. 1997, \\araa, 35, 445 \n\\end{thebibliography}"
}
] |
astro-ph0002138
|
Discovery of high proper motion ancient white dwarfs:\\ nearby massive compact halo objects?
|
[
{
"author": "Rodrigo Ibata"
}
] |
We present the discovery and spectroscopic identification of two very high proper motion ancient white dwarf stars, found in a systematic proper motion survey. Their kinematics and apparent magnitude clearly indicate that they are halo members, while their optical spectra are almost identical to the recently identified cool Halo white dwarf WD0346+246. Canonical stellar halo models predict a white dwarf volume density of two orders of magnitude less than the $\rho \sim 7\times 10^{-4} \msun\pc^{-3}$ inferred from this survey. With the caveat that the sample size is very small, it appears that a significant fraction, $\sim 10$\%, of the local dark matter halo is in the form of very old, cool, white dwarfs.
|
[
{
"name": "WD_Halo.tex",
"string": "%% AASTeX v5.0 LaTeX 2e\n\n\\documentclass[preprint2]{aastex}\n\\usepackage{graphicx}\n%\\usepackage[psfig]\n\n%% preprint produces a one-column, single-spaced document:\n\n% \\documentclass[preprint]{aastex}\n\n%% preprint2 produces a double-column, single-spaced document:\n\n% \\documentclass[preprint2]{aastex}\n\n\\def\\ltsima{$\\; \\buildrel < \\over \\sim \\;$}\n\\def\\simlt{\\lower.5ex\\hbox{\\ltsima}}\n\\def\\gtsima{$\\; \\buildrel > \\over \\sim \\;$}\n\\def\\simgt{\\lower.5ex\\hbox{\\gtsima}}\n%\n% MATH FUNCTIONS:\n\\def\\erf{\\mathop{\\rm erf}\\nolimits} %error function\n\\def\\sech{ \\mathop{\\rm sech}\\nolimits} %hyperbolic sec\n\\def\\csch{ \\mathop{\\rm csch}\\nolimits} %hyperbolic csc\n\\def\\arcsinh{\\mathop{\\rm arcsinh}\\nolimits} %arc hyperbolic sin\n\\def\\arccosh{\\mathop{\\rm arccosh}\\nolimits} %arc hyperbolic cos\n\\def\\arctanh{\\mathop{\\rm arctanh}\\nolimits} %arc hyperbolic tan\n\\def\\arccoth{\\mathop{\\rm arccoth}\\nolimits} %arc hyperbolic cot\n\\def\\arcsech{\\mathop{\\rm arcsech}\\nolimits} %arc hyperbolic sec\n\\def\\arccsch{\\mathop{\\rm arccsch}\\nolimits} %arc hyperbolic csc\n\\def\\arccot{\\mathop{\\rm arccot}\\nolimits} %arc cot\n\\def\\arcsec{\\mathop{\\rm arcsec}\\nolimits} %arc sec\n\\def\\arccsc{\\mathop{\\rm arccsc}\\nolimits} %arc csc\n\\def\\ylm{\\mathop{\\rm Y}_l^m\\nolimits} %spherical harmonic\n\\def\\ylmp{\\mathop{\\rm Y}_{l'}^{m'}\\nolimits} %spherical harmonic primed\n\\def\\real{\\Re e} %real part\n\\def\\imag{\\Im m} %imaginary part\n\n% UNITS:\n\\def\\km{{\\rm\\,km}}\n\\def\\kms{{\\rm\\,km\\,s^{-1}}}\n\\def\\mas{{\\rm\\,mas}}\n\\def\\masyr{{\\rm\\,mas/yr}}\n\\def\\kpc{{\\rm\\,kpc}}\n\\def\\mpc{{\\rm\\,Mpc}}\n\\def\\msun{{\\rm\\,M_\\odot}}\n\\def\\lsun{{\\rm\\,L_\\odot}}\n\\def\\rsun{{\\rm\\,R_\\odot}}\n\\def\\pc{{\\rm\\,pc}}\n\\def\\cm{{\\rm\\,cm}}\n\\def\\yr{{\\rm\\,yr}}\n\\def\\au{{\\rm\\,AU}}\n\\def\\g{{\\rm\\,g}}\n\\def\\om{\\Omega_0}\n\\def \\ca {{\\it ca.\\/}}\n\\def \\r {r$^{1/4}$ }\n\\def \\magnitude {$^{\\rm m}$}\n\\def\\kr{${\\cal K}_r$}\n\\def\\kz{${\\cal K}_z$}\n\\def\\kzz{${\\cal K}_z(z)$}\n\\def\\mss{{\\rm M}_\\odot \\rm pc^{-2}}\n\\def\\msss{{\\rm M}_\\odot \\rm pc^{-3}}\n\\newcommand{\\fmmm}[1]{\\mbox{$#1$}}\n\\newcommand{\\scnd}{\\mbox{\\fmmm{''}\\hskip-0.3em .}}\n\\newcommand{\\scnp}{\\mbox{\\fmmm{''}}}\n\\newcommand{\\mcnd}{\\mbox{\\fmmm{'}\\hskip-0.3em .}}\n\\def\\Aa{\\; \\buildrel \\circ \\over {\\rm A}}\n\\def\\AA{$\\; \\buildrel \\circ \\over {\\rm A}$}\n\\def\\yr{{\\rm yr}}\n\n\n% MISCELLANEOUS:\n% angles in degrees\n\\def\\deg{^\\circ}\n%\\degg produces degree symbol so that 3\\sec5 produces 3.`5 with the degree\n%symbol and the period aligned.\n\\def\\degg{\\hbox{$\\null^\\circ$\\hskip-3pt .}}\n%\\sec produces arcsec symbol so that 3\\sec5 produces 3.\"5 with the second\n%symbol and the period aligned.\n\\def\\sec{\\hbox{\"\\hskip-3pt .}}\n\\def\\half{{\\scriptstyle{1\\over2}}}\n%\\s produces tilde in mathmode or horizontal mode.\n\\def\\s{\\ifmmode \\widetilde \\else \\~\\fi}\n\\def\\={\\overline}\n\\def\\scre{{\\cal E}}\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\def\\larrow{\\leftarrow}\n\\def\\rarrow{\\rightarrow}\n\\def\\llangle{\\langle\\langle}\n\\def\\rrangle{\\rangle\\rangle}\n\\def\\etal{{\\it et al.\\ }}\n\\def\\cf{{\\it cf.\\ }}\n\\def\\eg{{ e.g.,\\ }}\n\\def\\ie{{ i.e.,\\ }}\n%\\lta and \\gta produce > and < signs with twiddle underneath\n\\def\\lta{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}}\n\\def\\gta{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}}\n%\\Dt and \\dt put Newton's notation dots above upper and lower case chars\n\\def\\Dt{\\spose{\\raise 1.5ex\\hbox{\\hskip3pt$\\mathchar\"201$}}}\t% upper case\n\\def\\dt{\\spose{\\raise 1.0ex\\hbox{\\hskip2pt$\\mathchar\"201$}}}\t% lower case\n\\def\\del{\\nabla}\n\\def\\delv{\\bb\\nabla}\n\\def\\r{${\\rm r^{1/4}}$}\n\n\\def\\jla{J_{\\lambda}}\n\\def\\jmu{J_{\\mu}}\n\\def\\jnu{J_{\\nu}}\n\\def\\pomega{\\varpi}\n\\def\\sigla{\\sigma_{\\lambda}}\n\\def\\sigmu{\\sigma_{\\mu}}\n\\def\\signu{\\sigma_{\\nu}}\n\\def\\dotsfill{\\leaders\\hbox to 1em{\\hss.\\hss}\\hfill}\n\\def\\sun{\\odot}\n\\def\\earth{\\oplus}\n\n\\def\\Gyr{{\\rm\\,Gyr}}\n\\def\\kmsd{{\\rm\\,km/s/degree}}\n\n\\def\\Rod#1{\\noindent{\\bf[$\\heartsuit$ #1]}}\n\\def\\Mike#1{\\noindent{\\bf[$\\clubsuit$ #1]}}\n\\def\\Oli#1{\\noindent{\\bf[$\\spadesuit$ #1]}}\n\\def\\Ralf#1{\\noindent{\\bf[$\\diamontsuit$ #1]}}\n\n\n\n\n\n%% You can insert a short comment on the title page using the command below.\n\n\\slugcomment{Submitted to ApJ Letters}\n\n%% If you wish, you may supply running head information, although\n%% this information may be modified by the editorial offices.\n%% The left head contains a list of authors,\n%% usually a maximum of three (otherwise use et al.). The right\n%% head is a modified title of up to roughly 44 characters. Running heads\n%% will not print in the manuscript style.\n\n\\shorttitle{Ibata et al.}\n\\shortauthors{Halo white dwarfs}\n\n\n\\begin{document}\n\n\\title{Discovery of high proper motion ancient white dwarfs:\\\\\nnearby massive compact halo objects?}\n\n\n%% Use \\author, \\affil, and the \\and command to format\n%% author and affiliation information.\n%% Note that \\email has replaced the old \\authoremail command\n%% from AASTeX v4.0. You can use \\email to mark an email address\n%% anywhere in the paper, not just in the front matter.\n%% As in the title, you can use \\\\ to force line breaks.\n\n\\author{Rodrigo Ibata}\n\\affil{Max-Plank Institut f\\\"ur Astronomie, \nK\\\"onigstuhl 17, D--69117 Heidelberg, Germany}\n\\email{ribata@mpia-hd.mpg.de}\n\n\\author{Michael Irwin}\n\\affil{Institute of Astronomy, Madingley Road, Cambridge, CB3 0HA, U.K.}\n\\email{mike@ast.cam.ac.uk}\n\n\\author{Olivier Bienaym\\'e}\n\\affil{Observatoire de Strasbourg, 11 rue de l'Universit\\'e,\nStrasbourg, 67000 France.}\n\\email{bienayme@newb6.u-strasbg.fr}\n\n\\author{Ralf Scholz}\n\\affil{Astrophysikalisches Institut Potsdam, An der Sternwarte 16,\nD--14482 Potsdam, Germany}\n\\email{rdscholz@aip.de}\n\n\\and\n\n\\author{Jean Guibert}\n\\affil{Centre d'Analyse des Images de l'INSU and Observatoire de Paris\n(DASGAL/UMR-8633), 77 avenue Denfert-Rochereau, F-75014 Paris, France}\n\\email{Jean.Guibert@obspm.fr}\n\n%% Notice that each of these authors has alternate affiliations, which\n%% are identified by the \\altaffilmark after each name. Specify alternate\n%% affiliation information with \\altaffiltext, with one command per each\n%% affiliation.\n\n%% Mark off your abstract in the ``abstract'' environment. In the manuscript\n%% style, abstract will output a Received/Accepted line after the\n%% title and affiliation information. No date will appear since the author\n%% does not have this information. The dates will be filled in by the\n%% editorial office after submission.\n\n\\begin{abstract}\nWe present the discovery and spectroscopic identification of two very high\nproper motion ancient white dwarf stars, found in a systematic proper motion\nsurvey. Their kinematics and apparent magnitude clearly indicate that they\nare halo members, while their optical spectra are almost identical to the\nrecently identified cool Halo white dwarf WD0346+246. Canonical stellar\nhalo models predict a white dwarf volume density of two orders of magnitude\nless than the $\\rho \\sim 7\\times 10^{-4} \\msun\\pc^{-3}$ inferred from this\nsurvey. With the caveat that the sample size is very small, it appears that\na significant fraction, $\\sim 10$\\%, of the local dark matter halo is in the\nform of very old, cool, white dwarfs.\n\\end{abstract}\n\n\\keywords{Galaxy: halo -- solar neighbourhood -- dark matter -- stars: white \ndwarfs}\n\n\\section{Introduction}\n\nUnless our present understanding of gravitation is incorrect, the Milky Way\nand most other galaxies, possess a halo of dark, or barely luminous, matter\nthat extends well beyond the visible boundaries of the galaxy. Present\ncosmological constraints strongly favour non-baryonic dark matter, though\nthe problem is complicated by the possibility that there may be several\ntypes of dark matter; for instance, galactic dark matter may have little to\ndo with dark matter in galaxy clusters or on larger scales \\citet{bosma}.\nIn our own Galaxy, this Halo component appears to extend out to at least 50\nkpc as traced by the Magellanic Clouds \\citep{lin}, and may well continue to\nbeyond the orbit of Leo~I at $\\sim 200\\kpc$ distance \\citep{zaritsky}.\nGiven the large uncertainty in the extent of these structures, their total\nmass is poorly constrained, but even within 50 kpc it is clear that they\nmust contain orders of magnitude more mass than the clearly visible baryons\nin the form of stars and gas.\n\nOne of the few direct constraints on the mass distribution of the\nconstituent particles of galactic halos comes from the Magellanic Cloud\nmicrolensing experiments \\citep{alcock97, afonso}. The most recent report\nof the detection rate of microlensing events \\citep{alcock00} supports a\nsimple model where approximately 20\\% of the Milky Way halo is made up of\nobjects of $\\sim 0.5\\msun$, consistent with the result of \\citet{afonso}.\nThough the halo fraction and object mass are model dependent, the main\nuncertainty arises from the possibility that the LMC may possess a\nsubstantial (dynamically hot) stellar halo of its own. Given the absence of\nevidence for this latter possibility, the microlensing conclusions must be\ntaken seriously. These MACHOs are most likely situated approximately\nhalf-way to the LMC, where the optical depth to microlensing is highest.\nHowever, unless the MACHOs were effectively decoupled from nucleosynthesis\n(as would presumably be the case for primordial black holes), it is unlikely\nthat MACHOs fill galactic halos entirely, as this would break\nnucleosynthesis constraints.\n\nApart from ancient white dwarfs (WDs), all stellar MACHO candidates can be\nsafely ruled out. Ancient WDs, which have stellar masses in the range\nmeasured by the MACHO experiment ($0.1$--$1.0 \\msun$), are not yet ruled out\nby direct starcount observations, but are difficult to envisage as a MACHO\npopulation due to several indirect constraints (see e.g., Fields, Freese \\&\nGraff 1998; Graff \\etal\\ 1999), including most importantly chemical\nenrichment of the early Galaxy \\citep{gibson}, though for a possible\nwork-around of this problem, see \\citet{chabrier}. This renewed interest in\nancient Halo WDs is mainly due to a theoretical reappraisal of the WD\ncooling function. New models with a self-consistent treatment of radiation\ntransfer and the inclusion of molecular hydrogen opacity\n\\citep{hansen,saumon} drastically change the predicted colours and\nmagnitudes of the oldest, and hence coolest, WDs. In particular, hydrogen\natmosphere (DA) WDs with ages $\\simgt 10\\Gyr$ have depressed red and NIR\nflux; contrary to previous expectations they become bluer in, for instance,\n${\\rm V-I}$, with age.\n\n\\citet{ibata} recently presented a proper motion analysis using two epochs\nof I-band imaging data in the Hubble Deep Field. They identified a small\nsample 2--5 faint, and relatively blue compact sources, that appear to move\nwith respect to the numerous background galaxies. The colours, motions, and\nnumber of these sources are consistent with the hypothesis that they are\nmembers of a numerous halo population of ancient WDs, with a spectral energy\ndistribution similar to that predicted by the Hansen models. The local mass\ndensity of this population appears similar to that of the ``standard'' halo\nmodel used by the MACHO and EROS collaborations \\citet{alcock97,\npalanque-delabrouille}. Unfortunately, the measured proper motions are at\nthe detection limit, and they are exceedingly faint (${\\rm V \\sim 29}$), so\nspectroscopic confirmation is currently impossible.\n\nStriking confirmation that the new WD models are more appropriate has been\ngiven by \\citet{hodgkin}. Their spectrum of WD0346+246 shows a large\nsupression of the NIR flux relative to a black-body model fit to the visible\nradiation, as predicted by \\citet{hansen} for ancient DA WDs. Furthermore,\nthe proper motion of WD0346+246 and the measured parallax, indicate that it\nis most likely a Halo member.\n\nTherefore, Halo WDs do seem to exist and the DA subset have bluer\ncolours than originally expected (WD0346+246 has ${\\rm V-I=1.52}$). The\nnext important question to address is the local mass density of this\npopulation, in particular, are they present in sufficient numbers to\ncontribute sgnificantly to the proposed Halo of MACHOs?\n\n\n\\section{Survey}\n\nTo detect the nearby counterparts of the population of WD MACHOs tentatively\ndetected by \\citet{ibata}, we have undertaken complementary wide field\nphotographic plate surveys of very high proper motion ($>1\\scnp/\\yr=$VHPM)\nstars. With a survey limit $\\sim 10$ magnitudes brighter than the HDF\nlimit, we need to cover a field one million times larger than the $1.4\\times\n10^{-3} \\Box^\\circ$ WFPC2 field to probe the same Halo volume. The expected\nproper motions can be several $\\scnp/\\yr$, and candidates will be\npredominantly at the faint limit of the plates, where existing catalogues\n(cf. LHS catalog, Luyten 1979) are heavily incomplete. Faced with the\ndifficulty of reliably identifying VHPM stars among thousands of potential\ncandidates, we have investigated three independent techniques to cross-check\nresults. These analyses are based on different combinations of existing\nplate material and probe different aspects of the problem; survey 1:- uses\nselected pairs of appropriate UK Schmidt Telescope (UKST) ${\\rm B_J}$ plates\nwith short epoch differences for sensitivity to ``blue'' VHPM stars; survey\n2:- uses standard UKST ${\\rm B_J}$ and R sky survey plate pairs and has the\npotential to probe all of the southern sky; and survey 3:- includes an extra\nthird epoch ESO-SRC survey R plate to enable searching to deeper limits\nfor $\\delta < -17^\\circ$.\n\nAll of the southern sky has been observed by the UKST in both blue (${\\rm\nB_J}$) and red (R) passbands, and the designated survey quality plates for\nmore than half of this area have been processed by the Automatic Plate\nMeasuring (APM) facility \\citep{kibblewhite}. This forms the basis for\npilot studies using the three survey methods. The total error in measuring\nthe relative proper motion is generally $<< 0.1\\scnp/\\yr$, negligible in the\ncontext of the survey.\n\n\\subsection{Survey 1}\n\nWhile the generic UKST ${\\rm B_J}$, R survey material is an excellent\nresource for locating objects of average colour (g--k type) and modest\nproper motions ($\\approx0.5-2.0\\scnp/\\yr$), it may not be ideal for the\ndetection of ancient Halo WDs given the colour uncertainty and the generally\nlarge epoch difference, 10--15~years. Consequently for survey~1 we have\nbased proper motion detection on only blue passband (${\\rm B_J}$) UKST\nplates with a shorter epoch difference 1$<$ T $<$ 10 years, to enhance the\nsensitivity to the oldest WDs. As would be expected, the available UKST\narchival non--survey grade plates are a heterogeneous mixture of plate\nqualities and epochs. With the help of Sue Tritton of the UKST Unit, we\nselected 21 deep ``b''-grade ${\\rm B_J}$ southern survey plates for\nscanning. This sample was chosen in fields with extant APM on-line UKST\n${\\rm B_J}$ and OR catalogue data.\n\nThe search algorithm works as follows: first the overall plate-to-plate\ntransformation is derived using all objects on the plates that match\n(iteratively) within $2\\scnp$. The extra ``b''-grade ${\\rm B_J}$ plate data\nis then matched to the exisiting survey ${\\rm B_J}$,R catalogue. Objects\nmatching within a radius of $2\\scnp$ for our purposes are taken to have\nnegligible proper motion and are discarded. This leaves a catalog of what\nare mostly spurious detections (noise, diffraction spikes, extended object\ndeblending problems, close object deblending problems, incompleteness\nproblems, etc.), among which there is a tiny proportion of actual VHPM\nobjects. To minimise contamination by spurious detections, unmatched\nobjects were only considered as possible HPM objects if they were stellar in\nappearance, and brighter than ${\\rm B_J} = 22$ on both blue plates.\nRemaining unmatched objects were then considered to be possible matches if\nthey were within a search radius of $30\\scnp$.\n\nIn this way we obtained a provisional list of 1426 candidates. After visual\nexamination of the APM object finding charts, DSS images of the field (if\navailable), and visual comparision with the R-band survey plates, we made a\nsub-selection of 101 candidate VHPM stars for followup observations. The\nmajority of the 1325 rejected candidates were from situations where there\nwas a clear error, for example, a detection on the APM plate scan which did\nnot appear on the DSS scan of the same plate, detections near large galaxies\nor bright stars. We note that some of the rejects at this stage were based\non less secure criteria having, for example, suspiciously elongated profiles\non the APM finding charts, or apparently different magnitudes after allowing\nfor the different plate depth between epochs. Unfortunately, the probity of\nrejection based on these last criteria is difficult to quantify,\nparticularly near the plate limits. Two plates proved to be unusable, giving\na total area of 19 fields in this survey.\n\n\\subsection{Survey 2}\n\nThis difficulty in probing to near the plate limits lead to our decision to\nundertake the 2nd complementary survey to shallower depths, using just the\nalready available APM online catalogue ${\\rm B_J}$ and R plate data. The\nresults from the first search technique plus the properties of the Halo WD\nWD0346+246 were used to fine tune the selection criteria. In a similar\nmanner to survey~1, brighter candidates, stellar in appearance, with 12 $<$\nR $<$ 19.5 and ${\\rm B_J} <$ 21.5, and with possible PM $\\simgt 1\\scnp/\\yr$,\nwere selected from a random sample of 24 equatorial region fields. The\nbright limit was imposed because on deep UKST sky survey plates images\nbrighter than this are heavily saturated, show strong diffraction spikes,\nand are imbedded in large reflection halos, making both accurate photometry\nand astrometry difficult to achieve. Equatorial fields were chosen because\non average they have much shorter epoch differences, $\\sim 5$ years, between\nthe R and ${\\rm B_J}$ survey plates compared to the so-called Southern\nsurvey plates, $\\delta \\le -20^\\circ$, where the average epoch difference is\n14 years.\n\nDue to storage limitations at the time of catalogue construction the extant\nAPM online catalogue recorded data on the coordinate system of the reference\nR plate and only recorded separate coordinate information for the ${\\rm\nB_J}$ plate data if there are no matches within $5\\scnp$, giving a lower\nlimit to the proper motions that can be observed. Of the 24 selected\nequatorial fields, 11 had epoch differences of 3 years or less, and although\nprocessed were not used in the sample. The remaining 13 fields had epoch\ndifferences between 4--9 \\yr\\ and produced a total of 87 candidates. After\ncareful visual inspection of the online catalogue data 36 candidates were\nleft. Finally, the remaining candidates were cross-checked with DSS images\nand visually inspected on first epoch (1950s) Palomar Sky Survey plates to\ncheck the reality of the candidate and the proper motion. This left a total\nof 9 guaranteed VHPM candidates.\n\n\\subsection{Survey 3}\n\nThe third strategy is based on a three epoch plate analysis from the UKST\nAPM on-line catalogue and ESO-R survey plates scanned by the MAMA (Guibert\net al. 1984, see also http://dsmama.obspm.fr) and is more sensitive to\nbright, red, extreme HPM objects. The survey covers 24 Schmidt plate fields\nat high Galactic latitude, selected according to the high-grade image\nquality of plates and with epoch differences between 3--15 \\yr. Of these, 4\nfields are in common with survey~1, so the effective additional area\nsurveyed is 20 fields.\n\nUnlike the APM candidate selection which used the $x$--$y$ pixel coordinates\nof the scanned plates, the ESO-R plate MAMA data matching used celestial\ncoordinates based on Tycho catalogue astrometric solutions \\citep{robichon}.\nVHPM candidates were selected by requiring a consistent alignement of\ncelestial coordinates at the three epochs. The candidates were selected to\nhave similar R magnitudes on UKST-R and ESO-R plates. Two regimes were\nconsidered: for ${\\rm R < 18}$, PMs of $\\mu <10\\scnp/\\yr$ were sought, while\nfor ${\\rm R > 18}$ a PM upper limit of $\\mu < 1.5\\scnp/\\yr$ was imposed.\nThe 417 candidates thus detected were inspected visually on DSS-I and II\nimages (when available) and also ESO-R plates, from which 20 objects were\nselected for observation, corresponding to the bluest detections (${\\rm\nB_J-R} < 2$) with the highest PM.\n\n\n\\section{Observations}\n\nAll of the 101 candidate VHPM stars detected in survey~1 were imaged with\nEFOSC2 on the ESO~3.6m telescope on the night of 1999 October 1. Short\ng-band exposures (to match the $\\rm B_J$ passband) were obtained centered on\nthe discovery positions. Of the 101 candidates; 72 detections were found to\nbe due to incompleteness of the photographic plates; 20 objects were\nconfirmed to be genuine VHPM stars, while a further 9 candidates were\nconsistent with objects that had moved out of the $5'$ field of view of the\ninstrument (that is, possibly amazingly high PM objects, but most likely\njust due to noise).\n\nOf the 20 candidates from survey~3, direct CCD exposures revealed that 18\nwere real moving stars with $\\mu<1\\scnp/\\yr$, while the 2 most extreme PM\ncandidates were rejected being in fact due to spurious alignments of 3\ndifferent stars, each one appearing alone on each plate, an expected\noccurence close to the detection limit of plates.\n\nOn the nights of 1999 October 2 and 3, four of the 20 confirmed candidates\nfrom survey~1 were observed with the spectroscopic mode of EFOSC2. Very high\nwinds limited our choice of targets, while the poor seeing conditions made\nus choose to set the slit width to $2\\scnp$, reducing the spectral\nresolution. All objects were first observed with grating \\#1 (3185\\AA\\ to\n10940\\AA), to obtain an identification spectrum, with follow-up with the\nhigher resolution gratings \\#9 (4700\\AA\\ to 6770\\AA), and \\#12 (6015\\AA\\ to\n10320\\AA).\n\nFinally, the spectrum of the most extreme high proper motion star of\nsurvey~2, in UKST field f821, was kindly observed for us by L.\nStorrie-Lombardi \\& C. Peroux at the CTIO 4m on the night of 1999 October 13\nusing the R-C spectrograph with the Loral 3k CCD and the KPGL-2 grating covering\nthe wavelength range 3350\\AA\\ to 9400\\AA, sampled at 2\\AA /pixel.\n\n\\section{Results}\n\nThe full results of these surveys will be presented in a forthcoming\npaper. Here we focus on two VHPM stars discovered in surveys~1 and 2.\n\nIn the left panel of Figure~1, we display the flux-calibrated low resolution\nspectrum of the highest proper motion star in survey~1, F351-50, a\nfeatureless WD with ${\\rm B_J=19.76}$, ${\\rm B_J-R=1.65}$, ${\\rm R-I= 0.31}$\n(I-band photometry from DENIS) and $\\mu=2.33\\scnp/\\yr$ at PA $130.1^\\circ$,\nlocated at $\\alpha_{\\rm J2000}=0$ 45 17.78, $\\delta_{\\rm J2000}=-33$ 29\n10.0, epoch 1987.88 . The upper panel of Figure~2 acts as a finder and also\ndemonstrates the high proper motion of the object. The absence of distinct\nabsorption lines and the colour of F351-50 are consistent with it being a\ncool DA WD. (Unfortunately, this absence of spectral lines makes it\nimpossible to measure a radial velocity for this object, even from the\nhigher spectral resolution data). Also superimposed in Figure~1 is a\n$3500$~K black body model, which provides a good fit to the visual region of\nthe spectrum with $\\lambda < 6500\\Aa$. It is readily apparent that there is\na substantial depression of the flux redward of $6500\\Aa$ in this object,\nprecisely as was originally seen in the now confirmed ancient halo WD star\nWD0346+246 (Hambly \\etal\\ 1997, their Figure~3).\n\nWhat Galactic population does this object belong to? Lacking a parallax, we\nmay still estimate its distance from other constraints. First, the Universe\nis not old enough for $0.5\\msun$ DA WDs to have cooled fainter than ${\\rm\nM_V = 18}$ \\citep{hansen} so F351-50 must be located at a distance $d > 15\n\\pc$. At this distance its total space velocity with respect to the Sun is\n$v > 170\\kms$, which clearly indicates that it is not a thin or thick disk\nmember. The only remaining alternative is that it is a Halo object.\nAssuming an upper limit to the space motion of $300\\kms$, its distance is\nconstrained to be closer than $26.5\\pc$ (this neglects the radial velocity\ncomponent). Finally, assuming, for now, a similar absolute magnitude to\nWD0346+246 places it at a distance of $\\sim 25\\pc$. At that distance the\nexpected reflex solar motion for a stationary Halo object is\n$\\mu=1.95\\scnp/\\yr$ at PA $145.2^\\circ$, in good agreement with the observed\nmotion.\n\nGiven the success of this initial ${\\rm B_J}$ plate survey and the similar\ncolour to WD0346+246, we subsequently checked whether the result was\nreproduced in survey~2, which used the extant APM catalog scans. The\nspectrum of F821-07, the most extreme HPM star found in survey~2 (${\\rm\nB_J=18.91}$, ${\\rm B_J-R=1.16}$, $\\mu=1.72\\scnp/\\yr$ at PA $201.2^\\circ$,\n$\\alpha_{\\rm J2000}=23$ 19 09.96, $\\delta_{\\rm J2000}=-6$ 12 32.5, epoch\n1988.92), is shown in the right hand panel of Figure~1 together with finding\ncharts and demonstrable high proper motion in the lower panel of Figure~2.\nF821-07 also has a similar spectral shape to WD0346+246 \\citep{hodgkin},\nshowing it to be another featureless WD star, and the very large proper\nmotion, $\\mu=1.72\\scnp/\\yr$ implies Halo membership for the same reasons as\nstated previously for F351-50.\n\nInterestingly, after careful inspection of the LHS catalogue it was clear\nthat F821-07 had the same proper motion within measurement errors, and was\nwithin 1~arcmin of the position of, the previously known HPM object LHS~542.\nF351-50 has no plausible counterpart in the LHS catalogue and remains a new\ndiscovery. As we will show in a forthcoming paper, the population of known\nnearby white dwarfs contains a previously unnoticed ancient Halo population,\nand LHS~542, in particular, is an excellent candidate for a cool Halo WD.\nFurthermore, the known parallax of LHS~542 implies a distance of $31 \\pm 3\n\\pc$ \\citep{leggett} and hence a high space motion typical of Halo objects.\n\n\n\\section{Conclusions}\n\nNo ancient WDs were found in survey 3. This is partly due to the added\nincompleteness from the requirement that a star be detected, and be\nclassified as stellar, on 3, rather than 2, plates. At each epoch, for $R\n\\sim 19$, the probability of detection and correct classification is $\\sim\n85$\\%. For rapidly moving sources, there is also a $\\sim 5$\\% chance that\nthey will randomly be situated close (within $3\\scnp$) to the detection\nisophote of a stationary source, and so not be detected as a point source.\nWe estimate the completeness of surveys~1 and 2 is, respectively, $\\sim\n65$\\% and $\\sim 80$\\%, while survey~3 is $\\sim 50$\\% complete. Survey~3 is\nalso not sensitive to faint ${\\rm R>18}$, high PM $\\mu>1.5\\scnp/\\yr$\nstars: one of the two detected HPM stars is outside of the selection limit\nof this survey. This implies that the efficiency of the detection is close\nto half the efficiency of the first two strategies, reducing the\ncompleteness of survey~3 to $\\sim 25$\\%.\n\nDiscounting the overlapping regions between adjacent plates, and the area\noccupied by bright stars and unusable regions of the plates, surveys 1, 2\nand 3 have, respectively, areas of $551\\Box^{\\circ}$, $377\\Box^{\\circ}$, and\n$506\\Box^{\\circ}$, giving a total effective area of $\\Omega \\sim\n790\\Box^{\\circ}$ explored.\n\nWe have only followed up obvious detections up to ${\\rm R=19}$. Model\npredictions (B. Hansen, priv. comm.) for $T>3500$~K DA WDs are that ${\\rm\nM_R<16.4}$, so we are sensitive to a distance modulus of ${\\rm m-M_0=2.7}$,\nthat is, a distance of $d=33\\pc$.\n\nThe finding of $n=2$ stars closer than $d=33\\pc$, over the $\\Omega \\sim 790\n\\Box^\\circ$ area of the survey implies a local density of:\n%\n\\begin{equation}\n\\rho \\sim n {{3} \\over {\\Omega d^{3}}} M_\\star \\,\n\\end{equation}\n%\nwhere $M_\\star$ are the individual object masses. Lacking any information on\nindividual masses, we assume a reasonable value of $M_\\star \\sim 1\\msun$\n\\citep{chabrier}. Thus the local mass density of this population is:\n\\begin{equation}\n\\rho \\sim 0.0007 \\msun\\pc^{-3} \\, .\n\\end{equation}\nThe expected mass density of white dwarfs in the stellar spheroid, given the\nsubdwarf star counts, and assuming a standard IMF, is $1.3\\times\n10^{-5}\\msun \\pc^{-3}$ \\citep{gould}, that is, approximately two orders of\nmagnitude lower than this estimate. This suggests that the IMF is not\nuniversal, and was substantially steeper in the progenitor population of\nthese WDs.\n\nThe density derived above is $\\sim 10$\\% of the local density ($0.0079\n\\msun\\pc^{-3}$) of the ``standard'' dark matter halo model used by the MACHO\ncollaboration \\citep{alcock97}. However, the halo mass fraction in WDs could\nbe even larger, as surveys 2 and 3 are probably not sensitive to the older\n(and bluer) DA WDs; while similar aged helium atmosphere (DB) WDs would be\ntoo faint to be detected by any of these methods (see Hansen 1998). We note\nthat our density estimate is consistent with the updated results from the\nMACHO collaboration \\citep{alcock00}, which appeared after the submission of\nthis paper.\n\nThus it appears that a significant fraction of galactic dark matter may be\nbaryonic, and in the form of cool and hence very old WDs, the remants of the\nfirst stellar populations. We caution that this analysis is based on very\nlow number statistics, and therefore requires confirmation. An all-sky\nsurvey to ${\\rm R \\sim 19}$ at Galactic latitudes $b > |30|$ (as is feasable\nto undertake with extant photographic plates), and with completeness similar\nto the present work, should find $\\sim 14$ such stars, providing a sample\nwith which the Halo may be age-dated in a way independent of isochrone fits\n\\citep{richer}. Also, very deep HST proper motion data towards the Galactic\ncenter and anticenter directions will constrain the radial density gradient\nof this population, thereby checking whether this is a local, perhaps\ntransient, feature, or a massive Galactic structure.\n\n\\begin{figure}\n\\includegraphics[width=\\hsize]{WD_Halo.fig01.ps}\n\\figcaption{The flux-calibrated spectra of the two VHPM stars (left:\nF351-50, right: F821-07). The black body SED models, fit to $\\lambda <\n6500\\Aa$) have been overlaid. The black body temperatures are 3500~K and\n4100~K for, respectively, F351-50 and F821-07.}\n\\end{figure}\n\n\\begin{figure}\n\\includegraphics[width=\\hsize]{WD_Halo.fig02.ps}\n\n\\figcaption{Plate direct images ($2\\mcnd5\\times2\\mcnd5$) of (top row)\nF351-50 (from left to right: ESO B, UKST ${\\rm B_J}$, UKST R) and (bottom\nrow) F821-07 (from left to right: Palomar O, UKST ${\\rm B_J}$, UKST R)\nshowing proper motion.}\n\\end{figure}\n\n\\acknowledgements{We would like to thank Sue Tritton at UKSTU, the MAMA\nteam, and our observers LSL and CP at CTIO for their invaluable help. RI is\ngrateful to Strasbourg Observatory for their kind hospitality during\nvisits.}\n\n\n\\begin{thebibliography}{}\n\\bibitem[Alcock et al.(1997)]{alcock97} Alcock, C. \\etal, 1997, \\apj\\ 486, 697\n\\bibitem[Alcock et al.(2000)]{alcock00} Alcock, C. \\etal, 2000, astro-ph/0001272\n\\bibitem[Afonso et al.(1999)]{afonso}Afonso, C. \\etal, 1999, A\\&A 344, 63\n\\bibitem[Bosma(1998)]{bosma} Bosma, A. 1998, CeMDA 72, 69\n\\bibitem[Chabrier(1999)]{chabrier} Chabrier, G., 1999, \\apj\\ 513, 103-106\n\\bibitem[Fields, Freese \\& Graff(1998)]{fields} Fields, B., Freese, K., \nGraff, D. 1998, New Astronomy 3, 347\n\\bibitem[Gibson \\& Mould(1997)]{gibson} Gibson, B. \\& Mould, J., 1997, \\apj\\ 482, 98-103\n\\bibitem[Graff et al.(1999)]{graff} Graff, D., Freese, K., Walker, T.,\nPinsonneault, M. 1999, \\apj\\ 523, 77L\n\\bibitem[Guibert et al.(1984)]{guibert} Guibert, J., Charvin, P., \nStoclet, P. 1984, in Astronomy with Schmidt-type Telescopes, Proc.~IAU Coll. 78,\nEd. M. Capaccioli (Reidel, Dordrecht) p.165\n\\bibitem[Gould, Flynn \\& Bahcall(1998)]{gould} Gould, A., Flynn, C.,\nBahcall, J. 1998, \\apj\\ 503, 798\n\\bibitem[Hansen(1998)]{hansen} Hansen, B., 1998, \\nat\\ 394, 860\n\\bibitem[Hambly et al.(1997)]{hambly} Hambly, N., Smartt, S., Hodgkin,\nS. 1997, \\apj\\ 489, L157\n\\bibitem[Hodgkin et al.(2000)]{hodgkin} Hodgkin, S., Oppenheimer, B., Hambly, N.,\nJameson, R., Smartt, S., Steele, I. 2000, \\nat\\ 403, 57\n\\bibitem[Ibata et al.(1999)]{ibata} Ibata, R., Richer, H., Gilliland, R., \nScott, D. 1999, \\apj\\ 524, 95L\n\\bibitem[Kibblewhite et al.(1994)]{kibblewhite} Kibblewhite, E., Bridgeland,\nM., Bunclark, P., Irwin, M. 1984, in \nProc.~Astron.~Microdensitometry Conf.~NASA-2317 (NASA, Washington DC) p277\n\\bibitem[Leggett, Ruiz, \\& Bergeron(1998)]{leggett} Leggett, S. K., Ruiz, M. R.,\nBergeron, P. 1998, \\apj\\ 497, 294\n\\bibitem[Lin et al.(1999)]{lin} Lin, D., Jones, B., Klemola, A. 1995, \\apj\\ 439, 652\n\\bibitem[Luyten(1979)]{luyten} Luyten, W. 1979, ``LHS catalogue'',\nMinneapolis: University of Minnesota\n\\bibitem[Palanque-Delabrouille et al.(1998)]{palanque-delabrouille}\nPalanque-Delabrouille, N. \\etal, 1998, A\\&A 332, 1\n\\bibitem[Richer et al.(1997)]{richer} Richer \\etal, 1997, \\apj\\ 484, 741\n\\bibitem[Robichon et al.(1995)]{robichon}Robichon, N. \\etal\\, 1995, A\\&A 304, 132\n\\bibitem[Saumon \\& Jacobson(1999)]{saumon} Saumon, D. \\& Jacobson, S., 1999, \\apj\\ 511, L107-110\n\\bibitem[Zaritsky(1999)]{zaritsky} Zaritsky, D. 1999, \nin The Third Stromlo Symposium: The Galactic Halo, eds. Gibson, B., Axelrod,\nT. \\& Putman, M., ASP Conference Series Vol. 165, p. 34\n\\end{thebibliography}\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002138.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[Alcock et al.(1997)]{alcock97} Alcock, C. \\etal, 1997, \\apj\\ 486, 697\n\\bibitem[Alcock et al.(2000)]{alcock00} Alcock, C. \\etal, 2000, astro-ph/0001272\n\\bibitem[Afonso et al.(1999)]{afonso}Afonso, C. \\etal, 1999, A\\&A 344, 63\n\\bibitem[Bosma(1998)]{bosma} Bosma, A. 1998, CeMDA 72, 69\n\\bibitem[Chabrier(1999)]{chabrier} Chabrier, G., 1999, \\apj\\ 513, 103-106\n\\bibitem[Fields, Freese \\& Graff(1998)]{fields} Fields, B., Freese, K., \nGraff, D. 1998, New Astronomy 3, 347\n\\bibitem[Gibson \\& Mould(1997)]{gibson} Gibson, B. \\& Mould, J., 1997, \\apj\\ 482, 98-103\n\\bibitem[Graff et al.(1999)]{graff} Graff, D., Freese, K., Walker, T.,\nPinsonneault, M. 1999, \\apj\\ 523, 77L\n\\bibitem[Guibert et al.(1984)]{guibert} Guibert, J., Charvin, P., \nStoclet, P. 1984, in Astronomy with Schmidt-type Telescopes, Proc.~IAU Coll. 78,\nEd. M. Capaccioli (Reidel, Dordrecht) p.165\n\\bibitem[Gould, Flynn \\& Bahcall(1998)]{gould} Gould, A., Flynn, C.,\nBahcall, J. 1998, \\apj\\ 503, 798\n\\bibitem[Hansen(1998)]{hansen} Hansen, B., 1998, \\nat\\ 394, 860\n\\bibitem[Hambly et al.(1997)]{hambly} Hambly, N., Smartt, S., Hodgkin,\nS. 1997, \\apj\\ 489, L157\n\\bibitem[Hodgkin et al.(2000)]{hodgkin} Hodgkin, S., Oppenheimer, B., Hambly, N.,\nJameson, R., Smartt, S., Steele, I. 2000, \\nat\\ 403, 57\n\\bibitem[Ibata et al.(1999)]{ibata} Ibata, R., Richer, H., Gilliland, R., \nScott, D. 1999, \\apj\\ 524, 95L\n\\bibitem[Kibblewhite et al.(1994)]{kibblewhite} Kibblewhite, E., Bridgeland,\nM., Bunclark, P., Irwin, M. 1984, in \nProc.~Astron.~Microdensitometry Conf.~NASA-2317 (NASA, Washington DC) p277\n\\bibitem[Leggett, Ruiz, \\& Bergeron(1998)]{leggett} Leggett, S. K., Ruiz, M. R.,\nBergeron, P. 1998, \\apj\\ 497, 294\n\\bibitem[Lin et al.(1999)]{lin} Lin, D., Jones, B., Klemola, A. 1995, \\apj\\ 439, 652\n\\bibitem[Luyten(1979)]{luyten} Luyten, W. 1979, ``LHS catalogue'',\nMinneapolis: University of Minnesota\n\\bibitem[Palanque-Delabrouille et al.(1998)]{palanque-delabrouille}\nPalanque-Delabrouille, N. \\etal, 1998, A\\&A 332, 1\n\\bibitem[Richer et al.(1997)]{richer} Richer \\etal, 1997, \\apj\\ 484, 741\n\\bibitem[Robichon et al.(1995)]{robichon}Robichon, N. \\etal\\, 1995, A\\&A 304, 132\n\\bibitem[Saumon \\& Jacobson(1999)]{saumon} Saumon, D. \\& Jacobson, S., 1999, \\apj\\ 511, L107-110\n\\bibitem[Zaritsky(1999)]{zaritsky} Zaritsky, D. 1999, \nin The Third Stromlo Symposium: The Galactic Halo, eds. Gibson, B., Axelrod,\nT. \\& Putman, M., ASP Conference Series Vol. 165, p. 34\n\\end{thebibliography}"
}
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astro-ph0002139
|
A NEARBY SUPERNOVAE SEARCH: EROS2
|
[
{
"author": "{N. REGNAULT} \\footnote{on behalf of the EROS2 Collaboration.}"
}
] |
Type Ia supernovae (SNIa) have been used as approximate standard candles to measure cosmological parameters such as the Hubble constant and the deceleration parameter. These measurements rely on empirical correlations between peak luminosities and other features that can be observed in the supernovae spectra and their light curves. Such correlations deserve further study since they have been established from small samples of nearby SNIa. Two years ago, the EROS2 collaboration launched an automated search for supernovae with the 1m Marly telescope operating at La Silla. In all, 57 SNe have been discovered in this EROS2 search and spectra have been obtained for 26 of them. We found that 75\% were of type Ia and 25\% of type II. Using this sample, a preliminary SN explosion rate has been obtained. Our most recent observation campaign took place in February and March 99. It was performed in the framework of a large consortium led by the {\em Supernova Cosmology Project}. The aim of this intensive campaign was to provide an independent set of high quality light curves and spectra to study systematic effects in the measurement of cosmological parameters. We will briefly describe our search procedure and present the status of our ongoing analysis.
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[
{
"name": "LAL9970.tex",
"string": "%====================================================================% \n% MORIOND.TEX 2-Feb-1995 % \n% This latex file rewritten from various sources for use in the % \n% preparation of the standard proceedings Volume, latest version % \n% for the Neutrino'96 Helsinki conference proceedings % \n% by Susan Hezlet with acknowledgments to Lukas Nellen. % \n% Some changes are due to David Cassel. % \n%====================================================================% \n \n%\\documentstyle[11pt,moriond,epsfig,tabularx]{article} \n\\documentclass[11pt]{article} \n\\usepackage{moriond,epsfig} \n\\usepackage{tabularx} \n\\usepackage{longtable} \n \n\\bibliographystyle{unsrt} \n% for BibTeX - sorted numerical labels by order of \n% first citation. \n \n% A useful Journal macro \n\\def\\Journal#1#2#3#4{{#1} {\\bf #2}, #3 (#4)} \n \n% Some useful journal names \n\\def\\NCA{\\em Nuovo Cimento} \n\\def\\NIM{\\em Nucl. Instrum. Methods} \n\\def\\NIMA{{\\em Nucl. Instrum. Methods} A} \n\\def\\NPB{{\\em Nucl. Phys.} B} \n\\def\\PLB{{\\em Phys. Lett.} B} \n\\def\\PRL{\\em Phys. Rev. Lett.} \n\\def\\PRD{{\\em Phys. Rev.} D} \n\\def\\ZPC{{\\em Z. Phys.} C} \n\\def\\AA{{\\em Astronomy \\& Astrophysics}} \n\\def\\AAS{{\\em Astronomy \\& Astrophysics Suppl. Ser.}} \n\\def\\AJ{{\\em The Astronomical Journal}} \n\\def\\APJ{{\\em Astrophysical Journal}} \n\\def\\MNRAS{{\\em Mon. Not. R. Astron. Soc.}} \n \n% Some other macros used in the sample text \n\\def\\st{\\scriptstyle} \n\\def\\sst{\\scriptscriptstyle} \n\\def\\mco{\\multicolumn} \n\\def\\epp{\\epsilon^{\\prime}} \n\\def\\vep{\\varepsilon} \n\\def\\ra{\\rightarrow} \n\\def\\ppg{\\pi^+\\pi^-\\gamma} \n\\def\\vp{{\\bf p}} \n\\def\\ko{K^0} \n\\def\\kb{\\bar{K^0}} \n\\def\\al{\\alpha} \n\\def\\ab{\\bar{\\alpha}} \n\\def\\be{\\begin{equation}} \n\\def\\ee{\\end{equation}} \n\\def\\bea{\\begin{eqnarray}} \n\\def\\eea{\\end{eqnarray}} \n\\def\\CPbar{\\hbox{{\\rm CP}\\hskip-1.80em{/}}} \n%temp replacement due to no font \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n% % \n% BEGINNING OF TEXT % \n% % \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n\\begin{document}\n%\\vspace*{-1.8cm}\n\\begin{flushright}{\\bf LAL 99-70}\\\\\n%\\vspace*{-0.5cm}\nNovember 1999\n\\end{flushright}\n%\\vskip 7.5 cm\n\n\n\\vspace*{4cm}\n\\title{\\large A NEARBY SUPERNOVAE SEARCH: EROS2}\n\n\\author{{\\bf N. REGNAULT} \\footnote{on behalf of the EROS2 Collaboration.}}\n%\\quad\\vspace{0.4cm}\n\\address{{\\bf \\large Laboratoire de l'Acc\\'el\\'erateur Lin\\'eaire,}\\\\\nIN2P3-CNRS et Universit\\'e de Paris-Sud, BP 34, F-91898 Orsay Cedex} \n \n\\maketitle\\abstracts{ \nType Ia supernovae (SNIa) have been used as \napproximate standard candles to measure cosmological parameters \nsuch as the Hubble constant and the deceleration parameter. \nThese measurements rely on empirical correlations between \npeak luminosities and other features that can be observed \nin the supernovae spectra and their light curves. \nSuch correlations deserve further study since they have been \nestablished from small samples of nearby SNIa. \nTwo years ago, the EROS2 collaboration launched an automated search \nfor supernovae with the 1m Marly telescope operating at La Silla. \nIn all, 57 SNe have been discovered in this EROS2 search \nand spectra have been obtained for 26 of them. We found that \n75\\% were of type Ia and 25\\% of type II. Using this sample, a preliminary SN \nexplosion rate has been obtained. Our most recent observation campaign \ntook place in February and March 99. It was performed in the framework \nof a large consortium led by the {\\em Supernova Cosmology Project}. \nThe aim of this intensive campaign was \nto provide an independent set of high quality light curves \nand spectra to study systematic effects in the measurement of \ncosmological parameters. We will briefly describe our search \nprocedure and present the status of our ongoing analysis. } \n \n\\section{Type Ia supernovae and cosmology} \n \n%\\subsection{}\\label{subsec:prod} \n \nSupernovae are classified in different subtypes, according to their \nspectral features. Type Ia supernovae (SNIa) are believed to be \nexplosions of carbon-oxygen white dwarfs. SNIa progenitors are \nlikely to be binary systems, composed of a red giant and an old \nC/O white dwarf. The latter accretes matter from its companion \nuntil it reaches the Chandrasekar mass ($\\sim 1.4 M_\\odot$), \nand then becomes unstable. \nThis process leads to the total thermonuclear explosive burning \nof the white dwarf. Thus, the total energy released should be nearly constant \nfrom one SNIa to another. These objects may therefore be used as \nstandard candles. \n% \nIndeed, photometric and spectroscopic studies have shown that SNIa \ncompose an homogeneous sample and their peak magnitudes present a small scatter \n($\\sim 20\\%$) in all colors. Furthermore, these \nobjects are very luminous --- they have been detected \nup to redshifts $z \\sim 1.2$ (Aldering {\\em et al.}~\\cite{ald}). \nThus they constitute powerful cosmological distance indicators. \n \n%For these objects, we can \n%define indeed a luminosity distance : $d_L^2 = \\frac{\\cal L}{4\\pi\\cal F}$, \n%where $\\cal F$ is the apparent flux of the supernova, and $\\cal L$, \n%the absolute luminosity of SNIa. For $z<0.1$ the $d_L-z$ relation is \n%quasi-linear, and depends mainly on $H_0$, which can be determined this way. \n%For $z>0.2$, this relation becomes non linear, and the deviations from the \n%Hubble law, depends on the cosmological parameters $\\Omega_0$ and $\\Lambda$. \n \nIt has been shown that the absolute maximum luminosities of SNIa correlate with other \nobservables, like the post maximum decline rate, the color at maximum, \nthe SN spectral features, or the galaxy type. When corrections based on such correlations \nare applied, the relative dispersion of the peak luminosities of SNIa can be reduced to 10\\% (Hamuy {\\it et al.}~\\cite{ham}). \n \nMeasurements of the cosmological parameters $H_0$, $\\Omega_0$ and \n$\\Lambda$ have been made by analysing the apparent peak magnitude \nversus redshift relation (Perlmutter {\\it et al.}~\\cite{perl}, \nSchmidt {\\it et al.}~\\cite{sch}). \nThese analyses rely heavily on the standardization procedure outlined \nabove. For example, the evidence for a non zero $\\Lambda$ arises from \na 20\\% flux decrease with respect to a ($\\Omega=0.2$) universe, \nwhich is comparable to the intrinsic luminosity spread. \n%whereas the corrections applied to $m^{max}$ is of about the same amount. \n% \nHowever, our SNIa knowledge is based on few objects, namely the 17 SNIa \n($z<0.1$) discovered before maximum during the Calan-Tololo search. This \nis why a number of nearby SN searches have been launched in order \nto increase the set of well sampled SNIa and study further the \nstandardization corrections mentionned above. \n \nSupernovae rates as a function of redshift are a useful tool for \nstudying the star formation history, or constraining the galactic chemical \nevolution scenarios. While probing the stellar evolution, they also bring valuable \ninformation on the SNIa progenitor system, and allow us to \nget a better insight into the physics processes involved in these events. \nSNIa rates have been measured at low redshift (see {\\em e.g.} Cappellaro \n{\\it et al.}~\\cite{cap}~) with SNe discovered using photographic plates, \nand at high redshift ($z \\sim 0.4$), with automatic subtraction of \nCCD images by Pain {\\it et al.}~\\cite{pain}. EROS2 has obtained the first \ndetermination of the SNIa rate at $z \\sim 0.15$ (Hardin {\\it et al.}~\\cite{delph}). \n \n\\section{The EROS2 nearby supernovae search} \n \nThe EROS2 experiment is mainly devoted to the search for \nmicrolensing events towards the Magellanic clouds, and towards the Galactic \nbulge and disk. For this purpose, the collaboration operates \na 1 meter telescope, installed at the {\\em European Southern Observatory} \nof La Silla (Chile). This instrument was specially refurbished and automated \nin view of a microlensing survey. It is equipped with a dichroic beam splitter \nand two cameras to take images simultaneously in two wide \npass-bands. Each camera comprises a mosaic of 8 $2k \\times 2k$ thick CCD's, \ncovering a field of view of $0.7^o(\\alpha) \\times 1.4^o(\\delta)$ \nwith a pixel size of 0.6 arcseconds. \n \nSince this setup is particularly well suited for discovering supernovae \nat $z \\sim 0.05-0.2$, the EROS2 collaboration launched in 1997 a systematic \nnearby SN search aimed at the measurement of the \nnearby SN explosion rates and a detailed study of the correlations between \nthe SNIa light curve shapes and their peak absolute luminosities. \n \n \n\\subsection{The search strategy} \n \nOur SN search technique consists in comparing an image of a given field \nwith a {\\em reference image} of the same field taken \ntwo or three weeks before. For this purpose, we subtract the {\\em reference \nframe} from the {\\em search frame}, after a geometric and a photometric alignment, \nand a matching of the seeing. We then perform an object detection \non the subtracted frame. \n%Most sources detected at this stage are hot pixels, \n%subtraction artifacts or variable stars. This background is rejected \n%by applying a set of cuts, \nGenuine candidates are selected among these objects by applying cuts \ntuned with a Monte-Carlo simulation, in order to reject variable stars, \nasteroids and subtraction artifacts. Finally, a visual scan allows \nus to eliminate the last spurious candidates. \n \n\\subsection{The first stage : 1997-1998} \n \nDuring the first two years, 7 search campaigns have been conducted. \nWe monitored fields from both celestial hemispheres. In order to avoid \ndust absorption they were chosen far from the Galactic plane. \n%The southern fields, covered by the {\\em Las Campanas \n%Redshift Survey} (LCRS) \nDuring these first searches, 35 SNe have been discovered. \nSpectra could be obtained for 10 of them with the ESO 3.6m and \nthe ARC 3.5m telescopes. 7 of the SN were of type Ia, 1 of type Ic and \n2 of type II. Using this first sample, a preliminary SNIa rate \nat $z \\sim 0.15$ has been obtained (see section \\ref{sec:snrate}). \n \n \n\\subsection{A worldwide SNIa search campaign} \n \nIn the spring of 1999, we participated in a worldwide search campaign \n\\footnote{Involving the following 9 groups : \n{\\bf The Nearby Galaxies SN Search Team} ($\\dagger$) (Strolger, Smith {\\em et al.}), \n{\\bf EROS2} ($\\ddagger$) (Spiro {\\em et al.}), \n{\\bf KAIT} (${\\dagger\\dagger}$) (Filippenko {\\em et al.}), \n{\\bf The Mount Stromlo Abell Cluster Supernovae Search} (${\\ddagger\\ddagger}$) (Schmidt, Germany \\& Reiss), \n{\\bf NEAT} ($\\bot$) (Helin, Pravdo \\& Rabinovitz), \n{\\bf QUEST} ($\\top$) (Schaefer {\\em et al.}), \n{\\bf SpaceWatch} ($\\ast$) (McMillan \\& Larsen), \n{\\bf The Tenagra Observatories} ($\\diamond$) (Schwartz), \nand {\\bf The Wise Observatories Supernovae Search} ($\\bigtriangledown$) (Gal-Yam {\\em et al.}).}, \nled by the {\\em Supernovae Cosmo\\-logy Project} and coordinated \nby Greg Aldering (SCP). The search involved 9 groups listed below. \n%\\footnote{{\\bf The CTIO Group} (Strolger, Smith {\\em et al.})\\label{fn:CTIO}} \n%\\footnote{{\\bf EROS2} (Spiro {\\em et al.})\\label{fn:EROS}} \n%\\footnote{{\\bf KAIT} (Fillippenko {\\em et al.})} \n%\\footnote{{\\bf The Mount Stromlo Abell Cluster Supernovae Search} (Schmidt, Germany \\& Reiss)} \n%\\footnote{{\\bf NEAT} (Helin, Pravdo \\& Rabinovitz)} \n%\\footnote{{\\bf QUEST} (Schaefer {\\em et al.})} \n%\\footnote{{\\bf SpaceWatch} (McMillan \\& Larsen)} \n%\\footnote{{\\bf The Tenagra Observatories} (Schwartz)} \n%\\footnote{{\\bf The Wise Observatories Supernovae Search} (Gal-Yam {\\em et al.}).} \n%The consortium aimed at discovering \n%and following-up photometrically and spectroscopically a set of \n%15 to 20 SNIa, found near maximum. \n% and more than XXX hours of photometric \n%and spectroscopic time was available, to follow-up the SNIa discovered. \n \n%\\begin{table}[t] \n%\\caption{The Spring 1999 search consortium, led by the \n%{\\em Supernovae Cosmology Project}\\label{tab:99search}} \n%\\vspace{0.4cm} \n%\\begin{center} \n%{\\scriptsize \n%\\begin{tabular}{|l|l|} \n%\\hline \n%CTIO group & Strolger, Smith \\& al \\\\ \n%EROS2 & \\\\ \n%KAIT & Fillippenko \\& al \\\\ \n%Mount Stromlo Abell Cluster SN Search & Schmidt, Germany \\& Reiss \\\\ \n%NEAT & Helin, Pravdo \\& Rabinovitz \\\\ \n%QUEST & Schaefer \\& all \\\\ \n%SpaceWatch & McMillan \\& Larsen \\\\ \n%Tenagra Observatories & Schwartz \\\\ \n%Wise Observatories Supernovae Search & Gal-Yam \\& al \\\\ \n%\\hline \n%\\end{tabular} \n%} \n%\\end{center} \n%\\end{table} \n \n\n \nEROS2 discovered a subset of 16 SN among the 41 supernovae found in \nthis campaign. Among them, 19 (7 from EROS2) turned out to be of type \nIa, discovered near maximum. An overview of the follow-up data for \neach SN can be found in table \\ref{tab:follow-up}. Photometric and \nspectroscopic data from both these SN together with discoveries \nannounced in the same period in IAU circulars are currently being \nanalysed. \n\n \n\\begin{table}[h] \n\\caption{An overview of the photometric follow-up of the SNIa discovered during \nthe Spring 1999 SN search.\\label{tab:follow-up}} \n\\vspace{0.4cm} \n\\begin{center} \n{\\scriptsize \n\\begin{tabular}{|c|cccccccccc|} \n\\hline \nSN & 99aa \n & 99ao(${\\ddagger\\ddagger}$) \n & 99ac(${\\dagger\\dagger}$) \n & 99af($\\ddagger$) \n & 99ar($\\dagger$) \n% & 99as($\\bot$) \n & 99at($\\bot$) \n & 99au($\\dagger$) \n & 99av($\\dagger$) \n & 99aw($\\dagger$) \n & 99ax($\\bigtriangledown$)\\\\ \n & & & & & & & & & & \\\\ \n%U & 15 & 14 & 20 & 4 & 5 & 7 & 8 & 13 & 15 & 13 \\\\ \n%B & 19 & 14 & 23 & 5 & 10 & 8 & 12 & 16 & 16 & 10 \\\\ \n%V & 19 & 14 & 23 & 6 & 10 & 9 & 11 & 15 & 17 & 14 \\\\ \n%R & 19 & 13 & 23 & 5 & 10 & 9 & 11 & 14 & 17 & 12 \\\\ \n%I & 14 & 12 & 16 & 2 & 4 & 6 & 10 & 9 & 11 & 7 \\\\ \nU & 22 & 17 & 23 & 8 & 6 & 7 & 10 & 15 & 19 & 13 \\\\ \nB & 27 & 16 & 27 & 9 & 11 & 8 & 13 & 19 & 18 & 10 \\\\ \nV & 27 & 16 & 28 & 11 & 11 & 9 & 12 & 18 & 19 & 16 \\\\ \nR & 27 & 15 & 27 & 10 & 11 & 9 & 12 & 17 & 19 & 15 \\\\ \nI & 22 & 14 & 19 & 7 & 5 & 6 & 12 & 11 & 13 & 9 \\\\ \n\\hline \n & 99be($\\ast$) \n & 99bf($\\ast$) \n & 99bh($\\dagger\\dagger$) \n & 99bi($\\ddagger$) \n & 99bk($\\ddagger$) \n & 99bm($\\ddagger$) \n & 99bn($\\ddagger$) \n & 99bp($\\ddagger$) \n & 99bq($\\ddagger$) \n & 99by($\\dagger\\dagger$) \\\\ \n & & & & & & & & & & \\\\ \n%U & 6 & -- & 7 & 8 & 5 & 1 & 5 & 10 & 1 & 7 \\\\ \n%B & 11 & 4 & 10 & 7 & 7 & 7 & 11 & 10 & 4 & 12 \\\\ \n%V & 11 & 5 & 9 & 6 & 11 & 6 & 9 & 10 & 5 & 7 \\\\ \n%R & 10 & 3 & 10 & 7 & 10 & 4 & 7 & 11 & 2 & 7 \\\\ \n%I & 7 & 1 & 6 & 5 & 8 & 1 & 6 & 6 & 2 & 7 \\\\ \nU & 7 & -- & 7 & 9 & 5 & 1 & 5 & 10 & 1 & 9 \\\\ \nB & 12 & 4 & 12 & 9 & 7 & 7 & 11 & 10 & 4 & 15 \\\\ \nV & 12 & 5 & 11 & 8 & 12 & 6 & 9 & 10 & 5 & 9 \\\\ \nR & 11 & 3 & 12 & 9 & 10 & 4 & 7 & 11 & 2 & 9 \\\\ \nI & 8 & 1 & 8 & 7 & 8 & 1 & 6 & 6 & 2 & 9 \\\\ \n \n\\hline \n\\end{tabular} \n} \n\\end{center} \n\\end{table} \n\n\n\\section{A first measurement of the SNIa rate at $z \\sim 0.15$}\\label{sec:snrate} \n \nOur preliminary determination of the SNIa rate at $z \\sim 0.15$ relies \non a sample of type Ia supernovae discovered during 2 search campaigns \nled in October and November 1997. 120 square degrees have been covered, \n8 supernovae discovered. Among them, 4 were of type Ia. \n \nSupernovae rates ${\\cal R}$ in the rest frame are usually expressed in SNu, \n{\\em i.e.} in supernovae per unit time and per unit blue luminosity \n($SNe / 10^{10} L_{\\odot_B} / 100 yr$). \n%The main work is thus to compute the total \n%luminosity of the galaxies our survey was sensitive to, and the control time \n%for each galaxy \nThe number of supernovae of a given type discovered during a search \nis related to the rate ${\\cal R}$ of this type of SNe through \n\\begin{equation} \n{\\cal N} \\ \\sim\\ \\ {\\cal R}\\ \n \\times\\ \\sum_{gal} L_{gal} \\times T_{gal} \n\\label{eq:snrate} \n\\end{equation} \nwhere $L_{_{gal}}$ is the absolute luminosity of the galaxy $gal$, and \n$T_{gal}$ is the {\\em control time} during which a SNIa could have \nbeen detected. If $\\varepsilon(t,z,\\ldots)$ is the search efficiency, \n{\\em i.e.} the probability to detect a SNIa with redshift $z$ whose maximum \noccured at a time $t$ before the observation, $T_{gal}$ can be written \nas $T_{gal} = \\int_{-\\infty}^{+\\infty} \\varepsilon(t,z,\\ldots) dt$. \n \nThe sum ${\\cal S} = \\sum_{gal} L_{gal} \\times T_{gal}$ is computed by \nMonte-Carlo integration. Firstly the galaxies in the search fields are \ndetected using the program {\\sf sextractor} (Bertin {\\it et \nal.}~\\cite{ber}). Their apparent magnitudes are derived in the $R_c$ \nband from the EROS2 magnitudes. Since the redshift of each galaxy is \nnot known, a value of $z$ is generated in the Monte-Carlo procedure, \nusing a $p(z|R_{c_{gal}})$ pdf derived from the Schechter law with \nparameter values measured by the LCRS (Lin {\\em et \nal.}~\\cite{lin}). The absolute luminosities of each galaxy can then be \ncalculated. The detection efficiency is fully simulated. The SN rate \nwe thus obtain is \n\\begin{equation} \n%{\\cal R} = 0.35 \\pm 0.17^{+0.11}_{-0.06}\\ h^2\\ {\\rm SNu}. \n%{\\cal R} = 0.44 \\pm 0.22^{+0.11}_{-0.07}\\ h^2\\ {\\rm SNu}. \n{\\cal R} = 0.44^{+0.35\\ +0.13}_{-0.21\\ -0.07}\\ h^2\\ {\\rm SNu}. \n\\end{equation} \n \nBy multiplying this value by the luminous density of the universe \n$\\rho_L = 1.4 \\pm 0.1\\ 10^8\\ h L_\\odot Mpc^{-3}$ (Lin {\\em et al.}~\\cite{lin}) \nwe obtain the rate expressed in $h^3\\ {\\rm Mpc}^{-3}\\ {\\rm year}^{-1}$ \n\\begin{equation} \n%{\\cal R} = 0.49 \\pm 0.24^{+0.15}_{-0.08} 10^{-4}\\ h^3 {\\rm Mpc}^{-3} {\\rm year}^{-1}. \n%{\\cal R} = 0.62 \\pm 0.31^{+0.16}_{-0.11} 10^{-4}\\ h^3 {\\rm Mpc}^{-3} {\\rm year}^{-1}. \n{\\cal R} = 0.62^{+0.49\\ +0.19}_{-0.29\\ -0.11} 10^{-4}\\ h^3 {\\rm Mpc}^{-3} {\\rm year}^{-1}. \n\\end{equation} \n \n \n\\begin{figure} \n%\\rule{5cm}{0.2mm}\\hfill\\rule{5cm}{0.2mm} \n%\\vskip 2.5cm \n%\\rule{5cm}{0.2mm}\\hfill\\rule{5cm}{0.2mm} \n\\begin{center} \n\\psfig{figure=fgrate.eps,height=0.75\\textwidth} \n\\end{center} \n\\vspace{-3mm} \n\\caption{SNIa and SNII explosion rates as a function of redshift. \n(After Madau {\\it et al.}$^9$) \n\\label{fig:fgrate}} \n\\end{figure} \n \n \n\\section*{Conclusion} \n \n Since 1997, the EROS2 collaboration has conducted several campaigns \n of supernovae searches. Our discovery rate is about 1 SN every two \n hours of observations, which makes us competitive with respect to \n other teams carrying on searches at the same $z$. In a first stage, \n 35 SNe were discovered, the light curves of 7 SNIa were studied, and \n a first SNIa explosion rate at $z \\sim 0.15$ was derived. In Spring \n 99, EROS2 participated in a worldwide search led by the {\\em \n Supernovae Cosmology Project}, and discovered 8 of the 19 SNIa near \n maximum found by the consortium. Photometric and spectroscopic \n follow-up data are currently been analyzed, and results are expected \n to come out soon.\n\n \n\\newpage \n\\section*{References} \n\\begin{thebibliography}{99} \n\\bibitem{ham} M. Hamuy {\\it et al.}, \\Journal{\\AJ}{112(6)}{2391}{1996}. \n\\bibitem{ald} G. Aldering {\\it et al.}, {\\em IAUC 7046} (1998).%\\Journal{IAUC}{7046}{1998}{}. \n\\bibitem{perl} S. Perlmutter {\\it et al.}, \\Journal{\\APJ}{517}{565P}{1999}. \n\\bibitem{sch} P. Schmidt {\\it et al.}, \\Journal{\\APJ}{507}{46S}{1998}. \n\\bibitem{cap} E. Cappellaro {\\it et al.}, \\Journal{\\AA}{322}{431C}{1997}. \n\\bibitem{pain} R. Pain {\\it et al.}, \\Journal{\\APJ}{473}{356P}{1996}. \n\\bibitem{delph} D. Hardin {\\it et al.}, {\\em Type Ia supernovae rate at $z \\sim 0.15$}, {\\em in preparation}. \n\\bibitem{ber} G. Bertin {\\it et al.}, \\Journal{\\AAS}{117}{393-404}{1996}. \n\\bibitem{mad} P. Madau {\\it et al.}, \\Journal{\\MNRAS}{297}{L17-L22}{1998}. \n\\bibitem{lin} H. Lin {\\it et al.}, \\Journal{\\APJ}{464}{60L}{1996}. \n \n\\bibitem{delphth} D. Hardin, {\\em PhD Thesis} DAPNIA/SPP 98-1002 (CEA 1998). \n\\bibitem{hami} J.-C. Hamilton, {\\em PhD Thesis} PCC 99-T1 (1999). \n \n%{\\em Recherches de supernov{\\ae} avec EROS2 et mesure du tax d'explosion de supernov{\\ae}}, \n%{\\em Recherche automatis\\'ee de supernov{\\ae} \\`a des distances \n% interm\\'ediaires, et analyse photom\\'etrique de leurs \n% courbes de lumi\\`ere}, \n%\\bibitem{ja}C Jarlskog in {\\em CP Violation}, ed. C Jarlskog \n%(World Scientific, Singapore, 1988). \n \n%\\bibitem{ma}L. Maiani, \\Journal{\\PLB}{62}{183}{1976}. \n \n%\\bibitem{bu}J.D. Bjorken and I. Dunietz, \\Journal{\\PRD}{36}{2109}{1987}. \n \n%\\bibitem{bd}C.D. Buchanan {\\it et al.}, \\Journal{\\PRD}{45}{4088}{1992}. \n \n\\end{thebibliography} \n \n\\end{document} \n \n%%%%%%%%%%%%%%%%%%%%%% \n% End of moriond.tex % \n%%%%%%%%%%%%%%%%%%%%%% \n \n \n \n%\\begin{table}[t] \n%\\caption{An overview of the follow-up of the SNIa discovered during \n%the Spring 1999 SN search\\label{tab:follow-up}} \n%\\vspace{0.4cm} \n%\\begin{center} \n%{\\scriptsize \n%\\begin{tabular}{|c|ccccc|c|} \n%\\hline \n%SN & \\multicolumn{5}{|c|}{Photometric followup} & Spectra \\\\ \n% & U & B & V & R & I & \\\\ \n%\\hline \n%99aa & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99ao & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99ac & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99af & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99ar & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99as & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99at & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99au & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99av & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99aw & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99be & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99bf & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99bh & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99bi & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99bk & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99bm & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99bn & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99bp & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99bq & ?? & ?? & ?? & ?? & ?? & \\\\ \n%99by & ?? & ?? & ?? & ?? & ?? & \\\\ \n%\\hline \n%\\end{tabular} \n%} \n%\\end{center} \n%\\end{table} \n"
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{
"name": "astro-ph0002139.extracted_bib",
"string": "\\begin{thebibliography}{99} \n\\bibitem{ham} M. Hamuy {\\it et al.}, \\Journal{\\AJ}{112(6)}{2391}{1996}. \n\\bibitem{ald} G. Aldering {\\it et al.}, {\\em IAUC 7046} (1998).%\\Journal{IAUC}{7046}{1998}{}. \n\\bibitem{perl} S. Perlmutter {\\it et al.}, \\Journal{\\APJ}{517}{565P}{1999}. \n\\bibitem{sch} P. Schmidt {\\it et al.}, \\Journal{\\APJ}{507}{46S}{1998}. \n\\bibitem{cap} E. Cappellaro {\\it et al.}, \\Journal{\\AA}{322}{431C}{1997}. \n\\bibitem{pain} R. Pain {\\it et al.}, \\Journal{\\APJ}{473}{356P}{1996}. \n\\bibitem{delph} D. Hardin {\\it et al.}, {\\em Type Ia supernovae rate at $z \\sim 0.15$}, {\\em in preparation}. \n\\bibitem{ber} G. Bertin {\\it et al.}, \\Journal{\\AAS}{117}{393-404}{1996}. \n\\bibitem{mad} P. Madau {\\it et al.}, \\Journal{\\MNRAS}{297}{L17-L22}{1998}. \n\\bibitem{lin} H. Lin {\\it et al.}, \\Journal{\\APJ}{464}{60L}{1996}. \n \n\\bibitem{delphth} D. Hardin, {\\em PhD Thesis} DAPNIA/SPP 98-1002 (CEA 1998). \n\\bibitem{hami} J.-C. Hamilton, {\\em PhD Thesis} PCC 99-T1 (1999). \n \n%{\\em Recherches de supernov{\\ae} avec EROS2 et mesure du tax d'explosion de supernov{\\ae}}, \n%{\\em Recherche automatis\\'ee de supernov{\\ae} \\`a des distances \n% interm\\'ediaires, et analyse photom\\'etrique de leurs \n% courbes de lumi\\`ere}, \n%\\bibitem{ja}C Jarlskog in {\\em CP Violation}, ed. C Jarlskog \n%(World Scientific, Singapore, 1988). \n \n%\\bibitem{ma}L. Maiani, \\Journal{\\PLB}{62}{183}{1976}. \n \n%\\bibitem{bu}J.D. Bjorken and I. Dunietz, \\Journal{\\PRD}{36}{2109}{1987}. \n \n%\\bibitem{bd}C.D. Buchanan {\\it et al.}, \\Journal{\\PRD}{45}{4088}{1992}. \n \n\\end{thebibliography}"
}
] |
astro-ph0002140
|
H{\,\LargeI}
|
[
{
"author": "T.A. Oosterloo"
},
{
"author": "R. Morganti\\altaffilmark{1}"
}
] |
We present 21-cm \HI\ line and 13-cm continuum observations, obtained with the Australian Long Baseline Array, of the Seyfert 2 galaxy IC~5063. This object appears to be one of the best examples of Seyfert galaxies where shocks produced by the radio plasma jet influence both the radio as well as the near-infrared emission. The picture resulting from the new observations of IC~5063 confirms and completes the one derived from previous Australia Telescope Compact Array (ATCA) lower resolution observations. A strong interaction between the radio plasma ejected from the nucleus and a molecular cloud of the ISM is occurring at the position of the western hot spot, about 0.6~kpc from the active nucleus. Because of this interaction, the gas is swept up forming, around the radio lobe, a cocoon-like structure where the gas is moving at high speed. Due to this, part of the molecular gas is dissociated and becomes neutral or even ionised if the UV continuum produced by the shocks is hard and powerful enough. In the 21-cm \HI\ line new data, we detect only part of the strong blue-shifted \HI\ absorption that was previously observed with the ATCA at lower resolution. In particular, the main component detected in the VLBI absorption profile corresponds to the most blue-shifted component in the ATCA data, with a central velocity of 2786 \kms\ and therefore blue-shifted $\sim$614 \kms\ with respect to the systemic velocity. Its peak optical depth is 5.4\%. The corresponding column density of the detected absorption, for a spin temperature of 100 K, is $N_{HI} \sim 2 \times 10^{21} $atoms cm$^{-2}$. Most of the remaining blue-shifted components detected in the ATCA \HI\ absorption profile are now undetected, presumably because this absorption occurs against continuum emission that is resolved out in these high-resolution observations. The \HI\ absorption properties observed in IC 5063 appear different from those observed in other Seyfert galaxies, where the \HI\ absorption detected is attributed to undisturbed foreground gas associated with the large-scale galaxy disk. In the case of IC~5063, only a small fraction of the absorption can perhaps be due to this. The reason for this can be that the western jet in IC~5063 passes through a particularly rich ISM. Alternatively, because of the relatively strong radio flux produced by this strong interaction, and the high spectral dynamic range of our observations, broad absorption lines of low optical depth as detected in IC 5063 may have remained undetected in other Seyferts that are typically much weaker radio emitters or for which existing data is of poorer quality.
|
[
{
"name": "oosterlooRevised.tex",
"string": "\\documentclass[preprint]{aastex}\n%\\documentclass[manuscript]{aastex}\n\n\\newcommand{\\HI}{H{\\,\\small I}}\n\\newcommand{\\MHILB}{$M_{\\ion{H}{1}}/L_B$}\n\\def\\ha{${\\rm H\\alpha}$}\n\\def\\hb{${\\rm H\\beta}$}\n\\def\\HaNii{H$\\alpha$+[\\ion{N}{2}] $\\lambda\\lambda6548,84$}\n\\def\\NII{[\\ion{N}{2}] $\\lambda\\lambda6548,84$}\n\\def\\OI{[\\ion{O}{1}] $\\lambda6300$}\n\\def\\oii{[\\ion{O}{2}] $\\lambda3727$}\n\\def\\OIII{[O{\\,\\small III}]}\n\\def\\NII{[N{\\,\\small II}]}\n\\def\\SII{[\\ion{S}{2}] $\\lambda\\lambda6717,31$}\n%\\newcommand{\\HI}{\\ion{H}{1}}\n\\newcommand{\\titleHI}{H{\\,\\Large\\bf I}}\n\\newcommand{\\eg}{{e.g.}}\n\\newcommand{\\ie}{{i.e.}}\n\\newcommand{\\cf}{{c.f.}}\n\\newcommand{\\etgal}{{et al.\\ }}\n\\newcommand{\\etc}{{etc.}}\n\\newcommand{\\kms}{km s$^{-1}$}\n\\newcommand{\\Mpc}{\\rm Mpc}\n\\newcommand{\\kpc}{\\rm kpc}\n\\newcommand{\\whz}{W Hz$^{-1}$}\n\\newcommand{\\ergs}{ergs s$^{-1}$}\n\\newcommand{\\mJybeam}{mJy beam$^{-1}$}\n\\newcommand{\\Msun}{{$M_\\odot$}}\n\\newcommand{\\Lsun}{{$L_\\odot$}}\n\\newcommand{\\ltae}{\\raisebox{-0.6ex}{$\\,\\stackrel{\\raisebox{-.2ex}{$\\textstyle <$}}{\\sim}\\,$}}\n%\\newcommand{\\gtae}{\\raisebox{-0.6ex}{$\\,\\stackrel{\\raisebox{-.2ex}{$\\textstyle >$}}{\\sim}\\,$}}\n%\\newcommand{\\etae}{\\raisebox{-0.6ex}{$\\,\\stackrel{\\raisebox{-.2ex}{$\\textstyle $\\sim$}}{$\\textstyle =}\\,$}\n\n\\input psfig\n\n\\slugcomment{Submitted to AJ, \\today}\n\n\\shorttitle{VLBI Observations of the Seyfert galaxy IC~5063}\n\\shortauthors{Oosterloo et al.}\n\\begin{document}\n\n\n\\title{A strong jet/cloud interaction\nin the Seyfert galaxy IC~5063: VLBI observations}\n\n\\author{T.A. Oosterloo, R. Morganti\\altaffilmark{1},}\n\\affil{Netherlands Foundation for\nResearch in Astronomy, Postbus 2, 7990 AA, Dwingeloo, NL}\n\\email{oosterloo@nfra.nl}\n\\email{morganti@nfra.nl}\n\n\\author{A. Tzioumis, J. Reynolds, E. King,}\n\\affil{ATNF-CSIRO, P.O. Box 76,\nEpping NSW 1710, Australia}\n\n\\author{P. McCulloch,} \n\\affil{Dept. of Physics, University of Tasmania,\nGPO Box 252-21, Hobart Tas 7001, Australia}\n\n\\and\n\n\\author{Z. Tsvetanov}\n\\affil{ Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218,\nUSA}\n\n\\altaffiltext{1}{Istituto di Radioastronomia, CNR, via Gobetti 101, 40129 Bologna, Italy}\n\n\n\\begin{abstract} \n\nWe present 21-cm \\HI\\ line and 13-cm continuum observations,\nobtained with the Australian Long Baseline Array, of the Seyfert 2 galaxy\nIC~5063. This object appears to be one of the best examples of Seyfert\ngalaxies where shocks produced by the radio plasma jet influence both the\nradio as well as the near-infrared emission. The picture resulting from the\nnew observations of IC~5063 confirms and completes the one derived from\nprevious Australia Telescope Compact Array (ATCA) lower resolution\nobservations. A strong interaction between the radio plasma ejected from the\nnucleus and a molecular cloud of the ISM is occurring at the position of the\nwestern hot spot, about 0.6~kpc from the active nucleus. Because of this\ninteraction, the gas is swept up forming, around the radio lobe, a cocoon-like\nstructure where the gas is moving at high speed. Due to this, part of the\nmolecular gas is dissociated and becomes neutral or even ionised if the UV\ncontinuum produced by the shocks is hard and powerful enough.\n\nIn the 21-cm \\HI\\ line new data, we detect only part of the strong\nblue-shifted \\HI\\ absorption that was previously observed with the ATCA at\nlower resolution. In particular, the main component detected in the VLBI\nabsorption profile corresponds to the most blue-shifted component in the ATCA\ndata, with a central velocity of 2786 \\kms\\ and therefore blue-shifted\n$\\sim$614 \\kms\\ with respect to the systemic velocity. Its peak optical depth\nis 5.4\\%. The corresponding column density of the detected absorption, for a\nspin temperature of 100 K, is $N_{\\rm HI} \\sim 2 \\times 10^{21} $atoms\ncm$^{-2}$. Most of the remaining blue-shifted components detected in the ATCA\n\\HI\\ absorption profile are now undetected, presumably because this absorption\noccurs against continuum emission that is resolved out in these\nhigh-resolution observations. \n\n The \\HI\\ absorption properties observed in IC 5063 appear different from those\nobserved in other Seyfert galaxies, where the \\HI\\ absorption detected is\nattributed to undisturbed foreground gas associated with the\nlarge-scale galaxy disk. In the case of IC~5063, only a small fraction\nof the absorption can perhaps be due to this. The reason for this can be that\nthe western jet in IC~5063 passes through a particularly rich ISM.\nAlternatively, because of the relatively strong radio flux produced by this\nstrong interaction, and the high spectral dynamic range of our observations,\nbroad absorption lines of low optical depth as detected in IC 5063 may have\nremained undetected in other Seyferts that are typically much weaker radio\nemitters or for which existing data is of poorer quality.\n\n\\end{abstract}\n\n\\keywords{galaxies: individual(IC~5063) --- galaxies: ISM --- galaxies: Seyfert}\n\n\n\\section{Introduction}\n\nThe study of the effects of interactions between the radio plasma ejected from\nan active nucleus and the interstellar medium (ISM) of the hosting galaxy is\npresently attracting a lot of interest. In particular, Seyfert and\nhigh-redshift radio galaxies appear to be the kind of objects where the\neffects of such interactions can be very important. They can range from\nshaping the morphology of the gas in the ISM (with the radio plasma sweeping\nup material as it advances in the ISM), to the ionisation of the gas itself. \nWhile there is little doubt on the presence of such interactions in objects\nlike Seyferts or high-$z$ radio galaxies, the actual importance of these\neffects in determining the overall characteristics of these sources is still\na matter of debate. \n\nIn some Seyfert galaxies the morphological association between the radio\nplasma and the optical line-emitting clouds, as well as the presence of\ndisturbed kinematics in these clouds, is striking. In particular, the\nnarrow-line regions (NLR) in Seyfert galaxies (i.e.\\ regions of highly\nionised, kinematically complicated gas emission that occupy the central area\n-- up to $\\sim 1$ kpc from the nucleus) often appears to form a `cocoon'\naround the radio continuum emission (see e.g.\\ Wilson 1997 for a review;\nCapetti et al.\\ 1996; Falcke, Wilson \\& Simpson (1998) and references\ntherein). Moreover, outflow phenomena are observed in the warm gas of several\nSeyfert galaxies (see Aoki et al.\\ 1996 for a summary). Thus, the NLRs\nrepresent some of the best examples of regions where interaction between the\nlocal ISM and the radio plasma takes place and can be studied in detail.\n\nThe situation appears to be different for the atomic hydrogen. Observations\nof the \\HI\\ 21-cm line, in absorption, can trace the distribution of this gas\nin front of the brightest radio components, that are usually observed in the\ncentral region of Seyferts (of kpc or sub-kpc size, i.e.\\ {\\sl co-spatial with\nthe NLRs}). Thus, the study of the distribution and kinematics of the {\\sl\ncold} component of the circumnuclear ISM can nicely complement the optical\ndata. Although \\HI\\ absorption has been detected in a number of Seyfert\ngalaxies (e.g.\\ NGC~4151 Pedlar et al.\\ 1992; NGC~5929, Cole et al.\\ 1998;\nMkn~6, Gallimore et al.\\ 1998 ; see also Brinks \\& Mundell 1996 and Gallimore\net al.\\ 1999 and references therein), most of the investigated objects show\nsingle localised \\HI\\ absorption components that can be explained as rotating,\ninclined disks or rings aligned with the outer galaxy disk (Gallimore et al.\\\n1999) and only very seldom with gas in a parsec-scale circumnuclear torus\n(NGC~4151, Mundell et al.\\ 1995). These components are therefore originated\nby gas that is not in interaction with the radio plasma. \n\nHowever, more complex {\\sc H\\,i} absorption profiles that cannot be explained\nby the above mechanism have been observed in at least one Seyfert galaxy,\nIC~5063. Australia Telescope Compact Array (ATCA) observations of this galaxy\n(Morganti, Oosterloo \\& Tsvetanov 1998, hereafter M98) have revealed a very interesting\nabsorption system with velocities up to $\\sim 700$ \\kms\\ blue-shifted with\nrespect to the systemic velocity. In this object, unlike in other Seyfert\ngalaxies, at least some of the observed \\HI\\ absorption is originating from\nregions of interaction between the radio plasma and the ISM, producing an\noutflow of the neutral gas. \nThis object, therefore, poses a number of interesting questions as:\nwhere is the interaction occurring, what are the physical conditions, why such\ninteraction is not seen more often in neutral gas in other Seyfert galaxies?\n\nPrevious \\HI\\ observations were limited by low spatial resolution. In this\npaper we\npresent the results from new VLBI observations aimed at investigating in more\ndetail its nuclear radio structure and locating where the complex \\HI\\ absorption\nobserved with ATCA is really occurring.\n\nThroughout the paper we adopt a Hubble constant of $H_\\circ = 50$ \\kms, so that\n1~arcsec corresponds to 0.32 kpc at the redshift of IC~5063.\n\n\\section{Summary of the properties of IC~5063}\n\nIC~5063 is a nearby ($z = 0.0110$) early-type galaxy that hosts a Seyfert 2\nnucleus that emits particularly strong at radio wavelengths ($P_{\\rm 1.4\\,GHz}\n= 6.3\\times 10^{23}$ W Hz$^{-1}$). This object has been recently studied,\nboth in radio continuum at 8 GHz and in the 21-cm line of {\\sc H\\,i}, using\nthe ATCA (M98). In the\ncontinuum, on the arcsecond scale, we find a linear triple structure (see\nFig.\\ 1) of about 4 arcsec size ($\\sim 1.3$ kpc), that shows a close spatial\ncorrelation with the optical ionised gas, very similar in nature to what is\nobserved in several other Seyfert galaxies (see e.g.\\ Wilson 1997) and\nindicating that the radio plasma is important in shaping the NLR.\n\n\nIn the \\HI\\ 21-cm line, apart from detecting the emission from the large-scale\ndisk of IC 5063, very broad ($\\sim 700$ km\\,s$^{-1}$), mainly blue-shifted\nabsorption was detected against the central continuum source. These line\nobservations could only be obtained with $\\sim 7$ arcsec resolution, the\nhighest resolution achievable with the ATCA at this wavelength. This\nresolution is too low to resolve the linear continuum structure detected in\nthe 8-GHz continuum image. However, and what makes this absorption\nparticularly interesting is that we were able to conclude (by a careful\nanalysis of the data, see M98 for the detailed discussion)\nthat at least the most blue-shifted absorption is likely to originate against\nthe western (and brighter) radio knot and not against the central radio\nfeature seen at 8 GHz. The large, blue-shifted velocities observed in the\nabsorption profile make it very unlikely that these motions have a\ngravitational origin (the most blue-shifted \\HI\\ emission associated with the\nlarge-scale \\HI\\ disk occurs at roughly $300$ \\kms with respect to the\nsystemic velocity), and are more likely to be connected to a fast outflow of\nthe ISM caused by an interaction with the radio plasma.\n\n\n\nThe identification of the central radio feature as the core, and hence that\nthe absorption is occurring against the western lobe, is an important element\nin interpreting the nature of the absorption detected in IC~5063. In the\nliterature, the core of this galaxy has sometimes been identified with the\nbright western knot (Bransford et al.\\ 1998), however in our opinion there is\ncompelling evidence that the identification of M98 is\ncorrect.\n\nThe superposition of the 8-GHz radio image with an optical {\\sl WFPC2} image available from the\n{\\sl HST} public archive and with a ground based narrow-band \\OIII\\ image\nsuggests that the nucleus coincides with the central radio knot (see Figs 3\nand 4 from M98). Although, as usual, there is some freedom\nin aligning the {\\sl WFPC2} image with the 8-GHz radio image, aligning the\nwestern radio knot with the nucleus would require too large a shift. Given\nthat the {\\sl WFPC2} image was taken through the F606W filter, it contains the\nbright emission lines of \\OIII$\\lambda 5007$, H$\\alpha$ and \\NII\n$\\lambda\\lambda 6548, 6584$, and it gives a good idea of the morphology of the\nionised gas. By aligning the nucleus with the central radio knot, a good\noverall correspondence between the radio morphology and the bright region of\noptical emission lines is obtained, both in the {\\sl WFPC2} image and the\nground-based \\OIII\\ image, similar in nature to what is observed in many other Seyfert\ngalaxies. Choosing this alignment, the western radio knot falls right on top\nof a very bright, unresolved, spike in the {\\sl WFPC2} image, i.e.\\ the western\nradio knot would also have a counterpart in the {\\sl WFPC2} image. The\nfilamentary morphology of the ionised gas of the region just around this spike\nis suggestive of an interaction between the radio plasma and the ISM and the\nidentification of the western radio lobe with this feature seems natural. \nUsing optical spectroscopy, Wagner \\& Appenzeller (1989) found off-centre\nblue-shifted broad emission lines with similar widths as the detected \\HI\\\nabsorption at a position 1-2 arcsec west of the nucleus, i.e.\\ coincident with\nthe spike seen in the {\\sl WFPC2} image. This also suggests that at this\nposition a violent interaction is occurring. \n\nThe identification of the core with the central radio knot has been recently\nconfirmed by Kulkarni et al.\\ (1998) from NICMOS images. Three well resolved\nknots were detected in the emission lines of [Fe\\,{\\small II}], Pa$\\alpha$ and\nH$_2$. This emission-line structure shows a direct correspondence with the\nradio continuum structure. In broad band near IR images they detected a very red\npoint source coincident with the central source seen in the emission lines,\nconsistent with previous suggestions of a dust-obscured active nucleus. The\nstrong [Fe\\,{\\small II}] and H$_2$ emission are usually interpreted as\nevidence for fast shocks and the direct correspondence between these regions\nand the radio emission suggest that shocks associated with the radio jet play\na role in the excitation of the emission-line knot. \n\nBy the same authors, an asymmetry in the H$_2$ distribution was found, with the\neastern lobe showing a much weaker emission than the western lobe. This\nasymmetry can be explained, e.g, if an excess of molecular gas is present on\nthe western side (for example, if the radio jet has struck a molecular cloud).\n\nIn the optical, IC5063 shows a very high-excitation emission line spectrum\n(including [Fe\\,{\\small VII}]$\\lambda\\lambda$5721, 6087; Colina, Spark \\&\nMacchetto 1991). The high-excitation lines are detected within 1 - 1.5 arcsec\non both sides of the nucleus, about the distance between the radio core and\nboth the lobes. These lines indicate the presence of a powerful and hard\nionising continuum in the general area of the nucleus and the radio knots in IC~5063. We have estimated\n(M98) the energy flux in the radio plasma to be an order of\nmagnitude smaller than the energy flux emitted in emission lines. The shocks\nassociated with the jet-ISM interaction are, therefore, unlikely to account\nfor the overall ionisation and the NLR must be, at least partly,\nphotoionised by the nucleus, unless the lobe plasma contains a significant\nthermal component (Bicknell et al.\\ 1998).\n\n\n\\section{VLBI observations}\n\n\nIC 5063 was observed with the Australian Long Baseline Array (LBA) initially in\ncontinuum at 13 cm (2.3 GHz), followed by spectral-line observations at the\nfrequency corresponding to the redshifted \\HI. \n\nThe 13-cm observations in June 1996 comprised five stations; Parkes (64 m),\nMopra (22 m), the Australia Telescope Compact Array (5$\\times$22-m dishes as\ntied-array), the Mount Pleasant 26-m antenna of the University of Tasmania and\nthe Tidbinbilla 70-m antenna of the Canberra Deep Space Communications Complex\n(CDSCC) near Canberra. The observations used the S2 recording system to\nrecord a single 16 MHz band in right-circular polarisation and were correlated\nat the LBA S2 VLBI correlator of the Australia Telescope National Facility at\nMarsfield, Sydney. \n\nThe 13-cm data were edited and calibrated using the AIPS processing system. After\nthis, the data were exported to DIFMAP (Sheperd 1997) for model fitting and\nimaging. The final image is presented in Fig.~2 and was made with uniform\nweighting. \n\nAlthough the observations were not phase-referenced, absolute position \ncalibration for the 13-cm LBA image was extracted from the delay and rate\ndata, allowing the radio image to be fixed at the $\\sim$0.1 arcsec level in \neach coordinate, adequate for registration with other images.\n\nThe 21-cm observations were made in September 1997 at the redshifted \\HI\\\nfrequency of 1407~MHz, recording 16~MHz bandwidths in each circular\npolarisation. The same array was used, except for the Tidbinbilla 70-m\nantenna, which has no 21~cm capability. Correlation was in spectral-line\nmode with 256 spectral channels on each baseline and polarisation.\n\nThe editing and part of the calibration of the 21-cm line data was done in\nAIPS and then the data were transfered to MIRIAD (Sault, Teuben \\& Wright\n1995) for the bandpass calibration. The calibration of the bandpass was done\nusing additional observations of the strong calibrators PKS~1921--293 and\nPKS~0537--441.\n\nProblems were encountered at Mopra which limited the usefulness of those data.\nIt proved not possible to image the source from the final dataset and instead\na simpler analysis using the time-averaged baseline spectra was employed.\n\n\n\n\n\\section{The sub-kpc structure}\n\n\\subsection{The radio continuum morphology}\n\n\nThe final 13-cm image, shown in Fig.~2, has a beam of $\\sim56\\times 15\\,$mas\nin position angle (p.a.) $-40^\\circ$. The r.m.s. noise is $\\sim 0.7$ mJy\nbeam$^{-1}$. The total flux is\n210 mJy. Because of the high accuracy of the astrometry of this VLBI image, we\nknow that the observed structure corresponds (as expected) to the brighter,\nwestern, lobe observed in the 8-GHz ATCA image (see Fig.~2). \nIt is therefore situated at about 0.6 kpc from the nucleus.\n\nThe image shows that the lobe appears to have a relatively bright peak ($77$\nmJy beam$^{-1}$) and some extended emission to the north-east in p.a.~$\\sim\n40^\\circ$ of total size of about 50 mas (or $\\sim 16$ pc). The p.a.\\ is quite\ndifferent from the p.a.\\ of the arcsecond sized structure seen in the ATCA\n8-GHz data (p.a.~$\\sim 295^\\circ$), so there appears to be structure\nperpendicular to the main radio structure. These kind of distortions are\noften seen in the radio structure of Seyfert galaxies (e.g. Falcke et al. \n1998) and could perhaps result from the interaction of the radio plasma with\nthe environment. \n\nFrom our data, a brightness temperature of $\\rm{T_{B}}\\sim 10^{7}$K can be\ninferred for the VLBI source. This brightness temperature is several orders\nof magnitude less than the typical values seen in milliarcsecond AGN cores or\ninner (pc-scale) jets that typically have brightness temperatures between\n$10^{9}$ and $10^{11}$K. However, this temperature is quite commonly found\nfor radio knots detected in Seyfert galaxies (e.g.\\ knot C in NGC~1068, Roy et\nal.\\ 1998). Unfortunately, we do not have a spectral index of this region on\nthe VLBI scale. The overall spectral index inferred from the ATCA 8.6 and\n1.4-GHz images is steep, $\\alpha\\sim -1$, and indeed consistent with a radio\nlobe or jet. However, unless a detailed multi-frequency spectral index study\ncan be carried out, it is difficult to derive conclusions from this result\nalone given the complexity often observed in the spectral index of the central\nregions of Seyfert galaxies. \n\nIn summary, we can conclude that the radio morphology, the spectrum and the\nbrightness temperature of the VLBI source are consistent with what expected in\na radio lobe.\n\n\n\\subsection{The \\HI\\ absorption}\n\nAs mentioned above, \nbecause from the 21-cm line observations useful data could only be obtained on\nthe Parkes-ATCA baseline, we will present only an time-integrated spectral\nprofile of the \\HI\\ on this baseline. These data correspond to a spatial\nscale of about 0.1 arcsec.\n\nFig.\\ 3 shows the continuum-weighted \\HI\\ absorption profile. \nHeliocentric,\noptical velocities are used. For comparison, the spectrum obtained from the\nprevious ATCA observations (with much lower spatial resolution) is\nsuperimposed (dashed line). In Fig.\\ 3 we have also indicated the range of\nthe velocities observed as measured for the \\HI\\ emission of the large-scale\ndisk of IC 5063, as well as the systemic velocity of the galaxy of $3400$ km\ns$^{-1}$ as derived from the kinematics of the \\HI\\ emission. The r.m.s.\nlimit to the optical depth is $\\sim 0.3$\\%.\n\nFig.\\ 3 shows that a strong absorption signal is detected against the VLBI\nsource. Since from the 13-cm data it followed that the VLBI source corresponds\nto the western radio lobe, these data now confirm what was believed to be the\ncase from the ATCA data, namely that the absorption is occurring against the\nwestern radio lobe.\nFig.\\ 4 shows the same data as in Fig.\\ 3, except that both profiles have been\nnormalised to the same optical depth for the most blue-shifted component.\n\nFigs 3 and 4 show quite clearly that the shape of the absorption profile\nobtained at the high resolution of the VLBI data is quite different in\ncharacter than that obtained with the ATCA. While in the ATCA data the\nabsorption is relatively uniform in velocity, in the VLBI spectrum the\nmost blue-shifted component is clearly the dominant one. This shows\nthat the most blue-shifted absorption is occurring against a compact\nradio source, while the absorption at lower velocities is against a more\ndiffuse source. Component ($A$) has a central velocity of 2786 \\kms,\nover 600 \\kms\\ blue-shifted with respect to the systemic velocity (3400\n\\kms), with its bluest wing extending to about 2650 \\kms, or --750 \\kms\\\nrelative to the systemic velocity. Component $A$ corresponds to the\nmost blue-shifted component found in the ATCA profile, as is illustrated\nin Fig.\\ 4. At slightly less blue-shifted velocities, but still outside\nthe range of velocities observed in emission, the VLBI data show a\nsecond component ($B$). The absorption with velocities within the range\nof the \\HI\\ emission, as detected in the ATCA profile, is only partly\ndetected in the VLBI spectrum with component $C$. No absorption is\ndetect in the velocity range 3000-3200 \\kms. Hence, the absorption seen\nin the ATCA data at velocities above 3000 \\kms\\ has become much less\nprominent compared to the more blue-shifted absorption. Note that this\neffect is probably even stronger than the data shows, since the low\nresolution of the ATCA will have caused some filling of the absorption\nwith emission of the \\HI\\ disk and the `true' absorption is likely to be\nstronger at these velocities. The ATCA spectrum also showed a faint\nred-shifted absorption component that is perhaps also detected in the\nVLBI spectrum. \n\n\nThe column density $N_{\\rm HI}$ of the obscuring neutral hydrogen is given by\n$N_{\\rm HI} = 1.823\\times 10^{18} T_s \\int \\tau dv$ cm $^{-2}$ where $T_{\\rm\ns}$ is the spin temperature of the electron. Assuming a spin temperature of\n100~K we derive a column density of $\\sim 1.7 \\times 10^{21}$ atoms cm$^{-2}$\nfor the components $A$ and $B$ and a column density of $\\sim 2.5 \\times\n10^{20}$ atoms cm$^{-2}$ for the component $C$. The main source of\nuncertainty for the derived column density comes from the assumption in the\nvalue of the spin temperature. The presence of a strong continuum source near\nthe \\HI\\ gas can make the radiative excitation of the \\HI\\ hyperfine state to\ndominate over the, usually more important, collisional excitation (see e.g.\\\nBahcall \\& Ekers 1969). Gallimore et al.\\ (1999) argue that the \\HI\\ causing\nthe absorption against Seyferts jets is in general at too high densities\n($\\sim$$10^5$ cm$^{-3}$) for these effects to be relevant. \nHowever, the argument used by Gallimore et al.\\ applies to \\HI\\ in pressure\nequilibrium with the NLR, while the absorbing gas in Seyferts in general is\n{\\sl not} co-spatial with the NLR, but is at larger radii. Because of this the\ndensity of the absorbing gas is lower, but the regions are also further\nremoved from the central engine and the spin temperature approaches the\nkinetic temperature at much lower densities.\nIn our model for IC 5063, the \\HI\\ causing the most blue-shifted absorption\nis the skin of a molecular cloud that is being stripped off by the jet (see\nalso \\S 5). Given that typical densities in molecular clouds are in the range\n$10^4$ - $10^6$ cm$^{-3}$, this is an upper limit to the density of the\nabsorbing gas. But given the large velocities involved, the actual density of\nthe blue-shifted gas could be substantially lower.\n\nThe effects on the excitation of the fine-structure line by the local\nradiation field were already discussed by M98 for the case\nof IC 5063, where it was concluded that these effects are perhaps\nimportant. The column density derived by Kulkarni et al.\\ \nfrom the NICMOS observation ($N_{\\rm HI} \\sim 5\n\\times 10^{21}$ atoms cm$^{-2}$) is slightly higher than our estimate based on \na $T_{\\rm spin}$ of 100 K, also suggesting that perhaps the spin temperature\nis somewhat higher than 100 K. For $T_{\\rm spin} = 100$ K the derived column\ndensity is much lower than the value of $\\sim10^{23}$atoms cm$^{-2}$ found\nfrom X-ray data (Koyama et al.\\ 1992).\n\n\n\\section{H{ \\small \\bf I}, H$_2$ and radio plasma: a possible scenario for the\ninteraction}\n\nSummarising, the main result from our new observations is that with the\nimproved spatial resolution, the absorption at velocities outside the range\nallowed by the rotational kinematics of the large-scale \\HI\\ disk has become\nmuch stronger, while the absorption in the range of velocities of the \\HI\\\ndisk has become much less prominent. \n\nFrom the 13-cm radio continuum VLBI data we have been able to image only the\nwestern part of the source observed by the ATCA, while the remaining structure\nis resolved out.\n\nThus, all this confirms and completes the picture we derived from the ATCA data,\nnamely that {\\sl a strong interaction between the radio plasma and the ISM is\noccurring at the position of the western radio lobe}. \n\nFig.\\ 5 gives a schematic diagram of what we believe is happening in the western\nlobe of IC~5063. Following the results from NICMOS (Kulkarni et al.\\ 1998),\nit is likely that the asymmetry observed in the brightness of the H$_2$\n(western side brighter than the eastern side) may be explained by an excess of\nmolecular gas on the western side. Thus, the radio plasma ejected from the\nnucleus appears to interact directly with such a molecular cloud. Because\nof this interaction, the jet is drilling a hole in the dense ISM, sweeping up\nthe gas and forming a cocoon-like structure\naround the radio lobe where the gas is moving at high speed and an outflow of\ngas is created. The increased ultraviolet radiation due to the presence of\nshocks generated from the interaction, can dissociate part of the molecular\ngas. This creates neutral hydrogen or even ionised gas if the UV continuum\nproduced by the shocks is hard and powerful enough. The region of ionised gas\nwould correspond to the part of the cocoon closer to where the interaction is\noccurring, possibly corresponding to both the shocked gas and to the precursor.\nThe complex kinematics of the emission lines in this region observed from\nthe optical emission lines (Wagner \\& Appenzeller 1989) is consistent with this.\n\nAs for the neutral gas, we will observe only the component in front of the\nradio continuum and therefore, as effect of the outflow produced by the\ninteraction, we will observe only the blue-shifted component. The most\nblue-shifted component will be seen against the hot spot where the interaction\nis most intense. Somewhat away from this location, the \\HI\\ will driven out by\nthe expanding cocoon, but since this is away from the hot spot, this will occur\nat lower velocities. Moreover, the radio continuum emission from this region\nis also more extended compared to the small-sized hot spot. Hence the VLBI\nobservation do not detect the absorption at lower velocities, but only the\nhighest velocities against the hot spot (as illustrated in Fig.5).\n\nThe origin of the H$_2$ emission can be related to UV or shocks (Draine,\nRoberge \\& Dalgano 1983, Sternberg \\& Dalgano 1989). Although we are not able\nto distinguish between these two mechanisms, this scenario suggest that there\nshould be in IC~5063 a strong shock component. The H$_2$ emission observed by NICMOS\nwould therefore come from the very dense region (again due to the compression\nof the gas associated with the interaction) of the molecular cloud. \n\nAs we noticed above, not all the components observed in the ATCA data are also\nvisible in the VLBI data. A possible explanation for this is that the\ncomponents that are missing from the VLBI \\HI\\ absorption are against\ncontinuum emission that is resolved out in our VLBI data, indicating that the\ncocoon of shocked gas is quite extended and cover at least all the western\nradio lobe. Alternatively, part of the absorption undetected in the VLBI\nspectrum can be due to the large-scale disk associated with the dust-lane and\nalso seen in \\HI\\ in emission, although the continuity of the ATCA absorption\nprofile does not suggest this. \n\nBy looking at the velocity field derived for this disk from the \\HI\\ emission\nobservations (see Fig.\\ 5 in M98) we can see as the western side\nis the approaching side, therefore showing a blue-shifted velocity relative to\nthe systemic. This means that the large-scale disk being in front of the hot\nspot could be responsible for component $C$, but that it cannot explain the\nweak red-shifted component unless non circular motions are present in the\nforeground gas associated with the dust lane. In M98 we\nhypothesised that the red-shifted component could be associated with a nuclear\ntorus/disk. This was motivated by the fact that the width of the red-shifted\ncomponent appeared to be similar to the width of the CO profile as observed by\nWiklind et al.\\ (1995). However, there seems to be no indication of detection\nof the nuclear component from the visibility of the continuum associated with\nthe 21-cm data (and by extrapolating the arcsec data, the core flux is\nprobably too weak to be detected and, even more, to produce an absorption) so\nthis hypothesis has to be ruled out. A final possibility is that, apart from\nthe bulk outflow, turbulent motions produced in the shocked region can give\nrise to clouds with red-shifted velocity. \n\n\n\\section{Comparison with other Seyfert galaxies}\n\nHow does IC~5063 compare with other Seyferts galaxies? The results on IC~5063\nconfirm the more general results obtained by Gallimore et al.\\ (1999) on a\nsample of Seyfert galaxies, that the \\HI\\ absorption is not occurring against\nthe core and that the absorbing gas in Seyferts does not trace (except for NGC\n4151) the pc-scale gas. In the galaxies studied by Gallimore et al., the\nabsorption is occurring at a few hundred parsec from the core and is caused by\nthe inner regions of, or gas associated with, the large-scale \\HI\\ disks.\nThis is also happening in IC 5063. The important difference is that in IC\n5063 the jet is physically strongly interacting with this \\HI\\ disk, causing\nthe fast outflow observed for the absorbing material. This makes IC 5063\nunique. Only component $C$ would exactly fit the scenario proposed by\nGallimore et al. It is quite likely a gas cloud at large radius (given its\ncolumn density), unrelated to the interaction, projected in front of the radio\nhot spot.\n\nOne obvious question is why such kind of absorption (i.e.\\ broad blue-shifted\nabsorption) is so rare. Are the physical conditions in IC 5063 rare, or is\nthere an observational bias?\n\nSome arguments suggest that IC 5063 is a special case. IC 5063 is a very\nstrong radio emitter compared to other Seyfert galaxies. Most of the strong\nradio flux of IC 5063 is produced in the western radio knot, indicating that\nthe interaction is particularly strong. Also the fact that the western radio\nknot is much brighter than the eastern one indicates that the conditions near\nthe western lobe are special. It has been noted that IC~5063 belongs to a\ngroup of \"radio-excess infrared galaxies\" (Roy \\& Norris 1997), objects that\ncould represent active galactic nuclei hosted in an unusual environment or\nperhaps dust-enshrouded quasars or their progenitors. \nIt appears that the jet-cloud interaction in IC 5063 is particularly strong. \nThis would make IC 5063 a very suitable object for further detailed studies of\njet-cloud interactions in Seyfert galaxies. \n\nOne factor is of course that in order to create the strong interaction and the\nvery broad absorption, the jet has to lie more or less in the plane of the\n\\HI\\ disk. Only then can the jet have a strong interaction with the ISM. The\norientation of the AGN in Seyferts is not correlated with that of the\nlarge-scale disk, so the effects seen in IC~5063 should then only occur in a\nminority of cases. \n\nOn the other hand, interactions between the radio plasma and the ISM are\ncommon in Seyferts, given that in many Seyfert galaxies, very large velocity\nwidths of the optical emission lines are observed in the NLR (e.g.\\ Aoki et\nal.\\ 1996 and references therein). Perhaps the high sensitivity in $\\tau$ of\nour observations also plays a role. IC~5063 is a strong radio source compared\nto other Seyfert galaxies that are between 10 and 100 times weaker at radio\nwavelengths. Therefore only \\HI\\ absorption with much higher optical depth\ncan be observed against those objects. For example, the Seyfert 2 galaxy NGC\n5929 shows a striking morphological similarity (both in the optical and radio)\nwith IC 5063. However, the peak of the radio emission in NGC~5929 is only 24\nmJy beam$^{-1}$, so in this object absorption of a few percent\nwould not be detectable with the noise level of the current observations (Cole\net al.\\ 1998). For almost all the galaxies in the sample studied by Gallimore\net al.\\ (1999) is the sensitivity not enough to have been able to detect\nfaint, broad absorption like in IC 5063. Moreover, in order to detect broad\nprofiles of the level as in IC 5063 even in strong sources, good spectral\ndynamic range is required, which is not always easy to obtain (e.g.\\ NGC 1068;\nGallimore et al.\\ 1999). It is quite well possible that more cases like IC\n5063 will be found if more sensitive observations are performed.\n\n\n\\section{Conclusions}\n\nUsing the Australian Long Baseline Array, we have detected a compact radio\nsource of about of 50 mas (or $\\sim 16$ pc) in size (at 13 cm) in the Seyfert\ngalaxy IC 5063. Because of the high positional accuracy of these\nmeasurements, we can unambiguously identify this radio knot with the western\nradio lobe. The hot spot is extended in a direction almost perpendicular to\nthe radio jet. \n\nIn 21-cm line observations, we detect absorption very much blue-shifted\n($\\sim$700 km s$^{-1}$) with respect to the systemic velocity. Together with\nthe 13-cm observations, this confirms that the \\HI\\ absorption is not taking\nplace against the core, but that it is against the western radio knot. At the\nposition of the western radio knot a very strong interaction must be occurring\nbetween the radio jet and the ISM. Various arguments suggest that this\ninteraction is particularly strong compared to other Seyfert galaxies. This\nmakes IC 5063 a good candidate for studying the physics of jet-cloud\ninteractions in Seyfert galaxies. \n\nThe HI absorption characteristics of IC 5063 are only partially\nconsistent with other absorption studies of Seyfert galaxies. The \nmajor absorption component is occuring against the bright radio \nknot offset a few hundred parsecs from the core. While there are \nindication that the absorbing material is associated with the large \nscale \\HI\\ disk, it is clearly (and violently) disturbed by the\npassage of the jet. We suspect that more sensitive observations \nmay reveal similar absorption profiles in other Seyfert galaxies \nwith fainter radio sources.\n\n\\acknowledgements\nWe wish to thank the referee, Jack Gallimore, for his useful comments.\n\n\\newpage\n\n\\begin{thebibliography}{}\n \n\\bibitem{} Aoki K., Ohtani H., Yoshida M. \\& Kosugi G. 1996, AJ 111, 140\n\\bibitem{} Bahcall J.N., Ekers R.D. 1969, ApJ 157, 1055\n\\bibitem{} Bicknell G.V., Dopita M. A., Tsvetanov Z.I., Sutherland R. S.\n1998, ApJ 495, 680\n\\bibitem{} Bransford M.A., Appleton P.N., Heisler C.A., Norris R.P., Marston\nA.P. 1998, ApJ 497, 133\n\\bibitem{} Brinks, E., \\& Mundell, C.~G. 1996, in {\\it The Minnesota\nLectures on Extragalactic Neutral Hydrogen}, ed.\\ E.~D.\\ Skillman, ASP\nConf.\\ Series, 106, 268 \n\\bibitem{} Capetti A., Macchetto F., Axon D.J., Sparks W.B. \\& Boksenberg\nA. 1996, ApJ 469, 554\n\\bibitem{} Cole G.H.J., Pedlar A., Mundell C.G.,\nGallimore J.F. \\& Holloway 1998, MNRAS 301,782 \n\\bibitem{} Colina L., Sparks W.B. \\& Macchetto F. 1991, ApJ 370, 102\n\\bibitem{} Draine B.T., Roberge W.G. \\& Dalgano A. 1983, ApJ 264, 485\n\\bibitem{} Falcke H., Wilson A.S., Simpson C. 1998, ApJ 502, 199\n\\bibitem{} Gallimore J.F., Holloway A.J., Pedlar A.,\nMundell C.G. 1998, A\\&A 333, 13 \n\\bibitem{} Gallimore J.F., Baum S.A., O`Dea C.P., Pedlar A., Brinks E. 1999,\nApJ in press (astro-ph/9905267)\n\\bibitem{} Koyama, K., Awaki, H., Iwasawa, K., \\& Ward, M. J. 1992, ApJ, 399, L129\n\\bibitem{} Kulkarni V.P. et al. 1998, ApJ 492, L121 \n\\bibitem{} Morganti R., Oosterloo T. \\& Tsvetanov Z., 1998, AJ, 115, 915 (M98)\n\\bibitem{} Pedlar A., Howley P., Axon D.J. \\& Unger\nS.W., 1992, MNRAS, 259, 369 \n\\bibitem{} Mundel C.G., Pedlar A., Baum\nS.A., O'Dea C.P., Gallimore J.F. \\& Brinks E. 1995, MNRAS 272, 355\n\\bibitem{} Roy A.L., Colbert E.J.M., Wilson A.S., Ulvestad J.S. 1998, ApJ 504,\n147\n\\bibitem{} Roy A.L. \\& Norris R.P. 1997, MNRAS 289, 824\n\\bibitem{} Sault R.J., Teuben P.J., Wright M.C.H. 1995, in {\\it ``Astronomical \nData Analysis Software and Systems IV''}, eds. R. Shaw, H.E. Payne and\nJ.J.E. haynes, ASP Conf. Series, 77, 433 \n\\bibitem{} Shepherd M.C. 1997, in ``Astronomical Data Analysis Software and\nSystems IV'', ASP Conf. Series Vol. 125, Hunt G. \\& Payne H.E. (eds.), p.77\n\\bibitem{} Sternberg A. \\& Dalgano A. 1989, ApJ 338, 197\n\\bibitem{} Wagner S.J. \\& Appenzeller I., 1989, A\\&A, 225, L13\n\\bibitem{} Wiklind T., Combes F. \\& Henkel C. 1995, A\\&A 297, 643\n\\bibitem{} Wilson A.S. 1997, in {\\it ``Emission lines in Active Galaxies: \nnew methods and techniques''}, eds.\\ B.M. Peterson, F.-Z.\\ Cheng and A.S.\\\nWilson, ASP Conf.\\ Series Vol.\\ 113, p.\\ 264\n\n\\end{thebibliography}\n\n\\newpage\n\n\\figcaption{ATCA 3 cm radio continuum image from Morganti et al.\\ (1998).}\n\\figcaption{VLBI 13 cm radio continuum image of (the western lobe of) IC~5063}\n\\figcaption{VLBI \\HI\\ absorption profile converted in optical depth.\nFor comparison, the ATCA profile is superimposed as dashed line.}\n\n\\figcaption{VLBI (solid line) and ATCA (dashed line) \\HI\\ absorption profile \nnormalised to the same optical depth of the main absorption component.}\n\n\\figcaption{Schematic diagram of the model presented in \\S 5 to explain the \ncharacteristics of the \\HI\\ absorption observed in the western lobe of\nIC~5063. See text for details.}\n\n\n% Fig. 1\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=oosterloo.fig1.ps,width=10cm,angle=-90}}\n{\\bf Fig.1}\n\\end{figure}\n\n\\newpage\n% Fig. 2\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=oosterloo.fig2.ps,width=9cm,angle=0}}\n{\\bf Fig.2}\n\\end{figure}\n\n% Fig. 3\n\\begin{figure}\n\\centerline{\\psfig{figure=oosterloo.fig3.eps,width=8.5cm,angle=-90}}\n{\\bf Fig.3}\n\\end{figure}\n\n\n% Fig. 4\n\\begin{figure}\n\\centerline{\\psfig{figure=oosterloo.fig4.eps,width=8.5cm,angle=-90}}\n{\\bf Fig.4}\n\\end{figure}\n\n\n% Fig. 5\n\\begin{figure}\n\\centerline{\\psfig{figure=oosterloo.fig5.eps,width=13cm}}\n{\\bf Fig.5}\n\\end{figure}\n\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002140.extracted_bib",
"string": "\\begin{thebibliography}{}\n \n\\bibitem{} Aoki K., Ohtani H., Yoshida M. \\& Kosugi G. 1996, AJ 111, 140\n\\bibitem{} Bahcall J.N., Ekers R.D. 1969, ApJ 157, 1055\n\\bibitem{} Bicknell G.V., Dopita M. A., Tsvetanov Z.I., Sutherland R. S.\n1998, ApJ 495, 680\n\\bibitem{} Bransford M.A., Appleton P.N., Heisler C.A., Norris R.P., Marston\nA.P. 1998, ApJ 497, 133\n\\bibitem{} Brinks, E., \\& Mundell, C.~G. 1996, in {\\it The Minnesota\nLectures on Extragalactic Neutral Hydrogen}, ed.\\ E.~D.\\ Skillman, ASP\nConf.\\ Series, 106, 268 \n\\bibitem{} Capetti A., Macchetto F., Axon D.J., Sparks W.B. \\& Boksenberg\nA. 1996, ApJ 469, 554\n\\bibitem{} Cole G.H.J., Pedlar A., Mundell C.G.,\nGallimore J.F. \\& Holloway 1998, MNRAS 301,782 \n\\bibitem{} Colina L., Sparks W.B. \\& Macchetto F. 1991, ApJ 370, 102\n\\bibitem{} Draine B.T., Roberge W.G. \\& Dalgano A. 1983, ApJ 264, 485\n\\bibitem{} Falcke H., Wilson A.S., Simpson C. 1998, ApJ 502, 199\n\\bibitem{} Gallimore J.F., Holloway A.J., Pedlar A.,\nMundell C.G. 1998, A\\&A 333, 13 \n\\bibitem{} Gallimore J.F., Baum S.A., O`Dea C.P., Pedlar A., Brinks E. 1999,\nApJ in press (astro-ph/9905267)\n\\bibitem{} Koyama, K., Awaki, H., Iwasawa, K., \\& Ward, M. J. 1992, ApJ, 399, L129\n\\bibitem{} Kulkarni V.P. et al. 1998, ApJ 492, L121 \n\\bibitem{} Morganti R., Oosterloo T. \\& Tsvetanov Z., 1998, AJ, 115, 915 (M98)\n\\bibitem{} Pedlar A., Howley P., Axon D.J. \\& Unger\nS.W., 1992, MNRAS, 259, 369 \n\\bibitem{} Mundel C.G., Pedlar A., Baum\nS.A., O'Dea C.P., Gallimore J.F. \\& Brinks E. 1995, MNRAS 272, 355\n\\bibitem{} Roy A.L., Colbert E.J.M., Wilson A.S., Ulvestad J.S. 1998, ApJ 504,\n147\n\\bibitem{} Roy A.L. \\& Norris R.P. 1997, MNRAS 289, 824\n\\bibitem{} Sault R.J., Teuben P.J., Wright M.C.H. 1995, in {\\it ``Astronomical \nData Analysis Software and Systems IV''}, eds. R. Shaw, H.E. Payne and\nJ.J.E. haynes, ASP Conf. Series, 77, 433 \n\\bibitem{} Shepherd M.C. 1997, in ``Astronomical Data Analysis Software and\nSystems IV'', ASP Conf. Series Vol. 125, Hunt G. \\& Payne H.E. (eds.), p.77\n\\bibitem{} Sternberg A. \\& Dalgano A. 1989, ApJ 338, 197\n\\bibitem{} Wagner S.J. \\& Appenzeller I., 1989, A\\&A, 225, L13\n\\bibitem{} Wiklind T., Combes F. \\& Henkel C. 1995, A\\&A 297, 643\n\\bibitem{} Wilson A.S. 1997, in {\\it ``Emission lines in Active Galaxies: \nnew methods and techniques''}, eds.\\ B.M. Peterson, F.-Z.\\ Cheng and A.S.\\\nWilson, ASP Conf.\\ Series Vol.\\ 113, p.\\ 264\n\n\\end{thebibliography}"
}
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astro-ph0002141
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Detection of deuterium Balmer lines in the Orion Nebula \thanks{Based on observations collected at the Canada-France-Hawaii Telescope, Hawaii, USA.}
|
[
{
"author": "G.~H\\'ebrard \\inst{1}"
},
{
"author": "D.~P\\'equignot \\inst{2}"
},
{
"author": "A.~Vidal-Madjar \\inst{1}"
},
{
"author": "J.~R.~Walsh \\inst{3}"
},
{
"author": "R.~Ferlet \\inst{1}"
}
] |
The detection and first identification of the deuterium Balmer emission lines, \da\ and \db, in the core of the Orion Nebula is reported. These lines are very narrow, have identical 11~\kms\ velocity shifts with respect to \ha\ and \hb, are probably excited by UV continuum fluorescence from the Lyman (\ion{D}{i}) lines and arise from the interface between the \hii\ region and the molecular cloud. \keywords{Line: formation -- Line: identification -- H\ts {\sc ii} regions -- ISM: individual objects: M42 -- ISM: atoms -- Cosmology: observations }
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[
{
"name": "Ca051.tex",
"string": "% article.tex\n% AA vers. 4.01, LaTeX class for Astronomy & Astrophysics\n% (c) Springer-Verlag HD\n%-----------------------------------------------------------------------\n%\n%\\documentclass[referee]{aa} % for a referee version\n%\n\\documentclass{aa}\n%\n\n\\usepackage{graphics}\n\n\\def \\dshism{${(\\rm{D/H})}_{ISM}$}\n\\def \\hii{\\ion{H}{ii}}\n\\def \\hi{\\ion{H}{i}}\n\\def \\di{\\ion{D}{i}}\n\\def \\nii{[\\ion{N}{ii}]}\n\\def \\oi{\\ion{O}{i}}\n\\def \\si{\\ion{Si}{ii}}\n\\def \\ha{H$\\alpha$}\n\\def \\hb{H$\\beta$}\n\\def \\hg{H$\\gamma$}\n\\def \\hd{H$\\delta$}\n\\def \\da{D$\\alpha$}\n\\def \\db{D$\\beta$}\n\\def \\dg{D$\\gamma$}\n\\def \\dd{D$\\delta$}\n\\def \\kms{${\\rm km}\\,{\\rm s}^{-1}$}\n\\def \\ie{{\\it i.e.}}\n\\def \\eg{{\\it e.g.}}\n\\def \\etc{{\\it etc}}\n\\def \\la{$\\lambda$}\n\\def \\cm2{cm$^2$}\n\\def \\lybd{Ly$\\beta_{{\\rm D}}$}\n\\def \\lyb{Ly$\\beta_{{\\rm H}}$}\n\n\n\\begin{document}\n\n \\thesaurus{08 % A&A Section 8: Diffuse matter in space\n (02.12.1 %Line: formation\n 02.12.2 %Line: identification\n 09.01.2 %ISM: atoms\n 09.08.1 %(ISM:) HII regions\n 09.09.1 M42 %ISM: individual object: M42\n 12.03.3)} %Cosmology: observations\n \n%\n%\\headnote{Letter to the Editor} \n%\n\n \\title{Detection of deuterium Balmer lines in the Orion Nebula\n\\thanks{Based on observations collected at the Canada-France-Hawaii\nTelescope, Hawaii, USA.}\n}\n\n \\author{ G.~H\\'ebrard \\inst{1}\n \\and\n D.~P\\'equignot \\inst{2}\n \\and\n A.~Vidal-Madjar \\inst{1}\n \\and\n J.~R.~Walsh \\inst{3}\n \\and\n R.~Ferlet \\inst{1}\n }\n\n \\offprints{Guillaume H\\'ebrard}\n% \\mail{hebrard@iap.fr}\n\n \\institute{Institut d'Astrophysique de Paris, CNRS,\n 98 bis Boulevard Arago, F-75014 Paris, France \n (hebrard@iap.fr, vidalmadjar, ferlet).\n \\and\n Laboratoire d'Astrophysique Extragalactique et de \n Cosmologie associ\\'e au CNRS (UMR 8631) et \\`a l'Universit\\'e \n Paris 7, DAEC, Observatoire de Paris-Meudon, F-92195 \n Meudon C\\'edex, France (daniel.pequignot@obspm.fr).\n \\and\n Space Telescope European Co-ordinating Facility, \n European Southern Observatory, Karl-Schwarzschild-Strasse 2,\n D-85748 Garching bei M\\\"unchen, Germany \n (jwalsh@eso.org).\n }\n\n\n \\date{Received ? / Accepted ?}\n\n \\maketitle\n\n \\begin{abstract}\n\nThe detection and first identification of the deuterium Balmer \nemission lines, \\da\\ and \\db, in \nthe core of the Orion Nebula is reported. \nThese lines are very narrow, have identical \n11~\\kms\\ velocity shifts with respect to \\ha\\ and \\hb, \nare probably excited by UV continuum \nfluorescence from the Lyman (\\ion{D}{i}) lines and arise from the \ninterface between the \\hii\\ region and the molecular cloud.\n\n\n \\keywords{Line: formation --\n Line: identification --\n H\\ts {\\sc ii} regions --\n ISM: individual objects: M42 -- \n ISM: atoms --\n Cosmology: observations\n }\n \\end{abstract}\n\n%\n%________________________________________________________________\n\n\\section{Introduction}\n\nDeuterium is believed to be entirely produced in the Big Bang \nand then steadily destroyed by astration \n(Epstein et al.~\\cite{epstein76}). \nStandard models predict a decrease of \nits abundance by a factor 2--3 in 15~Gyrs\n(\\eg,~Tosi et al.~\\cite{tosi98}). This picture is essentially \nconstrained by deuterium abundance determinations at $\\sim15$~Gyrs \n(primordial intergalactic clouds), 4.5~Gyrs (protosolar) and 0.0~Gyrs \n(interstellar medium). \nAlthough the evolution of the deuterium abundance seems to be \nqualitatively understood, the measurements \nshow some dispersion. \nThus, absorption in the Lyman series provides \ninterstellar deuterium abundance \n\\dshism$\\simeq1.5\\times10^{-5}$ \n(Linsky~\\cite{linsky98}), \nbut with fluctuations that may well be real \n(Vidal-Madjar et al. 1998). \nThese dispersions led to the development of non-standard \nmodels in which, for example, deuterium may either decrease \nby more than a factor 4 \nin 15~Gyrs (\\eg,~Vangioni-Flam et al.~\\cite{flam94}) \nor be created/destroyed by new mechanisms\n[\\eg, Lemoine et al.~(\\cite{lemoine99}) for a~review].\n\nA detailed appraisal of the evolution of deuterium is \ncrucial for cosmology and galactic chemical evolution. \nThe most reliable estimate of \\dshism\\ to date is based on \nfar-UV observation from space (Copernicus, IMAPS, HST or FUSE) \nof the Lyman lines of D and H in absorption. \nThese lines are also observed in the optical and near-UV \nto obtain D/H in high redshift quasar \nabsorbers. Other D/H determinations include {\\it in situ} measurements \nin the Solar System (\\eg,~Mahaffy et al.~\\cite{mahaffy98}), \nobservations of molecules such as HD \nor DCN (\\eg,~Bertoldi et al.~\\cite{bertoldi99}) \nand observations of \\ion{D}{i}~92~cm \n(\\eg,~Chengalur et al.~\\cite{chengalur97}).\n\nNew methods to determine D/H are of interest. One possibility \nis ground-based observation of the deuterium lines. \nThe isotope shift of the deuterium Balmer lines \nwith respect to the hydrogen Balmer lines \nis $-81.6$~\\kms. These \\di\\ lines have never been identified before. \nAttempts to detect \\da\\ \nin absorption in the Sun (Beckers~\\cite{beckers75}) \nand early-type stars \n(\\eg,~Vidal-Madjar et al.~\\cite{avm88}) \nwere unsuccessful (D is destroyed in stars).\nTraub et al.~(\\cite{traub74}) \nobserved \\ha\\ in the Orion Nebula using three-etalon Fabry-Perot \nspectrometers and reported D/H upper limits. \n\nHere we report on spectra of Orion, secured at the Canada-France-Hawaii \nTelescope (CFHT). Emission lines detected in the blue wings of \\ha\\ \nand \\hb\\ are identified with \\da\\ and \\db. A preliminary account \nwas presented by H\\'ebrard et al. (\\cite{hebrard99}). \nObservations \nare described in \nSect.~\\ref{observations}, the identification and the origin of \nthe lines in Sect.~\\ref{identification} \nand \\ref{origin} and the excitation mechanism in \nSect.~\\ref{fluo}. \n\n\n\\section{Observations, data reduction and results}\n\\label{observations}\n\nObservations of the Orion Nebula (\\object{M 42}, NGC~1976) were \nconducted at the 3.6m CFHT, using the Echelle spectrograph \nGecko at the Coud\\'e focus with a slit length of $\\sim40$\\arcsec.\nThe \\ha\\ and \\hb\\ spectral ranges were observed \nin October 1997 and September 1999 respectively. For \\ha, \nthe entrance slit was 1.2mm wide (3.5\\arcsec\\ on the sky), providing \na resolution $R=\\lambda/\\Delta\\lambda\\simeq40\\,000$ ($\\sim7.5$~\\kms); \nthe detector was the $2048\\times2048$ ``Loral~5'' thin CCD and \nthe spectral range was 6544\\AA\\ - 6576\\AA. \nFor \\hb, the slit was 0.8mm wide (2.3\\arcsec) leading to \n$R\\simeq50\\,000$ ($\\sim6$~\\kms); \nthe detector was the $2048\\times4500$ ``EEV2'' thin CCD and \nthe spectral range was 4832\\AA\\ - 4885\\AA. \n\nThe slit was centred 2.5\\arcmin\\ South of $\\theta^1$~Ori~C \n(\\object{HD 37022}), the brightest star of the Trapezium. \nThe slit orientation was slowly rotating during the exposures \n(Coud\\'e focus). \nTotals of 4.5 and 1.5 hours were devoted to \\ha\\ and \\hb\\ respectively,\ndivided in 30 -- 45~min sub-exposures. \nSmall rotations of the grating were applied between \\ha\\ sub-exposures \nin order to disclose ghosts that may depend on grating setting. \n\\ha\\ was also observed at higher resolution ($R\\simeq80\\,000$) \nin the same area for 20~min. \nFinally, \\hb\\ was observed \n2.5\\arcmin\\ North and 20\\arcsec\\ South of $\\theta^1$~Ori~C \nwith shorter exposures and $R\\simeq50\\,000$. \nBias, flats and Thorium-Neon lamp calibration \nexposures were secured regularly during the observations \nfor each instrument configuration. \n\n\nThe spectra were reduced using MIDAS software. \nThe steps of the data reduction were as follows:\n(1)~bias subtraction; \n(2)~flat division; \n(3)~bad pixel and cosmic cleaning; \n(4)~summing the rows to transform the 2D-spectra into \n1D-spectra; \n(5)~wavelength calibration;\n(6)~shift to the heliocentric frame; \n(7)~alignment of the different sub-exposures; and \n(8)~suming up of the sub-exposures. \nAfter shifting to the heliocentric frame, both \\ha\\ and \\hb\\ \nwere fitted by a Gaussian on each sub-exposure. The standard \ndeviation of the Gaussian peaks was less than 1~\\kms. \nSub-exposures were shifted to the average peak before summation \nin order to preserve the spectral resolution. \nAn interfering signal, instrumental in origin, appeared in \nthe \\hb\\ spectra, producing small oscillations in the dispersion \ndirection, which slightly increased the noise level. \nWavelengths are determined to better than 1.5~\\kms\\ and 1.0~\\kms\\ \nin the \\ha\\ and \\hb\\ final spectra respectively. \n\nTwo weak emission lines are obvious \nin the blue wings of \\ha\\ and \\hb\\ (Fig~\\ref{fig_detection}). \nAnticipating the conclusion of Sect.~\\ref{identification}, the weak \nlines are already identified with \\da\\ and \\db\\ in Table~\\ref{lines}, \nwhere results of Gaussian fits to \\ha, \\hb, \\da\\ and \\db\\ are given.\nThe full widths at half maximum (FWHM) of the deuterium lines are \nmuch smaller than those of the hydrogen lines. \nRelative fluxes (last row of Table~\\ref{lines}) are based on the \ntheoretical \\ha/\\hb\\ ratio, thus implicitly correcting for reddening. \nFor an H$^+$-weighted electron temperature \n(0.85$\\pm$0.10)$\\times$10$^4$K \nand electron density $\\sim$ 5$\\times$10$^3$~cm$^{-3}$\n(\\eg, Esteban et al.~\\cite{esteban98}), the \nCase~B recombination ratio \n$I({\\rm H}\\alpha)$/$I({\\rm H}\\beta)$ is 2.91$\\pm$0.03 \n(Storey \\& Hummer~\\cite{stohum95}). \nDeparture of this ratio from Case~B is expected to be much \nless than 1\\% in this thick nebula for any reasonable dust content \n(Hummer \\& Storey~\\cite{humsto92}). \n\n\\da\\ and \\db\\ are seen all along the 40\\arcsec\\ slit. \n\\db\\ is present at all three positions. \nThe velocity shifts between \\db\\ and \\hb\\ at \n2.5\\arcmin~N, 20\\arcsec~S and 2.5\\arcmin~S of $\\theta^1$~Ori~C \nare respectively 11.8, 9.1 and 10.0~\\kms\\ and the \\db\\ fluxes \n$4.2\\pm1.1$, $2.3\\pm0.6$ and \n$5.7\\pm1.1$ (\\hb$=10\\,000$). \n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{Ca051_fig.ps}}\n\\caption[]{Vicinity of \\ha\\ and \\hb\\ in Orion, showing \\da\\ and \\db\\ \nin emission. \nThe x-axis is in \\kms\\ relative to the rest wavelength of either \\ha\\ \nor \\hb. The vertical scale corresponds to peak fluxes $7250$ and $2500$ \nfor \\ha\\ and \\hb\\ respectively. \nThen $I$(\\ha)$/I$(\\hb)~=~2.91 and $I$(\\da)$/I$(\\db)~$\\simeq1.10$. \n}\n\\label{fig_detection}\n\\end{figure}\n\n\n\\begin{table*}\n\\caption[]{Gaussian fitted line profiles}\n\\label{lines}\n\\begin{tabular}{l|cc|cc}\n\\hline\nLine identification & \\ha & \\da & \\hb & \\db \\\\\nRest wavelength (\\AA) & $6562.796$ & $6561.010$ & $4861.325$ \n& $4860.003$ \\\\\n\\hline\nObserved wavelength (\\AA) & $6563.12\\pm0.03$ & $6561.59\\pm0.03$ \n& $4861.60\\pm0.02$ & $4860.44\\pm0.02$ \\\\\n$v_{\\odot}$ (\\kms)$^a$ & $14.8\\pm1.5$ & $26.5\\pm1.5$ \n& $17.0\\pm1.0$ & $27.0\\pm1.5$ \\\\\nFWHM (\\kms)$^b$ & $32.0\\pm0.5$ & $8.6\\pm1.0$ \n& $32.1\\pm0.5$ & $8.1\\pm1.5$ \\\\\nRelative flux$^c$ & \n$29\\,100\\pm300$ & $6.3\\pm0.6$ & $10\\,000\\pm200$ & $5.7\\pm1.1$ \\\\\n\\hline\n\\end{tabular}\n\\\\\n\\\\\n$^a$ Heliocentric velocity. \n\n$^b$ Full width at half maximum corrected for instrumental width \n(original FWHM: 32.9, 11.4, 32.7, 10.1~\\kms\\ respectively). \n\n$^c$ Using the theoretical $I($\\ha$)/I($\\hb$)$ (see text), \nthen $I($\\da$)/I($\\db$)=1.10\\pm0.22$.\n\n\\end{table*}\n\n\n\\section{Identification of \\da\\ and \\db}\n\\label{identification}\n\nAccording to Table~\\ref{lines}, the shift of both weak lines with \nrespect to the hydrogen lines is $-71$~\\kms\\ whereas the isotopic \nshift of deuterium is $-81.6$~\\kms. This significant difference \nforces us to consider alternative possibilities. \n\n$\\bullet$\n{\\sl Spectral artifact?} \\ \nNo feature equivalent to these lines is present in either the \nred wings of \\ha\\ and \\hb\\ or the wings of \\nii~$\\lambda6548.05$\\AA, \nobserved simultaneously. Small rotations of the grating \napplied between sub-exposures resulted in no change in \nprofile, position and intensity of the lines. Finally \nno such lines were detected in bright planetary \nnebulae we observed in September 1999 \n(H\\'ebrard et al.~\\cite{hebrard00b}), using the same instrument. \nThis also excludes possible sky-line emission. In fact, no sky-lines \nhave been reported at these wavelengths. \nThus, these lines are real features, specific to the Orion Nebula. \n\n$\\bullet$\n{\\sl Unidentified process or element?} \\ \nAttempts to find other identifications were unsuccessful. \nThese lines cannot be scattered stellar emission \n[for example, \\ha\\ from $\\theta^1$~Ori~C is variable \n(Stahl et al.~\\cite{stahl96})], as lines from hot stars are broad. \nFor the same reason, they cannot be Raman features. \nThe wavelengths do not correspond to any known quasi-molecular line. \nThe fact both lines have identical velocity shifts \nwith respect to \\hi\\ practically restricts the possibilities to \\hi\\ \nand \\di\\ emission (no \\ion{He}{ii} is detected in the Orion Nebula). \n\n$\\bullet$\n{\\sl High-velocity hydrogen emitting structure?} \\ \nTraub et al.~(\\cite{traub74}) reported the detection of a line \nin the blue wing of \\ha. This line may correspond to ours, although \nit was interpreted by these authors as high-velocity \n\\hi\\ emission, noting the existence of a similar component \nin [\\ion{O}{iii}] (Dopita et al.~\\cite{dopita73}). \nIndeed, our $R=80\\,000$ spectrum shows a blue component \nin [\\ion{N}{ii}] but with velocity shift only $\\sim-22$~\\kms. \nMore importantly, {\\it any component arising from the \\hii\\ region \nshould have a minimum width corresponding to thermal broadening}. \nThe thermal FWHM for hydrogen at 8500K \nis 20~\\kms, much larger than 8~\\kms\\ (Table~\\ref{lines}). \nThe $-22$~\\kms\\ ionized hydrogen emission \nshould be lost in the \\ha\\ and \\hb\\ wings. \n\nNonetheless, the fluorescence mechanism proposed below \nto explain the \\di\\ line excitation (Sect.~\\ref{fluo}) may \na priori apply to \\hi\\ as well. \nOne cannot formally exclude \\ion{H}{i} fluorescence emission \nfrom a neutral, cold (thermal FWHM is $\\sim7$~\\kms\\ at 10$^3$~K), \nhigh-velocity ($-74$~\\kms\\ LSR), low velocity dispersion ($<<10$~\\kms) \nlayer keeping the same kinematical properties over many arc minutes. \nHowever this is very unlikely as this hypothetical structure \nshould in addition have a small column density \n(no other fluorescent line is seen at that velocity) \n{\\sl and} lie sufficiently close to the Trapezium stars \n(fluorescence varies as the inverse square of the distance \nto the continuum source). \nThe survival of a neutral thin shell against photoionization \n(no low-ionization material is interposed; see Sect.~\\ref{origin}) \nis also in question. \nAs a matter of fact, Cowie et al. (\\cite{cowson79}) detected several \ncomponents of high-velocity gas in absorption against $\\iota$~Ori \n(a star located within half a degree of the region we observed), \nnotably a component at $-68$~\\kms, close to $-74$~\\kms. \nAccording to these authors, this component \ncorresponds to a very old highly ionized supernova remnant situated \nover 100~pc from the Trapezium, at any rate too far away to yield \nfluorescence. \n\nIt can therefore be safely concluded that these lines are \\da\\ and \\db. \nKinematics (Sect.~\\ref{origin}) brings out one more fundamental piece \nof evidence. \n\n\\section{Origin of the lines}\n\\label{origin}\n\nIn the Orion Nebula, the \\hii\\ region is essentially matter bounded \ntoward the observer and radiation bounded in the opposite direction\n(\\eg,~Rubin et al.~\\cite{rubsim91}). \nThe narrowness of the \\ion{D}{i} lines implies that they must originate \nin a cold, localised region along the line of sight, that is behind \nthe H$^+$ region, in the ``Photon Dominated Region'' (PDR) \nwhere deuterium is in atomic form. \n\nThis is borne out by available information on velocities. The \nheliocentric velocity of the \\ion{D}{i} lines is $\\sim27$~\\kms\\ compared \nto $\\sim16$~\\kms\\ for \\ion{H}{i}. In a blue spectrum of the Trapezium region \n(Kaler et al.~\\cite{kaler65}), the \\ion{Si}{ii} lines 3856+63\\AA, probably \nproduced by fluorescence in the PDR, appear shifted by +11~\\kms\\ relative \nto the neighbouring \\ion{H}{i} Balmer lines, a shift similar to the one \nfound for \\da\\ and \\db. Over a region close to the one we \nobserved, Esteban \\& Peimbert~(\\cite{esteban99}) measured \nheliocentric velocities \n6.4$\\pm$1.4, 14.0$\\pm$2.0, 24.6$\\pm$2.2 and 26.8$\\pm$1.4~\\kms\\ for \nAr$^{++}$, H$^+$, O$^0$ and N$^0$ respectively, \ntracing the free expansion of the \\hii\\ region, moving away \nfrom the molecular cloud. Over the same region, H\\\"anel~(\\cite{hanel87}) \nfound 20-23~\\kms\\ for [\\ion{N}{ii}] [in agreement with our measurement \n$v($[\\ion{N}{ii}]$)\\simeq21$~\\kms] and 23.5--28~\\kms\\ for [\\ion{S}{ii}], \nthus encompassing the velocity we found for \\da\\ and \\db. From \nmillimeter and submillimeter observations, \nHogerheijde et al.~(\\cite{hoger95}) found velocities $\\sim28$~\\kms\\ \nfor different molecules. \nObservations thus clearly imply that the \\ion{D}{i} lines could \narise from the boundary of the \\hii~region. \n\n\n\\section{Fluorescent excitation of \\da\\ and \\db}\n\\label{fluo}\n\nThe narrowness of \\da\\ and \\db\\ allows the possibility to be \nexcluded that the lines are excited \nby recombination in an ionized gas (Sect.~\\ref{identification}). \nThe H$^0$ column density of the PDR is \n$\\sim$~10$^{22}$cm$^{-2}$ (Tielens \\& Hollenbach \\cite{tiehol85}), \nso the D$^0$ column density is $\\sim$~10$^{17}$cm$^{-2}$ \n[assuming a typical \\dshism$\\simeq10^{-5}$] \nand the optical thickness in, \\eg, \\lybd\\ is over 100. \nSince the \\di\\ emission is confined to a layer coincident in velocity \nwith that of the PDR (Sect.~\\ref{origin}) and since the dust opacity \nthere is orders of magnitude less than the \\lybd\\ opacity, \nfluorescence from the Lyman lines is a viable process to produce \nthe deuterium Balmer lines. \n\nThe UV continuum is dominated by $\\theta^1$~Ori~C, whose effective \ntemperature is close to $4\\times10^4$K (Rubin et al.~\\cite{rubsim91}). \nLet us assume that both the ionization of the \n\\hii\\ region and the deuterium fluorescence are due to a \n$4\\times10^4$K black body and that half the ionizing photons \nescape from the \\hii\\ region in the matter bounded directions \n(Rubin et al.~\\cite{rubsim91}). \nIf each photon impinging on the PDR at the \\lybd\\ wavelengths \nultimately produces a \\da\\ photon by scattering on D$^0$, and \nonly \\lybd\\ photons lead to \\da\\ excitation \n(neglecting cascades), then the flux ratio \n$I$(\\da)/$I$(\\ha) is about $1.5\\times10^{-4}\\times(\\Delta v/5$\\kms), \nwhere $\\Delta v$ is the full velocity width of the zone where \\da\\ is \neffectively excited. According to Tielens and Hollenbach (\\cite{tiehol85}), \nthe turbulent pressure in the PDR corresponds to \n$\\Delta v\\simeq5$~\\kms\\ and according to Table~1, $\\Delta v$ is \nprobably less than 8~\\kms. The rather good agreement of this very \ncoarse estimate with the observed value $2.2\\times10^{-4}$ (Table~1) \nis fortuitous. This estimate \nmay be wrong in different ways. Many Ly$_{\\rm D}$ lines can a priori \nabsorb primary photons and feed \\da\\ by cascades, then leading to \nan overestimation. Conversely, part of the Ly$_{\\rm D}$ photons are \nabsorbed by dust and/or reflected back to the \\hii\\ region. \nAlso, our estimate is global in character and \nour particular line of sight may not intercept identical fractions \nof the \\hii\\ region and the PDR. Most importantly, \nthe stellar continuum may be depleted in the vicinity of the \nLy$_{\\rm H}$ lines, particularly for the first members of the series. \nNonetheless, since these different effects tend to partially \ncompensate one another, the above agreement indicates that the \nassumption of UV continuum fluorescence leads \nto the correct order of magnitude for the \\da\\ flux. \n\nUnlike \\da/\\ha, the flux ratio \\da/\\db\\ is little sensitive to \naspect effects. Assuming a ratio of visual extinction to column density \nof hydrogen nuclei $A_V$/$N_{\\rm H} = 5\\times$10$^{-22}$~mag$\\,$\\cm2\\ \nand $A_{FUV}$/$A_V = 5$ (Tielens and Hollenbach \\cite{tiehol85}), \nthe ratio of \\lybd\\ opacity to dust opacity is $\\sim$~240. \nOnly for large principal quantum numbers should dust absorption \ndecrease \\di\\ fluorescence (the photoexcitation cross section goes \nroughly as $n^{-3}$). Since the stellar continuum should be about flat \nover the Lyman line range (except possibly in the vicinity of strong \nlines), some insight into the excitation process \ncan be gained by assuming that all Ly$_{\\rm D}$($n$) lines, \nwith principal quantum number $n$ up to some given $n_0$, convert \nidentical numbers of UV photons by fluorescence and that \nno fluorescence occurs for $n > n_0$. Then, working out the \ncascades, the theoretical \\da/\\db\\ flux ratio is about 1.28, 1.41 \nand 1.51 for $n_0 =$ 4, 5 and 6 respectively and tends to level off \nfor larger $n_0$'s. Only for $n_0=4$ is this simple \ndescription compatible with the observed value $1.10\\pm0.22$ (Table~1). \nSince one would expect that a relatively large number of Ly$_{\\rm D}$ \nlines should contribute to the excitation, the suggestion is that \none of the above assumptions was oversimplified or some significant \nprocess has been overlooked. For example, the stellar continuum \nis probably depleted in the wings of the Ly$_{\\rm H}$ lines and \nthe vicinity of \\lyb\\ is likely to be most affected, \nthen selectively reducing the \\da\\ emission. \nObserving higher deuterium Balmer lines is essential before attempting \nany detailed modeling. \n\nNote that the \\da/\\db\\ of Table~\\ref{lines} \nwas obtained assuming that the reddening correction was the same \nfor the \\hi\\ and \\di\\ emitting zones. If extinction internal to the \nnebula is significant, then the actual (de-reddened) \\da/\\db\\ ratio \nwill be even smaller since the PDR, where the \\di\\ lines come from, \nis more deeply embedded than the \\hii\\ region. \n\nDust absorption will dominate Ly$_{\\rm D}$ fluorescence for sufficiently \nlarge $n$, the deuterium Balmer decrement then changing from very flat \nto very steep. This break can lead to a D/H value inasmuch as the \ndust opacity per hydrogen nucleus is known. On the other hand, \nfluorescence lines from species co-extensive with D$^0$ \nincluding \\ion{O}{i} and \\ion{Si}{ii} can provide \nindependent information on the primary continuum flux \nand on the competition of line scattering \nwith dust absorption for photons. \n\\ion{O}{i} fluorescence lines have been detected long ago in Orion \nand the excitation process was established by Grandi~(\\cite{grandi75}). \nComparing \\di\\ and \\oi\\ lines may lead to a D/O abundance ratio. \nDetailed observations and proper modeling of many deuterium Balmer \nlines and other fluorescence lines appear as a potentially \naccurate means to determine D/H in \\hii\\ regions. \n\n\\section{Conclusions}\n\nDeuterium is identified for the first time in a nebula from optical \nspectroscopy. The excitation mechanism of the observed lines, \n\\da\\ and \\db, is continuum fluorescence from Ly$_{\\rm D}$ lines in \nthe PDR. 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{
"name": "astro-ph0002141.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n \\bibitem[1975]{beckers75} Beckers, J. M.: 1975, ApJ 195, L43\n\n \\bibitem[1999]{bertoldi99} Bertoldi, F., \n%Timmermann, R., Rosenthal, D., Drapatz, S., \\& Wright, C. M.: \net al.: 1999, A\\&A 1999 346, 267\n\n \\bibitem[1997]{chengalur97} Chengalur, J. N., Braun, R., \n%\\& Burton, W. B.\net al.: 1997, A\\&A 318, L35\n\n \\bibitem[1979]{cowson79} Cowie, L. L., Songaila, A., \\& \nYork, D. G.: 1979, ApJ 230, 469\n\n \\bibitem[1973]{dopita73} Dopita, M. A., Gibbons, A. H., \n%Meaburn, J., \\& Taylor, K.: \net al.: 1973, {\\it Ap. Letters} 13, 55\n\n \\bibitem[1976]{epstein76} Epstein, R. I., Lattimer, J. M., \n%\\& Schramm, D. N.\net al.: 1976, Nature 263,~198\n\n \\bibitem[1999]{esteban99} Esteban, C. \\& Peimbert, M.: \n1999, A\\&A 349, 276\n\n \\bibitem[1998]{esteban98} Esteban, C., Peimbert, M., \n%Torres-Peimbert, S., \\& Escalante, V.\net al.: 1998, MNRAS 295, 401\n \n \\bibitem[1975]{grandi75} Grandi, S. A.: 1975, ApJ 196, 465\n\n \\bibitem[1987]{hanel87} H\\\"anel, A.: 1987, A\\&A 176, 347\n\n \\bibitem[1999]{hebrard99} H\\'ebrard, G., P\\'equignot, D., \nVidal-Madjar, A., %Walsh, J. R., \\& Ferlet, R.: \net al.: 1999, \nin {\\it The light elements and their evolution}, IAU Symp. 198\n\n \\bibitem[2000]{hebrard00b} H\\'ebrard, G., P\\'equignot, D., \n%Vidal-Madjar, A., %Walsh, J. R., \\& Ferlet, R.: \net al.: 2000, in preparation \n\n \\bibitem[1995]{hoger95} Hogerheijde, M. R., Jansen, D. J., \n%\\& van Dishoeck, E. F.: \net al.: 1995, A\\&A 294, 792\n\n \\bibitem[1992]{humsto92} Hummer, D. G. \\& Storey, P. J.: 1992, MNRAS\n254, 277\n\n \\bibitem[1965]{kaler65} Kaler, J. B., Aller, J. H., \\& Bowen, I. S.: \n1965, ApJ 141, 912\n\n \\bibitem[1999]{lemoine99} Lemoine, M., \n%Audouze, J., Ben~Jaffel, L., \n%Feldman, P., Ferlet, R., H\\'ebrard, G., Jenkins, E. B., Mallouris, C., \n%Moos, W., Sembach, K., Sonneborn, G., Vidal-Madjar, A., \\& York, D. G.: \net al.: 1999, {\\it New Astronomy} 4, 231\n\n \\bibitem[1998]{linsky98} Linsky, J. L.: 1998, \n{\\it Space Sci. Rev.} 84, 285\n\n \\bibitem[1998]{mahaffy98} Mahaffy, P. R., et al.: \n %Donahue, T. M., Atreya, S. K., \n %Owen, T. C., \\& Nieman, H. B.: \n 1998, {\\it Space Sci. Rev.} 84, 251\n\n \\bibitem[1991]{rubsim91} Rubin, R. H., Simpson, J. P., \n%Haas, M. R., Erickson, E. E.\net al.: 1991, PASP 103, 834\n\n \\bibitem[1996]{stahl96} Stahl, O., Kaufer, A., Rivinius, T., \n% etc\net al.: 1996, A\\&A 312, 539\n\n \\bibitem[1995]{stohum95} Storey, P. J. \\& Hummer, D. G.: 1995, MNRAS\n272, 41\n\n \\bibitem[1985]{tiehol85} Tielens, A. G. G. M. \\& Hollenbach, D. C.: \n1985, ApJ 291, 722\n\n \\bibitem[1998]{tosi98} Tosi, M., Steigman, G., \n%Matteucci, F., \\& Chiappini, C.: \net al.: 1998, ApJ 498, 226\n\n \\bibitem[1974]{traub74} Traub, W. A., Carleton, N. P., \n%\\& Hegyi, D. J.\net al.: 1974, ApJ 190, L81\n\n \\bibitem[1994]{flam94} Vangioni-Flam, E., \nOlive, K. A., %\\& Prantzos, N. \net al.: 1994, ApJ 427, 618\n\n \\bibitem[1988]{avm88} Vidal-Madjar, A., \nFerlet, R., %Spite, M., \\& Coupry, M. F.: \net al.: 1988, A\\&A 201, 273\n\n\\end{thebibliography}"
}
] |
astro-ph0002142
|
The Formation of Galaxies, the Formation of Old Globular Clusters and the Link with High-Redshift Objects
|
[
{
"author": "Denis Burgarella"
}
] |
In this paper, we are exploring the properties of old, metal-poor globular clusters in galaxies. We investigate whether their properties are related to the properties of their host galaxies, and whether we can constrain their formation. The main result is that the mean metallicities of old GC systems are found to lie in a narrow range -1.7 $<$ [Fe/H] $<$ -1.1 (80 \% of the population). Moreover, no correlations are found between the mean metallicities and other galaxy properties which implies a GC formation independent of the host galaxies. Further, we try to identify the sites of old, metal-poor GC formation, with any currently known high redshift objects. We find that the metalicities of damped Ly$\alpha$ systems in the redshift range 1.6 $<$ z $<$ 4 are consistent with our GC metalicities, which suggests that these high-density neutral gas objects may be the progenitors of the old, metal-poor globular clusters.
|
[
{
"name": "burgarellaD.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Burgarella, Kissler-Patig \\& Buat}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{The Formation of Galaxies, the Formation of Old Globular Clusters and the Link with High-Redshift Objects}\n\\author{Denis Burgarella, denis.burgarella@astrsp-mrs.fr}\n\\affil{Observatoire Astronomique Marseille-Provence, traverse du siphon, 13376 Marseille \ncedex 12, France}\n\\author{Markus Kissler-Patig, mkissler@eso.org}\n\\affil{ESO, Karl-Schwarzschild-Str. 2, 85748 Garching bei M�nchen, Germany}\n\\author{V\\'eronique Buat, veronique.buat@astrsp-mrs.fr}\n\\affil{Observatoire Astronomique Marseille-Provence, traverse du siphon, 13376 Marseille \ncedex 12, France}\n\n\\begin{abstract}\n In this paper, we are exploring the properties of old, metal-poor globular \n clusters in galaxies. We investigate whether their properties are related \n to the properties of their host galaxies, and whether we can constrain their \n formation. The main result is that \n the mean metallicities of old GC systems are found to lie in \n a narrow range -1.7 $<$ [Fe/H] $<$ -1.1 (80 \\% of the population). Moreover, no \n correlations are found between the mean metallicities and other galaxy \n properties which implies a GC formation independent of \n the host galaxies. Further, we try to identify the sites of old, metal-poor \n GC formation, with any currently known high redshift objects. \n We find that the metalicities of damped Ly$\\alpha$ systems in the redshift \n range 1.6 $<$ z $<$ 4 \n are consistent with our GC metalicities, which suggests that \n these high-density \n neutral gas objects may be the progenitors of the old, metal-poor globular \n clusters.\n\\end{abstract}\n\n\\keywords{Globular Clusters; Damped Ly$\\alpha$ systems; Lyman break galaxies;\ngalaxy formation}\n\n\\section{Introduction}\n\nStatistics is always a key-point in scientific studies and it is no surprise\nthat, as any scientist, the astronomer is looking for large, statistically\nsignificant samples to properly analyze the Universe and its content.\nUnfortunately, the intrinsic size of the Universe is turning this simple point\ninto a difficult brain teaser due to the faintness of the above objects.\nGlobular clusters are likely to contain some of the oldest known stellar\npopulations of the Universe. As such, they potentially hold a cosmologically\nsignificant information on their formation and more generally on the conditions\nthat prevailed more than 10~Gyrs ago.\n\nIn\nbrief, we have started a study that is heading at selecting the oldest globular\nclusters (GCs) from the largest available sample of extragalactic GC systems.\nPrevious studies often assumed the systems as an homogeneous population and \nused the mean properties (metallicity) of the GC systems as the main\nparameter. Only in the most recent works GCs have been split up\nin sub-populations (Forbes et al. 1997; C\\^ot\\'e et al. 1998). \nGoing back to the very formation of the galaxies\n(and maybe before), asks to make sure that only the oldest (i.e. reliable fossils) GCs are picked up. Our choice is to select the\nmetal-poor GCs. Indeed, if we can find old metal-rich globular\nclusters (Ortolani et al. 1995; Puzia et al. 1999), only in very limited cases\ncould we have a late formation of metal-poor GCs. An important step has\nbeen to discover that galaxies other than our own contain metal-poor\nsub-populations that can be associated to a halo component (Puzia et al. 1999).\n\nA more detailed report of this work will be published elsewhere (Burgarella, \nKissler-Patig \\& Buat, 2000).\n\n\\section{The compilation of Old Globular Cluster Populations}\n\nOur goal is to select the oldest GCs around galaxies and to\ncompare their metallicities with the host galaxy properties, as well as to \ncompare the systems with each other. The compilation\nincludes galaxies of all types, however spiral galaxies are under-represented\nwhile bright elliptical galaxies dominate the sample. The detection of\nseveral peaks in the metallicity distribution function is always a problem and\nwe use the mixture-modeling algorithm (KMM) developed by Ashman et al. (1994)\nto detect and quantify the bimodality and estimate the mean metallicity of the\nmetal-poor GC populations around the sampled galaxies. \nThis compilation of 38 GCs\nsystems includes galaxies of all types and our sample includes galaxies over 10\nmagnitudes in absolute brightness (see Burgarella et al. 2000).\n\n\\section{Mean metallicity against galaxy luminosity}\n\nBefore a clear separation of metal-poor and metal-rich populations could be\nperformed in other galaxies than in the Milky Way, the mean metallicities of the\nwhole GC system was thought to correlate with the galaxy luminosity (van den\nBergh 1975; Brodie \\& Huchra 1991). Actually, this apparent correlation was\nmainly due to the fact that the the brightest galaxies are ellipticals which\nhave, on average, a higher GC mean metallicity than spirals and dwarfs\n(e.g.~Ashman \\& Zepf 1998; Gebhardt \\& Kissler-Patig 1999).\n\nThe sample of GC systems presented in this paper is the largest\ndatabase to-date, and about 3 times more numerous than Forbes et al.'s (1997)\ninitial dataset. The mean [Fe/H] lies at [Fe/H]$=-1.40\\pm0.06$ with a\ndispersion of $\\sigma=0.24\\pm0.05$, that is slightly more metal-poor on average\nthan, and exhibiting a scatter similar to the Forbes et al. sample.\nFig.~1 shows the relative percentage of GC systems\nwithin each bin of the metallicity function. Indeed, the immediately apparent\nresult is that the mean-metallicities of metal-poor GCs are not\ndistributed at random: most of them are lying around [Fe/H]$\\sim-1.4$, with\n64~\\% within -1.5~$<$~[Fe/H]~$<$~-1.3 and 80~\\% within\n-1.7~$<$~[Fe/H]~$<$~-1.1. We plot in Fig.~1 the metallicities of the\nGC systems as a function of the absolute magnitude M$_V$. {\\it\nThe average metallicity of the metal-poor GCs is constant over a\nvery large range in absolute magnitude of the host galaxy ($-23<{\\rm\nM}_V<-16$)}.\n\n\\begin{figure} \\plottwo{burgarellaDfig1a.eps}{burgarellaDfig1b.eps} \\caption{ \na) Distribution of mean\nmetallicities for the GC system sample. Note the narrow \npeak at\n[Fe/H] $\\approx$ -1.4 with 80~\\% of the population within \n-1.7~$<$~[Fe/H]~$<$~-1.1.\nb) Mean metallicity of the old,\nmetal-poor GC systems plotted against the absolute magnitude of\nthe parent galaxy M$_V$ and the distance to the MW (right).}\n\\end{figure}\n\n\\begin{figure} \\plottwo{burgarellaDfig2a.eps}{burgarellaDfig2b.eps} \\caption{a) Mean \nmetallicities and\nb) peak $V-I$ colors of the metal-poor populations plotted against the host galaxy\nenvironment density $\\rho$. Black dots are new values.}\n\\end{figure}\n\n\\section{Consequences on the formation scenarios of GCs, globular\ncluster systems, and galactic halos}\n\nFollowing Fall \\& Rees (1988), GC formation models \n``{\\it can be classified as primary, secondary or tertiary depending on whether GCs are assumed to form\nbefore, during or after the collapse of proto-galaxies.}''.\nIt seems, however, that the borderline between the three classes is not always\nvery clear. To better identify the origins of GCs, we prefer to\nsplit the GCs on whether they are {\\it external} to the\ngalaxy, and not associated with the {\\it final} host galaxy, or whether they\nformed {\\it internally}, i.e. are associated in some form with the {\\it final}\nhost galaxy. This terminology is relatively unambiguous if we specify that\npre-galactic fragments are not considered to be galaxies. And since we consider\nonly old, metal-poor GCs assumed to have formed before or early in\nthe galaxy formation process, we do not take into account mergers of already\nformed galaxies.\n\nNow, if we concentrate our attention on the Milky Way GC system,\nit seems that halo GCs of the Milky Way host (at least) two\npopulations that Zinn (1993) distinguished from their horizontal branch\ntypes. He called them 'old' and 'younger' halo GCs. There are\nhints for a similar differentiation in M33 (Ashman \\& Bird 1993). A probable\ninternal halo old GC population which would have formed internally\nin the early galaxy lifetime by a dissipative collapse in a few Myr, and an\nexternal halo population which would have formed around other satellite galaxies\nand accreted afterwards. If such a complex GC formation history\nis valid for our own Galaxy and its nearest neighbors, it cannot be ruled out\nfor other galaxies either.\n\nWe could retain that~: i) the mean metallicity of\nhalo GCs is independent of the host galaxy properties (M$_V$,\ntype, environment (Fig.~2), metallicity) and ii) halo GC populations have\nvery similar mean metallicities in all galaxies. These two points can be added\nto the dynamical information available for a number of metal-poor outer globular\nclusters that tends to show that these clusters are on tangentially biased\norbits, as opposed to radially biased orbits expected if they had formed in a\ncollapse (Eggen et al. 1962). \n\nThe bottom line from the above facts, is that the early cluster and star\nformation was remarkably homogeneous in the local universe (within several tens\nof Mpc). The first collapsing fragments were extremely similar in mass and\nabundances over large scales and collapse in very similar fashions independently\nof the potential well (dark halo) in which they were located. Presumably, the\ndistinction between galaxy types only appeared after the first formation of\nstars and clusters in fragments.\n\n\\section{Time and sites of formation of the metal-poor GCs}\n\n\\subsection{The measurement of metallicity at high redshift} \n\nIn this section, we will look for measurements of metallicity at high redshift\nin order to compare with the average metallicity of our old GCs.\nIndeed, if the GC formation is the first stellar formation episode\nof what will become a new galaxy, the first-formed stars might have kept a\nmemory of the genuine intergalactic medium as it was before the galaxy\nformation. Among the objects observed at high redshifts for which the\nmetallicity can be estimated, two of them seem of interest: Damped Ly$\\alpha$\nsystems (DLAs), and Lyman Break Galaxies (LBGs). Both the typical column\ndensity in H{\\tt I} and the observed metallicities for DLAs and LBGs are plotted\nin Fig.~3, together with the same quantities for GCs (and the\nLyman $\\alpha$ forest for completeness). DLAs (Pettini et al. 1997) give a\nmeasurement for the metallicity as a function of redshift of high density\nneutral gas objects. Lyman Break Galaxies (Steidel et al. 1996) can, in\naddition, be used to estimate the star formation rate as a function of redshift.\nAssuming a metal ejection rate (Pettini et al. 1997),\nwe can infer a chemical evolution of the Universe and compare it with other\nestimates, in particular with the mean metallicity of the metal-poor globular\ncluster systems.\n\n\\begin{figure} \\plottwo{burgarellaDfig3a.eps}{burgarellaDfig3b.eps} \n\\caption{\na) This figure gives the rough location in \nmetallicity against column density of neutral hydrogen for different components \nof the high redshift universe. We have added the results from our GC \nsystems (80 \\% and 64 \\%) taking into account a low threshold \nN(HI) $\\approx$ 20 for the star formation to occur (left side).\nb) Comparative variation of the\nmetallicities with the redshift (H$_o$ = 50 km.s$^{-1}$.Mpc$^{-1}$ and q$_o$ =\n0.5). Right hand panel: GC system metallicity distribution.\nLeft hand panel~: the limits at 80 $\\%$ of the GC system\nmean-metallicity distribution are reported as dashed\nlines. The uppermost curves have been deduced from Steidel et al.'s (1999, \nFig.9) star formation history (continuous line); the dashed line includes Barger et\nal. 1999 FIR data. [Zn/H] (continuous line crosses) and [Fe/H] (dashed\ncrosses) values of DLAs are taken from Burgarella et al (2000). The age of \nthe oldest Galactic\nGCs are reported as an horizontal right-bound arrow. Pettini et al.\n1997 noted that assuming q$_0$ = 0.01 would shift the [M/H] by a factor of 2.\n}\n\\end{figure}\n\nHowever, [Fe/H] may not be a reliable estimate of the\nmetallicity of DLAs, since some Fe may be locked up in dust and thus the\nmeasured [Fe/H] too low. Pettini et al. (1997) showed that [Zn/H] is a more\nreliable estimator because it essentially measures the metallicity independently\nof dust depletion. From a [Zn/H] analysis of 34 DLAs, Pettini et al. (1997)\nshowed that z $>$ 1 DLAs are generally metal-poor (log ($<Z>/Z_\\odot$) $<$ -1.0)\nwith a possible trend for z $>$ 3 DLAs towards a lower metallicity. However,\nthe value at z = 3 is an upper limit and we would need better high redshift\nvalues. Although the dust depletion problem may make the direct use of DLA\n[Fe/H] questionable, we try here to use its variation with redshift in order to\ncompare it with the information from GC systems. The compilation is given in \nBurgarella et al. (2000). The [Zn/H] and [Fe/H]\nvariations as a function of the redshift are plotted in Fig.~3. We use the\ncolumn-density weighted abundances~: $ \\rm [<M/H_{DLA}>] = log <(M/H)_{DLA}> -\n~log (M/H)_\\odot $ where $\\rm <(M/H)_{DLA}$ (M = Fe or M = Zn) and the\nassociated standard deviations as defined in Pettini et al. (1997).\n\nThe data presented in Fig.~3 can be used to constrain the GC\nsystem formation. In the first place, the analysis of the CMDs of old Galactic\nGCs suggests the age of halo GCs to be more than 10\nGyr which corresponds to a GC formation not later than z $\\sim$\n1.6 (H$_0=50$ km.s$^{-1}$.Mpc$^{-1}$ and q$_0=0.5$). On the other hand, the \nchemical evolution of\nDLAs and LBGs is below the lower limit for 80 \\% of our metal-poor globular\nclusters at z $\\approx$ 4. The conclusion suggested by these data is that the\nGC formation occurred in average in the redshift range 1.6 $<$ z\n$<$ 4 (i.e approximately in the range 10 $<$ age (Gyrs) $<$ 12 with the assumed\ncosmology).\n\nFrom the above discussion we retain that DLAs (and LBGs) have approximately the\nsame range of metallicities and are observed in the redshift range expected for\nthe formation of metal-poor GCs. Note, however, that DLAs contain\nneutral gas while LBGs are star-forming objects. As already suggested by Fynbo\net al. (1999), we may wonder whether we are not observing the same objects at\ndifferent location in space or in time. For instance, DLAs would be the source\nof dense gas out of which old GCs formed while LBGs would be\nstar-forming regions e.g. spheroids as proposed by Giavalisco et al. (1996)\nand Steidel et al. (1996) but also surrounding fragments in the same potential\nwell which are only directly visible at high redshift when the star formation\nturns on. Eventually these\nfragments would be accreted by the large galaxy to produce a MW-like object.\n\n\\acknowledgements{We would like to thank K. Gebhardt for his help in handling\nthe data of the metal poor GCs and M. Pettini for helful discussions.}\n\n\\begin{references} \n\\reference Ashman K.M., Bird C.M. 1993 AJ 106, 2281\n\\reference Ashman K.M., Zepf S.E. 1998, Globular Cluster Systems, Cambridge Univ. Press\n\\reference Ashman K.M., Bird C.M., Zepf S.E. 1994 AJ 108, 2348\n\\reference Barger A.J., Cowie L.L., Sanders D.B. 1999, ApJ 518, 5\n\\reference Brodie J.P., Huchra J.P. 1991 ApJ 379,157\n\\reference Burgarella D., Kissler-Patig M., Buat V. 2000, A\\&A (subm.)\n\\reference C\\^ot\\'e P., Marzke R.O., West M.J. 1998, ApJ 501, 554\n\\reference Eggen O.J., Lynden-Bell D., Sandage A.R. 1962, ApJ 136, 748\n\\reference Fall S.M., Rees M.J. 1988, in \"Globular Clusters in Galaxies\", IAUS 126, eds. Grindlay J.E. and Davis A.G., p.323\n\\reference Forbes D.A., Brodie J.P., Grillmair C.J. 1997, AJ 113, 1652\n\\reference Fynbo J.U., Moller P., Warren S.J. 1999, MNRAS 305, 849\n\\reference Gebhardt K., Kissler-Patig M. 1999 AJ 118, 1526\n\\reference Giavalisco M., Steidel C.C., Macchetto F.D. 1996, ApJ 470, 189\n\\reference Ortolani S., Renzini A., Gilmozzi R., Marconi G., Barbuy B., Bica E., Rich R.M. 1995, Nat. 377, 701\n\\reference Pettini M., Smith L.J., King D.L., Hunstead R.W. 1997, ApJ 486, 665\n\\reference Puzia T.H., Kissler-Patig M., Brodie J.P., Huchra J.P. 1999, AJ 118,2734\n\\reference Steidel C.C., Giavalisco M., Adelberger K.L., Dickinson M. 1996, ApJ 462, L17\n\\reference Steidel C.C., Adelberger K.L., Giavalisco M., Dickinson M., Pettini M. 1999, ApJ 519,1\n\\reference van den Bergh S. 1975, IAU Symp. 58, \"The Formation and Dynamics of Galaxies\", J.R. Shakeshaft (ed.), p.157\n\\reference Zinn R. 1993, \"Stellar Populations\", eds. C.A. Norman, A. Renzini and M. Tosi, Cambridge Univ. Press, p.73\n\\reference \\hfil\n\\end{references}\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002143
|
Predicting the properties of binary stellar systems: \\ the evolution of accreting protobinary systems
|
[
{
"author": "Madingley Road"
},
{
"author": "Cambridge CB3 0HA"
},
{
"author": "$^{2}$ Max-Planck-Institut f\\\"ur Astronomie"
},
{
"author": "K\\\"onig\\-stuhl 17"
},
{
"author": "D-69117 Heidelberg"
},
{
"author": "Germany"
}
] |
We investigate the formation of binary stellar systems. We consider a model where a `seed' protobinary system forms, via fragmentation, within a collapsing molecular cloud core and evolves to its final mass by accreting material from an infalling gaseous envelope. This accretion alters the mass ratio and orbit of the binary, and is largely responsible for forming the circumstellar and/or circumbinary discs. Given this model for binary formation, we predict the properties of binary systems and how they depend on the initial conditions within the molecular cloud core. We predict that there should be a continuous trend such that closer binaries are more likely to have equal mass components and are more likely to have circumbinary discs than wider systems. Comparing our results to observations, we find that the observed mass-ratio distributions of binaries and the frequency of circumbinary discs as a function of separation are most easily reproduced if the progenitor molecular cloud cores have radial density profiles between uniform and $1/r$ (e.g. Gaussian) with near uniform-rotation. This is in good agreement with the observed properties of pre-stellar cores. Conversely, we find that the observed properties of binaries cannot be reproduced if the cloud cores are in solid-body rotation and have initial density profiles which are strongly centrally condensed. Finally, in agreement with the radial-velocity searches for extra-solar planets, we find that it is very difficult to form a brown dwarf companion to a solar-type star with a separation $\simless 10$ AU, but that the frequency of brown dwarf companions should increase with larger separations or lower mass primaries.
|
[
{
"name": "paper.tex",
"string": "\\documentstyle{mn}\n\n\\def\\etal{et al.}\n\\def\\simless{\\mathbin{\\lower 2pt\\hbox\n {$\\rlap{\\raise 5pt\\hbox{$\\char'074$}}\\mathchar\"7218$}}} % < or of order\n\\def\\simgreat{\\mathbin{\\lower 2pt\\hbox\n {$\\rlap{\\raise 5pt\\hbox{$\\char'076$}}\\mathchar\"7218$}}} % > or of order\n\\def\\be {\\begin{equation}}\n\\def\\ee {\\end{equation}}\n\n\\input psfig\n\n%\\pagerange{1--13}\n\\pubyear{2000}\n%\\volume{226}\n\n\\title[The properties of binary systems]{Predicting the properties of binary stellar systems: \\\\ the evolution of accreting protobinary systems}\n\n\\author[M. R. Bate]\n {Matthew R. Bate$^{1,2}$\\thanks{E-mail: mbate@ast.cam.ac.uk} \\\\\n $^{1}$ Institute of Astronomy, Madingley Road, Cambridge CB3 0HA \\\\\n $^{2}$ Max-Planck-Institut f\\\"ur Astronomie, K\\\"onig\\-stuhl 17, D-69117 Heidelberg, Germany}\n\n\\date{Accepted 1999 December 23. Received in original form 1999 September 16} \n%\\date{Accepted 1995 February 10. Received 1994 November 4} \n%\\date{Submitted 1999 September 9} \n\n\\begin{document}\n\\label{firstpage}\n\\maketitle\n\n\n\\begin{abstract}\n\nWe investigate the formation of binary stellar systems.\nWe consider a model where a `seed' protobinary system forms, via\nfragmentation, within a collapsing molecular cloud core and evolves\nto its final mass by accreting material from an infalling \ngaseous envelope. This accretion alters the mass ratio and orbit\nof the binary, \nand is largely responsible for forming the circumstellar and/or \ncircumbinary discs.\n\nGiven this model for binary formation, we predict the properties of \nbinary systems and how they depend on the initial conditions within \nthe molecular cloud core. We predict that there should\nbe a continuous trend such that closer binaries are more likely \nto have equal mass components and are more likely to have \ncircumbinary discs than wider systems. Comparing our results to observations, \nwe find that the observed mass-ratio distributions of binaries and the\nfrequency of circumbinary discs as a function of separation are most easily\nreproduced if the progenitor molecular cloud cores have radial density\nprofiles between uniform and $1/r$ (e.g. Gaussian) with near \nuniform-rotation. This is in good agreement with the observed properties\nof pre-stellar cores. Conversely, we find that the observed \nproperties of binaries cannot be \nreproduced if the cloud cores are in solid-body rotation and \nhave initial density profiles which are strongly centrally condensed. \nFinally, in agreement with the radial-velocity \nsearches for extra-solar planets, we find that it is very \ndifficult to form a brown dwarf companion \nto a solar-type star with a separation $\\simless 10$ AU, but that the\nfrequency of brown dwarf companions should increase with larger\nseparations or lower mass primaries.\n\n\n\\end{abstract}\n\n\\begin{keywords}\naccretion, accretion discs -- brown dwarfs -- binaries: general -- circumstellar matter -- stars: formation -- stars: mass function\n\\end{keywords}\n\n\n\\section{Introduction}\n\\label{introduction}\n\nThe favoured mechanism for producing most binary stellar systems\nis the fragmentation of a molecular cloud core during its gravitational\ncollapse. Fragmentation can be divided into two main classes: \ndirect fragmentation (e.g.~Boss \\& Bodenheimer 1979; Boss 1986; \nBonnell et al.~1991, 1992; Bonnell \\& Bastien 1992; \nNelson \\& Papaloizou 1993; Burkert \\& Bodenheimer 1993; Bate \\& Burkert 1997), \nand rotational fragmentation \n(e.g.~Norman \\& Wilson 1978; Bonnell 1994; Bonnell \\& Bate 1994a, 1994b;\nBurkert \\& Bodenheimer 1996; Burkert, Bate, Bodenheimer 1997). \nDirect fragmentation depends critically on \nthe initial density structure within the molecular cloud core \n(e.g.~non-spherical shape or density perturbations), whereas rotational\nfragmentation is relatively independent of the initial \ndensity structure of the cloud because the fragmentation occurs \ndue to nonaxisymmetric instabilities in a massive \nrotationally-supported disc or ring.\n\nThe main conclusion, from $\\approx 20$ years of fragmentation studies,\nis that it appears to be possible to form binaries with similar \nproperties to those that are observed. \nHowever, it has not been possible to use these calculations to \npredict the fundamental properties of stellar systems such as\nthe fraction of stellar systems which are binary or the properties of binary \nsystems (e.g.~the distributions of mass ratios,\nseparations, and eccentricities and the properties of \ndiscs in pre-main-sequence systems). \n\nThere are two primary reasons for this lack of predictive power. \nFirst, the results of fragmentation calculations depend sensitively\non the initial conditions, which are poorly constrained.\nThe second problem is that of accretion. In fragmentation calculations,\nthe binary or multiple protostellar systems that\nare formed initially contain only a small fraction of the total mass of the\noriginal cloud (e.g.~Boss 1986; Bonnell \\& Bate 1994b)\nwith the magnitude of this fraction decreasing with the \nbinary's initial separation (see Section \\ref{bmass_vs_sepsec}). \nTo obtain the final parameters of a stellar system, a calculation must\nbe followed until all of the original cloud material has been\naccumulated by one of the protostars or their discs.\nUnfortunately, due to the enormous range in densities and dynamical\ntime-scales in such a calculation, this is very difficult.\nThus far, only one calculation has followed the three-dimensional\ncollapse of a molecular cloud core until $>90$\\% of the initial\ncloud was contained in the protostars or circumstellar/circumbinary discs\n(Bate, Bonnell \\& Price 1995).\nBecause such calculations are so difficult to perform, it is\nimpossible to perform the number of calculations that would be\nrequired to predict the statistical properties of \nbinary stellar systems -- even if we knew the distribution of \ninitial conditions. On the other hand, if we can overcome this second\ndifficulty, we can use observations of binary systems to better constrain\nthe initial conditions for star formation.\n\nBate \\& Bonnell \\shortcite{BatBon97} quantified how \nthe properties of a binary system are affected by the accretion \nof a small amount of gas from an infalling gaseous envelope. \nThey found that the effects depend primarily on the specific \nangular momentum of the gas and the binary's mass ratio \n(see also Artymowicz 1983; Bate 1997). Generally, accretion of gas \nwith low specific angular momentum decreases the mass ratio and \nseparation of the binary, while accretion of gas with high \nspecific angular momentum increases the separation, drives the \nmass ratio toward unity, and can form a circumbinary disc. \nFrom these results, they predicted that closer binaries \nshould have mass ratios that are biased toward equal masses compared\nto wider systems.\n\nIn this paper, we use the results of Bate \\& Bonnell \\shortcite{BatBon97}\nto develop a protobinary evolution code that enables us to \nfollow the evolution of a protobinary system as it accretes \nfrom its initial to its final mass, but does so in far less time \nthan would be required for a full hydrodynamic calculation. \nUsing this code, we consider the following model for the formation of\nbinary stellar systems. We assume that a `seed' binary system is \nformed at the centre of a collapsing molecular cloud core, presumably \nvia some sort of fragmentation. The protobinary system initial consists \nof only a small fraction of the total mass of the core. \nSubsequently, it accretes the remainder of the initial cloud (which \nis falling on to the binary) and its properties evolve due to the \naccretion. We consider the formation process to be complete \nwhen all of the original cloud's material is contained\neither in one of the two stars or their surrounding discs.\nOur goal is to obtain\npredictions about the properties of binary stars that can be tested\nobservationally, and to determine how these properties depend on the \ninitial conditions (e.g.~the density and angular momentum profiles) \nin the progenitor molecular cloud cores\nso that the initial conditions can be better constrained.\n\nIn Section \\ref{commethod}, we describe the methods used to follow the\nevolution of accreting protobinary systems, and we present the\nresults of various test calculations in Section \\ref{comparison}.\nIn Sections \\ref{evolution} and \\ref{relax}, we present results from\ncalculations with a range of initial conditions which follow the \nevolution of accreting protobinary systems.\nFrom these results, in Section \\ref{predictions}, \nwe make predictions regarding the properties of binary systems and compare\nthem with the latest observations.\nThese predictions are briefly summarised in Section \\ref{conclusions}.\n\nThose readers more interested in our predictions of the\nproperties of binary stars, rather than the method by which these \npredictions have been obtained, may care to move directly \nto Section \\ref{evolution}.\n\n\n\\section{Computational methods}\n\\label{commethod}\n\n\\subsection{Protobinary evolution code}\n\\label{PBEcode}\n\nBate \\& Bonnell \\shortcite{BatBon97} considered the effects that \naccretion of a small amount of gas from an infalling gaseous envelope has\non the properties of a protobinary system. They quantified\nthese effects as functions of the mass ratio of the protobinary\nand the specific angular momentum of the infalling gas.\nTherefore, if a `seed' binary system is formed at the centre\nof a collapsing gas cloud, and we know its initial mass ratio and \nseparation, the mass infall rate on to the \nbinary, and the distribution of the specific angular momentum of the gas,\nthen we can determine how the binary will evolve as it accretes \ninfalling gas. Essentially, we can integrate the binary from its \ninitial mass to its final mass by accreting the gas in a series \nof small steps and altering the masses of the binary's components and \ntheir orbit by the amounts determined by Bate \\& Bonnell \n\\shortcite{BatBon97} after each step.\n\nWe now describe the implementation of the protobinary evolution (PBE) code.\nWe begin with the properties of the molecular cloud core, before it \nbegins to collapse dynamically, from which the binary system will form.\nFor simplicity, the progenitor cloud (see Figure \\ref{model}) is assumed to be \nspherical with mass $M_{\\rm c}$, radius $R_{\\rm c}$, density distribution\n\\be\n\\rho = \\rho_{\\rm 0} \\left(r/R_{\\rm c}\\right)^{\\lambda},\n\\ee\nand angular velocity\n\\be\n\\Omega_{\\rm c} = \\Omega_{\\rm 0} \\left(r/R_{\\rm c}\\right)^{\\beta},\n\\ee\nwhere $\\lambda$ controls the initial central condensation of the cloud,\nand $\\beta$ gives the amount of differential rotation of the cloud. Note\nthat $\\Omega_{\\rm c}$ is constant on spheres ($r$), \nnot cylinders ($r_{\\rm xy}$). \nNote also that if molecular cloud cores spend a large fraction of \ntheir lifetimes as magnetically-supported, quasistatic structures \nbefore undergoing dynamic collapse, they are likely to be in \nsolid-body rotation and significantly centrally-condensed \nbefore the dynamic collapse begins.\n\nWe assume that a `seed' binary is formed at the centre of this \nmolecular cloud core after it begins to collapse.\nThe `seed' binary contains only a small fraction of the total mass \nof the cloud. The masses of the primary and secondary are \n$M_1$ and $M_2$, respectively. The binary has a total mass $M_{\\rm b}$, \nmass ratio $q=M_2/M_1$, separation $a$ and is in a circular orbit. \nWe assume the binary has a circular orbit and that its axis of \nrotation is aligned with that of the cloud, since the PBE code makes \nuse of the results of Bate \\& Bonnell \\shortcite{BatBon97} and they \nonly studied such systems.\n\n\\begin{figure}\n%\\vspace{-0.2truecm}\n\\centerline{\\hspace{0.0truecm}\\psfig{figure=fig01.eps,width=8.0truecm,height=8.0truecm,rwidth=8.0truecm,rheight=8.5truecm}}\n%\\vspace{6.0truecm}\n\\caption{\\label{model} The model for binary star formation which is considered in this paper (see Section 2.1).}\n\\end{figure}\n\n\nThe `seed' binary is assumed to have formed from the gas that was \nin a spherical region at the centre of the progenitor \ncloud of radius $R_{\\rm b}$ (Figure \\ref{model}). \nUnless otherwise stated, we assume that this spherical region initially\nhad the same mass and angular momentum as the `seed' binary.\nThus, the initial angular momentum of the binary is given by\n\\be\n\\label{lbinary}\nL_{\\rm b} = \\sqrt{G M_{\\rm b}^3 a}~ \\frac{q}{(1+q)^2} = \\Lambda M_{\\rm b} R_{\\rm b}^2 \\Omega_{\\rm Rb} = L_{\\rm cen}\n\\ee\nwhere $\\Omega_{\\rm Rb}= \\Omega_{\\rm 0}(R_{\\rm b}/R_{\\rm c})^{\\beta}$ and,\nfor various values of $\\beta$ and $\\lambda$,\n\\be\n\\label{lambda}\n\\Lambda = \\frac{2\\left(3+\\lambda\\right)}{3\\left(5+\\lambda+\\beta\\right)}.\n\\ee\nFor example, for an initially uniform-density cloud in solid-body rotation,\n$\\Lambda$ = 2/5.\nAs in Bate \\& Bonnell \\shortcite{BatBon97}, we use natural units of \n$M_{\\rm b}=1$ and $a=1$ for the `seed' binary, with $G=1$.\n\nIn general, to evolve the binary under the accretion of gas from \nthe remainder of the collapsing cloud, we would need to know the \ninfall rate and the specific angular momentum distribution \nof the gas as functions of time (i.e.~we would need to \ncalculate how the cloud evolves as it collapses on to the binary).\nHowever, if we make two simple assumptions, we can calculate\nthe evolution of the binary knowing only the density and angular \nmomentum distributions of the cloud {\\it before} it began to collapse.\nFurthermore, we can consider the evolution of the binary as a \nfunction of the mass that has been accreted from the \nenvelope $M_{\\rm acc}$, and do not need to keep track of time explicitly.\nFirst, we assume that the specific angular momentum of each element \nof gas in the cloud is conserved during its fall until it gets\nvery close to the binary.\nSecond, we assume that the time it takes for gas to fall on to the binary\nfrom a radius $r$ from centre of the cloud is independent of direction\n(i.e.~the gas falls on to the binary in spherical shells).\n\nThese are reasonable assumptions if the molecular cloud core \nundergoes a dynamic collapse (i.e.~the magnitude of its \ngravitational energy dominates the thermal, rotational and magnetic \nenergies of the cloud). In principle, angular momentum transport \nbetween elements of gas could occur during collapse if the \ncloud has density inhomogeneities (via gravitational torques)\nor is threaded by magnetic fields (via magnetic torques).\nHowever, if the collapse is dynamic, these effects are unlikely to have\nenough time to transport a significant amount of angular momentum,\nand even cores which are initially magnetically sub-critical \ntypically evolve into configurations which undergo a dynamic \ncollapse (e.g.~Basu 1997).\n\nThe integration of the binary from its initial mass, $M_{\\rm acc}=M_{\\rm b}=1$,\nto its final mass $M_{\\rm acc}=M_{\\rm c} \\geq M_{\\rm b}$ \n(since some of the gas could be contained in a circumbinary disc)\nunder the accretion of the gas with $r>R_{\\rm b}$ \nproceeds as follows (Figure \\ref{model}). \nA spherical shell of gas with inner radius\n$r=R_{\\rm b}$ and thickness $\\Delta r$ is divided into many\nelements such that the gas in each element has the same specific\nangular momentum (i.e. each `element' consists of two rings of \ngas, one above and one below the orbital plane). The effect of\neach element of gas on the binary, when it is accreted, is determined\nusing the results of Bate \\& Bonnell \\shortcite{BatBon97}\nfrom its specific angular momentum, its mass, and $q$ (see below). \nThe effects on the binary\nfrom all the gas elements making up a shell are added together, and then the \nbinary's properties ($M_{\\rm b}$, $q$, $a$) are updated. \nThe mass of material that is not captured by one of the two protostars\nbut that remains in a circumbinary disc (if any) is also determined. \nThe process is\nrepeated for the shell of material at radius $r=R_{\\rm b} + \\Delta r$\nuntil the entire cloud of mass $M_{\\rm c}$ has been exhausted.\n\nThe results from Bate \\& Bonnell \\shortcite{BatBon97} are used to determine\nthe effects on the binary of the accretion of an element of gas. \nThe specific angular momentum of an element of gas relative to the \nspecific angular momentum required for gas\nto form a circular orbit at a radius equal to the binary's separation \nis given by \n\\be\n\\label{jrel}\nj_{\\rm rel} = \\frac{r_{\\rm xy}^2 \\Omega_{\\rm c}}{\\sqrt{G M_{\\rm b} a}}\n\\ee\nwhere $r_{\\rm xy}$ is the cylindrical radius of the gas element \nfrom the axis of rotation in the progenitor cloud. To evolve the binary, we\nneed to know the values of\n$\\dot M_1/\\dot M_{\\rm acc}$, \n$\\dot M_2/\\dot M_{\\rm acc}$ and \n$(\\dot a/a)/(\\dot M_{\\rm acc}/M_{\\rm b})$ as functions of $j_{\\rm rel}$\nand $q$,\nwhere $\\dot M_{\\rm acc}$ is the rate of accretion from the infalling envelope\non to the binary.\nNote that we consider gas to be `accreted' by one of \nthe protostars if it is actually accreted onto the protostar itself or\nif it is captured in the protostar's circumstellar disc \n(see also Section \\ref{method}).\nThese quantities were determined by\nBate \\& Bonnell \\shortcite{BatBon97} only at set intervals in\n$q$-$j_{\\rm rel}$-space. Interpolation between these points is performed \nto determine the quantities for any given $q$ and $j_{\\rm rel}$. \nBoundary conditions are used for $q=1$ and $q=0$. For $q=1$, we set\n$\\dot M_1/\\dot M_{\\rm acc} = \\dot M_2/\\dot M_{\\rm acc}$\nexplicitly, with $(\\dot a/a)/(\\dot M_{\\rm acc}/M_{\\rm b})$ \nbeing determined \nfrom Bate \\& Bonnell \\shortcite{BatBon97}. For $q=0$, we set \n$\\dot M_{\\rm 2}/\\dot M_{\\rm acc} = 0$ and \n\\be\n\\begin{array}{l}\n\\dot M_{\\rm 1}/\\dot M_{\\rm acc} = \\dot M_{\\rm b}/\\dot M_{\\rm acc} = \\cases {1 & ~~~~~if $j_{\\rm rel} \\le 1$, \\cr\n 0 & ~~~~~otherwise \\cr}\n\\end{array}\n\\ee\nand $(\\dot a/a)/(\\dot M_{\\rm acc}/M_{\\rm b})$ is set equal to the \nvalues for $q=0.1$. \nThe evolution of a binary with an initial mass ratio\n$q \\simgreat 0.05$ is insensitive to the assumptions for $q=0$. This\nwas tested by setting the primary and secondary accretion \nrates for $q=0$ equal to those for $q=0.1$ and repeating the calculations.\nNote that we use the values of \n$(\\dot a/a)/(\\dot M_{\\rm acc}/M_{\\rm b})$\nthat were derived by Bate \\& Bonnell \\shortcite{BatBon97} \nfor the effects of {\\it accretion only}. We do not include any\naffect on the binary's separation due to the loss of orbital \nangular momentum to the gas in a circumbinary disc (if one exists).\n\nFrom equation \\ref{lbinary}, we note that specifying the values \nof $\\Lambda$ and $q$ fixes the relationship between the mean\nspecific angular momentum of a {\\it shell} of gas, $J(r)$, at radius $r$,\nand the enclosed mass, $M(r)$, in the progenitor cloud.\nFor all $q$,\n\\be\n\\label{jr}\n\\frac{J(r)}{J_{\\rm b}} = \\frac{2}{3\\Lambda}\\left( \\frac{M(r)}{M_{\\rm b}} \\right)^{\\left(\\frac{2}{3\\Lambda} - 1 \\right)}\n\\ee\nwhere $J_{\\rm b}=L_{\\rm b}/M_{\\rm b}$ is the mean specific angular \nmomentum of the `seed' binary, which depends on $q$.\nEquation \\ref{jr} is plotted for various types of molecular cloud core in\nFigure \\ref{jrvsm}. With progenitor cores that are more centrally-condensed,\nthe specific angular momentum of the first gas to fall on to the \n`seed' binary from the envelope is greater and increases more rapidly\nas mass is accreted than in less centrally-condensed cores. \nFor cores which have a greater amount of differential rotation \n($\\beta \\leq 0$), the specific angular momentum of the gas is lower\nto begin with and increases more slowly as mass is accreted.\n\n\\begin{figure}\n%\\vspace{-0.2truecm}\n\\centerline{\\hspace{0.0truecm}\\psfig{figure=fig02.eps,width=8.0truecm,height=8.0truecm,rwidth=8.0truecm,rheight=8.0truecm}}\n%\\vspace{6.0truecm}\n\\caption{\\label{jrvsm} The relationship between angular momentum and mass for different types of molecular cloud core (equation 7). The values are normalised by the mean specific angular momentum and mass of the central region of gas from which the `seed' binary forms (which are also equal to the mean specific orbital angular momentum and mass of the `seed' binary itself). Notice that the angular momentum is greater initially and increases more rapidly with enclosed mass in clouds which are more centrally condensed or have less differential rotation ($\\beta \\leq 0$). Also, the relation between angular momentum and mass is the same for a cloud with $\\rho \\propto 1/r$ in solid-body rotation as it is for a cloud with $\\rho \\propto 1/r^2$ and $\\Omega_{\\rm c} \\propto 1/r$. }\n\\end{figure}\n\nSince $J_{\\rm b}$ in equation \\ref{jr} depends on the mass ratio, $q$, and\nseparation, $a$, of the `seed' binary, \nthe angular momentum of the cloud, $J(r)$ is linked to the \nproperties of the `seed' binary (due to our use of equation \\ref{lbinary}).\nThis can be viewed in two ways. First, if we consider a series \nof clouds with the same density and rotation profiles but that form\n`seed' binaries with different mass ratios, then the separations\nof the binaries will be somewhat larger for those with smaller \nmass ratios and $J_{\\rm b}$ is the same for all mass ratios.\nAlternately, if we choose `seed' binaries with the same \nseparations, their progenitor clouds must be rotating more slowly\nfor those binaries with lower mass ratios. We chose to use\nequation \\ref{lbinary} because, for a `seed' binary with a \ngiven mass ratio and separation, this gives the slowest possible\nrotation rate of the progenitor cloud. The progenitor cloud could\nbe rotating more rapidly than this if some of the angular momentum\nof the gas from which the `seed' binary formed is contained in \ncircumstellar discs, but it could not be rotating more slowly.\n\nFinally, since choosing $\\Lambda$ and $q$ fixes the relationship\nbetween angular momentum and mass in the progenitor cloud\n(independent of $M_{\\rm c}/M_{\\rm b}$, $R_{\\rm c}$\nand $\\Omega_0$), it follows that the evolution proceeds \nin the same way for any value of $M_{\\rm c}/M_{\\rm b}$. \nThus, a graph which shows the {\\it evolution} of a particular\nprotobinary system as it accretes gas from its initial to its final\nmass can {\\it also} be viewed as giving the \n{\\it final states} of binaries that have accreted a certain \namount of mass relative to their initial mass (e.g.~Figures \\ref{acc_d0_w0}\nto \\ref{acc_relax}). This is only the case because we have chosen\nclouds that have scale-free density and angular momentum profiles, \nand does not apply, for example, to clouds with Gaussian density\nprofiles that have a fixed inner to outer density contrast (e.g.~20:1).\n\n\n\\subsection{Smoothed particle hydrodynamics code}\n\\label{SPHcode}\n\nTo test the PBE code described above, we compare its results with those\nobtained from full hydrodynamic calculations using a three-dimensional, \nsmoothed particle hydrodynamics (SPH) code. The SPH code is \nbased on a version originally developed by Benz (Benz 1990; Benz et al.~1990).\nThe smoothing lengths of particles are variable in \ntime and space, subject to the constraint that the number of neighbours\nfor each particle must remain approximately constant at $N_{\\rm neigh}=50$. \nThe SPH equations are integrated using a second-order Runge-Kutta-Fehlberg \nintegrator with individual time steps for each particle (Bate et al.~1995).\nGravitational forces between particles and a particle's nearest neighbours \nare found by using either a binary tree, as in the original code, or the \nspecial-purpose GRAvity-piPE (GRAPE) hardware. \nThe implementation of SPH using the GRAPE\nclosely follows that described by Steinmetz \\shortcite{Steinmetz96}.\nUsing the GRAPE attached to a Sun workstation typically \nresults in a factor of 5 improvement in speed over the workstation alone.\n\nCalculations were performed using three different forms \nof artificial viscosity. The scatter in the results from\ncalculations with different viscosities is used to give indication of the\nuncertainty in the SPH results. \nThe viscosity, $\\Pi_{\\rm ij}$, between \nparticles $i$ and $j$ enters the momentum equation as\n\\be\n\\frac{{\\rm d}{\\bf v}_{\\rm i}}{{\\rm d}t} = - \\sum_{\\rm j}{ m_{\\rm j} \\left(\\frac{P_{\\rm i}}{\\rho_{\\rm i}^2} + \\frac{P_{\\rm j}}{\\rho_{\\rm j}^2} + \\Pi_{\\rm ij} \\right) \\nabla_{\\rm i} W(r_{\\rm ij}, h_{\\rm ij})},\n\\ee\nwhere ${\\bf v}$ is the velocity, $t$ is the time, $m$ is the particle's mass,\n$P$ is the pressure, $\\rho$ is the density, $W$ is the SPH smoothing kernel, \n$r_{\\rm ij}$ is the distance between particles $i$ and $j$, and $h_{\\rm ij}$\nis the mean of the smoothing lengths of particles $i$ and $j$.\nAll formulations of the viscosity have linear\nand quadratic terms which are parameterised by $\\alpha_{\\rm v}$ and \n$\\beta_{\\rm v}$, respectively. The first form of viscosity is the `standard'\nform, originally given by Monaghan \\& Gingold \n\\shortcite{MonGin83} (see also Monaghan 1992)\n\\be\n\\Pi_{\\rm ij} = \\cases {\\begin{array}{ll}\n(-\\alpha_{\\rm v} c_{\\rm ij} \\mu_{\\rm ij} + \\beta_{\\rm v} \\mu_{\\rm ij}^2)/\\rho_{\\rm ij} & {\\bf v}_{\\rm ij}\\cdot {\\bf r}_{\\rm ij} \\leq 0 \\cr\n0 & {\\bf v}_{\\rm ij}\\cdot {\\bf r}_{\\rm ij} > 0 \\cr\n\\end{array}}\n\\ee\nwhere $\\rho_{\\rm ij} = (\\rho_{\\rm i} + \\rho_{\\rm j})/2$, $c_{\\rm ij} = (c_{\\rm i} + c_{\\rm j})/2$ is the mean sound speed, ${\\bf v}_{\\rm ij} = {\\bf v}_{\\rm i} - {\\bf v}_{\\rm j}$, and\n\\be\n\\mu_{\\rm ij} = \\frac{h_{\\rm ij} {\\bf v}_{\\rm ij}\\cdot {\\bf r}_{\\rm ij}}{{\\bf r}_{\\rm ij}^2 + 0.01 h_{\\rm ij}^2}.\n\\ee\nThis form is known to have a large \nshear viscosity. The second form (Monaghan \\& Gingold 1983; \nHernquist \\& Katz 1989) \nhas much\nless shear viscosity but does not reproduce shocks quite as well as the \n`standard' formalism. It is given by\n\\be\n\\Pi_{\\rm ij} = \\frac{q_{\\rm i}}{\\rho_{\\rm i}} + \\frac{q_{\\rm j}}{\\rho_{\\rm j}}\n\\ee\nwhere\n\\be\nq_{\\rm i} = \\cases {\\begin{array}{ll}\n\\alpha_{\\rm v} h_{\\rm i} \\rho_{\\rm i} c_{\\rm i} |\\nabla\\cdot {\\bf v}|_{\\rm i} + \\beta_{\\rm v} h_{\\rm i}^2 \\rho_{\\rm i} |\\nabla\\cdot {\\bf v}|_{\\rm i}^2 & (\\nabla\\cdot {\\bf v})_{\\rm i} \\leq 0 \\cr\n0 & (\\nabla\\cdot {\\bf v})_{\\rm i} > 0 \\cr\n\\end{array}}\n\\ee\nThe third form is that proposed by Balsara \\shortcite{Balsara89} (see also\nBenz 1990), which is\nidentical to the `standard' form, except that $\\mu_{\\rm ij}$ is replaced by \n$\\mu_{\\rm ij}(f_{\\rm i}+f_{\\rm j})/2$ where\n\\be\nf_{\\rm i}=\\frac{|\\nabla\\cdot v|_{\\rm i}}{|\\nabla\\cdot v|_{\\rm i} + |\\nabla\\times v|_{\\rm i} + \\eta c_{\\rm i}/h_{\\rm i}}\n\\ee\nand $\\eta=1.0\\times 10^{-4}$.\nIn purely compressional flows this form gives the same results as that of\nthe `standard' viscosity, \nwhile in shearing flows the magnitude of the viscosity \nis reduced. The three forms of \nviscosity will be referred to as the Standard, $\\nabla\\cdot {\\bf v}$, \nand Balsara forms, respectively.\n\nModelling of non-gaseous bodies (in this paper, the protostars), and the\naccretion of gas on to them, is achieved by the inclusion of sink particles\n(Bate et al.~1995; Bate 1995). These were also used by Bate \\& Bonnell\n\\shortcite{BatBon97}. A sink particle is a non-gaseous particle\nwith a mass many times larger than that of an SPH gas particle. Any SPH gas\nparticle that passes within a specified radius of the sink particle,\nthe accretion radius $r_{\\rm acc}$, is accreted with its mass, linear \nmomentum, and spin angular momentum being added to those of the sink particle.\nSink particles interact with SPH gas particles only via\ngravitational forces. Boundary conditions can also be included for particles\nnear the accretion radius (Bate et al.~1995), but they are not used for\nthe calculations in this paper. Although boundary conditions are typically\nrequired to stop the erosion of discs near the accretion radius \n(Bate et al.~1995), this is not necessary here because once a disc forms\nit is replenished by the infalling gas more rapidly than it is eroded.\n\n\n\n\\section{Testing the Protobinary Evolution Code}\n\\label{comparison}\n\nTo test how accurately the protobinary evolution (PBE) code \n(Section \\ref{PBEcode}) describes the evolution \nof a `seed' binary as it accretes from its initial to \nits final mass we performed several full SPH calculations for comparison. \nTwo test cases were performed. The first follows the formation of a \nbinary system from the collapse of an initially uniform-density,\nspherical molecular cloud core in solid-body rotation. The \n`seed' binary is assumed to have a mass ratio of $q=0.6$ and a\nmass of $M_{\\rm b} = M_{\\rm c}/10 = 1$. The second test case\nis similar, except \nthat the progenitor cloud is centrally-condensed with a 1/r-density \ndistribution\nand there is less mass in the envelope relative to the initial binary's\nmass: $M_{\\rm b} = M_{\\rm c}/5 = 1$.\n\n\n\n\\subsection{SPH initial conditions}\n\n\\subsubsection{Test Case 1}\n\n\nThe evolutions given by the PBE code are scale-free. However, for \nthe SPH calculations, we choose to specify physical parameters. Test\ncase 1 consists of the collapse of a uniform-density\nmolecular cloud core in solid-body rotation with\n\\be\n\\begin{array}{ll}\nM_{\\rm c} = 1.0 ~{\\rm M}_{\\odot}, & R_{\\rm c} = 1.0 \\times 10^{17} ~{\\rm cm}, \\\\\nT = 10 ~{\\rm K}, & \\Omega_{\\rm c} = 3.13 \\times 10^{-14} ~{\\rm rad~s}^{-1},\n\\end{array}\n\\ee\nwhere $T$ is the temperature of the cloud, and it is assumed to consist of\nmolecular hydrogen. The `seed' binary\nis assumed to form from the mass initially contained within the sphere of \nradius $R_{\\rm b} = 4.64 \\times 10^{16}$ cm, which has 1/10 of the cloud's\ntotal mass.\n\nThe initial conditions are evolved with $2.0 \\times 10^5$ SPH gas particles\nuntil the particles that were initially within $R_{\\rm b}$ have collapsed\nto within \n$r=2 \\times 10^{15}$ cm of the centre. At this point, the calculation is\nstopped and the particles that were contained within $R_{\\rm b}$ are removed\nand replaced by a `seed' binary system with the same mass as those \nparticles that were removed ($M_{\\rm b}=0.1~{\\rm M}_{\\odot}$). The binary\nhas mass ratio $q=0.6$, separation $a=1.0 \\times 10^{15}$ cm and is in a \ncircular orbit. Note that the rotation rate of the cloud, $\\Omega_{\\rm c}$,\nis chosen so that the total angular momentum of the gas initially within \n$R_{\\rm b}$ is equal to the orbital angular momentum \nof the `seed' binary (the default used by the PBE code). \nThe calculation is then\nrestarted and the remaining gas begins to fall on to the binary.\nAs the binary increases it mass by 5\\%, its mass ratio and separation are\nforced to evolve as predicted by the PBE code (to allow time for the\ngas to establish its correct flow pattern on to the binary). After\nthis, however, the binary is free to evolve as the accretion of gas dictates.\n\n\\subsubsection{Test Case 2}\n\nThe second test case consists of a 1/r-density\nmolecular cloud core in solid-body rotation with\n\\be\n\\begin{array}{ll}\nM_{\\rm c} = 1.0 ~{\\rm M}_{\\odot}, & R_{\\rm c} = 1.0 \\times 10^{17} ~{\\rm cm}, \\\\\nT = 10 ~{\\rm K}, & \\Omega_{\\rm c} = 5.74 \\times 10^{-14} ~{\\rm rad~s}^{-1}.\n\\end{array}\n\\ee\nThe `seed' binary is assumed to form from the mass initially contained \nwithin the sphere of radius $R_{\\rm b} = 4.47 \\times 10^{16}$ cm, which\nhas 1/5 of the cloud's total mass.\n\nThe initial conditions are evolved with $1.0 \\times 10^5$ SPH gas particles\n(half the number that were used for test case 1 due to the smaller mass \nof the cloud\nrelative to the `seed' binary) in an identical manner to test case 1.\n\n\n\\subsection{Method}\n\\label{method}\n\nWhile the gas is modelled using SPH particles in the usual manner,\nthe binary's components (the protostars) are modelled with \nsink particles (Section \\ref{SPHcode}). Their accretion\nradii change in size as the mass ratio and separation of the \nbinary changes and are always equal to \n$r_{\\rm acc} = 0.1 R_{\\rm i}$ where $R_{\\rm i}$ are the \nsizes of the mean Roche lobes of the two protostars \\cite{FraKinRai85}\n\\be\nR_1/a = 0.38 - 0.20 ~{\\rm log}~q, ~~~~~~~~~~~0.05 < q \\leq 1,\n\\ee\nfor the primary and\n\\be\nR_2/a = \\cases{ \\begin{array}{ll}\n0.38 + 0.20 ~{\\rm log}~q, & ~0.5 \\leq q < 1, \\cr\n0.462~ (q/(1+q))^{1/3}, & ~~~\\,0 < q < 0.5, \\cr\n\\end{array}}\n\\ee\nfor the secondary. This enables circumstellar discs of size \n$\\simgreat 0.2 R_{\\rm i}$ to be resolved by the SPH calculations. Smaller \naccretion radii would allow smaller discs to be resolved, but would\nalso require more computational time due to the shorter dynamical\ntime-scales.\n\nAs in Bate \\& Bonnell \\shortcite{BatBon97}, we define the mass of a protostar\n($M_1$ or $M_2$) to be the mass of a sink particle {\\it and its circumstellar \ndisc} (if any). Hence, when stating the masses of the two components or \nmass ratio of the binary we are assuming that, in reality, all of the \nmaterial in a circumstellar disc will eventually be accreted by its\ncentral star.\nTherefore, the binary's mass $M_{\\rm b}$ is equal to the masses of the sink\nparticles and their circumstellar discs. The parameters of the binary's \norbit are calculated by considering these masses.\n\nA gas particle belongs to a circumstellar disc if\nits orbit, calculated considering only one sink particle at a time, has\neccentricity $<0.5$, and semi-major axis $<D/2$. This simple \ncriterion gives excellent extraction of the circumstellar discs.\nThe mass of material in a circumbinary disc $M_{\\rm cb}$ (if any),\nis defined as being the gas which has an outwards (positive) radial\nvelocity or which is falling on to the binary more slowly than 1/3 of the \nlocal free-fall velocity (i.e.~$v_{\\rm r} > -1/3 \\sqrt{2 G M_{\\rm b}/r}$) \nand which is not in one of the\ncircumstellar discs as defined above or within distance $a$ of the\nbinary's centre of mass. The amount of gas that has fallen on to the \nbinary from the envelope $M_{\\rm acc}$ is defined as $M_{\\rm b}+M_{\\rm cb}$\nplus the remaining gas within $a$ of the binary's centre of mass.\n\n\\begin{figure*}\n\\vspace{-0.7truecm}\n\\centerline{\\hspace{0.2truecm}\\psfig{figure=fig03.ps,width=17.0truecm,height=17.0truecm,rwidth=17.0truecm,rheight=11.0truecm}}\n%\\vspace{11.0truecm}\n\\caption{\\label{PBESPH1} First comparison of the results from the protobinary evolution (PBE) code with those from the full SPH calculations. The graphs show the evolution of a protobinary system that was formed in the centre of a collapsing molecular cloud core which initially had a uniform density profile and was in solid-body rotation. The evolution of the (a; upper left) mass ratio, (b; upper right) separation, (c; lower left) ratio of mass in a circumbinary disc to that of the binary, and (d; lower right) eccentricity are plotted as the binary accretes gas from the infalling envelope. The dot-dashed lines show results from the PBE code. The other lines show the results from the full SPH calculations with artificial viscosities of S1 (long-dashed), S2 (solid), and B1 (dotted) (see Section 3.3.2).}\n\\end{figure*}\n\nThe equation of state of the gas is given by\n\\be\nP = K \\rho^{\\gamma},\n\\ee\nwhere $P$ is the pressure, $\\rho$ is the density, and $K$ is a constant \nthat depends on the entropy of the gas. The ratio of specific heats $\\gamma$\nvaries with density as\n\\be\n\\gamma = \\cases{\\begin{array}{ll}\n1.0, & \\rho \\leq 10^{\\eta}~ {\\rm g~cm}^{-3}, \\cr\n1.4, & \\rho > 10^{\\eta}~ {\\rm g~cm}^{-3}. \\cr\n\\end{array}}\n\\ee\nThe value of $K$ is defined such that when the gas is \nisothermal $K=c_{\\rm s}^2$, with \n$c_{\\rm s} = 2.0 \\times 10^4$ cm s$^{-1}$ for molecular hydrogen at 10 K. \nWe choose $\\eta=-12$ for test case 1 and $\\eta=-13$\nfor test case 2. The heating of the gas at high densities inhibits\nfragmentation of the discs\n(e.g.~Bonnell 1994; Bonnell \\& Bate 1994a; Burkert \\& Bodenheimer 1996; \nBurkert et al.~1997). \nIn reality, this heating occurs when the gas becomes optically thick to\ninfrared radiation. The results are independent of the exact\ndensity at which heating starts, so long as the gas which falls on to the\nbinary from the envelope is `cold' (i.e.~pressure forces are not dynamically\nimportant so that the gas falls freely on to the binary), \nthe discs are relatively thin, and the discs do not fragment.\n\n\n\\subsection{Test Case 1}\n\\label{testcase1}\n\n\nThe evolutions of test case 1 as given by the PBE and SPH codes are\npresented in Figure \\ref{PBESPH1}. We give the binary's mass ratio $q$,\nseparation $a$, the ratio of the mass of the circumbinary disc (if one exists)\nto the mass of the binary $M_{\\rm cb}/M_{\\rm b}$, and the binary's eccentricity\n$e$, as functions of the mass which has been accreted from \nthe cloud $M_{\\rm acc}$ (up to 10 times the binary's initial mass).\nIn addition, for two of the SPH calculations, we show snapshots at various\ntimes during the calculations (Figures \\ref{UD_S2} and \\ref{UD_B1}).\n\n\\subsubsection{PBE calculation}\n\nThe PBE code predicts that after the binary has accreted all the gas in\nthe cloud, its mass ratio has increased from $q=0.6$\nto $q \\approx 0.84$ while its separation, after decreasing initially, has\nreturned to approximately the initial value. The binary's final \nmass is 8.8 times its initial mass\nwith the remaining 12\\% of the cloud \nlocated in a circumbinary disc. With the PBE\ncode, the binary is assumed to remain in a circular orbit throughout the\nevolution.\n\n\\subsubsection{SPH calculations}\n\nThree SPH calculations were performed using different formulations of\nthe artificial viscosity: \nS1: Standard, with $\\alpha_{\\rm v}=1$ and $\\beta_{\\rm v}=2$;\nS2: Standard, with $\\alpha_{\\rm v}=0.5$ and $\\beta_{\\rm v}=2$; and B1: Balsara,\nwith $\\alpha_{\\rm v}=0.25$ and $\\beta_{\\rm v}=1$. S1 and S2 have the same\nformulation, but S2 has approximately half the shear viscosity that is\npresent in S1 (the linear $\\alpha_{\\rm v}$-viscosity dominates the shear\nviscosity in the code; the $\\beta_{\\rm v}$-viscosity is only important\nin shocks). B1 has the lowest shear\nviscosity of the three, but also has a different formulation.\n\nUnfortunately, the SPH calculations cannot be evolved until all of the\noriginal cloud has been accreted. The reason is that as the \nevolution proceeds,\nthe rate at which mass falls on to the binary decreases and, thus,\nmore orbits of the binary \nmust be calculated for the same amount of mass to fall on to the binary.\nFor example, the increase from $M_{\\rm b}=1$ to $M_{\\rm b}=2$ takes $\\approx 5$\norbits, while the increase from $M_{\\rm b}=4$ to $M_{\\rm b}=5$ takes \n$\\approx 14$\norbits. The CPU time required to evolve the binary until the entire cloud\nfalls in is prohibitive, which, after all, is the reason that we\ndeveloped the PBE code in the first place. It takes $\\approx 60$ orbits\nfor the binary to increase its mass by a factor of 6 (i.e.~$\\approx 60$\\% \nof the total cloud was accreted).\nEach of the three SPH calculations took $4-5$ months on \na 170 MHz Sun Ultra workstation with a GRAPE board. \nThe evolution with the PBE code takes a few seconds!\n\n\\subsubsection{Evolution of the mass ratio and separation}\n\nAlthough the SPH calculations do not run to completion, \nwe can compare the evolution as the binary's mass increases \nby a factor of 5-6. Overall, there is excellent agreement \nbetween the PBE and SPH codes for the evolution of the mass ratio\nand separation. \nThe mass ratio is predicted to within 5\\% over the entire evolution\nand the separation to within 20\\%. Indeed, there is as much \nscatter between the different SPH results \nas there is between the PBE results and the SPH results. \nThus, {\\bf for the evolution of the mass ratio\nand separation, we conclude that the PBE code is at least\nas accurate as a full SPH calculation of this resolution.}\nNotice also that the PBE results (which assumed $e=0$) and SPH \nresults are in good agreement even though the eccentricity varies \nbetween $0<e\\simless 0.2$ during the SPH calculations. This implies\nthat the evolution given by the PBE code is satisfactory, not just for\ncircular binaries, but for binaries with $e \\simless 0.2$.\n\n\\begin{figure*}\n\\vspace{7.00truecm}\n%\\centerline{\\hspace{0.2truecm}\\psfig{figure=fig04.eps,width=17.0truecm,height=6.83truecm,rwidth=17.0truecm,rheight=7.00truecm}}\n%\\vspace{11.0truecm}\n\\caption{\\label{UD_S2} Snapshots of the evolution of test case 1 using the SPH code with artificial viscosity S2. The panels show the logarithm of column density, looking down the rotation axis, as the binary accretes infalling gas. The primary is on the right. The calculation starts when the mass accreted from the cloud is $M_{\\rm acc}=1$ and is followed until $M_{\\rm acc}=6$. Notice that, initially, the circumsecondary disc is too small to be resolved and it only begins to be resolved when $M_{\\rm acc}\\simgreat 2.0$. Each panel has a width of twice the binary's initial separation. Snapshots from calculations S1 and S2 look almost identical.}\n\\end{figure*}\n\n\\begin{figure*}\n\\vspace{7.00truecm}\n%\\centerline{\\hspace{0.2truecm}\\psfig{figure=fig05.eps,width=17.0truecm,height=6.83truecm,rwidth=17.0truecm,rheight=7.00truecm}}\n%\\vspace{11.0truecm}\n\\caption{\\label{UD_B1} The same as in Figure 4, except using artificial viscosity B1 and only following the binary until $M_{\\rm acc}=5.0$. With the different viscosity, the circumsecondary disc is unresolved for much longer (until $M_{\\rm acc}\\simgreat 4.0$) and a circumbinary disc starts to form earlier at $M_{\\rm acc}\\approx 4.4$. Each panel has a width of 4 times the binary's initial separation. }\n\\end{figure*}\n\n\\subsubsection{Evolution of the circumbinary disc}\n\nThe good agreement for the mass ratio and separation does not \nhold for the evolution of the circumbinary disc. The \nPBE code predicts that more gas will settle into a circumbinary \ndisc than is found in the SPH calculations. \nCases S1 and S2 do not form circumbinary discs \nat all for $M_{\\rm acc}<6$, while B1 only begins to form \na circumbinary disc when $M_{\\rm b}\\simgreat 4.3$ \n(Figures \\ref{PBESPH1}c and \\ref{UD_B1}). The difference between\nS1/S2 and B1 can be attributed to the much larger shear viscosity which\nis present in S1 and S2 compared to B1. Greater shear viscosity inhibits \nthe formation of a circumbinary disc by removing angular momentum \nfrom the gas which would otherwise settle into a circumbinary disc.\nAnother problem is that, in all of the SPH calculations, the binary\nhas a larger separation than is predicted by the PBE code when\n$M_{\\rm acc}\\simgreat 2.3$ which also inhibits the formation of\na circumbinary disc. These problems of circumbinary disc formation\nare the main reason that we performed test case 2\nand we defer further discussion to Section \\ref{testcase2}.\n\n\\subsubsection{Dependence of the results on the circumstellar discs}\n\nReturning to the evolution of the mass ratio and separation, \nalthough the overall agreement is good, there are two\ndifferences which need, briefly, to be commented on.\nThese differences are related to the way in which the PBE and \nSPH codes handle the circumstellar discs.\n\nFirst, S1 and S2 both give a slower rate of increase of the \nmass ratio initially than is predicted by the PBE code \n(Figure \\ref{PBESPH1}a; $1 \\leq M_{\\rm acc}\n\\simless 2$). This reflects a problem with the SPH calculations rather than\nwith the PBE code: namely, the size of the accretion radius \naround the secondary is initially of a similar size to that of the \ncircumstellar disc which should form. This stops a circumsecondary disc \nfrom forming which reduces the secondary's cross-section \nfor capturing infalling gas and, so, reduces the amount of gas captured\nby the secondary. Only when $M_{\\rm acc}\\simgreat 2.0$, is\nthe specific angular momentum of the gas being captured by the secondary\nlarge enough for it to form a circumsecondary disc outside the accretion\nradius (Figure \\ref{UD_S2}). From this point on, the mass \nratio increases at the rate predicted by the PBE code. \nB1 has a similar problem, but for a slightly different reason. B1\nhas much less shear {\\it and bulk} viscosity in shearing flows. In order\nfor infalling gas to form a resolved disc around the secondary, it\nmust, first, dissipate most of its kinetic energy so that it is captured\nby the secondary and, second, dissipate enough kinetic energy that the\ngas particles have roughly circular orbits. If the gas does not dissipate\nenough kinetic energy to be captured by the secondary on its first pass, \nit is likely to be captured by the primary instead which is deeper \nin the gravitational potential well. If a gas particle is captured by the\nsecondary but still has a very elliptical orbit, it will pass inside the\nsecondary's accretion radius and be removed. Thus, the low bulk \nviscosity of B1 means that the formation of a resolved \ncircumstellar disc around the secondary is delayed until \n$M_{\\rm acc}\\simgreat 3.9$ (Figure \\ref{UD_B1}) and the \ncross-section of the secondary is underestimated until this point.\nAs with S1 and S2, however, as soon as the circumsecondary disc is \nresolved ($M_{\\rm acc}\\simgreat 3.9$), the mass ratio begins to\nincrease at the rate predicted by the PBE code (Figure \\ref{PBESPH1}a).\n\nSecond, the PBE code does not include viscous \nevolution of the circumstellar discs. In reality, \nand in the SPH calculations, such viscous\nevolution results in the transfer of angular momentum from the \ndiscs to the orbit of the binary, increasing the separation.\n\nIn order for us to be able to neglect viscous evolution of the \ncircumstellar discs, this transfer of angular momentum must be negligible \nover the time for most of the envelope to be accreted. Viscous\nevolution of the circumstellar discs on a longer time-scale may \nincrease the final separation of the binary by a small factor, \nbut the masses of the binary's components will have been\ndetermined during the accretion phase.\n\nFor wide binaries, viscous evolution is unlikely to be significant.\nFor example, the free-fall time for a dense molecular cloud core \n($10^{-18}$ g cm$^{-3}$) is $\\sim 10^5$ years. The envelope\nwill fall on to the binary on this time-scale. The viscous time for\none of the circumstellar discs is of order \n\\be\nt_{\\rm v} \\sim \\frac{P}{2 \\pi \\alpha_{SS}}\\left(\\frac{R}{H}\\right)^2,\n\\ee\nwhere $P$ is the period of the binary, $\\alpha_{SS}$ measures the strength of\nthe shear viscosity using the standard Shakura--Sunyaev prescription, and\n$H/R$ is the ratio of the thickness of the disc to its radius (typically\n$\\sim 0.1$; Burrows et al.~1996; Stapelfeldt et al.~1998). Observationally,\nit is thought that the shear viscosity acting in protostellar accretion\ndiscs is of order $\\alpha_{\\rm ss} \\sim 0.01$ \\cite{Hartmannetal98}. \nThus, taking the median \nbinary separation of 30 AU \\cite{DuqMay91} and a typical protobinary mass\nof $0.1 {\\rm M}_\\odot$, the viscous time in one of the circumstellar \ndiscs is $\\sim 10^6$ years, an order of magnitude longer\nthan the free-fall time. For close binaries\n(separations $\\simless 5$ AU) viscous evolution may be expected to\nhave some effect during the accretion phase. However, in most cases, \na close binary is expected to have a circumbinary disc \n(see Section \\ref{circumbinary})\nand interactions between it and the binary will dominate the \ninteractions between the circumstellar discs and the binary \n(Section \\ref{testcase2cb}).\n\nIn SPH calculations S1 and S2, viscous evolution of the circumstellar discs\ndoes affect the binary's separation during the calculation.\nFor example, in calculation S1 when $M_{\\rm acc}\\simgreat 3$, \nthe separation increases\nmore rapidly than predicted by the PBE code and when $M_{\\rm acc}=6$,\nafter $\\approx 60$ orbits ($\\approx 4 \\times 10^4$ years) the separation \nis 20\\% larger than predicted. However, \nwe estimate (Pongracic 1988; Meglicki, Wickramasinghe \\& Bicknell 1993;\nArtymowicz \\& Lubow 1994)\nthe effective viscosity in the circumstellar discs \nto be $\\alpha_{\\rm SS}\\approx 0.2$.\nWith an orbital period of $\\approx 600$ years over most of the evolution, \nthis gives a viscous time of \n$\\sim 5 \\times 10^4$ years which is similar to the time over which \nthe calculation was followed. Therefore, \nit is not surprising that the separation was affected. We note,\nhowever, that this viscosity is $\\approx 20$ times stronger than is\nexpected in real protostellar discs and, thus, the effect on a real\nprotobinary system over this period would have been negligible,\nas is assumed by the PBE code. Calculation S2 has approximately\nhalf the shear viscosity of S1 and its separation is correspondingly\ncloser to the \nPBE code prediction. B1 has much less shear viscosity than S1 or S2.\nConsequently, the {\\it rate of change} of separation when \n$M_{\\rm acc}\\simgreat 3$ is very close to that predicted by the PBE \ncode. Instead, with B1, the differences in the evolution of the \nseparation occurred earlier in the evolution \n($1.5\\simless M_{\\rm acc} \\simless 2.5$).\n\nWe conclude that it is reasonable for the PBE code to neglect the \neffect on the separation due to viscous evolution of the \ncircumstellar discs\nsince it is only likely to have a significant effect for close \nbinaries and in these cases the effect is likely to be overwhelmed \nby the interaction between the binary and a circumbinary disc. \nWe also find that the small differences between the PBE and SPH results \nfor the evolution of the mass ratio and separation reflect \nthe unphysical treatment of the circumstellar \ndiscs by the SPH code rather than a problem with the PBE code.\n\n\\begin{figure*}\n\\vspace{-0.7truecm}\n\\centerline{\\hspace{0.2truecm}\\psfig{figure=fig06.ps,width=17.0truecm,height=17.0truecm,rwidth=17.0truecm,rheight=11.0truecm}}\n%\\vspace{11.0truecm}\n\\caption{\\label{PBESPH2} Second comparison of the results from the protobinary evolution (PBE) code with those from the full SPH calculations. The graphs show the evolution of a protobinary system that was formed in the centre of a collapsing molecular cloud core which initially had a $1/r$-density profile and was in solid-body rotation. The evolution of the (a; upper left) mass ratio, (b; upper right) separation, (c; lower left) ratio of mass in a circumbinary disc to that of the binary, and (d; lower right) eccentricity are plotted as the binary accretes gas from the infalling envelope. The dot-dashed lines show results from the PBE code. The other lines show the results from the full SPH calculations with artificial viscosities of B1 (dotted) and D1 (solid) (see Section 3.4.2).}\n\\end{figure*}\n\n\n\\subsubsection{Eccentricity evolution}\n\nFinally, we comment on the eccentricity of the binary as given by the\nSPH code. \nWe see that initially, independent of the viscosity, the binary\nbecomes eccentric due to the accretion of gas, with a peak eccentricity of\n$e \\approx 0.14$. The eccentricity then displays a secular decrease, \nas the accretion rate on to the binary also decreases,\nwhile oscillating\non an orbital time-scale. Such periodic changes of the orbital\nelements are known from analytic solutions of binary motion under a\nperturbing force (Kopal 1959), in this case, the accreting gas. \nLater in the evolution,\nthe eccentricity displays a secular increase which depends on the \nshear viscosity in the calculations: the greater the shear viscosity,\nthe earlier the increase begins. As with the overestimate of the\nrate of change of orbital separation that was given by S1 and S2 when \n$M_{\\rm acc}\\simgreat 3$, the eccentricity increases due to the \nunphysically-rapid transfer of angular momentum and energy from \nthe circumstellar discs into the binary's orbit.\n\n\n\\subsection{Test case 2}\n\\label{testcase2}\n\n\nThe second test case was chosen primarily to study the differences\nthat appeared in test case 1 between the PBE and SPH codes regarding\nthe formation of a circumbinary disc. A more centrally-condensed initial\ncloud results in the gas which first falls on to the binary having\nmore specific angular momentum than with a uniform-density \ncloud and in a more rapid increase of the specific angular momentum of\nthe gas as the accretion proceeds (see Section \\ref{soliddenr}). \nTherefore, a circumbinary disc should form earlier than with\ntest case 1 and provide us with a better test for the evolution of the \ncircumbinary disc.\nThe evolutions given by the PBE code and two different SPH calculations \nare given in Figure \\ref{PBESPH2}, with snapshots from the SPH calculations\nin Figures \\ref{1r_B1} and \\ref{1r_D1}.\n\n\n\\subsubsection{PBE calculation}\n\nThe PBE code predicts that at the end of the\nevolution the mass ratio should have increased from $q=0.6$\nto $q \\approx 0.88$ while the separation, after decreasing slightly\nat the beginning, finally ends up at $\\approx 2.3$ times the initial\nseparation. The mass of the circumbinary disc becomes significant\n($M_{\\rm cb}/M_{\\rm b} \\simgreat 1/20$) at $M_{\\rm acc} \\approx 1.5$,\nand at the end of the calculation the circumbinary disc contains\n$\\approx 13$\\% of the total mass.\n\n\n\\subsubsection{SPH calculations} \n\nThe SPH calculations had two different forms of artificial viscosity: \nB1: Balsara, with $\\alpha_{\\rm v}=0.25$ and $\\beta_{\\rm v}=1$;\nD1: $\\nabla\\cdot {\\bf v}$, also with $\\alpha_{\\rm v}=0.25$ and \n$\\beta_{\\rm v}=1$. Both formulations have low shear viscosity. The \nbulk viscosities are similar in non-shearing flows, but in shearing \nflows B1 has less bulk viscosity. We do\nnot use the Standard viscosity formulation (S1 or S2 in test case 1)\nbecause of our finding that its large shear viscosity inhibits \nthe formation of a circumbinary disc and leads to rapid evolution of \nthe circumstellar discs.\n\nAs with test case 1, due to the computational cost, the SPH \ncalculations are stopped before all of the gas has fallen on to the binary.\nEach calculation took $\\approx 4$ months on a 300 MHz Sun Ultra \nworkstation (using the binary tree, not a GRAPE board). During the\ncalculations, the binaries performed $\\approx 60$ orbits and $\\approx 70$\\%\nof the total mass was accreted by the binary or settled into a circumbinary\ndisc.\n\n\\begin{figure*}\n\\vspace{3.6truecm}\n%\\centerline{\\hspace{0.2truecm}\\psfig{figure=fig07.eps,width=17.0truecm,height=3.45truecm,rwidth=17.0truecm,rheight=3.60truecm}}\n%\\vspace{11.0truecm}\n\\caption{\\label{1r_B1} Snapshots of the evolution of test case 2 using the SPH code with artificial viscosity B1. The panels show the logarithm of column density, looking down the rotation axis, as the binary accretes infalling gas. The primary is on the right. The evolution starts when the mass accreted from the cloud is $M_{\\rm acc}=1$ and is followed until $M_{\\rm acc}=3.5$. Two circumstellar discs are formed as soon as the calculation begins and a circumbinary disc begins to form at $M_{\\rm acc}\\simgreat 1.4$. Each panel has a width of 8 times the binary's initial separation. }\n\\end{figure*}\n\n\\begin{figure*}\n\\vspace{3.6truecm}\n%\\centerline{\\hspace{0.2truecm}\\psfig{figure=fig08.eps,width=17.0truecm,height=3.45truecm,rwidth=17.0truecm,rheight=3.60truecm}}\n%\\vspace{11.0truecm}\n\\caption{\\label{1r_D1} The same as in Figure 7, except using artificial viscosity D1. With the different viscosity, the circumbinary disc forms earlier (at $M_{\\rm acc}\\approx 1.1$) and the spiral shocks in the disc are better resolved.}\n\\end{figure*}\n\n\n\\subsubsection{Evolution of the mass ratio} \n\nThe agreement for the evolution of the mass ratio is even better than it\nwas with test case 1 with differences of $\\simless 3$\\%. This\nis because, in this test case, the specific angular momentum \nof the gas being \ncaptured by the secondary is large enough for it to form a \ncircumsecondary disc outside the accretion radius as soon as the \nSPH calculations begin, regardless of the viscosity \n(Figures \\ref{1r_B1} and \\ref{1r_D1}). The SPH calculations\ngenerally give a slightly higher mass ratio than is predicted by the\nPBE code which is exactly what is expected because the PBE code \nignores the separation-decreasing effect of the interaction between\nthe binary and the circumbinary disc (a smaller binary separation means\nthat the specific angular momentum of the gas is higher relative to\nthat of the binary, resulting in more gas being captured by the \nsecondary).\n\n\\subsubsection{Circumbinary disc evolution and interactions} \n\\label{testcase2cb}\n\nFor test case 2, the differences between the PBE and SPH results involve the\nformation of the circumbinary disc and its interaction with the binary,\nthe latter of which is not accounted for in the PBE code. \nGenerally, a binary will interact with a circumbinary disc\nso as to transfer angular momentum from its orbit into the gas of\nthe circumbinary disc. This tends to decrease the separation of the\nbinary and increase its eccentricity (Artymowicz et al.~1991; Lubow\n\\& Artymowicz 1996). \nBoth these effects can be seen in the SPH calculations. The separation\nfollows the prediction of the PBE code to better than $3$\\%\nuntil the circumbinary disc begins to form, after which it is \nalways smaller than predicted by the PBE code. As in test case 1, \nthe eccentricity grows at the start of the\ncalculation and then displays a secular decrease with time. However,\nwhen the mass of the circumbinary disc exceeds $\\approx 0.05 M_{\\rm b}$,\nthe transfer of angular momentum from the binary to the circumbinary disc\noverwhelms the eccentricity-decreasing effect of the infalling gas and\nthe eccentricity increases.\n\nAs with test case 1, different formulations of the SPH viscosity give\nslightly different evolutions. \nD1 results in earlier formation of a circumbinary disc than B1, although\nat $M_{\\rm acc}=2$ and $M_{\\rm acc}=3.5$ \nthe circumbinary disc masses only differ by \n$\\approx 30$\\%. More importantly, we find that B1 gives very poor \nresolution of spiral shocks in the circumbinary disc (created by \ngravitational torques from the binary) due to its lower bulk viscosity\nin shearing flows \ncompared to D1 (c.f.~Figures \\ref{1r_B1} and \\ref{1r_D1}).\nThe better shock resolution of D1\nresults in more efficient angular momentum transport from the binary's\norbit to the circumbinary disc which leads to\na smaller binary separation and, consequently, more of the infalling gas\nsettles into the circumbinary disc than with B1. This can be seen in\nthe rapid decrease in separation of D1 compared to B1 when \n$2.0 \\simless M_{\\rm acc}\\simless 2.6$ (Figure \\ref{PBESPH2}b), and, \nsimultaneously, the more rapid \nincrease in the mass of the circumbinary disc for D1 (Figure \\ref{PBESPH2}c). \n\nFrom the point of view of the ability to resolve shocks in the \ncircumbinary disc, D1 is more realistic than B1\nand we emphasise that extreme care should be used when employing \nthe Balsara formulation of viscosity in shearing flows. Given that\nD1 appears to give more realistic results than B1, is it encouraging to\nnote that over the entire evolution the PBE code predicts the \ncircumbinary disc mass to within a factor of 2 of that given by the D1 SPH\ncalculation (Figure \\ref{PBESPH2}).\n\n\\begin{figure*}\n\\vspace{-0.7truecm}\n\\centerline{\\hspace{0.2truecm}\\psfig{figure=fig09.ps,width=17.0truecm,height=17.0truecm,rwidth=17.0truecm,rheight=11.0truecm}}\n%\\vspace{11.0truecm}\n\\caption{\\label{acc_d0_w0} The evolution of protobinary systems which were formed in the centres of collapsing molecular cloud cores as they accrete from their gaseous envelopes. The initial cores have uniform-density profiles and are in solid-body rotation. The evolution of the mass ratio (a; upper left), separation (b; upper right), and ratio of the circumbinary disc mass to that of the binary (c; lower left), and the relative accretion rate (d; lower right) are given as functions of the amount of gas that has been accreted from the envelope. The evolutions are given for binary systems with initial mass ratios of $q=0.1$ to $q=1.0$, with various different line types and/or line widths for each. The functions are all given by thin dotted lines once the circumbinary disc mass exceeds 5\\% of the binary's mass. Beyond this point, the binary's mass ratio and the mass in the circumbinary disc are likely to be underestimated, and the separation is likely to be overestimated. Masses are given in units of the binary's initial mass; separation is given in units of the binary's initial separation. }\n\\end{figure*}\n\n\\subsection{Conclusions and limitations of the PBE code}\n\nIn summary, in the absence of a massive circumbinary disc, \nthe PBE code gives results which are in good qualitative\nand quantitative agreement with the full hydrodynamic calculations.\nIn all cases, the binary's mass ratio is predicted to within 5\\% of\nthe SPH results {\\it over an increase in the binary's total mass \nby a factor of up to 6! } In test case 1, the binary's separation \nis predicted to within 20\\% by the PBE code. Furthermore, in test\ncase 1, even these small differences can be attributed to the \nSPH code's inability to resolve the circumsecondary disc during \nparts of the calculations or unphysically-rapid viscous evolution\nof the circumstellar discs, rather than a problem with the PBE code.\nThus, {\\bf the results from the PBE code are at least as accurate as \nthose given by a full SPH calculation, but the \nPBE code is $\\sim 10^6$ times faster}. \nThis makes it possible to investigate the\nstatistical properties of binary stars (see the next section).\n\nIn cases where a circumbinary disc forms around the binary,\nthe PBE code generally predicts that the \ndisc forms earlier than in the full SPH calculations, especially in the\nmore borderline case of \na progenitor molecular cloud core with uniform-density. However, in the\nbest case for studying the formation of a circumbinary disc \n(test case 2, D1) the time of formation of the circumbinary disc was\nin good agreement and its mass was predicted to within a factor of 2\nthroughout the evolution.\n\nThe main omission in the PBE code is that, if a massive circumbinary disc\nis formed ($M_{\\rm cb}/M_{\\rm b} \\simgreat 1/20$), the code ignores \nthe interaction between it and the binary. Omitting this interaction\nleads to the separation of the binary being {\\it overestimated} by the \nPBE code. From the SPH results, we find that {\\bf if a massive \ncircumbinary disc is formed, the binary's separation is likely \nto remain approximately constant as it accretes from a gaseous envelope}. \nThe overestimate of the separation by the PBE code means that\n{\\bf the mass of the circumbinary disc is likely to be underestimated and,\nfor the same increase in the binary's mass, the binary's mass ratio will be\nunderestimated}. We note, however, that this omission serves \nonly to {\\it strengthen} the predictions of the properties \nof binary stars that we obtain in Section \\ref{predictions}.\n\n\n\\begin{figure*}\n\\vspace{-0.7truecm}\n\\centerline{\\hspace{0.2truecm}\\psfig{figure=fig10.ps,width=17.0truecm,height=17.0truecm,rwidth=17.0truecm,rheight=11.0truecm}}\n%\\vspace{11.0truecm}\n\\caption{\\label{acc_d1_w0} The evolution of protobinary systems which were formed in the centres of collapsing molecular cloud cores as they accrete from their gaseous envelopes. The initial cores have {\\it either} $1/r$-density profiles and are in solid-body rotation, {\\it or} $1/r^2$-density profiles and are in differential rotation with $\\Omega_{\\rm c} \\propto 1/r$. These two types of core have the same relationship between angular momentum and mass (see Figure 2). See Figure 9 for a description of the plots. }\n\\end{figure*}\n\n\n\\section{Protobinary evolution}\n\\label{evolution}\n\nWe now use the PBE code to study the \nevolution and final states of binaries that are formed \nfrom the collapse of 6 types of molecular cloud core. We study \nbinaries that are formed from clouds with three different initial density\nprofiles: uniform-density, and power-law profiles of $\\rho \\propto 1/r$\nand $\\rho \\propto 1/r^2$ (i.e. $\\lambda$=0, -1, and -2). \nFor each of these three density profiles, we study two different initial\nrotation profiles: solid-body rotation, \nand $\\Omega_{\\rm c} \\propto 1/r$ (i.e. $\\beta$=0, and -1).\n\nThese initial conditions are highly idealised. However, we use them\nto illustrate how the properties of a binary depend on the \ndegree of central condensation and the amount of differential rotation\nin its progenitor molecular cloud core. In fact, in\nseveral cases the initial conditions represent extremes; the initial conditions\nbefore dynamic collapse occurs are almost certainly somewhat \ncentrally-condensed, but are almost certainly less centrally condensed than\n$\\rho \\propto 1/r^2$. In Section \\ref{predictions}, we use the conclusions\nreached from these calculations to predict the properties of binaries\nand to constrain the properties of the molecular cloud cores from which\nthey formed.\n\nFor each type of cloud (Figures \\ref{acc_d0_w0} to \\ref{acc_d1_w1}), \nwe consider the evolution of `seed' binaries that form with \ninitial mass ratios in the range $0.1 \\leq q \\leq 1.0$. \nWe give the mass ratio $M_{\\rm 2}/M_{\\rm 1}$, separation $a$, ratio\nof the mass of the circumbinary disc compared to the binary's mass\n$M_{\\rm cb}/M_{\\rm b}$,\nand relative accretion rate $\\dot M_{\\rm 2}/\\dot M_{\\rm 1}$,\nas functions of the total mass that has fallen on to the binary \nsystem from the envelope, $M_{\\rm acc}$. \nAs mentioned in Section \\ref{PBEcode},\nthe figures that are produced can be viewed in\ntwo ways: either as giving the \n{\\it evolution of individual protobinary systems} as\nthey evolve from their initial mass ($M_{\\rm acc}=M_{\\rm b}=1$) \nto a higher total mass\n(up to $M_{\\rm acc}=100$), or, for the first three panels in each figure, \nas giving the {\\it final states} of binaries\nthat initially began with masses ranging from 1\\% \n($M_{\\rm acc}=100$ when the accretion stops) to 100\\% \n($M_{\\rm acc}=1$ if there is no accretion on to the protobinary) \nof the cloud's total mass $M_{\\rm c}$.\n\n\n\n\\subsection{Solid-body rotation, uniform-density profile}\n\\label{soliddenuniform}\n\nFigure \\ref{acc_d0_w0} gives the results for binaries formed from initially\nuniform-density clouds in solid-body rotation. The long-term evolution of\nthe mass ratios is that they increase toward unity (equal mass components).\nThe separation initially decreases, due to accretion of gas with low mean \nspecific angular momentum, but increases in the long-term. \nBoth of these long-term effects are a consequence of the fact that \nthe specific angular momentum of the infalling gas increases \nquickly as mass is accreted (Figure \\ref{jrvsm}), \nsince the accretion of material with high \nspecific angular momentum increases the mass ratio and separation, while the\naccretion of material with low specific angular momentum decreases both\nthe mass ratio and separation\n(Artymowicz 1983; Bate 1997; Bate \\& Bonnell 1997).\n\nThe different evolutions for the different `seed' mass ratios are in\nlarge part due to the way we have chosen the initial conditions \n(Section \\ref{PBEcode}). \nWe assumed that the central region of the progenitor cloud from \nwhich the `seed' binary formed had the same angular \nmomentum as that contained in the orbit of the \n`seed' binary (equation \\ref{lbinary}). For a `seed'\nbinary with a given mass ratio and separation these initial\nconditions give the slowest possible rotation rate of the progenitor\ncore and, therefore, the {\\it slowest possible evolution toward \nequal mass ratios and the formation of circumbinary discs}. However,\nthey also mean that the gas which is accreted by a `seed'\nbinary with a low mass ratio has {\\it less} specific angular momentum \nthan for a binary with a high mass ratio. Hence, the mass ratio of a `seed'\nbinary with a small mass ratio tends to decrease initially, while that of \na binary with a large mass ratio tends to increase.\n\nThis dependence of the rotation rate of the progenitor cloud\non the mass ratio of the `seed' binary\nalso largely explains why the evolution of the separation \n(Figure \\ref{acc_d0_w0}b) and circumbinary disc (Figure \\ref{acc_d0_w0}c)\ndiffer for different initial \nmass ratios. In all cases, the separation decreases initially, but \nit does so quicker and for longer in systems with smaller initial mass \nratios because the specific angular momentum of the infalling gas is lower.\nLikewise, the formation of a circumbinary disc requires more accretion \nfor systems with lower initial mass ratios. However,\nfor the formation of a circumbinary disc, there is an additional effect.\nFor a system with a low mass ratio, the secondary is at a \nlarger radius from the binary's centre of mass than in a system with a\nhigh mass ratio. Therefore, the infalling gas must have more\nspecific angular momentum before it can form a circumbinary disc \nrather than be captured by the secondary.\n\n\\begin{figure*}\n\\vspace{0.15truecm}\n\\centerline{\\hspace{1.3truecm}\\psfig{figure=fig11.ps,width=15.8truecm,height=9.9truecm,rwidth=17.0truecm,rheight=10.15truecm}}\n%\\vspace{11.0truecm}\n\\caption{\\label{acc_d2_w0} The evolution of protobinary systems which were formed in the centres of collapsing molecular cloud cores as they accrete from their gaseous envelopes. The initial cores have $1/r^2$-density profiles and are in solid-body rotation. The binaries rapidly evolve to a state where most of the infalling gas accumulates in a massive circumbinary disc and the binary itself ceases to evolve. See Figure 9 for a description of the plots. }\n\\end{figure*}\n\nIn all cases, the long-term evolution is that the binary reaches a\nsteady-state in which a constant fraction of the infalling gas \nis captured by the binary with the rest going into the circumbinary\ndisc and $\\dot M_{\\rm cb}/\\dot M_{\\rm b} \\approx 0.17$. Since the \nspecific angular momentum of the gas that falls on to the binary is\nalways increasing (Figure \\ref{jrvsm}), \nthis indicates that a steady-state is established\nin which the binary continually adjusts to the accretion so that ratio\nof the specific angular momentum of the infalling gas to $\\sqrt{GM_{\\rm b}a}$\n(which is related to the specific angular momentum of the binary) \nis constant (see equation \\ref{jrel}). Of course,\nas shown by the test calculations (Section \\ref{comparison}), \nwhen the circumbinary disc becomes\nmassive ($M_{\\rm cb}/M_{\\rm b} \\simgreat 1/20$; dotted lines in Figures\n\\ref{acc_d0_w0} to \\ref{acc_relax}) the \ninteraction of the binary with the disc will not allow this same \nequilibrium to\nbe established. Instead the separations will be lower \nand more of the infalling gas will settle into the circumbinary \ndisc than is predicted here. In addition, for the same increase \nin the mass of the binary, the mass ratio will tend to increase even \nmore rapidly toward equal mass protostars because the smaller\nseparation of the binary means that the specific angular\nmomentum of the gas compared to that of the binary will be \nsomewhat larger. Thus, as with the assumption that the cloud rotates\nat the slowest possible rate, {\\it ignoring the interaction of the binary\nwith the circumbinary disc gives the slowest possible evolution \ntoward equal masses and the formation of a massive circumbinary disc}.\n\n\n\\subsection{Solid-body rotation, 1/r-density profile}\n\\label{soliddenr}\n\nFigure \\ref{acc_d1_w0} gives the results for binaries formed from progenitor\nclouds with $1/r$-density profiles in solid-body rotation.\nThe evolutions are similar to the uniform-density calculations, but\neverything evolves toward high-angular-momentum behaviour after the\naccretion of less gas. \nThe mass ratios evolve toward unity and a massive circumbinary disc\nis formed after less mass has been accreted. \nThe separations begin increasing earlier, \nand increase by a greater amount for the same amount of accretion.\n\nThe more rapid evolution toward high-angular-momentum behaviour \nthan with the uniform-density cloud is because the infalling gas \nhas a more specific angular momentum initially, and its \nspecific angular momentum increases more rapidly with mass\n(Figure \\ref{jrvsm}). This also means that, to reach a \nsteady-state, the binary must increase \n$\\sqrt{GM_{\\rm b}a}$ more rapidly. Hence, a steady-state is \nattained when the infalling gas has more specific angular momentum \nrelative to the binary than in the uniform-density case, and thus\n$\\dot M_{\\rm cb}/\\dot M_{\\rm b}$ is also higher at $\\approx 0.19$.\nAgain, however, the interaction of the binary with the circumbinary\ndisc, which is not taken into account by the PBE code, is likely to lead\nto: significantly smaller separations; more mass in \nthe circumbinary disc; and, for a given increase\nin the binary's total mass, a mass ratio that is even closer to unity.\n\n\n\\begin{figure*}\n\\vspace{-0.7truecm}\n\\centerline{\\hspace{0.2truecm}\\psfig{figure=fig12.ps,width=17.0truecm,height=17.0truecm,rwidth=17.0truecm,rheight=11.0truecm}}\n%\\vspace{11.0truecm}\n\\caption{\\label{acc_d0_w1} The evolution of protobinary systems which were formed in the centres of collapsing molecular cloud cores as they accrete from their gaseous envelopes. The initial cores have uniform-density profiles and differential rotation of $\\Omega_{\\rm c} \\propto 1/r$. See Figure 9 for a description of the plots. }\n\\end{figure*}\n\n\\begin{figure*}\n\\vspace{-0.7truecm}\n\\centerline{\\hspace{0.2truecm}\\psfig{figure=fig13.ps,width=17.0truecm,height=17.0truecm,rwidth=17.0truecm,rheight=11.0truecm}}\n%\\vspace{11.0truecm}\n\\caption{\\label{acc_d1_w1} The evolution of protobinary systems which were formed in the centres of collapsing molecular cloud cores as they accrete from their gaseous envelopes. The initial cores have $1/r$-density profiles and differential rotation of $\\Omega_{\\rm c} \\propto 1/r$. See Figure 9 for a description of the plots. }\n\\end{figure*}\n\n\\subsection{Solid-body rotation, 1/r$^2$-density profile}\n\\label{soliddenr2}\n\nFigure \\ref{acc_d2_w0} gives the results for binaries formed from progenitor\nclouds with $1/r^2$-density profiles in solid-body rotation.\nThe rate of increase of the specific angular momentum of the gas\nas mass is accreted is now so rapid (Figure \\ref{jrvsm}) \nthat the binary cannot evolve fast enough to keep up with it. \nThis results in the rapid formation and runaway growth of a \nmassive circumbinary disc (Figure \\ref{acc_d2_w0}c) because \nthe infalling gas has too much angular momentum to be \ncaptured by the individual components of the binary. \nThe binary only accretes a maximum of $1-3$ times its \ninitial mass, even if the cloud mass is 100 times the \ninitial binary mass -- the rest of the gas goes into the circumbinary disc. \n\nOf course, in reality, if the circumbinary disc becomes comparable \nin mass to the binary we would expect it to react in ways that are not \npossible to follow with the simple PBE calculations. \nInteraction between the binary and \ncircumbinary disc could lead to two possibilities.\nFirst, the disc may fragment to form one or more additional protostellar \nobjects (e.g.~Bonnell \\& Bate 1994a; Burkert \\& Bodenheimer\n1996; Burkert et al.~1997). In this case, the model\nhas completely broken down, since in this paper we assume\nthat a binary is formed by an initial binary fragmentation and subsequent \naccretion. There is no allowance made for additional\nfragmentation. The second possibility is that gas is accreted by\nthe circumstellar discs of the two protostars from the circumbinary \ndisc (Artymowicz \\& Lubow 1996; Lubow \\& Artymowicz 1996). If such \naccretion occurs, the binary's mass ratio will inevitably evolve \nrapidly toward unity because this material has high specific angular momentum\nand will preferentially be captured by the secondary. The mass ratios\nwould continue to follow the rapid increases seen early in \nFigure \\ref{acc_d2_w0}a (when $M_{\\rm acc} \\simless 2$), giving even\nfaster evolution toward equal masses than was seen for \ncores with $1/r$-density profiles.\n\n\n\\subsection{Differential rotation, uniform-density profile}\n\\label{omegaruniform}\n\nFigure \\ref{acc_d0_w1} gives the results for initially \nuniform-density clouds in differential rotation with\n$\\Omega_{\\rm c} \\propto 1/r$.\nThe specific angular momentum of the infalling gas is \nlow to begin with and only slowly increases as mass is accreted\n(Figure \\ref{jrvsm}). Thus, a binary's mass ratio takes longer to\nevolve toward unity, the separation continually decreases, \nand a circumbinary disc takes longer to form than in the solid-body case \n(Figure \\ref{acc_d0_w0}). Even after a binary has accreted 100 \ntimes its initial mass, its mass ratio depends primarily on its\ninitial value (Figure \\ref{acc_d0_w1}a). The ratio of the mass in the \ncircumbinary disc to the binary's mass is always less than 0.1, \nand in most cases less than 0.05, even after the infall of 100 times the\nbinary's initial mass.\n\n\n\\subsection{Differential rotation, 1/r-density profile}\n\\label{omegardenr}\n\nFigure \\ref{acc_d1_w1} gives the results for clouds with \n$1/r$-density profiles that are in differential\nrotation with $\\Omega_{\\rm c} \\propto 1/r$. Again, with\ndifferential rotation, the infall of gas with low specific\nangular momentum is maintained for longer than with solid-body rotation. \nThe mass ratios do all increase toward unity \nafter more than 10 times the binary's initial mass has fallen in, however,\nafter 100 times the initial binary's mass has fallen in, \na full range of mass ratios is still\npossible. The formation of a \ncircumbinary disc is again delayed with differential rotation, \nalthough in most cases a steady-state is reached eventually with \n$\\dot M_{\\rm cb}/\\dot M_{\\rm b} \\approx 0.15$. \n\n\n\\subsection{Differential rotation, 1/r$^2$-density profile}\n\\label{omegardenr2}\n\nFinally, we consider the evolution of binaries formed from progenitor\nclouds with $1/r^2$-density profiles that are in differential\nrotation with $\\Omega_{\\rm c} \\propto 1/r$. From Figure \\ref{jrvsm},\nthe relationship between angular momentum and mass in the progenitor\ncloud is identical to a cloud with a $1/r$-density \nprofile in solid-body rotation and, therefore, the evolution is\nidentical to that in Figure \\ref{acc_d1_w0}. \n\nCompared to $1/r^2$-density with solid-body rotation, \nthe effect of differential rotation is, once again, \nto decrease the rates of increase of the mass ratio and separation \n(at least while the binary is still accreting gas\nin Figure \\ref{acc_d2_w0}), and to delay the formation of a circumbinary\ndisc. The reduced rate of increase of the specific angular momentum of the\ninfalling gas means that, unlike in the case\nwith solid-body rotation, the binary can reach an equilibrium with the\ncloud; the runaway of the mass in the circumbinary disc is avoided.\nHowever, even such strong differential rotation is not enough\nto stop the mass ratios being driven toward unity with an initial\ndensity profile of $\\rho \\propto 1/r^2$.\n\n\n\\section{Relaxing some of the assumptions}\n\\label{relax}\n\n\\begin{figure*}\n\\vspace{-0.7truecm}\n\\centerline{\\hspace{0.2truecm}\\psfig{figure=fig14.ps,width=17.0truecm,height=17.0truecm,rwidth=17.0truecm,rheight=11.0truecm}}\n%\\vspace{11.0truecm}\n\\caption{\\label{acc_relax} The evolution of protobinary systems which were formed in the centres of collapsing molecular cloud cores as they accrete from their gaseous envelopes. As in Figure 9, the initial cores have uniform density profiles and are in solid-body rotation, but here the clouds are rotating more rapidly and are all rotating at the same rate, regardless of the binary's initial mass ratio (see Section 5.1). This type of evolution is appropriate for binaries that form via the fragmentation of a massive circumstellar disc surrounding single protostar. See Figure 9 for a description of the plots. }\n\\end{figure*}\n\n\n\\subsection{The rotation rate of the progenitor cloud}\n\\label{rotationrate}\n\nIn the previous section, we assumed that the orbital angular momentum\nof the `seed' binary system, $L_{\\rm b}$, was equal to the \nangular momentum of the spherical central region of the cloud, $L_{\\rm cen}$, \nfrom which the `seed' binary formed (equation \\ref{lbinary}). \nThis assumption gives a {\\it lower limit} to the rate of rotation of the\nprogenitor cloud, since it does not allow for the possibility \nof circumstellar discs around the `seed' binary which would\ncontain additional angular momentum. Furthermore, if the \n`seed' binary was formed via fragmentation of a circumstellar \ndisc surrounding a single \nprotostar, then the disc must have had a radius at least as big as the\nseparation of the `seed' binary which forms (i.e.~at least \nsome gas in the disc must have had a specific angular momentum of \n$j=\\sqrt{GM_{\\rm b}a}$). Thus, some of the gas which falls on to \nthe system from the envelope immediately after the `seed'\nbinary forms is expected to have at least this much specific\nangular momentum. As a comparison, the first gas to be accreted by the\nbinaries in Figure \\ref{acc_d0_w0} had at most $0.21-0.63$ of this \nvalue, depending on the initial mass ratios. \nTherefore, it is conceivable that the progenitor clouds may be \nrotating faster than we assumed in the previous section.\n\nTo demonstrate the effect of the progenitor cloud having a greater\nrate of rotation, we performed calculations which evolved binaries whose\nprogenitor clouds were rotating rapidly enough that some (that part of\nthe envelope which is in the plane of the binary) of the first gas to\nfall on to the binary had a specific angular\nmomentum of $j=\\sqrt{GM_{\\rm b}a}$. Thus, rather than setting \n$R_{\\rm b}^2 \\Omega_{\\rm Rb}$ using equation \\ref{lbinary}, we set\n\\be\nR_{\\rm b}^2 \\Omega_{\\rm Rb} = \\sqrt{G M_{\\rm b} a},\n\\ee\n{\\it regardless of the initial mass ratio of the binary}.\nThus, all the progenitor clouds have the same initial \ndensity profile and rotation rate and all the `seed' binaries have\nthe same separation, regardless of the mass ratio of the `seed' binary. \nThis also allows us to examine the degree to which the evolution \nof a binary depends on its mass ratio, and how much it depends on \nthe properties of the gas which it accretes from the infalling envelope.\nThese `seed' binaries could have formed via the fragmentation \nof a disc, where we assume that the angular momentum that \nis in excess of the `seed' binary's orbital angular \nmomentum, $L_{\\rm b}$, is contained in circumstellar discs.\n\nThe results for an initially uniform-density cloud in solid-body\nrotation are given in Figure \\ref{acc_relax}. Due to the greater \nrotation rate of the progenitor cloud and, hence, the higher specific \nangular momentum of the gas which falls on to the binary, \nthe mass ratios are driven toward unity after much less mass has been\naccreted compared with when the slowest possible\nrotation rate was used (Figure \\ref{acc_d0_w0}).\nThus, {\\bf the rates of increase toward mass ratios\nof unity that are given in Section \\ref{evolution} are lower limits}.\n\nIn contrast to the previous section, the evolutions of the \nseparation and the mass in a circumbinary disc are quite independent \nof the mass ratio of the binary, demonstrating that {\\bf the evolution\nof a binary's separation and the formation of a circumbinary disc \ndepend almost entirely on the properties of the infalling gas;\nthe mass ratio of the binary has almost no effect.} \nThe very small dependence of the mass of the circumbinary disc \non the binary's mass ratio\nis because the secondary is farther from the centre of mass \nin a binary with a lower mass ratio.\n\n\n\\subsection{Different density profiles}\n\nThe evolutions presented in Section \\ref{evolution} are for \nidealised progenitor cloud cores with power-law density and \nrotation profiles. These clearly illustrate the main dependencies of \nthe evolution of a protobinary system as it accretes to its final\nmass. However, the PBE code easily be applied to other types \nof progenitor cloud core.\nFor example, we have performed evolutions beginning with Gaussian\ncentrally-condensed cores with inner to outer density contrasts of 20:1.\nThese have density profiles that are similar to observed pre-stellar \nmolecular cloud cores in that they are steep on the outside and flatter\nnear the centre (Ward-Thompson et al.~1994;\nAndr\\'e, Ward-Thompson, Motte 1996; Ward-Thompson, Motte, \\& Andr\\'e 1999).\nAs one might expect, the evolutions lie between those for uniform-density\nclouds and those with $\\rho \\propto 1/r$, although they are \nclosest to the uniform-density case.\n\n\n\\subsection{Eccentric binary systems}\n\\label{eccentricity}\n\nIn this paper, strictly, we only consider the evolution \nof protobinary systems with circular orbits. However, in the test cases\nof Section \\ref{comparison}, where we compared the evolution given by \nthe PBE code with those from full SPH calculations, we obtained\ngood agreement even though the orbit of the binary in the SPH \ncalculation had eccentricities up to $e \\approx 0.2$. Therefore, we are\nconfident that the results in this paper are valid for binaries with \neccentricities $e \\simless 0.2$.\n\nFor larger eccentricities, we expect the evolution of the binaries\nshould be {\\bf qualitatively similar} to what we have found for circular\nbinaries. Hence, we still expect that the long-term effect of accretion\nwill be to drive the mass ratios toward unity and form circumbinary\ndiscs and that this evolution will be enhanced with more \ncentrally-condensed initial conditions and diminished by differential\nrotation.\n\nHowever, there will be quantitative differences. Most importantly,\nthe formation of a circumbinary disc will be delayed \nin an eccentric system for two reasons. First, for the same \nsemi-major axis, an eccentric binary has less angular momentum than a\ncircular one and, thus, the gas from which it first formed (and hence\nthe molecular cloud core as a whole) may have been rotating more slowly. \nThis is would also mean that more gas is able to be accreted \nbefore the binary's mass ratio is driven toward unity.\nSecond, for binaries with the same semi-major axis separation, \na circumbinary disc must be formed at a larger radius from the \ncentre of mass for an eccentric binary than for a circular binary \nto avoid disruption (e.g.~Artymowicz \\& Lubow 1994). \nThus, eccentric systems are expected to be able to accrete significantly more \nmaterial than circular binaries before forming a circumbinary disc. \n\nOther effects may include collisions between the protostars and their\ncircumstellar discs (e.g.~Hall, Clarke \\& Pringle 1996) \nand, of course, the eccentricity itself \nis expected to evolve due to accretion and the interactions \nbetween the protostars and the \ndiscs. These effects are beyond the scope of this paper, but \nwould certainly be well worth studying.\n\n\n\\section{The Properties of Binary Systems}\n\\label{predictions}\n\nThe aim of this paper is to determine, for a particular \nmodel of binary star formation, the properties of binaries and\nhow they depend on the initial conditions in their progenitor \nmolecular cloud cores. By comparing these predictions with \nobservations, we hope to determine whether this is a viable \nmodel for binary star formation and, if so, to constrain the \ninitial conditions for binary star formation.\nIn order to do so, however, we must first discuss the \nrelationship that is expected between the mass of a `seed' \nbinary system and its separation.\n\n\n\\subsection{Dependence of the mass of a `seed' protobinary on its separation}\n\\label{bmass_vs_sepsec}\n\nIn this paper, we consider the evolution of a `seed' binary system \nas it accretes gas from an infalling envelope, but we do not specify \nexactly how the protobinary is formed. Presumably, it is formed\nvia some sort of fragmentation process (see Section 1).\nIn order for binary fragmentation to occur, the Jeans radius at the \ntime of fragmentation must be less than or approximately equal to the \nseparation of the protobinary that is formed. Thus, \n$a \\simgreat 2 R_{\\rm J}$, where $R_{\\rm J}$ is the Jeans radius\n\\be\n\\label{jeansradius}\nR_{\\rm J} \\approx \\frac{2 G M_{\\rm frag} \\mu}{5 R_{\\rm g}T},\n\\ee\n$\\mu$ is the mean molecular weight, and $R_{\\rm g}$ is the gas constant.\nThe `seed' binary's initial mass is approximately twice the mass\nof each fragment, $M_{\\rm frag}$. Therefore, for a constant\ntemperature, $T$, we expect a roughly linear \nrelationship between the mass of a `seed' binary and its separation:\n$M_{\\rm b} \\approx 2 M_{\\rm frag} \\propto a$.\n\n\\begin{figure}\n\\vspace{-0.2truecm}\n\\centerline{\\hspace{0.2truecm}\\psfig{figure=fig15.ps,width=8.0truecm,height=8.0truecm,rwidth=8.0truecm,rheight=7.5truecm}}\n%\\vspace{6.0truecm}\n\\caption{\\label{bmass_vs_sep} The dependence of a protobinary's initial mass on its separation. The points give the results from 26 fragmentation calculations (Figure 13, Boss 1986). The solid and dotted lines give simple estimates (see Section 6.1) of the minimum mass that a `seed' protobinary system should have as a function of its separation.}\n\\end{figure}\n\n\nFigure \\ref{bmass_vs_sep} gives the initial mass of a binary versus \nits separation from a series of fragmentation calculations performed by\nBoss \\shortcite{Boss86}. Indeed, there is a strong, approximately linear, \nrelationship between the binary's mass and its separation.\n\nUsing equation \\ref{jeansradius}, we plot (solid line) the \nrelationship if $a = 2 R_{\\rm J}$. We use $\\mu=2.46$ with\n$T=10$ K for densities below $10^{-13}$ g cm$^{-3}$ and \n$T \\propto \\rho^{\\gamma-1}$ with $\\gamma=1.4$ for \n$10^{-13} \\leq \\rho < 6\\times 10^{-8}$ g cm$^{-3}$ and \n$\\gamma=1.1$ for $\\rho \\geq 6\\times 10^{-8}$ g cm$^{-3}$ (e.g.~Tohline\n1982). The numerical results generally lie above the solid line\nbecause the properties of the binaries were calculated somewhat after they\nfirst began to form and they have already accreted some gas.\nFor example, if we assume that the fragments are embedded in a sphere of \ngas with radius $2 R_{\\rm J}$ and a mean density of half the \nmean density of the fragments which is rapidly accreted by the\nfragments, then we obtain the dotted line for the masses of \nthe `seed' binaries.\nFurthermore, the fragments typically form on elliptical orbits \nand are initially falling toward each other (which moves\nthe numerical results to smaller separations). \n\nGenerally, for separations $\\simgreat 10$ AU, wider `seed' \nbinaries have larger initial masses, while for separations\n$\\simless 10$ AU the initial masses are $\\approx 0.01 {\\rm M}_\\odot$.\nTherefore, for example, in order to form binary systems with a solar-mass \nprimary, close systems ($\\simless 10$ AU) may have to \naccrete $\\sim 100$ times their initial mass. Systems with separations \n$10 \\simless a \\simless 100$ AU need to accrete between $100-10$ times\ntheir initial mass, and the widest systems need only accrete \na few times their initial mass.\n\nThis leads us to our first prediction: for binary systems with the \nsame total mass, {\\bf\nthe properties of close systems will be more heavily\ndetermined by accretion than those of wide systems}. In turn this means\nthat the mass ratios of wide binary systems are expected to be \ndetermined primarily from the initial density structure in the \nmolecular cloud cores and so they may enable us to better understand the\ninitial conditions for star formation by giving us a way to measure\nthe density structure. Therefore, \n{\\bf in order to study the initial conditions\nfor star formation we should consider the properties of wide binaries,\nwhile to learn more about the evolution due to accretion it is best to\nconsider close binaries}.\n\nA further prediction is: {\\bf if high and low mass stars form by the\nsame general process, and the initial mass of a `seed' binary\nis independent of the mass of the progenitor core, then the properties\nof massive binary systems should be more heavily influenced \nby accretion than those of lower mass systems with the same separation}.\n\n\n\\subsection{Binary mass ratios}\n\nIn sections \\ref{evolution} and \\ref{relax}, we found that\n{\\bf the long-term evolution of an accreting binary is for its \nmass ratio to approach unity}. \n\n\n\\subsubsection{Dependence of the mass ratio on separation}\n\nAs argued in Section \\ref{bmass_vs_sepsec}, for \nmolecular cloud cores of a given mass, the amount of mass accreted \nby a binary, relative to its initial fragmentation mass, will be greater\nfor close binaries than for wide systems. Thus, {\\bf closer binary\nsystems are more likely to have mass ratios near unity than wider \nsystems with the same total mass}.\n\nDuquennoy \\& Mayor \\shortcite{DuqMay91} surveyed main-sequence \nG-dwarf stellar systems. They found that the mass ratio \ndistribution, averaged over binaries with all separations, increases toward\nsmall mass ratios. However, there is mounting evidence that\nthe mass-ratio distributions differ between short and long-period\nsystems with the distribution for close binaries ($P <\n3000$ days; $a \\simless 5$ AU) consistent with\na uniform distribution (Mazeh et al.~1992; Halbwachs, Mayor \\& Udry~1998). \nThus, relative to wide systems, the close systems are biased toward\nmass ratios of unity, in agreement with the above prediction.\n\nThe fraction by which the mass of a `seed' binary must\nbe increased in order for its mass ratio to approach unity depends\non the conditions in the progenitor cloud core. In general, {\\bf the\nless centrally-condensed a core is and/or the more differential rotation\nit has ($\\beta \\leq 0$), \nthe easier it is to form binary systems with low mass ratios\nfor a given increase in the binary's initial mass}. By inquiring how\neasy it is to reproduce the observed mass-ratio distributions with\ndifferent types of progenitor molecular cloud core, \nwe can use these results to constrain the initial conditions for binary\nstar formation.\n\nDuquennoy \\& Mayor \\shortcite{DuqMay91} found that binaries containing\nG-dwarfs with\nseparations $\\simgreat 30$ AU generally have unequal mass ratios \n(typically $q\\approx 0.3$). From Figure \\ref{bmass_vs_sep}, typically,\nthese binaries may be expected to accrete $\\sim 10$ times their \n`seed' mass. For uniform-density progenitor \nclouds in solid-body rotation\n(Figure \\ref{acc_d0_w0}a), this observed mass \nratio distribution could be produced if the fragmentation process \ntypically produces `seed' binaries with low mass ratios ($q \\approx 0.2$).\nHowever, with more centrally-condensed cores it becomes progressively\nmore difficult to produce the observed mass-ratio distribution because\nthe accretion drives the initial mass ratios toward unity\n(Figures \\ref{acc_d1_w0}a and \\ref{acc_d2_w0}a). With\n$\\rho \\propto 1/r$ cores, the `seed' binaries must typically have\nmass ratios of $q \\approx 0.1$ in order to produce G-dwarf binaries\nthat have typical mass ratios of $q\\approx 0.3$. With \n$\\rho \\propto 1/r^2$ (assuming\nthe `seed' binaries manage to accrete from their circumbinary discs) it\nis difficult to see how the observed mass-ratio distribution could be\nproduced because of the rapid evolution toward equal mass protostars. \nIf the progenitor cores have significant differential\nrotation, uniform-density and $\\rho \\propto 1/r$ cores can easily\nproduce the observed mass ratios, but it is still difficult to \nproduce G-dwarf binaries with low mass ratios from cores with \n$\\rho \\propto 1/r^2$.\n\nFor close G-dwarf binary systems ($a \\simgreat 5$ AU), the constraints are\neven more pronounced. Typically, we expect such binaries to accrete\n$\\approx 100$ times their `seed' mass, yet the observed \nmass-ratio distribution is approximately flat (i.e.~approximately\n1/2 the binaries have $q<0.5$). It is effectively impossible\nfor cores in solid-body rotation to produce such a mass ratio \ndistribution if they are significantly centrally-condensed. Even for\nuniform-density cores, approximately 1/2 of the `seed' binaries\nwould need to have $q<0.1$, although taking into account the effect of\neccentricity (Section \\ref{eccentricity}) it is probable that cores\nwith nearly uniform-density profiles can reproduce the observations.\nIf the cores have significant differential rotation, the observed\nmass ratios can be produced with cores that are as \ncentrally-condensed as $\\rho \\propto 1/r$, but cores with\n$\\rho \\propto 1/r^2$ are still excluded.\n\nWe note that, as discussed in Section \\ref{relax}, the results \nin Section \\ref{evolution} give the slowest possible evolution \ntoward mass ratios of unity (unless the binary has a significant\neccentricity). Thus, it may be even more difficult to form \nunequal mass binaries than suggested by the above discussion.\nEven taking the above numbers, with solid-body rotation the mass\nratios of the `seed' binaries must typically be $q \\approx 0.1-0.2$.\nTo obtain such mass ratios via direct fragmentation requires\nthat the progenitor molecular cloud cores have significant \nasymmetries (e.g.~Bonnell \\& Bastien 1992) which implies that they\nare formed and/or triggered to collapse by dynamical processes.\nLow mass ratios can also be obtained via rotational fragmentation\n(Section \\ref{introduction}), but then the binary's mass ratio\nwill be driven toward unity even more rapidly. Thus, in reality,\nmolecular cloud cores may have a degree of differential rotation.\n\nIn summary, {\\bf the observed mass-ratio distributions are most\neasily explained by cores that have density profiles that are\nless centrally condensed than $\\rho \\propto 1/r$ (e.g.~Gaussian),\npossibly with a small amount of differential rotation.} \nThis is in good agreement with the observed density profiles of\npre-stellar cores \n(Ward-Thompson et al.~1994; Andr\\'e, Ward-Thompson, Motte 1996; \nWard-Thompson, Motte, \\& Andr\\'e 1999). If \nthe progenitor cores rotate as solid-bodies it is essentially \nimpossible to produce\nthe observed mass-ratio distribution of close binaries if the\ncores are much more centrally condensed than a Gaussian-density \nprofile. If differential rotation is allowed, cores with density\nprofiles as steep as $\\rho \\propto 1/r$ are feasible (with \nstrong differential rotation), but cores with\n$\\rho \\propto 1/r^2$ still cannot reproduce the observations. \n\n\n\\subsubsection{Dependence of the mass ratio on the binary's total mass}\n\nIf all binary systems form by the same general process, regardless \nof a system's final total mass (i.e.~from the collapse of molecular\ncloud cores with the same properties, only more massive), and if\nthe initial mass of a `seed' binary (Section \\ref{bmass_vs_sepsec})\nis independent of the mass of the core (depending only\non its initial separation), then {\\bf massive binaries should have\nmore-equal mass ratios than low-mass binaries of the same separation}.\nThis is because systems with a larger final mass would have had to\naccrete more, relative to their initial mass, than systems with a lower\nfinal mass.\n\nUnfortunately, unbiased surveys of stars more massive than G-dwarfs\nare only slowly becoming available. Preliminary results for O-star \nbinaries (e.g.~Manson et al.~1998) show a difference in the \nmass-ratio distribution between close \n($P \\simless 40$ days; $a \\simless 1/2$ AU) \nand wide ($P \\simgreat 10^4$ years; $a \\simgreat 1000$ AU) \nsystems, with close systems biased toward mass ratios of \nunity, but comparison between\nthe mass-ratio distributions of high and low-mass binaries is not\nyet possible. In addition, Bonnell, Bate \\& Zinnecker (1998) recently\nproposed that O-stars form in a different way to lower mass stars,\nfrom the collision of less massive stars in very dense star-forming \nregions. This theory predicts a large frequency of close binaries for\nO-stars (due to tidal capture) with a mass-ratio distribution that\nis not determined by accretion from an infalling envelope. Thus, we\nstrongly encourage surveys that will determine the mass-ratio distributions\nof B-, A-, and F-stars.\n\n\n\\subsubsection{Formation of brown dwarf companions to solar-type stars}\n\\label{browndwarfs}\n\nGiven that it becomes more difficult to form binaries with low mass ratios\nas more gas is accreted by a binary, \nit is of interest to ask how easy it is to form stars with brown-dwarf \ncompanions (see also Bate 1998). Since wider binaries should \nhave to accrete less gas, relative to their initial mass, to \nattain the same final total mass, then {\\bf the frequency of \nbrown dwarf companions to solar-type stars should increase with separation}.\nLikewise, we expect that systems with lower final masses also accrete\nless relative to their initial masses so that {\\bf for the same range of\nseparations, brown dwarf companions should be more frequent in \nsystems with a lower total mass than in higher-mass systems.}\n\nTaking the types of cores that most easily reproduce \nthe mass-ratio distributions\nof low-mass stars (i.e.~near-uniform density cores in solid-body rotation),\nwe find that a brown dwarf companion to a solar-type star could be formed \nif an extreme mass ratio ($q \\approx 0.1$) was produced at fragmentation and\nthe system subsequently increased its mass by a factor of $\\sim 20$ or\nless (Figure \\ref{acc_d0_w0}a). This implies that it may be quite easy to form\nbrown dwarf companions to stars of around a solar mass or less \nwith separations $\\simgreat 10$ AU. Indeed, two wide systems have \nbeen found: GL 229B\nis a brown dwarf companion ($0.02 - 0.06~ {\\rm M}_\\odot$) to a $0.6~\n{\\rm M}_\\odot$ M-dwarf with a separation of $\\approx 50$ AU (Nakajima\net al.~1995); G 196-3B is a brown dwarf companion ($0.02 - 0.04~ \n{\\rm M}_\\odot$) to a $0.4~{\\rm M}_\\odot$ \nM-dwarf with a separation of $\\approx 300$ AU (Rebolo et al.~1998).\n\nHowever, close systems ($\\simless 10$ AU) need to\naccrete $\\approx 100$ times their initial mass in order to obtain a\nsolar-mass primary and, due to the evolution of the mass ratio toward\nunity, it would be very difficult for the secondary to have the \nfinal mass of a brown dwarf after this amount of accretion.\n(Figure \\ref{acc_d0_w0}a). Therefore, {\\bf brown-dwarf companions\nto stars with masses $\\approx 1 {\\rm M}_\\odot$ and separations\n$\\simless 10$ AU are likely to be extremely rare or perhaps even nonexistent}.\nThis prediction is supported by the recent radial-velocity searches \nfor giant planets (see Marcy, Cochran \\& Mayor 1999 and references within).\nAlthough many planetary candidates \n($M \\sin i \\simless 0.013~{\\rm M}_\\odot $) have been found with \nseparations less than a few AU, there are currently only \n4 brown dwarf ($0.013~ {\\rm M}_\\odot \\simless \nM \\sin i \\simless 0.075~ {\\rm M}_\\odot $) candidates from $\\approx 600$\ntarget stars and even these could be stellar companions with orbits nearly\nperpendicular to the line of sight\n(Marcy, Cochran \\& Mayor 1999).\n\nWithin this model, the easiest way to obtain such close systems with extreme \nmass ratios would be that they formed from cores with significant \ndifferential rotation, or that the companion was formed significantly \n{\\it after} the primary. In the latter case, the primary would already \nhave a significant fraction of its final mass and, hence, the protobinary \nwould not have to increase its total mass by such a large factor.\nHowever, if this was achieved via the \nfragmentation of a circumstellar disc, then the fragmentation\nwould have to occur after the primary and its disc had accreted \na large fraction of the envelope, otherwise the secondary\nwould still end up with a stellar mass due to subsequent accretion \n(Section \\ref{rotationrate} and Figure \\ref{acc_relax}a).\n\n\n\n\\subsection{Binary separations}\n\nIn Section \\ref{evolution}, we found that a binary's separation can\nevolve significantly due to accretion, increasing \nor decreasing by up to 2 orders of magnitude (Figures \\ref{acc_d0_w0}b to\n\\ref{acc_relax}b). However, for most cases, if the binary's \nseparation is increasing the PBE code also predicts that a \nmassive circumbinary disc will be present. In test case 2\n(Section \\ref{testcase2}; Figure \\ref{PBESPH2}), we found that if a\nmassive circumbinary disc is present the interaction of the binary\nwith the circumbinary disc is likely to negate the separation-increasing\naffect of the accretion and the separation will remain approximately \nconstant.\n\nTherefore, {\\bf we conclude that a binary's separation is likely to \ndecrease or remain of the same order as \nits initial value during the accretion of\nthe gaseous envelope}. After the accretion phase, if a binary has a\ncircumbinary disc its separation is expected to decrease. Without a\ncircumbinary disc, its separation is likely to increase as the circumstellar\ndiscs evolve viscously and transfer their angular momentum to the orbit\nof the binary. However, the angular momentum contained in the \ncircumstellar discs is likely to be small compared to the orbital angular\nmomentum of the binary and, therefore, the binary's separation is expected to\nincrease by less than a factor of two.\n\n\n\\subsection{Circumstellar discs}\n\nBate \\& Bonnell \\shortcite{BatBon97} studied the disc formation \nprocess in accreting protobinary systems and established criteria \nfor the formation of circumstellar and circumbinary discs. \nThey found that if a protobinary system only accretes \ngas with low specific angular momentum after its formation, \nthe primary will have a circumstellar disc but the secondary may not.\nThe reverse is not true; if a circumstellar disc is formed\naround the secondary, the primary will also have a disc. \nThese conclusions can also be seen in the snapshots from the SPH test cases in \nFigures \\ref{UD_S2}, \\ref{UD_B1}, \\ref{1r_B1}, and \\ref{1r_D1}.\n\nWith the PBE code, we do not differentiate between gas that is directly\naccreted by a protostar and gas that is captured in its circumstellar\ndisc (presumably to be accreted by the protostar at a later time). \nHowever, we do\ndetermine the relative accretion rate on to the secondary and \nits circumstellar disc compared to the primary and its \ncircumstellar disc $\\dot M_2/\\dot M_1$ during formation of a binary\n(Figures \\ref{acc_d0_w0}d to \\ref{acc_relax}d). We find that the\nrelative accretion rate is $\\dot M_2/\\dot M_1 \\leq 1.3$\nand in the majority of cases is less than unity. Therefore,\n{\\bf we expect that in most cases the circumsecondary disc will have \na mass that is less than or similar to that of the circumprimary disc.} \nThis conclusion is valid\nunless the circumprimary disc accretes on a shorter time-scale than\nthe circumstellar disc. In fact, Armitage, Clarke \\& Tout (1999)\nshowed that the circumsecondary disc is expected to accrete {\\it more rapidly}\nthan the circumprimary disc and, therefore, this effect should only\nbe enhanced. This conclusion is in excellent agreement with the latest \nobservations of circumstellar material around young binary systems.\nGhez, White \\& Simon \\shortcite{GWS97} considered UV and NIR \nexcess emission from the components of young binary systems \nand found that the excesses are either comparable or \ndominated by the primary, suggesting that the gas in \ncircumstellar discs is either distributed similarly or \npreferentially around the primary.\n\nThe only cases where a circumsecondary disc may become significantly\nmore massive than the circumprimary disc are those where the \ngaseous envelope has effectively been exhausted and accretion \non to the circumstellar discs comes primarily from a circumbinary disc. \nIn these cases, because the \ngas has very high angular momentum with respect to the binary, it will\npreferentially be captured by the secondary (Artymowicz \\& Lubow 1996; \nBate \\& Bonnell 1997).\n\n\n\\subsection{Circumbinary discs}\n\\label{circumbinary}\n\nFrom the results in Section \\ref{evolution}, just as the mass \nratio of an accreting protobinary evolves toward unity in the long-term, \nthe more material that is accreted by a protobinary, the more \nlikely it is that a circumbinary disc is formed.\nTherefore, following the same argument that we made for the mass ratios\nof binary stars, {\\bf we predict that \ncloser binary systems are more likely to have circumbinary\ndiscs than wider systems with the same total mass}. \nFurthermore, if massive and low-mass binary\nsystems via the same process, and if the initial mass of\na `seed' binary is independent of the mass of the core, \nthen {\\bf massive binaries are more likely to have \ncircumbinary discs than low-mass binaries of the same separation}.\n\nThe first of these predictions is in good agreement with recent observations.\nJensen, Mathieu \\& Fuller \\shortcite{JMF96} surveyed 85 \npre-main-sequence binary systems and found that, while emission \npresumably associated with circumbinary discs could be found \naround many close binaries (separations less than a few AU), \ncircumbinary emission around binaries with separations of a\nfew AU to $\\approx 100$ AU is almost entirely absent. The only\nexception was GG-Tau with a separation of $\\approx 40$ AU \\cite{DutGuiSim94}.\nFurthermore, Dutrey et al.~(1996) performed an imaging survey of 18 \nmultiple systems that could resolve circumbinary discs with radii\n$\\simgreat 100$ AU and found only one circumbinary disc around UY-Aur\nwhich has a separation of $\\approx 120$ AU.\n\nAs with the mass-ratio evolution, the quantitative predictions depend on\nthe properties of the progenitor cloud cores: \n{\\bf the more centrally-condensed a core is and/or the\nless differential rotation it has ($\\beta \\leq 0$), the lower the \nfraction by which a binary has to increase its mass before a circumbinary\ndisc is formed}.\n\nFor cores in solid-body rotation, a uniform-density cloud leads \nto a significant circumbinary disc ($M_{\\rm cb}/M_{\\rm b} > 0.05$) \nafter a circular binary accretes $\\approx 2-40$ times its initial mass \n(depending on the initial mass ratio; Figure \\ref{acc_d0_w0}c). Using\nFigure \\ref{bmass_vs_sep}, we would expect most {\\it circular} binaries with \nseparations $a \\simless 100$ AU to have circumbinary discs, while many\nwith separations $a \\simgreat 100$ AU should not have circumbinary discs.\nHowever, most wide binaries have large eccentricities\n(e.g.~Duquennoy \\& Mayor 1991) and more material must be accreted\nby an eccentric binary before a circumbinary disc is formed \n(Section \\ref{eccentricity}). Taking this into account, uniform-density\ncores in solid-body rotation are likely to produce \ncircumbinary discs around most binaries with $a \\simless 10$ AU\nand some binaries with intermediate separations. However,\nvery few should exist around binaries with separations $a \\simgreat 100$ AU,\nin reasonable agreement with the observations.\n\nFor a core with $\\rho \\propto 1/r$ (Figure \\ref{acc_d1_w0}), \na binary can only increase its mass by a factor of $\\approx 1.5-6$\nbefore a circumbinary disc is formed. In this case, most \nbinaries with separations $a \\simless 100$ AU would be expected to \nhave circumbinary discs, even taking eccentricity into account.\nWith a $1/r^2$-density profile a binary can't even double its mass before\na circumbinary disc is formed (Figure \\ref{acc_d2_w0}) so that almost\nall binaries would be expected to have circumbinary discs, in strong \ndisagreement with observations.\n\nDifferential rotation allows a binary to accrete more mass before \na circumbinary disc is formed. In most cases, binaries formed from \nuniform-density cores (Figure \\ref{acc_d0_w1}) can accrete up to 100 times \ntheir initial mass without forming a massive circumbinary disc, \nmeaning that even the closest binaries would not have circumbinary discs. \nCores with $1/r$-density profiles (Figure \\ref{acc_d1_w1}) allow \nfrom $5-100$ times a binary's initial mass to be accreted so that\nmost binaries with separations $\\simless 10$ AU and many with separations \n$\\simless 100$ AU would have circumbinary discs. Cores with \n$1/r^2$-density profiles would still produce discs around most\nbinaries with separations $a \\simless 100$ AU.\n\nTherefore, as with our predictions concerning binary mass-ratio\ndistributions, {\\bf the circumbinary disc observations can be \nreasonably well explained\nif most binaries form from progenitor cores which are less centrally\ncondensed than $\\rho \\propto 1/r$ (e.g.~Gaussian), possibly with a\nsmall amount of differential rotation}.\nCores with $\\rho \\propto 1/r$ are possible if there is significant\ndifferential rotation, but the singular isothermal sphere ($\\rho \\propto\n1/r^2$) cannot reproduce the observations even with extreme differential\nrotation.\n\n\n\\section{Conclusions}\n\\label{conclusions}\n\nWe have considered a model for the formation of binary stellar\nsystems which has been inspired by the results obtained from \n$\\approx 20$ years of\nstudy of the fragmentation collapsing molecular cloud cores.\nIn the model, a `seed' protobinary system forms, presumably via\nfragmentation, within a collapsing molecular cloud core and evolves\nto its final mass by accreting material from an infalling \ngaseous envelope. \n\nWe developed and tested a method which can rapidly follow the\nevolution of the mass ratios, separations and circumbinary disc \nproperties of such binaries as they accrete to their final masses.\nUsing this protobinary evolution code, we predict \nthe properties of binary stars and how they depend\non the pre-collapse conditions in their progenitor molecular cloud\ncores. These predictions and their comparison with current observations\nare discussed in detail in Section \\ref{predictions}.\n\nBriefly, we conclude that, if most binary stars form via the above model,\nbinary systems with smaller separations or greater total masses\nshould have mass ratios which are biased toward equal masses when \ncompared to binaries with wider orbits or lower total masses. Similarly,\nthe frequency of circumbinary discs should be greater for \npre-main-sequence binaries with closer orbits or greater total masses.\nThese conclusions can be understood because: binaries which are closer or \nhave a greater final mass should accrete more gas relative to their \ninitial masses than wider or lower-mass binaries; \nthe specific angular momentum of the infalling gas relative to that of\nthe binary is expected to increase as the accretion proceeds; \nand the accretion of gas with high specific angular momentum tends\nto equalise the mass ratio and forms a circumbinary disc.\nWe also demonstrate that in a young binary which is accreting from \nan infalling gaseous envelope, the primary will generally have a\ncircumstellar disc which is more massive or similar in mass to that\nof the secondary. All of these\nconclusions are in good agreement with the latest observations.\n\nBy making rough quantitative predictions of the \nproperties of binary stars, we find that the observed properties \nof binary stars are most easily\nreproduced if the pre-collapse molecular cloud cores from which binaries\nform have radial density\nprofiles between uniform and $1/r$ (e.g.~Gaussian) with near \nuniform rotation. This is in excellent agreement with the observed properties\nof pre-stellar cores (Ward-Thompson et al.~1994;\nAndr\\'e, Ward-Thompson, Motte 1996; Ward-Thompson, Motte, \\& Andr\\'e 1999). \nConversely, the observed properties of binaries cannot be \nreproduced if the cores are in solid-body rotation and \nhave initial density profiles which are strongly centrally condensed\n(between $1/r$ and $1/r^2$), and the singular isothermal sphere \n($\\rho \\propto 1/r^2$) cannot\nfit the observations even with strong differential rotation.\n\n\n\\section*{Acknowledgments}\n\nI am grateful to Ian Bonnell, Cathie Clarke and Jim Pringle for \nmany helpful discussions and\ntheir critical reading of the manuscript. \n\n\n\\begin{thebibliography}{}\n\n%\\bibitem[\\protect\\citename{Adams, Ruden \\& Shu }1989]{AdaRudShu89}\n% Adams F. C., Ruden S. P., Shu, F. 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}
] |
[
{
"name": "astro-ph0002143.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n%\\bibitem[\\protect\\citename{Adams, Ruden \\& Shu }1989]{AdaRudShu89}\n% Adams F. C., Ruden S. P., Shu, F. H., 1989, ApJ, 347, 959\n \n\\bibitem[\\protect\\citename{Andr\\'e, Ward-Thompson \\& Motte }1996]{AWM96} \n Andr\\'e P., Ward-Thompson D., Motte F., 1996, A\\&A, 314, 625\n\n\\bibitem[\\protect\\citename{Armitage, Clarke \\& Tout }1999]{ACT99}\n Armitage P. J., Clarke C. J., Tout C. A., 1999, MNRAS, 304, 425\n\n\\bibitem[\\protect\\citename{Artymowicz }1983]{Arty83}\n Artymowicz P., 1983, Acta Astronomica, 33, 223\n \n%\\bibitem[\\protect\\citename{Artymowicz }1993]{Arty93}\n% Artymowicz P., 1993, PASP, 105, 1032\n \n\\bibitem[\\protect\\citename{Artymowicz et al. }1991]{ACLP91}\n Artymowicz P., Clarke C. J., Lubow S. H., Pringle J. E., 1991, ApJ, 370, L35\n \n\\bibitem[\\protect\\citename{Artymowicz \\& Lubow }1994]{ArtLub94}\n Artymowicz P., Lubow S. 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Cambridge University Press, Cambridge, p. 526\n\n\\end{thebibliography}"
}
] |
astro-ph0002144
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Formation of the optical spectra of the coolest M- and L-dwarfs and lithium abundances in their atmospheres
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[
{
"author": "Yakiv V. Pavlenko"
}
] |
Theoretical aspects of modeling of spectra of late M- and L-dwarfs are discussed. We show, that the processes of formation of spectra of M- and L-dwarfs are basically different. Instead of the case of M-dwarfs, atoms of Ti and V should be depleted into grains in the atmospheres of L-dwarfs. Overall shape of the L-dwarf spectra is governed by the K I + Na I resonance line wings of the huge strength. To fit lithium lines observed in spectra of the coolest dwarfs we used two additional suggestions: a) there are some {\em extra} depletions of molecular species absorbed in the optical spectra of L-dwarfs; b) there may be (a few?) additional (``dusty''?) opacity sources in their atmospheres. Problems of lithium line formation and the ``natural'' limitation of their use for the ``lithium test'' for the case of L-dwarfs are considered.
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[
{
"name": "ypavlenk.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,psfig]{article}\n\\markboth{Ya.Pavlenko}{Formation of the optical spectra}\n\\pagestyle{myheadings}\n\\nofiles\n\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{\nFormation of the optical spectra of the coolest M-\nand L-dwarfs and lithium abundances in their atmospheres\n}\n\\author{Yakiv V. Pavlenko}\n\\affil{\n Main Astronomical Observatory of NAS, Golosiiv woods, 03680, Kyiv-127,\n Ukraine}\n\n\n\\begin{abstract}\nTheoretical aspects of modeling of spectra of late M- and\nL-dwarfs are discussed. We show, that the processes of\nformation of spectra of M- and L-dwarfs are basically different.\nInstead of the case of M-dwarfs, atoms of Ti and V\nshould be depleted into grains in the atmospheres of L-dwarfs.\nOverall shape of\nthe L-dwarf spectra is governed by the K I + Na I resonance line\nwings of the huge strength. To fit lithium lines observed in\nspectra of the coolest dwarfs we used two additional suggestions:\na) there are some {\\em extra} depletions of molecular species\nabsorbed in the optical spectra of L-dwarfs; b) there may\nbe (a few?) additional (``dusty''?) opacity sources in their\natmospheres. Problems of lithium line formation and the\n``natural'' limitation of their use for the ``lithium test'' for\nthe case of L-dwarfs are considered.\n\n\\end{abstract}\n\n\\section{Introduction}\n\nA few definitions of the ``unconventional''\nspectral classification of low mass stars\nand substellar objects are used in this paper: \\\\\n\n{\\bf M-dwarfs~} are objects (stars + young brown dwarfs) with\n4000 $> T_{\\rm eff} >$ 2200 K. Their spectra are governed by\nmolecular bands of TiO and VO (in the optical part of the\nspectrum) , H$_2$O (in the red). \\\\\n\n{\\bf L-dwarfs~} are objects (brown dwarfs + stars) with 1000 $<$\n$T_{\\rm eff}$ $<$ 2200 K (cf. Martin et al. 1997).\n Optical spectra of L-dwarfs are governed by the K I + Na I\nlines and molecular bands of CrH + FeH (in the optical spectrum),\nH$_2$O (in the red). \\\\\n\n{\\bf T-dwarfs~} are super-giant, planet-like\nobjects (big Jupiters?)\nwith T$_{\\rm eff} <$ 1000 K. Their spectra are formed\nby the \"dusty opacities\" and methane + H$_2$O + ...? absorption\n(Strauss et al. 1999, Burgasser et al. 1999)\\\\\n\nFor the time being most of the known brown dwarfs are actually \nrecognized by the detection of the Li\\,{\\sc i} resonance \ndoublet in their spectra (Rebolo et al. 1996, Mart\\'\\i n et \nal. 1997a, Kirkpatrick et al. 1999). Indeed, temperatures in \nthe interiors of brown dwarfs are not high enough to burn lithium \n(Rebolo et al. 1992).\n\n\\section{Procedure}\n\nThe computations of synthetical spectra of M- and L-dwarfs are\ncarried out by program WITA5, which is a modified version of the\nprogram WITA31 used by Pavlenko (1997). The\nmodifications were aimed to incorporate ``dusty effects''\nthat affect the chemical equilibrium and radiative\ntransfer processes in very cool atmospheres.\n\nWe have used the set of Tsuji's (1999)\n``dusty'' (C-type) LTE model atmospheres. These models were\ncomputed for the case of segregation phase of dust and gas.\n\nChemical equilibrium was computed for the mix of $\\approx$100\nmolecular species.\nTo take into account the effect of the oversaturation, we\nreduced the abundances of those molecular species down to the\nequilibrium values (Pavlenko 1998).\n\nIn L-dwarf atmospheres the additional opacity (AdO) could appear due\nto molecular and/or dust absorption and/or scattering. We have\nmodelled the additional opacity with a simple law of the form\n$a_{\\circ} \\ (\\nu / \\nu_{\\circ})^N$, with $N$\\,= 1 -\\,4 (see\nPavlenko, Zapatero Osorio \\& Rebolo 2000 for more details).\n\n\\section{M-dwarf spectra}\n\nLithium lines observed in spectra of the late M-dwarfs are well\nknown tracers of their evolution.\nCompletely convective M-dwarfs are\nvery effective lithium destroyers, therefore cool pre-main\nsequence (PMS) stars are expected to preserve their initial\nlithium only during their first few million's years (Fig.3, see\nalso Magazzu, Rebolo \\& Pavlenko 1992,\nOppenheimer et al. 1997, Pavlenko (1997, 1997a),\nPavlenko \\& Oppenheimer 1998).\n\nLithium lines in spectra of M-dwarfs are formed at the background\nof mighty TiO bands (Fig.1). Only cores of the saturated Li\nlines may be observed in the real spectra (Pavlenko et al. 1995).\nTo estimate of the abundance of lithium one may use\n``pseudoequivalent widths'' of lithium lines, i.e. $W_{\\lambda}$\nmeasured in\nrespect to the local pseudocontinuum formed by molecular bands\naround Li lines (see also Pavlenko 1997a).\n\nSure, the better way of the quantitatively determination\nlog N(Li) is the use of synthetical spectra (Fig. 2).\n\n\\begin{figure}\n\\psfig{file=ypavlen1.eps,height=7cm,width=10cm}\n\\caption[]{\n Comparison of the observed\nspectrum of the Pleiade's young brown dwarf Teide1 (Rebolo et al. 1996) \nwith theoretical\nspectra computed\nusing C-model atmosphere ($T_{\\rm eff}$=2600~K, log g =5.0) of Tsuji (1999).\nThe strongest atomic lines which may be observed\nin M- and L- spectra and the real (theoretical) continuum are shown.}\n\\end{figure}\n\n\n\\begin{figure}\n%\\picplace{6.5cm}\n% \\epsfxsize=14cm \\epsfbox{fig3r.eps}\n\\psfig{file=ypavlen2.eps,height=7cm,width=10cm}\n\\caption[]{Fit to the observed Li I resonance doublet\nin UX Tau C spectrum (Magazzu et al. 1991) with the\nlist of TiO lines of Plez (1998) and\nmodel atmosphere 3100/4.5 (Allard \\& Hauschildt 1995)}\n\\end{figure}\n\n\n\\section{L-dwarf spectra}\n\nDue to depletion of the Ti and VO into grains a structure of the\noptical spectra of L-dwarfs becomes more simple in comparison with\nM-dwarfs. The overall spectral energy distribution (SED)\nis governed by absorption of\nresonance doublets of K I and Na I which have pressure broadened\nwings extended up to thousands \\AA (Fig.3). Furthermore, Pavlenko et al.\n(2000) showed that L-dwarf optical spectra are affected by\nthe additional\n(``dusty'') absorption and/or scattering.\n\n\n\\begin{figure}\n%\\picplace{6.5cm}\n%\\epsfysize=17cm \\epsfbox{1.eps}\n\\psfig{file=ypavlen3.eps,height=7cm,width=10cm}\n\\caption[]{Fit of theoretical SED's computed for C-model\natmosphere 2000/5.0 (Tsuji 1999) to Kelu1 spectrum. $D$ factors\nshowed in the Fig. are used to simulate the {\\em extra} depletion of several\nspecies into grains.}\n\\end{figure}\n\n\\begin{figure}\n%\\picplace{6.5cm}\n%\\epsfysize=17cm \\epsfbox{1.eps}\n\\psfig{file=ypavlen4.eps,height=7cm,width=10cm}\n\\caption[]{Fit to Li I $\\lambda$ 6708 nm\nresonance doublet in Kelu1 spectrum. Computations were carried\nout for log N (Li) = 3.0 and different parameters of the AdO}\n\\end{figure}\n\n\n Our computations show that lithium lines are very\nsensitive to the additional absorption (AdO) that we need to\nincorporate in the spectral synthesis if we want to explain\nthe observed broad spectral energy distribution(Fig.4).\nIn Table 1 we\ngive the predicted equivalent widths \n$W_{\\lambda}$ of the Li\\,{\\sc i} resonance doublet at\n670.8\\,nm for L-dwarf's model atmospheres\n(2000--1000\\,K) considered in this work. We found: \\\\\n\n-- In the AdO-free case\n(second column in the table), we would expect for the\n``cosmic'' values of log N(Li) rather strong neutral Li resonance\nlines in the spectra of objects as cool as DenisP\\,J0205--1159\nand Gl\\,229B. \\\\\n\n-- The chemical equilibrium of Li-contained\nspecies still allow a sufficient number of Li atoms to\nproduce a rather strong resonance feature.\n\n-- Our\ncomputations indicate that L -dwarfs with moderate dust\nopacities should show the\nLi\\,{\\sc i} resonance doublet if they had preserved this element\nfrom nuclear burning, and consequently the lithium test can still\nbe applied.\n\n-- Temporal variations of the dusty opacities may originate some\nkind of ``meteorological'' phenomena occurring in these cool\natmospheres. Lithium lines (as well other lines) may be severely\naffected by the effect (see Pavlenko et al. 2000 for more\ndetails).\n\n\n\\begin{table}\n\\caption[]{Equivalent widths of the Li\\,{\\sc\ni} resonance doublet at 670.8\\,nm computed for the C-type Tsuji's\n(1999) model atmospheres, cosmic Li abundance\n(log\\,$N$(Li)\\,=\\,3.2) and gravity log\\,$g$\\,=\\,5.0.}\n\\begin{center}\n\\begin{tabular}{crrr}\n\\hline\\hline\n\\multicolumn{1}{c}{} & \\multicolumn{3}{c}{$a_{\\circ}$} \\\\\n\\multicolumn{1}{c}{$T_{\\rm eff}$} &\n\\multicolumn{3}{c}{\\rule{2.5cm}{0.1mm}} \\\\ \\multicolumn{1}{c}{} &\n\\multicolumn{1}{c}{0.00} & \\multicolumn{1}{c}{0.01} &\n\\multicolumn{1}{c}{0.10} \\\\ \\multicolumn{1}{c}{} &\n\\multicolumn{3}{c}{\\rule{2.5cm}{0.1mm}} \\\\\n\\multicolumn{1}{c}{(K)} & \\multicolumn{3}{c}{$W_{\\lambda}$(\\AA)} \\\\\n\\hline\n 1000 & 17 & 8 & 0.6 \\\\\n 1200 & 30 & 12 & 0.7 \\\\\n 1400 & 42 & 21 & 0.9 \\\\\n 1600 & 40 & 24 & 1.6 \\\\\n 2000 & 23 & 16 & 3.6 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n\n\\section{Conclusions}\n\nFinally, we have arrived to the following conclusions:\n\n\\begin{itemize}\n\n\\item Processes of formation of Li lines in L- and M-spectra\ndiffer significantly:\n\n-- for M-dwarfs the main problem to be solved is blending of\nlithium lines by molecular lines,\n\n-- in the case of L-dwarfs we deal with a menagerie of different\nprocesses: depletion of lithium atoms into molecules and grains, \"dusty\neffects\", meteorological phenomena, stratification effects, etc...\n\n\\item We can fit the optical spectra of L-dwarfs in the frame of\n our simple model.\n\n\\item Using our model we may perform a numerical analysis of the\n L-dwarf spectra (at least in the sense of the Li abundance determination).\n\n\\item The basic algorithm of the ``lithium test'' may be used\neven for the assessment of the coolest L-dwarfs.\n\n\\end{itemize}\n\n\\section{Acknowledgements}\n\nI thank IAU, LOC and SOC of the IAU Symposium N 198\nfor the financial support of my participation. I'm grateful to\nR. Rebolo and M.R. Zapatero Ozorio\n(IAC) for the fruitful collaboration and for providing the\nobservational data in electronic form; to T.Tsuji, F. Allard and\nP.Hauschildt for providing model atmospheres in digital form.\nPartial financial support was provided by the Spanish DGES\nproject no. PB95-1132-C02-01.\n\n\\begin{references}\n\\reference Allard, F., Hauschildt, P.H. 1995 \\apj, 445, 433\n\\reference Burgasser, A. J., Kirkpatrick, J. D., Brown,\n M. E., et al. 1999, \\apj, 522, L65\n\\reference Basri, G., Mart\\'\\i n, E. L., 1999. \\aj, 118, 2460.\n\\reference Kirkpatrick, J. D., Reid, I. N., Liebert, J.,\n et al. 1999, ApJ, 519, 802\n\\reference Magazzu, A., Mart\\'\\i n, E. L., Rebolo, R. Ya. 1991,\n \\aap, 249, 149.\n\\reference Magazzu, A. Rebolo, R., Pavlenko, Ya. 1992, \\apj,\n\\reference Mart\\'\\i n, E. L., Basri, G., Delfosse, X.,\n Forveille, T. 1997, \\aap, 327, L29\n\\reference Oppenheimer, B., Basrii, G., Nakajima, T., Kulkarni, S.L.\n 1997, \\aj, 113, 296.\n\\reference Pavlenko, Ya.V. 1997, \\apss, 253, 43.\n\\reference Pavlenko, Y. V. 1997a. Astron. Rept.,\n 41, 537.\n\\reference Pavlenko, Ya. V. 1998, Astron. Reports, 42, 787\n\\reference Pavlenko, Ya.V., Zapapero Ozorio, M.R., Rebolo, R. 2000,\n \\aap, in press (astro-ph 0001060)\n\\reference Pavlenko, Ya.V., Oppenheimer, B. 1988,\n ASP Conf. Ser. 154, 1768.\n\\reference Pavlenko Ya.V. 1998b, Atronom. Report, 42, 787.\n\\reference Pavlenko et al. Pavlenko, Ya. V., Rebolo, R., Mart\\'\\i n, E. L,\n Garc\\'\\i a L\\'opez, G. 1995, \\aap, 303, 807.\n\\reference Plez, B. 1998, \\aap, 337, 495.\n\\reference Rebolo R., Mart\\'\\i n, E.L., Magazzu, A. 1992,\n\\reference Rebolo R., Mart\\'\\i n, E.L., Magazzu, A. 1992,\n \\apj, 389, L83.\n\\reference Rebolo, R., Mart\\'\\i n, E.L., Basri, G., G.W.\n Marcy, G.W. And Zapatero Osorio, M.R. 1996,\n \\apj, 469, L53.\n\\reference Strauss, M. A., Fan, X., Gunn, J. E. et al. 1999,\n \\apjl, 1999, 522, L61\n\\reference Tsuji, T. 1999a, in Low-Mass Stars and Brown Dwarfs\n in Stellar Clusters and Associations, La Palma, CUP, in press\n\n\\end{references}\n\n\\end{document}\n\n"
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astro-ph0002145
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On radial gas flows, the Galactic Bar \\ and chemical evolution in the Galactic Disc
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"author": "L.\\ Portinari and C.\\ Chiosi"
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We develop a numerical chemical model allowing for radial flows of gas, with the aim to analyse the possible role of gas flows in the chemical evolution of the Galactic Disc. The dynamical effects of the Galactic Bar on the radial gas profile of the Disc are especially addressed. \keywords{Galaxy: chemical evolution -- Galaxy: abundance gradients -- Galaxy: gas distribution -- Galaxy: Bar}
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"name": "paper.tex",
"string": "%% Paper on the chemical model with radial gas flows and the effects of the\n%% Galactic Bar\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\\documentclass[psfig]{aa}\n\\documentclass[psfig]{aa}\n\n\\input psfig.sty\n\n\\newcommand{\\gsim}{\\raisebox{-3.8pt}{$\\;\\stackrel{\\textstyle >}{\\sim}\\;$}}\n\\newcommand{\\lsim}{\\raisebox{-3.8pt}{$\\;\\stackrel{\\textstyle <}{\\sim}\\;$}}\n\\newcommand{\\Mbol}{\\mbox{${\\rm M_{bol}}$}}\n\\newcommand{\\Msol}{$M_{\\odot}$}\n\\newcommand{\\Zsol}{$Z_{\\odot}$}\n\\newcommand{\\MHe}{$M_{He}$}\n\\newcommand{\\MCO}{$M_{CO}$}\n\\newcommand{\\Mfin}{$M_{fin}$}\n\\newcommand{\\Teff}{\\mbox{${\\rm T\\sub{eff}}$}}\n\\newcommand{\\logT}{\\mbox{${\\rm \\log T\\sub{eff}}$}}\n\\newcommand{\\logL}{\\mbox{${\\rm \\log L/{\\rm L_{\\odot}}}$}}\n\\newcommand{\\etal}{\\mbox{{\\rm et~al.\\ }}}\n\\newcommand{\\Hydrogen}{\\mbox{${\\rm {\\rm ^{1}H}}$}}\n\\newcommand{\\Hetre}{\\mbox{${\\rm {\\rm ^{3}He}}$}}\n\\newcommand{\\Helium}{\\mbox{${\\rm {\\rm ^{4}He}}$}}\n\\newcommand{\\Carbon}{\\mbox{${\\rm {\\rm ^{12}C}}$}}\n\\newcommand{\\Ctredici}{\\mbox{${\\rm {\\rm ^{13}C}}$}}\n\\newcommand{\\Nitrogen}{\\mbox{${\\rm {\\rm ^{14}N}}$}}\n\\newcommand{\\Nquindici}{\\mbox{${\\rm {\\rm ^{15}N}}$}}\n\\newcommand{\\Oxygen}{\\mbox{${\\rm {\\rm ^{16}O}}$}}\n\\newcommand{\\Odiciassette}{\\mbox{${\\rm {\\rm ^{17}O}}$}}\n\\newcommand{\\Odiciotto}{\\mbox{${\\rm {\\rm ^{18}O}}$}}\n\\newcommand{\\Neon}{\\mbox{${\\rm {\\rm ^{20}Ne}}$}}\n\\newcommand{\\Neventidue}{\\mbox{${\\rm {\\rm ^{22}Ne}}$}}\n\\newcommand{\\Mgventicinque}{\\mbox{${\\rm {\\rm ^{25}Mg}}$}}\n\\newcommand{\\Magnesium}{\\mbox{${\\rm {\\rm ^{24}Mg}}$}}\n\\newcommand{\\Silicon}{\\mbox{${\\rm {\\rm ^{28}Si}}$}}\n\\newcommand{\\Sulfur}{\\mbox{${\\rm {\\rm ^{32}S}}$}}\n\\newcommand{\\Calcium}{\\mbox{${\\rm {\\rm ^{40}Ca}}$}}\n\\newcommand{\\Fe}{\\mbox{${\\rm {\\rm ^{56}Fe}}$}}\n\\newcommand{\\Nickel}{\\mbox{${\\rm {\\rm ^{56}Ni}}$}}\n\n%\\parindent 0pt\n\n\\def\\oneskip{\\vskip 8pt}\t\n\\def\\smallskip{\\vskip 6pt}\n\\def\\littleskip{\\vskip 4pt}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{document}\n\n\\thesaurus{ }\n\n\\title {On radial gas flows, the Galactic Bar \\\\\nand chemical evolution in the Galactic Disc} \n\n\\author{L.\\ Portinari and C.\\ Chiosi }\n\n\\institute{\nDepartment of Astronomy, University of Padova, Vicolo dell'Osservatorio 5, \n35122 Padova, Italy (portinari, chiosi@pd.astro.it)}\n\n\\offprints{L.\\ Portinari}\n\\date{Received 23 August 1999/ Accepted 14 January 2000}\n\n\\maketitle\n\\markboth{Portinari and Chiosi: On radial gas flows, the Galactic Bar\nand chemical evolution in the Galactic Disc}{}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{abstract}\n\nWe develop a numerical chemical model allowing for radial flows of gas,\nwith the aim to analyse the possible role of gas flows in the chemical \nevolution of the Galactic Disc.\nThe dynamical effects of the Galactic Bar on the radial gas profile of the\nDisc are especially addressed.\n\\keywords{Galaxy: chemical evolution -- Galaxy: abundance gradients -- \nGalaxy: gas distribution -- Galaxy: Bar}\n\n\\end{abstract}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Introduction}\n\nThe observed chemical and spectro--photometric properties of galaxies are\none of the main sources of information for our understanding\nof galaxy formation and evolution. The corresponding theoretical modelling \ninvolves star formation (SF) as a basic ingredient. Unfortunately, this process\nis rather poorly known on the large scales relevant to galaxy evolution.\nPortinari \\& Chiosi (1999, hereinafter PC99) analysed the effects of\nadopting different SF laws in a chemical model for the Galactic Disc, a\nsystem which we can study in great detail. In this\npaper we address another phenomenon which can bear interesting effects on the \nchemical evolution of galaxies:\nradial gas flows. A few papers in literature (Section~\\ref{previous}) \ndemonstrate that radial gas flows influence chemical models for the Disc, \nespecially in their predictions on the metallicity gradient.\nIt is therefore interesting to discuss the radial profile of the Disc\nwith models including also radial flows, in addition to various options for\nthe SF law. In particular, radial flows can help to overcome some\ndifficulties that ``static'' models find in reproducing, at the same time,\nthe metallicity gradient and the radial gas profile of the Disc\n(PC99).\n\nWe develop a chemical model with radial gas flows as a multi--dimensional\nextension of the model of Portinari \\etal (1998, hereinafter PCB98).\nThe model is described in Section~\\ref{discrete} and in the appendices.\nIn Section~\\ref{radfloweffects} we discuss the general qualitative effects \nof superposing radial flows upon a chemical model. In Section~\\ref{bestfit} \nwe present models \nfor the Galactic Disc with radial gas flows and different SF laws, showing \nthat radial flows provide an alternative or additional dynamical effect \nto the ``inside--out'' formation scenario to explain the metallicity gradient.\nSection~\\ref{bar} is dedicated to qualitative simulations of the dynamical \neffects of the Galactic Bar upon the gas distribution, with the aim to \nreproduce the molecular ring around 4 kpc, which static models cannot account \nfor (PC99). Section~\\ref{conclusions} contains a final summary and\nconclusions.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Radial flows: previous literature}\n\\label{previous}\n\nThe possibility that radial flows play a role in establishing the radial\nmetallicity gradients in galactic discs was first suggested by Tinsley \\& \nLarson (1978). Following Lacey \\& Fall (1985), we mention that radial gas \nflows in a disc can be driven by three main mechanisms:\n%\n\\begin{enumerate}\n\\item\nthe infalling gas has a lower angular momentum than the circular motions in\nthe disc, and mixing with the gas in the disc induces a net radial inflow with\na velocity up to a few km~sec$^{-1}$;\n\\item\nviscosity in the gas layer induces radial inflows in the inner parts of the \ndisc and outflows in the outer parts, with velocities of \n$\\sim$0.1~km~sec$^{-1}$;\n\\item\ngravitational interactions between gas and spiral density waves\nlead to large-scale shocks, dissipation \nand therefore radial inflows of gas (or outflows in the outer parts) with\ntypical velocities of $\\sim$0.3~km~sec$^{-1}$ (e.g.\\ Bertin \\& Lin 1996 and\nreferences therein); much larger velocities can be achieved in the\ninner few kpc in the presence of a barred potential.\n\\end{enumerate}\n%\nIn summary, radial flows are plausible with velocities of\n$\\sim$0.1--1~km~sec$^{-1}$, and they are expected to be inflows over most of \nthe disc. Observational upper limits permit radial inflows in the Galactic \nDisc with velocities up to 5~km~sec$^{-1}$ at the present time.\nFor further details, see Lacey \\& Fall (1985) and references therein.\n\nThe first of the above mentioned mechanisms was modelled in detail\nby Mayor \\& Vigroux (1980), and later by Pitts \\& Tayler (1989, 1996),\nChamcham \\& Tayler (1994). The effects of a generic inflow velocity profile \n%or efficiency \non chemical evolution models \nhas been explored by Lacey \\& Fall (1985), Tosi(1988), G\\\"otz \\& K\\\"oppen \n(1992), K\\\"oppen (1994), Edmunds \\& Greenhow (1995). \nA different approach is that of viscous disc models which, rather than imposing\narbitrary radial velocity patterns, describe the\nevolution of the gas distribution in the disc self--consistently, following\nthe model suggested by Lin \\& Pringle (1987). Viscous chemical models\nhave been developed by Clarke (1989), Yoshii \\& Sommer-Larsen (1989) and\nSommer-Larsen \\& Yoshii (1990), Thon \\& Meusinger (1998).\nAll these studies show how radial inflows can steepen the metallicity\ngradients with respect to static models, especially if an outer cut--off of\nSF is assumed.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Modelling radial flows}\n\\label{discrete}\n\nWe formulate our chemical model with radial flows as a multi-dimensional\nextension of the static model of PCB98 and PC99, an open model where the disc\nforms gradually by accretion of protogalactic gas. The disc is divided \nin $N$ concentric rings or shells; in each ring $k$ the gaseous component \nand its chemical abundances evolve due to:\n%\n\\begin{enumerate}\n\\item\ndepletion by SF, which locks up gas into stars;\n\\item\nstellar ejecta which shed back enriched material to the interstellar medium\n(ISM);\n\\item\ninfall of primordial protogalactic gas;\n\\item\ngas exchange with the neighbouring rings because of radial flows.\n\\end{enumerate}\n%\nThe set of equations driving the chemical evolution of the $k$-th shell is:\n%\n\\begin{equation}\n\\label{dGi/dt_radf}\n\\begin{array}{l l}\n\\frac{d}{dt} G_i(r_k,t) = & - X_i(r_k,t) \\Psi(r_k,t) \\,+ \\\\\n & \\\\\n & +\\, \\int_{M_l}^{M_u} \\Psi(r_k,t-\\tau_M)\\,R_i(M) \\Phi(M) dM \\,+ \\\\\n & \\\\\n& + \\, \\left[\\frac{d}{dt} G_i(r_k,t) \\right]_{inf} \\,+\\, \\\\\n & \\\\\n & +\\, \\left[\\frac{d}{dt} G_i(r_k,t) \\right]_{rf}\n\\end{array}\n\\end{equation}\n%\nwhere the various symbols are defined here below.\n\nPrimordial gas is accreted at an exponentially decreasing rate with time-scale \n$\\tau$:\n%, and contributes to the evolution of the surface mass density\n%$\\sigma(r_k,t)$ according to:\n%\n\\begin{equation}\n\\label{eqinfall}\n\\dot{\\sigma}_{inf}(r_k,t) = A(r_k) \\, e^{-\\frac{t}{\\tau(r_k)}}\n\\end{equation}\n%\n$A(r_k)$ is obtained by imposing that the integrated contribution of infall\nup to the present Galactic age $t_G=$15~Gyr, corresponds \nto an assumed exponential profile $\\sigma_A(r_k)$:\n%\n\\begin{equation}\n\\label{Arprofile}\n A(r_k) = \\frac{\\sigma_A(r_k)}{\\tau(r_k) (1-e^{-t_G/\\tau(r_k)})} = \n\\frac{\\sigma_A(r_{\\odot}) \\, e^{-\\frac{r_k-r_{\\odot}}{r_d}}}\n{\\tau(r_k) (1-e^{-t_G/\\tau(r_k)})}\n\\end{equation}\n%\nIndicating with $\\sigma_g(r_k,t)$ the surface gas density, we define the gas \nfraction: \n%\n\\begin{equation}\n\\label{Gkdefinition}\nG(r_k,t) = \\frac{\\sigma_g(r_k,t)}{\\sigma_A(r_k)}\n\\end{equation}\n%\nand the normalized surface gas density for each chemical species $i$:\n%\n\\begin{equation}\n\\label{Gikdefinition}\nG_i(r_k,t) = X_i(r_k,t) \\, G(r_k,t)\n\\end{equation}\n%\nwhere $X_i$ is the fractionary abundance by mass of $i$. \n\nThe 1$^{st}$ term on the right-hand side of Eq.~(\\ref{dGi/dt_radf}) represents\nthe depletion of species $i$ from the ISM due to star formation;\nsee PC99 for the various options concerning the SF rate, $\\Psi(r,t)$.\nThe 2$^{nd}$ term is the amount of species $i$ ejected back to the ISM \nby dying stars; the returned fractions $R_i(M)$ are calculated on the base \nof the detailed stellar yields from PCB98 and keep track of finite stellar \nlifetimes (no instantaneous recycling approximation IRA). The 3$^{rd}$ term\nis the contribution of infall, while the 4$^{th}$ term describes the effect\nof radial flows. \nFull details on the first three terms can be found in the original static\nmodel by PCB98 and PC99.\nThe novelty in Eq.~(\\ref{dGi/dt_radf}) is the radial flow term, which we \ndevelop here below. We will adopt the simplified notation \n$\\sigma_{g k} \\equiv \\sigma_g(r_k,t)$ and the like.\n\nLet the $k$-th shell be defined by the galactocentric radius $r_k$, its inner\nand outer edge being labelled as $r_{k-\\frac{1}{2}}$ and $r_{k+\\frac{1}{2}}$. \nThrough these edges, gas flows \nwith velocity $v_{k-\\frac{1}{2}}$ and $v_{k+\\frac{1}{2}}$, respectively \n(Fig.~\\ref{shellfig}). Flow velocities are taken positive outward;\nthe case of inflow is correspondingly \ndescribed by negative velocities. \n%\n%%%%%%%Figure 1%%%%%%%\n\\begin{figure}[t]\n\\centerline{\\psfig{file=fig1.ps,angle=-90,width=8truecm}}\n\\caption{Scheme of the gas flow through the $k$-th model shell}\n\\label{shellfig}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n%\nRadial flows through the borders, with a flux $F(r)$, contribute to alter \nthe gas surface density in the $k$-th shell according to:\n%\n\\begin{equation}\n\\label{dsigmarf1}\n\\left[ \\frac{d \\sigma_{g k}}{d t} \\right]_{rf} = \n - \\frac{1}{\\pi \\left( r^2_{k+\\frac{1}{2}} - r^2_{k-\\frac{1}{2}} \\right) }\n \\left[ F(r_{k+\\frac{1}{2}}) - F(r_{k-\\frac{1}{2}}) \\right]\n\\end{equation}\n%\nThe gas flux at $r_{k+\\frac{1}{2}}$ can be written:\n%\n\\begin{small}\n\\begin{equation}\n\\label{flux3}\nF(r_{k+\\frac{1}{2}}) = 2 \\pi r_{k+\\frac{1}{2}} \\, v_{k+\\frac{1}{2}} \\left[\n\\chi(v_{k+\\frac{1}{2}}) \\, \\sigma_{g k} + \\chi(-v_{k+\\frac{1}{2}}) \\,\n\\sigma_{g (k+1)} \\right]\n\\end{equation}\n\\end{small}\n%\nwhere $\\chi(x)$ is the step function: {\\mbox{$\\chi(x)=1$ or 0}} for \n{\\mbox{$x >$ or $\\leq 0$}}, respectively.\nEq.~(\\ref{flux3}) is a sort of ``upwind approximation'' for the advection\nterm to be included in the model equations (e.g.\\\nPress \\etal 1986), describing either inflow or outflow depending on the sign\nof $v_{k+\\frac{1}{2}}$. An analogous expression holds for \n$F(r_{k-\\frac{1}{2}})$.\n\nLet's take the inner edge $r_{k-\\frac{1}{2}}$\nat the midpoint between $r_{k-1}$ and $r_k$,\nand similarly for $r_{k+\\frac{1}{2}}$ (Fig.~\\ref{shellfig}).\nWriting Eq.~(\\ref{dsigmarf1}) separately for each chemical species $i$,\nin terms of the $G_i$'s we obtain\nthe radial flow term of Eq.~(\\ref{dGi/dt_radf}) as:\n%\n\\begin{equation}\n\\label{dGirf}\n\\begin{array}{l l}\n\\left[ \\frac{d}{dt} G_i(r_k,t) \\right]_{rf} = & \\alpha_k \\, G_i(r_{k-1},t) \n\\,-\\, \\beta_k \\, G_i(r_k,t) \\,+ \\\\\n & +\\, \\gamma_k \\, G_i(r_{k+1},t)\n\\end{array}\n\\end{equation}\n%\nwhere:\n%\n\\begin{equation}\n\\label{coeffradf}\n\\begin{array}{l l}\n\\alpha_k = & \\frac{2}{r_k + \\frac {r_{k-1} + r_{k+1}}{2}} \n\t \\left[ \\chi(v_{k-\\frac{1}{2}}) \\, v_{k-\\frac{1}{2}} \\, \n\t \\frac{r_{k-1}+r_k}{r_{k+1}-r_{k-1}} \\right] \\, \n\t \\frac{\\sigma_{A (k-1)}}{\\sigma_{A k}} \\\\\n & \\\\\n\\beta_k = & - \\, \\frac{2}{r_k + \\frac {r_{k-1} + r_{k+1}}{2}} \\times \\\\\n\t \\multicolumn{2}{l}{\n\t \\times \\left[ \\chi(-v_{k-\\frac{1}{2}}) v_{k-\\frac{1}{2}}\n\t \\frac{r_{k-1}+r_k}{r_{k+1}+r_{k-1}} - \\chi(v_{k+\\frac{1}{2}})\n\t v_{k+\\frac{1}{2}} \\frac{r_k+r_{k+1}}{r_{k+1}-r_{k-1}} \\right] } \\\\\n & \\\\\n\\gamma_k = & - \\frac{2}{r_k + \\frac {r_{k-1} + r_{k+1}}{2}} \n\t \\left[ \\chi(-v_{k+\\frac{1}{2}}) v_{k+\\frac{1}{2}}\n\t \\frac{r_k+r_{k+1}}{r_{k+1}-r_{k-1}} \\right] \n\t \\frac{\\sigma_{A (k+1)}}{\\sigma_{A k}}\n\\end{array}\n\\end{equation}\n%\nThe terms on the right-hand side of Eq.~(\\ref{dGirf}) \nevidence the contribution of the 3 contiguous shells involved: \nthe first term represents the gas being gained in shell $k$ from $k$--1, \nthe second term is the gas being lost from $k$ to $k$--1 and $k$+1, \nand the third term is the gas being gained in $k$ from $k$+1.\nThe coefficients~(\\ref{coeffradf}) are \nall $\\geq 0$ and depend only on the shell $k$, not on the chemical species $i$\nconsidered. If the velocity pattern is constant in time, $\\alpha_k$,\n$\\beta_k$ and $\\gamma_k$ are also constant in time.\n\nNotice that in the case of static models \nthe final surface mass density is completely determined by the\nassumed accretion profile, namely \n{\\mbox{$\\sigma(r_k,t_G) \\equiv \\sigma_A(r_k)$}}. Therefore, in static models \nthe radial profile for accretion can be directly chosen so as to match the \nobserved present--day surface density in the Disc (see PCB98 and PC99). \nThe inclusion of the term of radial gas flows alters the expected final density\nprofile\nand {\\mbox{$\\sigma(r_k,t_G) \\neq \\sigma_A(r_k)$}}.\nHence, $\\sigma(r,t_G)$ cannot be assumed in advance and is only known \n{\\it a posteriori} (see \\S\\ref{radfloweffects}); \nat the end of each simulation we need to check how much radial \nflows have altered the actual density profile $\\sigma(r_k,t_G)$ with respect \nto the pure accretion profile $\\sigma_A(r_k)$. With the slow \nflow speeds considered ($v \\lsim 1$~km~sec$^{-1}$), the two profiles will not \nbe too dissimilar anyways.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Boundary conditions}\n\nEq.~(\\ref{dGirf}) needs to be slightly modified in the case of the innermost\nand the outermost shell, since the shell $k$--1 or $k$+1 \nare not defined in these two respective cases.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsubsection{The innermost shell}\n\\label{shell1}\n\nOur disc models will extend down to where the Bulge becomes \nthe dominating Galactic component ($r_1=2.5$~kpc). As to the innermost edge, \nwe assume that the first \nshell is symmetric with respect to $r_1$:\n%\n\\[ r_{\\frac{1}{2}} = \\frac{3 r_1 - r_2}{2} \\]\n%\nand that {\\mbox{$v_{\\frac{1}{2}} \\leq 0$}} always, since\nwe cannot account for outflows from still inner shells, not included in the \nmodel. For {\\mbox{$k=1$}}, Eq.~(\\ref{dGirf}) then becomes:\n%\n\\begin{equation}\n\\label{dGirf1}\n\\left[ \\frac{d}{dt} G_i(r_1,t) \\right]_{rf} = - \\beta_1 G_i(r_1,t) \\, + \\, \n\\gamma_1 G_i(r_2,t)\n\\end{equation}\n%\nwith:\n%\n\\[ \\beta_1 = -\\frac{1}{2 r_1} \\left[ v_{\\frac{1}{2}}\\,\\frac{3 r_1-r_2}{r_2-r_1}\n\\,-\\, \\chi(v_{\\frac{3}{2}}) \\, v_{\\frac{3}{2}} \\, \\frac{r_1+r_2}{r_2-r_1} \n\\right] \\]\n%\n\\begin{equation}\n\\label{coeffradf1}\n\\gamma_1 = - \\chi(-v_{\\frac{3}{2}}) \\, v_{\\frac{3}{2}} \\, \\frac{1}{2 r_1} \\,\n\\frac{r_1+r_2}{r_2-r_1}\\, \\frac{\\sigma_{A 2}}{\\sigma_{A 1}}~~~~~~~~~~\n\\end{equation}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsubsection{Boundary conditions at the disc edge}\n\\label{boundary}\n\nAs to the outermost shell ($k=N$), \nwe need a boundary condition for the gas inflowing from the outer disc. \nWe assume\na SF cut-off in the outer disc, while the gaseous layer extends much further.\nIn fact, in external spirals HI discs are observed to extend much beyond the\noptical disc, out to 2 or even 3 optical radii. A threshold preventing \nSF beyond a certain radius is expected from gravitational stability\nin fluid discs (Toomre 1964, Quirk 1972) and has observational support as well\n(Kennicutt 1989). For the Galactic Disc we assume no SF \nbeyond the last shell at $r_N = 20$~kpc, which is the empirical limit for the\noptical disc and for HII regions and bright blue stars tracing active SF.\nGas can though flow in from the outer disc;\nextended gas discs might actually provide a much larger gas reservoir \nfor star--forming spirals than vertical infall, at least at the present time \nwhen the gravitational settling of the protogalactic cloud is basically over.\n\nIf no SF occurs in the outer disc, the evolution of the gas (and total) surface\ndensity can be expressed as:\n%\n\\begin{equation}\n\\label{radfnoSF}\n\\frac{\\partial \\sigma}{\\partial t} (r,t) = A(r) \\, e^{-\\frac{t}{\\tau(r)}} \n\\,-\\, \\frac{1}{r} \\, \\frac{\\partial}{\\partial r} (r v \\sigma)~~~~~~~\n\\forall \\, r>r_{N+\\frac{1}{2}}\n\\end{equation}\n%\n(e.g.\\ Lacey \\& Fall 1985, their model equation with the SF term dropped).\nHere, with no SF, $\\sigma \\equiv \\sigma_g$ and abundances always\nremain the primordial ones ($X_{i, inf}$).\nLet's assume the following simplifying conditions for the outer disc:\n%\n\\begin{enumerate}\n\\item\nthe infall time-scale is uniform: \n%\n\\[ \\tau(r) \\equiv \\tau(r_N)~~~~~~~~~~~~~~~~~~~~~\n\\forall \\, r>r_{N+\\frac{1}{2}} \\]\n%\n\\item\nthe inflow velocity is uniform and constant: \n%\n\\[ v(r,t) \\equiv v_{N+\\frac{1}{2}}~~~~~~~~~~~~~~~~~~~\n\\forall \\, r>r_{N+\\frac{1}{2}}, ~~\\forall \\, t\\]\n%\n\\item\nthe infall profile \nis flat:\n%\n\\[ A(r) \\equiv A_{ext} ~~~~~~~~~~~~~~~~~~~~~~~\\forall \\, r>r_{N+\\frac{1}{2}} \\]\n%\nin accordance with observed extended gas discs in spirals, showing a much \nlonger scale-length than the stellar component.\n\\end{enumerate}\n%\nWith these assumptions, \nEq.~(\\ref{radfnoSF}) becomes:\n%\n\\begin{equation}\n\\label{bordereq}\n\\frac{\\partial \\sigma}{\\partial t}\\,+\\,v\\,\\frac{\\partial \\sigma}{\\partial r}\n = A \\, e^{-\\frac{t}{\\tau}} \\,-\\, \\frac{v}{r} \\,\\sigma\n\\end{equation}\n%\nwhere we indicate $\\tau \\equiv \\tau(r_N)$, $v \\equiv v_{N+\\frac{1}{2}}$ and\n$A \\equiv A_{ext}$ to alleviate the notation.\nEq.~(\\ref{bordereq}) has a straightforward analytical solution \n(Appendix~B):\n%\n\\begin{equation}\n\\label{borderconditionTrf}\n\\begin{array}{l l}\n\\sigma(r,t) = & A \\, \\tau \\, \\times \\\\\n & \\\\\n\\multicolumn{2}{r}{ \\times \\left[ \\left( 1 - e^{-\\frac{t}{\\tau}} \\right)\n+ \\frac{v}{r} \\left( \\tau \\left( e^{-\\frac{T_{rf}}{\\tau}} - \ne^{-\\frac{t}{\\tau}} \\right) - (t - T_{rf}) \\right) \\right] }\n\\end{array}\n\\end{equation}\n%\nwhere $T_{rf} \\geq 0$ is the time when radial inflows are assumed to activate.\n%Eq.~(\\ref{bordercondition0}) or\nEq.~(\\ref{borderconditionTrf}) is our\nboundary condition at the outermost edge.\n\nNotice that (\\ref{borderconditionTrf})\nis the solution of (\\ref{bordereq}) \nin the idealized case of an infinite, flat gas layer extending boundless \nto any $r > r_N$ (see also Appendix~B).\nOf course, this\ndoes not correspond to gaseous discs surrounding real spirals; but since\nwe will consider only slow inflow velocities ($v \\lsim 1$~km~sec$^{-1}$), with\ntypical values of $r_N=20$~kpc and $t_G=15$~Gyr, the gas actually drifting into\nthe model disc shells will be just the gas originally accreted within \n$r \\sim 35$~kpc. Therefore, the boundary condition~(\\ref{borderconditionTrf})\nremains valid as long as the gas layer stretches out to $\\sim 35$~kpc,\na very plausible assumption since observed gaseous discs extend over \na few tens or even {\\mbox{$\\sim 100$~kpc}}.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsubsection{The outermost shell}\n\\label{shellN}\n\nWe take a reference external radius $r_{ext} > r_N$ in the outer disc where \nthe (total and gas) surface density \n$\\sigma(r_{ext},t) \\equiv \\sigma_{ext}(t)$ is given by the boundary condition\n(\\ref{borderconditionTrf}); typically, $r_N =20$~kpc and $r_{ext} \\sim 21$~kpc.\nWe take the outer edge of the shell at the midpoint:\n%\n\\[ r_{N+\\frac{1}{2}} = \\frac{r_N + r_{ext}}{2} \\]\n%\nand replace\n%\n\\[ X_{i (k+1)} \\, \\sigma_{g (k+1)} \\longrightarrow X_{i,inf} \\, \\sigma_{ext} \\]\n%\nin Eqs.~(\\ref{dsigmarf1}) and~(\\ref{flux3}), since \nthe primordial abundances $X_{i,inf}$ remain unaltered in the outer disc, \nin the absence of SF.\nWe thus write the radial flow term for the $N$-th shell as: \n%\n\\begin{equation}\n\\label{dGirfN}\n\\begin{array}{l l}\n\\left[ \\frac{d}{dt} G_i(r_N,t) \\right]_{rf} = & \\alpha_N \\, G_i(r_{N-1},t)\n\\,-\\, \\beta_N \\, G_i(r_N,t) \\,+ \\\\\n & +\\, \\omega_i(t)\n\\end{array}\n\\end{equation}\n%\nwhere:\n%\n\\begin{equation}\n\\label{coeffradfN}\n\\begin{array}{l l}\n\\omega_i = & - X_{i,inf} \\,\\,\\, \\chi(-v_{N+\\frac{1}{2}}) \\,\\, v_{N+\\frac{1}{2}}\n\\, \\times \\\\\n & \\times \\, \n\\frac{4}{r_{N-1} + 2 r_N + r_{ext}}\\,\\,\\frac{r_N+r_{ext}}{r_{ext}-r_{N-1}}\n\\,\\, \\frac{\\sigma_{ext}(t)}{\\sigma_{A N}}\n\\end{array}\n\\end{equation}\n%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{The numerical solution}\n\\label{numericalradf}\n\nUsing~(\\ref{dGirf}), (\\ref{dGirf1}) and (\\ref{dGirfN}), the basic set of \nequations~(\\ref{dGi/dt_radf}) can be written as:\n%\n\\[ \\left\\{ \\begin{array}{l l}\n\\frac{d}{dt} \\, G_i(r_1,t) = & \\vartheta_1(t) \\, G_i(r_1,t) +\n\t\t\t \\gamma_1 G_i(r_2,t) + W_i(r_1,t) \\\\\n & \\\\\n\\frac{d}{dt} \\, G_i(r_k,t) = & \\alpha_k G_i(r_{k-1},t) + \n\t\t\t \\vartheta_k(t) \\, G_i(r_k,t) + \\\\\n & + \\gamma_k G_i(r_k,t) + W_i(r_k,t) \\\\\n\\multicolumn{2}{r}{k=2,...N-1} \\\\\n & \\\\\n\\frac{d}{dt} \\, G_i(r_N,t) = & \\alpha_N G_i(r_{N-1},t) + \n\t\t\t \\vartheta_N(t) \\, G_i(r_N,t) + \\\\\n\t\t\t & + W_i(r_N,t) + \\omega_i(t)\n\\end{array} \\right. \\]\n%\nwhere we have introduced: \n%\n\\[ \\begin{array}{l c l}\n\\vartheta_k(t) & \\equiv & - \\left( \\eta(r_k,t) + \\beta_k \\right) \\leq 0 \\\\\n & \\\\\n\\eta(r_k,t) & \\equiv & \\frac{\\Psi}{G}(r_k,t) \\\\\n & \\\\\n\\medskip\nW_i(r_k,t) & \\equiv & \\int_{M_l}^{M_u} \\Psi(r_k,t-\\tau_M) \\, R_i(M) \\Phi(M) dM \n\\, + \\\\\n & & +\\, \\left[\\frac{d}{dt} G_i(r_k,t) \\right]_{inf}\n\\end{array} \\]\n%\nWe refer to PCB98 for further details on the quantities \n$\\eta$ and $W_i$, appearing also in the original static model.\nNeglecting, for the time being, that the $\\eta$'s and the $W_i$'s contain\nthe $G_i$'s themselves, we are dealing with a linear, first order, \nnon homogeneous system of\ndifferential equations with non constant coefficients, of the kind:\n%\n\\begin{equation}\n\\label{systemradf}\n\\frac{d \\vec{G}_i}{dt} \\,=\\,{\\cal A}(t) \\, \\vec{G}_i(t) \\,+\\, \\vec{W}_i(t)\n\\end{equation}\n%\nThere is a system~(\\ref{systemradf}) for each chemical species $i$, but the \nmatrix of the coefficients ${\\cal A}(t)$ is independent of $i$.\n\nWe solve the system by the same numerical method used for the original\nequation of the static model --- see Talbot \\& Arnett (1971) and PCB98\nfor details. We just need to extend the method to the present \nmulti--dimensional case~(\\ref{systemradf}). \nIf we consider the evolution of the $G_i$'s over a short enough timestep \n$t_1-t_0 = \\Delta t$, the various quantities $\\eta(r_k,t)$,\n$\\vartheta_k(t)$ and $W_i(r_k,t)$ will remain roughly constant within \n$\\Delta t$; similarly to the method for the static model (see PCB98),\nwithin $\\Delta t$ we approximate them with the values $\\overline{\\eta}_k$, \n$\\overline{\\vartheta}_k$ and $\\overline{W}_i(r_k)$ they assume at the midstep \n$t_{\\frac{1}{2}} = t_0 + \\frac{1}{2} \\Delta t$. Over $\\Delta t$,\n(\\ref{systemradf}) can then be considered a system with constant coefficients \n${\\cal A} \\equiv {\\cal A}(t_{\\frac{1}{2}})$, and $\\vec{W}_i (t)$ becomes a \nconstant vector, which allows for the analytical solution:\n%\n\\begin{equation}\n\\label{solsystemradf2}\n\\vec{G}_i (t_1) = e^{\\Delta t\\, {\\cal A}} \\, \\vec{G}_i (t_0) + \\left[\n\\int_{t_0}^{t_1} e^{(t_1-t) {\\cal A}} \\, dt \\right] \\,\\, \\vec{W}_i\n\\end{equation}\n%\nwhere \n$e^{t {\\cal A}}$ indicates the matrix:\n%\n\\begin{equation}\n\\label{e^tAformula}\ne^{t {\\cal A}} = \\pmatrix{ e^{\\lambda_1 t} \\vec{u}_1 & \n\\ldots & e^{\\lambda_N t} \\vec{u}_N } \n\\pmatrix{ \\vec{u}_1 & \n\\ldots & \\vec{u}_N }^{-1}\n\\end{equation}\n%\nwith $\\lambda_k$ the eigenvalues of ${\\cal A}$ and \n$\\vec{u}_k$ the corresponding eigenvectors.\nThe matrix $e^{t {\\cal A}}$ and the explicit expression of the \nsolution~(\\ref{solsystemradf2}) for the $G_i$'s are \ncalculated in Appendix~A,\nresulting in:\n%\n\\begin{equation}\n\\label{solradfN}\n\\begin{array}{l l}\nG_i(r_k,t_1) = & \\alpha_k \\, \\times \\\\ \n \t\\multicolumn{2}{r}{ \\times \\, \n\t \\frac{e^{-(\\overline{\\eta}_k+\\beta_k) \\Delta t}-\n\te^{-(\\overline{\\eta}_{k-1}+\\beta_{k-1}) \\Delta t}}\n\t{(\\overline{\\eta}_{k-1}+\\beta_{k-1})-(\\overline{\\eta}_k+\\beta_k)} \\, \n\tG_i(r_{k-1},t_0) \\,+} \\\\\n &\t+\\, e^{-(\\overline{\\eta}_k+\\beta_k) \\Delta t} \\, G_i(r_k,t_0) \\,+\\\\\n\\multicolumn{2}{r}{\n\t+\\, \\gamma_k \\,\\frac{e^{-(\\overline{\\eta}_{k+1}+\\beta_{k+1}) \\Delta t}-\n\te^{-(\\overline{\\eta}_k+\\beta_k) \\Delta t}}{(\\overline{\\eta}_k+\\beta_k)-\n\t(\\overline{\\eta}_{k+1}+\\beta_{k+1})} \\, G_i(r_{k+1},t_0) \\,+ }\\\\\n &\t+\\, \\alpha_k\\,\\frac{\\overline{W}_i(r_{k-1})}\n\t{(\\overline{\\eta}_{k-1}+\\beta_{k-1})-\n\t(\\overline{\\eta}_k+\\beta_k)} \\, \\times \\\\\n\t\\multicolumn{2}{r}{ \\times \\left(\n \\frac{1-e^{-(\\overline{\\eta}_k+\\beta_k) \\Delta t}}{\\overline{\\eta}_k+\\beta_k}\n\t- \\frac{1-e^{-(\\overline{\\eta}_{k-1}+\\beta_{k-1}) \\Delta t}}\n\t{\\overline{\\eta}_{k-1}+\\beta_{k-1}} \\right) \\,+ }\\\\\n & +\\, \\overline{W}_i(r_k)\\, \\frac{1-e^{-(\\overline{\\eta}_k+\\beta_k) \\Delta t}}\n\t{\\overline{\\eta}_k+\\beta_k} \\,+ \\\\\n &\t+\\, \\gamma_k\\,\\frac{\\overline{W}_i(r_{k+1})}\n\t{(\\overline{\\eta}_k+\\beta_k)-(\\overline{\\eta}_{k+1}+\\beta_{k+1})}\n\t\\, \\times \\\\\n &\t\\times\n\t \\left(\\frac{1-e^{-(\\overline{\\eta}_{k+1}+\\beta_{k+1}) \\Delta t}}\n\t{\\overline{\\eta}_{k+1}+\\beta_{k+1}} - \n\t\\frac{1-e^{-(\\overline{\\eta}_k+\\beta_k) \\Delta t}}\n\t{\\overline{\\eta}_k+\\beta_k} \\right) \\\\ \n\\end{array}\n\\end{equation}\n%\nwhere we intend $\\alpha_1 \\equiv 0$, $\\gamma_N \\equiv 0$, \n%$W_k \\equiv W_i(r_k,t)$, \nand for the outermost shell one should replace: \n%\n\\[ \\overline{W}_i(r_N) \\longrightarrow \n\\overline{W}_i(r_N) + \\overline{\\omega}_i = \\overline{W}_i(r_N) +\n\\frac{1}{\\Delta t} \\, \\int_{t_0}^{t_1} \\omega_i(t) \\, dt \\]\n%\n$\\omega_i$ being defined by~(\\ref{coeffradfN}).\n\nSimilarly to the case of an isolated shell (see PCB98) the \nsystem~(\\ref{solradfN}) \ndoes not provide the final solution for $G_i(r_k,t_1)$, since the \n$\\overline{\\eta}_k$'s and the $\\overline{W}_i$'s on the right--hand side\nactually depend on the $G_i$'s;\nit just represents \na set of implicit non--linear expressions in $G_i(r_k,t_1)$.\nAs in the original static model, we can neglect the dependence of \n$\\overline{W}_i(r_k)$ on the $G_i$'s and consider only that of \n$\\overline{\\eta}_k$ (see PCB98 for a detailed discussion). \nWe must finally find the roots of the system~(\\ref{solradfN}) by applying the \nNewton-Raphson method, generalized to many dimensions (cfr.\\ Press et~al., \n1986). \nSuch a system holds for each of the chemical species $i$ considered, so at \neach iteration we actually need to solve as many systems as the species \nincluded in the model.\nFull details on the mathematical development of the model and its numerical \nsolution can be found in the appendices and in Portinari (1998).\n\nWe tested the code against suitable analytical counterparts\nand obtained the following conditions for model consistency (Appendix~B).\n%\n\\begin{enumerate}\n\\item\nRather small timesteps are needed for the numerical model to keep stable;\nthe required timesteps get smaller and smaller the higher the flow velocities \nconsidered, and the thinner the shells.\n\\item\nTo describe gas flows in a disc with an exponential density profile, the shells\nshould be equispaced in the logarithmic, rather than linear, scale\n(so that they roughly have the same mass, rather than the same width).\n\\end{enumerate}\n%\nWe modelled the Galactic Disc using 35 shells\nfrom 2.5 to 20 kpc, equally spaced in the logarithmic scale, their width\nranging from $\\sim 0.2$~kpc for the inner shells to $\\sim 1$~kpc for the \noutermost ones. With such a grid spacing, and velocities up to \n{\\mbox{$\\sim 1$~km~sec~$^{-1}$}}, \nsuitable timesteps are of $10^{-4}$~Gyr (Appendix~B; see also \nThon \\& Meusinger 1998). This means that roughly {\\mbox{$1.5 \\times 10^5$}} \ntimesteps, times 35 shells, are needed to complete each model, which would\ntranslate in excessive computational times. This drawback was avoided \nby separating the time-scales in the code.\n%\n\\begin{enumerate}\n\\item\nThe timestep $\\Delta t$ used to update the ``chemical'' variables \n($\\eta$, $W_i$, etc.) is \nthe minimum\namong: $\\Delta t_1$ which guarantees that the relative variations \nof the $G_i$'s are lower than a fixed $\\epsilon$; $\\Delta t_2$ which\nguarantees that the total surface mass density $\\sigma(t)$ increases \nby no more than 5\\%; $\\Delta t_3$ which is twice the previous timestep of the\nmodel, to speed up the computation when possible;\n$\\Delta t_4$ which guarantees \nthe Courant condition {\\mbox{$\\Delta t < v \\, \\Delta r$}}, \nindispensable for the stability of a numerical algorithm describing\nflows. So, $\\Delta t$ is basically set by the requirement that\nthe chemical quantities do not vary too much within it, and it can get\nrelatively large (up to 0.2~Gyr), especially at late ages when the various \nchemical variables evolve slowly.\n\\item\nIt is only the numerical solution~(\\ref{solradfN}) which needs very short \ntimesteps to keep stable. Therefore, once the chemical variables are upgraded,\nthe main timestep $\\Delta t$ is subdivided in much shorter timesteps \n{\\mbox {$\\delta t = 10^{-4}$~Gyr}}, upon which the solution~(\\ref{solradfN})\nand its Newton-Raphson iteration\nare successively\napplied to cover the whole $\\Delta t$. Only then a new upgrade of all the\n$\\overline{\\eta}_k$'s and $\\overline{W}_i$'s is performed.\n\\end{enumerate}\n%\nThis trick keeps the code \nroughly as fast as if it would evolve with a single \ntime-scale $\\Delta t$, and yet it gives the\nsame results as the ``slow'' version in which all quantities are upgraded at\neach $\\delta t = 10^{-4}$~Gyr.\n\n%%%%%%%%%%%%%%Table 1%%%%%%%%%%%%%%%\n\\begin{table}[hb]\n\\caption{Parameter values and resulting metallicity gradients for models\n{\\sf S15RF}, {\\sf O10RF} and {\\sf DRRF}}\n\\label{modelRFtab}\n\\begin{tabular}{l|l|l|l|l|c|l}\n\\hline\n & & & & & & \\\\\n model & $r_d$ & $\\nu$ & $\\zeta$ & $\\tau$ & $v(r)$ & $\\frac{d[O/H]}{dr}$ \\\\\n & & & & & & \\\\\n\\hline\n\\multicolumn{7}{c}{} \\\\\n\\hline\n{\\sf S15a} & 4 & 0.35 & 0.2 & 3 & 0 & --0.03 \\\\\n\\hline\n{\\sf S15RFa} & 4 & 0.35 & 0.2 & 3 & --1 & --0.053 \\\\\n & & & & & & \\\\\n{\\sf S15RFb} & 5 & 0.4 & 0.32 & 3 & --1 & --0.047 \\\\\n\\hline\n{\\sf S15RFc} & 4 & 0.35 & 0.2 & 3 & $\\left\\{ \\begin{array}{c}\n\t\t\t\t\t\t-1 \\\\\n\t\t\t\t v_{N+\\frac{1}{2}}=0\n\t\t\t\t \\end{array} \\right.$ & --0.083 \\\\\n & & & & & & \\\\\n{\\sf S15RFd} & 7 & 0.35 & 0.35 & 3 & $\\left\\{ \\begin{array}{c}\n\t\t\t\t\t\t-1 \\\\\n\t\t\t\t v_{N+\\frac{1}{2}}=0\n\t\t\t\t \\end{array} \\right.$ & --0.073 \\\\\n\\hline\n{\\sf S15RFe} & 6 & 0.37 & 0.25 & 3 & Fig.~\\ref{velS15bestfit} & --0.063 \\\\\n\\hline\n\\multicolumn{7}{c}{} \\\\\n\\hline\n{\\sf O10a} & 4 & 0.19 & 0.2 & 3 & 0 & --0.03 \\\\\n\\hline\n{\\sf O10RFe} & 7 & 0.2 & 0.25 & 3 & Fig.~\\ref{velS15bestfit} & --0.07 \\\\\n\\hline\n\\multicolumn{7}{c}{} \\\\\n\\hline\n{\\sf DRa} & 4 & 0.42 & 0.2 & 3 & 0 & \n--0.07 {\\scriptsize ($r > r_{\\odot}$)} \\\\\n\t&\t& & & & & ~flat~~{\\scriptsize ($r < r_{\\odot}$)} \\\\\n\\hline\n{\\sf DRRFe} & 4 & 0.5 & 0.27 & 3 & Fig.~\\ref{velTA15bestfit} & --0.059 \\\\\n\\hline\n\\end{tabular}\n\\end{table}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%Figure 2%%%%%%%\n\\begin{figure*}[t]\n\\centerline{\\psfig{file=fig2.ps,angle=-90,width=17truecm}}\n\\caption{{\\it Left panels}: final profiles of the total surface density \nfrom models {\\sf S15RF} with inflow from the outer disc, in linear (upper \npanel) or logarithmic (lower panel) plot; the reference observed profile \nof models with scale length 4~kpc,\nas adopted in models with no flows (PC99), is shown as a thick solid line.\n{\\it Upper right panel}: radial gas density profiles compared to the\nobserved one. {\\it Lower right panel}: predicted radial metallicity profiles \ncompared to the observational data (data and symbols as in PC99).}\n\\label{s15rf}\n\\end{figure*}\n%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Effects of radial inflows on the disc}\n\\label{radfloweffects}\n\nAfter presenting our new model with radial flows, we investigate\ntheir general effects on the chemical evolution of the disc. \nHere we first analyse how the predicted metallicity gradient and gas and total \nsurface density profiles of a static model are\naltered by a superimposed uniform gas inflow,\nwhile in Section~\\ref{bestfit} we will suitably combine radial flows \nwith various SF laws to match the observed radial profile of the Disc.\n%\nThe characteristics and parameters of the various models presented in \nthis and in the next section are summarized in Table~\\ref{modelRFtab}.\n\nTo gain a qualitative understanding of the effects of radial gas inflows on \nchemical evolution, we impose a uniform inflow pattern $v=-1$~km~sec$^{-1}$\nupon a static chemical model\nand compare the new outcome with the original static case. \nRadial flows over the disc are expected to be mainly \ninflows, with velocities from 0.1 to $\\sim$1~km~sec$^{-1}$ \n(see \\S\\ref{previous}); imposing a uniform inflow\nof 1~km~sec$^{-1}$ is therefore a sort of ``extreme case'',\nconsidered here for the sake of qualitative analysis. Anyways, previous\nstudies in literature suggest that the effects of radial flows saturate\nfor much higher velocities (K\\\"oppen 1994). We will \nconsider both the case of inflow from the outer gaseous disc and not \n({\\mbox{$v_{N+\\frac{1}{2}}=-1$}} or 0, respectively).\n\nAll models with radial flows are rescaled \nso that the final surface density at the Solar ring ($r_{\\odot}=8.5$~kpc) \ncorresponds to 50~\\Msol~pc$^{-2}$. Namely, \nwith radial flows $\\sigma(r_{\\odot},t_G) \\neq \\sigma_A(r_{\\odot})$ \nand it cannot be imposed as an input datum (see \\S\\ref{discrete}), but the \nzero--point $A(r_{\\odot})$ of the exponential accretion \nprofile~(\\ref{Arprofile})\n%\n\\[ A(r) = A(r_{\\odot}) \\,\\, e^{-\\frac{r-r_{\\odot}}{r_d}} \\]\n%\n%%%%%%%Figure 3%%%%%%%\n\\begin{figure*}[t]\n\\centerline{\\psfig{file=fig3.ps,angle=-90,width=18truecm}}\n\\caption{Same as Fig.~\\protect{\\ref{s15rf}},\nbut for models {\\sf S15RF} with no inflow from the outer disc edge.}\n\\label{s15rfnoext}\n\\end{figure*}\n%%%%%%%%%%%%%%%%%%%%\n%\ncan be rescaled so that at the end of the simulation \n$\\sigma(r_{\\odot},t_G)=50$~\\Msol~pc$^{-2}$.\nThis zero--point does not influence the profile, nor the chemical \nevolution, so it can always be rescaled {\\it a posteriori}.\n\nFor our example, we take as the reference static case a model adopting\na Schmidt SF law with $\\kappa=1.5$ (Kennicutt 1998) and a uniform infall \ntime-scale of 3~Gyr (model {\\sf S15a} of PC99, see also \nTable~\\ref{modelRFtab}).\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Models with inflow from the outer disc}\n\nIn model {\\sf S15RFa} a uniform radial inflow pattern with \n{\\mbox{$v=-1$~km~sec$^{-1}$}}\nand inflow from the outer disc is imposed upon the static model {\\sf S15a},\nwith no further change in the model parameters (Table~\\ref{modelRFtab}). \nFig.~\\ref{s15rf} shows the effects of inflow \non the total surface density and gas density distribution, \nand on the oxygen gradient \n(details on the observational data in the plots can be found in PC99).\nBy comparing the solid line and the dashed line,\nwe notice the following main effects. \n%\n\\begin{itemize}\n\\item\nSince matter flows inward and accumulates toward the Galactic Centre, the \ndensity profile gets steeper in the inner parts, while in the outer parts \nit remains rather flat because gas is continuously poured in by the flat outer\ngaseous disc. The gas density distribution shows a similar behaviour.\n\\item\nThe overall metallicity gets much lower because of the dilution by\nprimordial gas inflowing from the outer disc. The gradient becomes steeper,\nespecially in the outermost shells,\nsince the discontinuity in metallicity between the star--forming \ndisc and the outer gaseous layer is smeared inward by radial inflows.\n\\end{itemize}\n%\nTo compensate for the steepening of the density distribution induced by radial\ninflows, we must adopt a shallower initial accretion profile; \nour simulations show that a scale length $r_d \\sim5$~kpc for the infall \nprofile reduces in the end to a density profile matching the desired scale \nlength of $\\sim$4~kpc at the Solar Neighbourhood. At the same\ntime, the chemical enrichment must get more efficient for the overall\nmetallicity to increase to the observed levels; the predicted metallicity \nis improved by adopting an IMF more\nweighted towards massive stars, i.e.\\ by increasing the ``IMF scaling \nfraction'' $\\zeta$ (see PCB98 and PC99 for a description of our model \nparameters). Together with the SF efficiency $\\nu$, $\\zeta$ is re-calibrated\nto match the observed gas surface density and metallicity at the Solar \nNeighbourhood (as for the models of PC99).\nIn this way we calibrate model {\\sf S15RFb} with respect to the Solar \nNeighbourhood; see Table~\\ref{modelRFtab} for details on the adopted \nparameters. Comparing now this re-calibrated model with radial flows (dotted\nline) to the original model {\\sf S15a}, the metallicity gradient is increased\nwith respect to the static case, but still a bit flat with respect to \nobservations. The gas density distribution peaks in the inner regions, as \nexpected, and remains quite high (much higher than observed) in the outer \nregions due to substantial replenishment from the outer disc.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Models with no inflow from the outer disc}\n\nLet's now consider the case when radial flows are limited within the star\nforming disc and there is no inflow from the external gaseous disc \n($v_{N+\\frac{1}{2}}=0$). If radial flows are mainly driven by shocks in spiral\narms, for instance, they might indeed occur only within the \nstellar disc, while the outer gas layer remains unperturbed.\n\nFig.~\\ref{s15rfnoext} (left panels) shows how the \nfinal density \nprofile becomes much steeper than the reference accretion profile \n(model {\\sf S15RFc}, dashed line), as expected since matter is efficiently\ndrifting inward with no replenishment from the outer disc.\nFor the final density profile to match the observed one, we must assume a much\nshallower initial accretion profile ($r_d \\sim 6-7$~kpc). \nThen the resulting local density profile is close to the observed one, \nwhile in the outer parts the profile remains steeper (model {\\sf S15RFd}, \ndotted line).\n\nThe gas density profile shows a similar behaviour, strongly peaked\ntoward the centre while dropping quickly (much more quickly than observed) \noutside the Solar ring (upper right panel).\n\nThe overall metallicity is reduced with respect to the original model\n{\\sf S15a} (lower right panel, model {\\sf S15RFc})\nand again we need to increase the IMF scaling fraction $\\zeta$ to raise\nthe chemical enrichment to the observed values (model {\\sf S15RFd}). \nThe resulting gradient is roughly comparable to the observed one.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Concluding remarks}\n\nWe can summarize the general effects of radial flows as follows.\n%\n\\begin{itemize}\n\\item\nSince matter flows inward and accumulates toward the Galactic Centre, the \ndensity profile in the inner parts gets steeper. A shallower intrinsic \naccretion profile is to be adopted, in order to recover the observed local\nscale--length at the end of the simulation.\n\\item\nIn the outer parts, the profile declines more or less sharply, depending on\nwhether the inflow occurs only within the star--forming disc or there is also\nsubstantial inflow from the outer, purely gaseous disc.\n\\item\nThe gas distribution shows a similar behaviour: it remains quite\nflat in the outer regions if gas is poured in by the flat outer gas disc,\nwhile it tends to drop sharply (more than observed) otherwise.\n\\item\nThe inner gas profile is very steep in the case of a Schmidt SF law (models\n{\\sf S15RF}) --- while with other SF laws with radially decaying efficiency\n(see PC99 and \\S\\ref{bestfit}) the effect would be somewhat compensated by\na larger gas consumption by SF in the inner regions.\n\\item\nThe overall metallicity gets much lower because of the dilution by\ngas inflowing from metal poor outer shells (and possibly\nthe primordial outer disc). A higher fraction of stars contributing to the\nchemical enrichment is needed in the model to match the observed metallicity.\n\\item\nThe metallicity gradient tends to steepen, in agreement with results by other \nauthors (see references in \\S\\ref{previous}).\n\\end{itemize}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Some ``successful'' models}\n\\label{bestfit}\n\nIn \\S\\ref{radfloweffects}\nwe have illustrated the qualitative effects of radial inflows using,\nfor the sake of example, models with a Schmidt SF law. We will now\nconsider models with various SF laws (see PC99) and\ntune the inflow velocity pattern, in each case, so as to match the\nobservational data on the radial profile of the Galactic Disc.\nThe various ``successful'' models presented here should not be taken\nas detailed, unique recipes to reproduce the Disc. Rather, they are meant\nas examples of how inclusion of radial flows in the chemical model\ncan improve the match with the data.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Models with Schmidt law}\n\nLet's first consider again the Schmidt SF law. \nInspection of \nmodels {\\sf S15RFb} and {\\sf S15RFd} (with and\nwithout radial inflows from the outer disc) suggests to proceed as follows.\n%\n%%%%%%%Figure 4%%%%%%%\n\\begin{figure}[hb]\n\\centerline{\\psfig{file=fig4.ps,angle=-90,width=8.5truecm}} \n\\caption{Inflow velocity pattern for the ``successful'' models {\\sf S15RFe} \nand {\\sf O10RFe}.}\n\\label{velS15bestfit}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n%\n\\begin{itemize}\n\\item\nSome inflow from the outer gaseous layer is needed to reproduce the \nshallow decline of the gas distribution observed out of the Solar ring, though\nthe inflow speed from the outer disc should be slower than --1~km~sec$^{-1}$ \notherwise the predicted gas density is too high in the outer parts (as in\nmodel {\\sf S15RFb}).\n\\item\nModels with radial inflows can predict metallicity gradients close to the \nobserved ones even with a Schmidt SF law, provided drift velocities within\nthe star--forming edge are relatively high (of the order of \n{\\mbox{--1~km~sec$^{-1}$}}).\nInflow patterns decelerating inward are particularly efficient in \nbuilding the metallicity gradient (G\\\"otz \\& K\\\"oppen 1992).\n\\end{itemize}\n%\n%%%%%%%Figure 5%%%%%%%\n\\begin{figure}[t]\n\\centerline{\\psfig{file=fig5.ps,width=8.9truecm}}\n\\caption{A ``successful'' {\\sf S15RFe} model compared to the case \nwith no flows. Data and symbols as in Fig.~\\protect{\\ref{s15rf}}.}\n\\label{s15rfbestfit}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n%\nAn example of a drift velocity profile shaped according to these considerations\nis shown in Fig.~\\ref{velS15bestfit}; the corresponding model gives indeed \na reasonable fit to the data (model {\\sf S15RFe}, Fig.~\\ref{s15rfbestfit}).\nThe gas profile keeps increasing \ninward, yet the model does not reproduce the peak of the molecular\nring, for which we need to include the peculiar radial flows induced \nby the Bar (see the discussion in PC99 and \\S\\ref{bar}). Model {\\sf S15RFe} \nshows how radial inflows \ncan in fact allow for metallicity gradients comparable with the observed\nones, even with a Schmidt SF law which would be excluded on the sole base of\nstatic models (PC99).\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Models with spiral--triggered SF laws}\n\nLet's consider now models adopting an Oort--type SF law, with\na SF efficiency inversely proportional to the galactocentric radius and a \nSchmidt--like exponent $\\kappa=1.0$ (Kennicutt 1998, PC99). The \nstatic and the ``successful'' model with this SF law are model {\\sf O10a} from \nPC99 and model {\\sf O10RFe}, respectively (Table~\\ref{modelRFtab}).\n\n%%%%%%%Figure 6%%%%%%%\n\\begin{figure}[t]\n\\centerline{\\psfig{file=fig6.ps,width=8.9truecm}}\n\\caption{A ``successful'' {\\sf O10RF} model compared to the case \nwith no flows.}\n\\label{ws10rfbestfit}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n\nAs in the static case, \n(see PC99), these models\nbehave somewhat similarly to models\nadopting the Schmidt SF law. Fig.~\\ref{ws10rfbestfit} shows \nthat a good fit is obtained with model {\\sf O10RFe}, where we applied\nthe velocity pattern of Fig.~\\ref{velS15bestfit} with inflows becoming slower\ninwar, very close to that used for model {\\sf S15RFe}. Notice that \nin this case the higher SF efficiency in the inner region and the slowdown of \ninflows conspire to accumulate gas around $r=3$~kpc while consuming it at\ninner radii, generating a peak in the predicted gas distribution which closely\nreminds the observed molecular ring.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Models with gravitational self--regulating SF laws}\n\nWe now investigate models adopting a self--regulating SF process driven by \ngravitational settling and feed--back from massive stars, implying a SF \nefficiency exponentially decaying outward in radius, such as the law by Dopita\n\\& Ryder (1994; see PC99). The reference static model\nin this case is model {\\sf DRa} of PC99, while the corresponding ``successful''\nmodel with radial flows is {\\sf DRRFe} (see Table~\\ref{modelRFtab} for the \nrelevant parameters).\n\n%%%%%%%Figure 7%%%%%%%\n\\begin{figure}[t]\n\\centerline{\\psfig{file=fig7.ps,angle=-90,width=8.4truecm}}\n\\caption{Inflow velocity pattern for the ``successful'' model {\\sf DRRF}}\n\\label{velTA15bestfit}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n\nTo reproduce the observed metallicity gradient with this SF law,\nnegligible inflow is required in the outer regions where static models\nalready predict a gradient with the right slope (see model {\\sf DRa}), \nwhile a moderate inflow velocity ($\\sim$0.3~km~sec$^{-1}$) in the inner parts \nis needed to maintain the observed slope also where the predicted gradient \nwould otherwise flatten (see PC99). Such a model is, for example, model\n{\\sf DRRFe}, obtained with the inflow velocity pattern shown in \nFig.~\\ref{velTA15bestfit}.\nIn Fig.~\\ref{drrfbestfit} the ``successful'' model {\\sf DRRFe} is compared \nto the original model {\\sf DRa} of PC99 with no radial flows.\n\n%%%%%%%Figure 8%%%%%%%\n\\begin{figure}[t]\n\\centerline{\\psfig{file=fig8.ps,width=8.9truecm}}\n\\caption{A ``successful'' {\\sf DRRF} model compared to the case with no flows.}\n\\label{drrfbestfit}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Concluding remarks}\n\nThe aim of the previous ``successful'' examples is to remark how, for each \nSF law considered,\nit is possible to tune the inflow velocity pattern so as to get\na good overall agreement with the observational\ndata. As an indication, suitable inflow profiles have the following \ncharacteristics.\n%\n\\begin{itemize}\n\\item\nWith a Schmidt SF law, relatively fast (but still plausible)\nflows are needed within the star--forming disc, with velocities of the order\nof 1~km~sec$^{-1}$. The required metallicity gradient is easily obtained,\nespecially if the inflow velocity is slowly decreasing inward. \\\\\nInflow from the outer gaseous disc must be less prominent (though present), \notherwise the predicted gas density in the outer regions is too high.\n\\item\nIn models adopting an Oort--type SF law with $\\kappa=1.0$, a good fit to the\ndata is obtained with an inflow profile of the same kind:\ninflow at $\\sim 0.5$~km~sec$^{-1}$ from the outer gaseous disc,\ndrift velocities raising at $\\sim 1$~km~sec$^{-1}$ at the stellar disc edge\nand declining inward. Curiously enough, in this case\nthe higher SF efficiency in the inner regions combines with the slowdown of \ninflows to predict a peak in the gas distribution around $r=3$~kpc, quite\nreminiscent of the observed molecular ring.\n\\item\nModels adopting the SF law by Dopita \\& Ryder give a good description of the \nouter regions of the Disc already in the absence of flows (PC99). Mild \nradial inflows can be assumed in the inner \nregions, where the radial gradient would otherwise flatten, to obtain the\nright slope throughout the disc. The required drift velocities are around\n0.3~km~sec$^{-1}$, which can be reasonably provided, for instance, by the \nshocks occurring within the spiral arms (see \\S\\ref{previous}).\n\\end{itemize}\n%\nThe various ``successful models'' presented here are not meant to be\ndefinitive recipes to reproduce the \nradial profile of the Galactic Disc. In fact, the adopted inflow velocity \nprofiles are quite\narbitrary and {\\it ad hoc}. These models are rather meant to show how radial \nflows can be a viable mechanism to interpret the properties of the \nDisc. In PC99 we showed how none of the various SF laws investigated\nis able, by itself, to reproduce the observed metallicity \ngradient throughout the whole extent of the Disc, unless some additional \n``dynamical'' assumption is included. In PC99 we considered \nthe classical case of an inside--out disc formation, namely of an\ninfall time-scale increasing outward. Here, we just show that radial inflows \ncan provide another viable \n``dynamical'' assumption to be combined with any SF law to reproduce the \nobserved gradient. In particular, if we adopt a Schmidt SF law \nwith $\\kappa=1.5$ or an Oort--type SF law with $\\kappa=1.0$, as\nrecent empirical evidence seems to support (Kennicutt 1998), the\nrequired variation of the accretion time-scale is too extreme in the\npure inside--out assumption (PC99), and radial inflows are then \nnecessary to explain the metallicity gradient. \nOf course, the two effects (inside--out formation and \nradial flows) can also play at the same time. We do not address here\ntheir combined outcome, because in our models this would merely translate into \nincreasing the number of parameters which one can tune to fit the observational\ndata. No further insight in the problem would be gained. With this kind of\nmodels we can just learn how the various players (different SF laws,\nradially varying accretion time-scales, radial gas inflows) enter the game of\nreconstructing the general picture, and analyse their effects one by one.\n\nIt is also worth stressing that even slow radial gas flows, with velocities \nwell plausible in terms of the triggering physical mechanisms and\nwithin the observational limits (\\S\\ref{previous}), \nhave non--negligible influence on chemical\nmodels, especially on the gas density distribution. It is therefore misleading\nto seek for a one--to--one relation between gas content and metallicity, or \nbetween gas profile and metallicity gradient, like the one predicted by simple\nmodels (e.g.\\ Tinsley 1980). When studying the chemical features of galaxies, \nit is very dangerous to assume that such a relation must hold, since even mild\nflows can easily alter the overall distribution.\n\nThe models with smooth radial inflows presented in this section (with the \npossible exception of model {\\sf O10RFe}) are still unable to reproduce the \ngas density peak corresponding to the molecular ring around 4~kpc, since that\nneeds to take into account the peculiar dynamical influence of the Galactic Bar\non gas flows. This will be the issue of the next section.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{The role of the Galactic Bar}\n\\label{bar}\n\nThere is by now substantial evidence that the Milky Way hosts a small Bar \nin its inner 3~kpc or so. The idea was originally suggested to explain the\nkinematics of the atomic and molecular gas near the Galactic Centre\n(de Vaucouleurs 1964, Peters 1975, Liszt \\& Burton 1980, Mulder \\& Liem 1986).\nIn recent years further evidence for a Galactic Bar has piled up from several\ntracers: gas dynamics (Binney \\etal 1991; Weiner \\& Sellwood 1996, 1999;\nYuan 1993; Wada \\etal 1994; Englmaier \\& Gerhard 1999; Fux 1999), IR photometry\nand star counts (Blitz \\& Spergel 1991, Weinberg 1992, Nikolaev \\& Weinberg \n1997, Dwek \\etal 1995, Binney \\etal 1997, Unavane \\& Gilmore 1998), stellar \nkinematics (Zhao \\etal 1994; Weinberg 1994; Fux 1997; Sevenster 1997, 1999;\nSevenster \\etal 1999; Raboud \\etal 1998), OGLE data (Stanek \\etal 1994, 1997; \nPaczynski \\etal 1994; Evans 1994;\nZhao \\etal 1995, 1996; Zhao \\& De Zeeuw 1998, Ng \\etal 1996). For a \nreview on the Galactic Bar see e.g. Gerhard (1996, 1999). \nThe determination of the characteristic parameters (size, \naxis ratio, rotation speed, orientation and so forth) is even more\ndifficult for the Bar of our own Milky Way than for external galaxies. Broadly\nspeaking, the various studies mentioned above indicate a Bar with a major axis\nof {\\mbox{2--4~kpc}} viewed at an angle of {\\mbox{15--45$^o$}} in the first \nlongitude quadrant, an axis ratio around 3:1 and a pattern speed \n{\\mbox{$\\Omega_p \\sim 60$~km sec$^{-1}$ kpc$^{-1}$}}.\n\nPC99 underlined that the dynamical influence of the Galactic Bar is likely to\naccount for the peak at 4~kpc displayed by the gas profile in the Disc, which\nstatic chemical models are unable to reproduce if other constraints, like the\nobserved metallicity gradient, are to be matched as well. In fact, \ngravitational torques in a barred, or non--axisymmetric, potential are thought\nto induce gas accumulation and formation of rings at the corresponding \nLindblad resonances (e.g. Combes \\& Gerin 1985; Schwarz 1981, 1984).\nIn brief, bar--induced flows sweep gas away from the co--rotation (CR) radius,\nwhere the bar roughly ends, toward the inner and outer Lindblad resonances \n(ILR, OLR).\nIn fact, we developed our new chemical model with radial flows also with \nthe aim to mimic such effects of the Bar upon the gas distribution, by\nsimulating suitable flow velocity profiles.\n\nAs mentioned above, though the existence and gross features of the \nGalactic Bar are by now established, there is no\ngeneral agreement on details like its size and pattern speed, and on the\ncorresponding radii for its CR and ILR, OLR. In this paper, with \nthe aim to reproduce the\nmolecular ring at 4--6~kpc, we will consider two Bar models covering\nthe range of scenarios suggested in literature:\n%\n\\begin{description}\n\\item[{\\bf case A)}]\nBar's CR around 3.5~kpc, so that the dip in the gas distribution between 1.5\nand 3.5~kpc is interpreted as a fast inward drift of gas from CR to the ILR\nand the nuclear ring;\n\\item[{\\bf case B)}]\nBar's CR around 2.5~kpc and OLR around 4.5~kpc, so that the molecular ring is\ninterpreted as accumulation of gas from CR toward the OLR.\n\\end{description}\n%\nIn any case, we will assume here that the Bar \ninfluences\nonly the inner {\\mbox{5--6~kpc} of the Galactic Disc, where its OLR is \nsupposed to lie at the outermost according to current understanding, \nwhile leaving regions outside the OLR unaffected (see also Gerhard 1999).\nActually, the possible influence of the Bar over a larger Disc region\nthan its formal extent is still an open problem, as we will \ncomment upon in the final conclusions (\\S\\ref{conclusions}).\n\nIn the framework of our chemical model, the inclusion of the Bar translates \ninto imposing a suitable velocity profile for the radial flows \nin the inner regions of the disc. \nNamely, we run the ``successful models'' with radial flows \npresented in \\S\\ref{bestfit}, but at a\nsuitable age the Bar is assumed to form and the radial velocity profile\nis altered correspondingly, by modifying\nthe coefficients $\\alpha_k$, $\\beta_k$, $\\gamma_k$ describing the radial flow \npattern (\\S\\ref{discrete}).\nIn case A, we will impose fast radial inflow velocities within CR at 3--4~kpc\nto mimic the rapid drift of the gas toward the ILR (\\S\\ref{caseA}). \nIn case B, we will impose outflows from CR to the OLR around 4.5~kpc\n(\\S\\ref{caseB}).\n\n%%%%%%%Figure 9%%%%%%%\n\\begin{figure}[t]\n\\centerline{\\psfig{file=fig9.ps,angle=-90,width=8truecm}}\n\\caption{Inflow velocity pattern adopted from the onset of the Bar at the time\n$t_G-T_{bar}$ upon the base ``no Bar'' model ({\\sf S15RFe}), to mimic case\nA for the Galactic Bar with models {\\sf S15RF}. The dotted line applies to the \nbase model {\\sf S15RFe}, and also to the ``barred'' models before\n$t_G-T_{bar}$.}\n\\label{vels15barA}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n%\n%%%%%%%Figure 10%%%%%%%\n\\begin{figure}[h]\n\\centerline{\\psfig{file=fig10.ps,width=8truecm}}\n\\caption{Models {\\sf S15RF} mimicking case A for the Galactic Bar, adopting\nthe inflow patterns of Fig.~\\protect{\\ref{vels15barA}}. The ``no Bar'' model \n{\\sf S15RFe} is also shown for comparison as a dotted line.}\n\\label{s15barA}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n\nAs to the age of the Bar, an upper limit is set by the typical age of its \nstellar\npopulation, 8--9~Gyr (Ng \\etal 1996); an age of 5 to 8~Gyr has been suggested \nby Sevenster (1997, 1999). The results from our simulations turned out to be\nquite\ninsensitive to a change in the Bar's age from 9 to 5~Gyr; therefore, we will\npresent simulations with a 5~Gyr old Bar \n($T_{bar}=5$) \nas representative of the generic case of age $\\gsim 5$~Gyr.\nWe will also consider, for the sake of completeness, the case of a much\nyounger Bar of 1~Gyr of age ($T_{bar}=1$).\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Modelling the effects of the Bar: case A}\n\\label{caseA}\n\nTo mimic case A, where the Bar induces fast inflows from CR to its ILR,\nthe inflow velocity is \ntypically increased for $r < 3.5-4$~kpc (the Bar's CR radius) with respect \nto the drift pattern adopted before the onset of the Bar.\n%\nModels corresponding to case A give good results when combined with a Schmidt\nSF law with radial inflows. Starting from the corresponding ``successful'' \nmodel {\\sf S15RFe} of \\S\\ref{bestfit} and changing the velocity law as in \nFig.~\\ref{vels15barA} at the onset of the Bar, we obtained\nthe models shown in Fig.~\\ref{s15barA}, compared to the original model \n{\\sf S15RFe} with no Bar's effects included. Obviously, if the Bar is younger\n($T_{bar}=1$~Gyr) faster induced inflows need to be assumed in the\ninner regions so that the observed sharp dip in the gas profile at \n$r \\lsim 3.5$~kpc is obtained in a shorter time (Fig.~\\ref{vels15barA}).\nAnyways, no extreme speeds need to be induced by the Bar ($|v| < 5$~km~sec) \nat these radii yet, to resemble the observed gas profile, so the models remain\nplausible.\n\nThis type of solution \nactually corresponds to \nthe one originally suggested by Lacey \\& Fall (1985), who in fact assumed a\nSchmidt SF law, radial inflows of the order of --1~km~sec$^{-1}$ to reproduce \nthe metallicity gradient, and for $r \\leq 4$~kpc a raise in the inflow speed \nup to {\\mbox{--10~km~sec$^{-1}$}} to reproduce the gas profile.\nWithout such a spike in the inflow velocity, the gas distribution keeps rising \ninward, with no depression (cfr.\\ model {\\sf S15RFe}).\nThis picture also corresponds to the situation for viscous models as suggested\nby Thon \\& Meusinger (1998): the detailed gas profile of the Disc \ncan be reproduced only by artificially increasing the viscosity\nin the inner regions, so as to mimic the influence of the Galactic Bar. \n\n%%%%%%%Figure 11%%%%%%%\n\\begin{figure}[ht]\n\\centerline{\\psfig{file=fig11.ps,angle=-90,width=8.5truecm}}\n\\caption{Inflow velocity pattern adopted from $t_G-T_{bar}$\nupon the base (``no Bar'') model {\\sf O10RFe}, to mimic\ncase A for the Galactic Bar with models {\\sf O10RF}.}\n\\label{velws10barA}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n%\n%%%%%%%Figure 12%%%%%%%\n\\begin{figure}[ht]\n\\centerline{\\psfig{file=fig12.ps,width=8.5truecm}}\n\\caption{Models {\\sf O10RF} mimicking case A for the Galactic Bar, adopting\nthe inflow patterns of Fig.~\\protect{\\ref{velws10barA}}.}\n\\label{ws10barA}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n\nCase A can also well combine with model {\\sf O10RFe}, namely with an \nOort--type SF law with $\\kappa=1$ plus the corresponding ``successful'' inflow\npattern. In fact, also in model {\\sf O10RFe} (which is actually the only model\nable to predict a peak in the gas profile reminding of the molecular ring \neven without including the Bar, see \\S\\ref{bestfit}) the gas profile \nrises inward,\nand by increasing the inflow velocities inside 4~kpc one can fit the observed\ngas depression. As an example, we show models {\\sf O10RF} with inflow patterns\nas in Fig.~\\ref{velws10barA}; the corresponding results are plotted in \nFig.~\\ref{ws10barA} together with the base model {\\sf O10RFe}.\n\nNotice how in all these ``case A'' models the metallicity gradient is only \nnegligibly affected by the switch of the inner inflow pattern \nat the time of onset of the Bar, $t_G-T_{bar}$ ($t_G=15$~Gyr is the present \nGalactic age). The effects are at most limited to $r \\lsim 3$~kpc, where\nthey are hard to check from observations, since in that region\nthe gas distribution is depressed and \nthe metallicity tracers are missing as well, since they are young objects \nstrongly correlated to present--day SF activity and therefore \nto the presence of gas. We remark that abundance data at $r=0$\nin the plots for the abundance gradient are to be disregarded \nas a constraint for the model, since\nthey refer to the Galactic Centre population, not to the Disc (see PC99).\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Modelling the effects of the Bar: case B}\n\\label{caseB}\n\nAccording to what we labelled above as ``case B'', the Galactic Bar ends \nin correspondence to its CR around 2.5~kpc, and it has an OLR around 4.5~kpc. \nTherefore, the gas is expected to drift from CR outward\nand accumulate at the OLR, while gas inflowing from outer regions slows down\nand accumulates as well at the level of the resonance at 4.5~kpc.\n\n%%%%%%%Figure 13%%%%%%%\n\\begin{figure}[b]\n\\centerline{\\psfig{file=fig13.ps,angle=-90,width=8.7truecm}}\n\\caption{Radial flow velocity pattern adopted from $t_G-T_{bar}$\nupon the base ``no Bar'' inflow pattern, to mimic case B \nfor the Galactic Bar with models {\\sf DRRF}. The dot--dashed \nhorizontal line at $v=0$ marks the transition from inflows (negative $v$) to \noutflows (positive $v$).}\n\\label{velta15barB}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n\nModels for case B will adopt, starting from $t_G-T_{bar}$, a radial\nflow pattern with positive velocities (outflow) from $r=2.5$~kpc to\n$r \\sim 4.5$~kpc, and negative velocities (inflow) from outside dropping to \nzero at $r \\sim 4.5$~kpc.\nCase B can be combined with model {\\sf DRRFe}, namely with the SF law by \nDopita \\& Ryder (1994) and the corresponding ``successful'' overall inflow \npattern (\\S\\ref{bestfit}). The relevant models with their detailed velocity \npatterns, for the usual two values of $T_{bar}$, are shown in \nFigs.~\\ref{velta15barB} and~\\ref{drbarB}. \n%\nNotice once again that rather low drift velocities \n{\\mbox{($|v| < 0.5$~km~sec)}}\nsuffice to reproduce the gas peak, which reinforces the plausibility of the\nmodels. \n\nIn case B models, the metallicity gradient is clearly affected in the\ninner regions by the switch in the gas flow pattern, at least if this lasted\nfor some time (Fig.~\\ref{drbarB}, case $T_{bar} = 5$). This feature,\nthough, is again hard to check from observations since there are no tracers of\nDisc metallicity for $r < 4$~kpc (see \\S\\ref{caseA}).\n\n%%%%%%%Figure 14%%%%%%%\n\\begin{figure}[t]\n\\centerline{\\psfig{file=fig14.ps,width=8.5truecm}}\n\\caption{Models {\\sf DRRF} mimicking case B for the Galactic Bar, adopting\nthe flow patterns of Fig.~\\protect{\\ref{velta15barB}}. Disregard abundance \ndata at $r=0$ (see text).}\n\\label{drbarB}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n\nCase B can also reproduce the observed gas profile combined with an Oort--type\nSF law with $\\kappa=1$ (model {\\sf O10RFe}), especially provided\nthe Bar formed recently, as displayed in Fig.~\\ref{ws10barB} with \n$T_{bar}=1$. If the Bar--induced flows activate much earlier, the predicted\npeak is very sharp and narrow (Fig.~\\ref{ws10barB}, case $T_{bar}=5$~Gyr),\ndue to the milder sensitivity of SF to the gas density in this\ncase (Schmidt-like exponent {\\mbox{$\\kappa=1$}}): with respect to other \nSF laws, this SF is relatively less efficient where the gas density is high, \nnamely where the gas accumulates around 4.5~kpc, while it is \nrelatively more efficient where the density drops, below 4~kpc.\nSuch a sharp peak seems in contrast with the observed, quite\nbroad distribution (the observational uncertainty on the gas density\nprofile in the inner Galactic region is less than a factor of 2, Dame 1993).\nModels {\\sf O10RF} with an ``old'' Bar are therefore less appealing in case B.\n\n%%%%%%%Figure 15%%%%%%%\n\\begin{figure}[t]\n\\centerline{\\psfig{file=fig15.ps,angle=-90,width=8.5truecm}}\n\\caption{Radial flow velocity pattern adopted from \n$t_G-T_{bar}$ upon the base ``no Bar'' inflow pattern, to mimic case B \nfor the Galactic Bar with models {\\sf O10RF}.}\n\\label{velws10barB}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n%\n%%%%%%%Figure 16%%%%%%%\n\\begin{figure}[t]\n\\centerline{\\psfig{file=fig16.ps,width=8.5truecm}}\n\\caption{Models {\\sf O10RF} mimicking case B for the Galactic Bar, adopting\nthe flow patterns of Fig.~\\protect{\\ref{velws10barB}}.}\n\\label{ws10barB}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Concluding remarks}\n\nWe referred to the current understanding of the structure and\nfeatures of the Galactic Bar to simulate its dynamical influence on the \nsurrounding gas flows and distribution. \nChemical models accounting for the effect of the Bar make it finally possible\nto reproduce the gas profile properly, which could not be accomplished by\nstatic models (PC99).\n\nBroadly speaking, two main scenarios are presented.\n%\n\\begin{enumerate}\n\\item\nThe Bar stretches to 3.5~kpc and the gas peak is due to a rapid\ndepletion of gas drifting from the Bar's CR to the Galactic Centre (case A).\nTo reproduce the gas profile, we need a gas distribution which keeps\nincreasing from the outer disc inward, down to $\\sim 4$~kpc where the Bar's\ninfluence produces the sharp depletion. This can be achieved only by means of\nefficient radial inflows over the whole disc, and in this case radial inflows\nare also the major source for the observed metallicity gradients (models\n{\\sf S15RFe} and {\\sf O10RFe}).\n\\item\nThe Bar ends around 2.5~kpc, where its CR is set, and the gas peak is due \nto the accumulation of gas from CR outward to its OLR at $\\sim 4.5$~kpc \n(case B). A rather \nlimited contribution of radial inflows from the outer regions suffices to \nobtain the peak. In this case, the metallicity gradients in the outer regions \nof the disc may be mainly due to the SF process itself, and to the intrinsic \nvariation of the SF efficiency with radius (model {\\sf DRRFe}).\n\\end{enumerate}\n%\n\nWithin these simplified models it is unfeasible to discuss any further\non the scenarios for Bar structure and age, and \nrelated gas flows. Only detailed dynamical simulations for Bar formation, \nevolution and potential can tell how the molecular ring consequently formed,\nwhich is beyond the goals of this paper (see also \\S\\ref{conclusions}). \nHere we were just interested in showing how even simple qualitative models for \nBar--induced gas flows in the inner disc solve in fact the puzzle encountered\nin PC99. Namely, they can reproduce at the same time both \nthe metallicity gradient and the gas distribution, in particular the peak \ncorresponding to the molecular ring around 4~kpc. This can be accomplished\nalready with quite slow, and largely plausible, flow velocities.\nThe present modelling therefore provides a simple tool for qualitative \nunderstanding of possible behaviours.\n\nRegardless of details, however, one condition is necessary for the scheme \nto work: there must be enough gas in the inner regions of the Disc, which the \nBar can then ``shape'' to resemble the detailed observed distribution. This \nfavours chemical models with radial inflows where the metallicity\ngradient can coexist with high gas fractions in the inner shells. Our\nsimulations showed that no Bar--induced gas flow\nsuperimposed on otherwise static models (as those by PC99) can produce \nthe observed gas peak: whatever the \nassumed age of the Bar or gas velocity profile, there is not enough gas\nleft in the inner Galactic regions if we are to \nreproduce the metallicity gradient as well. Gas must be continuously \nreplenished by inflows from outer regions;\nthat's why we presented here\n``barred'' models based only on the ``successful'' models with radial inflows \nfrom \\S\\ref{bestfit} and never on the static models of PC99.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Summary and conclusions}\n\\label{conclusions}\n\nFrom the results of static chemical models, PC99 underlined the need to \nintroduce radial flows to explain some features of the Galactic Disc. In fact,\nstatic models are unable to reproduce, at the same time, both the\nmetallicity gradient and the radial gas profile; in particular, the peak\ncorresponding to the molecular ring at 4--6~kpc is likely to be a consequence \nof gas drifts induced by the dynamical influence of the Galactic Bar.\nTherefore, in the present paper we introduced a new chemical model including \nradial gas flows, developed as a multi--dimensional generalization of the \noriginal static model (\\S\\ref{discrete}).\nOur model is conceived so as to adapt to any imposed radial velocity \nprofile, describing both inflows and outflows in any part of the disc. \nThe model is carefully tested \nagainst instability problems and \nspatial resolution, by comparing it to suitable exact analytical cases\n(Appendix~B). In this paper we applied the model to the Galactic Disc;\nmore in general, such models allowing for gas drifts are meant to be used\nas fast and handy interfaces between detailed dynamical galaxy\nmodels (predicting the velocity profiles) and parametric chemical\nand spectro--photometric models.\n\nAn overview of the behaviour of chemical models with radial inflows of gas\nshows that these provide an alternative ``dynamical'' assumption to the\ninside--out disc formation scenario to explain the metallicity gradient\n(\\S\\ref{radfloweffects}).\nWith radial gas flows, the model can reproduce the metallicity\ngradient even in the case of a Schmidt or an {\\mbox{Oort--type}} SF law,\nwhich were excluded in the case of static models (see PC99).\nIn addition, it appears that even low radial flow velocities,\nwell within observational limits and theoretical expectations \n(see~\\S\\ref{previous}), have non--negligible \neffects upon model predictions on the metallicity\ngradient and moreover on the gas distribution. In particular,\nif radial gas inflows are allowed for, a metallicity gradient can coexist \nwith a high gas fraction in the inner regions, at odds with simple static \nmodels. This is indispensable to reproduce the observed gas distribution \nin the inner Galaxy (see point 2 below).\n%\nThe remarkable effects of even slow radial flows upon observable quantities,\nmainly upon the gas distribution, should be kept in mind as a caveat when \ncomparing real galaxies to simple analytical models which predict a \none--to--one relationship between metallicity and gas fraction (e.g.\\ Tinsley \n1980). Our models show that small dynamical effects, like slow gas flows, \ncan easily make real systems depart from the behaviour of simple models.\n\nWith our model it is possible to mimic the dynamical influence of the\nGalactic Bar and reproduce the peak in the gas distribution around 4~kpc\n(\\S\\ref{bar}).\nTwo scenarios, related to two different models for the structure of the\nBar, are qualitatively suggested.\n%\n\\begin{description}\n\\item[{\\bf A.}]\nWith a Schmidt or an Oort--type SF law, slow radial inflows in the disc \npile up gas inward down to {\\mbox{$r=3.5-4$~kpc}}. Here, the Bar CR\nradius is found and the gas is quickly swept inward from CR toward an ILR, \nwhich causes the drop in the gas profile at 3.5~kpc.\n\\item[{\\bf B.}]\nWith a SF law like that by Dopita \\& Ryder (1994),\nsmaller inflow rates suffice\nto reproduce the metallicity gradient, leading to a lower concentration of gas \nin the inner regions than in the previous case. The peak corresponding to the\nmolecular ring can be reproduced with a Bar CR around 2.5~kpc and its\nOLR around 4.5~kpc, so that all the gas external to $r=2.5$~kpc tends to pile\nup around the OLR.\n\\end{description}\n%\nThough these models are just qualitative and cannot\ndescribe the detailed dynamical process of Bar formation nor the\nevolution of the related gas flows to form the molecular ring, they provide\ntwo interesting indications. \n%\n\\begin{enumerate}\n\\item\nOnly when introducing the effects of the Bar, the model is able to reproduce \nthe radial gas profile properly. The only possible exception resides in a \nparticular combination of an Oort-type SF law with a radial inflow pattern \nwhose velocity decreases inward (model {\\sf O10RFe}; this combination may lead\nto a peak of the gas distribution in the inner Galactic regions,\nclosed to the observed molecular ring. But this particular, fortunate case \ndoes not diminish the general conclusions about the role of the Galactic Bar.\n\\item\nIn any case (A or B above), overall radial inflows in the disc are \nindispensable to replenish the inner regions with enough gas that the observed\nmolecular ring can form\nunder the influence of the Bar. This seems to favour disc models with radial \ninflows, unless one assumes that the gas in the ring has \nsome different origin (gas swept from the Bulge, or accreted later).\t\n\\end{enumerate}\n%\nTo investigate these issues any further, detailed gas--dynamical models\nare obviously required. Unfortunately, most studies on Bar--induced \ngas dynamics \n(see references in \\S\\ref{bar}) concentrate on the observed features of the\nvery inner regions, such as the nuclear ring, the 3~kpc expanding arm, and so\nforth. Little discussion can be found about the effects of the Bar on more\nexternal regions, and on the formation of the molecular ring in particular:\nwhether it is due to gas depletion inside CR as in our case A, or due to\ngas accumulation at some resonance (e.g.\\ Binney \\etal 1991, Fux 1999) as in \nour case B, or whether it just consists of two or more tightly wound spiral\narms (e.g. Englmaier \\& Gerhard 1999). Further gas--dynamical studies \nsuggesting detailed scenarios, time-scales, and velocity profiles\nfor the formation of the molecular ring would be welcome, for the sake of \nincluding the effects of the Bar in chemical evolution \nmodels more consistently. \n\nFurther investigation of gas--dynamical models on the influence \nof the Bar on even larger scales (namely, outside its OLR) should be pursued\nas well, since this is a clue issue related to\na claimed discrepancy between\nthe characteristics of the Galactic Bar and the observed metallicity gradient.\nIt is well known that barred galaxies display systematically shallower\ngradients than ordinary spirals (e.g.\\ Alloin \\etal 1981, Vila--Costas \\& \nEdmunds 1992, Martin \\& Roy 1994). This is likely a consequence of\nthe radial mixing induced by bars; in fact, Martin \\& Roy (1994) found\na correlation for external galaxies between the strength of a bar \nand the metallicity gradient. Taking this empirical relation at face value, \nthe Galactic Bar with an axial ratio of {\\mbox{$\\sim 0.5$}} should induce \na metallicity gradient of {\\mbox{--0.03~dex/kpc}}, much shallower than the \nobserved one of --0.07~dex/kpc, which is typical of a {\\it normal} Sbc galaxy.\nTo overcome such a puzzle, it has been suggested that the Galactic Bar must\nbe very young ($<$1~Gyr), so that there was not enough time yet to flatten \nthe gradient (Gummersbach \\etal 1998); but this is in conflict with other\nestimates of the Bar's age (e.g.\\ Sevenster 1997, 1999). Alternatively,\nwe suggest that the discrepancy might be only apparent, since the Galactic Bar\nis quite small, and the Milky Way cannot be properly considered a barred \nspiral.\nIt might be unlikely that the Bar can influence the metallicity \ngradient all over the Disc, as in really barred galaxies: Bar--induced \nradial drifts and corresponding chemical mixing are expected to occur from CR \ntoward the ILR (inflows) and to the OLR (outflows; e.g.\\ Schwarz 1981, 1984; \nFriedli \\etal 1994).\nPresent understanding of the Galactic Bar sets its OLR between 4.5 and 6~kpc\n(\\S\\ref{bar} and references therein), so in our models we presumed \nthat the Bar induces negligible mixing beyond these radii, regardless\nof its age (see also Gerhard 1999). If the situation is as in the models \nwe presented here, in fact,\nthe metallicity gradient in the outer regions\nis unperturbed and just related to intrinsic Disc properties and/or \nlarge--scale viscous flows.\n\nHowever, gas--dynamical simulations dedicated to the effects of the Galactic\nBar over the whole Disc would be necessary, so as to investigate \nthe relation between the Bar, radial mixing and the metallicity \ngradient more consistently.\nMore in general, including the effects of {\\mbox{bar--induced}} \nradial flows in the \npicture of the chemical evolution of spiral galaxies might turn out to be\nof wide interest, since it is likely that all spirals develop at some point, \nor have developed in the past, some bar--like structure (Binney 1995). \nInfrared observations indeed reveal that a large fraction of spirals \nhost a barred structure (e.g.\\ Eskridge \\etal 1999), and \nrecent numerical simulations suggest that even weak bars or oval distortions \nmay be able to induce radial drifts to form multiple gaseous rings at the \ncorresponding Lindblad resonances (Jungwiert \\& Palou\\v{s} 1996). \nBars could even drive secular evolution of spiral discs from late to early type\n(e.g.\\ Dutil \\& Roy 1999). \nBar--driven radial gas flows might therefore play a fundamental role \nin the chemical evolution of spiral discs.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\acknowledgements{We thank Joachim K\\\"oppen for his advice on \nnumerical modelling of radial gas flows, Yuen K.\\ Ng and Antonella Vallenari\nfor useful discussions\nabout Galactic structure, and our referee, Mike Edmunds, whose suggestions \nmuch improved the presentation of our paper. \n\n\\noindent\nL.P.\\ acknowledges kind hospitality from the \nNordita Institute in Copenhagen, from the Observatory of Helsinki and from \nSissa/Isas in Trieste. This study has been financed by the Italian \nMURST through a PhD \ngrant and the contract ``Formazione ed evoluzione delle galassie'', \nn.~9802192401.}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\appendix\n\\section{The explicit expression of Eq.~(\\protect{\\ref{solsystemradf2}})}\n\\label{appendixA}\n\nHere we sort out the explicit expression~(\\protect{\\ref{solradfN}})\nof the solution~(\\protect{\\ref{solsystemradf2}}) for $G_i(r_k,t)$, by \ncalculating the\nmatrix $e^{t {\\cal A}}$. Let us first introduce the simplified notation:\n%\n\\begin{equation}\n\\label{notation}\nG_k(t) = G_i(r_k,t),~~~~~~~~~~~\\overline{W_k} = \\overline{W}_i(r_k)\n\\end{equation}\n%\nFor the sake of example, we present here the detailed solution in the case \nof three shells ($N=3$). The relevant system of \nequations~(\\protect{\\ref{systemradf}}) becomes:\n%\n\\begin{equation}\n\\label{systemradf3}\n\\left\\{ \\begin{array}{l}\n\\frac{d}{dt} \\, G_1(t) = \\vartheta_1 G_1(t) + \\gamma_1 G_2(t) + W_1 \\\\\n\\\\\n\\frac{d}{dt} \\, G_2(t) = \\alpha_2 \\, G_1(t) + \\vartheta_2 G_2(t) +\n\t\t\t \\gamma_2 G_3(t) + W_2 \\\\\n\\\\\n\\frac{d}{dt} \\, G_3(t) = \\alpha_3 \\, G_2(t) + \\vartheta_3 G_3(t) + W_3 +\n\\overline{\\omega_i}\\\\\n\\end{array} \\right.\n\\end{equation}\n%\nwhere all the coefficients are considered as constants \n(see \\S\\ref{numericalradf}), though we have \nomitted the bar over $W_k$ and $\\vartheta_k$ for simplicity. \nA system like~(\\protect{\\ref{systemradf3}}) holds for each chemical species \n$i$, but the characteristic matrix ${\\cal A}$ is the same for any $i$\n(see \\S\\protect{\\ref{numericalradf}}); in this case:\n%\n\\[ {\\cal A} = \\pmatrix{\n\\vartheta_1 & \\gamma_1 & 0 \\cr\n \\alpha_2 & \\vartheta_2 & \\gamma_2 \\cr\n 0 & \\alpha_3 & \\vartheta_3 \\cr} \\]\n%\nLet's first notice, from the definition~(\\protect{\\ref{coeffradf}}),\nthat $\\gamma_k$ and $\\alpha_{k+1}$ can never be both positive: at least one of \nthem must be zero since\nthey are ``activated'' in the opposite cases of inflow or outflow at\n$r_{k+\\frac{1}{2}}$, respectively; if there is no flow at all through \n$r_{k+\\frac{1}{2}}$, they both reduce to zero. Therefore, in our calculations\nwe are always entitled to use the condition:\n%\n\\begin{equation}\n\\label{gammacondition}\n\\gamma_k \\, \\alpha_{k+1} = 0 ~~~~~~~~~~~~~~~~~~\\forall k\n\\end{equation}\n%\nThe eigenvalues of the matrix ${\\cal A}$ are\n%\n\\[ \\lambda_{1,2,3} = \\vartheta_{1,2,3} \\]\n%\nand the associated eigenvectors are:\n%\n\\[ {\\bf u}_1 = \\pmatrix{\n1 \\cr\n\\cr\n\\frac{\\alpha_2}{\\vartheta_1 - \\vartheta_2} \\cr \n\\cr\n\\frac{\\alpha_3}{\\vartheta_1 - \\vartheta_3} \n\\frac{\\alpha_2}{\\vartheta_1 - \\vartheta_2} \\cr} \n%\n{\\bf u}_2 = \\pmatrix{\n\\frac{\\gamma_1}{\\vartheta_2 - \\vartheta_1} \\cr\n\\cr\n1 \\cr\n\\cr\n\\frac{\\alpha_3}{\\vartheta_2 - \\vartheta_3} \\cr} \n{\\bf u}_3 = \\pmatrix{\n\\frac{\\gamma_1}{\\vartheta_3 - \\vartheta_1}\n\\frac{\\gamma_2}{\\vartheta_3 - \\vartheta_2} \\cr\n\\cr\n\\frac{\\gamma_2}{\\vartheta_3 - \\vartheta_2} \\cr\n\\cr\n1 \\cr} \\]\n%\nFrom~(\\protect{\\ref{e^tAformula}}) we get:\n%\n\\[ \n%\\begin{array}{l l}\ne^{t {\\cal A}} \n\\\\\n= {\\scriptsize \\pmatrix{ \ne^{\\vartheta_1 t} & \\gamma_1 f_{21}(t) &\n\\frac{\\gamma_1 \\gamma_2}{\\vartheta_3-\\vartheta_2} [f_{31}(t)-f_{21}(t)] \\cr\n & \\cr\n\\alpha_2 f_{21}(t) & e^{\\vartheta_2 t} & \\gamma_2 f_{32}(t) \\cr\n & \\cr\n\\frac{\\alpha_2 \\alpha_3}{\\vartheta_2-\\vartheta_1} [f_{32}(t)-f_{31}(t)] &\n\\alpha_3 f_{32}(t) & e^{\\vartheta_3 t} \\cr}}\n\\]\n%\nwhere we have indicated with:\n%\n\\[ f_{kl}(t) = f_{lk}(t) \\equiv\n\\frac{e^{\\vartheta_k t}-e^{\\vartheta_l t}}{\\vartheta_k-\\vartheta_l},\n~~~~~~~~~~~~~~~~~~k,l=1,2,3 \\]\n%\nDefining:\n%\n\\[ g_k(\\Delta t) \\equiv \\int_{t_0}^{t_1} e^{\\vartheta_k (t_1-t)} \\, dt \\,=\\, \n\\frac{e^{\\vartheta_k \\Delta t} -1}{\\vartheta_k} \\]\n%\nthe solution~(\\protect{\\ref{solsystemradf2}}) in the case $N=3$ becomes:\n%\n\\begin{equation}\n\\label{solradf3}\n\\left\\{ \n\\begin{array}{l l}\nG_1(t_1) = & e^{\\vartheta_1 \\Delta t} \\, G_1(t_0) \\,+ \\\\ \n & +\\, \\gamma_1 \\, \\frac{e^{\\vartheta_2 \\Delta t}-e^{\\vartheta_1 \\Delta t}}\n {\\vartheta_2-\\vartheta_1} \\, G_2(t_0) \\,+ \\\\ \n &\t+\\, \\gamma_1 \\, \\gamma_2 \\, \\frac{f_{31}(\\Delta t)-f_{21}(\\Delta t)}\n\t{\\vartheta_3-\\vartheta_2} \\,G_3(t_0) \\,+ \\\\\n &\t+\\, W_1 \\, \\frac{e^{\\vartheta_1 \\Delta t} -1}{\\vartheta_1} \\,+ \\\\\n & \t+\\, \\gamma_1 \\, \\frac{W_2}{\\vartheta_2-\\vartheta_1} \\left( \n \\frac{e^{\\vartheta_2 \\Delta t} -1}{\\vartheta_2} -\n \\frac{e^{\\vartheta_1 \\Delta t} -1}{\\vartheta_1} \\right) \\,+ \\\\\n & +\\, \t \\gamma_1 \\gamma_2 \\, \\frac{W_3}{\\vartheta_3-\\vartheta_2} \\left[\n \\frac{g_3(\\Delta t) - g_1(\\Delta t)}{\\vartheta_3-\\vartheta_1} -\n\\frac{g_2(\\Delta t) - g_1(\\Delta t)}{\\vartheta_2-\\vartheta_1} \\right] \\\\\n & \\\\\nG_2(t_1)= & \\alpha_2\\, \\frac{e^{\\vartheta_2 \\Delta t}-e^{\\vartheta_1 \\Delta t}}\n {\\vartheta_2-\\vartheta_1} \\, G_1(t_0) \\,+ \\\\\n & \t+\\, e^{\\vartheta_2 \\Delta t} \\, G_2(t_0) \\,+ \\\\ \n & +\\, \\gamma_2 \\, \\frac{e^{\\vartheta_3 \\Delta t}-e^{\\vartheta_2 \\Delta t}}\n {\\vartheta_3-\\vartheta_2} \\, G_3(t_0) \\,+ \\\\\n & +\\, \\alpha_2 \\, \\frac{W_1}{\\vartheta_2-\\vartheta_1} \\left( \n\t \\frac{e^{\\vartheta_2 \\Delta t} -1}{\\vartheta_2} -\n \\frac{e^{\\vartheta_1 \\Delta t} -1}{\\vartheta_1} \\right) \\,+ \\\\ \n & + \\, W_2 \\, \\frac{e^{\\vartheta_2 \\Delta t} -1}{\\vartheta_2} \\,+ \\\\\n & + \\,\t \\gamma_2 \\, \\frac{W_3}{\\vartheta_3-\\vartheta_2} \\left( \n\\frac{e^{\\vartheta_3 \\Delta t} -1}{\\vartheta_3} -\n\\frac{e^{\\vartheta_2 \\Delta t} -1}{\\vartheta_2} \\right)\\\\\n & \\\\\nG_3(t_1) = & \\alpha_2 \\, \\alpha_3 \n\\frac{f_{32}(\\Delta t)-f_{31}(\\Delta t)}{(\\vartheta_2-\\vartheta_1)}\\,G_1(t_0)\n \\,+ \\\\ \n & +\\, \\alpha_3 \\, \\frac{e^{\\vartheta_3 \\Delta t}-e^{\\vartheta_2 \\Delta t}}\n\t {\\vartheta_3-\\vartheta_2} \\, G_2(t_0) \\,+ \\\\\n & +\\,\te^{\\vartheta_3 \\Delta t} \\, G_3(t_0) \\,+ \\\\ \n & \t+ \\alpha_2 \\alpha_3 \\frac{W_1}{\\vartheta_2-\\vartheta_1} \\left[\n \t\\frac{g_3(\\Delta t) - g_2(\\Delta t)}{\\vartheta_3-\\vartheta_2} -\n \\frac{g_3(\\Delta t) - g_1(\\Delta t)}{\\vartheta_3-\\vartheta_1} \\right] + \\\\\n & +\\, \\alpha_3 \\, \\frac{W_2}{\\vartheta_3-\\vartheta_2} \\left( \n \\frac{e^{\\vartheta_3 \\Delta t} -1}{\\vartheta_3} -\n \\frac{e^{\\vartheta_2 \\Delta t} -1}{\\vartheta_2} \\right) \\,+ \\\\\n & + \\,\t(W_3 + \\overline{\\omega_i}) \\, \n\t\\frac{e^{\\vartheta_3 \\Delta t} -1}{\\vartheta_3}\n\\end{array} \n\\right.\n\\end{equation}\n%\nWith zero flow velocity {\\mbox{($\\alpha_k=\\beta_k=\\gamma_k=0$),}}\n(\\protect{\\ref{solradf3}}) \nreduces to the solving formula of the original static model (see PCB98).\nNotice that the solution $G_1(t_1)$ for the $1^{st}$ shell includes not\nonly the contribution of the contiguous $2^{nd}$ shell, but also a contribution\nfrom the $3^{rd}$ shell ``scaled'' by its passage through the $2^{nd}$ shell.\nSimilarly, the $3^{rd}$ shell is affected not only by the $2^{nd}$, but also\nby the $1^{st}$ shell though they are not contiguous.\n\nWith analogous procedure, for an arbitrary number $N$ of shells the solution \nis of the kind:\n%\n\\begin{equation}\n\\label{generalNsol}\nG_k(t) = \\sum_{l=1}^N F_{kl}(\\Delta t) \\, G_l(t_0) \\,+\\, \n \\sum_{m=0}^N H_{km}(\\Delta t) \\, W_m\n\\end{equation}\n%\nwhere:\n%\n\\[ \\begin{array}{l l r}\nF_{kk}(\\Delta t) = & e^{\\vartheta_k \\Delta t}\\\\\nF_{kl}(\\Delta t) = & \\gamma_k \\, \\gamma_{k+1} ....... \\gamma_{l-1} \\,\n{\\cal F}_{k (k+1)....l}(\\Delta t) & ~~~~l > k \\\\\nF_{kl}(\\Delta t) = & \\alpha_{l+1} ....... \\alpha_{k-1} \\, \\alpha_k \n{\\cal F}_{l (l+1)....k}(\\Delta t) & ~~~~l < k \\\\\nH_{kk}(\\Delta t) = & g_k(\\Delta t) \\\\\nH_{kl}(\\Delta t) = & \\gamma_k \\, \\gamma_{k+1} ....... \\gamma_{l-1}\n{\\cal H}_{k (k+1)....l}(\\Delta t) & ~~~~l > k \\\\\nH_{kl}(\\Delta t) = & \\alpha_{l+1} ....... \\alpha_{k-1} \\, \\alpha_k \n{\\cal H}_{k (k-1)....l}(\\Delta t) & ~~~~l < k\n\\end{array} \\]\n%\nand the quantities ${\\cal F}$ and ${\\cal H}$ are constructed by means of \nrecursive formul\\ae:\n%\n\\[ \\begin{array}{l l}\n{\\cal F}_{ki}(\\Delta t) = f_{ki}(\\Delta t)~~~~~~~~~~~~~~~~~~~~ &\n{\\cal H}_{ki}(\\Delta t) = \n\\frac{g_k{\\Delta t}-g_i{\\Delta t}}{\\vartheta_k-\\vartheta_i} \\\\\n & \\\\\n{\\cal F}_{kij} = \\frac{{\\cal F}_{ki}-{\\cal F}_{kj}}{\\vartheta_i-\\vartheta_j} &\n{\\cal H}_{kij} = \\frac{{\\cal H}_{ki}-{\\cal H}_{kj}}{\\vartheta_i-\\vartheta_j}\\\\\n & \\\\\n{\\cal F}_{kijm} = \n\\frac{{\\cal F}_{kij}-{\\cal F}_{kim}}{\\vartheta_j-\\vartheta_m} &\n{\\cal H}_{kijm} = \n\\frac{{\\cal H}_{kij}-{\\cal H}_{kim}}{\\vartheta_j-\\vartheta_m}\\\\\n & \\\\\n{\\cal F}_{kijmn} = \n\\frac{{\\cal F}_{kijm}-{\\cal F}_{kijn}}{\\vartheta_m-\\vartheta_n} &\n{\\cal H}_{kijmn} = \n\\frac{{\\cal H}_{kijm}-{\\cal H}_{kijn}}{\\vartheta_m-\\vartheta_n}\\\\\n & \\\\\n\\vdots & \\vdots\n\\end{array} \\]\n%\nThe coefficients $F_{kl}$ and $H_{kl}$ \ndescribe the contribution of the generic shell $l$ to the chemical\nevolution of $k$. Notice that a shell external to $k$ ($l>k$) can influence $k$\nonly if all the inflow coefficients $\\gamma$ in between $l$ and $k$ are \nnon-zero, namely if there is a continuous inflow from $l$ to $k$, as expected.\nThe same holds for inner shells $l<k$, whose contribution $F_{kl}$, $H_{kl}$ \nis non-zero only if none of the intermediate outflow coefficients $\\alpha$ is \nzero. \n%Evidently,\nThe solution~(\\protect{\\ref{generalNsol}}) gets more and more \ncomplicated the larger the number $N$ of shells considered, since each shell \nformally feels the contribution of all the other shells\n(as already noticed in the above case $N=3$). \nThis occurs because~(\\protect{\\ref{generalNsol}}) \nwould be the \\underline{exact} analytical solution in the case of a\ndifferential system with constant coefficients, namely \\underline{if} the \n${\\cal A}$ matrix in~(\\protect{\\ref{systemradf}}) were constant. Then, \n(\\protect{\\ref{generalNsol}})\nwould describe the complete evolution of any shell $k$, which over a \ngalaxy's lifetime would indeed process and exchange gas drifting from or \nto rather distant shells. But ${\\cal A}(t)$ is not constant even when \nthe flow pattern $\\alpha$, $\\beta$, $\\gamma$ is constant, because \n$\\eta_k(t)$ and therefore $\\vartheta_k(t)$ evolve in time due to SF; \nin fact, we apply \n(\\protect{\\ref{generalNsol}}) only upon short timesteps $\\Delta t$, within \nwhich ${\\cal A}(t)$ can be considered approximately constant.\nIf $\\Delta t$ is short enough with respect to the radial flow velocities\n--- as guaranteed by the Courant condition {\\mbox{$\\Delta t < v \\Delta r$}},\nsee \\S\\protect{\\ref{numericalradf}} ---,\nwe can assume that within $\\Delta t$ the $k$-th shell is affected just by the\nflows from the contiguous shells $k$+1 and $k$--1, and not from more distant\nshells, although all of them formally contribute to the solution.\nIn this approximation we neglect all higher order terms in\n$\\alpha$ and $\\gamma$, namely all the terms \n${\\cal O}(\\alpha_i \\alpha_j)$ and ${\\cal O}(\\gamma_i \\gamma_j)$, keeping\nonly the ``linear'' terms of the kind $\\alpha_k f_{k (k-1)}$ and \n$\\gamma_k f_{k (k+1)}$; so the general \nsolution~(\\protect{\\ref{generalNsol}}) reduces in fact to~(\\ref{solradfN}).\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Testing the numerical model}\n\\label{tests}\n\nSince discretized numerical solutions for partial differential equations \ncontaining an ``advection term''\ntend to be affected by instability problems (e.g.\\ Press \\etal 1986),\nwe tested our numerical code with gas flows against suitable analytical cases.\nWe report here two representative tests involving pure gas\nflows (no SF) which allow for exact analytical solutions; to these\nwe compare the predictions of our numerical code with a SF efficiency \ndropped virtually to zero.\n\n%%%%%%%Figure B1%%%%%%%\n\\begin{figure}[ht]\n\\centerline{\\psfig{file=figB1.ps,width=8.9truecm}}\n\\caption{Numerical models compared to the exact analytical solution for a flat\naccretion profile with inflows. Different models correspond\nto different typical timesteps (see legend on top right) and to different \nshell spacing (upper to lower panel).}\n\\label{testflatfig}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n\n\\medskip\n{\\it Selecting the timestep}.\nThe first reference analytical case is that of a purely \ngaseous disc of infinite radial extent and flat profile, where the gas is:\n%\n\\begin{enumerate}\n\\item\naccreting uniformly with a time-scale $\\tau$;\n\\item\nflowing inward with a constant (in time) and uniform (in space) velocity $v$,\nstarting from the ``inflow onset time'' $T_{rf}$.\n\\end{enumerate}\n%\nSuch a system is governed by the same differential \nequation~(\\protect{\\ref{bordereq}})\ndescribing the adopted boundary condition at the outer disc edge in the \nchemical model (\\S\\protect{\\ref{boundary}}). Eq.~(\\protect{\\ref{bordereq}}) \nis a linear, first order, partial differential equation, equivalent to the \nsystem:\n%\n\\begin{equation}\n\\label{bordersystem}\n\\left\\{ \\begin{array}{l r}\n\\frac{dr}{dt} = v & (a) \\\\\n & \\\\\n\\frac{d \\sigma}{dt} \\,= \\, A \\, e^{-\\frac{t}{\\tau}} \\,-\\, \\frac{v}{r} \\,\n\\sigma & (b)\n\\end{array}\n\\right.\n\\end{equation}\n%\nEq.~(\\protect{\\ref{bordersystem}}a) is solved as:\n%\n\\[ r = v \\, (t-t_0) \\,+\\, r_0 \\]\n%\nand substitution into Eq.~(\\protect{\\ref{bordersystem}}b) \nyields:\n%\n\\begin{equation}\n\\label{bordereq(b)}\n\\frac {d \\sigma}{d t} \\,+\\, \\frac{1}{t + p} \\, \\sigma \\,=\\, \nA e^{-\\frac{t}{\\tau}}~~~~~~~~~~~~~~~~~~~~~~p \\equiv \\frac{r_0}{v} - t_0\n\\end{equation}\n%\nThis \nlinear, first order, ordinary differential equation\nis solved as:\n%\n\\[ \\begin{array}{l l}\n\\sigma(t) & = \\sigma(t_0) \\, e^{- \\int_{t_0}^{t} \\frac{1}{\\xi + p} d\\xi} \\,+\\,\n \\int_{t_0}^{t} e^{- \\int_{\\xi}^{t} \\frac{1}{\\theta + p} d\\theta} \\,\n A \\, e^{-\\frac{\\xi}{\\tau}} d\\xi\\\\\n & \\\\\n & = \\sigma(t_0) \\, \\frac{t_0+p}{t+p} \\,+\\, \\frac{A}{t+p} \\, \\tau \n\t\\, \\times \\\\\n & \\times \\left[ (t_0+p) \\, e^{-\\frac{t_0}{\\tau}} \\,-\\, \n(t+p) \\, e^{-\\frac{t}{\\tau}}\\,+\\,\n\\tau \\left( e^{-\\frac{t_0}{\\tau}} \\,-\\, e^{-\\frac{t}{\\tau}} \\right) \\right] \n\\end{array} \\]\n%\nFinally, replacing back:\n%\n\\[ r_0 = r - v \\, (t-t_0) \\, ,~~~~~~~~~~~~~~~t + p = \\frac{r}{v} \\]\n%\nwe get:\n%\n\\begin{equation}\n\\label{bordersolv}\n\\begin{array}{l l}\n\\sigma(r,t) = & \\left[ 1 - \\frac{v}{r} (t-t_0) \\right] \\sigma(r-v(t-t_0),t_0) \n\\,+\\, A \\, \\tau \\, \\times \\\\\n & \\\\\n\\multicolumn{2}{r}{\n\\times \\left[ \\left( 1 - \\frac{v}{r} (t-t_0) \\right)\\, e^{-\\frac{t_0}{\\tau}}\n\\,-\\, e^{-\\frac{t}{\\tau}} \\,+\\, \\frac{v}{r} \\, \\tau \n\\left( e^{-\\frac{t_0}{\\tau}} \\,-\\, e^{-\\frac{t}{\\tau}} \\right) \\right]}\n\\end{array}\n\\end{equation}\n%\nLet's now set the initial conditions at $t_0$. If radial flows ``activate'' \nat a time {\\mbox{$t_0=T_{rf} \\geq 0$}} \nthe surface density distribution for $t \\leq T_{rf}$ is determined just\nby the accretion profile:\n%\n\\[ \\sigma(r,T_{rf})=A\\, \\tau\\, \\left( 1\\,-\\,e^{-\\frac{T_{rf}}{\\tau}} \\right) \\]\n%\n(see Eq.~\\protect{\\ref{eqinfall}}) and Eq.~(\\protect{\\ref{bordersolv}})\nbecomes in fact Eq.~(\\protect{\\ref{borderconditionTrf}}). \nHere in our test case, Eq.~(\\protect{\\ref{borderconditionTrf}}) \nis the exact analytical description of the surface density profile over \nthe whole disc (a part from the centre $r=0$, which is a singular point).\n\nAs a representative test, let's consider the case {\\mbox{$\\tau=3$~Gyr}},\n$T_{rf}=0$ and\n$v=-1$~km~sec$^{-1}$.\nThe relevant analytical solution is plot in\nFig.~\\protect{\\ref{testflatfig}} for $t=t_G=15$~Gyr (thick solid line).\nThe numerical models used for comparison cover the radial range 2\nto 20~kpc and adopt a flat accretion profile $A(r) \\equiv A$. \nTheir outer edge does match exactly with the analytical counterpart, since the\nboundary condition at $r=20$~kpc is given by the analytical \nexpression~(\\protect{\\ref{borderconditionTrf}}) itself.\nBut the predictions of numerical models at inner radii tend to deviate\nfrom the reference density profile, and the mismatch is larger:\n%\n\\begin{enumerate}\n\\item\nthe larger the typical timestep of the model;\n\\item\nfor a fixed timestep, the thinner the shells (compare upper to lower panel).\n\\end{enumerate}\n%\nFor a typical shell width of 1~kpc, for instance, a good match is obtained \nwith model timesteps of $2 \\times 10^{-2}$~Gyr, while \nmodel shells of\n0.5~kpc an acceptable profile is obtained only with timesteps of \n$2 \\times 10^{-3}$~Gyr.\n%\nTherefore, a reliable representation of radial gas flows is obtained only\nwith a suitably small timestep; how small, is related to the \nwidth of the shells, namely to the resolution of the grid spacing. \n\n\\medskip\n{\\it Selecting the grid spacing.}\nSince our \nmodels are to simulate a disc with an exponential profile,\nas a second test we consider a gaseous disc with uniform and constant infall \ntime-scale and inflow velocity, analogous to the previous case, but with an \nexponential profile. Namely, in the representative differential \nequation~(\\protect{\\ref{radfnoSF}})\nthe accretion profile $A(r)$ declines exponentially outward:\n%\n\\[ A(r) = A(r_{\\odot}) \\,\\, e^{-\\frac{r-r_{\\odot}}{r_d}} \\]\n%\nEq.~(\\protect{\\ref{radfnoSF}}) can then be written:\n%\n\\[ \\frac{\\partial \\sigma}{\\partial t}\\,+\\,v\\,\\frac{\\partial \\sigma}{\\partial r}\n = \nA(r_{\\odot}) \\, e^{\\frac{r_{\\odot}}{r_d}}\n\\, e^{-\\frac{r}{r_d}} \\, e^{-\\frac{t}{\\tau}} \\,-\\, \n\\frac{v}{r} \\,\\sigma \\]\n%\n%%%%%%%Figure B2%%%%%%%\n\\begin{figure}[ht]\n\\centerline{\\psfig{file=figB2.ps,angle=-90,width=8.9truecm}}\n\\caption{Exact analytical solution for an exponential accretion profile \nwith inflows compared to a numerical model with 40 shells \nequally spaced in logarithmic scale.}\n\\label{bestexpfig}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%\n%\nThis is another linear, first order, partial differential equation of the same\nkind as (\\protect{\\ref{bordereq}}), and can be solved with analogous procedure\ninto:\n%\n\\begin{equation}\n\\label{borderexpgen}\n\\begin{array}{l l}\n\\sigma(r,t) \\, = & \\left[ 1 - \\frac{v}{r} (t-t_0) \\right] \n\\sigma(r-v(t-t_0),t_0) \\,+\\, \\\\\n & +\\, \\frac{ A(r_{\\odot}) \\, e^{-\\frac{r-r_{\\odot}}{r_d}}} \n{\\frac{1}{\\tau}+\\frac{v}{r_d}} \\, \n\\left[ \\left( 1-\\frac{v}{r} (t-t_0) \\right) e^{ - \\frac{t_0}{\\tau} +\n\\frac{v}{r_d}(t-t_0)} \\,+ \\right. \\\\\n & \\left. -\\, e^{-\\frac{t}{\\tau}} \\,+\\, \n\\frac{v}{r} \\frac{ e^{-\\frac{t_0}{\\tau}+ \\frac{v}{r_d}(t-t_0)} -\ne^{-\\frac{t}{\\tau}} }{\\frac{1}{\\tau}+\\frac{v}{r_d}} \\right]\n\\end{array}\n\\end{equation}\n%\nNotice that Eq.~(\\protect{\\ref{bordersolv}}) for a flat profile is recovered\nfrom~(\\protect{\\ref{borderexpgen}}) for $r_d \\longrightarrow \\infty$. \nIf radial inflows set in at time $t_0=T_{rf} \\geq 0$, \nfrom \n%\n\\[ \\sigma(r,T_{rf}) = A(r_{\\odot}) \\,\\, e^{-\\frac{r-r_{\\odot}}{r_d}} \\, \n\\tau \\, ( 1- e^{-\\frac{T_{rf}}{\\tau}}) \\]\n%\nwe get:\n%\n\\begin{equation}\n\\label{borderexp}\n\\begin{array}{l l}\n\\sigma(r,t) & = A(r_{\\odot}) \\, e^{-\\frac{r-r_{\\odot}}{r_d}} \\left\\{\n\\tau \\, \\left( 1 \\,-\\, e^{-\\frac{T_{rf}}{\\tau}} \\right) \\, \ne^{\\frac{v}{r_d} (t-T_{rf})} \\,+ \\right. \\\\\n & \\left. +\\, \n\\frac{ e^{ \\frac{v}{r_d} t - \\left(\\frac{1}{\\tau}+\\frac{v}{r_d}\\right) T_{rf}} \n\\,-\\, e^{-\\frac{t}{\\tau}} }\n{\\frac{1}{\\tau}+\\frac{v}{r_d}} \\,+ \\right. \\\\\n\\\\\n & \\left. + \\frac{v}{r} \\left[ \\frac{ e^{ \\frac{v}{r_d} t - \n\\left( \\frac{1}{\\tau} + \\frac{v}{r_d} \\right) T_{rf}} - e^{-\\frac{t}{\\tau}}}\n{\\left( \\frac{1}{\\tau}+\\frac{v}{r_d} \\right)^2} \\,-\\, (t-T_{rf}) \\times\n\\right. \\right. \\\\\n\\multicolumn{2}{c}{ \\left. \\left. \\times \\left(\n\\tau \\left( 1 \\,-\\, e^{-\\frac{T_{rf}}{\\tau}} \\right) \ne^{\\frac{v}{r_d} (t-T_{rf})} \\,+\\,\n\\frac{ e^{ \\frac{v}{r_d} t - \\left(\\frac{1}{\\tau}+\\frac{v}{r_d}\\right) T_{rf}}}\n{\\frac{1}{\\tau}+\\frac{v}{r_d}} \n\\right) \\right] \\right\\} } \n\\end{array}\n\\end{equation}\n\nWe compared this second analytical case to our\nnumerical model, where an exponential accretion profile was adopted between \n2 and 20~kpc, and at the outer edge the boundary condition\n(\\protect{\\ref{borderconditionTrf}}) was replaced\nby~(\\protect{\\ref{borderexp}}).\nOur tests showed that in this case the analytical profile is better \nreproduced the larger the number of shells, i.e.\\ the finer the grid spacing.\nA good match \nis obtained especially when model shells\nare equally spaced in the logarithmic, rather than linear, scale; namely when \nthe shells are chosen, in this case of an exponential accretion profile, so as\nto contain roughly the same mass, rather than cover the same radial width. \nFig.~\\protect{\\ref{bestexpfig}} shows in fact the analytical solution\n(\\ref{borderexp})\n(for $r_d=4$~kpc, $\\tau=3$, $T_{rf}=0$ and $v=-1$) together with a \ncorresponding numerical model with 40 shells logarithmically spaced\n(from 0.1~kpc wide for the inner ones to \n$\\sim$1~kpc wide for the outer ones).\n\nWith such a grid spacing, our tests with the reference flat profile \nof Fig.~\\protect{\\ref{testflatfig}}\nindicate $10^{-4}$~Gyr as a suitable timestep \nto obtain stable solutions for velocities up to the order of \n{\\mbox{1~km~sec$^{-1}$}}.\n\nIn the light of all these tests, in our chemical models we adopted a\ngrid spacing of 35 shells from 2.5 to 20~kpc, equally spaced in \nlogarithmic scale and a typical timestep \nof $10^{-4}$~Gyr (see \\S\\protect{\\ref{numericalradf}}).\nOf course, the suitable timestep depends also on the velocity field: \nflows with higher velocities require shorter integration timesteps.\nWhenever we need to consider much larger speeds than {\\mbox{1~km~sec$^{-1}$}},\nas might be the case for the strong flows induced by the Bar, we reduce the \ntimestep in proportion.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{thebibliography}{}\n\n\\bibitem{}\nAlloin D., Edmunds M.G., Lindblad P.O., Pagel B.E.J., A\\&A 101, 377\n\n\\bibitem{}\nBertin G., Lin C.C., 1996, {\\em Spiral structure in galaxies -- A density\nwave theory}, MIT Press, Cambridge, Massachusetts\n\n\\bibitem{}\nBinney J.J., 1995, S\\&T 89, 20\n\n\\bibitem{}\nBinney J.J., Gerhard O.E., Stark A.A., Bally J., Uchida K.I., 1991,\nMNRAS 252, 210\n\n\\bibitem{}\nBinney J.J., Gerhard O.E., Spergel D.N., 1997, MNRAS 288, 365\n\n\\bibitem{}\nBlitz L., Spergel D.N., 1991, ApJ 379, 631\n\n\\bibitem{}\nChamcham K., Tayler R.J., 1996, MNRAS 266, 282\n\n\\bibitem{}\nClarke C.J., 1989, MNRAS 238, 283\n\n\\bibitem{}\nCombes F., Gerin M., 1985, A\\&A 150, 327\n\n\\bibitem{}\nDame T.M., 1993, in {\\em Back to the Galaxy} S.\\ Holt, F. Verter (eds.),\np.~267\n\n\\bibitem{}\nDopita M.A., Ryder S.D., 1994, ApJ 430, 163\n\n\\bibitem{}\nDutil Y., Roy J.R., 1999, ApJ 516, 62\n\n\\bibitem{}\nDwek E., Arendt R.G., Hauser M.G., et~al., 1995, ApJ 445, 716\n\n\\bibitem{}\nEdmunds M.G., Greenhow R.M., 1995, MNRAS 272, 241\n\n\\bibitem{}\nEnglmeier P., Gerhard O.E., 1999, MNRAS 304, 512\n\n\\bibitem{}\nEskridge P.B., Frogel J.A., Pogge R.W., Quillen A.C., Davies~R.L., et~al.,\n1999, ApJ in press {\\sf (astro--ph 9910479)}\n\n\\bibitem{}\nFich M., Silkey M., 1991, ApJ 366, 107\n\n\\bibitem{}\nFriedli D., Benz W., Kennicutt R.C., 1994, ApJ 430, L10\n\n\\bibitem{}\nFux R., 1997, A\\&A 327, 983\n\n\\bibitem{}\nFux R., 1999, A\\&A 345, 787\n\n\\bibitem{}\nGerhard O.E., 1996, IAU Symp.~169, 79\n\n\\bibitem{}\nGerhard O.E., 1999, ASP Conf.\\ Ser.\\ 182 {\\sf (astro--ph 9902247)}\n\n\\bibitem{}\nG\\\"otz M., K\\\"oppen J., 1992, A\\&A 262, 455\n\n\\bibitem{}\nGummersbach C.A., Kaufer A., Sch\\\"afer A.D., Szeifert T., Wolf~B., 1998,\nA\\&A 338, 881\n\n\\bibitem{}\nJungwiert B., Palou\\v{s} J., 1996, A\\&A 311, 397\n\n\\bibitem{}\nKennicutt R.C., 1989, ApJ 344, 685\n\n\\bibitem{}\nKennicutt R.C., 1998, ApJ 498, 541\n\n\\bibitem{}\nK\\\"oppen J., 1994, A\\&A 281, 26\n\n\\bibitem{}\nLacey C.G., Fall M., 1985, ApJ 290, 154\n\n\\bibitem{}\nLin \\& Pringle, 1987, ApJ 320, L87\n\n\\bibitem{}\nLiszt H.S., Burton W.B., 1980, ApJ 236, 779\n\n\\bibitem{}\nMartin P., Roy J.R., 1994, ApJ 424, 599\n\n\\bibitem{}\nMartinet L., Friedli D., 1997, A\\&A 323, 363\n\n\\bibitem{}\nMayor M., Vigroux L., 1981, A\\&A 98, 1\n\n\\bibitem{}\nMulder W.A., Liem B.T., 1986, A\\&A 157, 148\n\n\\bibitem{}\nNg Y.K., Bertelli G., Chiosi C., Bressan A., 1996, A\\&A 310, 771\n\n\\bibitem{}\nNikolaev S., Weinberg M.D., 1997, ApJ 487, 885\n\n\\bibitem{}\nPaczynski B., Stanek K.Z., Udalski A., et~al., 1994, ApJ 435, L113\n\n\\bibitem{}\nPeters W.L., 1975, ApJ 195, 617\n\n\\bibitem{}\nPitts E., Tayler R.J., 1996, MNRAS 280, 1101\n\n\\bibitem{}\nPitts E., Tayler R.J., 1989, MNRAS 240, 373\n\n\\bibitem{}\nPortinari L., 1998, PhD Thesis, University of Padova, Italy\n\n\\bibitem{}\nPortinari L., Chiosi C., 1999, A\\&A 350, 827 (PC99)\n\n\\bibitem{}\nPortinari L., Chiosi C., Bressan A., 1998, A\\&A 334, 505 (PCB98)\n\n\\bibitem{}\nPress W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P., 1986,\n{\\em Numerical recipes}, Cambridge University Press\n\n\\bibitem{}\nQuirk W.J., 1972, ApJ 176, L9\n\n\\bibitem{}\nRaboud D., Grenon M., Martinet L., Fux R., Udry S., 1998, A\\&A 335, L61\n\n\\bibitem{}\nRubin R.H., Simpson J.P., Haas M.R., Erickson E.F., 1991, ApJ 374, 564\n\n\\bibitem{}\nRudolph A.L., Simpson J.P., Haas M.R., Erickson E.F., Fich~M., 1997,\nApJ 489, 94\n\n\\bibitem{}\nSchwarz M.P., 1981, ApJ 247, 77\n\n\\bibitem{}\nSchwarz M.P., 1984, MNRAS 209, 93\n\n\\bibitem{}\nSevenster M., 1997, PhD thesis, Leiden University (the Netherlands)\n\n\\bibitem{}\nSevenster M., 1999, MNRAS 310, 629\n\n\\bibitem{}\nSevenster M., Saha P., Valls--Gabaud D., Fux R., 1999, {\\mbox{MNRAS 307, 584}}\n\n\\bibitem{}\nShaver P.A., McGee R.X., Newton M.P., Danks A.C., Pottasch~S.R., 1983,\nMNRAS 204,53\n\n\\bibitem{}\nSimpson J.P., Colgan S.W.J., Rubin R.H., Erickson E.F., Hass~M.R., 1995,\nApJ 444, 721\n\n\\bibitem{}\nSmartt S.J., Rolleston W.R.J., 1997, ApJ 481, L47\n\n\\bibitem{}\nSommer-Larsen J., Yoshii Y., 1990, MNRAS 243, 468\n\n\\bibitem{}\nStanek K.Z., Mateo M., Udalski A., et~al., 1994, ApJ 429, L73\n\n\\bibitem{}\nStanek K.Z., Udalski A., Szymanski M., et~al., 1997, ApJ 477, 163\n\n\\bibitem{}\nTalbot R.J., Arnett D.W., 1971, ApJ 170, 409\n\n\\bibitem{}\nThon R., Meusinger H., 1998, A\\&A 338, 413\n\n\\bibitem{}\nTinsley B.M., 1980, Fund.\\ Cosmic Phys.\\ 5, 287\n\n\\bibitem{}\nTinsley B.M., Larson R.B., 1978, ApJ 221, 554\n\n\\bibitem{}\nToomre A., 1964, ApJ 139, 1217\n\n\\bibitem{}\nTosi M., 1988, A\\&A 197, 33\n\n\\bibitem{}\nUnavane M., Gilmore G., 1998, MNRAS 295, 145\n\n\\bibitem{}\nVila--Costas M.B., Edmunds M.G., 1992, MNRAS 259, 121\n\n\\bibitem{}\nVilchez J.M., Esteban C., 1996, MNRAS 280, 720\n\n\\bibitem{}\nde Vaucouleurs G., 1964, IAUS 20, 195\n\n\\bibitem{}\nWada K., Taniguchi Y., Habe A., Hasegawa T., 1994, ApJ 437, L123\n\n\\bibitem{}\nWeinberg M.D., 1992, ApJ 384, 81\n\n\\bibitem{}\nWeinberg M.D., 1994, ApJ 420, 597\n\n\\bibitem{}\nWeiner B., Sellwood J.A., 1996, IAU Symp.~169, 145\n\n\\bibitem{}\nWeiner B., Sellwood J.A., 1999, ApJ 524, 112\n\n\\bibitem{}\nYuan C., 1993, PASP 105, 657\n\n\\bibitem{}\nYoshii Y., Sommer-Larsen J., 1989, MNRAS 236, 779\n\n\\bibitem{}\nZhao H.S., de Zeeuw P.T., 1998, MNRAS 297, 449\n\n\\bibitem{}\nZhao H.S., Spergel D.N., Rich R.M., 1994, AJ 108, 2154\n\n\\bibitem{}\nZhao H.S., Spergel D.N., Rich R.M., 1995, ApJ 440, L13\n\n\\bibitem{}\nZhao H.S., Rich R.M., Spergel D.N., 1996, MNRAS 282, 175\n\n\\end{thebibliography}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002145.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem{}\nAlloin D., Edmunds M.G., Lindblad P.O., Pagel B.E.J., A\\&A 101, 377\n\n\\bibitem{}\nBertin G., Lin C.C., 1996, {\\em Spiral structure in galaxies -- A density\nwave theory}, MIT Press, Cambridge, Massachusetts\n\n\\bibitem{}\nBinney J.J., 1995, S\\&T 89, 20\n\n\\bibitem{}\nBinney J.J., Gerhard O.E., Stark A.A., Bally J., Uchida K.I., 1991,\nMNRAS 252, 210\n\n\\bibitem{}\nBinney J.J., Gerhard O.E., Spergel D.N., 1997, MNRAS 288, 365\n\n\\bibitem{}\nBlitz L., Spergel D.N., 1991, ApJ 379, 631\n\n\\bibitem{}\nChamcham K., Tayler R.J., 1996, MNRAS 266, 282\n\n\\bibitem{}\nClarke C.J., 1989, MNRAS 238, 283\n\n\\bibitem{}\nCombes F., Gerin M., 1985, A\\&A 150, 327\n\n\\bibitem{}\nDame T.M., 1993, in {\\em Back to the Galaxy} S.\\ Holt, F. Verter (eds.),\np.~267\n\n\\bibitem{}\nDopita M.A., Ryder S.D., 1994, ApJ 430, 163\n\n\\bibitem{}\nDutil Y., Roy J.R., 1999, ApJ 516, 62\n\n\\bibitem{}\nDwek E., Arendt R.G., Hauser M.G., et~al., 1995, ApJ 445, 716\n\n\\bibitem{}\nEdmunds M.G., Greenhow R.M., 1995, MNRAS 272, 241\n\n\\bibitem{}\nEnglmeier P., Gerhard O.E., 1999, MNRAS 304, 512\n\n\\bibitem{}\nEskridge P.B., Frogel J.A., Pogge R.W., Quillen A.C., Davies~R.L., et~al.,\n1999, ApJ in press {\\sf (astro--ph 9910479)}\n\n\\bibitem{}\nFich M., Silkey M., 1991, ApJ 366, 107\n\n\\bibitem{}\nFriedli D., Benz W., Kennicutt R.C., 1994, ApJ 430, L10\n\n\\bibitem{}\nFux R., 1997, A\\&A 327, 983\n\n\\bibitem{}\nFux R., 1999, A\\&A 345, 787\n\n\\bibitem{}\nGerhard O.E., 1996, IAU Symp.~169, 79\n\n\\bibitem{}\nGerhard O.E., 1999, ASP Conf.\\ Ser.\\ 182 {\\sf (astro--ph 9902247)}\n\n\\bibitem{}\nG\\\"otz M., K\\\"oppen J., 1992, A\\&A 262, 455\n\n\\bibitem{}\nGummersbach C.A., Kaufer A., Sch\\\"afer A.D., Szeifert T., Wolf~B., 1998,\nA\\&A 338, 881\n\n\\bibitem{}\nJungwiert B., Palou\\v{s} J., 1996, A\\&A 311, 397\n\n\\bibitem{}\nKennicutt R.C., 1989, ApJ 344, 685\n\n\\bibitem{}\nKennicutt R.C., 1998, ApJ 498, 541\n\n\\bibitem{}\nK\\\"oppen J., 1994, A\\&A 281, 26\n\n\\bibitem{}\nLacey C.G., Fall M., 1985, ApJ 290, 154\n\n\\bibitem{}\nLin \\& Pringle, 1987, ApJ 320, L87\n\n\\bibitem{}\nLiszt H.S., Burton W.B., 1980, ApJ 236, 779\n\n\\bibitem{}\nMartin P., Roy J.R., 1994, ApJ 424, 599\n\n\\bibitem{}\nMartinet L., Friedli D., 1997, A\\&A 323, 363\n\n\\bibitem{}\nMayor M., Vigroux L., 1981, A\\&A 98, 1\n\n\\bibitem{}\nMulder W.A., Liem B.T., 1986, A\\&A 157, 148\n\n\\bibitem{}\nNg Y.K., Bertelli G., Chiosi C., Bressan A., 1996, A\\&A 310, 771\n\n\\bibitem{}\nNikolaev S., Weinberg M.D., 1997, ApJ 487, 885\n\n\\bibitem{}\nPaczynski B., Stanek K.Z., Udalski A., et~al., 1994, ApJ 435, L113\n\n\\bibitem{}\nPeters W.L., 1975, ApJ 195, 617\n\n\\bibitem{}\nPitts E., Tayler R.J., 1996, MNRAS 280, 1101\n\n\\bibitem{}\nPitts E., Tayler R.J., 1989, MNRAS 240, 373\n\n\\bibitem{}\nPortinari L., 1998, PhD Thesis, University of Padova, Italy\n\n\\bibitem{}\nPortinari L., Chiosi C., 1999, A\\&A 350, 827 (PC99)\n\n\\bibitem{}\nPortinari L., Chiosi C., Bressan A., 1998, A\\&A 334, 505 (PCB98)\n\n\\bibitem{}\nPress W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P., 1986,\n{\\em Numerical recipes}, Cambridge University Press\n\n\\bibitem{}\nQuirk W.J., 1972, ApJ 176, L9\n\n\\bibitem{}\nRaboud D., Grenon M., Martinet L., Fux R., Udry S., 1998, A\\&A 335, L61\n\n\\bibitem{}\nRubin R.H., Simpson J.P., Haas M.R., Erickson E.F., 1991, ApJ 374, 564\n\n\\bibitem{}\nRudolph A.L., Simpson J.P., Haas M.R., Erickson E.F., Fich~M., 1997,\nApJ 489, 94\n\n\\bibitem{}\nSchwarz M.P., 1981, ApJ 247, 77\n\n\\bibitem{}\nSchwarz M.P., 1984, MNRAS 209, 93\n\n\\bibitem{}\nSevenster M., 1997, PhD thesis, Leiden University (the Netherlands)\n\n\\bibitem{}\nSevenster M., 1999, MNRAS 310, 629\n\n\\bibitem{}\nSevenster M., Saha P., Valls--Gabaud D., Fux R., 1999, {\\mbox{MNRAS 307, 584}}\n\n\\bibitem{}\nShaver P.A., McGee R.X., Newton M.P., Danks A.C., Pottasch~S.R., 1983,\nMNRAS 204,53\n\n\\bibitem{}\nSimpson J.P., Colgan S.W.J., Rubin R.H., Erickson E.F., Hass~M.R., 1995,\nApJ 444, 721\n\n\\bibitem{}\nSmartt S.J., Rolleston W.R.J., 1997, ApJ 481, L47\n\n\\bibitem{}\nSommer-Larsen J., Yoshii Y., 1990, MNRAS 243, 468\n\n\\bibitem{}\nStanek K.Z., Mateo M., Udalski A., et~al., 1994, ApJ 429, L73\n\n\\bibitem{}\nStanek K.Z., Udalski A., Szymanski M., et~al., 1997, ApJ 477, 163\n\n\\bibitem{}\nTalbot R.J., Arnett D.W., 1971, ApJ 170, 409\n\n\\bibitem{}\nThon R., Meusinger H., 1998, A\\&A 338, 413\n\n\\bibitem{}\nTinsley B.M., 1980, Fund.\\ Cosmic Phys.\\ 5, 287\n\n\\bibitem{}\nTinsley B.M., Larson R.B., 1978, ApJ 221, 554\n\n\\bibitem{}\nToomre A., 1964, ApJ 139, 1217\n\n\\bibitem{}\nTosi M., 1988, A\\&A 197, 33\n\n\\bibitem{}\nUnavane M., Gilmore G., 1998, MNRAS 295, 145\n\n\\bibitem{}\nVila--Costas M.B., Edmunds M.G., 1992, MNRAS 259, 121\n\n\\bibitem{}\nVilchez J.M., Esteban C., 1996, MNRAS 280, 720\n\n\\bibitem{}\nde Vaucouleurs G., 1964, IAUS 20, 195\n\n\\bibitem{}\nWada K., Taniguchi Y., Habe A., Hasegawa T., 1994, ApJ 437, L123\n\n\\bibitem{}\nWeinberg M.D., 1992, ApJ 384, 81\n\n\\bibitem{}\nWeinberg M.D., 1994, ApJ 420, 597\n\n\\bibitem{}\nWeiner B., Sellwood J.A., 1996, IAU Symp.~169, 145\n\n\\bibitem{}\nWeiner B., Sellwood J.A., 1999, ApJ 524, 112\n\n\\bibitem{}\nYuan C., 1993, PASP 105, 657\n\n\\bibitem{}\nYoshii Y., Sommer-Larsen J., 1989, MNRAS 236, 779\n\n\\bibitem{}\nZhao H.S., de Zeeuw P.T., 1998, MNRAS 297, 449\n\n\\bibitem{}\nZhao H.S., Spergel D.N., Rich R.M., 1994, AJ 108, 2154\n\n\\bibitem{}\nZhao H.S., Spergel D.N., Rich R.M., 1995, ApJ 440, L13\n\n\\bibitem{}\nZhao H.S., Rich R.M., Spergel D.N., 1996, MNRAS 282, 175\n\n\\end{thebibliography}"
}
] |
astro-ph0002146
|
Near infrared observations of E+A galaxies
|
[
{
"author": "Gaspar Galaz\\altaffilmark{1}"
}
] |
We present near-IR photometry of a selected sample of southern hemisphere E+A galaxies. The sample includes 50 galaxies from nearby ($z \sim 0.05$) and distant ($z \sim 0.3$) clusters as well as E+A galaxies from the field ($z \sim 0.1$). We also observed 13 normal early-type galaxies from the field and from clusters to be compared with the E+A sample. The photometry includes $J$, $H$ and $K_s$ apparent magnitudes and colors. Observed colors are obtained from the apparent total magnitudes and compared to spectrophotometric models of galaxy evolution GISSEL96. There is an overall agreement between integrated colors of models and observed ones, for both the E+A located in clusters and in the field, at $z \lesssim 0.1$. However, large differences are found between colors predicted from models and those observed in E+A galaxies located in clusters at $z \sim 0.3$. We also compute rest-frame colors for all the galaxies using two different sets of K-corrections, and obtain average colors for all the samples. We investigate systematic properties of the E+A sample as a function of their environment. Results seem to indicate that cluster E+As (at low redshift) are bluer than field E+As at $z \sim 0.1$. Even this conclusion does not depend whether we use comoving or rest-frame colors, nor on the models used to obtain rest-frame colors; the difference is not significant enough, considering color dispersions between the samples. If differences are real, they could imply different stellar content for the E+A galaxies located in the field, compared to the cluster E+A.
|
[
{
"name": "galaz.tex",
"string": "\\def\\etal{{\\em et al.~}}\n\\def\\H0{$H_0$ = 100 {\\it h} km s$^{-1}$ Mpc$^{-1}$}\n\\def\\wl{wavelength~}\n%\\documentstyle[12pt,epsfig,apjpt4]{article}\n%\\documentstyle[12pt,epsfig,aj_pt4]{article}\n%\\documentstyle[12pt,epsfig,aasms4]{article}\n%\\documentclass[preprint]{aastex}\n\\documentclass[flushrt]{aastex}\n%\\documentclass[preprint2]{aastex}\n%\\renewcommand{\\baselinestretch}{1.1}\n\\singlespace\n%\\doublespace\n%\\topmargin=-1.0cm\n\\usepackage{psfig}\n\\usepackage{natbib}\n\n%\\documentclass[]{article}\n\n%\\tighten \n\n%\\received{16 May 1999}\n%\\accepted{20 June 1999}\n%\\journalid{400}{1 January 2000}\n%\\articleid{11}{14}\n\n\\slugcomment{Accepted for publication in the {\\em Astronomical Journal}}\n\n\\shortauthors{Gaspar Galaz}\n\\shorttitle{E+A galaxies in the near-IR}\n\n\\begin{document}\n%\\baselineskip 2.5ex\n\n%-------------------- TITLE -----------------\n%\\title{Near infrared observations of E+A galaxies}\n\\title{E+A galaxies in the near-IR: Broad band photometry}\n\\author{Gaspar Galaz\\altaffilmark{1}} \n\\affil{Carnegie Observatories. Las Campanas \nObservatory, Casilla 601, La Serena, Chile} \n\\altaffiltext{1}{Andes-Carnegie Fellow}\n\\email{gaspar@azul.lco.cl}\n\n%\\baselineskip 1.0ex\n\\begin{abstract}\n\nWe present near-IR photometry of a selected sample of southern hemisphere E+A\ngalaxies. The sample includes 50 galaxies from \nnearby ($z \\sim 0.05$) and distant ($z \\sim 0.3$) clusters \nas well as E+A galaxies from the field ($z \\sim 0.1$).\nWe also observed 13 normal early-type galaxies from the field and from clusters\nto be compared with the E+A sample. \nThe photometry includes $J$, $H$ and $K_s$ apparent magnitudes and colors. \nObserved colors are obtained from the apparent total magnitudes and compared\nto spectrophotometric models of galaxy evolution GISSEL96. There is an \noverall agreement between integrated colors of models and observed ones, for \nboth the E+A located in clusters and in the field, at $z \\lesssim 0.1$. However, \nlarge differences are found between colors predicted from models and those observed in E+A \ngalaxies located in clusters at $z \\sim 0.3$. \n\nWe also compute \nrest-frame colors for all the galaxies using two different \nsets of K-corrections, and obtain average colors for all the samples.\n\nWe investigate systematic properties of the E+A sample as a \nfunction of their environment. Results seem \nto indicate that cluster E+As (at low redshift) are bluer than field\nE+As at $z \\sim 0.1$. Even this conclusion does not depend whether \nwe use comoving or rest-frame colors, nor\non the models used to obtain rest-frame colors; the difference is not \nsignificant enough, considering color dispersions between the samples. \nIf differences are real, they could imply different stellar content for the\nE+A galaxies located in the field, compared to the cluster E+A. \n\\end{abstract}\n\n\\keywords{galaxies: fundamental parameters --- galaxies: photometry\n \t galaxies: stellar content}\n\n\\section{Introduction}\n\nThe attention drawn to E+A galaxies (or post-starbursts) has \nincreased since it was claimed that \ntheir fraction observed in clusters is correlated with the Butcher-Oemler \neffect \\citep{butcher78, dressler83, rakos95}.\nThe E+A galaxies present a peculiar spectrum in the optical:\nstrong Balmer absorption lines, representative of a large population of A and B\nstars, but a {\\em lack} of\nemission lines typical of blue, star forming galaxies, like \n[OII]$\\lambda3727$, [OIII]$\\lambda$5007, and H$\\alpha$. \nBecause of the further detection \nof metallic absorption lines such as Mg b $\\lambda 5175$, Ca H \\& K \n$\\lambda 3934$, 3968 and Fe $\\lambda5270$, indicative of an old \npopulation dominated by G, K and M spectral types they were \ncalled E+A \\citep{dressler83}.\nIn addition, their spectra in the {\\em optical} cannot be reproduced simply by \na young stellar component without nebular emission lines: it is necessary to add an old\npopulation of stars, like the one present in \nquiescent elliptical galaxies \\citep{liu96}. \n\nDuring the last 3 years, research on the E+A galaxies has seen a revival\nafter the discovery of more such galaxies not only in nearby clusters,\nlike Coma and others (e.g. see \\citet{caldwell97} and references\ntherein), but also in the field; in particular those discovered \nduring the Las Campanas Redshift Survey (LCRS, Shectman \\etal 1996)\nby \\citet{zabludoff96}. An interesting feature\nis the apparent existence of two classes of E+A galaxies \\citep{couch87}. One \nis formed by ``blue'' post-starburst galaxies \nand the other by redder, H$\\delta$-strong (HDS)\ngalaxies \\citep{fabricant91}. These subclasses\nof E+As have colors and absorption line features related to the \nmorphology: HDS E+As have in general a noticeable bulge and/or\nspheroidal component when compared with the blue class. In addition, the\nHDS class can be divided into 2 subclasses: bulge and disk HDSs (as \nobserved in A665 and in Coma \\citep{franx93}). \n\nAn almost unexplored domain of these E+A galaxies is their \nnear-IR properties. In fact, no catalogue or systematic observations\nexist on this subject. Is the bright, red population, dominated mainly \nby giants and stars of the asymptotic giant branch (AGB) of the E+As, different\nfrom the red population of other elliptical galaxies, in particular the \nperturbed ellipticals? Is there any conspicuous signature in the \nnear-IR colors of the E+A galaxies, as in the \noptical wavelengths? Do the cluster E+A galaxies have bluer colors\nthan those in the field at these wavelengths? Are the near-IR colors of the E+A \ngalaxies similar to the colors of normal galaxies, as predicted \nby spectrophotometric models? \n\nIn this paper, we investigate these\nquestions with new data taken at Las Campanas\nObservatory, in Chile. The sample includes E+A galaxies from the \nfield (most of them from the LCRS) and from nearby clusters as well as \nclusters at $z \\sim 0.3$. \n\nThe paper is organized as follows. In \\S 2 we present the \ngalaxies selected for this work. In \\S 3 we explain the \nobservations, and in \\S 4 the data reduction procedures. In \\S 5 we present\nthe results of the photometry, the apparent\nmagnitudes, colors, and K-corrections. Both, {\\em observed} and {\\em rest-frame} \ncolors are compared\nwith colors obtained from spectrophotometric models of galaxy evolution in \\S 6. In \\S 7\nwe discuss the limitations of our results and the implications for some properties\nof the E+A galaxies from our near-IR colors. Conclusions are presented in \\S 8. \n\n\\section{The Sample}\n\nAll of the galaxies selected for this study have been spectroscopically\nclassified as E+A galaxies from the analysis of their Balmer absorption lines \n(particularly the equivalent widths of H$\\delta$ and H$\\beta$) \nand the lack of nebular emission lines, \nrepresentative of an ongoing stellar formation process. We have selected\nmost of the southern E+A galaxies existent in the literature \nat present. The sample of galaxies\nis divided into 4 subsamples. The first subsample corresponds to 21 field \nE+A galaxies from the LCRS selected from a catalogue of $\\sim 19000$ galaxies \nwith redshift between $z \\sim 0.07$ and $z \\sim 0.18$ \\citep{zabludoff96}.\nThe second subsample contains 22 E+As from the nearby clusters\nDC2048-52, DC1842-63, DC0329-52, and DC0107-46 \\citep{caldwell97} \nat $z \\sim 0.05$. \nSeven E+A galaxies from rich clusters at $z \\sim 0.31$ \n(AC103 and AC114) constitute the 3rd subsample \\citep{couch87}.\n%Three E+A galaxies from the\n%ESO-Sculptor Survey (ESS hereafter, \\citet{delapparent97, \\citet{galaz98}) \n%were also observed ($z = 0.18$, 0.23 and 0.45). \nSome ``control'' galaxies \nwere observed also (the 4th subsample, 13 galaxies). These galaxies have \nwell-known properties and provide a reference sample to compare the observables of \nthe E+A sample. The control sample includes mostly elliptical\nand lenticular galaxies (from clusters and the field), as well \nas a few galaxies between $z \\sim 0.01$ to $z \\sim 0.04$.\nTable \\ref{samples} summarizes the sample of 63 galaxies which have been observed.\n\n%%placetable{samples}\n\n\\section{Observations}\n\nAll of the observations presented here were carried out at Las Campanas Observatory, Chile,\nduring photometric conditions. Most of the images were obtained with \nthe 40-inch Swope telescope, using a NICMOS3 HgCdTe array (256 $\\times$ 256 pixels, \n0.599 arcsec/pix, $2.5 \\times 2.5$ arcmin FOV), in \nMarch, July, August and November 1998. We employed also \nthe 100-inch du Pont telescope in September 1998, with a \nNICMOS3 detector, yielding a scale of 0.42 arcsec/pix ($1.8 \\times 1.8$ arcmin FOV). \nWe use the following filters: $J$, $H$, and $K$ short ($K_s$), centered \nat 1.24$\\mu m$, 1.65$\\mu m$, and 2.16$\\mu m$, \nrespectively, and bandwidths of 0.22$\\mu m$, 0.30$\\mu m$, and 0.33$\\mu m$. \n%$J_s$ is a new variant of $J$ that has been designed to cut off \n%more of the water vapor absorption near both edges of the passband, but \n%in practice is equivalent to the $J$ band, and therefore we will call it simply $J$.\n%With the same philosophy, Ks is a variant of the Johnson K passband that \n%reduces the thermal background, by about a factor of two. However, in this\n%case there are some differences between the $K_s$ and $K$ magnitudes (depending \n%on color). \nFor a detailed discussion of the photometric system see \\citet{persson98}. \n\nBetween 5 and 8 standard stars from \\citet{persson98} were observed each night. \n%As usual, the observing methods in the NIR has to provide images corrected \n%for thermal scattered light. \nThe observation procedure for all the objects (standards included) was as follows.\nEach object was observed at several positions on the array,\nsome amount of time in each position (I call this an {\\em observing sequence} \nfor a given object in a given filter). The amount\nof time depended on the magnitude of the object, on the sky\nbrightness, and on the linearity regime of the array. The NICMOS3 becomes noticeably\nnon-linear when the total counts (sky + object) exceed 17000 ADU.\n% and the time to reach this \n%level depends on the thermal brightness of the sky and/or the brightness of the\n%object. \nWe exposed in each position between 60 and 120 seconds in $J$, \nbetween 30 and 60 seconds in $H$, and\nbetween 30 and 50 seconds in $K_s$. Total exposure times for a given observing \nsequence and filter varied between 10 and 45 minutes. For the standard stars (with magnitudes \nbetween $K_s \\approx 10 - 12$), the exposure time ranged between \n5 and 20 seconds in each position, for both telescopes. \nTypically, the number of non-redundant \npositions at which each object was observed varied between 4 and 10, depending \non the size and/or magnitude of the object. \nA pre-reduction was made at the beginning of each observing sequence\nin order to estimate the total exposure time required to reach a minimum\ncentral S/N $\\approx 12-15$. This pre-reduction consisted in the construction of a \nsky image averaging all of the stacked images for a given object (with \na sigma-clipping rejection threshold), the subtraction of the sky \nimage from each individual image, and the combination after registration\nof the individual sky-subtracted images. \n\n\\section{Data Reduction}\n\n%Before performing the photometry, and in order to remove all the instrumental \n%effects. \nThe images have to be corrected for all of the instrumental effects, namely,\nnon-linear deviations, dark-current contribution (dark subtraction),\nand pixel-to-pixel response differences (flat-field division).\n\nFor the determination of the linearity corrections, we \ntake several dome-flats with different exposure time. \nThen, we plot the ratio of the average counts and the integration time of each\nframe, as a function of the average counts. After normalizing, we \ntransform the count value I$_{in}$ of each pixel into \nI$_{out}$ = I$_{in}$ [1 + C$\\times$I$_{in}$], and we solve for the {\\em constant} C which \nproved to vary between $1.0 \\times 10^{-6}$ and \n$5.0 \\times 10^{-6}$. At 14000 counts, for example, which corresponds to \n$\\sim 75\\%$ of the whole range of the signal, the departure from linearity is \nonly 2\\%.\n\nAt the beginning of the night we took series of 20 dark frames, the\nnumber of series depending on the number of different exposure times we\nused through the night.\nThe flat-field images were constructed from (a) dome-flats and twilight \nsky-flats and (b) the raw science images \nof the night, which allowed us to construct {\\em super-flats} from the combination of \nthe individual frames.\nThe useful images for these super-flats were those where the \nobjects were faint and/or a small number of objects were observed. \nBecause galaxy fields were\nin general uncrowded, it was always possible to construct super-flats.\nTypically, each super-flat was constructed from no less than 30 science \nimages, for each filter. \nThe results show that the super-flats allow to correct for fringes appearing \nin the stacked and combined images. The fringes are present in the 3 filters ($J$, $H$ \nand $K_s$), but are particularly prominent in the H images. Except for the presence of\nfringes, the dome- and sky-flats are quite similar to the super-flats (at the\n0.6\\% level). However,\ngiven the better photon statistics of the super-flats and the fact that \nthe fringes are better represented by the super-flats\n% than %in any other kind of flat-fielding \n%procedure, \nwe chose the super-flats to remove the pixel-to-pixel variations. \nFrom the object frames, the dark and flat-fielding corrections were made \non the images using the SQIID\\footnote{Simultaneous Quad-color Infrared Imaging\nDevice software package, developed by Michael Merrill and John Mac Kenty.} reduction package,\nimplemented under IRAF\\footnote{IRAF is distributed by the National Optical Astronomy\nObservatories, which are operated by the Association of Universities \nfor Research in Astronomy, Inc., under cooperative agreement with\nthe National Science Foundation.}. \nAt this stage, a mask with the bad pixels was created (using the dark images)\nto correct those pixels by interpolation with their neighbor pixels \nin all the images. \n\nOnce the linearity corrections were done, as well as the dark correction\nand flat-fielding procedures in all the raw images, the \nprocedure to obtain stacked and combined sky-subtracted images began. This\npart was done using DIMSUM\\footnote{DIMSUM is the Deep Infrared Mosaicing Software\npackage developed by Peter Eisenhardt, Mark Dickinson, Adam Stanford, and John Ward, and\nis available via ftp from {\\tt ftp://iraf.noao.edu/iraf/contrib/dimsumV2/dimsum.tar.Z}}, \nalso implemented under IRAF. The general procedure for a \ngiven {\\em observing sequence} follows.\n\\begin{enumerate}\n\\item[(a)] A scaling factor for each image was computed using a 5$\\sigma$ iterated\nrejection method about the mean. The scaling factor is the median of the\nunrejected pixels, and is stored as a descriptor in the image header. \nThis provides a first estimate for the sky level. \n\\item[(b)] For each image in the observing sequence, a specified number of neighboring images \nof the sequence were selected. To construct a sky image, we selected only the \nneighboring images taken within $\\pm 5$ min from the given image.\nThis provides a sample of sky images within a short-period of time \nduring which the variations of the sky level are not larger than 1\\% to 3\\% \nof the mean, in order to reduce the r.m.s. variation in \nthe thermal emission background as well as the OH sky lines, \ncharacteristic of the NIR (see Figure \\ref{sky}). Furthermore, \nthe higher background in $K_s$ produces higher shot noise\neven if this background did not vary with time. This is a key step.\n%\\begin{figure}\n%\\figurenum{0}\n%\\%epsscale{0.6}\n%\\plotfiddle{/export/data1/gaspar/postscripts/sky.ps}{10cm}{-90}{50}{50}{-256}{313}\n%\\plotone{/data1/gaspar/postscripts/sample_spec.ps}\n%\\caption{Figure showing typical sky variations in the near-IR passbands \n%$J$, $H$, and $K_s$ during 1 hour. Each point represents the mean sky\n%level for an individual image during an {\\em observing sequence}. The error bars\n%are given by the standard deviation in the image counts. Note the \n%larger error bars for the $K_s$ band, where the thermal variations are\n%in fact larger. This behavior limits the sky subtraction procedure to be\n%applied for the near-IR filters (see text).}\n%\\label{sky}\n%\\end{figure}\n\n%%placefigure{sky}\n\nAt each pixel a specified number\nof low and high values in the scaled images were rejected and the\naverage of the remainder values was taken as the sky for that pixel. The resulting sky\nimage was subtracted from the object image to create a sky subtracted object\nimage. \n\\item[(c)] Cosmic rays were found using a threshold algorithm applied to the\nratio of the image and a median filtered image. The detected cosmic rays\nwere replaced by the local median. A cosmic ray mask was\ncreated to record the location of the cosmic rays. \n\\item[(d)] For a given observing sequence, a shift list is created to define \nthe offsets between the images. To create this\nlist it is first necessary to have at least one object in common among \nall of the images of the observing sequence (usually a star). \nNext we selected a set of additional objects to improve the determination\nof the relative shifts. These objects were used\nin constructing the shift list using a centroid-based algorithm. \n\\item[(e)] A registration stage\nwas done by shifting and combining the images of the sequence.\nA matching exposure map was also created, which allows to obtain a final\nmosaic properly weighted by the effective exposure time of each section\nof the mosaic. \n\\item[(f)] To provide combined images free of ``holes''\narising from the sky subtraction, two different masks are created for \neach registered image of the observing sequence. The detailed procedure is explained \nin the DIMSUM package. \n%a mask has to be created for each registered\n%image of the sequence. The algorithm creates two different masks. \n%The first mask uses a higher threshold to identify only the brighter parts\n%of the objects. This is used to check that the cores of the objects\n%not seen in the individual images were not identified earlier as cosmic\n%rays. The second mask uses a lower threshold to identify extended\n%regions of the images covered by the objects. This mask is used to\n%exclude those regions from the sky subtraction. \n%A mask is made from the first pass image as follows. The image is\n%divided by the square root of the exposure map to account for variations\n%in the sky noise due to varying exposure times at each pixel. The sky\n%r.m.s. is computed using iterative sigma rejection and a threshold value\n%in terms of this r.m.s. is determined. Finally, an algorithm which tracks the\n%sky and threshold detections above the sky is applied. A mask of zero ADU\n%(sky) and one ADU (object) is created from the pixels above the threshold.\n%Once the masks are made for the objects in the first pass mosaic, the\n%shift list is used to make masks for every original image. Any cosmic\n%rays identifications in the cosmic ray masks of the object which are\n%within the individual object masks are then removed. \n\\item[(g)] The sky subtraction\nis repeated as in the first pass, before the masking procedure, \nexcept that the pixels in the individual masks derived from (f) are ignored. \n\\item[(h)] Finally, all the sky-subtracted images of an observing \nsequence are shifted and combined, and the different parts of the mosaic \nare scaled to an exposure time of 1 s. \n\\end{enumerate}\n\n\\section{Photometry}\n\n\\subsection{Photometric calibrations}\n\nThe photometric calibrations were done using the faint standard stars\nfrom the list of \\citet{persson98}. This list includes \nstandard magnitudes in $J$, $H$, $K$ and $K_s$ for equatorial and southern \nphotometric standard stars. Five to eight standards were observed \nevery night at airmasses similar to those of the galaxies (no larger than 1.2). \nThis minimizes the dimming and reddening due to the airmass contribution, especially in \ncolors involving the $J$ filter. \n\nInstrumental magnitudes were computed using the code SExtractor \n\\citep{bertin96}, which computes isophotal, isophotal corrected,\nand total magnitudes for all the objects detected above a given \nthreshold. We have also computed instrumental aperture magnitudes using \nDAOPHOT, and verified that DAOPHOT\naperture magnitudes for the standards do not differ by more than $0.5\\%$ from the total\nmagnitudes yielded by SExtractor. The aperture used for \nthe standards in DAOPHOT is the maximum aperture after \nanalyzing the shape of the grow curve for the instrumental magnitudes, and \ntypically take radii values $\\sim 6.0$ arcsec. We conclude that the instrumental magnitudes \ngiven by SExtractor are reliable, which we adopt hereafter. \n\nThe adopted photometric transformations between the instrumental and the calibrated \nmagnitudes are:\n\\begin{eqnarray}\n\\label{phot}\nJ & = & A_1 + j - 0.10 X \\\\ %- B_1 (j_s - k_s) \\\\\nH & = & A_2 + h - 0.04 X \\\\ %- B_2 (h - k_s) \\\\\nK_s & = & A_3 + k_s - 0.08 X %- B_3 (j_s - k_s),\n%\\addtocounter{equation}{1}\n\\end{eqnarray}\nwhere the $A_N$ coefficients ($N$ = 1, 2, 3) are the zero points,\n$X$ is the airmass, and the extinction coefficients are from \\citet{persson98}. \nNote that we do not try to solve for airmass corrections night by night, as this\ncan lead to spurious values for coefficients if the extinction is variable \nand non-gray. The latter is relevant at the filter passband edges where water\nvapor influences the effective width of the passband \\citep{persson98}. \n\nThe zero points $A_1$, $A_2$ and $A_3$ were\ndetermined on a nightly basis, and proved to vary between $1\\%$ and $7\\%$. \nWe do not include color terms in these transformations (equations 1, 2, and 3)\nsince they are smaller than 0.04 mag, a value close to the observational\nmagnitude errors. We emphasize\nthat all of the standards and the galaxies reported in this paper\nwere observed during completely photometric nights. The photometric transformations\nhave typical r.m.s. residuals of $\\sim 0.02 - 0.05$ mag on \nboth telescopes (see Figure \\ref{stds_error}). This gives an internal error\nin the photometric calibrations around 2\\% to 5\\%.\n%\\begin{figure}\n%\\figurenum{0}\n%\\epsscale{0.6}\n%\\plotfiddle{/export/data1/gaspar/postscripts/stds_errors.ps}{10cm}{-90}{50}{50}{-256}{313}\n%\\plotone{/data1/gaspar/postscripts/sample_spec.ps}\n%\\caption{Average errors in the photometric calibrations, for the standards\n%observed with the 100-inch du Pont telescope (triangles), and for the \n%standards observed with the 40-inch Swope telescope (circles). \n%Each data point corresponds to an average error of several (typically no less than 3)\n%magnitude errors for the same standard, observed in different nights.}\n%\\label{stds_error}\n%\\end{figure}\n%----------------------\n%where the $A_N$ coeficients ($N$ = 1, 2, 3) are the zero points, the $B_N$ \n%are the color terms and the $\\xi_{j_s}$, $\\xi_{h}$, and $\\xi_{k_s}$\n%are the airmasses for the filters $J_s$, $H$ and $K_s$, \n%respectively. We adopted two sets of color terms, one for the \n%40-inch runs and another for the 100-inch runs. For the 40-inch\n%runs the color terms are $B_1 = 0.07$, $B_2 = 0.01$, and $B_3 = 0.04$. \n%For the 100-inch runs they are $B_1 = 0.32$, $B_2 = 0.30$, and\n%$B_3 = 0.27$. The standard deviation for these color terms \n%from one night to another is typically 8\\% for observations \n%done at both telescopes. The zero points, on the other hand, were\n%determined nightly, and they vary from 4\\% to 12\\%. We emphasize\n%that all the standards and the galaxies reported in this paper\n%were observed during photometric nights. \n%----------------------\n\n%placefigure{stds_error}\n\nThe main source of error are, in fact, the short-term sky fluctuations (in particular\nin $K_s$), which are of the order of 3\\% to 6\\% in time intervals spanning\nthe longest exposure time of individual frames during each of the observing sequences \n(120 s in $J$, 60 s in $H$, and 50 s in $K_s$). \nSome galaxies were observed twice, even using the two telescopes, and therefore\nthere is a good estimate of the global photometric errors, which proves to be around \n7\\% for photometric nights. The observation of the same object during two \nphotometric nights but with different telescope/instrument is the best \nway to estimate the photometric quality of the data (see \\S 5.2), and the \nreal dispersion of magnitudes.\n\n\\subsection{Galaxy photometry}\n\nInstrumental apparent magnitudes for all the galaxies \nwere obtained on the registered and \ncombined images using the code SExtractor \\citep{bertin96}. \nGiven the differences in size, shape\nand luminosity of the galaxies, the total magnitude is a better \nestimator than the aperture or isophotal magnitudes. \nSExtractor computes aperture magnitudes, isophotal magnitudes\nand ``total'' magnitudes for all of the objects detected above a given threshold. \nThe total apparent instrumental magnitude for a given object is given by\none of the two following approaches. (1) It is computed using an {\\em adaptive}\naperture magnitude or (2), using a {\\em corrected} isophotal magnitude. \nIn order to give the best estimate of the total magnitude, the adaptive \naperture method is performed, except if a neighbor is suspected to \nbias the magnitude by more than 0.1 mag. If this happens, the \ncorrected isophotal magnitude is taken as the total magnitude. \nThis leads to the so-called MAG\\_BEST magnitude, in the \nSExtractor output catalogue.\n\nIn order to check the calibrated magnitudes for our galaxies, and\nto have an idea of the accuracy of our total magnitudes, we\nobserved some of the galaxies on two different nights, with the \n40-inch and the 100-inch telescopes.\nFor the 8 galaxies which were observed twice (2 for each subsample), \nwe found r.m.s differences $\\Delta J = 0.037$, \n$\\Delta H = 0.042$ and $\\Delta K_s = 0.061$. These differences, \nalthough large when taken at face value, represent the most \nrealistic errors in the total magnitudes, \nsince they were obtained with different instrumental set-ups during\ndifferent observing runs.\n\n\\subsection{Apparent magnitudes and K-corrections}\n\nOnce the instrumental magnitudes are calculated using SExtractor, they\nare transformed to the standard system using the package PHOTCAL in IRAF. \nTable \\ref{all_calib} shows the apparent\ncalibrated total magnitudes for all of the galaxies of the 4 subsamples. \n%Galaxies with values NC (Not Calibrated) in some of the magnitude \n%entries, have been\n%observed during non photometric nights, and then the magnitude is not \n%reliable (the unique case is the galaxy \\# 25, AC114\\_89, for its $K_s$ magnitude).\nThe $K_s$ magnitude for galaxy \\# 25, AC114\\_89, was not computed since it was\nobserved under possibly non-photometric conditions, and \nwas marked with a NC (not calibrated). \nNo internal reddening correction was applied to these magnitudes, nor a Galactic\nforeground extinction correction: both corrections are smaller than the photometric \nerror and, in particular, are smaller than the uncertainty given by the \nK-correction, as \nwe show in \\S 5.6. The reddening by dust is $\\Delta(J - H) \\lesssim 0.03$ and \n$\\Delta(H - K_s) \\lesssim 0.02$, if we consider a simple screen model \nbased on the reddening law of \\citet{cardelli89}. If we consider a more\ncomplicated extinction model, following the star-dust mixture recipe by\n\\citet{wise96}, the amount of reddening is similar. The correction \ndue to Galactic extinction is also small for \nthe 3 passbands ($\\lesssim 0.03$), which proves to be well within the photometric \nuncertainties (for the Galactic reddening corrections in the \nnear-IR photometric bands see \\citet{schlegel98}). We emphasize, however, that \nGalactic and internal reddening corrections are systematic effects, while the \nphotometric uncertainty is random. \nGiven their small values, no attempt is made to correct for the extinctions. \nIf we include foreground and internal extinction, \nthe $J - H$ color redden probably no more than 0.03 -- 0.05 \n(but see discussion at the end of \\S 6). \n\n%placetable{all_calib}\n\nSince the K-terms can significantly modify the intrinsic colors of the \ngalaxies, they are critical in correcting the observed colors and magnitudes\nto the galaxy rest-frame. If $m_1$ and $m_2$ are the apparent magnitudes \nin the passbands 1 and 2, respectively, for a galaxy at a redshift $z$ and with a \nknown spectral type $T$, then the rest-frame color for this galaxy is\n\\begin{equation}\nM_1 - M_2 = m_1 - m_2 - \\left\\{K_1(z,T) - K_2(z,T)\\right\\},\n\\label{rest_col}\n\\end{equation}\nwhere $M_1$ and $M_2$ are the corresponding absolute magnitudes,\n$K_1(z,T)$ and $K_2(z,T)$ are the K-corrections for the passband\n1 and 2, respectively, for the galaxy with spectral type $T$ at redshift $z$.\nK-corrections are not included in the magnitudes and colors presented in Table\n\\ref{all_calib} since they can have a wide range of values depending on \nthe spectral energy distribution (SED) employed in their computation.\nWhen the SED is not available for a given object, it is common practice (although risky) \nto adopt K-terms from the correlation between spectral type\nand morphological classification, provided the latter is available.\n\nIn our case, we only have approximate morphological types for the E+As\nfrom the literature, nor do we have spectral information for the galaxies\nin the near-infrared part of the spectra. Even though most of our E+A galaxies \nare early types, we can ask the following. How will the near-IR \nK-corrections depend on the spectrophotometric model of galaxy evolution used\nto compute them? In order to study the model dependence in $J$, $H$ and\n$K$, take for example 2 SED models which \nprovide (or allow us to compute) K-terms in the near-IR.\n%Most of the synthetic spectra lack from absorption bands which \n%actually exist between 1$\\mu m$ and 3$\\mu m$. \nThe first K-terms were taken directly from \\citet{poggianti97}, who \ncomputed K-corrections from the \nnear-UV to the infrared. \\citet{poggianti97} provides K-corrections in several bands in the \nJohnson-Bessel \\& Brett photometric system, up to $z = 3$ as a \nfunction of morphological type. The values are computed according \nto an evolutionary synthesis model that reproduces the integrated \ngalaxy spectrum in the range 1000-25000 \\AA, and uses the code of \nGISSEL93 \\citep{bruzual93}. The models are instantaneous bursts with \nsolar metallicity and Scalo IMF \\citep{scalo86}. The age after the \nburst gives the SED which is compared with galaxies of known morphological\ntype through colors. Note that the comparison is done in the optical part of the \nspectrum, mostly between 3000 and 8000 \\AA. \nThe second set of K-corrections were derived using the model PEGASE\\footnote{Projet \nd'Etude des GAlaxies par Synth\\`ese Evolutive.}\n\\citep{fioc97} to generate synthetic spectra between 7000 \\AA~\nand 30000 \\AA, and convolving these SEDs with the filter response functions\n(see Persson \\etal 1998), using the definition of the K-correction \\citep{oke68}. \n%This allows also us to compute a transformation between $K$ and \n%$K_s$ magnitudes (see below). \n\nFigure \\ref{K_poggianti} shows the K-corrections in $J$, $H$ and $K$, calculated by \n\\citet{poggianti97} for 3 different morphological types, namely, \nE (solid line), Sa (dotted line) and Sc (dashed line).\nNote that the K-corrections in the near-IR are not necessarily\nsmall. Nevertheless, in most of\nthe photometric bands they do not depend strongly on the spectral type\nor the morphological type. \nK-corrections are large (and negative) for the \n$K$ band, for $z \\lesssim 0.5$, for all galaxy types (this makes galaxies to appear\nbrighter than they really are). The average \nredshift in our sample is $\\approx$ 0.08, and K-corrections \nin all the bands are less than 0.1 mag for most of the cases. The \nexceptions are the E+A galaxies in AC103 and AC104 (at $z \\sim 0.3$). \nFor these objects K-corrections can be larger and around $-0.3$ mag in $K$\nfor the late type galaxies. \nFigure \\ref{K_pegase} shows the K-term calculated from PEGASE. \nThese K-corrections are calculated from SEDs with solar metallicity\nand also instantaneous bursts. The IMF is from \\citet{scalo86}.\nIn PEGASE, the authors define their morphological types by directly comparing \nspectra generated from their models with \\citet{kennicutt92} optical \nspectra of nearby galaxies. \\citet{poggianti97}, on the other hand, matches \ncolors obtained from her model with observed colors of galaxies, taken \nfrom \\citet{persson79} and \\citet{bower92a, bower92b}. \n\n\n%placefigure{K_poggianti}\n%placefigure{K_pegase}\n\nComparing Figure \\ref{K_poggianti} and \\ref{K_pegase}, we conclude that although\nthe K-corrections are quite different from one model to another, they are similar\nfor $z \\lesssim 0.1$. For $z \\gtrsim 0.2$, differences are larger. \nK-corrections for different Hubble types are more similar if they are derived \nfrom PEGASE than from the models of Poggianti. Figure \\ref{K_diff} shows the\ndifferences between these K-corrections for the two models, in the 3 passbands,\nand for the 3 Hubble types. Up to $z \\sim 0.5$ the difference for the E type\nin $J$ and $H$ is less than 0.05 mag. However, the difference is $\\sim \n0.1$ mag for the later types. Equation (\\ref{rest_col}) implies that the \ndifferences in $J - H$ will be less than 0.05 mag. However, this is not\nthe case for colors involving the $K$ band ($J - K$ and $H - K$), due \nto the large difference in the K-corrections, for all the Hubble types, \nas shown also in Figure \\ref{K_diff}. The difference in $K$ for the K-corrections\nreaches values $\\sim 0.4$ mag at $z \\sim 0.3$. This shows that K-correction \nuncertainty will have the largest impact on rest-frame colors. \nOther studies also show large differences between their K-corrections, although some \nof them are comparable to the values of this work, showing also large negative K-corrections\nin $K$ \\citep{frogel78, persson79, bershady95}. For example, \\citet{bershady95} \nobtains type-averaged K-corrections in $K$,\nreaching $-0.33$ and $-0.60$ at $z = 0.14$ and $z = 0.30$, respectively. These values\nare larger than values from \\citet{poggianti97}, but similar to those obtained \nfrom PEGASE (see Figure \\ref{K_poggianti} and \\ref{K_pegase}). \n\n%placefigure{K_diff}\n\n\\section{Comparison with models}\n\nAs shown in the preceding section, K-corrections in the near-IR can be \nvery different depending on the spectrophotometric models used. Therefore,\nwe do not use rest-frame colors, i.e. we do not de-redshift the data. \nInstead, we {\\em redshift} current epoch SEDs. Although this approach is similar\nto work with rest-frame colors, it is more robust, since the SEDs of the current \nepoch models can be determined absolutely. In order to give an idea whether\nsynthetic SEDs compare well with spectra of galaxies at the current \nepoch, we consider GISSEL96 models \\citep{charlot96}\nand compare them with real, local galaxy spectra of known morphological types, \ngiven by \\citet{kennicutt92}. As it is well-known, the \nage-metallicity degeneracy prevents us for deriving age and metallicity directly \nfrom colors, as was shown by \\citet{worthey94, ferreras98}. Therefore, we consider \ninstantaneous bursts of fixed (solar) metallicity. Subsequent evolution \nis determined by adopting passive stellar evolution, measured in Gyrs and \nindicated by the label ``age'' for each model spectrum in Figure \\ref{spectra}. \nA simple $\\chi^2$ test is used to determine the model spectra closest to the \nobserved (Kennicutt) sample. We use a starting sample of 20 GISSEL96 spectra\nand 27 spectra representative of normal galaxies of known Hubble types \n\\citep{galaz98}. Figure \\ref{spectra} shows the better spectral match between some \nKennicutt spectra and the 20 selected GISSEL96 models.\n\n%placefigure{spectra}\n\nThe Hubble sequence fits well with an evolutionary sequence in the optical,\nbut care has to be taken in the interpretation since \nmore than one solution can be obtained from a synthetic set where both age and\nmetallicity vary \\citep{ronen99}. Even though metallicity can vary from one galaxy\nto another, it is realistic to set metallicity close to solar. Extremely metal-poor\n(Z $\\lesssim 0.5$ Z$_\\odot$) or metal-rich (Z $\\gtrsim 1.5$ Z$_\\odot$) cases are unlikely\nin this set of galaxies \\citep{liu96}. Moreover, the fact that colors are obtained \nfrom {\\em integrated} total apparent magnitudes, imply that colors are an average\nover the whole galaxy light and therefore likely to be representative of\nsolar metallicity or lower in the luminosity weighted mean (see for\nexample \\citet{edmunds92}). \n\nIn order to compare the observed colors with models, we take the 20 spectra from \nGISSEL96 and we ``redshift'' them to several redshift values (from the rest-frame to \n$z = 0.5$). Afterwards, we compute synthetic colors using $J$, $H$ and $K_s$ passbands\n\\citep{persson98} for the 20 synthetic spectra. \nFigure \\ref{obs_colors} shows the color-color diagram for the E+A sample and the \ncontrol sample (indicated as filled circles), as well as for the model spectra \n(indicated as open symbols) situated at different redshifts (as indicated by labels). \nWe include 3 different evolving tracks in figure \\ref{obs_colors}, for instantaneous\nbursts after 1 Gyr, 3 Gyr and 16 Gyr indicated by circles, squares, and triangles,\nrespectively. After 10 Gyr, the near-IR colors are almost \nindependent of age, for a given redshift. \n\nFigure \\ref{obs_colors} shows that there is an overall agreement between near-IR \ncolors of all subsamples and models, except for subsample 3. The average \ncolor $<H - K_s> = 0.41$ $(\\sigma = 0.05)$ of subsample 1 (average redshift \n$<z> = 0.09$, $\\sigma = 0.02$) agrees well with any model older than 3 Gyr at $z = 0.10$.\nHowever, the average $<J - H> = 0.66$ $(\\sigma = 0.06)$ appears bluer than the same\nmodels by $\\sim 0.1$ mag. Otherwise, $<J - H>$ is well fitted by a \nmodel with age $\\lesssim 3$ Gyr at $z = 0.10$, but then $<H - K_s>$ of \nsubsample 1 is redder by $\\sim 0.1$ mag. These differences are twice the\ncolor dispersion for this subsample. Therefore we can conclude that colors\nof the models and the data do not differ by more than $2\\sigma$. \nIn subsample 2, the average\ncolors $<H - K_s> = 0.29$ $(\\sigma = 0.07)$ and \n$<J - H> = 0.69$ $(\\sigma = 0.05)$, with average redshift $<z> = 0.046$ $(\\sigma = 0.014)$, \nare well fitted by a model at $z = 0.05$ and 2.8 Gyr. Subsample 3, having\n$<H - K_s> = 0.61$ $(\\sigma = 0.23)$, \n$<J - H> = 0.75$ $(\\sigma = 0.25)$, and average redshift $<z> = 0.31$ $(\\sigma = 0.01)$\nis not fitted by the GISSEL96 models, even though the average color $<H - K_s>$\nis closer to the $z = 0.3$ redshifted color of models. Subsample 4 (the \ncontrol sample) matches the models colors well, despite the rather large scatter. \nThis subsample has average colors $<H - K_s> = 0.29$ $\\sigma = 0.08)$, \n$<J - H> = 0.74 (\\sigma = 0.06)$, and average redshift $<z> = 0.030$ $(\\sigma = 0.012)$.\nThese average colors correspond to a model located at $z = 0.05$ and age 3 Gyr.\nThis subsample shows a larger scatter in the color-color diagram. \nMost of these galaxies are nearby\ngalaxies (from the PGC and NGC catalogues) and some \ngalaxies from DC clusters \\citep{caldwell97}. All have\nsecure Hubble types, and most of them have known photometric properties in the\noptical (for $B$ and $R$ total magnitudes see Table \\ref{all_calib}). \nThe majority of these galaxies are well matched by the \ncolors provided by the spectrophotometric models, for ages representative of\nearly type galaxies. These\ngalaxies have large apparent radii, and therefore, their\nphotometry is more sensitive to color gradients. This is not a problem for more\ndistant galaxies because of the poorer spatial resolution. \n\n%placefigure{obs_colors}\n\nNow we compare color properties of subsample 1 (field E+As from the LCRS) \nand 2 (cluster E+As). From Figure \\ref{obs_colors} it is apparent that subsample 1\nhas the same average $<J - H>$ (with a difference of 0.03), but a \nredder $<H - K_s>$ than subsample 2 (see above). The difference of\n0.12 mag is $2.4\\sigma$ and $\\sim 1.7\\sigma$ away from the \nintrinsic dispersion of subsample 1 and subsample 2, respectively. \nThe expected color difference due to K-corrections between $<z> = 0.09$ (subsample 1)\nand $<z> = 0.046$ (subsample 2) is $\\sim 0.06$ mag, \nfor a 2 Gyr model \n(half of the 0.12 color difference between the two subsamples), which fits\nthe average colors of both subsamples 1 and 2 better. Therefore, we can only \nconclude with a $\\sim 1.5\\sigma$ confidence level that E+A galaxies from \nthe field are redder than cluster E+As. The fact that dust extinction is much more \nnotorious in $J - H$ than in $H - K_s$ suggest that the color difference\nobserved in $H - K_s$ between subsample 1 and subsample 2 is not due to \ndifferential internal dust extinction. However, because of the observed \ncolor dispersion, we cannot give a robust answer\nsupporting stellar population differences instead of internal reddening \ndifferences due to extinction. We stress\nthat our differences are only at $1.5\\sigma$ significance level. \nIt is worth noting that $J - H$ color would {\\em redden systematically} \n$\\sim 0.03 - 0.05$ if we account for foreground or internal extinction\n(see \\S 5.3).\nThis would make ages inferred from colors (see Figure \\ref{obs_colors})\nslightly older (0.5 to 1 Gyr), but in any case alter the results of \nthe analysis, since changes are the same for all the galaxy samples. \n\n\\section{Further analysis and discussion}\n\n\\subsection{Photometry uncertainties}\n\nIn order to interpret correctly the color properties\nof the observed galaxy sample, it is important to keep in mind\nthe sources of uncertainty which affect the colors. \nThe first source of uncertainty is of course the \ndata acquisition itself. Given the nature of the near-IR imaging,\nthe thermal variation of the sky affects the photometry for the faint\nobjects, which require longer integration time than the brighter ones, \nsometimes much longer than the typical time of the \nsky fluctuations (see Figure \\ref{sky}). However, the nature of these variations is well\nunderstood and the fact that the sky fluctuations are sampled in {\\em real-time} \nand subtracted for each image can reduce this error to 5\\% \n(see \\S 3). The second important source of errors is the procedure employed to compute the\nmagnitude. It is well known that total magnitudes depend on the cut\nlevel where the light contribution is null or\nnot significant. In our case, SExtractor computes total magnitudes\nintegrating all the light up to a given threshold above the sky \n(typically 1.5$\\sigma$), and fitting elliptical isophotes to the profiles.\nAn elliptical aperture for a given galaxy, defined by \nthe elongation $\\epsilon$ and position angle $\\theta$, is computed \nfrom the 2nd order moment in the light distribution, above the \nisophotal threshold. The ``first moment'' $r_1$ is then \ncomputed\\footnote{$r_1$ is defined as $r_1 = \\frac{\\sum_r r I(r)}{\\sum_r I(r)}$.} \nwithin an aperture twice as large as the isophotal aperture, in \norder to reach the light distribution in the wings. This approach is very\nsimilar to the approach of \\citet{kron80}. The parameter $r_1$ is then used to define \nthe adaptive aperture where the total magnitude will be computed. The \nmain axes of the ellipse are defined as $\\epsilon k r_1$ and\n$k r_1 / \\epsilon$, where $k$ is a value to be fixed by the user. We\ncarried out some tests with both faint and bright galaxies and found that the\nvalue $k = 2.5$ allows us to include between $90\\%$ and $95\\%$\nof the total flux without introducing additional noise within the \naperture. Further details can be found in \\citet{arnouts96}. This\nprocedure ensures that not more than 5\\% of the light is lost.\n%reducing then the error due to loss of light from the wings. \n\nAnother source of uncertainty is the photometric errors due to the \ntransformation of the instrumental magnitudes to calibrated \nmagnitudes. This process is well understood and in general the \nscatter is small. The errors of the zero points are $\\sim 2\\%$ to\n$\\sim 7\\%$. \n\nThe largest uncertainties (now for rest-frame colors) \nare due to the K-corrections. These\nuncertainties, as shown in the previous section, can be very large\nfor galaxies with $z \\gtrsim 0.25$, where the change in magnitude\nproduced by the computation of K-corrections assuming one or another\nSED can reach differences as large as 30\\%, \npropagating these differences to the rest-frame colors (see Figure \\ref{K_diff}). \nFor galaxies with $z \\lesssim 0.2$, differences\nare smaller: $\\sim 10\\%$ for $0.15 \\lesssim z \\lesssim 0.2$ and \n$\\sim 5\\%$ for $0 \\le z \\lesssim 0.15$. In order to compute reliable K-corrections,\nit is fundamental to obtain calibrated spectra at 9000 \\AA $\\lesssim \\lambda\n\\lesssim$ 25000 \\AA~ for different spectral types, including E+A galaxies.\nOf course, the nature of the \nuncertainties lies in the fact that K-corrections are expressed in \nterm of the morphological type instead of the spectral type. The\nmorphological type relies on a subjective classification procedure, often\ndependent on the passband through which the images are obtained (more or less \nsensitive to the star population which delineates the galaxy\nmorphology) and is always strongly dependent on the image quality. On the other\nhand, there is no unique and reliable relationship between the spectral\ntype and the morphological type of the galaxies. Even though this is \napproximately true for normal Hubble types \\citep{folkes96, galaz98},\nthe dispersion can be large for some spectral types \nor active galaxies \\citep{sodre99}, leading to large uncertainties in the\nK-correction = $f(z$, T-type). However, we note that independently of what\nspectrophotometric models are used in obtaining rest-frame colors,\nthe K-corrections in $K$ (or $K_s$ band), are only {\\em weakly}\ndependent on the spectral type for $z \\lesssim 0.2$ (see Figures \n\\ref{K_poggianti}, \\ref{K_pegase}, and \\ref{K_diff}).\n\n\\subsection{Implications from near-IR colors}\n\nWe now examine some color properties of the E+A galaxies observed \nin the near-IR, keeping in mind the limitations of the accuracy\nof our photometry, as discussed above.\n\nStudying the position of the E+A galaxies in the $H - K_s$/$J - H$\nplane shown in Figure \\ref{obs_colors}, we see that {\\em field}\ngalaxies located at $<z> \\sim 0.09$ (subsample 1), have an average\n$J - H$ color similar to that of E+A galaxies located in nearby clusters \n($<z> \\sim 0.05$, subsample 2), but are slightly {\\em redder} in the \naverage $H - K_s$ color (see preceding section). The fact that the color\ndifference of 0.12 mag in only significant at $\\sim 1.5\\sigma$ level \nprevents us from proposing a robust conclusion. However, we can now ask \nhow the K-corrections can change this result. Here we examine the answer\nto this question using the two sets of K-corrections show in \\S 5.3\nthe PEGASE and the Poggianti K-corrections. \n\nFigure \\ref{color_average} shows average rest-frame colors for our sample\nof galaxies computed using both sets of K-corrections. Also shown are the colors\nof the sample of elliptical galaxies from \\cite{silva98}. We show the average\ncolors for the {\\em cluster} and the {\\em field} galaxies separately. This \nFigure demonstrates that, although the color differences are small, the same \ntrend is observed, independently of which set of K-corrections is used. The color\ndifference in $<H - K_s>$ between field and cluster E+As is \nabout 0.04 mag using PEGASE K-corrections and 0.15 mag\nusing Poggianti K-corrections. Note that in \nFigure \\ref{color_average} we compare cluster-field colors also for the \nLCRS sample (3 LCRS E+As belong to clusters). The field E+As from LCRS are also\nredder in $<H - K_s>$ than the LCRS cluster E+As. \n\n%placefigure{color_average}\n\nAs demonstrated by \\citet{persson83}, stellar\npopulations containing a large fraction of AGB stars (1 to 3\nGyr old), have redder $H - K$ color (but similar $J - H$ index), compared\nwith populations that lack such stars. This might suggest that the \nE+A galaxies in the field have a larger fractions of AGB stars than those in \nclusters. We emphasize that, although the difference given by the K-correction between \n$z \\sim 0.1$ and $z \\sim 0.05$ for subsamples 1 and 2, respectively, does\nchange the corresponding average colors, the observed color trend field/cluster\ndoes not change. \n%The \n%differences in the average $J - K_s$ and $H - K_s$ colors between \n%subsamples 1 and 2 are similar if one considers rest-frame colors\n%K-corrected using the PEGASE models. The same conclusion can \n%be inferred comparing the colors of the E+A galaxies in subsamples 1 and 2\n%with the colors of the sample of elliptical galaxies from \n%\\citet{silva98}. \n\nNote that three out 21 LCRS E+As are embedded in clusters (LCRS \\# 4, 11 and 20, \n%represented by solid points in Figures \\ref{rest_colors1}\n%and \\ref{rest_colors2}). \nThese galaxies have an average color $<H - K_s> = 0.160 \\pm 0.041$,\nusing the PEGASE K-corrections, and $<H - K_s> = 0.260 \\pm 0.005$, using the Poggianti\nK-corrections. These values are $35\\%$ and $22\\%$ bluer, respectively, than \nthe average $H - K_s$ color for the LCRS E+A galaxies located in the field, and \nare consistent with the comparison field/cluster between subsamples 1 and 2. \n\n%On the other hand, the models suggest that $J - H$ is an age indicator \n%and $H - K_s$ a metallicity indicator. Furthermore, \n%different spectral types in the optical with the same age have extremely similar \n%$H - K_s$ color. Therefore, our data suggest that E+A galaxies located in the \n%field (subsample 1) may have higher metallicity than those located in \n%nearby clusters (subsample 2).\n%It has been shown that galaxies in groups tend to have a higher probability to \n%merge than galaxies in clusters \\citep{binney87}, and as a result the metallicity\n%of galaxies in groups is higher than the metallicity of galaxies in clusters. \n%Three out of 21 LCRS E+As are embedded in clusters. \n%Could the $H - K_s$ color of these E+A galaxies, compared to the\n%same color index of the nearby cluster E+A galaxies, be redder because of a larger \n%metallicity content ? The observed color difference \n%is probably not large enough to conclude this\n%and, also, the possibility that other factors can redden the $H - K_s$ color, as an \n%excess in the AGB population. \n\nGalaxies in more distant clusters (subsample 3), \nappear redder in $J - H$ (at 2$\\sigma$ significance level) \nthan those at lower redshift (compared with both\nsubsamples 1 and 2). As discussed above, although for this subsample \nK-corrections are critical, the $J - H$ color does not change if one uses\na different set of K-corrections. This could be interpreted as a temperature\nchange of the first-ascent giant branch (FAGB) in the \nstellar populations of these $z \\sim 0.3$ E+A galaxies (see \\citet{charlot96}). A\nfurther spectroscopic analysis in the near-IR would settle this question, \nand also will help to disentangle possible significant extinction in the \n$J$ band.\n\nOne can also compare the integrated rest-frame \ncolors between the E+A galaxies from subsample 2 with the control galaxies which \n{\\em also} belong to these nearby clusters (e.g. galaxies \\# 52, 53, 59, \n60 and 61 in Table \\ref{all_calib}.\n% and plotted as solid dots in Figure \n%\\ref{rest_colors1} and \\ref{rest_colors2}). \nWe note that the average $H - K_s$ color\nfor both sets of galaxies is similar, and therefore any difference (in the mean)\nis observed between E+A galaxies and elliptical galaxies belonging to the \nsame cluster.\nThis is not the case if one compares the \ncolors between subsamples 1 and 2, as shown before. \nWe emphasize that the average $J - H$ color of the E+A galaxies of subsamples 1 and 2\nis similar to the average $J - H$ of the control sample \n(at $1\\sigma$ significance level, see Figure \\ref{obs_colors}). \n%This could indicate a \n%change in temperature for the FAGB population, and imply that in these E+A galaxies \n%the G/K stellar populations have suffered a temperature change, hence a\n%color change in $J - H$. \n\nIt is worth noting that all the K-corrections used to obtain average rest-frame colors, \nas shown in Figure \\ref{color_average}, have been computed using solar\nmetallicity models, assuming that K-corrections, for a given IMF, age\nand SFR scenario do not depend strongly on metallicity. We tested this\nassumption using GISSEL96 SEDs with different\nmetallicity. Several tests were carried out for different ages, \nIMFs, and SFRs, and metallicity between the extreme values of \n[Fe/H] $=-1.65$ and [Fe/H] $= +1.00$. \nDifferences in K-corrections between these two extreme metal-poor and metal-rich models \ncan reach up to 0.3 mag in $J$ at $z = 0.3$, for a large range of fundamental \nparameters (age, IMF, and SFR). For more modest metallicity differences \nbetween models (probably more realistic), variations in K-corrections, for the different near-IR\nphotometric bands, are between 0.15 mag for $J$ and 0.05 mag for $H$ and $K_s$, at $z = 0.3$. \nFor smaller redshifts, these differences are even smaller. \nFigure \\ref{diff_metal} shows K-correction differences in near-IR bands, as a function of redshift,\nfor two SEDs (shown in the inset) with different metallicity ([Fe/H] $= -0.30$ and \n[Fe/H] $= +0.1$), derived from instantaneous bursts with \nthe same age and IMF (in both cases Scalo IMF). These K-corrections differences \nimply $J - H$ and $H - K_s$ colors shifts no larger than 0.08 mag up to $z \\sim 0.3$, given \nthat differences in K-corrections, due to different \nmetallicity have the same sign. We conclude that for a typical interval of \nmetallicity found in the field and in clusters, the effect of varying metallicity should \nnot be significant on the K-correction uncertainties, and hence on rest-frame colors. \nHowever, for more accurate estimates of near-IR colors from broad band photometry, \nespecially at higher redshift ($z \\gtrsim 0.5$), metallicity does play a \nsignificant role on the K-corrections. \n\n%placefigure{diff_metal}\n\n\\section{Summary and conclusions}\n\nThe E+A galaxies reported here include 32 galaxies\nfrom clusters and 18 galaxies from the field. In addition, 13 nearby galaxies\nwhich do not present post-starburst activity, were observed (5 located in clusters\nat $z \\sim 0.05$ and 8 located in the field at very low redshift). All the galaxies\nhave been observed in the near-IR bands $J$, $H$ and $K_s$ during \nphotometric nights at Las Campanas Observatory.\nTotal apparent magnitudes and colors were derived. The color-color \ndiagram $H - K_s$/$J - H$ of the observed galaxies is compared to\nthe expected corresponding colors of spectrophotometric models of galaxy \nevolution, at different redshifts. The models are those generated by\nGISSEL96 \\citep{charlot96}. There is an overall agreement between these\nexpected colors and the observed ones, for the E+A located in nearby \nclusters ($<z> \\sim 0.05$) and for E+As located in the field ($<z> \\sim 0.1$).\nThe comparison of the colors of these two samples shows that even though \ncluster E+As appear bluer than field E+As, the color difference is only significant at\n$\\sim 1.5\\sigma$ level, and therefore we cannot strongly affirm that stellar \npopulation differences are observed between these two populations. \n\nThe colors of the E+A galaxies located in more distant clusters $z = 0.3$, \non the other hand, do not agree with the color expected from models. In the \nmean, they appear bluer than expected in $H - K_s$ (by $\\sim 0.3$mag) \nand redder in $J - H$ (by $\\sim 0.15$ mag). The possible interpretation of\nthe failure is strong internal reddening (mostly in the $J$ band), not \nconsidered in models. \n\nIn order to derive a more complete comparison with models, \nrest-frame colors were also obtained using two different sources of K-corrections:\none based on the work of \\citet{poggianti97}, and the other computed using\nthe spectrophotometric model PEGASE \\citep{fioc97}. \nWe have shown that such K-corrections can be significant for $z \\sim 0.2$ in the\n$K$ bands (or any band centered at 2$\\mu m$), although they are not a strong function\nof spectral type. In addition, large differences\nexist in the K-corrections between these two models, having a large impact on\nthe derived quantities, like rest-frame colors for high redshift galaxies. \nWe have compared average rest-frame colors of E+A galaxies located in the \nfield and in clusters. Results show that average rest-frame near-IR colors of E+A\ngalaxies located in clusters at $z \\sim 0.05$ \\citep{caldwell97} \nand field E+As located at $z \\sim 0.1$ (from the LCRS, Zabludoff \\etal 1996), \nfollow the same color trend in $J - H$ and $H - K_s$ observed in the comoving\ncolor-color diagram: E+A galaxies located in nearby clusters appear \nbluer than field E+As ($z \\sim 0.1$). \n\n%If models are \n%correct, the rest-frame colors favor a higher metallicity content for the \n%E+A galaxies located in the field. Indeed, both the E+A galaxies and \n%the control galaxies (some of these galaxies also from the clusters \n%investigated by Caldwell \\& Rose (1997)) favor a high metallicity environment.\n%Nevertheless, this redder color could also be interpreted as a higher fraction\n%of AGB stars present in the E+A galaxies located in the field (Persson \\etal 1983).\n\nAs well as comparing the observed colors with the GISSEL96 colors at\ndifferent redshifts, the models do not fit the rest-frame colors \nof the E+A galaxies observed in clusters\nat $z \\sim 0.3$. Their $H -K_s$ colors appear bluer (using the K-corrections \nof PEGASE), or redder (using the K-corrections of Poggianti) compared to\nthe models. Their $J - H$ color index, although not particularly sensitive to\none or the other K-correction, is also redder than the colors predicted by the \nmodels. The color of control galaxies, most of them ellipticals at $z \\lesssim 0.01$, and\nthe others from clusters at $z \\sim 0.05$, agree with the near-IR colors predicted\nby models. \n\nIntegrated colors between the {\\em field} E+As and the {\\em cluster} \nE+As of the LCRS (LCRS \\# 4, 11 and 20; see Table \\ref{all_calib}) are\nsimilar, although those in clusters seem to be slightly ($\\sim 25\\%$) bluer in $H - K_s$ \nthan the average color. This result is the same for both sets of rest-frame \ncolors, the set corrected by the PEGASE K-corrections and the set corrected \nby the Poggianti K-corrections (see Figure \\ref{color_average}). \nOn the other hand, the corresponding $J - H$ color is similar for \nthe cluster and field E+As in subsample 1. \n\nIn order to build more robust results, more field and cluster \nE+A galaxies have to be observed between $z = 0.1 - 1.0$. Spectroscopic \nobservations of normal and E+A galaxies at different redshifts \nin the near-IR are necessary to (1) obtain calibrated SEDs and \nrealistic K-corrections, and (2) to compare the spectra of the E+A galaxies \nwith those of normal galaxies in the whole spectral range \n3500 \\AA~ $\\lesssim \\lambda \\lesssim 25000$ \\AA. We expect to continue this \nresearch by imaging new E+A galaxies in the near-IR at higher redshift, as\nwell as obtaining near-IR spectra in order to construct a useful and larger database of \nnormal and post-starburst galaxies in a large spectral range. In order to\nincrease the number of E+A galaxies, some field galaxies already classified\nas E+As, are being observed in the near-IR at Las Campanas.\nSome of these galaxies \nbelong to the ESO-Sculptor Survey \\citep{delapparent97}, and results\nwill be published soon. Other wide-field surveys will provide a wealth of data \nfor E+A galaxies at $0.01 \\lesssim z \\lesssim 0.2$, like SLOAN \\citep{loveday98,fan98}, \nand the 2DF survey \\citep{colless98}, whose \ndata are expected to become available to the public. In a forthcoming paper, \nwe shall investigate systematic properties on the surface photometry and \ncolors of the E+A galaxies. \n\n\\acknowledgements\n\nI would like to thank the anonymous referee for useful comments and suggestions on how to improve \nthis paper. I thank Ron Marzke, Eric Persson, and Ann Zabludoff for fruitful discussions\non the nature of the E+A galaxies. I acknowledge Mauro Giavalisco for his help\nwith the DIMSUM software. I also acknowledge Mario Hamuy, Ren\\'e M\\'endez,\nMark Phillips, Miguel Roth, and Bill Kunkel \nin helping to improve the preliminary version of this paper. \nIt is a pleasure to thank all the staff at Las Campanas Observatory. \nThis research has made use of the NASA/IPAC Extragalactic Database (NED), \nwhich is operated by the Jet Propulsion Laboratory, California Institute\nof Technology, under contract with the National Aeronautics and Space\nAdministration. This work is made possible through the fellowship \\# C-12927, under \nagreement between Fundaci\\'on Andes and Carnegie Institution of\nWashington. \n\n\\clearpage\n\\begin{thebibliography}{99}\n\\bibitem[Arnouts (1996)]{arnouts96} Arnouts, S. 1996, PhD thesis, Universit\\'e\n\tParis VII. \n\\bibitem[Bershady (1995)]{bershady95} Bershady, M. 1995, \\aj, 109, 87\n\\bibitem[Bertin \\& Arnouts (1996)]{bertin96} Bertin, E., \\& Arnouts, S. 1996,\n\t\\aaps, 117, 393\n%\\bibitem[Binney \\& Tremaine (1987)]{binney87} Binney, J., \\& Tremaine, S. 1987, \n%\tGalactic Dynamics, Princeton University Press\n\\bibitem[Bower, Lucey \\& Ellis (1992a)]{bower92a} Bower, R., Lucey, J., \\&\n\tEllis, R. 1992a, \\mnras, 254, 589\n\\bibitem[Bower, Lucey \\& Ellis (1992b)]{bower92b} Bower, R., Lucey, J., \\&\n\tEllis, R. 1992b, \\mnras, 254, 601\n\\bibitem[Bruzual \\& Charlot (1993)]{bruzual93} Bruzual, G., \\& Charlot, S. 1993,\n\t\\apj, 405, 538 (GISSEL93). \n\\bibitem[Butcher \\& Oemler (1978)]{butcher78} Butcher, H., \\& Oemler, A. 1978,\n\t\\apj, 219, 18\n\\bibitem[Caldwell \\& Rose (1997)]{caldwell97} Caldwell, N., \\& Rose,\n\tJ. 1997, \\aj, 113, 492\n\\bibitem[Cardelli, Clayton \\& Mathis (1989)]{cardelli89} Cardelli, J., \n\tClayton, G., \\& Mathis, J. 1989, \\apj, 345, 245 \n\\bibitem[Charlot, Worthey \\& Bressan (1996)]{charlot96} Charlot, S., Worthey,\n\tG., \\& Bressan, A. 1996, \\apj, 457, 625 (GISSEL96)\n\\bibitem[Colless (1998)]{colless98} Colless, M. 1998, in Wide Field Surveys in \n\tCosmology, 14th IAP meeting, Paris. 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21\n\\bibitem[Persson \\etal (1998)]{persson98} Persson, E., Murphy, D., \n\tKrzeminski, W., Roth, M., \\& Rieke, M. 1998, \\apj, 116, 2475\n\\bibitem[Persson \\etal (1983)]{persson83} Persson, E., Cohen, J., Matthews, K., \n\tFrogel, J., \\& Aaronson, M. 1983, \\apj, 266, 105\n\\bibitem[Persson, Frogel \\& Aaronson (1979)]{persson79} Persson, E., Frogel, J., \n\t\\& Aaronson, M. 1979, \\apjs, 39, 61\n\\bibitem[Poggianti (1997)]{poggianti97} Poggianti, B. 1997, \\aaps, 122, 399\n\\bibitem[Prugniel \\& H\\'er\\'edeau (1998)]{prugniel98} Prugniel, P., \\& \n\tH\\'er\\'edeau, P. 1998, \\aaps, 128, 299 \n\\bibitem[Rakos \\& Schombert (1995)]{rakos95} Rakos, K., \\& Schombert, J. \n\t1995, \\apj, 439, 47\n%\\bibitem[Rana \\& Basu (1992)]{rana92} Rana, N., \\& Basu, S. 1992,\n%\t\\aap, 265, 499\n\\bibitem[Ronen, Aragon-Salamanca \\& Lahav (1999)]{ronen99} Ronen, S., \n\tAragon-Salamanca, A., \\& Lahav, O. 1999, \\mnras, 303, 284\n\\bibitem[Scalo (1986)]{scalo86} Scalo, J. 1986, \\fcp, 11, 1 \n\\bibitem[Schlegel, Finkbeiner \\& Davis (1998)]{schlegel98} Schelegel, D., \n\tFinkbeiner, P. \\& Davis, M. 1998, \\apj, 500, 525\n\\bibitem[Shectman \\etal (1996)]{shectman96} Shectman, S., Landy, S., Oemler,\n\tA., Tucker, D., Lin, H., Kirshner, R., \\& Schechter, P. 1996, \\apj, 470, 172\n\\bibitem[Silva \\& Bothun (1998)]{silva98} Silva, D., \\& Bothun, G. 1998,\n\t\\aj, 116, 85\n\\bibitem[Sodre \\& Stasinska (1999)]{sodre99} Sodre, L., \\& Stasinska, G. 1999,\n\tastro-ph/9903130\n\\bibitem[Spellman, Madore \\& Helou (1989)]{spellman89} Spellman, K., \n\tMadore, B., \\& Helou, G. 1989, \\pasp, 101, 360\n\\bibitem[Wise \\& Silva (1996)]{wise96} Wise, M., \\& Silva, D. 1996, \\apj, 461,\n\t155\n\\bibitem[Worthey (1994)]{worthey94} Worthey, G. 1994, \\apjs, 95, 107\n\\bibitem[Zabludoff \\etal (1996)]{zabludoff96} Zabludoff, A., Zaritsky, D., \n\tLin, H., Tucker, D., Hashimoto, Y., Shectman, S., Oemler, A., \\& \n\tKirshner, R. 1996, \\apj, 466, 104 \n\\end{thebibliography}\n\n\\clearpage \n\n%\\makeatletter\n%\\def\\jnl@aj{AJ}\n%\\ifx\\revtex@jnl\\jnl@aj\\let\\tablebreak=\\\\\\fi\n%\\makeatother\n\n%\\ptlandscape{}\n\\begin{deluxetable}{lllccclcc}\n\\tablewidth{0pt}\n\\renewcommand{\\baselinestretch}{1.4}\n\\tablecaption{The sample. \\label{samples}}\n\\tablenum{1}\n%\\tableheigh{15cm}\n\\tablehead{\n\\colhead{ID\\tablenotemark{(1)}} &\n\\colhead{S-ID\\tablenotemark{(2)}} &\n\\colhead{Name\\tablenotemark{(3)}} &\n\\colhead{RA\\tablenotemark{(4)}} & \n\\colhead{DEC\\tablenotemark{(5)}} & \n\\colhead{$z$\\tablenotemark{(6)}} & \n\\colhead{Cluster/Field\\tablenotemark{(7)}} & \n\\colhead{T-type\\tablenotemark{(8)}} & \n\\colhead{Reference\\tablenotemark{(9)}}}\n\\startdata\n%(1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) \\\\\n\\cutinhead{E+A galaxies} \n1 & 1 & g515 & 15:24:26 & +08:09:06 & 0.0870 & Abell 665 & 0 & (1) \\\\\n2 & 1 & dc204852\\_26 & 20:49:52 & $-$53:02:58 & 0.0397 & ACO 3716 & $-$2 & (2) \\\\\n3 & 1 & dc184263\\_39m & 18:42:49 & $-$63:12:28 & 0.0144 & DC1842-63 & $-$3 & (2) \\\\\n4 & 1 & dc204852\\_100 & 20:51:49 & $-$52:44:45 & 0.0493 & ACO 3716 & $-$2 & (2) \\\\\n5 & 1 & dc204852\\_148 & 20:49:13 & $-$52:33:51 & 0.0429 & ACO 3716 & $-$2 & (2) \\\\\n6 & 1 & dc204852\\_39 & 20:50:01 & $-$52:59:56 & 0.0489 & ACO 3716 & $-$2 & (2) \\\\\n7 & 1 & dc204852\\_45 & 20:52:10 & $-$52:56:09 & 0.0484 & ACO 3716 & $-$2 & (2) \\\\\n8 & 1 & dc204852\\_104 & 20:51:07 & $-$52:43:34 & 0.0493 & ACO 3716 & 0 & (2) \\\\\n9 & 1 & dc204852\\_149 & 20:48:30 & $-$52:33:07 & 0.0569 & ACO 3716 & 0 & (2) \\\\\n10 & 1 & dc204852\\_192 & 20:51:56 & $-$52:03:45 & 0.0473 & ACO 3716 & $-$5 & (2) \\\\\n11 & 1 & dc204852\\_77 & 20:52:54 & $-$52:47:28 & 0.0452 & ACO 3716 & $-$2 & (2) \\\\\n12 & 1 & dc204852\\_174 & 20:51:46 & $-$52:16:09 & 0.0448 & ACO 3716 & $-$5 & (2) \\\\\n13 & 1 & dc204852\\_184 & 20:54:00 & $-$52:08:15 & 0.0469 & ACO 3716 & $-$2 & (2) \\\\\n14 & 1 & dc204852\\_216 & 20:49:24 & $-$51:56:56 & 0.0490 & ACO 3716 & $-$2 & (2) \\\\\n15 & 1 & dc204852\\_231 & 20:51:40 & $-$51:45:22 & 0.0459 & ACO 3716 & $-$2 & (2) \\\\\n16 & 1 & dc032952\\_135a & 03:29:31 & $-$52:27:18 & 0.0519 & ACO 3128 & $-$2 & (2) \\\\\n17 & 1 & dc032952\\_156a & 03:31:15 & $-$52:22:28 & 0.0604 & ACO 3128 & $-$2 & (2) \\\\\n18 & 1 & dc010746\\_30b & 01:10:51 & $-$45:51:52 & 0.0267 & ACO 2877 & $-$5 & (2) \\\\\n19 & 1 & dc032952\\_82a & 03:31:09 & $-$52:36:49 & 0.0576 & ACO 3128 & $-$5 & (2) \\\\\n20 & 1 & dc032952\\_158b & 03:29:35 & $-$52:39:58 & 0.0500 & ACO 3128 & 0 & (2) \\\\\n21 & 1 & dc010746\\_22m & 01:08:23 & $-$46:09:09 & 0.0200 & ACO 2877 & 0 & (2) \\\\\n22 & 1 & dc010746\\_45m & 01:09:07 & $-$45:44:29 & 0.0300 & ACO 2877 & 0 & (2) \\\\\n23 & 2 & ac103\\_132 & 20:57:18 & $-$64:38:48 & 0.3047 & AC 103 & 0 & (3) \\\\\n24 & 2 & ac114\\_22 & 22:58:50 & $-$34:48:13 & 0.3354 & AC 114 & 0 & (3) \\\\\n25 & 2 & ac114\\_89 & 22:58:49 & $-$34:46:57 & 0.3169 & AC 114 & 0 & (3) \\\\\n26 & 2 & ac103\\_03 & 20:56:55 & $-$64:40:11 & 0.3118 & AC 103 & 0 & (3) \\\\\n27 & 2 & ac103\\_106 & 20:56:47 & $-$64:40:56 & 0.3091 & AC 103 & 0 & (3) \\\\\n28 & 2 & ac103\\_280 & 20:57:26 & $-$64:42:11 & 0.3111 & AC 103 & 0 & (3) \\\\\n29 & 2 & ac103\\_145 & 20:57:07 & $-$64:38:29 & 0.3105 & AC 103 & $-$2 & (3) \\\\\n30 & 3 & lcrs01 & 11:01:19 & $-$12:10:18 & 0.0746 & Field & 1 & (4) \\\\\n31 & 3 & lcrs17 & 10:13:52 & $-$02:55:47 & 0.0609 & Field & 0 & (4) \\\\\n32 & 3 & lcrs21 & 11:15:24 & $-$06:45:13 & 0.0994 & Field & 0 & (4) \\\\\n33 & 3 & lcrs13 & 11:19:52 & $-$12:52:39 & 0.0957 & Field & 1 & (4) \\\\\n34 & 3 & lcrs14 & 13:57:01 & $-$12:26:47 & 0.0704 & Field & 0 & (4) \\\\\n35 & 3 & lcrs12 & 12:05:59 & $-$02:54:32 & 0.0971 & Field & 1 & (4) \\\\\n36 & 3 & lcrs03 & 12:09:05 & $-$12:22:37 & 0.0810 & Field & 1 & (4) \\\\\n37 & 3 & lcrs16 & 12:19:55 & $-$06:14:01 & 0.0764 & Field & 1 & (4) \\\\\n38 & 3 & lcrs15 & 14:40:44 & $-$06:39:54 & 0.1137 & Field & 0 & (4) \\\\\n39 & 3 & lcrs06 & 11:53:55 & $-$03:10:36 & 0.0884 & Field & 0 & (4) \\\\\n40 & 3 & lcrs08 & 14:32:03 & $-$12:57:31 & 0.1121 & Field & $-$2 & (4) \\\\\n41 & 3 & lcrs07 & 22:41:09 & $-$38:34:35 & 0.1141 & Field & 0 & (4) \\\\\n42 & 3 & lcrs20 & 00:38:44 & $-$38:57:12 & 0.0632 & Cluster & $-$2 & (4) \\\\\n43 & 3 & lcrs18 & 00:22:46 & $-$41:33:37 & 0.0598 & Field & 0 & (4) \\\\ \n44 & 3 & lcrs05 & 01:58:01 & $-$44:37:14 & 0.1172 & Field & $-$2 & (4) \\\\\n45 & 3 & lcrs19 & 02:07:49 & $-$45:20:50 & 0.0640 & Field & 0 & (4) \\\\\n46 & 3 & lcrs11 & 01:14:49 & $-$41:22:30 & 0.1216 & Cluster & 0 & (4) \\\\\n47 & 3 & lcrs02 & 02:17:39 & $-$44:32:47 & 0.0987 & Field & 2 & (4) \\\\\n48 & 3 & lcrs09 & 01:17:38 & $-$41:24:23 & 0.0651 & Field & 0 & (4) \\\\\n49 & 3 & lcrs10 & 02:11:43 & $-$44:07:39 & 0.1049 & Field & 0 & (4) \\\\\n50 & 3 & lcrs04 & 04:00:00 & $-$44:35:16 & 0.1012 & Cluster & 1 & (4) \\\\ \n\\cutinhead{Control galaxies} \n51 & 4 & pgc35435 & 11:30:05 & $-$11:32:47 & 0.0178 & Field & $-$3 & (5) \\\\\n52 & 4 & dc204852\\_116 & 20:51:19 & $-$52:40:41 & 0.0441 & ACO 3716 & $-$5 & (2) \\\\\n53 & 4 & dc204852\\_66 & 20:51:45 & $-$52:51:19 & 0.0410 & ACO 3716 & $-$5 & (2) \\\\\n54 & 4 & pgc60102 & 17:20:28 & $-$00:58:46 & 0.0304 & Field & $-$2 & (6) \\\\\n55 & 4 & eso290-IG\\_050& 23:06:46 & $-$44:15:06 & 0.0290 & Field & $-$2 & (7) \\\\\n56 & 4 & pgc62615 & 18:57:41 & $-$52:31:46 & 0.0280 & Field & 2 & (8) \\\\\n57 & 4 & pgc57612 & 16:15:04 & $-$60:54:26 & 0.0183 & Field & $-$5 & (9) \\\\\n58 & 4 & ngc6653 & 18:44:39 & $-$73:15:47 & 0.0172 & Field & $-$5 & (9) \\\\\n59 & 4 & dc204852\\_115 & 20:51:21 & $-$52:39:17 & 0.0440 & ACO 3716 & $-$5 & (2) \\\\\n60 & 4 & dc204852\\_126 & 20:51:44 & $-$52:37:57 & 0.0489 & ACO 3716 & $-$2 & (2) \\\\\n61 & 4 & dc204852\\_38 & 20:50:05 & $-$53:00:28 & 0.0454 & ACO 3716 & $-$2 & (2) \\\\ \n62 & 4 & ngc6328 & 17:23:41 & $-$65:00:37 & 0.0142 & Field & 2 & (6) \\\\\n63 & 4 & pgc62765 & 19:05:59 & $-$42:21:59 & 0.0193 & Field & $-$2 & (6) \\\\ \n\\tablenotetext{(1)}{Correlative number of the galaxy.}\n\\tablenotetext{(2)}{Sample ID. Sample 1, Nearby cluster E+As; sample 2, distant cluster E+As;\n\t\t\tsample 3, LCRS E+As; sample 4, control galaxies.}\n\\tablenotetext{(3)}{Galaxy Identification used in this paper.}\n\\tablenotetext{(4)}{Right ascension in hh:mm:ss (J2000).}\n\\tablenotetext{(5)}{Declination in \\arcdeg:\\arcmin:\\arcsec (J2000).}\n\\tablenotetext{(6)}{Redshift.}\n\\tablenotetext{(7)}{Column indicating whether the galaxy belongs to a \ncluster or to the field.}\n\\tablenotetext{(8)}{Morphological type in T-type units, from the \nde Vaucouleurs classification system \\citep{devaucouleurs76}.}\n\\tablenotetext{(9)}{Reference where quantities other than magnitudes\nhave been extracted.}\n\\tablerefs{\n(1) \\citet{franx93}; \n(2) \\citet{caldwell97};\n(3) \\citet{couch87};\n(4) \\citet{zabludoff96};\n(5) \\citet{fairall92};\n(6) \\citet{devaucouleurs91};\n(7) \\citet{loveday96};\n(8) \\citet{spellman89};\n(9) \\citet{prugniel98}}\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n%\\setlength{\\topmargin}{1.0cm}\n%\\setlength{\\leftmargin}{-5.0cm}\n%\\setlength{\\rightmargin}{0.5cm}\n\n\\begin{deluxetable}{llccccccccccc}\n\\tablewidth{0pt}\n%\\tabletail{10cm}\n\\scriptsize\n\\rotate\n\\scriptsize\n\\renewcommand{\\baselinestretch}{0.90}\n\\tablecaption{Apparent magnitudes and colors. \\label{all_calib}}\n\\tablenum{2}\n\\tablecolumns{13}\n\\tablehead{\n\\colhead{ID\\tablenotemark{(1)}} &\n\\colhead{Name\\tablenotemark{(2)}} &\n\\colhead{$J$\\tablenotemark{(3)}} & \n\\colhead{$H$\\tablenotemark{(4)}} & \n\\colhead{$K_s$\\tablenotemark{(5)}} &\n\\colhead{$(J - H)$\\tablenotemark{(6)}} &\n\\colhead{$(H - K_s)$\\tablenotemark{(7)}} &\n\\colhead{$(J - K_s)$\\tablenotemark{(8)}} &\n\\colhead{$z$\\tablenotemark{(9)}} &\n\\colhead{$B$\\tablenotemark{(10)}} &\n\\colhead{$R$\\tablenotemark{(11)}} &\n\\colhead{S-ID\\tablenotemark{(12)}} &\n\\colhead{T-Type\\tablenotemark{(13)}}}\n%\\tiny\n\\startdata\n%(1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) & (11) & (12) & (13) \\\\ \\hline \n%# E+A galaxies: Whole sample\n%#\n%# Object Js H Ks Js-H H-Ks Js-Ks z B R Flag T-Type \n%# (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) \n%#\n&&&&&&&&&&&& \\\\\n1 & g515 & 13.86 0.02 & 13.11 0.05 & 12.75 0.05 & 0.75 0.05 & 0.36 0.07 & 1.11 0.05 & 0.0870 & \\nodata & \\nodata & 1 & 0 \\\\\n2 & dc204852\\_26 & 13.82 0.03 & 13.16 0.04 & 12.99 0.03 & 0.66 0.05 & 0.17 0.05 & 0.83 0.04 & 0.0397 & 16.99 & 15.38 & 1 & $-$2 \\\\\n3 & dc184263\\_39m & 11.01 0.02 & 10.27 0.06 & 10.05 0.03 & 0.74 0.06 & 0.22 0.07 & 0.96 0.04 & 0.0144 & \\nodata & \\nodata & 1 & $-$3 \\\\\n4 & dc204852\\_100 & 14.62 0.04 & 13.95 0.06 & 13.64 0.03 & 0.67 0.07 & 0.31 0.07 & 0.98 0.05 & 0.0493 & 17.61 & 16.19 & 1 & $-$2 \\\\\n5 & dc204852\\_148 & 14.44 0.04 & 13.74 0.06 & 13.44 0.04 & 0.70 0.07 & 0.30 0.07 & 1.00 0.06 & 0.0429 & 17.57 & 16.01 & 1 & $-$2 \\\\\n6 & dc204852\\_39 & 14.50 0.03 & 13.81 0.05 & 13.48 0.03 & 0.69 0.06 & 0.33 0.06 & 1.02 0.04 & 0.0489 & 17.77 & 16.16 & 1 & $-$2 \\\\\n7 & dc204852\\_45 & 15.04 0.04 & 14.39 0.05 & 14.03 0.03 & 0.65 0.06 & 0.36 0.06 & 1.01 0.05 & 0.0484 & \\nodata & \\nodata & 1 & $-$2 \\\\\n8 & dc204852\\_104 & 14.99 0.05 & 14.25 0.05 & 13.95 0.04 & 0.74 0.07 & 0.30 0.06 & 1.04 0.06 & 0.0493 & \\nodata & \\nodata & 1 & 0 \\\\\n9 & dc204852\\_149 & 13.91 0.03 & 13.24 0.05 & 12.91 0.04 & 0.67 0.06 & 0.33 0.06 & 1.00 0.05 & 0.0569 & \\nodata & \\nodata & 1 & 0 \\\\\n10 & dc204852\\_192 & 13.83 0.05 & 13.13 0.04 & 12.80 0.05 & 0.70 0.06 & 0.33 0.06 & 1.03 0.07 & 0.0473 & 16.98 & 15.40 & 1 & $-$5 \\\\\n11 & dc204852\\_77 & 14.88 0.03 & 14.16 0.04 & 13.90 0.04 & 0.72 0.05 & 0.26 0.06 & 0.98 0.05 & 0.0452 & \\nodata & \\nodata & 1 & $-$2 \\\\\n12 & dc204852\\_174 & 14.84 0.03 & 14.15 0.05 & 13.88 0.03 & 0.69 0.06 & 0.27 0.06 & 0.96 0.04 & 0.0448 & 18.09 & 16.43 & 1 & $-$5 \\\\\n13 & dc204852\\_184 & 14.29 0.02 & 13.60 0.04 & 13.25 0.04 & 0.69 0.04 & 0.35 0.06 & 1.04 0.04 & 0.0469 & 17.36 & 15.78 & 1 & $-$2 \\\\\n14 & dc204852\\_216 & 13.87 0.04 & 13.18 0.03 & 12.88 0.02 & 0.69 0.05 & 0.30 0.04 & 0.99 0.04 & 0.0490 & \\nodata & \\nodata & 1 & $-$2 \\\\\n15 & dc204852\\_231 & 13.58 0.03 & 12.88 0.03 & 12.58 0.03 & 0.70 0.04 & 0.30 0.04 & 1.00 0.04 & 0.0459 & 16.72 & 15.18 & 1 & $-$2 \\\\\n16 & dc032952\\_135a & 14.34 0.02 & 13.52 0.04 & 13.09 0.04 & 0.82 0.04 & 0.43 0.06 & 1.25 0.04 & 0.0519 & 18.09 & 16.21 & 1 & $-$2 \\\\\n17 & dc032952\\_156a & 13.22 0.04 & 12.48 0.03 & 12.15 0.03 & 0.74 0.05 & 0.33 0.04 & 1.07 0.05 & 0.0604 & 16.61 & 14.93 & 1 & $-$2 \\\\\n18 & dc010746\\_30b & 14.99 0.07 & 14.42 0.04 & 14.21 0.03 & 0.57 0.08 & 0.21 0.05 & 0.78 0.08 & 0.0267 & 17.90 & 16.41 & 1 & $-$5 \\\\\n19 & dc032952\\_82a & 14.96 0.03 & 14.35 0.03 & 14.18 0.03 & 0.61 0.04 & 0.17 0.04 & 0.78 0.04 & 0.0576 & 17.81 & 16.42 & 1 & $-$5 \\\\\n20 & dc032952\\_158b & 14.13 0.03 & 13.41 0.02 & 13.02 0.04 & 0.72 0.04 & 0.39 0.04 & 1.11 0.05 & 0.0500 & 17.26 & 15.76 & 1 & 0 \\\\\n21 & dc010746\\_22m & 14.49 0.04 & 13.87 0.04 & 13.60 0.02 & 0.62 0.06 & 0.27 0.04 & 0.89 0.04 & 0.0200 & \\nodata & \\nodata & 1 & 0 \\\\\n22 & dc010746\\_45m & 14.98 0.03 & 14.32 0.04 & 14.16 0.03 & 0.66 0.05 & 0.16 0.05 & 0.82 0.04 & 0.0300 & 17.37 & 16.24 & 1 & 0 \\\\\n23 & ac103\\_132 & 18.45 0.08 & 18.24 0.07 & 17.23 0.06 & 0.21 0.10 & 1.01 0.09 & 1.22 0.10 & 0.3047 & \\nodata & 19.34 & 2 & 6 \\\\\n24 & ac114\\_22 & 18.26 0.08 & 17.57 0.06 & 16.76 0.07 & 0.69 0.10 & 0.81 0.09 & 1.50 0.11 & 0.3354 & \\nodata & 19.85 & 2 & 0 \\\\\n25 & ac114\\_89 & 17.79 0.09 & 17.24 0.07 & NC NC & 0.55 0.11 & \\nodata \\nodata & \\nodata \\nodata & 0.3169 & \\nodata & 19.78 & 2 & 0 \\\\\n26 & ac103\\_03 & 16.33 0.08 & 15.44 0.08 & 15.09 0.05 & 0.89 0.11 & 0.35 0.09 & 1.24 0.09 & 0.3118 & 19.95 & 18.12 & 2 & 0 \\\\\n27 & ac103\\_106 & 17.15 0.09 & 16.34 0.07 & 15.76 0.06 & 0.81 0.11 & 0.58 0.09 & 1.39 0.11 & 0.3091 & \\nodata & \\nodata & 2 & 0 \\\\\n28 & ac103\\_280 & 17.21 0.06 & 16.23 0.07 & 15.76 0.07 & 0.98 0.09 & 0.47 0.10 & 1.45 0.09 & 0.3111 & 21.00 & 18.93 & 2 & 0 \\\\\n29 & ac103\\_145 & 17.20 0.08 & 16.31 0.08 & 15.90 0.07 & 0.89 0.11 & 0.41 0.11 & 1.30 0.10 & 0.3105 & \\nodata & 19.66 & 2 & 3 \\\\\n30 & lcrs01 & 16.18 0.04 & 15.57 0.05 & 15.10 0.04 & 0.61 0.06 & 0.47 0.06 & 1.08 0.06 & 0.0746 & \\nodata & 17.05 & 3 & 1 \\\\\n31 & lcrs17 & 15.83 0.03 & 15.19 0.03 & 14.75 0.05 & 0.64 0.04 & 0.44 0.06 & 1.08 0.06 & 0.0609 & \\nodata & 16.99 & 3 & 0 \\\\\n32 & lcrs21 & 15.55 0.03 & 14.94 0.04 & 14.53 0.04 & 0.61 0.05 & 0.41 0.06 & 1.02 0.05 & 0.0994 & \\nodata & 16.93 & 3 & 0 \\\\\n33 & lcrs13 & 14.49 0.03 & 13.67 0.02 & 13.29 0.03 & 0.82 0.04 & 0.38 0.04 & 1.20 0.04 & 0.0957 & \\nodata & 12.97 & 3 & 1 \\\\\n34 & lcrs14 & 14.90 0.03 & 14.20 0.05 & 13.77 0.03 & 0.70 0.06 & 0.43 0.06 & 1.13 0.04 & 0.0704 & \\nodata & 16.05 & 3 & 0 \\\\\n35 & lcrs12 & 15.02 0.03 & 14.35 0.04 & 13.82 0.03 & 0.67 0.05 & 0.53 0.05 & 1.20 0.04 & 0.0971 & \\nodata & 16.78 & 3 & 1 \\\\\n36 & lcrs03 & 14.11 0.04 & 13.47 0.03 & 13.04 0.03 & 0.64 0.05 & 0.43 0.04 & 1.07 0.05 & 0.0810 & \\nodata & 15.03 & 3 & 1 \\\\\n37 & lcrs16 & 15.35 0.04 & 14.75 0.04 & 14.41 0.03 & 0.60 0.06 & 0.34 0.05 & 0.94 0.05 & 0.0764 & \\nodata & 16.69 & 3 & 1 \\\\\n38 & lcrs15 & 15.84 0.05 & 15.16 0.05 & 14.73 0.04 & 0.68 0.07 & 0.43 0.06 & 1.11 0.06 & 0.1137 & \\nodata & 17.19 & 3 & 0 \\\\\n39 & lcrs06 & 15.64 0.05 & 15.09 0.04 & 14.72 0.03 & 0.55 0.06 & 0.37 0.05 & 0.92 0.06 & 0.0884 & \\nodata & 16.81 & 3 & 0 \\\\\n40 & lcrs08 & 15.63 0.04 & 15.01 0.03 & 14.55 0.04 & 0.62 0.05 & 0.46 0.05 & 1.08 0.06 & 0.1121 & \\nodata & 17.87 & 3 & $-$2 \\\\\n41 & lcrs07 & 13.62 0.05 & 12.89 0.03 & 12.45 0.04 & 0.73 0.06 & 0.44 0.05 & 1.17 0.06 & 0.1141 & \\nodata & 15.00 & 3 & 0 \\\\\n42 & lcrs20 & 14.48 0.03 & 13.89 0.03 & 13.53 0.05 & 0.59 0.04 & 0.36 0.06 & 0.95 0.06 & 0.0632 & \\nodata & 15.96 & 3 & $-$2 \\\\\n43 & lcrs18 & 14.70 0.04 & 14.02 0.03 & 13.62 0.03 & 0.68 0.05 & 0.40 0.04 & 1.08 0.05 & 0.0598 & \\nodata & 16.09 & 3 & 0 \\\\\n44 & lcrs05 & 15.36 0.05 & 14.80 0.03 & 14.32 0.05 & 0.56 0.06 & 0.48 0.06 & 1.04 0.07 & 0.1172 & \\nodata & 16.73 & 3 & $-$2 \\\\\n45 & lcrs19 & 14.95 0.03 & 14.24 0.04 & 13.90 0.03 & 0.71 0.05 & 0.34 0.05 & 1.05 0.04 & 0.0640 & \\nodata & 16.42 & 3 & 0 \\\\\n46 & lcrs11 & 15.48 0.04 & 14.78 0.04 & 14.38 0.03 & 0.70 0.06 & 0.40 0.05 & 1.10 0.05 & 0.1216 & \\nodata & 16.96 & 3 & 0 \\\\\n47 & lcrs02 & 14.95 0.03 & 14.28 0.03 & 13.95 0.03 & 0.67 0.04 & 0.33 0.04 & 1.00 0.04 & 0.0987 & \\nodata & 16.36 & 3 & 2 \\\\\n48 & lcrs09 & 15.98 0.05 & 15.30 0.04 & 14.96 0.03 & 0.68 0.06 & 0.34 0.05 & 1.02 0.06 & 0.0651 & \\nodata & 17.47 & 3 & 0 \\\\\n49 & lcrs10 & 15.29 0.04 & 14.65 0.05 & 14.27 0.04 & 0.64 0.06 & 0.38 0.06 & 1.02 0.05 & 0.1049 & \\nodata & 16.68 & 3 & 0 \\\\\n50 & lcrs04 & 14.49 0.04 & 13.80 0.05 & 13.41 0.03 & 0.69 0.06 & 0.39 0.06 & 1.08 0.05 & 0.1012 & \\nodata & 15.68 & 3 & 1 \\\\\n51 & pgc35435 & 11.75 0.03 & 10.98 0.04 & 10.66 0.02 & 0.77 0.05 & 0.32 0.04 & 1.09 0.04 & 0.0178 & 13.75 & \\nodata & 4 & $-$3 \\\\\n52 & dc204852\\_116 & 12.62 0.06 & 11.92 0.05 & 11.65 0.02 & 0.70 0.08 & 0.27 0.05 & 0.97 0.06 & 0.0441 & 15.84 & 14.06 & 4 & $-$5 \\\\\n53 & dc204852\\_66 & 14.45 0.05 & 13.62 0.04 & 13.36 0.03 & 0.83 0.06 & 0.26 0.05 & 1.09 0.06 & 0.0410 & 17.48 & 15.88 & 4 & $-$5 \\\\\n54 & pgc60102 & 12.96 0.06 & 12.13 0.03 & 11.65 0.04 & 0.84 0.07 & 0.47 0.05 & 1.31 0.07 & 0.0304 & 15.36 & \\nodata & 4 & $-$2 \\\\\n55 & eso290-IG\\_050& 13.46 0.03 & 12.74 0.03 & 12.39 0.03 & 0.72 0.04 & 0.35 0.04 & 1.07 0.04 & 0.0290 & 15.18 & 14.21 & 4 & $-$2 \\\\\n56 & pgc62615 & 12.65 0.04 & 11.92 0.04 & 11.63 0.04 & 0.73 0.06 & 0.29 0.06 & 1.02 0.06 & 0.0280 & \\nodata & \\nodata & 4 & 2 \\\\\n57 & pgc57612 & 10.99 0.03 & 10.22 0.03 & 10.10 0.03 & 0.77 0.04 & 0.11 0.04 & 0.88 0.04 & 0.0183 & 13.30 & 11.33 & 4 & $-$5 \\\\\n58 & ngc6653 & 11.53 0.04 & 10.79 0.01 & 10.59 0.04 & 0.74 0.04 & 0.20 0.04 & 0.94 0.06 & 0.0172 & \\nodata & \\nodata & 4 & $-$5 \\\\\n59 & dc204852\\_115 & 14.98 0.03 & 14.33 0.03 & 14.04 0.03 & 0.65 0.04 & 0.29 0.04 & 0.94 0.04 & 0.0440 & 18.13 & 16.53 & 4 & $-$5 \\\\\n60 & dc204852\\_126 & 15.01 0.04 & 14.29 0.04 & 14.01 0.04 & 0.72 0.06 & 0.28 0.06 & 1.00 0.06 & 0.0489 & 18.21 & 16.60 & 4 & $-$2 \\\\\n61 & dc204852\\_38 & 13.49 0.05 & 12.90 0.03 & 12.56 0.04 & 0.59 0.06 & 0.34 0.05 & 0.93 0.06 & 0.0454 & 16.73 & 15.12 & 4 & $-$2 \\\\ \n62 & ngc6328 & 11.33 0.03 & 10.57 0.04 & 10.24 0.04 & 0.77 0.05 & 0.32 0.06 & 1.09 0.05 & 0.0142 & 13.17 & 11.45 & 4 & 2 \\\\ \n63 & pgc62765 & 11.42 0.04 & 10.68 0.04 & 10.36 0.03 & 0.74 0.06 & 0.32 0.05 & 1.06 0.05 & 0.0193 & \\nodata & \\nodata & 4 & $-$2 \\\\\n\\tablenotetext{(1)}{Correlative number.}\n\\tablenotetext{(2)}{Name of the galaxy.}\n\\tablenotetext{(3)}{$J_s$ apparent magnitude and photometric error.}\n\\tablenotetext{(4)}{$H$ apparent magnitude and photometric error.}\n\\tablenotetext{(5)}{$K_s$ apparent magnitude and photometric error.}\n\\tablenotetext{(6)}{$J - H$ color index and its error.}\n\\tablenotetext{(7)}{$H - K_s$ color index and its error.}\n\\tablenotetext{(8)}{$J - K_s$ color index and its error.}\n\\tablenotetext{(9)}{Redshift.}\n\\tablenotetext{(10)}{$B$ apparent total magnitude in the Johnson system. This magnitude\n\tis provided by NED.}\n\\tablenotetext{(11)}{$R$ apparent total magnitude in the Cousins system. This\n\tmagnitude is provided by NED.}\n\\tablenotetext{(12)}{Sample ID (see Table \\ref{samples}).} \n\\tablenotetext{(13)}{Morphological T-type provided by NED.}\n\\enddata\n\\end{deluxetable}\n\\clearpage\n\n\\figcaption[galaz.fig1.ps]{Typical sky \nvariations in the near-IR passbands \n$J$, $H$, and $K_s$ during 1 hour. Each point represents the mean sky\nlevel for an individual image during an {\\em observing sequence}. The error bars\nare given by the standard deviation in the image counts. Note the \nlarger error bars for the $K_s$ band, where the thermal variations are\nin fact larger (where also the shot noise is higher, compared to that\nof other filters). This behavior limits the accuracy of the sky subtraction \nprocedure applied to the near-IR images (see text). \\label{sky}}\n\n\\figcaption[galaz.fig2.ps]{Average errors \nin the photometric calibrations for the standards\nobserved with the 100-inch du Pont telescope (triangles), and for the \nstandards observed with the 40-inch Swope telescope (circles). \nEvery point corresponds to an average error of several (typically no less than 3)\nmeasurements for the same standard, observed in different nights.\n\\label{stds_error}}\n\n\\figcaption[galaz.fig3.ps]{K-corrections \nfrom the models of \\citet{poggianti97} \nfor passbands $J$, $H$ and $K$, as\na function of redshift and for Hubble types E, Sa and Sc.\nNote the large and negative K-corrections for\nthe $K$ band for $z \\gtrsim 0.5$. \\label{K_poggianti}}\n\n\\figcaption[galaz.fig4.ps]{K-corrections \nderived from the PEGASE models \\citep{fioc97} \nfor the $J$, $H$, $K$ and $K_s$ bands as \na function of redshift and Hubble type (lines as in Figure \n\\ref{K_poggianti}). Compare with Figure \\ref{K_poggianti}. \\label{K_pegase}}\n\n\\figcaption[galaz.fig5.ps]{K-correction\ndifferences obtained from 2 spectrophotometric models of galaxy evolution, \nindicated in Figures \\ref{K_poggianti} and \\ref{K_pegase}. Differences are computed\nfor $J$, $H$, and $K$ and for Hubble types E, Sa and Sc. Note the large\ndifference for the K-corrections in the $K$ band. \\label{K_diff}}\n\n%\\figcaption[/export/data1/gaspar/postscripts/rest_colors1.ps]{\n%Rest-frame colors for the 4 subsamples of \n%observed galaxies (open and solid circles). \n%Colors have been K-corrected using \n%the PEGASE models \\citep{fioc97}, and assuming a relationship\n%between the morphological type of the observed galaxies and the spectral type of\n%the models. Solid circles in subsample 1 represent {\\em cluster} E+As from the \n%LCRS sample. Solid circles in subsample 4 represent control galaxies observed\n%in the same clusters which contain the E+A galaxies of subsample 2.\n%Lines represent different color tracks for \n%spectrophotometric models of galaxy evolution. In all of them, age\n%increases as $J - H$ became redder. The green and magenta lines \n%represent the color track between 1 Gyr and 19 Gyr for a \n%model representative of an elliptical and an irregular\n%galaxy, respectively (different stellar formation rates, see text). \n%The red and blue lines, on the other hand, represent the color \n%evolution for the same range of ages but for an\n%instantaneous burst of star formation with different \n%metallicity: [Fe/H] = +0.0932 (red line) and \n%[Fe/H] = +0.5595 (blue line). These last two models \n%were generated using GISSEL96 \\citep{charlot96}. Photometric errors\n%in the colors for each subsample are indicated by the corresponding \n%error bars at the lower left corner. \n%Asterisks show the elliptical galaxies observed by \\citet{silva98}.\n%See text for further details.\n%\\label{rest_colors1}}\n\n%\\figcaption[/export/data1/gaspar/postscripts/rest_colors2.ps]{The same as \n%Figure \\ref{rest_colors1} but with \n%the observed colors transformed to rest-frame colors (circles with error bars) \n%using the models of \\citet{poggianti97}. See text\n%for details. \\label{rest_colors2}}\n%\n\n\\figcaption[galaz.fig6.ps]{Some \\citet{kennicutt92} spectra\nof observed normal galaxies (as indicated in each panel) \nwith known Hubble types (thick lines), and fitted synthetic\nspectra from GISSEL96 \\citep{charlot96} (thin lines). The fitted models correspond\nto instantaneous bursts of solar metallicity and different ages of the passively\nevolving stellar populations. The closest model spectrum \nis obtained using a simple $\\chi^2$ fitting algorithm between the Kennicutt spectra and 20 \nmodel spectra. The good match shows that at the \noptical wavelengths models agree with observations. The same kind of models are\ncompared to the near-IR colors. See text for details. \\label{spectra}}\n\n\\figcaption[galaz.fig7.ps]{Observed colors of the \nE+A galaxies reported in this paper (filled circles) compared with spectrophotometric models\nof galaxy evolution (open symbols joint by lines). Each panel corresponds to a different\nE+A sample (as indicated in each panel). Each line represent a redshift track of \nan instantaneous burst of solar metallicity, at a given age of 1, 3 and 16 Gyr, \nindicated by circles, squares, and triangles, respectively, for the \nredshifts indicated in the lower right panel. The crosses are the error bars in the\ncolors. See text for explanations \\label{obs_colors}}\n\n\\figcaption[galaz.fig8.ps]{Averaged rest-frame \ncolors of E+As lying in different environments. The LCRS symbols \ncorresponds to the 21 E+As from the \nsample of Las Campanas Redshift Survey \\citep{zabludoff96}. Most of these galaxies \nare located in the field (at $<z> \\sim 0.1$), but 3 of them lie in clusters. \nThe DC cluster E+As correspond to the E+As from the sample of \n\\citet{caldwell97}, and all of them are located in clusters with $<z> \\sim 0.05$. \nFilled symbols indicate that rest-frame colors have been obtained using the \n\\citet{poggianti97} K-corrections. Open symbols are averaged rest-frame colors\nobtained using the PEGASE \\citep{fioc97} K-corrections. Asteriscs correspond \nto elliptical galaxies observed by \\citet{silva98}. The solid line \ncorrespond to colors of a GISSEL96 \\citep{charlot96} instantaneous burst of\nsolar metallicity at $z = 0$ and at different ages (indicated by solid dots and\nlabeled). See text for details. \\label{color_average}}\n\n\\figcaption[galaz.fig9.ps]{K-correction differences in $J$, $H$,\n$K$ and $K_s$, as a function of redshift, for two SEDs having different metallicity. \nThe two SEDs, shown in the inset, are simple instantaneous bursts with a Scalo \ninitial mass function \\citep{scalo86} and with an age of 10 Gyr. Differences in K-corrections\nare expressed as the difference between K-correction for SED 1 ([Fe/H] $= -0.30$) \nand K-correction for SED 2 ([Fe/H] $= +0.10$). \\label{diff_metal}}\n\n\n%\\include{figures}\n\n\\begin{figure}\n\\plotone{galaz.fig1.ps}\n\\end{figure}\n\\begin{figure}\n\\plotone{galaz.fig2.ps}\n\\end{figure}\n\\begin{figure}\n\\plotone{galaz.fig3.ps}\n\\end{figure}\n\\begin{figure}\n\\plotone{galaz.fig4.ps}\n\\end{figure}\n\\begin{figure}\n\\plotone{galaz.fig5.ps}\n\\end{figure}\n\\begin{figure}\n\\plotone{galaz.fig6.ps}\n\\end{figure}\n\\begin{figure}\n\\plotone{galaz.fig7.ps}\n\\end{figure}\n\\begin{figure}\n\\plotone{galaz.fig8.ps}\n\\end{figure}\n\\begin{figure}\n\\plotone{galaz.fig9.ps}\n\\end{figure}\n\n\n\n\\end{document}\n"
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{
"name": "astro-ph0002146.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem[Arnouts (1996)]{arnouts96} Arnouts, S. 1996, PhD thesis, Universit\\'e\n\tParis VII. \n\\bibitem[Bershady (1995)]{bershady95} Bershady, M. 1995, \\aj, 109, 87\n\\bibitem[Bertin \\& Arnouts (1996)]{bertin96} Bertin, E., \\& Arnouts, S. 1996,\n\t\\aaps, 117, 393\n%\\bibitem[Binney \\& Tremaine (1987)]{binney87} Binney, J., \\& Tremaine, S. 1987, \n%\tGalactic Dynamics, Princeton University Press\n\\bibitem[Bower, Lucey \\& Ellis (1992a)]{bower92a} Bower, R., Lucey, J., \\&\n\tEllis, R. 1992a, \\mnras, 254, 589\n\\bibitem[Bower, Lucey \\& Ellis (1992b)]{bower92b} Bower, R., Lucey, J., \\&\n\tEllis, R. 1992b, \\mnras, 254, 601\n\\bibitem[Bruzual \\& Charlot (1993)]{bruzual93} Bruzual, G., \\& Charlot, S. 1993,\n\t\\apj, 405, 538 (GISSEL93). \n\\bibitem[Butcher \\& Oemler (1978)]{butcher78} Butcher, H., \\& Oemler, A. 1978,\n\t\\apj, 219, 18\n\\bibitem[Caldwell \\& Rose (1997)]{caldwell97} Caldwell, N., \\& Rose,\n\tJ. 1997, \\aj, 113, 492\n\\bibitem[Cardelli, Clayton \\& Mathis (1989)]{cardelli89} Cardelli, J., \n\tClayton, G., \\& Mathis, J. 1989, \\apj, 345, 245 \n\\bibitem[Charlot, Worthey \\& Bressan (1996)]{charlot96} Charlot, S., Worthey,\n\tG., \\& Bressan, A. 1996, \\apj, 457, 625 (GISSEL96)\n\\bibitem[Colless (1998)]{colless98} Colless, M. 1998, in Wide Field Surveys in \n\tCosmology, 14th IAP meeting, Paris. Publisher: Editions Fronti\\`eres.\n\\bibitem[Couch \\& Sharples (1987)]{couch87} Couch, W., \\& Sharples, \n\tR. 1987, \\mnras, 229, 423\n\\bibitem[de Lapparent \\etal (1997)]{delapparent97} de Lapparent, V., Galaz, G., \n\tArnouts, S., Bardelli, S., \\& Ramella, M. 1997, The Messenger, 89, 21\n\\bibitem[de Vaucouleurs \\etal (1991)]{devaucouleurs91} de Vaucouleurs, G., \n\tde Vaucouleurs, A., Corwin, H., Buta, R., Paturel, G., \\& Fouqu\\'e, P.\n\t1991, {\\em Third Reference Catalogue of Bright Galaxies}, Springer-Verlag, \n\tBerlin, Heidelberg, New York (RC3)\n\\bibitem[de Vaucoulers, de Vaucouleurs \\& Corwin (1976)]{devaucouleurs76}\n\tde Vaucouleurs, G., de Vaucouleurs, A., \\& Corwin, H. 1976,\n\t{\\em Second Reference Catalogue of Bright Galaxies (Austin: University of\n\tTexas Press)}\n\\bibitem[Dressler \\& Gunn (1983)]{dressler83} Dressler, A., \\& Gunn, J. \n\t1983, \\apj, 270, 7\n\\bibitem[Edmunds (1992)]{edmunds92} Edmunds, M. G. 1992, in The Stellar\n\tPopulations of Galaxies, ed. B. Barbuy \\& A. Renzini (Dordrecht:\n\tKluwer Academic), 277\n\\bibitem[Fabricant, McClintock \\& Bautz (1991)]{fabricant91} Fabricant, D., \n\tMcClintock, J., \\& Bautz, M. 1991, \\apj, 381, 33\n\\bibitem[Fairall \\etal (1992)]{fairall92} Fairall, A., Willmer, C., \n\tCalder\\'on, J., Latham, D., da Costa, L., Pellegrini, P., Nunes,\n\tM., Focardi, P., \\& Vettolani, G. 1992, \\aj, 103, 11\n\\bibitem[Fan \\etal (1998)]{fan98} Fan, X., Strauss, M., Gunn, J., Hennessy, G., \n\tIvezic, Z., Knapp, G., Lupton, R., Newberg, H., \\& Schneider, D. 1998, \n\tAmerican Astronomical Society Meeting no. 193, 02.05\n\\bibitem[Ferreras, Charlot \\& Silk (1998)]{ferreras98} Ferreras, I., \n\tCharlot, S., \\& Silk, J. 1998, \\apj, in press \n\\bibitem[Fioc \\& Rocca-Volmerange (1997)]{fioc97} Fioc, M., \\& \n\tRocca-Volmerange, B. 1997, \\aap, 326, 950 (PEGASE)\n\\bibitem[Folkes, Lahav \\& Maddox (1996)]{folkes96} Folkes, S., Lahav, O., \n\t\\& Maddox, S. 1996, \\mnras, 283, 651\n\\bibitem[Franx (1993)]{franx93} Franx, M. 1993, \\apjl, 407, L5\n\\bibitem[Galaz \\& de Lapparent (1998)]{galaz98} Galaz, G., \\& de Lapparent, V. \n\t1998, \\aap, 332, 459\n\\bibitem[Frogel \\etal (1978)]{frogel78} Frogel, J., Persson, E., Matthews, K., \n\t\\& Aaronson, M. 1978, \\apj, 220, 75\n\\bibitem[Kennicutt (1992)]{kennicutt92} Kennicutt R. 1992, \\apjs, 79, 255\n%\\bibitem[Kinney \\etal (1996)]{kinney96} Kinney, A., Calzetti, D., Bohlin, R., \n%\tMcQuade, K., Storchi-Bergmann, T.,and Schmitt, H. 1996, \\apj, 467, 38\n\\bibitem[Kron (1980)]{kron80} Kron, R. 1980, \\apjs, 43, 305\n\\bibitem[Liu \\& Green (1996)]{liu96} Liu, C., \\& Green, R. 1996, \\apj, 468, L63\n\\bibitem[Loveday \\& Pier (1998)]{loveday98} Loveday, J., \\& Pier, J. 1998, in\n\tWide Field Surveys in Cosmology, 14th IAP meeting, Paris. \n\tPublisher: Editions Fronti\\`eres.\n\\bibitem[Loveday (1996)]{loveday96} Loveday, J. 1996, \\mnras, 278, 1025\n\\bibitem[Oke \\& Sandage (1968)]{oke68} Oke, J., \\& Sandage, A. 1968, \\apj, 154, 21\n\\bibitem[Persson \\etal (1998)]{persson98} Persson, E., Murphy, D., \n\tKrzeminski, W., Roth, M., \\& Rieke, M. 1998, \\apj, 116, 2475\n\\bibitem[Persson \\etal (1983)]{persson83} Persson, E., Cohen, J., Matthews, K., \n\tFrogel, J., \\& Aaronson, M. 1983, \\apj, 266, 105\n\\bibitem[Persson, Frogel \\& Aaronson (1979)]{persson79} Persson, E., Frogel, J., \n\t\\& Aaronson, M. 1979, \\apjs, 39, 61\n\\bibitem[Poggianti (1997)]{poggianti97} Poggianti, B. 1997, \\aaps, 122, 399\n\\bibitem[Prugniel \\& H\\'er\\'edeau (1998)]{prugniel98} Prugniel, P., \\& \n\tH\\'er\\'edeau, P. 1998, \\aaps, 128, 299 \n\\bibitem[Rakos \\& Schombert (1995)]{rakos95} Rakos, K., \\& Schombert, J. \n\t1995, \\apj, 439, 47\n%\\bibitem[Rana \\& Basu (1992)]{rana92} Rana, N., \\& Basu, S. 1992,\n%\t\\aap, 265, 499\n\\bibitem[Ronen, Aragon-Salamanca \\& Lahav (1999)]{ronen99} Ronen, S., \n\tAragon-Salamanca, A., \\& Lahav, O. 1999, \\mnras, 303, 284\n\\bibitem[Scalo (1986)]{scalo86} Scalo, J. 1986, \\fcp, 11, 1 \n\\bibitem[Schlegel, Finkbeiner \\& Davis (1998)]{schlegel98} Schelegel, D., \n\tFinkbeiner, P. \\& Davis, M. 1998, \\apj, 500, 525\n\\bibitem[Shectman \\etal (1996)]{shectman96} Shectman, S., Landy, S., Oemler,\n\tA., Tucker, D., Lin, H., Kirshner, R., \\& Schechter, P. 1996, \\apj, 470, 172\n\\bibitem[Silva \\& Bothun (1998)]{silva98} Silva, D., \\& Bothun, G. 1998,\n\t\\aj, 116, 85\n\\bibitem[Sodre \\& Stasinska (1999)]{sodre99} Sodre, L., \\& Stasinska, G. 1999,\n\tastro-ph/9903130\n\\bibitem[Spellman, Madore \\& Helou (1989)]{spellman89} Spellman, K., \n\tMadore, B., \\& Helou, G. 1989, \\pasp, 101, 360\n\\bibitem[Wise \\& Silva (1996)]{wise96} Wise, M., \\& Silva, D. 1996, \\apj, 461,\n\t155\n\\bibitem[Worthey (1994)]{worthey94} Worthey, G. 1994, \\apjs, 95, 107\n\\bibitem[Zabludoff \\etal (1996)]{zabludoff96} Zabludoff, A., Zaritsky, D., \n\tLin, H., Tucker, D., Hashimoto, Y., Shectman, S., Oemler, A., \\& \n\tKirshner, R. 1996, \\apj, 466, 104 \n\\end{thebibliography}"
}
] |
astro-ph0002147
|
UBV(RI)$_{C}$ photometric comparison sequences for symbiotic stars
|
[
{
"author": "Arne Henden\\inst{1}"
},
{
"author": "Ulisse Munari\\inst{2}"
}
] |
We present accurate UBV(RI)$_{C}$ photometric sequences around 20 symbiotic stars. The sequences extend over wide brightness and color ranges, and are suited to cover quiescence as well as outburst phases. The sequences are intended to assist both present time photometry as well as measurement of photographic plates from historical archives. \keywords {Catalogs -- Binaries: symbiotic}
|
[
{
"name": "paper.tex",
"string": "\\documentstyle[psfig]{l-aa}\n\n\\begin{document}\n\n\\thesaurus {06 (04.03.1, 08.02.5)}\n\n\\title{UBV(RI)$_{\\rm C}$ photometric comparison sequences for symbiotic stars}\n\n\\author{\n Arne Henden\\inst{1}\n\\and Ulisse Munari\\inst{2}\n }\n\\offprints{U.Munari}\n\n\\institute {\nUniversities Space Research Association/U. S. Naval Observatory\nFlagstaff Station, P. O. Box 1149, Flagstaff AZ 86002-1149, USA\n\\and\nOsservatorio Astronomico di Padova, Sede di Asiago, \nI-36012 Asiago (VI), Italy\n}\n\\date{Received date..............; accepted date................}\n\n\\maketitle\n\n\\markboth{A.Henden and U.Munari: UBV(RI)$_{\\rm C}$ photometric comparison sequences for \nsymbiotic stars}{A.Henden and U.Munari: UBV(RI)$_{\\rm C}$ photometric comparison \nsequences for symbiotic stars}\n\n\\begin{abstract}\nWe present accurate UBV(RI)$_{\\rm C}$ photometric sequences around 20 symbiotic stars.\nThe sequences extend over wide brightness and color ranges, and are suited\nto cover quiescence as well as outburst phases. The sequences are intended\nto assist both present time photometry as well as measurement of\nphotographic plates from historical archives.\n\\keywords {Catalogs -- Binaries: symbiotic}\n\\end{abstract}\n\\maketitle\n\n\\section{Introduction}\n\nSymbiotic stars are binary systems composed of a cool giant and a hot,\nluminous white dwarf. They show variability over any time scale from minutes\n(flickering) to several decades (outbursts of symbiotic novae), with\nphenomena related to the orbital motion having periodicities generally\nbetween 1 and 4 years (or a few decades in the systems harbouring a\nMira variable, $\\sim$20\\% of all known symbiotic stars).\n\nSuch long time scales tend to discourage stand--alone photometric campaigns\nfrom a single Observatory (which would require observational programs\nrunning up to $\\sim$10 years in order to derive - for example - a firm orbital\nperiod). Most of the current photometric investigations of symbiotic stars\ntherefore try to assemble as much as possible data from the widest set of\ncurrent and archival sources. A template example is the recent\nreconstruction of the 1890-1996 lightcurve and orbital period determination\nfor YY~Her by Munari et al. (1997).\n\nThe data so collected are generally very heterogeneous in nature, with large\ndifferences caused for example by ($a$) the non-standard photometric bands,\n($b$) the adopted comparison sequences and standard stars, ($c$) lack of\nadherence to and transformation into a system of general use, like the\nUBV(RI)$_{\\rm C}$, and ($d$) telescope focal length or pixel scale\nthat causes blending with images of nearby field stars. These\ndifferences generally may introduce such a large scatter in the data that\nall but the strongest details are washed out.\n\nThe establishment of suitable and accurate photometric comparison sequences\ncovering a wide range in magnitude and colors should alleviate considerably\nsome of the above problems, and could encourage small observatories and/or\noccasional observers to obtain new data as well as to encourage \nthose with access to plate archives to search for valuable historical data.\n\nTo this aim we present here suitable, UBV(RI)$_{\\rm C}$ comparison sequences\nfor 20 symbiotic stars (all but a few accessible from both hemispheres. See\nTable~1 for a list of the program stars). The sequences are basically\nintended to allow a general observer to capture on a single CCD frame or to\nhave in the same eyepiece field of view when inspecting archival\nphotographic plates: ($a$) enough stars to cover the whole range of known or\nexpected variability for the given symbiotic star, ($b$) stars of enough\ndifferent colors to be able to calibrate the instrumental color equations\nand therefore reduce to the standard UBV(RI)$_{\\rm C}$ system the collected\ndata, and ($c$) stars well separated from surrounding ones to avoid blending\nat all but the shortest telescope focal lengths.\n\n\\begin{table*}\n\\caption[]{List of program symbiotic stars. The coordinates for the symbiotic stars\nare from our observations (equinox J2000.0, mean epoch 1999.5). \nThe $e_\\alpha$ and $e_\\delta$ columns list the errors in milliarcsec\nfor right ascension and declination, respectively. The last two\ncolumns list the coordinates of the field centers in Figures~1 and 2.}\n\\centerline{\\psfig{file=tab_1.ps,width=18cm}}\n\\end{table*}\n\n\\begin{figure*}[h!]\n\\centerline{\\psfig{file=fig_1.ps,width=17.5cm}}\n\\caption[]{Finding charts for the UBV(RI)$_{\\rm C}$ comparison\nphotometric sequence around the program symbiotic stars. The fields are\nin the same order as in Table~1. North is up and East to the left,\nwith an imaged field of view of 5.16$\\times$5.16 arcmin and\na 5.4$\\times$5.4 coordinate grid (see bottom-right panel of Figure~2).\nStars are plotted as open circles of diameter proportional to the\nbrightness in the $V$ band. The stars making up the photometric sequence\n(see Table~2) are plotted as filled circles.}\n\\end{figure*}\n\n\n\\section{Observations}\n\nAll observations were made with the 1.0-m Ritchey-Chr\\'etien telescope of\nthe U. S. Naval Observatory, Flagstaff Station. A Tektronix/SITe 1024x1024\nthinned, backside--illuminated CCD was used, along with Johnson UBV and\nKron--Cousins RI filters. Images were processed using IRAF, with nightly\nmedian sky flats and bias frames. Aperture photometry was performed with\nroutines similar to those in DAOPHOT (Stetson 1987). Astrometry was\nperformed using SLALIB (Wallace 1994) linear plate transformation routines\nin conjunction with the USNO--A2.0 reference catalog. Errors in coordinates\nwere typically under 0.1 arcsec in both coordinates, referred to the mean\ncoordinate zero point of the reference stars in each field.\n\nThe telescope scale is 0.6763 arcsec/pixel, with a total field of view of\naround 11.4x11.4 arcmin. Typical seeing was $\\sim$2 arcsec. A 9 arcsec\nextraction aperture with concentric sky annulus was commonly used.\n\nThe reported photometry only uses data collected on photometric nights\n(transformation errors under 0.02mag). For each such night, symbiotic field\nobservations were interspersed with observations of Landolt (1983, 1992)\nstandard fields, selected for wide color and airmass range. The mean\ntransformation coefficients (cf. Henden \\& Kaitchuck\n1990, eqns. 2.9ff) are:\n\n\\begin{eqnarray}\n V:& -0.020& \\pm 0.007 \\\\\nB-V:& ~0.949& \\pm 0.007 \\\\\nU-B:& ~1.072& \\pm 0.018 \\\\\nV-R:& ~1.017& \\pm 0.005 \\\\\nR-I:& ~0.971& \\pm 0.013 \n\\end{eqnarray}\n\nSecond order extinction was negligible except for {\\sl B--V}, where a\ncoefficient of --0.03 was used.\n\nThe symbiotic field photometry was usually performed as the field transited. \nIn a few rare cases, observations were made at higher airmass to the West. \nIn these cases, care was taken to obtain extinction measures at equivalent\nor higher airmass. Each field was observed on at least three nights. Since\nall primary standards used the same aperture as the secondary standards\nbeing established, and the apertures were large, no aperture corrections\nwere necessary.\n\n\n\\section{The photometric sequences}\n\nBetween 10 and 15 stars around each symbiotic star have been selected to\nform the comparison sequences, given in Table~2. The sequences have been\nselected and ordered on the basis of the $B$ magnitude. The $B$ magnitude is\nreproducible by most filter-equipped CCD cameras, it is the closest one to\nthe $m_{pg}$ band of the historical photographic observations and the $B$\nband is particularly well suited to investigate the variability of\nsymbiotic stars (see next section).\n\nThe range in magnitude of the sequences is large enough to cover both\noutburst and quiescence phases (eclipses included) of each symbiotic star.\nThe comparison sequences are tighter around the usual brightness of the\nsymbiotic stars and become looser away from it. In most cases the sequences\nextend to much fainter magnitudes (down to $B \\geq 19$ mag or $B \\geq 20$\nmag) than reached by the respective symbiotic stars because they could be of\ninterest to other observational projects as well as in assisting in the\ncalibration of sky survey projects on photographic plates.\n\nFor 9 objects (Draco C-1, ALS~2, K~3-9, V919~Sgr, Ap~3-1, V335~Vul,\nHen~3-468, V627~Cas and StH$\\alpha$~32) the symbiotic star and the\ncomparison sequence both lie inside a 5.16$\\times$5.16 arcmin field (see\nFigure~1), which match in dimension the Allen (1984) finding charts. For the\nremaining 11 program objects, comparison stars bright enough to cover the\noutburst phases had to be found at greater distance from the symbiotic star.\nThey are given in Table~2 at the end of each sequence, separated by an empty\nline from the other comparison stars, and are plotted on the less deep and\nwider finding charts of Figure~3.\n\nThe stars included in the comparison sequences have been checked on at least\nthree different nights for variability (see column $N$ of Table~2). We\ncannot rule out beyond doubt that some of them are indeed variable (they\ncould be eclipsing systems observed outside eclipse, for example), but the\nfairly good \n\n\\begin{figure*}[!h]\n\\centerline{\\psfig{file=fig_2.ps,width=17.5cm}}\n\\caption[]{Same as Figure~1.}\n\\end{figure*}\n\n\\begin{figure*}[!h]\n\\centerline{\\psfig{file=fig_3.ps,width=17.5cm}}\n\\caption[]{Comparison stars bright enough to cover the outburst phases\nlay outside the fields of Figures~1 and 2 for eleven symbiotic stars.\nThey are identified in these wider finding charts, where the portion \nplotted in greater detail in Figures~1 and 2 is outlined by\na dashed square. The symbols are the same as in Figures~1 and 2, with\nan imaged field of view of about 11.4$\\times$11.4 arcmin and a\n12$\\times$12 arcmin coordinate grid. To avoid overcrowding, the limiting\nmagnitude is much brighter ($V \\sim$16 mag) than in Figures~1 and 2.}\n\\end{figure*}\n\n\\clearpage\n\n\\noindent\nagreement (at a few millimag level) of their magnitudes as measured on\ndifferent nights over some months gives some confidence in their use. \nFinally, to avoid problems of blending with nearby stars on plates or CCD\nimages from short focus telescopes, the comparison stars have been selected\nso as to avoid those with close companions.\n\n\\section{The type of variability in symbiotic stars}\n\nAs a guideline for observers not familiar with the symbiotic stars, a few\nsimplified notes may be of interest concerning the types of variability one\nmay expect from the latter and the best way to observe them. We will limit\nthe discussion to the photometric bands of the UBV(RI)$_{\\rm C}$ system.\n\nThe variability ascribed to the {\\sl cool giant} is best observed at longer\nwavelengths (i.e. the $I$ band. The $R$ band is affected by the usually\nvery strong H$\\alpha$ emission), where the contamination from the white\ndwarf companion and the circumstellar material become less important.\nBasically, two types of variability of the cool giant may be observed:\\\\\n \\underline{\\sl intrinsic}, like the pulsations of a Mira variable (about\n $\\sim$ 20\\% of the known symbiotics harbor a Mira). The amplitude of\n variability generally decreases toward longer wavelengths. Popular examples\n are R~Aqr (pulsation period of 386 days, minima as faint as $V$=12, maxima\n as bright as $V$=5 mag) or UV Aur (pulsation period of 395 days, minima as\n faint as $V$=11, maxima as bright as $V$=7.5 mag);\\\\\n \\underline{\\sl ellipsoidal}, when the cool giant fills its Roche lobe.\n Due to the orbital motion the area of the Roche lobe projected onto\n the sky varies continuously, with two maxima (when the binary system is\n seen at quadrature) and two minima (when the cool giant passes at superior\n or inferior conjunctions) per orbital cycle. Because the reason for\n variability is a geometrical one, the amplitude of variability is not strongly\n dependent upon wavelength. Popular examples of symbiotic stars showing\n ellipsoidal distortion of their lightcurve are T~CrB (orbital period 227\n days, amplitude $\\bigtriangleup m$= 0.3 mag) and BD--21.3873 (orbital\n period 285 days, amplitude $\\bigtriangleup m$= 0.2 mag).\n\nThe variability ascribed to the {\\sl hot white dwarf} companion to the cool\ngiant is best observed at shorter wavelengths. There are several type of\nmanifestations, among which :\\\\\n \\underline{\\sl outbursts}, with amplitudes $\\bigtriangleup B = 2 -\n 5$ mag and duration from half a year to many decades. The amplitude,\n duration and lightcurve shape are usually unpredictable. The same system\n might show completely different type of outbursts one after the other. \n For example, QW~Sge had an outburst extending from July 1962 to March 1972\n characterized by a rapid rise and a linear and smooth decline, followed by\n another one from May 1982 to September 1989 showing a complex lightcurve\n with more than one maximum and deep minima in between;\\\\\n \\underline{\\sl reflection effect}, when the hard radiation field of the\n hot and luminous white dwarf (radiating mainly in the X-ray and far\n ultraviolet domains) illuminates and heats up the facing side of the cool\n giant (which reprocesses to the optical domain the energy received by the\n white dwarf). The heated side of the cool giant is therefore a bit\n brighter and bluer than the opposite one (which is not illuminated by the\n white dwarf radiation field). During an orbital period the heated side comes\n and goes from view, causing a sinusoidal lightcurve. The effect is strongly\n wavelength dependent, being maximum in the $U$ band and undetectable in\n $R$ and $I$ bands. The amplitude may be fairly large, as in LT~Del where\n $\\bigtriangleup U$=1.6, $\\bigtriangleup B$=0.5 and $\\bigtriangleup V$= 0.2\n mag. It should be observable in the majority of symbiotic stars (more and\n more easily as the white dwarf gets hotter and the orbital inclination\n increases) and it is a powerful way to measure orbital periods;\\\\\n \\underline{\\sl eclipses} of the white dwarf by the cool giant. In\n quiescence the eclipses generally escape detection by optical photometry\n because the white dwarf is radiating mostly at shorter wavelengths (X-rays\n and far ultraviolet). During the outbursts the white dwarf emission\n shifts to longer wavelengths and becomes conspicuous in the optical, thus\n allowing the eclipses to be detected if the orbital inclination is\n sufficiently high. Classical examples of symbiotic stars for which the\n eclipses passed undetected in quiescence and instead became outstanding\n features of the outburst lightcurve are FG~Ser and V1413~Aql. Because\n the eclipsing body is cool and the eclipsed one is hot, the visibility of\n eclipses increases toward shorter wavelengths (for example for FG Ser in\n outburst it was $\\bigtriangleup V$=1.4, $\\bigtriangleup B$=1.9 and\n $\\bigtriangleup U$=2.3 mag);\\\\\n \\underline{\\sl re-processing} by the circumstellar nebula of the energy\n radiated by the white dwarf. Sometimes there is so much circumstellar gas\n ionized by the radiation field of the white dwarf that its brightness\n completely overwhelms that of the binary system, as it is for the popular\n cases of V1016~Cyg and V852~Cen (the {\\sl Southern Crab}). Both these symbiotic\n binaries harbor a Mira variable, whose variability however does not at all\n affect the optical photometry because of the immensely brighter\n circumstellar ionized gas. When the white dwarf becomes progressively\n cooler and dimmer, the amount of ionizing photons that it releases goes\n down, and the ionized fraction of the circumstellar nebula decreases and\n consequently its brightness (the scenario is valid for radiation bounded\n nebulae). This is the case for HM~Sge that over the last 25 years has\n gradually become fainter by $\\bigtriangleup V$ = 0.031 and\n $\\bigtriangleup B$ = 0.086 mag~yr$^{-1}$.\n \n\\section{Notes on individual symbiotic stars}\n\nA few individual notes follow on the photometric behavior of the program\nsymbiotic stars, to the aim of assisting the interested reader in planning\nan observing strategy. An inspiring reading would also be the collected\nhistory of symbiotic stars assembled by Kenyon (1986).\n\nWhile calibrating the photometric comparison sequences for this paper we\nhave also collected data on the program symbiotic stars. These UBV(RI)$_{\\rm\nC}$ data will be presented and discussed elsewhere together with similar\ndata for more than another 100 symbiotic stars observed from ESO and Asiago.\nTo the reader's benefit we report in this section mean $B$ and {\\sl B-V}\nvalues for 1999 from the UBV(RI)$_{\\rm C}$ survey (hereafter indicated as\nMHZ: Munari, Henden and Zwitter, in preparation).\n\n\\underline{\\sl Draco C-1}. This carbon symbiotic star belongs to the Draco\ndwarf galaxy (Aaronson et al. 1982). Infrared photometry by \n\n\\begin{table*}\n\\caption[]{The comparison sequences around the 20 program symbiotic stars. Positions\nfor J2000 equinox and a mean epoch 1999.5 are given (errors in arcsec are\nderived from different exposures in different bands), together with\nmagnitudes and colors (errors in magnitudes). The stars in each sequence are ordered \naccording to fainter $B$ magnitudes. $N$ is the number of observing nights.\nThe sequences are given in the same order as in Table~1 and Figures~1 and 2.\nThe comparison stars laying outside the field of view of Figures~1 and 2\nand plotted in Figure~3 are given at the bottom of each sequence, separated by\nan empty line.}\n\\centerline{\\psfig{file=tab_2a.ps,height=23.5cm}}\n\\end{table*}\n\n\\setcounter{table}{1}\n\\begin{table*}\n\\caption[]{({\\sl continues})}\n\\centerline{\\psfig{file=tab_2b.ps,height=24.5cm}}\n\\end{table*}\n\n\\setcounter{table}{1}\n\\begin{table*}\n\\caption[]{({\\sl continues})}\n\\centerline{\\psfig{file=tab_2c.ps,height=24.5cm}}\n\\end{table*}\n\n\\setcounter{table}{1}\n\\begin{table*}\n\\caption[]{({\\sl continues})}\n\\centerline{\\psfig{file=tab_2d.ps,height=24.5cm}}\n\\end{table*}\n\n\\noindent\nMunari (1991a) proves C-1 to be at the tip of the Draco AGB with very blue\nIR colors for a carbon star, probably caused bythe low metal content of the\nparent galaxy (Munari 1991b). No outburst has been so far recorded and the\norbital period is unknown. {\\sl BVI} photometry by Munari (1991c) seems to\nsupport a variability of the carbon giant with a period of $\\sim$ 55 days.\nIf confirmed, this would be among the shortest period known for carbon\npulsating variables (cf. Claussen et al. 1987). MHZ report $B$=18.6 and\n{\\sl B--V}=+1.5 mag.\n \n\\underline{\\sl ALS 2}. Its symbiotic nature has been discovered by Acker et\nal. (1988). MHZ lists $B$=16.2 and {\\sl B--V}=+1.9 mag. The orbital\nperiod, type of variability and presence of historical outburst are unknown.\n\n\\underline{\\sl FG Ser}. After the 1988--1994 outburst when it rose to\n$B$=10.4 and {\\sl B--V}=+1.1, it is now back toward the quiescent $B$=13.8\nand {\\sl B--V}=+2.0 mag values. MHZ list $B$=13.5 and {\\sl B--V}=+1.7 mag.\nMunari et al. (1992b) discovered eclipses during the outburst phase (of\namplitude $\\bigtriangleup V$=1.4, $\\bigtriangleup B$=1.9, $\\bigtriangleup\nU$=2.3 mag and 120 days between first and fourth contact). From three\nconsecutive mimina Munari et al. (1995) derived the following ephemeris\n\\begin{equation}\nT(min) = 2448492 (\\pm 4) \\ + \\ 658 (\\pm 4) \\times E\n\\end{equation}\nwhere 658 is the period in days, as usual.\nFrom 250 archive blue plates covering the period 1949-1987, Kurockin (1993)\nfound a large and sinusoidal variability at quiescence ($\\bigtriangleup\nB$=1.5 mag), following the ephemeris\n\\begin{equation}\nT(min) = 2446591 \\ + \\ 630 \\times E\n\\end{equation}\nwhich could be interpreted in terms of a reflection effect. The difference\nbetween the two periods (both should trace the orbital period) has to be\ninvestigated. It should also be noted that the cool component does not show\nintrinsic or ellipsoidal variability in excess of 0.1 mag. The eclipses have\nnot yet been searched for during quiescence. Their detection and monitoring\nwould be of interest to measure the size, temperature and luminosity\nof the white dwarf now that it is returning back to quiescence dimensions.\n\n\\underline{\\sl V443 Her}. No outburst has ever been recorded from this\nfairly bright symbiotic star. Its behavior in quiescence has been investigated by\nKolotilov et al. (1995) who found a lightcurve dominated by a reflection effect \nof $\\bigtriangleup U$=0.9, $\\bigtriangleup B$=0.4 and $\\bigtriangleup V$= 0.1 mag\namplitude. The minima follow the ephemeris\n\\begin{equation}\nT(min) = 2443660 (\\pm 30) \\ + \\ 594 (\\pm 3) \\times E\n\\end{equation}\nThere seems to be another periodicity of no easy interpretation at 430 days.\nThe mean values in quiescence are $B$=12.5 and {\\sl B--V}=+1.0. Limited\ninfrared observations by Kolotilov et al. (1998) seems to argue against\nvariability of the cool giant or an ellipsoidal distortion of it.\n\n\\underline{\\sl K 3-9}. Originally classified among the planetary nebulae,\nits symbiotic star nature has been discovered by Acker et al. (1983).\nAccording to Ivison and Seaquist (1995) K 3-9 is among the brightest\nsymbiotic radio sources, and could harbor a Mira variable and a WD locked in\na permanent outburst state. A thick dust cocoon should encircle the binary\nsystem, and a huge external ionized nebular material completely dominates\nthe optical spectra. The photometric properties, history and orbital period\nare unknown. MHZ report $B$=18.3 and {\\sl B--V}=+1.3.\n\n\\underline{\\sl MWC 960}. This is a bright symbiotic star neglected by the\nobservers. Munari et al. (1992a) report $B$=13.6 and {\\sl B--V}=+1.5 and MHZ\nlist $B$=13.8 and {\\sl B--V}=+1.6. The photometric properties, history and\norbital period are unknown.\n\n\\underline{\\sl AS 323}. Another object originally classified as a planetary\nnebula which later turned out to be a symbiotic star (Sabbadin 1986, Acker et\nal. 1983). MHZ report $B$=15.2 and {\\sl B--V}=+1.0. The photometric\nproperties, history and orbital period are unknown.\n\n\\underline{\\sl FN Sgr}. Another bright symbiotic star that has been\noverlooked by most observers even though reports of large variability date\nback to Ross (1926). Outbursts have been recorded in 1924-1926 and\n1936-1941. The brightness in quiescence seems to vary by a large amplitude\n($\\bigtriangleup m \\sim$2 mag) with possible periodicities between 1 and 3\nyears (cf. Kenyon 1986 and references therein). Amateur visual observations\nover the last few years show a pattern reminiscent of an eclipsing binary\nfollowing the ephemeris (Munari et al., in preparation):\n\\begin{equation}\nT(min) = 2451410 (\\pm 15) \\ + \\ 1120 (\\pm 20) \\times E\n\\end{equation}\nThe mean brightness is $V \\sim$13.5 in eclipse and $V \\sim$11.0 outside.\nNext minimum is scheduled for mid September 2002. MHZ list $B$=12.7 and {\\sl\nB--V}=+0.7.\n\n\\underline{\\sl V919 Sgr}. Another bright object ignored by observers.\nAccording to literature review and new observations by Ivison et al. (1993),\nV919 Sgr varies between $B$=12 and $B \\geq$ 14.2 mag. Its cool giant is\ndefinitively variable in the infrared by at least $\\bigtriangleup K$=0.7\nmag. The announcement of an outburst was made in 1991, but it is not yet\nproven it actually occurred (see Ivison et al. 1993). MHZ report $B$=14.2\nand {\\sl B--V}=+1.2. The past photometric history and orbital period are\nunknown.\n\n\\underline{\\sl CM Aql}. Another relatively bright symbiotic star that has\nbeen overlooked by most observers. Its range of variability extend from\n$B$=13.0 to $B$=16.5. Outbursts have been reported for 1914, 1925, 1934,\n1950. CM Aql also attracted some attention in late 1992 when from the usual\n$V=13.2$ it rose for a short period to $V\\sim 12$ mag. The orbital period is\nunknown. MHZ report $B$=14.6 and {\\sl B--V}=+1.3\n\n\\underline{\\sl V1413 Aql}. The star erupted into a symbiotic nova in late\n1981, and has not yet returned to quiescence conditions. According to\nMunari (1992), V1413 Aql presented in quiescence \none of the largest known reflection effects ($B$ varying between 16.5 and\n14.0 mag). When the star erupted into outburst, deep eclipses appeared\nperfectly in phase with the minima of the reflection effect according the\nephemeris\n\\begin{equation}\nT(min) = 2446650 (\\pm 15) \\ + \\ 434.2 (\\pm 0.2) \\times E\n\\end{equation}\nAt outburst maximum the star peaked at $B$=11.2 and {\\sl B--V}=+0.7\n(compared to $B$=15.5 and {\\sl B--V}=+1.5 in quiescence). The decline has\nbeen very slow but smooth until late 1992 when V1413 Aql went back on the\nrise and returned to peak brightness ($V$=10.5) by summer of 1995 and\nstarted to decline again in a very smooth way (Munari 1996). The\neclipses have always been visible during the whole outburst phases since\n1982, and at minimum the star shines at $V\\sim$15.0. Outside eclipses the\nstar is currently at $V$=13.1 and {\\sl B--V}=+0.9. If the present rate of\ndecline of $\\bigtriangleup V$=0.56 mag yr$^{-1}$ will be maintained in the\nfuture, the star should return to quiescence brightness by late 2002. A\ndetailed multi-band monitoring of successive eclipses would be of great\ninterest to model the radius, temperature and luminosity of the outbursting\ncomponent while it is returning back to quiescence conditions.\n\n\\underline{\\sl Ap 3-1}. Another example of an object originally classified \nas a planetary nebula, and which later turned out to be a symbiotic star (Allen 1984).\nIts photometric properties are unknown. MHZ list $B$=19.1 and\n{\\sl B--V}=+2.1\n\n\\underline{\\sl ALS 1}. Its symbiotic nature has been discovered by Acker et\nal. (1988), who report $V$=14.8 mag. MHZ lists $V$=13.5 and {\\sl\nB--V}=+1.4 mag. The photometric properties, history and orbital period are\nunknown.\n\n\\underline{\\sl V335 Vul}. A symbiotic nature for this carbon star has been\nsuggested only recently (Munari et al. 1999a). The star colors are very\nred, with MHZ giving $V$=12.9 mag and {\\sl B-V}=+5.1 for quiescence.\nMunari et al. (1999b) caught the star on the rising branch of an\napparent outburst, with $V$=11.3 and {\\sl B--V}=+3.1 and a ten-fold increase\nin the intensity of emission lines. The orbital period is unknown.\nAccording to Dahlmark (1993) the carbon star is a Mira variable of\n10.5 $< V <$ 13.2 range, and maxima given by the ephemeris\n\\begin{equation}\nT(min) = 2446740 \\ + \\ 342 (\\pm 0.2) \\times E\n\\end{equation}\nThe possible outburst reported by Munari et al. (1999b) for the end of 1999\nhappened at the time of maximum brightness for the Mira variable (O.Pejcha\nand P.Sobota, private communication). The puzzling coincidence of the two\nevents should be studied in more details.\n\n\\underline{\\sl QW Sge}. Examining 438 archive blue plates covering the\nperiod 1960-1992, Kurockin (1993) has discovered two outbursts: one extending\nfrom July 1962 to March 1972 with $B$=11.5 at maximum, the other from May\n1982 to September 1989 with a much more complex lightcurve and a peak\nbrightness $B$=12.0. \nOutside outburst phases the star is since first observations in 1898 at\n$B\\sim 13.1\\div 13.3$. MHZ lists $B$=13.2 and {\\sl B--V}=+0.81 mag. QW Sge\nhas an optical companion 3.5 arcsec to the north, that Munari and Buson\n(1991) classified as an F0~V star with $B$=13.59 and {\\sl B--V}=+0.45. Our\nphotometry gives different values, $B$=13.18 and {\\sl B--V}=+0.83, with a\nlarge scatter of 0.25 mag between three different measurements (compared to\nthe few millimag for nearby stars of similar brightness). All this suggests\nthat the optical companion is itself a variable star, and this complicates\nthe interpretation of photometry made with moderate or short focus\ntelescopes that are not able to separate QW~Sge from the close optical\ncompanion (as it is the case for most of the archive photographic plates).\nIt seems relevant to observe QW Sge with enough spatial resolution to avoid\ncontamination from the nearby companion and to characterize the type and\namplitude of variability of the latter. If the companion should turn out to\nbe a moderate-amplitude variable and/or of a predictable type (like an\neclipsing system), it would be possible to remove its contribution from the\nphotographic photometry collected on QW Sge over the last century. No\norbital period has been determined for QW Sge.\n\n\\underline{\\sl LT Del}. A large reflection effect ($\\bigtriangleup U$=1.6,\n$\\bigtriangleup B$=0.5 and $\\bigtriangleup V$= 0.2 mag) following the\nephemeris\n\\begin{equation}\nT(min) = 2445910 (\\pm 5) \\ + \\ 478.5 (\\pm 2) \\times E\n\\end{equation}\nhas been discovered by Arkhipova et al. (1995), who lists $B$ = 14.4 and\n{\\sl B--V}=+1.3 mag as mean values for the quiescence. MHZ report $B$=14.3\nand {\\sl B--V}=+1.3. The only recorded outburst of LT~Del has been\ndiscovered in the summer of 1994 by Passuello et al. (1994), when the star\nrose to $B$=12.8 and {\\sl B--V}=+0.5. The star has returned to quiescence by\nearly 1998.\n\n\\underline{\\sl Hen 2-468}. The photometric properties, history and orbital\nperiod are unknown. MHZ list $B$=16.6 and {\\sl B--V}=+1.8 mag.\n\n\\underline{\\sl V407 Cyg}. Discovered as Nova Cyg 1936, it was found by\nMeinunger (1966) to harbor a Mira variable with one of the longest pulsation\nperiod known and maxima following the ephemeris\n\\begin{equation}\nT(max) = 2429710 \\ + \\ 745 \\times E\n\\end{equation}\nWhile reconstructing the historical lightcurve, Munari et al. (1990)\ndiscovered that brightness at the maximum of the pulsation cycle is strongly\nmodulated by a sinusoidal variation with a possible period around 43 years\nand extrema at $B_{max}=13.3$ and $B_{max}=17.0$. The 43 year periodicity\nwas interpreted as the orbital period of the system. V407~Cyg was discovered\nagain in outburst in the summer of 1994 by Munari et al. (1994), when it\nrose to $B=14.0$ and $B-V$=+1.0 (same value as in the 1936 outburst) at a\ntime when contemporaneous infrared photometry confirmed that the Mira was at\na minimum in its pulsation cycle. According to VSNET databank the last\nminimum of the Mira has been in the very early 1998 ($V >$ 16.0) and the\nlast maximum in June 1999 ($V \\sim$11.2). The lightcurve is however quite\ncomplicated with humps as large as one magnitude superimposed to the much\nsmoother lightcurve of the Mira. The humps are possibly connected with the\ncurrent enhanced activity phase of the white dwarf and would deserve close\nmonitoring over the whole UBV(RI)$_{\\rm C}$ range. MHZ list $B$=13.2 and\n{\\sl B-V}=+1.5.\n\n\\underline{\\sl V627 Cas}. Originally classified among the T~Tau pre-main\nsequence variables, its symbiotic star nature was discovered by Kolotilov\n(1988). Kolotilov et al. (1996) has summarized the optical and infrared\nphotometric properties of V627 Cas. The cool component seems to be a M2\nsupergiant in a post-AGB phase, pulsating with a 466 day period. The hot\ncomponent presents flickering activity superimposed onto several different\ntypes of variability, including a secular dimming by $\\bigtriangleup B$=2.0\nmag in 60 years. This is a peculiar type of symbiotic star which needs\nmore effort to be better characterized from a photometric point of view. To\nnull the effect of flickering, the star should be observed more times per\nnight and over a few consecutive nights in all the UBV(RI)$_{\\rm C}$ bands.\n\n\\underline{\\sl StH$\\alpha$ 32}. Its symbiotic star nature has been\ndiscovered by Downes and Keyes (1988). The photometric properties are\nunknown. MHZ list $B$=14.2 and {\\sl B-V}=+1.4.\n\n\\begin{thebibliography}{}\n\\bibitem{} Allen D.A., 1984, Proc.A.S.A. 5, 369\n\\bibitem{} Aaronson M., Liebert, J., Stocke, J., 1982, Ap.J. 254, 507\n\\bibitem{} Acker A., Lundstr\\\" om I., Stenholm B., 1988, A\\&AS 73, 325\n\\bibitem{} Arkhipova V.P., Ikonnikova, N.P., Noskova, R.I., 1995 1995 PAZh 21, 379\n\\bibitem{} Clausaen M.J., Kleinmann S.G., Joyce R.R., Jura M., 1987, Ap.J.Suppl. 65,385\n\\bibitem{} Dahlmark L., 1993, IBVS 3855\n\\bibitem{} Downes R.A., Keyes C.D. 1988, AJ 96, 777\n\\bibitem{} Henden, A. A., Kaitchuck, R. H. 1990, Astronomical\n Photometry (Richmond: Willmann-Bell).\n\\bibitem{} Ivison R.J., Seaquist E.R. 1995, MNRAS 272, 878\n\\bibitem{} Ivison R.J., Munari U., Marang F., 1993, A\\&A 277, 510\n\\bibitem{} Kenyon 1986, The Symbiotic Stars, Cambridge University Press\n\\bibitem{} Kolotilov E.A. 1988, Astrofizika 9, 458\n\\bibitem{} Kolotilov E.A., Munari U., Yudin B.F. 1995, A\\&A 293, 815 \n\\bibitem{} Kolotilov E.A., Munari U., Yudin B.F., Tatarnikov A.M. 1996, Sov.Astron. 40, 812\n\\bibitem{} Kolotilov E.A., Munari U., Popova A.A., Yudin B.F. 1998, Astron. Lett. 24, 34\n\\bibitem{} Kurochkin N.E. 1993, Astron.Astrophys.Transactions 3, 295\n\\bibitem{} Landolt, A. U. 1983, AJ, 88, 439.\n\\bibitem{} Landolt, A. U. 1992, AJ, 104, 340.\n\\bibitem{} Meinunger L., 1966, Mitt.Veranderl.Sterne 3, 111\n\\bibitem{} Munari U., 1991a, Inf.Bull.Var.Stars 3605\n\\bibitem{} Munari U., 1991b, A\\&A 251, 103\n\\bibitem{} Munari U., 1991c, Inf.Bull.Var.Stars 3648\n\\bibitem{} Munari U., 1992, A\\&A 257, 163\n\\bibitem{} Munari U., 1996, in Physical Processes in Symbiotic Binaries and Related\n Systems, ed.s J.Mikolajewska, Polish Academy of Sciences, pag. 37\n\\bibitem{} Munari U., Margoni R., Stagni R. 1990, MNRAS 242, 653\n\\bibitem{} Munari U., Buson L.M. 1991, A\\&A 249, 141\n\\bibitem{} Munari U., Yudin B.F., Taranova O.G., Massone G., Marang F., Roberts G.,\n Winkler H., Whitelock P.A. 1992a, A\\&AS 93, 383\n\\bibitem{} Munari U., Whitelock P.A., Gilmore A.C., Blanco C., Massone G.,\n Schmeer P.K. 1992b, AJ 104, 262\n\\bibitem{} Munari U, Bragaglia A., Guarnieri M.D., Sostero G., Lepardo A.,\n Yudin B.F., 1994, IAU Circ 6049\n\\bibitem{} Munari U., Yudin B.F., Kolotilov E.A., Gilmore A.C. 1995, AJ 109, 1740 \n\\bibitem{} Munari U., Rejkuba M., Mattei J., Hazen M., Luthardt R., Yudin B.F. 1997,\n A\\&A 323, 113\n\\bibitem{} Munari U., Tomov T., Rejkuba M., 1999a, IBVS 4668\n\\bibitem{} Munari U., Tomov T., Moro D., Henden A. 1999b, IAU Circ.\n\\bibitem{} Passuello R., Saccavino S., Munari U. 1994, IAU Circ 6065\n\\bibitem{} Ross F.E. 1926, AJ 36, 122\n\\bibitem{} Sabbadin F., 1986, A\\&AS 65, 301\n\\bibitem{} Stetson, P. B. 1987, PASP 99, 191.\n\\bibitem{} Wallace, P. 1994, in Astronomical Data Analysis Software\n and Systems III, PASP conference series, vol 61\n (San Francisco: ASP), ed. Crabtree, D. R., Hanisch, R. J.\n and Barnes, J., p. 481.\n\\end{thebibliography}\n\n \n\n\\end{document}\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002147.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem{} Allen D.A., 1984, Proc.A.S.A. 5, 369\n\\bibitem{} Aaronson M., Liebert, J., Stocke, J., 1982, Ap.J. 254, 507\n\\bibitem{} Acker A., Lundstr\\\" om I., Stenholm B., 1988, A\\&AS 73, 325\n\\bibitem{} Arkhipova V.P., Ikonnikova, N.P., Noskova, R.I., 1995 1995 PAZh 21, 379\n\\bibitem{} Clausaen M.J., Kleinmann S.G., Joyce R.R., Jura M., 1987, Ap.J.Suppl. 65,385\n\\bibitem{} Dahlmark L., 1993, IBVS 3855\n\\bibitem{} Downes R.A., Keyes C.D. 1988, AJ 96, 777\n\\bibitem{} Henden, A. A., Kaitchuck, R. H. 1990, Astronomical\n Photometry (Richmond: Willmann-Bell).\n\\bibitem{} Ivison R.J., Seaquist E.R. 1995, MNRAS 272, 878\n\\bibitem{} Ivison R.J., Munari U., Marang F., 1993, A\\&A 277, 510\n\\bibitem{} Kenyon 1986, The Symbiotic Stars, Cambridge University Press\n\\bibitem{} Kolotilov E.A. 1988, Astrofizika 9, 458\n\\bibitem{} Kolotilov E.A., Munari U., Yudin B.F. 1995, A\\&A 293, 815 \n\\bibitem{} Kolotilov E.A., Munari U., Yudin B.F., Tatarnikov A.M. 1996, Sov.Astron. 40, 812\n\\bibitem{} Kolotilov E.A., Munari U., Popova A.A., Yudin B.F. 1998, Astron. Lett. 24, 34\n\\bibitem{} Kurochkin N.E. 1993, Astron.Astrophys.Transactions 3, 295\n\\bibitem{} Landolt, A. U. 1983, AJ, 88, 439.\n\\bibitem{} Landolt, A. U. 1992, AJ, 104, 340.\n\\bibitem{} Meinunger L., 1966, Mitt.Veranderl.Sterne 3, 111\n\\bibitem{} Munari U., 1991a, Inf.Bull.Var.Stars 3605\n\\bibitem{} Munari U., 1991b, A\\&A 251, 103\n\\bibitem{} Munari U., 1991c, Inf.Bull.Var.Stars 3648\n\\bibitem{} Munari U., 1992, A\\&A 257, 163\n\\bibitem{} Munari U., 1996, in Physical Processes in Symbiotic Binaries and Related\n Systems, ed.s J.Mikolajewska, Polish Academy of Sciences, pag. 37\n\\bibitem{} Munari U., Margoni R., Stagni R. 1990, MNRAS 242, 653\n\\bibitem{} Munari U., Buson L.M. 1991, A\\&A 249, 141\n\\bibitem{} Munari U., Yudin B.F., Taranova O.G., Massone G., Marang F., Roberts G.,\n Winkler H., Whitelock P.A. 1992a, A\\&AS 93, 383\n\\bibitem{} Munari U., Whitelock P.A., Gilmore A.C., Blanco C., Massone G.,\n Schmeer P.K. 1992b, AJ 104, 262\n\\bibitem{} Munari U, Bragaglia A., Guarnieri M.D., Sostero G., Lepardo A.,\n Yudin B.F., 1994, IAU Circ 6049\n\\bibitem{} Munari U., Yudin B.F., Kolotilov E.A., Gilmore A.C. 1995, AJ 109, 1740 \n\\bibitem{} Munari U., Rejkuba M., Mattei J., Hazen M., Luthardt R., Yudin B.F. 1997,\n A\\&A 323, 113\n\\bibitem{} Munari U., Tomov T., Rejkuba M., 1999a, IBVS 4668\n\\bibitem{} Munari U., Tomov T., Moro D., Henden A. 1999b, IAU Circ.\n\\bibitem{} Passuello R., Saccavino S., Munari U. 1994, IAU Circ 6065\n\\bibitem{} Ross F.E. 1926, AJ 36, 122\n\\bibitem{} Sabbadin F., 1986, A\\&AS 65, 301\n\\bibitem{} Stetson, P. B. 1987, PASP 99, 191.\n\\bibitem{} Wallace, P. 1994, in Astronomical Data Analysis Software\n and Systems III, PASP conference series, vol 61\n (San Francisco: ASP), ed. Crabtree, D. R., Hanisch, R. J.\n and Barnes, J., p. 481.\n\\end{thebibliography}"
}
] |
astro-ph0002148
|
Spectral Analysis of the Ly$\alpha$ Forest Using Wavelets
|
[
{
"author": "A. Meiksin"
},
{
"author": "Blackford Hill"
},
{
"author": "Edinburgh EH9 3HJ"
},
{
"author": "UK"
}
] |
It is shown how wavelets may be used to analyse the absorption properties of the \Lya forest. The Discrete Wavelet Transform of a QSO spectrum is used to decompose the light fluctuations that comprise the forest into orthogonal wavelets. It is demonstrated that most of the signal is carried by the moderate to lower frequency wavelets in high resolution spectra, and that a statistically acceptable description of even high signal--to--noise spectra is provided by only a fraction (10--30\%) of the wavelets. The distributions of the wavelet coefficients provide a statistical basis for discriminating between different models of the \Lya forest. The method is illustrated using the measured spectrum of Q1937--1009. The procedure described is readily automated and may be used to process both measured spectra and the large number of spectra generated by numerical simulations, permitting a fair comparison between the two.
|
[
{
"name": "meiksin.tex",
"string": "\\documentstyle{mn}\n\\topmargin-0.2in\n\n\\input epsf\n\n\\begin{document}\n\n\\newcommand{\\Lya}{Ly$\\alpha\\ $}\n\\newcommand{\\HI}{\\hbox{H~$\\scriptstyle\\rm I\\ $}}\n\\newcommand{\\NHI}{$N_{\\rm HI}\\, $}\n\\newcommand{\\rchi}{\\chi_{\\rm red}^2\\, }\n\\newcommand{\\hMpc}{$h^{-1}\\, {\\rm Mpc}\\, $}\n\\newcommand{\\Mpch}{$h\\, {\\rm Mpc}^{-1}\\, $}\n\\newcommand{\\kms}{${\\rm km\\, s}^{-1}\\, $}\n\n\\newcommand{\\etal}{~et al.\\ }\n\n\\journal{Mon. Not. R. Astron. Soc. {\\bf 000}, 1--8 (2000)}\n\n\\title{Spectral Analysis of the Ly$\\alpha$ Forest Using Wavelets }\n\n\\author[A.Meiksin]{A. Meiksin \\\\\nInstitute for Astronomy, University of Edinburgh,\\\\\nBlackford Hill, Edinburgh EH9 3HJ, UK}\n\n\\date{Accepted 1999 December 17. Received 1999 July 26}\n\n\\maketitle\n\n\\begin{abstract}\nIt is shown how wavelets may be used to analyse the absorption properties\nof the \\Lya forest. The Discrete Wavelet Transform of a QSO spectrum\nis used to decompose the light fluctuations that comprise the forest into\northogonal wavelets. It is demonstrated that most of the signal is carried\nby the moderate to lower frequency wavelets in high resolution spectra, and\nthat a statistically acceptable description of even high signal--to--noise\nspectra is provided by only a fraction (10--30\\%) of the wavelets. The\ndistributions of the wavelet coefficients provide a statistical basis for\ndiscriminating between different models of the \\Lya forest.\nThe method is illustrated using the measured spectrum of Q1937--1009. The\nprocedure described is readily automated and may be used to process both\nmeasured spectra and the large number of spectra generated by numerical\nsimulations, permitting a fair comparison between the two.\n\n\\end{abstract}\n\n\\begin{keywords}\nintergalactic medium -- methods:data analysis -- quasars:absorption lines\n\\end{keywords}\n\n\\section{Introduction}\n\nMeasurements of QSO spectra show that the Intergalactic Medium (IGM) is\ncomposed of highly inhomogeneous structures. Ever since their identification\nby Lynds (1971) and the pioneering survey of Sargent \\etal (1980), these\ninhomogeneities have been described as discrete absorption systems, the \\Lya\nforest. With the view that the systems arise from individual intervening gas\nclouds, the \\Lya forest has been characterized using traditional absorption\nline statistics, most notably the line equivalent widths and, as the spectra\nimproved in resolution and signal--to--noise ratio, the Doppler widths and \\HI\ncolumn densities through Voigt profile line fitting to the features.\n\nIn the past few years, numerical simulations have successfully modelled many\nof the measured properties of the forest, showing that the absorption systems\nmay arise as a consequence of cosmological structure formation\n(Cen \\etal 1994; Zhang, Anninos \\& Norman 1995; Hernquist \\etal 1996;\nBond \\& Wadsley 1997; Zhang \\etal 1997; Theuns, Leonard \\& Efstathiou 1998).\nThe simulations have shown, contrary to the picture in which the systems are\nisolated intergalactic gas clouds, that most of the systems originate in an\ninterconnected web of sheets and filaments of gas and dark matter\n(Cen \\etal 1994; Bond \\& Wadsley 1997; Zhang \\etal 1998). Alternative\nstatistical methods were subsequently\nintroduced for describing the forest using the more direct measurements of the\ninduced light fluctuations. These include the 1-point distribution of the\nfluctuations (Miralda-Escud\\'e \\etal 1996; Zhang \\etal 1997), and a quantity\nrelated to the 2-point distribution based on a weighted difference of the light\nfluctuations in neighbouring wavelength pixels (Miralda-Escud\\'e \\etal).\nA direct estimate of the 2-point transmission correlation function was made by\nZuo \\& Bond (1994).\n\nWhile the newer methods for analysing the \\Lya forest avoid the identification\nof absorption lines and the fitting of Voigt profiles, they are not\nnecessarily fundamentally different in their description of\nthe spectra. For instance, Zhang \\etal (1998) find that the distribution of\noptical depth per pixel in their simulation may be recovered by modelling the\nspectra entirely by discrete absorption lines with Voigt profiles. Rather the\nmore direct methods circumvent a difficulty that has long plagued attempts to\ncharacterize the absorbers in terms of Voigt profiles: the sensitivity of the\nresulting line statistics to noise and to the fitting procedure. Absorption\nline fitting of necessity requires arbitrary decisions to be made regarding\nthe setting of the continuum level, the deblending of features, and a decision\non the acceptability of a fit. Different observational\ngroups report different distributions for the line parameters. Most\ndiscrepant has been the inferred distribution of line widths. Even with the\nhighest quality data gathered to date using the Keck HIRES, agreement is still\nlacking, with Hu \\etal (1995) finding a narrower Doppler parameter distribution\nwith a significantly higher mean than found by Kirkman \\& Tytler (1997).\nThe differences are important, as cosmological simulations predict comparable\ndifferences for a range of plausible cosmological models (Machacek \\etal 2000;\nMeiksin \\etal 2000).\n\nThe purpose in this paper is to develop a method that provides an alternative\nobjective description of the statistics of the \\Lya forest. Ultimately the\ngoal is to employ the same method for analysing both observational data and\ndata derived from numerical simulations in order to compare the two on a fair\nbasis. Because of the large number of synthetic spectra generated from a\nsimulation necessary to provide a correct average description of the forest,\ntwo principal requirements of the procedure are that it be fast and easily\nautomated. Although automated or semi--automated Voigt profile fitting\nprocedures exist (AutoVP, Dav\\'e \\etal 1997; VPFIT, developed by Carswell and\ncollaborators), these procedures still\nrequire arbitrary decisions to be made to obtain acceptable fits. The\ncomplexity of the codes makes it difficult to assess the statistical\nsignificance of differences between the measured distributions of the\nabsorption line parameters and those predicted. The codes also are\ncomputationally expensive, making very costly their application to the large\nnumber of simulated spectra required to obtain a statistically valid average\nof the line parameters. For these reasons, a faster less complex method would\nbe desirable. The Voigt profile fitting codes yield important parameters, like\nthe linewidths, which contain physical information (eg, gas temperature and\nturbulent velocities), that the direct-analysis methods do not. It\nwould thus be desirable for an alternative method to retain some of this\ninformation. The method presented here utilizes wavelets to characterize the\nabsorption statistics of the \\Lya forest. It is not intended to be a\nreplacement for Voigt profile fitting, but a fast alternative that allows\na ready comparison between the predictions of numerical models and measured\nspectra and a clear statistical analysis of the results.\n\nThe outline of the paper is as follows: in \\S\\ref{sec:wavelets} it is shown\nhow the statistics of the \\Lya forest may be characterized using wavelets.\nIn \\S\\ref{sec:results} the method is applied to the measured spectrum of a\nhigh redshift QSO. The results are summarized in \\S\\ref{sec:summary}.\n\n\\section{Analysing the \\Lya Forest with Wavelets} \\label{sec:wavelets}\n\n\\subsection{Terminology} \\label{sec:terms}\n\nAlthough wavelets have been used in signal processing, image analysis, and the\nstudy of fluid dynamics for a decade, they are only beginning to enter the\nvernacular of astronomers. Accessible introductions are provided in\nPress \\etal (1992), and in Slezak, Bijaoui \\& Mars (1990) and\nPando \\& Fang (1996), who apply wavelets to study the clustering of galaxies\nand \\Lya absorbers, respectively. More complete accounts of wavelet\nmethodology are Chui (1992), Daubechies (1992), and Meyer (1993). The\ndescription here is confined to those elements necessary to introduce the\nnotation and terminology that will be used below.\n\nWavelets are defined variously in the literature. The definition of most use\nhere, somewhat restrictive but appropriate to a multiresolution analysis\nusing the Discrete Wavelet Transform (DWT), is (Meyer):\n\n\\begin{quote}\nA {\\it wavelet} is a square--integrable function $\\psi(x)$ defined in real\nspace such that $\\psi_{jk}\\equiv2^{j/2}\\psi(2^jx-k)$, where $j$ and $k$ are\nintegers, is an orthonormal basis for the set of square--integrable functions.\n\\end{quote}\nThe wavelet $\\psi(x)$ satisfies $\\int_{-\\infty}^{\\infty} dx\\, \\psi(x)=0$,\nand is generally chosen to be concentrated near $x=k2^{-j}$.\nIts defining properties permit it to perform two operations\ngoverned by the values of $j$ and $k$. Smaller values of $j$ correspond to\ncoarser variations in $f(x)$, while differing values of $k$ correspond to\nshifting the centre of the transform.\n\nThe {\\it wavelet coefficients} of a function $f(x)$ are defined by\n\\begin{equation}\nw_{jk}\\equiv\\int dx\\, f(x)\\psi_{jk}(x).\n\\end{equation}\nThe set of coefficients $\\{w_{jk}\\}$\ncomprises the wavelet transform of the function $f(x)$. The function may then\nbe recovered through the inverse transform\n\\label{eq:wavelet_trans}\n\\begin{equation}\nf(x) = \\sum_{j,k} w_{jk}\\psi_{jk}(x),\n\\label{eq:wavelet_inv}\n\\end{equation}\nsince the set of functions $\\psi_{jk}$ forms a complete orthonormal basis.\nThe wavelet coefficients at a level $j$ express the changes between the\nsmoothed representations of $f(x)$ at the resolution scales $j+1$ and $j$.\n\nSeveral functions may serve as wavelets. A set that has proven particularly\nuseful was developed by Daubechies (Daubechies 1992). These functions are\nconstructed to have vanishing moments up to some value $p$, and the functions\nthemselves vanish outside the range $0<x<2p+1$. The wavelet coefficients\ndecrease rapidly with $p$ for smooth functions. Accordingly, the higher order\nDaubechies wavelets are the most suitable for analyzing smooth data. The DWT\nis computed using the pyramidal algorithm as implemented in Numerical Recipes\n(Press \\etal). The Daubechies wavelet of order 20 is chosen throughout.\n\n\\subsection{Monte Carlo simulations} \\label{sec:Monte}\n\nThe properties of the wavelet transform of the \\Lya forest are examined by\nperforming Monte Carlo realizations of spectra. The spectra are constructed\nfrom discrete lines with Voigt profiles using the \\HI column density and\nDoppler parameter distributions found by Kirkman \\& Tytler. Specifically, the\n\\HI column densities \\NHI are drawn from a power law distribution of slope 1.5\nbetween $12.5<\\log_{10}N_{\\rm HI}<16$ and the Doppler parameters $b$ from a\ngaussian with mean 23~\\kms and standard deviation 14~\\kms. A cut--off in $b$ is\nimposed according to $b>14 + 4(\\log_{10} N_{\\rm HI} - 12.5)$~\\kms. The\nresulting average Doppler parameter is 31~\\kms. The number density of lines\nper unit redshift matches that of Kirkman \\& Tytler at $z=3$. The resolution is\nset at $\\lambda/d\\lambda=5\\times10^4$, and gaussian noise is added according to\na specified continuum signal--to--noise ratio per pixel. This is the fiducial\nmodel used in all the simulations unless stated otherwise. Segments 128 pixels\nwide were found adequate for extracting the statistical properties of the\nwavelet coefficients.\n\nA representative spectrum and its discrete wavelet transform are shown in\nFigure~\\ref{fig:spec}. A block at resolution $j$ is $128/2^j$ pixels wide and\n$2^j$ pixels long for $j=1$ to 6. The resolution becomes finer as $j$ increases\nfrom 1 to 6 (downwards). The uppermost level ($j=0$) corresponds to smoothed\naverages of the spectrum. The wavelet coefficients tend to increase in\nmagnitude with decreasing resolution (decreasing $j$). The low values indicate\nthat only small changes occur in the spectrum when smoothed at one resolution\nlevel to the next higher. The small values are desirable, as they signify\nthe dominant absorption features in the spectra are adequately resolved. \n\n\\begin{figure}\n\\centering\n\\epsfxsize=3.3in \\epsfbox{fig1a.eps}\n\\caption{(a)\\ A representative synthetic spectrum showing the \\Lya forest at\n$z=3.0$ at a resolution of $\\lambda/d\\lambda=5\\times10^4$. (b)\\ The absolute\nmagnitudes of the wavelet coefficients are shown in the grayscale map. The map\nis linear and ranges between 0 (white) and 0.5 (black).}\n\\label{fig:spec}\n\\end{figure}\n\nBecause the wavelet functions form a complete set of basis functions,\nthe full set of wavelet coefficients completely describes the\nspectrum: the spectrum may be reconstructed identically from the\ninverse transform. For noisy spectra, however, it will generally be\nunnecessary to retain the full set of coefficients. Indeed, this is\nthe motivation for multi--resolution data compression. By\nemploying a judicious set of basis functions, a signal may be\ncompressed into only a small fraction of its original size. The method\nof chosing the optimal basis set such that the compressed signal matches the\noriginal as closely as possible in a least squares sense with the least\nnumber of retained basis elements is known as Proper\nOrthogonal Decomposition or the Karhunen--Lo\\'eve procedure (see Berkooz,\nHolmes \\& Lumley 1993 for a review). The basis set, however, will in general\ndiffer from signal to signal if its components are highly variable, as in the\ncase of the \\Lya forest. Although not optimal in the least squares sense,\nthe wavelet basis nonetheless achieves a large amount of data compression and\nhas the advantage of generality. Next is described how wavelets may be applied\nto assessing the amount of useful information in a spectrum.\n\nTwo measures of the information content of a noisy spectrum are considered,\none based on $\\chi^2$ and the second on entropy. If $s(x_i)$ is the original\nspectrum defined at $N$ points $x_i$ (eg, wavelength or velocity), and\n$s_n(x_i)$ is the spectrum reconstructed from the $n$ largest (in magnitude)\nwavelet coefficients, then\n\\begin{equation}\n\\chi^2=\\sum_{i=1}^{N}\\left[\\frac{s(x_i)-s_n(x_i)}{\\sigma_i}\\right]^2\n\\label{eq:chi2}\n\\end{equation}\nwhere $\\sigma_i$ is the measurement error associated with pixel $i$. For\ngaussian distributed measurements, the expectation value of $\\chi^2$ is\nthe number of degrees--of--freedom. If $n$ wavelet coefficients are retained,\nthe number of degrees--of--freedom is $N-n$. (Hence, for example, $\\chi^2=0$\nis expected for $n=N$.) The reduced $\\rchi=\\chi^2/(N-n)$ then\ndefines the optimal value of $n$ for truncating the wavelet coefficients.\n\nThe information content may also be expressed in terms of the wavelet\ncoefficients directly as an ``entropy''\\footnote{Meyer (1993)\ndefines the entropy to be the exponential of $S$.}\n\\begin{equation}\nS=-\\sum_{jk}\\, \\alpha^2_{jk}\\log \\alpha^2_{jk},\n\\label{eq:entropy}\n\\end{equation}\nwhere the $\\alpha_{jk}$ are the normalized coefficients\n\\begin{equation}\n\\alpha_{jk}=\\frac{w_{jk}}{\\left(\\sum_{jk} w^2_{jk}\\right)^{1/2}}.\n\\label{eq:alphajk}\n\\end{equation}\nThis quantity behaves like a physical entropy in the sense that it is\nmaximum when the signal is completely random so that the full set of\ncoefficients $\\{w_{jk}\\}$ is required to describe it, while it vanishes\nwhen the signal may be entirely described by a single coefficient.\n\nThe reduced $\\chi^2$ for an ensemble of Monte Carlo realizations is shown in\nFig.~\\ref{fig:chi2} as a function of the fraction $(N-n)/N$ of the wavelet\ncoefficients discarded. As the signal--to--noise ratio per pixel increases,\nthe value of $\\rchi$ for a given $n$ increases. In all cases,\nhowever, there is some $n<N$ for which $\\rchi=1$. This suggests\nthat an acceptable fit to a noisy spectrum may be provided by only a fraction\n$n/N$ of the full set of coefficients, with the fraction required increasing as\nthe noise level decreases.\n\nThe entropy $S$ is shown in Figure~\\ref{fig:entropy}.\nThe entropy stays nearly constant out to $\\chi_{\\rm red}^2=1$,\nindicating that little information has been lost by discarding the small\ncoefficients. As $\\rchi$ increases, eventually the entropy decreases\nas information is lost. Due to the greater information content of the less\nnoisy spectra, as the noise level is decreased, the entropy remains constant\nto increasingly higher values of $\\rchi$ before declining.\n\n\\begin{figure}\n\\begin{center}\n\\leavevmode \\epsfxsize=3.3in \\epsfbox{fig2.eps}\n\\end{center}\n\\caption{The dependence of the reduced $\\rchi$ on the fraction\nof discarded wavelet coefficients. The curves increasing from the bottom\nare for signal--to--noise ratios of 10, 30, 50, 100, 300, and 1000.\nAs the noise level increases, an increasing\nfraction of the coefficients may be discarded with the remainder still\nproviding a statistically acceptable fit to the spectra.}\n\\label{fig:chi2}\n\\end{figure}\n\n\\begin{figure}\n\\begin{center}\n\\leavevmode \\epsfxsize=3.3in \\epsfbox{fig3.eps}\n\\end{center}\n\\caption{The entropy of the spectra defined in\nterms of the wavelet coefficients. Little information is lost from the\nspectra for $\\rchi\\le1$, as measured by the entropy. The entropy curves from\nleft to right are for signal--to--noise ratios of 10, 30, 50, 100, 300, and\n1000.}\n\\label{fig:entropy}\n\\end{figure}\n\n\\subsection{Statistics of the wavelet coefficients}\n\nIt was shown above how wavelets may be used to characterize the noise\nproperties of a spectrum. The wavelet coefficients, however, may also be\nused to characterize the statistics of the \\Lya forest itself.\n\nThe distributions of the coefficients (in absolute value) for the several\nresolution levels are shown in Fig.~\\ref{fig:wcdist} for a set of simulated\nspectra with $S/N=50$, typical of the Keck HIRES spectra. The number of\ncoefficients at a level $j$ is $2^j$, with $j=1$ corresponding to the\ncoarsest resolution, and $j=6$ to the finest for the $2^7=128$ pixels used in\na spectrum. The finest resolution ($j=6$) curve is the steepest. As the\nresolution becomes increasingly coarse, the amplitude of the coefficients\nincreases, as was found in Fig.~\\ref{fig:spec}. This indicates that most of\nthe information in the spectrum is carried by the coarser levels (as well as\nby the two course scale averages, not shown). The finest level has\nresolved the spectral structures, with little difference between the smoothed\nrepresentations of the spectrum at resolution levels $j=5$ and 6.\nApplying a cut--off in the coefficients corresponding to\n$\\rchi=1$ yields for the average number retained of the initially\n$2^j$ coefficients for $j=1\\dots6$ the respective values 1.9, 3.8, 7.4, 11.6,\n6.9, and 3.4. While almost all of the coefficients for $j\\le3$ are needed,\na decreasing fraction is required to describe the spectra at higher resolution.\n\n\\begin{figure}\n\\begin{center}\n\\leavevmode \\epsfxsize=3.3in \\epsfbox{fig4.eps}\n\\end{center}\n\\caption{The normalized distribution of the wavelet coefficients at the levels\n$j=1\\dots6$. The coefficients increase in magnitude at the coarser\n(lower $j$) resolutions, indicating that they carry most of the information\nin the spectra.}\n\\label{fig:wcdist}\n\\end{figure}\n\n\\begin{figure}\n\\begin{center}\n\\leavevmode \\epsfxsize=3.3in \\epsfbox{fig5.eps}\n\\end{center}\n\\caption{The normalized distribution of the wavelet coefficients for the levels\n$j=3, 4,$ and 5 for signal--to--noise ratios of 10, 30, 50, 100, 300, and\n1000. Except for $S/N=10$ (dotted lines), the distributions overlap.}\n\\label{fig:dist_snr}\n\\end{figure}\n\nThe distributions are insensitive to the signal--to--noise ratio, as shown\nin Fig.~\\ref{fig:dist_snr}. Except for the lowest ratio of 10, the curves\ncoincide, showing that they may be measured accurately even for a varying\nsignal--to--noise ratio in a spectrum, provided it is not too low.\n\nTo demonstrate that the wavelet coefficient distributions may be used to\ndiscriminate between different predictions for the statistical properties\nof the \\Lya forest, a second set of Monte Carlo realizations with alternative\ncolumn density and Doppler parameter distributions is generated. The\nparameters adopted are those reported by Hu \\etal They found that the forest\nstatistics are consistent with an \\HI column density distribution with a slope\nof $1.5$ for clouds with $12.3<\\log N_{\\rm HI}<14.5$ and a Gaussian Doppler\nparameter distribution with mean 28~\\kms, standard deviation 10~\\kms, and\na sharp cut--off below 20~\\kms. The resulting average Doppler parameter is\n37~\\kms. The simulation is normalized to the same line density per unit\nredshift at $z=3$ as found by Hu \\etal, but the column density distribution\nis extended to $\\log N_{\\rm HI}=16$ to be consistent with the previous set of\nsimulations. The resulting wavelet coefficient distributions are compared with\nthose from the previous simulation for $j=3,4,$ and 5 in\nFig.~\\ref{fig:dist_KTH}. The wavelet coefficients are able to distinguish\nbetween the two models.\n\n\\begin{figure}\n\\begin{center}\n\\leavevmode \\epsfxsize=3.3in \\epsfbox{fig6.eps}\n\\end{center}\n\\caption{The normalized frequencies of the wavelet coefficients for the levels\n$j=3, 4,$ and 5 for two different statistical descriptions of the \\Lya forest.\nThe solid lines are based on the Voigt parameter distributions inferred by\nKirkman \\& Tytler, and the dashed on the distributions inferred by Hu \\etal\nA signal--to--noise ratio of 50 is used in both sets of simulations. The\ndistributions of wavelet coefficients distinguish between the two models.}\n\\label{fig:dist_KTH}\n\\end{figure}\n\nThe Kolmogorov--Smirnov test may be used to assess the probability that the\nwavelet coefficients of a measured spectrum match a given distribution for each\nresolution level $j$. The most stringent test, however, is given by combining\nthe probabilities for all the distributions. Because any given absorption\nfeature may be expected to affect the coefficients at more than a single\nresolution level $j$, it is possible that the coefficients corresponding\nto a given set of nested blocks for different $j$ (see Fig.~\\ref{fig:spec})\nmay be correlated. In this case, the probabilities of matching the various\ndistributions may not be combined as if they were independent. To determine\nthe degree to which the distributions may be treated as independent, the\ncorrelations are measured for coefficients between the various levels $j$\ncorresponding to the same hierarchy of blocks, and then averaged over all the\nhierarchies, for a set of Monte Carlo\nrealizations using the fiducial forest model. The results are shown in\nTable~\\ref{tab:corr}. (The level $j=0$ refers to the correlations with the\npair of coefficients corresponding to the course scale averages.)\nA signal--to--noise ratio of 50 is assumed, and a cut-off in the coefficients\nis applied to ensure $\\rchi=1$. The error on the correlations is\n$\\sim0.1$\\%. Although the correlations are small, they are not absent. They\nare sufficiently small, however, that treating the probabilities for the\ndifferent distributions as independent should be an adequate approximation\nfor model testing.\n\n\\begin{table*}\n\\caption{Wavelet coefficient correlation matrix for resolution levels\n$j=6,\\dots,0$.}\n\\begin{tabular}{lrrrrrrr}\n$j$ & 6 & 5 & 4 & 3 & 2 & 1 & 0 \\\\\n\\\\\n6 & 1.000 & 0.003 & 0.009 & 0.013 & 0.009 & 0.003 & 0.001 \\\\\n5 & 0.003 & 1.000 & -0.020 & -0.013 & -0.005 & -0.001 & -0.001 \\\\\n4 & 0.009 & -0.020 & 1.000 & 0.026 & 0.018 & 0.012 & 0.000 \\\\\n3 & 0.013 & -0.013 & 0.026 & 1.000 & 0.046 & 0.025 & 0.002 \\\\\n2 & 0.009 & -0.005 & 0.018 & 0.046 & 1.000 & 0.035 & 0.005 \\\\\n1 & 0.003 & -0.001 & 0.012 & 0.025 & 0.035 & 1.000 & -0.002 \\\\\n0 & 0.001 & -0.001 & 0.000 & 0.002 & 0.005 & -0.002 & 1.000 \\\\\n\\end{tabular}\n\\label{tab:corr}\n\\end{table*}\n\n\\subsection{Data compression} \\label{sec:compress}\n\nOne of the key features of wavelets is their ability to compress data.\nFigs.~\\ref{fig:chi2} and \\ref{fig:entropy} show that it is possible to fit a\nspectrum using only a subset of the wavelets used in its DWT at a statistically\nacceptable level ($\\rchi=1$), without significantly degrading the\ninformation content of the spectrum as measured by the wavelet entropy.\nThis suggests that filtering the spectrum in this way may provide a usable\nspectrum that is relatively noiseless and suitable for absorption line fitting.\n\nThis is illustrated by performing Voigt profile fitting to Monte Carlo\nrealisations of the fiducial line model, with an assumed signal--to--noise\nratio of 50. A wavelet filtered representation of each realised spectrum is\ngenerated with coefficients truncated to give a reduced $\\rchi=1$ for the\ndifference between the original and wavelet filtered spectra. This\ncorresponds on average to retaining only 30\\% of the full set of coefficients.\nA representative spectrum is shown in Fig.~\\ref{fig:specwfit}.\n\nAbsorption lines are then identified in the filtered spectrum and fit\nusing AutoVP. The results of $10^4$ realisations are shown in\nFigs.~\\ref{fig:NHIdist} and \\ref{fig:bdist}. Also shown are the\ndistributions obtained from AutoVP using the original spectra with no\nwavelet filtering applied. The distributions are nearly identical. A\nnegligible loss is incurred in the recovery of the line parameters\ndespite the exclusion of 70\\% of the information in the original spectra.\n\n\\begin{figure}\n\\begin{center}\n\\leavevmode \\epsfxsize=3.3in \\epsfbox{fig7.eps}\n\\end{center}\n\\caption{Synthetic spectrum with $S/N=50$ (heavy solid histogram). The wavelet\nfiltered spectrum with $\\rchi=1$ is shown by the lighter\nline (shown as a smooth curve for clarity).}\n\\label{fig:specwfit}\n\\end{figure}\n\n\\begin{figure}\n\\begin{center}\n\\leavevmode \\epsfxsize=3.3in \\epsfbox{fig8.eps}\n\\end{center}\n\\caption{The recovered \\HI column density distribution from a set of Monte\nCarlo realizations. The dotted curve corresponds to the Voigt fits obtained\nusing the original unfiltered spectra. The solid curve shows the recovered\ndistribution obtained from the wavelet filtered spectrum for which only 30\\%\nof the wavelet coefficients are retained, corresponding to a reduced $\\rchi=1$\nfor the difference between the original and wavelet filtered spectra. The heavy\nsolid line shows the input model distribution.}\n\\label{fig:NHIdist}\n\\end{figure}\n\n\\begin{figure}\n\\begin{center}\n\\leavevmode \\epsfxsize=3.3in \\epsfbox{fig9.eps}\n\\end{center}\n\\caption{The recovered Doppler parameter distribution, as in\nFig.~\\ref{fig:NHIdist}. The heavy solid line shows the input model\ndistribution.}\n\\label{fig:bdist}\n\\end{figure}\n\n\\section{Application to Q1937--1009} \\label{sec:results}\n\nIn this section, the Discrete Wavelet Transform is used to analyse the \\Lya\nforest as measured in the $z=3.806$ QSO Q1937--1009. The spectrum was taken\nwith the Keck HIRES at a resolution of $\\sim8.5$~\\kms (Burles \\& Tytler 1997).\nThe signal--to--noise ratio per pixel was $\\sim50$. The spectrum covers the\nrange between \\Lya and Ly$\\beta$ in the QSO restframe. (The region analysed\nis restricted to the redshift interval $3.055<z<3.726$ to avoid any possible\ninfluence by the QSO.)\n\nThe distribution of wavelet coefficients is shown in Fig.~\\ref{fig:wcKeck} for\n$j=2$, 3, 4, and 5. As in Fig.~\\ref{fig:wcdist}, the high frequency\ncoefficients are generally smaller than at lower frequencies, indicating that\nthe fluctuations that dominate the spectra have been resolved.\n\n\\begin{figure}\n\\begin{center}\n\\leavevmode \\epsfxsize=3.3in \\epsfbox{fig10.eps}\n\\end{center}\n\\caption{The normalized distributions of the wavelet coefficients for the\nspectrum of Q1937--1009. The distributions are shown for the levels\n$j=2$ (dot--dashed), $j=3$ (long--dashed), $j=4$ (solid), and $j=5$\n(short--dashed). The faster decline at higher frequencies demonstrates that\nthe absorption features dominating the spectrum have been adequately\nresolved.}\n\\label{fig:wcKeck}\n\\end{figure}\n\nThe cumulative distributions of the coefficients are compared with the\npredicted distributions for the fiducial model in Fig.~\\ref{fig:wcumdKeck}.\nThe predicted distributions were generated by simulating spectra with\nthe same pixelization, resolution, signal--to--noise ratio and wavelength\ncoverage as for the measured spectrum of Q1937--1009. An increase in line\ndensity per unit redshift proportional to $(1+z)^{2.6}$ (Kirkman \\& Tytler)\nwas included to match to the redshift range of Q1937--1009. While the\ndistributions generally agree well, a large variation is found for $j=4$,\ncorresponding to fluctuations on the scale of $17-34$~\\kms, suggesting some\ndifferences from the line model of Kirkman \\& Tytler. Effects neglected in\nthe simulations that could produce a difference are the presence of metal\nsystems and redshift correlations between the \\Lya absorption systems. The\nchanges that would be produced, however, are most likely small:\\ the number of\nmetal systems is small, and the correlations appear weak or absent (Meiksin \\&\nBouchet 1995; Kim \\etal 1997). Still, the sensitivity of the wavelet\ncoefficient distributions to these effects may be worth more careful\nconsideration.\n\n\\begin{figure}\n\\begin{center}\n\\leavevmode \\epsfxsize=3.3in \\epsfbox{fig11.eps}\n\\end{center}\n\\caption{The cumulative distributions of the wavelet coefficients for the\nspectrum of Q1937--1009, along with the predicted distributions according\nto the line model of Kirkman \\& Tytler (1997). The frequency levels shown\nare $j=2$ (dot--dashed), $j=3$ (long--dashed), $j=4$ (solid), and $j=5$\n(short--dashed).}\n\\label{fig:wcumdKeck}\n\\end{figure}\n\n\\section{Summary} \\label{sec:summary}\n\nWavelets may be usefully employed to provide a statistical\ncharacterizaton of the absorption properties of the \\Lya forest. An\napproach is presented that performs a multiresolution analysis of the\nforest using the Discrete Wavelet Transform of the QSO spectrum. The\ntransform decomposes the local frequency dependence of the light\nfluctuations into an orthogonal hierarchy of basis functions, the\nwavelets. It is found that in spectra of better than 10~\\kms\nresolution, most of the information of the spectrum is carried by\nthe lower frequency wavelets. For a signal--to--noise ratio typical of\neven the highest quality spectra ($S/N=10-100$), only 10--30\\% of the\nwavelets are required to provide a statistically acceptable\ndescription of the spectrum, corresponding to a data compression factor\nof 3--10. It is shown that a Voigt profile line analysis performed on\nthe wavelet filtered spectra yields nearly identical line parameter\ndistributions as obtained from the original unfiltered spectra.\n\nThe distributions of the wavelet coefficients offer an alternative statistical\ndescription of the \\Lya forest while retaining information on the line widths.\nIt is demonstrated that the correlations of\ncoefficients between different levels in the wavelet hierarchy are weak (a few\npercent or smaller). Consequently, each of the distributions may be treated as\nstatistically independent to good approximation.\n\nThe method is applied to a Keck HIRES spectrum of Q1937--1009. The\nwavelet coefficient distributions behave qualitatively\nsimilarly to those found in Monte Carlo simulations based on the line\nparameter distributions reported by Kirkman \\& Tytler. The measured\ndistributions, however, show some differences on the scale $17-34$~\\kms.\n\n\nThe results demonstrate that Multiresolution Analysis using the\nDiscrete Wavelet Transform provides an alternative objective, easily\nautomated procedure for analysing the \\Lya forest suitable for basing\na comparison between the measured properties of the \\Lya forest and\nthe predictions of numerical models.\n\n\\bigskip\nThe author thanks S. Burles and D. Tytler for kindly providing the spectrum of\nQ1937--1009, and R. Dav\\'e for permission to use AutoVP.\n\n\\begin{thebibliography}{99}\n\n\\bibitem[\\protect\\citename{Berkooz, Holmes \\& Lumley }1993]{Ber93}\n\tBerkooz G., Holmes P., Lumley J.~L., 1993,\nAnn. Rev. Fluid Mech., 25, 539\n\n\\bibitem[\\protect\\citename{Bond \\& Wadsley }1997]{Bon97}\n Bond J.~R., Wadsley J.~W., 1997, in Petitjean, P., Charlot, S., eds,\nProc. 13th IAP Astro. Colloq., Structure and Evolution of the Intergalactic\nMedium from QSO Absorption Line Systems. Editions Fronti\\`eres, Paris, p. 143\n\n\\bibitem[\\protect\\citename{Burles \\& Tytler }1998]{bur98}\n Burles S., Tytler D., 1997, AJ, 114, 1330\n\n\\bibitem[\\protect\\citename{Cen et al. }1994]{Cen94}\n Cen R., Miralda-Escud\\'e J., Ostriker J. P., Rauch M.,\n 1994, ApJ, 437, L9\n\n\\bibitem[\\protect\\citename{Chui }1992]{Chu92}\n\tChui C.~K., 1992, An Introduction to Wavelets. Academic Press, San\n\tDiego\n\n\\bibitem[\\protect\\citename{Daubechies }1992]{Dau92}\n\tDaubechies I., 1992, Ten Lectures on Wavelets. SIAM, Philadelphia\n\n\\bibitem[]{dav97}\n Dav\\'e R., Hernquist L., Weinberg D.~H., Katz N., 1997, ApJ,\n 477, 21\n\n\\bibitem[\\protect\\citename{Hernquist et al. }1996]{Her96}\n Hernquist L., Katz N., Weinberg D., Miralda-Escud\\'e J.,\n 1996, ApJ, 457, L51\n\n\\bibitem[\\protect\\citename{Hu et al. }1995]{Hu95}\n Hu E.~M., Kim T.~S., Cowie L.~L., Songaila A., Rauch M.,\n 1995, AJ, 110, 1526\n\n\\bibitem[\\protect\\citename{Kim et al. }1997]{kim97}\n Kim T.-S., Hu E.~M. Cowie L.~L., Songaila A., 1997, AJ, 114, 1\n\n\\bibitem[\\protect\\citename{Kirkman \\& Tytler }1997]{Kir97}\n Kirkman D., Tytler D., 1997, ApJ, 484, 672\n\n\\bibitem[\\protect\\citename{Lynds }1971]{Lyn71}\n\tLynds R., 1971, ApJ, 164, L73\n\n\\bibitem[\\protect\\citename{Machacek \\etal }2000]{mac00}\n\tMachacek M.~E., Bryan G.~L., Meiksin A., Anninos P., Thayer D.,\nNorman M., Zhang Y., 2000, ApJ (in press)\n\n\\bibitem[\\protect\\citename{Meiksin \\& Bouchet }1995]{mei95}\n\tMeiksin A., Bouchet F.~R., 1995, ApJ, 448, L85\n\n\\bibitem[\\protect\\citename{Meiksin \\etal }2000]{mei00}\n Meiksin A. \\etal, 2000, in preparation\n\n\\bibitem[\\protect\\citename{Meyer }1993]{Mey93}\n\tMeyer Y., 1993, Wavelets:\\ Algorithms and Applications.\n\tSIAM, Philadelphia\n\n\\bibitem[\\protect\\citename{Miralda-Escud\\'e et al. }1996]{Mir96}\n Miralda-Escud\\'e J., Cen R., Ostriker J.~P., Rauch M.,\n 1996, ApJ, 471, 582\n\n\\bibitem[]{pf96}\n\tPando J., Fang L.-Z., 1996, ApJ, 459, 1\n\n\\bibitem[\\protect\\citename{Press et al. }1992]{NumRec}\n\tPress W.~H., Teukolsky, S.~A, Vetterling, W.~T., Flannery, B.~P., 1992,\nNumerical Recipes, 2nd edn. Cambridge Univ. Press, Cambridge\n\n\\bibitem[\\protect\\citename{Sargent et al. }1980]{Sar80}\n\tSargent W.~L.~W., Young P.~J., Boksenberg A., Tytler D., 1980,\n\tApJS, 42, 41\n\n\\bibitem[]{sbm90}\n\tSlezak E., Bijaoui A., Mars G., 1990, AA, 227, 301\n\n\\bibitem[\\protect\\citename{Theuns, Leonard \\& Efstathiou }1998]{The98}\n Theuns T., Leonard A., Efstathiou G., 1998, MNRAS, 297, L49\n\n\\bibitem[\\protect\\citename{Zhang, Anninos \\& Norman }1995]{Zha95}\n Zhang Y., Anninos P., Norman M.~L., 1995, ApJ, 453, L57\n\n\\bibitem[\\protect\\citename{Zhang et al. }1997]{Zha97}\n Zhang Y., Anninos P., Norman M.~L., Meiksin A.,\n 1997, ApJ, 485, 496\n\n\\bibitem[\\protect\\citename{Zhang et al. }1998]{Zha98}\n Zhang Y., Meiksin A., Anninos P., Norman, M.~L.,\n 1998, ApJ, 495, 63\n\n\\bibitem[\\protect\\citename{Zuo \\& Bond }1994]{Zuo94}\n Zuo L., Bond J.~R. 1994, ApJ, 423, 73\n\n\\end{thebibliography}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002148.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem[\\protect\\citename{Berkooz, Holmes \\& Lumley }1993]{Ber93}\n\tBerkooz G., Holmes P., Lumley J.~L., 1993,\nAnn. Rev. Fluid Mech., 25, 539\n\n\\bibitem[\\protect\\citename{Bond \\& Wadsley }1997]{Bon97}\n Bond J.~R., Wadsley J.~W., 1997, in Petitjean, P., Charlot, S., eds,\nProc. 13th IAP Astro. Colloq., Structure and Evolution of the Intergalactic\nMedium from QSO Absorption Line Systems. Editions Fronti\\`eres, Paris, p. 143\n\n\\bibitem[\\protect\\citename{Burles \\& Tytler }1998]{bur98}\n Burles S., Tytler D., 1997, AJ, 114, 1330\n\n\\bibitem[\\protect\\citename{Cen et al. }1994]{Cen94}\n Cen R., Miralda-Escud\\'e J., Ostriker J. P., Rauch M.,\n 1994, ApJ, 437, L9\n\n\\bibitem[\\protect\\citename{Chui }1992]{Chu92}\n\tChui C.~K., 1992, An Introduction to Wavelets. Academic Press, San\n\tDiego\n\n\\bibitem[\\protect\\citename{Daubechies }1992]{Dau92}\n\tDaubechies I., 1992, Ten Lectures on Wavelets. SIAM, Philadelphia\n\n\\bibitem[]{dav97}\n Dav\\'e R., Hernquist L., Weinberg D.~H., Katz N., 1997, ApJ,\n 477, 21\n\n\\bibitem[\\protect\\citename{Hernquist et al. }1996]{Her96}\n Hernquist L., Katz N., Weinberg D., Miralda-Escud\\'e J.,\n 1996, ApJ, 457, L51\n\n\\bibitem[\\protect\\citename{Hu et al. }1995]{Hu95}\n Hu E.~M., Kim T.~S., Cowie L.~L., Songaila A., Rauch M.,\n 1995, AJ, 110, 1526\n\n\\bibitem[\\protect\\citename{Kim et al. }1997]{kim97}\n Kim T.-S., Hu E.~M. Cowie L.~L., Songaila A., 1997, AJ, 114, 1\n\n\\bibitem[\\protect\\citename{Kirkman \\& Tytler }1997]{Kir97}\n Kirkman D., Tytler D., 1997, ApJ, 484, 672\n\n\\bibitem[\\protect\\citename{Lynds }1971]{Lyn71}\n\tLynds R., 1971, ApJ, 164, L73\n\n\\bibitem[\\protect\\citename{Machacek \\etal }2000]{mac00}\n\tMachacek M.~E., Bryan G.~L., Meiksin A., Anninos P., Thayer D.,\nNorman M., Zhang Y., 2000, ApJ (in press)\n\n\\bibitem[\\protect\\citename{Meiksin \\& Bouchet }1995]{mei95}\n\tMeiksin A., Bouchet F.~R., 1995, ApJ, 448, L85\n\n\\bibitem[\\protect\\citename{Meiksin \\etal }2000]{mei00}\n Meiksin A. \\etal, 2000, in preparation\n\n\\bibitem[\\protect\\citename{Meyer }1993]{Mey93}\n\tMeyer Y., 1993, Wavelets:\\ Algorithms and Applications.\n\tSIAM, Philadelphia\n\n\\bibitem[\\protect\\citename{Miralda-Escud\\'e et al. }1996]{Mir96}\n Miralda-Escud\\'e J., Cen R., Ostriker J.~P., Rauch M.,\n 1996, ApJ, 471, 582\n\n\\bibitem[]{pf96}\n\tPando J., Fang L.-Z., 1996, ApJ, 459, 1\n\n\\bibitem[\\protect\\citename{Press et al. }1992]{NumRec}\n\tPress W.~H., Teukolsky, S.~A, Vetterling, W.~T., Flannery, B.~P., 1992,\nNumerical Recipes, 2nd edn. Cambridge Univ. Press, Cambridge\n\n\\bibitem[\\protect\\citename{Sargent et al. }1980]{Sar80}\n\tSargent W.~L.~W., Young P.~J., Boksenberg A., Tytler D., 1980,\n\tApJS, 42, 41\n\n\\bibitem[]{sbm90}\n\tSlezak E., Bijaoui A., Mars G., 1990, AA, 227, 301\n\n\\bibitem[\\protect\\citename{Theuns, Leonard \\& Efstathiou }1998]{The98}\n Theuns T., Leonard A., Efstathiou G., 1998, MNRAS, 297, L49\n\n\\bibitem[\\protect\\citename{Zhang, Anninos \\& Norman }1995]{Zha95}\n Zhang Y., Anninos P., Norman M.~L., 1995, ApJ, 453, L57\n\n\\bibitem[\\protect\\citename{Zhang et al. }1997]{Zha97}\n Zhang Y., Anninos P., Norman M.~L., Meiksin A.,\n 1997, ApJ, 485, 496\n\n\\bibitem[\\protect\\citename{Zhang et al. }1998]{Zha98}\n Zhang Y., Meiksin A., Anninos P., Norman, M.~L.,\n 1998, ApJ, 495, 63\n\n\\bibitem[\\protect\\citename{Zuo \\& Bond }1994]{Zuo94}\n Zuo L., Bond J.~R. 1994, ApJ, 423, 73\n\n\\end{thebibliography}"
}
] |
astro-ph0002149
|
The Analysis of Cosmic Ray Data
|
[
{
"author": "K J Orford"
}
] |
[
{
"name": "Review.tex",
"string": "\\documentclass[12pt]{iopart} \n\\usepackage{iopams}\n\\usepackage{psfig}\n\\usepackage{graphpap}\n\n\\newcommand{\\chisq}{$\\chi^{2}$}\n\n\\begin{document} \n\\title{The Analysis of Cosmic Ray Data}\n\\author{K J Orford}\n\\address{Physics Department\\\\ Durham University\\\\Durham DH1 3LE, UK}\n\\maketitle \n% MAIN SECTION INTRODUCTION MAIN SECTION\n% MAIN SECTION INTRODUCTION MAIN SECTION\n% MAIN SECTION INTRODUCTION MAIN SECTION\n\\section{Introduction}\n\nA statement of statistical belief not uncommon in cosmic ray work is: \"you need five sigmas to convince me\". \nThis has some justification, in that the history of cosmic rays contains many instances when a source \nor effect is claimed but not subsequently substantiated. \nFrequently this has been due to incorrect application of some statistical technique, often a failure to account \nfully for the 'degrees of freedom'.\n\nMost of the present body of statistical knowledge has been developed for specific problems, few of which occur in cosmic \nrays, although one of the most useful of texts\\cite{kn:eadie} was produced for experimental particle physicists. \nThe analyser of cosmic ray data has particular problems: cosmic ray data requires great effort in collection and they\nare unlikely, once analysed, to be repeated. \nThe numbers are frequently small and there are usually data missing and frequently there is significant contamination \nby noise. \nIdeally, a statistical measure should be developed specifically for each application. This is the only way in which \nall of the parameters of the experiment can be allowed for in the analysis. \nIt is more usual for a general statistical tool to be applied, for example \\chisq, which may not be optimal for the \npurpose, and for some experimental variables to be ignored.\n\nThe focus of this review will be on methods of determining the presence of a signal rather than estimating some parameters \nof the data.\nThe aim is to gather together the recent developments in methods of analysis of the temporal and spatial features of \ncosmic ray data, especially where the methods used are not 'traditional'. \n\nSeveral new methods have been published recently which depend on Bayesian ideas, and these ideas have been introduced \nbefore the description of the methods.\n\n\n\n% MAIN SECTION ON/OFF COUNTS\n% MAIN SECTION ON/OFF COUNTS\n% MAIN SECTION ON/OFF COUNTS\n\n\\section{On/Off Counts}\n\n\\subsection{Introduction}\n\nThe subject of detecting the presence of a source in counting rate data, using off-source control data has appeared \nmany times\\cite{kn:eadie,kn:hearn,kn:omongain,kn:gibsona,kn:lima}. \nDespite these numerous airings, erroneous statistical significances are occasionally still being published.\nIn principle the question is easy to pose: if $N_{ON}$ counts are detected when an instrument is pointed at a source \nand there is also a background counting rate, and $N_{OFF}$ counts are detected when it is collecting background counts \nonly under otherwise identical conditions, what is the likelihood that there is a genuine source?\n\nA common treatment is to give for the significance of the excess counts:\n\\begin{equation}\nN_{SIGMA}=\\frac{N_{ON}-\\alpha N_{OFF}}{\\sqrt{N_{ON}+\\alpha^{2}N_{OFF}}} \\label{eq:dcxs}\n\\end{equation}\nwhere $\\alpha$ is the ratio of time on-source to time off-source, $t_{ON}=\\alpha t_{OFF}$.\nThis is based on the supposition that the best estimate of the observed 'signal' is $N_{ON}-\\alpha N_{OFF}$, \nthe variances of the ON and OFF counts for a Poisson distribution are $N_{ON}$ and $N_{OFF}$ and the \nvariance of the difference between $N_{ON}$ and $\\alpha N_{OFF}$ is the weighted sum of the variances. \nThe statistic used is $Student's$ $t$ which in the limit of large numbers is Gaussian. \nSince the distributions of $N_{ON}$ and $N_{OFF}$ are Poissonian, this expression should be used only if the numbers\nof events is sufficiently large for a Gaussian approximation to Poissonian to be valid.\n\nIt is an example of only one type of statistic which could be used in $ON/OFF$ situations - a \\emph{goodness-of-fit} \nstatistic to determine whether the observed data could have arisen from an \\emph{a priori} distribution.\nOther statistics could have been used, for example \\chisq, which in this instance would have one degree of freedom. \nAsymptotically they should have the same result, that is they both should reject or accept the null hypothesis\nequally.\nIn these tests the \\emph{null hypothesis} is that the observations were both samples from the same population and\nthat any difference arose merely by chance. \nThere is no explicit alternative hypothesis, but an implicit one: that if the difference between the counts\nwas unlikely to be due to chance, it arose because of a genuine source, strength unspecified.\n\n\n% Subsection LIKELIHOOD ANALYSIS\n% Subsection LIKELIHOOD ANALYSIS\n\\subsection{Likelihood Analysis}\n\nAn optimal test exists for the intermediate case where there are two completely specified hypotheses: $H_{0}$: \nthe \\emph{null hypothesis} as described above, and $H_{1}$: a hypothesis involving another model, usually including \na specific 'signal'. \nIn this rare (in cosmic rays) case, the Neyman/Pearson theorem shows that the likelihood ratio is optimal for any \ndistribution function for the errors.\n\nIn the more usual case, $H_{1}$ is not fully specified, but has one or more free parameters. \nThe null hypothesis $H_{0}$ is that $N_{OFF}$ and $N_{ON}$ are both samples of the same population for which the source \nstrength $S=0$.\nThe alternative hypothesis $H_{1}$ is that $N_{ON}$ contains an \\emph{unknown} source component, $S>0$.\nIn this case there is no optimal test, except that for errors of the exponential family, such as a Gaussian, the \nlikelihood ratio is expected to be near-optimal. \n\nThe problem was discussed at length twenty five years ago by O'Mongain\\cite{kn:omongain} and Hearn\\cite{kn:hearn} but \nwas not solved satisfactorily, at least in this field, until the maximum likelihood treatment of Gibson et al.\n\\cite{kn:gibsona} and Dowthwaite et al.\\cite{kn:dowthwaite} and later by a similar treatment by Li and Ma\\cite{kn:lima}. \nIn these treatments the observed $ON$ and $OFF$ counts are due to (i) an unknown background $B$ plus an unknown source \n$S$ and (ii) the same unknown background $B$ alone. The likelihood ratio is maximised with respect to the possible \nsource counts:\n\\begin{eqnarray}\n\\lambda & = & \\left(\\frac{P\\left(N_{ON},N_{OFF}\\mid S=0\\right)}{P\\left(N_{ON},N_{OFF}\\mid S=N_{ON}-\\alpha N_{OFF} \n\\right)}\\right) \\nonumber\n\\\\\n & = & \\left[ \\frac{\\alpha}{1+\\alpha}\\left(\\frac{N_{ON}+N_{OFF}}{N_{ON}}\\right)\\right]^{N_{ON}} \\left[\\frac{1}{1+\\alpha}\n\\left(\\frac{N_{ON}+N_{OFF}}{N_{OFF}}\\right)\\right]^{N_{OFF}} \\label{eq:lambda}\n\\end{eqnarray}\nA standard result\\cite{kn:eadie} is that the probability of obtaining a given $\\lambda$ is obtained from\n\\begin{equation}\n-2\\ln(\\lambda) \\sim \\chi^{2}(1) \\label{eq:lamchi}\n\\end{equation}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}[hb]\n\\psfig{file=LiMa.eps,angle=90,height=6cm}\n\\label{fig:1a}\n\\footnotesize\n\\caption{Ratio of probabilities from equation~\\ref{eq:dcxs} (full circles) and equation~\\ref{eq:lambda} (full triangles)\nto Monte Carlo results for various values of $N_{OFF}$ and $N_{ON}=N_{OFF}+S_{3}$} \\label{fig:limacomp}\n\\end{figure}\n\\normalsize \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n% Subsection COMPARISON\n% Subsection COMPARISON\n\\subsection{Comparison of methods}\nBoth equations~\\ref{eq:dcxs} and~\\ref{eq:lamchi} are valid asymptotically: only for large values of $N_{OFF}$ and $N_{ON}$.\nEquation~\\ref{eq:dcxs} assumes that the error distributions of $N_{ON}$ and $N_{OFF}$ are gaussian and equation~\n\\ref{eq:lamchi} assumes that $-2\\log(\\lambda)$ is distributed as $\\chi_{2}(1)$.\nTo check the region of validity, random data sets have been generated for each of a number of values of $N_{OFF}$.\nFor each data set $\\alpha$ has been set to $1.0$ and a value of $S_{3}=3\\sqrt{2B+S_{3}}$ has been calculated, \nwhich is the $3\\sigma$ value of $S=S_{3}$ assuming the validity of equation~\\ref{eq:dcxs}.\nAt each value of $N_{OFF}$, $10^{6}$ data sets were generated using a poissonian random number algorithm\\cite{kn:numreps}.\nThe fraction of samples $N$ of $N_{OFF}$ where $N > N_{OFF}+S_{3}$ is used as an estimate of the true probability of \nobtaining $N_{ON}=N_{OFF}+S_{3}$ by chance.\nThe results are shown in figure~\\ref{fig:limacomp} where both equations~\\ref{eq:dcxs} and \\ref{eq:lamchi} are shown\nto overestimate the probability near the $3\\sigma$ level almost equally likely, the former slightly less so.\nIt is evident that, near the $3\\sigma$ level, there is little to choose and both equations are adequate for values of \n$N_{OFF}$ and $N_{ON}$ of a few hundred or more. \nSince good algorithms are available for Poissonian random number generation it is likely to be better to determine\nthe probability of $N_{ON}$ and $N_{OFF}$ for values less than $\\sim 100$ using Monte Carlo methods tailored for the \nexact values of $N_{ON}$ and $N_{OFF}$.\n\n\n% MAIN SECTION TIME SERIES MAIN SECTION \n% MAIN SECTION TIME SERIES MAIN SECTION \n% MAIN SECTION TIME SERIES MAIN SECTION \n\n\\section{Time Series}\n\n\\subsection{Introduction}\n\nTime series analysis has been the subject of very many books and articles and has been applied in very many fields. \nThe term covers a wide range of concepts, including Change Point Analysis, Fourier Analysis and Trend Analysis.\nIn cosmic ray studies, there are several areas of application, such as sidereal/solar effects on low energy cosmic \nrays on the ground, periodicity in data from point sources, either from satellite X- and $\\gamma$-ray data, \nor from ground-based \\v{C}erenkov detectors, and sporadic emission of a wide range of cosmic ray energies. \nIn these cases, the raw data is usually in the form of time-tagged events. \n\n\n\n% Sub Section BURSTS\n% Sub Section BURSTS\n\n\\subsection{Bursts of Events}\n\nThis section will be concerned with the problem of deciding whether the counting rate of a detector has deviated from \nthe expected rate due to a real outburst of events.\nThe problem is usually most difficult in data comprising time-tagged events.\nAn initial analysis could start with binning the data and looking for a deviation from the expected Poissonian\ndistribution of the counts.\nOne problem with this approach is that in the model of a single Poisson process generating the counts, each bin is\nindependent, the experimenter often has the freedom to place the bins, both in position and width, arbitrarily.\nThis alters the 'degrees of freedom' and experience suggests that more bursts have been 'detected' in the past than\ncould have been justified from the data.\n\nThe problem mentioned above is a specific one but in general most statistical problems associated with sporadic emission \nrelate to the lack of a specific model for the form, duration and amplitude of emission, and the feeling is often that, \ngiven a free hand with the parameters, any pure noise series could made to disclose a 'burst'.\nA recent paper by Scargle\\cite{kn:scargle98} suggests that existing methods for searching for rapid variability in $X-$ray \nand $\\gamma$-ray astronomy do not fully extract all of the information contained in photon counts. \nThe reasons given included 'binning fallacies', in that the data were widely binned and the size of the bins must be \nlarge enough to give 'good statistics'. \nFurther, global methods such as autocorrelations and power spectra used on large data sets dilute the effects of sporadic \nbursts. The Bayesian response to these problems is discussed later. \n\nThe problem at first sight does not seem insolvable using classical statistical theory. \nThe statistical treatment of \\emph{point processes}: data occurring as points on the real line, or as discrete times, \nis covered by several texts, for example Cox and Isham\\cite{kn:cox}. \nThe general treatment covers a variety of statistical processes, including Poisson (which is of most application here), \ndoubly stochastic Poisson (where the average Poisson rate is itself a variable) and renewal processes where the distribution \nfunction for intervals between points is not exponential. \nIn analysing data in the form of time-tagged photons without appreciable dead time, classical statistics would \nlook for a powerful goodness-of-fit test of the pure Poisson process, if possible avoiding the loss of information and \nthe arbitrary choices associated with binning.\n\nGiven such a series of times, the problem posed here is: is there evidence for 'bunching' or 'bursts'?\nAlternatively, are the data consistent with a uniform distribution in time which, for events not affected by counter \ndead-time, would be governed by a pure Poisson process? \nSome recent papers such as McLaughlin et al.\\cite{kn:mclaughlin} use just this assumption to classify sources into 'steady' \nor 'variable'. Others use \\emph{ad hoc} methods to estimate the probability of bursts\\cite{kn:katayose}.\n\n\\subsubsection{The Scan Statistic}\n\nThe test statistic postulated above exists: the Scan Statistic has been extensively studied by Parzen\\cite{kn:parzen}, \nBarton and David\\cite{kn:barton}, Huntington and Naus\\cite{kn:huntington}, Neff and Naus\\cite{kn:neff}, Naus\\cite{kn:naus66},\nGlaz\\cite{kn:glaz93}, Wallenstein, Naus and Glaz\\cite{kn:wallenstein73,kn:wallenstein94}, Chen and Glaz\\cite{kn:chen97} and M\\aa nsson\n\\cite{kn:mansson}.\nIt is a statistic for detecting clustering in time or one dimension in space. \nIt is usually described as the maximum (or minimum) number of events which can be found in a window of fixed duration \nscanning smoothly through a much longer interval containing discrete events following some random process, for example \nPoissonian. \nAn example of the scan statistic is shown in figure~1 for window lengths of 1\\% and 10\\% of the duration of the data. \nThe random test data has a constant mean rate except for the third quarter which has double the rate.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}[h]\n\\psfig{file=Fig1b.eps,angle=90,height=6cm}\n\\label{fig:1b}\n\\footnotesize\n\\caption{Example of the Scan Statistic for windows of 1\\% and 10\\% of the data duration}\n\\end{figure}\n\\normalsize \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nThe scan statistic $S$ has a probability $P(S)$ which depends on the rate of events, the duration and the width of\nthe scanning window.\nSome exact solutions for the probability $P(S)$ have been provided.\nOne of them, by Huntington and Naus\\cite{kn:huntington}, provides the probability of a related statistic: \n\\begin{equation}\nP\\left(a_{n}\\leq a\\right)=1-\\sum_{Q}R \\det\\mid\\!\\!1/h_{ij}!\\!\\mid \\det\\mid\\!\\!1/l_{ij}!\\!\\mid\n\\label{eq:scanexact}\n\\end{equation}\n\nwhere $a_{n}$ is the smallest interval $a$ containing $n$ events in the range $[0,1]$, where this range contains $N$ \nevents in all. \nThe summation extends over the set $Q$ of all partitions of $N$ into $2L+1$ integers satisfying $n_{i}+n_{i+1}<n, i=1,\\ldots,2L$ and $R=N!b^{M}(a-b)^{N-M}$ with $M=\\sum_{k=0}^{L}n_{2k+1}$, and \n\\begin{eqnarray*}\nh_{ij} & = & \\;\\;\\;\\sum_{k=2j-1}^{2i-1}\\!\\!n_{k}-(i-j)n\\;\\;\\;\\; L+1\\geq i\\geq j\\geq 1\n\\\\\n & = & -\\sum_{k=2i}^{2j-2}\\!\\!n_{k}+(j-i)n\\;\\;\\;\\; 1\\leq i<j\\leq L+1\n\\\\\nl_{ij} & = & \\;\\;\\;\\sum_{k=2j}^{2i}n_{k}-(i-j)n\\;\\;\\;\\;L\\geq i\\geq j\\geq 1\n\\\\\n & = & -\\sum_{k=2i+1}^{2j-1}\\!\\!n_{k}+(j-i)n\\;\\;\\;\\;1\\leq i<j\\leq L\n\\end{eqnarray*}\nEquation~\\ref{eq:scanexact}, although exact, is computationally expensive for large $N$ and small $a$, that is a large \ndata set with a small scanning window, but several approximations have been provided which are designed to be valid for \ncertain combinations of parameters.\n \n\\subsubsection{Newell-Ikeda Approximation for the Scan Statistic}\n\nThe Newell-Ikeda\\cite{kn:newell,kn:ikeda} asymptotic formula is suitable for small probabilities. \nIt gives the probability of finding a section of length $t$ in a data set of length $T$, given a Poisson process of \naverage rate $\\lambda$:\n\\begin{equation}\nP\\left( n;\\lambda T,t/T \\right) \\doteq 1-\\exp \\left( -\\lambda^{n}t^{n-1}T/(n-1)! \\right)\n\\label{eq:newell}\n\\end{equation}\nAs shown in table~\\ref{tab:scanstats}, it significantly overestimates larger probabilities.\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{|l|l|l|} \\hline\n%\\multicolumn{3}{l}{ } \\\\\n$n$ & exact & Newell-Ikeda \\\\ \\hline\n$5$ & $0.711$ & $0.984$ \\\\ \\hline \n\n$6$ & $0.225$ & $0.565$ \\\\ \\hline\n$7$ & $0.0425$ & $0.129$ \\\\ \\hline\n$8$ & $6.31\\times10^{-3}$ & $0.0196$ \\\\ \\hline\n$9$ & $8.04\\times10^{-4}$ & $2.48\\times10^{-3}$ \\\\ \\hline\n$10$ & $9.05\\times10^{-5}$ & $2.76\\times10^{-4}$ \\\\ \\hline\n\\end{tabular}\n\\caption{Comparison of Scan Statistic probabilities} \\label{tab:scanstats}\n\\end{center}\n\\end{table}\nBetter approximations, although not as easy to calculate, are available, for example Conover, Bement and Iman\n\\cite{kn:conover} and Naus\\cite{kn:naus82}. \n\n\\subsubsection{Naus Approximation for the Scan Statistic}\nThe more exact treatment of Naus\\cite{kn:naus82} will be given without derivation.\nFor an average rate of events $\\lambda$, data of total duration $T$ and scanning window of duration $t$, define $L=T/t$. \nThen the probability that the number of events in a scanning window never exceeds $n$ is $Q^{*}\\left(n;\\lambda L,1/L\\right)$\n and is accurately approximated by:\n\\begin{equation}\nQ^{*}\\left(n;\\lambda L,1/L\\right) \\doteq Q^{*}\\left(n;2\\lambda,\\frac{1}{2}\\right)\\left[Q^{*}\\left(n;3\\lambda,\\frac{1}{3}\n\\right)/Q^{*}\\left(n;2\\lambda,\\frac{1}{2}\\right)\\right]^{L-2}\n\\label{eq:naus}\n\\end{equation}\nNote that this approximation is valid for a wide range of types of distribution for the time between events.\nExact formulae for $Q^{*}\\left(n;2\\lambda,\\frac{1}{2}\\right)$ and $Q^{*}\\left(n;3\\lambda,\\frac{1}{3}\\right)$ are given for \na Poisson process:\n\\begin{eqnarray*}\nQ^{*}\\left(n;2\\lambda,\\frac{1}{2}\\right) & = & F_{n-1}^{2}-\\left(n-1\\right)p_{n}p_{n-2}-\\left(n-1-\\lambda\\right)p_{n}F_{n-3}\n\\\\\nQ^{*}\\left(n;3\\lambda,\\frac{1}{3}\\right) & = & F_{n-3}^{2}-A_{1}+A_{2}+A_{3}-A_{4}\n\\end{eqnarray*}\nwhere\n\\begin{eqnarray*}\nA_{1} & = & 2p_{n}F_{n-1}\\left(\\left(n-1\\right)F_{n-2}-\\lambda F_{n-3}\\right)\n\\\\\nA_{2} & = & 0.5p_{n}^{2}\\left(\\left(n-1\\right)\\left(n-2\\right)F_{n-3}-2\\left(n-2\\right)\\lambda F_{n-4}+\\lambda^{2}F_{n-5}\n\\right)\n\\\\\nA_{3} & = & \\sum_{r=1}^{n-1}p_{2n-r}F_{r-1}^{2}\n\\\\\nA_{4} & = & \\sum_{r=2}^{n-1}p_{2n-r}p_{r}\\left(\\left(r-1\\right)F_{r-2}-\\lambda F_{r-3}\\right)\n\\end{eqnarray*}\n\nand $p_{i}$,$F_{n}$ are the Poisson probability and distribution functions: $p_{i}=e^{-\\lambda t}(\\lambda t)^{i}/i!$ and \n$F_{n}=\\sum_{i=0}^{n}p_{i}$. \n\nTight bounds for $Q^{*}(n)$ have been given by Glaz and Naus\\cite{kn:glaz91} and a recursive method proposed\\cite{kn:karwe} \nfor calculating $Q^{*}(n;2t)$ and $Q^{*}(n;3t)$ for situations where the random quantity $X_{i}$ may take on values other \nthan $0,1$, that is situations where an 'event' cannot be given as either present or absent but only with a non-zero \nprobability.\n\nOther approximations for the tail of the scan statistics and the moments of its distribution have been given by Glaz\n\\cite{kn:glaz93} and Chen and Glaz\\cite{kn:chen97}. \nSample tables of the scan statistic have been given for $n\\leq 500$ by Glaz\\cite{kn:glaz92,kn:glaz93}. \n\nThis treatment of the scan statistic is for an interval of length $t$, specified in advance. \nWhen searching for a 'burst' of events, an \\emph{a priori} length cannot always be specified. \nAn extension to the treatment above has been described by Nargawalla\\cite{kn:nargarwalla} in which the length need \nnot be pre-assigned.\n\n\\subsubsection{Alm Approximation for the Scan Statistic}\nA new approximation has been given recently by Alm\\cite{kn:alm} which is accurate and easy to calculate for large values \nof $T/t$ and $\\lambda t$. \nThis treatment examines the distribution of upcrossings, that is occurrences where the number of\nevents in the scanning window increases by 1 as the window is moved. \nBy separating these events into \\emph{primary} and \\emph{secondary} upcrossings, the dependence of the second type from the \nfirst (almost) independent events allows significant simplifications.\nIf each window of length $t$ were independent, the expected number of events would be $\\lambda t$\nwith a Poisson probability function $F_{\\lambda t}(n)$ and distribution function \n$p_{\\lambda t}(n)$. \nThe approximation based on the ideas above gives the simple modification:\n\n\\begin{equation}\nP\\left(N\\geq n\\right) = 1 - F_{\\lambda t}(n)\\exp\\left[-\\left(1-\\frac{\\lambda t}{n+1}\\right)\\lambda\\left(T-t\\right)p_{\\lambda \nt}(n)\\right] \n\\label{eq:alm}\n\\end{equation}\n\nEquation~\\ref{eq:alm} has been tested for $\\lambda t=40$ and $T/t=3600$ using 10000 Monte Carlo simulations.\nThe results are shown in table~\\ref{tab:montecarlo} for $13 \\leq n \\leq 23$.\nIt can be seen that equation~\\ref{eq:alm} is a good approximation within the sampling errors. \n\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{|l|l|l|} \\hline\n%\\multicolumn{3}{l}{ } \\\\\n$n$ & Monte Carlo & Equation~\\ref{eq:alm} \\\\ \\hline\n$13$ & $0.9984$ & $0.9993$ \\\\ \\hline\n$15$ & $0.9429$ & $0.9478$ \\\\ \\hline\n$16$ & $0.6654$ & $0.6635$ \\\\ \\hline\n$17$ & $0.3094$ & $0.3087$ \\\\ \\hline\n$18$ & $0.1055$ & $0.1098$ \\\\ \\hline\n$19$ & $0.0307$ & $0.0337$ \\\\ \\hline\n$20$ & $0.0093$ & $0.0095$ \\\\ \\hline\n$21$ & $0.0021$ & $0.0025$ \\\\ \\hline\n$22$ & $0.0006$ & $0.0006$ \\\\ \\hline\n$23$ & $0.0002$ & $0.0001$ \\\\ \\hline\n\\end{tabular}\n\\caption{Comparison of 1-D Scan Statistic probabilities for 10000 samples with $T/t=3600$ and $\\lambda t = 40$} \\label{tab:montecarlo}\n\\end{center}\n\\end{table}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\\begin{figure}[hb]\n%\\psfig{file=Almcomb.eps,height=6cm}\n%\\label{fig:11}\n%\\footnotesize\n%\\caption{Comparison of ratio: actual/approximate probability for various approximate formulae}\n%\\end{figure}\n%\\normalsize \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsubsection{Other Approximations for the Scan Statistic}\nOther methods have been published, for example the Burst Expectation Search by Giles\\cite{kn:giles} and CUSUM by \nVanStekelenborg and Petrakis\\cite{kn:vanstekelenborg}. \nThe first follows earlier work\\cite{kn:rothschild} which used binned times of events and calculates Poisson probabilities \nof bin counts from a running average of a sample of bins. \nThe BES inverts this process and, for each possible bin count from zero to several hundreds, calculates the mean rate \nbelow which the possible count could be a significant burst using a fixed sample of bins around the trial bin. \nThe aim of keeping a fixed sample was to avoid problems arising from a step function edge entering a moving average.\n\n\\subsubsection{Bursts: Summary}\nIn summary, of possible methods suggested for searching for bursts using classical statistics, the Scan Statistic is \nrecommended, both for time-tagged data and for time-binned data.\nFor small data sets or large window sizes, equation~\\ref{eq:scanexact} provides an exact probability of the largest\nnumber in any window arising due to chance.\nMany approximate formulae are available, depending on whether the probability of the scan statistic is expected to \nbe large or small.\nIn most practical cases in cosmic rays the statistic is used to search for a possible outburst and so the probability\nof a given value of the scan statistic arising due to chance will be small in order to be useful.\nIt becomes a matter of computational convenience which of the formulae above is used but equation~\\ref{eq:alm} delivers \na good approximation over a wide range of probability values and is easy to calculate.\nIt also has the advantage, in terms of understanding the principles, of starting from the naive initial Poissonian \nformula with non-overlapping (independent) windows.\nIts use is therefore recommended here.\n\n\n\n\n% Sub Section PERIODICITY\n% Sub Section PERIODICITY\n\\subsection{Periodicity}\n\nMost of the methods for time-series analysis, including trend analysis and auto-regressive moving average (ARMA), \nhave been developed for fields other than cosmic rays, for example \\cite{kn:bell,kn:lathi,kn:lewis93}. \nFourier methods suitable for data at equally spaced times are well developed but are usually not suitable, although \nthese have been extended to discuss unequal intervals and missing data\\cite{kn:scargle82}. \nA bibliography of astronomical time series analysis has been given by Koen\\cite{kn:koen}.\n\n\\subsubsection{The Rayleigh test and Dependants}\n\nThe spur for the introduction of the Rayleigh test into $\\gamma$-ray astronomy was the unsatisfactory nature of the \nstatistics being used before. \nEarly tests on $\\gamma$-ray data used epoch-folding to produce a histogram in phase, and \n$\\chi^{2}$ as a statistic for goodness of fit to a uniform distribution. \nThis suffers from several disadvantages:\n\\begin{enumerate}\n\\item the freedom to select the number of bins, \n\\item the freedom to define the starting phase, \n\\item the failure to use the information contained in the order of the bins.\n\\end{enumerate}\nThis last problem can be overcome to some degree by using the Run Test, which is independent and therefore whose \nprobability may be combined with that from \\chisq. \nThe result of the freedoms listed above is that different authors could return quite different chance probabilities, \ngiven the same data, despite using the same test statistic.\nThe analysis of $\\gamma$-ray data from the Crab pulsar by Gibson et al.\\cite{kn:gibsonb} contained the first known use \nof the Rayleigh statistic\\cite{kn:mardia,kn:fisher} in cosmic ray work. \nIt is still a goodness-of-fit statistic, which has no explicit hypothesis as an alternative to the null hypothesis.\n\nThe time of each event is treated as a unit vector in the plane, with an angle equal to the pulsar phase. \nIf $N$ unit vectors of random orientations (random phases) are added, the distribution of the resultant $R$ may \nbe obtained from the distribution of the orthogonal components of the vectors, $\\sin \\phi_{i} $ , $\\cos \\phi_{i}$\nwhere $\\phi_{i}$ is the phase of the $i^{th}$ vector. \nThe means of these components are :\n\\begin{displaymath}\nC = \\frac{1}{N}\\sum_{i=1}^{N} \\cos \\phi_{i} \\ \\ \\ \\ \\ S = \\frac{1}{N}\\sum_{i=1}^{N} \\sin \n\\phi_{i}\n\\end{displaymath}\n\nFrom the Central Limit Theorem (CLT) means of samples of $C$ are distributed, for large $N$, as a Gaussian with $var_{C} = \n\\sigma_{C}^{2}/N$.\nFor vectors uniformly covering the circle:\n\\begin{displaymath}\n \\sigma_{C}^{2} = \\int_{0}^{2\\pi} \\cos^{2}(\\phi) d\\phi / 2\\pi = 0.5\n\\end{displaymath}\n therefore $var_{C} = var_{S} = 1/2N$.\nThe quantities $C$ and $S$ are asymptotically uncorrelated and have zero means. \nThe statistic \\(2NR^{2} = 2NC^{2}+2NS^{2}\\) is therefore the sum of the squares of two zero-mean, unit-variance \nuncorrelated variables and is distributed as $\\chi^{2}$ with 2 degrees of freedom \\cite{kn:priestley, kn:bloomfield}. \nThe probability distribution function (pdf) of $R$ is : \n\\begin{equation}\n%*}\n f(R)dR = 2NR e^{-NR^{2}} dR \n\\label{eq:pdf}\n\\end{equation}\n%*}\nand its cumulative probability distribution is :\n\\begin{equation} \n F(R) = e^{-NR^{2}} \\label{eq:probab}\n\\end{equation}\nThe quantity $NR^{2}$ is known as the Rayleigh power.\n\nIf a data set spans a time interval $T$ the number of independent frequency trials in the frequency range $f_{1}$ to $f_{2}$\n is $\\nu=T\\left(f_{1}-f_{2}\\right)$ if $T >> f_{1}$,$f_{2}$, with the independent frequencies separated by $1/T$. \nIn practice allowance must be made for leakage: the possible effect of a signal at frequency $f_{0}$ on trial frequencies \n$f$ with $\\mid \\!f-f_{0}\\mid\\!>1/T$, and oversampling: the possibility of obtaining a larger value of $NR^{2}$ by\nvarying the frequency between adjacent independent frequencies. \nThis has been done using by de Jager et al.\\cite{kn:dejager89} by Monte Carlo techniques and analytically by \nOrford\\cite{kn:orford91}. \nBoth methods agree that the number of trials is $nT\\left(f_{1}-f_{2}\\right)$ where $n$ is a slowly \nvarying function of $F(R)$ in the range $2$ to $4$, with a value approximately $3$ for $F(R) \\sim 10^{-3}$.\n\n\n% THE Zn TEST\n\\subsubsection{The $Z_{n}^{2}$ Test}\n\nThe $Z_{n}^{2}$ test is the extension of the Rayleigh test to include harmonics.\nIF \\textbf{n} separate harmonics are included with independent coefficients, the statistic is \n\\begin{equation}\nZ_{n}^{2}=2N\\sum_{i=1}^{n} R^{2}(i\\omega) \\label{eq:zn}\n\\end{equation}\nwhere $2NR^{2}(i\\omega)$ is the Rayleigh power for the $i^{th}$ harmonic.\n$Z_{n}^{2}$ is distributed as $\\chi^{2}(2n)$.\nVariations on this technique depend on the method used to select the number and weighting of harmonics. \nA similar principle is used in radio astronomy where a pulse of width $W$ is searched for using $P/2W$ harmonics \nwhich improves the signal to noise by a factor of up to $(P/2W)^{0.5}$\\cite{kn:lyne}.\nA search for $\\gamma$-ray emission from radio pulsars proposed the use of $Z_{2}^{2}$ as a relatively powerful but\ngeneral test for periodicity\\cite{kn:buccheri}.\nThe power of the Rayleigh test for light curves from sinusoids to $\\delta$-functions was explored by Protheroe\n\\cite{kn:protheroe3}.\nA variant of $Z_{n}^{2}$ is the H-test\\cite{kn:dejager89} in which the value of $n$ is obtained objectively from the data\nand $Z_{n}^{2}$ is suitably rescaled.\nThis last test is most suitable for multi-mode light curves.\n\n% RED NOISE IN RAYLEIGH TESTING\n\\subsubsection{Limitations of the Rayleigh and associated statistics}\n\nThe foregoing results for the Rayleigh ($Z_{1}^{2}$) and $Z_{n>1}^{2}$ tests are for the asymptotic case, that is: uncorrelated \n$C$ and $S$ with zero means. \nIn most practical applications, these conditions are not strictly met. \nGround-based gamma-ray observations of long-period pulsars are limited by: \n\\begin{enumerate}\n\\item being only a few hours in duration and \n\\item variations in zenith angle, producing changing counting rates.\n\\end{enumerate} \nThe requirement for large sample size is usually met - typical counting rates are $\\approx$~1 per second over several hours. \nThe result is an enhancement of \\chisq\\ in pure noise data for longer test periods - red noise.\nThe first limitation listed above may be overcome by truncating the dataset so that only integral multiples of the trial \nperiod are tested - see Carrami\\~{n}ana et al.\\cite{kn:alberto} and Raubenheimer and \\\"{O}gelman\\cite{kn:raub1}. \nAs a result, the two trigonometric terms have zero expectations, given a constant mean counting rate. \nThis truncation is easy to accomplish, but results in a variable data selection depending on the test period and therefore \nall periods are not accorded the same treatment. \nSince the periodogram is the convolution of the power spectral density with the Fourier transform of the data window, any \nspectral estimate based on a truncated data set is biased\\cite{kn:kay,kn:priestley,kn:jenkins}. \nFurther, any correlation introduced by the second limitation above will not be removed this way. \nAn attempt to remove the results of the counting rate variation has been made by Raubenheimer et al.\\cite{kn:raub2} by \nfitting a parameter $a$ in an \\emph{ad hoc} modification of the Rayleigh probability distribution: \n\\begin{equation}\n F(R) = e^{-2aNR^{2}} \n\\label{eq:raubenheimer}\n\\end{equation}\nto random data sets containing no signal, but with the same parameters as the test data set. \nFor data taken on Vela X-1 (period $\\approx$~ 5 minutes) they found that equation~\\ref{eq:raubenheimer} with $a=0.4$ \n(as opposed to 0.5 from simple theory) gave a probability distribution which was a good fit to the distribution in \n\\chisq\\ for noise at periods near to 5 minutes in simulated data sets.\n% MODIFIED RAYLEIGH STATISTIC\n\n\\subsubsection{Modified Rayleigh Statistic}\n\nIf the expectations of $C$ and $S$, their variances and their covariance are not assumed to be zero, $\\frac{1}{2N}$ and \nzero respectively, but are calculated for a specific dataset, then the asymptotic probability equation~\\ref{eq:probab} \nmay be valid, given a sufficiently large number of events\\cite{kn:orford96}. \n\nThe expression for \\chisq\\ in the case of samples of two correlated variables $C$ and $S$ is :\n\\begin{eqnarray} \n \\chi^{2}&=&\n \\left[\n \\begin{array}{c} \n \\overline{C}-E(C) \\\\ \\overline{S}-E(S) \n \\end{array} \n \\right] ^{T}\n \\left[ \n \\begin{array}{cc} \n \\sigma_{C}^{2} & cov_{S,C} \\\\ cov_{S,C} & \\sigma_{S}^{2} \n \\end{array} \n \\right] ^{-1} \n \\left[ \n \\begin{array}{c} \n \\overline{C}-E(C) \\\\ \\overline{S}-E(S) \n \\end{array} \n \\right] \\label{eq:chisq}\n\\end{eqnarray}\n\nFor any data set, the substitution of the actual values of $E(C)$, $E(S)$, $\\sigma_{C}$, $\\sigma_{S}$ and $cov_{S,C}$ will \nresult in a value of \\chisq\\ corrected for the correlation of the variables $C$ and $S$ and with a probability distribution,\nfor large sample size, given by $\\exp(-\\chi^{2}/2)$.\n\nIn the case of a box-car data set with a constant average counting rate, a starting time $t_{1}$ and ending time $t_{2}$ \nwith $T=t_{2}-t_{1}$ and a trial period $P = 2\\pi/\\omega$ :\n\\begin{eqnarray*}\n E(C) & = & \\frac{\\left[\\sin\\omega t\\right]_{t_{1}}^{t_{2}}}{\\omega T} \\label{eq:exc} \n\\\\\n E(S) & = & \\frac{\\left[-\\cos\\omega t\\right]_{t_{1}}^{t_{2}}}{\\omega T} \\label{eq:exs}\n \\\\\n Nvar_{C} & = & \\frac{1}{2} + \\frac{\\left[\\sin \\omega t \\cos \\omega t\\right]_{t_{1}}^{t_{2}}}{2\\omega T} - [E(C)]^{2}\n\\label{eq:varc}\n \\\\ \n Nvar_{S} & = & \\frac{1}{2} - \\frac{\\left[\\sin \\omega t \\cos \\omega t\\right]_{t_{1}}^{t_{2}}}{2\\omega T} - [E(S)]^{2}\n\\label{eq:vars}\n \\\\\n Ncov_{S,C} & = & \\frac{\\left[\\sin^{2}\\omega t\\right]_{t_{1}}^{t_{2}}}{2\\omega T} - {E(C)E(S)} \\label{eq:covsc}\n\\end{eqnarray*} \nThese depend solely on $\\omega$, $t_{1}$ and $t_{2}$ and their substitution in equation~\\ref{eq:chisq} gives a \\chisq\\ \nvalue corrected for the finite length of the data set. \nIf it is known that there is no secular change in counting rate the substitution of the above equations \ninto equation~\\ref{eq:chisq} would give the correct formal probability of chance occurrence, even if the duration of the \ndata set is less than the trial period, as long as the number of events was high enough for the CLT to be valid. \nIt is more usually the case in ground-based gamma-ray observations that the box-car function is only an approximation.\nMonte Carlo simulations of data sets have been carried out to test the validity of data set truncation and the above \nformulations for the case of secular variations of counting rate superimposed on noise. \nIn order to test the validity of the probability distribution equation~\\ref{eq:probab} down to probabilities \n$\\approx 10^{-6}$, data sets were generated using a multiplicative congruential algorithm with shuffling, chosen to \navoid serial correlations. \nThe repeat period is longer than $2\\times10^{18}$. \nThe time of each event $t_{i}$ was generated from the previous event:\n$t_{i}=t_{i-1}-\\Delta(t)\\ln(rnd)$ where $\\Delta(t)$ is the mean separation of events as a function of time.\nA group of $10^{6}$ data sets of duration 8000 s were simulated with a counting rate profile \\mbox{$R=R_{0}(1-0.3t/4000)$} \nand \\mbox{$R_{0}=1s^{-1}$}. \nEach data set was tested for periodicity at a trial period of 295s by finding $C$ and $S$ with reference to the time \nof the first event.\n These values were substituted into equation~\\ref{eq:chisq} for various assumptions about the form of $E(C)$, $E(S)$, \n$var_{C}$, $var_{S}$ and $cov_{S,C}$. The probability of chance occurrence was calculated from $e^{-\\chi^{2}/2}$.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\\begin{figure}[h]\n%\\begin{center}\n%\\psfig{file=Fig2.eps,angle=90,height=6cm}\n%\\footnotesize\n%\\caption{Frequency distribution of \\chisq\\ probabilities from $10^{6}$ Monte Carlo data sets} \\label{fig:monte2}\n%\\end{center}\n%\\end{figure}\n%\\normalsize \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nThe resulting cumulative frequency distributions for $e^{-\\chi^{2}/2}$\n% are shown in figure~\\ref{fig:monte2} \nhave been calculated for the cases \nof (a) a truncation of the data set to integral multiple of the trial period, (b) box-car \nfunction and (c) a linear fit to the counting rate profile. \nThe ratios of the observed to expected frequencies of occurrence of \\chisq\\ chance probabilities is shown in \nfigure~\\ref{fig:cumfreq}, as functions of $\\log{(\\chi^{2} probability)}$.\nNote that the duration of the data set is corrected for equally well by (b) and (c).\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}[ht]\n\\center\n\\psfig{file=Fig3a.eps,angle=90,height=6cm}\n\\footnotesize\n\\caption{Ratio of cumulative frequency of \\chisq\\ probabilities to expectation} \\label{fig:cumfreq}\n\\end{figure} \n\\normalsize\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nThe boxcar and truncated statistics both make corrections for the finite length of a data set, but give a residue which \nmay be identified as being caused by the change of counting rate during the trial period. \nLonger trial periods or greater rates of change in counting rate would amplify their biases. \nThe truncation method has a distribution which may be fitted, for this simulated data set, by a form such as \nequation~\\ref{eq:raubenheimer} with $a=0.45$. \nThe linear fit model is seen to be a good representation of the noise spectrum down to chance probabilities of \n$\\approx 10^{-5}$.\n% OTHER TESTS\n% OTHER TESTS\n\\subsubsection{Other Tests}\n\nLeahy et al.\\cite{kn:leahy} pointed out that the unmodified Rayleigh test was powerful for detecting wide peaks in a \nlight curve, in fact it is identical with a likelihood ratio test of a sinewave plus uniform against a uniform phase \ndistribution \\cite{kn:bai}. \nIn addition, for a light curve of a von Mises form (the circular generalisation of the Gaussian), the Rayleigh statistic\nexhausts the data's information on periodicity if the concentration parameter $\\kappa$ is allowed to vary freely\n\\cite{kn:loredo92}.\n\nNarrow periodic pulse detection, with significant power in the higher harmonics, is bound to be quite difficult because \nthe number of degrees of freedom increases with the trial frequency range. \nProtheroe\\cite{kn:protheroe1} proposed a test statistic \n\\begin{equation}\nT_{n} =\\frac{2}{n(n-1)}\\sum_{i=1}^{n-1}\\sum_{j=i+1}^{n}(\\Delta_{ij}+1/n)^{-1}\n\\end{equation}\nwhich looked for close clustering of points on the circle. In this statistic $\\Delta_{ij}$ is the distance between the \nangles $x_{i}$ and $x_{j}$ of two events on the circle:\n\\begin{displaymath}\n\\Delta_{ij}=0.5-\\mid\\left[\\mid(x_{i}-x_{j})\\mid-0.5\\right]\\mid\n\\end{displaymath}\nThe null distribution was found using Monte Carlo methods for $n\\leq200$ and critical values given. \nThe context of the test was the search for ultra-high energy $\\gamma$-rays from Cygnus X-3 and was therefore not \ndesigned for large $n$. \nIn this limitation it is similar to the exact expression scan statistic described above. \nOthers have suggested variants which are designed to be powerful for certain classes of pulsed emission\n\\cite{kn:swanepoel}.\n\nThe Scan Statistic may also be used for searching for non-uniformity in phase. \nFor narrow windows its probability distribution is well approximated by the scan statistic on the line\\cite{kn:nauspriv}.\nNo systematic work on the use of the Scan Statistic in periodic analysis has been traced.\n% SEARCHING FOR PERIODICITY\n% SEARCHING FOR PERIODICITY\n\\subsubsection{Searching for a Periodicity}\n\nIt is usually only the case that a unique periodic ephemeris is available for high energy photons from an isolated radio \npulsar.\nIn other cases, a search must be made in period, and the test used must allow for the freedoms associated with the\ntrial period range.\nA rule-of-thumb arising from the number of 'degrees of freedom' implicit in a periodicity search using the Rayleigh\ntest\\cite{kn:dejager89,kn:orford91} is that the search should be at intervals in period of $(IFI)/3$ ($IFI$ = \nIndependent Fourier Interval).\nFor a period of $P$ in a data set of duration $T$ this corresponds to a trial period step of $\\sim P^{2}/3T$.\nThis step size has the advantage that the number of degrees of freedom to be used to interpret the peak periodic amplitude\nfound is approximately the number of periods tried.\nIf harmonics of the test period are to be included, the spacing would be correspondingly reduced and hence the number of\ntrial periods increased.\nFor the $Z_{n}^{2}$ test, the reduction in period step, and consequent increase in both computation and the degrees of\nfreedom to be accounted for, is by a factor $n$.\n\nWhen searching for pulsed emission from some sources, in particular binary sources, there is frequently poor knowledge of \nthe both the pulsar period and period derivative. \nIn this case the light curve will be narrow only if the correct period $P$ and period derivative $\\dot{P}$ is offered to \nthe test.\nA nearby, but not correct, trial period and the ignorance of a period derivative will smear the light curve.\nIf a true light curve were a $\\delta$ function at period $P=P_{o}$ and the trial period was $P=P_{o}+\\Delta$, the light\ncurve would be a rectangular distribution in phase of length $T\\Delta /P_{o}^{2}$.\nThis effectively limits the number of harmonics which may be realistically added to $P_{o}^{2}/T\\Delta-1$.\n\nSome searches for periodicity are combined with a search for a DC excess. This is common in \\v{C}erenkov telescope \nsearches where ON-source data is compared with OFF-source control data to detect any DC component. \nThe combined analysis of this situation was proposed by Lewis\\cite{kn:lewis89} in which a statistic $\\alpha$ is defined as the \nsum of the Rayleigh statistic and the square of equation~\\ref{eq:dcxs}, distributed as \\chisq(3). \nThe assumption in this case is that all of the excess is pulsed; if there is an unpulsed component the test statistic \nwill be biased. \nAgain, the presence of a possible unpulsed component could be built into a Bayesian analysis.\n% CONCLUSION\n\\subsubsection{Conclusion on Periodicity}\nThe question of the best classical test for the presence of periodicity is a complex one.\nThe selection of the most sensitive test requires a knowledge of \n\\begin{itemize}\n\\item the pulsar ephemeris\n\\item the light curve shape\n\\item the background noise distribution\n\\end{itemize}\nIf all of these are known in advance, a most powerful test, based on the $Z_{n}^{2}$ extension of the Rayleigh test\nis likely to be close to optimum.\nFrequently some or all of these will be unknown or poorly known.\nIn this case, some allowance must be made for the lack of knowledge and the test selected should not contain any\nassumption which causes a significant bias.\nIt has sometimes been claimed that the Rayleigh test is 'biased' towards broad light curves and that a test which\nis more sensitive to narrow light curves should be used when such a light curve is suspected.\nThis raises the problem, discussed in the previous section, of the smearing of a light curve if the pulsar's ephemeris is\nuncertain. \n\nProtheroe has suggested\\cite{kn:protheroe2} that if one has no information about the nature of the phase distribution \none should be conservative and adopt the Rayleigh test. \nA rational for this is that if one is searching for an unknown period and an unknown light curve, which is quite common \nin $\\gamma$-ray work, and there is no significant power in the fundamental, then a test involving the addition of an \nunknown number of higher harmonics is unlikely to be successful.\nThis point will be revisited later in discussing a Bayesian method of searching for periodicity.\n\nA simple suggestion made before and reiterated here is that if $Z_{n}^{2}$ does not show evidence for periodicity,\nthat is: there is no significant power in the fundamental or the first harmonic, either in addition or separately, then it \nis unlikely that the data will contain a strong periodic signal.\n\n% MAIN SECTION SPATIAL ANALYSIS MAIN SECTION \n% MAIN SECTION SPATIAL ANALYSIS MAIN SECTION \n% MAIN SECTION SPATIAL ANALYSIS MAIN SECTION \n\n\\section{Spatial Analysis}\n\n\\subsection{Introduction} \n\nSpatial analysis of arrival direction data is of great interest for X- and $\\gamma$-rays from satellites and for \ncosmic rays of the highest energies, which may not be greatly deflected in the galactic magnetic field. \n\nSimple methods rely on a grid placed on the events and counts in the grid cells taken as independent Poisson-distributed \nevents.\nIf the cells are fixed absolutely, there is no problem in ascribing a suitable Poissonian probability to the largest\nnumber detected in any cell.\nIf there is freedom to incrementally move the cell containing the largest count, a larger number is generally found.\nIn this case the new cells created are correlated and the assumption of independence is incorrect: simple application\nof Poissonian probabilities is inappropriate.\nThe problem of having the freedom to move the boundaries of the cells was pointed out for cosmic ray 'sources' by \nHillas\\cite{kn:hillas} who suggested a conservative number of 'sigmas'.\nLarge scale anisotropy in gamma ray bursts were sought using dipole and quadrapole analysis\\cite{kn:briggs}. \nA 'pair matching' statistic was used by Bennett and Rhie\\cite{kn:bennett} to check for gamma ray burst repeaters rather \nthan 'nearest neighbour' methods used by others\\cite{kn:brainerd} and criticised by Nowak\\cite{kn:nowak}.\nMany methods have been used which are based upon a known point-spread function (PSF). \nAmongst these are Maximum Entropy methods such as those used for satellite X-ray imaging\\cite{kn:cheng}, maximum\nlikelihood\\cite{kn:mattox} and Hough Transforms\\cite{kn:ballester}. \n\nIn the next section it is suggested that the scan statistic is a powerful and general statistic for which good approximations\nexist for the chance probabilities.\nIt has recently been extended to two dimensions by Loader\\cite{kn:loader}, Chen and Glaz\\cite{kn:chen96} and \nAlm\\cite{kn:alm}. Kulldorf\\cite{kn:kulldorff} has extended this further to higher dimensional searches.\n\n\n% sub section 2-D SCAN STATISTIC\n% sub section 2-D SCAN STATISTIC\n\\subsection{2-Dimensional Scan Statistic}\nThis is the two-dimensional development of the Scan Statistic introduced above.\nIt will be introduced using a notion of 'elemental' cells from which a two-dimensional scanning window is constructed.\nIn effect, the scanning window may be moved by discrete steps of the size of the elemental cell.\nAssume that a two-dimensional square region $R=\\left[0,L\\right]\\times\\left[0,L\\right]$ of side $L$ is inspected for \noccurrences of 'sources'\\cite{kn:chen96}. \nThe region is partitioned into $n\\times n$ elemental cells so that the size of a cell $h=L/n$. \nThe contents of each of the $n^{2}$ cells are independent.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}[ht]\n\\psfig{file=Draw2dc.eps,height=6cm}\n\\label{fig:2dscan}\n\\footnotesize\n\\caption{Two-dimensional Scan.\nThe region [0,L]X[0,L] is partitioned into $n\\times n$ cells ($n=16$) and an $m\\times m$ window ($m=4$) is scanned over it.}\n\\end{figure}\n%\\end{picture}\n\\normalsize\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n\nFor $1\\leq i\\leq n$ and $1\\leq j\\leq n$, define a random variable $Y_{i,j}$ as the number of events in the elemental cell \n$\\left[(i-1)h,ih\\right] \\times \\left[ (j-1)h,jh\\right] $. \nA square box of $m\\times m$ small cells is scanned over the whole of region $R$.\nThere will be $\\nu$ such boxes, partially dependent if $m \\geq 2$, with $\\nu = 0, (n-m+1)^{2}$.\n\nDefine \\[ S(i_{1},i_{2})=\\sum_{j=i_{2}}^{i_{2}+m-1}\\sum_{i=i_{1}}^{i_{1}+m-1}Y_{i,j} \\]\nto be the number of events in the square box of $m^{2}$ adjacent cells starting at $i=i_{1}$, $j=i_{2}$. \nIf, during the scanning of the $m-$box, $S(i_{1},i_{2})$ exceeds a particular value $k$, a 'source' has been detected.\nFor $1\\leq i_{1},i_{2}\\leq n-m+1$ define an 'event' $A_{i_{1},i_{2}}$ as an occurrence of $S(i_{1},i{_2})\\geq k$ and \nas a member of the set $A$ of all such occurrences.\n\nThe two-dimensional scan statistic is defined as:\n\\[S_{m}=\\max\\left\\{S(i_{1},i_{2});1\\leq i_{1}\\leq n-m+1,1\\leq i_{2}\\leq n-m+1\\right\\}\\]\nand the probability that $S_{m}$ has at least a value $k$ is:\n\\begin{eqnarray*}\nP(S_{m}\\geq k) & = & P\\left(\\bigcup_{i_{1}=1}^{n-m+1}\\bigcup_{i_{2}=1}^{n-m+1}A_{i_{1},i_{2}}\\right)\n%\\\\ & = & P\\left(A_{1,i_{2}} or A_{2,i_{2}} or ..... or A_{n+m-1,i_{2}}\\right)\n\\\\\n & = & P\\left(\\bigcap_{i_{1}=1}^{n-m+1}\\bigcap_{i_{2}=1}^{n-m+1}A_{i_{1},i_{2}}^{c}\\right)\n\\end{eqnarray*}\nwhere $A_{i_{1},i_{2}}^{c}$ is the occurrence of $S(i_{1},i_{2}) < k$.\n\n\\subsubsection{Glaz Approximation to 2-D Scan Statistic}\nFor a fixed value of $1\\leq i_{1}\\leq n-m+1$ the one-dimensional approximation holds:\n\\[P\\left(\\bigcap_{i_{2}=1}^{n-m+1}A_{i_{1}i_{2}}^{c}\\right)\\approx q_{2m}\\left(\\frac{q_{2m}}{q_{2m-1}}\\right)^{n-2m}\\]\nand since $n-m+1$ square regions of $m\\times m$ are scanned, a reasonable approximation is\\cite{kn:glaz91}:\n\\begin{equation}\nP(S_{m}\\geq k)\\approx 1-q_{2m-1}\\left(\\frac{q_{2m}}{q_{2m-1}}\\right)^{(n-2m+1)(n-m+1)}\n\\label{eq:2dapprox}\n\\end{equation}\nFor a Poissonian distribution of events the following expression was found to be a good approximation\\cite{kn:chen96}:\n\\begin{equation}\nP(S_{m}\\geq k)\\approx 1-\\exp(-\\lambda^{*}) \\label{eq:2dapproxb}\n\\end{equation}\nwhere the approximate mean for the asymptotic Poisson distribution is\n\\[\\lambda^{*}=1-q_{2m-2}+(n-2m+2)(n-m+1)(q_{2m-2}-q_{2m-1})\\]\nand\n\\[q_{m+l-1}=P(A_{1,1}^{c}\\cap A_{1,1}^{c}\\ldots \\cap A_{1,l}^{c})\\]\nTables are given\\cite{kn:chen96} of this and other approximations, for the Poisson model of $m\\leq 20$ and $n\\leq 500$.\n\n\\subsubsection{Alm Approximation to 2-D Scan Statistic}\nA recent paper\\cite{kn:alm} has given an approximation based on a modification of the method\nof counting \\emph{upcrossings} used in equation~\\ref{eq:alm}, which is easy to calculate and \nmoreover is given for a more generally useful rectangular scanning window $[0,a]\\times [0,b]$ in a \nrectangular region $[0,S]\\times [0,T]$. \nThe scan statistic $L$ is the maximum content of a scanning window with a two-dimensional\nPoissonian process $X$ with event density $\\lambda$:\n\\[L=L(\\lambda,a,b,S,T)=\\max_{a\\leq t\\leq T, b\\leq s \\leq S}X([t-a,t]\\times [s-b,s]\\]\nThe probability of observing at least $n$ events in a scanning window is:\n\\begin{equation}\nP(L\\geq n) \\approx 1 - F_{N(a)} e^{-\\gamma_{n+1}} \\label{eq:alm2d}\n\\end{equation}\nwhere\n\\[\\gamma_{n+1} \\approx \\left(1-\\frac{\\lambda ab}{n+1}\\right)\\left(T-a\\right)b\\lambda \\left(\\mu_{n}-\\mu_{n+1}\\right)e^\n{-\\mu _{n+1}}\\]\n\n\\[\\mu_{n} \\approx \\left(1-\\frac{\\lambda ab}{n}\\right)\\lambda a\\left(S-b\\right)p_{\\lambda ab}(n-1)\\]\nand\n\\[F_{N(a)} \\approx F_{\\lambda ab}\\exp\\left[1-\\left(1-\\frac{\\lambda ab}{n+1}\\right)\\lambda a\\left(S-b\\right)p_{\\lambda ab}(n)\n\\right]\\]\n$p_{\\mu}$ and $F_{\\mu}$ are the Poisson probability and cumulative probability distributions. \n\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{|l|l|l|l|} \\hline\n%\\multicolumn{4}{l}{ } \\\\\n$n$ & Monte Carlo & Equation~\\ref{eq:alm2d} & Poisson \\\\ \\hline\n$ 7$ & $0.9990$ & $0.9975$ & $3\\times 10^{-3}$\\\\ \\hline\n$ 8$ & $0.8658$ & $0.8795$ & $10^{-3}$ \\\\ \\hline\n$ 9$ & $0.4271$ & $0.4501$ & $2\\times 10^{-4}$ \\\\ \\hline\n$10$ & $0.1351$ & $0.1346$ & $4\\times 10^{-5}$ \\\\ \\hline\n$11$ & $0.0326$ & $0.0304$ & $7\\times 10^{-6}$ \\\\ \\hline\n$12$ & $0.0089$ & $0.0059$ & $10^{-6}$ \\\\ \\hline\n$13$ & $0.0021$ & $0.0011$ & $2\\times 10^{-7}$ \\\\ \\hline\n$14$ & $0.0005$ & $0.0002$ & $3\\times 10^{-8}$ \\\\ \\hline\n\\end{tabular}\n\\caption{Comparison of 2-D Scan Statistic probabilities for 100000 samples with N=800, S=T=40, a=b=2. Also shown are the\nsimple Poissonian probabilities assuming independent cells} \\label{tab:2dscan}\n\\end{center}\n\\end{table}\n\nThe predictions of equation~\\ref{eq:alm2d} have been compared with the results of $10^{5}$ Monte Carlo simulations in \ntable~\\ref{tab:2dscan} for $S=T=20$, $a=b=2$ and $N=800$.\nThe agreement is good, allowing for the errors inherent in the Monte Carlo results.\nFor interest, the final column shows the Poissonian probability obtained if the cells were treated as independent.\nIn this particular case, the result of assuming independence of the cells would be a fairly consistent overestimate of\nthe significance of the 'source' by about '$3\\sigma$'.\nThe precise amount of underestimate of the chance probability will depend on the number of elemental cells in the\nscanning window.\nFinally, the treatment of \\cite{kn:alm} has been extended to other shapes of scanning window, such as circular.\n\n\\subsubsection{Summary}\nIn summary, the 2-D Scan Statistic is a preferred general statistic for those cases where events are located \nrandomly on a plane, within fixed bounds, and where there is no \\emph{a priori} expectation such as a known source with \nknown instrumental spread function.\nIn most practical situations a good approximation is obtained by using equation~\\ref{eq:alm2d}.\n\n\n% MAIN SECTION BAYESIAN METHODS MAIN SECTION \n% MAIN SECTION BAYESIAN METHODS MAIN SECTION \n% MAIN SECTION BAYESIAN METHODS MAIN SECTION\n \n\\section{Bayesian Methods}\n\\label{sec:bayes}\n\n\\subsection{Introduction}\n\nFor many workers in cosmic rays, Bayesian methods are relatively novel and the following section attempts to \nsummarise the main ideas and methods.\nA much fuller development of the ideas discussed below is given by Loredo\\cite{kn:loredo90,kn:loredo92,kn:loredo94}.\n\n\\subsubsection{Statistics}\nThe term 'statistics' arises from the concept of a \\emph{statistic}. \nA statistic is a number derived from observed data and which obeys certain rules, some of which depend on a hypothesis\nabout the system under observation, some of which are extraneous. \nFrom this number, one can say how likely it is that the data was drawn from a population obeying rules specified by the \nparticular hypothesis, assuming that all extraneous quantities are allowed for.\nFrom that, by an inversion of logic, it is inferred how likely is the hypothesis.\nIn many cases, a particular statistic is used because the experimental results appear to be presented, or may be rearranged to\nbe presented, in a form which allows an easy calculation of that statistic.\nAn example is the epoch-folding of time-tagged photon times above, followed by \\chisq\\ calculated from the binned\nphases. \nAs was pointed out in that example, some arbitrary choices had to be made which rendered the results unsatisfactory.\nAlso, the aspects of the experimental data which were used to calculate a statistic may not be all that are available,\nor the most discriminating aspects.\nThis should, with careful design, be evident from a consideration of the statistic's 'power' but not necessarily.\nIt is the claim of Bayesians that such problems are inherent in 'classical' statistics and derive from a misunderstanding\nof the meaning of Probability.\n\n\\subsubsection{The Meaning of Probability}\n\nThere were at the beginnings of the subject, and still are, two schools of thought.\nThe first school maintains that the term \\emph{probability} is a statement of the frequency of occurrence of data, \nsuch as that taken in a very large number of repeats of an experiment, under the assumption that random factors \nare at work causing the possibility that the results could be different every time. \nTake, as an example, coin-tossing: the probability of heads is obviously 0.5 in a single toss. \nEveryone would agree that, assuming no trickery, an unbiased coin would land equally likely as 'heads' or 'tails'. \nBut there are forces at work which affect the way a coin would land - all amenable to analysis.\nIn fact a coin-tossing machine could be made which obtained 'heads' or 'tails' every time. \nWe regard coin-tossing as a random activity only because we expect humans to apply unconscious variability to the force and \ndirection of the flip which is much greater than that needed in the initial conditions to obtain one more extra turns before \nlanding.\nThis illustrates an important point: unless the hypothesis is clear and specifies all pertinent factors there could be an \napparent randomness. \nThat is not to say that true randomness does not exist, only that it is often used as an alibi for lack of knowledge or \nprecision in stating the experimental conditions.\n\nAn alternative definition of \\emph{probability} is 'a measure of belief in a certain hypothesis'.\nThis is, and was, a much easier idea to grasp but one which was felt from an early date not to be capable of exact or \nscientific analysis. \nOne consequence of this idea is that for a unique set of data, perhaps taken on a naturally-occurring phenomenon, \nthe idea of a very large set of repeated experiments to plot out the 'frequency distribution necessary to use a \n'statistic' was unrealistic.\nIt is this definition which underlies Bayesian thought, and indeed is the definition which more closely accords with\nthe questions for which measurements are made. \nInterestingly, this meaning of probability explains the frequency version as a special case using de Finetti's representation \ntheorem for exchangeable sequences of events\\cite{kn:goldstein}.\n\nThe main difference between the two philosophical approaches is how the data are related to the hypotheses.\n\\begin{enumerate}\n\\item The 'Frequentist' approach:\nWe obtain $P(D\\mid H)$, the conditional probability of obtaining the observed data, given a particular hypothesis. \nThe hypothesis is frequently a model $M$ which has a parameter space $\\theta$ and $P(D\\mid M,\\theta)$ is the \n'sampling distribution' for the data, given the model.\nA frequently met hypothesis is the 'null' hypothesis $H_{o}$ in which the parameters are set to zero.\nFor any hypothesis, a statistic is formed which is 'locally most powerful' or even better 'uniformly most powerful' \nand the probability of observing the data is assigned from a knowledge of the statistic's distribution function.\nThis is now used to give a range of values in which the value of a statistic may fall by chance, with given probability\n(i.e. frequency).\nAs an interesting aside, it is most usually the case for continuous measures, and frequently for discrete measures, for a\nrange of values of the statistic, including that observed (but also including many values \\emph{not} observed), to be\nused to derive the probability.\nThis is frequently performed by integrating $P(D\\mid M,\\theta)$ over the sample (data) space.\nThat is to say, the probability of a hypothesis is determined by the data taken, plus a whole range of values of\ndata which were \\emph{not} observed.\nThis curious situation is not often questioned by ordinary users of 'statistics'.\n\n\\item The 'Bayesian' approach:\n We obtain $P(H\\mid D)$, the probability of a hypothesis, given the data - apparently a more difficult matter.\n However Bayes Theorem gives: \n\\begin{eqnarray*}\n P(H\\mid D)P(D) & = & P(D\\mid H)P(H) \\mbox{leading to}\n\\\\ \n P(H\\mid D) & = & P(D\\mid H) P(H)/P(D)\n\\end{eqnarray*}\n $P(D\\mid H)$ is the likelihood function, \n $P(D)$ is the global likelihood, usually treated as an ignorable normalising constant,\n $P(H)$ is the 'prior' probability of the hypothesis. \nIn addition to the extra terms not used in frequentist analysis, a crucial difference between the approaches is that\nBayesian methods would integrate the likelihood function over the parameters space, rather than the sampling (data) space. \nBayesian methods have been criticised for the inclusion of an apparently subjective quantity $P(H)$ but a trivial\nexample demonstrates that frequentist analyses are not free from this. \nFrequentists would determine if the hypothesis $H_{o}$ of a histogram having all the cells identical were true by taking \n\\chisq\\ as a statistic. \nThey would use no prior information or knowledge. \nBut we know that histogram cells cannot contain negative numbers, and so some relevant background information is ignored \nwhen using \\chisq. \n\\end{enumerate}\n\n\\subsubsection{An Example}\n\n An example of the different approaches is an experiment in which a coin is tossed $N$ times. \nIt lands heads $H$ times. The question is: is it biased?\nIn the Frequentist approach a hypothesis (the 'null' hypothesis) is formed that the coin is unbiased and that the result is \na function of randomness only. \nA sufficiently low probability which is obtained for a suitable statistic would be evidence that the 'null hypothesis' \nshould be abandoned.\nThe binomial distribution describes the result of such discrete, bounded experiments.\nThe probability of $H$ heads in $N$ tosses is $0.5^{H} \\times 0.5^{N-H} \\times C_{H}^{N}$. \nOne then calculates the probability of obtaining $0,1,2,\\ldots H-1$ heads and add them to the probability of $H$ heads and \nsay: 'if the null hypothesis is true, getting $H$ \\emph{or fewer} heads in $N$ tosses can occur due to chance, \nwith a given probability. \nThis could be interpreted as some evidence against the 'null hypothesis', hence evidence that the coin is biased.\n\n\\subsubsection{Stopping Rules}\n\nSetting aside for the moment the fact that we did not see $0,1,2,\\ldots H-1$ heads, the last conclusion supposes that the\ncoin was tossed, irrespective of the result, $N$ times and that the number of heads $H$ was the random variable. \nBut suppose the coin was actually tossed by a person until $H$ heads were obtained, and that happened to occur after $N$ \ntosses. \nIn this case the number of tosses $N$ is the random variable and the number of heads $H$ is fixed. \nThe probability is then derived by combining the individual probabilities of obtaining $H$ heads from $h \\geq H$ tosses,\nand may be significantly different from the first probability calculated.\n\nLoredo\\cite{kn:loredo92} gives a more apposite example: a theorist predicts that $f=10\\%$ of the stars in a cluster should\nbe of type \\textbf{A}.\nAn observer reports 5 stars of type \\textbf{A} out of 96 observed.\nThe theorist calculates as follows: $N=96$ and $f=0.1$ gives $9.6$ predicted type \\textbf{A} stars.\nThe probability of the value of $\\chi^{2}=2.45$ of this information is $P=0.073$, which is acceptable at the $95\\%$ level.\nThe observer however decided in advance to stop when he had found 5 stars of type \\textbf{A}.\nThe expected value of $N$ is then $5/0.1=50$ with variance $5(1-f)/f^{2}=450$.\nThe probability of the value of $\\chi^{2}=4.7$ of this information is $P=0.032$, which is \\emph{not} acceptable at the \n$95\\%$ level.\nThis ambiguity arises because of the stopping rule used by the experimenter that is - what data sets \\emph{might}\nhave been observed.\n\nThe stopping rule can therefore be important in classical statistical analysis, and ignorance of the actual rule used\nmay lead to an erroneous or at least ambiguous conclusion. \nKnowledge of the exact stopping rule is less important in Bayesian analysis, but is valuable in particular when it \ncontains useful information about the unknown quantities.\nIn other cases, the stopping rule could be important if the existence of some data is unknown to the analyser, perhaps \nbecause its analysis did not show it to be significant and it was suppressed by the experimenter.\nThe message from this example is that for Frequentist analysis to be possible, an experiment must be precisely defined \nand if the execution is different in any way from the plan, the data could be worthless.\n\n\\subsubsection{Conclusion}\nIn summary, frequentist methods establish $P(D\\mid \\theta M)$ as the sampling distribution of the data, given a model\n$M$ with parameters $\\theta$ and perform integration over the data space.\nBayesian methods start with the same function $P(D\\mid \\theta M)$ but treat it is a likelihood with integrations\nperformed over the parameter space of the model.\nIn particular, parameters which are necessary for the specification of the model but are not of interest (for example\nthe phase when looking for a periodic signal) are integrated out, or marginalised.\n\nIn Bayesian theory, the notion of a 'random variable' is absent so ambiguity does not arise for many types of \nstopping rule and there is no need for a 'reference set' of hypothetical data.\nThis state of affairs results from the need in Bayesian methods to be specific about all the hypotheses, or to \nintegrate away any unspecifiable variable.\nTaking again the example of a histogram, and the question of whether its cells are consistent with uniformity using\n\\chisq\\.\nIf the null hypothesis is the only hypothesis available, the use of \\chisq\\ is as a 'goodness-of-fit' test for the \nsupposition of flatness. \nThe number observed in the $i^{th}$ bin of $n$ bins is $x_{i}$. \nThe number expected in each bin, under the null hypothesis, is $avg=\\sum_{i=1}^{n}x_{i}/n$ and $\\chi^{2}=\n\\sum_{i=1}^{n}(x_{i}-avg)^{2}/avg$, assuming $avg$ is large enough (usually 10 or so) for asymptotic normality.\nThe probability of \\chisq\\ for $n-1$ degrees of freedom is interpreted as supporting or otherwise the null hypothesis. \nThis statistic suffers from a major problem in that it ignores information - the order of the bins may be significant, \nand so it implicitly assumes a class of alternative models in which the order is unimportant.\nThis can be partially rectified by applying an independent test which is only determined by the order of the bins - \nthe Run Test. \nThis is only applying a patch, since the Run test is most powerful against monotonicity and not other patterns. \nFrequentists acknowledge this problem in general by using the idea of the power of a statistic, that is its ability \nto identify correctly a true model from a particular alternative.\nBoth approaches have subjective factors: Bayesian in assigning prior probabilities to hypotheses, Frequentist in the \nnotion of randomness and its applicability in a mathematical sense to cover for a lack of knowledge of the exact \nexperimental conditions.\nA consequence of this is that different experts in both fields may come to different conclusions given the same data.\nAnother way of putting this is that the result of analysing data will be a conclusion within a range, depending on\n(a) the Bayesian priors, or (b) the estimate of the degrees of freedom and unknown factors.\n\n\n% Sub Section BAYESIAN ON/OFF\n\n\\subsection{Bayesian On/Off Analysis}\n\nThe Bayesian ideas in the above section have recently been applied to the ON/OFF problem treated earlier.\nAs in all Bayesian analyses, some judgement must be made of the priors to be used, but in the cases discussed here \nthe results do not depend critically on how these priors are chosen.\n\nAn initial Bayesian analysis of the problem of detecting a source in an ON/OFF counting experiment has been given by \nLoredo\\cite{kn:loredo90}.\nUsing the same notation as in the ON/OFF section above, the probability of the background rate $b$ (the posterior density) \nfrom the OFF-source data is:\n\\[p\\left(b\\mid N_{OFF}\\right) = p\\left(N_{OFF}\\mid b\\right)\\frac{p\\left(b\\right)}{p\\left(N_{OFF}\\right)}\\]\nThe Poisson likelihood for $N_{OFF}$ is:\n\\[p(N_{OFF}\\mid b)=\\frac{(bT)^{N_{OFF}}e^{-bT}}{N_{OFF}!}\\] \nThe parameter $b$ is unknown and so the 'prior' probability would appear to be a matter of guesswork.\nIf the range of $b$ were pre-specified in some non-arbitrary way, at least the scale of $b$ would be known, and a flat\nprior would be reasonable.\nIf even the scale of $b$ is unknown, the 'least informative' prior for $b$ is $p(b)=1/b$, which is uniform in $\\log b$, \nand then\n\\[p(N_{OFF})=\\frac{T^{N_{OFF}}}{N_{OFF}!}\\int_{0}^{\\infty}b^{N_{OFF}-1}e^{-bT} db\\]\nThis leads to\n\\[p\\left(b\\mid N_{OFF}\\right) = \\frac{T_{OFF}\\left(bT_{OFF}\\right)^{N_{OFF}-1}e^{bT_{OFF}}}{\\left(N_{OFF}-1\\right)!}\\]\nNote that the expectation of the background $\\hat{b}=N_{OFF}/T$ and that the assumption of $p(b)=1/b$ does not strongly \naffect the result, Loredo pointing out that a prior uniform in $b$ only marginally alters the expectation \n$\\hat{b}=(N_{OFF}+1)/T$.\nThe joint probability of the background rate $b$ and a source rate $s$, given $N_{ON}$ and $N_{OFF}$, is:\n\\[p\\left(sb\\mid N_{ON}\\right)=p\\left(s\\mid b\\right)p\\left(b\\right)\\frac{p\\left(N_{ON}\\mid sb\\right)}{p\\left(N_{ON}\\right)}\\]\nThe probability of the source rate $s$ is obtained by marginalising $b$, that is $p\\left(s\\mid N_{ON}\\right)=\\int p\n\\left(sb\\mid N_{ON}\\right) db$:\n\\begin{equation}\np\\left(s\\mid N_{ON}\\right)=\\sum_{i=1}^{N_{ON}}C_{i}\\frac{ T_{ON}\\left(sT_{ON}\\right)^{i-1}e^{-sT_{ON}} }{ \\left(i-1\\right)\n! }\n\\label{eq:bayesonoff}\n\\end{equation}\nwhere\n\\[C_{i}=\\frac{ \\left(1+\\frac{1}{\\alpha}\\right)^{i}\\frac{\\left(N_{ON}+N_{OFF}-i-1\\right)!}{\\left(N_{ON}-i\\right)!}}{ \n\\sum_{j=1}^{N_{ON}}\\left(1+\\frac{1}{\\alpha}\\right)^{j}\\frac{\\left(N_{ON}+N_{OFF}-j-1\\right)!}{\\left(N_{ON}-j\\right)!}}\\]\nThis result is formally correct for all positive values of $N_{ON}$ and $N_{OFF}$ and is particularly useful for small\nvalues when the asymptotic treatments fail.\n\nIts main value is to illustrate the completely different approach and result of the application of Bayesian ideas.\nHowever, there are some computational problems for values of $N_{ON}$ and $N_{OFF}$ which exceed $\\sim 100$.\nFor values of $N_{ON}$ and $N_{OFF}$ which are less than $\\sim 100$ evaluation of equation~\\ref{eq:lambda} and equation\n~\\ref{eq:bayesonoff} shows small differences in the derived probabilities.\n\n% Sub Section BAYESIAN BURSTS\n% Sub Section BAYESIAN BURSTS\n\\subsection{Bayesian Change Point Analysis - Bursts}\n\nA recent paper by Scargle\\cite{kn:scargle98} has used Bayesian methods to analyse structure in photon counting data. \nIt is worth noting that the ON/OFF problem dealt with above is a special case of change point analysis, where there is \nonly one change point and its location is known in advance.\nThe principles are the same as those outlined above, with the added simplicity of having simpler alternatives to the uniform \nmodel. \nThe uniform counting rate model $M_{1}$ assumes a constant intensity over a particular time interval $T$. \nAn alternative model $M_{2}$ has the interval $T$ broken into two regions $T_{1}$ and $T_{2}$, $T=T_{1}+T_{2}$, each with \na different counting rate. \nIn general, a model $M_{k}$ may be constructed with $k$ regions. \nBayes Theorem give the probability of a model\n\\[p\\left(M_{k}\\mid D,I\\right)=\\frac{p\\left(D\\mid M_{k},I\\right)p\\left(M_{k}\\mid I\\right)}{p\\left(D\\mid I\\right)}\\]\nDropping the explicit appearance of the background information $I$, the odds ratio $O_{kj}$ between two competing models \n$M_{k}$ and $M_{j}$ is then\n\\[\\frac{p(M_{k}\\mid D)}{p(M_{j}\\mid D)}=\\frac{p(D\\mid M_{k})p(M_{k})}{p(D\\mid M_{j})p(M_{j})}\\]\nThe parameter $\\theta$ or vector of parameters $\\vec{\\theta}$ of the model $M_{k}$ enter when $p(D\\mid M_{k})$ is \ncalculated\n\\[p(D\\mid M_{k}) = \\int p(D\\mid \\vec{\\theta},M_{k})p(\\vec{\\theta}\\mid M_{k})d\\vec{\\theta}\\]\nThe odds ratio $O_{kj}$ is then\n\\begin{eqnarray}\n O_{kj} & = & \\frac{p(M_{k}\\mid D)}{p(M_{j}\\mid D)} \\nonumber\n\\\\ & = & \\frac{p(M_{k})}{p(M{j})}\\frac{\\int p(D\\mid \\vec{\\theta},M_{k})p(\\vec{\\theta}\\mid M_{k})d\\vec{\\theta} }\n{\\int p(D\\mid \\vec{\\theta},M_{j})p(\\vec{\\theta}\\mid M_{j})d\\vec{\\theta}} \\nonumber\n\\\\ & = & \\frac{p(M_{k})}{p(M{j})} \\frac{\\mbox{$\\mathcal{L}$}(M_{k},D)}{\\mbox{$\\mathcal{L}$}(M_{j},D)}\n\\end{eqnarray} \nwhere $\\mbox{$\\mathcal{L}$}(M_{k},D)$ is the global likelihood of model $M_{k}$.\n\nFor the constant-rate model $M_{1}$, $N$ events arrive in a time $T$ which is treated as being divided into $M$ intervals \nof duration $\\delta t$, the justification being that photon counting apparatus always has a resolving time. \nNote that the number of events in any particular interval $\\delta t$ can be $0$ or $1$ only.\nThe author shows that the global likelihood for this constant-rate model of Time Tagged Events (TTE) is\n\\[\\mbox{$\\mathcal{L}$}(M_{1}\\mid TTE)=\\frac{\\Gamma(N+1)\\Gamma(M-N+1)}{\\Gamma(M+2)}\\]\nIf the data is time-binned into $M$ equal bins, but such that any number of events may occur in any bin, given an overall \nrate $\\lambda = N/T$ and mean number per bin of $\\mu=\\lambda T/M$, the global likelihood is:\n\\[\\mbox{$\\mathcal{L}$}(M_{1}\\mid Binned)=\\frac{\\Gamma(N+1)}{(M+1)^{N+1}}\\]\nNote that the bins are fixed and may not be scanned to maximise $\\mathcal{L}$.\n\nThe alternative model $M_{k}$ has a likelihood which is the product of the likelihoods of the individual constant-rate \nregions of $T$. \nFor a two-rate model with the time of the change of rate being $t_{cp}$\n\\begin{eqnarray*}\n\\mbox{$\\mathcal{L}$}(M_{2}\\!\\!\\mid\\!\\!D) & = &\\int\\!\\!dt_{cp}\\int\\!\\!d\\Lambda_{1}\\int\\!\\!d\\Lambda_{2} p_{cp}(t_{cp}) \n\\times p[D_{1}\\!\\!\\mid\\!M_{1}(\\Lambda_{1},\\!T_{1})]p(\\Lambda_{1}) \n\\\\\n& & \\times p[D_{2}\\!\\!\\mid\\!M_{2}(\\Lambda_{2},\\!T_{2})]p(\\Lambda_{2})\n\\end{eqnarray*}\nwhere $\\Lambda=\\lambda \\delta t$, $P(\\Lambda)$ is the prior for the rate $\\Lambda$ and $P_{cp}$ is the prior for the \nchange-point time $t_{cp}$.\nFor time-tagged data with resolution $\\delta t$ the integrals are sums and the change-point location is $m_{cp}\\delta t$.\nSince the change-point can be tested only at the arrival time of a photon, the photon number of the change-point $n_{cp}$ \nis used as an index. The number of events in the first section, up to the change-point, is $N_{1}=n_{cp}$, $N_{2}=N-N_{1}$ \nand $M_{1}=m_{n_{cp}}$\nThe global likelihood is then\n\\begin{eqnarray*}\n\\mbox{$\\mathcal{L}$}(M_{2}\\mid D) & = &\\sum_{n_{cp}}\\frac{\\Gamma(n_{cp}\\!\\!+1)\\Gamma(m_{n_{cp}}\\!\\!-n_{cp}\\!+1)}{\n\\Gamma(n_{cp}\\!\\!+2)} \\nonumber\n\\\\\n & & \\times \\frac{\\Gamma(N\\!-n_{cp}\\!\\!+\\!1)\\Gamma(m_{N-n_{cp}}\\!-(N\\!-n_{cp})+1)}{\\Gamma(N\\!-n_{cp}\\!+2)}\\Delta t_{n_{cp}}\n\\end{eqnarray*}\n\nThe paper\\cite{kn:scargle98} gives a coding in a popular mathematical package to implement the above ideas.\n\n% Sub Section BAYESIAN PERIODICITY\n% Sub Section BAYESIAN PERIODICITY\n\n\\subsection{Bayesian Periodicity Analysis}\n\n\\subsubsection{Introduction}\n\nFrequentist statistical theory allows more than one test to be applied to any situation.\nAny statistic, or function of the data, may be defined and the 'best' is selected depending on its 'power' or likelihood \nof selecting the 'correct' hypothesis. \nOne of the problems of the frequentist approach to looking for evidence of periodicity is that, in the absence of a \nspecific light curve, the alternative hypothesis (to one of uniformity in the phase distribution) is unknown and the \npower of a statistical test is difficult to specify except for a narrow class of alternative light curves. \nThe Rayleigh statistic, $Z_{1}^{2}$, is powerful only for the fundamental period and is formally the most powerful test \nfor alternatives to uniformity from the Von Mises distribution - the circular equivalent of the Gaussian on the line.\nThe $Z_{n}^{2}$ test allows the addition of $n-1$ harmonics but needs a protocol to decide when to stop adding harmonics \nand therefore degrees of freedom (the $H$ test mentioned above suggests such a protocol).\nFinally, Protheroe's test is powerful for very narrow light curves. \nEach could be tried in succession to look for evidence of periodicity, but a method which is indifferent to the shape \nof the light curve, without any penalty, would be of great advantage.\n\n\\subsubsection{Gregory \\& Loredo Method}\n\nSuch a method based on Bayesian analysis, is claimed by Gregory and Loredo\\cite{kn:gregory}. \nThe essence of the method is to compare a uniform model for the distribution in phase at a trial frequency with a \nperiodic model. \nThe great difference between this and other methods is how the periodic model is proposed and how the necessary \nuncertainties and their associated 'degrees of freedom' of classical theory are accounted for. \nIn particular, since an arbitrary postulated light curve may be of any shape, the method automatically applies Ockham's \nrazor, in that models with fewer variables are automatically favoured unless the evidence from the data more than \ncompensates. \nMore complicated light curves (not necessarily with small number of harmonics, a $\\delta$-function is uncomplicated in \nthis context) are penalized for their greater complexity.\n\nBayes Theorem is used to compare the probabilities of two parameterised models of the phase distribution. \nIn the notations of the authors, the probability that a model $M$ describes the data, given the data $D$ and any \nbackground information $I$ is \n\\begin{equation}\np\\left(M\\mid D,I\\right) = p\\left(M\\mid I\\right) \\frac{p\\left(D\\mid M,I\\right)}\n{p\\left( D\\mid I\\right)}\n\\end{equation}\nThe first term on the right, $p\\left(M\\mid I\\right)$, is the prior probability of the model $M$, which may seem to be \nsubjective but may be estimated in some cases from the permissible range of the parameters. \nThe numerator in the second term, $p\\left(D\\mid M,I\\right)$, is the sampling probability of the data $D$, or the \nlikelihood of the model $M$. The denominator, $p\\left( D\\mid I\\right)$, is the global likelihood of the entire class of \nmodels. \nIf the model contains a parameter $\\theta$, or in the case two or more parameters a vector $\\vec{\\theta}$, the \nlikelihood of the model can be calculated:\n\\[p\\left (D\\mid M\\right)=\\int_{\\vec{\\theta}}p\\left( D\\mid \\vec{\\theta},M\\right)p\\left(\\vec{\\theta} \\mid M\\right)\\]\n\nFor time-tagged photon data with $N$ events detected over a time $T$, the probability of $D$ for a particular rate model \n$r(t)$ can be calculated. \nFor the time $T$ divided into very small intervals of length $\\Delta t$, the probability of $n$ events in $\\Delta t$ is:\n\\[p_{n}=\\frac{\\left[r(t)\\Delta t\\right]^{n}e^{-r(t)\\Delta t}}{n!}\\]\nIf $\\Delta t$ is small enough for $p_{i}=0, i\\geq 2$ then the sequence of $T/\\Delta t$ time samples will contain $N$ \ncontaining one event and $Q=T/\\Delta t - N$ containing no event. \nThe likelihood is then:\n\\[p\\left(D\\mid r,I\\right)=\\prod_{i=1}^{N}p_{1}(t_{i})\\prod_{k=1}^{Q}p_{0}(t_{k})\\]\nUsing $p_{0}(t)=e^{-r(t)\\Delta t}$ and $p_{1}(t)=r(t)\\Delta te^{-r(t)\\Delta t}$ the likelihood function is\n\\[p\\left(D\\mid r,I\\right) = \\Delta t^{N}\\left[\\prod_{i=1}^{N}r(t_{i})\\right]\\exp\\left[-\\sum_{k=1}^{N+Q}r(t_{k})\\Delta \nt\\right]\\]\n\nIn the case of a periodic model, the non-uniformity in phase is characterised by the varying contents of the phase bins. \nAlthough the number of phase bins needed to detect any light curve and the origin of phase are unknowns, these will be \nmarginalised or integrated out. \nIf there are $m$ phase bins the average rate $A=\\frac{1}{m}\\sum_{j=1}^{m}r_{j}$ and the fraction of the total rate per \nperiod in phase bin $j$ is $f_{j}=\\frac{r_{j}}{mA}$.\nThe likelihood function is shown to reduce to\n\\[P\\left(D\\mid \\omega,\\phi,A,{\\bf f},M_{m}\\right)=\\Delta t^{N}(mA)^{N}e^{-AT}\\left(\\prod_{j=1}^{m}f_{j}^{n_{j}}\\right)\\]\nwhere $\\omega$ is the postulated angular frequency, $\\phi$ the starting phase, ${\\bf f}$ the set of $m$ values of $f_{j}$ \nand $n_{j}$ being the number of events occurring in bin $j$.\n\nThe joint prior density for the parameters $\\omega,\\phi,A,{\\bf f}$ is\n\\[p\\left(\\omega,\\phi,A,{bf f}\\mid M_{m}\\right)=p\\left(\\omega\\mid M_{m}\\right)p\\left(\\phi\\mid M_{m}\\right)p\\left(A\\mid \nM_{m}\\right)p\\left({\\bf f}\\mid M_{m}\\right)\\]\nThe prior densities are:\n\\begin{enumerate}\n\\item $p(\\phi \\mid M_{m})=1/2\\pi$, this assumes that any starting phase is equally likely,\n\\item $p(A\\mid M_{m})=1/A_{max}$, this assumes that $A$ does not change during the observation and any value of $A$ \nfrom $A=0$ to $A=A_{max}$ is possible,\n\\item $p(\\omega \\mid M_{m})=\\/\\omega \\ln(\\omega_{hi}/\\omega_{lo})$, where $\\left[\\omega_{hi},\\omega_{lo}\\right]$ is \na prior range for $\\omega$,\n\\item $p({\\bf f})=(m-1)!\\delta\\left(1-\\sum_{j=1}^{m}f_{j}\\right)$.\n\\end{enumerate}\n\nThe assignment of the priors of the models themselves is all that is needed before comparing the likelihoods of the models. \nThe two models are equally likely \\emph{a priori} and so the prior likelihood of the non-periodic model \n($M_{1}$), $p(M_{1})=1/2$ and that for the periodic model ($M_{m}$, $m=2,m_{max}$), $p(M_{m}\\mid I)=1/2\\nu$ \nwhere $\\nu = m_{max}-1$.\n\nThe final result for the odds $O$ against a uniform model of phase and in favour of a periodic model with phase and \nperiod unknown (a common case) is:\n\\begin{equation}\nO=\\frac{1}{2\\pi\\nu\\ln\\left(\\omega_{hi}/\\omega_{lo}\\right)}\\frac{N!(m-1)!}{(N+m-1)!}\\int_{\\omega_{lo}}^{\\omega_{hi}}\n\\frac{d\\omega}{\\omega}\\int_{0}^{2\\pi}d\\phi\\frac{m^{N}}{W_{m}\\left(\\omega,\\phi\\right)} \\label{eq:odds}\n\\end{equation}\nwhere $W_{m}\\left(\\omega,\\phi\\right)$ is the number of ways that the set of $n_{j}$ observed counts can be made by \ndistributing $N$ counts in $m$ bins:\n\\[W_{m}\\left(\\omega,\\phi\\right)=\\frac{N!}{\\prod_{j=1}^{m}n_{j}!}\\]\nand $n_{j}$, the number of events placed in the $j^{th}$ phase bin depends on $\\omega$, $\\phi$ and $m$.\n\nIf the period is known, this reduces to:\n\\begin{equation}\nO(\\omega)=\\frac{1}{2\\pi\\nu}\\frac{N!(m-1)!}{(N+m-1)!}\\int_{0}^{2\\pi}d\\phi \\frac{m^{N}}{W_{m}\\left(\\omega,\\phi\\right)}\n\\label{eq:odds2}\n\\end{equation}\n\nIn order to illustrate the difference between the information available from this treatment and from the Rayleigh\ntest, a data set has been generated containing time-tagged random events with a constant mean rate, plus a periodic\ncomponent.\nThe results are shown in figure~\\ref{fig:bcomp}.\nA particular point to note is that although the Rayleigh power is always positive, even for pure noise, in the case\nof LOG(Bayesian odds), peaks do not become 'interesting' until they become positive. \nThis is because the 'degrees of freedom' have been accounted for automatically and cause the offset seen in \nfigure~\\ref{fig:bcomp} so that peaks falling below $\\log(Odds)=0$ are just those expected from noise.\nIt can be seen much more clearly in the Bayesian Odds diagram that there is only one significant peak, at the period\nsimulated. \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}[ht]\n\\psfig{file=GLcomp3.eps,angle=90,height=6cm}\n\\label{fig:bcomp}\n\\footnotesize\n\\caption{A comparison of Rayleigh Power and Bayesian Odds using random simulated data with a periodic signal at $P=8.2s$}\n\\end{figure}\n\\normalsize \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nThe method has been used to detect a weak pulsar signal from SNR 0540-693 in ROSAT data, which could not be detected \nusing a standard FFT technique\\cite{kn:gregory96}. \nMoreover, the precision of determining the frequency was much higher for the Bayesian method than for $\\chi^{2}$ \nusing epoch-folding. \nThe frequency precision of the latter is determined mainly by the duration of the data and is not strongly influenced \nby the number of photons.\nGregory and Loredo show\\cite{kn:gregory96} that the Bayesian method obtains greater precision in parameter estimation \nwith more photons.\nThe method has also been used to detect 1600 day modulation in the long-term radio emission of an X-ray binary, \nwith very non-uniformly sampled data and a Gaussian noise of unknown magnitude \\cite{kn:gregory99a,kn:gregory99b}.\nThere has been a recent independent use of a Bayesian method to calculate the upper limit to a pulsed flux at a\nknown period, independent of pulse width and pulse phase\\cite{kn:VLAbayes}.\n\n\\section{Conclusions}\n\nThe hope of this review is that the more commonly met data analysis problems may be approached by the cosmic ray\nworker with a more consistent and up to date approach.\nThere have been a number of advances in recent years in the tools, and more importantly in the methods, available to \ncosmic ray experimenters to ensure that the maximum use is made of hard-won data. \nThe traditional statistical methods have resulted in a measure of agreement on the 'correct' way to look for sources\nfrom ON/OFF data, change points (bursts) in 1- and 2-dimensions and in periodicity.\nThe application of these methods requires care to ensure that the 'degrees of freedom' are kept under control and \nproperly accounted for: many of the criticisms of claimed sources have been based on the latter.\n\nNew Bayesian methods of testing hypotheses have recently been proposed.\nA central theme of these methods is that classical methods often cloak ignorance in a way which distorts the results.\nThere are claimed to be significant benefits to the use of Bayesian methods which derive from the requirement to be \nabsolutely specific about the hypotheses and the methodology of marginalising nuisance parameters.\nIn contrast to classical statistical methods, where various \\emph{statistics} may be generated from the same data, each\nwith different assumptions, \\emph{degrees of freedom} and {power}, Bayesian methods provide a framework for describing\ncompletely the data and allow the direct comparison of specified hypotheses.\nA practical result of the philosophical differences between the approaches is that, rather than relying on a relatively \neasy-to-use, pre-packaged test statistic, with the accompanying dangers of hidden degrees of freedom, a Bayesian\nmethod requires the data interpreter to model the hypotheses precisely.\nThe obvious disadvantages of this are claimed to be more than compensated by the directness of the link between the\nhypotheses and the data.\nBayesian methods may require some time to become accepted in the field, in that the methodologies and ideas have not\ntraditionally been part of the training of physicists; indeed may not have been as useful if physicists' training\nin classical methods had been better. \n\n\n\n\\section{Acknowledgements}\n\nThe author would like to acknowledge useful discussions with P.S.Craig and M.Goldstein.\n\n\\section{References}\n\n\\begin{thebibliography}{99}\n\\bibitem{kn:eadie} Eadie W T et al. 1971 \\emph{Statistical Methods in Experimental Physics} North-Holland.\n\\bibitem{kn:hearn}Hearn D 1969 \\emph{Nuclear Inst. Meth.} \\textbf{70} 200.\n\\bibitem{kn:omongain}O'Mongain E 1973 \\emph{Nature} \\textbf{241} 376.\n\\bibitem{kn:gibsona}Gibson I A et al. 1982 \\emph{Proc. Int. Workshop on VHE $\\gamma$-ray Astronomy, Ootacamund, India} \nTata Institute/Harvard Smithsonian Institution. 97.\n\\bibitem{kn:lima}Li T-P and Ma Y-Q 1983 \\emph{Astrophys.J.} \\textbf{272} 317.\n\\bibitem{kn:dowthwaite}Dowthwaite J C et al. 1983 \\emph{Astron.Astrophys.} \\textbf{126} 1.\n\\bibitem{kn:numreps} Press WH et al., \\emph{Numerical Recipes} Cambridge University Press.\n\\bibitem{kn:scargle98}Scargle J D 1998 \\emph{Astrophys.J.} \\textbf{504} 405.\n\\bibitem{kn:cox}Cox DR and Isham V 1980 \\emph{Point Processes} Chapman and Hall, London.\n\\bibitem{kn:mclaughlin} McLaughlin M A et al. 1998 \\emph{Astrophys.J.} \\textbf{473} 703.\n\\bibitem{kn:katayose}Katayose Y et al. 1997 \\emph{Proc.25th Int. Cosmic Ray Conf. Durban}\n\\bibitem{kn:parzen}Parzen E 1960 \\emph{Modern Probability Theory and its Applications} New York:Wiley.\n\\bibitem{kn:barton}Barton D E and David F N 1956 \\emph{J. Roy. Stat. Soc. Series A} \\textbf{18} 79.\n\\bibitem{kn:huntington}Huntington R J and Naus J I 1975 \\emph{Ann. Probability} \\textbf{3} 895.\n\\bibitem{kn:neff}Neff N D and Naus J I 1980 \\emph{Selected tables in Mathematical Statistics} \\textbf{VI} AMS Providence \nRI.\n\\bibitem{kn:naus66}Naus J I 1966 \\emph{J. Amer. Stat. Assn.} \\textbf{61} 1191.\n\\bibitem{kn:glaz93}Glaz J 1993 \\emph{Statistics in Medicine} \\textbf{12} 1845.\n\\bibitem{kn:wallenstein73}Wallenstein S and Naus J I 1973 \\emph{Ann.Probability} \\textbf{1} 188.\n\\bibitem{kn:wallenstein94}Wallenstein S Naus J and Glaz J 1994 \\emph{Biometrika} \\textbf{81} 595.\n\\bibitem{kn:chen97}Chen J and Glaz J 1997 \\emph{Chap. 16 in: Advances in the Theory and Practice of Statistics, ed. \nJohnson N L and Balakrishnan N} New York:Wiley.\n\\bibitem{kn:mansson}M\\aa nsson M 1999 \\emph{Ann.Appl.Probability} \\textbf{9} 465.\n\\bibitem{kn:newell}Newell GF 1963 \\emph{Time Series Analysis, Proc. Conf. at Brown Univ.} ed M.Rosenblatt, Academic Press.\n\\bibitem{kn:ikeda}Ikeda S 1965 \\emph{Ann.Inst.Stat.Math.} \\textbf{17} 295.\n\\bibitem{kn:conover} Conover W J Bement T R and Iman R L 1979 \\emph{Technometrics} \\textbf{21} 277.\n\\bibitem{kn:naus82}Naus J I 1982 \\emph{J.Amer.Stat.Ass.} \\textbf{77} 177.\n\\bibitem{kn:glaz91}Glaz J and Naus J I 1991 \\emph{Ann.Appl.Probability} \\textbf{1} 306.\n\\bibitem{kn:karwe}Karwe V V and Naus J I 1997 \\emph{Computational Statistics and Data Analysis} \\textbf{23} 389.\n\\bibitem{kn:glaz92}Glaz J 1992 \\emph{Computational Statistics and Data Analysis} \\textbf{14} 213.\n\\bibitem{kn:nargarwalla}Nargarwalla N 1996 \\emph{Statistics in Medicine} \\textbf{15} 845.\n\\bibitem{kn:alm}Alm S E 1997 \\emph{Adv.Appl.Prob.} \\textbf{29} 1.\n\\bibitem{kn:giles}Giles A B 1996 \\emph{Astrophys.J.} \\textbf{474} 464.\n\\bibitem{kn:vanstekelenborg}Vanstekelenborg J T P M and Petrakis J P 1993 \\emph{Nucl.Inst.Meth.} \\textbf{328} 559.\n\\bibitem{kn:rothschild}Rothschild R E et al. 1974 \\emph{Astrophys.J.} \\textbf{189} L13.\n\\bibitem{kn:bell}Bell D A 1968 \\emph{Information Theory} London:Pitman.\n\\bibitem{kn:lathi}Lathi B P 1968 \\emph{Random Signals and Communication Theory}, \n Scranton, Pennsylvania: International Textbook Company.\n\\bibitem{kn:lewis93}Lewis D A 1993 \\emph{Statistical Methods for Physical Sciences} chap. 12, London:Academic Press.\n\\bibitem{kn:scargle82} Scargle J D 1982 \\emph{Astrophys.J.} \\textbf{263} 835.\n\\bibitem{kn:koen}Koen C 1995 \\emph{Astrophys.Space Sci.} \\textbf{230} 307.\n\\bibitem{kn:gibsonb}Gibson I A et al. 1982 \\emph{Nature} \\textbf{296} 833.\n\\bibitem{kn:mardia}Mardia K V 1972 \\emph{Statistics of Directional Data} London:Academic Press.\n\\bibitem{kn:fisher}Fisher N I 1993 \\emph{Statistical Analysis of Circular Data} Cambridge University Press.\n\\bibitem{kn:priestley}Priestley M B 1981 \\emph{Spectral Analysis and Time Series} - Volume 1 \\emph{Univariate Series} \nLondon:Academic Press.\n\\bibitem{kn:bloomfield}Bloomfield P 1976 \\emph{Fourier Analysis of Time Series} New York:Wiley.\n\\bibitem{kn:dejager89}DeJager O C, Swanepoel J W H and Raubenheimer B C 1989 \\emph{Astron.Astrophys.} \\textbf{221} 180.\n\\bibitem{kn:orford91}Orford K J 1991 \\emph{Exper.Astron.} \\textbf{1} 305.\n\\bibitem{kn:lyne} Lyne AG and Graham-Smith F 1998 \\emph{Pulsar Astronomy} Cambridge University Press.\n\\bibitem{kn:buccheri}Buccheri R et al. 1983 \\emph{Astron.Astrophys.} \\textbf{128} 245.\n\\bibitem{kn:protheroe3}Protheroe R J 1987 \\emph{Proc.Astron.Soc.Australia} \\textbf{7} 167.\n\\bibitem{kn:dejager94} deJager O C 1994 \\emph{Astrophys.J.} \\textbf{436} 239.\n\\bibitem{kn:alberto}Carrami\\~{n}ana A et al. 1989 {\\em Astrophys.J.(Letters)} \\textbf{346} 967.\n\\bibitem{kn:raub1}Raubenheimer B C and \\\"{O}gelman H 1990 {\\em Astron.Astrophys.} \\textbf{230} 73.\n\\bibitem{kn:kay}Kay S M 1988 \\emph{Modern Spectral Estimation - Theory and Applications} New Jersey:Prentice-Hall.\n\\bibitem{kn:jenkins}Jenkins G M and Watts D G 1968 {\\em Spectral Analysis and its Applications}, San Fransisco:Holden-Day.\n\\bibitem{kn:raub2}Raubenheimer B C et al. 1994 {\\em Astrophys.J.} \\textbf{428} 77.\n\\bibitem{kn:orford96}Orford K J 1996 \\emph{Astropart.Phys.} \\textbf{4} 235.\n\\bibitem{kn:leahy}Leahy D A, Elsner R F and Weisskopf W C 1983 \\emph{Astrophys.J.} \\textbf{272} 256.\n\\bibitem{kn:bai}Bai T 1992 \\emph{Astrophys.J.} \\textbf{397} 584.\n\\bibitem{kn:loredo92} Loredo T J 1992 \\emph{Statistics Challenges in Modern Astronomy} eds. \nFeigelson E D and Babu G J, Springer verlag, New York, 275.\n\\newline http://astrosun.tn.cornell.edu/staff/loredo/bayes/promise.ps.gz\n\\bibitem{kn:protheroe1}Protheroe R J 1985 \\emph{Proc. 19th ICRC (La Jolla)} \\textbf{3} 485.\n\\bibitem{kn:nauspriv}Naus J I 1998 private communication.\n\\bibitem{kn:swanepoel}Swanepoel J W H and deBeer C F 1990 \\emph{Astrophys.J.} \\textbf{350} 754.\n\\bibitem{kn:protheroe2}Protheroe R J 1986 \\emph{NATO Advanced Research Workshop, Durham}\n\\bibitem{kn:lewis89}Lewis D A 1989 \\emph{Astron.Astrophys.} \\textbf{219} 352.\n\\bibitem{kn:cheng}Cheng L X et al. 1997 \\emph{Astrophys.J.} \\textbf{481} L43.\n\\bibitem{kn:hillas}Hillas A M 1975 \\emph{Proc. 14th ICCR Munich} 3439.\n\\bibitem{kn:briggs}Briggs M S 1996 \\emph{Astrophys.J.} \\textbf{459} 40.\n\\bibitem{kn:bennett}Bennett D P and Rhie S H 1996 \\emph{Astrophys.J.} \\textbf{458} 293.\n\\bibitem{kn:brainerd}Brainerd J J 1996 \\emph{Astrophys.J.} \\textbf{473} 974.\n\\bibitem{kn:nowak}Nowak M A 1994 \\emph{Mon.Not.R.Astron.Soc.} \\textbf{266} L45.\n\\bibitem{kn:mattox}Mattox J R et al. 1996 \\emph{Astrophys.J.} \\textbf{461} 396.\n\\bibitem{kn:ballester}Ballester P 1994 \\emph{Astron.Astrophys.} \\textbf{286} 1011.\n\\bibitem{kn:loader}Loader C R 1991 \\emph{Advances in Applied Probability} \\textbf{23} 751.\n\\bibitem{kn:chen96}Chen J and Glaz J 1996 \\emph{Statistics and Probability Letters} \\textbf{31} 59.\n\\bibitem{kn:kulldorff}Kulldorff M 1997 \\emph{Comms. in Statistics - Theory and Methods} \\textbf{6} 1481.\n\\bibitem{kn:loredo90} Loredo T J 1990 \\emph{Maximum Entropy and Bayesian Methods} \nKluwer Academic Publishers, Dordrecht.\n\\newline http://astrosun.tn.cornell.edu/staff/loredo/bayes/articles.ps.gz\n\\bibitem{kn:loredo94} Loredo T J 1994 \\emph{Bayesian Inference in Astrophysics} Bayesian Statistics 5, Valencia. \n\\newline http://astrosun.tn.cornell.edu/staff/loredo/bayes/return.ps.gz\n\\bibitem{kn:goldstein} Goldstein M, private communication.\n\\bibitem{kn:gregory}Gregory P C and Loredo T J 1992 \\emph{Astrophys.J.} \\textbf{398} 146.\n\\bibitem{kn:gregory96}Gregory PC and Loredo T J 1996 \\emph{Astrophys.J.} \\textbf{473} 1059.\n\\bibitem{kn:gregory99a}Gregory PC, \\emph{Astrophys.J.} \\textbf{520} 361.\n\\bibitem{kn:gregory99b}Gregory PC, Peracaula M and Taylor AR, \\emph{Astrophys.J.} \\textbf{520} 376.\n\\bibitem{kn:VLAbayes} McLaughlin M A et al., 1999 \\emph{Astrophys.J.} \\textbf{512}, 929\n\\end{thebibliography}\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002149.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{kn:eadie} Eadie W T et al. 1971 \\emph{Statistical Methods in Experimental Physics} North-Holland.\n\\bibitem{kn:hearn}Hearn D 1969 \\emph{Nuclear Inst. Meth.} \\textbf{70} 200.\n\\bibitem{kn:omongain}O'Mongain E 1973 \\emph{Nature} \\textbf{241} 376.\n\\bibitem{kn:gibsona}Gibson I A et al. 1982 \\emph{Proc. Int. Workshop on VHE $\\gamma$-ray Astronomy, Ootacamund, India} \nTata Institute/Harvard Smithsonian Institution. 97.\n\\bibitem{kn:lima}Li T-P and Ma Y-Q 1983 \\emph{Astrophys.J.} \\textbf{272} 317.\n\\bibitem{kn:dowthwaite}Dowthwaite J C et al. 1983 \\emph{Astron.Astrophys.} \\textbf{126} 1.\n\\bibitem{kn:numreps} Press WH et al., \\emph{Numerical Recipes} Cambridge University Press.\n\\bibitem{kn:scargle98}Scargle J D 1998 \\emph{Astrophys.J.} \\textbf{504} 405.\n\\bibitem{kn:cox}Cox DR and Isham V 1980 \\emph{Point Processes} Chapman and Hall, London.\n\\bibitem{kn:mclaughlin} McLaughlin M A et al. 1998 \\emph{Astrophys.J.} \\textbf{473} 703.\n\\bibitem{kn:katayose}Katayose Y et al. 1997 \\emph{Proc.25th Int. Cosmic Ray Conf. Durban}\n\\bibitem{kn:parzen}Parzen E 1960 \\emph{Modern Probability Theory and its Applications} New York:Wiley.\n\\bibitem{kn:barton}Barton D E and David F N 1956 \\emph{J. Roy. Stat. Soc. Series A} \\textbf{18} 79.\n\\bibitem{kn:huntington}Huntington R J and Naus J I 1975 \\emph{Ann. Probability} \\textbf{3} 895.\n\\bibitem{kn:neff}Neff N D and Naus J I 1980 \\emph{Selected tables in Mathematical Statistics} \\textbf{VI} AMS Providence \nRI.\n\\bibitem{kn:naus66}Naus J I 1966 \\emph{J. Amer. Stat. Assn.} \\textbf{61} 1191.\n\\bibitem{kn:glaz93}Glaz J 1993 \\emph{Statistics in Medicine} \\textbf{12} 1845.\n\\bibitem{kn:wallenstein73}Wallenstein S and Naus J I 1973 \\emph{Ann.Probability} \\textbf{1} 188.\n\\bibitem{kn:wallenstein94}Wallenstein S Naus J and Glaz J 1994 \\emph{Biometrika} \\textbf{81} 595.\n\\bibitem{kn:chen97}Chen J and Glaz J 1997 \\emph{Chap. 16 in: Advances in the Theory and Practice of Statistics, ed. \nJohnson N L and Balakrishnan N} New York:Wiley.\n\\bibitem{kn:mansson}M\\aa nsson M 1999 \\emph{Ann.Appl.Probability} \\textbf{9} 465.\n\\bibitem{kn:newell}Newell GF 1963 \\emph{Time Series Analysis, Proc. Conf. at Brown Univ.} ed M.Rosenblatt, Academic Press.\n\\bibitem{kn:ikeda}Ikeda S 1965 \\emph{Ann.Inst.Stat.Math.} \\textbf{17} 295.\n\\bibitem{kn:conover} Conover W J Bement T R and Iman R L 1979 \\emph{Technometrics} \\textbf{21} 277.\n\\bibitem{kn:naus82}Naus J I 1982 \\emph{J.Amer.Stat.Ass.} \\textbf{77} 177.\n\\bibitem{kn:glaz91}Glaz J and Naus J I 1991 \\emph{Ann.Appl.Probability} \\textbf{1} 306.\n\\bibitem{kn:karwe}Karwe V V and Naus J I 1997 \\emph{Computational Statistics and Data Analysis} \\textbf{23} 389.\n\\bibitem{kn:glaz92}Glaz J 1992 \\emph{Computational Statistics and Data Analysis} \\textbf{14} 213.\n\\bibitem{kn:nargarwalla}Nargarwalla N 1996 \\emph{Statistics in Medicine} \\textbf{15} 845.\n\\bibitem{kn:alm}Alm S E 1997 \\emph{Adv.Appl.Prob.} \\textbf{29} 1.\n\\bibitem{kn:giles}Giles A B 1996 \\emph{Astrophys.J.} \\textbf{474} 464.\n\\bibitem{kn:vanstekelenborg}Vanstekelenborg J T P M and Petrakis J P 1993 \\emph{Nucl.Inst.Meth.} \\textbf{328} 559.\n\\bibitem{kn:rothschild}Rothschild R E et al. 1974 \\emph{Astrophys.J.} \\textbf{189} L13.\n\\bibitem{kn:bell}Bell D A 1968 \\emph{Information Theory} London:Pitman.\n\\bibitem{kn:lathi}Lathi B P 1968 \\emph{Random Signals and Communication Theory}, \n Scranton, Pennsylvania: International Textbook Company.\n\\bibitem{kn:lewis93}Lewis D A 1993 \\emph{Statistical Methods for Physical Sciences} chap. 12, London:Academic Press.\n\\bibitem{kn:scargle82} Scargle J D 1982 \\emph{Astrophys.J.} \\textbf{263} 835.\n\\bibitem{kn:koen}Koen C 1995 \\emph{Astrophys.Space Sci.} \\textbf{230} 307.\n\\bibitem{kn:gibsonb}Gibson I A et al. 1982 \\emph{Nature} \\textbf{296} 833.\n\\bibitem{kn:mardia}Mardia K V 1972 \\emph{Statistics of Directional Data} London:Academic Press.\n\\bibitem{kn:fisher}Fisher N I 1993 \\emph{Statistical Analysis of Circular Data} Cambridge University Press.\n\\bibitem{kn:priestley}Priestley M B 1981 \\emph{Spectral Analysis and Time Series} - Volume 1 \\emph{Univariate Series} \nLondon:Academic Press.\n\\bibitem{kn:bloomfield}Bloomfield P 1976 \\emph{Fourier Analysis of Time Series} New York:Wiley.\n\\bibitem{kn:dejager89}DeJager O C, Swanepoel J W H and Raubenheimer B C 1989 \\emph{Astron.Astrophys.} \\textbf{221} 180.\n\\bibitem{kn:orford91}Orford K J 1991 \\emph{Exper.Astron.} \\textbf{1} 305.\n\\bibitem{kn:lyne} Lyne AG and Graham-Smith F 1998 \\emph{Pulsar Astronomy} Cambridge University Press.\n\\bibitem{kn:buccheri}Buccheri R et al. 1983 \\emph{Astron.Astrophys.} \\textbf{128} 245.\n\\bibitem{kn:protheroe3}Protheroe R J 1987 \\emph{Proc.Astron.Soc.Australia} \\textbf{7} 167.\n\\bibitem{kn:dejager94} deJager O C 1994 \\emph{Astrophys.J.} \\textbf{436} 239.\n\\bibitem{kn:alberto}Carrami\\~{n}ana A et al. 1989 {\\em Astrophys.J.(Letters)} \\textbf{346} 967.\n\\bibitem{kn:raub1}Raubenheimer B C and \\\"{O}gelman H 1990 {\\em Astron.Astrophys.} \\textbf{230} 73.\n\\bibitem{kn:kay}Kay S M 1988 \\emph{Modern Spectral Estimation - Theory and Applications} New Jersey:Prentice-Hall.\n\\bibitem{kn:jenkins}Jenkins G M and Watts D G 1968 {\\em Spectral Analysis and its Applications}, San Fransisco:Holden-Day.\n\\bibitem{kn:raub2}Raubenheimer B C et al. 1994 {\\em Astrophys.J.} \\textbf{428} 77.\n\\bibitem{kn:orford96}Orford K J 1996 \\emph{Astropart.Phys.} \\textbf{4} 235.\n\\bibitem{kn:leahy}Leahy D A, Elsner R F and Weisskopf W C 1983 \\emph{Astrophys.J.} \\textbf{272} 256.\n\\bibitem{kn:bai}Bai T 1992 \\emph{Astrophys.J.} \\textbf{397} 584.\n\\bibitem{kn:loredo92} Loredo T J 1992 \\emph{Statistics Challenges in Modern Astronomy} eds. \nFeigelson E D and Babu G J, Springer verlag, New York, 275.\n\\newline http://astrosun.tn.cornell.edu/staff/loredo/bayes/promise.ps.gz\n\\bibitem{kn:protheroe1}Protheroe R J 1985 \\emph{Proc. 19th ICRC (La Jolla)} \\textbf{3} 485.\n\\bibitem{kn:nauspriv}Naus J I 1998 private communication.\n\\bibitem{kn:swanepoel}Swanepoel J W H and deBeer C F 1990 \\emph{Astrophys.J.} \\textbf{350} 754.\n\\bibitem{kn:protheroe2}Protheroe R J 1986 \\emph{NATO Advanced Research Workshop, Durham}\n\\bibitem{kn:lewis89}Lewis D A 1989 \\emph{Astron.Astrophys.} \\textbf{219} 352.\n\\bibitem{kn:cheng}Cheng L X et al. 1997 \\emph{Astrophys.J.} \\textbf{481} L43.\n\\bibitem{kn:hillas}Hillas A M 1975 \\emph{Proc. 14th ICCR Munich} 3439.\n\\bibitem{kn:briggs}Briggs M S 1996 \\emph{Astrophys.J.} \\textbf{459} 40.\n\\bibitem{kn:bennett}Bennett D P and Rhie S H 1996 \\emph{Astrophys.J.} \\textbf{458} 293.\n\\bibitem{kn:brainerd}Brainerd J J 1996 \\emph{Astrophys.J.} \\textbf{473} 974.\n\\bibitem{kn:nowak}Nowak M A 1994 \\emph{Mon.Not.R.Astron.Soc.} \\textbf{266} L45.\n\\bibitem{kn:mattox}Mattox J R et al. 1996 \\emph{Astrophys.J.} \\textbf{461} 396.\n\\bibitem{kn:ballester}Ballester P 1994 \\emph{Astron.Astrophys.} \\textbf{286} 1011.\n\\bibitem{kn:loader}Loader C R 1991 \\emph{Advances in Applied Probability} \\textbf{23} 751.\n\\bibitem{kn:chen96}Chen J and Glaz J 1996 \\emph{Statistics and Probability Letters} \\textbf{31} 59.\n\\bibitem{kn:kulldorff}Kulldorff M 1997 \\emph{Comms. in Statistics - Theory and Methods} \\textbf{6} 1481.\n\\bibitem{kn:loredo90} Loredo T J 1990 \\emph{Maximum Entropy and Bayesian Methods} \nKluwer Academic Publishers, Dordrecht.\n\\newline http://astrosun.tn.cornell.edu/staff/loredo/bayes/articles.ps.gz\n\\bibitem{kn:loredo94} Loredo T J 1994 \\emph{Bayesian Inference in Astrophysics} Bayesian Statistics 5, Valencia. \n\\newline http://astrosun.tn.cornell.edu/staff/loredo/bayes/return.ps.gz\n\\bibitem{kn:goldstein} Goldstein M, private communication.\n\\bibitem{kn:gregory}Gregory P C and Loredo T J 1992 \\emph{Astrophys.J.} \\textbf{398} 146.\n\\bibitem{kn:gregory96}Gregory PC and Loredo T J 1996 \\emph{Astrophys.J.} \\textbf{473} 1059.\n\\bibitem{kn:gregory99a}Gregory PC, \\emph{Astrophys.J.} \\textbf{520} 361.\n\\bibitem{kn:gregory99b}Gregory PC, Peracaula M and Taylor AR, \\emph{Astrophys.J.} \\textbf{520} 376.\n\\bibitem{kn:VLAbayes} McLaughlin M A et al., 1999 \\emph{Astrophys.J.} \\textbf{512}, 929\n\\end{thebibliography}"
}
] |
|
astro-ph0002151
|
Effect of Reionization on Structure Formation in the Universe
|
[
{
"author": "Nickolay Y.\\ Gnedin"
}
] |
I use simulations of cosmological reionization to quantify the effect of photoionization on the gas fraction in low mass objects, in particular the characteristic mass scale below which the gas fraction is reduced compared to the universal value. I show that this characteristic scale can be up to an order of magnitude lower than the linear theory Jeans mass, and that even if one defines the Jeans mass at a higher overdensity, it does not track the evolution of this characteristic suppression mass. Instead, the filtering mass, which corresponds directly to the scale over which baryonic perturbations are smoothed in linear perturbation theory, provides a remarkably good fit to the characteristic mass scale. Thus, it appears that the effect of reionization on structure formation in both the linear and nonlinear regimes is described by a single characteristic scale, the filtering scale of baryonic perturbations. In contrast to the Jeans mass, the filtering mass depends on the full thermal history of the gas instead of the instantaneous value of the sound speed, so it accounts for the finite time required for pressure to influence the gas distribution in the expanding universe. In addition to the characteristic suppression mass, I study the full shape of the probability distribution to find an object with a given gas mass among all the objects with the same total mass, and I show that the numerical results can be described by a simple fitting formula that again depends only on the filtering mass. This simple description of the probability distribution may be useful for semi-analytical modeling of structure formation in the early universe.
|
[
{
"name": "jed.tex",
"string": "\\documentstyle[11pt,aaspp4,nick]{article}\n\\begin{document}\n\n%\\pagestyle{myheadings}\n%\\markright{DRAFT: \\today\\hfill}\n\n\\title{Effect of Reionization on Structure Formation in the Universe}\n\\author{Nickolay Y.\\ Gnedin}\n\\affil{CASA, University of Colorado, Boulder, CO 80309;\ne-mail: \\it gnedin@casa.colorado.edu}\n\n%$$\\framebox{$\\displaystyle\\phantom{\\prod}$DRAFT: \\today}$$\n\n\\load{\\scriptsize}{\\sc}\n\n\n\\def\\A{{\\cal A}}\n\\def\\B{{\\cal B}}\n\\def\\ion#1#2{\\rm #1\\,\\sc #2}\n\\def\\HI{{\\ion{H}{i}}}\n\\def\\HII{{\\ion{H}{ii}}}\n\\def\\GI{{\\ion{He}{i}}}\n\\def\\GII{{\\ion{He}{ii}}}\n\\def\\GIII{{\\ion{He}{iii}}}\n\\def\\MH{{{\\rm H}_2}}\n\\def\\Hp{{{\\rm H}_2^+}}\n\\def\\Hm{{{\\rm H}^-}}\n\n\\def\\dim#1{\\mbox{\\,#1}}\n\n\\def\\figdir{.}\n\\def\\placefig#1{#1}\n\n\\begin{abstract}\nI use simulations of cosmological reionization to quantify\nthe effect of photoionization on the gas fraction in low mass\nobjects, in particular the characteristic mass scale below which\nthe gas fraction is reduced compared to the universal value.\nI show that this characteristic scale can be up to an order of\nmagnitude lower than the linear theory Jeans mass, and that even\nif one defines the Jeans mass at a higher overdensity,\nit does not track the evolution of this characteristic suppression\nmass. Instead, the filtering mass, which corresponds directly \nto the scale over which baryonic perturbations are smoothed in linear\nperturbation theory, provides a remarkably good fit to the characteristic \nmass scale. Thus, it appears that the effect of reionization on structure\nformation in both the linear and nonlinear regimes is described\nby a single characteristic scale, the filtering scale of baryonic \nperturbations. In contrast to the Jeans mass, the filtering mass depends\non the full thermal history of the gas instead of the instantaneous\nvalue of the sound speed, so it accounts for the finite time required\nfor pressure to influence the gas distribution in the expanding universe.\nIn addition to the characteristic suppression mass, I study the full shape\nof the probability distribution to find an object with a given gas mass \namong all the objects with the same total mass, and I show that the\nnumerical results can be described by a simple fitting formula that again\ndepends only on the filtering mass. This simple description of the \nprobability distribution may be useful for semi-analytical modeling of \nstructure formation in the early universe.\n\\end{abstract}\n\n\\keywords{cosmology: theory - cosmology: large-scale structure of universe -\ngalaxies: formation - galaxies: intergalactic medium}\n\n\n\\section{Introduction}\n\nThe effect of cosmological reionization on the formation and evolution of\nlow mass objects has been under the scrutiny of theorists for a long time,\never since Ikeuchi (1986) and Rees (1986) independently pointed out that\nthe increase in the temperature of the cosmic gas during reionization will\nsuppress the formation of small galaxies with masses below the Jeans\nmass. Several attempts to quantify the effect of reionization on \nlow mass galaxies have been made since using semi-analytical calculations\n(Babul \\& Rees 1992; Efstathiou 1992; Shapiro, Giroux, \\& Babul 1994), \nspherically symmetric modeling\n(Haiman, Thoul, \\& Loeb 1996; Thoul \\& Weinberg 1996), and \nthree-dimensional cosmological hydrodynamic simulations (Quinn, Katz, \\&\nEfstathiou 1996; Weinberg, Hernquist, \\& Katz 1997; Navarro \\& Steinmetz\n1997). \n\nWhile confirming the general proposition that reionization\nsuppresses formation of low mass galaxies, these studies \ndo not give the full description of the impact of reionization on\nthe gas fraction in the low mass objects. Particularly, one can expect\nthat the effect of reionization depends on the reionization history,\nand thus is not universal at a given redshift.\n\nThus, it would be useful to attempt to quantify the effect of reionization\non the formation and evolution of the low-mass objects in a more complete\nmanner, relating the effective mass below which an object is a subject\nto reionization feedback to the characteristic scales present at\neach given moment of time.\n\n\\def\\tableone{\n\\begin{deluxetable}{cccccc}\n\\tablecaption{Simulation Parameters\\label{tabone}}\n\\tablehead{\n\\colhead{Run} & \n\\colhead{$N$} & \n\\colhead{Box size} & \n\\colhead{Baryonic mass res.} & \n\\colhead{Total mass res.} & \n\\colhead{Spatial res.} }\n\\startdata\nA & $128^3$ & $4h^{-1}{\\rm\\,Mpc}$ & $10^{5.7}\\dim{M}_{\\sun}$ & \n$10^{6.6}\\dim{M}_{\\sun}$ &$1.0h^{-1}{\\rm\\,kpc}$ \\\\\nB & $128^3$ & $2h^{-1}{\\rm\\,Mpc}$ & $10^{4.8}\\dim{M}_{\\sun}$ & \n$10^{5.7}\\dim{M}_{\\sun}$ &$0.5h^{-1}{\\rm\\,kpc}$ \\\\\n\\enddata\n\\end{deluxetable}\n}\n\\placefig{\\tableone}\nThis paper attempts to accomplish precisely that based on the new simulations\nof cosmological reionization. The \nsimulations of a representative Cold Dark Matter cosmological \nmodel\\footnote{With the following cosmological parameters: $\\Omega_0=0.3$,\n$\\Omega_\\Lambda=0.7$, \n$h=0.7$, $\\Omega_b=0.04$, $n=1$, $\\sigma_8=0.91$, where the amplitude and\nthe slope of the primordial spectrum are fixed by the COBE and cluster-scale\nnormalizations.}\nwere performed with the \n``Softened Lagrangian Hydrodynamics'' (SLH-P$^3$M) code (Gnedin 1995, 1996;\nGnedin \\& Bertschinger 1996)\nand fully described in Gnedin (2000).\nTable \\ref{tabone} lists two simulations used in this paper. Parameter $N$\ngives the number of the dark matter particles; the quasi-Lagrangian baryonic \nmesh has the same size. Baryonic mass resolution is an average mass of a\nbaryonic cell, and the total mass resolution is the mass of a dark matter\nparticle plus the average mass of a baryonic cell. The spatial resolution\nis measured as the gravitational softening length (the real resolution of\nboth the gravity solver and the gas dynamics solver is\na factor of two worse). Reionization by stars (i.e.\\ with a soft UV \nbackground spectrum) is modeled with the Local Optical Depth approach,\nwhich is able to approximately follow the three-dimensional radiative transfer\nin the cosmological density distributions.\n\nThe two simulations from Table 1 allow me to investigate the sensitivity\nof my results to the missing small and large scale power: run A has a larger\nbox whereas run B has a higher resolution. \nThey also have different reionization histories, which allows me to test the \ngenerality of my results.\n\nBoth simulations\nhave sufficient mass resolution and the box size to resolve the relevant\ncharacteristic mass scales during reionization and thus can be used\nfor the purpose of this paper. Since both simulations have\nbox sizes comparable to the nonlinear scale at the present time, they cannot\nbe continued until $z=0$. Rather, run A is stopped at $z=4$ and run B at\n$z=6.5$.\n\nThe goal of this paper is to quantify the relationship between the\ntotal mass of an object $M_{\\rm t}$ and its gas mass $M_{\\rm g}$.\nThe advantage of using the simulations listed in Table \\ref{tabone} is that\nthey have enough resolution (both in mass and space) to actually map the\nfull two-dimensional distribution of objects in the $M_{\\rm t}-M_{\\rm g}$\nplane. But before this can be done, I need to discuss what characteristic\nmass scales are relevant for the evolution of the cosmic gas. This is\nparticularly important because, as the reader is reminded in the next section,\nthe Jeans mass, initially proposed as the characteristic scale, is essentially\nirrelevant in the expanding universe.\n\n\n\n\\section{Reminder: the Linear Theory}\n\nThe effect of the reionization of the universe and the associated reheating\nof the cosmic gas on the evolution of linear perturbations was comprehensively\ndiscussed in Gnedin \\& Hui (1998). As they showed, the relationship between\nthe linear overdensity of the dark matter $\\delta_d(t,k)$ and the\nlinear overdensity of the cosmic gas $\\delta_b(t,k)$ as a function of\ntime and the comoving wavenumber $k$, in the limit of small $k$ \n($k\\rightarrow0$), \ncan be written as\n\\begin{equation}\n {\\delta_b(t,k)\\over\\delta_d(t,k)} = 1-{k^2\\over k_F^2} +\n\tO(k^4),\n \\label{defkf}\n\\end{equation}\nwhere $k_F$ is in general a function of time. They called the physical scale\nassociated with the comoving wavenumber $k_F$ the {\\it filtering scale\\/},\nsince it is the characteristic scale over which the baryonic perturbations\nare smoothed as compared to the dark matter.\n\nThe filtering scale is related to the Jeans scale $k_J$,\n\\begin{equation}\n k_J \\equiv {a \\over c_S}\\sqrt{4\\pi G\\bar\\rho}\n \\label{defkj}\n\\end{equation}\n(here $\\bar\\rho$ is the average total mass density of the universe, \n$c_S$ is the sound speed, which is uniquely defined in linear theory,\nand $a$ is the cosmological scale factor), by\nthe following relation:\n\\begin{equation}\n {1\\over k_F^2(t)} = {1\\over D_+(t)} \\int_0^t dt^\\prime \n a^2(t^\\prime)\n {\\ddot{D}_+(t^\\prime)+2H(t^\\prime)\\dot{D}_+(t^\\prime) \n \\over k_J^2(t^\\prime)} \n \\int_{t^\\prime}^t{dt^{\\prime\\prime}\\over a^2(t^{\\prime\\prime})},\n \\label{kfaskj}\n\\end{equation}\nwhere $D_+(t)$ is the linear growing mode in a given cosmology.\n\nFor a flat universe at high redshift $z\\ga2$, the scale factor $a$\nis well approximated by the power-law in time, $a\\propto t^{2/3}$,\nand the growing mode $D_+$ is proportional to $a$. In this case equation \n(\\ref{kfaskj}) can be substantially simplified:\n\\begin{equation}\n {1\\over k_F^2(a)} = {3\\over a} \\int_0^a {da^\\prime \n \\over k_J^2(a^\\prime)} \\left[1-\\left(a^{\\prime}\\over a\n\t\\right)^{1/2}\\right].\n \\label{kfaskjflat}\n\\end{equation}\n\nInspection of equation (\\ref{kfaskj}) shows that the filtering scale {\\it as a\nfunction of time\\/} is related to the Jeans scale {\\it as a function of \ntime\\/}, but\nat {\\it a given moment in time\\/} those two scales are unrelated and can be\nvery different. Thus, given the Jeans scale at a specific moment in time,\nnothing can be said about the scale over which the baryonic perturbations\nare smoothed. It is only when the whole time evolution of the Jeans\nscale up to some moment in time is known that can the filtering scale at this\nmoment be\nuniquely defined.\\footnote{In general it is also true that the filtering \nscale is equal to the Jeans scale at some earlier moment in time.}\n\nThe physical explanation of this result is very simple: the gas temperature\n(and thus the Jeans scale) can increase very quickly, but the gas density\ndistribution can only change on the dynamical time scale, which is about\nthe Hubble time for the linear perturbations. Thus, the effect of the\nincreased pressure on the gas density distribution will be delayed and can\nonly occur over the Hubble time.\n\nWhile formally the filtering scale is only defined on large scales, as \n$k\\rightarrow0$, the following formula\n\\begin{equation}\n {\\delta_b(t,k)\\over\\delta_d(t,k)} \\approx e^{-k^2/k_F^2}\n \\label{approxkf}\n\\end{equation}\nprovides a remarkably accurate fit on all scales up to at least \n$k=k_F$, and is also very accurate when one needs to calculate the\nintegrals over the baryonic power spectrum $P_b(k)=\\delta_b(t,k)^2$.\nThere is no obvious physical reason why equation (\\ref{approxkf}) should be a\ngood fit to the full solution of the linear theory equations, but it was\nextensively tested over a very large region of the parameter space\nof possible cosmological models and\nwas always found to work well.\n\nSince my task is to compare the baryonic versus the total mass\nfor small objects, it is convenient to switch from spatial to mass scales.\nIn linear theory, of course, there exists a one-to-one relationship between\nthe two. Thus, I can define the Jeans mass,\n$$\n\tM_J \\equiv {4\\pi\\over3}\\bar\\rho\\left(2\\pi a\\over k_J\\right)^3,\n$$\nand the filtering mass,\n$$\n\tM_F \\equiv {4\\pi\\over3}\\bar\\rho\\left(2\\pi a\\over k_F\\right)^3,\n$$\nas the mass enclosed in the sphere with the comoving \nradius equal to the corresponding spatial scale. The relationship between \nthe two mass scales for $D_+\\propto a\\propto t^{2/3}$\ncan be easily obtained from equation (\\ref{kfaskjflat}):\n\\begin{equation}\n M_F^{2/3} = {3\\over a} \\int_0^a da^\\prime \n\tM_J^{2/3}(a^\\prime) \\left[1-\\left(a^{\\prime}\\over a\n\t\\right)^{1/2}\\right].\n \\label{mfasmj}\n\\end{equation}\n\n\n\n\\section{Main Results}\n\n\\def\\capTE{\nThe evolution of the mass- ({\\it dotted line\\/}) and volume-\n({\\it solid line\\/}) weighted temperature from run A. Also shown is\nthe volume-averaged temperature for run B ({\\it long-dashed line\\/}).\nThe filled circles with error-bars label the virial temperature of \nobjects that on average have the baryonic fraction of\n50\\% of the universal value. The triangles show\nthe Jeans temperature at the virial overdensity of 180\nthat corresponds to this virial temperature (eq.\\ [\\protect{\\ref{tjdef}}]).\nThe right $y$ axis shows the circular velocity that corresponds to the\nvirial temperature marked by filled circles (the right $y$ axis has no meaning\nfor other curves on this plot).\n}\n\\placefig{\n\\begin{figure}\n\\epsscale{0.65}\n\\insertfigure{\\figdir/figTE.ps}\n\\caption{\\label{figTE}\\capTE}\n\\end{figure}\n}\nFigure \\ref{figTE} shows the evolution of the volume- and mass-weighted \ntemperature in the simulations. Since the\ngas density and temperature are not uniform in the simulation, the definition\nof the linear sound speed (or linear temperature) is somewhat ambiguous.\nI therefore adopt the volume-averaged temperature as a substitute for\nthe linear theory temperature, so that the linear theory sound speed,\nwhich enters the definition of the linear theory Jeans mass, is defined as\n$$\n\tc_S^2 = {5\\over 3} {k_B\\langle T\\rangle_V\\over \\mu m_p},\n$$\nwhere $\\mu=0.59$ is the mean molecular weight of the fully ionized gas.\n\nHowever, the specific definition of the linear sound speed\nis not very important. For example, if I used the mass-weighted\nmean temperatures instead of the volume-weighted one, or instead, I\n calculate the mass- or \nvolume-weighted Jeans mass directly from the simulation,\nthe difference in the computed\nJeans and filtering masses would be smaller than the statistical uncertainty \ndue to a finite number of objects in my simulation (i.e.\\ smaller than the\nerror-bars in Fig.\\ \\ref{figME}).\n\n\\def\\capMM{\nThe gas versus the total mass for all objects from run A taken at\nfour different redshifts ({\\it dark grey points\\/}; redshift decreases\nin the counter-clockwise direction). Also shown\nwith the light grey color the gas versus total mass at $z=15$.\nThe straight line marks the position of the universal baryon\nfraction, $M_{\\rm g}=(\\Omega_b/\\Omega_0) M_{\\rm t}$, and three\ncurved lines show the fit to the function $\\overline{M}_{\\rm g}(M_{\\rm t})$\ntogether with 95\\% confidence levels. The inserted axes show the\ncircular velocity corresponding to the total mass at each redshift.\n}\n\\placefig{\n\\begin{figure}\n\\epsscale{0.70}\n\\insertfigure{\\figdir/figMM.ps}\n\\caption{\\label{figMM}\\capMM}\n\\end{figure}\n}\nThe relationship between the gas and the\ntotal mass of cosmological objects in the simulations\nis now shown in Figure \\ref{figMM}.\\footnote{In all \ncases the stellar mass\nmakes only a small correction to the total gas mass and is \nignored.} Bound objects are identified using the DENMAX algorithm of\nBertschinger \\& Gelb (1991) with the gaussian density smoothing length\nequal to one fifth of the mean interparticle separation, which \ncorresponds to the characteristic overdensity of about 100.\n\nBefore reionization ($z=15$, light grey color) the gas\nmass is directly proportional to the total mass of all objects, and the\ncoefficient of proportionality is the universal baryon fraction\n$f_b\\equiv\\Omega_b/\\Omega_0$. In the simulation shown (run A) \nreionization occurs\nat $z\\approx7$, and at that redshift the effects of reheating start to appear.\nAs time progresses, larger and larger mass objects are affected by the\nincrease in the gas temperature.\n\nWithout additional analysis, it is impossible to say whether the\nreduction of the gas mass in low mass objects is due to the expulsion\nof the already accreted gas, or due to the suppression of the accretion.\nIt is likely that both effects play a role - for example, essentially all\nobjects with masses below $2\\times 10^8{\\rm M}_{\\sun}$ lost their gas\nbetween $z=7$ and $z=6$, and since the average mass of a cosmological object\ndoes not increase significantly during this short time interval, it is\nclear that the gas was expelled from the low-mass objects. \n\nThe first quantity of interest is the average baryonic mass of all objects\nwith given total mass, $\\overline{M}_{\\rm g}(M_{\\rm t})$. This quantity\nwould be useful for semi-analytical modeling since it can be directly\nplugged into the Press-Schechter approximation. Before reionization this\nfunction has a very simple form, $\\overline{M}_{\\rm g}=f_b M_{\\rm t}$, but\nafter reionization the small mass end of $\\overline{M}_{\\rm g}$ is suppressed.\nIn order to obtain a practically useful result, I approximate the mean \nbaryonic mass with the following fitting formula,\n\\begin{equation}\n\t\\overline{M}_{\\rm g} = {f_b M_{\\rm t}\\over \n\t\\left[1+(2^{1/3}-1)M_C/M_{\\rm t}\\right]^3},\n\t\\label{mcdef}\n\\end{equation}\nwhich depends on a single parameter - the characteristic mass $M_C$, which is\nthe total mass of objects that on average retain 50\\% of their gas mass.\n\nIn order to measure $M_C$ from the simulation, I first measure \nthe average gas mass and its error-bars \nas a function of the total mass\nfrom the simulation by \naveraging the gas mass of all objects within 0.1 dex around the\ngiven value of the total mass. \nThen the value of $M_C$ and the corresponding error-bars are found by a\nstandard $\\chi^2$ minimization.\n\nThe rationale for the particular choice of the fitting function is the \nfollowing: it is clear from Fig.\\ \\ref{figMM} that at small masses the\nmean baryonic mass goes as $M_{\\rm t}^4$. I have therefore tried\nfitting formulae of the following kind,\n$$\n\t\\overline{M}_{\\rm g} = {f_b M_{\\rm t}\\over \n\t\\left[1+(2^{\\alpha/3}-1)\\left(M_C/M_{\\rm t}\\right)^\\alpha\n\t\\right]^{3/\\alpha}},\n$$\nand $\\alpha=1$ gives the best values for the $\\chi^2$ test over the whole\ntime evolution.\\footnote{At selected moments in time an equally good fit\ncan be obtained with different $\\alpha$. For example, at $z=4$, $\\alpha=2$\ngives as good a fit as $\\alpha=1$. By eye it appears that $\\alpha=2$\nmight be better than $\\alpha=1$, but this appearance is misleading;\nFig.\\ \\ref{figMM} is shown\non log-log scale, while $\\overline{M}_{\\rm g}$ is the average mass, and not\nthe exponent of the average logarithm of mass.}\n\n\n\\def\\capME{\nThe evolution of various mass scales for two simulations: run A\n({\\it a\\/}) and run B ({\\it b\\/}). The two thin lines show from the top\ndown the linear theory Jeans mass ($M_J$)\nand the Jeans mass at the virial overdensity of 180 \n($M_J/\\sqrt{180}$). The bold line shows the filtering mass ($M_F$), and the \nsymbols\nwith error-bars show the characteristic mass $M_C$\nat which $\\overline{M}_{\\rm g} = 0.5 f_b M_{\\rm t}$,\n as measured from the \nsimulations.\n}\n\\placefig{\n\\begin{figure}\n%\\epsscale{0.65}\n\\inserttwofigures{\\figdir/figMEa.ps}{\\figdir/figMEb.ps}\n\\caption{\\label{figME}\\capME}\n\\end{figure}\n}\nFigure \\ref{figME} now shows the evolution of the Jeans mass $M_J$, the\nfiltering mass $M_F$, and the characteristic mass $M_C$ for both simulations.\nOne can immediately see that the filtering mass provides a good fit for\nthe characteristic mass $M_C$,\nwhereas the linear theory Jeans mass is much larger.\nOne could, however, argue that the linear theory Jeans mass is the wrong scale\nto use, and that the Jeans mass at the virial overdensity\n$1+\\delta=18\\pi^2$ should be used instead. \nThe lower thin line shows the virial overdensity Jeans mass, which provides a \ngood\nfit to the characteristic scale at the end of run A.\nHowever, and this is the most important point of this paper,\n{\\it the overall shape is \nwrong\\/}, which indicates that the agreement between the Jeans mass at the \nvirial density and the characteristic mass scale at $z\\sim4$ is a mere\ncoincidence. Rather, a linear theory filtering mass should be used\nas an \napproximation to the characteristic mass $M_C$,\n\\begin{equation}\n\t\\overline{M}_{\\rm g}(M_{\\rm t},t) \\approx {f_b M_{\\rm t}\\over \n\t\\left[1+(2^{1/3}-1)M_F(t)/M_{\\rm t}\\right]^3}.\n\t\\label{fitfor}\n\\end{equation}\n\nThis result can also be cast in the temperature units. The circles with\nthe error-bars in Fig.\\ \\ref{figTE} show the virial temperature,\n$$\n\tT_{\\rm vir} \\equiv {\\mu m_p\\over 2 k_B} v_c^2 =\n\t{\\mu m_p\\over k_B} G M_{\\rm t}^{2/3} (3\\pi^3\\bar\\rho)^{1/3}\n$$\n(Thoul \\& Weinberg 1996) that corresponds to the characteristic mass $M_C$\nfor run A (the right $y$ axis shows the respective circular velocity).\nThe same mass corresponds to the \nJeans mass at the virial overdensity for \ngas with the temperature of\n\\begin{equation}\n\tT_J \\equiv {\\mu m_p\\over k_B}{3^{7/3}\\over 10\\pi}\n\tG M^{2/3} \\bar\\rho^{1/3} = \n\t{9\\over 10\\pi^2} T_{\\rm vir}.\n\t\\label{tjdef}\n\\end{equation}\nThe value of $T_J$ is shown in \nFig.\\ \\ref{figTE} with the filled triangles.\nThus, if one wants to use the\nJeans mass at the virial overdensity to quantify the effect of \nreionization on structure\nformation, one must use the effective temperature $T_{\\rm eff}$ of\nreheated gas so that $M_{J,\\rm eff} = M_F$,\nwhich in terms of temperature translates into\n$T_{\\rm eff} \\sim 8\\times10^3 \\dim{K}$\nat $z\\sim4$ and $T_{\\rm eff} \\sim 2\\times10^3 \\dim{K}$ during reionization,\nrather that $T_{\\rm eff}=(1-2)\\times10^4\\dim{K}$ at all times.\n\nThus, the effect of the expansion of the\nuniverse (which causes the delay of the growth of the\nfiltering mass $M_F$ with respect to the linear Jeans mass $M_J$)\non the gas fraction suppression in low mass objects\nhas the same appearance as the non-expanding universe with the\nreheating temperature of only a few thousand degrees.\n\nFor most practical applications the knowledge of \n$\\overline{M}_{\\rm g}(M_{\\rm t},t)$\nmay be sufficient, but the resolution of my simulations is also sufficient\nto approximately characterize the whole distribution function\n$P(M_{\\rm g},M_{\\rm t})$. Using the product rule of probability theory,\nthis distribution function can be written as the product of the\nprobability to find an object with the total mass $M_{\\rm t}$\nand the probability distribution of the gas masses for all\nobjects with a given total mass,\n$$\n\tP(M_{\\rm g},M_{\\rm t}) = P(M_{\\rm t})P(M_{\\rm g}|M_{\\rm t}).\n$$\nThe former probability depends on the cosmological model, whereas the latter\nmay be conjectured to be independent of the specific model, and\ndepend only on the characteristic mass scales present at this moment.\nThe physical reason for this conjecture is simple: the number density\nof cosmological objects of a given mass depends on the cosmological model,\nbut as long as this number density is not exceedingly high, different objects\nas virialized entities are independent of each other and the rest of\nthe universe, and thus a probability for an object to lose a given fraction\nof its gas mass should not depend strongly on the abundance of other objects\nsomewhere else in the universe.\n\nThe number of objects in the simulations is not high enough\nto accurately measure the probability distribution function\n$P(M_{\\rm g}|M_{\\rm t})$, but it appears that for any $M_{\\rm t}$ and \nat any given\ntime this distribution is compatible with a lognormal distribution.\nAssuming that it is indeed lognormal, I can write it down as follows:\n\\begin{equation}\n\tP(M_{\\rm g}|M_{\\rm t}) = {1\\over \\sigma \\sqrt{2\\pi}}\n\t\\exp\\left[-{1\\over2\\sigma^2}\\left(\\ln M_{\\rm g} - \n\t\\ln\\overline{M}_{\\rm g}+\\sigma^2/2\\right)^2\\right],\n\t\\label{ln}\n\\end{equation}\nwhere $\\sigma$ is the rms dispersion of the logarithm of the gas mass,\nand is a function of the total mass, as is $\\overline{M}_{\\rm g}$\n(eq.\\ [\\ref{fitfor}]).\n\n\\def\\capMS{\nThe same as Fig.\\ \\protect{\\ref{figME}}, except that the symbols now\nshow the characteristic mass $M_C^*$ from the fitting formula for the\nrms dispersion $\\sigma$ of the lognormal distribution \n$P(M_{\\rm g}|M_{\\rm t})$\nat a given $M_{\\rm t}$.\n}\n\\placefig{\n\\begin{figure}\n%\\epsscale{0.65}\n\\inserttwofigures{\\figdir/figMSa.ps}{\\figdir/figMSb.ps}\n\\caption{\\label{figMS}\\capMS}\n\\end{figure}\n}\nIn order to come up with a closed form fitting formula, I approximate $\\sigma$\nby the following power-law:\n$$\n\t\\sigma(M_{\\rm t}) = {M_C^*\\over 3 M_{\\rm t}},\n$$\nwhere $M_C^*$ is another characteristic mass, which is plotted in Figure\n\\ref{figMS} together with the Jeans mass and the filtering mass. Again,\nas one can see, the characteristic mass $M_C^*$ is approximately equal\nto the filtering mass, so that the rms dispersion of the logarithm of\ngas mass at a given total mass is given by the following fit:\n\\begin{equation}\n\t\\sigma(M_{\\rm t},t) \\approx {M_F(t)\\over 3 M_{\\rm t}}.\n\t\\label{sigfit}\n\\end{equation}\nThe last equation is not very well constrained by my simulations. For example,\nthe coefficient in the denominator is determined with only 30\\% accuracy,\nso replacing it with 2 or 4 also gives an acceptable fit to the data.\n\nEquations (\\ref{fitfor}-\\ref{sigfit}) give in a closed form the probability\ndistribution function\n$P(M_{\\rm g}|M_{\\rm t},t)$ for any cosmological model and \nreionization history (which are specified through the filtering mass\n$M_F(t)$ as a function of time).\n\n\n\n\\section{Low Redshift Evolution}\n\n\\def\\capMF{\n({\\it a\\/})\nExtrapolation of Fig.\\ \\protect{\\ref{figME}a} to $z=0$. Lower solid curves\nshow the extrapolation assuming the temperature\nevolution $T\\propto a^{-0.88}$, whereas the upper curves\nalso include a second reheating at $z=3$ as indicated by the\nobservations. ({\\it b\\/}) The same plot with masses converted into circular \nvelocities. The triangle shows the results of Thoul \\& Weinberg (1996) and\nQuinn et al.\\ (1996) for the model without reheating (lower solid curves).}\n\\placefig{\n\\begin{figure}\n%\\epsscale{0.65}\n\\inserttwofigures{\\figdir/figMF.ps}{\\figdir/figVF.ps}\n\\caption{\\label{figMF}\\capMF}\n\\end{figure}\n}\nGiven the thermal history of the universe, the evolution of the linear theory\nJeans mass and thus the filtering mass can be calculated up to the present\ntime. In a universe with a single (hydrogen) reionization epoch\nthe temperature\nat late times is theoretically predicted to evolve as $\\propto a^{-0.88}$\n(Miralda-Escud\\'{e} \\& Rees 1994; Hui \\& Gnedin 1997). However, \nrecent analyses of Lyman-alpha forest data indicate that the universe\nunderwent a second reheating at $z\\approx 3$ (Ricotti, Gnedin, \\& Shull\n2000; Schaye et al.\\ 2000), possibly as the result of helium reionization\nby quasars.\nIn order to account for it, I also consider\na thermal history for which the gas temperature is increased sharply\nat $z=3$ by a factor of 2.5. Figure \\ref{figMF} shows the predicted\nevolution of the filtering mass, the linear theory Jeans mass, and the\nJeans mass at the virial overdensity for the two cases (the upper curves\ncorrespond to the secondary reheating model) in an $\\Omega_0=1$ universe\n(for a flat universe with the cosmological constant, the result is almost\nindistinguishable). This paper therefore makes a \nprediction that objects as massive as $10^{11}{\\rm M}_{\\sun}$ have on average\na baryon fraction of only 50\\% of the universal value. (The baryonic\ncontent of these objects is likely to be dominated by stars at the present\ntime.) Note, however, that in terms of circular velocities, \nthe characteristic scale is essentially independent of redshift, and is\nabout $50\\dim{km/s}$, \nin agreement with previous investigations (Thoul \\& Weinberg 1996;\n(Quinn, Katz, \\& Efstathiou 1996; Weinberg, Hernquist, \\& Katz 1997). \nThe Jeans mass\nat the virial overdensity is, however, a decreasing function of time,\nand corresponds to a circular velocity of only about $30\\dim{km/s}$\nat $z=2$ in the model without the secondary reheating, contrary to the \nnumerical results. This gives a\nfurther illustration of the fact that the Jeans mass (at any\noverdensity) is not the proper scale that controls the gas fraction\nin low mass objects.\n\n\n\n\\section{Conclusions}\n\nBased on cosmological simulation of reionization, I showed that the \nlinear Jeans\nmass does not control the mass scales over which reionization suppresses\nthe gas fraction in low mass cosmological objects, and may overestimate\nthe characteristic mass scale by an order of magnitude. \nSince the Jeans mass is\na function of the density, at the virial overdensity of 180 the\nJeans mass is able to match the characteristic scale at later times,\nbut the general shape of the Jeans mass vs redshift and the characteristic\nmass vs redshift do not match. \nInstead, the\nfiltering mass, which directly corresponds to the length scale over which\nthe baryonic perturbations are smoothed in linear theory, provides\na good fit to the characteristic mass scale. This conclusions supports\na very simple picture (proposed by Shapiro et al.\\ 1994)\nin which the effect of reionization on structure\nformation in the universe is controlled by a single mass scale\nboth in the linear and the nonlinear regime. However, this work \ndemonstrates that it is not the Jeans mass (as was previously thought)\nbut the filtering mass that is the approriate mass scale.\n\nThe distribution of the\ngas fractions of all cosmological objects with the same total mass at any\ngiven moment during the evolution of the universe\nis approximately lognormal, is fully specified by the filtering mass\nat this moment, and is given by equations (\\ref{fitfor}-\\ref{sigfit}).\n\nThese equations, supplemented with the total-mass function of cosmological\nobjects, fully describe the full probability distribution to find an object\nwith given values of its gas and total mass. This probability distribution\ncan be conveniently used in semi-analytical modeling of the evolution\nof low mass objects in the universe.\n\nAdmittedly, the simulations used in this paper consider only one cosmological\nmodel, but all cosmological models (including those that are\ncurvature- or vacuum-dominated today) have an expansion law that approaches\n$a\\propto t^{2/3}$ at sufficiently\nhigh redshift, and follow similar behavior. Thus, while the \napplicability of equations (\\ref{fitfor}-\\ref{sigfit}) for a wide range of\ncosmological models is not rigorously proven, the physical reasoning\nsuggests that this is likely to be the case.\n\nMy simulations also do not cover all the possible reionization histories, but\nat least runs A and B have different reionization histories and different\nresolutions, which gives some credibility to the conjecture that equations\n(\\ref{fitfor}-\\ref{sigfit}) work for different reionization histories and are\nalso free from numerical artifacts.\n\n\\acknowledgements\n\nI am grateful to the referee David Weinberg for fruitful comments that\nsubstantially improved the original manuscript.\nThis work was partially supported by National Computational Science\nAlliance under grant AST-960015N and utilized the SGI/CRAY Origin 2000 array\nat the National Center for Supercomputing Applications (NCSA).\n\n\n\n\\begin{references}\n\n\\reference{BR92}\nBabul, A., \\& Rees, M.\\ J. 1992, \\mnras, 255, 346\n\n\\reference{BG91}\nBertschinger, E., \\& Gelb, J. 1991, J.\\ Comput.\\ Phys., 5, 164\n\n\\reference{E92}\nEfstathiou, G. 1992, \\mnras, 256, 43P\n\n\\reference{G95}\nGnedin, N.\\ Y. 1995, \\apjs, 97, 231\n\n\\reference{G96}\nGnedin, N.\\ Y. 1996, \\apj, 456, 1\n\n\\reference{G96}\nGnedin, N.\\ Y. 2000, \\apj, in press (astro-ph/9909383)\n\n\\reference{GB96}\nGnedin, N.\\ Y., \\& Bertschinger, E. 1996, \\apj, 470, 115\n\n\\reference{GH98}\nGnedin, N.\\ Y., \\& Hui, L. 1998, \\mnras, 296, 44\n\n\\reference{HTL96}\nHaiman, Z., Thoul, A.\\ A., \\& Loeb, A. 1996, \\apj, 464, 523\n\n\\reference{HG97}\nHui, L., \\& Gnedin, N.\\ Y. 1997, \\mnras, 292, 27\n\n\\reference{I86}\nIkeuchi, S. 1986, Ap\\&SS, 118, 509\n\n\\reference{MR94}\nMiralda-Escud\\'{e}, J., \\& Rees, M.\\ J. 1994, \\mnras, 266, 343\n\n\\reference{NS97}\nNavarro, J., \\& Steinmetz, M. 1997, \\apj, 478, 13\n\n\\reference{QKE96}\nQuinn, T., Katz, N., \\& Efstathiou, G. 1996, \\apj, 278, 49P\n\n\\reference{R86}\nRees, M.\\ J. 1986, \\mnras, 218, 25P\n\n\\reference{RGH00}\nRicotti, M., Gnedin, N.\\ Y., \\& Shull, J.\\ M. 2000, \\apj, in press \n(astro-ph/9906413)\n\n\\reference{Sea00}\nSchaye, J., Theuns, T., Rauch, M., Efstathiou, G., \\& Sargent, W.\\ L.\\ W. 2000,\n\\mnras, submitted (astro-ph 9912432)\n\n\\reference{SGB94}\nShapiro, P.\\ R., Giroux, M.\\ L., \\& Babul, A. 1994, \\apj, 427, 25\n\n\\reference{TW96}\nThoul, A.\\ A., \\& Weinberg, D.\\ H. 1996, \\apj, 465, 608\n\n\\reference{WHK97}\nWeinberg, D.\\ H., Hernquist, L., \\& Katz, N. 1997, \\apj, 477, 8\n\n\\end{references}\n\n\\placefig{\\end{document}}\n\n\\clearpage\n\n\\newcounter{figurecap}\n\\setcounter{figurecap}{0}\n\n\\begin{center}\n\\bf Figure Captions\n\\end{center}\n\n\\refstepcounter{figurecap}\nFig.\\ \\thefigurecap---\\label{figTE}\\capTE\n\n\\refstepcounter{figurecap}\nFig.\\ \\thefigurecap---\\label{figMM}\\capMM\n\n\\refstepcounter{figurecap}\nFig.\\ \\thefigurecap---\\label{figME}\\capME\n\n\\refstepcounter{figurecap}\nFig.\\ \\thefigurecap---\\label{figMS}\\capMS\n\n\\refstepcounter{figurecap}\nFig.\\ \\thefigurecap---\\label{figMF}\\capMF\n\n\\clearpage\n\n\\tableone\n\n\\end{document}\n"
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astro-ph0002152
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The observational evidence for the existence of a non-zero cosmological constant is getting stronger. It is therefore timely to address the question of its eventual effect on the dynamics of galaxies, clusters and larger structures in the Universe. We find, contrary to a recent claim, that the influence of the cosmological constant has to be negligible for, e.g., the rotation curves of galaxies. On larger scales, starting with large galaxy clusters, there are potentially measurable effects from the repulsive addition to the Newtonian gravitational force caused by the cosmological constant.
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"string": "\\documentclass[12pt]{article}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{document}\n\\begin{titlepage}\n\\null\n\\vskip 1cm\n\\begin{center}{\\Large Dynamical effects of a cosmological constant}\\\\\n\\vskip 1cm {\\bf Lars Bergstr\\\"om}\\\\\n\\vskip .2cm\n{\\em Department of Physics,\nStockholm University,\\\\\n Box 6730, SE-113 85 Stockholm, Sweden,}\\\\ {\\tt lbe@physto.se}\\\\\n\n\\vskip .2cm\nand\\\\\n\\vskip.2cm\n{\\bf Ulf Danielsson}\\\\\n\\vskip .2cm\n{\\em Department of Theoretical Physics,\nUppsala University,\\\\\n Box 807, SE-751 08 Uppsala, Sweden,}\\\\ {\\tt ulf@teorfys.uu.se}\n\\end{center}\n\\vskip .2cm\n\\centerline{{\\bf \\today}}\n\n\\begin{abstract}\nThe observational evidence for the existence of a non-zero cosmological\nconstant is getting stronger. It is therefore timely to address the\nquestion of its eventual effect on the dynamics of galaxies, clusters\nand larger structures in the Universe. We find, contrary to a recent\nclaim, that the influence of the cosmological constant has to be\nnegligible for, e.g., the rotation curves of galaxies. On larger scales,\nstarting with large galaxy clusters, there are potentially measurable\neffects from the repulsive addition to the Newtonian gravitational force\ncaused by the cosmological constant.\n\\end{abstract}\n\\end{titlepage}\n\nDuring the past few years, remarkable progress has been made in cosmology,\nboth observational and theoretical. One of the outcomes of these rapid\ndevelopments is the increased confidence that most of the energy density of\nthe observable universe is of an unusual form, i.e., not made up of the\nordinary matter (baryons and electrons) that we see around us in our\neveryday world.\n\nThere are convincing arguments for the existence of a large amount of\nnon-luminous, i.e., dark, matter. The matter content of the universe is at\nleast a factor of 5 higher than the maximum amount of baryonic matter\nimplied by big bang nucleosynthesis. This dark matter is thus highly likely\nto be ``exotic'', i.e, non-baryonic.\n\nThere are also indications, although still not entirely conclusive, of the\nexistence of vacuum energy, corresponding to the famous ``cosmological\nconstant'' that Einstein introduced but later rejected (although without\nvery good reasons) in his theory of general relativity. This possibility has\nrecently been given increased attention due to results from Type Ia\nsupernova surveys \\cite{ariel,kirshner2}. (For a recent review of the\nobservational status of dark matter and dark energy, see \\cite{triangle}.)\n\nIt may be interesting to investigate possible consequences of the\ncosmological constant besides its influence on the geometry of the universe,\nand the redshift-dependence of the luminosity-distance relation for standard\ncandles \\cite{BGbook}. This is the subject of the present paper. We find\ndisagreement with a recent paper \\cite{kraniotis} where the cosmological\nconstant was claimed to influence the rotation curves of galaxies strongly.\nHowever, some small effects on the dynamcis of galaxy clusters do not seem\nexcluded.\n\nLet us first set our conventions. Einstein's equations read \n\\begin{equation}\nR^{\\mu \\nu }-{\\frac{1}{2}}g^{\\mu \\nu }-\\Lambda g^{\\mu \\nu }=8\\pi G_{N}T^{\\mu\n\\nu }.\n\\end{equation}\nThe energy density in the form of a co{smological constant $\\Lambda $ can be\nconveniently written in units of the density scaled to the critical density, \n\\begin{equation}\n\\Omega _{\\Lambda }\\equiv {\\frac{\\rho _{\\Lambda }}{\\rho _{\\mathrm{crit}}}},\n\\end{equation}\nwhere \n\\begin{equation}\n\\rho _{\\Lambda }={\\frac{\\Lambda }{8\\pi G_{N}}} \\label{eq:rhol}\n\\end{equation}\nwith $G_{N}=1/m_{\\mathrm{Pl}}^{2}$ (the numerical value of the Planck mass\nis $m_{\\mathrm{Pl}}=1.2\\cdot 10^{19}$ GeV) and the present value of the\ncritical density \n\\begin{equation}\n\\rho _{\\mathrm{crit}}={\\frac{3H_{0}^{2}}{8\\pi G_{N}}}.\n\\end{equation}\nThus, \n\\begin{equation}\n\\Omega _{\\Lambda }={\\frac{\\Lambda }{3H_{0}^{2}}}.\n\\end{equation}\nWriting $H_{0}=100h$ km\\thinspace s$^{-1}$\\thinspace Mpc$^{-1}$ (with $h\\sim\n0.6\\pm 0.1$ from observations), the present numerical value of the critical\ndensity is \n\\begin{equation}\n\\rho _{\\mathrm{crit}}\\simeq 8\\cdot 10^{-47}h^{2}\\ \\mathrm{GeV}^{4}.\n\\end{equation}\n}\n\nThis was derived using particle physics units ($c=\\hbar =1$). Expressed in $%\ncgs$ units, the presently observationally favoured value \\cite{triangle} $%\n\\Omega _{\\Lambda }\\simeq 0.7\\pm 0.2$ then translates to \n\\begin{equation}\n\\Lambda _{\\mathrm{obs}}\\simeq 10^{-56}\\ \\mathrm{cm}^{-2}.\n\\label{eq:lambda_obs}\n\\end{equation}\nIn a recent preprint \\cite{kraniotis}, an attempt was made to explain the\nflat rotation curves of galaxies as being due to the effect of a\ncosmological constant instead of the ``traditional'' explanation in terms of\ndark matter. However, values some three to four orders of magnitude \nlarger than\nthat in (\\ref{eq:lambda_obs}) were needed, something which is clearly in\nextreme disagreement with observations. In fact, there seems to be a further\nmistake, a sign error, in \\cite{kraniotis}. A positive cosmological\nconstant, as favored by the observations, will tend to accelerate the\nexpansion of the universe and, if anything, make matter in the outer\nregions of galaxies less rather than\nmore bound.\n\nWhile the effects of a cosmological constant thus are negligible on the\nlength scale of galaxies, one might expect observable consequences for\ngalaxy clusters. As a first attempt to see such an effect, we will consider\nthe fate of circular orbits in a flat, expanding universe with a\ncosmological constant. To do this we start with the equation of motion for a\nparticle in an expanding universe with an additional gravitational\npotential, \n\\[\n\\ddot{\\overline{\\chi }}+\\frac{2\\dot{a}}{a}\\overline{\\chi }=-\\frac{\\overline{g%\n}}{a},\n\\]\nwhere $\\overline{\\chi }$ is the comoving coordinate and $a$ is the scale\nfactor. In terms of physical distances, $\\overline{R}=a\\overline{\\chi }$,\none finds \n\\[\n\\ddot{\\bar{R}}-\\bar{R}\\frac{\\ddot{a}}{a}=-\\overline{g}.\n\\]\nAs an example we consider the de Sitter case with $\\Omega _{\\Lambda }=1$,\ni.e. a universe totally dominated by the cosmological constant. We then use \n\\[\na(t)=e^{Ht}\n\\]\nwhere $H=\\sqrt{\\frac{\\Lambda }{3}}$ is constant, to obtain \n\\begin{equation}\n\\frac{v^{2}}{R}=\\frac{G_{N}m}{R^{2}}-\\frac{\\Lambda }{3}R.\n\\label{bandesitter}\n\\end{equation}\nfor an object in orbit around a central mass $m$. One might note that the\nsame result may be obtained by starting with the static form of the de\nSitter metric, i.e. \n\\[\nds^{2}=\\left( 1-\\frac{2G_{N}m}{r}-\\frac{\\Lambda }{3}r^{2}\\right) dt^{2}-%\n\\frac{dr^{2}}{\\left(1-\\frac{2G_{N}m}{r}-\\frac{\\Lambda }{3}r^{2}\\right)}-r^{2}d\\Omega ^{2},\n\\]\nand using a Newtonian analysis. This form of the metric is related to the\ncosmological form through a coordinate transformation. Equation (\\ref\n{bandesitter}) shows that for large enough $R,$ i.e. \n\\[\nR>\\left( \\frac{3G_{N}m}{\\Lambda }\\right) ^{1/3},\n\\]\nthere are no longer bound orbits. Does this have observable consequences?\nUnfortunately it is easy to see that the effect becomes important only for\norbits that are such that they have periods of the order of the age of the\nuniverse. Furthermore, the effect of the cosmological constant decreases\nrapidly for smaller orbits. Hence the concept of a rotation curve loses its\nmeaning and we had better look elsewhere for a better approach to the\npossible effect of a cosmological constant. One possibility is the way\nclusters and superclusters of galaxies form.\n\nAs a first step, one may consider the infall of matter onto a galaxy cluster\nin the regime where linear perturbation theory is valid. This has in fact\nbeen treated by Peebles \\cite{jim}, in the case $\\Omega_M+\\Omega_\\Lambda=1$\n(i.e. zero curvature) which is the natural case in view of inflation, and\nwhich, incidentally, is now also indicated by the recent balloon\nmeasurements of the cosmic microwave background \\cite{boomerang}. Peebles\nshowed that, unfortunately, the dependence of the infall peculiar velocity $%\nv $ for a cluster of proper radius $R$ and overdensity $\\delta$ on $%\n\\Omega_\\Lambda$ is quite weak, being well parametrized by \n\\begin{equation}\nv=0.3H_0R\\delta\\Omega_M^{0.6}\n\\end{equation}\nfor $0.03 < \\Omega_M < 0.3$ and $1< \\delta < 3$, essentially independent of $%\n\\Omega_\\Lambda$. This formula was generalized to arbitrary \n$\\Omega_M+\\Omega_\\Lambda$ in \\cite{lahav}.\n\nIn the non-linear, collapsing phase, we may obtain an estimate of the\ninfluence of $\\Lambda$ by adapting the simple constant density, spherical\ncollapse model \\cite{kolbturner} to the situation when the cosmological\nconstant is present. We thus look at the situation when an overdense region\nexpands to a maximal radius $R_{\\mathrm{max}}$, and then contracts to a\nviral radius $R_{\\mathrm{vir}}$.\n\nTo analyse this situation, we use the equation for the energy per unit mass (%\n\\emph{cf.} \\cite{jim}, Eq.~(20) or our equation (\\ref{bandesitter})) of a\nmass shell of proper radius $R(t)$ containing a fixed mass $m$: \n\\begin{equation}\nE={\\frac{\\dot{R}^{2}}{2}}-{\\frac{G_{N}m}{R}}-{\\frac{\\Lambda R^{2}}{6}},\n\\end{equation}\nwhere the three terms correspond to the kinetic energy, Newtonian\ngravitational energy, and vacuum energy, respectively. As in the standard\nanalysis \\cite{kolbturner}, we may employ the virial theorem relating the\naverage value of the kinetic energy $T$ to the potential energy $V$ \n\\begin{equation}\n\\langle 2T\\rangle =\\langle \\vec{r}\\cdot {\\frac{\\partial V}{\\partial \\vec{r}}}%\n\\rangle .\n\\end{equation}\n\nTaking the average over a sphere of constant density of the energy equation\n(at the turn-around radius $R_{\\mathrm{max}}$ the kinetic energy is zero) \n\\begin{equation}\nE=T_{\\mathrm{vir}}+V^G_{\\mathrm{vir}}+V^\\Lambda_{\\mathrm{vir}}=V^G_{\\mathrm{%\nmax}}+V^\\Lambda_{\\mathrm{max}},\n\\end{equation}\nutilizing \n\\begin{equation}\n{\\langle \\Lambda r^2 \\rangle}= {\\frac{3\\Lambda}{R^3}}\\int_0^R r^{4}dr= {%\n\\frac{3R^2}{5}}\n\\end{equation}\nand \n\\begin{equation}\n{\\langle G_NM(r)r^{-1} \\rangle} = {\\frac{3G_NM}{R^6}}\\int_0^R r^{4}dr= {%\n\\frac{3G_NM}{5 R}}\n\\end{equation}\nwe recover in the case $\\Lambda=0$ the well-known result \\cite{kolbturner} \n\\begin{equation}\n{\\frac{3G_NM}{5 R_{\\mathrm{max}}}}={\\frac{3G_NM}{10 R_{\\mathrm{vir}}}},\n\\end{equation}\ni.e., $R_{\\mathrm{vir}}=R_{\\mathrm{max}}/2$. For a non-vanishing $\\Lambda$,\nthe corresponding equation is \n\\begin{equation}\n{\\frac{3G_NM}{5 R_{\\mathrm{max}}}}+{\\frac{\\Lambda}{10}}R^2_{\\mathrm{max}}= {%\n\\frac{3G_NM}{10 R_{\\mathrm{vir}}}}+{\\frac{\\Lambda}{5}}R^2_{\\mathrm{vir}}.\n\\label{eq:virial}\n\\end{equation}\n\nSuppose that the mass overdensity contrast compared to the cosmological\naverage mass density at the maximal (turn-around) radius is $\\omega$ ($=5.6$\nin the standard case), and assume $\\Omega_M+\\Omega_\\Lambda=1$. Then we can\nwrite $M=4\\pi R_{\\rm max}^3\\omega\\rho_M/3$, and this inserted into (\\ref\n{eq:virial}) gives, by use of (\\ref{eq:rhol}) \n\\begin{equation}\n1+\\kappa={\\frac{1}{2\\mu}}+2\\kappa\\mu^2 \\label{eq:simple}\n\\end{equation}\nwhere we have introduced $\\mu= R_{\\mathrm{vir}}/R_{\\mathrm{max}}$ ($=0.5$ in\nthe standard case) and \n\\[\n\\kappa={\\frac{1}{\\omega}}{\\frac{\\Omega_\\Lambda}{(1-\\Omega_\\Lambda)(1+z)^3}}. \n\\]\nThis result is written in a somewhat different form than, but agrees with,\nEq.~(26) of \\cite{lahav}.\nIf we assume as a first approximation $\\omega=5.6$ as in the $\\Lambda=0$\ncase, and $\\Omega_\\Lambda=0.7$, we find by solving (\\ref{eq:simple})\nnumerically for $z=0$ that $\\mu$ has decreased from 0.5 to around 0.39.\n\nThis means that the virialized radius is smaller, which is not unreasonable,\nsince for a given mass, only more compact clusters can ``survive'' the \nrepulsive force from a\npositive cosmological constant.\n\nWe can improve this analysis somewhat by taking into account the fact that $%\n\\omega $ also depends on $\\Lambda $. It can be seen that this has the effect\nof increasing $\\omega $ at intermediate redshifts. This increase causes an\nincrease in $\\mu $, meaning that we have overestimated the effect of $%\n\\Lambda $ above. The effect is, however, small. One can also estimate what\nthe final density contrast of the cluster will be. To do this we have\nobtained an expression comparing the density at maximum expansion with the\ndensity of the universe today. This is given by \n\\begin{equation}\n\\widetilde{\\omega }={\\frac{9\\pi ^{2}}{16}}{\\frac{1}{f(a)^{2}}}{\\frac{1}{%\n(1-\\Omega _{\\Lambda })}}\n\\end{equation}\nwith \n\\begin{equation}\nf(a)={\\frac{3}{2}}\\int_{0}^{a}{\\frac{da}{\\sqrt{(1-\\Omega _{\\Lambda\n})/a+\\Omega _{\\Lambda }a^{2}}}}.\n\\end{equation}\nThe result is a further net relative compression of the clusters \ndue to the cosmological constant above the\none given by $\\mu $.\n\nSince we have been dealing with an imagined situation where one can compare\nbetween a ``standard'' scenario without a cosmological constant, and one\nwhere $\\Lambda \\neq 0$, and found only small effects on cluster scales, it\nseems difficult, but maybe not excluded, to draw conclusions about the value\nof $\\Omega _{\\Lambda }$ in the real universe where observational\nuncertainties have to be taken into account. The effect to search for, is a\ntendency for virialized clusters to get smaller and more overdense for a\npositive $\\Lambda $.\n\nIt seems clear, however, that the effects on galactic scales are extremely\ntiny and negligible for rotation curves.\n\n\\vskip .2cm \n\\begin{flushleft}\n{\\bf\\large Acknowledgements}\n\\vskip .2cm\nWe wish to thank H. Rubinstein for discussions, and P. Lilje and\nM. Rees for informing us about reference \\cite{lahav}. This work\nwas supported in part by the Swedish Natural Science Research Council\n(NFR).\n\\end{flushleft}\n\n\\bigskip\n\n\\bigskip\n\n\\begin{thebibliography}{9}\n\\bibitem{ariel} S. Perlmutter et al., Astrophys. J. \\textbf{517} (1999) 565.\n\n\\bibitem{kirshner2} P.M. Garnavich et al., Astrophys. J. \\textbf{509}\n(1998) 74.\n\n\\bibitem{triangle} N.~Bahcall, J.P.~Ostriker, S.~Perlmutter and\nP.J.~Steinhardt, Science {\\bf 284}, 1481 (1999).\n\n\\bibitem{BGbook} L. Bergstr\\\"om and A. Goobar, \\emph{Cosmology and Particle\nAstrophysics}, Wiley/Praxis (Chichester), 1999.\n\n\\bibitem{kraniotis} S.B. Whitehouse and G.V. Kraniotis, astro-ph/9911485\n(1999).\n\n\\bibitem{jim} P.J.E. Peebles, Astrophys. J. \\textbf{284} (1984) 439.\n\n\\bibitem{boomerang} P.D. Mauskopf et al., astro-ph/9911444 (1999).\n\n\\bibitem{lahav} O. Lahav, P.B. Lilje, J.R. Primack and M.J. Rees,\nMonth. Not. Roy. Astr. Soc. {\\bf 251} (1991) 128.\n\n\\bibitem{kolbturner} E.W. Kolb and M.S. Turner, \\emph{The Early Universe},\nAddison-Wesley Publishing Co., 1990.\n\\end{thebibliography}\n\n\\end{document}\n\n"
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"name": "astro-ph0002152.extracted_bib",
"string": "\\begin{thebibliography}{9}\n\\bibitem{ariel} S. Perlmutter et al., Astrophys. J. \\textbf{517} (1999) 565.\n\n\\bibitem{kirshner2} P.M. Garnavich et al., Astrophys. J. \\textbf{509}\n(1998) 74.\n\n\\bibitem{triangle} N.~Bahcall, J.P.~Ostriker, S.~Perlmutter and\nP.J.~Steinhardt, Science {\\bf 284}, 1481 (1999).\n\n\\bibitem{BGbook} L. Bergstr\\\"om and A. Goobar, \\emph{Cosmology and Particle\nAstrophysics}, Wiley/Praxis (Chichester), 1999.\n\n\\bibitem{kraniotis} S.B. Whitehouse and G.V. Kraniotis, astro-ph/9911485\n(1999).\n\n\\bibitem{jim} P.J.E. Peebles, Astrophys. J. \\textbf{284} (1984) 439.\n\n\\bibitem{boomerang} P.D. Mauskopf et al., astro-ph/9911444 (1999).\n\n\\bibitem{lahav} O. Lahav, P.B. Lilje, J.R. Primack and M.J. Rees,\nMonth. Not. Roy. Astr. Soc. {\\bf 251} (1991) 128.\n\n\\bibitem{kolbturner} E.W. Kolb and M.S. Turner, \\emph{The Early Universe},\nAddison-Wesley Publishing Co., 1990.\n\\end{thebibliography}"
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astro-ph0002153
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Can we predict the fate of the Universe?
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We re-analyze the question of the use of cosmological observations to infer the present state and future evolution of our patch of the universe. In particular, we discuss under which conditions one might be able to infer that our patch will enter an inflationary stage, as a {\em prima facie} interpretation of the Type Ia supernovae and CMB data would suggest. We then establish a `physical' criterion for the existence of inflation, to be contrasted with the more `mathematical' one recently proposed by Starkman {\em et al.} \cite{STV}.
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"name": "future.tex",
"string": "%\\documentstyle[preprint,prd,aps]{revtex}\n\\documentstyle[prd,aps,a4]{revtex}\n\\input epsf\n\n\\newcommand\\lsim{\\mathrel{\\rlap{\\lower4pt\\hbox{\\hskip1pt$\\sim$}}\n \\raise1pt\\hbox{$<$}}}\n\\newcommand\\gsim{\\mathrel{\\rlap{\\lower4pt\\hbox{\\hskip1pt$\\sim$}}\n \\raise1pt\\hbox{$>$}}}\n\\newcommand\\esim{\\mathrel{\\rlap{\\raise2pt\\hbox{\\hskip0pt$\\sim$}}\n \\lower1pt\\hbox{$-$}}}\n\n\\begin{document}\n\\title{Can we predict the fate of the Universe?}\n\n\\author{P. P. Avelino${}^{1,2}$\\thanks{\nElectronic address: pedro\\,@\\,astro.up.pt},\nJ.\\ P.\\ M.\\ de Carvalho${}^{1,3}$\\thanks{\nElectronic address: mauricio\\,@\\,astro.up.pt}\nand C. J. A. P. Martins${}^{4}$\\thanks{Also at C.A.U.P.,\nRua das Estrelas s/n, 4150 Porto, Portugal.\nElectronic address: C.J.A.P.Martins\\,@\\,damtp.cam.ac.uk}}\n\n\\address{${}^1$ Centro de Astrof\\'{\\i}sica, Universidade do Porto\\\\\nRua das Estrelas s/n, 4150 Porto, Portugal}\n\n\\address{${}^2$ Dep. de F\\'{\\i}sica da Faculdade de Ci\\^encias da Univ. do Porto,\\\\\nRua do Campo Alegre 687, 4169-007 Porto, Portugal}\n\n\\address{${}^3$Dep.\\ de Matem\\'atica Aplicada da Faculdade de Ci\\^encias da Univ.\\ do Porto,\\\\\nRua das Taipas 135, 4050 Porto, Portugal}\n\n\\address{${}^4$ Department of Applied Mathematics and Theoretical Physics\\\\\nCentre for Mathematical Sciences, University of Cambridge\\\\\nWilberforce Road, Cambridge CB3 0WA, U.K.}\n\n\\maketitle\n\\begin{abstract}\nWe re-analyze the question of the use of cosmological observations\nto infer the present state and future\nevolution of our patch of the universe. In particular,\nwe discuss under which conditions one might be able to infer that our\npatch will enter an inflationary stage, as a {\\em prima facie}\ninterpretation of the Type Ia supernovae and CMB data would suggest.\nWe then establish a `physical' criterion for the existence of inflation, to be\ncontrasted with the more `mathematical' one recently proposed by Starkman\n{\\em et al.} \\cite{STV}.\n\\end{abstract}\n\\pacs{98.80.Es, 98.80.Cq, 98.62.Py\\\\\nKeywords: Gravitation; Cosmology; Inflation; Observational Tests}\n\n\\section{\\bf Introduction}\n\\label{intro}\nThe issue of the present state,\nfuture dynamics and final fate of the Universe, or at least our patch\nof it, has been\nrecently pushed to the front line of research in cosmology. This is mostly\ndue to observations of high redshift type Ia supernovae, performed by\ntwo independent groups (the\n``Supernova Cosmology Project'' and the ``High-Z Supernova Team''), which\nallowed accurate measurements of the luminosity-redshift relation out to\nredshifts up to about $z \\sim 1$ \\cite{Perlmu,Riess1,Garnavich}.\nIt should be kept in mind that these\nmeasurements are done on the assumption that these\nsupernovae are standard candles, which is by no means demonstrated and\ncould conceivably be wrong.\nThere are concerns about the evolution of these objects\nand the possible dimming caused by intergalactic dust \\cite{Drell,Riess2}, but\nwe will ignore these for the purposes of this paper, and assume that the\nquoted results are correct.\n\nThe supernovae data, when combined with the ever growing\nset of CMBR anisotropy observations,\nstrongly suggest an accelerated expansion of the Universe\nat the present epoch, with cosmological parameters\n$\\Omega_\\Lambda \\sim 0.7$ and $\\Omega_{\\rm m} \\sim 0.3$. A further cause of\nconcern here is the model dependence of the CMBR\nanalysis, but we shall again accept the above results for the\npurpose of this paper.\n\nTaken at face value, these results would seem to show that the universe \nwill necessarily enter an inflationary stage in the near future. \nHowever, as pointed out by Starkman, Trodden and\nVachaspati \\cite{STV} this is not necessarily so. We could be living in a\nsmall, sub-horizon bubble, for example. And even if we were indeed inflating,\nit would not be trivial to demonstrate it. \nIn the above work, these authors looked\nat the crucial question of `How far out must we look to infer that\nthe patch of the\nuniverse in which we are living is inflating?' Their analysis is based on\nprevious work by Vachaspati and Trodden \\cite{VT} which shows that the onset of\ninflation can in some sense be identified with the comoving contraction of\nour minimal anti-trapped surface (MAS)\\footnote{The MAS of each comoving\nobserver is a sphere centered on him/her, on which the velocity of comoving\nobjects is $c$. For the particular case of an homogeneous universe, the MAS\nhas a physical radius $cH^{-1}$.}.\nThey then argue that if one can confirm cosmic acceleration\nup to a redshift $z_{MAS}$ and detect the contraction of our MAS, then our\nuniverse must be inflating. Unfortunately, even if we can do the former (for\n$\\Omega_\\Lambda=0.8$ the required redshift is $z_{MAS}\\sim1.8$), it turns\nout that there is no way to presently\nconfirm the latter, because the accelerated\nexpansion hasn't been going for long enough for the MAS to contract. Only if\nwe had $\\Omega_\\Lambda\\ge0.96$ would we be able to demonstrate inflation\ntoday.\n\nAs in the proverbial mathematicians joke, the method outlined by Starkman\n{\\em et al.} provides an answer that is completely accurate but will take a\nlong time to find, and hence is of no immediate use to us. In this paper, \nhowever, we will explore a different possibility.\nOur main aim is to provide what could be called a physicists\nversion of the ``mathematical'' question of Starkman {\\em et al.} \\cite{STV}.\nIn other words, we are asking, {\\em `If we can't know for sure\nthe fate of the universe at\npresent, what is our best guess today?'}. As we will discuss, we can answer\nthis question, although it will involve making\nsome crucial additional assumptions.\n\nIn order to answer the above question we compare the particle and event\nhorizons. We show that for a flat universe with $\\Omega_\\Lambda \\gsim 0.14$\nthe particle horizon is greater than the distance to the \nevent horizon meaning that today\nwe may be able to observe a larger portion of the Universe than that which\nwill ever be able to influence us. We argue that if we find evidence for\na constant vacuum density up to a distance from us equal to the event\nhorizon then our Universe will necessarily enter an inflationary phase\nin the not too distante future, {\\em assuming} that the potential \nof the scalar field which\ndrives inflation is time-independent and that the content of the\nobservable universe will remain `frozen' in comoving coordinates.\n\nNote that Starkman {\\em et al.}\nargue that inflation can only take place if the vacuum energy dominates\nthe energy density on a region with physical radius not smaller than\nthat of the MAS at that time. However, they did not assume that the \ncontent of the observable universe would remain frozen in comoving\ncoordinates and so they found that the larger is the contribution of a\ncosmological constant for the total density of the Universe, the\nlarger is the redshift out to which one has to look in order to infer\nthat our portion of the universe is inflating.\nThis result seems paradoxical, until one realizes that the size of the MAS\nat a given time {\\em does not}, by itself, say anything about inflation.\nThe main reason why $z_{MAS}$ grows with $\\Omega_\\Lambda$ is\nsimply because the scale factor has grown more.\n\nThe plan of this paper is as follows. In the next section we introduce the\nvarious lengthscales that are relevant to our discussion, and\nprovide a qualitative discussion of our\ntest for inflation. We also discuss the assumptions involved and compare our\n`physical' test with the `mathematical' one recently proposed by\nStarkman {\\em et al.} \\cite{STV}. In section \\ref{biaf} we provide a more\nquantitave analysis of our criterion. We also discuss in more detail our \ncrucial assumption of an energy-momentum distribution which remains \nfrozen in comoving coordinates. Finally, in section \\ref{conc} we \nsummarize our results and discuss some other outstanding issues.\n\n\\section{A `physical' test for inflation}\n\\label{horizon}\nThe dynamical equation which describes the evolution of the scale factor\n$a$ in a Friedmann-Robertson-Walker (FRW) universe containing matter, \nradiation and a cosmological constant can be written as\n\\begin{equation}\n H^2=H_0^2(\\Omega_{m0} a^{-3} + \\Omega_{r0} a^{-4} +\n\\Omega_{\\Lambda0} + \\Omega_{k0} a^{-2}).\n\\label{one}\n\\end{equation}\nwhere $H={\\dot a / a}$ and the density parameters $\\Omega_m$, $\\Omega_r$ and\n$\\Omega_\\Lambda$ express respectively the densities in matter, radiation and\ncosmological constant as fractions of the critical density\\footnote{A dot\nrepresents a derivative with respect to the cosmic time $t$. The\nsubscript `$0$' means that the quantities are to be evaluated at\npresent epoch, and we have also taken $a_0=1$.}.\nNaturally one has $\\Omega_k = 1 - \\Omega_m-\\Omega_r-\\Omega_\\Lambda$.\n\nThe distance $d$, to a comoving observer at a redshift $z$ is\ngiven by\n\\begin{equation}\n d(z)= c \\int_{t(z)}^{t_0} {{d t'} \\over a(t')} = c H_0^{-1}\n\\int_0^z {{dz'} \\over { \\left[ \\Omega_{m0} (1+z')^3 + \\Omega_{r0} (1+z')^4 +\n\\Omega_{\\Lambda0} + \\Omega_{k0} (1+z')^{2}\n\\right]^{1/2}}} \\, ,\n\\label{two}\n\\end{equation}\nand is related to the `radius' of the local universe which we can in\nprinciple observe today. The distance to the \n{\\em event horizon} can be defined as\n\\begin{equation}\n d_e= c \\int_{t_0}^\\infty {{d t'} \\over a(t')} = c H_0^{-1}\n\\int_1^\\infty {{da} \\over { (\\Omega_{m0} a + \\Omega_{r0} + \n\\Omega_{\\Lambda0} a^4 + \\Omega_{k0} a^{2})^{1/2}}}.\n\\label{three}\n\\end{equation}\nand represents the portion of the Universe which will ever be able to\ninfluence us\\footnote{In writing the upper integration limit as infinity we are\nof course assuming that the universe will keep expanding forever; an\nanalogous formal definition could be given for an universe ending in a\n`big crunch'.}. On the other hand,\nthe {\\em particle horizon}, $d_p$, is defined by (from eqn. (\\ref{two}))\n\\begin{equation}\nd_p\\equiv \\lim_{z \\to \\infty} d(z)\\, ,\n\\label{five}\n\\end{equation}\nand it represents the maximum distance which we can observe today.\n\nIf today the distance to the event horizon is smaller than \nthe particle horizon ($d_e <\nd_p$) this means that today we are able to observe a larger portion of\nthe Universe than that which will ever be able to influence us.\nWe can do this if we look at a redshift greater than $z_*$ defined by\n(see also \\cite{staro})\n\\begin{equation}\nd(z_*)=d_e\\, .\n\\label{four}\n\\end{equation}\nIn a flat universe solutions to this equation are only\npossible for $z_* \\ge 1$ and for $\\Omega_{\\Lambda0} \\gsim 0.14$.\nHence, assuming that the energy-momentum distribution within the \npatch of the Universe which we are able to see remains unchanged \nin comoving coordinates, our Universe will\nnecessarily enter an inflationary phase in the future if there is a\nuniform vacuum density permeating the Universe up to a redshift\n$z_*$.\n\nThis assumption obviously requires\nsome further discussion. One can certainly think of a\nuniverse made up of different `domains', each with its own values of\nthe matter and vacuum energy\ndensity. Furthermore, by cleverly choosing the field dynamics, one can\nalways get patches with time-varying vacuum energy densities, or patches\nwhere the vacuum energy density is non-zero for only short periods.\nIn all such cases, the domain walls separating these\npatches can certainly have a very complicated dynamics, and in\nparticular it is always\npossible that a domain wall will suddenly get inside our horizon sometime\nbetween the epoch corresponding to our observations and the present day.\nOn the other hand, it should also be pointed out that a certain amount of\nfine-tuning would be required to have a bubble coming inside our horizon \nright after we have last observed it.\nIn these circumstances, the best that can be done is to impose constraints\non the characteristics of any bubble wall that could plausibly have entered\nthe patch of the universe we are currently able to observe, given that we\nhave so far seen none. We shall analyse this point in a more quantitative\nmanner in the following section.\n\nWe think that the results obtained in this way, even if less robust from\na formal point of view, are intuitively more meaningful than\nthose obtained in \\cite{STV} in the sense that, among other things,\nin this case the minimum \nredshift $z_*$ out to which one must observe in order to be able to\npredict an inflationary phase (subject to the conditions mentioned earlier)\ndecreases as $\\Omega_\\Lambda$ increases---see Fig. \\ref{fig1}. In other\nwords, the larger the present value of the cosmological constant, the easier\nit should be to notice it.\n\nIt is perhaps instructive to compare our test with that of \\cite{STV}\nin more detail. Starkman {\\em et al.} require\nthe contraction of the MAS. Now, in order to see the MAS one\nhas to look at a redshift defined by:\n\\begin{equation}\na(z_{MAS})d(z_{MAS}) - c H^{-1}(z_{MAS})=0\\, .\n\\label{six}\n\\end{equation}\nThis finds the redshift, $z_{MAS}$, for which the physical distance to a\ncomoving observer at that redshift, evaluated at\nthe corresponding time $t_{MAS}$, is equal to the Hubble radius at that time.\nHowever, if the vacuum density already dominates\nthe dynamics of the Universe at the redshift $z_*$ then eqn.\n(\\ref{four}) reduces to:\n\\begin{equation}\nd(z_*) - c H^{-1}(z_*)=0.\n\\label{seven}\n\\end{equation}\n(recall that $a_0=1$)\nbecause during inflation the physical size of the event horizon is \nsimply equal\\footnote{This is only exactly true when the vacuum energy\ndensity is the only contributor to the energy density, in which case\nexponential inflation occurs.}\nto $cH^{-1}$ (this is ultimately the reason for the choice of \ncriterium for inflation by Vachaspati and Trodden \\cite{VT}). \nAs has been discussed above, eqns. (\\ref{six}) and (\\ref{seven}) \nhave totally different solutions ($z_*=1$ while $z_{MAS} \\to \\infty$).\n\nTo put it in another way,\nthe main difference between our approach and that of\nref.\\cite{STV} lies on the fact that we assume that the energy-momentum\ncontent of the observable Universe does not change\nsignificatively in comoving coordinates. This allows us to use the \nequation of state of the local universe\nobserved for a redshift $z$ (looking back at a physical time $t(z)$) \nto infer the equation of state of the local universe at the present time.\nIn the following section, we shall discuss these points in somewhat\nmore detail.\n\nWe should also point out that if we were to relax the assumption of a\nco-movingly frozen content of the observable universe, then the\nequation---analogous to (\\ref{four})---specifying the redshift out to which\none should look in order to be able to predict the future of the Universe\nwould be\n\\begin{equation}\nd(z_+)=d_e(z_+)\\, .\n\\label{fourtwo}\n\\end{equation}\nThis equation has no solution, so a stronger test of this kind is not feasible\nin practice.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{\\bf Discussion}\n\\label{biaf}\n\nHere we go through some specific aspects of our test in more\nquantitative detail. To begin with, we\nhave solved numerically eqn. (\\ref{four});\nthe numerical results were obtained for choices of cosmological\nparameters such that $\\Omega_m+\\Omega_\\Lambda=0.7, 1.0, 1.3$,\nwith an additional $\\Omega_m=0.3$ for illustration.\nWe are interested only in a matter--dominated or $\\Lambda-$dominated\nepoch of the evolution of the universe, and therefore we have dropped the\nradiation density parameter $\\Omega^{\\rm r}_0$ of eqn. (\\ref{one}), in the\ncalculations.\n\nThese results are displayed in Fig. \\ref{fig1} as a function of\n$\\Omega_{\\Lambda0}$. The cases with constant total density\nare shown in solid curves (with the top curve corresponding to the higher\nvalue of the density), while the case of a fixed $\\Omega_{\\rm m}$,\nis shown, for comparison purposes, by a dotted curve.\n\nAs expected, as the universe becomes more $\\Lambda-$dominated and/or\nless matter--dominated, the comoving distance to the event\nhorizon decreases, which is reflected in the decrease of the redshift\n$z_*$ of a comoving source located at that distance\\footnote{Note that\npushing $\\Omega_{\\Lambda0}$ down to zero, the value of $z_*$ tends\nto infinity, since in such universes an event horizon does not exist.}.\nFor the observationally preferred values of $\\Omega_m=0.3$\nand $\\Omega_\\Lambda=0.7$, the required redshift will be $z_*\\sim 1.8$.\n\nFor comparison, the redshift, $z_{MAS}$, defined by eqn. (\\ref{six}), \nwhich is the analogous relevant quantity\nfor the criterion of Starkman {\\em et al.} is shown, for the same choices\nof cosmological parameters, in Fig. \\ref{fig2}. Note that in this case,\nas the universe becomes more $\\Lambda-$dominated and/or\nless matter--dominated, the redshift of the MAS will increase.\nAs we already pointed out our test will not be applicable for very low\nvalues of the vacuum energy density, and for intermediate values,\nit requires a higher redshift than $z_{MAS}$.\nHowever, for high values of the cosmological constant and/or low\nmatter contents, the fact that the universe will be expanding much faster\nmakes the redshift of the MAS increase significantly, and even become\nlarger than $z_*$ for some combinations of cosmological parameters.\nFor the same observationally preferred values of $\\Omega_m$\nand $\\Omega_\\Lambda$ quoted above,\nthe required redshift will be $z_{MAS}\\sim 1.6$. A comparison of the\nvalues of $z_*$ and $z_{MAS}$ for the spatially flat model is shown in\nFig. \\ref{FNEW}.\n \nWe now return to our assumption about the \nenergy-momentum content of the universe, considering the possibility that\ndifferent regions of space may have \ndifferent values for the vacuum energy density, which are\nseparated by domain walls. This means that we are assuming the\nexistence of a scalar field, say $\\phi$, which within each region\nsits in one of a number of possible minima of a \ntime-independent potential. It is obvious that if the potential \ndepends on time or if the scalar field did not have time to roll to\nthe minimum of the potential, then it is not possible to predict the fate of\nthe universe without knowing more about the particle physics model which\ndetermines its dynamics. For simplicity, we shall assume\nthat we live in a spherical domain with constant vacuum energy density \n(effectively a cosmological constant) that is\nsurrounded by a much larger region in \nwhich the the vacuum density has a different value---for the present \npurposes we will assume it to be zero. Note that this is the case where\nthe dynamics of the wall will be faster (more on this below). \n\nIs it possible that a region \nwith a radius $d(z)$, say centred on a nearby observer,\ncan be inside a given domain at the conformal time $\\eta(z)$,\nbut outside that domain at the present time, $\\eta_0$? This\nproblem can provide some measure of how good the assumption of \na frozen energy-momentum distribution in comoving coordinates is. \nIn other words, is it likely that a domain \nwall may have entered this region at a redshift smaller than $z$?\nIn order to provide a more quantitative answer to this question,\nwe have performed numerical simulations of domain wall evolution using\nthe PRS \\cite{PRS} algorithm, in which the thickness of the domain walls\nremains fixed in comoving coordinates for numerical convenience.\nSee also \\cite{AM} for a description of the simulations.\n\nWe assume that the domain wall has spherical symmetry, thereby\nreducing a three-dimensional problem to a one-dimensional \none. We perform simulations of this wall in a flat universe on a\none-dimensional $8192$ grid. The comoving grid spacing is $\\Delta x=c \\eta_i$\nwhere $\\eta_i=1$ is the conformal time at the beginning of the simulation. \nThe initial comoving radius of the spherical domain was chosen to\nbe $R=2048 \\Delta x$, and the comoving thickness of \nthe domain wall was set to be $10 \\Delta x$. In these simulations \nwe neglect the gravitational effect induced by the different domains and\ndomain walls on \nthe dynamics of the universe, and we also do not consider the possibility of\nan open universe. We must emphasise, however, that both these effects would\nslow down the defects, thereby helping to justify our assumption of a constant\nequation of state in comoving coordinates even more.\n\nWe have obtained the following \nfit for the radius of the domain wall as a function of the conformal \ntime $\\eta$\n\\begin{equation}\nR(\\eta)=R_\\infty\\left(1-\\left({{c \\eta} \\over {\\alpha R_\\infty}}\\right)^n\\right)^{2/n}\\, ,\n\\label{fit1}\n\\end{equation}\nwhere\n\\begin{equation}\n\\alpha=2.5\\, , \\qquad n=2.1\\,\n\\label{powers}\n\\end{equation}\nand $R_\\infty$ is the initial comoving radius of the domain wall \n(with $R_\\infty \\gg c \\eta_i$). \nThis fit is accurate to better than $5 \\%$, except for the final stages of collapse.\nIn a flat universe with no cosmological constant\nthe comoving distance to a comoving object at a redshift $z$ is given by\n\\begin{equation}\nd(z)=c \\eta_0\\left(1-1/\\sqrt{1+z}\\right)\\, ,\n\\label{reldz}\n\\end{equation}\nwhereas the radius of the spherical domain wall can be written as\na function of the redshift $z$, given its initial radius $R_\\infty$,\nas follows\n\\begin{equation}\nR(z)=R_\\infty\\left(1-\\left({{c \\eta_0} \\over {\\alpha R_\\infty \\sqrt{1+z} }}\\right)^n\\right)^{2/n}\\, .\n\\label{reldz2}\n\\end{equation}\n\nNow, by solving the equation\n\\begin{equation}\nR(z=0)=d(z)\\, \n\\label{tosolve}\n\\end{equation}\nwe can find the initial comoving radius of our domain\n(in units of the present conformal time, that is $R_i(z)/{\\eta_0}$)\nwhich it would be required to have so that its comoving size today is\nequal to the comoving distance to an object at a redshift $z$.\nFinally, we can calculate the radius of this domain at the present time \n$\\eta_0$ and at the redshift $z$ (call it $R_{\\rm max}(z)$)\nwith the value of $R_i(z)/\\eta_0$ obtained from the previous equation.\nIn Fig. \\ref{fig3} we plot the value of $R_{\\rm max}(z) / d(z)$ as a function \nof the redshift, $z$.\n\nIf the radius of our domain at a redshift $z$ was smaller than $d(z)$ the\ndomain wall would be in causal contact with us at the present time and we\ncould in principle detect the gravitational effect both of the domain wall and\nof the different vacuum density outside our bubble.\nOn the other hand, if the radius of our domain at a redshift $z$ was greater\nthan $R_{max}$ then it would not have time to enter the sphere of radius\n$d(z)$ before today. \n\nWhen the redshift of the cosmological object we\nare looking at is small, that is ($z \\to 0$), its comoving distance from us,\n$d(z)$, is much smaller than the comoving horizon, $\\eta(z)$,\nat the time at which the light was emitted. Consequently, a domain \nwall with a comoving size equal to $d(z)$ at the present time would already\nhave a velocity very close to the speed of light by the redshift $z$.\nIt is easy to calculate the maximum comoving \nsize, $R_{max}$, which our domain would need to have at the redshift $z$,\nin order for the domain wall to enter a sphere of\ncomoving radius $d(z)$ centred on a nearby observer\nsometime between today and redshift $z$.\nThis is simply given by\n\\begin{equation}\n\\frac{R_{max}(z)}{d(z)}\\longrightarrow 2\\, \n\\label{assimp00}\n\\end{equation}\nwhen $z \\to 0$, because \n$d(z)$ is the distance travelled by light from a redshift $z$ until today \n(see fig. \\ref{fig3}).\n\nIf we assume that the comoving radius of our bubble at a redshift $z$ is\nlarger than $\\eta(z)$, \nthen it will remain frozen in comoving coordinates until its size gets smaller\nthan the horizon. This means that in this case the value\nof $R_{max} / d(z)$ is even smaller, approaching \n\\begin{equation}\n\\frac{R_{max}(z)}{d(z)}\\longrightarrow\\frac{\\alpha^{-2} \\times ({\\sqrt {1+4\\alpha^{-n}}}-1)^{-2/n}}{2^{-2/n}}, \n\\label{assimp}\n\\end{equation}\nwhen $z \\to \\infty$ (see fig. \\ref{fig3}). For a spherical domain we have\n\\begin{equation}\n\\frac{R_{max}(z)}{d_\\infty} \\approx 1.12\\, . \n\\label{assimpsph}\n\\end{equation}\n\nWe thus see that for the purposes of predicting the fate of the universe it\nmay be a plausible assumption to assume a fixed content \nin comoving coordinates. The above discussion also suggests, in\nparticular, that one may find {\\em a posteriori} that it is\nindeed a reasonable assumption if we can observe the dynamical effects of\na uniform vacuum density up to a redshift $z \\ge 1$.\n\n\\section{\\bf Conclusions}\n\\label{conc}\nWe have provided a simple analysis of the use of cosmological observations\nto infer the state and fate of our patch of the universe. In particular,\nin the same spirit of Starkman {\\em et al. } \\cite{STV}, we have discussed\npossible criteria for inferring the present or future existence of an\ninflationary epoch in our patch of the universe.\n\nWe have presented a `physical' criterion for the existence of inflation,\nand contrasted it with the `mathematical' one that has been introduced\nin \\cite{STV}. Ours has the advantage of being able to provide (in principle)\na definite answer at the present epoch, but the disadvantage of\nultimately relying on assumptions on the content of the local universe and on field dynamics. We consider our\nassumptions to be plausible, but we can certainly conceive of (arguably\ncontrived or fine-tuned) mechanisms that would be capable of violating it.\n\n\n\\acknowledgments\nC. M. is funded by FCT (Portugal) under `Programa PRAXIS XXI' (grant\nno. PRAXIS XXI/BPD/11769/97). We thank Centro de Astrof\\'{\\i}sica da\nUniversidade do Porto (CAUP) for the facilities provided. \n\n\\begin{thebibliography}{99}\n\\bibitem{STV}\nG. Starkman, M. Trodden and T. Vachaspati, {\\em Phys. Rev. Lett. } {\\bf 83}, 1510 (1999).\n\\bibitem{Perlmu}\nS. Perlmutter {\\em et al. }, {\\em Astrophys. J. }, 517, 565 (2000).\n\\bibitem{Riess1}\nA.G. Riess {\\em et al. }, {\\em Astron. J. } {\\bf 116}, 1009 (1998).\n\\bibitem{Garnavich}\nP.M. Garnavich {\\em et al. }, {\\em Ap. J. Lett. } {\\bf 493}, L53 (1998).\n\\bibitem{Drell}\nP.S. Drell, T.J. Loredo and I. Wasserman, , {\\em Ap. J. }, to appear (astro-ph/9905027).\n\\bibitem{Riess2}\nA.G. Riess, A.V. Filippenko, W. Li and B.P. Schmidt, {\\em Astron. J. }, to appear (astro-ph/9907038).\n\\bibitem{VT}\nT. Vachaspati and M. Trodden, {\\em Phys. Rev. } {\\bf D61}, 023502 (2000).\n\\bibitem{staro}\nA.A. Starobinsky, astro-ph/9912054.\n\\bibitem{PRS} \nW.H. Press, B.S. Ryden and D.N. Spergel, {\\it Ap.\\ J.\\ } {\\bf 347}, 590 (1994).\n\\bibitem{AM}\nP.P. Avelino and C.J.A.P: Martins, {\\em Phys. Rev. }{\\bf D62}, 103510 (2000).\n\\end{thebibliography}\n\n\\begin{figure}\n\\vbox{\\centerline{\n\\epsfxsize=0.8\\hsize\\epsfbox{figure1.eps}}\n\\vskip.2in}\n\\caption{The solution of eqn. (\\ref{four}) for cosmologies with $\\Omega_m+\\Omega_\\Lambda=0.7, 1.0, 1.3$ (solid curves, bottom to top)\nand $\\Omega_m=0.3$ for illustration (dotted curve). Observing a uniform\nvacuum energy density up to a redshift $z_*$ will imply that our universe\nwill enter an inflationary phase in the future, subject to the conditions\nspecified in the text.}\n\\label{fig1}\n\\end{figure}\n\n\\begin{figure}\n\\vbox{\\centerline{\n\\epsfxsize=0.8\\hsize\\epsfbox{figure2.eps}}\n\\vskip.2in}\n\\caption{The redshift of the MAS, relevant for the inflationary criterion\nof Starkman {\\em et al.}, for the same cosmological models as\nin Fig. \\ref{fig1}. Note that the solid curves\nfor $\\Omega_m+\\Omega_\\Lambda=0.7, 1.0, 1.3$ now appear in the\ngraph from top to bottom.}\n\\label{fig2}\n\\end{figure}\n\n\\begin{figure}\n\\vbox{\\centerline{\n\\epsfxsize=0.8\\hsize\\epsfbox{figure3.eps}}\n\\vskip.2in}\n\\caption{Comparing the values of the critical redshifts $z_*$ and $z_{MAS}$,\nas a function of the vacuum energy density,\nfor the spatially flat models ($\\Omega_m+\\Omega_\\Lambda=1.0$).}\n\\label{FNEW}\n\\end{figure}\n\n\\begin{figure}\n\\vbox{\\centerline{\n\\epsfxsize=0.8\\hsize\\epsfbox{figure4.eps}}\n\\vskip.2in}\n\\caption{The comoving radius of a domain wall at redshift $z$ whose present\ncomoving size equals the comoving distance to an object at\nredshift $z$---denoted $d(z)$, see (\\ref{reldz})---in units of $d(z)$,\nas a function of redshift.}\n\\label{fig3}\n\\end{figure}\n\n\\end{document}\n\\end\n"
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{
"name": "astro-ph0002153.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{STV}\nG. Starkman, M. Trodden and T. Vachaspati, {\\em Phys. Rev. Lett. } {\\bf 83}, 1510 (1999).\n\\bibitem{Perlmu}\nS. Perlmutter {\\em et al. }, {\\em Astrophys. J. }, 517, 565 (2000).\n\\bibitem{Riess1}\nA.G. Riess {\\em et al. }, {\\em Astron. J. } {\\bf 116}, 1009 (1998).\n\\bibitem{Garnavich}\nP.M. Garnavich {\\em et al. }, {\\em Ap. J. Lett. } {\\bf 493}, L53 (1998).\n\\bibitem{Drell}\nP.S. Drell, T.J. Loredo and I. Wasserman, , {\\em Ap. J. }, to appear (astro-ph/9905027).\n\\bibitem{Riess2}\nA.G. Riess, A.V. Filippenko, W. Li and B.P. Schmidt, {\\em Astron. J. }, to appear (astro-ph/9907038).\n\\bibitem{VT}\nT. Vachaspati and M. Trodden, {\\em Phys. Rev. } {\\bf D61}, 023502 (2000).\n\\bibitem{staro}\nA.A. Starobinsky, astro-ph/9912054.\n\\bibitem{PRS} \nW.H. Press, B.S. Ryden and D.N. Spergel, {\\it Ap.\\ J.\\ } {\\bf 347}, 590 (1994).\n\\bibitem{AM}\nP.P. Avelino and C.J.A.P: Martins, {\\em Phys. Rev. }{\\bf D62}, 103510 (2000).\n\\end{thebibliography}"
}
] |
astro-ph0002154
|
Morphology and kinematics of Planetary Nebulae\\ II. A \diab/ model for NGC~3132
|
[
{
"author": "H. Monteiro\\altaffilmark{1}"
},
{
"author": "C. Morisset\\altaffilmark{1,2}"
},
{
"author": "R. Gruenwald\\altaffilmark{1}"
},
{
"author": "S. M. Viegas\\altaffilmark{1}"
}
] |
We use a 3D photoionization modeling tool to study the morpho-kinematic properties of the Planetary Nebula (PN) NGC~3132. We show that it is possible to reproduce the low resolution observations (spectra and images) with an ellipsoidal shell. However, high resolution observations, as those showing a density variation along the nebula and the \forb{O}{3}{5007} velocity profiles, definitively rule out this description. We show that a bipolar Diabolo shape with a 40\degre/ rotation of the symmetry axis relative to the line of sight successfully reproduces the observed images, as well as the high resolution observations.
|
[
{
"name": "pap2.tex",
"string": "%\\documentstyle[12pt,aasms4,flushrt]{article}\n\\documentstyle[apjpt4]{article} % APj\n%\\documentstyle[12pt,aasms4]{article}\n\n\\newcommand{\\etal}{} \\def\\etal/{et al.} \n\\newcommand{\\kms}{} \\def\\kms/{km s$^{-1}$} \n\\newcommand{\\degre}{} \\def\\degre/{$^\\circ$}\n\\newcommand{\\halpha}{} \\def\\halpha/{H$\\alpha$} \n\\newcommand{\\hbeta}{} \\def\\hbeta/{H$\\beta$} \n\\newcommand{\\flux}{} \\def\\flux/{erg cm$^{-2}$ s$^{-1}$} \n\\newcommand{\\allo}[3]{\\ion{#1}{#2}$\\lambda$\\-#3} \n\\newcommand{\\forb}[3]{[\\ion{#1}{#2}]$\\lambda$\\-#3} \n\\newcommand{\\sforb}[3]{\\ion{#1}{#2}]$\\lambda$\\-#3} \n\\newcommand{\\dforb}[4]{[\\ion{#1}{#2}]$\\lambda\\lambda$\\-#3,#4} \n\n\\newcommand{\\mvelo}[1]{$<V>_{#1}$} \n\\newcommand{\\diab}{} \\def\\diab/{Diabolo} \n \n\\begin{document} \n\\twocolumn \n \n\\title{Morphology and kinematics of Planetary Nebulae\\\\ \nII. A \\diab/ model for NGC~3132 \n} \n\n\\author{H. Monteiro\\altaffilmark{1}, C. Morisset\\altaffilmark{1,2},\nR. Gruenwald\\altaffilmark{1}, \\and S. M. Viegas\\altaffilmark{1} } \n\n\\altaffiltext{1}{Instituto Astron\\^omico e Geof\\'{\\i}sico, USP,\nAvenida Miguel Stefano, 4200 CEP 04301-904 S\\~ao Paulo, SP, Brazil}\n\\altaffiltext{2}{Laboratoire d'Astronomie Spatiale, Traverse du Siphon, Les \nTrois Lucs, 13012 Marseille, France }\n\n \n\\begin{abstract} \n\nWe use a 3D photoionization modeling tool to study the\nmorpho-kinematic properties of the Planetary Nebula (PN) NGC~3132. We\nshow that it is \npossible to reproduce the low resolution observations (spectra and \nimages) with an ellipsoidal shell. \nHowever, high resolution observations, as those showing a density variation \nalong the nebula and the\n\\forb{O}{3}{5007} velocity profiles, definitively rule out this\ndescription.\nWe show that a bipolar Diabolo shape with a 40\\degre/ rotation\nof the symmetry axis relative to the line of sight successfully\nreproduces the observed images, as well as the high resolution observations. \n\n\\end{abstract} \n \n\\keywords{Methods: numerical -- planetary nebulae: NGC~3132} \n \n\\section{Introduction} \n \nThe determination of the three-dimensional matter distribution in planetary \nnebulae is essential for a knowledge of the nebula ejection mechanism.\nA precise understanding of the nebula geometry which produces the observed \nmorphology can also provide constraints on stellar evolution theories.\nThe geometry and the density \ndistribution of PNe are generally derived from line imaging, assuming that \na surface brightness enhancement corresponds to a density enhancement. \nAfter a first descriptive study of the morphology of PNe (Curtis 1918), \nmore detailed studies indicate two different interpretations for the \nobserved morphology of these objects:\na) the different observed morphologies are due to different projections\nof a same common basic structure (Minkowski \\& Osterbrock 1960, Khromov \\& \nKohoutek 1968); b) the different types in which PNe can be classified \n(bipolar, elliptical, etc.) correspond to different evolutionary stages \n(Balick 1987). In this second approach, the morphology can also be related \nto the \nnebular and stellar properties, particularly the mass of the progenitor star\n(e.g. Peimbert \\& Torres-Peimbert 1983, Calvet \\& Peimbert 1983, \nStanghellini, Corradi \\& Schwarz 1993, Corradi \\& Schwarz 1995). This \npoint of view is corroborated by the studies of Zhang \\& Kwok (1998). These\nauthors, assuming a three-dimensional ellipsoidal shell with density variations\nand a complete absorption of the ionizing photons,\nwhich are reconverted in H recombination photons, \nproduce simulated radio and H$\\alpha$ images which are compared to the \nobservations.\nThe visual appearence of PNe were also compared with models obtained for \nionization-bounded prolate shells by Masson (1990). Assuming \nan ellipsoidal shell with constant thickness and that the \nionizing radiation is geometrically diluted, Masson (1990) compared\ntheoretical and observed H$\\alpha$ images.\nHowever, a given emission line image results from \nthe sum of line intensities along the line of sight. \nThe exact location of the regions which produce each line depends \non the gas density distribution, but also on the \nionization distribution, which, in turn, depends on the characteristics \nof the ionizing star and on the nebular gas abundance. Consequently, \ndifferent emission lines provides information on different \nregions of the nebula, and only a consistent photoionization model \napplied to a realistic gas structure can give an accurate density distribution \non the nebula.\n\nIn this paper we show that the geometry of a PN derived by fitting \nthe observed image of a line emission and/or a line intensity \nratio is misleading, since different geometries can reproduce the \nsame observational data. Other constraints, coupled with a detailed 3D \nphotoionization model, must be used for better defining the geometry, as \nillustrated by the planetary nebula NGC~3132.\n\nBased on emission line imaging, an ellipsoidal geometry for NGC~3132 \nis assumed by various authors. Such a geometry is then suggested in a\nfirst approach. Studies similar to that of Masson (1990) using a prolate \nshell could explain the observed morphology of NGC~3132. Notice that \nthe ellipsoidal shell model of \nZhang \\& Kwok (1998) also reproduces the general trends of the observed \nH$\\alpha$ image of NGC~3132. \nUsing a geometry defined by two concentric ellipsoids and a\n3D photoionization code,\nB\\\"assgen, Diesch \\& Grewing (1990, hereafter \\cite{B90}) \nfit the observed [\\ion{O}{3}] and [\\ion{N}{2}] line images, \nas well as the emission line spectra taken through four slits. \n\nSpatio-kinematic models for NGC~3132 \nwere proposed by Sahu \\& Desai (1986, hereafter \\cite{SD86}) to explain\nthe observed asymmetric double-peaked \\forb{O}{3}{5007} line profiles in \nfive positions. \n\\cite{SD86} assert that an ellipsoidal model \nwith velocity and density asymmetries reproduces the observed expansion \nvelocities and correctly explains the nature of the profile asymmetries.\nHowever, in their paper, only the fit to the line profile at the central \nposition is shown. \nLine profiles, as a powerful tool for studying the nebula geometry, \nare discussed by Morisset, Gruenwald \\& Viegas (2000, hereafter MGV2000).\n\nAs it will be shown below, all the models assuming an ellipsoidal emitting \nshell lead to the same problems: neither \ncan reproduce the low central density observed by \\cite{SD86} and \n\\cite{J88} nor the observed asymmetric double-peaked profiles \nin regions far from the center of the nebula. \nAfter a description of the available\nobservations of NGC~3132 (\\S \\ref{sec-obs}), we show that \nellipsoidal shell models do not reproduce all the available\nobservations (\\S \\ref{sec-bass}). A ``\\diab/'' nebula \nsuccessfully explaining all the main observational trends is presented in \n\\S \\ref{sec-diab}. The conclusions are outlined in \\S \\ref{sec-concl}. \n\n\\section{Observational data for NGC~3132} \n\\label{sec-obs} \n\nA consistent photoionization model giving a realistic description \nof a PN has to account for all the observational data coming from \ndifferent types of observation. In the following, a summary of \nthe data available for NGC~3132 is presented. \n \nThe logarithm of the observed H$\\beta$ flux ranges from -10.49\n(\\cite{P71}) to -10.20 (\\cite{P77}). The extinction E(B-V) is of the order \nof 0.1 (\\cite{P77}, Mendez 1978, Feibelman 1982, Gathier, Pottasch \\& \nPel 1986).\n \nThe calculated values for the Zanstra \\ion{He}{2} temperature of the\nionizing star \nof NGC~3132 ranges from 73 000 K (de Freitas Pacheco, Codina \\& Viadana 1986) \nto 110 000 K (\\cite{P96}).\nDistance determinations indicate values from\n$\\sim$ 0.51 kpc (\\cite{DF86}, Pottasch 1996) to 1.63 kpc \n(Torres-Peimbert \\& Peimbert 1977). The ionizing star \nluminosity available in the literature is 72 L$_{\\odot}$ (Mendez 1978) or \n$\\sim$ 125 L$_{\\odot}$ (\\cite{P84}).\n\nHST/WFPC2 images for \\halpha/, \\forb{O}{1}{6300}, \\forb{O}{3}{5007}, \n\\forb{N}{2}{6583}, and \\dforb{S}{2}{6717}{6731} are available at the CADC \nserver from the Trauger's proposal \\# 6221\\footnote{Guest User, Canadian \nAstronomy Data Center, which is operated by the \nNational Research Council, Herzberg Institute of Astrophysics, Dominion \nAstrophysical Observatory}. Lower resolution images and contours were \nobtained by \\cite{J88}, \\cite{B90}, \\cite{P90}, \n\\cite{C81}, and \\cite{S92}.\n \nSpectroscopic observations of NGC~3132 can be found in \\cite{A64}, \n\\cite{K76}, \\cite{T77}, and \\cite{B90}. \nExpansion velocities of 14.7 \\kms/ for \\forb{O}{3}{5007} and 21.0\n\\kms/ for \n\\dforb{O}{2}{3726}{3729} were obtained by Meatheringham, Wood \\& Faulkner \n(1988), for slits along \nthe major axis. High resolution spectra for \\forb{O}{3}{5007} in five \npositions were obtained by \\cite{SD86}, who also deduced \na velocity of 14 \\kms/ at the central position. \nThe line profiles are all asymmetrical and double peaked. \nSince the observed red peak is more intense towards the center,\nthe asymmetry can not be due to local absorption.\n\nElectronic densities are generally obtained from the [\\ion{O}{2}] or\n[\\ion{S}{2}] line \nintensity ratios corresponding to intensities integrated on a slit. \n\\cite{T77} obtained 1000 cm$^{-3}$, while \\cite{M88} and \nStanghellini \\& Kaler (1989) give, respectively, 600 cm$^{-3}$ and 430 \ncm$^{-3}$.\nMore detailed observations show a variation \nof the electronic density measured in different positions.\nDensity determination by \\cite{J88}, from the \\dforb{S}{2}{6717}{6731} \nline intensity ratio, shows\na double-peaked distribution along the NS direction, \nreaching up to 1300 cm$^{-3}$ at the periphery of the nebula and \ndecreasing to 300 cm$^{-3}$ at the central position. \nRecent observations have confirmed this density distribution trend \n(Monteiro, Gruenwald \\& de Souza, in preparation). \n{\\it It will be shown that the decrease in density at the central \nregion is the key observation that rules out the description \nof NGC~3132 as a geometrical ellipsoidal shell.} \n\n\\section{The ellipsoidal model} \n\\label{sec-bass} \n\nThe 3D photoionization code used in this paper \nis described in Gruenwald, Viegas \\& Brogui\\`ere (1997). \nThe output of the code is \ntreated by IDL tools performing rotations, projections, and \nvelocity profiles. A full description of these tools is given by \nMGV2000. \n\nIn order to fit the observed morphology of NGC~3132 (\\forb{O}{3}{5007} \nand \\forb{N}{2}{6583} line images), as well as the emission line spectra taken \nthrough 4 slits, \\cite{B90} proposed a model obtained\nby a 3D photoionization code.\nThe geometry and input parameters proposed \nby \\cite{B90} are taken as a starting point for our 3D model \nof NGC~3132. Elements heavier than Ne were not included in \\cite{B90} model.\nFor S, Cl, and Ar we assumed a solar abundance (\\cite{GA89}), while Mg, S, Cl, \nand Fe are depleted by one hundred (Stasinska \\& Tylenda 1986).\nThus, the gas chemical abundance, in number, is: \nH: 1.0, He: 0.126, C: 7.1(-4), \nN: 2(-4), O: 6(-4), Ne: 8.2(-5), \nMg: 3.8(-7), Si: 3.55(-7), S: 1.62(-5), Cl: 3.16(-7), Ar: 3.6(-6), Fe: \n4.7(-7). \nThe central ionizing radiation is a black-body of 90~000~K \nand 150~L$_\\odot$. % = 5.85e35. \nThe model consists of two prolate ellipsoids defining a \nshell and an inner cavity (the outer zone being empty). \nThe inner ellipsoid has a semi-minor axis of 1.27 $10^{17}$cm and a \nsemi-major axis of 2.32 $10^{17}$cm, while the outer one has \n1.96 $10^{17}$cm and 2.45 $10^{17}$cm, respectively. \nThe density in the inner cavity is constant (464 \ncm$^{-3}$). In \\cite{B90}, the shell density varies along the three directions.\nHere only the most important density gradient (along the major axis Z) \nis assumed. It varies from $\\sim$ 1200\ncm$^{-3}$ at one pole to $\\sim$ 900 cm$^{-3}$ at the opposite \npole. This gradient is needed in order to reproduce\nthe observed asymmetrical brightness enhancement \nshown by the optical images. \n\nThe calculations are performed assuming the on-the-spot \napproximation (see MGV2000).\nInitially the cube containing 1/8 the nebula is divided \nin $36^3$ cells. In order to \nimprove the numerical resolution, some \nof these cells are subdivided, resulting in 133 000 cells. \nOnce the \ncalculations converged, the whole nebula is recovered (see MGV2000).\nFollowing \\cite{B90}, the images are obtained after a 7\\degre/.5\nrotation around the X axis \n(perpendicular to the line of sight). \n\n\\subsection{Matter- and Radiation-bound models}\n\\label{sub-bas-MRmod} \nThe results obtained by \\cite{B90} for the line intensities are not \nreproduced by our ellipsoidal model. \nFirst, the geometrical thickness of the shell, adopted by these authors, \nis not large enough to absorb all the photons. \nOur model with the \\cite{B90} geometry leads to a matter-bound (M-bound) \nnebula. The model is then unable \nto reproduce the observed \\dforb{N}{1}{5198}{5200} strong lines,\ncharacteristic of a radiation bound nebula.\nNotice that the measured intensity for \\forb{O}{1}{6300}, $\\sim$ 0.3 \\hbeta/ \n(Torres-Peimbert \\& Peimbert 1977), also indicates that the nebula must\nbe mainly radiation-bound (R-bound). \nAlthough the details of the \\cite{B90} \ncode are not available in their paper, the difference with our results \nmay come from the optical depth calculation, which is the \nkey-parameter determining the model. Models with a low number \nof cells (which implies too large cells) tend to overestimate the optical \ndepth. In this case, for the same \ngeometrical thickness, the model would be R-bound instead of M-bound.\nOur model has 40 times more cells than \\cite{B90}.\nThis can explain why, using the same input parameters, our model is M-bound \nwhile theirs is R-bound.\nIn order to have a R-bound shell, \nreproducing the observed low-ionization emission lines, \nthe outer ellipsoid size must be increased by at least 20\\%.\nA second reason for the discrepancies between our model and that of\n\\cite{B90} is the lack of elements heavier than Ne in their \ncode, which leads to \nan underestimation of the cooling processes. In order to test this \neffect, a heavy-element free-\\cite{B90} model was \nbuilt. The \\forb{O}{3}{5007} and \\forb{N}{2}{6583} line intensities\n(relative to \\hbeta/) increase, respectively, by 30$\\%$ and 16$\\%$.\nThis can partly explain the differences with \\cite{B90} results, \nsince the optical depth effect, discussed above, must be also important. \n\nIn the following, we will refer to the\nmatter-bound model using the dimensions of \\cite{B90} as the \nM-\\cite{B90} model and to the 20$\\%$ ``extended'' radiation-bound model as the \nR-\\cite{B90} model. The results of both models \nare presented in Table \\ref{tab-obs}. As expected, the \nstronger differences \nappear for the low ionization lines (\\dforb{N}{1}{5198}{5200} and \n\\forb{O}{1}{6300}). Nevertheless, \neven the R-\\cite{B90} model is far from reproducing the results \nobtained by \\cite{B90}, as discussed below. \n\\placetable{tab-obs}\n\n\\subsection{Ellipsoidal model results}\n\\label{sub-bas-res}\nThe superposition of the \\forb{N}{2}{6583} HST image and the \ntheoretical isophotes obtained from the R-\\cite{B90} model \nis shown in Fig. \\ref{fig-hst-b90}. \nThe shape is well reproduced, as well as the variation of \nthe surface brightness along the major axis. To adjust the modeled \nshape and dimensions to the observed ones, a reduction of 4$\\%$ \nin the distance used by \\cite{B90} (670 pc) is necessary. Note that \nthis new value for the distance is in the range of the calculated distances\nto NGC~3132 (\\S 2) \n%\\placefigure{fig-hst-b90}\n\nFor a comparison of our results with the observations of \\cite{J88}, \nthe theoretical N-S \ndensity distribution is calculated from the theoretical \n\\dforb{S}{2}{6717}{6731} ratio (using the \\cite{AB97} fit)\nfor a 4\" width slit, centered on the nebula.\nAs seen from Fig. \\ref{fig-sii-dens}, this model assuming an \nellipsoidal geometry (dashed line) does not reproduce the observed central \ndecrease in density.\n%\\placefigure{fig-sii-dens}\n\nIn order to obtain the theoretical \\forb{O}{3}{5007} emission line \nprofiles, \na radial velocity law \n$\\vec V = \\alpha . \\vec r / r + \\beta . \\vec r $ \nis used.\nThree possible sets of $\\alpha$ and $\\beta$ values are assumed:\n$\\alpha = 14.7, 9.1, 0$ \\kms/ and \n$\\beta = 0, 9.1/r_o, 23.8/r_o$ km s$^{-1}$ cm$^{-1}$, respectively. \nThe normalization factor, $r_o$ = 3 10$^{17}$cm, is of \nthe order of the size of the nebula.\nThe \\mvelo{5007} and \\mvelo{3726} emission line mean velocities \nfor the whole nebula (as defined in MGV2000) are given in Table\n\\ref{tab-velo}.\nFor the three sets of values defining the velocity law, the parameters \nwere chosen in order to give \n\\mvelo{5007} = 14.7 \\kms/, as obtained \nfrom the observed profile reported by \\cite{M88}. The \ncorresponding theoretical \\mvelo{3726} mean velocity \ndepends on the parameters $\\alpha$ and $\\beta$ and is always \nslightly lower than the observed value (21 \\kms/). \nThe five positions at which the \\forb{O}{3}{5007}\nline profiles were observed are shown in \\cite{SD86} (their Fig. 1a)\nsuperposed\non an U-band image (Kohoutek \\& Lausten 1977).\nThe calculated velocity profiles for \\forb{O}{3}{5007} \nare shown in Fig. \\ref{fig-velo-b90}. \nSince the three sets of parameters of the adopted velocity law \ngive similar line profiles, only the results for the $\\alpha = 9.1$ \\kms/ \nand $\\beta = 9.1/r_o$ km s$^{-1}$ cm$^{-1}$ law is shown.\nIn the upper-right panel the aperture is shifted from the center\nby 2.8'' NE. This \nshift corresponds to the pointing accuracy of the \ntelescope used by \\cite{SD86} and it allows to check if \nthe effect of the pointing precision on the profile is important.\nThe central double peak is reproduced. However,\nthe observed asymmetry can only be obtained if the nebula is \ntilted by about 30\\degre/, whereas the results shown in \nFig. \\ref{fig-velo-b90} were obtained assuming a rotation angle of\n7\\degre/.5, as proposed by BDG90. \nThe observed double peaks at the four external \npositions are not reproduced. Note that the observed profiles were taken by SD86 \nat positions where the U band emission is strongest. In the U band, the \nnebular emission is dominated by the \\forb{O}{2}{3726} line, so the \nobservations were taken \nat the extreme outer part of the nebula. \nThus, the radial velocity at these \npositions is quasi-perpendicular to the line of sight and an \napparent velocity of $\\sim$ 10 \\kms/ would require an unrealistic \nhigh radial velocity. \n\n\\placetable{tab-velo}\n\n%\\placefigure{fig-velo-b90}\n\nFinally, a simple way to verify the inadequacy of the ellipsoidal model \nin reproducing the density gradient and the low ionization lines is the \nfollowing: let us consider a dense shell ($\\sim$ 1000 cm$^{-3}$) with a\ngeometrical thickness $t$ and \nradius $R$, around a less dense cavity ($\\sim$ 300 cm$^{-3}$). \nThe line emissivity is proportional to the square of the density. Thus, \nin order to reproduce \nthe observed density distribution, the main contribution to the \ncentral emission must come from the low density gas, implying $t < 0.02 R$. \nSuch a thin shell will have a total emissivity far below the observed \none, and will be matter-bound, not producing the \nlow ionization lines. A radiation-bound model, necessary to explain the low \nionization lines cannot reproduce the density gradient as shown above. \nThis rules out the description of NGC~3132 as a \n{\\it closed ellipsoidal shell}. \nAn ellipsoidal shell with a hole just aligned to the \ncentral line of sight could be proposed, but such an {\\sl ad hoc} \ngeometry seems unrealistic. \n\nFrom all the results presented above we conclude that \nan ellipsoidal model for NGC~3132 is not appropriate to explain the \nobservational data. Thus, a new model is proposed below.\n \n\\section{The \\diab/ model} \n \\label{sec-diab}\n\nPNe imaging suggests that several objects can have a ``Diabolo'' shape (e.g.\nHour-Glass nebula and NGC 2346). \nIn order to reproduce this shape, we adopt a two-zone \ngas distribution, illustrated in Fig. \\ref{fig-densh4}: a) a dense\nzone (with a density of 1300 cm$^{-3}$) \ndefined by the intersection of two spheres of the same radius \n(3. 10$^{17}$ cm) but with centers shifted by 10$^{17}$ cm, defining \nthe ``Diabolo-shape'', and b) a low-density gas, 300 cm$^{-3}$, \nfilling the rest of the nebula. The shadowing in the figure is just used \nto give a better 3D visualization and does not correspond to a density \nvariation. \nThe model was calculated for 1/8 of\nthe nebula and the whole nebula was reconstructed in a 10$^6$ cells\ncube.\n%\\placefigure{fig-densh4}\nWe keep the chemical abundances and ionizing star characteristics of \n\\cite{B90} model (\\S \\ref{sec-bass}). No attempt to adjust these \nparameters were made in order to improve the fit of the emission line\nratios. In fact, the scope of this paper is just to show that a strong \nconstraint on the geometry is the density distribution. \nOnce this distribution is reproduced, other observed features, \nunexplained by previous models, can also be explained.\n \n\\subsection{The Diabolo model results}\n\\label{sub-diab-res}\n\nThe effect of varying the angle of view of the nebula is shown in \nFig. \\ref{fig-diab-rot}.\nPractically all the observed regular morphologies of PNe are reproduced:\nfrom a clearly butterfly image (axis of symmetry\nperpendicular to the line of sight) to a well round\nnebula (axis of symmetry aligned to the line of sight) through an ellipsoidal\none.\nWith an appropriate orientation of 40\\degre/ relative to the line\nof sight, the observed optical shape of NGC~3132 (ellipsoidal shape) can be\nreproduced. As said above (\\S 1), such feature can also be reproduced by \nthe ellipsoidal shell model of Zhang \\& Kwok (1998), as well as by a model\nsimilar to that of Masson (1990). However, these models are not \nself-consistent with respect to the ionization balance and, as will be shown \nbelow, other constraints will rule out an ellipsoidal model for this nebula.\n\n%\\placefigure{fig-diab-rot}\n\nWith a \\diab/ morphology the contribution from the dense region \nto the central emission is reduced, helping to solve the close ellipsoidal \nshell problems.\nAt the same time, the projected velocity of the gas in the\nexternal parts of the nebula will be high enough, reproducing \nthe observed double peak, as shown below. \n\nRegarding the emission line ratios, the results of the \\diab/ model \n(fourth column of Table \\ref{tab-obs}) are similar to \nthose obtained from the R-\\cite{B90} model. In addition, \nHST line images in H$\\beta$, \\forb{O}{3}{5007}, \n\\forb{N}{2}{6583} and \\forb{O}{1}{6300} are shown \nFig. \\ref{fig-ima-diab} (four upper panels) and can be compared to\nthe corresponding \\diab/ model images (four lower panels).\nThe observed ellipsoidal shape is well \nreproduced, as well as the ionization \nstratification. The brightness asymmetry along the major axis\nis not reproduced by the adopted axi-symmetrical \nmodel of the nebula. Such asymmetry could be explained either by a \ndensity gradient\nor an ionization source that is not in the geometrical center of the Diabolo.\n\n%\\placefigure{fig-ima-diab}\n\nThe electronic density distribution obtained from the\n\\dforb{S}{2}{6717}{6731} ratio is also shown in\nFig. \\ref{fig-sii-dens} (solid line). \n{\\it The observed decrease of the density (\\S 2) in the central part \nof the nebula is reproduced}.\nThis and the line profiles discussed below are the main improvements \nobtained by the Diabolo shape.\n\nThe same velocity laws applied for the R-BDG90 model are used (\\S3.2) \nwith $r_o$ = 5 10$^{17}$cm.\nThe three different \\forb{O}{3}{5007} profiles obtained with the \nthree sets of parameters of the velocity \nlaw are shown in Fig. \\ref{fig-prof-diab} and can be compared to \nthe observations (\\cite{SD86}). \nThe profiles show the double peaks \nat the six positions, {\\it a feature not reproduced by the ellipsoidal shell \nmodel}. \nThe asymmetry is well reproduced at the four external positions.\nThe asymmetry at the central position is not reproduced, as long as \nan axi-symmetric nebula is used, even considering a shift of 2.8'' \nas shown in the upper right panel. \nNotice that at the central position only the low\ndensity gas contributes to the emission. Thus, any asymmetry in \nthe velocity field and/or in the low\ndensity distribution will lead to the observed asymmetry, requiring no \nchange in the higher density distribution associated to the \\diab/ shape.\n%\\placefigure{fig-prof-diab}\n\nThe three sets of parameters for the velocity law were chosen in order to \nobtain the same \\mvelo{5007} (14.7 \\kms/, Table \\ref{tab-velo}; the results \nfor \\mvelo{3726} remain the same as for\nthe R-BDG90 models); however, for $\\alpha$ = 0 (dashed lines), \nthe peaks of the observed \nprofiles at the central part of the nebula occur for a lower \nvelocity (Fig. \\ref{fig-prof-diab}, upper panels).\nFurthermore, in this case, the velocity law \ndoes not reproduce the observed profiles since one of the peaks is almost \ninexistent.\nThe results obtained with the other two sets of parameters (solid and \ndot-dashed lines) are very similar. Nevertheless, for $\\alpha$ $\\not=$ 0 and \n$\\beta$ $\\not=$ 0, \\mvelo{3726} is higher than \\mvelo{5007}, approaching the \nobserved result (Table \\ref{tab-velo}) of \\cite{M88}.\n\n\\section{Concluding remarks} \n\\label{sec-concl}\n\nWe have shown in this paper that the lack of high resolution observations \n(spatial and spectroscopic) may lead to a wrong conclusion about \nthe morphology of a PN.\n\nA new modeling tool based on a 3D photoionization code is used to \nconsistently reproduce all the available observations of NGC~3132. \nUsing an ellipsoidal geometry, all the low resolution observations \n(flux, emission line spectrum, imaging) could be reproduced.\nHowever, neither the density variations indicated by\nthe \\dforb{S}{2}{6717}{6731} ratio, nor the \n\\forb{O}{3}{5007} velocity profiles could be explained by such a model. \nTo account for these observations, a drastic change in the geometry of \nthe nebula is necessary. The proposed Diabolo shape offers the \nsolution to the density distribution, as well as to the asymmetric \ndouble-peaked emission line profiles, while also explaining the low\nresolution observations.\n\nA Diabolo shape may reproduce the observed bipolar morphology of many PNe. \nIn fact, Bryce, Balick \\& Meaburn (1994) suggested that NGC~6720 \nis not a spherical expanding shell as often assumed, but must be bipolar in \nnature, since the observed [NII] emission line profiles are split in two \ncomponents.\nA bipolar shape emerges from studies of the formation and \nevolution of PNe, in particular those\nrelated to the interacting wind model (Kwok, Purton, \\& Fitzgerald 1978). \nRecent hydrodynamical models (e.g. Dwarkadas, Chevalier \\& Blondin 1996;\n\\cite{M97}) \nsuggest that a Diabolo type shape \ncan be produced in the accepted scenario of PNe formation\n(post AGB envelope ejection with wind interaction). In fact,\nrecent high resolution images taken with the Hubble Space Telescope show \nthat PNe with this type of structure is not uncommon. Some nice examples \nare the Hour-Glass nebula, NGC~2346, NGC~6537 and Hb-5.\n\nNo attempt was made to fine tuning the emission line ratios. This \ncan be achieved through changes in the ionizing star characteristics, in \nthe chemical abundances, as well as through small adjustments in the density \ndistribution, which will not change the main conclusions of this paper, \nin particular the Diabolo shape.\nFurthermore, in the models presented here, the \nionizing source is assumed to be at the center of symmetry of the nebula. \nHowever, there are evidences that the star should be shifted \nby $\\sim$ 1.7'' from the geometrical center of the nebula \n(Kohoutek \\& Lausten 1977 and \\cite{SD86}).\nA model accounting for this \nout-of-center ionizing star may still improve the results, leading \nto a better agreement with the observations regarding the \nbrightness asymmetry and the emission line profile at the central \nposition. \n\nWe have shown here the importance of a 3D photoionization model, combined \nwith imaging results and also with high resolution observations, to impose\nrelevant constraints on the PN geometry. \nThe misclassification of NGC~3132 as an ellipsoidal PN instead\nof a bipolar one casts doubts on the \nstatistical results correlating the morphology and other PNe\nproperties, such as abundances or progenitor type.\n\n\\acknowledgements\nThe authors would like to thank the referee, Dr. Sun Kwok, for his \nvaluable comments and suggestions. \nC. Morisset is thankful to IAGUSP for the hospitality during his \npost-doctoral visit.\nThis work was supported by CNPq (n.~304077/77-1, n.~306122/88-0, and \nn.~150162/96-0), FAPESP (n.~97/13428-4 and n.~98/01922-7), and \nPRONEX/FINEP (n.~41.96.0908.00). \n\n\\begin{thebibliography}{} \n\\bibitem[Alexander \\& Balick 1997]{AB97} \n\tAlexander, J. \\& Balick, B. 1997, AJ, 114, 713\n\\bibitem[Aller \\& Faulkner (1964)]{A64} Aller, L. H., \\& Faulkner, \n\tD. J. 1964, IAU Symp. 20, 45 \n\\bibitem[Balick 1987]{B87} Balick, B. 1987, AJ, 94, 671 \n\\bibitem[BDG90]{B90} B\\\"assgen, M., Diesch, \n\tC. \\& Grewing, M. 1990, BDG90, A\\&A 237, 201\n\\bibitem{ }Bryce, M., Balick, B. \\& Meaburn, J. 1994, \\mnras, 266, 721 \n\\bibitem[Calvet \\& Peimbert 1983]{C83} Calvet, N., \\& Peimbert,\n\tM. 1983, Rev. Mexicana Astron. Astrofis., 5, 319\n\\bibitem[Condal \\etal/ (1981)]{C81} Condal, A., Pritchet, C., Fahlman,\n\tG.G. \\& Walker, G.A.H. 1981, PASP, 93, 695\n\\bibitem[Corradi \\& Schwarz 1995]{CS95} Corradi, R. L. M. \\& \n\tSchwarz, H. E. 1995, \\aap, 293, 871\n\\bibitem{ }Curtis, H. D. 1918, Pub. Lick Obs. 13, 55\n\\bibitem[Dwarkadas \\etal/ 1996]{D96} \n\tDwarkadas, V. V., Chevalier, R. A. \\& Blondin, J. M. 1996,\n\t\\apj, 457, 773 \n\\bibitem{ }Feibelman, W. A. 1982, AJ, 87, 555 \n\\bibitem[de Freitas Pacheco \\etal/ 1986]{DF86} de \n\tFreitas Pacheco, J. A., Codina, S. J. \\& Viadana, L. 1986, \n\t\\mnras, 220, 107 \n\\bibitem[Gathier \\etal/ 1986]{G86} Gathier, R., \n\tPottasch, S. R. \\& Pel, J. W. 1986, \\aap, 157, 171 \n\\bibitem[Grevesse \\& Anders 1989]{GA89} Grevesse, N. \\& \n\tAnders, E. 1989, American Institute of Physics Conference\n\tSeries, 183, 1 \n\\bibitem[Gruenwald \\etal/ (1997)]{G97} Gruenwald, R., Viegas, \n\tS. M. \\& Brogui\\`ere, D. 1997, ApJ, 480, 283 \n\\bibitem[Juguet \\etal/ (1988)]{J88} Juguet, \n\tJ. L., Louise, R., Macron, A. \\& Pascoli, G. 1988, A\\&A, 205, 267 \n\\bibitem[Kaler (1976)]{K76} Kaler, J. B. 1976, \\apjs, 31, 517 \n\\bibitem{ }Khromov, G. S. \\& Kohoutek, L. 1968, IAU Symp. 34, Planetary \n\tNebulae (Dordrecht: Reidel), 227\n\\bibitem[Kohoutek \\& Lausten (1977)]{K77} Kohoutek, L. \\& Lausten, \n\tS. 1977, A\\&A, 61, 761\n\\bibitem[Kwok \\etal/ 1978]{K78} Kwok, S., \n\tPurton, C. R. \\& Fitzgerald, P. M. 1978, \\apjl, 219, L125\n\\bibitem{ }Masson, C. R. 1990, ApJ, 348, 580\n\\bibitem[Mea\\-theringham \\etal/ (1988)]{M88} \n\tMeatheringham, S. J., Wood, P. R. \\& Faulkner, D. J. 1988, \n\tApJ, 334, 862\n\\bibitem[Mellema 1997]{M97} Mellema, G. 1997, \\aap, 321, L29\n\\bibitem{ }Minkowski, R. \\& Osterbrock, D. E. 1960, ApJ, 131, 537\n\\bibitem{ }Mendez, R. H. 1978, \\mnras, 185, 647\n\\bibitem[Morisset \\etal/ (2000)]{M99} Morisset, C., Gruenwald, R. \\& \n\tViegas, S. M. 2000, MGV2000, ApJ, submitted \n\\bibitem[Pascoli (1990)]{P90} Pascoli, G. 1990, AAS, 83, 27\n\\bibitem[Peimbert \\& Torres-Peimbert 1983]{PTP83} Peimbert, M., \\&\n\tTorres-Peimbert, S. 1983, IAU Symp. 103, Planetary \n\tNebulae (Dordrecht: Kluwer), 233\n\\bibitem[Perek 1971]{P71} Perek, L. 1971, Bulletin of the \n\tAstronomical Institutes of Czechoslovakia, 22, 103 \n\\bibitem[Pottasch \\etal/ 1977]{P77} \n\tPottasch, S. R., Wesselius, P. R., Wu, C. -C. \\& Van Duinen, \n\tR. J. 1977, \\aap, 54, 435 \n\\bibitem[Pottasch 1984]{P84} Pottash 1984, Planetary Nebulae, \n\tReidel, Dordrecht \n\\bibitem[Pottasch 1996]{P96} Pottasch, S. R. 1996, \\aap, \n\t307, 561 \n\\bibitem[SD86]{SD86} Sahu, K. C. \\& Desai, J. N. 1986, SD86, \n\tA\\&A, 161, 357 \n\\bibitem[Schwarz \\etal/ (1992)]{S92} Schwarz, H. \n\tE., Corradi, R. L. M. \\& Melnick, J. 1992, \\aaps, 96, 23 \n\\bibitem[Stanghellini \\etal/ 1993]{S93} Stanghellini, L., Corradi,\n\tR. L. M., \\& Schwarz, H. E. 1993, \\aap, 279, 521\n\\bibitem{ } Stanghellini, L. \\& Kaler, J. B. 1989, 343, 811\n\\bibitem{ } Stasinska, G. \\& Tylenda, R. 1986, A\\&A, 155, 137\n\\bibitem[Torres-Peimbert \\& Peimbert (1977)]{T77} Torres-Peimbert, \n\tS. \\& Peimbert, M. 1977, Revista Mexicana de Astronomia y \n\tAstrofisica, 2, 181 \n\\bibitem[Zhang \\& Kwok (1998)]{ZK98} Zhang, C.Y. \\& Kwok, S. 1998,\n\tApJS, 117, 341 \n\\end{thebibliography} \n \n\\newpage\n\\figcaption[fig1.ps]{Superposition of the HST and the theoretical images\nof \\forb{N}{2}{6583}. The theoretical results correspond to the\nR-\\cite{B90} model.\n\\label{fig-hst-b90}} \n\n\\figcaption[fig2.ps]{N$\\leftrightarrow $S variation of\n\\dforb{S}{2}{6717}{6731} density from the R-\\cite{B90} model (dashed\nline) and from the \\diab/ model (solid line). \n\\label{fig-sii-dens}} \n\n\\figcaption[fig3.ps]{\\forb{O}{3}{5007} velocity profiles obtained from the\nR-\\cite{B90} model. The positions and the size aperture are the same as\nin \\cite{SD86} (their Fig. 2). In the upper-right panel the aperture \nis shifted from the center by 2.8'' (see text).\n\\label{fig-velo-b90}} \n\n\\figcaption[fig4.ps]{Gas distribution for the \\diab/ model. Only the\ndenser zone (1300 cm$^{-3}$) is shown. \n\\label{fig-densh4}} \n\n\\figcaption[fig5.ps]{\\hbeta/ images from the \\diab/ model. \nFrom the upper-left to the lower-right panel the \nangle between the axis of symmetry and the sky plane increases by 10\\degre/\nfrom 0\\degre/ to 80\\degre/.\n\\label{fig-diab-rot}}\n\n\\figcaption[fig6.ps]{ The top panels correspond to\nHST images of NGC~3132 while the botton panels to the \n\\diab/ model. \n\\label{fig-ima-diab}} \n\n\\figcaption[fig7.ps]{\\forb{O}{3}{5007} velocity profiles for the\n\\diab/ model using the velocity law \n$\\vec V = \\alpha . \\vec r / r + \\beta . \\vec r $, with r$_0 = 3 10^{17}$cm, \nand\n($\\alpha$, $\\beta$ ) = (14.7, 0), (9.1, 9.1/r$_o$), and (0, 23.8/r$_o$) are \nshown, respectively, by dashed, solid, and dot-dashed lines.\n\\label{fig-prof-diab}} \n\n\\newpage\n \n\\begin{table}[h] \n\\caption{Emission line intensities relative to \\hbeta/ \\label{tab-obs}} \n\\begin{tabular}{rccc} \n\\tableline \nLine \\AA & M-\\cite{B90} & R-\\cite{B90} & \\diab/\\nl \n\\tableline \n\\forb{O}{3}{4363} \t& 0.022\t& 0.018\t& 0.013\t\\nl \n\\allo{He}{2}{4686} \t& 0.085\t& 0.059\t& 0.065\t\\nl \n\\forb{O}{3}{5007} \t& 6.045\t& 4.700\t& 3.690\t\\nl \n\\forb{N}{1}{5200} \t& 0.010\t& 0.159\t& 0.200\t\\nl \n\\allo{He}{1}{5876} \t& 0.175\t& 0.189\t& 0.190\t\\nl \n\\forb{O}{1}{6300} \t& 0.037\t& 0.320\t& 0.353\t\\nl \n\\forb{N}{2}{6583} \t& 2.792\t& 5.090\t& 5.337 \\nl \n\\forb{S}{2}{6717} \t& 0.193\t& 0.689\t& 0.825\t\\nl \n\\forb{S}{2}{6731} \t& 0.236\t& 0.745 & 0.846\t\\nl \nH$\\alpha $ \t& 2.904\t& 2.915\t& 2.917\t\\nl \nH$\\beta^1 $ \t& 6.553\t& 9.651\t& 9.050\t\\nl \n\\tableline \n\\end{tabular} \n \n$^1$ {\\footnotesize In $10^{-11}$ \\flux/, for a distance of 670 pc.} \n% 4piD2 = 5.372e43 \n\\end{table} \n\n\\begin{table}[h] \n\\caption{Mean line velocities for the adopted velocity law \\label{tab-velo}} \n\\begin{tabular}{rrcc} \n\\tableline \n$\\alpha^a$& $\\beta^b$ & \\mvelo{5007}$^a$ & \\mvelo{3726}$^a$\\nl \n\\tableline \n14.7 & 0. & 14.7 & 14.7 \\nl \n9.1 & 9.1 & 14.7 & 15.9 \\nl \n0. & 23.8 & 14.7 & 17.8 \\nl \n\\tableline \n\\end{tabular} \n \n$^a$ {\\footnotesize in \\kms/} \n \n$^b$ {\\footnotesize in \\kms//r$_0$, with r$_0 = 3 10^{17}$cm for the R-BDG90 \nmodel and r$_0 = 5 10^{17}$cm for the Diabolo model} \n\n\\end{table} \n\\newpage\n\\setcounter{figure}{0}\n\\begin{figure} \n\\plotone{fig1.ps}\n\\caption{}\n\\end{figure} \n\n\\begin{figure} \n\\plotone{fig2.ps} \n\\caption{}\n\\end{figure} \n\n\\begin{figure} \n\\plotone{fig3.ps} \n\\caption{}\n\\end{figure} \n\n\\begin{figure} \n\\plotone{fig4.ps} \n\\caption{}\n\\end{figure} \n\n\\begin{figure} \n\\plotone{fig5.ps} \n\\caption{}\n\\end{figure} \n \n\\begin{figure} \n\\plotone{fig6.ps}\n\\caption{}\n\\end{figure} \n \n\\begin{figure} \n\\plotone{fig7.ps} \n\\caption{}\n\\end{figure} \n\n\n\\end{document} \n\n\n"
}
] |
[
{
"name": "astro-ph0002154.extracted_bib",
"string": "\\begin{thebibliography}{} \n\\bibitem[Alexander \\& Balick 1997]{AB97} \n\tAlexander, J. \\& Balick, B. 1997, AJ, 114, 713\n\\bibitem[Aller \\& Faulkner (1964)]{A64} Aller, L. H., \\& Faulkner, \n\tD. J. 1964, IAU Symp. 20, 45 \n\\bibitem[Balick 1987]{B87} Balick, B. 1987, AJ, 94, 671 \n\\bibitem[BDG90]{B90} B\\\"assgen, M., Diesch, \n\tC. \\& Grewing, M. 1990, BDG90, A\\&A 237, 201\n\\bibitem{ }Bryce, M., Balick, B. \\& Meaburn, J. 1994, \\mnras, 266, 721 \n\\bibitem[Calvet \\& Peimbert 1983]{C83} Calvet, N., \\& Peimbert,\n\tM. 1983, Rev. Mexicana Astron. Astrofis., 5, 319\n\\bibitem[Condal \\etal/ (1981)]{C81} Condal, A., Pritchet, C., Fahlman,\n\tG.G. \\& Walker, G.A.H. 1981, PASP, 93, 695\n\\bibitem[Corradi \\& Schwarz 1995]{CS95} Corradi, R. L. M. \\& \n\tSchwarz, H. E. 1995, \\aap, 293, 871\n\\bibitem{ }Curtis, H. D. 1918, Pub. Lick Obs. 13, 55\n\\bibitem[Dwarkadas \\etal/ 1996]{D96} \n\tDwarkadas, V. V., Chevalier, R. A. \\& Blondin, J. M. 1996,\n\t\\apj, 457, 773 \n\\bibitem{ }Feibelman, W. A. 1982, AJ, 87, 555 \n\\bibitem[de Freitas Pacheco \\etal/ 1986]{DF86} de \n\tFreitas Pacheco, J. A., Codina, S. J. \\& Viadana, L. 1986, \n\t\\mnras, 220, 107 \n\\bibitem[Gathier \\etal/ 1986]{G86} Gathier, R., \n\tPottasch, S. R. \\& Pel, J. W. 1986, \\aap, 157, 171 \n\\bibitem[Grevesse \\& Anders 1989]{GA89} Grevesse, N. \\& \n\tAnders, E. 1989, American Institute of Physics Conference\n\tSeries, 183, 1 \n\\bibitem[Gruenwald \\etal/ (1997)]{G97} Gruenwald, R., Viegas, \n\tS. M. \\& Brogui\\`ere, D. 1997, ApJ, 480, 283 \n\\bibitem[Juguet \\etal/ (1988)]{J88} Juguet, \n\tJ. L., Louise, R., Macron, A. \\& Pascoli, G. 1988, A\\&A, 205, 267 \n\\bibitem[Kaler (1976)]{K76} Kaler, J. B. 1976, \\apjs, 31, 517 \n\\bibitem{ }Khromov, G. S. \\& Kohoutek, L. 1968, IAU Symp. 34, Planetary \n\tNebulae (Dordrecht: Reidel), 227\n\\bibitem[Kohoutek \\& Lausten (1977)]{K77} Kohoutek, L. \\& Lausten, \n\tS. 1977, A\\&A, 61, 761\n\\bibitem[Kwok \\etal/ 1978]{K78} Kwok, S., \n\tPurton, C. R. \\& Fitzgerald, P. M. 1978, \\apjl, 219, L125\n\\bibitem{ }Masson, C. R. 1990, ApJ, 348, 580\n\\bibitem[Mea\\-theringham \\etal/ (1988)]{M88} \n\tMeatheringham, S. J., Wood, P. R. \\& Faulkner, D. J. 1988, \n\tApJ, 334, 862\n\\bibitem[Mellema 1997]{M97} Mellema, G. 1997, \\aap, 321, L29\n\\bibitem{ }Minkowski, R. \\& Osterbrock, D. E. 1960, ApJ, 131, 537\n\\bibitem{ }Mendez, R. H. 1978, \\mnras, 185, 647\n\\bibitem[Morisset \\etal/ (2000)]{M99} Morisset, C., Gruenwald, R. \\& \n\tViegas, S. M. 2000, MGV2000, ApJ, submitted \n\\bibitem[Pascoli (1990)]{P90} Pascoli, G. 1990, AAS, 83, 27\n\\bibitem[Peimbert \\& Torres-Peimbert 1983]{PTP83} Peimbert, M., \\&\n\tTorres-Peimbert, S. 1983, IAU Symp. 103, Planetary \n\tNebulae (Dordrecht: Kluwer), 233\n\\bibitem[Perek 1971]{P71} Perek, L. 1971, Bulletin of the \n\tAstronomical Institutes of Czechoslovakia, 22, 103 \n\\bibitem[Pottasch \\etal/ 1977]{P77} \n\tPottasch, S. R., Wesselius, P. R., Wu, C. -C. \\& Van Duinen, \n\tR. J. 1977, \\aap, 54, 435 \n\\bibitem[Pottasch 1984]{P84} Pottash 1984, Planetary Nebulae, \n\tReidel, Dordrecht \n\\bibitem[Pottasch 1996]{P96} Pottasch, S. R. 1996, \\aap, \n\t307, 561 \n\\bibitem[SD86]{SD86} Sahu, K. C. \\& Desai, J. N. 1986, SD86, \n\tA\\&A, 161, 357 \n\\bibitem[Schwarz \\etal/ (1992)]{S92} Schwarz, H. \n\tE., Corradi, R. L. M. \\& Melnick, J. 1992, \\aaps, 96, 23 \n\\bibitem[Stanghellini \\etal/ 1993]{S93} Stanghellini, L., Corradi,\n\tR. L. M., \\& Schwarz, H. E. 1993, \\aap, 279, 521\n\\bibitem{ } Stanghellini, L. \\& Kaler, J. B. 1989, 343, 811\n\\bibitem{ } Stasinska, G. \\& Tylenda, R. 1986, A\\&A, 155, 137\n\\bibitem[Torres-Peimbert \\& Peimbert (1977)]{T77} Torres-Peimbert, \n\tS. \\& Peimbert, M. 1977, Revista Mexicana de Astronomia y \n\tAstrofisica, 2, 181 \n\\bibitem[Zhang \\& Kwok (1998)]{ZK98} Zhang, C.Y. \\& Kwok, S. 1998,\n\tApJS, 117, 341 \n\\end{thebibliography}"
}
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astro-ph0002155
|
Ultra-High-Energy Cosmic Ray Acceleration by Magnetic Reconnection in Newborn Accretion Induced Collapse Pulsars
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[
{
"author": "Elisabete M. de Gouveia Dal Pino\\altaffilmark{1,2} \\& Alex Lazarian\\altaffilmark{3}"
}
] |
We here investigate the possibility that the ultra-high energy cosmic ray (UHECR) events observed above the GZK limit are mostly protons accelerated in reconnection sites just above the magnetosphere of newborn millisecond pulsars which are originated by accretion induced collapse (AIC). %AL We formulate the requirements for the acceleration mechanism and show that % AIC-pulsars with surface magnetic fields $10^{12} $ G $< \, B_{\star} \lesssim $ $10^{15}$ G and spin periods 1 ms $\lesssim \, P_{\star} \, < \, $ 60 ms, are able to accelerate particles to energies $\geq \, 10^{20} $ eV. %AL %due to lack of space %We speculate that reconnection is able to provide the necessary %conditions. % %These limits can be %summarized by the condition $ P_{\star} \, \simeq \, 2 $ ms %($B_{\star}/10^{13}^{3/4}$ G). Because the expected rate of AIC sources in our Galaxy is very small ($\sim \, 10^{-5}$ yr$^{-1}$), the corresponding contribution to the flux of UHECRs is neglegible, and the total flux is given by the integrated contribution from AIC sources produced by the distribution of galaxies located within the distance which is unaffected by the GZK cutoff ($\sim \, 50 $ Mpc). We find that reconnection % AL %efficiency factor needs to be only should convert a fraction % %$ \xi \, \gtrsim \, 3.6 \times 10^{-3}$ $ \xi \, \gtrsim \, 0.1$ of magnetic energy %AL into UHECR % in order to reproduce the observed flux. %As data collection %improves, we must expect some sign of %correlation of the distribution of %events with the local %distribution of galaxies.
|
[
{
"name": "ms.tex",
"string": "% Ultra-High-Energy Cosmic Rays Acceleration by Magnetic Reconnection \n%in Young\n%Born Pulsars\n% by E.M. de Gouveia Dal Pino & A. Lazarian\n%revised version: 29/3/2000\n%accepted version: 12/4/2000\n%\\documentstyle[11pt,aaspp4]{article}\n%\\documentstyle[aas2pp4]{article}\n%\\documentstyle[11pt,eqsecnum,aaspp4]{article}\n%\\documentstyle[12pt,amssym,aasms4]{article}\n%\\journalid{337}{}\n%\\articleid{11}{14}\n\n\\documentstyle[12pt,aasms4]{article}\n\n\\received{}\n\\accepted{}\n%\\slugcomment{to appear in \\it{The Astrophysical Journal Letters}}\n%\\input tcilatex\n\n\\begin{document}\n\\title { Ultra-High-Energy Cosmic Ray Acceleration by Magnetic \nReconnection in Newborn Accretion Induced Collapse Pulsars}\n\n\\author{Elisabete M. de Gouveia Dal Pino\\altaffilmark{1,2}\n\\& Alex Lazarian\\altaffilmark{3} } \n\\altaffiltext{1}{Instituto Astron\\^omico e Geof\\'{\\i}sico, University \nof S\\~ao Paulo, Av. Miguel St\\'efano, 4200, S\\~ao Paulo\n04301-904, SP, Brasil; \nE-mail: dalpino@iagusp.usp.br, } \n\\altaffiltext{2}{\nAstronomy Department,\nTheoretical Astrophysics Center,\nUniversity of California,\n601 Campbell Hall,\nBerkeley, CA 94720-3411} \n\\altaffiltext{3}{Department of Astronomy, \nUniversity of Wisconsin, \nMadison, USA; \nE-mail: lazarian@dante.astro.wisc.edu }\n\n\n\\begin{abstract}\nWe here investigate the possibility that the \nultra-high energy cosmic ray (UHECR) events observed above the GZK \nlimit are mostly protons accelerated in reconnection sites just above \nthe \nmagnetosphere of newborn millisecond pulsars \nwhich are originated by accretion \ninduced collapse (AIC). \n%AL\nWe formulate the requirements for the acceleration mechanism\nand show that\n%\nAIC-pulsars with surface\nmagnetic fields \n $10^{12} $ G $< \\, B_{\\star} \\lesssim $ $10^{15}$ G \nand spin periods\n1 ms $\\lesssim \\, P_{\\star} \\, < \\, $ 60 ms, \nare able to accelerate\nparticles to energies $\\geq \\, 10^{20} $ eV.\n%AL\n%due to lack of space\n%We speculate that reconnection is able to provide the necessary\n%conditions. \n%\n%These limits can be \n%summarized by the condition $ P_{\\star} \\, \\simeq \\, 2 $ ms \n%($B_{\\star}/10^{13}^{3/4}$ G).\nBecause the expected rate of AIC sources in our Galaxy \nis very small ($\\sim \\, 10^{-5}$ yr$^{-1}$), \nthe corresponding contribution to\nthe \nflux of UHECRs is neglegible, \nand the total flux \nis given by the integrated contribution from AIC sources \nproduced by the distribution of galaxies located within the distance \nwhich \nis unaffected by the GZK cutoff ($\\sim \\, 50 $ Mpc). \nWe find that reconnection \n% AL\n%efficiency factor needs to be only\nshould convert a fraction \n% \n%$ \\xi \\, \\gtrsim \\, 3.6 \\times 10^{-3}$ \n$ \\xi \\, \\gtrsim \\, 0.1$ \nof magnetic energy\n%AL\ninto UHECR\n%\nin order to reproduce the observed flux.\n\n%As data collection \n%improves, we must expect some sign of \n%correlation of the distribution of\n%events with the local \n%distribution of galaxies. \n\\end{abstract}\n\n\\keywords{\\bf \n%ultra-high energy cosmic rays: theory, \nacceleration of particles - \nstars: magnetic fields -\npulsars: general- \nstars: neutron - white dwarfs \n}\n\n\\section{Introduction}\nThe detection of cosmic ray events with energies beyond 10$^{20}$eV\nby AGASA (Takeda et al. 1999), Fly's Eye (Bird et al. 1995), and \nHaverah \nPark\n(Lawrence, Reid, \\& Watson 1991)\nexperiments still poses a challenge for the understanding of their \nnature\nand sources. These ultra-high energy cosmic rays (UHECRs) show no major\ndifferences in their air shower characteristics to cosmic rays at lower\nenergies and thus one would expect them to be mostly protons \n%particularly if, as is most likely, they are extragalactic in origin \n(Protheroe\n1999). \n%although the possibility that they are heavy nuclei, $\\gamma -\n%$rays,\n%neutrinos, or exotic particles cannot be totally\n%disregarded at the present. \nIf UHECRs are charged particles, or \nprotons, then they should be \naffected \nby\nthe expected Greisen-Zatsepin-Kuzmin (GZK) energy cutoff ($\\sim 5\\times\n10^{19}$ eV), which is due to photomeson production by interactions \nwith \nthe\ncosmic microwave background radiation, unless they are originated at\ndistances closer than about 50 Mpc (e.g., Protheroe \\& Johnson 1995,\nMedina Tanco, de Gouveia Dal Pino \\& Horvath 1997). On the other hand, \nif\nthe UHECRs are mostly protons from nearby sources \n(located within $\\sim $\n 50 Mpc), then the arrival directions of the events should point toward\ntheir sources since they are expected to be little deflected by the\nintergalactic and Galactic magnetic fields (e.g., Stanev 1997, Medina \nTanco,\nde Gouveia Dal Pino \\& Horvath 1998). The present data shows no \nsignificant\nlarge-scale anisotropy in the distribution related to the Galactic disk \nor\nthe local distribution of galaxies, although some clusters of events \nseem \nto\npoint to the supergalactic plane (Takeda et al. 1999, \nMedina Tanco 1998). \n\nA number of source candidates and acceleration mechanisms have been \ninvoked but all of them have their shortcomings \n(see, e.g.,\n%AL \n%Hillas 1984, Protheroe 1999, Cronin 1999,\n% \nOlinto 2000 for a review).\n%and \n% both galactic and extragalactic environments are, in principle, \n%allowed. \n%Although\n%at the present the observed events \n%(above 55 with $E > 4 \\times 10^{19}$ eV; Takeda et al. 1999)\n%seem to favor an extragalactic origin,\n%further events \n%must still be accumulated in order to improve the statistical analysis \n%and\n%make the arrival direction distribution\n%more clear \n%(Medina Tanco 1998, Takeda et al. 1999).\n%\n%Possible\n%acceleration mechanisms require either direct accelerators (involving\n%compact sources with high magnetic fields and rotation rates) or \n%stochastic\n%accelerators (in powerful shocks), each one with their own \n%difficulties for\n%reaching UHE (Hillas 1984).\n%\n%Among the source candidates, shock acceleration\n%in the radio lobes and jets of powerful radio sources and AGNs may \n%appear \n%as an\n%attractive possibility (e.g., Rachen \\& Bierman 1993), but the lack of \n%direct\n%correlation of the arrival directions of most of the observed UHECRs \n%events\n%with nearby radio galaxies or AGNs poses some difficulties to these\n%candidates. The production of UHECRs by hadronization of quarks and \n%glouns\n%generated during the evaporation of primordial black holes located \n%mainly \n%at\n%an extended Galactic halo has been also recently examined as an \n%alternative\n%mechanism (Barrau 1999). \n%Other potential sources are millisecond pulsars\n%with very strong magnetic fields (B $>10^{12} $ G), or magnetars.\n% \n%Here, we investigate whether \n%magnetars ( \n%millisecond pulsars\n%with very strong magnetic fields $B >10^{12} $ G can produce \n%UHECR. \nParticles can,\nin principle, extract the required energies from an induced e.m.f. in a\ncircuit connected between the polar and the last open field line of a \nrapidly\nrotating pulsar, although it is not clear how the large voltages can \nbe maintained (e.g., Hillas 1984), or be accelerated in reconnection\nsites of magnetic loops, $if$ these can be produced, e.g., \nby Parker instability, \non the surface of a pulsar (Medina Tanco, de Gouveia Dal Pino \\& \nHorvath \n1997), but the accelerated particles will probably lose\nmost of their energy gain by curvature radiation while dragged along by \nthe magnetic dipole field (Sorrell 1987). Alternatively, Olinto, \nEpstein, \\& Blasi (1999) have recently proposed that UHECRs could be \niron nuclei\nstripped by strong electric fields from the surface of highly \nmagnetized\nneutron stars and accelerated in a relativistic MHD wind. It is \nnot clear however, how the accelerated particles can\nescape from the magnetosphere of the star, for although efficient power\n extraction may be\npossible, there is a dense positron-electron plasma generated with the\nrelativistic wind (Gallant \\& Arons 1994) \nthat will possibly modify the electric fields and also\ninteract with the energetic particles. Their model also predicts that \na\ncorrelation with the Galactic plane should become evident as data \ncollection\nat the highest energies improves.\n%AL\n%We here discuss an alternative model in which UHECRs are mostly protons\nIn this paper we discuss an alternative model in which UHECRs are \naccelerated in\nmagnetic reconnection sites outside the magnetosphere of very young \nmillisecond pulsars being produced by accretion induced collapse (AIC) \nof a \nwhite dwarf.\n%AL \n%In the following section, we discuss the basic\n%assumptions of our model and evaluate the \n%particle spectrum of UHECRs emerging from individual sources, \n%and the integrated\n%particle flux due to AIC-pulsars produced in all galaxies located \n% within the volume where the UHECRs are almost unaffected by the GZK \n%cutoff \n%(i.e., within a\n%radius $\\sim $ 50 Mpc). In \\S 3\n%we draw our conclusions and discuss the results.\n\\section{The model}\nWhen a white dwarf reaches the critical Chandrasekhar mass $\\sim 1.4$\nM$_{\\odot }$ through mass accretion, in some cases it does not explode \ninto\na type Ia supernova, but instead collapses directly to a neutron star \n(e.g.,\n Woosley \\& Baron 1992 and references therein). \n%Neutron \n%stars\n%formed through accretion induced collapse (AIC) have been proposed as \n%an \n%alternate channel to explain the birthrate of millisecond pulsars in \n%globular \n%clusters and in the Galactic disk,\n% and \n%the properties of low-mass X-ray binaries (Fryer et al. 1999).\nThe accretion flow spins up the star and confines the magnetosphere \nto a radius $R_X$ where plasma stress in the accretion disk and \nmagnetic \nstress \nbalance\n(Arons 1993). At this radius, which also defines the inner radius of \nthe \naccretion disk, the equatorial flow will divert into a funnel inflow\nalong the closed \nfield-lines toward the star (Gosh and Lamb 1978), and \na centrifugally \ndriven wind outflow (Arons 1986). \nRecently, Shu et al. (1994, 1999)\nhave studied the detailed field geometry \nof magnetized stars accreting matter from a disk. \nTwo surfaces of null poloidal field lines are required\nto mediate the geometry of dipole-like field lines of the star with \nthose\nopened by the wind and those trapped by the funnel inflow emanating \nfrom\nthe $R_X$ region. Labeled as \"$helmet$ $streamer$\" and \"$reconnection$ \n$ring$\" \nin\nFigure 1, these magnetic null surfaces begin or end on $Y$ points. \nAcross each null surface, the poloidal field suffers a sharp reversal\nof direction. \n%According to the Amp\\`ere's law, large electric currents\n%must flow out of the plane shown in Figure 1, along the null \n%surfaces, and\n%In the presence of finite electric resistivity, \nDissipation of \nthe large \nelectric currents that develop along the null surfaces\nwill lead to reconnection of the oppositely directed \nfield lines (e.g., Biskamp 1997, Lazarian \\& Vishniac 1999).\n%We here investigate the possibility that the magnetic energy \n%released by\n%reconnection from the helmet streamer region in an AIC-pulsar \n%is able to accelerate particles \n%to the UHEs.\nHelmet streamers (or flare loops) are also present in the magnetic \nfield configuration\n of the \nsolar corona. \n%(e.g., Kahler 1992). \nThe magnetic\nenergy released by reconnection in the helmet streamer \n drives violent\noutward motions in the surrounding plasma\nthat accelerate copious \namounts \nof solar cosmic rays without producing many photons (Reames 1995).\nA similar process may take place in the helmet streamer of \nyoung born AIC-pulsars and the magnetic energy released may \naccelerate particles to the UHEs.\nThe reconnection rings in the disk would\nalso, in principle, be able to accelerate UHECRs, \nhowever, as we will see below,\n%the required disk accretion rates are super-Eddington and, \n%in such a condition, \nthe intense radiation field produced in the disk must \nprevent accelerated UHE particles to escape from it.\n%The acceleration via reconnection process should be efficient\n%to compensate for the inevitable curvature losses.\nThe particular mechanism of particle acceleration\nduring the reconnection events is still unclear in spite of \nnumerous attempts\nto solve the problem \n(see \n%Holman 1985, \nLaRosa et al 1996, Litvinenko 1996).\nCosmic rays from the Sun confirm that the process is sufficiently \nefficient in spite of the apparent theoretical difficulties for its\nexplanation.\nSolar flares observations indicate that \nthe reconnection speed \ncan \nbe \nas high as one tenth of the Alfv\\'en velocity. \nAs in the conditions we deal with this speed\napproaches $c$, the expected acceleration rate is large. \nWe discuss the details of particle acceleration during \nreconnection events in \nLazarian \\& de Gouveia Dal Pino (2000). \nWe argue that \n protons can be accelerated by the large induced electric field\nwithin the reconnection region \n(e.g., Haswell, Tajima, \n\\& Sakai 1992, Litvinenko 1996) over a time scale \n$\\sim \\Delta R_X/c$,\nwhere $\\Delta R_X$ is the size of the reconnection zone (see\nbelow).\nThe required electric field is less than the critical value for pair\nproduction and therefore is sustainable (see also \\S 3).\n%Among the\n%potential mechanisms, the induction of an \n%effective accelerating \n%electric \n%voltage, and\n%\n%we describe a promising\n%process by which the particles may be accelerated in \n%the reconnection region but it is still not clear\n%whether the particular process can explain the mystery of cosmic \n%particle acceleration.\n%where we show that \n%first order Fermi acceleration\n%of cosmic rays when they bounce back and forth between the \n%oppositely directed and approaching magnetic field fluxes\n%in the reconnection zone,\n%may appear as promising candidates. \n%In the latter,\n%the reconnecting fluxes play the role of approaching mirrors \n%increasing\n%the energy of a proton by $\\sim V_{\\rm rec}/c$ any time the proton is \n%bounced\n%back. \n\nFor a Keplerian disk, the inner disk edge $R_X$ rotates at \nan angular speed\n($G M_{\\star}/R_X^3)^{1/2}$, and equilibrium between gravity \nand centrifugal\nforce at $R_X$ will lead to co-rotation of the star\nwith the inner disk edge, i.e., \n$R_X \\, = \\, (G M_{\\star}/\\Omega _{\\star}^2)^{1/3}$,\nwhich for typical millisecond pulsars with \nrotation periods \n$P_{\\star} = 2\\pi/\\Omega_{\\star} \\simeq 1.5 - 10$ ms, mass\n$M_{\\star} \\, \\simeq \\, $1 M$_{\\odot}$, \nand radius $R_{\\star} = 10^6$ cm, \ngives \n$R_X \\simeq (2 $ to $ 7) \\times 10^{6}$ cm $R_{6}$,\nwhere $R_{6} = R_{\\star}/ 10^6$ cm.\n\n%AL\n%It is customary to \nThe primary condition usually assumed \n%the reconnection \non the region \n% for it to be\n%able \nto accelerate particles of charge $Ze$ to energies $E$ \n is that its width\n$\\Delta R_X \\, \\geq \\, 2 \\, r_L$, \nwhere \n$r_L$ is the particle Larmour radius \n$r_L = E /Z e \\, B_X$ (Hillas 1984) and\n$B_X$ is the magnetic \nfield (normal to particle velocity) at the $R_X$ region,\n%\\begin{equation}\n$B_X \\, \\simeq \\, B_{dipole}(R_X) \\left( {\\frac{R_X}{ \\Delta R_X} \n}\\right)^{1/2}$\n%\\end{equation}\n%\\noindent\n(e.g., Arons \n1993), where $B_{dipole}(R_X) = B_{\\star} \\, (R_{\\star}/R_X)^{3}$ is the \nmagnetic field that would be\npresent in the absence of the shielding disk, and \n$B_{\\star}$ is the magnetic field at the surface \nof the star. \n%AL\nWhile this condition on $\\Delta R_X$ is usually invoked to allow\n particles to bounce back and forth thus gaining energy, we find\nthat for accelerated protons the synchrotron losses\nmay be too large if they bounce within the reconnection\nzone. Then, in our model \nthe condition above is invoked to assure that the \nfield $B_X$ will focus\nparticles to move within a small angle into the reconnection zone.\n%We also assume that at the center of the reconnection zone the magnetic\n%field goes to zero which means that the reconnected fluxes\n%have a marginal shared magnetic field component, i.e. nearly\n%antiparallel.\n%\nBesides, \none \nshould also expect that: \n$\\Delta R_X/ R_X << 1$. Both conditions above imply that\n%\\begin{equation}\n%1 \\, > > \\, \\left({\\frac{\\Delta R_X}{R_X } }\\right) \\, \\gtrsim \\, 0.1 \n%\\, Z^{-2} \\, E_{20}^{2} \\, B_{13}^{-2} \\, \\Omega_{2.5k}^{-8/3} \n%\\end{equation}\n$1 \\, > > \\, \\left({\\frac{\\Delta R_X}{R_X } }\\right) \\, \\geq \\, 4 e^{-\n2} \n\\, Z^{-2} \\, R_{\\star}^{-6} \\, (G \\, M_{\\star})^{4} \\, \nE^{2} \\, B_{\\star}^{-2} \\, \\Omega_{\\star}^{-8/3}$. \nThis relation indicates that for a given ratio $\\Delta R_X/R_X$ and \nparticle \nenergy $E$, the stellar magnetic field $B_{\\star}$ must \nsatisfy \n\\begin{equation}\nB_{13} \\, \\gtrsim \\, Z^{-1} \\, E_{20} \\, \\Omega_{2.5k}^{-4/3} \\, \n \\left({\\frac{\\Delta R_X/R_X } { 0.1}}\\right)^{-1/2} \n\\end{equation}\n\\noindent \nwhere we have assumed \n$M_{\\star} \\, = \\, 1 M_{\\odot}$, \n$R_{\\star} = R_6$,\n$E_{20} \\, = \\, E/10^{20} $ eV, \n$\\Omega_{2.5k} = \\Omega_{\\star}/ 2.5 \\times 10^3$ s$^{-1}$,\nand $B_{13} = B_{\\star}/10^{13}$ G.\nThe corresponding allowed zones in the $B_{\\star} - \\Omega_{\\star}$\nplane are shown in Figure 2 for $E_{20} = 1$ and $E_{20} = 10$,\nand different values of the ratio $\\Delta R_X/R_X$. \n%As expected, the smaller the size of the acceleration zone, the larger\n% the magnetic field strength that is required to accelerate the \n%particles. \nThe curves with $\\Delta R_X/R_X = 1 $ determine extreme lower bounds \non the stellar surface magnetic field and the angular speed. \nWe note that stellar magnetic fields \n $10^{12} $ G $ < B_{\\star} \\lesssim $ $10^{15}$ G \nand angular speeds \n$4 \\times 10^{3}$ s$^{-1}$ $\\gtrsim \\Omega_{\\star} \\, > \\, 10^{2} $ \ns$^{-1}$,\n%which correspond to spin periods\n%1 ms $\\lesssim \\, P_{\\star} \\, < \\, $ 60 ms, \nare able to accelerate\nparticles to energies $E_{20} \\, \\gtrsim $ 1. \n%Slower pulsars with \n%angular \n%frequencies $\\Omega_{\\star} \\lesssim 10^{2} $ s$^{-1}$\n%require too large surface magnetic fields ($B_{\\star} > \\, 10^{15}$ \n%G) \n%to efficiently accelerate the\n%particles. \n%(We note that this upper bound on $\\Omega_{\\star}$\n%is actually much larger than the break-up frequency \n%of the white dwarf progenitor, for which \n%$\\Omega_{WD} \\simeq$ 11.5 s$^{-1}$ $ M_{\\odot} R_{8}$.)\nThe values above are perfectly compatible with the parameters \nof young pulsars and\nEq. (1) is thus a good representation of the typical conditions \nrequired \nfor particle acceleration to the UHEs in reconnection zones of AIC-\npulsars.\n%\n%cut due to lack of space\n%Also, we will see later that reconnection regions with \n%$\\Delta R_X/R_X \\, \\lesssim \\, 0.1$\n% have sizes that are under the length scales\n%for which interactions of the accelerated protons \n%with the radiation field become significant. \n%\nThe substitution of Eq. (1) into the equation for $B_X$ \nimplies a magnetic field \nin the acceleration zone \n$B_X \\, \\simeq \\, 1.5 \\times 10^{12}$ G $B_{13} \\, \\Omega_{2.5k}^2 \\, \n\\left({\\frac{\\Delta R_X/R_X } { 0.1}}\\right)^{-1/2}$.\n\nA newborn millisecond pulsar spins down due to \nmagnetic \ndipole radiation in a time scale given by\n$\\tau_{\\star} = \\Omega_{\\star}/\\dot \\Omega_{\\star} \\simeq \n\\left({\\frac{ I c^3 }{B_{\\star}^2 R_{\\star}^6 \\Omega_{\\star}^2 } \n}\\right)$, \nwhich for a moment of inertia \n$I = 10^{45}$ g cm$^2$\n%$I = 0.4 M_{\\star} R_{\\star}^2 \\simeq 8 \\times 10^{44}$ g cm$^2$,\n%and $R_{\\star} = R_6 $ cm \ngives\n%\\begin{equation}\n$\\tau_{\\star} \\simeq 4.3 \\times 10^7 $ s $ B_{13}^{-2} \\, \n\\Omega_{2.5k}^{-2}$. \n%Considering the magnetohydrodynamics equations \nWe can show that the \ncondition that the magnetosphere and \nthe disk stresses are in equilibrium \nat \nthe inner disk edge results a disk mass accretion rate \n%$\\dot M_D \\, \\simeq \\, \\alpha_X^{-2} \\, R_X^{-7/2} \\, (\\mu_{\\star}^4/G \n%M_{\\star})^{1/2}$, \n$\\dot M_D \\, \\simeq \\, \\alpha_X^{-2} \\, I c^3 \\, \n(G \\, M_{\\star})^{-5/3} \\, \\Omega_{\\star}^{1/3} \\, \n\\tau_{\\star}^{-1} $, \nwhere \n%$\\mu_{\\star} \\, = \\, B_{\\star} \\, R_{\\star}^3$ is the stellar magnetic \n%dipole \n%moment and\n$2 \\gtrsim \\alpha_X > 1$\n measures the amount of \nmagnetic dipole flux that has been pushed by the disk accretion flow to \nthe inner edge of the disk \n(Gosh \\& Lamb 1978, \n%Arons 1993,\n Shu et al. 1994). \nSubstitution of the \nprevious equations yields \n$\\dot M_D \\, \\simeq \\, 3 \\times 10^{-8} M_{\\odot} $ s$^{-1} \\, \n{\\alpha_2}^{-2} \\,\nB_{13}^2 \\, \\Omega_{2.5k}^{7/3}$ \n(where $\\alpha_2 = \\alpha_X/2$),\n which is much larger than the \nEddington accretion rate \n$\\dot M_{Edd} \\simeq 7.0 \\times 10^{-17} M_{\\odot} $ s$^{-1}\n(M_{\\star}/ M_{\\odot}) $.\nHowever, this \"super-Eddington\" accretion \n(which is correlated to $\\tau_{\\star}$) will \nlast for a time $\\tau_{D}$, which is only\na small fraction ($f_D$) of $\\tau_{\\star}$. \nThe strong radiation pressure from the accreted material will \n cause most of the infalling material to be ejected from the system,\n%(at approximately the same rate). \nand this will in turn cause the accretion rate \n%onto \n%the central object \nto rapidly decrease to\na value nearly equal to the Eddington limit\n(e.g., Lipunova\n1999). \nAdvection dominated inflow-outflow solutions involving \nsupercritical accretion onto neutron stars predict a \ntotal mass \ndepostion on the star \n$\\sim $ few $0.01 M_{\\odot}$ (e.g., Brown et al. 1999). \n%Van den Heuvel, Savonijc 1999).\nThus assuming that a mass $M \\sim 0.04 M_{\\odot}$ \nis accreted during the supercritical phase, \nwe find \n$\\tau_D \\simeq M/\\dot M_D \\simeq 1.3 \\times 10^6 $ s, and\n$f_D \\simeq 0.03$. \n%too long during \n% the AIC phase. As indicated by the equation above, \n%its duration is \n%essentially determined by $\\tau_{\\star}$ which is in turn very short. \n%On the other hand, \nThe acceleration of UHECRs in the reconnection zone, \non the other hand, will \nlast as long as the\nsupercritical accretion. \nIt is well known that the most violent solar flares \ncan live up to several hours and the more energetic the \nlonger-lived they are. In our scenario, \nconsidering that the reconnecting magnetic fields \nare several orders of magnitude larger than\nin the solar corona, \nit is reasonable to expect that\nthe most violent reconnection events can live\nat least for several days, \nas required by $\\tau_D$. \n%As the supercritical \n%accretion approaches the \n%end, the \n%newborn pulsar decreases its rotation speed due to electromagnetic \n%radiation at a rate $\\tau_{\\star}^{-1}$. \nThe spectrum evolution of \nthe \naccelerated UHECRs will be, therefore, determined by \n$\\tau_D = f_D \\tau_{\\star}$ \n(see below). \n\nIn order to derive the spectrum of accelerated particles, let us first \nevaluate the rate of magnetic energy that can be extracted from the \nreconnection region, \n$\\dot W_B \\simeq (B_X^2/ 8\\pi) \\, \\xi v_A \\, (4\\pi R_X \\,\\Delta R_X \n)$,\nwhere $v_A \\sim \\, c$ is the Alfv\\'en velocity,\nand $\\xi \\, < \\, $1 is a factor that determines the amount of magnetic \nenergy released in the reconnection that will accelerate the \nparticles. \n%(Lazarian \\& Vishniac 1999). \nSubstituting the previous relations into this equation, one finds\n%\\begin{equation}\n$\\dot W_B \\, \\simeq \\, 2.6 \\times 10^{46} $ erg s$^{-1} \\, \\xi \n\\, B_{13}^2 \\, \\Omega_{2.5k}^{8/3}$. \n%\\end{equation}\n%\\noindent\nAccording to our model assumptions, in a reconnection burst an electric\nfield arises inductively \n%(and emerges mostly perpendicularly from page in Fig. 1) \nbecause of plasma fow across the $\\vec B$ lines. The corresponding\nmaximum voltage drop is\n$ V \\, \\simeq \\, \\epsilon \\, \\Delta R_X \\, \\simeq (v_A/c) B_X \\Delta R_X \n\\simeq B_X \\Delta R_X $\nwhere $\\epsilon$ is the electric field strength \n(e.g., Bruhwiller and Zweibel 1992).\nOnce a particle decouples from the injected fluid, it \nwill be ballistically accelerated by the electric field and the\nmomentum attained will depend on the intensity of the electromagnetic\nburst and on the time and location at which it decouples from the\ninjected fluid motion (e.g., Haswell et al. 1992).\nIt is out of the scope of this work to quantitatively constrain the\nburst characteristics and thus to deduce the detailed spectrum of particle\nenergies. Clearly, however, the more energetic bursts \nwill give rise to a \nhigher average energy for the ejected particles \n(Haswell et al. 1992). In these extreme cases, the induced electric \nvoltage will dominate and the particles will be accelerated to an \naverage energy \n$E \\simeq V \\, Z e $, which \naccording to the equation above and consistently with \nrelation (1) is \n$E \\simeq 10^{20}$ eV.\nThe UHECR flux emerging from the reconnection site can then be \nestimated as\n%\\begin{equation}\n$\\dot N \\, \\simeq \\, {\\frac {\\dot W_B } { E}} \\, \\simeq \\, 1.6 \n\\times 10^{38} \\, {\\rm s}^{-1} \\, \\xi \\, B_{13}^2 \\, \n\\Omega_{2.5k}^{8/3} \\,E_{20}^{-1}$\n%\\end{equation}\n%\\noindent \nfor particles with energy $E \\gtrsim 10^{20} $ eV, and\n the particle spectrum $N(E)$ is obtained from \n%(see also Olinto et \n%al. 1999 for similar treatment)\n%\\begin{equation}\n$\\dot N \\, = \\, N(E) \\, {\\frac {dE } { dt}} \\, \n\\simeq \\, N(E) \\, {\\frac {dE } { d \\Omega_{\\star} } } \\, \\dot \n\\Omega_{\\star}/f_D$,\n%\\end{equation}\n%\\noindent\nor \n\\begin{equation}\nN(E) \\, \\simeq \n% {\\frac { d \\Omega_{\\star} }{dE } } } \\, \n%{\\frac { \\dot N }{\\dot \\Omega_{\\star}} } }\n%\\, 5.8 \\times 10^{34} \\, {\\rm GeV}^{-1} \\, \\xi \\, Z^{-1/2} \\, \n\\, 1.7 \\times 10^{33} \\, {\\rm GeV}^{-1} \\, \\xi \\, Z^{-1/2} \\, \nB_{13}^{-\n1/2} \\, E_{20}^{-3/2} \\, \\left({\\frac{\\Delta R_X/R_X } \n{0.1}}\\right)^{-1/4}\n\\end{equation}\n\\noindent \nwhere Eq. (1) \n has \ngiven \n$ d \\Omega_{\\star}/dE \\simeq 2.1 \\times 10^{-17} \\, Z^{-3/4} \\, \nE_{20}^{-1/4} \\, B_{13}^{-3/4} \\, \\left({\\frac{\\Delta R_X/R_X } { \n0.1}}\\right)^{-3/8}$ \n (with the signal made equal in Eq. 1). \nEq. (2) above predicts that \n$N(E) \\propto E^{-3/2} = E^{-1.5}$, which is a flat spectrum\n%AL (otherwise eq.(5) is questionable)\n%\\footnote{ }\n%\nin \ngood\nagreement with observations (e.g., Olinto 2000).\n%AL\n%We note that the derivation above which is valid for the most\n%extreme accelerations may break down in cases in which the \n%particles are, for ex., not well collimated along the electric \n%field directions \n%(Hasweel et al. 1992; see however, Litvinenko (1996) and LG2000 for \n%a generalization of the calculation above and the evaluation of \n%have focused on the conditions at which reconnection allows for the\n%production of particles with extremely high energies. \n%AL\n%Of course,\n%it is not unlikely that a large number of particles with lower\n%energy will be also produced.\n%However, a precise determination of the entire spectrum \n%produced in a single reconnection event is dependent on the properties \n%of the particular acceleration \n%process that is taking place in the reconnection site and will \n%be discussed elsewhere, for different potential acceleration\n%mechanisms (LG2000). Nonetheless, as the derived spectrum is reasonably \n%flat our present assumption that the bulk\n%of the energy is mostly consumed for acceleration of the ultra high \n%energy cosmic rays is justifiable.\n%The fact that the derived spectrum is flat may serve as {\\it \n%a posteriori}\n%justification for our assumption. \n\nThe particle distribution emerging from the source will not be \nisotropic. Thanks to the magnetic field geometry in the reconnection \nsite (see Fig. 1), it will be confined to a ring (above and below the \naccretion disk)\nof thickness and \nheight given both by $\\sim \\Delta R_X$. \nThe distribution will thus be beamed in a solid angle \n$\\Delta \\Omega \\, \\simeq \\, 4 \\pi (\\Delta R_X/R_X)^2$.\nLet us now, estimate the resulting flux of UHECRS at the Earth. \n%cut due to lack of space\n%A \n%complete and exact derivation of this flux is a \n%complex task well beyond the scope of this letter, nonetheless, we can \n%estimate at least the magnitudes involved.\nThe total number of objects formed via AICs \nin our Galaxy is limited by nucleosynthesis constraints to a very small \nrate \n$ \\sim \\, (10^{-7} \\, - \\, 10^{-4}$) yr$^{-1}$, \nor in other words, less \nthan 0.1 \\% of \nthe total \ngalactic neutron star population (Fryer et al. 1999). \nAssuming then that the rate of AICs in the Galaxy is\n${\\tau_{AIC} }^{-1} \\, \\simeq \\, 10^{-5}$ yr$^{-1}$, we can evaluate \nthe probability $a $ $priori$ of having UHECRs events produced in the \nGalaxy. \nThe beaming mentioned above\nwill reduce the probability\nof detection of the events of a source by a factor \n$f_b \\sim \\, (\\Delta R_X/R_X)^2 \\simeq 10^{-2}$.\nThus the probability \nwill be only\n$P \\, \\simeq \\, f_b \\, {\\tau_{AIC}}^{-1} \\, t \\, \\simeq \\, 2 \\times \n10^{-\n6}$, where $t = 20 $\nyears accounts for the time the UHECR events have been collected in \nEarth detectors since the operation of the first experiments. \nSince the individual contribution to the observed UHECRs due to \nAICs in our Galaxy is so small we must evaluate the integrated \ncontribution due to AICs from all the galaxies located within a\nvolume \nwhich is not affected by the GZK effect, i.e., within a radius \n$R_{50} = R_G/ 50$ Mpc.\nAssuming that each galaxy has essentially the\nsame rate of AICs as our Galaxy and taking the standard galaxy \ndistribution \n$n_G \\simeq \\, 0.01 \\, e^{\\pm 0.4}\\, h^3 $ Mpc$^{-3}$ (Peebles 1993)\n(with the Hubble parameter defined as $H_o = h$ 100 km s$^{-1} $ \nMpc$^{-1}$), the resulting flux at $E_{20} \\, \\geq $ 1 is\n%AL 25.09 (please check)\n%$F(E) \\, \\simeq \\, f_b \\, N(E) \\, n_G \\, {\\tau_{AIC}}^{-1} \\, R_{G}$, \n%which gives\n$F(E) \\, \\simeq \\, \\, N(E) \\, n_G \\, {\\tau_{AIC}}^{-1} \\, R_{G}$, \nwhich gives\n\\begin{equation}\n%F(E) \\, \\simeq \\, 1.1 \\times 10^{-27} \\xi \\, {\\rm GeV}^{-1} \nF(E) \\, \\simeq \\, 3.3 \\times 10^{-29} \\xi \\, {\\rm GeV}^{-1} \n{\\rm cm}^{-2} {\\rm s}^{-1} \\,\nZ^{-1/2} \\, B_{13}^{-1/2} \\, \nE_{20}^{-3/2} \\, {\\tau_{AIC,5}}^{-1} \\, n_{0.01} \\, \nR_{50} \\left({\\frac{\\Delta R_X/R_X } {0.1}}\\right)^{-1/4} \n\\end{equation}\n\\noindent \nwhere ${\\tau_{AIC,5}}^{-1} \\, = \\, {\\tau_{AIC}}^{-1}/ 10^{-5}$ yr$^{-\n1}$,\n and \n$n_{0.01} = n_G/0.01 $ h$^3$ Mpc$^{-3}$.\nObserved data by the AGASA experiment (Takeda et al. 1999) gives a flux \nat \n$E = $10$^{20}$ eV of \n$F(E) \\, \\simeq \\, 4 \\times \\, 10^{-30}$ Gev$^{-1}$ cm$^{-2}$ s$^{-\n1}$, so \nthat the efficiency of converting magnetic energy into UHECR should be \n%the reconnection efficiency factor needs to be only\n%AL \n%$ \\xi \\, \\gtrsim \\, 3.6 \\times 10^{-3}$\n$ \\xi \\, \\gtrsim \\, 0.1$\nin order to reproduce such a signal.\n%AL (this is still very uncertain) \n%(reconnection theory predicts \n%$ \\xi \\, \\sim \\, 0.1 - 1$; e.g., Lazarian \\& Vishniac 1999).\n% \n%AIC-pulsars do \n%not receive the same large kicks observed in neutron stars formed in \n%type \n%II SN and they are expected be the prime candidates for pulsar \n%population in \n%the globular clusters. \n%\n\\section{Conclusions and Discussion}\nWe have discussed the possibility that the UHECR events observed above \nthe GZK limit are protons accelerated in reconnection sites just above \nthe magnetosphere of very young millisecond pulsars originated by \naccretion induced collapse.\nAIC-pulsars with surface\nmagnetic fields \n $10^{12} $ G $< \\, B_{\\star} \\lesssim $ $10^{15}$ G \nand spin periods\n1 ms $\\lesssim \\, P_{\\star} \\, < \\, $ 60 ms, \nare able to accelerate\nparticles to energies $\\geq \\, 10^{20} $ eV. These limits can be \nsummarized by the condition \n$B_{\\star} \\, \\gtrsim \\, 10^{13}$ G $ (P_{\\star}/2.5 $ ms)$^{4/3}$ \n%which is \n%valid for \n%fiducial stellar and accretion disk/reconnection parameters \n(Eq. 1 and \nFig. 2).\nBecause the expected rate of AIC sources in our Galaxy \nis very small, \n%($\\sim \\, 10^{-5 }$ yr$^{-1}$),\n% its isolated \n%contribution \n%to the observed flux of UHECRs is negligible and \nthe total flux is \ngiven by the integrated contribution from AIC sources produced in the \ndistribution of galaxies within a volume which is unaffected by the \nGZK cutoff (of\nradius $R_G \\simeq 50 $ Mpc). \nWe find that the reconnection efficiency factor needs to be \n%$ \\xi \\, \\gtrsim \\, 3.6 \\times 10^{-3}$\n$ \\xi \\, \\gtrsim \\, 0.1$\nin order to reproduce the observed flux.\n%AL\n%cut due to lack of space\n%A further study of the reconnection mechanism \n%is necessary to understand\n%whether this efficiency is attainable.\nThis result is appealing because it predicts \nno correlation of UHECR events with the Galactic plane, in agreement \nwith present observations. \n%cut due to lack of space\n%Unfortunately,\n%the conditions within the acceleration region \n%we are studying\n%are very different from whatever we know and therefore the Sun\n%data is of marginal help.\n%\nHowever, as data collection improves, we \nshould expect some sign of correlation with the local distribution of \ngalaxies and the supergalactic plane. \n%Although statistically limited, present data base provides \n%some evidence which supports this prediction \n%and\n%indicates that the arrival directions of the\n%UHECRs are compatible with a scenario in which their sources\n%trace the inhomogeneous distribution of luminous matter in the\n%local universe \n%(Medina Tanco 1998),\nThese predictions \n%but it \ncan be ultimately tested by coming experiments such as \nthe AUGER Observatory which will provide high statistics samples of \nUHECRs.\n% (AUGER Projet Design report 1997).\n\n%cut due to lack of space\n%On deriving the flux of UHECRs (eq. 3), we have neglected propagation \n%effects, as the particles are produced essentially within the GZK \n%sphere. But we should note that particles with energies \n%smaller than $10^{20}$ eV will have a larger pathlength that may\n% result in a spectrum at lower energies which is somewhat \n%steeper than the source\n%spectrum. A similar steepening may also occur for energies \n%above $10^{20}$ eV because a smaller volume must contribute for this\n%part of the spectrum. \n%Moreover, particles with E $ > 10^{20}$ eV \n%interacting at distances above 50 Mpc will produce lower energy \n%particles that may also add to the steepening.\n%AL \n%These propagation \n%effects are evaluated in LG2000 where the \n% the entire source spectrum produced during a \n%reconnection \n%event is derived taking into account the details of the \n%acceleration mechanism%. \n\n\n%A disadvantage of the model is that it \n%invokes to yet unclear details\n%of the reconnection acceleration mechanism. \nThe model \n%discussed here \npredicts a highly super-Eddington accretion \nmass \nrate during part of the AIC process. In such a regime, one \nshould \nexpect a large mass outflow from the stellar surface itself\nwhich might \nalter the coronal conditions near the helmet streamer region. However,\nthe strong closed magnetic fields in the pulsar magnetosphere can \ninhibit \nthe gas \noutflow from the stellar surface if the \nsurface temperature does not exceed the value at which the radiation \nenergy \ndensity ($a \\, T^4$) equals the magnetic field energy density \n($B_{\\star}^2/8 \\pi$), i.e., \n$T_{\\star} \\lesssim 5 \\times 10^9 $ K $ B_{13}^{1/2}$; this upper limit \nis \nconsistent with the predicted values for a neutron star that is formed\nby AIC (Woosley \\& Baron 1992).\n\nLet us consider now the energy loss mechanisms that may \naffect the efficiency of the acceleration of the particles to the UHEs. \nEnergy losses by curvature radiation which occur when cosmic rays have to \nstream along magnetic field lines with a finite radius of curvature \n$R_c$, have \na cooling time \n$t_{rc} \\propto R_c^2 $. \n%This time can be very short near the surface of the pulsar \n%where particles have to stream along the curved trajectories provided by the \n%strong dipole field lines, but \nIn our model, the reconnection takes place in the helmet streamer \nregion\n(see Fig. 1) where $R_c \\rightarrow \\infty$ and \ntherefore, $t_{rc} > > t_a$, where \n$t_a$ is the acceleration time for a proton in the reconnection site.\n[We can \nuse the dimensions of the reconnection site derived in \\S 2 \nto estimate the order of magnitude of \n$t_a \\simeq \\Delta R_X/ c \\, \\simeq 8 \\times 10^{-6} {\\rm s} \\,\n\\left({\\frac{\\Delta R_X/R_X}{0.1} }\\right) \\, \\left({ \\frac{R_X} {2.45 \n\\times 10^6 {\\rm cm} } }\\right)$.]\n%For an induced electric voltage in the reconnection site \n%$V \\simeq B_X \\, \\Delta R_X$, the acceleration time scale \n%can be determined from the momentum balance \n%$(\\gamma m_p c) \\, t_a^{-1} \\simeq V e/ \\Delta R_X$, which gives \n%$ t_a \\simeq 8 \\times 10^{-6}$ s $E_{20} \\, \n%(B_X/1.5 \\times 10^{12} G)^{-1}$.)\nThe time for synchrotron losses is \n$t_{syn} \\propto \\theta^{-2}$, where \n $\\theta$ is the particle pitch angle. \n Since we require that the protons in the reconnection zone\n are accelerated by an induced electric field \nrather than by a scattering process, \nthey are expected to \nmaintain \nbeamlike pitch angles while escaping along the magnetic field lines,\n i.e., \n$\\theta < < 1$ and $t_{syn} > > \nt_a$. \n%\n% cut due to lack of space\n%We note that synchrotron losses will be also \n%negligible in stochastic processes, like Fermi acceleration, in the course \n%of reconnection events, if heavy nuclei rather than protons are \n%being accelerated. \n\nThe accelerated protons may also undergo energy loss by pion \nand $e^{\\pm}$ \npair production \ndue to interactions with photons from the \naccretion disk radiation field.\nThe characteristic distance scales for these processes \n%to occur \n%efficiently \ncan be estimated by \n$\\lambda_{p \\gamma} \\simeq (\\sigma_{p \\gamma} n_{\\gamma})^{-1}$ and \n$\\lambda_{pair} \\simeq (\\sigma_{pair} n_{\\gamma})^{-1}$ \nfor \nphoto-pion and pair production, respectively,\nwhere $n_{\\gamma}$ is the photon number \ndensity at the reconnection site, \n$\\sigma_{p \\gamma} \\simeq 2.5 \\times 10^{-28} $ cm$^{-2}$ is the cross \nsection \nfor pion production, \n%(with an inelasticity $K_p \\sim$ 1),\n and \n$\\sigma_{pair} \\simeq 10^{-26} $ cm$^{-2}$ is the cross section \nfor pair production \n%(with an inelasticity $K_p \\sim \\, 2 \\times 10^{-3}$)\n(e.g., \n%Sorrell 1987, \nBednarek and Protheroe 1999). \nIn order to estimate $n_{\\gamma}$,\nwe must determine the luminosity in the accretion disk. \nAt super-Eddington accretion rates, the disk is thicker \nand heat is radially advected \nwith matter. The luminosity of such advective supercritical accreting \ndisks\n%has been evaluated numerically (e.g., Lipunova 1999) and \nis given by \n$L_D \\simeq [0.6 + 0.7 \\, ln (\\dot M_D/\\dot M_{Edd})] \\, L_{Edd}$\n(e.g., Lipunova 1999),\nwhere \n$L_{Edd} \\simeq 1.25 \\times 10^{38} $ erg s$^{-1}$ $(M_{\\star}/ \nM_{\\odot})$.\n%is the Eddington luminosity.\nUsing the value obtained in \\S 2 for \n$\\dot M_D/ \\dot M_{Edd} \\simeq 1.8 \\times 10^{9}$, we\n%find $L_D \\simeq 1.9 \\times 10^{39}$ erg s$^{-1}$.\nfind $L_D \\simeq 1.8 \\times 10^{39}$ erg s$^{-1}$.\nInside the disk, where the optical depth is much larger than unity, \nphotons \nand particles are in thermodynamic equilibrium and the disk radiates \nlike a \nblack-body with a temperature \n%$T_D \\simeq 1.5 \\times 10^9 $ K \n$T_D \\simeq 1.1 \\times 10^9 $ K \n%$\\left({ \\frac {\\dot M_D } {1.3 \\times 10^{-7} M_{\\odot} \\, {\\rm s}^{-\n$\\left({ \\frac {\\dot M_D } {3 \\times 10^{-8} M_{\\odot} \\, {\\rm s}^{-\n1} } }\\right)^{1/4} \\,\n\\left({ \\frac{ M_{\\star}} {M_{\\odot} } }\\right)^{1/4} \\, \n\\left({ \\frac{ R_X} {2.45 \\times 10^6 {\\rm cm} } }\\right)^{-3/4}$.\nAt a distance $R_X$, \n$n_{\\gamma} \\simeq L_D/ (\\pi R_X^2 \\bar \\epsilon_{\\gamma})$\n(e.g., Sorrell 1987),\nwhere $\\bar \\epsilon_{\\gamma} \\, \\simeq \\, 2.8 k_B T_D \\sim 0.35 MeV$ \nis the \nmean photon energy, or\n %$n_{\\gamma} \\simeq 6 \\times 10^{21} {\\rm cm}^{-3} \\,\n $n_{\\gamma} \\simeq 8 \\times 10^{21} {\\rm cm}^{-3} \\,\n\\left({ \\frac{ L_D} { 1.9 \\times 10^{39} {\\rm erg} \\, {\\rm s}^{-1} } }\\right) \\,\n\\left({ \\frac{ R_X} {2.45 \\times 10^{6} {\\rm cm} } }\\right)^{-2} \\, \n\\left({ \\frac{ T_D} { 1.5 \\times 10^9 {\\rm K} } }\\right)^{-1}$. \nWe note that beyond the disk, \nthe luminosity can be substantially smaller as the matter \njust above the disk surface can be partially opaque to the outgoing \nradiation. \nThus, the value above\nof $n_{\\gamma} $ for the\n%for the \n%photon \n%number density at the \nhelmet streamer is probably overestimated. \nSubstitution of $n_{\\gamma}$ \ninto the equation for $\\lambda_{p \\gamma}$ gives\n%$\\lambda_{p \\gamma}/R_X \\, \\gtrsim \\, 0.3 \\, > 0.1 \n$\\lambda_{p \\gamma}/R_X \\, \\gtrsim \\, 0.22 \\, > 0.1 \n\\left({\\frac{\\Delta R_X/R_X } { \n0.1}}\\right)$, \nso that the \n%$p-\\gamma$ \ninteraction distance scale for pion production \nis \nlarger than the width of the acceleration region. For pair production, \nalthough the interaction distance $\\lambda_{pair} $ is shorter, \nthe inelasticity of this process is so small \n(inelasticity $K_p \\sim \\, 2 \\times 10^{-3}$) that the corresponding \nenergy \nloss rates of the UHECR protons are even smaller than in the case of \npion production (e.g., Bednarek \\& Protheroe 1999).\n%Nonetheless, this process may become relevant at lower energies. \nHowever, the injected $e^{\\pm}$ pairs can initiate inverse Compton pair \ncascades in the reconnection region that may saturate an induced \nelectric field if the width of the reconnection region is larger than \n$\\lambda_{sat} \\simeq 100 \\, (\\sigma_{trip} n_{\\gamma})^{-1}$,\nwhere $\\sigma_{trip} \\simeq 1.3 \\times 10^{-26} $ cm$^{-2}$ \nis the cross section \nfor the triple $e^{\\pm}$ pair production by electron-photon collisions. \n%(e.g., Bednarek \\& Protheroe 1999). \nWe find that\n%$\\lambda_{sat}/R_X \\gtrsim 0.5 > 0.1 \\left({\\frac{\\Delta R_X/R_X } { \n$\\lambda_{sat}/R_X \\gtrsim 0.4 > 0.1 \\left({\\frac{\\Delta R_X/R_X } { \n0.1}}\\right)$, \nso that the width of the reconnection site is smaller than \n$\\lambda_{sat}$. \n\n\n%Finally, we should note that although we have essentially discussed the \n%acceleration of protons in the AICs, Eqs. (1) and (3) indicate that \n%the \n%proposed mechanism is, in principle, also applicable to heavier nuclei \n%(e.g., Fe, for which $Z = $ 26). However, since most of the UHECR \n%events from AICs must come from extragalactic sources, it would be \n%more difficult to propagate the nuclei than the protons, because of the \n%additional photonuclear disintegration they suffer. \n%(Elbert \\& Sommers \n%1995).\n\n% comentar: sobre a questao de outflows na superficie e no disco que\n%podem atrapalhar a emissao\n\\acknowledgements\nThis paper has benefited from many valuable comments \n%and suggestions \nof \nan \nanonymous referee, and \nJ. Arons, A.E. Glassgold, J. A. de Freitas Pacheco,\nJ. Horvath, A. Melatos, and F.H. 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Phys. Nucl. \nPart. Phys., \n17, 733\n\n\\bibitem[]{} \nLipunova, G.V., 1999, Astronomy Letters, 25, 508\n\n\\bibitem[]{} \nLitvinenko, Y.E. 1996, ApJ, 462, 997\n\n\n\\bibitem[] { }\nMedina Tanco, G.A. 1998, \\apj, 495, L71\n\n\\bibitem[] { }\nMedina Tanco, G.A., de Gouveia Dal Pino, E.M., \\& Horvath, J. 1997, \nAstropart. \nPhys., 6, 337\n\n\\bibitem[] { }\nMedina Tanco, G.A., de Gouveia Dal Pino, E.M., \\& Horvath, J. 1998, \n\\apj, 492, \n200\n\\bibitem[] { }\nOlinto, A. 2000, astro-ph/0002006\n\n\\bibitem[] { }\nOlinto, A., Epstein, R.I. \\& Blasi, P. 1999, astro-ph/9906338\n\n\\bibitem[] { }\nPeebles, P.J.E. 1993, in Principles of Physical Cosmology, Princeton \nUniv. Press\n\n\\bibitem[] { }\nProtheroe, R.J. 1999, astro-ph/9812055\n\n\\bibitem[] { }\nProtheroe, R.J., \\& Johnson, P.A. 1995, Astropart. Phys., 4, 253\n\n%\\bibitem[] { }\n%Rachen, J.P., \\& Biermann, P.L. 1993, A\\&A, 272, 161\n \n\\bibitem[] { }\nReames, D.V. 1995, Rev. Geophys., 33 (suppl.), 585\n\n\\bibitem[] { }\nSorrell, W.H. 1987, \\apj, 323, 647\n\n\\bibitem[] { }\nShu, F.H., Najita, J., Ostriker, e., Wilkin, F., Ruden, S., and Lizano, \nS. 1994, \n\\apj, 429, 781\n\n\\bibitem[] { }\nShu, F.H. et al. 1999, in The Origin of Stars and \nPlanetary Systems, eds.\nCharles J. Lada \\& Nikolaos D. Kylafis, Kluwer Acad. Publs., p.193\n \n\\bibitem[] { }\nStanev, T. 1997,\\apj, 479, 290\n\n\\bibitem[] { }\nTakeda, M. et al. 1999, \\apj, 522, 225 \n\n\\bibitem[] { }\nWoosley, S.E., \\& Baron, E. 1992, \\apj, 391, 228 \n\n\\end{thebibliography}\n\n\\newpage\n{\\bf Figure Caption}\n\n\\noindent\nFigure 1. Schematic drawing of the magnetic field geometry and the gas \naccretion flow in the inner disk edge at $R_X$. UHECRs are accelerated \nin \nthe magnetic reconnection site at the helmet streamer (see text). The \nfigure also indicates that coronal winds from the star and the disk \nhelp the magnetocentrifugally driven wind at $R_X$ to open the field \nlines \naround the helmet streamer (adapted from Shu et al. 1999). \n\n\\noindent\nFigure 2. Allowed zones in the parameter space for UHECR\nacceleration for \n$E = 10^{20}$ and $10^{21}$ eV. The vertical line in each plot\nindicates the upper \nlimit on\nthe stellar angular speed \n$\\Omega_{\\star, max} \\, = \\, (G \\, M_{\\star}/R_{\\star}^3)^{1/2} \\, \n\\simeq 1.15 \\times 10^4 $ s$^{-1}$. The allowed zone in each plot \nis above the solid line\nfor which \n$\\Delta R_X/R_X = 1$; the dash-dotted line has \n$\\Delta R_X/R_X = 0.1$; and the dashed line has\n$\\Delta R_X/R_X = 0.01$.\n\n\n\\end{document}\n\n\n\n"
}
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[
{
"name": "astro-ph0002155.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n%\\bibitem[] { }\n%Aly, J. 1980, A\\&A, 86, 192\n\n\\bibitem[] { }\nArons, J. 1993, \\apj, 408, 160\n\n\\bibitem[] { }\nArons, J. 1986, in Plasma Penetration into Magnetospheres, eds. N. \nKylafis, J. \nPapamastorakis, and J. Ventura (Iraklion: Crete Univ. Press), 115\n\n%\\bibitem[] { }\n%AUGER, P. Projet Design Report 1997, Fermilab; \n%http://www.auger.org/admin/DesignReport/index.html/\n\n%\\bibitem[] { }\n%Barrau, A. 1999, Astroparticle Phys., in press\n\n\\bibitem[] { }\nBednarek, W., \\& , Protheroe, R.J. 1999, MNRAS, 302, 373\n\n\n\\bibitem[] { }\nBird, D.J. et al. 1995, \\apj, 441, 144\n\n\\bibitem[] { }\nBiskamp, D. 1997, in Advanced Topics in Astrophysical and Space \nPlasmas, eds. \nE.M. de Gouveia Dal Pino, A. Perat, G.A. Medina Tanco, and A.C.L. Chian \n(The \nNetherlands: Kluwer), \n\n\\bibitem[] { }\nBrown, C.E., Lee, C.-H., Portegies Zwart, S.F., \\& Bethe, H.A 1999 \n(astro-ph/9911130)\n\n\\bibitem[] { }\nBruhwiller, D.L., \\& Zweibel, E. 1992, Journal of Geophys. Res., 97, 10825\n\n\\bibitem[] { }\nCronin, J.W. 1999, Rev. Mod. Phys., 71, 165\n\n%\\bibitem[] { }\n%Dar, A. 1999, astro-ph/9905315\n\n%\\bibitem[] { }\n%Dere, K.P. 1996, ApJ, 472, 864\n\n%\\bibitem[] { }\n%Elbert, J.W., \\& Sommers, P. 1995, \\apj, 441, 151\n\n\\bibitem[] { }\nFryer, C.L., Benz, W., Herant, M., \\& Colgate, S. 1999, \n\\apj, 516, 892\n\n\\bibitem[] { }\nGallant, Y.A. \\& Arons, J. 1994, \\apj, 435, 230 \n\n\\bibitem[] { }\nGosh, P., \\& Lamb, F.K. 1978, \\apj, 223, L83\n\n\\bibitem[] { }\nHaswell, C.A., Tajima, T., \\& Sakai, J.-L., 1992, \\apj, 401, 495\n\n\\bibitem[] { }\nHillas A.M., 1984, ARAS, 22, 425\n \n%\\bibitem[]{} \n%Holman, G.D. 1985, ApJ, 293, 584\n\n%\\bibitem[] { }\n%Kahler, S.W., 1992, ARAA, 30, 113\n\n\\bibitem[]{} \nLaRosa, T.N., Moore, R.L., Miller, J.A., \\&\nShore, S.N. 1996, ApJ, 467, 454\n\n\\bibitem[] { }\nLazarian A., \\& de Gouveia Dal Pino, E.M. 2000 (LG2000) (in \npreparation)\n\n\\bibitem[] { }\nLazarian, A. \\& Vishniac, E. 1999, \\apj 1999a, ApJ, 517, 700\n\n\\bibitem[] { }\nLawrence, M.A., Reid, R.J.O., \\& Watson, A.A. 1991, J. Phys. Nucl. \nPart. Phys., \n17, 733\n\n\\bibitem[]{} \nLipunova, G.V., 1999, Astronomy Letters, 25, 508\n\n\\bibitem[]{} \nLitvinenko, Y.E. 1996, ApJ, 462, 997\n\n\n\\bibitem[] { }\nMedina Tanco, G.A. 1998, \\apj, 495, L71\n\n\\bibitem[] { }\nMedina Tanco, G.A., de Gouveia Dal Pino, E.M., \\& Horvath, J. 1997, \nAstropart. \nPhys., 6, 337\n\n\\bibitem[] { }\nMedina Tanco, G.A., de Gouveia Dal Pino, E.M., \\& Horvath, J. 1998, \n\\apj, 492, \n200\n\\bibitem[] { }\nOlinto, A. 2000, astro-ph/0002006\n\n\\bibitem[] { }\nOlinto, A., Epstein, R.I. \\& Blasi, P. 1999, astro-ph/9906338\n\n\\bibitem[] { }\nPeebles, P.J.E. 1993, in Principles of Physical Cosmology, Princeton \nUniv. Press\n\n\\bibitem[] { }\nProtheroe, R.J. 1999, astro-ph/9812055\n\n\\bibitem[] { }\nProtheroe, R.J., \\& Johnson, P.A. 1995, Astropart. Phys., 4, 253\n\n%\\bibitem[] { }\n%Rachen, J.P., \\& Biermann, P.L. 1993, A\\&A, 272, 161\n \n\\bibitem[] { }\nReames, D.V. 1995, Rev. Geophys., 33 (suppl.), 585\n\n\\bibitem[] { }\nSorrell, W.H. 1987, \\apj, 323, 647\n\n\\bibitem[] { }\nShu, F.H., Najita, J., Ostriker, e., Wilkin, F., Ruden, S., and Lizano, \nS. 1994, \n\\apj, 429, 781\n\n\\bibitem[] { }\nShu, F.H. et al. 1999, in The Origin of Stars and \nPlanetary Systems, eds.\nCharles J. Lada \\& Nikolaos D. Kylafis, Kluwer Acad. Publs., p.193\n \n\\bibitem[] { }\nStanev, T. 1997,\\apj, 479, 290\n\n\\bibitem[] { }\nTakeda, M. et al. 1999, \\apj, 522, 225 \n\n\\bibitem[] { }\nWoosley, S.E., \\& Baron, E. 1992, \\apj, 391, 228 \n\n\\end{thebibliography}"
}
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astro-ph0002156
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Inflation and Eternal Inflation
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[
{
"author": "Alan H. Guth"
}
] |
The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. Vilenkin's proposal for avoiding these problems is also discussed.
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[
{
"name": "ahg-phrp.tex",
"string": "%RE: ``Inflation and Eternal Inflation,'' final version,\n% submitted to Physics Reports, 1/20/00.|\n\n\\documentstyle[epsf]{elsart}\n\n\\def\\lta{\\mathrel{\\vcenter{\\vbox{\\offinterlineskip \\hbox{$<$}\n \\vskip 0.2 pt \\hbox{$\\sim$}}}}}\n\\def\\tot{{\\rm tot}}\n\\newcommand{\\subsect}[1]{\\goodbreak \\vskip 3.25ex plus\n1ex minus 0.2ex \\noindent {\\large \\bf #1}\\par\\nobreak \\vskip\n1.5ex plus 0.2ex}\n\n\\begin{document}\n\n\\flushright{MIT-CTP-2948, astro-ph/0002156}\n\n\\begin{frontmatter}\n\n\\title{Inflation and Eternal Inflation}\n\n\\author{Alan H. Guth}\n\n\\address{Center for Theoretical Physics, Laboratory for Nuclear\nScience, and \\\\\nDepartment of Physics, Massachusetts Institute of Technology, \\\\\nCambridge, Massachusetts 02139, USA\\protect\\footnote{Present\naddress.} \\\\ and \\\\\nIsaac Newton Institute for Mathematical Sciences, \\\\\nClarkson Road, Cambridge CB3 0EH, UK} \n\n\\begin{abstract}\nThe basic workings of inflationary models are summarized, along\nwith the arguments that strongly suggest that our universe is the\nproduct of inflation. The mechanisms that lead to eternal\ninflation in both new and chaotic models are described. Although\nthe infinity of pocket universes produced by eternal inflation\nare unobservable, it is argued that eternal inflation has real\nconsequences in terms of the way that predictions are extracted\nfrom theoretical models. The ambiguities in defining\nprobabilities in eternally inflating spacetimes are reviewed,\nwith emphasis on the youngness paradox that results from a\nsynchronous gauge regularization technique. Vilenkin's proposal\nfor avoiding these problems is also discussed.\n\\end{abstract}\n\n\\thanks{This work is supported in part by funds provided by the\nU.S. Department of Energy (D.O.E.) under cooperative research\nagreement \\#DF-FC02-94ER40818, and in part by funds provided by\nNM Rothschild \\& Sons Ltd and by the EPSRC.}\n\n\\end{frontmatter}\n\n\\setcounter{footnote}{0}\n\n\\section{Introduction}\n\n There are many fascinating issues associated with eternal\ninflation, so I can think of no subject more appropriate to\ndiscuss in a volume commemorating David Schramm. The shock of\nDave's untimely death showed that even the most vibrant of human\nlives is not eternal, but his continued influence on our entire\nfield proves that in many ways David Schramm is truly eternal. \nDave is largely responsible for creating the interface between\nparticle physics and cosmology, and is very much responsible for\ncementing together the community in which this interface\ndeveloped. His warmth, his enthusiasm, and the efforts that he\nmade to welcome young scientists to the field have strengthened\nour community in a way that will not be forgotten. \n\nI will begin by summarizing the basics of inflation, including a\ndiscussion of how inflation works, and why many of us believe\nthat our universe almost certainly evolved through some form of\ninflation. This material is not new, but I think it should\ncertainly be included in any volume that attempts to summarize\nthe important advances that Dave helped to develop and promote. \nThen I will move on to discuss eternal inflation, attempting to\nemphasize that this topic has important implications, and raises\nimportant questions, which should not be dismissed as being\nmetaphysical.\n\n\\section{How Does Inflation Work?}\n\nThe key property of the laws of physics that makes inflation\npossible is the existence of states of matter that have a high\nenergy density which cannot be rapidly lowered. In the original\nversion of the inflationary theory \\cite{Guth1}, the proposed\nstate was a scalar field in a local minimum of its potential\nenergy function. A similar proposal was advanced by Starobinsky\n\\cite{Starobinsky}, in which the high energy density state was\nachieved by curved space corrections to the energy-momentum\ntensor of a scalar field. The scalar field state employed in the\noriginal version of inflation is called a {\\it false vacuum},\nsince the state temporarily acts as if it were the state of\nlowest possible energy density. Classically this state would be\ncompletely stable, because there would be no energy available to\nallow the scalar field to cross the potential energy barrier that\nseparates it from states of lower energy. Quantum mechanically,\nhowever, the state would decay by tunneling \\cite{Coleman}. \nInitially it was hoped that this tunneling process could\nsuccessfully end inflation, but it was soon found that the\nrandomness of false vacuum decay would produce catastrophically\nlarge inhomogeneities. These problems were summarized in\nRef.~\\cite{Guth1}, and described more fully by Hawking, Moss, and\nStewart \\cite{HMS} and by Guth and Weinberg\n\\cite{GuthWeinberg}. \n\nThis ``graceful exit'' problem was solved by the invention of the\nnew inflationary universe model by Linde \\cite{Linde1} and by\nAlbrecht and Steinhardt \\cite{Albrecht-Steinhardt1}. New\ninflation achieved all the successes that had been hoped for in\nthe context of the original version. In this theory inflation is\ndriven by a scalar field perched on a plateau of the potential\nenergy diagram, as shown in Fig.~\\ref{newinf}. Such a scalar\nfield is generically called the {\\it inflaton}. If the plateau\nis flat enough, such a state can be stable enough for successful\ninflation. Soon afterwards Linde showed that the inflaton\npotential need not have either a local minimum or a gentle\nplateau: in the scenario he dubbed {\\it chaotic inflation}\n\\cite{chaotic}, the inflaton potential can be as simple as\n\\begin{equation}\n V(\\phi)={1 \\over 2} m^2 \\phi^2, \n \\label{eq:1}\n\\end{equation}\nprovided that $\\phi$ begins at a large enough value so that\ninflation can occur as it relaxes. For simplicity of language, I\nwill stretch the meaning of the phrase ``false vacuum'' to\ninclude all of these cases; that is, I will use the phrase to\ndenote any state with a high energy density that cannot be\nrapidly decreased. Note that while inflation was originally\ndeveloped in the context of grand unified theories, the only real\nrequirement on the particle physics is the existence of a false\nvacuum state.\n\n\\begin{figure}\n\\epsfxsize=201pt\n\\centerline{\\epsfbox{newinf2.eps}}\n\\caption{Generic form of the potential for the new inflationary\nscenario.}\n\\label{newinf}\n\\end{figure}\n\n\\subsection{The New Inflationary Scenario:}\n\nIn this section I will summarize the workings of new inflation,\nand in the following section I will discuss chaotic inflation. \nWhile more complicated possibilities (e.g. hybrid inflation\n\\cite{hyb1,hyb2,hyb3,hyb4,hyb5} and supernatural inflation\n\\cite{RSG}) appear very plausible, the basic scenarios of new and\nchaotic inflation will be sufficient to illustrate the physical\neffects that I want to discuss in this article.\n\nSuppose that the energy density of a state is approximately equal\nto a constant value $\\rho_f$. Then, if a region filled with this\nstate of matter expanded by an amount $dV$, its energy would have\nto increase by\n\\begin{equation}\n d U = \\rho_f \\, d V \\ . \n \\label{eq:2}\n\\end{equation}\nThis energy must be supplied by whatever force is causing the\nexpansion, which means that the force must be pulling against a\nnegative pressure. The work done by the force is given by\n\\begin{equation}\n dW = - p_f \\, d V \\ ,\n \\label{eq:3}\n\\end{equation}\nwhere $p_f$ is the pressure inside the expanding region. \nEquating the work with the change in energy, one finds\n\\begin{equation}\n p_f = - \\rho_f \\ . \n \\label{eq:4}\n\\end{equation}\nThis negative pressure is the driving force behind inflation. \nWhen one puts this negative pressure into Einstein's equations,\none finds that it leads to a repulsion, causing such a region to\nundergo exponential expansion. If the region can be approximated\nas isotropic and homogeneous, this result can be seen from the\nstandard Friedmann-Robertson-Walker (FRW) equations:\n\\begin{equation}\n {d^2 a \\over d t^2} = - {4 \\pi \\over 3} G ( \\rho + 3 p ) a \\ \n = { 8 \\pi \\over 3 } G \\rho_f a \\ .\n \\label{eq:5}\n\\end{equation}\nwhere $a(t)$ is the scale factor, $G$ is Newton's constant, and\nwe adopt units for which $\\hbar = c = 1$. For late times the\ngrowing solution to this equation has the form\n\\begin{equation}\n a(t) \\propto e^{\\chi t} \\ , \\hbox{ where } \\chi = \\sqrt{{8 \\pi\n \\over 3} G \\rho_f } \\ .\n \\label{eq:6}\n\\end{equation}\nOf course inflationary theorists prefer not to assume that the\nuniverse began homogeneously and isotropically, but there is\nconsiderable evidence for the ``cosmological no-hair conjecture''\n\\cite{Jensen-Stein-Schabes}, which implies that a wide class of\ninitial states will approach this exponentially expanding\nsolution. \n\nThe basic scenario of new inflation begins by assuming that at\nleast some patch of the early universe was in this peculiar false\nvacuum state. In the original papers\n\\cite{Linde1,Albrecht-Steinhardt1} this initial\ncondition was motivated by the fact that, in many quantum field\ntheories, the false vacuum resulted naturally from the\nsupercooling of an initially hot state in thermal equilibrium. \nIt was soon found, however, that quantum fluctuations in the\nrolling inflaton field give rise to density perturbations in the\nuniverse \\cite{Starobinsky2,GuthPi,Hawking1,BST,BFM}, and that\nthese density perturbations would be much larger than observed\nunless the inflaton field is very weakly coupled. For such weak\ncoupling there would be no time for an initially nonthermal state\nto reach thermal equilibrium. Nonetheless, since thermal\nequilibrium describes a probability distribution in which all\nstates of a given energy are weighted equally, the fact that\nthermal equilibrium leads to a false vacuum implies that there\nare many ways of reaching a false vacuum. Thus, even in the\nabsence of thermal equilibrium---even if the universe started in\na highly chaotic initial state---it seems reasonable to assume\nthat some small patches of the early universe settled into the\nfalse vacuum state, as was suggested for example in\nRef.~\\cite{Guth-RS}. Linde \\cite{chaotic} pointed out that even\nhighly improbable initial patches could be important if they\ninflated, since the exponential expansion could still cause such\npatches to dominate the volume of the universe. One might hope\nultimately to calculate the probability of regions settling into\nthe false vacuum from a quantum description of cosmogenesis, but\nI will argue in Sec.~\\ref{implications} that this probability is\nquite irrelevant in the context of eternal inflation.\n\nOnce a region of false vacuum materializes, the physics of the\nsubsequent evolution is rather straightforward. The gravitational\nrepulsion caused by the negative pressure will drive the region\ninto a period of exponential expansion. If the energy density of\nthe false vacuum is at the grand unified theory scale ($\\rho_f\n\\approx (2 \\times 10^{16}\\ \\hbox{GeV})^4)$, Eq.~(\\ref{eq:6})\nshows that the time constant $\\chi^{-1}$ of the exponential\nexpansion would be about $10^{-38}$ sec. For inflation to achieve\nits goals, this patch has to expand exponentially for at least 60\ne-foldings. Then, because the false vacuum is only metastable\n(the inflaton field is perched on top of the hill of the\npotential energy diagram of Fig.~\\ref{newinf}), eventually it\nwill decay. The inflaton field will roll off the hill, ending\ninflation. When it does, the energy density that has been locked\nin the inflaton field is released. Because of the coupling of the\ninflaton to other fields, that energy becomes thermalized to\nproduce a hot soup of particles, which is exactly what had always\nbeen taken as the starting point of the standard big bang theory\nbefore inflation was introduced. From here on the scenario joins\nthe standard big bang description. The role of inflation is to\nestablish dynamically the initial conditions which otherwise have\nto be postulated. \n\nThe inflationary mechanism produces an entire universe starting\nfrom essentially nothing, so one needs to answer the question of\nwhere the energy of the universe comes from. The answer is that\nit comes from the gravitational field. The universe did not\nbegin with this colossal energy stored in the gravitational\nfield, but rather the gravitational field can supply the energy\nbecause its energy can become negative without bound. As more\nand more positive energy materializes in the form of an\never-growing region filled with a high-energy scalar field, more\nand more negative energy materializes in the form of an expanding\nregion filled with a gravitational field. The total energy\nremains constant at some very small value, and could in fact be\nexactly zero. There is nothing known that places any limit on\nthe amount of inflation that can occur while the total energy\nremains exactly zero.\\footnote{In Newtonian mechanics the energy\ndensity of a gravitational field is unambiguously negative; it\ncan be derived by the same methods used for the Coulomb field,\nbut the force law has the opposite sign. In general relativity\nthere is no coordinate-invariant way of expressing the energy in\na space that is not asymptotically flat, so many experts prefer\nto say that the total energy is undefined. Either way, there is\nagreement that inflation is consistent with the general\nrelativistic description of energy conservation.}\n\n\\subsection{Chaotic Inflation:}\n\nChaotic inflation \\cite{chaotic} can occur in the context of a\nmore general class of potential energy functions. In particular,\neven a potential energy function as simple as\nEq.~(\\ref{eq:1})---describing a scalar field with a mass and no\ninteraction---is sufficient to describe chaotic inflation. \nChaotic inflation is illustrated in Fig.~\\ref{chaoticinf}. In\nthis case there is no state that bears any obvious resemblance to\nthe false vacuum of new inflation. Instead the scenario works by\nsupposing that chaotic conditions in the early universe produced\none or more patches in which the inflaton field $\\phi$ was at\nsome high value $\\phi = \\phi_0$ on the potential energy curve. \nInflation occurs as the inflaton field rolls down the hill. As\nlong as the initial value $\\phi_0$ is sufficiently large, there\nwill be sufficient inflation to solve all the problems that\ninflation is intended to solve. \n\n\\begin{figure}\n\\epsfxsize=275pt\n\\centerline{\\epsfbox{eipot1.eps}}\n\\caption{Generic form of the potential for the chaotic inflationary\nscenario.}\n\\label{chaoticinf}\n\\end{figure}\n\nThe equations describing chaotic inflation can be written simply,\nprovided that we assume that the universe is already flat enough\nso that we do not need to include a curvature term. The field\nequation for the inflaton field in the expanding universe is\n\\begin{equation}\n \\ddot \\phi + 3 H \\dot \\phi = - {\\partial V \\over \\partial\n \\phi } \\ ,\n \\label{eq:7}\n\\end{equation}\nwhere the overdot denotes a derivative with respect to time $t$,\nand $H$ is the time-dependent Hubble parameter given by\n\\begin{equation}\n H^2 = {8 \\pi \\over 3} G V \\ .\n \\label{eq:8}\n\\end{equation}\nFor the toy-model potential energy of Eq.~(\\ref{eq:1}), these\nequations have a very simple solution:\n\\begin{equation}\n \\phi = \\phi_0 - {m \\over \\sqrt{12 \\pi G}} \\, t \\ .\n \\label{eq:9}\n\\end{equation}\nOne can then calculate the number $N$ of inflationary e-foldings,\nwhich is given by\n\\begin{equation}\n N = \\int\\nolimits_{\\phi = \\phi_0}^{\\phi = 0} H(t) \\, dt = 2 \\pi G\n \\phi_0^2 \\ .\n \\label{eq:10}\n\\end{equation}\nIn this toy model $N$ depends only on $\\phi_0$ and not on the\ninflaton mass $m$. Thus the number of e-foldings will exceed 60\nprovided that\n\\begin{equation}\n \\phi_0 > \\sqrt{60 \\over 2 \\pi} \\, M_{\\rm P} \\approx 3.1 M_{\\rm P} \\ ,\n \\label{eq:11}\n\\end{equation}\nwhere $M_{\\rm P} \\equiv 1/\\sqrt{G} = 1.22 \\times 10^{19}$ GeV is\nthe Planck mass. Although this is a super-Planckian value for\nthe scalar field, the energy density need not be super-Planckian:\n\\begin{equation}\n \\rho_0 = {1 \\over 2} m^2 \\phi_0^2 > {60 \\over 4 \\pi} M_{\\rm P}^2 m^2\n \\ .\n \\label{eq:12}\n\\end{equation}\nFor example, if $m = 10^{16}$ GeV, then the potential energy\ndensity is only $3 \\times 10^{-6}\\, M_{\\rm P}^4$. Since it is\npresumably the energy density and not the value of the field that\nis relevant to gravity, it seems reasonable to assume that the\nchaotic inflation scenario will not be dramatically affected by\ncorrections from quantum gravity.\n\n\\section{Evidence for Inflation}\n\nNo matter which form of inflation we might envision, we would\nlike to know what is the evidence that our universe underwent a\nperiod of inflation. The answer is pretty much the same no\nmatter which form of inflation we are discussing. In my opinion,\nthe evidence that our universe is the result of some form of\ninflation is very solid. Since the term {\\it inflation}\nencompasses a wide range of detailed theories, it is hard to\nimagine any reasonable alternative. The basic arguments are as\nfollows:\n\n\\begin{enumerate}\n\\item{\\it The universe is big}\n\nFirst of all, we know that the universe is incredibly large: the\nvisible part of the universe contains about $10^{90}$ particles. \nSince we have all grown up in a large universe, it is easy to\ntake this fact for granted: of course the universe is big, it's\nthe whole universe! In ``standard'' FRW cosmology, without\ninflation, one simply postulates that about $10^{90}$ or more\nparticles were here from the start. However, in the context of\npresent-day cosmology, many of us hope that even the creation of\nthe universe can be described in scientific terms. Thus, we are\nled to at least think about a theory that might explain how the\nuniverse got to be so big. Whatever that theory is, it has to\nsomehow explain the number of particles, $10^{90}$ or more. \nHowever, it is hard to imagine such a number arising from a\ncalculation in which the input consists only of geometrical\nquantities, quantities associated with simple dynamics, and\nfactors of 2 or $\\pi$. The easiest way by far to get a huge\nnumber, with only modest numbers as input, is for the calculation\nto involve an exponential. The exponential expansion of\ninflation reduces the problem of explaining $10^{90}$ particles\nto the problem of explaining 60 or 70 e-foldings of inflation. \nIn fact, it is easy to construct underlying particle theories\nthat will give far more than 70 e-foldings of inflation. \nInflationary cosmology therefore suggests that, even though the\nobserved universe is incredibly large, it is only an\ninfinitesimal fraction of the entire universe.\n\n\\item{\\it The Hubble expansion}\n\nThe Hubble expansion is also easy to take for granted, since we\nhave all known about it from our earliest readings in cosmology. \nIn standard FRW cosmology, the Hubble expansion is part of the\nlist of postulates that define the initial conditions. But\ninflation actually offers the possibility of explaining how the\nHubble expansion began. The repulsive gravity associated with\nthe false vacuum is just what Hubble ordered. It is exactly the\nkind of force needed to propel the universe into a pattern of\nmotion in which each pair of particles is moving apart with a\nvelocity proportional to their separation.\n\n\\item{\\it Homogeneity and isotropy}\n\nThe degree of uniformity in the universe is startling. The\nintensity of the cosmic background radiation is the same in all\ndirections, after it is corrected for the motion of the Earth, to\nthe incredible precision of one part in 100,000. To get some\nfeeling for how high this precision is, we can imagine a marble\nthat is spherical to one part in 100,000. The surface of the\nmarble would have to be shaped to an accuracy of about 1,000\nangstroms, a quarter of the wavelength of light. \n\nAlthough modern technology makes it possible to grind lenses to\nquarter-wavelength accuracy, we would nonetheless be shocked if\nwe unearthed a stone, produced by natural processes, that was\nround to an accuracy of 1,000 angstroms. If we try to imagine\nthat such a stone were found, I am sure that no one would accept\nan explanation of its origin which simply proposed that the stone\nstarted out perfectly round. Similarly, I do not think it makes\nsense to consider any theory of cosmogenesis that cannot offer\nsome explanation of how the universe became so incredibly\nisotropic. \n\nThe cosmic background radiation was released about 300,000 years\nafter the big bang, after the universe cooled enough so that the\nopaque plasma neutralized into a transparent gas. The cosmic\nbackground radiation photons have mostly been traveling on\nstraight lines since then, so they provide an image of what the\nuniverse looked like at 300,000 years after the big bang. The\nobserved uniformity of the radiation therefore implies that the\nobserved universe had become uniform in temperature by that time. \nIn standard FRW cosmology, a simple calculation shows that the\nuniformity could be established so quickly only if signals could\npropagate at 100 times the speed of light, a proposition clearly\ncontradicting the known laws of physics. In inflationary\ncosmology, however, the uniformity is easily explained. The\nuniformity is created initially on microscopic scales, by normal\nthermal-equilibrium processes, and then inflation takes over and\nstretches the regions of uniformity to become large enough to\nencompass the observed universe.\n\n\\item{\\it The flatness problem}\n\nI find the flatness problem particularly impressive, because of\nthe extraordinary numbers that it involves. The problem concerns\nthe value of the ratio\n\\begin{equation}\n \\Omega_\\tot \\equiv {\\rho_\\tot \\over \\rho_c} \\ ,\n \\label{eq:13}\n\\end{equation}\nwhere $\\rho_\\tot$ is the average total mass density of the\nuniverse and $\\rho_c = 3 H^2 / 8 \\pi G$ is the critical density,\nthe density that would make the universe spatially flat. (In the\ndefinition of ``total mass density,'' I am including the vacuum\nenergy $\\rho_{\\rm vac} = \\Lambda/ 8 \\pi G$ associated with the\ncosmological constant $\\Lambda$, if it is nonzero.)\n\nThere is general agreement that the present value of\n$\\Omega_\\tot$ satisfies\n\\begin{equation}\n 0.1 \\lta \\Omega_0 \\lta 2 \\ ,\n \\label{eq:14}\n\\end{equation}\nbut it is hard to pinpoint the value with more precision. Despite\nthe breadth of this range, the value of $\\Omega$ at early times\nis highly constrained, since $\\Omega=1$ is an unstable\nequilibrium point of the standard model evolution. Thus, if\n$\\Omega$ was ever {\\it exactly} equal to one, it would remain\nexactly one forever. However, if $\\Omega$ differed slightly from\none in the early universe, that difference---whether positive or\nnegative---would be amplified with time. In particular, it can\nbe shown that $\\Omega - 1$ grows as\n\\begin{equation}\n \\Omega - 1 \\propto \\cases{t &(during the radiation-dominated era)\\cr\n t^{2/3} &(during the matter-dominated era)\\ .\\cr}\n \\label{eq:15}\n\\end{equation}\nAt $t=1$ sec, for example, when the processes of big bang\nnucleosynthesis were just beginning, Dicke and Peebles\n\\cite{dicke} pointed out that $\\Omega$ must have equaled one to\nan accuracy of one part in $10^{15}$. Classical cosmology\nprovides no explanation for this fact---it is simply assumed as\npart of the initial conditions. In the context of modern\nparticle theory, where we try to push things all the way back to\nthe Planck time, $10^{-43}$ sec, the problem becomes even more\nextreme. If one specifies the value of $\\Omega$ at the Planck\ntime, it has to equal one to 58 decimal places in order to be\nanywhere in the allowed range today. \n\nWhile this extraordinary flatness of the early universe has no\nexplanation in classical FRW cosmology, it is a natural\nprediction for inflationary cosmology. During the inflationary\nperiod, instead of $\\Omega$ being driven away from one as\ndescribed by Eq.~(\\ref{eq:15}), $\\Omega$ is driven towards one,\nwith exponential swiftness:\n\\begin{equation}\n \\Omega - 1 \\propto e^{-2 H_{\\rm inf} t} \\ ,\n \\label{eq:16}\n\\end{equation}\nwhere $H_{\\rm inf}$ is the Hubble parameter during inflation. \nThus, as long as there is a long enough period of inflation,\n$\\Omega$ can start at almost any value, and it will be driven to\nunity by the exponential expansion. \n\n\\item{\\it Absence of magnetic monopoles}\n\nAll grand unified theories predict that there should be, in the\nspectrum of possible particles, extremely massive particles\ncarrying a net magnetic charge. By combining grand unified\ntheories with classical cosmology without inflation, Preskill\n\\cite{preskill} found that magnetic monopoles would be produced\nso copiously that they would outweigh everything else in the\nuniverse by a factor of about $10^{12}$. A mass density this\nlarge would cause the inferred age of the universe to drop to\nabout 30,000 years! Inflation is certainly the simplest known\nmechanism to eliminate monopoles from the visible universe, even\nthough they are still in the spectrum of possible particles. The\nmonopoles are eliminated simply by arranging the parameters so\nthat inflation takes place after (or during) monopole production,\nso the monopole density is diluted to a completely negligible\nlevel.\n\n\\item{\\it Anisotropy of the cosmic background radiation}\n\nThe process of inflation smooths the universe essentially\ncompletely, but density fluctuations are generated as inflation\nends by the quantum fluctuations of the inflaton field. \nGenerically these are adiabatic Gaussian fluctuations with a\nnearly scale-invariant spectrum\n\\cite{Starobinsky2,GuthPi,Hawking1,BST,BFM}. New data is\narriving quickly, but so far the observations are in excellent\nagreement with the predictions of the simplest inflationary\nmodels. For a review, see for example Bond and Jaffe\n\\cite{bond-jaffe}, who find that the combined data give a slope\nof the primordial power spectrum within 5\\% of the preferred\nscale-invariant value.\n\n\\end{enumerate}\n\n\\section{Eternal Inflation: Mechanisms}\n\nThe remainder of this article will discuss eternal\ninflation---the questions that it can answer, and the questions\nthat it raises. In this section I discuss the mechanisms that\nmake eternal inflation possible, leaving the other issues for the\nfollowing sections. I will discuss eternal inflation first in\nthe context of new inflation, and then in the context of chaotic\ninflation, where it is more subtle. \n\n\\subsection{Eternal New Inflation:}\n\nThe eternal nature of new inflation was first discovered by\nSteinhardt \\cite{steinhardt-nuffield} and Vilenkin\n\\cite{vilenkin-eternal} in 1983. Although the false vacuum is a\nmetastable state, the decay of the false vacuum is an exponential\nprocess, very much like the decay of any radioactive or unstable\nsubstance. The probability of finding the inflaton field at the\ntop of the plateau in its potential energy diagram does not fall\nsharply to zero, but instead trails off exponentially with time\n\\cite{guth-pi2}. However, unlike a normal radioactive substance,\nthe false vacuum exponentially expands at the same time that it\ndecays. In fact, in any successful inflationary model the rate of\nexponential expansion is always much faster than the rate of\nexponential decay. Therefore, even though the false vacuum is\ndecaying, it never disappears, and in fact the total volume of\nthe false vacuum, once inflation starts, continues to grow\nexponentially with time, ad infinitum. \n\n\\begin{figure}\n\\centerline{\\epsfbox{eternpr.eps}}\n\\caption{A schematic illustration of eternal inflation.} \n\\label{eternalline}\n\\end{figure}\n\nFig.~\\ref{eternalline} shows a schematic diagram of an eternally\ninflating universe. The top bar indicates a region of false\nvacuum. The evolution of this region is shown by the successive\nbars moving downward, except that the expansion could not be\nshown while still fitting all the bars on the page. So the\nregion is shown as having a fixed size in comoving coordinates,\nwhile the scale factor, which is not shown, increases from each\nbar to the next. As a concrete example, suppose that the scale\nfactor for each bar is three times larger than for the previous\nbar. If we follow the region of false vacuum as it evolves from\nthe situation shown in the top bar to the situation shown in the\nsecond bar, in about one third of the region the scalar field\nrolls down the hill of the potential energy diagram,\nprecipitating a local big bang that will evolve into something\nthat will eventually appear to its inhabitants as a universe. \nThis local big bang region is shown in gray and labelled\n``Universe.'' Meanwhile, however, the space has expanded so much\nthat each of the two remaining regions of false vacuum is the\nsame size as the starting region. Thus, if we follow the region\nfor another time interval of the same duration, each of these\nregions of false vacuum will break up, with about one third of\neach evolving into a local universe, as shown on the third bar\nfrom the top. Now there are four remaining regions of false\nvacuum, and again each is as large as the starting region. This\nprocess will repeat itself literally forever, producing a kind of\na fractal structure to the universe, resulting in an infinite\nnumber of the local universes shown in gray. There is no\nstandard name for these local universes, but they are often\ncalled bubble universes. I prefer, however, to call them pocket\nuniverses, to avoid the suggestion that they are round. While\nbubbles formed in first-order phase transitions are round\n\\cite{coleman-deluccia}, the local universes formed in eternal\nnew inflation are generally very irregular, as can be seen for\nexample in the two-dimensional simulation by Vanchurin, Vilenkin,\nand Winitzki in Fig.~2 of Ref.~\\cite{vvw}.\n\nThe diagram in Fig.~\\ref{eternalline} is of course an\nidealization. The real universe is three dimensional, while the\ndiagram illustrates a schematic one-dimensional universe. It is\nalso important that the decay of the false vacuum is really a\nrandom process, while the diagram was constructed to show a very\nsystematic decay, because it is easier to draw and to think\nabout. When these inaccuracies are corrected, we are still left\nwith a scenario in which inflation leads asymptotically to a\nfractal structure \\cite{aryal-vilenkin} in which the universe as\na whole is populated by pocket universes on arbitrarily small\ncomoving scales. Of course this fractal structure is entirely on\ndistance scales much too large to be observed, so we cannot\nexpect astronomers to see it. Nonetheless, one does have to\nthink about the fractal structure if one wants to understand the\nvery large scale structure of the spacetime produced by\ninflation. \n\nMost important of all is the simple statement that once inflation\nhappens, it produces not just one universe, but an infinite\nnumber of universes. \n\n\\subsection{Eternal Chaotic Inflation:}\n\nThe eternal nature of new inflation depends crucially on the\nscalar field lingering at the top of the plateau of\nFig.~\\ref{newinf}. Since the potential function for chaotic\ninflation, Fig.~\\ref{chaoticinf}, does not have a plateau, it is\nnot obvious how eternal inflation can happen in this context. \nNonetheless, Andrei Linde \\cite{linde-eternal} showed in 1986\nthat chaotic inflation can also be eternal. \n\nThe important point is that quantum fluctuations play an\nimportant role in all inflationary models. Quantum fluctuations\nare invariably important on very small scales, and with inflation\nthese very small scales are rapidly stretched to become\nmacroscopic and even astronomical. Thus the scalar field\nassociated with inflation has very evident quantum effects. \n\n\\begin{figure}\n\\epsfxsize=275pt\n\\centerline{\\epsfbox{eipot2.eps}}\n\\caption{Evolution of the inflaton field during eternal chaotic\ninflation.}\n\\label{chaotic-eternal}\n\\end{figure}\n\nWhen the mass of the scalar field is small compared to the Hubble\nparameter $H$, these quantum effects are accurately summarized by\nsaying that the quantum fluctuations cause the field to undergo a\nrandom walk. It is useful to divide space into regions of\nphysical size $H^{-1}$, and to discuss the average value of the\nscalar field $\\phi$ within a given region. In a time $H^{-1}$,\nthe effect of the quantum fluctuations is equivalent to a random\nGaussian jump of zero mean and a root-mean-squared magnitude\n\\cite{random-vil-ford,random-linde,Starobinsky2,random-starobinsky}\ngiven by\n\\begin{equation}\n \\Delta \\phi_{\\rm qu} = {H \\over 2 \\pi} \\ .\n \\label{eq:17}\n\\end{equation}\nThis random quantum jump is superimposed on the classical motion,\nas indicated in Fig.~(\\ref{chaotic-eternal}).\n\nTo illustrate how eternal inflation happens in the simplest\ncontext, let us consider again the free scalar field described by\nthe potential function of Eq.~(\\ref{eq:1}). We consider a region\nof physical radius $H^{-1}$, in which the field has an average\nvalue $\\phi$. Using Eq.~(\\ref{eq:9}) along with\nEqs.~(\\ref{eq:8}) and (\\ref{eq:1}), one finds that the magnitude\nof the classical change that the field will undergo in a time\n$H^{-1}$ is given in by\n\\begin{equation}\n \\Delta \\phi_{\\rm cl} = {M_{\\rm P} m \\over \\sqrt{12 \\pi}} \\,\n H^{-1} = {1 \\over 4 \\pi} {M_{\\rm P}^2 \\over \\phi} \\ .\n \\label{eq:18}\n\\end{equation}\nLet $\\phi^*$ denote the value of $\\phi$ which is sufficiently\nlarge so that\n\\begin{equation}\n \\Delta \\phi_{\\rm qu} (\\phi^*) = \\Delta \\phi_{\\rm cl}(\\phi^*) \\ ,\n \\label{eq:19}\n\\end{equation}\nwhich can easily be solved to find\n\\begin{equation}\n \\phi^* = \\left( {3 \\over 16 \\pi} \\right)^{1/4} {M_{\\rm P}^{3/2} \\over\n m^{1/2}} \\ .\n \\label{eq:20}\n\\end{equation}\n\nNow consider what happens to the region if its initial average\nvalue of $\\phi$ is equal to $\\phi^*$. In a time interval\n$H^{-1}$, the volume of the region will increase by $e^3 \\approx\n20$. At the end of the time interval we can divide the original\nregion into 20 regions of the same volume as the original, and in\neach region the average scalar field can be written as\n\\begin{equation}\n \\phi = \\phi^* + \\Delta \\phi_{\\rm cl} + \\delta \\phi \\ ,\n \\label{eq:21}\n\\end{equation}\nwhere $\\delta \\phi$ denotes the random quantum jump, which is\ndrawn from a Gaussian probability distribution with standard\ndeviation $\\Delta \\phi_{\\rm qu} = \\Delta \\phi_{\\rm cl}$. \nGaussian statistics imply that there is a 15.9\\% chance that a\nGaussian random variable will exceed its mean by more than one\nstandard deviation, and therefore there is a 15.9\\% chance that\nthe net change in $\\phi$ will be positive. Since there are now\n20 regions of the original volume, on average the value of $\\phi$\nwill exceed the original value in 3.2 of these regions. Thus the\nvolume for which $\\phi \\ge \\phi^*$ does not (on average)\ndecrease, but instead increases by more than a factor of 3. \nSince this argument can be iterated, the expectation value of the\nvolume for which $\\phi \\ge \\phi^*$ increases exponentially with\ntime. Typically, therefore, inflation never ends, but instead\nthe volume of the inflating region grows exponentially without\nbound. The minimum field value for eternal inflation is slightly\nbelow $\\phi^*$, since a volume increase by a factor of 3.2 is\nmore than necessary---any factor greater than one would be\nsufficient. A short calculation shows that the minimal value for\neternal inflation is $0.78 \\phi^*$.\n\nWhile the value of $\\phi^*$ is larger than $M_{\\rm P}$, it is\nimportant to note that the energy density can still be much\nsmaller than Planck scale:\n\\begin{equation}\n V(\\phi^*) = {1 \\over 2} m^2 \\phi^{*2} = \\sqrt{3 \\over 64 \\pi}\n \\, m M_{\\rm P}^3 \\ ,\n \\label{eq:22}\n\\end{equation}\nwhich for $m = 10^{16}$ GeV gives an energy density of $1 \\times\n10^{-4} \\, M_{\\rm P}^4$. \n\nIf one repeats the argument with a potential function\n\\begin{equation}\n V(\\phi) = {1 \\over 4} \\lambda \\phi^4 \\ ,\n \\label{eq:23}\n\\end{equation}\none finds \\cite{linde-book} that\n\\begin{equation}\n \\phi^* = \\left( 3 \\over 2 \\pi \\lambda \\right)^{1/6} M_{\\rm P} \\ ,\n \\label{eq:24}\n\\end{equation}\nand\n\\begin{equation}\n V(\\phi^*) = \\left( 3 \\over 16 \\pi \\right)^{2/3} \\lambda^{1/3}\n M_{\\rm P}^4 \\ .\n \\label{eq:25}\n\\end{equation}\nSince one requires $\\lambda$ to be very small in any case so that\ndensity perturbations are not too large, one finds again that\neternal inflation is predicted to happen at an energy density\nwell below the Planck scale.\n\n\\section{Eternal Inflation: Implications}\n\\label{implications}\n\nIn spite of the fact that the other universes created by eternal\ninflation are too remote to imagine observing directly, I\nnonetheless claim that eternal inflation has real consequences in\nterms of the way we extract predictions from theoretical models. \nSpecifically, there are three consequences of eternal inflation\nthat I will discuss.\n\nFirst, eternal inflation implies that all hypotheses about the\nultimate initial conditions for the universe---such as the\nHartle-Hawking \\cite{hartle-hawking} no boundary proposal, the\ntunneling proposals by Vilenkin \\cite{tunnel-vilenkin} or Linde\n\\cite{tunnel-linde}, or the more recent Hawking-Turok instanton\n\\cite{hawking-turok}---become totally divorced from observation.\nThat is, one would expect that if inflation is to continue\narbitrarily far into the future with the production of an\ninfinite number of pocket universes, then the statistical\nproperties of the inflating region should approach a steady state\nwhich is independent of the initial conditions. Unfortunately,\nattempts to quantitatively study this steady state are severely\nlimited by several factors. First, there are ambiguities in\ndefining probabilities, which will be discussed later. In\naddition, the steady state properties seem to depend strongly on\nsuper-Planckian physics which we do not understand. That is, the\nsame quantum fluctuations that make eternal chaotic inflation\npossible tend to drive the scalar field further and further up\nthe potential energy curve, so attempts to quantify the steady\nstate probability distribution \\cite{LLM,GBLinde} require the\nimposition of some kind of a boundary condition at large $\\phi$. \nAlthough these problems remain unsolved, I still believe that it\nis reasonable to assume that in the course of its unending\nevolution, an eternally inflating universe would lose all memory\nof the state in which it started.\n\nEven if the universe forgets the details of its genesis, however,\nI would not assume that the question of how the universe began\nwould lose its interest. While eternally inflating universes\ncontinue forever once they start, they are presumably not eternal\ninto the past. (The word {\\it eternal} is therefore not\ntechnically correct---it would be more precise to call this\nscenario {\\it semi-eternal} or {\\it future-eternal}.) While the\nissue is not completely settled, it appears likely that eternally\ninflating universes must necessarily have a beginning. Borde and\nVilenkin \\cite{borde-vilenkin} have shown, subject to various\nassumptions, that spacetimes that are future-eternal must have an\ninitial singularity, in the sense that they cannot be past null\ngeodesically complete. The proof, however, requires the weak\nenergy condition, which can be violated by quantum fluctuations\n\\cite{borde-vilenkin2}. In any case, no one has constructed a\nviable model without a beginning, and certainly nothing that we\nknow can rule out the possibility of a beginning. The\npossibility of a quantum origin of the universe is very\nattractive, and will no doubt be a subject of interest for some\ntime. Eternal inflation, however, seems to imply that the entire\nstudy will have to be conducted with literally no input from\nobservation. \n\nA second consequence of eternal inflation is that the probability\nof the onset of inflation becomes totally irrelevant, provided\nthat the probability is not identically zero. Various authors in\nthe past have argued that one type of inflation is more plausible\nthan another, because the initial conditions that it requires\nappear more likely to have occurred. In the context of eternal\ninflation, however, such arguments have no significance.\n\nTo illustrate the insignificance of the probability of the onset\nof inflation, I will use a numerical example. We will imagine\ncomparing two different versions of inflation, which I will call\nType A and Type B\\relax. They are both eternally inflating---but\nType A will have a higher probability of starting, while Type B\nwill be a little faster in its exponential expansion rate. Since\nI am trying to show that the higher starting probability of Type\nA is irrelevant, I will choose my numbers to be extremely\ngenerous to Type A\\relax. First, we must choose a number for how\nmuch more probable it is for Type A inflation to begin, relative\nto type B\\relax. A googol, $10^{100}$, is usually considered a\nlarge number---it is some 20 orders of magnitude larger than the\ntotal number of baryons in the visible universe. But I will be\nmore generous: I will assume that Type A inflation is more likely\nto start than type B inflation by a factor of $10^{1,000,000}$. \nType B inflation, however, expands just a little bit faster, say\nby 0.001\\%. We need to choose a time constant for the\nexponential expansion, which I will take to be a typical grand\nunified theory scale, $\\tau = 10^{-37}$ sec. ($\\tau$ represents\nthe time constant for the overall expansion factor, which takes\ninto account both the inflationary expansion and the exponential\ndecay of the false vacuum.) Finally, we need to choose a length\nof time to let the system evolve. In principle this time\ninterval is infinite (the inflation is eternal into the future),\nbut to be conservative we will follow the system for only one\nsecond.\n\nWe imagine starting a statistical ensemble of universes at $t=0$,\nwith an expectation value for the volume of Type A inflation\nexceeding that of Type B inflation by $10^{1,000,000}$. For\nbrevity, I will use the term ``weight'' to refer to the ensemble\nexpectation value of the volume. Thus, at $t=0$ the weights of\nType A inflation and Type B inflation will have the ratio\n\\begin{equation}\n \\left.{W_B \\over W_A}\\right|_{t=0} = 10^{-1,000,000} \\ .\n \\label{eq:26}\n\\end{equation}\nAfter one second of evolution, the expansion factors for Type A\nand Type B inflation will be\n\\begin{eqnarray}\n \\label{eq:27}\n Z_A & = & e^{t/\\tau} = e^{10^{37}} \\\\\n \\label{eq:28}\n Z_B & = & e^{1.00001\\,t/\\tau} = e^{0.00001\\,t/\\tau} Z_A\n \\nonumber \\\\\n & = & e^{10^{32}} Z_A \\approx 10^{4.3 \\times 10^{31}} Z_A\n\\end{eqnarray}\nThe weights at the end of one second are proportional to these\nexpansion factors, so\n\\begin{equation}\n \\left.{W_B \\over W_A}\\right|_{t=1\\ \\rm sec} = 10^{\\left(4.3\n \\times 10^{31} - 1,000,000\\right)} \\ .\n \\label{eq:29}\n\\end{equation}\nThus, the initial ratio of $10^{1,000,000}$ is vastly superseded\nby the difference in exponential expansion factors. In fact, we\nwould have to calculate the exponent of Eq.~(\\ref{eq:29}) to an\naccuracy of 25 significant figures to be able to barely detect\nthe effect of the initial factor of $10^{1,000,000}$. \n\nOne might criticize the above argument for being naive, as the\nconcept of time was invoked without any specification of how the\nequal-time hypersurfaces are to be defined. I do not know a\ndecisive answer to this objection; as I will discuss later, there\nare unresolved questions concerning the calculation of\nprobabilities in eternally inflating spacetimes. Nonetheless,\ngiven that there is actually an infinity of time available, it is\nseems reasonable to believe that the form of inflation that\nexpands the fastest will always dominate over the slower forms by\nan infinite factor.\n\nA corollary to this argument is that new inflation is not dead. \nWhile the initial conditions necessary for new inflation cannot\nbe justified on the basis of thermal equilibrium, as proposed in\nthe original papers \\cite{Linde1,Albrecht-Steinhardt1}, in the\ncontext of eternal inflation it is sufficient to conclude that\nthe probability for the required initial conditions is nonzero. \nSince the resulting scenario does not depend on the words that\nare used to justify the initial state, the standard treatment of\nnew inflation remains valid.\n\nA third consequence of eternal inflation is the possibility that\nit offers to rescue the predictive power of theoretical physics. \nHere I have in mind the status of string theory, or the theory\nknown as M theory, into which string theory has evolved. The\ntheory itself has an elegant uniqueness, but nonetheless it is\nnot at all clear that the theory possesses a unique vacuum. \nSince predictions will ultimately depend on the properties of the\nvacuum, the predictive power of string/M theory may be limited. \nEternal inflation, however, provides a possible mechanism to\nremedy this problem. Even if many types of vacua are equally\nstable, it may turn out that one of them leads to a maximal rate\nof inflation. If so, then this type of vacuum will dominate the\nuniverse, even if its expansion rate is only infinitesimally\nlarger than the other possibilities. Thus, eternal inflation\nmight allow physicists to extract unique predictions, in spite of\nthe multiplicity of stable vacua.\n\n\\section{Difficulties in Calculating Probabilities}\n\nIn an eternally inflating universe, anything that can happen will\nhappen; in fact, it will happen an infinite number of times. \nThus, the question of what is possible becomes trivial---anything\nis possible, unless it violates some absolute conservation law. \nTo extract predictions from the theory, we must therefore learn\nto distinguish the probable from the improbable.\n\nHowever, as soon as one attempts to define probabilities in an\neternally inflating spacetime, one discovers ambiguities. The\nproblem is that the sample space is infinite, in that an\neternally inflating universe produces an infinite number of\npocket universes. The fraction of universes with any particular\nproperty is therefore equal to infinity divided by infinity---a\nmeaningless ratio. To obtain a well-defined answer, one needs to\ninvoke some method of regularization.\n\nTo understand the nature of the problem, it is useful to think\nabout the integers as a model system with an infinite number of\nentities. We can ask, for example, what fraction of the integers\nare odd. Most people would presumably say that the answer is\n$1/2$, since the integers alternate between odd and even. That\nis, if the string of integers is truncated after the $N$th, then\nthe fraction of odd integers in the string is exactly $1/2$ if\n$N$ is even, and is $(N+1)/2N$ if $N$ is odd. In any case, the\nfraction approaches $1/2$ as $N$ approaches infinity.\n\nHowever, the ambiguity of the answer can be seen if one imagines\nother orderings for the integers. One could, if one wished,\norder the integers as\n\\begin{equation}\n 1,3,\\ 2,\\ 5,7,\\ 4,\\ 9,11,\\ 6\\ ,\\ldots, \n \\label{eq:30}\n\\end{equation}\nalways writing two odd integers followed by one even integer. \nThis series includes each integer exactly once, just like the\nusual sequence ($1,2,3,4, \\ldots$). The integers are just\narranged in an unusual order. However, if we truncate the\nsequence shown in Eq.~(\\ref{eq:30}) after the $N$th entry, and\nthen take the limit $N \\to \\infty$, we would conclude that 2/3 of\nthe integers are odd. Thus, we find that the definition of\nprobability on an infinite set requires some method of\ntruncation, and that the answer can depend nontrivially on the\nmethod that is used.\n\nIn the case of eternally inflating spacetimes, the natural choice\nof truncation might be to order the pocket universes in the\nsequence in which they form. However, we must remember that each\npocket universe fills its own future light cone, so no pocket\nuniverse forms in the future light cone of another. Any two\npocket universes are spacelike separated from each other, so some\nobservers will see one as forming first, while other observers\nwill see the opposite. One can arbitrarily choose equal-time\nsurfaces that foliate the spacetime, and then truncate at some\nvalue of $t$, but this recipe is not unique. In practice,\ndifferent ways of choosing equal-time surfaces give different\nresults. \n\n\\section{The Youngness Paradox}\n\nIf one chooses a truncation in the most naive way, one is led to\na set of very peculiar results which I call the {\\it youngness\nparadox.}\n\nSpecifically, suppose that one constructs a Robertson-Walker\ncoordinate system while the model universe is still in the false\nvacuum (de Sitter) phase, before any pocket universes have\nformed. One can then propagate this coordinate system forward\nwith a synchronous gauge condition,\\footnote{By a synchronous\ngauge condition, I mean that each equal-time hypersurface is\nobtained by propagating every point on the previous hypersurface\nby a fixed infinitesimal time interval $\\Delta t$ in the\ndirection normal to the hypersurface.} and one can define\nprobabilities by truncating at a fixed value $t_f$ of the\nsynchronous time coordinate $t$. That is, the probability of any\nparticular property can be taken to be proportional to the volume\non the $t = t_f$ hypersurface which has that property. This\nmethod of defining probabilities was studied in detail by Linde,\nLinde, and Mezhlumian, in a paper with the memorable title ``Do\nwe live in the center of the world?'' \\cite{center-world}. I\nwill refer to probabilities defined in this way as synchronous\ngauge probabilities.\n\nThe youngness paradox is caused by the fact that the volume of\nfalse vacuum is growing exponentially with time with an\nextraordinary time constant, in the vicinity of $10^{-37}$ sec.\nSince the rate at which pocket universes form is proportional to\nthe volume of false vacuum, this rate is increasing exponentially\nwith the same time constant. That means that in each second the\nnumber of pocket universes that exist is multiplied by a factor\nof $\\exp\\left\\{10^{37}\\right\\}$. At any given time, therefore,\nalmost all of the pocket universes that exist are universes that\nformed very very recently, within the last several time\nconstants. The population of pocket universes is therefore an\nincredibly youth-dominated society, in which the mature universes\nare vastly outnumbered by universes that have just barely begun\nto evolve. Although the mature universes have a larger volume,\nthis multiplicative factor is of little importance, since in\nsynchronous coordinates the volume no longer grows exponentially\nonce the pocket universe forms.\n\nProbability calculations in this youth-dominated ensemble lead to\npeculiar results, as discussed in Ref.~\\cite{center-world}. \nThese authors considered the expected behavior of the mass\ndensity in our vicinity, concluding that we should find ourselves\nvery near the center of a spherical low-density region. Here I\nwould like to discuss a less physical but simpler question, just\nto illustrate the paradoxes associated with synchronous gauge\nprobabilities. Specifically, I will consider the question: ``Are\nthere any other civilizations in the visible universe that are\nmore advanced than ours?''. Intuitively I would not expect\ninflation to make any predictions about this question, but I will\nargue that the synchronous gauge probability distribution\nstrongly implies that there is no civilization in the visible\nuniverse more advanced than us.\n\nSuppose that we have reached some level of advancement, and\nsuppose that $t_{\\rm min}$ represents the minimum amount of time\nneeded for a civilization as advanced as we are to evolve,\nstarting from the moment of the decay of the false vacuum---the\nstart of the big bang. The reader might object on the grounds\nthat there are many possible measures of advancement, but I would\nrespond by inviting the reader to pick any measure she chooses;\nthe argument that I am about to give should apply to all of them. \nThe reader might alternatively claim that there is no sharp\nminimum $t_{\\rm min}$, but instead we should describe the problem\nin terms of a function which gives the probability that, for any\ngiven pocket universe, a civilization as advanced as we are would\ndevelop by time $t$. I believe, however, that the introduction of\nsuch a probability distribution would merely complicate the\nargument, without changing the result. So, for simplicity of\ndiscussion, I will assume that there is some sharply defined\nminimum time $t_{\\rm min}$ required for a civilization as\nadvanced as ours to develop.\n\nSince we exist, our pocket universe must have an age $t_0$\nsatisfying\n\\begin{equation}\n t_0 \\ge t_{\\rm min} \\ . \n \\label{eq:31}\n\\end{equation}\nSuppose, however, that there is some civilization in our pocket\nuniverse that is more advanced than we are, let us say by 1\nsecond. In that case Eq.~(\\ref{eq:31}) is not sufficient, but\ninstead the age of our pocket universe would have to satisfy\n\\begin{equation}\n t_0 \\ge t_{\\rm min} + 1 \\hbox{\\ second}\\ . \n \\label{eq:32}\n\\end{equation}\nHowever, in the synchronous gauge probability distribution,\nuniverses that satisfy Eq.~(\\ref{eq:32}) are outnumbered by\nuniverses that satisfy Eq.~(\\ref{eq:31}) by a factor of\napproximately $\\exp\\left\\{10^{37}\\right\\}$. Thus, if we know\nonly that we are living in a pocket universe that satisfies\nEq.~(\\ref{eq:31}), it is extremely improbable that it also\nsatisfies Eq.~(\\ref{eq:32}). We would conclude, therefore, that\nit is extraordinarily improbable that there is a civilization in\nour pocket universe that is at least 1 second more advanced than\nwe are.\n\nPerhaps this argument explains why SETI has not found any signals\nfrom alien civilizations, but I find it more plausible that it is\nmerely a symptom that the synchronous gauge probability\ndistribution is not the right one.\n\n\\section{An Alternative Probability Prescription}\n\nSince the probability measure depends on the method used to\ntruncate the infinite spacetime of eternal inflation, we are not\nforced to accept the consequences of the synchronous gauge\nprobabilities. A very attractive alternative has been proposed\nby Vilenkin \\cite{vilenkin-proposal}, and developed further by\nVanchurin, Vilenkin, and Winitzki \\cite{vvw}.\n\nThe key idea of the Vilenkin proposal is to define probabilities\nwithin a single pocket universe (which he describes more\nprecisely as a connected, thermalized domain). Thus, unlike the\nsynchronous gauge method, there is no comparison between old\npocket universes and young ones. To justify this approach it is\ncrucial to recognize that each pocket universe is infinite, even\nif one starts the model with a finite region of de Sitter space. \nThe infinite volume arises in the same way as it does for the\nspecial case of Coleman-de Luccia bubbles\n\\cite{coleman-deluccia}, the interior of which are open\nRobertson-Walker universes. From the outside one often describes\nsuch bubbles in a coordinate system in which they are finite at\nany fixed time, but in which they grow without bound. On the\ninside, however, the natural coordinate system is the one that\nreflects the intrinsic homogeneity, in which the space is\ninfinite at any given time. The infinity of time, as seen from\nthe outside, becomes an infinity of spatial extent as seen on the\ninside. Thus, at least for continuously variable parameters, a\nsingle pocket universe provides an infinite sample space which\ncan be used to define probabilities. The second key idea of\nVilenkin's method is to use the inflaton field itself as the time\nvariable, rather than the synchronous time variable discussed in\nthe previous section.\n\nThis approach can be used, for example, to discuss the\nprobability distribution for $\\Omega$ in open inflationary\nmodels, or to discuss the probability distribution for some\narbitrary field that has a flat potential energy function. If,\nhowever, the vacuum has a discrete parameter which is homogeneous\nwithin each pocket universe, but which takes on different values\nin different pocket universes, then this method does not apply. \n\n\\begin{figure}\n\\centerline{\\epsfbox{vilsp2.eps}}\n\\caption{A schematic picture of a pocket universe, illustrating\nVilenkin's proposal for the calculation of probabilities.}\n\\label{vilenkin-space}\n\\end{figure}\n\nThe proposal can be described in terms of\nFig.~\\ref{vilenkin-space}. We suppose that the theory includes\nan inflaton field $\\phi$ of the new inflation type, and some set\nof fields $\\chi_i$ which have flat potentials. The goal is to\nfind the probability distribution for the fields $\\chi_i$. We\nassume that the evolution of the inflaton $\\phi$ can be divided\ninto three regimes, as shown on the figure. $\\phi < \\phi_1$\ndescribes the eternally inflating regime, in which the evolution\nis governed by quantum diffusion. For $\\phi_1 < \\phi < \\phi_{\\rm\nend}$, the evolution is described classically in a slow-roll\napproximation, so that $\\dot \\phi \\equiv {\\rm d} \\phi / {\\rm d}\nt$ can be expressed as a function of $\\phi$. For $\\phi >\n\\phi_{\\rm end}$ inflation is over, and the $\\phi$ field no longer\nplays an important role in the evolution. The $\\chi_i$ fields\nare assumed to have a finite range of values, such as angular\nvariables, so that a flat probability distribution is\nnormalizable. They are assumed to have a flat potential energy\nfunction for $\\phi > \\phi_{\\rm end}$, so that they could settle\nat any value. They are also assumed to have a flat potential\nenergy function for $\\phi < \\phi_1$, although they might interact\nwith $\\phi$ during the slow-roll regime, however, so that they\ncan affect the rate of inflation. \n\nSince the potential for the $\\chi_i$ is flat for $\\phi < \\phi_1$,\nwe can assume that they begin with a flat probability\ndistribution $P_0(\\chi_i) \\equiv P(\\chi_i, \\phi_1)$ on the $\\phi\n= \\phi_1$ hypersurface. If the kinetic energy function for the\n$\\chi_i$ is of the standard form, we take $P_0(\\chi_i) = const$. \nIf, however, the kinetic energy is nonstandard,\n\\begin{equation}\n {\\cal L}_{\\rm kinetic} = g^{ij}(\\chi) \\partial_\\mu \\chi_i\n \\partial^\\mu \\chi_j \\ ,\n \\label{eq:33}\n\\end{equation}\nas is plausible for a field described in angular variables, then\nthe initial probability distribution is assumed to take the\nreparameterization-invariant form\n\\begin{equation}\n P_0(\\chi_i) \\propto \\sqrt{ \\det g} \\ .\n \\label{eq:34}\n\\end{equation}\nDuring the slow-roll era, it is assumed that the $\\chi_i$ fields\nevolve classically, so one can calculate the number of e-folds of\ninflation $N(\\chi_i)$ as a function of the final value of the\n$\\chi_i$ (i.e., the value of $\\chi_i$ on the $\\phi =\n\\phi_{\\rm end}$ hypersurface). \nOne can also calculate the final values $\\chi_i$ in terms of the\ninitial values $\\chi_i^0$ (i.e., the value of $\\chi_i$ on the\n$\\phi=\\phi_1$ hypersurface). One then assumes that the\nprobability density is enhanced by the volume inflation factor\n$e^{3 N (\\chi_i)}$, and that the evolution from $\\chi_i^0$ to\n$\\chi_i$ results in a Jacobian factor. The (unnormalized) final\nprobability distribution is thus given by\n\\begin{equation}\n P(\\chi_i, \\phi_{\\rm end}) = P_0(\\chi_i^0) e^{3 N (\\chi_i)} \\,\n \\det {\\partial \\chi_j^0 \\over \\partial \\chi_k} \\ .\n \\label{eq:35}\n\\end{equation}\nAlternatively, if the evolution of the $\\chi_i$ during the\nslow-roll era is subject to quantum fluctuations, Ref.~\\cite{vvw}\nshows how to write a Fokker-Planck equation which is equivalent\nto averaging the result of Eq.~(\\ref{eq:35}) over a collection of\npaths that result from interactions with a noise term.\n\nThe Vilenkin proposal sidesteps the youngness paradox by defining\nprobabilities by the comparison of volumes within one pocket\nuniverse. The youngness paradox, in contrast, arose when one\nconsidered a probability ensemble of all pocket universes at a\nfixed value of the synchronous gauge time coordinate---an\nensemble that is overwhelmingly dominated by very young pocket\nuniverses.\n\nThe proposal has the drawback, however, that it cannot be used to\ncompare the probabilities of discretely different alternatives. \nFurthermore, although the results of this method seem reasonable,\nI do not at this point find them compelling. That is, it is not\nclear what principles of physics or probability theory ensure\nthat this particular method of regularizing the spacetime is the\none that leads to correct predictions. Perhaps there is no way\nto answer this question, so we may be forced to accept this\nproposal, or something similar to it, as a postulate.\n\n\\section{Conclusion}\n\nIn this paper I have summarized the workings of inflation, and\nthe arguments that strongly suggest that our universe is the\nproduct of inflation. I argued that inflation can explain the\nsize, the Hubble expansion, the homogeneity, the isotropy, and\nthe flatness of our universe, as well as the absence of magnetic\nmonopoles, and even the characteristics of the nonuniformities. \nThe detailed observations of the cosmic background radiation\nanisotropies continue to fall in line with inflationary\nexpectations, and the evidence for an accelerating universe fits\nwell with the inflationary preference for a flat universe.\n\nNext I turned to the question of eternal inflation, claiming that\nessentially all inflationary models are eternal. In my opinion\nthis makes inflation very robust: if it starts anywhere, at any\ntime in all of eternity, it produces an infinite number of pocket\nuniverses. Eternal inflation has the very attractive feature,\nfrom my point of view, that it offers the possibility of allowing\nunique predictions even if the underlying string theory does not\nhave a unique vacuum. I have also emphasized, however, that\nthere are important problems in understanding the implications of\neternal inflation. First, there is the problem that we do not\nknow how to treat the situation in which the scalar field climbs\nupward to the Planck energy scale. Second, the definition of\nprobabilities in an eternally inflating spacetime is not yet a\nclosed issue, although important progress has been made. And\nthird, I might add that the entire present approach is at best\nsemiclassical. A better treatment may not be possible until we\nhave a much better handle on quantum gravity, but eventually this\nissue will have to be faced.\n\n\\section*{Acknowledgments}\n\nThe author particularly thanks Andrei Linde, Alexander Vilenkin,\nNeil Turok, and other participants in the Isaac Newton Institute\nprogramme {\\it Structure Formation in the Universe} for very\nhelpful conversations. This work is supported in part by funds\nprovided by the U.S. Department of Energy (D.O.E.) under\ncooperative research agreement \\#DF-FC02-94ER40818, and in part\nby funds provided by NM Rothschild \\& Sons Ltd and by the EPSRC.\n\n% Macros that control the format for all references:\n\\newcommand{\\jf}{\\it} % Journal name font\n\\newcommand{\\jt}{\\/} % Journal name spacing correction\n % Replace by {} if Journal name font is not italics\n\\newcommand{\\VPY}[3]{{\\bf #1}, #2 (#3)} % Volume Page Year\n\\newcommand{\\ispace}{\\thinspace} % Space between multiple initials\n\n% Macro to implement the \\. command for spacing \\ispace between initials\n% LaTeX uses \\.{o} for an o with an overdot, but I want to use \\. for\n% periods separating multiple initials. Use \\U{o} for an o with an \n% overdot:\n\\let\\U=\\.\n\\def\\.{.\\nobreak\\ispace\\ignorespaces}\n\n% Macros for individual journal names:\n\\newcommand{\\IJMODPHYS}[3]{{\\jf Int. J. Mod. Phys.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\JETP}[3]{{\\jf JETP Lett.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\MPL}[3]{{\\jf Mod. Phys. Lett.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\NC}[3]{{\\jf Nuovo Cim.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\NP}[3]{{\\jf Nucl. Phys.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\PHYREP}[3]{{\\jf Phys. Rept.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\PL}[3]{{\\jf Phys. Lett.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\PRD}[3]{{\\jf Phys. Rev. D\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\PRL}[3]{{\\jf Phys. Rev. Lett.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\PTRSLA}[3]{{\\jf Phil. Trans. R. Soc. Lond.\\jt\\ A}\n\\VPY{#1}{#2}{#3}}\n\\newcommand{\\ZhETF}[3]{{\\jf Zh. Eksp. Teor. Fiz.\\jt} \\VPY{#1}{#2}{#3}}\n\n\\begin{thebibliography}{99}\n\n\\bibitem{Guth1}\nA\\.H.~Guth, \\PRD{23}{347--356}{1981}.\n% The Inflationary Universe: A Possible Solution to the Horizon\n% and Flatness Problems\n\n\\bibitem{Starobinsky}\nA\\.A.~Starobinsky, \\ZhETF{30}{719}{1979} [\\JETP{30}{682}{1979}];\nA\\.A.~Starobinsky, \\PL{91B}{99--102}{1980}.\n% A New Type of Isotropic Cosmological Models without Singularity\n% (yes, that really is ``Models''; reprinted in Abbott & Pi)\n\n\\bibitem{Coleman}\nS.~Coleman, \\PRD{15}{2929--2936}{1977} [see errata\n\\VPY{16}{1248}{1977}];\n% The Fate of the False Vacuum. 1. Semiclassical Theory\nC\\.G.~Callan and S.~Coleman,\n\\PRD{16}{1762--1768}{1977}.\n% The Fate of the False Vacuum. 2. First Quantum Corrections\n\n\\bibitem{HMS}\nS\\.W.~Hawking, I\\.G.~Moss, and J\\.M.~Stewart,\n\\PRD{26}{2681--2693}{1982}.\n% Bubble Collisions in the Very Early Universe\n\n\\bibitem{GuthWeinberg}\nA\\.H.~Guth and E\\.J.~Weinberg, \\NP{B212}{321--364}{1983}.\n% Could the Universe Have Recovered from a Slow First Order Phase\n% Transition?\n\n\\bibitem{Linde1}\nA\\.D.~Linde, \\PL{108B}{389--393}{1982}.\n% A New Inflationary Universe Scenario: A Possible Solution of the\n% Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole\n% Problems\n\n\\bibitem{Albrecht-Steinhardt1}\nA.~Albrecht and P\\.J.~Steinhardt, \\PRL{48}{1220--1223}{1982}.\n% Cosmology for Grand Unified Theories with Radiatively Induced\n% Symmetry Breaking\n\n\\bibitem{chaotic}\nA\\.D.~Linde, \\ZhETF{38}{149--151}{1983} [\\JETP{38}{176--179}{1983}];\n% Chaotic inflating universe\nA\\.D.~Linde, \\PL{129B}{177--181}{1983}.\n% Chaotic inflation\n\n\\bibitem{hyb1} \nA\\.D.~Linde, \\PL{B259}{38--47}{1991}.\n% Axions in Inflationary Cosmology\n\n\\bibitem{hyb2}\nA\\.R.~Liddle and D\\.H.~Lyth, \\PHYREP{231}{1--105}{1993},\nastro-ph/9303019.\n% The Cold Dark Matter Density Perturbation\n\n\\bibitem{hyb3}\nA\\.D.~Linde, \\PRD{49}{748--754}{1994}, astro-ph/9307002.\n% Hybrid Inflation\n\n\\bibitem{hyb4}\nE\\.J.~Copeland, A\\.R.~Liddle, D\\.H.~Lyth, E\\.D.~Stewart, and\nD.~Wands, \\PRD{49}{6410-6433}{1994}, astro-ph/9401011.\n% False Vacuum Inflation with Einstein Gravity\n\n\\bibitem{hyb5}\nE.~Stewart, \\PL{B345}{414--415}{1995}, astro-ph/9407040.\n% Mutated Hybrid Inflation\n\n\\bibitem{RSG}\nL.~Randall, M.~Solja\\v{c}i\\'{c}, and A\\.H.~Guth,\n\\NP{B472}{377--408}{1996}, hep-ph/9512439; also hep-ph/9601296.\n% Supernatural Inflation: Inflation from Supersymmetry\n% with No (Very) Small Parameters\n% Supernatural Inflation (hep-ph/9601296).\n\n\\bibitem{Jensen-Stein-Schabes}\nL\\.G. Jensen and J\\.A. Stein-Schabes, \\PRD{35}{1146--1150}{1987},\nand references therein.\n% Is inflation natural?\n% Lars Gerhard Jensen and Jaime A. Stein-Schabes \n\n\\bibitem{Starobinsky2}\nA\\.A.~Starobinsky, \\PL{117B}{175--178}{1982}.\n% Dynamics of phase transition in the new inflationary universe\n% scenario and generation of perturbations\n\n\\bibitem{GuthPi}\nA\\.H.~Guth and S.-Y.~Pi, \\PRL{49}{1110--1113}{1982}.\n% Fluctuations in the new inflationary universe\n\n\\bibitem{Hawking1}\nS\\.W.~Hawking, \\PL{115B}{295--297}{1982}.\n% The development of irregularities in a single bubble\n% inflationary universe\n\n\\bibitem{BST}\nJ\\.M.~Bardeen, P\\.J.~Steinhardt, and M\\.S.~Turner,\n\\PRD{28}{679--693}{1983}.\n% Spontaneous creation of almost scale-free density perturbations\n% in an inflationary universe\n\n% For the current line width settings, the spacing TeX gives is\n% ridiculous if one doesn't lower \\hyphenpenalty so that\n% ``Brandenberger'' can be hyphenated:\n{\\hyphenpenalty=100\n\\bibitem{BFM}\nFor a modern review, see\nV\\.F.~Mukhanov, H\\.A.~Feldman, and R\\.H.~Brandenberger,\n\\PHYREP{215}{203--333}{1992}.\\par}\n% Theory of Cosmological Perturbations\n\n\\bibitem{Guth-RS}\nA\\.H.~Guth, \\PTRSLA{307}{141--148}{1982}.\n% Phase transitions in the embryo universe\n\n\\bibitem{dicke}\nR\\.H.~Dicke and P\\.J\\.E.~Peebles, in {\\bf General\nRelativity: An Einstein Centenary Survey}, eds: S\\.W.~Hawking and\nW.~Israel (Cambridge University Press, 1979).\n\n\\bibitem{preskill}\nJ\\.P.~Preskill, \\PRL{43}{1365--1368}{1979}.\n% Cosmological production of superheavy magnetic monopoles\n\n\\bibitem{bond-jaffe}\nJ\\.R.~Bond and A\\.H.~Jaffe, talk given at Royal Society Meeting\non {\\bf The Development of Large Scale Structure in the\nUniverse,} London, England, 25-26 Mar 1998, submitted to {\\jf\nPhil. Trans. Roy. Soc. Lond. A}, astro-ph/9809043.\n\n\\bibitem{steinhardt-nuffield}\nP\\.J. Steinhardt, in {\\bf The Very Early Universe}, Proceedings\nof the Nuffield Workshop, Cambridge, 21 June -- 9 July, 1982,\neds: G\\.W.~Gibbons, S\\.W.~Hawking, and S\\.T\\.C.~Siklos (Cambridge\nUniversity Press, 1983), pp. 251--266.\n% Natural Inflation\n\n\\bibitem{vilenkin-eternal}\nA.~Vilenkin, \\PRD{27}{2848--2855}{1983}.\n% The Birth of Inflationary Universes.\n\n\\bibitem{guth-pi2}\nA\\.H.~Guth and S.-Y.~Pi, \\PRD{32}{1899--1920}{1985}.\n% Quantum Mechanics of the Scalar Field in the New Inflationary\n% Universe\n\n\\bibitem{coleman-deluccia}\nS.~Coleman \\& F.~De~Luccia, \\PRD{21}{3305--3315}{1980}.\n% Gravitational effects on and of vacuum decay\n\n\\bibitem{vvw}\nV.~Vanchurin, A.~Vilenkin, \\& S.~Winitzki, gr-qc/9905097.\n% Predictability crisis in inflationary cosmology and its\n% resolution\n\n\\bibitem{aryal-vilenkin}\nM.~Aryal and A.~Vilenkin, \\PL{199B}{351--357}{1987}.\n% The Fractal Dimension of Inflationary Universe.\n% Mukunda Aryal\n\n\\bibitem{linde-eternal}\nA\\.D.~Linde, \\MPL{A1}{81}{1986};\n% Eternal Chaotic Inflation\nA\\.D.~Linde, \\PL{175B}{395--400}{1986};\n% Eternally Existing Selfreproducing Chaotic Inflationary Universe\nA\\.S.~Goncharov, A\\.D.~Linde, and V\\.F.~Mukhanov,\n\\IJMODPHYS{A2}{561--591}{1987}.\n% The Global Structure of the Inflationary Universe.\n\n\\bibitem{random-vil-ford}\nA.~Vilenkin and L\\.H.~Ford, \\PRD{26}{1231--1241}{1982}.\n% Gravitational Effects Upon Cosmological Phase Transitions.\n\n\\bibitem{random-linde}\nA\\.D.~Linde, \\PL{B116}{335}{1982}.\n% Scalar Field Fluctuations in Expanding Universe and the New\n% Inflationary Universe Scenario.\n\n\\bibitem{random-starobinsky}\nA.~Starobinsky, in {\\bf Field Theory, Quantum Gravity and\nStrings}, eds: H.J. de Vega \\& N. S\\'anchez, {\\jf Lecture Notes\nin Physics\\jt} (Springer Verlag) Vol.~246, pp.~107--126 (1986).\n\n\\bibitem{linde-book}\nSee for example A\\.D.~Linde, {\\bf Particle Physics and\nInflationary Cosmology} (Harwood Academic Publishers, Chur,\nSwitzerland, 1990) Secs.~1.7--1.8.\n\n\\bibitem{hartle-hawking}\nJ\\.B.~Hartle \\& S\\.W.~Hawking, \\PRD{28}{2960--2975}{1983}.\n% Wave Function of the Universe\n\n\\bibitem{tunnel-vilenkin}\nA.~Vilenkin, \\PRD{30}{509--511}{1984};\n% Quantum Creation of Universes\nA.~Vilenkin, \\PRD{33}{3560--3569}{1986};\n% Boundary Conditions in Quantum Cosmology\nA.~Vilenkin, gr-qc/9812027, to be published in {\\bf Proceedings\nof COSMO 98}, Monterey, CA, 15-20 November, 1998.\n% The Quantum Cosmology Debate\n\n\\bibitem{tunnel-linde}\nA\\.D. Linde, \\NC{39}{401--405}{1984};\n% Quantum Creation of the Inflationary Universe\nA\\.D. Linde, \\PRD{58}{083514}{1998}, gr-qc/9802038.\n% Quantum Creation of an Open Inflationary Universe\n\n\\bibitem{hawking-turok}\nS\\.W.~Hawking \\& N\\.G.~Turok, \\PL{B425}{25--32}{1998}, hep-th/9802030.\n% Open Inflation Without False Vacua.\n\n\\bibitem{LLM}\nA.~Linde, D.~Linde, \\& A.~Mezhlumian, \\PRD{49}{1783--1826}{1994},\ngr-qc/9306035.\n% From the Big Bang Theory to the Theory of a Stationary\n% Universe\n\n\\bibitem{GBLinde}\nJ.~Garcia-Bellido \\& A.~Linde, \\PRD{51}{429--443}{1995},\nhep-th/9408023.\n% Stationarity of Inflation and Predictions of Quantum Cosmology\n\n\\bibitem{borde-vilenkin}\nA.~Borde \\& A.~Vilenkin, \\PRL{72}{3305--3309}{1994}, gr-qc/9312022.\n% Eternal inflation and the initial singularity\n\n\\bibitem{borde-vilenkin2}\nA.~Borde \\& A.~Vilenkin, \\PRD{56}{717--723}{1997}, gr-qc/9702019.\n% Violations of the Weak Energy Condition in Inflating\n% Space-Times.\n\n\\bibitem{center-world}\nA.~Linde, D.~Linde, \\& A.~Mezhlumian, \\PL{B345}{203--210}{1995},\nhep-th/9411111.\n\n\\bibitem{vilenkin-proposal}\nA.~Vilenkin, \\PRL{81}{5501--5504}{1998}, hep-th/9806185.\n% Unambiguous Probabilities in an Eternally Inflating Universe\n\n\\end{thebibliography}\n\n\\end{document}\n"
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{
"name": "astro-ph0002156.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{Guth1}\nA\\.H.~Guth, \\PRD{23}{347--356}{1981}.\n% The Inflationary Universe: A Possible Solution to the Horizon\n% and Flatness Problems\n\n\\bibitem{Starobinsky}\nA\\.A.~Starobinsky, \\ZhETF{30}{719}{1979} [\\JETP{30}{682}{1979}];\nA\\.A.~Starobinsky, \\PL{91B}{99--102}{1980}.\n% A New Type of Isotropic Cosmological Models without Singularity\n% (yes, that really is ``Models''; reprinted in Abbott & Pi)\n\n\\bibitem{Coleman}\nS.~Coleman, \\PRD{15}{2929--2936}{1977} [see errata\n\\VPY{16}{1248}{1977}];\n% The Fate of the False Vacuum. 1. Semiclassical Theory\nC\\.G.~Callan and S.~Coleman,\n\\PRD{16}{1762--1768}{1977}.\n% The Fate of the False Vacuum. 2. First Quantum Corrections\n\n\\bibitem{HMS}\nS\\.W.~Hawking, I\\.G.~Moss, and J\\.M.~Stewart,\n\\PRD{26}{2681--2693}{1982}.\n% Bubble Collisions in the Very Early Universe\n\n\\bibitem{GuthWeinberg}\nA\\.H.~Guth and E\\.J.~Weinberg, \\NP{B212}{321--364}{1983}.\n% Could the Universe Have Recovered from a Slow First Order Phase\n% Transition?\n\n\\bibitem{Linde1}\nA\\.D.~Linde, \\PL{108B}{389--393}{1982}.\n% A New Inflationary Universe Scenario: A Possible Solution of the\n% Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole\n% Problems\n\n\\bibitem{Albrecht-Steinhardt1}\nA.~Albrecht and P\\.J.~Steinhardt, \\PRL{48}{1220--1223}{1982}.\n% Cosmology for Grand Unified Theories with Radiatively Induced\n% Symmetry Breaking\n\n\\bibitem{chaotic}\nA\\.D.~Linde, \\ZhETF{38}{149--151}{1983} [\\JETP{38}{176--179}{1983}];\n% Chaotic inflating universe\nA\\.D.~Linde, \\PL{129B}{177--181}{1983}.\n% Chaotic inflation\n\n\\bibitem{hyb1} \nA\\.D.~Linde, \\PL{B259}{38--47}{1991}.\n% Axions in Inflationary Cosmology\n\n\\bibitem{hyb2}\nA\\.R.~Liddle and D\\.H.~Lyth, \\PHYREP{231}{1--105}{1993},\nastro-ph/9303019.\n% The Cold Dark Matter Density Perturbation\n\n\\bibitem{hyb3}\nA\\.D.~Linde, \\PRD{49}{748--754}{1994}, astro-ph/9307002.\n% Hybrid Inflation\n\n\\bibitem{hyb4}\nE\\.J.~Copeland, A\\.R.~Liddle, D\\.H.~Lyth, E\\.D.~Stewart, and\nD.~Wands, \\PRD{49}{6410-6433}{1994}, astro-ph/9401011.\n% False Vacuum Inflation with Einstein Gravity\n\n\\bibitem{hyb5}\nE.~Stewart, \\PL{B345}{414--415}{1995}, astro-ph/9407040.\n% Mutated Hybrid Inflation\n\n\\bibitem{RSG}\nL.~Randall, M.~Solja\\v{c}i\\'{c}, and A\\.H.~Guth,\n\\NP{B472}{377--408}{1996}, hep-ph/9512439; also hep-ph/9601296.\n% Supernatural Inflation: Inflation from Supersymmetry\n% with No (Very) Small Parameters\n% Supernatural Inflation (hep-ph/9601296).\n\n\\bibitem{Jensen-Stein-Schabes}\nL\\.G. Jensen and J\\.A. Stein-Schabes, \\PRD{35}{1146--1150}{1987},\nand references therein.\n% Is inflation natural?\n% Lars Gerhard Jensen and Jaime A. Stein-Schabes \n\n\\bibitem{Starobinsky2}\nA\\.A.~Starobinsky, \\PL{117B}{175--178}{1982}.\n% Dynamics of phase transition in the new inflationary universe\n% scenario and generation of perturbations\n\n\\bibitem{GuthPi}\nA\\.H.~Guth and S.-Y.~Pi, \\PRL{49}{1110--1113}{1982}.\n% Fluctuations in the new inflationary universe\n\n\\bibitem{Hawking1}\nS\\.W.~Hawking, \\PL{115B}{295--297}{1982}.\n% The development of irregularities in a single bubble\n% inflationary universe\n\n\\bibitem{BST}\nJ\\.M.~Bardeen, P\\.J.~Steinhardt, and M\\.S.~Turner,\n\\PRD{28}{679--693}{1983}.\n% Spontaneous creation of almost scale-free density perturbations\n% in an inflationary universe\n\n% For the current line width settings, the spacing TeX gives is\n% ridiculous if one doesn't lower \\hyphenpenalty so that\n% ``Brandenberger'' can be hyphenated:\n{\\hyphenpenalty=100\n\\bibitem{BFM}\nFor a modern review, see\nV\\.F.~Mukhanov, H\\.A.~Feldman, and R\\.H.~Brandenberger,\n\\PHYREP{215}{203--333}{1992}.\\par}\n% Theory of Cosmological Perturbations\n\n\\bibitem{Guth-RS}\nA\\.H.~Guth, \\PTRSLA{307}{141--148}{1982}.\n% Phase transitions in the embryo universe\n\n\\bibitem{dicke}\nR\\.H.~Dicke and P\\.J\\.E.~Peebles, in {\\bf General\nRelativity: An Einstein Centenary Survey}, eds: S\\.W.~Hawking and\nW.~Israel (Cambridge University Press, 1979).\n\n\\bibitem{preskill}\nJ\\.P.~Preskill, \\PRL{43}{1365--1368}{1979}.\n% Cosmological production of superheavy magnetic monopoles\n\n\\bibitem{bond-jaffe}\nJ\\.R.~Bond and A\\.H.~Jaffe, talk given at Royal Society Meeting\non {\\bf The Development of Large Scale Structure in the\nUniverse,} London, England, 25-26 Mar 1998, submitted to {\\jf\nPhil. Trans. Roy. Soc. Lond. A}, astro-ph/9809043.\n\n\\bibitem{steinhardt-nuffield}\nP\\.J. Steinhardt, in {\\bf The Very Early Universe}, Proceedings\nof the Nuffield Workshop, Cambridge, 21 June -- 9 July, 1982,\neds: G\\.W.~Gibbons, S\\.W.~Hawking, and S\\.T\\.C.~Siklos (Cambridge\nUniversity Press, 1983), pp. 251--266.\n% Natural Inflation\n\n\\bibitem{vilenkin-eternal}\nA.~Vilenkin, \\PRD{27}{2848--2855}{1983}.\n% The Birth of Inflationary Universes.\n\n\\bibitem{guth-pi2}\nA\\.H.~Guth and S.-Y.~Pi, \\PRD{32}{1899--1920}{1985}.\n% Quantum Mechanics of the Scalar Field in the New Inflationary\n% Universe\n\n\\bibitem{coleman-deluccia}\nS.~Coleman \\& F.~De~Luccia, \\PRD{21}{3305--3315}{1980}.\n% Gravitational effects on and of vacuum decay\n\n\\bibitem{vvw}\nV.~Vanchurin, A.~Vilenkin, \\& S.~Winitzki, gr-qc/9905097.\n% Predictability crisis in inflationary cosmology and its\n% resolution\n\n\\bibitem{aryal-vilenkin}\nM.~Aryal and A.~Vilenkin, \\PL{199B}{351--357}{1987}.\n% The Fractal Dimension of Inflationary Universe.\n% Mukunda Aryal\n\n\\bibitem{linde-eternal}\nA\\.D.~Linde, \\MPL{A1}{81}{1986};\n% Eternal Chaotic Inflation\nA\\.D.~Linde, \\PL{175B}{395--400}{1986};\n% Eternally Existing Selfreproducing Chaotic Inflationary Universe\nA\\.S.~Goncharov, A\\.D.~Linde, and V\\.F.~Mukhanov,\n\\IJMODPHYS{A2}{561--591}{1987}.\n% The Global Structure of the Inflationary Universe.\n\n\\bibitem{random-vil-ford}\nA.~Vilenkin and L\\.H.~Ford, \\PRD{26}{1231--1241}{1982}.\n% Gravitational Effects Upon Cosmological Phase Transitions.\n\n\\bibitem{random-linde}\nA\\.D.~Linde, \\PL{B116}{335}{1982}.\n% Scalar Field Fluctuations in Expanding Universe and the New\n% Inflationary Universe Scenario.\n\n\\bibitem{random-starobinsky}\nA.~Starobinsky, in {\\bf Field Theory, Quantum Gravity and\nStrings}, eds: H.J. de Vega \\& N. S\\'anchez, {\\jf Lecture Notes\nin Physics\\jt} (Springer Verlag) Vol.~246, pp.~107--126 (1986).\n\n\\bibitem{linde-book}\nSee for example A\\.D.~Linde, {\\bf Particle Physics and\nInflationary Cosmology} (Harwood Academic Publishers, Chur,\nSwitzerland, 1990) Secs.~1.7--1.8.\n\n\\bibitem{hartle-hawking}\nJ\\.B.~Hartle \\& S\\.W.~Hawking, \\PRD{28}{2960--2975}{1983}.\n% Wave Function of the Universe\n\n\\bibitem{tunnel-vilenkin}\nA.~Vilenkin, \\PRD{30}{509--511}{1984};\n% Quantum Creation of Universes\nA.~Vilenkin, \\PRD{33}{3560--3569}{1986};\n% Boundary Conditions in Quantum Cosmology\nA.~Vilenkin, gr-qc/9812027, to be published in {\\bf Proceedings\nof COSMO 98}, Monterey, CA, 15-20 November, 1998.\n% The Quantum Cosmology Debate\n\n\\bibitem{tunnel-linde}\nA\\.D. Linde, \\NC{39}{401--405}{1984};\n% Quantum Creation of the Inflationary Universe\nA\\.D. Linde, \\PRD{58}{083514}{1998}, gr-qc/9802038.\n% Quantum Creation of an Open Inflationary Universe\n\n\\bibitem{hawking-turok}\nS\\.W.~Hawking \\& N\\.G.~Turok, \\PL{B425}{25--32}{1998}, hep-th/9802030.\n% Open Inflation Without False Vacua.\n\n\\bibitem{LLM}\nA.~Linde, D.~Linde, \\& A.~Mezhlumian, \\PRD{49}{1783--1826}{1994},\ngr-qc/9306035.\n% From the Big Bang Theory to the Theory of a Stationary\n% Universe\n\n\\bibitem{GBLinde}\nJ.~Garcia-Bellido \\& A.~Linde, \\PRD{51}{429--443}{1995},\nhep-th/9408023.\n% Stationarity of Inflation and Predictions of Quantum Cosmology\n\n\\bibitem{borde-vilenkin}\nA.~Borde \\& A.~Vilenkin, \\PRL{72}{3305--3309}{1994}, gr-qc/9312022.\n% Eternal inflation and the initial singularity\n\n\\bibitem{borde-vilenkin2}\nA.~Borde \\& A.~Vilenkin, \\PRD{56}{717--723}{1997}, gr-qc/9702019.\n% Violations of the Weak Energy Condition in Inflating\n% Space-Times.\n\n\\bibitem{center-world}\nA.~Linde, D.~Linde, \\& A.~Mezhlumian, \\PL{B345}{203--210}{1995},\nhep-th/9411111.\n\n\\bibitem{vilenkin-proposal}\nA.~Vilenkin, \\PRL{81}{5501--5504}{1998}, hep-th/9806185.\n% Unambiguous Probabilities in an Eternally Inflating Universe\n\n\\end{thebibliography}"
}
] |
astro-ph0002157
|
Structure of the Sagittarius dwarf galaxy at low Galactic latitudes \thanks{Based on observations obtained at the European Southern Observatory, La Silla, Chile}
|
[
{
"author": "P. Cseresnjes \\inst{1,2}"
},
{
"author": "C. Alard \\inst{1,2}"
},
{
"author": "J. Guibert \\inst{1,2}"
}
] |
We report the detection of $\sim$1\,500 RR Lyrae of Bailey type ab located in the Sagittarius dwarf galaxy (Sgr). These variables have been detected on two ESO Schmidt fields centred on (l,b)=(3.1\de,-7.1\de) and (6.6\de,-10.8\de), covering an area of $\sim$50 deg$^{2}$. We present a surface density map of Sgr based on the spatial distribution of these RRab, allowing us to trace its structure in a region that was still almost unexplored between b=-14\de and b=-4\de. We present the results of the fit of different models to the density profile of Sgr. The best fit to the core of Sgr is an exponential with a scale length of 4.1\de along the major axis. When we look at the extension of Sgr we find a break (significant at the $\sim$2$\sigma$ level) in the slope of the surface density along the main axis of Sgr. The nearly flat (or at least very slowly decreasing) profile in the outer region of Sgr shows that this dwarf galaxy is probably extending even further out our fields. \keywords{Galaxies: dwarf - Galaxies: individual: Sagittarius dwarf - Local group - Stars: Variables: RR Lyr}
|
[
{
"name": "paper.tex",
"string": "\\documentclass{aa}\n\\usepackage{graphics}\n\\usepackage{amssymb}\n%\\usepackage{babel}\n\n%\\renewcommand{\\arraystretch}{0.75}\n\\newcommand{\\de}{$^{\\circ}$}\n\\newcommand{\\sag}{\\textit{SAG }}\n\\newcommand{\\duo}{\\textit{DUO }}\n\\newcommand{\\majd}{\\textit{Maj10}}\n\\newcommand{\\majs}{\\textit{Maj6}}\n\\newcommand{\\mini}{\\textit{Min} }\n\n\\setlength{\\parindent}{10pt}\n\n\\begin{document}\n\n\\thesaurus{11(08.22.4; %Stars: variables: RR Lyr\n 11.09.1 Sagittarius; %Galaxies: individual: Sagittarius\n 11.04.2; %Galaxies: dwarf\n 11.12.1)} %Local Group\n \n\n\\title{Structure of the Sagittarius dwarf galaxy at low Galactic latitudes \\thanks{Based on observations obtained at the European Southern Observatory, La Silla, Chile}}\n\n\\author{P. Cseresnjes \\inst{1,2} \\and C. Alard \\inst{1,2} \\and J. Guibert \\inst{1,2}}\n\n\\offprints{patrick.cseresnjes@obspm.fr}\n\n\\institute{DASGAL, Observatoire de Paris, 61 Avenue de l'Observatoire, F-75014 Paris\n \\and Centre d'Analyse des Images - INSU}\n\t \n\n\\date{Received .../ Accepted ...}\n\n\\titlerunning{Structure of the Sgr dwarf at low Galactic latitudes}\n\\authorrunning{P. Cseresnjes et al.}\n\n\\maketitle\n\n\\begin{abstract}\nWe report the detection of $\\sim$1\\,500 RR Lyrae of Bailey type ab located in the Sagittarius dwarf galaxy (Sgr). These variables have been detected on two ESO Schmidt fields centred on (l,b)=(3.1\\de,-7.1\\de) and (6.6\\de,-10.8\\de), covering an area of $\\sim$50 deg$^{2}$. We present a surface density map of Sgr based on the spatial distribution of these RRab, allowing us to trace its structure in a region that was still almost unexplored between b=-14\\de and b=-4\\de. We present the results of the fit of different models to the density profile of Sgr. The best fit to the core of Sgr is an exponential with a scale length of 4.1\\de along the major axis. When we look at the extension of Sgr we find a break (significant at the $\\sim$2$\\sigma$ level) in the slope of the surface density along the main axis of Sgr. The nearly flat (or at least very slowly decreasing) profile in the outer region of Sgr shows that this dwarf galaxy is probably extending even further out our fields.\n\\keywords{Galaxies: dwarf - Galaxies: individual: Sagittarius dwarf - Local group - Stars: Variables: RR Lyr}\n\\end{abstract}\n%\n%++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n%\n\\section{Introduction}\n%\n The Sagittarius dwarf galaxy is the closest known member of the Local Group orbiting around the Milky Way ($\\sim$25 kpc from the sun, $\\sim$16 kpc from the Galactic Centre), but as a consequence of its location behind the Galactic Centre, it has been discovered only recently (Ibata, Gilmore, Irwin 1994, 1995). Since this discovery it turned out that Sgr presents typical features of a dwarf spheroidal: domination of an old ($\\gtrsim$10 Gyr) metal poor stellar population (Mateo et al. \\cite{muskkk}; Fahlman et al. \\cite{fahlman}; Marconi et al. \\cite{marconi}; Bellazzini et al \\cite{bfb1}) and absence of gas (Burton \\& Lockman \\cite{bl}). Its highest surface density region is centred on the Globular Cluster M54 (l=5.6\\de, b=-14.0\\de) and it is oriented roughly perpendicular to the Galactic plane so that its Northern extension (in Galactic coordinates) is completely hidden by the MW.\\\\\nThe mapping of Sgr is difficult to achieve because of the combination of its low surface brightness ($\\mu_{V}\\ge 25.5$ mag.arcsec$^{-2}$), contamination by foreground Galactic stars and its large spatial extent (at least 22$^{\\circ}\\times$8\\de) (Ibata et al. \\cite{iwgis}, hereafter IWGIS). Evidence for the presence of Sgr has been established over 45\\de from b$\\sim -3^{\\circ}$ (Alard \\cite{a96}, hereafter A96; Alcock et al. 1997, hereafter Alc97) down to b$\\sim -48^{\\circ}$ (Mateo et al. \\cite{mom}, hereafter MOM), but it is difficult to assess whether these regions still correspond to the main body of Sgr or if we are merely encountering tidal debris (as suggested by Johnston et al. \\cite{johnston99}). IWGIS proposed a map of the Southern part of Sgr based on the spatial distribution of the bright main sequence stars in Sgr and covering an area of $\\sim 150$ deg$^{2}$ from $b\\sim -11^{\\circ}$ down to $b\\sim -26^{\\circ}$. However, their method based on statistical decontamination fails at low Galactic latitudes ($|$b$|\\lesssim$12\\de) where differential reddening and high density of foreground stars (only $\\sim$1 star in 1\\,000 is in Sgr in these regions) preclude any reliable decontamination, leaving the structure of the Northern extension of Sgr almost unknown. To this point, the detection of RR Lyrae constitutes an essential tool to trace the structure of Sgr in these regions as they can be clearly separated from the RR Lyrae of the MW. This method has already proven successful and $\\sim 350$ RRab were detected between b=-10\\de and b=-4\\de (A96; Alc97). However, a connection between these stars and the centre of Sgr was necessary in order to offer a clear vision of this important region strongly interacting with the MW.\\\\\nIn this paper we report the detection of $\\sim$1\\,500 RRab members of Sgr and located in its Northern extension. We present a surface density map of Sgr covering $\\sim$50 deg$^{2}$ between b=-14\\de and b=-4\\de, based on the spatial distribution of these variables. \\\\\nThe paper is organized as follows : in section 2 we present our data (observations and reduction). Section 3 is devoted to the description of the selection process of RR Lyrae stars as well as a study of its completeness. We then describe the structure of Sgr (section 4). Finally we summarize our results and conclude in section 5.\n%\n%++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n%\n\\section{Data}\n%\n\\subsection{Observations}\n The data discussed in this paper consist of two sets of photographic plates and films taken with the ESO 1m Schmidt telescope at La Silla Observatory (see Table 1), each of them covering an area of $\\sim 25$ deg$^{2}$ on the sky.\\\\\nThe first set of plates was part of the DUO project aimed at detecting microlensing events towards the Galactic Bulge (Alard \\& Guibert \\cite{a97}, hereafter AG97). This field, centred on Galactic coordinates (l=3.1\\de, b=-7.1\\de), has already been processed and presented in A96. The second set is new and includes 69 films centred on a field shifted towards the centre of density of the Sagittarius dwarf galaxy and slightly overlapping with the former (l=6.6\\de, b=-10.8\\de). Throughout the remainder of this paper, we will call the first field \\duo field while the new field will be referred to as the \\sag field.\n%\n\\begin{table}\n \\caption{{\\bf Table 1.} Observations}\n \\begin{tabular}{l @{ } l @{ } l} \\\\ \n \\hline\n Field & DUO & SAG \\\\\\hline\\\\\n Season & 1994 & 1996 \\\\\n Number of plates & 82 & 69 \\\\\n Field centre (l,b) & ($3.1^{\\circ},-7.1^{\\circ})$ & $(6.6^{\\circ},-10.8^{\\circ})$\\\\\n Emulsion & III$_{a}$J, III$_{a}$F & 4415 \\\\\n Filter & GG385, RG630 & BG12 \\\\\n Limiting Magnitude & B$_{J}\\sim$20.5 & V$\\sim$20.0\n \\end{tabular}\n\\end{table}\n%\n\\subsection{Data reduction}\n The plates were scanned at CAI/Paris Observatory with the high speed microdensitometer MAMA\\footnote{MAMA (http://dsmama.obspm.fr) is operated by INSU (Institut National des Sciences de l'Univers) and Observatoire de Paris.} (Machine Automatique \\`a Mesurer pour l'Astronomie), yielding images with a pixel size of 10$\\mu$m ($\\sim 0.6 \\arcsec$.).\\\\\nThe photometric reduction has been performed with the software \\textit{Extractor} written by Alard. The process is as follows: first a reference catalogue is extracted from a plate of good quality (seeing$< 1 \\arcsec$). For all the other plates, a new extraction is performed (implying a new detection of each object) and the new catalogue associated to the reference catalogue. The light curves were built in this way plate by plate and stored in a database. For more details on the photometric reduction process see AG97. The final sample contains light curves for $\\sim14.10^{6}$ stars in the \\duo field and $\\sim6.10^{6}$ stars in the \\sag field.\n%\n\\subsection{Photometry}\n%\n\\subsubsection{Calibration}\n The \\duo field has been calibrated with a CCD sequence taken at the ESO/Danish 1.5 m telescope at La Silla. The photometric system for this field is ${\\rm B}_{\\rm J}={\\rm B} - 0.28({\\rm B} - {\\rm V})$ (Blair \\& Gilmore \\cite{bg}) . The Emulsion/Filter combination was different for the \\sag field and consisted of a Kodak Tech-Pan 4415 emulsion together with a BG12 Filter. The Tech-Pan 4415 emulsion is an extremely fine-grained, high resolution film with a sensitivity extending to 0.69 $\\mu$m. For more informations about the 4415 emulsion, see Phillipps \\& Parker (\\cite{pp}) and references therein. We were not aware of any photometric relation published for the band used in \\sag. \n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{bpass.ps}}\n \\caption {Approximate bandpasses used in \\sag (solid line) and \\duo (dotted line).}\n \\label{bpass}\n\\end{figure}\nThe resulting bandpasses for both fields are shown on Fig. \\ref{bpass}. The calibration in \\sag has been performed with a sequence provided by Sarajedini \\& Layden (\\cite{sl}), located $12\\arcsec$ north of the globular cluster M54 and consisting of 1638 stars calibrated in V and I bands. A polynomial fit to the instrumental magnitude of these stars yielded the photometric system ${\\rm B}_{\\rm i}={\\rm V} + 1.47({\\rm V}-{\\rm I})$, where B$_{\\rm i}$ stands for the magnitude in the color band used in \\sag . The scatter about this relation is 0.17 mag. \n\\subsubsection{Correction for extinction}\n%\n The reddening has been estimated separately for each field. For the \\duo field we used the well known property that the color of RR Lyrae stars at minimum magnitude is approximately constant and depends only slightly on the period and the metallicity (Sturch, \\cite{sturch}). A reddening map has been estimated for this field by computing the mean colors (B$_{\\rm J}$-R) of RRab in small regions of 10$\\arcmin \\times$10$\\arcmin$. The corrected magnitude is ${\\rm B}_{J_{0}}={\\rm B}_{\\rm J}-2.84\\,{\\rm E(B-R)}$ (Wesselink \\cite{wes}). For the \\sag field, where no color information was available, we used the extinction map of Schlegel et al. (\\cite{sfd}, hereafter SFD) which provides reddening estimates with a precision of 16$\\%$ for $|$b$|>$10\\de. However, the \\sag field extends to b$\\sim$ -8\\de where, according to SFD, the reddening map might become inaccurate. From the relation ${\\rm E(V-R)}=0.74\\,{\\rm E(B-V)}$ (Cardelli et al. \\cite{car}; hereafter CCM) we derive ${\\rm E(B_{\\rm J}-R)}/{\\rm E(B-V)}=1.46$. This ratio in the overlap between \\duo and \\sag yields 1.32 $\\pm$ 0.24, in reasonable agreement with the theoretical expectation, showing that even at the western edge of the \\sag field the SFD map provides a satisfactory estimation for the extinction. Assuming E(V-I)=1.55 E(B-V) from CCM and a normal extinction law ${\\rm A_{V}}$=3.10 E(B-V) we obtain ${\\rm B_{{\\rm i}_{0}}}={\\rm B}_{i}$ - 5.38 E(B-V) for the de-reddened magnitude in the \\sag field.\n%\n\\section{Detection of RRab}\n%\n\\subsection{The selection process}\n We will describe here the selection process of RRab stars. For the sake of homogeneity, we reprocessed the stars of the \\duo field, using the same selection criteria as for the \\sag field. The search for RRab in \\duo has been performed through the B$_{J}$ band.\\\\\n A first selection was performed by calculating the $\\chi^{2}$ about the mean magnitude ($\\chi^{2}_{mean}$) for each light curve. \nStars with $\\chi_{mean}^{2} >$ 8 were then searched for periodicity. This cut should select all variables with an amplitude $\\gtrsim$ 0.3 mag. A first estimate of the period was done with the string minimization method of Renson (\\cite{renson}). A more accurate period was then searched in a small window spanning 0.1 day around the first estimate, using a multi-harmonic periodogram method (Schwarzenberg-Czerny \\cite{czerny}). The next step was to fit a Fourier series (with up to five harmonics) to the folded light curve:\n\\begin{center}\n \\begin{displaymath}\n B_{\\rm i}=A_{0}+\\sum_{n=1}^{n\\leq 5}A_{n}\\cos(n\\omega t+\\phi_{n})\n \\end{displaymath}\n\\end{center} \nThe $\\chi_{fit}^{2}$ about the fitted light curve was then calculated and all the stars for which $\\chi_{ratio}=\\sqrt{\\chi_{mean}^{2}/\\chi_{fit}^{2}}>2$ have been selected as variable stars. At this step of the process the sample contained $\\sim$ 7\\,000 variables.\\\\\n The selection for RR Lyrae stars has been performed through the Fourier coefficients: for each variable we calculated the ratio of the amplitude of the first harmonic relative to the amplitude of the fundamental harmonic $R_{21}=A_{2}/A_{1}$, and the phase difference $\\phi_{21}=\\phi_{2}-2\\phi_{1}$. Fig.\\ref{r21phi21} shows a plot of $R_{21}$ versus $\\phi_{21}$ for all stars satisfying $\\chi_{mean}^{2}>8$ and $\\chi_{ratio}>2$.\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{r21phi21.ps}}\n \\caption {R$_{21}$ versus $\\phi_{21}$ for all variables with a large amplitude ($\\chi_{mean}^{2}>$8) and a well fitted light curve ($\\chi_{ratio} > 2$). Also shown is the ellipse for selection of RRab.}\n \\label{r21phi21}\n\\end{figure}\n Several clumps lie in this figure. The most obvious one is located at $R_{21}\\sim$ 0.45 , $\\phi_{21}\\sim$ 0.7. This clump corresponds to RR Lyrae stars of Bailey type ab (hereafter RRab). For lower values of $R_{21}$ (\\textit{i.e.} for more symmetric light curves) we can distinguish two other clumps: one centred on ($R_{21}\\sim$0.2, $\\phi_{21}\\sim$3.2) and a shallower one at ($R_{21}\\sim$0.15, $\\phi_{21}\\sim$ 1.75), corresponding respectively to contact binaries and RR Lyrae of Bailey type c (RRc). A faint strip across the plot at $\\phi_{21}\\sim 3.1$ is also visible and represents eclipsing binaries of Algol type. The selection of the RRab has been made with an ellipse centred on the clump (see Fig. \\ref{r21phi21}) and finally a cut on periods ($0.40^{d} > P > 0.85^{d}$) has been applied. The final sample contains $\\sim$ 3\\,000 RRab.\\\\\nThe selected RRab may belong either to the MW or to the Sagittarius dwarf galaxy and we separated them through their distance modulus, assuming absolute magnitudes M$_{B_{\\rm J}}$=0.79 (Wesselink \\cite{wes}) and M$_{V}$=0.6 (Mateo et al \\cite{muskkk}). Furthermore, we take the mean color (V-I)$_{0}$=0.46$\\pm$0.06 after averaging over 27 RRab covering a wide range of metallicities from Table 1 of McNamara (1997). The apparent magnitude of each RRab has been estimated with the constant term of the Fourier series. Taking into account errors on the absolute magnitudes, apparent magnitudes, extinction and colors of RRab, the error on a single distance modulus is $\\sim$0.3 mag in both field, the main source of uncertainty coming from extinction. Fig.\\ref{maghisto} shows the histogram of distance modulus for both fields before and after correction for extinction.\\\\\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{mag_histo.ps}}\n \\caption{Upper panels (a): apparent magnitude histogram of the RRab stars. Lower panels (b): distance modulus histogram of the RRab stars. The dotted line indicates the distance modulus cut (16.3) adopted for membership of the Sagittarius dwarf galaxy. Note the reinforcement of the separation of the two bumps after correction for extinction.}\n \\label{maghisto}\n\\end{figure} \nThe histograms were smoothed by estimating the mean magnitude every 0.1 mag in a 0.3 mag bin. Both histograms exhibit similar features: a broad bump centred on (m-M)$_{0}\\sim$14.5 (8 kpc) corresponding to RRab of the MW, and a sharp bump centred on (m-M)$_{0}\\sim$16.9 (24 kpc) representing RRab members of Sgr. According to current models of RRab densities in the Halo the Galactic contribution to the histograms for (m-M)$_{0}>$16.3 should be no more than 5-10$\\%$ (Wetterer \\& McGraw \\cite{wet}).\\\\\n The 2D spatial distribution of all the RRab with a distance modulus greater than 16.3 is displayed on Fig.\\ref{rawmap}. This map includes $\\sim$ 1\\,500 RRab.\n\\begin{figure*}\n \\resizebox{12cm}{!}{\\includegraphics{rrab_dist.ps}}\n \\hfill\n \\parbox[b]{55mm}{\n \\caption{RRab detected in the Sagittarius dwarf galaxy. The eastern box centred on (l,b)=(6.6\\de,-10.8\\de) represents the \\sag field and the western box centred on (3.1\\de,-7.1\\de) is the \\duo field. Each field covers an area of $\\sim$ 25 deg$^{2}$. This map contains about 1500 RRab. The slight discontinuity in the density between \\duo and \\sag is due to the different completeness levels of the plates (see text). Also shown are the RRab detected by the MACHO team (asterisks). This map confirms that these RRab are the continuation of Sgr. Seven of their RRab are in common with ours.}\n \\label{rawmap}}\n\\end{figure*} \nThe eastern and western box represents respectively the \\sag field and the \\duo field. The total area covered is about $50$ deg$^{2}$, and comprises the globular cluster M54 at (l=5.5\\de,b=-14.0\\de) which is associated to Sgr and located in its highest density region. The image of M54 is completely saturated until $\\sim$1.5 half mass radius on our plates, thus we do not expect this globular cluster to contribute significantly to our RRab sample. The spatial distribution of RRab reveals a density gradient in the SE-NW direction. We also show in Fig. \\ref{rawmap} the RRab discovered by the MACHO team (Alc97), confirming that these stars are the continuation of Sgr\\\\\n%\n\\subsection{Completeness}\n%\nThere are two steps where the completeness of the RRab sample might be affected: first, the detection of stars becomes difficult towards the Galactic Centre because of the increasing stellar density, and some RRab blended by a neighbouring stars are missed. Second, we might miss some RRab during the selection process. \n\\subsubsection{Completeness of the extraction process}\n To quantify the loss induced by the first effect we simulated a set of 250\\,000 artificial stars with the same apparent magnitude than the detected RRab. These stars were then injected in small regions of 10$\\arcmin \\times$ 10$\\arcmin$ uniformly spread over the fields and we tried to retrieve them with the same detection process as for the real stars. The lower panel of Fig.\\ref{complete} displays the fraction of stars re-detected as a function of Galactic latitude.\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{complete.ps}}\n \\caption{Upper panel (a): detection efficiency for point sources as a function of amplitude. Each curve has been averaged over 50 000 simulated light curves. The full line corresponds to the \\sag field and the dashed line corresponds to the \\duo field. The vertical dotted (resp. dash-dotted) line shows the amplitude cut adopted in \\duo (resp. \\sag ) for the construction of the surface density map. Lower panel (b): fraction of simulated stars re-detected as a function of Galactic latitude. Filled circles represent fields in \\sag whereas crosses correspond to fields in \\duo .}\n \\label{complete}\n\\end{figure} \n Filled circles are stars injected onto the \\sag field whereas crosses are stars simulated in the \\duo field. The dispersion reflects mainly the dependence on Galactic longitude. One can see that while the fraction of stars re-detected in \\sag stays at a high level (above 90$\\%$) and varies slowly, this is not the case in \\duo where this fraction drops abruptly to reach 40$\\%$ at b$\\sim$-5\\de. The reason for the higher variation rate in \\duo is that the stellar density gradient increases at a higher rate towards the Galactic Centre (the mean density gradient is $\\sim$15 stars.arcmin$^{-2}$.deg$^{-1}$ in \\sag and $\\sim$25 stars.arcmin$^{-2}$.deg$^{-1}$ in \\duo ). Another feature visible on Fig.\\ref{complete}b is that the loss induced by crowding is intrinsically higher in \\duo than in \\sag as can be seen in the range -10$^{\\circ}<$b$<$-8\\de ($\\sim$10$\\%$ offset). This can be explained by the lower resolution of the III$_{aJ}$ emulsion in \\duo relative to the finer grained 4415 emulsion in \\sag (Parker \\& Malin \\cite{pm}). Furthermore, the lower extinction in \\duo (A$_{B_{\\rm J}}$/A$_{B_{\\rm i}}\\sim$0.7) results in a higher number of stars detected (N$_{stars}$(DUO)/N$_{stars}$(SAG)$\\sim$1.25 in the overlap), increasing by this way the crowding.\n\\subsubsection{Completeness of the selection process}\n\\paragraph{Amplitudes:} \n Our selection process might not be able to detect variable of low amplitude. To check the dependency of completeness on amplitude we simulated a set of 1\\,000 RRab light curves with the same time sampling as the real ones, the Fourier coefficients have been taken from Simon \\& Teays (1982). The distributions in amplitude, magnitude and period (excluding integer fractions of a day) of the simulated light curves were chosen in a way to match the actual distributions of the detected RRab, and the phasing was uniformly distributed between 0 and $2\\pi$. This set of simulated light curves was then injected in 100 regions of $10\\arcmin \\times 10\\arcmin$ (uniformly distributed over the fields) from which we took the errors to deteriorate the light curves. These light curves were then reduced in the same way as the real RRab. Fig.\\ref{complete}a shows the completeness levels of our selection process as a function of amplitude for the two fields, averaged over 50\\,000 simulated light curves.\n The shapes of the completeness curves are nearly identical for both fields and the difference is not significant. Fig.\\ref{complete}a shows that the detection rate stays above 95$\\%$ for amplitude $>$0.8 mag, and then drops abruptly down to $\\sim$ 20$\\%$ at amplitude=0.5 mag. These results signify that our selection process would detect almost all the RRab with an amplitude above 0.8 mag if these were point sources.\\\\\n\\indent However, the completeness levels will differ between \\sag and \\duo because the amplitudes of the RRab measured in each filter are different, being more important on average for \\sag than for \\duo . This difference occurs because the color band of \\sag peaks at shorter wavelength than the color band used for \\duo whereas the amplitude of RRab decreases with increasing wavelength (Smith \\cite{smith}). A least square fit between the amplitudes of 30 RRab in common in the overlap yielded the relation \n\\begin{equation}\\label{amprel}\n {\\rm A}_{DUO}=0.98 (\\pm 0.10) {\\rm A}_{SAG} - 0.05 (\\pm 0.11)\n\\end{equation}\nwhere A$_{\\tiny DUO}$ and A$_{\\tiny SAG}$ represent respectively the amplitudes measured in \\duo and in \\sag . {\\em In order to construct a consistent density map, we will consider in the remainder of this paper only those RRab satisfying amplitude $>0.60$ mag in SAG and amplitude $>0.54$ mag in DUO}, where 0.54 has been derived from the above relation (\\ref{amprel}). These cuts have been chosen both to ensure the largest sample as possible and to keep the completeness corrections at a manageable level. The corresponding corrections are 3.7\\% in \\sag and 12.3\\% in \\duo .\n\\paragraph{Periods:}\n Some RRab are missed because their periods are close to an integer fraction of a day, this causes points of the folded light curve to accumulate in a narrow phase range. The fitted Fourier series is then poorly constrained over a large fraction of the light curve and some of these stars might lie outside the ellipse of our selection process (see Fig.\\ref{r21phi21}). Monte-carlo simulations shows that we miss about $\\sim 30\\%$ of the RRab within the range 0.49$^{d}$ to 0.51$^{d}$ for both fields, corresponding to a total loss of $\\sim 3\\%$.\\\\\n\\subsection{Homogeneity between the fields}\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{overlap.ps}}\n \\caption{Overlap region between \\duo and \\sag . The RRab detected in \\duo (amplitude(B$_{\\rm J}$)$>$0.54) and \\sag (amplitude(B$_{i}$)$>$0.60) are shown respectively as crosses and open circles. The dashed lines represent the plate limits. Note that the scales are different in $\\alpha$ and $\\delta$.}\n \\label{overlapcomp}\n\\end{figure}\n An important point to inspect for checking the consistency between the two fields is the overlap (Fig.\\ref{overlapcomp}). Open circles correspond to RRab detected in the \\sag field with an amplitude(B$_{i}$) $>$ 0.60 mag. while crosses represent RRab detected in the \\duo field and having an amplitude(B$_{\\rm J}$) $>$ 0.54 mag. The dashed lines indicate the limit of each plate, their inclination is due to a slight tilt between the two plates. Note that this overlap applies to the reference frames and is not necessarily constant from plate to plate. Fig.\\ref{overlapcomp} reveals that most of the RRab are detected independently in the \\sag field and in the \\duo field. However, some RRab are not detected twice and it is important to understand the reasons why these stars are missed by one of the fields:\n\\begin{enumerate}\n \\item RRab not detected in the \\sag field (crosses)\n \\begin{itemize}\n \\item Eight RRab are located very close to the edge of the \\sag plate. Such stars usually have fewer points in their light curves because the centre of the plate is not exactly the same at each exposure. For example the three westernmost stars in the \\sag field have respectively 47, 55 and 47 points in their light curve (instead of 69 for most of the other light curves).\n \\item Two RRab did not pass through the selection process (one because of its estimated B$_{\\rm J}$ amplitude and the other one because of its $\\chi_{ratio}$).\n \\end{itemize}\n \\item RRab not detected in the \\duo field (open circles)\n \\begin{itemize}\n \\item One RRab has not been detected probably because of its low amplitude (0.61 mag in \\sag ).\n \\item Two RRab have a period of nearly $\\sim$ 0.50$^{d}$ and were detected in \\sag only by chance.\n \\item Three RRab were blended by a nearby star. As stated above, \\duo is more sensitive to crowding than \\sag and the relative loss of three RRab in the overlap is fully consistent with the $\\sim$10$\\%$ offset observed in Fig.\\ref{complete}b in the range -10$^{\\circ}<$b$<$-8\\de.\n \\end{itemize}\n\\end{enumerate}\nMost of the missed RRab will therefore have no statistical incidence and should not bias the density map. The only concern is for the greater sensitivity of the \\duo field to crowding. However this effect should be lowered by the crowding correction. Turning now to the western edge of \\duo we re-detect 7 RRab out of the 8 detected by the MACHO team in our field (disregarding two RRab located close to the edge). This is a satisfactory result. \n\\section{Structure of the Sagittarius dwarf galaxy}\n%\n\\subsection{Surface density of Sgr}\n%\nA surface density map is constructed from RRab with the amplitude cuts stated above. The spatial distribution of these RRab has been convolved with a Gaussian on a grid with a step of $0.1^{\\circ}$ and a variable filter size adapted to the local surface density $\\sigma \\propto \\rho^{-1/2}$, constrained between 0.2\\de and 0.5\\de . This map was then corrected for the different completeness in amplitude and crowding (see section 3.2).\n\\begin{figure*}\n \\resizebox{\\hsize}{!}{\\includegraphics{sgr_contour.ps}}\n \\caption{Smoothed map of the Sagittarius dwarf galaxy. This map is based upon the spatial distribution of RRab with distance modulus greater than 16.3. Only those RRab with (amplitude in B$_{i}$)$>$0.60 in \\sag and (amplitude in B$_{\\rm J}$)$>$0.54 in \\duo have been used. Completeness corrections have also been applied (see text). Contours are labelled as number of RRab per square degree. The dotted line (labelled 5) is not equidistant from the other contours.}\n \\label{contmap}\n\\end{figure*}\nThe resulting map is shown on Fig \\ref{contmap} where the elongated shape of Sgr is clearly visible. This is the first map of Sgr in these regions, showing that Sgr extends far beyond the outer limit of the map previously published by IWGIS. One of the most striking features of this map is the slow decrease (if any ?) of the density along the main axis of Sgr for $|$b$|\\lesssim$9\\de.\\\\\nThe main source of uncertainty in the surface density is the Poissonian noise in the star counts, which is variable over the field and tends to increase towards lower $|$b$|$.\nTo estimate this noise we simulated 1\\,000 maps by injecting 1\\,400 stars (corresponding to the number of RRab actually used to construct the final map) onto the field with a probability density matching the surface density of the real map. These spatial distributions were then processed exactly in the same manner as the real one and a 1$\\sigma$ ``noise map'' has been deduced.\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{pnoise.ps}}\n \\caption{ Uncertainty of the density map of Sgr based on 1$\\sigma$ Poissonian error in the star counts. The contours are labelled in percentage. The dotted line (labelled 15) is not equidistant with the other contours.}\n \\label{sigma_map}\n\\end{figure}\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{sgr_profile.ps}}\n \\caption{Cross-section along the main axis of Sgr based on a density map smoothed with a constant filter size of 0.5\\de. The thick line represents the density after completeness corrections and the dotted line is the uncorrected density. The shaded region corresponds to the 1$\\sigma$ uncertainty issued from simulated maps. Note the discontinuity in the density gradient at $\\sim$6\\de, also perceptible in the uncorrected density.}\n \\label{sgrprof}\n\\end{figure}\n This map is shown on Fig.\\ref{sigma_map} where the contours are labelled in percent. The typical (relative) uncertainty is constrained between 10$\\%$ and 15$\\%$ over the main part of the field, but increases up to $\\sim$40$\\%$ towards the edges where the number of RRab drops.\n\\subsection{Surface density profile of the main axis}\n The position angle of Sgr has been determined by fitting an exponential to the surface density along various directions. The highest scale length was reached for an angle of 108.4\\de, which we choosed as the direction of the major axis. Fig.\\ref{sgrprof} displays the density profile of Sgr along that axis. This figure is based on a map smoothed on a constant scale of 0.5\\de. The thick line is the density after correction for completeness whereas the dotted line is the density before that correction. The shaded region represents the 1$\\sigma$ uncertainty issued from simulated maps. A discontinuity in the slope is clearly visible at $\\sim$6\\de from the centre. After this point the surface density seems to be almost constant. It is however disconcerting that this discontinuity occurs near the limit between \\duo and \\sag and we may wonder if this is not an experimental effect. We have shown in section 3 that the crowding correction in \\sag and \\duo were consistent with the completeness of each field in the overlap. Furthermore the break is also perceptible in the uncorrected density so it cannot be an effect of the crowding correction. Another possibility is that our amplitude cut in \\duo is to low to be consistent with \\sag. This is difficult to check and we can only rely on those 30 RRab in common in the overlap, from which we derived the relation in amplitude between \\duo and \\sag (Eq. \\ref{amprel}). However, if we make the assumption that the RRab population is homogeneous over the field, it is possible to search for the relation ${\\rm A}_{DUO}=a\\,{\\rm A}_{SAG}+b$ for which the amplitude distributions are the most similar (through Kolmogorov-Smirnov test). The resulting coefficients were a=0.95 and b=-0.08 and are within the error bars stated in Eq. \\ref{amprel}. The corresponding cuts are ${\\rm A}_{SAG}=0.6 \\leftrightarrow {\\rm A}_{DUO}=0.49$. These cuts would have reinforced the discontinuity, showing that our adopted amplitude cuts are not responsible for the break observed in Fig. \\ref{sgrprof}. We conclude that the discontinuity in the slope of the density profile is probably real and not a consequence of the change of field.\\\\\n It is also possible to derive an upper limit for the extension of Sgr along the line of sight: the distance modulus histogram can be roughly fitted by a Gaussian with a width of 0.2 mag, corresponding to a depth of $\\sim$4.5 kpc for an assumed distance of 24 kpc.\n\\begin{figure}[!h]\n \\resizebox{\\hsize}{!}{\\includegraphics{boxes.ps}}\n \\caption{ Location of the axes on which various models have been fitted. Each point is represented by the number of RRab (corrected for completeness) within a box of size 0.5\\de$\\times$1.0\\de. The vertical dashed line at $\\alpha \\sim$18.55 indicates the limit of the \\majs axis (see text).}\n \\label{axis}\n\\end{figure}\n\\begin{table}[!h]\n \\caption{{\\bf Table 2.} Results of the model fitting to the surface density of Sgr. The three first columns give respectively the axis, model and parameter considered. Column 4 gives the result of the fit. Column 5 gives the uncertainty on the parameter value as given by the covariance matrix issued from the fitting procedure. Column 6 gives the $\\chi^{2}$ of the fit normalized by the number of degree of freedom. All values given in kpc assume a distance to Sgr of 24 kpc.}\n \\begin{tabular}{l @{ } l @{ } l @{ } l @{ } l @{ } l}\n \\hline\n Axis & Models & Parameters & Value & $\\sigma$ & $\\chi^{2}_{fit}/{\\rm N}_{\\rm DOF}$\\\\\n \\hline\n \\majd & K & k & 178.32 & 68.28 & 4.11 \\\\\n & & r$_{c}$(kpc) & 2.69 & 0.56 & \\\\\n & & r$_{t}$(kpc) & $\\infty$ & ... & \\\\ \\\\\n\n & E & $\\rho_{e}$ & 120.87 & 5.96 & 3.08 \\\\\n & & r$_{e}$(kpc) & 2.42 & 0.15 & \\\\ \\\\\n\n & G & $\\rho_{g}$ & 84.53 & 3.75 & 5.10 \\\\\n & & $\\sigma_{g}$(kpc) & 2.13 & 0.08 & \\\\ \\\\\n\n & L & a$_{0}^{\\rm (in)}$ & 117.51 & 5.64 & 1.77 \\\\\n & & a$_{1}^{\\rm (in)}$ & -15.40 & 1.38 & \\\\\n & & a$_{0}^{\\rm (out)}$ & 32.13 & 11.33 & \\\\\n & & a$_{1}^{\\rm (out)}$ & -0.50 & 1.36 & \\\\ \\\\\n \\hline\n \\majs & K & k & 139.91 & 99.88 & 2.59 \\\\\n & & r$_{c}$(kpc) & 1.77 & 0.65 & \\\\\n & & r$_{t}$(kpc) & $\\infty$ & ... & \\\\ \\\\\n\n & E & $\\rho_{e}$ & 138.62 & 14.09 & 2.05 \\\\\n & & r$_{e}$(kpc) & 1.73 & 0.21 & \\\\ \\\\\n\n & G & $\\rho_{g}$ & 104.43 & 5.04 & 2.46 \\\\\n & & $\\sigma_{g}$(kpc) & 1.50 & 0.08 & \\\\ \\\\\n\n & L & a$_{0}$ & 117.51 & 5.64 & 2.08 \\\\\n & & a$_{1}$ & -15.40 & 1.38 & \\\\ \\\\ \n \\hline\n \\mini & K & k & 344.84 & 108.04 & 2.00 \\\\\n & & r$_{c}$(kpc) & 1.45 & 0.27 & \\\\\n & & r$_{t}$(kpc) & 2.98 & 0.30 & \\\\ \\\\\n\n & E & $\\rho_{e}$ & 160.12 & 11.79 & 5.03 \\\\\n & & r$_{e}$(kpc) & 0.79 & 0.05 & \\\\ \\\\\n\n & G & $\\rho_{g}$ & 107.04 & 6.01 & 1.75 \\\\\n & & $\\sigma_{g}$(kpc) & 0.84 & 0.03 & \\\\ \\\\\n\n & L & a$_{0}$ & 99.30 & 4.69 & 3.16 \\\\\n & & a$_{1}$ & -18.97 & 1.00 & \\\\ \\\\ \n \\hline\n \\end{tabular}\n\\end{table}\n%\n\\subsection{Model fitting}\nWe define the following analytical functions to fit to the density profile:\n\n\\begin{equation} \\label{e_K}\n \\rho_{K}=k\\, \\bigg\\{ \\frac{1}{[1+(r/r_{c})^{2}]^{1/2}}-\\frac{1}{[1+(r_{t}/r_{c})^{2}]^{1/2}}\\bigg\\}^{2}\n\\end{equation}\n\n\\begin{equation} \\label{e_E}\n \\rho_{E}=\\rho_{e}\\, e^{-\\frac{r}{r_{e}}}\n\\end{equation}\n\n\\begin{equation} \\label{e_G}\n \\rho_{G}=\\rho_{g}\\, e^{-r^{2}/2\\sigma_{g}^{2}}\n\\end{equation}\n\n\\begin{equation} \\label{e_L}\n \\rho_{L}=a_{0}+a_{1}r \n\\end{equation}\n\nWhere $r$ represents the distance from the Centre of Sgr, and all other parameters are variables to be fitted. Eq. \\ref{e_K} refers to the empirical King model (K) with a core radius r$_{c}$ and tidal radius r$_{t}$ (King \\cite{king}). Eq. \\ref{e_E} refers to an exponential model (E) with a radius r$_{e}$. Eq. \\ref{e_G} refers to a Gaussian (G) with a width of $\\sigma_{g}$. Finally, Eq. \\ref{e_L} refers to a linear model (L) where the density profile is modeled by a straight line. These models have been fitted along three segments. Two of these segments are located on the main axis: one corresponding to the main axis over its entire length ($\\sim$10\\de), referred to as \\majd; and another one corresponding to the portion of the main axis contained within \\sag ($\\leq$6\\de from the center), referred to as \\majs. The latter segment has been chosen in order to avoid fitting the stars past the break and also because it is more consistent since it is entirely contained within \\sag. Finally the minor axis is not present within our field and instead we fitted an axis making a large angle relative to the main axis (50 \\de), referred to as \\mini. The fit of model L on \\majd has been performed by fitting the density before 6\\de and after 6\\de separately. \nIn order to get uncorrelated points for the fit, we took the densities (after correction for completeness) of RRab inside boxes with a size of 0.5\\de$\\times$1.0\\de located along each axis (see Fig.\\ref{axis}). The results of the fit are shown in Table 2 and in Fig.\\ref{lfit}.\\\\\n\\begin{figure*}\n \\resizebox{\\hsize}{!}{\\includegraphics{fitprof.ps}}\n \\caption{Results of the fit to the surface density of Sgr. Left panels: density profile along the main axis. The solid line is the fit to the whole main axis (\\majd) while the dotted line corresponds to the fit to the inner part of the main axis (\\majs). The dotted line is prolonged beyond 6\\de to allow visual comparison between the data and the inner fit. Right panel: density profile along an axis rotated 50\\de relative to the main axis (\\mini). The errors bars represent the Poissonian noise. The fitted model is indicated in each panel.}\n \\label{lfit}\n\\end{figure*}\nThe single function model that best fits \\majd is model E ($\\chi^{2}_{fit}/N_{DOF}$=3.08). However, the fit is significantly improved if we consider the model L (($\\chi^{2}_{fit}/N_{DOF}$=1.77) which reproduces the break already observed in Fig. \\ref{sgrprof}. A Fisher test shows that the probability for the ratio of the $\\chi^{2}_{fit}/N_{DOF}$ of these two fits to be lower than the observed value by chance is only $\\sim$13$\\%$. Note that we were unable to fit any convergent two-component model to \\majd: this is due to the almost constant density of the external region which causes one of the component to increase as we move away from the centre in order to compensate the decrease of the other component.\\\\\n Concerning the core of Sgr (\\majs), the density profile is equally well fitted by model E and L ($\\chi^{2}_{fit}/N_{DOF}\\approx$2.1). The scale length derived from model E is $\\sim$4.1\\de$\\pm$0.5\\de (1.7$\\pm$0.2 kpc). This value is slightly lower to the one derived by MOM who find an inner scale length of 4.7\\de in the Southern part of Sgr. Model K and G also give an acceptable fit to the core of Sgr but they fail to reproduce the high density in the first bin. Furthermore, the uncertainties on the parameters of the empirical King model are quite large and the infinite tidal radius is rather unrealistic.\\\\\n Finally, the best fit on \\mini is achieved by model G ($\\chi^{2}_{fit}/N_{DOF}$=1.75), but again it fails to reproduce the high density of the first bin. The only model that reproduces the high central density is model E but the $\\chi^{2}_{fit}/N_{DOF}$ of this model is worsened by the poor fit on the three last bins. However these bins contain only very few points (between 1 and 5), introducing uncertainties induced by small-numbers statistics.\\\\\n\\section{Conclusion}\n To summarize, we presented the detection of $\\sim$1\\,500 RRab stars located in the Sgr dwarf galaxy. A surface density map based on the spatial distribution of these variables unveiled the structure of this dwarf galaxy in a region that was still almost unexplored so far between b=-14\\de and b=-4\\de. The core of Sgr is best fitted by an exponential with a scale length of 4.1\\de along the major axis. A cross section of this density map revealed a break in the slope occurring at $\\sim$6\\de from the highest density region of Sgr and an almost flat density past the break.\\\\ \n Although the break coincided with the change of field we have shown that this is unlikely to be an experimental effect since it is also perceptible in the uncorrected density, whereas the \\duo field is intrinsically more sensitive to crowding than \\sag (lower resolution, lower extinction). Also, as shown in Section 4.2, the amplitude cuts used in this study cannot be considered as responsible for the break. Finally, could this break be a consequence of an overestimation of the completeness correction in \\duo relative to \\sag ? Though not excluded, this would be in conflict with what is observed in the overlap where 3 RRab blended by a neighbouring star were detected in \\sag and missed in \\duo, a result that is quite consistent with the corrections actually applied. We argue therefore that the break is real. The significance of the break relative to an exponential with a scale length of 4.1\\de is $\\sim$2$\\sigma$. MOM also observed a break in their density profile in the Southern extension of Sgr. However neither the location (20\\de from the centre) nor the density at the break location ($\\Sigma_{V}\\sim$29.0 mag.arcsec$^{-2}$) are consistent with our values (6\\de and $\\sim$26.7 mag.arcsec$^{-2}$) implying that either the main body of Sgr is not symmetric or these ``post-break'' stars are not directly related to it.\\\\\nAnother striking feature revealed by the surface density profile is its flatness past the break. This feature relies on the accuracy of the completeness correction over the field, a correction that becomes quite important at low Galactic latitudes (up to 60$\\%$). Yet, the difficulty of modeling point spread functions on photographic plates (due to non-linear response of the emulsion) and potential systematic errors caused by differential sensitivity over the plate makes the crowding correction rather uncertain. Therefore, although our completeness corrections are fairly consistent within the overlap, we cannot exclude that the flatness of the density profile in the outer regions is a consequence of an overcorrection. Wide-field high resolution imaging would be necessary in these extremely crowded regions (up to $\\sim$10$^{6}$ stars per square degree at our magnitude limit) to confirm or to rule out this issue. Nevertheless, even if we consider that our completeness corrections are overestimated by a factor of 2 (a quite conservative estimate), it remains that the density profile decreases slowly in the outer regions and Sgr may well be extending even further out towards (beyond ?) the Galactic plane. \\\\\nJohnston et al. (\\cite{johnston99}) recently modeled the Sgr stream as a superposition of a main body and tidal streams of stars stripped on previous peri-centric passages. This scenario has been worked out to explain both the break observed by MOM and the possible detection of stars in the outer region of Sgr with different radial velocities relative to those of the main body (Majewski et al. \\cite{maj}). Similarly, spectroscopic observations on our RR Lyrae catalogue could allow to determine the nature of the stars in the outer region: if these stars are linked to the main body of Sgr, then they should share almost the same radial velocities as the main body (apart of a gradient along the main axis due to the rapidly varying Galactic potential). On the other hand, if the break we observe corresponds to a transition between the main body and an unbound tidal stream from a previous orbit, it is likely that the two objects will have different radial velocities. This new catalogue of RR Lyrae is an interesting opportunity to study further a region of Sgr that has been poorly investigated so far.\\\\\n\\begin{acknowledgements}\n We thank Ren\\'e Chesnel for scanning most of the plates used in this paper. We would also like to thank Rodrigo Ibata and St\\'ephane L\\'eon for interesting discussions. Finally, we thank the anonymous referee for valuable comments which helped to improve this paper.\n\\end{acknowledgements}\n%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n\\begin{thebibliography}{}\n\\bibitem[1996]{a96}\n Alard C., 1996, ApJ, 458, L17, (A96)\n\\bibitem[1997]{a97}\n Alard C., Guibert J.: 1997, A\\&A, 326, 1, (AG97)\n\\bibitem[1997]{alcock}\n Alcock C. et al. (The MACHO Collaboration): 1997, ApJ, 474, 217, (Alc97)\n\\bibitem[1999]{bfb1}\n Bellazzini M., Ferraro F., Buonanno R.: 1999, MNRAS, 304, 633\n\\bibitem[1982]{bg}\n Blair M., Gilmore G.: 1982, PASP, 94, 742\n\\bibitem[1999]{bl}\n Burton W., Lockman F., 1999, A\\&A, 349, 7\n\\bibitem[1989]{car}\n Cardelli J., Clayton G., Mathis J.: 1989, ApJ, 345, 245, (CCM)\n\\bibitem[1996]{fahlman}\n Fahlman G., Mandushev G., Richer H., Thompson I., Sivaramakrisiinan A., 1996, ApJL, 459, 65\n\\bibitem[1994]{igi1}\n Ibata R., Gilmore G., Irwin M.: 1994, Nature, 370, 194\n\\bibitem[1995]{igi2}\n Ibata R., Gilmore G., Irwin M.: 1995, MNRAS, 277, 781\n\\bibitem[1997]{iwgis}\n Ibata R., Wyse R., Gilmore G., Irwin M., Suntzeff N.: 1997, AJ, 113, 634, (IWGIS)\n\\bibitem[1999]{johnston99}\n Johnston K., Majewski S., Siegel M., Reid I., Kunkel W., 1999, AJ, 118, 1719\n\\bibitem[1962]{king}\n King I., 1962, AJ, 67, 471\n\\bibitem[1997]{mcn}\n McNamara D.H.: 1997, PASP, 109, 857\n\\bibitem[1999]{maj}\n Majewski S., Siegel M., Kunkel W., Reid I., Johnston K., Thompson I., Landolt A., Palma C.: 1999, AJ, 118, 1709\n\\bibitem[1998]{marconi}\n Marconi G., Buonanno R., Castellani M., Iannicola G., Molaro P., Pasquini L., Pulone L.: 1998, A\\&A, 330, 453\n\\bibitem[1995]{muskkk}\n Mateo M., Udalski A., Szyma\\'nski M., Ka\\l u\\.zny J., Kubiak M, Krzemi\\'nski W.: 1995, AJ, 109, 588\n\\bibitem[1998]{mom}\n Mateo M., Olszewski E., Morrison H.: 1998, ApJL, 508, L55, (MOM)\n\\bibitem[1999]{pm}\n Parker Q., Malin D.: 1999, Publ. Astron. Soc. Aust., 16, 288\n\\bibitem[1993]{pp}\n Phillipps S., Parker Q.: 1993, MNRAS, 265, 385\n\\bibitem[1978]{renson}\n Renson P.: 1978, A\\&A, 63, 125\n\\bibitem[1995]{sl}\n Sarajedini A., Layden A.: 1995, AJ, 109, 1086\n\\bibitem[1998]{sfd}\n Schlegel D., Finkbeiner D., Davis M.: 1998, ApJ, 500, 525\n\\bibitem[1996]{czerny}\n Schwarzenberg-Czerny A.: 1996, ApJL, 460, L107\n\\bibitem[1982]{simon}\n Simon R., Teays T.: 1982, ApJ, 261, 586\n\\bibitem[1995]{smith}\n Smith H., 1995, \\textit{RR Lyrae stars}, Cambridge Astrophysics Series, 27, p.15\n\\bibitem[1966]{sturch}\n Sturch C., 1966, ApJ, 224, 953\n\\bibitem[1987]{wes}\n Wesselink Th.J.H.: 1987, Ph.D. thesis, Catholic Univ. Nijmegen\n\\bibitem[1996]{wet}\n Wetterer C., McGraw J.: 1996, AJ, 112, 1046\n\\end{thebibliography}\n \n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002157.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[1996]{a96}\n Alard C., 1996, ApJ, 458, L17, (A96)\n\\bibitem[1997]{a97}\n Alard C., Guibert J.: 1997, A\\&A, 326, 1, (AG97)\n\\bibitem[1997]{alcock}\n Alcock C. et al. (The MACHO Collaboration): 1997, ApJ, 474, 217, (Alc97)\n\\bibitem[1999]{bfb1}\n Bellazzini M., Ferraro F., Buonanno R.: 1999, MNRAS, 304, 633\n\\bibitem[1982]{bg}\n Blair M., Gilmore G.: 1982, PASP, 94, 742\n\\bibitem[1999]{bl}\n Burton W., Lockman F., 1999, A\\&A, 349, 7\n\\bibitem[1989]{car}\n Cardelli J., Clayton G., Mathis J.: 1989, ApJ, 345, 245, (CCM)\n\\bibitem[1996]{fahlman}\n Fahlman G., Mandushev G., Richer H., Thompson I., Sivaramakrisiinan A., 1996, ApJL, 459, 65\n\\bibitem[1994]{igi1}\n Ibata R., Gilmore G., Irwin M.: 1994, Nature, 370, 194\n\\bibitem[1995]{igi2}\n Ibata R., Gilmore G., Irwin M.: 1995, MNRAS, 277, 781\n\\bibitem[1997]{iwgis}\n Ibata R., Wyse R., Gilmore G., Irwin M., Suntzeff N.: 1997, AJ, 113, 634, (IWGIS)\n\\bibitem[1999]{johnston99}\n Johnston K., Majewski S., Siegel M., Reid I., Kunkel W., 1999, AJ, 118, 1719\n\\bibitem[1962]{king}\n King I., 1962, AJ, 67, 471\n\\bibitem[1997]{mcn}\n McNamara D.H.: 1997, PASP, 109, 857\n\\bibitem[1999]{maj}\n Majewski S., Siegel M., Kunkel W., Reid I., Johnston K., Thompson I., Landolt A., Palma C.: 1999, AJ, 118, 1709\n\\bibitem[1998]{marconi}\n Marconi G., Buonanno R., Castellani M., Iannicola G., Molaro P., Pasquini L., Pulone L.: 1998, A\\&A, 330, 453\n\\bibitem[1995]{muskkk}\n Mateo M., Udalski A., Szyma\\'nski M., Ka\\l u\\.zny J., Kubiak M, Krzemi\\'nski W.: 1995, AJ, 109, 588\n\\bibitem[1998]{mom}\n Mateo M., Olszewski E., Morrison H.: 1998, ApJL, 508, L55, (MOM)\n\\bibitem[1999]{pm}\n Parker Q., Malin D.: 1999, Publ. Astron. Soc. Aust., 16, 288\n\\bibitem[1993]{pp}\n Phillipps S., Parker Q.: 1993, MNRAS, 265, 385\n\\bibitem[1978]{renson}\n Renson P.: 1978, A\\&A, 63, 125\n\\bibitem[1995]{sl}\n Sarajedini A., Layden A.: 1995, AJ, 109, 1086\n\\bibitem[1998]{sfd}\n Schlegel D., Finkbeiner D., Davis M.: 1998, ApJ, 500, 525\n\\bibitem[1996]{czerny}\n Schwarzenberg-Czerny A.: 1996, ApJL, 460, L107\n\\bibitem[1982]{simon}\n Simon R., Teays T.: 1982, ApJ, 261, 586\n\\bibitem[1995]{smith}\n Smith H., 1995, \\textit{RR Lyrae stars}, Cambridge Astrophysics Series, 27, p.15\n\\bibitem[1966]{sturch}\n Sturch C., 1966, ApJ, 224, 953\n\\bibitem[1987]{wes}\n Wesselink Th.J.H.: 1987, Ph.D. thesis, Catholic Univ. Nijmegen\n\\bibitem[1996]{wet}\n Wetterer C., McGraw J.: 1996, AJ, 112, 1046\n\\end{thebibliography}"
}
] |
astro-ph0002158
|
Ultra-High-Energy Cosmic Ray Acceleration by Magnetic Reconnection in Newborn Pulsars
|
[
{
"author": "Elisabete M. de Gouveia Dal Pino\\altaffilmark{1,2} \\& Alex Lazarian\\altaffilmark{3}"
}
] |
We here investigate the possibility that the ultra-high energy cosmic ray (UHECR) events observed above the GZK limit are mostly protons accelerated in reconnection sites just above the magnetosphere of newborn millisecond pulsars that are originated by accretion induced collapse (AIC).
|
[
{
"name": "rmuhecr.tex",
"string": "%% dalpino2.tex\n%% for the proc. of the Conference on Astrophysical Plasmas...\n%% October, 1999, Mexico City\n%%% Converted to RMAA(SC) style and annotated by Will Henney \n%%% (04 Oct1999) \n\n%% This file contains examples of many of the commands in the LaTeX\n%% document class rmaa.cls, such as the commands for specifying data\n%% for the title page and the commands for including postscript\n%% figures. For more details, you should consult the accompanying\n%% Author Guide (`rmuser.tex'). A further sample document\n%% (`rmtest.tex') contains examples of some commands not used in this\n%% file, eg. for marking up tables. You may also want to use this file\n%% as a template for your own article. \n%% All proceedings articles must begin with the following line\n\\documentclass[proceedings]{rmaa}\n%%\n%% The file `rmaa.cls' should be somewhere in your TeX search path\n%% (e.g, in the current directory, or in a personal or system-wide\n%% directory of LaTeX packages. \n%%\n%% This will not work with old versions of LaTeX: any version\n%% of LaTeX2e should be OK, but LaTeX209 is too old. If LaTeX\n%% complains that it doesn't recognise the command `\\documentclass'\n%% then your LaTeX installation needs updating!\n\n%% The following package allows one to do the citations\n%% semi-automatically. It defines the commands \\cite{KEY},\n%% \\scite{KEY}, and \\pcite{KEY} which respectively produce citations\n%% in the following styles: \n%% (AUTHOR YEAR)\n%% AUTHOR (YEAR)\n%% AUTHOR YEAR\n%% For this to work, you need to pay attention to the formatting of\n%% the `\\bibitem's in your `thebibliography ' environment, qv.\n%%\\usepackage{rmaacite}\n%% If you would rather do your citations by hand, then comment out the \n%% above line\n\n%% Here, you can put the definitions of your own personal macros.\n%% All the special commands defined in AASTEX 4.0 (e.g. \\ion{}{},\n%% \\gtrsim, \\arcsec, \\apj, etc) are already defined. I haven't checked \n%% if there are any new ones in AASTEX 5.0 yet. \n\\newcommand{\\thOr}{$\\theta^1\\,$C~Ori}\n\\newcommand{\\zero}{_0}\n\\newcommand{\\kms}{\\,\\mbox{km s$^{-1}$}}\n\\newcommand{\\Othree}{[\\ion{O}{3}]~5007\\AA}\n\\renewcommand{\\P}[1]{%\n\\ifnum#1=1\\hbox{OW~168--326E}\\fi\n\\ifnum#1=2\\hbox{OW~167--317}\\fi\n\\ifnum#1=3\\hbox{OW~163--317}\\fi\n\\ifnum#1=5\\hbox{OW~158--323}\\fi\n\\ifnum#1=0\\hbox{OW~171--334}\\fi}\n\n%%\n%% The following commands specify the title, authors etc\n%%\n\\title { Ultra-High-Energy Cosmic Ray Acceleration by Magnetic \nReconnection in Newborn Pulsars}\n\\author{Elisabete M. de Gouveia Dal Pino\\altaffilmark{1,2}\n\\& Alex Lazarian\\altaffilmark{3} } \n% \\affil{Instituto de Astronom\\'{\\i}a, UNAM, Morelia} }\n\\altaffiltext{1}{Instituto Astron\\^omico e Geof\\'{\\i}sico, University \nof S\\~ao Paulo, E-mail: dalpino@iagusp.usp.br } \n\\altaffiltext{2}{\nAstronomy Department,\nUniversity of California at Berkeley} \n\\altaffiltext{3}{Department of Astronomy, \nUniversity of Wisconsin }\n%\\altaffiltext{1}{Just to see that the affiliation subscripts work OK}\n%% Note that the \\affil{} command is inside the argument of the\n%% \\author{} command and that a short version of the address should go \n%% here. More complicated author/address examples are discussed in the \n%% Author Guide (`rmuser.tex') and illustrated in the example document\n%% `rmtest.tex' \n\n%% The full postal addresses are specified here - they will be typeset \n%% at the end of the article. Here is also the place to put email\n%% addresses. \n\\fulladdresses{\n\\item E. M. de Gouveia Dal Pino: \n%Instituto Astron\\^omico e Geof\\'{\\i}sico, \n%University \n%of S\\~ao Paulo, \nIAG-USP, Av. Miguel St\\'efano, 4200, S\\~ao Paulo\n04301-904, SP, Brasil} \n%E-mail: dalpino@iagusp.usp.br }\n%\\item A. Lazarian:Department of Astronomy, \n%University of Wisconsin, \n%Madison, USA } \n%% Note that the `\\fulladdresses' command defines a list-like\n%% environment, so each separate address must be preceded by the\n%% `\\item' command (here there is only one, since the authors share the \n%% same address). \n\n%% Title/author for running headers\n\\shortauthor{de Gouveia Dal Pino \\& Lazarian}\n\\shorttitle{UHECR Acceleration by Reconnection}\n%% These will automatically be converted to upper case in the current\n%% style. \n\n%% No more than 5 keywords, chosen from the standard list\n\\keywords{magnetohydrodynamics --- cosmic ray acceleration --- Stars:\n pulsars}\n\n%% The abstract:\n\\abstract{ We here investigate the possibility that the \nultra-high energy cosmic ray (UHECR) events observed above the GZK \nlimit are mostly protons accelerated in reconnection sites just above \nthe \nmagnetosphere of newborn millisecond pulsars \nthat are originated by accretion \ninduced collapse (AIC).\n }\n%% If your spanish is up to it, you may want to supply the resumen by\n%% uncommenting the following line:\n%\\resumen{Versi\\'on espa\\~nol del ``abstract''}\n%% Alternatively, you can leave the translation to the editors. \n\n\n%% This command is so LaTeX won't stop on errors. I've put it in so\n%% you will still be able to compile the file even if you have lost\n%% the associated PS files of the figures. \n\\nonstopmode\n\n%% The following command is necessary before beginning the text of\n%% your article. There should be a matching \\end{document} at the end\n%% of the file. \n\\begin{document}\n\n%% This command is necessary to typeset the title, abstract, etc. \n\\maketitle\n\n%%\n%% And here starts the text....\n%%\n\\section{Introduction}\n\\label{sec:intro}\n\nThe detection of cosmic ray events with energies beyond 10$^{20}$ eV\n(UHECRs) poses a challenge for the understanding of their \nnature\nand sources. If UHECRs are mostly\nprotons, then they should be \naffected \nby\nthe expected Greisen-Zatsepin-Kuzmin (GZK) energy cutoff \n($\\sim 5\\times\n10^{19}$ eV), which is due to photomeson production by interactions \nwith \nthe\ncosmic microwave background radiation, unless they are originated at\ndistances closer than about 50 Mpc (e.g., \nMedina Tanco, de Gouveia Dal Pino \\& Horvath 1997). On the other hand, \nif\nthe UHECRs are mostly protons from nearby sources \n(located within $\\sim $\n 50 Mpc), then the arrival directions of the events should point toward\ntheir sources since they are expected to be little deflected by the\nintergalactic and Galactic magnetic fields (e.g., Medina \nTanco, de Gouveia Dal Pino \\& Horvath 1998). The present data shows no \nsignificant\nlarge-scale anisotropy in the distribution related to the Galactic disk \nor\nthe local distribution of galaxies, although some clusters of events \nseem \nto\npoint to the supergalactic plane (Takeda et al. 1999). \n\n\nWe here discuss a model in which UHECRs are mostly protons \naccelerated in\nmagnetic reconnection sites outside the magnetosphere of very young \nmillisecond pulsars being produced by accretion induced collapse (AIC) \nof a \nwhite dwarf (de Gouveia Dal Pino \\& Lazarian 2000; hereafter GL2000). \nWhen a white dwarf reaches the critical Chandrasekhar mass $\\sim 1.4$\nM$_{\\odot }$ through mass accretion, in some cases it collapses directly to\n a neutron star instead of exploding\ninto\na supernova. The accretion flow spins up the star and confines the \nmagnetosphere \nto a radius $R_X$ where plasma stress in the accretion disk and \nmagnetic \nstress \nbalance\n(Arons 1993). At this radius the equatorial flow will divert into a\nfunnel inflow\nalong the closed \nfield-lines toward the star, and \na centrifugally \ndriven wind outflow (see Fig. 1 of GL2000). \nTo mediate the field lines of the star with \nthose\nopened by the wind and those trapped by the funnel inflow emanating \nfrom\nthe $R_X$ region a surface of null poloidal field forms \n(e.g., Shu et al. 1994). \nThis reconnection region dominated \"$helmet$ $streamer$\",\nwill release magnetic energy that will accelerate particles to \nthe UHEs.\n\nA primary condition on the reconnection region \n for it to be\nable to accelerate particles of charge $Ze$ to energies $E$ \n is that its width\n$\\Delta R_X \\, \\geq \\, 2 \\, r_L$, \nwhere \n$r_L$ is the particle Larmour radius \n$r_L = E /Z e \\, B_X$ , and \n$B_X$ is the magnetic \nfield (normal to particle velocity) at the $R_X$ region. \nThis condition and the field geometry imply (GL2000):\n\\begin{equation}\nB_{13} \\, \\gtrsim \\, Z^{-1} \\, E_{20} \\, \\Omega_{2.5k}^{-4/3} \\, \n \\left({\\frac{\\Delta R_X/R_X } { 0.1}}\\right)^{-1/2} \n\\end{equation}\n\\noindent \nwhere $B_{13}$ is the stellar magnetic field in units of \n$10^{13}$ G, \n$\\Omega_{2.5k}$ is the stellar angular speed in units of 2500 s$^{-1}$,\nand $E_{20}$ is the particle energy in units of 10$^{20}$ eV.\n We find that stellar magnetic fields \n $10^{12} $ G $ < B_{\\star} \\lesssim 10^{15}$ G \nand angular speeds \n$4 \\times 10^{3}$ s$^{-1}$ $\\gtrsim \\Omega_{\\star} \\, > \\, 10^{2} $ \ns$^{-1}$\n(or spin periods\n1 ms $\\lesssim \\, P_{\\star} \\, < \\, $ 60 ms), are able to accelerate\nparticles to energies $E_{20} \\, \\gtrsim $ 1.\n%These above are perfectly compatible with the parameters \n%of young pulsars and\n%Eq. (1) is thus a good representation of the typical conditions \n%required \n%for particle acceleration to the UHEs in reconnection zones of AIC-pulsars.\n\nA newborn millisecond pulsar spins down due to \nmagnetic \ndipole radiation in a time scale given by\n$\\tau_{\\star} \\equiv \\Omega_{\\star}/\\dot \\Omega_{\\star}\n\\simeq 4.3 \\times 10^7 $ s $ B_{13}^{-2} \\, \n\\Omega_{2.5k}^{-2}$. \nWe can show that the \ncondition that the magnetosphere and disk stresses are in equilibrium \nat \nthe inner disk edge results a disk mass accretion rate \nthat is \n super-Eddington. This supercritical accretion will \n last for $\\sim $ $\\tau_{\\star}$. \n As it approaches the \nend, the \nnewborn pulsar decreases its rotation speed due to electromagnetic \nradiation at a rate $\\tau_{\\star}^{-1}$. \nThe spectrum evolution of \nthe \naccelerated UHECRs is thus determined by \n$\\tau_{\\star}^{-1}$. \nThe particle spectrum $N(E)$ is obtained from\n%\\begin{equation}\n$\\dot N \\, = \\, N(E) \\, {\\frac {dE } { dt}} \\, \n= \\, N(E) \\, {\\frac {dE } { d \\Omega_{\\star} } } \\, \\dot \n\\Omega_{\\star}$\n (GL2000):\n\\begin{equation}\nN(E) \\, \\simeq \n% {\\frac { d \\Omega_{\\star} }{dE } } } \\, \n%{\\frac { \\dot N }{\\dot \\Omega_{\\star}} } }\n\\, 5.8 \\times 10^{34} \\, {\\rm GeV}^{-1} \\, \\xi \\, Z^{-1/2} \\, \nB_{13}^{-\n1/2} \\, E_{20}^{-3/2} \\, \\left({\\frac{\\Delta R_X/R_X } \n{0.1}}\\right)^{-1/4}\n\\end{equation}\n\\noindent \nwhere $\\xi$ is the reconnection efficiency factor; \nthe derived spectrum above is\n very flat which is in \nagreement with the observations.\n\n\nThe total number of objects formed via AICs \nin our Galaxy is limited by nucleosynthesis constraints to a very small \nrate \n$ \\sim \\, 10^{-5} $ yr$^{-1}$. \nHence, the probability of having UHECR events produced in the Galaxy \nwill be only\n$P \\, \\simeq \\, f_b \\, {\\tau_{AIC}}^{-1} \\, t \\, \\simeq \\, 2 \\times \n10^{-\n6}$, where $f_b \\sim \\, (\\Delta R_X/R_X)^2 \\simeq 10^{-2}$ is\n the emission beaming factor caused by the magnetic field geometry, and\n$t = 20 $\nyr accounts for the time the UHECR events have been collected in \nEarth detectors so far. \nSince the individual contribution to the observed UHECRs due to \nAICs in our Galaxy is so small we must evaluate the integrated \ncontribution due to AICs from all the galaxies located within a\nvolume \nwhich is not affected by the GZK effect, i.e., within a radius \n$R_{50} = R_G/ 50$ Mpc.\nAssuming that each galaxy has essentially the\nsame rate of AICs as our Galaxy and taking the standard galaxy \ndistribution \n$n_G \\simeq \\, 0.01 \\, e^{\\pm 0.4}\\, h^3 $ Mpc$^{-3}$ \n(with the Hubble parameter defined as $H_o = h$ 100 km s$^{-1} $ \nMpc$^{-1}$), the resulting flux at $E_{20} \\, \\geq $ 1 is\n$F(E) \\, \\simeq \\, \\, N(E) \\, n_G \\, {\\tau_{AIC}}^{-1} \\, R_{G}$, \nwhich gives\n\\begin{equation}\nF(E) \\, \\simeq \\, 1.1 \\times 10^{-27} \\xi \\, {\\rm GeV}^{-1} \n{\\rm cm}^{-2} {\\rm s}^{-1} \\,\nZ^{-1/2} \\, B_{13}^{-1/2} \\, \nE_{20}^{-3/2} \\, {\\tau_{AIC,5}}^{-1} \\, n_{0.01} \\, \nR_{50} \\left({\\frac{\\Delta R_X/R_X } {0.1}}\\right)^{-1/4} \n\\end{equation}\n\\noindent \nwhere ${\\tau_{AIC,5}}^{-1} \\, = \\, {\\tau_{AIC}}^{-1}/ 10^{-5}$ yr$^{-\n1}$,\n and \n$n_{0.01} = n_G/0.01 $ h$^3$ Mpc$^{-3}$.\nObserved data by the AGASA experiment (Takeda et al. 1999) gives a flux \nat \n$E = $10$^{20}$ eV of \n$F(E) \\, \\simeq \\, 4 \\times \\, 10^{-30}$ Gev$^{-1}$ cm$^{-2}$ s$^{-\n1}$, so \nthat the reconnection efficiency factor needs to be only\n$ \\xi \\, \\gtrsim \\, 3.6 \\times 10^{-3}$\nin order to reproduce the observed signal.\n\n\n \n%\\begin{figure}\n% \\begin{center}\n% \\leavevmode\n% \\includegraphics[width=\\textwidth]{fig1.ps}\n% \\caption{Schematic diagram of the magnetic field\n%geometry and the gas \n%accretion flow in the inner disk edge at $R_X$ for an AIC pulsar. \n% UHECRs are accelerated in \n%the magnetic reconnection site at the helmet streamer (see text). \n% (adapted from Shu et al. 1998). }\n% \\label{fig:cartoon}\n% \\end{center}\n%\\end{figure}\n\n\n\\acknowledgements E.M.G.D.P. has been partially supported by a grant of the Brazilian \nAgency FAPESP and by the PRONEX. \n\n%% When using the rmaacite package, the \\bibitem command should be of\n%% the format: \n%%\n%% \\bibitem[AUTHOR<YEAR>]{KEY} \n%%\n%% so that the \\cite{KEY}, etc. commands will work properly. \n%% \n%% If you are doing the citations manually, then you can just use\n%% `\\bibitem{}' instead. This will give you a warning about\n%% `multiply-defined labels' which you can safely ignore.\n%% \n\\begin{thebibliography}\n\n\n\\bibitem { }\nArons, J. 1993, \\apj, 408, 160\n\n\n\n\\bibitem { }\nde Gouveia Dal Pino, E. M., \\& Lazarian A. 2000, ApJ (GL2000) \n\n\n\n\\bibitem { }\nMedina Tanco, G.A., de Gouveia Dal Pino, E.M., \\& Horvath, J. 1997, \nAstropart. \nPhys., 6, 337\n\n\\bibitem { }\nMedina Tanco, G.A., de Gouveia Dal Pino, E.M., \\& Horvath, J. 1998, \n\\apj, 492, \n200\n\n\\bibitem { }\nShu, F.H., Najita, J., Ostriker, e., Wilkin, F., Ruden, S., and Lizano,\nS. 1994,\n\\apj, 429, 781\n\n\n\\bibitem { }\nTakeda, M. et al. 1999, \\apj, 522, 225\n\n\\end{thebibliography}\n\n\\end{document}\n"
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] |
[
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"name": "astro-ph0002158.extracted_bib",
"string": "\\begin{thebibliography}\n\n\n\\bibitem { }\nArons, J. 1993, \\apj, 408, 160\n\n\n\n\\bibitem { }\nde Gouveia Dal Pino, E. M., \\& Lazarian A. 2000, ApJ (GL2000) \n\n\n\n\\bibitem { }\nMedina Tanco, G.A., de Gouveia Dal Pino, E.M., \\& Horvath, J. 1997, \nAstropart. \nPhys., 6, 337\n\n\\bibitem { }\nMedina Tanco, G.A., de Gouveia Dal Pino, E.M., \\& Horvath, J. 1998, \n\\apj, 492, \n200\n\n\\bibitem { }\nShu, F.H., Najita, J., Ostriker, e., Wilkin, F., Ruden, S., and Lizano,\nS. 1994,\n\\apj, 429, 781\n\n\n\\bibitem { }\nTakeda, M. et al. 1999, \\apj, 522, 225\n\n\\end{thebibliography}"
}
] |
astro-ph0002159
|
Proper motion of water masers associated with\\ IRAS 21391+5802: Bipolar Outflow\\ and an AU-scale Dusty Circumstellar Shell
|
[
{
"author": "Nimesh A. Patel\\altaffilmark{1}"
}
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We present VLBA observations of water maser emission associated with the star forming region IRAS 21391+5802, which is embedded in a bright rimmed cometary globule in IC1396. The angular resolution of the maps is $\sim$ 0.8 mas, corresponding to a spatial resolution of $\sim$0.6 AU, at an estimated distance of 750 pc. Proper motions are derived for 10 maser features identified consistently over three epochs, which were separated by intervals of about one month. The masers appear in four groups, which are aligned linearly on the sky, roughly along a northeast--southwest direction, with a total separation of $\sim$520 AU ($\sim$0$\rlap{.}''$7). The 3D velocities of the masers have a maximum value of $\sim$42 km~s$^{-1}$ ($\sim$9 AU yr$^{-1}$). The average error on the derived proper motions is $\sim$4 km~s$^{-1}$. The overall pattern of proper motions is indicative of a bipolar outflow. Proper motions of the masers in a central cluster, with a projected extent of $\sim$ 20 AU, show systematic deviations from a radial outflow. However, we find no evidence of Keplerian rotation, as has been claimed elsewhere. A nearly circular loop of masers lies near the middle of the cluster. The radius of this loop is 1 AU and the line-of-sight velocities of the masers in the loop are within 2 km~s$^{-1}$ of the systemic velocity of the region. These masers presumably exist at the radial distance where significant dust condensation occurs in the outflow emanating from the star.
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{
"name": "motions-patel.tex",
"string": "\\documentstyle[12pt,aaspp4]{article}\n\\input psfig\n\n\\newcommand{\\masyr}{mas$\\,$yr$^{-1}$}\n\\newcommand{\\fn}[1]{\\tablenotemark{#1}}\n\\newcommand{\\p}{\\phm{mai)}}\n\\newcommand{\\z}{\\phm{mai}}\n\\newcommand{\\y}{\\phm{masi}}\n\\newcommand{\\w}{\\phm{ma}}\n\\newcommand{\\m}{\\phm{ma)}}\n\\newcommand{\\n}{\\phm{mi}}\n\n\\begin{document}\n\\def\\i{\\item}\n\\def\\beq{\\begin{equation}}\n\\def\\eeq{\\end{equation}}\n\\def\\plotfiddle#1#2#3#4#5#6#7{\\centering \\leavevmode\n\\vbox to#2{\\rule{0pt}{#2}}\n\\special{psfile=#1 voffset=#7 hoffset=#6 vscale=#5 hscale=#4 angle=#3}}\n \n\\title{Proper motion of water masers associated with\\\\\nIRAS 21391+5802: Bipolar Outflow\\\\\nand an AU-scale Dusty Circumstellar Shell} \n\\author{Nimesh A. Patel\\altaffilmark{1}\\\\(npatel@cfa.harvard.edu)}\n\\author{Lincoln J. Greenhill\\altaffilmark{1}\\\\(lgreenhill@cfa.harvard.edu)}\n\\author{James Herrnstein\\altaffilmark{2}\\\\(jherrnstein@nrao.edu)}\n\\author{Qizhou Zhang\\altaffilmark{1}\\\\(qzhang@cfa.harvard.edu)}\n\\author{James M. Moran\\altaffilmark{1}\\\\(jmmoran@cfa.harvard.edu)}\n\\author{Paul T. P. Ho\\altaffilmark{1}\\\\(pho@cfa.harvard.edu)}\n\\author{Paul F. Goldsmith\\altaffilmark{3}\\\\(pfg@astrosun.tn.cornell.edu)}\n\\altaffiltext{1}{Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138}\n\\altaffiltext{2}{National Radio Astronomy Observatory, P.O. Box 0, Socorro, NM\n87801} \n\\altaffiltext{3}{National Astronomy and Ionosphere Center, Cornell University, Department of Astronomy, Ithaca, NY 14853}\n\n\\begin{abstract}\n\nWe present VLBA observations\nof water maser emission associated with the star forming region\nIRAS 21391+5802, which is embedded in a bright rimmed cometary globule \nin IC1396. \nThe angular resolution of the maps is $\\sim$ 0.8 mas, \ncorresponding to a spatial resolution of $\\sim$0.6 AU, at an estimated\ndistance of 750 pc. Proper motions \nare derived for 10 maser features identified consistently over\nthree epochs, which were separated by intervals of about one month.\nThe masers appear in four groups, which are aligned \nlinearly on the sky, roughly along a northeast--southwest direction, \nwith a total separation of $\\sim$520 AU ($\\sim$0$\\rlap{.}''$7). \nThe 3D velocities of the masers have a maximum value of $\\sim$42 km~s$^{-1}$ \n($\\sim$9 AU yr$^{-1}$).\nThe average error on the derived proper motions is $\\sim$4 km~s$^{-1}$.\nThe overall pattern of proper motions is indicative of a bipolar \noutflow. \nProper motions of the\nmasers in a central cluster, with a projected extent of $\\sim$ 20 AU, \nshow systematic deviations from a radial outflow.\nHowever, we find no evidence of Keplerian rotation, as has\nbeen claimed elsewhere. A nearly circular loop of masers lies near the \nmiddle of the cluster. The radius of this loop is 1 AU and the \nline-of-sight velocities of the masers in the loop are within \n2 km~s$^{-1}$ of the systemic velocity of the region. \nThese masers presumably exist at the radial distance where\nsignificant dust condensation occurs in the outflow emanating from\nthe star. \n\\end{abstract}\n\n\\keywords{ISM: jets and outflows --- masers --- stars: formation}\n\n\\setcounter{footnote}{0}\n\\section{Introduction}\n \nAn important phase in the evolution of young stellar objects (YSO) \nis the one during which they exhibit energetic mass outflows, and \nsimultaneous accretion of material onto the\nstar-forming core. Since the discovery of bipolar outflows (Snell et\nal. 1980), much progress has been made in the study of the large scale \nand phenomenological characteristics of such outflows (e.g. Bachiller 1996),\nbut relatively fewer studies have probed the regions within \n$\\sim$ 100 AU of the YSOs, where the winds that drive the outflows,\noriginate (e.g., Shu et al. 1994).\n\nA significant fraction of all YSOs exhibit water maser emission,\nand the maser luminosity appears to be correlated with the\nmechanical luminosity of the outflows (Felli et al. 1992).\nThe maser emission is thought to arise from dust-laden shocked gas \nclose to the exciting YSOs, where\ndensities are $\\sim$ 10$^{9}$ cm$^{-3}$ and temperatures are $\\sim$400 K \n(e.g. Elitzur et al. 1989). Since such conditions are likely to be\nhighly localized, and since the velocity coherence required for building\nup large path lengths for the maser amplification is also likely to\noccur over relatively smaller regions, the water maser emission provides\nan excellent tool for probing the kinematics of the gas with high\nangular resolution ($\\sim$1 mas). Radio interferometric \nobservations of the water maser emission \nand measurements of maser proper motions have been carried out mostly towards \nhigh-mass star forming regions such as Orion-KL, W49N, W51 Main, W51\nNorth, Sgr B2 and W3~(OH) (Genzel et al. 1981a; Gwinn et al. 1992; Genzel\net al. 1981b; Schneps et al. 1981; Reid et al. 1988; Alcolea et al.\n1993).\nSimilar studies of low\nand intermediate-mass ($<$10 M$_{\\odot}$) star forming regions with\nvery high spatial resolution are only now becoming available \n(Claussen et al. 1998, Furuya et al. 1999, Wootten et al. 1999). \n\nIRAS 21391+5802 is an infrared source\nembedded in a bright-rimmed globule appearing on the northern periphery\nof the giant H {\\sc ii} region IC1396.\nSeveral observational studies of this object at various wavelengths \nsuggest that it is an intermediate-mass \nstar forming region (Sugitani et al. 1989, Wilking et al. 1993, \nPatel et al. 1995, Cesaroni et al. 1999). \nIts far-infrared luminosity is 235 L${_\\odot}$ (Saraceno\net al. 1996).\nWater maser emission from this source was first detected by Felli et al.\n(1992) and interferometric observations \nwere made by Tofani et al. (1995) using the NRAO\\footnote{The National Radio Astronomy Observatory is a facility\nof the National Science Foundation operated under a cooperative agreement\nwith Associated Universities, Inc.}\nVery Large Array (VLA)\nat a resolution of 0$\\rlap{.}''$1 resolution.\nThese observations\nrevealed a linear distribution\nof masers, with a systematic velocity gradient along its length.\nMore recently, Slysh et al. (1999) reported single-epoch \nobservations of these masers with mas angular resolution.\nHowever, interpretation of the kinematics has remained ambiguous\nwithout proper motion data.\n\nWe present here the results of a multi-epoch program of interferometric\nobservations of the water maser\nemission from IRAS21391+5802.\nIn the next section, we summarize the observational details, followed\nby results and our interpretation using a simple model of\na bipolar outflow. \n%Our conclusions are summarized in section 5.\n\n%------------------------------end of introduction-------------------\n\\section{Observations and data reduction}\n\nWe observed the $6_{16}-5_{23}$\nmaser line at 22.23508 GHz, \nusing the Haystack 37m telescope, the NRAO 140-foot antenna at \nGreenbank, WV, \nthe VLA in its largest and smallest configurations,\nand the NRAO Very Large Baseline Array (VLBA).\nThe single-dish observations in 1994-1995 provided a time-series of\nspectra, while we determined absolute astrometric positions of the masers\nusing the VLA observations. \n\nThe VLBA observations were made for 6 hours on \n1996 March 17, 1996 April 20 and 1996 May 19.\nWe observed a single 4 MHz bandpass in left circular polarization,\n covering $-$27 to +27 km~s$^{-1}$ in velocity, \nand divided \n%which was\n%spectroscopically analyzed \ninto 256 channels of 0.21 km~s$^{-1}$ each.\nThe systemic velocity of the source, based on observations of \n$^{13}$CO J=1-0 emission, with a velocity resolution of 0.7\nkm~s$^{-1}$, is about 0~km~s$^{-1}$ with respect to the Local Standard\nof Rest (LSR) (Patel et al. 1995).\n The data were \n correlated at the\nNRAO Array Operation Center at Socorro, NM with an averaging time of\n1.3 seconds, which provided a field-of-view of $\\sim 1''$ for the whole\narray.\n\nThe data were reduced and imaged with standard techniques using the\nNRAO AIPS package.\nObservations of 3C345, 1739+522, 2007+777, BL LAC, and 3C454.3\nprovided delay and phase calibration.\nThe sources 3C345 and BL Lac were used for bandpass \ncalibration. \n%The AIPS tasks CALIB and IMAGR were used iteratively on this channel\n%and the solutions were applied to all the channels. \nThe synthesized beam in \nall three epochs \nwas $\\sim0.8\\times 0.4$ mas at a position angle of $\\sim20^{\\circ}$.\nThe rms noise in the final images was $\\sim$ 6 mJy in all 3\nepochs.\n\nInitially, maps with reduced 1 $\\times$ 1 mas resolution were made \nto identify the approximate locations of all the maser \nspots in a 1$'' \\times 1''$ field. \nWe define a maser ``spot'' as emission occurring in\na given velocity channel. A maser ``feature'' is a collection of spots\nover contiguous channels.\nMaps with the highest resolution were made for\nselected regions and two dimensional elliptical Gaussians were fitted \nto each identified maser spot.\nThe positions of the masers were measured with respect to the spot at\n$-$14.6 km~s$^{-1}$ in maser feature {\\sc a}, which was used as \na reference for self-calibration in all three epochs (i.e., for \ncalibration of atmospheric path length fluctuations). \nThe resulting position measurements have a mean formal uncertainty of\n$\\sim10 \\mu$as.\nFor each spot, the adopted uncertainty is the larger of 1) the\ntheoretical uncertainty\nfrom the beam-width and the signal-to-noise ratio,\nand 2) the measured uncertainty from the profile fit.\nContributions to the position uncertainties from the\ninterferometric calibration (e.g., clock, astrometry, or baseline errors)\nwere negligible.\nFor each epoch, maser spot positions and line-of-sight velocities were \ninspected graphically to identify \ndistinct features.\nThe number of identifiable maser features in the\nthree epochs was 21, 19, and 20, respectively. \n\nTen maser features persisted in all three epochs, with mean line-of-sight\nvelocities changing by less than 0.5 km~s$^{-1}$ ($\\sim{1\\over 2}$ linewidth).\nProper motions were estimated by a least-squares fit to position as a \nfunction of time, with weights that were inversely proportional to the\nsquare of the uncertainties in position measurement. The weights were\nscaled to achieve unit reduced $\\chi^{2}$. A noise floor of 80 $\\mu$as\nwas added in quadrature to the uncertainties to account for possible \nunresolved structure within the maser spots. The noise floor\ncorresponded approximately to the observed wander in the motion of the\nmaser features about a straight-line trajectory. Proper motions for\nfeatures observed at only two epochs were discarded because their\ndeviations from the straight-line motion could not be estimated.\n\n%-----------------------end of observations and data reduction-----\n\n\\section{Results}\n\nA time-series of spectra obtained during the time-monitoring observations \nof the water maser emission from IRAS 21391+5802 are shown in Fig. 1. \nThe epochs are separated by $\\ga$ 1 month. \nThe spectral-lines change significantly from epoch to epoch. \nThe center velocities of some lines\nseem to change as well.\nHowever, data obtained over shorter time intervals ($\\le$ 2 weeks; not shown\nhere), do not show any significant changes.\n\nThe velocity structure of the spectra\nare symmetric around the systemic velocity\nof $\\sim0$ km~s$^{-1}$, but the VLA images show that \nthe 10 km~s$^{-1}$ emission is offset\nsoutheast by $\\sim$10$''$ (7500 AU) (see also\nTofani et al. 1995). Earlier interferometric observations of \nthermal continuum emission at 3mm, and C$^{18}$O J=1-0 line emission\nmade by Wilking et al. (1993), show\nan extension from the central peak towards this \n$10$ km~s$^{-1}$ maser feature. We suggest that this\nis a separate star forming condensation, \nunrelated to the rest of the masers in our map. \nWilking et al. (1993) identified four near-infrared sources\ntowards IRAS21391+5802. IRS2 (Wilking et al. 1993) which is \nassociated with the 3 mm peak radio continuum emission, is closest to\nthe water masers shown in Fig. 2.\nIn the observations by Wilking et al. (1993), there does\nnot appear to be an infrared source associated with the $10$ km~s$^{-1}$\nmaser feature that is offset 10'' from the bulk of the maser\nemission.\n\nFig. 2 shows the results of our VLBA observations over the three epochs. \nThe groups of maser features labeled {\\sc a}, {\\sc c} and {\\sc d} are isolated.\nThese masers have line-of-sight velocities differing by more than \n$\\pm4$ km~s$^{-1}$ from the systemic velocity. \n{\\sc a} and {\\sc d} are the most extremely blue and red-shifted masers, respectively, \nand they also appear at the extrema of the distribution of masers on the sky.\nMost of the masers in {\\sc b} appear to be aligned along\nan eastwest line near $\\Delta\\delta=0\\rlap{.}''17$. We refer\nto these hereafter as the ``inner\" masers.\nThe integrated intensity maps of the inner\nmasers are shown in Fig. 3. From an analysis of fringe rates, we\nestimate that the \nposition of the reference emission is \n$\\alpha_{J2000}=21^{h}40^{m}41^{s}.791\\pm0^{s}.004,\n\\delta_{J2000}=58^{o}16'11\\rlap{.}''737\\pm0\\rlap{.}''030$.\nOur VLA A array observations made on 6 July 1995, add\ninformation on the variability of maser emission in this region.\nThe maser features {\\sc a} and {\\sc b} appear roughly in the same\npositions and line-of-sight velocities as in the VLBA observations.\nTwo different maser features appear in the VLA A array observations.\nOne at a position offset of $(0\\rlap{.}''41,0\\rlap{.}''11)$ with a\nline-of-sight velocity of -8 km s$^{-1}$ and the other at\n$(0\\rlap{.}''63,0\\rlap{.}''25)$ and velocity of 22 km s$^{-1}$.\nMaser features {\\sc c} and {\\sc d} do not appear in the VLA map.\nBecause the position uncertainties are about $0\\rlap{.}''1$ in\nthe VLA map, registered with respect to the VLBA map, the VLA data\nare not useful in estimation of motions.\n\nThe proper motions in clumps {\\sc a}, {\\sc c} and {\\sc d} are suggestive\nof largely radial outflow from a center of expansion in clump {\\sc b}.\nWithin clump {\\sc b} there is a roughly circular loop of masers at \n$\\Delta\\alpha=0\\rlap{.}''515-0\\rlap{.}''519$ and \n$\\Delta\\delta=0\\rlap{.}''16-0\\rlap{.}''17$. The line-of-sight\nvelocities of these masers are the closest to the systematic velocity of\nthe region, and the velocities in the plane of the sky are consistent\nwith a radial outflow. \nFrom these results we propose that the loop signifies the radius of dust\nsublimation in a circumstellar shell of outward flowing stellar wind material. \nMaser emission is beamed along the line-of-sight by the long gain paths \ntangent to the edge of the relatively dust-free inner cavity. \n\nFrom each feature, we have subtracted the mean \nmeasured proper motion for the whole source, to reduce the effect of \nthe proper motion of the reference feature.\nIn principle, an arbitrary\nvelocity vector may be added to the proper motions since they are\nobtained from positions to the feature at $-14.6$ km~s$^{-1}$. \nIf we add a proper motion of 6.8 km~s$^{-1}$ at a\nposition angle of 29$^{\\circ}$ to each maser feature, then the two proper\nmotion vectors associated with the loop become radial and outward.\nHowever, with the addition of this largely northward motion, the proper\nmotions of the three easternmost features in {\\sc b} deviate\nsignificantly from a radial outflow. Although the assignment of zero \nnet proper motion may be somewhat arbitrary, it is the most straight-forward \nway to compensate at least partly for the relatively large apparent motion \nof the reference maser feature. \n\n%--------------------------------end of results------------------------\n\n\\section{Discussion}\n\nThe positions and 3D space velocities in Fig. 2 clearly show that\nsystematic motions dominate over turbulent motions in this system.\nThe masers trace bulk gas kinematics within 0$\\rlap{.}''6$ or 500 AU\nof the possible YSO. \nIn principle, within such close proximity, both \n infall along an accreting\ncircumstellar disk and an orthogonal bipolar outflow \nmay be anticipated (e.g., Shu et al. 1987).\nRelying on interpretation of spectra and a single \nepoch VLBA observation of these masers, Slysh et al.\n(1999) conclude that the maser kinematics might represent\nKeplerian rotation of a circumstellar disk around a YSO. \nHowever, in such a scenario the masers with line-of-sight velocity\nnearest \nthe systemic velocity should \nshow the largest proper motions.\nOur data clearly rule out a disk model and support a\n bipolar outflow model.\n\nThe loop of masers that we propose pinpoints the possible YSO (Figs. 2 \\& 3) \nhas a radius of $\\sim$1 AU. \nThe bolometric luminosity of IRAS 21391+5802 is 235 L$_{\\odot}$,\nimplying a mass of 3 to 5 M$_{\\odot}$. Gravitationally bound gas within\na radius of a few AU of a 3 M$_{\\odot}$ object should exhibit orbital\nvelocities of a few tens of km~s$^{-1}$. \nHowever, all the features in the loop have line-of-sight velocities that \nare an order of magnitude less. Furthermore, \ntwo of the features in the loop for which proper motions could be determined\nshow 3D space velocities of only $\\sim$5 km~s$^{-1}$. \nIf the masers lie at about the radius where\nsubstantial condensation of dust grain occurs, then this is also\nthe radius at which acceleration of the outflow by radiation pressure\nbegins; the low 3D space velocities are reasonable and may be upper limits\non bulk outflow speeds closer to the YSO. \nSince the earliest observations of the maser source \n(Felli et al. 1992, Brand et al. 1994) the maser emission \nat line-of-sight velocities corresponding to the loop masers\nhas been persistent, in contrast to the higher velocity \nmaser features, which apparently lie downstream in the\noutflow.\nThe masers in\nthe loop may thus represent a standing pattern in outward flowing \nmaterial, wherein masers are born, track outflowing and cooling\nmaterial, and fade, to be replaced by new masers at smaller radii.\nMasers downstream are products of shocks and local heating possibly in\ncollisions between the outflow and ambient media.\n\nThe spectral energy distribution of the infrared emission from IRAS\n21391+5802 has been studied by Correia et al. (1999). According\nto their model, the temperature of the gas at a distance of 1 AU from\nthe YSO is predicted to be about 1800 K. This is in excess by at least a\nfactor of two higher than the temperature expected from the occurrence \nof the water masers in the loop. However, the calculated temperature depends\nsensitively on grain properties such as size. If the grains are\nlarger than 1$\\mu$m in size, the dust envelope would be optically\nthin very close to the star, and lower temperatures would be possible\n($\\sim$1000 K).\n\nThe 3D space velocities of masers {\\sc a}, {\\sc c} and {\\sc d} shown \nin Fig. 2 indicate an outflow away from the inner masers ({\\sc b}). \nTo estimate the position and inclination angles of the outflow, we fit \na simple model to the data in which we assume an outflow \nvelocity that is linearly proportional to the distance from \nthe outflow center, with a proportionality constant, $k$. \nWe choose a coordinate system with its origin at the center of the \nloop.\n% the abscissa along the right ascension and the ordinate to be along \n%the declination, and the z axis is\n%along the line of sight. \nThe purpose of this model is only to \nestimate the position and inclination angles and the value of $k$. \nA straight line fitted\nto the observed maser positions alone provides\nthe position angle $\\phi\\approx 70^{\\circ}$.\nFrom the positions and 3D velocities, we obtain\nan inclination angle $\\theta\\approx 70^{\\circ}$ \nwith respect to the line of sight, \n$k$, and $z_{i}$, the distance of each maser spot along\nthe line of sight, \nand $k\\approx5\\times 10^{-10} s^{-1}$ (0.07 km~s$^{-1}$ AU$^{-1}$).\nThe inclination and position angle are difficult to measure well because\nthe outflow appears to have an opening angle of at least 40$^{\\circ}$,\njudging from the motions and line-of-sight velocities of {\\sc c} \\& {\\sc\nD}, and from the distribution of maser spots in {\\sc B}.\n\nThe fitted value of $k$ implies an overall e-folding time of $\\sim$65 yrs.\nThe dynamical times obtained from the de-projected radii of the masers\nand the 3D space velocities are\n43, 38 and 14 yrs for the masers {\\sc a}, {\\sc d} and {\\sc c}. \nThe inner masers ({\\sc b}) have a dynamical time\nof only 2 to 9 yrs. \nThese different dynamical times are inconsistent with the masers \nbeing ejected ballistically at the same time but with different initial \nvelocities.\nInstead, there is possibly true acceleration \nin the flow as a function of distance away from the\nYSO. Another possibility is that the flow is ballistic but episodic.\nHowever, as noted earlier, maser emission at velocities close\nto the systemic velocity (corresponding to {\\sc b} \\& {\\sc l}) seems to\nhave persisted since the earliest observations in 1988 \n(Brand et al. 1994). Thus, the mass\noutflow represented by the clumps of gas that are masing today, may be a\ncontinuous process, rather than a consequence of a singular event of \nmass ejection. \n\n\n%-----------------------------end of discussion-----------------------\n\n\\section{Conclusions}\n\nWe have detected proper motion of 10 water maser features associated \nwith the star-forming region IRAS 21391+5802. \nThe water masers trace a bipolar outflow\nfrom an intermediate mass young stellar object. \n%The masers have a mean \n%magnitude of 3D space velocity of $\\sim$13 km~s$^{-1}$ (2.7 AU yr$^{-1}$). \nWe estimate position and inclination angles of $\\sim 70^{\\circ}$ for the\noutflow axis, though the opening angle may exceed 40$^{\\circ}$.\nThe maximum observed 3D space velocity of the masers is 42 km~s$^{-1}$. \nThe observed 3D space velocities of the masers suggest the presence of \nacceleration within the outflow, but we cannot rule out episodic ballistic\nejection.\nNear the center of the flow, there is a roughly circular loop of masers \nwith a radius of $\\sim$1 AU. \nThe masers in this loop are most likely to be\ntangentially amplified within a shell of dense gas\nsurrounding the YSO. Because there is no evidence for rotation in the\nsource (as in a disk), the shell probably comprises wind material\nalone.\nHowever, dynamics of the IRAS 21391+5802 region are poorly sampled,\nespecially in the loop. Additional \nobservations may still reveal some rotation, or even infall.\n\n\\acknowledgments\nWe thank Lee Hartmann, Nuria Calvet, T. K. Sridharan and Masao Saito for \nhelpful discussions.\nWe are grateful to Shoshana Rosenthal for help with the management of the\nAlpha workstations and AIPS in the Radio and Geoastronomy division \nat the Center for Astrophysics. \n\n\n%--------------------------------end of conclusion------------------\n\n\\begin{references}\n\n\\reference{} Alcolea, J., Menten, K. M., Moran, J. M. \\& Reid, M. J.,\n1993, in Astrophysical Masers, Lecture Notes in Physics, Vol. 412, \n The Proper Motions of the H$_{2}$O Masers Near W3(OH), \n ed. A. Clegg and G. 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Nakamoto,\n(Nagoya: Nagoya University), in press \n\n\\end{references}\n\\newpage\n\\clearpage\n\n\\begin{deluxetable}{rcccrrrrc}\n\\tablecaption{Positions, velocities and proper motions of masers}\n\\tablewidth{0pt}\n\\tablehead{\n\\colhead{} & \\multicolumn{2}{c}{Position offset\\fn{a}} && \\multicolumn{4}{c}{Proper motion\\fn{b}} & Maser\\fn{c}\\\\\n\\cline{2-3} \\cline{5-9} \\\\\n\\colhead{V$_{LSR}$} & \\colhead{$\\Delta \\alpha$} & \\colhead{$\\Delta \\delta$} &&\n \\colhead{$\\dot{\\alpha}$} & \\colhead{Error} &\n \\colhead{$\\dot{\\delta}$} & \\colhead{Error}& \\\\\n\\colhead{(km$\\,$s$^{-1}$)} & \\colhead{(mas)} & \\colhead{(mas)} &&\n\t\t \\colhead{(\\masyr)} & \\colhead{(\\masyr)} & \\colhead{(\\masyr)} & \\colhead{(\\masyr)} &}\n\\startdata\n-14.6 \\n & 0.9 & 0.2 && -10.2\\z & 1.2 \\p & -2.5 \\y & 0.2\\w & A\\\\\n-10.0 \\n & 529.4 & 191.6 &&&&&&B\\\\\n-9.4 \\n & 527.0 & 225.2 && 3.2\\z & 3.8 \\p & 2.4 \\y & 0.2\\w & C\\\\\n-9.1 \\n & 529.0 & 190.1 &&&&&&B\\\\\n-8.6 \\n & 529.0 & 190.1 &&&&&&B\\\\\n-8.0 \\n & 528.4 & 190.0 &&&&&&B\\\\\n-7.6 \\n & 527.7 & 189.7 &&&&&&B\\\\\n-7.6 \\n & 529.3 & 190.0 &&&&&&B\\\\\n-3.7 \\n & 536.9 & 183.7 &&&&&&B\\\\\n-1.9 \\n & 535.0 & 182.3 &&&&&&B\\\\\n-1.4 \\n & 506.8 & 167.6 && -1.8\\z & 0.6 \\p & -1.7 \\y & 0.02\\w & B\\\\\n-1.0 \\n & 509.1 & 168.6 && -0.3\\z & 0.5 \\p & -2.2 \\y & 0.1\\w & B\\\\\n-0.9 \\n & 528.0 & 178.5 &&&&&&B\\\\\n-0.5 \\n & 515.3 & 168.1 &&&&&&B\\\\\n-0.5 \\n & 506.9 & 167.9 &&&&&&L\\\\\n-0.0 \\n & 516.6 & 168.0 &&&&&&L\\\\\n0.0 \\n & 516.4 & 167.8 &&&&&&L\\\\\n0.2 \\n & 516.5 & 167.8 &&&&&&L\\\\\n0.3 \\n & 516.7 & 167.8 &&&&&&L\\\\\n0.4 \\n & 515.5 & 169.3 && 0.3\\z & 0.3 \\p & -1.3 \\y & 0.4\\w & L\\\\\n0.4 \\n & 517.8 & 168.9 &&&&&&L\\\\\n0.4 \\n & 516.9 & 168.0 &&&&&&B\\\\\n0.4 \\n & 507.0 & 168.0 &&&&&&B\\\\\n0.8 \\n & 522.4 & 162.7 &&&&&&L\\\\\n0.8 \\n & 516.2 & 167.0 &&&&&&L\\\\\n\\tablebreak\n0.9 \\n & 517.1 & 166.9 &&&&&&L\\\\\n1.0 \\n & 517.1 & 169.8 && 1.5\\z & 0.7 \\p & -0.8 \\y & 0.2\\w & L\\\\\n1.0 \\n & 517.6 & 167.9 &&&&&&L\\\\\n1.1 \\n & 516.5 & 166.9 &&&&&&L\\\\\n1.1 \\n & 517.4 & 167.5 &&&&&&L\\\\\n1.4 \\n & 527.0 & 168.8 && 0.2\\z & 1.0 \\p & 1.7 \\y & 0.1\\w & B\\\\\n1.5 \\n & 526.3 & 161.2 &&&&&&B\\\\\n2.0 \\n & 528.5 & 175.8 &&&&&&B\\\\\n2.1 \\n & 531.6 & 169.6 && 1.6\\z & 0.2 \\p & 0.7 \\y & 0.2\\w & B\\\\\n2.5 \\n & 523.0 & 168.7 && 1.0\\z & 0.4 \\p & 0.8 \\y & 0.4\\w & B\\\\\n7.5 \\n & 615.9 & 334.9 && 4.5\\z & 0.3 \\p & 3.0 \\y & 1.2\\w & D\\\\\n\\enddata\n\\tablenotetext{a}{Position in right ascension and declination offset\nfrom the reference feature (V$_{LSR}$=-14.6 km~s$^{-1}$), the estimated\nposition of which is \n$\\alpha_{J2000}=21^{h}40^{m}41^{s}.791\\pm0^{s}.004,\n\\delta_{J2000}=58^{o}16'11\\rlap{.}''737\\pm0\\rlap{.}''030$}\n\\tablenotetext{b}{A proper motion vector of 38.7 km~s$^{-1}$ at a\nposition angle of 256$^{\\circ}$ has been added to the gross motions to\nachieve a zero mean (see text).}\n\\tablenotetext{c}{See labels in Figure 2}\n\\end{deluxetable}\n\\newpage\n\n% FIGURE 1\n\\begin{figure}[t]\n\\plotfiddle{patel-fig1.eps}{6.75in}{0}{70}{70}{-220}{-50}\n\\caption{\\setlength{\\baselineskip}{8 pt} \\footnotesize\nTotal power spectra obtained at the Green Bank 140-foot and Haystack 37m\nantennas and integrated VLA and VLBA spectra of water maser \nemission associated with IRAS 21391+5802.\nThe maser features vary significantly in intensity on time scales\ngreater than a month. Line-of-sight velocities may also change on\ntime scales of months. The VLBA spectra covered the velocity range of\n$-$27 to 27 km~s$^{-1}$ but no emission was found at velocities less than\n$-$14 km~s$^{-1}$ and greater than 8 km~s$^{-1}$. (The VLBA data are\n shown only for the range of spectral\n channels that display maser emission on the dates indicated).\nThe vertical lines indicate the range of line-of-sight velocities of the\nmasers occurring in the loop shown in Fig. 2. The systemic velocity of\nthe source is $\\sim$ 0 km~s$^{-1}$.\n}\n\\end{figure}\n\\newpage\n\n% FIGURE 2\n\\begin{figure}[t]\n\\plotfiddle{patel-fig2.eps}{5.9in}{0}{75}{75}{-225}{-140}\n\\caption{\\setlength{\\baselineskip}{8 pt} \\footnotesize\nMaps of fitted water maser spots and maser feature proper motions \nfrom all 3 VLBA epochs superposed. {\\it Upper right:} \nPositions and proper motions of the water masers\nare largely indicative of a bipolar outflow motion.\nThe formal and systematic errors in these positions are\nmuch smaller than the size of the symbols in the plot. \nThe $1\\sigma$ uncertainties in the direction of proper motion \nare indicated by the angle\nindicated at the tails of the arrows. The length of the cones\nimply $1\\sigma$ uncertainties in the magnitude of the proper motion.\nLine-of-sight velocities are indicated by symbol colors, according to\nthe scale bar at the bottom left.\nThe maser labeled {\\sc a} is the reference feature in all three epochs.\n{\\it Middle left:} The proper motions and positions of the inner masers ({\\sc b}), are shown \non an enlarged scale in the lower panel. \n{\\it Lower right:} The masers roughly in the center of the\n{\\sc b} trace a nearly circular loop; the YSO is probably located at the\ncenter. The radius of the loop of masers is $\\sim$1 AU. \nThe loop most likely represents the inner\nradius of dust condensation in a shell of outflowing material around the YSO.\n}\n\\end{figure}\n\\newpage\n\n% FIGURE 3\n\\begin{figure}[t]\n\\plotfiddle{patel-fig3.eps}{7.25in}{0}{80}{80}{-265}{-40}\n\\caption{\\setlength{\\baselineskip}{8 pt} \\footnotesize\nIntegrated intensity images at three epochs, for emission between\nV$_{LSR}=-$4.6 and 1.7 km~s$^{-1}$ within the central clump of masers.\nThe overall variability of features in the spectra (Fig. 1) is consistent with\nchanges among the maps.\nThe masers near the position offset $\\Delta\\alpha=0\\rlap{.}''516,\n\\Delta\\delta=0\\rlap{.}''168$ correspond to the loop pictured in Fig. 2.\n}\n\\end{figure}\n\\newpage\n\n% FIGURE 4\n\\begin{figure}[t]\n\\plotfiddle{patel-fig4.eps}{5in}{0}{100}{100}{-310}{0}\n\\caption{\\setlength{\\baselineskip}{8 pt} \\footnotesize\nVariation of 3D space velocity as a function of distance from the \nposition of the YSO\n(which is assumed to be at the center of the loop of masers shown in Fig. 2).\nThis figure shows that 1) the masers that are more distant from the YSO,\nmove relatively faster than the closer ones and 2) the dynamical time for\nthe inner masers ({\\sc b} \\& {\\sc l}) is less than \nthat for the outer masers ({\\sc a}, {\\sc c} \\& {\\sc d}).\n}\n\\end{figure}\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002160
|
Lyman-${\bmath \alpha}$ Imaging of a Very Luminous ${\bmath z=2.3} $ Starburst Galaxy with WFPC2\footnote
|
[
{
"author": "Nathan Roche$^{1,3}$"
},
{
"author": "James Lowenthal$^{1,4}$ and Bruce Woodgate$^{2,5}$"
},
{
"author": "$^1$Department of Physics and Astronomy"
},
{
"author": "Box 34525"
},
{
"author": "Amherst MA 01003"
},
{
"author": "USA."
},
{
"author": "$^2$NASA Goddard Space Flight Center"
},
{
"author": "Laboratory for Astronomy and Solar Physics"
},
{
"author": "Code 681"
},
{
"author": "Greenbelt MD 20771"
}
] |
We investigate the $Ly\alpha$ and UV continuum morphology of one of the most luminous known Lyman $\alpha$ emitting galaxies (the `Coup Fourr\'e Galaxy'), associated with a $z=2.3$ damped $Ly\alpha$ absorption system in the spectrum of the QSO PHL 957 (Lowenthal et al. 1991). The galaxy is observed with the HST WFPC2, through a narrow filter (F410M) corresponding to rest-frame $Ly\alpha$ for a total exposure time of 41.2 ksec, plus shorter exposures in F555W and F814W. In all three passbands, the galaxy is resolved into a close ($\sim 0.35$ arcsec) pair of two components, CFgA and CFgB, both of which are extended and elongated. The profile of CFgA is consistent with an exponential disk of similar scale-length in $Ly\alpha$ ($r_{exp}=0.23$ arcsec) and continuum ($r_{exp}=0.20$ arcsec), and no evidence of a central point source. In contrast, CFgB is closer to a bulge profile. We find that CFgA has by far the higher ratio of $Ly\alpha$ to continuum flux, and from the observed colours estimate rest-frame equivalent widths of $W(Ly \alpha) =151\pm 16 \AA$ for CFgA and $33\pm 13 \AA$ for CFgB. From the F814W and F555W magnitudes we estimate rest-frame blue-band absolute magnitudes (for $H_0=50$ km $s^{-1}Mpc^{-1}$ and $q_0=0.05$) of -23.12 for CFgA and -23.24 for CFgB, significantly brighter than local galaxies of the same size. CFgA shows a remarkable 3.9 magnitudes of surface brightness enhancement relative to local spirals. This object appears to be at the upper limit of both the range of surface brightness evolution observed in $z>2$ galaxies and the range of $W(Ly \alpha)$ in any star-forming galaxy. We speculate that its extreme surface brightness results from a very luminous starburst ($\sim 200 M_{\odot}yr^{-1}$), triggered by the merger of the two components, and the high $W(Ly \alpha)$ from a brief phase of the starburst in which most $Ly\alpha$ photons can escape, as predicted in the models of Tenorio-Tagle et al. (1999). We also investigate the F410M image of the QSO PHL 957. Subtraction of a normalized point-spead function leaves no significant residuals -- the QSO is consistent with a pure point source and we do not detect either the host galaxy or the damped $Ly\alpha$ absorbing galaxy. We search for other galaxies with strong $Ly\alpha$ emission at $z\sim 2.3$--2.4, selecting these by a colour $(m_{410}-V_{555})_{AB}<-0.2$. Eight candidate $Ly\alpha$ sources, all fainter than the Coup Fourr\'e galaxy, are identified in our field. One is a point-source and may be an AGN; the others are of similar size to the Coup Fourr\'e Galaxy but lower surface brightness, knotty and asymmetric. They appear typical of Lyman break galaxies but with colours indicating $W(Ly\alpha)\sim 100\AA$.
|
[
{
"name": "lym.tex",
"string": "\\documentstyle{mn}\n\n\n\\title[Ly$\\alpha$ Imaging of a $z=2.3$ Galaxy] \n{Lyman-${\\bmath \\alpha}$ Imaging of a Very Luminous ${\\bmath z=2.3}\n$ Starburst Galaxy with WFPC2\\footnote}\n\n\n\\author[N. Roche, J.Lowenthal and B. Woodgate]{Nathan \nRoche$^{1,3}$, James Lowenthal$^{1,4}$ and Bruce Woodgate$^{2,5}$\\\\\n$^1$Department of Physics and Astronomy,\n University of Massachusetts,\n Box 34525,\n Amherst MA 01003,\n USA.\\\\\n$^2$NASA Goddard Space Flight Center, Laboratory for Astronomy and Solar Physics, Code 681, Greenbelt MD 20771, USA.\\\\\n{$^3$ \\verb\"ndr@wigeon.astro.umass.edu\"}\\hspace{8mm}\n{$^4$ \\verb\"james@velo.astro.umass.edu\"}\\hspace{8mm}\n{$^5$ \\verb\"woodgate@s2.gsfc.nasa.gov\"}\\hspace{8mm} \n}\n\\bibliographystyle{unsrt}\n\\input{psfig.sty}\n\n\\begin{document}\n\\maketitle\n \n\\begin{abstract}\nWe investigate the $\\rm Ly\\alpha$ and UV continuum morphology of one of the most luminous known Lyman $\\alpha$ emitting galaxies (the `Coup Fourr\\'e Galaxy'), associated with a $z=2.3$ damped $\\rm Ly\\alpha$ absorption system in the spectrum of the QSO PHL 957\n (Lowenthal et al. 1991). The galaxy is observed with the HST WFPC2, through a narrow filter (F410M) corresponding to\nrest-frame $\\rm Ly\\alpha$ for a total exposure time of 41.2 ksec, plus shorter exposures in F555W and F814W.\n\nIn all three passbands, the galaxy is resolved into a close ($\\sim 0.35$ arcsec) pair of two components, CFgA and CFgB, both of which are extended and elongated.\n The profile of CFgA is consistent with an exponential disk of similar scale-length in $\\rm Ly\\alpha$ ($r_{exp}=0.23$ arcsec) and continuum ($r_{exp}=0.20$ arcsec), and no evidence of a central point source. In contrast, CFgB is closer to a bulge profile.\n We find that CFgA has by far the higher ratio of $\\rm Ly\\alpha$ to continuum flux, and from the observed colours estimate rest-frame equivalent widths of $W(\\rm Ly \\alpha) =151\\pm 16 \\AA$ for CFgA and $\\rm 33\\pm 13 \\AA$ for CFgB. \n\nFrom the F814W and F555W magnitudes we estimate rest-frame blue-band absolute magnitudes (for $H_0=50$ km $\\rm s^{-1}Mpc^{-1}$ and $q_0=0.05$) of -23.12 for CFgA and -23.24 for CFgB, significantly brighter than local galaxies of the same size. CFgA shows a remarkable 3.9 magnitudes of surface brightness enhancement relative to local spirals. This object appears to be at the upper limit of both the range of \nsurface brightness evolution observed in $z>2$ galaxies and the range of $W(\\rm Ly \\alpha)$ in any star-forming galaxy. We speculate that its extreme surface brightness results from a very luminous starburst ($\\sim 200 M_{\\odot}\\rm yr^{-1}$), triggered by the merger of the two components, and the high $W(\\rm Ly \\alpha)$ from a brief phase of the starburst in which most $\\rm Ly\\alpha$ photons can escape, as predicted in the models of Tenorio-Tagle et al. (1999).\n \nWe also investigate the F410M image of the QSO PHL 957. Subtraction of a normalized point-spead function leaves no significant residuals -- the QSO is consistent with a pure point source and we do not detect either the host galaxy or the damped $\\rm Ly\\alpha$ absorbing galaxy. \n \nWe search for other galaxies with strong $\\rm Ly\\alpha$ emission at $z\\sim 2.3$--2.4, selecting these by a colour $(m_{410}-V_{555})_{AB}<-0.2$. Eight candidate $\\rm Ly\\alpha$ sources, all fainter than the Coup Fourr\\'e galaxy, are identified in our field. One is a point-source and may be an AGN; the others are of similar size to the Coup Fourr\\'e Galaxy but lower surface brightness, knotty and asymmetric. They appear typical of Lyman break galaxies but with colours indicating $W(\\rm Ly\\alpha)\\sim 100\\rm \\AA$. \n\\end{abstract}\n \n\\begin{keywords}\nGalaxies -- evolution: galaxies -- starburst: ultraviolet -- galaxies\n\\end{keywords}\n{\\thefootnote Based on observations with the NASA/ESA Hubble Space Telescope obtained at the\nSpace Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555.}\n\\section{Introduction}\n\n\nClouds of neutral hydrogen detected as Lyman $\\alpha$ ($\\rm Ly\\alpha$, $1216\\rm \\AA$) absorption lines in the spectra of\ndistant QSOs sample gas in the early universe, without bias towards\nluminosity or the presence of stars. They are therefore useful as\nsensitive indicators of the distribution, metallicity, and ionization\nof gas at redshifts as high as the most distant QSOs ($z>5$),\nand they complement galaxies selected by emission, such as Lyman break\ngalaxies. In particular, damped $\\rm Ly\\alpha$ absorption systems (hereafter DLAs), with neutral hydrogen\ncolumn densities $N_{\\rm HI} > 10^{20}\\rm cm^{-2}$, although rare, contain most of the\nHI in the universe at high redshift, and have been postulated to\ncorrespond to the sites of young, possibly primeval galaxies, and of cluster formation (e.g.,\nWolfe 1993). Despite intense efforts to\nimage dozens of DLA clouds directly in optical continuum or\nemission lines, only a few systems at $z>2$ have yielded any\nassociated emission (e.g., Djorgovski et al 1996;\nFrancis et al. 1996; M\\o ller and Warren 1998; Fynbo, M\\o ller,\nand Warren 1999; Leibundgut and Robertson 1999)\n -- note that the latter three cases\nhave $z_{abs} \\simeq z_{em}$, so the cloud is presumably influenced by\nthe QSO close by.\n\n\nThe QSO PHL 957, at $z=2.681$, shows the spectral signature of damped \n$\\rm Ly\\alpha$ \nabsorption from a neutral hydrogen cloud ($N_{\\rm HI}=2.5\\times 10^{21}\\rm cm^{-2}$) at $z=2.309$.\n Meyer and Roth (1990) detected the NiII, CrII and ZnII absorption lines from the cloud and from the relative line strengths concluded that this DLA has a metallicity (Zn/H) only 4 per cent solar, and a dust-to-gas ratio\nonly 3 per cent Galactic. \nThis very low metallicity and dust content implies that any $\\rm Ly \\alpha$ emission from within, or associated with, the system, e.g. from star-forming galaxies, might suffer very little dust obscuration, allowing its direct observation.\n \n To investigate this possibility, the PHL 957 field was observed (Lowenthal et al. 1991) at the KPNO 4m telescope through a Fabry-Perot filter tuned to $4023\\pm 28\\rm \\AA$ (rest-frame $\\rm Ly\\alpha$). Significant emission was detected from a small ($<3$ arcsec) source 48 arcsec from PHL 957. Spectroscopic investigation at the Multiple-Mirror telescope (MMT) revealed a faint ($V\\simeq 23.6$) continuum with a strong $\\rm Ly\\alpha$ line of flux $5.6\\times 10^{-16}$ ergs $\\rm s^{-1}cm^{-2}$, or rest-frame equivalent width $W(\\rm Ly\\alpha)\\simeq 140\\rm \\AA$. The line gave a \nredshift $z=2.3128\\pm 0.0004$ -- indicating a velocity $346\\pm 20$ km $\\rm s^{-1}$ relative to the absorbing cloud -- and showed Doppler broadening corresponding to ${\\rm FWHM}\\sim 600$ km $\\rm s^{-1}$. \nThe $\\rm Ly\\alpha$ source was therefore a galaxy, later named the Coup Fourr\\'e galaxy (hereafter, CFg), separate from but associated with the absorbing cloud.\nThe CFg spectrum also showed less luminous CIV($\\rm 1549\\AA$) and HeII($\\rm 1640\\AA$) emission lines, which might indicate the presence of an Active Galactic Nucleus (AGN), but could also be produced by Wolf-Rayet stars. \n\n\nObserving CFg in the near infra-red, Hu et al. (1993) obtained a marginal detection of $\\rm H\\alpha$ emission, confirmed at higher significance by \nBunker et al. (1995, 1999). \n Wolfe et al. (1994) confirmed that $\\rm[O/H]<-0.97$ solar for the damped absorption cloud, indicating that the system's metallicity is sufficiently low that there is at least a possibility for any $\\rm Ly\\alpha$ photons to escape (Charlot and Fall 1993).\nHowever, these\nground-based observations were not able to reveal either the spatial distribution of the $\\rm Ly\\alpha$ emission or the morphology of the underlying galaxy, and it remained unclear whether the $\\rm Ly\\alpha$ flux was produced by an AGN, by more extended star-formation, or some combination of the two.\n\nA number of other $\\rm Ly\\alpha$ emitting galaxies have now been identified\nat high redshifts. One of the most luminous, at $z=3.428$, was observed in the $V$-band (Giavalisco et al. 1995) with the pre-refurbishment HST WFPC, \nand found to have \na compact ($r_{hl}=0.09\\pm 0.02$ arcsec) bulge-profile morphology.\nM\\o ller and Warren (1993) investigated three $\\rm Ly\\alpha$ emitting galaxies at $z=2.81$, associated with the DLA towards QSO PKS0528-250. HST WFPC2 imaging\nin broad-band $B$ and $I$ revealed these also to be compact,\n$r_{hl}\\simeq 0.1$ arcsec, in the rest-frame UV continuum (one consisted of two components separated by 0.3 arcsec), although ground-based narrow-band imaging suggested that one source was more extended in $\\rm Ly\\alpha$ ($r_{hl}\\simeq 0.51$ arcsec).\n\nThe obvious next step in the study of this type of galaxy is deep space-based,\nnarrow-band imaging at the redshifted $\\rm Ly\\alpha$ wavelength, combined with broad-band imaging. This will \nenable the $\\rm Ly\\alpha$ and continuum structures to be investigated and compared at sub-kpc scales, revealing whether the $\\rm Ly\\alpha$ emission is from a point-source or extended region, and if extended whether it traces the distribution of stars, and indicating the morphology (e.g. disk, bulge or merger) of the underlying galaxy. Fortunately, one of the WFPC2 filters, the medium-width F410M, covers the desired wavelength, but a very long exposure time is needed.\nWe were allocated a total of 21 orbits of WFPC2 time for the detailed study of CFg, of which 16 orbits were dedicated to acquiring the $\\rm Ly\\alpha$ image. \n\n In addition, any other strong\n$\\rm Ly\\alpha$ sources on our field at redshifts close to CFg will be distinguishable from other galaxies by an enhanced ratio of F410M to broad-band flux. \nPascarelle, Windhorst and Keel (1998) applied this technique to a field centred on the $z=2.4$ radio galaxy 53W002, plus three randomly chosen fields, which were imaged with WFPC2 in F410M, F450W and F814W. In the 4 fields, a total of 35 galaxies were selected as probable $\\rm Ly\\alpha$ emitters on the basis of blue $m_{410}-B_{450}$ colours, with the greatest number (17) in the 53W002 field. \nSimilarly, a narrow-band $5007\\rm \\AA$ survey of Kudritzki et al. (2000) revealed 9 $\\rm Ly\\alpha$ emitters at $z=3.1$.\nHowever, not all high-redshift galaxies are $\\rm Ly\\alpha$ emitters --\nSteidel et al. (1999) performed\nground-based $\\rm Ly\\alpha$ imaging of a field with many identified Lyman break\ngalaxies at $2.7\\leq z \\leq 3.4$ and estimated that only $\\sim 20$--25 per cent of these have $W(\\rm Ly\\alpha)>20 \\AA$. \n\nLastly, \nsubtracting a normalized point-spread function from the image of a QSO may reveal the host galaxy (e.g. McLure et al. 1999), although this is more difficult for high-redshift QSOs (e.g. Lowenthal et al. 1995), and/or show a galaxy at the centre of the DLA system. We attempt this with the F410M image of PHL 957.\n\nSection 2 describes the observational data and its reduction. In Section 3 we present contour plots and radial profiles of CFg, and estimate the scalelength and morphological type of this galaxy. In Section 4 we investigate the F410M image of PHL 957. In Section 5, model galaxy spectra are used to interpret our results in terms of $W(\\rm Ly \\alpha)$, surface brightness evolution etc. \nIn Section 6, colour-selection is used to identify other possible $\\rm Ly\\alpha$ emitters. In Section 7 we discuss\nour results concerning the morphology, environment and evolution of CFg, the\n$\\rm Ly\\alpha$ properties of high-redshift galaxies in general, and possible future observations.\n\n\\section{Observations}\n\\subsection{Data}\nWith the HST WFPC2, a field centred on RA $01^h03^m8.4^s$, Dec. $+13:16:40$ (equinox 2000.0) - to include both the CFg and the QSO PHL 957 -- \nwas observed through 3 filters.\nThe F410M observations consist of 32 ($4\\times 1200$ sec and $28\\times$ 1300 sec) exposures (41.2 ksec total) obtained during\n16 HST orbits on 3 and 5 December 1998. The F555W and F814W (wide-band) observations were made during 5 HST orbits on 16 January 1999, and consist of $2\\times 1200$ sec and \n$4\\times 1300$ sec exposures (7.6 ksec total) in F555W (hereafter $V_{555}$) and $4\\times 1300$ sec (5.2 ksec total) in F814W (hereafter $I_{814}$, the standard WFPC2 $I$-band). \n\n\\subsection{Filters}\nFigure 1 shows the response curves for the three, non-overlapping filters of our observations, together with a low-resolution ($\\rm FWHM\\simeq 24\\AA$) CFg spectrum obtained in a 3423 sec exposure with the MMT (Lowenthal et al. 1991).\nFigure 2 shows the $\\rm Ly\\alpha$ line on a medium-resolution ($\\rm FWHM\\simeq 2.6\\AA$) 3350 sec MMT spectrum, with the F410M curve overplotted. Evidently, the strong $\\rm Ly\\alpha$ line will dominate the flux observed through F410M, while the broad-band filters sample a relatively featureless UV continuum. \n At the CFg redshift of $z=2.3128$, the FWHM ranges of the filters are 1206--$1261\\rm \\AA$ for F410M, 1348--$1828\\rm \\AA$ for F555W and 2137--$2909\\rm \\AA$ for F814W. The $\\rm Ly\\alpha$ line will lie within the FWHM of F410M for sources at $2.286<z<2.436$. \n\\begin{figure}\n\\psfig{file=resp.ps,width=95mm}\n\\caption{Response curves for the F410M (left,dotted), F555W (centre, short-dash) and F814W (right, long-dash) filters, together with the low-resolution MMT spectrum of the CFg (Lowenthal et al. 1991), here shown slightly smoothed.}\n\\end{figure}\n\\begin{figure}\n\\psfig{file=gal_line.ps,width=95mm}\n\\caption{Medium-resolution spectrum of the $\\rm Ly\\alpha$ line of the CFg\n(Lowenthal et al. 1991), unsmoothed, with the F410M response curve (dotted).}\n\\end{figure}\n\n\\subsection{Data Reduction}\n\nData reduction was carried out using the {\\sevensize IRAF} package with some additional routines. We received \nthe data, already debiased, flat-fielded and calibrated, for the 42 individual\nexposures.\n\n The first problem was the removal of the large numbers of cosmic rays\nfrom the images. For this purpose we used the `nukecr' {\\sevensize IRAF} \nroutine developed by Luke Simard specifically for HST data. This generates a median-filter smoothed image from the pair of exposures from each HST orbit, and detects cosmic rays as pixels discrepant from this by more than a pre-set threshold. Pixels within 0.2 arcsec of each cosmic ray detection, in both exposures of the pair, are then replaced by the correponding pixels from the smoothed image.\nWith a careful choice of thresholds, it was possible to completely remove the majority of visible cosmic rays and reduce the others to a few pixels, with no effect on the photon counts from the real stars and galaxies.\n\n WFPC2 images consist of 4 chips (c1--c4), each with $800\\times 800$ pixels, with the pixel size 0.0996 arcsec on c2--c4 and 0.0455\narcsec on c1 (the PC). The PC data proved to be of poorer signal-to-noise and hereafter we are concerned only with c2--c4. The pixel size of these chips undersamples the point-spread function (PSF), but when stacking a large number of slightly offset exposures, it is possible to regain much of the `lost' resolution by first rebinning all images into a smaller pixel grid.\n\nDuring the observations, the WFPC2 field centre was shifted by 1 or 2 arcsec between each orbit (dithering) so as to minimize the effects of bad pixels on the stacked images.\nThese positional offsets were measured to $< 0.01$ arcsec accuracy using the cross-correlation technique of {\\sevensize IRAF} `precor', `crossdriz' and `shiftfind'. \nWith the {\\sevensize IRAF} `drizzle' routine, all exposures (together with their data quality files) were rebinned by a factor 0.42, into 0.0418 arcsec pixels, \nand simultaneously positionally registered using our measured offsets. \n\nIn each passband, the drizzled exposures are then stacked using {\\sevensize IRAF} `imcombine'. At each pixel position, counts discrepant by chosen thresholds (approximately $2.5\\sigma$) from the median of the stack, and those\n from `bad pixels' as listed in the data quality files, are rejected from the\naveraging. This `sigclip' rejection was effective in removing almost all of the remaining cosmic ray contamination from the combined F410M and F555W data. It was less effective in F814W, where there were only 4 exposures, so the combined F814 image was further cleaned \n using {\\sevensize IRAF} 'cosmicrays'. Again, we checked that these procedures\n did not remove any of the signal from the real objects. \n \n\\subsection{Source Detection and Photometry}\n\n\nSources on the combined images were detected and catalogued using the most recent version of SExtractor (Bertin and Arnauts 1996), which begins by fitting a sky background and estimating the sky noise $\\sigma_{sky}$. We chose \na detection criterion of $\\geq 2\\sigma_{sky}$ above the background in $\\geq 16$ contiguous pixels, with a Gaussian 2.5 pixel FWHM filter. The contrast threshold for source deblending was set to a relatively high 0.1.\n\n \n\n Photometric zero-points are derived from the \n`photflam' parameters in the image headers, multiplied by $\\lambda_{pivot}^2$\nto convert from $F_{\\lambda}$ to $F_{\\nu}$. Throughout this paper (unless stated otherwise) all magnitudes are given in the AB system, in which the magnitude for any passband is \n\n$m_{AB}=-2.5~{\\rm log}_{10}~F_{\\nu}-48.60$,\n\n where \n$F_{\\nu}$ is flux in units ergs $\\rm s^{-1} cm^{-2} Hz^{-1}$. The stacked images are normalized to the mean exposure time of 1287.5, 1266.7 and 1300.0 sec in F410M, F555W and F814W respectively. One count on these images then corresponds to $m_{410}=27.273$, $V_{555}=30.315$ and\n$I_{814}=29.864$. \nOn the basis of these zero-points the mean sky brightness is $m_{410}=23.20$,\n$V_{555}=21.95$ and $I_{814}=21.49$ mag $\\rm arcsec^{-2}$ and our surface brightness detection thresholds ($2\\sigma_{sky}$) are $m_{410}=23.55$,\n$V_{555}=24.71$ and $I_{814}=24.17$ mag $\\rm arcsec^{-2}$.\n\nSExtractor detected \na total of 71 sources on the 3 chips of the F410M data, 411 in $V_{555}$ and 491 in $I_{814}$. For each detection, \nSExtractor gives fluxes in circular apertures of fixed diameter (here 2.0 arcsec) and `Kron' fluxes (in elliptical apertures fitted to each object), and converts these to magnitudes using the photometric zero-points.\n\n \\section{The Nature of the Coup Fourr\\'{e} Galaxy}\n\\subsection{General Appearence}\nThe CFg lies at $z=2.3128$, where for $q_0=0.05$ and $H_0=50h_{50}$ km $\\rm s^{-1} \nMpc^{-1}$ (assumed throughout the paper) , 1.0 arcsec is $12.2 h_{50}^{-1}$ kpc. In F410M\nit is detected as one of the brighter sources on chip 3, at a position which the astrometry supplied with the WFPC2 data \ngives as RA $01^m03^m8.45^s$ Dec. $+13:16:41.42$, close to the spectroscopy position of RA $01^m03^m8.43^s$ Dec. $+13:16:39.61$ from Lowenthal et al. (1991) (converted to equinox 2000.0).\n\n\n\nWith SExtractor, the CFg is a $\\sim 14.5\\sigma$ significance detection in F410M, with $m_{410}=23.18\\pm 0.07$ in a 2 arcsec diameter aperture. It is clearly extended, with a Gaussian FWHM of 0.70 arcsec compared to 0.14 arcsec for the point-spread function (PSF), and elongated (ellipticity of 0.402). On the broad-band images, it is detected with aperture magnitudes $V_{555}=23.80\\pm 0.03$ and $I_{814}=23.48\\pm 0.03$, and appears\nsimilar in size. \n\n To best estimate the colours of the $\\rm Ly\\alpha$ emitting galaxy, SExtractor is run in a `double-image mode' whereby detection and Kron aperture-fitting are performed in F410M, but fluxes measured from the corresponding pixels of the F555W and F814W images. \nComparing the Kron magnitudes from this method gives $m_{410}-V_{555}=-0.56\\pm 0.08$ and \n$V_{555}-I_{814}=0.36\\pm 0.01$, consistent with the colours from the larger circular apertures.\n\\begin{figure}\n\\psfig{file=cgL_rot.eps,width=95mm}\n\\caption{ Contour plot of the $2.1\\times 2.1$ arcsec area centred on CFg\nin F410M, with contours linearly spaced in flux from the $2\\sigma_{sky}$ detection threshold to the peak intensity. Plot is oriented N at the top, E at the left.}\n\\end{figure}\n\\begin{figure}\n\\psfig{file=cgV_rot.eps,width=95mm}\n\\caption{As Figure 3, in F555W.}\n\\end{figure}\n\\begin{figure}\n\\psfig{file=cgI_rot.eps,width=95mm}\n\\caption{As Figure 3, in F814W.}\n\\end{figure}\nFigures 3, 4 and 5 show contour plots of the CFg in the three passbands. On chip 3 North is $71.7^{\\degr}$ anticlockwise of the y-axis, but these plots are rotated to show North at the top and East at the left.\nThe CFg is seen to consist of two similarly-sized and elongated components within a\ncommon envelope, of which the northwestern \n(hereafter CFgA) is the more prominent in F410M, whereas in $V_{555}$ and $I_{814}$ the southeastern (hereafter CFgB) has the higher surface brightness.\n\\subsection{Surface Brightness and Colour Profiles}\nThe profile of CFg is investigated using the {\\sevensize IRAF} `isophote' package, which fits the isophotes surrounding a chosen intensity peak with a series of concentric ellipses. We first fit isophotes to the F410M profile, which is peaked at the CFgA nucleus, and show on Figure 6 the mean surface brightness of the F410M isophotes as a function of semi-major axis. \n\\begin{figure}\n\\psfig{file=Lprof.ps,width=89mm}\n\\caption{F410M surface brightness (above sky background) of isophotes centred on the CFgA nucleus, as a function of semi major axis, with the best-fitting exponential (dotted) and bulge (short-dashed) profiles, and the PSF normalized to the same total flux as CFg (long-dash).}\n\\end{figure}\n\n Figure 6 also shows the profile given by applying the same analysis to the F410M PSF at the CFg position, as simulated using the `Tinytim' package (Krist 1995).\nThe observed FWHM of the CFg is $\\sim 5$ times that of the PSF, so estimation of the galaxy size from the observed profile should (on the basis of subtracting the FWHM in quadrature) overestimate by only $\\sim 2$ per cent. Hence we neglect the effect of the PSF, and quantify the galaxy size by fitting (by the least-squares method) the observed relation of surface brightness ($\\mu$, in mag $\\rm arcsec^{-2}$) to semi-major axis ($r$) with (i) an exponential (disk) profile\n$$\\mu=\\mu_0~{\\rm exp}(-r/r_{exp})$$\nand (ii) a bulge (elliptical) profile\n$$\\mu=\\mu^b_0~{\\rm exp}(-7.688[r/r_e]^{0.25}).$$ \n\\begin{figure}\n\\psfig{file=colprofile.ps,width=91mm}\n\\caption{Mean $m_{410}-V_{555}$ (above) and $V_{555}-I_{814}$ (below) colours (AB system) on the F410M isophotes of the CFg.}\n\\end{figure}\n\n As the closely-spaced isophotes and the resampled pixels are non-independent, the $\\chi^2$ of the fits will be overestimates, and we instead quantify the goodness of fit in terms of the rms residual in magnitudes. The F410M profile is fitted at 28 isophotes in the range $0.063\\leq r\\leq 0.83$ arcsec.\n\\onecolumn\n\\begin{figure}\n\\psfig{file=profAB.ps,width=180mm}\n\\caption{Surface brightness as a function of semi-major axis, for isophotes fitted in F410M (top), F555W (mid) and $I$ (lower) to CFgA (left) and CFgB (right), with the other component masked out. The higher signal-to-noise of the broad-band images allows isophotes to be fitted to larger radii. The dotted and dashed lines show the exponential and bulge profiles best-fitting each observed profile.}\n\\end{figure}\n\\twocolumn\nThe exponential fit gives $\\mu_0=21.73$ and $r_{exp}=0.27$ arcsec, with rms\nresiduals 0.16 mag. The bulge fit gives $\\mu^b_0=19.90$ with an implausibly large $r_e$ (as typically results from attempting to fit a disk galaxy with a bulge profile) of 17.99 arcsec and much larger residuals of 0.48 mag. \n\nFirstly, the CFg profile is evidently closer to an exponential than to a bulge, although it shows a `bump' at $r\\simeq 0.3$ arcsec produced by the fainter (in F410M) CFgB nucleus. \nSecondly, there is\nno indication of any central point-source of $\\rm Ly\\alpha$ emission in excess of the exponential profile. Any point-source would have to be $>2$ mag fainter than the underlying galaxy so as not to produce a visible ($\\geq 0.3$ mag) turn-up in the profile at $r<0.15 $ arcsec. \n\nUsing `isophote', we measure the mean $V_{555}$ and $I_{814}$ surface brightness on the fitted F410M isophotes, to obtain colour profiles (Figure 7).\nA colour $m_{410}-V_{555}\\simeq -0.7$ is seen at all radii from the CFgA nucleus out to $\\simeq 0.27$ arcsec, where the isophotes become significantly redder due to the contribution of CFgB.\nIn contrast, $V_{555}-I_{814}\\simeq 0.3$--0.4 over the whole galaxy, \nto $\\geq 0.7$ arcsec, and if anything the CFgB nucleus causes a slight bluening.\n\n\nThe marked bimodality of the surface brightness profile (even greater in the broad-bands), and the uniformity of $m_{410}-V_{555}$ within CFgA compared to the large CFgA/CFgB difference, imply that the CFg\nis a system of two distinct components, which might have very different properties, and might be best studied by \nconsidering CFgA and CFgB separately.\n\\subsection{The CFg as a Double System}\nRunning SExtractor with a lower contrast threshold for deblending of 0.005 demerges (in all three passbands) CFg into two detections, with the flux apportioned between CFgA and CFgB. Table 1 gives Kron magnitudes for the deblended CFgA and CFgB. In F410M, the centroids are separated by 0.335 arcsec, with CFgB \n0.224 arscec south and 0.249 arcsec east of CFgA. To estimate colours, \nSExtractor is used in the double-image mode to measure the magnitudes of the deblended components in F410M-fitted Kron apertures. Absolute magnitudes are estimated in Section 5.3.\n\n\\begin{table}\n\\caption{Kron magnitudes for the two deblended components of the CFg, and colours measured in Kron apertures fitted in F410M.}\n\\begin{tabular}{lccccccc}\n\\hline\n & CFgA & CFgB \\\\\n\\hline\n $m_{410}$ & $23.50\\pm 0.08$ & $24.63\\pm 0.14$\\\\\n $V_{555}$ & $24.67\\pm 0.04$ & $24.34\\pm 0.03$\\\\ \n $I_{814}$ & $24.24\\pm 0.04$ & $24.08\\pm 0.04$\\\\\n$m_{410}-V_{555}$ & $-0.74\\pm 0.08$ & $0.05\\pm 0.14$ \\\\\n$V_{555}-I_{814}$ & $0.43\\pm 0.01$ & $0.22\\pm 0.01$\n \\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\n\nThe surface brightness profiles of CFgA and CFgB are investigated individually, using `isophote', by centering the isophotes on the centroid position of one component\nand masking out the area covered by the other (by eye, dividing approximately at the saddle-point). This analysis is repeated in all three passbands, fitting a new set of isophotes in each. Figure 8 shows the resulting profiles, with the best-fitting exponential and bulge models, and\nTable 2 gives the parameters of the best-fit profiles.\n\n(The $I$ band images are of slightly lower resolution, presumably as the number of exposures is too few for drizzling to effectively\nsample the PSF. This appears to cause a flattening of the $I$-band profiles at\n$r<0.08$ arcsec, so the two isophotes within this radius are excluded from the\n$I$-band model fits). \n\n\n\\begin{table}\n\\caption{Best-fitting exponential profiles (central surface brightness\n$\\mu_0$, scalelength ($r_{exp}$) and bulge-profiles (central surface brightness\n$\\mu_0^b$, effective radius ($r_e$) for CFgA and CFgB, as plotted on Figure 8, with the rms residuals ($\\sigma_{res}$) of each fit in magnitudes.}\n\\begin{tabular}{lccccccc}\n\\hline\nGalaxy & Band & \\multispan{3} \\hfil Exponential \\hfil & \\multispan{3} \\hfil Bulge \\hfil \\\\\n & & $\\mu_0$ & $r_{exp}$ & $\\sigma_{res}$ & $\\mu_0^b$ & $r_{e}$\n& $\\sigma_{res}$ \\\\\n\\hline\nCFgA & $m_{410}$ & 21.67 & 0.23 & 0.11 & 21.55 & 19.99 & 0.24 \\\\\nCFgA & $V_{555}$ & 22.18 & 0.20 & 0.12 & 19.63 & 5.00 & 0.30 \\\\ \nCFgA & $I_{814}$ & 21.61 & 0.20 & 0.17 & 18.97 & 4.69 & 0.37 \\\\\nCFgB & $m_{410}$ & 22.06 & 0.21 & 0.11 & 20.20 & 14.1 & 0.18 \\\\\nCFgB & $V_{555}$ & 21.53 & 0.13 & 0.41 & 17.59 & 0.84 & 0.17 \\\\\nCFgB & $I_{814}$ & 21.56 & 0.15 & 0.21 & 17.88 & 1.24 & 0.09 \\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\nThese profiles show that:\n\n(i) On the basis of its UV continuum (presumably from young, massive stars) morphology, CFgA is an exponential galaxy (i.e. most likely a disk) with consistent scalelengths in F555W and $I$, and no evidence for a significant bulge component or central point-source. The F555W $r_{exp}$ corresponds to \n2.42 $h_{50}^{-1}$ kpc.\n \n (ii) The F410M flux from CFgA follows an exponential profile of similar scalelength, indicating that the $\\rm Ly\\alpha$ emission closely traces the distribution of \nyoung stars.\n\n(iii) In contrast, the broad-band profiles of CFgB are closer to a bulge than an exponential, showing an obvious concavity not seen for CFgA. The $V_{555}$ bulge-model $r_{e}$ corresponds to 10.2 $h_{50}^{-1}$ kpc, although this will be an overestimate if there is also an exponential disk component.\n \n(iv) The F410M profile of CFgB appears closer to an exponential. Furthermore, CFgB appears smaller in F410M. One possibility is that CFgB is primarily a bulge galaxy with a relatively small\ndisk component, but only the disk is a $\\rm Ly\\alpha$ source. \n\n\n\n\\section{The QSO PHL 957 in F410M}\n\nThe QSO PHL 957, at $z=2.681$ is detected close to the RA $01^h03^m11.28^s$ Dec. $+13:16:16.95$ position (equinox 2000.0) of Bunker et al. (1995), originally from Hewitt and Burbridge (1987). It is \nthe brightest source on the F410M image, with an aperture magnitude $m_{410}=17.86\\pm 0.01$. It is saturated on our broad-band images, but through the F410M filter its peak intensity is only $\\sim 7$ per cent of the chip saturation level, allowing its profile to be studied.\n\nIn F410M, the QSO, with a Gaussian FWHM of $\\sim 0.18$ arcsec, is clearly point-source dominated, but it is possible that subtraction of a normalized PSF may reveal the underlying host galaxy, if it is sufficiently luminous\nat $\\lambda_{rest}\\simeq 1110\\rm \\AA$. Secondly, if the $\\rm Ly\\alpha$ absorbing cloud on the line-of-sight to the QSO contains a galaxy, it may be revealed close to the QSO position. \n\nTo investigate these possibilities, a model F410M WFPC2 PSF from `Tinytim' is resampled (drizzled) into the smaller pixels of our stacked data, registered (by cross-correlation) to the QSO position, and normalized to the same flux as the QSO within a 1.0 arcsec radius aperture. We then (i) subtract the normalized PSF from the image of the QSO and look for\nevidence of any extended structures in the residual, (ii) compare the QSO and PSF radial profiles, using `isophote'.\n\\begin{figure}\n\\psfig{file=qsominuspsf.eps,angle=90,width=95mm}\n\\caption{Greyscale plot of the $6.3\\times 6.3$ arcsec area centred on the QSO\n PHL 957 in F410M, after subtraction of a PSF normalized to the QSO intensity. No significant emission residuals are detected.}\n\\end{figure}\n\nFigure 9 shows a greyscale plot of the PSF-subtracted QSO image. There is an irregular ring pattern of positive and negative regions near the centre, but this may be due simply to slight differences beweeen the model PSF and that of our data (which will inevitably become less sharp in the process of combining exposures). There are also patches at the positions of the diffraction spikes (which appear to be slightly \nbrighter in the data than in the model PSF), but no obvious indications of any real galaxies. \n\nFigure 10 shows the radial profiles of the QSO and model PSF. The observed QSO profile is slightly flatter than the model at $r<0.12$ arcsec but otherwise very close to it at all radii, and both profiles have half-light radii of \n$\\simeq 3$ pixels $\\simeq 0.125$ arcsec.\nAgain, the QSO appears consistent with a pure point-source.\nHowever, the pixel-to-pixel noise in the background ($\\sigma$) is greatly increased near the QSO centre. Figure 10 also shows the pixel-to-pixel rms intensity variation, $\\sigma$, as a function of distance from the AGN, and for comparison, the surface brightness profile of CFgA. \n To be visible at $>2\\sigma$ against the PSF of the AGN, a host galaxy would require a surface brightness 1.5--2.0\nmagnitudes brighter than CFgA. Similarly, we estimate by eye that an image of the CFg, superimposed on the PSF-subtracted QSO, had to be increased in normalization by a factor of $\\sim 5$ before there is any visible sign of a galaxy.\n\\begin{figure}\n\\psfig{file=qsoprofile.ps,width=95mm}\n\\caption{F410M surface brightness as a function of semi-major axis, for the QSO\nPHL 957 (solid squares), the `TinyTim' model PSF for F410M (long-dashed) and \nthe CFg (open triangles). The dotted line shows the rms pixel-to-pixel intensity variation on the observed QSO profile.} \n\\end{figure}\n\n\n\nWe conclude that PHL 957 appears on our F410M image to be consistent with a pure point-source. However, a QSO host galaxy would need to be at least $\\sim 2$ mag brighter than CFgA at $r\\sim 0.2$--0.4 arcsec to be visible. At this upper limit, the $\\lambda\\simeq 1100\\rm \\AA$ luminosity of the host galaxy would still be exceeded by a factor $\\sim 20$ by the AGN. The host galaxies of radio-quiet QSOs are typically $\\sim 1$ mag above $L^*$ (McLure et al. 1999), so the \nnon-detection may not be unexpected. \n\nWe also find no visible emission from the intervening DLA. A few DLAs have identified optical counterparts, typically $\\sim 8$--16$h^{-1}_{50}$ kpc from the QSO (M\\o ller and Warren 1993; Fynbo et al. 1999), $\\sim 0.65$--1.3 arcsec at the CFg redshift, although these examples differ from the DLA under consideration in that their absorption is at the same redshift as the QSO.\nAny galaxy of similar surface brightness to the CFgA would become visible if centred $>0.45$ arcsec from the AGN. If offset by 0.65--1.3 arcsec, it would have to be fainter than CFgA to avoid detection, by as much as $\\sim 2 $ mag towards the upper limit of this range. Any galaxy at the centre of the DLA must therefore be compact and almost concentric with the QSO, or of a relatively low surface brightness in the rest-frame UV (see Section 7.3). \n\n\\section{Galaxy Colours and ${\\rm Ly}\\alpha$ Emission}\n\\subsection{Expected Equivalent Widths}\nStar-forming galaxies produce $\\rm Ly\\alpha $ emission primarily from circumstellar HII regions, excited by Lyman continuum ($\\lambda<912\\rm \\AA$) UV from the hottest ($T_{eff}>30000$K) and most massive stars. In the absence of absorption or scattering, the fluxes in both $\\rm Ly\\alpha$ and the underlying continuum approximately follow the\nimmediate star-formation rate, and hence the equivalent width $W(\\rm Ly\\alpha)$ would be relatively insensitive to star-formation history. Charlot and Fall (1993) predict $W(\\rm Ly\\alpha)$ to decrease during the first $\\sim 30$ Myr of star-formation, but thereafter remain approximately constant in a steadily star-forming galaxy. \n\nThe Bruzual and Charlot `bc96' models (e.g. Charlot, Worthey and Bressan 1996), which assume a Salpeter IMF and \n neglect the effect of dust, predict $W(\\rm Ly\\alpha)\\simeq 100\\AA$\nfor all steadily star-forming galaxies of age $>0.1\\rm Gyr$, increasing to\n$W(\\rm Ly\\alpha)\\simeq 150$--$\\rm 300\\AA$ only in the initial $\\sim 12$ Myr.\nThe `Pegase' models of Fioc and Rocca-Volmerange (1997) incorporate observationally-based dust extinction and a steeper IMF at $M>6M_{\\odot}$, and therefore predict a lower $W(\\rm Ly\\alpha)$. They assume that 70 per cent of Lyman continuum photons are absorbed by the nebulae, and thus may be re-radiated as $\\rm Ly\\alpha$. Their template spectra give $W(\\rm Ly\\alpha)\\simeq 32\\AA$ -- where $W(\\rm Ly\\alpha)$ is defined relative to the continuum at $1165<\\lambda<1265\\rm \\AA$ -- for steadily star-forming galaxies of age $>0.1$ Gyr. As in the `bc96' models, $W(\\rm Ly\\alpha)$ \nincreases by factors 2--4 in the very early ($<12$ Myr) stages of star-formation.\nLastly, the low-metallicity Salpeter IMF models of Kudritzki et al. (2000) predict, with 70 per cent Lyman continuum absorption, upper limits (i.e. with no extinction of $\\rm Ly\\alpha$) of $W(\\rm Ly\\alpha)\\simeq 160\\AA$ for a 3 Myr \nstarburst and $W(\\rm Ly\\alpha)\\simeq 75\\AA$ for continuous star-formation.\n \nObservationally, some local star-forming galaxies with $\\rm [O/H]<-0.8$ solar show emission of $W(\\rm Ly\\alpha)=30$--$120\\rm \\AA$ \n (Hartmann et al. 1988; Charlot and Fall 1993; Giavalisco et al. 1996). Significantly, the DLA the CFg is associated with is below this abundance threshold (Wolfe et al. 1994). In more metal-rich galaxies, $W(\\rm Ly\\alpha)<30\\rm \\AA$ \nand may be decreased to zero. The situation at high redshifts may be similar;\n Steidel et al. (1999) estimate only 20--25 per cent of star-forming Lyman break galaxies at $z\\simeq 3.09$ have $W(\\rm Ly\\alpha)> 20\\rm \\AA$, and Lowenthal et al. (1997) detect $\\rm Ly\\alpha$ emission in only 6/13 $z\\sim 3$ galaxies, with these giving a relatively moderate $W(\\rm Ly\\alpha)=6.2$--$\\rm 34.1\\rm \\AA$.\nIt appears that for real star-forming galaxies, the moderate $W(\\rm Ly\\alpha)$ of the Pegase models may be typical, but there is a very wide range in $\\rm Ly\\alpha$ properties, perhaps with the `bc96' models approximating an upper limit.\n\n\n\\subsection{Model Galaxy Colours}\nFioc and Rocca-Volmerange (1997) present a set of template spectral energy distributions (continuum and emission-line fluxes) produced using their Pegase models, to fit the observed spectral properties of 8 types of present-day galaxy. Model galaxy SEDs are given at 68 time steps of evolution. \nUsing the `Pegase' template SEDs and the response functions of our 3 filters,\nwe model the observer-frame $m_{410}-m_{555}$ and $m_{F555}-I$ colours of the evolving galaxies. For the assumed cosmology, the redshift of observation ($z=2.3128$) of the CFg corresponds to a lookback time 13.226 Gyr. \n\\begin{figure}\n\\psfig{file=bvcol.ps,width=95mm}\n\\caption{Observed $m_{410}-V_{555}$ as a function of redshift for Pegase \nmodels of passive galaxies (long-dash), E and S0 galaxies (short-dash, upper and lower), Sa/Sb/Sc/Sd and Im spirals (solid, top to bottom), and a 1 Gyr age starburst (dotted) galaxy. Also shown are the Sa model with $W(\\rm Ly\\alpha)$\nreduced to zero (dot-short dash) and the Im model with $W(\\rm Ly\\alpha)$\nincreased to $108\\rm \\AA$ (dot-long dash).}\n\\end{figure} \n\nIn the reddest model (`Passive')\nconsidered here, galaxies begin \nstar-formation 16 Gyr ago, at $z=6.36$, and cease \n1 Gyr later at $z=4.04$, thereafter evolving passively. In other models the SFR decreases in an approximately exponential fashion with timescales lengthening from E to Im. The E and S0 models form 16 Gyr ago, the Sa, Sb, Sbc, Sd and Im models 15 Gyr ago. We also compute a Burst model in which the SED of a 1.0 Gyr age constant-SFR burst is redshifted without evolving, to represent the bluest locally observed galaxies (e.g. Gronwall and Koo 1995). \n\n\nThe F410M flux is computed in two separate parts, (i) the $\\rm Ly\\alpha$ contribution from the product of the Pegase model $\\rm Ly\\alpha$ flux and the filter response function at its redshifted wavelength, and (ii) the integration of the continuum over F410M.\nFigure 11 shows the predicted $m_{410}-V_{555}$ as a function of redshift.\nAt $z\\sim 2.3$--2.4, all the models (except the $W(\\rm Ly\\alpha)=0$ Passive model) have $W(\\rm Ly\\alpha)\\simeq 32\\rm \\AA$, which produces a blueward shift in $m_{410}-V_{555}$. An Sa model with $W(\\rm Ly\\alpha)$ set to zero (shown on Figure 11) becomes redder by 0.46 mag at the CFg redshift and 0.56 mag at $z=2.38$.\nAlso included is the contribution of the [OII]$3727\\rm \\AA$ line, which is redshifted through F410M at $z\\sim 0.1$, but its effects are small, $\\Delta(m_{410}-V_{555})=-0.16$ mag\nmag for starbursts and $-0.10$ mag for spirals, and star-forming galaxies at this redshift remain redder than those at $z>1$.\n\nNone of these models approach the extremely blue colour of CFgA. However, a\nlow-metallicity, dust-free `bc96' model predicts $W(\\rm Ly\\alpha)=108\\rm \\AA$\nfor a constant-SFR galaxy at $z\\sim 2.3$, and is represented on Figure 11 as the Pegase \nIm (i.e. a near-constant SFR) model with $W(\\rm Ly\\alpha)$ increased to $108\\rm \\AA$. This gives $m_{410}-V_{555}=-0.84$ at the redshift of CFgA and hence could account for its colour. \n\\begin{figure}\n\\psfig{file=vicol.ps,width=89mm}\n\\caption{Observed $V_{555}-I_{814}$ as a function of redshift for Pegase \nmodels of passive galaxies (long-dash), E and S0 galaxies (short-dash, upper \nand lower), Sa/Sb/Sc/Sd and Im galaxies (solid, top to bottom), and a 1 Gyr age starburst (dotted).}\n\\end{figure} \n\nFigure 11 shows that firstly, at $z\\simeq 2.3$--2.4, $m_{410}-V_{555}$ is much more sensitive to $W(\\rm Ly\\alpha)$ \nthan to star-formation history (over the range from Sa to Burst models). Secondly, while starburst galaxies at $0.8<z<2.3$ may be as blue as $m_{410}-V_{555}\\sim -0.05$, any galaxy with $m_{410}-V_{555}< -0.2$ is likely to be a strong $\\rm Ly\\alpha$ emitter at $2.27<z<2.44$, and it should be possible to use this colour criterion to select for these (Section 6.1). \n\nFigure 12 shows the $V_{555}-I_{814}$ colours of the models. At $z\\sim 2.3$ the star-forming models lie in the\n$V_{555}-I_{814}=-0.1$--0.25 range, but in real galaxies dust extinction may produce larger variations. This colour will give an indication of the star-formation history and/or dust extinction of candidate $\\rm Ly\\alpha$ sources, and thus help to refine estimates of $W(\\rm Ly\\alpha)$.\n\n\n\n\\subsection{Interpreting the CF Galaxy Colours}\nWe measured \n$m_{410}-V_{555}=-0.74\\pm 0.08$ and $V_{555}-I_{814}=0.43\\pm 0.01$ for CFgA and \n$m_{410}-V_{555}=0.05\\pm 0.14$ and $V_{555}-I_{814}=0.22\\pm 0.01$ for CFgB. These are now interpreted by comparison with the Pegase template spectra. \n\nAssuming CFgA to be a rapidly star-forming disk galaxy, the most appropriate Pegase model is probably a late-type spiral or Im.\nThe $m_{410}-V_{555}$ is consistent with the Im model with\n$W(\\rm Ly\\alpha)=93\\pm 11\\rm \\AA$, but the $V_{555}-I_{814}$ is much redder than the Im and spiral models. Bunker et al. (1994) detected the $\\rm H\\alpha$ emission line of the CFg and estimated that the $\\rm Ly\\alpha/H\\alpha$ ratio is reddened by 1.27 ($\\pm 0.3$) mag relative to a dust-free starburst. Assuming the Calzetti et al.(1995) extinction law, this is $A_V\\simeq 0.49$ mag and when added to the Pegase spiral models at $z=2.3$, gives reddening of $\\Delta(m_{410}-V_{555})\\simeq 0.26$ mag and $\\Delta(V_{555}-I_{814})=0.33$ mag.\nThe `dereddened' colours of CFgA are then $m_{410}-V_{555}\\simeq -1.00$ and $E(V_{555}-I_{814})=0.10$, corresponding to the Sc model with \n $W(\\rm Ly\\alpha)=151\\pm 16\\rm \\AA$.\n\nFor CFgB, the measured colours are consistent with the unmodified Pegase Sa model, with $m_{410}-V_{555}$ best-fit by \n$W(\\rm Ly\\alpha)=33\\pm 13\\rm \\AA$.Combining these estimates for the two components, weighted by $m_{410}$, gives $W(\\rm Ly\\alpha)=120\\pm 17\\rm \\AA$ for the whole CFg, consistent with the \n $W(\\rm Ly\\alpha)\\simeq 140\\rm \\AA$ estimated (Lowenthal et al. 1991) from the MMT spectrum. \n\nThe observed and model colours can also be used to estimate the $\\rm Ly\\alpha$ luminosities. If CFgA is represented by the Sc model with 0.26 mag of additional reddening, and CFgB by the Sa model, models with $W(\\rm Ly\\alpha)$ set to zero predict $m_{410}-V_{555}=0.60$ and 0.51, respectively, at $z=2.3128$.\nThe observed colours indicate that 70.9 per cent and 34.5 per cent of their respective F410M fluxes are $\\rm Ly\\alpha$, rather than continuum. The $\\rm Ly\\alpha$ components of their \nF410M magnitudes are then $m_{410}=23.87\\pm 0.08$ for CFgA and $25.78\\pm 0.14$\nfor CFgB, equivalent to \n$10.3\\times 10^{-30}$ and $1.77\\times 10^{-30}$ ergs $\\rm s^{-1}cm^{-2}Hz^{-1}$ averaged over the bandwidth.\n\n The restframe photometric bandwidth in frequency units is $c(1+z)\\Delta\\lambda/\\lambda_{pivot}^2$ -- where for F410M, $\\Delta\\lambda=93.73\\rm\\AA$ and $\\lambda_{pivot}=4092.7\\rm\\AA$ (from image header) -- giving $5.558\\times 10^{13}$ Hz. Multiplying, the $\\rm Ly\\alpha$ line fluxes are then $5.71\\pm 0.43\\times 10^{-16}$ ergs $\\rm s^{-1} cm^{-2}$ for CFgA and $0.984\\pm 0.127\\times 10^{-16}$ ergs $\\rm s^{-1}\ncm^{-2}$ for CFgB.\n This is consistent with the Lowenthal et al. (1991) estimates of \n$6.5\\times 10^{-16}$ (Fabry-Perot) and $5.6\\times 10^{-16}$ (MMT spectrograph) ergs $\\rm s^{-1} cm^{-2}$ for the whole source. For $q_0=0.05$, the $\\rm Ly\\alpha$ luminosities are\n$5.21\\times 10^{43}h_{50}^{-2}$ ergs $\\rm s^{-1}$ for CFgA and $8.99\\times 10^{42}$ ergs $\\rm s^{-1}h_{50}^{-2}$ for CFgB (this is discussed further in Section 7.1).\n \nLastly, the Pegase models can be used to estimate absolute magnitudes, e.g.\n$M_B$ in the rest-frame blue-band. At $z=2.3128$ the Sa model spectrum gives a k-correction $B_{rest}-I_{obs}=-0.05$ mag and the reddened Sc model, $B_{rest}-I_{obs}=-0.14$ mag. Adding the demerged Kron magnitudes of $I_{814}=24.24\\pm 0.04$ for CFgA and $I_{814}=24.04\\pm 0.04$ for CFgB, the distance modulus $-47.20+5~{\\rm log}~h_{50}$ and these corrections, we estimate $M_B=-23.10+5~{\\rm log}~h_{50}$ for CFgA and $-23.21+5~{\\rm log}~h_{50}$ for CFgB. Both components are approximately 2 magnitudes brighter than the present-day\n$L^*$. \n\n\\section{Other $\\rm Ly\\alpha$ Emitting Galaxies}\nOne aim of imaging the CFg field in narrow band and continuum filters was to identify other $\\rm Ly\\alpha$ emitters at the same redshift, and thus determine if the CFg is in a cluster of these sources. Pascarelle et al. (1998) found evidence of a concentration of $\\rm Ly\\alpha$ emitters near a high-redshift radio galaxy, and we would expect a local overdensity to be associated with a damped $\\rm Ly\\alpha$ cloud.\n \n\\subsection{Selection}\nThe models of Section 5.2 predicted that high $W(\\rm Ly\\alpha$) galaxies at $z\\sim 2.3$--2.4 would be identifiable by a colour\n$m_{410}-V_{555}<-0.2$. \nA total of 71 sources are detected on the three chips of the F410M image. As before, colours are measured from Kron magnitudes in apertures matched to the F410M detection. There are a total of 15, including the CFg, with $m_{410}=V_{555}<-0.2$, but the brightest two are PHL 957 and a bright star\n-- both saturated in F555W giving an unreliable colour -- and three of the faintest appeared to be spurious detections. Excluding these leaves the CFg and 9 fainter sources.\n\n\\begin{figure}\n\\psfig{file=bvkron.ps,width=95mm}\n\\caption{Observed $m_{410}-V_{555}$ for all F410M detections (from Kron magnitudes with detection in F410M), against $m_{410}$ magnitude. Filled symbols indicate the candidate $\\rm Ly\\alpha$ emitters. The CFg is plotted twice, as a single source and as the deblended galaxies.}\n\\end{figure} \n\n Table 3 gives the F410M magnitudes and colours of the candidate $\\rm Ly\\alpha$ emitters, numbered as `Lc:n' where c is the chip number and n the SExtractor detection number, and also the $I$ magnitudes in $I$-band fitted Kron apertures, which (if the sources are at $z\\sim 2.3$) indicate $\\lambda \\sim 2500\\rm \\AA$ luminosites ($\\sim$ mass of young stars) independent of the $\\rm Ly\\alpha$ properties. Figure 13 shows $m_{410}-V_{555}$ against $m_{410}$ for the candidate $\\rm Ly\\alpha$ emitters and the other F410M detections.\n\\begin{table}\n\\caption{The F410M magnitudes and colours (Kron, in F410M apertures), and $I_{814}$\nmagnitudes (Kron, measured in $I$ apertures) of \ncandidate $\\rm Ly\\alpha$ emitters at\n$z\\sim 2.3$--2.4 ($nd=$ not detected in $I$), with CFgA/B for comparison.} \n\\begin{tabular}{lcccc}\n\\hline\n\\smallskip\nSource No. & $m_{410}$ & $m_{410}-V_{555}$ & $V_{555}-I_{814}$ & $I_{814}$ \\\\\nL2:03 & 25.13 & $-0.22\\pm 0.20$ & 0.64 & 24.39 \\\\\nL2:09 & 25.19 & $-0.88\\pm 0.19$ & 0.12 & 25.99 \\\\\nL2:12 & 24.73 & $-0.21\\pm 0.14$ & 0.83 & 23.25\\\\\nL2:16 & 26.35 & $-1.27\\pm 0.31$ & -1.09 & nd \\\\\nL3:10 & 23.91 & $-0.24\\pm 0.09$ & 0.06 & 24.02\\\\\nL3:19 & 25.36 & $-0.26\\pm 0.21$ & 0.60 & 24.74\\\\\nL4:07 & 25.82 & $-0.31\\pm 0.23$ & -0.15 & 25.80 \\\\\nL4:11 & 24.90 & $-1.08\\pm 0.17$ & -0.04 & 25.74 \\\\\nL4:12 & 26.02 & $-0.42\\pm 0.28$ & 1.28 & 24.78 \\\\\nCFgA & 23.50 & $-0.74\\pm 0.08$ & 0.43 & 24.24 \\\\\nCFgB & 24.64 & $0.05\\pm 0.14$ & 0.22 & 24.08 \\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\nSource L2:12, which only just satisfies the colour criterion, is uncertain -- the F410M detection forms only part of a much larger, morphologically complex galaxy, the remainder of which is redder in $m_{410}-V_{555}$, and the large $I$-band FWHM of 1.68 arcsec may be implausible for an object at this redshift. It may be a lower redshift starburst galaxy. \nThe other 8 candidate sources have continuum sizes and magnitudes consistent with $z\\sim 2.3$ galaxies, and are definitely blue in $m_{410}-V_{555}$.\n\n\\subsection{Colours and Morphology}\n\n\nCFgA is $>0.4$ mag brighter in F410M than any of the candidate sources, and remains the most powerful $\\rm Ly\\alpha$ emitter in the field and redshift range of observation. The $I_{814}$ magnitudes of the candidate sources (excluding L2:12) range from 0.22 mag brighter to $>2$ mag fainter than CFgA; assuming a similar k-correction as for CFgA gives their mean absolute magnitude as\n $M_B\\sim -22.3$, $\\sim 1$ mag brighter than the present-day $L^*$.\n\nFigure 14 shows a colour-colour plot ($m_{410}-V_{555}$ against $V_{555}-I_{814}$), for\nthe F410M detections. Of the candidate $\\rm Ly\\alpha$ emitters, L3:10 and L4:07 lie only slightly below the Pegase models at $z=2.3128$, suggesting $W(\\rm Ly\\alpha)\\simeq 30$--$50\\rm \\AA$. \nFour sources (including L2:12) have $V_{555}-I_{814}>0.5$, and if genuinely at $z\\sim 2.3$ are probably dust-reddened and hence stronger $\\rm Ly\\alpha$ emitters than would be thought from their $m_{410}-V_{555}$ alone. \n\\begin{figure}\n\\psfig{file=bvi.ps,width=91mm}\n\\caption{Colour-colour plot of all F410M detections, with the CFg plotted as a single source and as two deblended galaxies. The long-dashed, short-dashed and solid lines represent the Pegase models as on Figures 11 and 12. The model galaxies follow these loci clockwise with increasing redshift, from $z=0$ to \n$z\\sim 3.5$. The heavy solid diagonal line connects the positions of the Pegase spiral models at $z=2.3128$, from Im (left) to Sa (right). The dot-dash diagonal line intersects an Im model with $W(\\rm Ly\\alpha)=108\\AA$ and follows the slope of the dust-reddening vector.} \n\\end{figure} \n\n The dot-dash line passes through the colours of an \nIm model with $W(\\rm Ly\\alpha)=108\\rm \\AA$ (the `bc96' prediction), and follows the slope of the dust-reddening vector, estimated as $\\Delta(m_{410}-V_{555})\\simeq 0.80 \\Delta(V_{555}-I_{814})$. Several candidate $\\rm Ly\\alpha$ emitters lie close to this line - one possible interpretation is that they (and the CFg) have rather similar\n $\\rm Ly\\alpha$ properties but dust reddening ranging from near-zero to $\\Delta(V_{555}-I_{814})\\sim 1$ mag. \n\n\\begin{figure}\n\\psfig{file=lyquiltL.eps,width=95mm}\n\\caption{Contour plots of $2.1\\times 2.1$ arcsec areas of the F410M image, centred on each of the 9 $\\rm Ly\\alpha$ candidates; (top, left to right) \nL2:03, L2:09, L2:12;(middle) L2:16, L3:10, L3:19; (bottom) L4:07, L4:11, L4:12).\nContours are linearly spaced, the lowest being $2\\sigma$ above the sky.}\n\\end{figure}\n \n\\begin{figure}\n\\psfig{file=lyquiltV.eps,width=95mm}\n\\caption{As Figure 15 in F555W.}\n\\end{figure}\n\n\nFigures 15 and 16 show contour plots of the 9 candidate $\\rm Ly\\alpha$ sources in F410M and F555W. Most have the typical appearence of Lyman-break objects or `chain galaxies' -- small bright nuclei and a number of secondary intensity peaks, presumably knots of star-formation, within\nan asymmetric outer envelope. They are generally more irregular than either component of the CFg, and appear to be single galaxies rather than interacting\npairs. They appear even more `knotty' in F410M than in the broad bands, as expected if the $\\rm Ly\\alpha$ emission is from multiple star-forming hotspots. However, L3:10, the brightest after CFgA, differs from the others in being a single-peaked, compact, high central surface brightness source in all 3 passbands. \n\nThe F410M sizes and central surface brightnesses of these sources are estimated by fitting exponential profiles to the F410M isophotes, determined using {\\sevensize IRAF} `isophote'. \n Table 4 gives the best-fit parameters, with our previous results for CFgA/B, and also gives the centroid positions as RA and Dec from WFPC2 astrometry, which is accurate to $<2$ arcsec for the absolute positions and will be much more precise than this for their relative positions. To aid in finding \nthe objects, we also give the position of the QSO PHL 0957, in the same \nco-ordinate system.\n\nSome objects, with multiple peaks, show large residuals from an exponential\nprofile, but none appear to\nbe bulge galaxies. The profile of L3:10 resembles the PSF, and subtracting a normalized PSF from its image appeared to leave no significant residuals. Hence L3:10 must be almost a pure point-source, and may be a QSO. The $r_{exp}$ of the other candidate sources are generally comparable to the CFgA. The brighter F410M magnitude of the CFgA is not the result of a larger size, but of a higher surface brightness, $>1$ mag above most of these galaxies. \n \n \\begin{table}\n\\caption{The RA and Dec positions (equinox 2000.0) from WFPC2 astronomy, best-fitting exponential\nscalelengths ($r_{exp}$, in arcsec) F410M central surface brightnesses ($\\mu_{410}$, in AB mag $\\rm arcsec^{-1}$), of candidate $z\\sim 2.3$--2.4 $\\rm Ly\\alpha$ emitters, with CFgA/B and PHL 957 for comparison. No corrections are applied for the PSF, which for a pure point-source gives $r_{exp}=0.063$ arcsec.} \n\\begin{tabular}{lcccc}\n\\hline\n\\smallskip\nSource & R.A. & Dec. & $r_{exp}$ & $\\mu_{410}$ \\\\\nL2:03 & $01^h 03^m 09.87^s$ & $13:16:38.84$ & 0.39 & 23.38 \\\\\nL2:09 & $01^h 03^m 09.88^s$ & $13:16:29.97$ & 0.31 & 22.86 \\\\\nL2:12 & $01^h 03^m 10.13^s$ & $13:16:19.77$ & 0.21 & 22.57 \\\\\nL2:16 & $01^h 03^m 12.86^s$ & $13:15:45.31$ & 0.09 & 22.38 \\\\\nL3:10 & $01^h 03^m 07.67^s$ & $13:16:30.61$ & 0.07 & 19.92 \\\\\nL3:19 & $01^h 03^m 05.55^s$ & $13:16:40.85$ & 0.35 & 22.99 \\\\\nL4:07 & $01^h 03^m 09.15^s$ & $13:17:17.24$ & 0.17 & 22.71 \\\\\nL4:11 & $01^h 03^m 10.17^s$ & $13:18:00.53$ & 0.39 & 22.79 \\\\ \nL4:12 & $01^h 03^m 06.88^s$ & $13:17:44.18$ & 0.23 & 22.93 \\\\\nCFgA & $01^h 03^m 08.45^s$ & $13:16:41.50$ & 0.23 & 21.67 \\\\\nCFgB & $01^h 03^m 08.47^s$ & $13:16:41.27$ & 0.21 & 22.06 \\\\\nPHL957 & $01^h 03^m 11.30^s$ & $13:16:17.99$ & 0.063 & 14.62 \\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\nFigure 17 shows the distribution of the candidate $\\rm Ly\\alpha$ sources on the field. They appear to be evenly distributed, without obvious clustering about CFg or any other position, and none are closely paired (except the two components of CFg). \n \n\n\\begin{figure}\n\\psfig{file=lposn.ps,width=90mm}\n\\caption{Distribution on the sky of the $\\rm Ly/alpha$ candidates (solid circles) and other F410M detections (open circles), with the CFg (solid square) and the QSO PHL 957 (asterisk). The three boxes show the observed areas (chips\n2, 3 and 4).}\n\\end{figure}\n\\section{Discussion}\n\\subsection{The CFg - a Starbursting Merger?}\nWe have investigated a $z=2.3128$ $\\rm Ly\\alpha$ emitting galaxy with high-resolution, deep WFPC2 imaging in narrowband $\\rm Ly\\alpha$ (F410M) and\nthe UV continuum (F555W and $I$). The galaxy, in all 3 passbands, is resolved into two components of similar size, CFgA and CFgB, with projected separation 0.335 arcsec ($\\sim 4.1 h_{50}^{-1}$ kpc). It is probable that the CFg is a merging pair of \ngalaxies. Firstly, both components are extended and moderately elongated; neither resembles a point source or jet that might just be a region of star formation in a single galaxy. Each component, investigated individually, shows the radial profile of a normal galaxy, CFgA being exponential while CFgB is closer to a bulge. Secondly, the two components differ in colour, CFgA being much bluer in $m_{410}-V_{555}$ but\nslightly redder in $V_{555}-I$, while the colours within each component are relatively uniform.\n\nFrom the narrowband magnitudes and colours of the deblended components, $m_{410}=23.50\\pm 0.08$ and $m_{410}-V_{555}=-0.74\\pm 0.08$ for CFgA, $m_{410}=24.64\\pm 0.14$ and $m_{410}-V{555}=0.05\\pm 0.14$ for CFgB, we estimate $\\rm Ly\\alpha$ luminosities of \n $5.21\\times 10^{43}h^{-2}_{50}$ ergs $\\rm s^{-1}$ for CFgA and $8.99\\times 10^{42}h^{-2}_{50}$ ergs $\\rm s^{-1}$ for CFgB.\n\nKennicutt (1983) found $L(\\rm H\\alpha)\\sim 1.12\\times 10^{41} \\times$ SFR ($\\rm M_{\\odot} yr^{-1})$ ergs $\\rm s^{-1}$ for spiral galaxies, where SFR is the total star-formation rate for a Salpeter IMF. For star-formation in the absence of dust, $L({\\rm Ly}\\alpha)\\simeq 8.3 L({\\rm H}\\alpha)$ (Osterbrock 1989, Bunker et al. 1995), so that the SFR would be $L(\\rm Ly\\alpha)/(9.296\\times 10^{41}$ ergs $\\rm s^{-1})$, giving 56.0 $h^{-2}_{50}\\rm M_{\\odot}yr^{-1}$ for CFgA and 9.7 $h^{-2}_{50}\\rm M_{\\odot}yr^{-1}$ for CFgB. Bunker et al. (1995) estimate that the $\\rm Ly\\alpha/ H\\alpha$ ratio of the CFg is dust-reddened by 1.27 mag, which corresponds to 1.56 mag of $\\rm Ly\\alpha$ extinction and increases the estimated SFR of CFgA to $\\sim 236 h^{-2}_{50} \\rm M_{\\odot} yr^{-1}$. \n\nThe SFR in CFgA is very high, as might be expected for a gas-rich disk galaxy at the peak of a merger-induced starburst (e.g. Mihos and Hernquist 1996; Read and Ponman 1998). In contrast, the $L(\\rm H\\alpha)$ of CFgB is consistent with a SFR in the range of normal spirals (Kennicutt 1983). One possible explanation is that the starbursts in the two galaxies peak at different times due to the bulge morphology of CFgB -- in simulations (e.g. Mihos and Hernquist 1996; Tissera 1999), the presence of a massive bulge delays the SFR maximum to a later stage of a merger.\n\n\n\n\\subsection{Surface Brightness Evolution}\nWe fitted radial profiles to both components in all three passbands, and \nestimated rest-frame blue-band absolute magnitudes from the broad-band magnitudes and Pegase model spectra. These two measurements provide an estimate of the surface brightness evolution, independent of the $\\rm Ly\\alpha$ properties, and of $q_0$ and $H_0$.\n The size-luminosity relations for local \ngalaxies, from Roche et al. (1998) with $B_{Vega}=B_{AB}+0.077$, are\n$${\\rm log}~r_{hl}=-0.2M_B-3.235$$ for spirals (derived from Freeman 1970) and $${\\rm log}~r_{e}=-0.3M_B-5.594$$ for ellipticals (from Binggeli, Sandage and\nTarenghi 1984). \n\nFor CFgA, best-fitted by a pure exponential profile, we estimate $r_{exp}=2.42\nh_{50}^{-1}$ \nand $M_B=-23.10 +5~{\\rm log}~h_{50}^{-1}$.\nFor an exponential profile $r_{hl}=1.68 r_{exp}= 4.07h_{50}^{-1}$ kpc for CFgA, and for a local spiral of this size $M_B=-19.22+5 {\\rm log}~h_{50}$. \nThis observed luminosity is greater by 3.88 mag or a factor 35.6.\nThis surface brightness evolution exceeds the evolutionary brightening of the Pegase spiral models , e.g. $\\Delta(M_B)=-0.75$ mag for Sc and $-1.80$ mag for Sa galaxies from $z=2.3128$ to\n $z=0$, but is consistent with a 1 Gyr starburst ending at $z\\sim 2.3$, which would subsequently fade by 3.98 mag.\nHence the continuum surface brightness of CFgA, like the $\\rm Ly\\alpha$ luminosity, implies that the SFR greatly exceeds the time-averaged rate and that an intense short-term burst is occurring. \n\nLyman break galaxies tend to be small in size but very high in surface brightness. Roche et al.(1998) estimated that the rest-frame blue surface brightness of 16 Hubble Deep Field galaxies at $2.26<z<3.43$ averaged $2.79\\pm 0.31$ mag higher than $z<0.35$ galaxies, with $\\sim 1$ mag dispersion. Lowenthal et al. (1997) found the mean $r_{hl}$ of $z\\sim 3$\nLyman break galaxies to be 3.6 kpc with $M_B$ ranging from -21.6 to -23.1. The surface brightness of CFgA is still a factor $\\sim 2$\nhigher than the average for Lyman break galaxies (in these flux-limited samples), and near the maximum of the\nobserved range. Again, this is most likely the result of a particularly luminous merger-triggered starburst.\n\n\nThe effective radius of CFgB was estimated as $10.2 h_{50}^{-1}$ kpc, from fitting a pure bulge (${\\rm exp}~ [r^{-0.25}]$) profile, and its absolute magnitude as $M_B=-23.20+5 {\\rm log}~h_{50}$. For a local elliptical of this size, $M_B=-22.01+5 {\\rm log}~h_{50}$, indicating surface brightness evolution of 1.21 mag. This is slightly less than predicted by the Sa model, but is a lower limit as the presence of any disk component would cause \n$r_e$ to be overestimated. The surface brightness of CFgB, like the $\\rm Ly\\alpha$ luminosity, suggests a more moderate evolution for this component, essentially consistent with the Pegase models.\n\n\\subsection{Environment of the CFg}\nModels predicted that $W(\\rm Ly\\alpha)>30\\rm \\AA$ sources at $2.27<z< 2.44$ would be separable from other star-forming galaxies by a colour $m_{410}-m_{555}<-0.2$. We used this colour criterion to search for other $\\rm Ly\\alpha$ emitters at the same redshift as the CFg, and found nine candidate sources (in addition to the CFg) to the faint limits of the F410M data. One (L2:12) is suspected to be a foreground galaxy. Of the other 8, it is not yet known which, if any, are physically associated with the CFg, and which are field galaxies distributed over \n$2.27<z<2.44$. To interpret these results in terms of the environment of the CFg, the total number of candidates must be compared with both random and known cluster fields. \n\n Pascarelle et al. (1998) imaged four fields with WFPC2 through F410M, F450W ($B$) and F606M ($V$) filters. The use of the same F410M filter means that $\\rm Ly\\alpha$ sources will be selected in exactly the same redshift range as in our observations. On a field containing the $z=2.4$ radio galaxy\n53W002, 17 galaxies were selected as $\\rm Ly\\alpha$ candidates, and \nspectroscopy confirmed that some of these did form a cluster with 53W002. \nThree randomly selected fields contained 3, 11 and 4 $\\rm Ly\\alpha$ candidates (it was thought the second of these had by chance contained a cluster). The F410M exposure times of these fields differed and all were shorter than for our image. To a common magnitude limit $B=25$, they give the numbers of candidates per field as 10, 1, 8 and 2, and we would (counting the CFg as one galaxy) find 4. \n\nOn this basis it seems that the CFg environment is likely to be less rich than that of 53W002. On the other hand, the number of $\\rm Ly\\alpha$ candidates in our field may still be about twice that expected from random fields. Detecting $\\rm Ly\\alpha$ emission is not a good estimator of cluster richness as, even if most cluster galaxies are star-forming at these redshifts, only a small and uncertain fraction will have strong $\\rm Ly\\alpha$ emission (Steidel et al. 1999). Mannucci et al. (1998) instead imaged the PHL 957 field through a $1.237\\rm \\mu m$ filter designed to detect redshifted $\\rm [OII]3737\\rm \\AA$,\ntogether with a broadband filter. This revealed two candidate [OII] sources, close to the CFg in both position and redshift, although just outside the area studied here. They would fall on the PC chip of our image, on which no $\\rm Ly\\alpha$ sources could be seen. Whether or not these galaxies are significant $\\rm Ly\\alpha$ emitters, the [OII] fluxes estimated by Mannucci et al. (1998) \ncorrespond to very high SFRs, similar to the CFg.\nTaking this and our findings into account it seems probable that the CFg does lie within some sort of high-redshift group or cluster, in which a large amount of star-formation is taking place.\n\nThe CFg is also known to be associated with a\nDLA cloud. We attempted, unsucessfully, to find the DLA optical counterpart on our F410M image. On the basis of previous observations (e.g. Fynbo et al. 1999; Djorgovski et al. 1995), it is most likely to lie close ($\\sim 1$ arcsec) to the QSO PHL 957, but due to the increased noise in this region of the data, the upper limits on its central surface brightness are relatively high -- about equal to CFgA 0.45 arcsec from the QS0 and $\\sim 2 $ mag fainter 1.3 arcsec from it. As CFgA is a particularly high surface brightness galaxy, these limits may allow a spiral or irregular galaxy to have formed in the cloud. The optical counterparts of high-redshift DLAs may typically be of low/moderate luminosity, e.g. the\n`S1' object discovered by M\\o ller and Warren (1998) at $z=2.81$ is fainter than the CFg, with $I_{AB}=25.3$, the $\\rm Ly\\alpha$ luminosities of DLAs so far detected are also lower than CFgA, and Fynbo et al. (1999) predict the majority of DLAs to be at $R>28$. \n\n\\subsection{The Lyman $\\alpha$ Properties}\n\\subsubsection{Comparison with other $Ly\\alpha$ Galaxies}\nWe estimate rest-frame $\\rm Ly\\alpha$\nequivalent widths of $W(\\rm Ly\\alpha)=151\\pm 16\\rm \\AA$ for CFgA and $W(\\rm Ly\\alpha)=33\\pm 13\\rm \\AA$ for CFgB. \nThe $W(\\rm Ly\\alpha)$ of CFgA is, on the basis of the Charlot and Fall (1993)\nmodels, close to the maximum possible for a non-AGN starburst, but is not\nunprecedented. The most obvious comparison is with the `G2' galaxy ($z=3.428$) described by \nGiavalisco at al. (1995), with $W(\\rm Ly\\alpha)=175\\pm 16\\AA$, an estimated SFR of 50--100 $M_{\\odot}\\rm yr^{-1}$, and a luminosity only slightly lower than the CFg,\n$M_B=-22.7$. This object differs markedly from CFgA in showing a compact\n($r_e=1.3$ kpc) bulge profile, but as in the CFg there is no evidence of a central point source. \n\nThe candidate $\\rm Ly\\alpha$ sources on our field are also of lower luminosity than CFgA, but in contrast to `G2', tend to be more irregular and of lower surface brightness (with the exception of the possible AGN, L3:10). Their colours suggest a wide $\\sim 30$--$150\\rm \\AA$ range of $W(\\rm Ly\\alpha)$, with a distribution approximately centred on a locus corresponding to\n$W(\\rm Ly\\alpha)\\sim 108\\rm \\AA$ and dust extinction $0<A_V<1.5$ mag. \nSimilarly, the 35 candidate $\\rm Ly\\alpha$ sources on the 4 fields of\n Pascarelle et al. (1998), at the same redshifts, have $m_{410}-B$ and $B-V$ consistent\nwith $W(\\rm Ly\\alpha)\\sim 20$--$180\\rm \\AA$ and extinction $0<A_V<2$ mag. These vary in size but most are smaller than either component of the CFg (28/35 have $r_{hl}<0.3$ arcsec).\n\nMalkan, Teplitz and McLean (1996) investigate by spectroscopy a $z=2.498$ galaxy\nwith a similar $W(\\rm Ly\\alpha)$ and luminosity to `G2', thought to be a \n$\\sim 100$ $\\rm M_{\\odot}\\rm yr^{-1}$ starburst with high dust extinction ($A_V\\sim 0.9$). Steidel et al. (1999) identify 15 $\\rm Ly\\alpha$ emitting galaxies at $z\\sim 3.09$, with W($\\rm Ly\\alpha)_{median}=67\\rm \\AA$, and a continuum luminosity function the same shape as for other Lyman break galaxies. \n At even higher redshifts, Dey et al. (1998) measure $W(\\rm Ly\\alpha)=95\\rm\\AA$ for a galaxy at $z=5.34$.\nKudritzki et al (2000) identify 9 $\\rm Ly\\alpha$ emitters at $z\\simeq 3.1$ in a narrow-band survey originally aiming to detect planetary nebulae, and confirm the redshifts by spectroscopy. These sources have $W(\\rm Ly\\alpha)\\simeq 33$--$175\\rm \\AA$ and $\\rm Ly\\alpha$ luminosities about 8--66 per cent that of CFgA.\nLastly, Taniguchi and Shoiya (2000) propose that the recently discovered large ($\\sim 100$ kpc) $\\rm Ly\\alpha$ nebulae are powered by primordial ellipticals, with starbursts which can exceed even CFgA in $\\rm Ly\\alpha$ luminosity. \n \nTogether, these results indicate that (i) a significant number of high redshift\nstar-forming galaxies have $W(\\rm Ly\\alpha)$ exceeding the $30\\rm \\AA$ of the Pegase models, and ranging up to an upper limit of\n$\\sim 150$--$180\\rm \\AA$, and (ii) these strong $\\rm Ly\\alpha$ emitters cover a wide range of luminosity, size, age and dust extinction and include both bulge and disk galaxies. The $W(\\rm Ly\\alpha)$ and luminosity of CFgA are near the upper limit of this distribution. \n\n\\subsubsection{Interpretation}\nAs many low metallicity and high-redshift star-forming galaxies reach $W(\\rm Ly\\alpha)\\sim 30\\AA$ (Hartmann et al. 1988; Lowenthal et al. 1997),\nthe moderately high SFR typical at these redshifts may be sufficient to explain the $\\rm \nLy\\alpha$ emission from CFgB. The much greater $W(\\rm Ly\\alpha)$ of CFgA and\nthe other sources discussed above cannot be explained by further reducing the dust -- many of these \nhave colours indicating they are more reddened than CFgB -- and there must be an additional property of galaxies influencing $\\rm Ly\\alpha$ emission. \n\n\nKunth et al. (1998) propose that the most important factor in determining the escape of $\\rm Ly\\alpha$ photons from star-formation is not the dust, but the velocity structure of the gas. Using high resolution spectroscopy, they found 4 of a sample of\n8 starburst galaxies, including the very low metallicity IZw18, showed only a broad absorption trough at the $\\rm Ly\\alpha$ wavelength. In the 4 with $W(\\rm Ly\\alpha) >0$, the trough is still present but shifted to the blue side of the emission line, producing an asymmetric `P Cygni' line profile.\nThis indicates a galactic wind, in which the neutral gas is outflowing at some hundreds of km $\\rm s^{-1}$ relative to the star-forming central regions. This velocity difference greatly reduces resonant scattering of the $\\rm Ly\\alpha$ photons, which would otherwise increase the effects of dust extinction and \nobscure the emission line.\n\nPettini et al. (1998) perform near-infra-red spectroscopy of 5 galaxies at $z\\sim 3$, of which 3 show $\\rm Ly\\alpha$ in emission. They also find evidence of high-velocity ($\\sim 500$ km $\\rm s^{-1}$)\nlarge-scale outflows, seen as a blueshifting of metal absorption lines and a \nredshifting of $\\rm Ly\\alpha$ relative to the H$\\beta$ and [OII] emission lines of the star-forming nebulae.\n \nTenorio-Tagle et al. (1999) develop a model of an instantaneous $10^6M_{\\odot}$ starburst that produces a rapidly expanding bubble inside a galactic disk.\nThey predict a sequence in which (a) at the start of the burst, $\\rm Ly\\alpha$ photons are trapped, \n(b) after $\\sim 2.5$ Myr the expanding bubble breaks throught the galactic disk, producing a cone of ionization through which most UV photons can escape, (c) at $\\sim 4$ Myr, recombination in the expanding shell produces a secondary $\\rm Ly\\alpha$ emission line, blueshifted with respect to the first, (d) at $>5$ Myr the ionization front becomes trapped behind the recombining shell and the secondary emission becomes an absorption trough, giving a P Cygni profile, (iv) at $>9$ Myr continuing recombination in the galaxy halo again cuts off the $\\rm Ly\\alpha $ photons, and for the remainder of the\nburst, $\\rm Ly\\alpha$ is seen only as an absorption feature.\n\n\nFor the more massive and prolonged starbursts in the CFg and other high-redshift sources, the period of $\\rm Ly\\alpha$ emission is likely to exceed that in this model, although it is probably shorter than the $\\sim 100$ Myr\npredicted for a much more extended ($\\sim 100 \\rm kpc$) source \n(Taniguchi and Shioya 2000). While evolutionary timescales may vary, the most important prediction of this model is that powerful starbursts would pass through a phase of strong $\\rm Ly\\alpha$ emission -- perhaps attaining the $\\rm W(Ly\\alpha)\\sim 150\\AA$ of unobscured models (Section 5.1) -- which is relatively brief compared to \nmerging and other dynamical timescales. This would explain why strong $\\rm Ly\\alpha$ emitters are diverse in morphology and have a similar luminosity function to other star-forming galaxies, but form only a small fraction of any\nsample of these (Steidel et al. 1999). \nIt also means that CFgA and CFgB need be only slightly mismatched in the timing of their peak SFR to explain their large difference in $W(\\rm Ly\\alpha$).\n\nA further prediction is that in galaxies near the beginning of the $\\rm Ly\\alpha$ emission phase (the first $\\sim 1$ Myr in the model), the $\\rm Ly\\alpha$ profile shows one or more secondary emission lines -- in massive starbursts, a `network of shells` produces a `forest of $\\rm Ly\\alpha$ in emission` -- while later stages give a P Cygni line profile. The Lowenthal et al. (1991) MMT spectra (Figure 1 and 2) of the CFg may be of insufficient depth and resolution to unambiguously detect either of these features, but the medium-resolution ($\\rm FWHM\\simeq 2.6\\rm \\AA$) spectrum does indicate an intrinsic Gaussian FWHM of $\\simeq \\rm 8 \\AA$ corresponding to high velocity FWHM of $\\sim 600$ km $\\rm s^{-1}$. The line is sharp-peaked with no obvious asymmetry. \nFitting a Voigt model suggests that the profile is closer to a $\\rm FWHM\\simeq 6\\rm \\AA$ Lorentzian than a Gaussian. We hypothesize that CFgA is in the earlier starburst stage, with multiple outflowing shells with high relative velocities giving the appearence of a single broadened $\\rm Ly\\alpha$ emission line, but no P Cygni profile. To confirm this, more data are needed; see Section 7.5i. \n\n\n We find no positive evidence for an AGN contribution to the $\\rm Ly\\alpha$ emission. The F410M flux of CFgA (of which $\\sim 70$ per cent is from the $\\rm Ly\\alpha$ line) appeared to trace the exponential profile\nof the UV continuum, with no evidence of a point source, as expected if the $\\rm Ly\\alpha$ emission is from extensive star-formation. However, if the $\\rm Ly\\alpha$ photons were primarily from an AGN, resonant scattering would be required\nto redistribute the $\\rm Ly\\alpha$ from a point-source to a profile \nreflecting that of the gas (and hence the star-formation). These multiple scatterings of each photon would increase the dust extinction of $\\rm Ly\\alpha$ above that of the UV continuum, reducing $W(\\rm Ly\\alpha$), so it might be difficult for even an AGN to produce the observed $\\sim 150\\rm \\AA$.\nIn contrast, models\n(Tenorio-Tagle et al. 1999) and observed sources (e.g. Pettini et al. 1998) suggest that starbursting, with resonant scattering suppressed by outflows, can account for this $W(\\rm Ly\\alpha)$.\n\nHowever, some $\\rm Ly\\alpha$-emitting galaxies do appear to be AGN-dominated. \nFrancis, Woodgate and Danks (1997) report 3 galaxies close to a $z=2.38$ QSO, \nwith similar $\\rm Ly\\alpha$ equivalent widths and velocity widths to CFgA.\nThese galaxies differ from the CFg in that the $\\rm Ly\\alpha$ emission is displaced $\\sim 10$ kpc from the continuum, and the colours are very red, suggesting old stellar populations. On this basis they were thought to be obscured AGN rather than\nstarburst galaxies. \n\n The high-excitation emission lines, \nCIV($1549\\rm \\AA$) and HeII($1640\\rm\\AA$), seen in the MMT spectrum might be interpreted as evidence for an AGN, although the equivalant widths, estimated as $\\sim 12\\rm \\AA$ and $\\sim 6\\rm \\AA$ respectively, are smaller than typical of Seyferts. However, the $\\sim 3$ Myr starburst age at which Tenori-Tagle et al. (1999) predict secondary emission from shells corresponds to a similarly brief phase in which starburst galaxies may produce CIV($1549\\rm \\AA$) and HeII($1640\\rm\\AA$) in emission\n(Leitherer, Roberts and Heckman 1995), due to a peak in the numbers of \nWolf-Rayet stars. Interestingly, the $z=2.498$, $W(\\rm Ly \\alpha \\simeq 170\\AA)$ starburst galaxy investigated\nby Malkan et al. (1996) also showed these emission lines, with similar equivalent widths ($\\sim 21$ and $7\\rm \\AA$ for CIV and HeII), so may\n be another example of this stage of evolution.\n \n\\subsection{Future Investigations}\nIt is evident that the Coup Fourr\\'e Galaxy, especially its A component, is of special interest in that both its surface brightness evolution and Lyman $\\alpha$ emission are at the upper extreme of the class of Lyman break galaxies, or of star-forming galaxies at any redshift, and furthermore it is one of the most luminous galaxies of its type. Our WFPC2 investigations have revealed much about its morphology, but many questions remain unanswered about its nature, and might be addressed as described below:\n\n(i) Further near-infrared spectroscopy of the CFg (Bunker et al. 1995) to detect the redshifted [OII]$3727\\rm\\AA$, H$\\beta(4861\\rm \\AA$), [OIII]$ 5007\\rm\\AA$ and H$\\alpha(6565\\rm \\AA)$. The equivalent widths of [OII] and H$\\alpha$\nshould give less dust-dependent estimates of the SFR, the \n$\\rm H\\beta/H\\alpha$ ratio may give a direct estimate of the dust extinction,\nand\nthe ratios of the first three lines provide a standard AGN diagnostic (e.g. Tress\\'e et al. 1996). The line widths may provide an estimate of the rotation velocity. The relative velocities of these lines and \n$\\rm Ly\\alpha$ may indicate gaseous outflows, and should help to explain the high velocity width of $\\rm Ly\\alpha$ (e.g. Pettini et al. 1998). We have now obtained these observations using the Keck NIRSPEC.\n\n\n(ii) Deeper and higher resolution spectroscopy at $\\sim 4000\\rm\\AA$ to reveal the structure of the $\\rm Ly\\alpha$ line in detail, the strength and profile of the high-excitation emission lines \nCIV($1549\\rm \\AA$) and HeII($1640\\rm\\AA$), and other emission or absorption features. The \nspectral index of the UV continuum would provide an improved estimate of the dust extinction (e.g. Calzetti et al. 1995).\n\n(iii) Ideally, a spectrum would be obtained along the CFgA--CFgB axis with sufficient spatial resolution ($<0.4$ arcsec) to separate the two \ncomponents. This may reveal differences in their star-formation histories. Spatial resolution of $\\rm Ly\\alpha$ will provide information on the interaction kinematics, and indicate the contributions of velocity gradient and radial velocity dispersion \nto the broadening of $\\rm Ly\\alpha$. A velocity gradient of $\\Delta\\lambda\\simeq 7\\rm \\AA$ -- similar to the line broadening in the CFg -- has already been detected across a lensed $\\rm Ly\\alpha$ galaxy at an even higher redshift \n(Franx et al. 1997).\n\n(iv) Multi object spectroscopy of the fainter $\\rm Ly\\alpha$ candidate sources,\nto determine the true numbers of strong $\\rm Ly\\alpha$ emitters, which galaxies are associated with the CFg, and\nwhether L3:10 is a QSO. If several of these galaxies are found to be clustered at the CFg redshift, their velocity dispersion will provide a rough estimate of cluster richness. \n\n \n(v) Deep imaging of the CFg field in near-infra red $J$ ($1.25\\mu \\rm m$) and $K$ ($2.2\\mu \\rm m$) may reveal (or set upper limits on) \nclustering around this galaxy. 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{
"name": "astro-ph0002160.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem{}\n Bertin E., Arnouts S., 1996, A\\&AS 117, 393.\n\\bibitem{}\n Binggeli B., Sandage A., Tarenghi M., 1984, AJ, 89, 64.\n\\bibitem{}\n Bunker A. J., Warren S., Clements D.L., Williger, G.M., Hewett P., 1995, MNRAS, 309, 875.\n\\bibitem{}\n Bunker A. J., Warren S., Hewett P., Clements D. L., 1995, MNRAS, 273, 513.\n\\bibitem{}\n Calzetti D., Bohlin R., Kinney, A. L., Storchi-Bergmann T., Heckman T. M., 1995, ApJ, 443, 136.\n\\bibitem{}\n Charlot S., Fall S. M., 1993, ApJ, 415, 580.\n\\bibitem{}\n Charlot S., Worthey G., Bressan A., 1996, ApJ, 457, 625.\n\\bibitem{}\n Clements D. L., Sutherland W. J., McMahon R. G., Saunders W.,\n 1996, MNRAS, 279, 477.\n\\bibitem{}\n Dey A., Spinrad H., Stern D., Graham J., Chaffee F., 1998, ApJ, 498, L93.\n\\bibitem{}\n Djorgovski S.G., Pahre M., Bechtold J., Elston R., 1996, Nature, 382, 234. \n\\bibitem{}\n Fioc M., Rocca-Volmerange B., 1997, A\\&A, 326, 950.\n\\bibitem{}\n Francis P., Woodgate B., Danks A. 1997, ApJ, 482, L25. \n\\bibitem{}\n Franx M., Illingworth G., Kelson D., van Dokkum P., Tran K., 1997, ApJ, 486, L75. \n\\bibitem{}\n Freeman K., 1970, ApJ, 160, 811.\n\\bibitem{}\n Fynbo J., M\\o ller P, Warren S. J., 1999, MNRAS, 305, 849. \n\\bibitem{}\n Giavalisco M., Macchetto F., Madau P., Sparks W., 1995, ApJ, 441, L13.\n\\bibitem{}\n Giavalisco M., Anuradha K., Calzetti D., 1996, 466,831.\n\\bibitem{}\n Gronwall C., Koo, D. C., 1995, ApJ, 440, L1.\n\\bibitem{}\n Hartmann L. W., Huchra J. P., Geller M. J., O' Brien P., Wilson P., 1988, ApJ, 326, 101.\n\\bibitem{}\n Hewitt A., Burbridge G., 1987, ApJS, 63, 1.\n\\bibitem{}\n Hu E. M., Songaila A., Cowie L., Hodapp K.-W., 1993, ApJ, 419, L13.\n\\bibitem{}\n Kennicutt R. C., 1983, ApJ 272, 54.\n\\bibitem{}\n Krist J., 1995, `Astronomical Data Analysis Software and Systems IV', ASP\nConf. Series, Vol 77, eds. R.A. Shaw, H. Payne, J. Hayes, p. 349.\n\\bibitem{}\n Kudritzki R.P., et al., 2000, ApJ, in press. (astro-ph/0001156)\n\\bibitem{}\n Leibundgut B., Robertson J.G., 1999, MNRAS, 303, 711.\n\\bibitem{}\n Leitherer C., Robert C., Heckman T. M., 1995, ApJS, 99, 173.\n\\bibitem{}\n Leitherer C., Robert C., Heckman T. M., 1995, ApJS, 99, 173.\n\\bibitem{}\n Lowenthal J. D., Hogan C., Green R. , Caulet A., Woodgate B., Brown L., \nFoltz C., 1991, ApJ, 377, L73.\n\\bibitem{}\n Lowenthal J. D., Heckman T. M., Lehnert M., Elias J., 1995, ApJ, 439, 588.\n\\bibitem{}\n Lowenthal J. D., Koo D. C., Guzm\\'{a}n R., Gallego J., Phillips A C., Faber S. M., Vogt N. P., Illingworth G. D., Gronwall C., 1997, ApJ, 481, 673.\n\\bibitem{}\n Malkan M. A., Teplitz H., McLean I. S., 1996, ApJ, 468, L9.\n\\bibitem{}\n Manning C., Stern D., Spinrad H, Bunker A. J., 1999. (astro-ph/9911442) \n\\bibitem{}\n Mannucci F., Thompson D., Beckwith S., Williger G.M., 1998, ApJ, 501, L11. \n\\bibitem{}\n McLure R., Kukula M., Dunlop J., Baum S., O'Dea C., Hughes D., MNRAS, 308, 377.\n\\bibitem{}\n Meyer D. M., Roth K. C., 1990, ApJ 363, 57. \n\\bibitem{}\n Mihos J. C., Hernquist L., 1996, ApJ, 464, 641.\n\\bibitem{}\n M\\o ller P, Warren S. J., 1998, MNRAS, 299, 661. \n\\bibitem{}\n Osterbrock D.E., 1989, `Astrophysics of Gaseous Nebulae and Active Galactic Nuclei', Mill Valley, CA, University Science Books.\n\\bibitem{}\n Pascarelle S. M., Windhorst R., Keel W. C., 1998, AJ, 116, 2659.\n\\bibitem{}\n Pettini M., Kellogg M., Steidel C., Dickinson M., Adelberger K., Giavalisco M., 1998, ApJ, 508, 539. \n\\bibitem{}\n Read A. M., Ponman T. J., 1998, MNRAS, 291, 143.\n\\bibitem{}\n Roche N., Ratnatunga K., Griffiths R. E., Im M., Naim A., 1998,\nMNRAS, 293, 197.\n\\bibitem{}\n Steidel C., Adelberger K., Shapley A., Pettini M., Dickinson M., Giavalisco M., 1999.\n\\bibitem{}\n Taniguchi Y., Shioya Y., 2000. (astro-ph/0001522).\n\\bibitem{}\n Tenorio-Tagle G., Silich S., Kunth D., Terlevich E., Terlevich R., 1999, MNRAS, in press. (astro-ph/9905324) \n\\bibitem{}\n Tissera P., `Clustering at High Redshift', ASP Conf. Series, eds. A. Mazure, O. Le Fevre, V. Lebrun, 1999. (astro-ph/9911009)\n\\bibitem{}\n Tress\\'e L., Rola C., Hammer F., Stasinska G. Le Fevre O., Lilly S.J., Crampton D., 1996, MNRAS, 281, 847.\n\\bibitem{}\n Wolfe A., 1993, ApJ 402, 411. \n\\bibitem{}\n Wolfe A., Fan X-M., Tytler D., Vogt S., Keane M., Lanzetta K., 1994, ApJ 435, L101. \n\\end{thebibliography}"
}
] |
astro-ph0002161
|
Patterns of Super Star Cluster Formation in `Clumpy' Starburst Galaxies
|
[
{
"author": "J.S. Gallagher"
},
{
"author": "N.L. Homeier"
},
{
"author": "C.J. Conselice"
}
] |
We present preliminary results from a Hubble Space Telescope (HST) WFPC2 investigation of spatial and temporal distributions of star clusters in the clumpy irregular galaxy NGC~7673 and the starburst spirals NGC 3310 and Haro~1. We compare the spectral energy distributions of star clusters in the large clumps in NGC 7673 to model calculations of stellar clusters of various ages. We also propose that the presence of super star clusters in clumps seems to be a feature of intense starbursts.
|
[
{
"name": "gallagherj.tex",
"string": "\\documentstyle[11pt,newpasp,twoside, epsf]{article}\n\\markboth{Gallagher et al.}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{Patterns of Super Star Cluster Formation in `Clumpy' Starburst Galaxies}\n \\author{J.S. Gallagher, N.L. Homeier, C.J. Conselice}\n\\affil{Department of Astronomy, University of Wisconsin-Madison, 475 N. Charter\nSt. Madison WI., 53706}\n\\author{WFPC-2 Investigation Definition Team}\n\n\\begin{abstract}\n\nWe present preliminary results from a\nHubble Space Telescope (HST) WFPC2 investigation of spatial and\ntemporal distributions of star clusters in the \nclumpy irregular galaxy NGC~7673 and the starburst spirals NGC 3310 and\n Haro~1. We compare\nthe spectral energy distributions of star clusters in the large\nclumps in NGC 7673 to model calculations of\nstellar clusters of various ages. We also propose that the presence of \nsuper star clusters in clumps seems to be a feature of intense starbursts.\n\n\\end{abstract}\n\n\\keywords{stars -- clusters, galaxies -- starbursts, galaxies -- evolution}\n\n\\section{Introduction}\n\n The optical morphologies of active star forming galaxies are often\ndominated by kpc-scale star-forming regions, which appear as luminous\n`clumps' or `islands'. These clumps can have very high optical and UV\nsurface brightnesses, making them visible signatures of intense star\nformation over cosmological distances. High angular resolution imaging\nwith the {\\it Hubble Space Telescope} (HST) and ground-based telescopes,\nreveals that clumps consist of associations of dense star clusters.\nThese are usually superimposed on a more diffuse background, probably\nmade up of massive stars. \n\nThe presence of numerous star clusters influences the evolution of \nclumps through their\ninteractions with the surrounding ISM, that must respond to\nphotoionization, as well as mechanical energy and momentum inputs from\nthe evolving star clusters. These processes can trigger star formation\nand simultaneously remove ISM from the clump. Since star clusters can\nbe age-dated from their spectra, their presence also offers the\npossibility of measuring the history of\nstar-forming activity in starburst galaxies.\n\nStarbursts are well-known producers of dense, massive star clusters and thus\nare an excellence place to study these interactions. In \nthis paper we explore the spatial and temporal patterns of massive \nstar cluster formation in a small sample of relatively nearby starburst \ngalaxies.\n\nThe primary objects in this study are NGC 2415 (Haro 1), NGC 3310 and\nNGC 7673. The Haro 1 and NGC 7673 data are HST WFPC2 ultraviolet (UV)\nand optical images, while we use\nground-based optical images from the WIYN 3.5-m telescope for NGC 3310.\nDetails are presented in Gallagher et al. (2000).\n\n\\begin{table}\n\\begin{center}\nProperties of Studied Starbursts\n\\begin{tabular}{rlll} \\hline\nGalaxy & Distance & Magnitude & Size \\\\ \\hline \\hline \nNGC 2415 & D=50 Mpc & M$_B$=-20.8 & A=13 kpc \\\\\n\nNGC 3310 & D=19 Mpc & M$_B$=-19.9 & A=17 kpc \\\\\n\nNGC 7673 & D=46 Mpc & M$_B$=-20 & A=17 kpc \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\section{Star Clusters in Starbursts}\n\nWe begin with NGC 3310, the least intense example in our sample (Figure 1). \nWIYN optical images reveal compact star clusters in the ring and along the \narms of this galaxy, \nwith a wider distribution of fainter cluster candidates outside of these\nregions. While clusters are numerous, their spatial distribution in this \nnon-clumpy starburst resembles that of a normal spiral galaxy. \n\nHaro 1 is an intense starburst with high optical brightness, producing \na luminous galaxy with a diameter of only about 13 kpc. The spectrum shows\nstrong Balmer absorption lines indicating that this is a relatively \nevolved starburst. High quality ground-based images with the WIYN\nTelescope suggest a transition to a clumpy structure. Our WFPC2 image\nin the emission line-free F547M filter displays a moderate\ndegree of clustering of dense, luminous star clusters, and high surface \nbrightness regions usually containing more than one compact star cluster.\n{\\small\n\\begin{figure}\n\\plottwo{gallagherj1a.eps}{gallagherj1b.eps}\n\\caption{WFPC2 image of NGC 7673 (left) showing the clumpy star formation\nappearance that is occurring in distinct star clusters. A WIYN image\nof the center of NGC 3310 (right) displays a more normal circumnuclear ring \nof star formation.}\n\\end{figure}\n}\n\n\\begin{figure}\n\\plottwo{gallagherj2a.eps}{gallagherj2b.eps}\n\\caption{Spectral Energy distributions for super star clusters\nwithin two clumps in NGC 7673.}\n\\end{figure}\n\n\\begin{figure}\n\\plotone{gallagherj3.eps}\n\\vspace{1cm}\n\\caption{Model calculation for an aging cluster from 4 Myr to 100 Myr (right\ny-axis) vs. wavelength. Fluxes from Starburst99, and magnitudes from\nmodels by A. Watson.}\n\\end{figure}\n\n\nNGC 7673 is a star bursting clumpy irregular galaxy.\n Colors and magnitudes derived for star\ncluster candidates in the F255W, F555W, and F814W WFPC2 bands indicate\nthat young clusters are mixed through the optically prominent clumps; \ntheir colors appear to be\ndriven at least as much by locally variable extinction as by ages. A low\nlevel of organization may be present, with clusters near the galaxy's center\npossibly being made in a linear structure by bar-induced gas flows. Some\nclumps are roughly circular, and so propagating star formation could be \npresent. Figure 2 shows the spectral energy distribution (SED) of two\nclumps in NGC 7673, while Figure 3 shows model calculation SEDs\nfor star clusters at various ages. \nProbably more than one mechanism structures the distribution of star\nclusters within clumps, but in most cases populations of star clusters \nare formed over relatively short time scales of $<$ 100 Myr.\n\n\\section{Discussion}\n\nClumps seem to be features of active star bursts with high intensities.\nThis fits with theoretical models (Elmegreen \\& Efrenov 1997; Noguchi\n1999) where stellar clumps form in gas-rich galactic disks\nwith higher than average internal velocity dispersions, leading to large\nJeans masses and lengths. Such conditions could be natural consequences of\ncollisional perturbations of gassy disk galaxies. They would be more\ncommon in less evolved galaxies with higher gas contents and lower degrees\nof organization, providing a possible explanation for the clumpy\nappearances of high redshift galaxies (Noguchi 1997).\nAlthough super star clusters can form in a range of conditions, clumps may\nbe particularly important in unevolved galaxies; observations of nearby\nclumps then may provide insight into the formation of globular clusters.\n\nOnce star formation begins in a clump, the subsequent evolution must be\ncomplex. Energy and momentum inputs from massive stars and star clusters\nproduce obvious observational signatures in emission line profiles\n(Homeier \\& Gallagher 1999) will disturb the ISM, and\nlikely lead to compressed regions which are excellent sites for further\ncluster formation (eg., Scalo \\& Chappell 1999). The close\nspacing between clusters and high densities of gas clouds may also lead to\ncluster-cluster mergers or cluster rejuvenations due to gas cloud\ncaptures. These possibilities reinforce the capabilities for massive star\nforming clumps to be prime producers of massive super star clusters. Once\nmade these clusters will be the most likely to survive and \nobserved at later times.\n\nWe thank the WFPC2 Investigation Definition Team, and the Space Telescope\nScience Institute Archival Observer program for providing support\nthrough the National Aeronautics and Space Administration for this work.\n\n\\begin{references}\n\n\\reference Elmegreen, B.G. \\& Efrenov, Y.N., 1997, ApJ, 480, 235\n\\reference Gallagher, J.S., Homeier, N.L., Conselice, C.J., et al., 2000, \nin Preparation\n\\reference Homeier, N.L. \\& Gallagher, J.S., 1999, ApJ, 522, 199 \n\\reference Noguchi, M., 1999, ApJ, 514, 77\n\\reference Noguchi, M., 1997, Nature, 392, 253\n\\reference Scalo, J. \\& Chappell, D., 1999, ApJ, 510, 258\n\n\n\\end{references}\n\\end{document}\n"
}
] |
[] |
astro-ph0002162
|
Characterizing the Peak in the \\ Cosmic Microwave Background Angular Power Spectrum
|
[
{
"author": "Lloyd\\ Knox$^1$ and Lyman Page$^2$"
}
] |
A peak has been unambiguously detected in the cosmic microwave background (CMB) angular spectrum. Here we characterize its properties with fits to phenomenological models. We find that the TOCO and BOOM/NA data determine the peak location to be in the range 175--243 and 151--259 respectively (both ranges 95\% confidence) and determine the peak amplitude to be between $\approx70~{and}~90$ $\muK$. By combining all the data, we constrain the full-width at half-maximum to be between 180 and 250 at 95\% confidence. Such a peak shape is consistent with inflation-inspired flat, cold dark matter plus cosmological constant models of structure formation with adiabatic, nearly scale-invariant initial conditions. It is inconsistent with open and defect models.
|
[
{
"name": "peak.tex",
"string": "%====================================================================\n% Trail:\n% Original version by Lloyd.\n% Some notes by L. P.\n% More note by Lloyd\n% Some minor additions by LP\n% Added LK's email, edited some and sent back to LK Jan 25 '00 -LP\n% Further editing by LK, table fixed. Jan 27 '00\n% Minor editing by LP Jan 27 '00 Soma words and notes\n% Fran Lloyd Jan 29\n% OK edits throughout Feb 1 \n% LP made some edits to shorten paper and included fig2_feb2.ps\n%(available on the web).\n% LK slightly modified Fig. 1 available on web as kpfig1_feb03.eps\n% commented out Fig. 3, edited throughout\n%\n% LP edited for length and to try and make room for the LK width plot.\n% I took some liberties with the discussion. Please undo anything bad.\n% Also, I added a reference to the Pen/Turok,Seljak work on textures.\n% I put {\\bf TDB} next to questions.\n% I removed previous editorial comments to make this version easier to\n% read.\n%\n%\n% Final changes from LP. Sunday Feb 5. Have not spell checked\n% also saw that in the reference for LK's PASCOS talk, astro-ph\n% had an xxx. 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P}}\n\\def\\hz{{\\hat z}}\n\\def\\la{\\mathrel{\\mathpalette\\fun <}}\n\\def\\ga{\\mathrel{\\mathpalette\\fun >}}\n\\def\\fun#1#2{\\lower3.6pt\\vbox{\\baselineskip0pt\\lineskip.9pt\n \\ialign{$\\mathsurround=0pt#1\\hfil##\\hfil$\\crcr#2\\crcr\\sim\\crcr}}}\n%%%%%%%%%\n\\def\\boldsymbol{\\bf}\n\n\\def\\boldcdot{\\mathbin{{\\boldsymbol\\cdot}}}\n\\def\\boldnabla{{\\boldsymbol\\nabla}}\n\\font\\BF=cmmib10\n\\def\\gam{\\hat{\\gamma}}\n\\def\\k{{\\hbox{\\BF k}}}\n\\def\\x{{\\hbox{\\BF x}}}\n\\def\\r{{\\hbox{\\BF r}}}\n\\def\\u{{\\hbox{\\BF u}}}\n\\def\\v{{\\hbox{\\BF v}}}\n\\def\\d{\\delta}\n\\def\\dD{\\delta_{\\rm D}}\n\\newcommand{\\lexp}{\\mathop{\\langle}}\n\\newcommand{\\rexp}{\\mathop{\\rangle}}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%% end local macros %%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{document}\n\\twocolumn[\\hsize\\textwidth\\columnwidth\\hsize\\csname @twocolumnfalse\\endcsname\n\\draft\n\\title{Characterizing the Peak in the \\\\\nCosmic Microwave Background Angular Power Spectrum}\n\\author{Lloyd\\ Knox$^1$ and Lyman Page$^2$}\n\\address{$^1$ Department of Astronomy and Astrophysics\\\\\nUniversity of Chicago, 5640 S. Ellis Ave., Chicago, IL 60637, USA}\n\\address{$^2$ Department of Physics\\\\\nPrinceton University, Princeton, NJ, USA}\n\\date{\\today}\n\\maketitle\n\n\\begin{abstract}\n A peak has been unambiguously detected in the cosmic microwave\n background (CMB) angular spectrum. Here we characterize its\n properties with fits to phenomenological models. We find that the\n TOCO and BOOM/NA data determine the peak location to be in the range\n 175--243 and 151--259 respectively (both ranges 95\\% confidence) and\n determine the peak amplitude to be between $\\approx70~{\\rm and}~90$\n $\\muK$. By combining all the data, we constrain the full-width at\n half-maximum to be between 180 and 250 at 95\\% confidence. Such a\n peak shape is consistent with inflation-inspired flat, cold dark\n matter plus cosmological constant models of structure formation with\n adiabatic, nearly scale-invariant initial conditions. It is\n inconsistent with open and defect models.\n\\end{abstract}\n\\pacs{98.70.Vc}\n%\\narrowtext\n] \n\n{\\parindent0pt\\it Introduction.} If the adiabatic cold dark matter\n(CDM) models with scale-invariant initial conditions describe our\ncosmogony, then an analysis of the anisotropy in the CMB can reveal the\ncosmological parameters to unprecedented accuracy\n\\cite{forecast}. A number of studies have aimed at\ndetermining, with various prior assumptions, a subset of the $\\sim 10$\nfree parameters that affect the statistical properties of the CMB\n\\cite{paramest,dodknox99}. The parameter most robustly determined\nfrom current data is $\\Omega$, the ratio of the mean matter/energy\ndensity to the critical density (that for which the mean spatial\ncurvature is zero). These investigations show that\n$\\Omega$ is close to one. This result, combined with other\ncosmological data, implies the existence of some smoothly distributed\nenergy component with negative pressure such as a cosmological constant.\n\nA weakness of previous approaches \\cite{paramest,dodknox99} is that\nthe conclusions depend on the validity of the assumed model. In this\n{\\it Letter} we take a different tack and ask what we know independent\nof the details of the cosmological model. We find the peak location,\namplitude and width are consistent with those expected in adiabatic\nCDM models. Furthermore, as $l_{\\rm peak} \\simeq 200 \\Omega^{-1/2}$\nin these models, the observed peak location implies $\\Omega \\simeq 1$.\nThe determination of the peak location is robust; it does not depend\non the parametrization of the spectrum, assumptions about the\ndistribution of the power spectrum measurement errors, nor on the\nvalidity of any one data set. The model-dependent determinations of\n$\\Omega$ are further supported by the {\\it inconsistency} of the data\nwith competing models, such as topological defects, open\nmodels with $\\Omega < 0.4$, or the simplest isocurvature models.\n\n{\\parindent0pt\\it The Data.} \nThe last year of the 1000's saw new\nresults from MSAM\\cite{wilson99}, PythonV\\cite{coble99}, MAT/TOCO\n\\cite{toco,tocoexplained}, \nViper\\cite{peterson}, CAT\\cite{bak99}, IAC\\cite{dicker99}\nand BOOM/NA\\cite{mauskopf}, all of which have bearing on the properties of the \npeak. These results are plotted in Fig. 1. We have known for several\nyears that there is a rise toward towards $l=200$ \nbut it is now clear that the spectrum also falls significantly towards\n$l=400$.\n\nFor all the medium angular scale experiments, the largest systematic\neffect is the calibration error which is roughly 10\\% for each.\nContamination from foreground emission is also important and not yet\nfully accounted for in some experiments ({\\it e.g.} TOCO). A\ncorrection for this contribution, for which $\\delta T_l \\sim\nl^{-1/2}$, will affect the amplitude of the peak though will not\nstrongly affect its position. Thorough analyses by the\nMSAM\\cite{cheng} and PYTHON\\cite{coble99} teams show that the level of\ncontamination in those experiments was $<3\\%$.\n\nThe three experiments that have taken data that span the peak are\nMSAM, TOCO, and BOOM/NA. All\nexperiments exhibit a definite increase over the Sachs-Wolfe plateau\nthough the significance of a feature based on the data alone, e.g. a\npeak, differs between experiments. We may assess the detection of a\nfeature by examining the deviation from the best fit flat line,\n$\\overline{\\delta T}$. For the three MSAM points, we find \n$\\overline{\\delta T}=46\\pm 4.9~\\mu$K with a reduced $\\chi^2$ of 0.43 \n(Probability to\nexceed, $P_{>\\chi^2} = 0.65$. The calibration error is not included.). \nThus, no feature is detected with these data alone though\nthere is a clear increase over DMR\\cite{DMR}. \nFor the seven BOOM/NA points, we\nfind $\\overline{\\delta T}=55.3\\pm 4.2~\\mu$K with a reduced $\\chi^2$ of 1.94\n($P_{>\\chi^2} = 0.05$, assuming the data are anti-correlated at\nthe 0.1 level\\cite{mauskopf}). \nFor the ten TOCO\npoints, $\\overline{\\delta T}=69.3\\pm 2.7~\\mu$K with a reduced $\\chi^2$ of 4.86\n($P_{>\\chi^2} <10^{-5}$)\nCalibration errors will not\nchange $\\chi^2/\\nu$, however a correction for foreground emission will \nhave a slight effect.\nThough we examine all data in the following, we focus particularly on\nBOOM/NA and TOCO because of their detections of a feature.\n\n{\\parindent0pt\\it Fits to Phenomenological Models.} \nTo characterize the peak amplitude and location we fit the\nparameters of two different phenomenological models. \nFor the first, we start with the best fit DK99\\cite{dodknox99} adiabatic\nCDM model, $\\delta T_l^{DK}$, and form\n$\\delta T_l = (\\delta T_l^{DK}-\\delta T_{l=10}^{DK})\\alpha + \\delta T_{l=10}^{DK}$\nby varying $\\alpha$, and then stretching in $l$\\cite{barth96}. We characterize\neach stretching with the peak position and peak amplitude. \nThis method has the virtue that the resulting\nspectra resemble adiabatic models and so if one assumes that\nthese models describe Nature, then these results are the\nones to which we should pay the most attention.\n\n\n\\begin{figure}[htbp]\n \\plotone{kpfig1.eps} \n \\caption{Bandpowers from TOCO97 (cyan open triangles), \nTOCO98 (blue filled triangles), BOOM/NA (green filled squares),\nMSAM (red open squares), CAT (black open pentagon), IAC (black \nfilled pentagon), PyV (black open circles) and Viper\n(green filled circles). The y-axis is \n$\\delta T_l \\equiv \\sqrt{l(l+1)C_l/(2\\pi)}$ where $C_l$ is the\nangular spectrum. The models\nare, peaking at left to right, the best fit models\nof \\protect\\cite{dodknox99} for $\\Omega=1$, $\\Omega=0.4$ and $\\Omega=0.2$. \nThe $\\Omega=1$ model has a mean density of non-relativistic matter, \n$\\Omega_m=0.31$, a cosmological constant density of $\\Omega_\\Lambda=0.69$,\na baryon density of $\\Omega_b=0.019h^{-2}$ \\protect\\cite{BNTT99}, a Hubble\nconstant of $H_0 =65 \\ {\\rm km/sec/Mpc}$, \nan optical depth to reionization\nof $\\tau = 0.17$ and a power spectrum power-law index of $n=1.12$, where\n$n=1$ is scale-invariant.\nThe shaded areas are the results of \nfitting the power in 14 bands of $l$ to all the data (from 1999 and previous years) as in \\protect\\cite{bjk98}.\nMany of the bands are at low $l$ and cannot be discerned on this plot.\nCalibration errors are not shown though are included in the best fit.\n}\n\\label{fig:data}\n\\end{figure}\n\nOur second model for $\\delta T_l^2$ is a Gaussian:\n$\\delta T_l^2 = A^2 \\exp\\left(-\\left(l-l_c\\right)^2/(2\\sigma_l^2)\\right)$.\nDepending on the width, this spectrum can look\nvery much like, or unlike, the spectra of adiabatic models \n\\cite{gaussmod}.\nWe view this versatility as a virtue since we are interested \nin a characterization of the peak which is independent of physical models.\n\nWe fit to these phenomenological models in two ways. For the stretch\nmodel, we examine the $\\chi^2$ of the residuals between the \npublished data and each model.\nThe widths of the window functions are ignored and we assume the data\nare normally distributed in $\\delta T_l$ with a dispersion\ngiven by the average of the published error bars (GT in Table 1). This is an admittedly\ncrude method but it works well because the likelihoods as a function of\n$\\delta T_l$ are moderately well approximated by a normal distribution. \n\n\nFor both the Gaussian shape and the stretch model, we also perform\nthe full fit as outlined in BJK\\cite{bjk98} (RAD in Table 1). \nFor the Gaussian shape model, the\nconstraints on the amplitude and\nlocation are given below after marginalization over the width $\\sigma_l$.\nIn all fitting, we ignore the experiments that are affected by $l< 30$\n(DMR, FIRS\\cite{firs} and Tenerife\\cite{tenerife}) because\nwe want the parameters of\nour Gaussian to be determined by behavior in the peak region.\n\n\n\\vskip 0.15in\n\\begin{tabular}{cccccccc}\n\\hline\n\\hline\nData & Model & Fit & $N/\\nu$ & $\\chi^2/\\nu$ & $P_{>\\chi^2}$ &$l_{peak}$ &$\\delta T_{peak}$ \\\\\n& & & & & & & $~\\mu$K \\\\\n\\hline\nAll & G & Rad & 58/55 & 1.25 &0.10 &$229 \\pm 8.5$ & 78 \\\\ \nT & G & Rad & 10/7 & 0.41 &0.89 & $206 \\pm 16$ & 95 \\\\\nT & S & GT & 10/8 & 0.94 & 0.48 & $214\\pm 14$ & 88 \\\\\nT & S & Rad & 10/8 & 0.84 & 0.57 & $209\\pm 17$ & 92 \\\\\nB & G & Rad & 7/4 & 0.19 &0.94&$208 \\pm 21$ & 69 \\\\\nB & S & GT & 7/5 & 0.39 & 0.85 & $215\\pm 24$ & 69 \\\\\nB & S & Rad$_0$ & 7/5 & 0.23 & 0.95 & $205\\pm 27$ & 72 \\\\\nB & S & Rad$_\\infty$ & 7/5 & 0.39 & 0.85 & $206\\pm 26$ & 68 \\\\\nP & G & Rad & 33/30 & 1.13 & 0.28 & $262\\pm 24$ & 68 \\\\\n\\hline\n\\end{tabular}\n\\footnotemark{ALL stands for all publically available data sets (except\nfor VIPER which was not used because of unspecified \npoint-to-point correlations), the T\nis for the TOCO data, the B for BOOM/NA and the P is for ``Previous'',\nmeaning all data prior to BOOM/NA and TOCO.}\n\\footnotemark{G and S are for the Gaussian shape and stretch methods\nrespectively}\n\\footnotemark{$N$ is the number of data points and $\\nu$ the degrees of freedom.}\n\\footnotemark{Rad$_0$ and Rad$_\\infty$ corresponds to log\nnormal and normal distributions for the likelihood respectively.}\n\\vskip 0.15in\n%All2 & S & Rad & 45 & 1.56 &0.008 &$216 \\pm 12$ & 80 \\\\ \n\nThe main thing to notice in the Table is that the position of the peak\nis robustly determined by {\\it either} TOCO or BOOM/NA to be in the\nrange 185 to 235, regardless of the method. For the quoted errors, we\nhave marginalized over all parameters except the position. The\npeak amplitudes are subject to change as\nthere is some dependence on the model parametrization and the\nforeground contamination has not been thoroughly assessed.\n\nWe account for the calibration uncertainty through a convolution\nof the likelihood of the fits with a normal distribution of the fractional\nerror \\cite{ganga97,bjk98}. BOOM/NA, TOCO97 and TOCO98 have\ncalibration uncertainties of \n8\\%, 10.5\\% and 8\\% respectively. However, 5\\% of this is\ndue to uncertainty in the temperature of Jupiter and therefore,\nassuming that these uncertainties add in quadrature, we get\n$\\sigma_{\\rm Jup} = 0.05$, $\\sigma_{T97}=0.092$, $\\sigma_{T98}=0.062$ \nand $\\sigma_{B97} = 0.062$. We then find, for TOCO, that the full likelihood\nin $\\delta T_l$ and $l$ is given by\n\n\\bea\n\\label{eqn:margi}\nL(l_c,\\delta T_l) &=& \\int d\\sigma_l du_{\\rm Jup} du_{T97} du_{T98} \nL_{T97}(l_c,\\delta T_lu_{\\rm Jup}u_{T97},\\sigma_l) \\nonumber \\\\\n& & \\times L_{T98}(l_c,\\delta T_lu_{\\rm\nJup}u_{T98},\\sigma_l)P_G(u_{97}-1;\\sigma_{T97})\n \\nonumber \\\\\n& & \\times P_G(u_{T98}-1;\\sigma_{T98})\nP_G(u_{\\rm Jup}-1;\\sigma_{\\rm Jup}) \n\\eea\nwhere $P_G(x;\\sigma)= \\exp\\left(-x^2/(2\\sigma^2)\\right)/ \\sqrt{2\\pi\\sigma^2}$,\n$u$ is integrated from 0 to $\\infty$\nand, e.g., $L_{T97}(l_c,\\delta T_l,\\sigma_l) = \\exp(-\\chi^2/2)$\nwhere $\\chi^2$ is evaluated on a grid of $\\delta T_l^2$, $l_c$ \\&\n$\\sigma_l$ using RADPACK\\cite{radpack} as discussed in BJK.\nWe get similar results for TOCO when simply using a combined\ntotal calibration error of 8.5\\%.\n\nFor the Gaussian model we can also marginalize over $A$ and $l_c$ to\nplace 95\\% confidence bounds on the width:\n$75 < \\sigma_l < 105$ for ALL, $50 < \\sigma_l < 105$ for TOCO\nand $55 < \\sigma_l < 145$ for BOOM/NA.\n\n%% figure 2\n\\begin{figure}[bthp]\n \\plotone{kpfig2.ps}\n \\caption{Likelihood contours for $l$ vs $\\delta T_l$ for the position\nof the peak. For BOOM/NA and TOCO, we use the stretch \nmethod using RADPACK\\protect\\cite{radpack} and include\nthe calibration error. \nFor Previous and ALL (tightest contours) we have {\\it not} used generalizations\nof Eq.~\\ref{eqn:margi}, but instead have fixed the calibration \nparameters. All contour levels correspond to 5\\%, 68\\%,\nand 95\\% enclosed, or roughly the peak, $1\\sigma$,\n$2\\sigma$. }\n\\label{fig:Avl}\n\\end{figure}\n\nAre the\ndata in Fig 1 consistent? DK99 found that the best-fit model, given all the\ndata at the time, had a $\\chi^2$ of 79 for 63 degrees of freedom,\nwhich is exceeded 8\\% of the time. Here we see that the $\\chi^2$ for\nthe fit of the Gaussian model is 69 for 55 degrees of freedom, which\nis exceeded 10\\% of the time. We conclude that, although there may\nwell be systematic error in some of these data sets, we have no\ncompelling evidence of it. However, we take caution from the fact\nthat we had to adjust the calibration parameters from their nominal\nvalues to their best-fit values in order to reduce the $\\chi^2$ to 69.\nLeft at their nominal values with calibration uncertainty ignored, the\ndata are not consistent with each other. Thus we believe that the\ncompilation results are perhaps less reliable than those for either\nBOOM/NA or TOCO.\n\n{\\parindent0pt\\it Implications for Physical Models.} \nFlat, adiabatic, nearly scale-invariant models \nhave similar peak properties to those of our best-fit \nphenomenological models. Most importantly the peak location,\nas determined by three independent data sets (``Previous'',\nTOCO, BOOM/NA), is near $l \\simeq 210$, as expected. Depending on\nthe data set chosen, the amplitude is higher than expected but\ncan easily be accommodated, within the uncertainties, \nwith a cosmological constant.\nCombining all the data, there is a preference \nfor $l_{\\rm peak} > 210$ which suggests a cosmological constant\\cite{pascos}\n(at $h=0.65$, $l_{\\rm peak}$ goes\nfrom 200 at $\\Omega_\\Lambda=0$ to 220 at $\\Omega_\\Lambda=0.7$).\nHowever, this result is not seen in any individual data set.\n\nA good approximation to the first peak in the DK99 best-fit model is\ngiven by the Gaussian model with $\\sigma_l=95$. From the $\\sigma_l$\nconstraints quoted earlier we see that the data have no significant\npreference for peaks that are either narrower or broader than those in\ninflation-inspired CDM models.\n\nA general perturbation is a combination of adiabatic and isocurvature\nperturbations. Adiabatic perturbations are such that at each point in\nspace, the fractional fluctuations in the number density of each\nparticle species is the same for all species. Isocurvature\nperturbations are initially arranged so that, despite fluctuations in\nindividual species, the total energy density fluctuation is zero.\nGiven multiple components, there\nare a number of different ways of maintaining the isocurvature condition.\nBelow we assume the isocurvature condition\nis maintained by the dark matter compensating everything else.\n\nIsocurvature initial conditions result in shifts to the CMB power\nspectrum peak locations. For\na given wavenumber, the temporal phase of oscillations in the\nbaryon-photon fluid depends on the initial relation between\nthe dark matter and the fluid. \nThose waves with oscillation frequencies\nsuch that they hit an extremum at the time of last-scattering in\nthe adiabatic case, will hit a null in the isocurvature case\\cite{husugwhite}.\nThe effect on the first peak is a shift from \n$l \\simeq 200\\Omega^{-1/2}$ to $l \\simeq 350\\Omega^{-1/2}$.\nGiven the observation of $l_{\\rm peak} \\simeq 210$, simple isocurvature\nmodels require $\\Omega > 2$---which is inconsistent with\na number of observations\\cite{montypython}.\n\nCritical to the Doppler peak structure, in either adiabatic or\nisocurvature models, is the temporal phase coherence for \nFourier modes of a given wavenumber\\cite{coherence}. In topological defect\nmodels, the continual generation of new perturbations by\nthe non-linear evolution of the defect network destroys this\ntemporal phase coherence and the acoustic peaks blend into a\nbroad hump which is wider and peaks at higher $l$ than\nthe observed feature. \n\nOne can make defect model power spectra with less power at $l=400$\nthan at $l=200$ with ad-hoc modifications to the standard \nionization history\\cite{WBA}. But even for these models the drop\nis probably not fast enough\\cite{Albrechtpascos}. \nThe contrast between the power at $l=200$ and\n$l=400$ is a great challenge for these models.\n\nThere are scenarios with initially isocurvature conditions\nthat can produce CMB power spectra that look much\nlike those in the adiabatic case. This can be done by adding\nto the adiabatic fluctuations (of photons, neutrinos, baryons and\ncold dark mater) another component, with a non-trivial stress\nhistory, which maintains\nthe isocurvature condition\\cite{postmodernisocurv}. \n\n{\\parindent0pt\\it Conclusions.} Our phenomenological \nmodels have allowed for rapid, model-independent,\ninvestigation of the consistency of CMB datasets, and of the\nrobustness of the properties of the peak in the CMB power spectrum.\nThe peak has been observed by two different instruments, and can be\ninferred from an independent compilation of other data sets. The\nproperties of this peak are consistent with those of the first peak in\nthe inflation-inspired adiabatic CDM models, and inconsistent with a\nnumber of competing models, with the possible exception of the more\ncomplicated isocurvature models mentioned above. It is perhaps\ninstructive that where the confrontation between theory and\nobservation can be done with a minimum of theoretical uncertainty, the\nadiabatic CDM models have been highly successful.\n\n\\acknowledgements \n%\\vskip 0.2in\n%\\noindent \nLK wishes to thanks S. Meyer and M. Tegmark for useful conversations and \nis supported by the DOE, NASA grant NAG5-7986 and NSF grant OPP-8920223.\nLP wishes to thank MAT/TOCO team members Mark Devlin, Randy Dorwart,\nRob Caldwell, Tom Herbig, Amber Miller, Michael Nolta, Jason Puchalla, \nEric Torbet, \\& Huan Tran,\nfor insights and encouragement, and Chuck Bennett for comments on\nan earlier version of this work. LP is supported by NSF grant PHY\n96-00015 and NASA grant NAS5-96021.\n\n\\begin{thebibliography}{ucsc}\n%\\begin{thebibliography}{}\n\\bibitem{forecast} e.g., L.\\ Knox, {\\sl Phys.\\ Rev.}\\/ {\\bf D52} 4307 (1995);\n G.\\ Jungman, M.\\ Kamionkowski,\n A.\\ Kosowsky \\& D.N.\\ Spergel, {\\sl Phys.\\ Rev.\\ Lett.}\\/ {\\bf 76},\n 1007 (1996); {\\sl ibid}, {\\sl Phys.\\ Rev.}\\/ {\\bf D54},\n 1332 (1996); J.R.\\ Bond, G.\\ Efstathiou \\& M.\\ Tegmark, Mon. Not. R. Astron.\nSoc. {\\bf 33}, 291L (1997);\n M.\\ Zaldarriaga, D.\\ Spergel \\& U.\\ Seljak, Astrophys.J. {\\bf 488}, 1 (1997);\nD. Eisenstein, W. Hu and M. Tegmark, Astrophys. J. {\\bf 518}, 2 (1999).\n\\bibitem{paramest} M. Tegmark and M. Zaldarriaga, astro-ph/0002091; \nA. Melchiorri \\etal, astro-ph/9911445;\nN. Bahcall, J.P. Ostriker, S. Perlmutter, and\nP. J. Steinhardt, Science, {\\bf 284} 1481 (1999) (astro-ph/9906463);\nJ.G. Bartlett, A. Blanchard, M. Douspis, M. Le Dour,\nProc Evol of Large Scale Structure, Garching, Aug 1998, astro-ph/9810318;\nJ. R. Bond, A.H. Jaffe, Phil.\nTrans. R. Soc. Lond. astro-ph/9809043;\nC. H. Lineweaver, Science {\\bf 284}, 1503 (1999); \nB. Ratra, {\\it et al.} Astrophys. J. {\\bf 517}, 549 (1999);\nM. Tegmark, Astrophys. J. {\\bf 514}, L69 (1999).\n\\bibitem{dodknox99}S. Dodelson \\& L. Knox, %submitted to Phys. Rev. Lett.\nastro-ph/9909454.\n\\bibitem{wilson99} G. Wilson, \\etal\\ Astrophys. J., in press, astro-ph/9902047.\n\\bibitem{coble99} K. Coble et al., Astrophys. J. {\\bf 519}, L5 (1999)\n(astro-ph/9902195); K. Coble, Ph.D. Thesis, astro-ph/9911419.\n\\bibitem{toco} [TOCO97] E. Torbet \\etal\\ Astrophys. J. {\\bf 521} L79 \n(1999)(astro-ph/9905100); [TOCO98] A. Miller et al., \nAstrophys. J. {\\bf 524} L1 (1999) astro-ph/9906421.\n\\bibitem{tocoexplained} The Mobile Anisotropy Telescope\n(MAT), while situated on Cerro Toco, Chile, produced two data sets using\nthe same instrument and observing\nstrategy, TOCO97 \\& TOCO98. We refer to these collectively as TOCO.\n\\bibitem{peterson} J. B. Peterson et al., astro-ph/9910503.\n\\bibitem{bak99} J. C. Baker et al.,\n%, K. Grainge, M.P. Hobson,\n%M.E. Jones, R. Kneissl, A.N. Lasenby, C.M.M. O'Sullivan, G. Pooley,\n%G. Rocha, R. Saunders, P.F. Scott, E.M. Waldram, \nsubmitted to MNRAS, astro-ph/9904415.\n\\bibitem{dicker99}Dicker et al. Submitted to MNRAS 1999. (astro-ph/9907118) \n\\bibitem{mauskopf} P. D. Mauskopf et al., astro-ph/9911444. \n\\bibitem{cheng} \nE.S. Cheng\\ \\etal\\, \\apjl, {422}, L37 (1994);\nE.S. Cheng\\ \\etal\\ , \\apjl, {456}, L71 (1995);\nE.S. Cheng\\ \\etal\\, \\apjl, {488}, L59 (1997).\n\\bibitem{DMR} C.L. Bennett, A.J. Banday, K.M. Gorski, \nG. Hinshaw, P.D. Jackson, P. Keegstra, A. Kogut, G.F. Smoot,\nD. Wilkinson, and E.L. Wright,\\apjl, {464}, L1 (1996), and\n 4-year COBE/DMR references therein.\n\\bibitem{barth96} Barth Netterfield, 1996, Private communication.\n\\bibitem{BNTT99} S. Burles, K. N. Nollett, J. M. Truran, M. S. Turner,\n{\\em Phys. Rev. Lett.} {\\bf 82} 4176 (1999).\n\\bibitem{bjk98} J. R. Bond, A. H. Jaffe and L. Knox,\nAstrophys. J., in press, astro-ph/9808264.\n\\bibitem{gaussmod}We modify the Gaussian by taking for $500 < l <\n1000$, $\\delta T_l^2 = 2000 \\mu{\\rm K}^2$\nand for $l > 1000$, $\\delta T_l^2 = 0$. Assuming a Gaussian out\nto $l=1000$ gives bad $\\chi^2$ values.\n\\bibitem{firs} K. Ganga, L. Page, E.S. Cheng, \n S.S. Meyer, Astrophys. J. {\\bf 432}, L15 (1994).\n\\bibitem{tenerife} S.M. Gutierrez de la\n Cruz, \\etal, Astrophys. J., {\\bf 442}, 10 (1995). \n\\bibitem{ganga97}Ganga, K., Ratra, B., Gundersen, J. \\& Sugiyama, N. \nAstrophys. J. {\\bf 484} 517-522 (1997) See also astro-ph/9602141\n\\bibitem{radpack} http://flight.uchicago.edu/knox/radical.html\n\\bibitem{pascos} L. Knox, Proceedings of PASCOS 1999, astro-ph/0002163.\n\\bibitem{husugwhite} e.g., W. Hu and N. Sugiyama, Phys. Rev. D {\\bf 51}, \n2599 (1995); % Toward Understanding CMB Anisotropies and Their Implications\nW. Hu and M. White, Astrophys. J. {\\bf 471}, 30 (1996). \n%Acoustic Signatures in the CMB\n\\bibitem{coherence} e.g., J. Magueijo, A. Albrecht, P. Ferreira and\nD. Coulson, Phys. Rev. D {\\bf 54}, 3727 (1996).\n\\bibitem{WBA} J. Weller, R.A. Battye and A. Albrecht, \nPhys.Rev. D60, 103520 (1999).\n%Reionization by active sources and its effects on the cmb astro-ph/9808269.\n\\bibitem{montypython}D. Scott and M. White, Publ.Astron.Soc.Pac. \n{\\bf 111}, 525 (1999).\n\\bibitem{Albrechtpascos} A. Albrecht, \nProceedings of PASCOS 1999.\n\\bibitem{postmodernisocurv} W. Hu, {\\em Phys. Rev. D} {\\bf 59}, 121301 (1999);\nW. Hu, P.J.E. Peebles, astro-ph/9910222; \nN. Turok, Phys. Rev. Lett. {\\bf 77}, 4138 (1996).\n%A Causal Source which mimics inflation\n\\end{thebibliography}\n\\end{document}\n\n\n\n\n\n\n\n"
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{
"name": "astro-ph0002162.extracted_bib",
"string": "\\begin{thebibliography}{ucsc}\n%\\begin{thebibliography}{}\n\\bibitem{forecast} e.g., L.\\ Knox, {\\sl Phys.\\ Rev.}\\/ {\\bf D52} 4307 (1995);\n G.\\ Jungman, M.\\ Kamionkowski,\n A.\\ Kosowsky \\& D.N.\\ Spergel, {\\sl Phys.\\ Rev.\\ Lett.}\\/ {\\bf 76},\n 1007 (1996); {\\sl ibid}, {\\sl Phys.\\ Rev.}\\/ {\\bf D54},\n 1332 (1996); J.R.\\ Bond, G.\\ Efstathiou \\& M.\\ Tegmark, Mon. Not. R. Astron.\nSoc. {\\bf 33}, 291L (1997);\n M.\\ Zaldarriaga, D.\\ Spergel \\& U.\\ Seljak, Astrophys.J. {\\bf 488}, 1 (1997);\nD. Eisenstein, W. Hu and M. Tegmark, Astrophys. J. {\\bf 518}, 2 (1999).\n\\bibitem{paramest} M. Tegmark and M. Zaldarriaga, astro-ph/0002091; \nA. Melchiorri \\etal, astro-ph/9911445;\nN. Bahcall, J.P. Ostriker, S. Perlmutter, and\nP. J. Steinhardt, Science, {\\bf 284} 1481 (1999) (astro-ph/9906463);\nJ.G. Bartlett, A. Blanchard, M. Douspis, M. Le Dour,\nProc Evol of Large Scale Structure, Garching, Aug 1998, astro-ph/9810318;\nJ. R. Bond, A.H. Jaffe, Phil.\nTrans. R. Soc. Lond. astro-ph/9809043;\nC. H. Lineweaver, Science {\\bf 284}, 1503 (1999); \nB. Ratra, {\\it et al.} Astrophys. J. {\\bf 517}, 549 (1999);\nM. Tegmark, Astrophys. J. {\\bf 514}, L69 (1999).\n\\bibitem{dodknox99}S. Dodelson \\& L. Knox, %submitted to Phys. Rev. Lett.\nastro-ph/9909454.\n\\bibitem{wilson99} G. Wilson, \\etal\\ Astrophys. J., in press, astro-ph/9902047.\n\\bibitem{coble99} K. Coble et al., Astrophys. J. {\\bf 519}, L5 (1999)\n(astro-ph/9902195); K. Coble, Ph.D. Thesis, astro-ph/9911419.\n\\bibitem{toco} [TOCO97] E. Torbet \\etal\\ Astrophys. J. {\\bf 521} L79 \n(1999)(astro-ph/9905100); [TOCO98] A. Miller et al., \nAstrophys. J. {\\bf 524} L1 (1999) astro-ph/9906421.\n\\bibitem{tocoexplained} The Mobile Anisotropy Telescope\n(MAT), while situated on Cerro Toco, Chile, produced two data sets using\nthe same instrument and observing\nstrategy, TOCO97 \\& TOCO98. We refer to these collectively as TOCO.\n\\bibitem{peterson} J. B. Peterson et al., astro-ph/9910503.\n\\bibitem{bak99} J. C. Baker et al.,\n%, K. Grainge, M.P. Hobson,\n%M.E. Jones, R. Kneissl, A.N. Lasenby, C.M.M. O'Sullivan, G. Pooley,\n%G. Rocha, R. Saunders, P.F. Scott, E.M. Waldram, \nsubmitted to MNRAS, astro-ph/9904415.\n\\bibitem{dicker99}Dicker et al. Submitted to MNRAS 1999. (astro-ph/9907118) \n\\bibitem{mauskopf} P. D. Mauskopf et al., astro-ph/9911444. \n\\bibitem{cheng} \nE.S. Cheng\\ \\etal\\, \\apjl, {422}, L37 (1994);\nE.S. Cheng\\ \\etal\\ , \\apjl, {456}, L71 (1995);\nE.S. Cheng\\ \\etal\\, \\apjl, {488}, L59 (1997).\n\\bibitem{DMR} C.L. Bennett, A.J. Banday, K.M. Gorski, \nG. Hinshaw, P.D. Jackson, P. Keegstra, A. Kogut, G.F. Smoot,\nD. Wilkinson, and E.L. Wright,\\apjl, {464}, L1 (1996), and\n 4-year COBE/DMR references therein.\n\\bibitem{barth96} Barth Netterfield, 1996, Private communication.\n\\bibitem{BNTT99} S. Burles, K. N. Nollett, J. M. Truran, M. S. Turner,\n{\\em Phys. Rev. Lett.} {\\bf 82} 4176 (1999).\n\\bibitem{bjk98} J. R. Bond, A. H. Jaffe and L. Knox,\nAstrophys. J., in press, astro-ph/9808264.\n\\bibitem{gaussmod}We modify the Gaussian by taking for $500 < l <\n1000$, $\\delta T_l^2 = 2000 \\mu{\\rm K}^2$\nand for $l > 1000$, $\\delta T_l^2 = 0$. Assuming a Gaussian out\nto $l=1000$ gives bad $\\chi^2$ values.\n\\bibitem{firs} K. Ganga, L. Page, E.S. Cheng, \n S.S. Meyer, Astrophys. J. {\\bf 432}, L15 (1994).\n\\bibitem{tenerife} S.M. Gutierrez de la\n Cruz, \\etal, Astrophys. J., {\\bf 442}, 10 (1995). \n\\bibitem{ganga97}Ganga, K., Ratra, B., Gundersen, J. \\& Sugiyama, N. \nAstrophys. J. {\\bf 484} 517-522 (1997) See also astro-ph/9602141\n\\bibitem{radpack} http://flight.uchicago.edu/knox/radical.html\n\\bibitem{pascos} L. Knox, Proceedings of PASCOS 1999, astro-ph/0002163.\n\\bibitem{husugwhite} e.g., W. Hu and N. Sugiyama, Phys. Rev. D {\\bf 51}, \n2599 (1995); % Toward Understanding CMB Anisotropies and Their Implications\nW. Hu and M. White, Astrophys. J. {\\bf 471}, 30 (1996). \n%Acoustic Signatures in the CMB\n\\bibitem{coherence} e.g., J. Magueijo, A. Albrecht, P. Ferreira and\nD. Coulson, Phys. Rev. D {\\bf 54}, 3727 (1996).\n\\bibitem{WBA} J. Weller, R.A. Battye and A. Albrecht, \nPhys.Rev. D60, 103520 (1999).\n%Reionization by active sources and its effects on the cmb astro-ph/9808269.\n\\bibitem{montypython}D. Scott and M. White, Publ.Astron.Soc.Pac. \n{\\bf 111}, 525 (1999).\n\\bibitem{Albrechtpascos} A. Albrecht, \nProceedings of PASCOS 1999.\n\\bibitem{postmodernisocurv} W. Hu, {\\em Phys. Rev. D} {\\bf 59}, 121301 (1999);\nW. Hu, P.J.E. Peebles, astro-ph/9910222; \nN. Turok, Phys. Rev. Lett. {\\bf 77}, 4138 (1996).\n%A Causal Source which mimics inflation\n\\end{thebibliography}"
}
] |
astro-ph0002163
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Adiabatic CDM Models and the Competition
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[
{
"author": "Lloyd Knox"
}
] |
The inflation-inspired flat, cold dark matter-dominated models of structure formation with adiabatic, nearly scale-invariant initial conditions agree very well with current CMB anisotropy data. The success of these models is highlighted by the failure of alternatives; we argue that there are no longer any viable competitors (with the exception of models with more complicated matter content which are still flat and which still require inflation). CMB data will soon be of sufficient quality that, if one {assumes} inflation, one can detect a non-zero cosmological constant by combining a determination of the peak location with Hubble constant measurements.
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[
{
"name": "pascos.tex",
"string": "%%UNIX --- UPDATED ON 13/8/97\n%====================================================================%\n% sprocl.tex 27-Feb-1995 %\n% This latex file rewritten from various sources for use in the %\n% preparation of the standard proceedings Volume, latest version %\n% by Susan Hezlet with acknowledgments to Lukas Nellen. %\n% Some changes are due to David Cassel. %\n%====================================================================%\n\n\\documentstyle[sprocl]{article}\n\n\\font\\eightrm=cmr8\n\n\\input{psfig}\n\n\\bibliographystyle{unsrt} %for BibTeX - sorted numerical labels by\n %order of first citation.\n\n\\arraycolsep1.5pt\n\n% A useful Journal macro\n\\def\\Journal#1#2#3#4{{#1} {\\bf #2}, #3 (#4)}\n\n% Some useful journal names\n\\def\\NCA{\\em Nuovo Cimento}\n\\def\\NIM{\\em Nucl. Instrum. Methods}\n\\def\\NIMA{{\\em Nucl. Instrum. Methods} A}\n\\def\\NPB{{\\em Nucl. Phys.} B}\n\\def\\PLB{{\\em Phys. Lett.} B}\n\\def\\PRL{\\em Phys. Rev. Lett.}\n\\def\\PRD{{\\em Phys. Rev.} D}\n\\def\\ZPC{{\\em Z. Phys.} C}\n\n% Some other macros used in the sample text\n\\def\\st{\\scriptstyle}\n\\def\\sst{\\scriptscriptstyle}\n\\def\\mco{\\multicolumn}\n\\def\\epp{\\epsilon^{\\prime}}\n\\def\\vep{\\varepsilon}\n\\def\\ra{\\rightarrow}\n\\def\\ppg{\\pi^+\\pi^-\\gamma}\n\\def\\vp{{\\bf p}}\n\\def\\ko{K^0}\n\\def\\kb{\\bar{K^0}}\n\\def\\al{\\alpha}\n\\def\\ab{\\bar{\\alpha}}\n\\def\\be{\\begin{equation}}\n\\def\\ee{\\end{equation}}\n\\def\\bea{\\begin{eqnarray}}\n\\def\\eea{\\end{eqnarray}}\n\\def\\CPbar{\\hbox{{\\rm CP}\\hskip-1.80em{/}}}%temp replacemt due to no font\n\n\\def\\TBD{{\\bf TBD}}\n\\def\\la{\\mathrel{\\mathpalette\\fun <}}\n\\def\\ga{\\mathrel{\\mathpalette\\fun >}}\n\\def\\fun#1#2{\\lower3.6pt\\vbox{\\baselineskip0pt\\lineskip.9pt\n \\ialign{$\\mathsurround=0pt#1\\hfil##\\hfil$\\crcr#2\\crcr\\sim\\crcr}}}\n%%%%%%%%%\n\n\\def\\etal{{\\it et. al.}}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%BEGINNING OF TEXT\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{document}\n\n\\title{Adiabatic CDM Models and the Competition}\n\n\\author{Lloyd Knox}\n\n\\address{Department of\nAstronomy and Astrophysics, The University of Chicago\\\\5640 So. Ellis Avenue,\nChicago, IL~~60637-1433, USA}\n\\vskip 0.05in\n\\address{E-mail: knox@flight.uchicago.edu}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% You may repeat \\author \\address as often as necessary %\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\maketitle\\abstracts{The inflation-inspired flat, cold\ndark matter-dominated models of structure formation with\nadiabatic, nearly scale-invariant initial conditions agree very well\nwith current CMB anisotropy data. The success of these models\nis highlighted by the failure of alternatives; we argue\nthat there are no longer any viable competitors (with the\nexception of models with more complicated matter content \nwhich are still flat and which still require inflation). \nCMB data will soon be of sufficient quality that, if one {\\it assumes}\ninflation, one can detect a non-zero cosmological constant by\ncombining a determination of the peak location with \nHubble constant measurements.\n}\n\n\\section{Introduction}\n\nThe aim of this paper is to demonstrate the success of\ninflation-inspired models of structure formation. The CMB data are\npointing us towards models in which the mean spatial curvature is\nzero, and in which the ``initial'' perturbations were adiabatic and\nnearly scale-invariant. These three properties are all predictions of\nthe simplest models of inflation. We will discuss them below and how\nthey influence the properties of the CMB. Since we are never able to\nprove a model to be true, just that it is more probable than other\nmodels, much of the demonstration of the success of inflation-inspired\nmodels is a discussion of what goes wrong with other ones.\n\nWe begin with a very quick review\\cite{swrev} of the basics\nand then move on to a brief description of current data.\nThe subsequent discussion of adiabatic models explains what adiabatic,\nflat and nearly scale-invariant mean and how these properties\ninfluence the CMB power spectrum. With this discussion complete we\nare then ready to see how isocurvature and defect models \ndiffer, and that they do so in ways that conflict with the data. \nFinally, the strong constraint on the peak\nlocation given all data, prompts a discussion about what we can learn\nfrom the peak location besides the geometry.\n\n\\section{Preliminaries}\n\nAt sufficiently early times, a thermal distribution of photons kept\nall the atoms in the Universe ionized. Because of the strength of the\nThomson cross section and the large number density of electrons, the\nphotons were tightly coupled to the electrons (and through them to the\nnuclei) and therefore these components could be treated as a single\nfluid called the photon-baryon fluid. As the photon temperature\ncooled (due to the expansion of the Universe) below one Rydberg\n(actually well below one Rydberg due to the enormous photon-to-baryon\nratio), the electrons combined with the nuclei thereby decoupling the\nphotons from the baryons. The Universe became transparent to the\nphotons that are now the CMB. Thus when we look at the CMB, we are\nseeing the Universe as it was at the time of decoupling---also\nreferred to as ``last-scattering''.\n\nThe temperature of the CMB is the same in all directions, to 1 part in\n100,000. The most interesting statistical property of these tiny\nfluctuations is the angular power spectrum, $C_l$, which tells us how\nmuch fluctuation power there is at different angular scales, or\nmultipole moments $l$ (where $l \\sim \\pi/\\theta$). Because the\ndepartures from isotropy are so small, linear perturbation theory is\nan excellent approximation and the angular power spectrum can be\ncalculated for a given model with very high precision. Thus the CMB\noffers a very clean probe of cosmology---one where the basic physics\nis much better understood than is the case for galaxies or even\nclusters of galaxies.\n\nThroughout, $\\Omega_i$ is the mean density\nof component $i$, $\\bar \\rho_i$, in units of the critical density\nwhich divides negatively and positively curved models.\nNote that $\\Omega \\equiv \\sum_i \\Omega_i = 1$ corresponds to the\ncase of zero mean spatial curvature.\n\n\\section{The Data}\n\nThe last year of the 1000's was a very exciting one for those\ninterested in measurements of the angular power spectrum. \nNew results came from MSAM\\cite{wilson99}, PythonV\\cite{coble99a,coble99b}, \nCAT\\cite{bak99}, MAT\\cite{mat97,mat98,tocoexplained}, \nIAC\\cite{dicker99}, Viper\\cite{peterson}, and BOOM/NA\\cite{mauskopf}, all of\nwhich have bearing on the properties of the peak. \nThese data make a convincing case\nthat we have indeed observed a peak---which not only rises towards\n$l=200$ (as we have known for several years\\cite{risedetect}) but also falls\ndramatically towards $l=400$. Figure 1 shows the results from 1999\nplus, in background shading, a fit\\cite{BJKII} \nof the power in 14 bands of $l$ to\nall the data. Many of the bands are at\nlow enough $l$ that they cannot be discerned on a linear x-axis plot.\nThe $\\Omega=1$ model in the figure \nhas a mean density of non-relativistic matter, \n$\\Omega_m=0.31$, a cosmological constant density of $\\Omega_\\Lambda=0.69$,\na baryon density of $\\Omega_b=0.019h^{-2}$ \\protect\\cite{BNTT99}, a Hubble\nconstant of $H_0 = 100 h\\ {\\rm km/sec/Mpc}$ with $h=0.65$, \nan optical depth to reionization\nof $\\tau = 0.17$ and a power spectrum power-law index of $n=1.12$, where\n$n=1$ is scale invariant.\n\n%% figure 1\n\\begin{figure}\n\\label{fig:data}\n{\\psfig{figure=kpfig1_alt.eps,width=4in}}\n\\caption{Bandpowers from TOCO97 (cyan open triangles), \nTOCO98 (blue filled triangles), BOOM/NA (green filled squares),\nMSAM (red open squares), CAT (black open pentagon), IAC (black \nfilled pentagon), PyV (black open circles) and Viper\n(green filled circles). The y-axis is \n$\\delta T_l \\equiv \\sqrt{l(l+1)C_l/(2\\pi)}$ where $C_l$ is the\nangular power spectrum. The models\nare (from peaking at left to peaking at right) the best fit models\nof \\protect\\cite{dodknox99} for $\\Omega=1$, $\\Omega=0.4$ and $\\Omega=0.2$. \nCalibration errors are not shown. \n}\n\\end{figure}\n\nKnox and Page \\cite{KP00} have recently characterized the peak with\nfits of phenomenological models to the data. They find the peak to\nbe localized by TOCO and BOOM/NA at $175 < l_{\\rm peak} < 243$ and\n$151 < l_{\\rm peak} < 259$ respectively (both ranges 95\\% confidence).\nThis location is also indicated by combining the PythonV and Viper\ndata, as can be seen in Fig. 1 and a significant bound can also be\nderived by combining all other data, prior to these four data sets. \nIn sum, a peak near $l \\sim 200$, is robustly detected. \nCombining all the data, we can also constraint its full-width at \nhalf-maximum to be between 180 and 250 at 95\\% confidence. \n\n\\section{Physical Models}\n\nIn this section we describe three classes of physical models\n(adiabatic CDM, topological defects and isocurvature dark matter) and\ntheir predictions for the angular power spectrum\\cite{whatweknow}. \n\n\\subsection{Adiabatic CDM}\n\nThe simplest models of inflation lead to a post-reheat Universe with\ncritical density (to exponential precision) and adiabatic, nearly\nscale-invariant fluctuations\\cite{KT}. Although inflation does not require\ncold dark matter, the prediction of critical density, combined with\nupper limits on the mean baryonic density, push one in that direction.\nWithin the last few years, the observations have developed to strongly\nprefer the gap between $\\Omega_b$ $(b \\equiv {\\rm baryons})$\nand unity to be filled with not just cold dark matter, \nbut a sizeable helping of dark energy too, e.g., \n\\cite{dodknox99,bahcall,mturner,SNe}.\nLet's examine more precisely each of these three predictions.\n\n\\subsubsection{Adiabatic}\n\nAdiabatic (or, equivalently, isentropic) means that there are no\nspatial fluctuations in the total entropy {\\it per particle of each type}. \nThat is, $\\delta\n(s/n_i) = 0$ for all species $i$. From this, we see that $\\delta\nn_i/n_i = \\delta s/s$ and therefore all species have the same\nfractional fluctuation in their number densities. For example, where\nthere are more dark matter particles there are more photons, etc. A\ngeneral perturbation\\cite{generalperturb} is a\nlinear combination of isocurvature and adiabatic modes. Isocurvature\nperturbations are arranged so that $\\delta \\rho = \\sum_i \\delta \\rho_i = 0$.\n\nThe evolution of a single Fourier mode is initially a competition\nbetween the pressure of the baryon-photon fluid trying to decrease\ndensity contrasts, and gravity trying to enhance them.\nFor adiabatic modes the gravitational term is initially dominant, \nincreasing the amplitude of the mode, until the restorative\nforce of the pressure gradients pushes it back. Despite the\ninitial growth in the density contrast, the potential decays.\nThis\nis because the photon pressure prevents the growth from happening\nquickly enough to counteract the effects of the expansion. It is this\ndecay of the potential that leads to excitation of a cosine mode\n(after the initial transient) for the acoustic oscillation. For\nisocurvature modes, the potential is initially zero, until there is\nsufficient time for pressure gradients to evolve into density\ngradients. The initially growing potential excites a sine mode\n\\cite{husug,HW}.\n\nAll adiabatic modes of given wavenumber, $k=\\sqrt{k_x^2+k_y^2+k_z^2}$,\nalthough they have different {\\it spatial} phases, will all have the\nsame {\\it temporal} phase, because they all start off with the same\nrelationship between the dark matter and photons. In other words,\nalthough spatially incoherent, they are temporally coherent. This\ncoherence is essential to the familiar Doppler peak structure of the\nCMB power spectrum \\cite{coherence}. \nFigure 2 illustrates the point by showing the\nspatial dependence of three different modes with varying wave numbers\nat five different stages of their evolution. \n\n%% figure 2\n\\begin{figure}\n\\centerline{\\psfig{figure=doppler_alt.eps,width=3.5in}}\n\\caption{Spatial dependence of the photon-baryon fluid temperature\nfor three different modes at five different times. Shown is the evolution\nfrom very early when the wavelengths are much larger than the Hubble\nradius and causal processes have not had time to change\nthe ``initial conditions'' as left by inflation (top panels) to the\ntime of decoupling between matter and radiation (bottom panels). \nThe longest wavelength mode is shown on the left. \nIt reaches its\nfirst maximum just at the time of decoupling. The peak-to-trough\ndistance, as seen by us today, subtends about a degree on the\nlast-scattering surface. The fact that this mode (and all modes \nwith the same wavelength) reach an extremum just at the time\nof decoupling is the reason for the first peak in the\nCMB power spectrum at $l \\sim 200$. Contrast this behavior \nwith that of a mode with half the wavelength\n(shown in the five middle panels) which therefore oscillates in\ntime twice as fast and hits a null at the time of decoupling.\nModes like this one have a peak-to-trough distance of about half\na degree and are responsible for the first trough at $l=400$.\nFinally, the right-most panels are for the \neven faster and shorter modes responsible for the\nsecond peak.\n}\n\\end{figure}\n\n\\subsubsection{Flat}\n\nInflation generically produces flat Universes---ones where the mean\nspatial curvature is exponentially close to zero (e.g., $e^{-100}$ is\na particularly large residual curvature). The CMB is sensitive to\ncurvature because the translation of a linear distance on the last-scattering\nsurface to an angular extent on the sky depends on it. \nOne can see this by noting that\nin a negatively curved space the surface area of a sphere of radius\n$r$ is larger than $4\\pi r^2$ and therefore objects at fixed\ncoordinate distance of fixed size appear smaller than they would in\nthe case of zero curvature (the larger-than-$4\\pi r^2$ sphere must be\nsqueezed into a local $4\\pi$ steradians). This geometrical effect\nshifts the CMB power spectrum peak locations by a factor of\n$\\Omega^{-1/2}$. Other parameters also affect the peak locations by\naltering the coordinate distance to the last-scattering surface and\nthe size of features there; these are subdominant effects which will\nbe discussed later.\n\n\\subsubsection{Nearly Scale Invariant}\n\nThe power spectrum of fluctuations produced by the simplest models of\ninflation is\nwell-described by a power law, $P(k) \\propto k^n$, with $n$ near\nunity. The case $n=1$ is called scale-invariant because the\ndimensionless quantity $k^3 P(k)$ is the same for all modes when the\ncomparison is done at ``horizon crossing'' (when the mode wavelength\nbecomes smaller than the Hubble radius)\\cite{KT}. \n\n\n\\subsection{Topological Defects}\n\nThe usual scenario for topological defects is that a phase transition\nin an initially homogeneous Universe gives rise to a scalar field with\na spatially-varying stress-energy tensor. In most such scenarios, the\nscalar field configuration evolves into a network of regions which are\ntopologically incapable of relaxing to the true ground state.\nCausality implies that these models have isocurvature initial\nconditions.\n\nIn defect models, the temporal coherence is lost due to continual\nsourcing of new perturbations by the non-linearly evolving scalar\nfield. This generically leads to one very broad peak with a maximum\nnear $l=400-500$\\cite{coherence}. Thus the drop in power from $l=200$\nto $l=400$ is a very challenging feature of the data. \nOne can get lower power at $l=400$ than at $l=200$ with\nmodifications to the ionization history\\cite{WBA}, but even for\nthese models the drop probably is not fast enough. See A. Albrecht's\ncontribution to these proceedings.\n\n\\subsection{Isocurvature Dark Matter Models}\n\nNote that isocurvature is more general than adiabatic. Given numerous\ncomponents, there are a number of different ways of maintaining the\nisocurvature condition, $\\sum_i \\delta \\rho_i = 0$. In what follows we\nwill assume that the isocurvature condition is maintained by the dark\nmatter compensating everything else.\n\nIsocurvature models have at least two strikes against them. First,\nscale-invariant models produce far too much fluctuation power on large\nangular scales, when normalized to galaxy fluctuations at smaller\nscales as has been known for over a decade \\cite{EB86}. \n%The relative\n%quietness on large angular scales of adiabatic models is due to the\n%different ways in which the {\\it Sachs-Wolfe effect} plays out in\n%these two models. So far we have only discussed the effects of\n%intrinsic temperature fluctuations in last-scattering surface---and\n%this is the principally important effect for understanding the Doppler\n%peaks. But at large angular scales ($l \\la 60$) the gravitational\n%redshift of a photon climbing out of a potential well is important.\n%For adiabatic models, at large angular scales, the potential wells are\n%also where the photon over densities are. Therefore the gravitational\n%redshift is coherently destructive with the intrinsic temperature and\n%the combined effect results in the Sachs-Wolfe result: $\\delta T/T =\n%-1/3 \\phi$, where $\\phi$ is the Newtonian potential. For isocurvature\n%models, the opposite relation holds: where there are more photons\n%corresponds to potential hills. This is because pressure gradients\n%are moving photons out of the higher pressure regions. The\n%gravitational redshift and intrinsic effects are coherently\n%constructive with the result: $\\delta T/T = -2\\phi$. Thus for the\n%same small-scale normalization isocurvature models produce {\\bf 36}\n%times more power on large scales than do adiabatic models. \nOne might\nhope to save isocurvature models by tilting them far from\nscale invariant, but this fix cannot simultaneously get galaxy scales,\nCOBE-scales and Doppler peak scales right.\n\nThe second strike has to do with the location of the acoustic peaks.\nAs mentioned above, the isocurvature oscillations are 90 degrees out\nof phase with the adiabatic ones. The peaks get shifted to {\\it\n higher} $l$ ($l = 350$ to $400$ for the first peak) \\cite{HW}. Geometrical\neffects could shift it back, to make it agree with the data, but this\nwould require $\\Omega > 2$ which is inconsistent with a number of \nobservations\\cite{whatweknow}. \n\nThere are scenarios with initially isocurvature conditions that can\nproduce CMB power spectra that look much like those in the adiabatic\ncase. This can be done by adding to adiabatic fluctuations, another\ncomponent which maintains the isocurvature condition and then by\ngiving this extra component a non-trivial stress history\n\\cite{postmodernisocurv}. These alternatives will be interesting to\npursue further if improvements to the data cause troubles for the\ncurrently successful adiabatic models. Even these alternatives are\nflat models that require some mechanism, such as inflation, for\ncreating the super-horizon correlations in their initial conditions.\n\nTurok has shown that even super-horizon correlations are not a necessary\ncondition for CMB power spectra that mimic those of inflation\\cite{turok}.\nAlthough no specific model is constructed, this work demonstrates that\ncausality alone does not preclude one from getting inflation-like\npower spectra without inflation. For a discussion of the physical plausibility\nof models that could do this, see \\cite{HSW97}.\n\n\\section{Peak Location and $\\Omega_\\Lambda$}\n\nIf we {\\it assume} \nflatness, adiabaticity and near scale-invariance we can \nthen determine $\\Omega_\\Lambda$ from the location of the first peak\n\\cite{marc}.\nWith these assumptions, the peak position just depends on the\ncoordinate distance to the last-scattering surface divided by the\nsound horizon at last-scattering. How this ratio depends on $\\Omega_\\Lambda$\ndepends on what else we hold fixed. If we have high-precision\nCMB data over several peaks then $w_b \\equiv \\Omega_b h^2$ and\n$w_c \\equiv \\Omega_c h^2$ would be good things to keep fixed, since\nthose are what affect the acoustic peak morphology\\cite{EB99}. \nHowever, without\nsuch high precision data, $w_b$ and $H_0$ are good things to fix because\nwe know these fairly well from other measurements. With $w_b$ and $H_0$\nfixed, increasing $\\Omega_\\Lambda$ increases the sound horizon (because\n$w_c$ must decrease) but increases the coordinate distance to the\nlast-scattering surface by more and the peak moves out to higher $l$. With\n$w_b$ and $w_c$ fixed, the sound-horizon stays the same but $H_0$ increases\nand the coordinate distance to the last-scattering surface drops: the\npeak shifts to lower $l$.\n\n%% figure 4\n\\begin{figure}\n\\label{fig:lambdaVlpeak}\n\\centerline{\\psfig{figure=lambdaVlpeak_alt.eps,width=3.5in}}\n\\caption{We find $l_{\\rm peak}$ as we vary $\\Omega_\\Lambda$\nfor three values of the Hubble constant. We always fix\n$\\Omega_b h^2 = 0.019$, no reionization, no gravity waves, no tilt.\nThe horizontal lines show 1$\\sigma$ constraint on $l_{\\rm peak}$ of\n$220 \\pm 5$ that\nshould be possible from Boom98 data, just using $100< l < 300$. The\ncorresponding bound for MAP will be about $\\pm 1$.\n}\n\\end{figure}\n\nIf we take all the data, the peak\nlocation is $l_{\\rm peak} =229\\pm 9$\\cite{KP00}. \nThus, if we assume $h=0.65$ then\nthis is evidence for a positive cosmological constant. It is weak\nevidence because inclusion of possible systematic errors would \nprobably widen the peak bound significantly. \nHowever, for a sample-variance dominated measurement of the first\npeak (specifically, $C_l$ from\n$l=100$ to $l=300$) derived from observations of 1000 square\ndegrees of sky (comparable to the Antarctic Boomerang coverage)\none can determine the peak to be at, e.g., $l_c = 220 \\pm 5$. \nOne can see from Fig.~\\ref{fig:lambdaVlpeak} that we may soon have\na strong determination of non-zero $\\Omega_\\Lambda$ based\nsolely on Hubble constant and CMB measurements. Note that\nthis determination \nwill not suffer from calibration uncertainty.\n\n\\section{Conclusion}\nThe peak has been observed by two\ndifferent instruments, and can be inferred from an independent\ncompilation of other data sets. The properties of this peak are\nconsistent with those of the first peak in the inflation-inspired\nadiabatic CDM models, and inconsistent with competing models, with the\npossible exception of the more complicated isocurvature models\nmentioned above. It is perhaps instructive that where the\nconfrontation between theory and observation can be done with a\nminimum of theoretical uncertainty, the adiabatic CDM models have been\nhighly successful.\n\n\n\\section*{Acknowledgments}\nI thank A. Albrecht, L. Page and J. Ruhl for useful conversations and\nD. Eisenstein for comments on the manuscript.\nI used CMBAST\\cite{cmbfast} and am supported by the DoE, NASA grant NAG5-7986,\nand NSF grant OPP-8920223. \n\n\\section*{References}\n\\begin{thebibliography}{99}\n\n\\bibitem{swrev} For a longer review, see M. White, D. Scott and J. Silk, \nAnnual Review of Astronomy and Astrophysics, {\\bf 32}, 315 (1994). For\na textbook treatment see, e.g., P.J.E. Peebles, ``Principles of Physical\nCosmology'', Princeton University Press, Princeton, NJ (1993).\n\\bibitem{wilson99} G. Wilson, \\etal\\ 1999, astro-ph/9902047.\n\\bibitem{coble99a} K. Coble et al., Astrophys. J. {\\bf 519}, L5 (1999)\n(astro-ph/9902195)\n\\bibitem{coble99b} K. Coble, Ph.D. Thesis, astro-ph/9911419.\n\\bibitem{bak99} J. C. Baker et al., Submitted to MNRAS,\nastro-ph/9904415.\n\\bibitem{mat97} E. Torbet \\etal\\ Astrophys. J. {\\bf 521} L79 \n(1999)(astro-ph/9905100)\n\\bibitem{mat98} A. Miller et al., Astrophys. J. {\\bf 524} L1 astro-ph/9906421.\n\\bibitem{tocoexplained} The Mobile Anisotropy Telescope\n(MAT) has produced two data sets \nreferred to as TOCO97 \\& TOCO98, or TOCO collectively. \n\\bibitem{dicker99}Dicker et al. Submitted to MNRAS 1999. (astro-ph/9907118) \n\\bibitem{peterson} J. B. Peterson et al., astro-ph/9910503.\n\\bibitem{mauskopf} P. D. Mauskopf et al., astro-ph/9911444. \n\\bibitem{risedetect} D. Scott and M. White, astro-ph/9407073, \n%THE EXISTENCE OF BARYONS AT z=1000, \nProceedings of the CWRU CMB Workshop `2 years after COBE' \neds. L. Krauss \\& P. Kernan (1994).\n\\bibitem{BJKII} J.R. Bond, A.H. Jaffe and L. Knox, Astrophys. J. in press, \nastro-ph/9808204 (1998).\n\\bibitem{KP00} L. Knox and L. Page, astro-ph/0002162.\n\\bibitem{whatweknow} For further discussion\nof the implications of CMB data, see \nD. Scott and M. White, Publ.Astron.Soc.Pac. {\\bf 111},\n525 (1999), astro-ph/9810446 and references therein..\n\\bibitem{KT} For a textbook treatment of inflation, see, e.g., E.W. Kolb and\nM.S. Turner, ``The Early Universe'', Addison-Wesley, New York, NY (1990).\n\\bibitem{dodknox99}Dodelson, S. \\& Knox, L., 1999, astro-ph/9909454.\n\\bibitem{bahcall}Bahcall, N., Ostriker, J. P., Perlmutter, S., and\nSteinhardt, P. J., 1999, Science, 284, 1481-1488 (astro-ph/9906463);\n\\bibitem{mturner} M.S. Turner, ``The Third Stromlo Symposium: The Galactic\nHalo'', eds. B.K. Gibson, T.S. Axelrod and M.E. Putman, ASP Conference\nSeries {\\bf 165}, 431 (1999); astro-ph/9811454.\n\\bibitem{generalperturb} We are here restricting ourselves to a\ntwo-component description (dark matter and baryon-photon fluid).\nWith more components, there may be more modes. See\nM. Bucher, K. Moodley and N. Turok, astro-ph/9904231.\n\\bibitem{husug} W. Hu and N. Sugiyama, Phys. Rev. D {\\bf 51}, 2599 (1995).\n% Toward Understanding CMB Anisotropies and Their Implications\n\\bibitem{HW} W. Hu and M. White, Astrophys. J. {\\bf 471}, 30 (1996).\n%Acoustic Signatures in the CMB\n\\bibitem{coherence} e.g., J. Magueijo, A. Albrecht, P. Ferreira and\nD. Coulson, Phys. Rev. D {\\bf 54}, 3727 (1996).\n\\bibitem{WBA} J. Weller, R.A. Battye and A. Albrecht, \nPhys.Rev. D60, 103520 (1999).\n%Reionization by active sources and its effects on the cmb astro-ph/9808269.\n\\bibitem{EB86} G. Efstathiou and J. R. Bond, MNRAS {\\bf 218}, 103 (1986).\n%Constraints on Isocurvature CDM Models\n\\bibitem{EB99} G. Efstathiou and J. R. Bond, MNRAS {\\bf 304}, 75 (1999).\n\\bibitem{H0} See e.g., J.R. Mould et al, astro-ph/9909260.\n\\bibitem{SNe} A.G. Riess, et al., {\\em Astron. J.} {\\bf 116}, 1009 (1998);\nS. Perlmutter et al, {\\em Astrophys. J.} {\\bf 517}, 565\n(1999) (astro-ph/9812133).\n\\bibitem{BNTT99} S. Burles, K. N. Nollett, J. M. Truran, M. S. Turner,\n{\\em Phys. Rev. Lett.} {\\bf 82} 4176 (1999).\n%\\bibitem{CBF} J. Mohr et al, {\\em Astrophys. J.}, in press (1999)\n%(astro-ph/9901281).\n%\\bibitem{montypython}D. Scott and M. White, Publ.Astron.Soc.Pac. \n%{\\bf 111}, 525 (1999).\n\\bibitem{postmodernisocurv} W. Hu, {\\em Phys. Rev. D} {\\bf 59}, 121301 (1999);\nW. Hu, P.J.E. Peebles, astro-ph/9910222.\n\\bibitem{turok}N. Turok, Phys. Rev. Lett. {\\bf 77}, 4138 (1996).\n%A Causal Source which mimics inflation\n\\bibitem{HSW97} W. Hu, D. Spergel and M. White, \nPhys. Rev. {\\bf D55}, 3288 (1997).\n\\bibitem{marc} Or, from the second peak: M. Kamionkowski and A. Buchalter, \nastro-ph/0001045 \n\\bibitem{cmbfast} U. Seljak \\& M. Zaldarriaga, Astrophys. J. {\\bf 469}, \n437 (1996).\n\\end{thebibliography}\n\n\\end{document}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% End of sprocl.tex\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002163.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{swrev} For a longer review, see M. White, D. Scott and J. Silk, \nAnnual Review of Astronomy and Astrophysics, {\\bf 32}, 315 (1994). For\na textbook treatment see, e.g., P.J.E. Peebles, ``Principles of Physical\nCosmology'', Princeton University Press, Princeton, NJ (1993).\n\\bibitem{wilson99} G. Wilson, \\etal\\ 1999, astro-ph/9902047.\n\\bibitem{coble99a} K. Coble et al., Astrophys. J. {\\bf 519}, L5 (1999)\n(astro-ph/9902195)\n\\bibitem{coble99b} K. Coble, Ph.D. Thesis, astro-ph/9911419.\n\\bibitem{bak99} J. C. Baker et al., Submitted to MNRAS,\nastro-ph/9904415.\n\\bibitem{mat97} E. Torbet \\etal\\ Astrophys. J. {\\bf 521} L79 \n(1999)(astro-ph/9905100)\n\\bibitem{mat98} A. Miller et al., Astrophys. J. {\\bf 524} L1 astro-ph/9906421.\n\\bibitem{tocoexplained} The Mobile Anisotropy Telescope\n(MAT) has produced two data sets \nreferred to as TOCO97 \\& TOCO98, or TOCO collectively. \n\\bibitem{dicker99}Dicker et al. Submitted to MNRAS 1999. (astro-ph/9907118) \n\\bibitem{peterson} J. B. Peterson et al., astro-ph/9910503.\n\\bibitem{mauskopf} P. D. Mauskopf et al., astro-ph/9911444. \n\\bibitem{risedetect} D. Scott and M. White, astro-ph/9407073, \n%THE EXISTENCE OF BARYONS AT z=1000, \nProceedings of the CWRU CMB Workshop `2 years after COBE' \neds. L. Krauss \\& P. Kernan (1994).\n\\bibitem{BJKII} J.R. Bond, A.H. Jaffe and L. Knox, Astrophys. J. in press, \nastro-ph/9808204 (1998).\n\\bibitem{KP00} L. Knox and L. Page, astro-ph/0002162.\n\\bibitem{whatweknow} For further discussion\nof the implications of CMB data, see \nD. Scott and M. White, Publ.Astron.Soc.Pac. {\\bf 111},\n525 (1999), astro-ph/9810446 and references therein..\n\\bibitem{KT} For a textbook treatment of inflation, see, e.g., E.W. Kolb and\nM.S. Turner, ``The Early Universe'', Addison-Wesley, New York, NY (1990).\n\\bibitem{dodknox99}Dodelson, S. \\& Knox, L., 1999, astro-ph/9909454.\n\\bibitem{bahcall}Bahcall, N., Ostriker, J. P., Perlmutter, S., and\nSteinhardt, P. J., 1999, Science, 284, 1481-1488 (astro-ph/9906463);\n\\bibitem{mturner} M.S. Turner, ``The Third Stromlo Symposium: The Galactic\nHalo'', eds. B.K. Gibson, T.S. Axelrod and M.E. Putman, ASP Conference\nSeries {\\bf 165}, 431 (1999); astro-ph/9811454.\n\\bibitem{generalperturb} We are here restricting ourselves to a\ntwo-component description (dark matter and baryon-photon fluid).\nWith more components, there may be more modes. See\nM. Bucher, K. Moodley and N. Turok, astro-ph/9904231.\n\\bibitem{husug} W. Hu and N. Sugiyama, Phys. Rev. D {\\bf 51}, 2599 (1995).\n% Toward Understanding CMB Anisotropies and Their Implications\n\\bibitem{HW} W. Hu and M. White, Astrophys. J. {\\bf 471}, 30 (1996).\n%Acoustic Signatures in the CMB\n\\bibitem{coherence} e.g., J. Magueijo, A. Albrecht, P. Ferreira and\nD. Coulson, Phys. Rev. D {\\bf 54}, 3727 (1996).\n\\bibitem{WBA} J. Weller, R.A. Battye and A. Albrecht, \nPhys.Rev. D60, 103520 (1999).\n%Reionization by active sources and its effects on the cmb astro-ph/9808269.\n\\bibitem{EB86} G. Efstathiou and J. R. Bond, MNRAS {\\bf 218}, 103 (1986).\n%Constraints on Isocurvature CDM Models\n\\bibitem{EB99} G. Efstathiou and J. R. Bond, MNRAS {\\bf 304}, 75 (1999).\n\\bibitem{H0} See e.g., J.R. Mould et al, astro-ph/9909260.\n\\bibitem{SNe} A.G. Riess, et al., {\\em Astron. J.} {\\bf 116}, 1009 (1998);\nS. Perlmutter et al, {\\em Astrophys. J.} {\\bf 517}, 565\n(1999) (astro-ph/9812133).\n\\bibitem{BNTT99} S. Burles, K. N. Nollett, J. M. Truran, M. S. Turner,\n{\\em Phys. Rev. Lett.} {\\bf 82} 4176 (1999).\n%\\bibitem{CBF} J. Mohr et al, {\\em Astrophys. J.}, in press (1999)\n%(astro-ph/9901281).\n%\\bibitem{montypython}D. Scott and M. White, Publ.Astron.Soc.Pac. \n%{\\bf 111}, 525 (1999).\n\\bibitem{postmodernisocurv} W. Hu, {\\em Phys. Rev. D} {\\bf 59}, 121301 (1999);\nW. Hu, P.J.E. Peebles, astro-ph/9910222.\n\\bibitem{turok}N. Turok, Phys. Rev. Lett. {\\bf 77}, 4138 (1996).\n%A Causal Source which mimics inflation\n\\bibitem{HSW97} W. Hu, D. Spergel and M. White, \nPhys. Rev. {\\bf D55}, 3288 (1997).\n\\bibitem{marc} Or, from the second peak: M. Kamionkowski and A. Buchalter, \nastro-ph/0001045 \n\\bibitem{cmbfast} U. Seljak \\& M. Zaldarriaga, Astrophys. J. {\\bf 469}, \n437 (1996).\n\\end{thebibliography}"
}
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astro-ph0002164
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Is There a Detectable Vishniac Effect?
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[
{
"author": "Evan Scannapieco"
}
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The dominant linear contribution to cosmic microwave background (CMB) fluctuations at small angular scales ($\lesssim 1'$) is a second-order contribution known as the Vishniac or Ostriker-Vishniac effect. This effect is caused by the scattering of CMB photons off free electrons after the universe has been reionized, and is dominated by linear perturbations near the $R_V =2$ Mpc/($h \Gamma/0.2)$ scale in the Cold Dark Matter cosmogony. As the reionization of the universe requires that nonlinear objects exist on some scale, however, one can compare the scale responsible for reionization to $R_V$ and ask if a linear treatment is even feasible in different scenarios of reionization. For an $\Omega_0 = 1$ cosmology normalized to cluster abundances, only $\sim 65 \%$ of the linear integral is valid if reionization is due to quasars in halos of mass $\sim 10^9 M_\odot$, while $\sim 75\%$ of the integral is valid if reionization was caused by stars in halos of $\sim 10^6 M_\odot$. In $\Lambda$ or open cosmologies, both the redshift of reionization and $z_V$ are pushed further back, but still only $\sim 75 \%$ to $\sim 85 \%$ of the linear integral is valid, independent of the ionization scenario. We point out that all odd higher-order moments from Vishniac fluctuations are zero while even moments are non-zero, regardless of the gaussianity of the density perturbations. This provides a defining characteristic of the Vishniac effect that differentiates it from other secondary perturbations and may be helpful in separating them.
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[
{
"name": "apj.tex",
"string": " \\documentstyle[11pt,aaspp4,psfig]{article}\n%\\documentstyle[emulateapj,psfig]{article}\n\\begin{document} \n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ba}{\\begin{eqnarray}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\ea}{\\end{eqnarray}} \n\n\\title{Is There a Detectable Vishniac Effect?}\n \n\\author{Evan Scannapieco}\n\n\\affil{Departments of Physics and Astronomy,\nUniversity of California, Berkeley, CA 94720-7304} \n%\\altaffiltext{1}{\n%Departments of Physics and Astronomy,\n%University of California, Berkeley, CA 94720-7304}\n\n\\begin{abstract}\nThe dominant linear contribution to cosmic microwave background (CMB)\nfluctuations at small angular scales ($\\lesssim 1'$) is a\nsecond-order contribution known as the Vishniac or Ostriker-Vishniac\neffect. This effect is caused by the scattering of CMB photons off\nfree electrons after the universe has been reionized, and is dominated\nby linear perturbations near the $R_V =2$ Mpc/($h \\Gamma/0.2)$ scale\nin the Cold Dark Matter cosmogony. As the reionization of the\nuniverse requires that nonlinear objects exist on some scale, however,\none can compare the scale responsible for reionization to $R_V$ and\nask if a linear treatment is even feasible in different scenarios of\nreionization. For an $\\Omega_0 = 1$ cosmology normalized to cluster\nabundances, only $\\sim 65 \\%$ of the linear integral is valid\nif reionization is due to quasars in halos of mass\n$\\sim 10^9 M_\\odot$, while $\\sim 75\\%$ of the integral is valid if\nreionization was caused by stars in halos of $\\sim 10^6 M_\\odot$. In\n$\\Lambda$ or open cosmologies, both the redshift of reionization and\n$z_V$ are pushed further back, but still only $\\sim 75 \\%$ to $\\sim 85\n\\%$ of the linear integral is valid, independent of the ionization\nscenario. We point out that all odd higher-order moments from\nVishniac fluctuations are zero while even moments are non-zero,\nregardless of the gaussianity of the density perturbations. This\nprovides a defining characteristic of the Vishniac effect that\ndifferentiates it from other secondary perturbations and may be\nhelpful in separating them.\n\n\\end{abstract}\n\\keywords{cosmic background radiation -- cosmology: theory}\n\n\\newpage\n\n\\section{Introduction}\n\nWhile recombination at $z \\approx 1100$ marked the end of ionized\nhydrogen from the viewpoint of a linearly evolving universe, the\nnonlinear evolution of small-scale perturbations resulted in the\nreionization of the intergalactic medium at much lower redshifts. The\nfact that quasar spectra show an absence of an absorption trough from\nLy$\\alpha$ resonant scattering by neutral H atoms distributed\ndiffusely along the line of sight, the Gunn-Peterson effect (Gunn \\&\nPeterson 1965), means that this reionization must have occurred with a\nhigh degree of efficiency before a redshift of 5.\n\nOne of the necessary consequences of this reionization is the presence\nof secondary anisotropies in the cosmic microwave background (CMB)\ndue to the scattering of photons off ionized electrons. These\nsecondary fluctuations can be divided into two classes: anisotropies\ndue to nonlinear structures and linear anisotropies.\n\nNonlinear secondary anisotropies are of several types. Some of the\nmore studied of these include the scattering of photons off the hot\nintracluster medium of galaxy clusters (Sunyaev \\& Zel'dovich 1970,\n1972; or for more recent treatments see, e.g., Evrard \\& Henry 1991;\nColfrancesco et al.\\ 1994; Aghanim et al.\\ 1997), gravitational\nlensing (see, e.g., Linder 1997; Metcalf \\& Silk 1997), \nthe impact of inhomogeneous reionization\n(Aghanim et al.\\ 1995; Peebles \\& Juszkiewicz 1998; Knox, Scoccimarro,\n\\& Dodelson 1998), and the Rees-Sciama effect due to the bulk motions\nof collapsing nonlinear structures (see, e.g., Rees \\& Sciama 1968;\nKaiser 1982; Seljak 1996).\n\nSmall-scale linear anisotropies come in fewer flavors. Detailed\nanalyses of linear perturbations have uncovered a single dominant\neffect known as the Vishniac or Ostriker-Vishniac effect\n(Hu, Scott, \\& Silk 1994; Dodelson \\& Jubas 1995; Hu \\& White 1995; Hu\n\\& Sugiyama 1996). The level of these perturbations has been\ncalculated by several authors (Ostriker \\& Vishniac 1985; Vishniac\n1987; Jaffe \\& Kamionkowski 1998, hereafter JK).\n\nThese investigations raise the question of whether a detectable\nVishniac effect even exists since nonlinear structures must exist on\n{\\em some} length scale at the time of secondary scattering of CMB\nphotons, as it is only by the formation of nonlinear objects that the\nuniverse is able to reionize itself. If these scales are comparable\nto those making the dominant contribution to the Vishniac effect, then\na linear analysis is inappropriate and a calculation of secondary\nanisotropies must incorporate nonlinear effects.\n\nIn this work we determine the minimum length scale, $R_V$, which must\nremain linear in order for a linear approach to scattering by ionized\nregions with varying bulk motions to be accurate for the range of\nangular scales over which one can hope to measure secondary fluctuations.\nIn hierarchical\nscenarios of structure formation, such as the Cold Dark Matter (CDM)\nmodel, smaller structures assemble at early times, later merging to\nform larger objects. This allows us to place limits on the time\nbetween the formation of structures large enough to reionize the\nuniverse and the time at which $R_V$ becomes nonlinear.\nAt that point, while peculiar\nvelocities of ionized gas continue to be imprinted on the microwave\nbackground, the nature of this signature is qualitatively different\nand is best interpreted from another perspective.\n\nThe structure of this work is as follows. In Sec.\\ 2 we describe the\nVishniac effect and determine the physical length scale on which it\ndepends. In Sec.\\ 3 we compare this to the scale of reionizing\nobjects in different reionization scenarios and discuss the\napplicability of linear theory. In Sec.\\ 4 we examine how\nthe Vishniac effect is distinguished from other effects. Conclusions\nare given in Sec.\\ 5, and the various cosmological expressions used\nthroughout are summarized in the appendix.\n\n\\section{Analysis}\n\n\\subsection{Approximations}\n\nThe Vishniac effect is caused by the scattering of CMB photons\n by ionized regions with varying bulk motions. The temperature \nfluctuations induced along a line of sight are given by \n\\begin{equation}\n\\frac {\\Delta T}{T}(\\vec{\\theta}) = \n- \\int^{t_0}_0 dt \\sigma_T e^{-\\tau(\\vec{\\theta},t)} n_e(\\vec{\\theta},t) \n{\\bf \\hat{\\theta}} \\cdot {\\bf v}(\\vec{\\theta},t), \n\\end{equation}\nwhere $\\tau (\\vec{\\theta},t)$,\n$n_e(\\vec{\\theta},t)$, and ${\\bf v}(\\vec{\\theta},t)$ \nare the optical depth along the line of sight, \nelectron density, and bulk velocity,\n$\\sigma_T$ is the cross section for Thomson scattering,\n$t$ is the age of the universe, and $t_0$ is the present age.\nFollowing JK, we choose a coordinate system in which \n${\\bf \\hat{\\theta}}$ represents a three-dimensional unit vector along the \nline of sight, $\\vec{\\theta}$ represents a two-dimensional unit\nvector in the plane perpendicular to it, and bold letters represent fully \nthree-dimensional vectors. Thus ${\\bf v} = (v_x,v_y,v_z)$,\n$\\vec{\\theta} = (\\theta_1, \\theta_2, 0)$, and\n${\\bf \\hat{\\theta}} = (\\theta_1, \\theta_2, \\sqrt{1 - \\theta_1^2 - \\theta_2^2})\n\\approx (\\theta_1, \\theta_2, 1)$, \nthe validly of the approximation deriving from the small-scale\nnature of the effect. Note that $n_e$, ${\\bf v}$, and $\\tau$ are all functions\nof position, the optical depth being given by\n$\\tau(\\vec{\\theta},t) = \\int^{t_0}_t\n\\sigma_T n_e(\\vec{\\theta},t) c dt' $, where $c$ is the speed of light.\n\nIf we decompose the density field into average and fluctuating\ncomponents, we obtain, to leading order,\n\\begin{equation}\n\\frac {\\Delta T}{T}(\\vec{\\theta}) =\n- \\frac{\\sigma_T n_0}{c} \n\\int_0^1 dw a_0^3\\frac{x_e({\\bf \\hat{\\theta}} w_{\\rm ang},w)}{a(w)^2}\n(1+\\delta({\\bf \\hat{\\theta}} w_{\\rm ang},w)-\n\\Delta \\tau({\\bf \\hat{\\theta}} w_{\\rm ang},w))\n{\\bf \\hat{\\theta}} \\cdot \n{\\bf v}({\\bf \\hat{\\theta}} w_{\\rm ang},w) e^{-\\tau_0(w)}, \n\\label{eq:deltat}\n\\end{equation}\nwhere $x_e({\\bf x},w)$ is the ionization fraction, $\\tau_0$ and\n$\\Delta \\tau({\\bf x},w)$ are the optical depths due to the average and\nfluctuating density components respectively, $a(w)$ is the scale\nfactor with $a_0 \\equiv a(0)$, $\\delta({\\bf x},w)$ is the overdensity\nfield defined such that $\\delta({\\bf x},w) \\equiv \\rho({\\bf\nx},w)/\\bar{\\rho}(w) - 1$ where $\\rho({\\bf x},w)$ is the density field\nand $\\bar{\\rho}(w)$ the average density as a function of comoving\ndistance, $n_0$ is the present average electron density, and $w_{\\rm\nang}$ is the comoving angular distance, given by Eq.\\\n(\\ref{eq:wangle}). Note that we have replaced time by $w$, the\ncomoving distance defined by $dw \\equiv c dt/a(t)$, and rewritten\n${\\bf v}$, and $\\tau$ in comoving coordinates, ${\\bf x}$. Taking\nthe mass fraction of He to be $\\sim 25 \\%$, and approximating helium\nreionization as simultaneous to that of hydrogen, $n_0 = \\Omega_b\n\\rho_c /m_p \\times 7/8 = 9.9 \\times 10^{-6} \\Omega_b h^2 {\\rm\ncm}^{-3}$, where $\\rho_c$ is the critical density, $m_p$ is the mass\nof the proton, $h$ is Hubble's constant normalized to $100 \\, {\\rm km}\n\\, {\\rm s}^{-1} \\, {\\rm Mpc}^{-1}$, and $\\Omega_b$ is the present\nbaryonic matter density in units of the critical density.\n\nThe Vishniac effect arises by considering the\nhomogeneously-reionizing, low optical depth case. In this case\n$x_e({\\bf x},w)$ is independent of position and $\\Delta\n\\tau$ can be ignored. In practice, realistic\nreionization scenarios lead to low values of optical depth and hence\ndropping $\\Delta \\tau$ is a safe assumption (Hu,\nScott, \\& Silk 1994). Indeed, the measurement of CMB fluctuations at\nlarge scales precludes the high degree of damping that would be \ncaused by a high optical depth \n(Scott \\& White 1994; Hancock et al.\\ 1998). The\nhomogeneity of reionization, however, is a question of scales and thus\nrepresents a basic assumption on which the Vishniac analysis is based.\n\nIn this limit Eq.\\ (\\ref{eq:deltat})\nbecomes\n\\be\n\\frac {\\Delta T}{T}(\\vec{\\theta}) =\n- \\int_0^1 dw g(w) {\\bf \\hat{\\theta}} \\cdot \n\\left( {\\bf v}({\\bf \\hat{\\theta}} w_{\\rm ang},w) \n+ {\\bf q}({\\bf \\hat{\\theta}} w_{\\rm ang},w) \\right),\n\\label{eq:thin}\n\\ee\nwhere \n${\\bf q}({\\bf x},t) \\equiv {\\bf v}({\\bf x},w) \\delta({\\bf x},w)$\nand $g(w)$ is the visibility function\n\\be\ng(w) \\equiv \\frac{a_0^3 n_0 x_e(w)}{c a(w)^2} \\sigma_T e^{-\\tau}\n= \\frac{.121 \\Omega_b h}{c} (1+z(w))^2 x_e(w) e^{-\\tau},\n\\ee\nwith our conventions for the scale factor as in Appendix A.\nThis gives the probability of scattering off reionized electrons\nand is a slowly-varying function of $w$.\n\nFinally, we must approximate both ${\\bf v}$ and ${\\bf q}$ using linear\ntheory. In this case,\nthe density contrast at a comoving coordinate ${\\bf x}$ \nand comoving distance $w$ from the observer\nis a random field with Fourier transform given by\n$\n \\tilde \\delta({\\bf k},w) \\equiv \\int \\,d^3 {\\bf x} \\exp(-i\n {\\bf k} \\cdot {\\bf x})\\, \\delta({\\bf x},w).$\nThe spatial and time dependence of $\\tilde \\delta({\\bf k},w)$\ncan be factorized, so $\\tilde \\delta({\\bf k},w)=\n\\tilde \\delta_0({\\bf k})D(w)/D_0$\nwhere $\\tilde \\delta_0({\\bf k}) \\equiv \\tilde \\delta({\\bf k},0)$, \n$D(w)$ is the linear\ngrowth factor, given by Eq.\\ (\\ref{eq:growth}), and $D_0 \\equiv D(0)$. \nThe power spectrum is then defined by the relation\n\\be\n\\langle \\tilde{\\delta_0}({\\bf k}) \\tilde{\\delta_0}({\\bf k'}) \\rangle =\n\\langle \\tilde{\\delta_0}({\\bf k}) \\tilde{\\delta_0}^*(-{\\bf k'}) \\rangle =\n(2 \\pi)^3 \\delta^3({\\bf k} + {\\bf k'}) P(k),\n\\label{eq:deltadelta}\n\\ee \nwhere $\\delta^3( {\\bf k} + {\\bf k'})$ denotes the\nthree-dimensional Dirac delta function. This completely specifies the\nprobability density functional from which $\\delta({\\bf k})$ is drawn\nin gaussian theories. In the CDM cosmogony, $P(k)$\nis given by Eq.\\ (\\ref{eq:pk}) and Eq.\\ (\\ref{eq:cdm}), and is\ndependent on the `shape parameter' $\\Gamma$, which is given as a\nfunction of cosmological parameters by Eq.\\ (\\ref{eq:shapep}) and\nconstrained by observations of the galaxy correlation function to be\n$0.23^{+0.042}_{-0.034}$ (Viana and Liddle 1996). The overall\nnormalization of $P(k)$ can be fixed by the amplitude of mass\nfluctuations on the 8 $h^{-1}$ Mpc scale as defined in Eq.\\\n(\\ref{eq:sig}).\n\nThe linear velocity field is simply related to the density field by\nthe continuity equation ${\\bf \\nabla \\cdot v}({\\bf x}) \n= - a(w) {\\dot {\\delta}} ({\\bf x},w)$ which in Fourier space gives\n\\be\n \\tilde {\\bf v}({\\bf k},t) = {i a(w) \\over k^2}\\, {\\dot D(w)\n \\over D_0} \\,{\\bf k} \\, \\tilde \\delta_0({\\bf k}),\n\\label{eq:veckeqn}\n\\ee\nwhere $\\dot D(w)$ denotes the derivative of $D$ with respect to time\nrather than $w$, and is given by Eq.\\ (\\ref{eq:growthdot}).\nAs the velocity always points along the direction of ${\\bf k}$, only\n${\\bf k}$ modes with large values along the line of sight can have\nlarge peculiar velocities in the ${\\bf \\hat{\\theta}}$ direction. But\nthese modes are varying with wavelengths much smaller than variations\nin the window function and cancel when projected along the line of\nsight. It is only the second order (${\\bf q}$) term then, that\ncontributes to the integral in Eq.\\ (\\ref{eq:thin}).\n\nA simple real-space argument gives a different way of understanding\nthis cancellation. As gravitational perturbations to a pressureless\nfluid can be written in terms of the gradient of a scalar potential\nfield (${\\bf v} \\propto {\\bf \\nabla} \\phi$ where $\\phi$ is the\ngravitational potential) the curl of the velocity field is zero to all\norders. Thus a line integral of ${\\bf v}$ along a line of sight is\napproximately the integral of a gradient and is zero except for a\nsmall contribution at the end points. From all the terms\nin Eq.\\ \\ref{eq:deltat}, only the \n$\\delta \\times {\\bf \\hat{\\theta}} \\cdot {\\bf v}$ survives to\ncontribute to $\\frac{\\Delta T}{T}$.\n\n\\subsection{Power Spectrum}\n\nDropping the velocity term from Eq.\\ \\ref{eq:thin},\nwe can analytically construct the\npower spectrum of the angular fluctuations in the linear limit.\nLet us define $\\tilde{\\frac{\\Delta T}{T}}({\\vec \\kappa})$ as the\nFourier transform of the temperature fluctuations such that\n$\n \\tilde{\\frac{\\Delta T}{T}}({\\vec \\kappa}) \n= \\int \\,d^2 {\\vec \\theta} \\exp(-i{\\vec \\kappa} \\cdot {\\vec \\theta})\\, \n\t\\frac{\\Delta T}{T}({\\vec \\theta}),$\nwith the angular power spectrum defined as\n$P_{\\rm ang}(\\kappa_1) (2 \\pi)^2 \n\\delta^2({\\vec \\kappa_1} + {\\vec \\kappa_2}) \\equiv \\langle \n\\left( \\tilde{\t\\frac{\\Delta T}{T}}({\\vec \\kappa_1}) \n \\tilde{ \\frac{\\Delta T}{T}}({\\vec \\kappa_2}) \n\\right) \\rangle$.\nAt the small angular scales appropriate to the Vishniac effect, \n$P_{\\rm ang}(\\kappa)$ is simply related to the usual $C_\\ell$s \nused to express CMB fluctuations by $C_\\ell = P_{\\rm ang}(\\kappa=\\ell)$ \n(JK).\n\nSeveral authors (Vishniac 1987; Kaiser 1992; JK) have derived\nexpressions for the Vishniac $C_\\ell$s. Here we provide a new\napproach that, unlike other techniques, is easily extended to \ncalculate higher-order moments, as is shown in \\S4.\nOur method is a simple extension of\nthe usual formalism used to calculate single-point moments of the\n$\\frac{\\Delta T}{T}(\\vec \\theta)$ distribution.\n\nThe simplest quantity of this sort is the second moment\n$\\langle \\left[\\frac{\\Delta T_B}{T}(0)\\right]^2\\rangle$, where we use\n$B$ to denote convolution with a beam profile.\nGiven such a profile in Fourier space $B({\\vec \\kappa})$, \nthe second moment can be calculated as\n\\be\n\\langle\n\\left[ \\frac{\\Delta T_B}{T}(0) \\right]^2\n\\rangle = \n\\int \\frac{d^2 {\\vec \\kappa}}\n{(2 \\pi)^2}\n B({\\vec \\kappa})^2 \nP_{\\rm ang}(\\kappa).\n\\label{eq:po} \n\\ee\nSuppose, however, that instead of asking about the second moment \ncalculated from a single map observed with a beam \n$B({\\vec \\kappa})$, we instead compute the single-point function as \ncalculated from the convolution of two maps, observed by\nbeams $B_1({\\vec \\kappa})$ and $B_2({\\vec \\kappa})$. As these profiles\nare arbitrary, we are free to take\n\\be\nB_1({\\vec \\kappa}) \\equiv (2 \\pi)^2\n\\delta^2({\\vec \\kappa}-{\\vec \\kappa_1}) \n\\qquad \\qquad\nB_2({\\vec \\kappa}) \\equiv (2 \\pi)^2\n\\delta^2({\\vec \\kappa}-{\\vec \\kappa_2}),\n\\label{eq:deltawin}\n\\ee\nwhere $\\delta^2({\\vec \\kappa})$ is the two-dimensional delta function.\nIn this case we find\n\\be\n\\langle\n\\frac{\\Delta T_{B_1}}{T}(0)\n\\frac{\\Delta T_{B_2}}{T}(0)\n\\rangle = (2 \\pi)^2 P_{\\rm ang}(\\kappa_1) \n\\delta^2({\\vec \\kappa_1}+ {\\vec \\kappa_2}),\n\\ee\nrecovering the angular power spectrum.\nThus the power spectrum of the Vishniac effect can be computed\nfrom the single-point correlation if we are careful to\nexpress the beam profiles in sufficient generality.\n\n\nLet us consider then\n\\ba\n\\langle\n\\frac{\\Delta T_{B_1}}{T}(0)\n\\frac{\\Delta T_{B_2}}{T}(0) \n\\rangle = \n& &\n\\int_0^1 dw_1 g(w_1) \\int_0^1 dw_2 g(w_2)\n\\int \\frac{d^3{\\bf k_a}}{(2 \\pi)^3} \\int \\frac{d^3{\\bf k_b}}{(2 \\pi)^3}\n\\nonumber \\\\ & &\nB_1({\\vec k_a} w_{1,{\\rm ang}})\nB_2({\\vec k_b} w_{2,{\\rm ang}})\ne^{i k_{a,z} w_1 + i k_{b,z} w_2}\n\\langle\n\\tilde{q}_z({\\bf k_a},w_1) \\tilde{q}_z({\\bf k_b},w_2) \n\\rangle,\n\\label{eq:b1b2}\n\\ea\nwhere $\\tilde{\\bf q}({\\bf k},w)$ is the Fourier transform of\n${\\bf q}({\\bf x},w)$.\nSubstituting in the expression for $\\tilde{\\bf q}$ in terms of\n$\\tilde{\\delta}$:\n\\be\n{\\bf {\\tilde q}}({\\bf k},w) = \n\\frac{ i a(w) \\dot D(w) D(w)}{D_0^2} \n\\int \\frac{d^3 {\\bf k'}}{(2 \\pi)^3} \n\\tilde{\\delta}_0({\\bf k'})\n\\tilde{\\delta}_0({\\bf k} - {\\bf k'}) \\frac{{\\bf k'}}{k'^2},\n\\ee\nEq.\\ (\\ref{eq:b1b2}) becomes\n\\ba\n\\langle\n\\frac{\\Delta T_{B_1}}{T}(0)\n\\frac{\\Delta T_{B_2}}{T}(0) \n\\rangle = \n&-& \n\\int_0^1 dw_1 G(w_1)\n\\int_0^1 dw_2 G(w_2)\n\\prod_{j=1}^4 \n\\left[\n\\int \\frac{d^3 {\\bf k_j}}{(2 \\pi)^3} \n\\right] B_1(({\\vec k_1}+{\\vec k_2}) w_{1,{\\rm ang}})\n\\nonumber \\\\\n& &\nB_2(({\\vec k_3}+{\\vec k_4}) w_{2,{\\rm ang}}) \ne^{i (k_1+k_2) w_1+ i (k_3+k_4) w_2}\n\\frac{k_{1,z}}{k_1^2}\n\\frac{k_{3,z}}{k_3^2} \n\\langle\n\\prod_{l=1}^4 \\tilde{\\delta}_0({\\bf k_l})\n\\rangle,\n\\ea\nwhere\n\\be\nG(w) \\equiv \\frac{ g(w) a(w) D(w) \\dot D(w)}{D_0^2}.\n\\label{eq:bigg(w)}\n\\ee\nAs $G(w)$ is slowly varying, we can follow Kaiser (1992) in dividing\nthe integrals over comoving distance into $N$ statistically\nindependent intervals of width $\\Delta w$, over each of which $G(w)$ is\nwell approximated by a constant. In this case\n\\ba\n\\langle\n\\frac{\\Delta T_{B_1}}{T}(0)\n\\frac{\\Delta T_{B_2}}{T}(0) \n\\rangle = \n-\\sum_{n=1}^{N}\nG(w_n)^2 \\Delta w^2\n\\prod_{j=1}^4 \n\\left[\n\\int \\frac{d^3 {\\bf k_j}}{(2 \\pi)^3} \n\\right] \\qquad \\qquad \n\\nonumber \\\\ \n B_1(({\\vec k_1}+{\\vec k_2})w_{n,{\\rm ang}})\n B_2(({\\vec k_3}+{\\vec k_4})w_{n,{\\rm ang}})\n\\nonumber \\\\ \nj_0 \\left(\\frac{(k_{1,z}+k_{2,z}) \\Delta w}{2} \\right)\nj_0 \\left(\\frac{(k_{3,z}+k_{4,z}) \\Delta w}{2} \\right)\n\\frac{k_{1,z}}{k_1^2}\n\\frac{k_{3,z}}{k_3^2}\n\\langle\n\\prod_{l=1}^4 \\tilde{\\delta}_0({\\bf k_l})\n\\rangle.\n\\ea\nAs the density fluctuations are taken to be gaussian, we can expand the \nexpectation value of the product of overdensities by Wick's theorem, \nkeeping only the terms in which $k_1$ is paired with $k_3$ or $k_4$.\nIf we then define $k'_2 \\equiv k_1 + k_2$, we find\n\\ba\n\\langle\n\\frac{\\Delta T_{B_1}}{T}(0)\n\\frac{\\Delta T_{B_2}}{T}(0) \n\\rangle = \n\\sum_{n=1}^{N}\nG(w_n)^2 \\Delta w^2\n\\int \\frac{d^3{\\bf k_1}}{(2 \\pi)^3}\n\\int \\frac{d^3{\\bf k_2'}}{(2 \\pi)^3}\nB_1({\\vec k'_2} w_{n,{\\rm ang}})\nB_2(-{\\vec k'_2} w_{n,{\\rm ang}}) \\nonumber \\\\\n\\left[ \\frac{k_{1,z}^2}{k_1^4} + \\frac{k_{1,z} \n(k'_{2,z} - k_{1,z})}{k_1^2 || {\\bf k_2'} - {\\bf k_1} ||^2}\n\\right]\nP(k_1) P(|| {\\bf k'_2} - {\\bf k_1} ||) \nj_0^2 \\left(\\frac{ k'_{2,z} \\Delta w}{2} \\right).\n\\ea\nThe Bessel function has a width $\\delta k_z \\sim 1/\\Delta w$\nso $k_{2,z} << \\kappa/w_{\\rm ang}$ wherever $j^2_0$ is appreciable.\nWe can neglect terms that are smaller by a factor of \n$w_{\\rm ang}^2 \\kappa^2/\\Delta w^2$ to obtain \n\\ba\n\\langle\n\\frac{\\Delta T_{B_1}}{T}(0)\n\\frac{\\Delta T_{B_2}}{T}(0) \n\\rangle & = &\n\\sum_{n=1}^{N} G(w_n)^2 \\Delta w \n\\int \\frac{d^3{\\bf k_1}}{(2 \\pi)^3}\n\\int \\frac{d^2{\\vec k'_2}}{(2 \\pi)^2} \nB_1({\\vec k'_2} w_{\\rm ang})\nB_2(-{\\vec k'_2} w_{\\rm ang}) \\nonumber \\\\\n& &\n\\frac{k_{1,z}^2}{k_1^4} - \n\\frac{k_{1,z}^2}{k_1^2 || ({\\vec k_2'},0) - {\\bf k_1} ||^2}\nP(k_1) P(|| ({\\vec k'_2},0) - {\\bf k_1} ||).\n\\ea\nTaking \n\\be\nB_1({\\vec \\kappa}) =\nB_2({\\vec \\kappa}) = \n2 \\pi \\sigma^2 e^{-\\frac{\\sigma^2 \\kappa^2}{2}}\n\\ee\ngives the second moment as observed by a beam of gaussian width\n$\\sigma$, while choosing beam profiles as given in Eq.\\\n(\\ref{eq:deltawin}) yields the angular power spectrum. In this case\n\\be\nC_\\ell = P_{\\rm ang}(\\kappa = \\ell) \n= \\int_0^1 dw \\frac{G(w)^2}{w^2_{\\rm ang}} \nP_{\\rm V}(\\ell / w_{\\rm ang}),\n\\label{eq:clcalc}\n\\ee\nwhere\n\\be\nP_{\\rm V}({k}) =\n\\int \\frac{d^3{\\bf k_1}}{(2 \\pi)^3}\nP(k') P(|| ((k,0,0) - {\\bf k_1} ||) \n\\left[\n\\frac{k_{1,z}^{'2}}{k_1^{'4}} \n- \\frac{k_{1,z}^{'2}}{k_1^{'2} ||(k,0,0) - {\\bf k_1} ||^2 } \n\\right],\n\\ee\nwhich, choosing a coordinate system in which the $z'$ axis points\nalong the direction of $(k,0,0)$ becomes\n\\be\nP_{\\rm V}(k) =\n\\frac{k}{8 \\pi^2} \\int_0^\\infty dx \\int_{-1}^{1} \nd \\mu P(k x) P(k \\sqrt{1 - 2 x \\mu + x^2})\n(1 - \\mu^2) \n\\left[1 - \n\\frac{x^2}{1 - 2 x \\mu + x^2}\n\\right].\n\\ee\nThis is equivalent to the usual expression for the Vishniac power spectrum\n\\be\nP_{{\\rm V}} (k) = \n\\frac{k}{8 \\pi^2} \n\\int_0^\\infty dx \\int_{-1}^{1} d \\mu P(k x) \nP( k \\sqrt{ 1 - 2 x \\mu + x^2}) \n\\frac{ (1 - \\mu^2)(1 - 2 x \\mu)^2}{(1 - 2 x \\mu + x^2)^2},\n\\label{eq:pperp}\n\\ee\nas can be seen by rewriting both integrals in rectangular coordinates\nand applying an origin shift.\nThus the $C_\\ell$s are dependent on an integral along the line of\nsight of a term, $P_{\\rm V}(k)$, that is independent of redshift and\narises from the convolution of the ${\\bf q}$ fields.\nWe note in passing that our results are in agreement with \nDodelson and Jubas (1995) and are twice the values found in JK.\n\n\\subsection{Physical Scales}\n\nHaving outlined the approximations which are used to calculate\nthis effect and constructed the resulting power spectrum of\nfluctuations,\nwe now examine which physical scales contribute most to $P_{\\rm V}(k)$.\nTypically, Eq.\\ (\\ref{eq:clcalc})\nis used to calculate the Vishniac effect by integrating over a\nparticular matter power spectrum. To study the dependence of the\neffect on physical scale, we replace the power spectrum that appears\nin Eq.\\ (\\ref{eq:pperp}) with $P(k) W^2(k R)$ where $P(k)$ is the CDM\npower spectrum and $W(x)$ is the spherical top-hat window function,\ngiven by Eq.\\ (\\ref{eq:tophat}). Here we consider a $\\Lambda$CDM\nmodel in which the current nonrelativistic matter, vacuum, and\nbaryonic densities in units of the critical density are $\\Omega_0$ =\n0.35, $\\Omega_\\Lambda$ = 0.65, and $\\Omega_b$ = 0.06 respectively, and\nthe ``tilt'' in the power spectrum as parameterized in Eq.\\\n(\\ref{eq:pk}) is taken to be flat, $n = 1.0$. If the other parameters\nare taken to be $h$ =0.65, $\\sigma_8$ = 1.05, $\\Gamma = 0.2$ and\nreionization occurs instantaneously and completely at $z_{\\rm re} =\n18$, this results in $P_{\\rm V}(k)$ and $C_\\ell$ as plotted in Fig.\\\n\\ref{fig:sk}. Note that these values correspond to $\\frac{\\Delta T}{T}$s \na full order of magnitude smaller than large-scale primary\nanisotropies, pointing out the experimental challenges that must be\novercome before secondary anisotropies can be measured (see, e.g.,\nSubrahmanyan et al.\\ 1993; Church et al.\\ 1997). For reference\nwe also plot the COBE-normalized primary fluctuations as computed by \nthe CMBFAST code V2.4.1\n(Seljak \\& Zaldarriaga 1996; Hu et al.\\ 1998; Zaldarriaga \\& Seljak 1998),\nfor the same cosmological model.\nNote that the position of this line is sensitive only to the Silk\ndamping scale and thus is largely independent of the shape of the\nprimordial power spectrum.\n\n\n\\begin{figure}\n\\centerline{\\psfig{file=f1.ps,width=4.5in}}\n\\caption{\nUpper panel: $P_{\\rm V} (k)$ from $\\Lambda$CDM density\nfluctuations convolved with top-hat window functions of various\nscales. The solid line is the exact analytic expression, the dotted\nline corresponds to a top-hat filtering scale of $R$ = 1 Mpc/h, the\nshort-dashed to $R$ = 2 Mpc/h, and the long dashed to $R$ = 4 Mpc/h.\nThe overall normalization is arbitrary as it is dependent on the\nchoice of the scale factor. Lower panel: $\\ell^2 C_\\ell/2\\pi$ from density\nfluctuations convolved with top-hat window functions of various\nscales. Window functions are as in the upper panel.\nThe sharply falling solid line shows the primary anisotropies \nas calculated by CMBFAST.}\n\\label{fig:sk}\n\\end{figure}\n\nIn this figure we see that even when filtered at the $1$ Mpc/$h$\nscale, the power spectrum is appreciably changed, especially at higher\nwavenumbers. While low $\\ell$ fluctuations are not affected,\na comparison with the solid line shows that these fluctuations\nare lost in the CMB primary signal and are very difficult to measure.\nNote that the damping shown in this graph represents not\nonly a loss of power in linear theory, but also an increase of\nnonlinear power. Thus, at the point that the $1$ Mpc/$h$ scale has\nbecome nonlinear, the Vishniac effect is competing with nonlinear\neffects over the range of angular scales in which it is able to be detected.\n\nBy the time the $2$ Mpc/$h$ scale becomes nonlinear, however, the peak\nwavelength of the Vishniac effect has been shifted by a factor of\n$1/2$ and $\\sim 50 \\%$ of the power of $P_{\\rm V}(k)$ has been lost.\nAt this point, linear calculations are unlikely to be \nreliable at measurable $\\ell$ values $\\gtrsim 4000$, and a more\ncareful theoretical approach becomes necessary.\nThese length scales are inversely proportional to the `shape\nparameter' $\\Gamma$ which is $0.2$ for this model. Thus we can\nconservatively fix $R_V =$ 2 Mpc/$h \\Gamma_{0.2}$ where\n$\\Gamma_{0.2} \\equiv \\Gamma/0.2$, as the maximum nonlinear length\nscale that still allows a linear analysis to be appropriate.\n\n\\section{Redshift of applicability}\n\nHaving determined $R_V$, we now consider what scenarios of\nreionization are compatible with a Vishniac effect. These scenarios\ncan be roughly divided into two classes: those in which the dominant\nsource of ionizing photons is due to stars formed in dwarf galaxies\nwith halo masses $\\gtrsim 10^6 M_\\odot$ (Couchman \\& Rees 1986;\nFukugita \\& Kawakasi 1994; Shapiro, Giroux, \\& Babul 1994; Haiman \\&\nLoeb 1997) and models in which reionization occurs due to active\nnuclei in galaxies with halo masses $\\gtrsim 10^9 M_\\odot$ (Efstathiou\n\\& Rees 1988; Haehnelt \\& Rees 1993; Aghanim et al.\\ 1995; Haiman \\&\nLoeb 1998; Valageas \\& Silk 1999). See also, however, the issues\nraised in Madau, Haardt, \\& Rees (1998) and Miralda-Escud\\'e,\nHaehnelt, \\& Rees (1998), and the more exotic scenarios of\nreionization described in Scott, Rees, \\& Sciama (1991) and Adams,\nSarkar, \\& Sciama (1998).\n\nModels in which smaller objects are the most important predict\nredshifts of reionization of $z_{\\rm re} \\approx 20$ while models in\nwhich reionization is due to objects on scales $\\gtrsim 10^9 M_\\odot$\npredict more modest values of $z_{\\rm re}$. All models of\nreionization, however, are constrained by the lack of a Gunn-Peterson\nabsorption trough in the spectra of high-redshift quasars, implying\nthat the intergalactic medium was highly deficient in neutral hydrogen\nat redshifts $\\lesssim 5.$ Thus, high-mass reionization scenarios can only be\nsuccessful in cosmologies in which the parameters are such that\nrelatively large objects became nonlinear at high redshifts, precisely\nthose models where the linear approximation is on the most shaky\nground.\n\nUsing our value for $R_V$ from Sec.\\ 2, we\nare able to determine a redshift of applicability, $z_V$, below\nwhich the Vishniac approximation is invalid over the measurable\nrange of $\\ell$ scales. \nThe number density of objects above a critical over-density,\n$\\delta_c$, is given by Press-Schechter theory \n(Press \\& Schechter 1974) as\n\\be\n\\frac{d n(M,z)}{dM} = -\\sqrt{\\frac{2}{\\pi}} \\frac{\\rho(z)}{M}\n\\frac{\\delta_c D_0}{\\sigma(M)^2 D(z)} \n\\exp \\left(\n-\\frac{\\delta_c^2 D_0^2}{2 \\sigma^2(M) D(z)^2}\n\\right) \\frac{d \\sigma}{dM}(M),\n\\ee\nwhere $n(M,z)$ is the number density of collapsed objects per unit mass at a\nredshift of $z$, $\\rho(z)$ is the comoving density of the universe at\na redshift of $z$, $D(z)$ is the linear growth factor of fluctuations,\nand $\\sigma(M)$ is the level of fluctuations on the mass scale\ncorresponding to a sphere containing a mass $M$, which can be computed\nfrom Eq.\\ (\\ref{eq:sig}). Typically, this formula is used to\ndetermine the number density of virialized halos. In this case\n$\\delta_c(z)$ is a weak function of $z$ for open models and $\\Lambda$\nmodels and a fixed value of $3 (12 \\pi)^{2/3}/20 \\simeq 1.69$ in the\n$\\Omega_0 = 1$ case (Kitayama \\& Suto 1996).\n\nAs a rough rule of thumb we can assume that reionization \ntakes place when the 2$\\sigma$ fluctuations at the relevant \nscale have collapsed. In this case,\n$D(z_{\\rm re})/D_0 = \\delta_c(z_{\\rm re})/ (2 \\sqrt{2} \\sigma(M))$ which is\n$\\approx 0.6 /\\sigma(M)$ in the flat case. We take the linear approximation\nto be valid up the point at which the 1$\\sigma$ scale fluctuations at the\n$R_V$ scale have reached an overdensity of 1. This gives \n$D(z_V)/D_0 = 1/(\\sqrt{2} \\sigma(R_V)) \\approx \n0.7/\\sigma(R_V).$ \n\nIn Fig.\\ \\ref{fig:sigmas} we plot both $z_{\\rm re}$ and $z_V$ as\nfunctions of mass, as it is the mass scale rather than the length scale\nthat is most easily identified with different reionization scenarios.\nWe consider three cosmologies, representative of\nparameters that favor both low mass-scale and high mass-scale\nscenarios of reionization. In order to compare with a scenario that\nis representative of stellar reionization, we consider a flat model\nnormalized at the 8 Mpc/$h$ scale (Viana \\& Liddle 1996). Here\n$\\Omega_0$ = 1.0, $\\Omega_\\Lambda$ = 0.0, $\\Omega_b$ = 0.07, $h$ =\n0.5, $\\sigma_8$ = 0.60, and $n$ = 1.0. In this\nscenario $\\Gamma = 0.44$, shifting the CDM line and decreasing $R_V$\nby a factor of $\\sim 2$. Note that this value of $\\Gamma$ is\nincompatible with the observed galaxy correlation function. Typical\nof high-mass reionization scenarios, we consider the ``concordance\nmodel'' of Ostriker \\& Steinhart (1995), which was used by Haiman \\&\nLoeb (1998a) in their modeling of reionization by quasars. In this\ncase the parameters are taken to be $\\Omega_0$ = 0.35,\n$\\Omega_\\Lambda$ = 0.65, $\\Omega_b$ = 0.04, $h$ = 0.65, $\\sigma_8$ =\n0.87, $\\Gamma = 0.20$, and $n$ = 0.96. Finally, we examine an open\nmodel with $\\Omega_0 = 0.35$, again normalized at 8 Mpc/$h$. In this\ncase $\\Omega_\\Lambda$ = 0.0, $\\Omega_b$ = 0.04, $h$ = 0.65, $\\sigma_8$\n= 1.02, $\\Gamma = 0.20$, and $n$ = 1.0.\n\n\n\\begin{figure}\n\\centerline{\\psfig{file=f2.ps,width=4.5in}}\n\\caption{\nIn each pair of horizontal lines the upper \ncorrespond to the ionization redshift\n$D(z_{\\rm re})/D_0 = \\delta(z_{\\rm re})/ (2 \\sqrt{2} \\sigma(M))$, and \nthe lower lines correspond to the redshift at which a linear treatment\nis no longer valid, $D(z_V)/D_0 = 1/(\\sqrt{2}\\sigma(M))$.\nThe solid lines correspond to the flat model, the dotted lines to\nthe ``concordance model,'' and the dashed lines to the open model,\nwith parameters as described in the text. The nearly vertical lines show the\nmass scales corresponding to spheres of radius $R_V$ for each of the\nmodels. }\n\\label{fig:sigmas}\n\\end{figure}\n\nLet us first consider the $\\Omega_0 = 1$ model, represented by the lowest pair\nof lines. In this model $\\sigma_8$ is the lowest of all \nthe cosmologies considered and the perturbations evolve the most quickly.\nThe combination of these two effects moves the \nredshift of applicability down to a value of $z_V \\approx 2$,\nand thus one might expect to find an appreciable Vishniac effect.\nThe problem, however, is that the low\nnormalization and rapid evolution of perturbations also lowers the\ncollapse redshift of the objects responsible for reionization. In this \nscenario, the $2 \\sigma$, $10^9 M_\\odot$ peaks collapse at\n$z_{\\rm re} \\approx 7$. As reionization must have occurred with a high degree \nof efficiency by $z = 5$, this scenario is only marginally \nconsistent with quasar absorption-line observations. Thus a flat cosmology \nis most compatible with low-mass reionization scenarios.\nIf the collapse of $10^6 M_\\odot$ halos is responsible for reionization, then\n$z_{\\rm re} \\approx 13$ for this model, yielding a larger range\nof redshifts over which the Vishniac effect could be imprinted on the microwave\nbackground. This redshift is comparable to the revised values calculated\nin the stellar reionization scenario of Haiman and Loeb (1997; 1998b), although\nthey consider a somewhat higher range of $\\sigma_8$ values.\n\n\nTo quantify this further, \nin Figs.\\ \\ref{fig:width1} and \\ref{fig:width2} we replot \nFig.\\ \\ref{fig:sigmas}, replacing the vertical axis with \n$\\int_0^{w(z)} dw G(w)^2/w_{{\\rm ang}}^2 P_V(\\ell/w_{{\\rm ang}})$,\nthe contribution to $C_\\ell$ due to bulk motions within\na redshift of $z$. We take $\\ell = 4000$ in Fig.\\ \\ref{fig:width1}\nand $\\ell = 12000$ in Fig.\\ \\ref{fig:width2}, and normalize\nthe $y$ axis such that the integral is equal to 1 at a redshift of \n$z_{\\rm re}(10^6 M_\\odot)$. The magnitude of the Vishniac $C_\\ell$ is \nthen directly proportional to the vertical width of the gap between \n$\\int_0^{w(z_{\\rm res})} dw \nG(w)^2/w_{{\\rm ang}}^2 P_V(\\ell/w_{{\\rm ang}})$, and\n$\\int_0^{w(z_V)} dw \nG(w)^2/w_{{\\rm ang}}^2 P_V(\\ell/w_{{\\rm ang}})$,\nallowing us to judge the linear and nonlinear \ncontributions to Eq.\\ (\\ref{eq:clcalc}) in arbitrary scenarios of \nreionization at a glance.\n\nFrom this point of view, reionization by $10^6 M_\\odot$ objects\nresults in only a marginal improvement the accuracy of a linear\ntreatment. While 35\\% of the $\\ell = 4000$ integral is nonlinear if\n$M_{\\rm re} = 10^9 M_\\odot$, the $M_{\\rm re} = 10^6 M_\\odot$ case is\nstill 25\\% inaccurate. These numbers are somewhat lower in the\nhigh-$\\ell$ case, in which 18\\% of the integral is nonlinear in the\nlow mass case, and 25\\% in the high mass. Note however, that our\ndefinition of $R_V = 2 \\, {\\rm Mpc}(h \\Gamma/0.2)$ was based on the\ndamping of perturbations at $\\ell = 4000.$ From Fig.\\ \\ref{fig:sk} we\nsee that perturbations at $\\ell = 12000$ are largely damped when the\nmatter power spectrum is filtered at the $R = 1 \\, {\\rm\nMpc}(h \\Gamma/0.2)$ scale, and a more fair comparison between Figs.\\\n\\ref{fig:width1} and \\ref{fig:width2} would be to shift the vertical\nlines in Fig.\\ \\ref{fig:width2} to masses lower by a factor of 8,\nyielding much the same numbers as in the $\\ell = 4000$ case.\n\n\\begin{figure}\n\\centerline{\\psfig{file=f3.ps,width=3.2in}}\n\\caption{\nFig.\\ \\protect\\ref{fig:sigmas} replotted in terms of\n$\\int_0^{w(z(M))} dw G(w)^2/w_{{\\rm ang}}^2 P_V(\\ell/w_{{\\rm ang}})$ \nwith $\\ell = 4000$ for three different cosmologies. Lines are as in \nFig.\\ \\protect\\ref{fig:sigmas}.}\n\\label{fig:width1}\n\\end{figure}\n\n \n\\begin{figure}\n\\centerline{\\psfig{file=f4.ps,width=3.2in}}\n\\caption{\nSame as Fig.\\ \\protect\\ref{fig:width1} but with $\\ell = 12000$. \nThe onset of nonlinearity at the $R = 1 \\, {\\rm Mpc}(h \\Gamma/0.2)$ \nscale can be estimated by shifting the nearly vertical lines to\nmasses lower by a factor of 8.}\n\\label{fig:width2}\n\\end{figure}\n\nMore typical of high-mass reionization scenarios is the $\\Lambda$CDM\nmodel represented by the dotted lines in Figs.\\\n\\ref{fig:sigmas}-\\ref{fig:width2}. In this model, $\\sigma_8$ is\nslightly higher than in the flat case and the evolution of $D(z)$ is\nslowed. These effects raise the collapse redshift of $10^9 M_\\odot$\npeaks to $z_{\\rm re} \\approx 11$, easily compatible with Gunn-Peterson\ntests. Note that our crude estimate of the redshift of reionization\nis almost the same as the redshift of $\\approx 12$ calculated\nby Haiman \\& Loeb (1998a) for the same set of cosmological parameters,\nusing a more sophisticated Press-Schechter based argument for the\nionizing flux from quasars. In this scenario $z_V$ is also pushed\nback, although this is lessened by the shift of $\\Gamma$ as compared\nto the flat case. Thus $z_V \\approx 2.5$.\n\nOne might imagine that in this case, a much wider margin of \nredshifts would lead to an accurate linear calculation.\nFig.\\ \\ref{fig:width1} indicates otherwise. \nIn this case almost 20\\% of the low-mass and over 25\\% of the \nhigh-mass integral comes from redshifts at which $R_V$ is nonlinear. \nThe high-$\\ell$ values are slightly lower, with 12\\% of \nthe $10^6 M_\\odot$ and 17\\% of the $10^9 M_\\odot$ integral taking \nplace when $R_V$ is nonlinear, but again these numbers become\nroughly the same as the $\\ell = 4000$ case for a more fair comparison.\n\nThe most extreme case we consider is the cluster-normalized open\nmodel, in which $\\sigma_8$ is the highest and $D(z)$ the most slowly\nevolving. In this case $z_V \\approx 4$, the $10^9 M_\\odot$ and the\n$10^6 M_\\odot$ schemes reionize at $z_{\\rm re} \\approx 22$ and $z_{\\rm\nre} \\approx 33$ respectively. This cosmology yields the largest\nregime of redshift space over which a linear analysis is valid and the\nmost accurate results. Here nonlinear $R_V$ scale fluctuations\ncontaminate 15\\% of the low-mass and 20\\% of the high-mass $C_{4000}$\nintegrals. Again these numbers are lower at higher\n$\\ell$ but roughly the same after accounting for the smaller filtering\nscale of $R = 1 \\, {\\rm Mpc}(h \\Gamma/0.2)$.\n\n\n\\begin{figure}\n\\centerline{\\psfig{file=f5.ps,width=4.5in}}\n\\caption{\nRatio of the contribution to $C_\\ell$ from the linear regime to the total\ncalculated contribution as a function of $\\ell$.\nThe solid lines correspond to the flat model, the dotted lines to\nthe ``concordance model,'' and the dashed lines to the open model,\nand in each pair of lines the upper line corresponds to reionization\nby $10^6 M_\\odot$ objects and the lower line to reionization by\n$10^9 M_\\odot$ objects.}\n\\label{fig:nailincofin}\n\\end{figure}\n\nAs a final check of the validity of our analysis, we construct\n$C_{\\ell,{\\rm filtered}}$ defined as the angular power spectrum as given\nby Eq.\\ (\\ref{eq:clcalc}) but replacing $P(k)$ with $P(k) W^2(k R_{\\rm nl}(z))$\nwhere $R_{\\rm nl}(z)$ is now the nonlinear length scale {\\em at each redshift}\nas in Fig.\\ 2 ($D(z)/D_0 =0.7/\\sigma(R_{\\rm nl}(z))$). In Fig.\\\n\\ref{fig:nailincofin} we plot the ratio of $C_{\\ell,{\\rm filtered}}$ \nto $C_\\ell$ calculated from the unfiltered CDM power spectrum. While\nonly a few reionization scenarios are represented in this graph, this\nnevertheless gives us some feel of the accuracy of the linear treatment\nover different scales, and unlike Figs.\\ 2 - 4, is completely\nindependent of our definition of $R_V$. Here we see that\nin the range of $\\ell$\nvalues at which the effect is most likely to be measured \n($4000 \\lesssim \\ell \\lesssim 120000$) this estimate is in good agreement\nwith the accuracies given in the previous figures. Note also\nthat a linear treatment becomes increasingly inaccurate with $\\ell$,\nand thus measurements of fluctuations at angular scales just below\nthis Silk damping scale will be most easy to interpret.\n\nFrom these results we can safely conclude that even given our present\nignorance as to the cosmological parameters, no more than $\\approx 85\n\\%$ of the contribution to Eq.\\ (\\ref{eq:clcalc}) for measurable\n$\\ell$ values can be calculated by linear theory in a CDM cosmogony. This\ndepends only on the shape of the CDM power spectrum and the lack of \ndiffuse L$\\alpha$ absorption in quasar spectra out to $z \\gtrsim 5$.\n\n\n\\section{Is There a Detectable Vishniac Effect, Really?}\n\nAt this point, one may raise the objection that our argument is a bit\nsemantic, as there will still be scattering due to bulk motions even\nwhen linear theory breaks down. Indeed, the\nKinetic Sunyaev-Zel'dovich effect, which is due to the peculiar\nvelocities of clusters, can be viewed as a nonlinear counterpart\nto the Vishniac effect. Is there not, then, a sort of\ndetectable Vishniac effect\nin cosmological scenarios in which $R_V$ is nonlinear during the\nepoch of reionization, albeit under a different name?\n\nThe problem with this point of view is that it overlooks some\nimportant physical distinctions between these effects. The Vishniac\neffect is due to the presence of a redshift regime in which $G(w)$ is\nslowly varying and a delicate cancellation takes place due to the lack\nof curl in the peculiar velocity field. As it can be calculated\nprecisely, it provides a unique probe of the reionization history of\nthe universe that is not available from measurements of nonlinear\nfluctuations.\n\nFurthermore, the Vishniac effect displays a distinct signature\nof higher-order moments that allows it to be distinguished from \nother contributions. In order to understand why this occurs,\nlet us consider the bispectrum $B({\\vec \\kappa_1},{\\vec \\kappa_2}) \n(2 \\pi)^2 \\delta^2({\\vec \\kappa_1} + {\\vec \\kappa_2} + \n\t{\\vec \\kappa_3}) \\equiv\n\\langle\n\\tilde{\\frac{\\Delta T}{T}}({\\vec \\kappa_1})\n\\tilde{\\frac{\\Delta T}{T}}({\\vec \\kappa_2}) \n\\tilde{\\frac{\\Delta T}{T}}({\\vec \\kappa_3})\n\\rangle$.\nWe can apply our $\\delta$-function beam approach in\nthe linear regime to calculate this as\n\\ba\n\\langle\n\\tilde{\\frac{\\Delta T}{T}}({\\vec \\kappa_1})\n\\tilde{\\frac{\\Delta T}{T}}({\\vec \\kappa_2}) \n\\tilde{\\frac{\\Delta T}{T}}({\\vec \\kappa_3})\n\\rangle \n = -i\n\\prod_{i=1}^3 \n\\left[\\int_0^{w_0} dw_i G(w_i) \\right]\n\\prod_{j=1}^6 \n\\left[\n\\int \\frac{d^3 {\\bf k_j}}{(2 \\pi)^3} \n\\right]\n\\nonumber \\\\ \\qquad (2 \\pi)^6\n \\delta^2(({\\vec k_1}+{\\vec k_2})w_{1,{\\rm ang}}-{\\vec \\kappa_1})\n \\delta^2(({\\vec k_3}+{\\vec k_4})w_{2,{\\rm ang}}-{\\vec \\kappa_2})\n \\delta^2(({\\vec k_5}+{\\vec k_6})w_{3,{\\rm ang}}-{\\vec \\kappa_3})\n\\nonumber \\\\ \\qquad \\qquad\ne^{i(k_{1,z}+k_{2,z})w_1 + i (k_{3,z}+k_{4,z})w_2 + i(k_{5,z}+k_{6,z})w_3}\n\\frac{k_{1,z}}{k_1^2}\n\\frac{k_{3,z}}{k_3^2}\n\\frac{k_{5,z}}{k_5^2}\n\\langle\n\\prod_{l=1}^6 \\tilde{\\delta_0} ({\\bf k_l},w_i)\n\\rangle.\n\\label{eq:bispec}\n\\ea\nIf $G(w)$ is slowly varying,\nwe can again follow Kaiser (1992) in dividing\nthe integrals over comoving distance into $N$ statistically\nindependent intervals of width $\\Delta w$, \n\\ba\n\\langle\n\\tilde{\\frac{\\Delta T}{T}}({\\vec \\kappa_1})\n\\tilde{\\frac{\\Delta T}{T}}({\\vec \\kappa_2}) \n\\tilde{\\frac{\\Delta T}{T}}({\\vec \\kappa_3})\n\\rangle\n = -i\n\\sum_{n=1}^{N}\nG(w_n)^3 \\Delta w^3\n\\prod_{j=1}^6 \n\\left[\n\\int \\frac{d^3 {\\bf k_j}}{(2 \\pi)^3} \n\\right] (2 \\pi)^6\n \\delta^2(({\\vec k_1}+{\\vec k_2})w_{n,{\\rm ang}}-{\\vec \\kappa_1})\n\\nonumber \\\\ \n \\delta^2(({\\vec k_3}+{\\vec k_4})w_{n,{\\rm ang}}-{\\vec \\kappa_2})\n \\delta^2(({\\vec k_5}+{\\vec k_6})w_{n,{\\rm ang}}-{\\vec \\kappa_3})\nj_0 \\left(\\frac{(k_{1,z}+k_{2,z}) \\Delta w}{2} \\right)\n\\nonumber \\\\ \nj_0 \\left(\\frac{(k_{3,z}+k_{4,z}) \\Delta w}{2} \\right)\nj_0 \\left(\\frac{(k_{5,z}+k_{6,z}) \\Delta w}{2} \\right)\n\\frac{k_{1,z}}{k_1^2}\n\\frac{k_{3,z}}{k_3^2}\n\\frac{k_{5,z}}{k_5^2}\n\\langle\n\\prod_{l=1}^6 \\tilde{\\delta_0} ({\\bf k_l},w_n)\n\\rangle.\n\\label{eq:bispec2}\n\\ea\nAs there are an odd number of $k_z$ terms, there is no pairing of density\nfields that does not result in an odd $k_z$ term. As all the $k$ \nintegrals are even, \n$\\langle \\tilde{\\frac{\\Delta T}{T}}({\\vec \\kappa_1}) \n \t \\tilde{\\frac{\\Delta T}{T}}({\\vec \\kappa_2}) \n\t \\tilde{\\frac{\\Delta T}{T}}({\\vec \\kappa_3}) \\rangle $ = 0.\n\nThis cancellation can be understood from a more general perspective.\n$B({\\vec \\kappa_1},{\\vec \\kappa_2})$ is generated\nby the expectation value of the triple product of the field ${\\bf q}$.\nAs ${\\bf q}$ is an isotropic vector field, \n$\\langle \\tilde{q}_{i}({\\bf k_1}) \\tilde{q}_{j}({\\bf k_2}) \n\t \\tilde{q}_{k}({\\bf k_3}) \\rangle$\ncan depend on no vectors other than the ${\\bf k}$ vectors themselves\nand must therefore be proportional to at least one of \nthe them (Monin \\& Yaglom 1971). This means that \nthe $i = j = l = z$ component of this product must be proportional\nto $k_{1,z}$, $k_{2,z}$, or $k_{3,z}$. Thus the \nodd $k_z$ term that results in $B({\\vec \\kappa_1},{\\vec \\kappa_2}) = 0$ \nis due to the isotropy of the\ndensity fluctuations. By a similar argument, all odd moments \nof the temperature fluctuations must be zero as these also depend on the\nexpectation value of the product of an odd number\nof ${\\bf q}$'s. Note that this is true independent of the gaussianity\nof the probability distribution functional of ${\\tilde \\delta}({\\bf k})$.\n\n\nThis cancellation does not apply to the even moments, however, as an\neven number of ${\\bf q}$'s can be arranged in a way that is not proportional\nto one of the ${\\bf k}$ vectors. Thus the Vishniac effect is unique in that\nit is nongaussian independent of the gaussianity of the probability\ndistribution functional of $\\tilde{\\delta}({\\bf k})$, but this\nnongaussianity is expressed only in the even higher-order moments.\nThis alternation of zero-and-nonzero higher-order moments provides a\nunique signal that distinguishes the Vishniac effect from other\nsecondary anisotropies, and provides us with the opportunity to use\nnongaussian statistics as a discriminator between these contributions.\nNote however, that the difficulty of measuring secondary anisotropies\nmay make such an analysis difficult to apply in practice.\n\n\\section{Conclusions}\n\nDue to the tremendous predictive power of linear theory, comparisons\nbetween linear predictions and large-scale cosmic microwave background\nmeasurements promise to constrain cosmological parameters to the order\nof a few percent (Jungman et al.\\ 1996; Bond, Efstathiou, \\& Tegmark\n1997; Zaldarriaga, Spergel, \\& Seljak 1997). The natural extension of\nthis approach is to try to measure small-scale secondary anisotropies\nand match them to linear predictions to study the reionization history\nof universe. The situation in this case is more muddled, however, as\na number of nonlinear secondary effects also contribute at these\nscales.\n\nThe dominant secondary linear anisotropy is a\nsecond-order contribution known as the Vishniac or Ostriker-Vishniac\neffect. As this effect can be predicted accurately as a function of\ncosmological parameters, several authors have proposed that its\nmeasurement will prove to be a sensitive probe of the reionization\nhistory of the universe. Reionization occurs by the formation of\nnonlinear structures, however, raising the question of whether a\nregime of redshift space exists in which these objects have collapsed\nbut a linear analysis is still appropriate.\n\nIn this work, we have determined the relevant physical scales that\ngive rise to the Vishniac effect in a Cold Dark Matter cosmogony,\nshowing that approximations are already compromised when $1$ Mpc/($h\n\\Gamma_{0.20}$) scales have become nonlinear, and break down when $2$\nMpc/($h \\Gamma_{0.20}$) dark matter halos reach overdensities of 1.\nThe width of the redshift regime over which the effect can be\nimprinted on the CMB is dependent on the cosmological parameters and\nthe reionizing mass scale. Schemes in which reionization is due to\nradiation from active galactic nuclei associated with dark matter\nhalos of masses $\\gtrsim 10^9 M_\\odot$ are limited by the absence of a\nGunn-Peterson absorption trough. As reionization must have occurred\nwith a high degree of efficiency before a redshift of 5, such models\nare successful only if one assumes a large value of $\\sigma_8$, or\nconsiders open models with slowly-changing linear growth factors.\nBoth these assumptions push back the redshift at which $R_V$ becomes\nnonlinear, limiting the range over which a linear analysis is\nappropriate.\n\nScenarios in which reionization is due to much smaller objects, such\nas stars formed in dwarf galaxies associated with dark matter halos of\nmasses $\\gtrsim 10^6 M_\\odot$, are able to reionize the universe at\nmuch larger redshifts even in cosmologies in which $\\sigma_8$ is small\nand $D(z)$ quickly evolving. This represents only a marginal gain\nhowever, as the high redshift contribution to the \nVishniac integral is roughly proportional to comoving\ndistance, and comoving distances are \nsmall at high redshifts. Thus low-mass scenarios of reionization are\nmore compatible with a linear analysis not so much because they\nreionize earlier as because they allow $R_V$ to become nonlinear more\nrecently without violating Gunn-Peterson limits.\n\nThe Vishniac effect arises from physical processes that are distinct\nfrom nonlinear secondary anisotropies. Its detection indicates the\npresence of a redshift regime in which a delicate cancellation takes\nplace due to the lack of curl in the peculiar velocity field and slow\nvariations in $G(w)$. This leaves a unique signature in the\nhigher-order moments of the temperature fluctuations that is absent\nfrom its nonlinear counterparts. Furthermore, due to the predictive\npower of linear theory, it represents a sensitive probe of the\nreionization history not available from measurements of nonlinear\ncontributions.\n\nAs with measurements of large angular scale anisotropies, small-scale\nmicrowave background anisotropy measurements have the potential to\nuncover much about the history of our universe. Also as with\nlarge-scale measurements, whether this potential will be realized\nremains to be seen. While the Vishniac effect represents a possible\nprobe of the reionization epoch, the analysis will, as always, be more\ninvolved than first suggested. Ultimately it will only be through the\nmeasurement and analysis of small-scale microwave background\nanisotropies that we will be able to know if there is a detectable Vishniac\neffect.\n\n\n\\acknowledgments I wish to thank Nabila Aghanim, Fran\\c cois Bouchet,\nRychard Bouwens, Andrew Jaffe, Douglas Scott, and Naoshi Sugiyama for\nhelpful discussions and am particularly indebted to Joseph Silk, whose\ncomments and suggestions have been invaluable during the preparation\nof this work. I thank Uro\\v{s} Seljak and Matias Zaldarriaga for the use of\nCMBFAST and acknowledge partial support by the NSF.\n\n\n\\section*{Appendix}\n\nIn this appendix, we provide explicit expressions for the\ncosmological factors used throughout this paper. We allow both \n$\\Omega_0$ and $\\Omega_\\Lambda$ to be free. \nIn this case the Friedman equations for the evolution of \nthe scale factor of the Universe, $a(z)$ are\n\\begin{equation}\n {\\dot a \\over a} = H_0 E(z) \\equiv H_0 \\sqrt{\\Omega_0 (1+z)^3 +\n \\Omega_\\Lambda + (1-\\Omega_0-\\Omega_\\Lambda)(1+z)^2},\n\\end{equation}\nand\n\\begin{equation}\n {\\ddot a \\over a} = H_0^2 [\\Omega_\\Lambda - \\Omega_0\n (1+z)^3/2],\n\\end{equation}\nwhere $H_0 = 100\\, h$ km~sec$^{-1}$~Mpc$^{-1}$ is the Hubble\nconstant, and the overdot denotes a derivative with respect to\ntime. \n\nWe choose the scale factor such that $a_0 H_0=2 c$. If we are\nlocated at the origin, $w = 0$, then an object at redshift $z$\nis at a comoving distance,\n$w(z) = {1\\over 2} \\int_0^z \\, dz' E^{-1}(z')$\nand at a time\n$t(z) = {1 \\over H_0} \\int_z^\\infty \\, dz' (1+z')^{-1} E^{-1}(z').$\nNote that this is different than conformal time,\ndefined by $d\\eta=dt/a$, such that \n$c \\eta(z) = w(\\infty)-w(z)$. \nFor any flat universe the angular size distance $w_{\\rm ang} = w$,\nand in an open universe\n\\be\n w_{\\rm ang} = \\frac{\\sinh(2 w \\sqrt{1 - \\Omega_0 - \\Omega_\\Lambda})}\n {2 \\sqrt{1 - \\Omega_0 - \\Omega_\\Lambda}} .\n\\label{eq:wangle}\n\\ee\nThe growth factor as a function of redshift is \n\\begin{equation}\n D(z) = {5 \\Omega_0\\, E(z) \\over 2} \\, \\int_z^\\infty \\, {1+z' \\over\n [E(z')]^3} \\, dz',\n\\label{eq:growth}\n\\end{equation}\nwhile \n\\be\n {\\dot D \\over D} = {\\ddot a \\over \\dot a} - {\\dot a\n \\over a} + {5 \\Omega_0 \\over 2} {\\dot a \\over a} {(1+z)^2\n \\over [E(z)]^2\\,D(z)}.\n\\label{eq:growthdot}\n\\ee\nThe evolution of $\\Omega$ is given by\n\\be\n\\Omega(z) = \\Omega_0 (1+z)^3 E^{-2}(z)\n\\ee\nwhere $\\Omega_0 = \\Omega(0).$\n\nFor the power spectrum, we use\n\\begin{eqnarray}\n P(k) &=& {2 \\pi^2 \\over 8} \\delta_H^2 (k/2)^n T^2(k_p\\,{\\rm\n Mpc}/h \\Gamma),\n\\label{eq:pk}\n\\end{eqnarray}\nwhere $T(q)$ is the CDM transfer function, $k_p= k/a_0 =k\nH_0/2 c$ is the physical wavenumber, and\nthe shape parameter $\\Gamma$ is defined as (Sugiyama 1995)\n\\be\n\\Gamma \\equiv \\Omega_0 (h/0.5) \\exp(-\\Omega_b-\\Omega_b/\\Omega_0).\n\\label{eq:shapep}\n\\ee\nThe factor of 8 in the denominator in\nEq.\\ (\\ref{eq:pk}) arises because we are using $a_0\nH_0=2 c$. For the transfer function, we use the analytic fit given \nby Bardeen et al.\\ (1986) for the CDM cosmogony,\n\\begin{equation}\n T(q)= {\\ln(1+2.34q)/(2.34 q)\\over [1+3.89 q + (16.1 q)^2 +\n (5.46 q)^3 + (6.71 q)^4]^{1/4}}.\n\\label{eq:cdm}\n\\end{equation}\nThe normalization factor $\\delta_H$ can be fixed by specifying \n$\\sigma(8{\\rm Mpc}/h)$, where\nthe variance of the mass enclosed in a sphere of radius $R$ is given by \n\\be\n\\sigma^2(R) = \\frac{1}{2 \\pi^2} \\int_0^\\infty k^2 dk P(k) W^2(k_p R).\n\\label{eq:sig}\n\\ee\nHere $W(x)$ is the spherical top-hat window function, defined in\nFourier space as\n\\be\nW(x) \\equiv 3 \\left[ \\frac{\\sin(x)}{x^3} - \\frac{\\cos(x)}{x^2} \\right].\n\\label{eq:tophat}\n\\ee\n\n\\fontsize{9}{11pt}\\selectfont\n\n\\begin{references}\n\n\\reference{}Adams, J. A., Sarkar, S., \\& Sciama, D. W. 1998, MNRAS, 301, 210\n\\reference{} Aghanim, N., De Luca, A., Bouchet, F. R., Gispert, R., \\& \n\tPuget, J. 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astro-ph0002165
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Beaming and Jets in Gamma Ray Bursts
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[
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"author": "Re'em Sari"
}
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The origin of GRBs have been a mystery for almost 30 years. The afterglow observed in the last few years enabled redshift determination for a handful of bursts, and the cosmological origin is now firmly established. Though the distance scale is settled, there still remains orders of magnitude uncertainty in their rate and in the total energy that is released in the explosion due to the possibility that the emission is not spherical but jet-like. Contrary to the GRB itself, the afterglow can be measured up to months and even years after the burst, and it can provide crucial information on the geometry of the ejecta. We review the theory of afterglow from jets and discuss the evidence that at least some of the bursts are not spherical. We discuss the prospects of polarization measurements, and show that this is a powerful tool in constraining the geometry of the explosion.
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"name": "proc.tex",
"string": "\\documentstyle[epsfig]{aipproc}\n\n% \\address{$^*$National Center for Atmospheric Research\\thanks{The National\n% Center for Atmospheric Research is sponsored by the National\n% Science Foundation.}\\\\\n% Boulder Colorado 80307\\\\\n% $^{\\dagger}$National Standards Institute, Boulder, Colorado 11543}\n\n%\\lefthead{LEFT head}\n%\\righthead{RIGHT head}\n\n%remove this (******)\n%\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n%\\markboth{Re'em Sari}{APS Conf. Ser. Style}\n%\\pagestyle{myheadings}\n%\\nofiles\n\n% Some definitions I use in these instructions.\n\n% \\def\\emphasize#1{{\\sl#1\\/}}\n% \\def\\arg#1{{\\it#1\\/}}\n% \\let\\prog=\\arg\n\n% \\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n% \\marginparwidth 1.25in\n% \\marginparsep .125in\n% \\marginparpush .25in\n% \\reversemarginpar\n\n\\begin{document}\n\\title{Beaming and Jets in Gamma Ray Bursts}\n \\author{Re'em Sari}\n\\address{Theoretical Astrophysics 130-33, California institute of Technology, Pasadena CA 91125}\n\\maketitle\n\n\\begin{abstract}\nThe origin of GRBs have been a mystery for almost 30 years. The\nafterglow observed in the last few years enabled redshift\ndetermination for a handful of bursts, and the cosmological origin is\nnow firmly established. Though the distance scale is settled, there\nstill remains orders of magnitude uncertainty in their rate and in the\ntotal energy that is released in the explosion due to the possibility\nthat the emission is not spherical but jet-like. Contrary to the GRB\nitself, the afterglow can be measured up to months and even years\nafter the burst, and it can provide crucial information on the\ngeometry of the ejecta. We review the theory of afterglow from jets\nand discuss the evidence that at least some of the bursts are not\nspherical. We discuss the prospects of polarization measurements, and\nshow that this is a powerful tool in constraining the geometry of the\nexplosion.\n\\end{abstract}\n\n\\section{Jets? - A fundamental question}\n\nThe study of $\\gamma$-ray bursts was revolutionized when the\nItalian-Dutch satellite BeppoSAX delivered arcminutes positioning of\nsome GRBs, within a few hours after the event. This enabled other ground\nand space instruments to monitor the relatively narrow error\nboxes. Emission in X-ray, infrared, optical and radio, so called\n``afterglow'', was observed by now for more than a dozen of bursts.\n\nThe current understanding of the GRBs phenomenon is that a compact source\nemits relativistic flow with Lorentz factor $\\gamma$ of at least a few\nhundreds. This flow emits, probably by internal shocks (see e.g. \\cite{SP97,FMN96}),\nthe GRB. After these internal shocks have produced the GRB, the ultra\nrelativistic flow interacts with the surrounding medium and\ndecelerates. Synchrotron radiation is emitted by the heated\nsurrounding matter. As more and more of the surrounding mass is\naccumulating, the flow decelerates and the emission shifts to lower\nand lower frequencies. Excitingly, the afterglow theory is relatively\nsimple. It deals with the emission on timescales much longer than those\nof the GRBs. The details of the complex initial conditions are\ntherefore forgotten and the evolution depends only on a small number of\nparameters.\n\nWe begin by clarifying some of the confusing terminology. There are\ntwo distinct, but related, effects. The first, {\\bf ``jets''},\ndescribes scenarios in which the relativistic flow emitted from the\nsource is not isotropic but collimated towards a finite solid\nangle. The term jet refers to the geometrical shape of the\nrelativistic flow emitted from the inner engine. The second effect is\nthat of {\\bf ``relativistic beaming''}. The radiation from any object\nthat is radiating isotropically in its own rest frame, but moving with\na large Lorentz factor $\\gamma$ in the observer frame, is collimated\ninto a small angle $1/\\gamma$ around its direction of motion. This is\nan effect of special relativity. It has nothing to do with the\nejecta's geometry (spherical or jet) but only with the fact that the\nejecta is moving relativisticly. The effect of relativistic beaming\nallows an observer to see only a small angular extent, of size\n$1/\\gamma$ centered around the line of sight. Unfortunately, the term\nbeaming was also used for ``jets'' by many authors (including myself).\nWe will keep a clear distinction between the two in this paper. Since\nwe know the flow is ultra-relativistic (initially $\\gamma>100$), there\nis no question that the relativistic beaming is always relevant for\nGRBs. The question we are interested in is that of the existence of\n``jets''.\n\nThe idealized description of a jet is a flow that occupies only a\nconical volume with half opening angle $\\theta_0$. In fact the\nrelativistic dynamics is such that the width of the matter in the\ndirection of its propagation is much smaller than its distance from\nthe source by a factor of $1/\\gamma^2$. The flow, therefore, does not\nfill the whole cone. Instead it occupies only a thin disk at its base,\nlooking more like a flying pancake \\cite{P99} - see figure\n\\ref{grbjets}. If the ``inner engine'' emits two such jets in\nopposite directions then the total solid angle towards which the flow\nis emitted is $\\Omega=2\\pi \\theta_0^2$. The question whether the\nrelativistic flow is in the form of a jet or a sphere has three\nimportant implications.\n \n\\begin{figure*}\n%\\centerline{\\epsfig{file=grbjets3.eps,width=3.6in}}\n\\centerline{\\epsfig{file=f3.eps,width=3.0in}}\n\\vspace{10pt}\n\\caption{Schematic geometric description of jets in GRBs. The scheme shows\nthe multiple shells before internal shocks have occurred. After that they \nall merge to one shells with typical width a factor of $\\gamma^2$ thinner\nthan their distance from the source. \n}\n\\label{grbjets}\n\\end{figure*}\n\n\\noindent {\\bf The Total Emitted Energy.} Optical observations of\nafterglows enabled redshift determination, and therefore a reasonably\naccurate estimate of the distance, $D$, to these events (the\nuncertainty is now in the cosmological parameters of the\nuniverse). The so called ``isotropic energy'' can then be inferred\nfrom the fluence $F$ (the total observed energy per unit area at\nearth) as $E_{iso}=4\\pi D^2 F$ (taking cosmological corrections into\naccount, $D=D_L/\\sqrt{1+z}$ where $D_L$ is the luminosity distance and\n$z$ is the redshift). The numbers obtained in this way range from\n$10^{51}$erg to $10^{54}$erg with the record of $3\\times 10^{54}$erg\nheld by the famous GRB~990123. These huge numbers approach the\nequivalent energy of a solar mass, all emitted in a few tens of\nseconds!\n\nThese calculations assumed that the source emitted the\nsame amount of energy towards all directions. If instead the emission\nis confined to some solid angle $\\Omega$ then the true energy is\n$E=\\Omega D^2 F$. As we show later $\\Omega$ is very weakly constrained\nby the GRB itself and can be as low as $10^{-6}$. If so the true\nenergy in each burst $E \\ll E_{iso}$. We will show later that\ninterpretation of the multi-wavelength afterglow lightcurves indeed indicates\nthat some bursts are jets with solid angles considerably less than $4 \\pi$.\nThe isotropic energy estimates may be fooling us by a few orders of \nmagnitudes! Clearly this is of fundamental importance when considering \nmodels for the sources of GRBs.\n\n\\noindent {\\bf The Event Rate.} BATSE sees about one burst per\nday. With a few redshifts measured this translates to about $10^{-7}$\nbursts per year per galaxy. However,\nif the emission is collimated to $\\Omega \\ll 4\\pi$ then we do not see\nmost of the events. The true event rate is then larger than that measured by\nBATSE by a factor of $4\\pi /\\Omega$. Again this is of fundamental importance. \nClearly, the corrected GRB\nevent rate must not exceeds that of compact binary mergers or \nthe birth rate of massive stars if these are to produce the majority \nof the observed GRBs.\n\n\\noindent {\\bf The Physical Ejection Mechanism.} Clearly, different\nphysical models are needed to explain collimated and isotropic\nemission. For example, in the collapsar model (e.g. \\cite{MW99}), \nrelativistic ejecta\nthat is capable of producing a GRB is produced only around the\nrotation axis of the collapsing star with half opening angle of about\n$\\theta_0 \\cong 0.1$. Such models would have difficulties to explain\nisotropic bursts as well as very narrow jets.\n\nWith these uncertainties we are therefore left with\nhuge ignorance in how, how much and how many GRBs are produces. The\nquestion as to whether the emission of GRBs is spherical or collimated in jets is fundamental to almost all aspects of the GRB\nphenomenon.\n\n\n\n\\section{Afterglow Spectrum - Basic Theory}\n\nWhen the ejecta interacts with the surrounding medium, a shock waves\n(so called the forward shock) is going through the cold ambient medium\nand heating it up to relativistic temperatures. The basic afterglow\nmodel assumes that electrons are accelerated by the shock into a\npowerlaw distribution of their Lorentz factor $\\gamma_e$: $N(\\gamma\n_{e})\\sim \\gamma _{e}^{-p}$ for $\\gamma _{e}>\\gamma _{m}$. The lower\ncutoff of this distribution is assumed to be a fixed fraction of\nequipartition. It is also assumed that a considerable magnetic field\nis being built behind the shock, again characterized by a certain\nfraction of equipartition. The relativistic electrons then emit\nsynchrotron radiation and produce the observed afterglow. The broad\nband spectrum of such emission was given by Sari, Piran \\& Narayan\n\\cite{SPN98} (see figure \\ref{SPNspec}).\n\n\\begin{figure*}\n\\centerline{\\epsfig{file=SPNfcspec.eps,width=2.8in}\\ \\\n\\epsfig{file=SPNscspec.eps,width=2.8in}}\n\\vspace{10pt}\n\\caption{Theoretical spectra of synchrotron emission from fast cooling\n($\\nu_c<\\nu_m$ left) and slow cooling ($\\nu_m<\\nu_c$ right) powerlaw\ndistribution of electrons. This spectrum is robust and holds for jets\nas well as spherical ejecta. In general, the break frequencies change\nin time as well as the overall normalization. The arrows on the figure\nindicate the evolution of these break frequencies for a spherical\nemission in a constant density environment. $p=2.2-2.4$ fits the\nobserved spectra well.}\n\\label{SPNspec}\n\\end{figure*}\n\nAt each instant, there are three characteristic frequencies: (I) $\\nu\n_{m}$ which is the synchrotron frequency of the minimal energy\nelectron, having a Lorentz factor $\\gamma _{m}$. (II) The cooling time\nof an electron is inverse proportional to its Lorentz factor $\\gamma\n_{e}$. Therefore, electrons with a Lorentz factor higher than some\ncritical value $\\gamma _{e}>\\gamma _{c}$ can cool on the dynamical\ntimescale of the system. This characteristic Lorentz factor\ncorresponds to the ``cooling frequency'' $\\nu _{c}$. (III) Below some\ncritical frequency $\\nu _{a}$ the flux is self absorbed and is given\nby the Rayleigh-Jeans portion of a black body spectrum. The broad band\nspectrum of the well studied GRB 970508 \\cite{G+98} is in very good\nagreement with the theoretical picture.\n\nWe stress that the spectrum given above is quite robust. The only\nassumption is synchrotron radiation from a powerlaw distribution of\nrelativistic electrons. The same spectrum will hold whether the shocks\npropagates into a constant density interstellar medium or a decreasing\nsurrounding density produced earlier by the progenitor's wind. It will\nbe valid whether the ejecta is spherical or jet-like, whether the\nequipartition parameters are constant with time or not.\n\nOn the contrary, the temporal evolution of the spectrum is more subtle. \nThe simplest evolution, which well describes the\ndata of some bursts, is the spherical adiabatic model with a constant\ndensity ambient medium. In this scenario, $\\gamma \\sim R^{-3/2}$\nor in terms of the observer time, $t=R/\\gamma^2c$, $\\gamma \\sim\nt^{-3/8}$. Given the evolution of $\\gamma(t)$ one can derive the \ntemporal evolution of the break frequencies and the results are indicated\nin figure \\ref{SPNspec}. The peak flux, in the adiabatic, spherical \nconstant ambient density model is constant with time.\n\n\\section{Hydrodynamics of Jets}\n\nInterestingly, due to the effect of relativistic beaming (which is independent\nof jets) we are only able to see an angular extent of $1/\\gamma <0.01$\nduring the GRB itself where the Lorentz factor $\\gamma\n>100$. Moreover, it is only regions of size $1/\\gamma$ that are\ncausally connected. Therefore, each fluid element evolves as if it is\npart of a sphere as long as $1/\\gamma<\\theta_0$. Combining these two\nfacts, we cannot distinguish a jet from spherical ejecta as long as\n$1/\\gamma<\\theta_0$.\n\nHowever, as the afterglow evolves, $\\gamma$ decreases and it will eventually\nfall below the initial inverse opening angle of the jet. The observer\nwill notice that some of the sphere is missing from the fact that\nless radiation is observed. This effect alone, will produce a significant\nbreak, steepening the lightcurve decay by a factor of $\\gamma^2 \\sim\nt^{-3/4}$ even if the dynamics of each fluid element has not\nchanged. The transition should occur at the time $t_{jet}$ when\n$1/\\gamma \\cong \\theta_0$. Observing this time can therefore provide\nan estimate of the jet's opening angle according to\n\\begin{equation} \\label{t_jet}\nt_{{\\rm jet}}\\approx 6.2 (E_{52}/n_{1})^{1/3}(\\theta _{0}/0.1)^{8/3}\n{\\rm hr}.\n\\end{equation}\n\nAdditionally, Rhoads \\cite{R99} has shown that at about the same time\n(see however \\cite{PM99,MR99,MSB99}),\nthe jet will begin to spread laterally so that its opening angle \n$\\theta (t\\grave{)}\\sim 1/\\gamma$. \nThe ejecta now encounters more surrounding matter and\ndecelerates faster than in the spherical case. The Lorentz factor \nnow decays exponentially with the radius and as $\\gamma\\sim t^{-1/2}$ \nwith observed time. Taking this into account, the observed \nbreak is even more significant. The slow cooling spectrum given in figure \n\\ref{SPNspec} evolves now with decreasing peak flux $F_{\\nu,m} \\sim t^{-1}$ \nand the break frequencies evolve as $\\nu_m \\sim t^{-2}$, $\\nu_c \\sim t^0$ and\n$\\nu_a \\sim t^{-1/5}$. \nThis translate to a temporal decay in a given frequency as\nlisted in table \\ref{t:afterglow}.\n\n\\begin{table}[b]\n\\begin{tabular}{|c||c||c|c|}\n\\hline\n& spectral index & \\multicolumn{2}{|c|}{light curve index $\\alpha$, $F_{\\nu}\\propto\nt^{-\\alpha}$} \\\\\n& $\\beta$, $F_{\\nu}\\propto \\nu^{-\\beta}$ & sphere & jet \\\\ \\hline\\hline\n$\\nu<\\nu_a$ & $\\beta=-2$ & $\\alpha=-1/2$ & $\\alpha=0$ \\\\ \\hline\n$\\nu_a<\\nu<\\nu_m$ & $\\beta=-1/3$ & $\\alpha=-1/2$ & $\\alpha=1/3$ \\\\ \\hline\n& & $\\alpha=3(p-1)/4\\cong 1.05$ & $\\alpha=p\\cong 2.4$ \\\\\n\\raisebox{1.5ex}[0pt]{$\\nu_m<\\nu<\\nu_c$} & \\raisebox{1.5ex}[0pt]{$(p-1)/2\n\\cong0.7$} & $\\alpha=3\\beta/2$ & $\\alpha=2\\beta+1$ \\\\ \\hline\n& & $\\alpha=(3p-2)/4\\cong 1.3$ & $\\alpha=p\\cong 2.4$ \\\\\n\\raisebox{1.5ex}[0pt]{$\\nu>\\nu_c$} & \\raisebox{1.5ex}[0pt]{$ p/2\n\\cong1.2$} & $\\alpha=3\\beta/2-1/2$ & $\\alpha=2\\beta$ \\\\ \\hline\n\\end{tabular}\n\\caption{The spectral index $\\beta$ and the temporal index $\\alpha$ as\nfunction of $p$ for a spherical and a jet-like evolution. Typical values are \nquoted using $p=2.4$. The parameter free relation between $\\alpha$ and \n$\\beta$ is given for each case (eliminating $p$). The difference in $\\alpha$\nbetween a jet and a sphere is always substantial at all frequencies.}\n\\label{t:afterglow}\n\\end{table}\n\nThe jet break is a hydrodynamic one. It should therefore appear at\nthe same time at all frequencies - an achromatic break. Though an achromatic\nbreak is considered to be a strong signature of a jet, one should keep\nin mind that any other hydrodynamic transition will also produce an\nachromatic break. To name a few: the transition from relativistic to \nnon-relativistic dynamics, a jump in the ambient density or \nthe supply of new energy\nfrom slower shells that catch up with the decelerated flow. However,\nthe breaks produced by the transition from a spherical like evolution\n(when $1/\\gamma<\\theta_0$) to a spreading jet has a well defined\nprediction for the change in the temporal decay indices. The amount of \nbreak depends on the spectral regime that is observed. It can be seen\nfrom table \\ref{t:afterglow} that the break is substantial $\\Delta\n\\alpha >0.5$ in all regimes and should be easily identified.\n\nFinally we note that if jet's opening angle is of order unity, the\ntotal energy may still be about an order of magnitude lower than the\nisortropic estimate. However, in this case the break will be\n``hidden'' as it will overlap the transition to non-relativistic\ndynamics. It was suggested that this is the case for GRB~970508\n\\cite{FWK99}\n\n\\section{Observational Evidence for Jets}\n\n\n\nEvidence of a break from a shallow to a steep power law was first seen\nin GRB 990123 \\cite{K+99a,F+99}. Unfortunately the break was observed\nonly in one optical band while the infrared data was ambiguous. Yet,\nthe strongest evidence for this burst being a jet does not come from\nthis optical break but rather from radio observations, as explained\nbelow. A famous and exciting event this year was the first detection\nof a bright (9th magnitude) optical emission simultaneous with GRB\n990123 \\cite{A99}. Another new ingredient in GRB 990123 is a radio\nflare \\cite{K+99b}. Contrary to previous afterglows, where the radio\npeaks around few weeks and then decays slowly, this burst had a fast\nrising flare, peaking around a day and then decaying quickly. Sari and\nPiran \\cite{SP99c} have shown that the bright optical flash and the\nradio flare are related. Within a day the emission from the\nadiabatically cooling ejecta, that produced the $60$s optical flash\nshifts into the radio frequencies. Given this interpretation, the\nregular forward shock emission should have come later, on the usuall\nfew weeks timescale. The fact that this ``usual'' forward shock radio\nemission did not show up is in agreement with the interpretation of\nthis burst as a ``jet'' which causes the emission to considerably\nweaken by the time the typical frequency $\\nu_m$ arrives to radio\nfrequencies.\n\\begin{figure}\n\\centerline{\\epsfig{file=grb990123opt.eps,width=2.2in}\\ \\\n\\epsfig{file=grb990123rad.eps,width=3.4in}}\n\\vspace{10pt}\n\\caption{GRB~990123: Optical data (left) shows some break in the light\ncurve at Gunn-r band. K band seems to have no break but the\ncontribution of the host galaxy is less certain.\nRadio ``flare'' (right) seen a day after the burst agrees with \ntheoretical scaling \nof the optical flash (heavy solid line marked R). \nIn the jet interpretation, only\nfaint radio emission is expected on late times as given by the heavy\nsolid line marked R+F, in agreement with observations. Thin and\ndashed lines indicate the theoretical expectations if the radio signal\nat day two is interpreted as the forward shock (independent of the optical flash) and if jets are not\ntaken into account. These will largely over predict the late radio \nupper limits, marked by triangles \\protect\\cite{K+99b} (see however \n\\protect\\cite{G+99}).}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\epsfig{file=grb990510opt.eps,width=2.6in}\\ \\ \n\\epsfig{file=grb990510rad.eps,width=3.0in}}\n\\vspace{10pt}\n\\caption{GRB~990510, the best evidence for a ``jet'': an achromatic\nbreak in optical and radio at $t_{jet} = 1.2$ days implying\n$\\theta_0 = 0.08$. The temporal slope before and after the break\nagree well with theory if $p=2.2$. For this burst\n$E_{iso}=2.9\\times 10^{53}$erg but the true total energy is only\n$E=10^{51}$erg.\n}\n\\end{figure}\n\nGRB~990510 had a very clear break simultaneously in all optical bands\nand in radio \\cite{S+99,H+99}. In GRB~990123 and GRB~990510 the\ntransition times were about $2.1$ days and $1.2$ days reducing the\nisotropic energy estimate by a factor of $\\sim 200$ and $\\sim 300$,\nrespectively. The total energy is now well below a solar rest mass!\n\nSari, Piran \\& Halpern \\cite{SPH99} have noted that the observed\ndecays in GRB afterglows that do not show a break are either of a\nshallow slope of $\\sim t^{-1.2}$ or a very steep slope of $\\sim\nt^{-2.1}$. They argued that the rapidly decaying bursts are those in\nwhich the ejecta was a narrow jet and the break in the light curve was\nbefore the earliest observation. Interestingly, evidence for jets are\nfound when the inferred energy $E_{iso}$ (which does not take jets\ninto account) is the largest. This implies that jets may account for a\nconsiderable fraction of the wide luminosity distribution seen in\nGRBs, and that the true energy distribution is less wide than it seems\nto be.\n\nAn alternative explanation for these afterglows with fast decline\nis propagation into a medium with decreasing density, i.e. a wind produced earlier by the progenitor \\cite{CL99}. We favor the jet \ninterpretation for two reasons: (I) decreasing density only \nenhance the decay by $t^{-1/2}$ for $\\nu_m<\\nu<\\nu_c$ and does \nnot enhance the decay at all for $\\nu>\\nu_c$ \n(with typical parameters the optical \nand certainly the x-ray bands are above $\\nu_c$). The rest of the needed \neffect, in the wind interpretation, is associated with a higher value of\nthe electron powerlaw distribution index $p$ ($p \\cong 3$ instead of\n$p\\cong 2.2-2.4$). Why should the value of $p$ be different for shocks\npropagating into winds? With the jet interpretation one can explain all\nafterglows with a single value of $p$, as in \\cite{SPH99}. (II) The\njets interpretation makes the luminosity distribution of GRBs more narrow,\nsince evidence for jets are found in bright events.\nClearly, these are circumstantial evidence. A more clear cut between these\ntwo possible interpretations can be done with the use of early afterglow\nobservation, preferably at radio frequencies (see \\cite{FKS+99}).\n\n\nIn summary, there are several kind of afterglows:\n\n\\noindent\n{\\bf Shallow decline} $\\sim t^{-1.2}$ for as long as the afterglow\ncan be observed. These are probably spherical or at least have a large \nopening angle (e.g. GRB~970508).\n\n\\noindent\n{\\bf Fast decline} $\\sim t^{-2.1}$ (e.g. GRB~980519 and GRB~980326). \nThese are either narrow jets, in which the break was very early or \nthey have high values of $p$ and propagate into decreasing density medium.\n\n\\noindent\n{\\bf Breaks}: Initially slow decline that changes into a fast decline. These\nare the best candidates for jets (e.g. GRB~990510).\n\n\n\\section{Polarization - A promising tool}\n\nAn exciting possibility to further constrain the models and obtain a\nmore direct proof of the geometrical picture of ``jets'' is to measure\nlinear polarization. High levels of linear polarization are usually\nthe smoking gun of synchrotron radiation. The direction of the\npolarization is perpendicular to the magnetic field and can be as high\nas $70\\%$. Gruzinov \\& Waxman and Medvedev \\& Loeb \\cite{GW99,ML99}\nconsidered the emission from spherical ejecta which by symmetry should\nproduce no polarization on the average, except for fluctuations of\norder of a few percent. Polarization is more natural if the ejecta is\na ``jet'' and the line of sight from the observer is with in the jet\nbut does not coincide with its axis. In this case, the spherical\nsymmetry is broken \\cite{G99,GL99,S99}, and the natural polarization\nproduced by synchrotron radiation should not vanish. For simplicity,\nlets assume that the magnetic field behind the shock is directed along\nthe shock's plane (the results hold more generally, unless the\nmagnetic field has no preferred direction). The synchrotron\npolarization from each part of the shock front, which is perpendicular\nto the magnetic field, is therefore directed radially.\n\nAs long as the relativistic beaming angle $1/\\gamma$ is narrower\nthan the physical size of the jet $\\theta_0$, one is able to see a\nfull ring and therefore the radial polarization averages to zero \n(the first frame, with $\\gamma\\theta_0=4$ of the left plot in \nfigure \\ref{polfig}). As\nthe flow decelerates, the relativistic beaming $1/\\gamma$ becomes\ncomparable to $\\theta_0$ and only a part of the ring is visible; net\npolarization is then observed. Note that due to the radial direction\nof the polarization from each fluid element, the total polarization is\nmaximal when a quarter ($\\gamma\\theta_0=2$ in figure \\ref{polfig}) \nor when three quarters ($\\gamma\\theta_0=1$ in figure \\ref{polfig}) \nof the ring are missing (or radiate less efficiently) \nand vanishes for a full and for half ring. The\npolarization when more than half of the ring is missing is\nperpendicular to the polarization direction when less than half of it\nis missing.\n\n\\begin{figure*}\n\\centerline{\\epsfig{file=polevol.eps,width=2.8in}\\ \\ \\epsfig{file=pollight.eps,width=2.8in}}\n\\vspace{10pt}\n\\caption{Left: Shape of the emitting region.\nDash line marks the physical extent\nof the jet while solid lines give the viewable region $1/\\gamma$.\nThe observed radiation is coming from the gray region.\nOn each frame, the percentage of \npolarization is given on the top right and the initial size of the jet\nrelative to $1/\\gamma$ is given on the left.\nThe frames are scaled so that the size of the jet is unity.\nRight: observed and theoretical polarization lightcurve for three possible\noffsets of the observer relative to the jet axis\nObservational data for GRB~990510 is marked by x, assuming $t_{jet}=1.2$\\,d.\nThe upper limit for GRB~990123 is given by a triangle, assuming\n$t_{jet}=2.1$\\,d.}\n\\label{polfig}\n\\end{figure*}\n\nAt late stages the jet expands and since the offset of the observer\nfrom the physical center of the jet is constant, spherical symmetry is\nregained. The vanishing and re-occurrence of significant parts of the\nring results in a unique prediction: there should be three peaks of\npolarization, with the polarization position angle during the central\npeak rotated by $90^{\\circ }$ with respect to the other two peaks. In\ncase the observer is very close to the center, more than half of\nthe ring is always observed, and therefore only a single direction of\npolarization is expected. A few possible polarization light curve are\npresented in figure \\ref{polfig}.\n\n\\section{Summary}\nNow when redshifts for GRBs are routinely measured, the largest\nuncertainty in their energy budget and event rate is the possibility\nthat the emission is not spherical but jet-like. We discussed the\ntheory of afterglow from jet-like event. These should produce a\nsubstantial break at all frequencies. The time where this break occurs\nis an indication of the jets opening angle. GRB~990510 seems to be a\nperfect example for this behavior. The inferred opening angle is\nabout $0.1$ consistent with upper limits from searches of orphan X-ray\nafterglows \\cite{GHV+99}. Several other candidate for jets are bursts\nwith fast decline, where the break presumably took place before the\nearliest observation. This question will be settled when more frequent\nearly observations are available. We have shown that afterglow from\njets should show a unique signature of polarization, at detectable\nlevels. Observing such signature will confirm the jet interpretation\nand the synchrotron model in general.\n\n{\\bf Acknowledgements} I thank Titus Galama for very useful comments, and \nthe Sherman Fairchild foundation for support.\n\n\\begin{references}\n\n%\\bibitem{KSO73} Klebesadel, R. W.; Strong, I. B. \\& Olson, Roy A. 1973, ApJ, 182, 85\n\n%\\bibitem{P+99} Paciesas, W. S. et al. 1999, ApJS, 122, 465\n\n%\\bibitem{B93} Band, D. et al., 1993, ApJ, 413, 281\n\n\n%\\bibitem{MR93} M\\'esz\\'aros, P., \\& Rees, M. J. 1993, ApJ, 405, 278\n\n%\\bibitem{NPP92} Narayan, R., Paczy\\'nski, B. \\& Piran, T. 1992, ApJ, 395, 83\n\n%\\bibitem{RM94} Rees M. J. \\& M\\'esz\\'aros P. 1994, ApJ, 430, L93\n\n\\bibitem{MW99} MacFadyen, A. I., Woosley, S. E. 1999, ApJ, 526, 152.\n\n%\\bibitem{ELPS89} Eichler, D., Livio, M., Piran, T., Schramm, D. N. 1989, Nature, 340, 126.\n\n\\bibitem{SP97} Sari, R., \\& Piran T. 1997, ApJ, 485, 270\n\n\\bibitem{FMN96} Fenimore, E. E., Madras, C., \\& Nayakshine, S. 1996, ApJ, 473, 998\n\n\\bibitem{P99} Piran, T. 1999, in the proceedings of the \nGr\\\"aft{\\aa}vallen workshop `Gamma Ray Bursts: \nThe First Three Minutes', Ed. Juri Poutanen.\n\n%\\bibitem{RF99} Ramirez-Ruiz, E., \\& Fenimore, E. E. 1999, A\\&A, 138, 521\n\n%\\bibitem{KPS97} Kobayashi, S., Piran, T., \\& Sari, R. 1997, ApJ, 490, 92\n\n%\\bibitem{B+94} Barthelmy, S.D., et al. 1994, in ``Proceeding of the Second\n%Huntsville Workshop\"; eds. G.Fishman, J.Brainerd, K.Hurley; 307; 643\n\n%\\bibitem{PR93} Paczy\\'nski, B. \\& Rhoads, J. 1993, ApJ, 418, L5\n\n%\\bibitem{K94} Katz, J. I., 1994, ApJ, 422, 248\n\n%\\bibitem{V97} Vietri, M. 1997, ApJ, 478, L9\n\n%\\bibitem{MR97} M\\'esz\\'aros, P., \\& Rees M. J. 1997, ApJ, 476, 232\n\n\\bibitem{SPN98} Sari, R., Piran, T. \\& Narayan, R. 1998, 497, L17 \n\n\\bibitem{G+98} Galama, T. J. et al. 1998, ApJ, 500, 101\n\n\\bibitem{R99} Rhoads, J. E. 1999, ApJ, 525, 737\n\n\\bibitem{PM99} Panaitescu, A. \\& M\\'esz\\'aros, P., 1999, ApJ, 503, 314\n\n\\bibitem{MR99} M\\'esz\\'aros, P., \\& Rees M. J. 1999, MNRAS, 299, L10\n\n\\bibitem{MSB99} Moderski, R., Sikora, M., Bulik, T. 1999, astro-ph/9904310\n\n\\bibitem{FWK99} Frail, D. A., Waxman, E. \\& Kulkarni, S. R. 1999, astro-ph/9910319\n\n\\bibitem{K+99a} Kulkarni, S. R., et al. 1999, Nature, 398, 389\n\n\\bibitem{F+99} Fruchter, A. S., et al., 1999, ApJ, 519, L13\n\n\\bibitem{A99} Akerlof, C. et al., 1999, Nature. 398, 400\n\n\\bibitem{K+99b} Kulkarni, S. R., et al. 1999, ApJ, 522, L97\n\n\\bibitem{SP99c} Sari, R., \\& Piran T. 1999c, ApJ, 517, L109\n\n\\bibitem{S+99} Stanek, K. Z., Garnavich, P. M., Kaluzny, J.,\n Pych, W. \\& Thompson, I. 1999, ApJ, 522, L39\n\n\\bibitem{H+99} Harrison F. A., et al. 1999, ApJ, 1999, 523, L121\n\n\\bibitem{SPH99} Sari, R., Piran, T., \\& Halpern, J. 1999, ApJ, 519, L17\n\n\\bibitem{G+99} Galama, T. J. et al. 1999, Nature, 398, 394.\n\n\\bibitem{CL99} Chevalier, R. A. \\& Li, Z. Y., 2000, ApJ in press, \nastro-ph/9908272\n\n%\\bibitem{SP99a} Sari, R., \\& Piran T. 1999a, A\\&AS, 138, 537\n\n%\\bibitem{SP99b} Sari, R., \\& Piran T. 1999b, ApJ, 520, 641\n\n%\\bibitem{SP95} Sari, R., \\& Piran T. 1995, ApJ, 455, L143\n\n%\\bibitem{MR99} M\\'esz\\'aros, P., \\& Rees M. J. 1999, MNRAS, 306, L39\n\n\\bibitem{FKS+99} Frail, D. A. et al. 1999, astro-ph/9910060\n\n\\bibitem{GW99} Gruzinov A., \\& Waxman E., 1999, ApJ, 511, 852\n\n\\bibitem{ML99} Medvedev, M. V., \\& Loeb A., 1999, astro-ph/9904363\n\n\\bibitem{G99} Gruzinov A. 1999, ApJ, 525, L29\n\n\\bibitem{GL99} Ghisellini, G., \\& Lazzati, D., 1999, MNRAS, 309, L7\n\n\\bibitem{S99} Sari, R. 1999, ApJ, 524, L43\n\n\\bibitem{GHV+99} Greiner et al., these proceedings.\n\n\\end{references}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002165.extracted_bib",
"string": "\\bibitem{KSO73} Klebesadel, R. W.; Strong, I. B. \\& Olson, Roy A. 1973, ApJ, 182, 85\n\n%\n\\bibitem{P+99} Paciesas, W. S. et al. 1999, ApJS, 122, 465\n\n%\n\\bibitem{B93} Band, D. et al., 1993, ApJ, 413, 281\n\n\n%\n\\bibitem{MR93} M\\'esz\\'aros, P., \\& Rees, M. J. 1993, ApJ, 405, 278\n\n%\n\\bibitem{NPP92} Narayan, R., Paczy\\'nski, B. \\& Piran, T. 1992, ApJ, 395, 83\n\n%\n\\bibitem{RM94} Rees M. J. \\& M\\'esz\\'aros P. 1994, ApJ, 430, L93\n\n\n\\bibitem{MW99} MacFadyen, A. I., Woosley, S. E. 1999, ApJ, 526, 152.\n\n%\n\\bibitem{ELPS89} Eichler, D., Livio, M., Piran, T., Schramm, D. N. 1989, Nature, 340, 126.\n\n\n\\bibitem{SP97} Sari, R., \\& Piran T. 1997, ApJ, 485, 270\n\n\n\\bibitem{FMN96} Fenimore, E. E., Madras, C., \\& Nayakshine, S. 1996, ApJ, 473, 998\n\n\n\\bibitem{P99} Piran, T. 1999, in the proceedings of the \nGr\\\"aft{\\aa}vallen workshop `Gamma Ray Bursts: \nThe First Three Minutes', Ed. Juri Poutanen.\n\n%\n\\bibitem{RF99} Ramirez-Ruiz, E., \\& Fenimore, E. E. 1999, A\\&A, 138, 521\n\n%\n\\bibitem{KPS97} Kobayashi, S., Piran, T., \\& Sari, R. 1997, ApJ, 490, 92\n\n%\n\\bibitem{B+94} Barthelmy, S.D., et al. 1994, in ``Proceeding of the Second\n%Huntsville Workshop\"; eds. G.Fishman, J.Brainerd, K.Hurley; 307; 643\n\n%\n\\bibitem{PR93} Paczy\\'nski, B. \\& Rhoads, J. 1993, ApJ, 418, L5\n\n%\n\\bibitem{K94} Katz, J. I., 1994, ApJ, 422, 248\n\n%\n\\bibitem{V97} Vietri, M. 1997, ApJ, 478, L9\n\n%\n\\bibitem{MR97} M\\'esz\\'aros, P., \\& Rees M. J. 1997, ApJ, 476, 232\n\n\n\\bibitem{SPN98} Sari, R., Piran, T. \\& Narayan, R. 1998, 497, L17 \n\n\n\\bibitem{G+98} Galama, T. J. et al. 1998, ApJ, 500, 101\n\n\n\\bibitem{R99} Rhoads, J. E. 1999, ApJ, 525, 737\n\n\n\\bibitem{PM99} Panaitescu, A. \\& M\\'esz\\'aros, P., 1999, ApJ, 503, 314\n\n\n\\bibitem{MR99} M\\'esz\\'aros, P., \\& Rees M. J. 1999, MNRAS, 299, L10\n\n\n\\bibitem{MSB99} Moderski, R., Sikora, M., Bulik, T. 1999, astro-ph/9904310\n\n\n\\bibitem{FWK99} Frail, D. A., Waxman, E. \\& Kulkarni, S. R. 1999, astro-ph/9910319\n\n\n\\bibitem{K+99a} Kulkarni, S. R., et al. 1999, Nature, 398, 389\n\n\n\\bibitem{F+99} Fruchter, A. S., et al., 1999, ApJ, 519, L13\n\n\n\\bibitem{A99} Akerlof, C. et al., 1999, Nature. 398, 400\n\n\n\\bibitem{K+99b} Kulkarni, S. R., et al. 1999, ApJ, 522, L97\n\n\n\\bibitem{SP99c} Sari, R., \\& Piran T. 1999c, ApJ, 517, L109\n\n\n\\bibitem{S+99} Stanek, K. Z., Garnavich, P. M., Kaluzny, J.,\n Pych, W. \\& Thompson, I. 1999, ApJ, 522, L39\n\n\n\\bibitem{H+99} Harrison F. A., et al. 1999, ApJ, 1999, 523, L121\n\n\n\\bibitem{SPH99} Sari, R., Piran, T., \\& Halpern, J. 1999, ApJ, 519, L17\n\n\n\\bibitem{G+99} Galama, T. J. et al. 1999, Nature, 398, 394.\n\n\n\\bibitem{CL99} Chevalier, R. A. \\& Li, Z. Y., 2000, ApJ in press, \nastro-ph/9908272\n\n%\n\\bibitem{SP99a} Sari, R., \\& Piran T. 1999a, A\\&AS, 138, 537\n\n%\n\\bibitem{SP99b} Sari, R., \\& Piran T. 1999b, ApJ, 520, 641\n\n%\n\\bibitem{SP95} Sari, R., \\& Piran T. 1995, ApJ, 455, L143\n\n%\n\\bibitem{MR99} M\\'esz\\'aros, P., \\& Rees M. J. 1999, MNRAS, 306, L39\n\n\n\\bibitem{FKS+99} Frail, D. A. et al. 1999, astro-ph/9910060\n\n\n\\bibitem{GW99} Gruzinov A., \\& Waxman E., 1999, ApJ, 511, 852\n\n\n\\bibitem{ML99} Medvedev, M. V., \\& Loeb A., 1999, astro-ph/9904363\n\n\n\\bibitem{G99} Gruzinov A. 1999, ApJ, 525, L29\n\n\n\\bibitem{GL99} Ghisellini, G., \\& Lazzati, D., 1999, MNRAS, 309, L7\n\n\n\\bibitem{S99} Sari, R. 1999, ApJ, 524, L43\n\n\n\\bibitem{GHV+99} Greiner et al., these proceedings.\n\n"
}
] |
astro-ph0002166
|
A spatially resolved plerionic X-ray nebula around \psr
|
[
{
"author": "E. V. Gotthelf$^1$ and Q. Daniel Wang$^2$"
}
] |
We present a high resolution \Chandra\ X-ray observation of \psr, the Crab-like 50 msec pulsar in the Large Magellanic Cloud. We use phase-resolved imaging to decompose the extended X-ray emission, as expected of a synchrotron nebula, from the point-like emission of the pulsar. The image of the pulsed X-ray emission shows a well-defined point-spread function of the observation, while the resolved nebula has a morphology and size remarkably similar to the Crab nebula, including evidence for a jet-like feature from \psr. The patchy outer shell, which most likely represents the expanding blast-wave of the supernova, is reminiscent of that seen in radio. Based on morphology, size, and energetics there can be little doubt that \snr\ is an analogous system to the Crab but located in our neighboring galaxy.
|
[
{
"name": "psr0540_paper1_000309.tex",
"string": "\\documentstyle[emulateapj,psfig]{article}\n%\\documentstyle[11pt,aaspp,tighten]{article}\n%\\documentstyle[12pt,aasms4,psfig]{article}\n%\\documentstyle[11pt,~/aas/aaspp4,tighten]{article}\n\n\\def\\rosat{{\\sl ROSAT}}\n\\def\\asca{{\\sl ASCA}}\n\\def\\chandra{{\\sl Chandra}}\n\\def\\Chandra{{\\sl Chandra}}\n\\def\\ha{H$\\alpha$}\n\\newcommand\\psr{\\hbox{PSR~B0540$-$69}}\n\\newcommand\\snr{\\hbox{SNR~B0540$-$69}}\n\\newcommand{\\as}{$^{\\prime\\prime}~$}\n\\newcommand{\\am}{$^{\\prime}~$}\n\n%\\received{7 January 2000}\n%\\accepted{23 September 1988}\n%\\journalid{337}{15 January 1989}\n%\\articleid{11}{14}\n\\slugcomment{To appear in the Astrophysics Journal Letters}\n\n\\lefthead{Gotthelf \\& Wang}\n\\righthead{X-ray nebula around \\psr}\n\n\\begin{document}\n\n\\title{A spatially resolved plerionic X-ray nebula around \\psr}\n\n\\author{E. V. Gotthelf$^1$ and Q. Daniel Wang$^2$}\n\\altaffiltext{1}{Columbia Astrophysics Laboratory, Columbia University, 550 \nWest 120$^{th}$ Street, New York, NY 10027, USA; evg@astro.columbia.edu}\n\\altaffiltext{2}{Astronomy Department, University of Massachusetts, B-524 \nLGRT, Amherst, MA 01003, USA; wqd@astro.umass.edu}\n\n\\begin{abstract}\n\n We present a high resolution \\Chandra\\ X-ray observation of\n\\psr, the Crab-like 50 msec pulsar in the Large Magellanic Cloud. We\nuse phase-resolved imaging to decompose the extended X-ray emission,\nas expected of a synchrotron nebula, from the point-like emission of\nthe pulsar. The image of the pulsed X-ray emission shows a\nwell-defined point-spread function of the observation, while the\nresolved nebula has a morphology and size remarkably similar to the\nCrab nebula, including evidence for a jet-like feature from \\psr. The\npatchy outer shell, which most likely represents the expanding\nblast-wave of the supernova, is reminiscent of that seen in\nradio. Based on morphology, size, and energetics there can be little\ndoubt that \\snr\\ is an analogous system to the Crab but located in our\nneighboring galaxy.\n\n\\end{abstract}\n\\keywords{pulsars: general --- pulsars: individual (\\psr) --- X-rays:\ngeneral --- supernova remnant --- stars: neutron}\n\n\\section {Introduction}\n\n\nThe X-ray-bright 50 ms pulsar \\psr\\ was discovered in the N158A nebula\nof the Large Magellanic Cloud (LMC) and has long been compared to the\nCrab pulsar (Seward, Harnden, \\& Helfand 1984). Based on its timing\nand spectral properties, the two rotation powered pulsars are very\nsimilar with a spin period of 50 vs. 33 ms and a spin-down rate of\n$4.8 \\times 10^{-13}$ vs. $4.0 \\times 10^{-13}$ s/s for \\psr\\ and the\nCrab, respectively. From these quantities, assuming the standard\nmagnetic dipole pulsar model, one can infer a characteristic age (1.7\nvs. 1.2 kyr), spin-down energy ($2.0 \\times 10^{38}$ vs. $6.5 \\times\n10^{38}$ ergs s$^{-1}$), and surface magnetic field strength ($5.0\n\\times 10^{12}$ vs. $3.8 \\times 10^{12}$ G) for \\psr\\ and the\nCrab, respectively. This similarity suggests that \\psr\\ could be\naccompanied by a ``plerion'', a pulsar driven wind nebula (Weiler \\&\\\nSramek 1988), reminiscent of that seen for the Crab.\n\nIndeed, there are several lines of evidence indicating the presence of\na plerion in the vicinity of \\psr. Chanan, Helfand, \\& Reynolds (1984)\ndetected a polarized optical nebula of half-power diameter $\\sim\n4^{\\prime\\prime}$ around the pulsar. This apparent synchrotron nebula\nwas also resolved (though barely) in a radio image presented by\nManchester et al. (1993) and in a \\rosat\\ high resolution imager\nobservation by Seward \\& Harnden (1994). Furthermore, the overall\nX-ray spectrum of \\psr\\ and its remnant (\\snr) is well characterized by a\npower law, as expected if the emission is predominantly non-thermal\n(Clark et al. 1982; Wang \\& Gotthelf 1998a).\n\nThe \\rosat\\ observation also revealed a faint X-ray emitting shell,\n$\\sim 15$~pc in size surrounding the pulsar. This shell contributes\nless than $ 20\\%$ to the total luminosity of $\\sim 1.0 \\times 10^{37}\n{\\rm~ergs~s^{-1}}$ in the \\rosat\\ 0.1-2~keV band and is likely the SNR\nassociated with the pulsar (Seward \\& Harden 1994). However, no\nevidence has yet been found for a similar X-ray-emitting shell or a\nshell-like SNR around the Crab (e.g. see discussion in Jones et\nal. 1998).\n\nIn this Letter, we report new results on \\snr\\ based on a recent\nobservation acquired with the \\Chandra\\ High Resolution Camera. This\nobservation enables us for the first time to distinguish morphological\ndetails of the nebula around \\psr. We analyze phase dependent images\nand resolve the expected plerion-like nebula from the point-like\npulsar emission. This allows us to identify features similar to those\nseen from the Crab nebula; we present morphological evidence for a\ntorus of X-ray emission, which most likely represents shocked pulsar wind \nmaterials and a likely X-ray jet emanating from the pulsar. We discuss the\nimplications of the results in the context of the pulsar-nebula\nsystem. Throughout the paper we adopt a distance of $51$~kpc for the\nLMC.\n\n\\section {Observation}\n\nThe \\Chandra\\ observatory (Weisskopf et al. 1996) observed \\snr\\ on\nAug 31 1999 as part of the initial calibration of the High Resolution\nCamera (HRC; Murray et al. 1997). A total of 19.4 ksec of data were\ncollected during a portion of the orbit which avoided regions of high\nbackground contamination such as from bright Earth and radiation belt\npassages. The remnant was centered on the on-axis position of the HRC\nwhere the point-spread function (PSF) has a half power radius (the\nradius enclosing 50\\% of total source counts) of $\\sim 0\\farcs5$.\n%over the face of the pulsar's extended X-ray nebula. \nTime-tagged photons were acquired with 15.6 $\\mu$s precision, and the\narrival times were corrected to the solar system barycenter using a beta\nversion of {\\tt AXBARY} available from the \\Chandra\\ X-ray Center FTP\nsite (A. Rots 1999, private communication). While the detector is sensitive\nto X-rays over a $0.1-10.0$ keV range, there is essentially no energy\ninformation available. We analyzed event data calibrated by the\ninitial processing and dated 1999 September 12, which was made\navailable through the \\Chandra\\ public archive. In addition to the\nstandard processing, the event data was further filtered to reduce the\ninstrumental background and to remove ``ghost image'' artifacts using a\nbeta version of {HRC\\_SCREEN} (S. Murray 2000, private\ncommunication). We extracted $1024 \\times 1024$ pixel images centered\non the pulsar rebinned by a factor of two from the native HRC pixel\nsize of 0\\farcs13175 per side.\n\n\\section {Results}\n\nA global view of N158A and its environment as seen by the \\Chandra\\\nHRC is shown in Figure~$1$ (contours) and Figure~$2$ (greyscale). The\nlarge-scale X-ray enhancement on scales up to $\\sim 1^\\prime$ is the\npreviously resolved shell-like emission (Seward \\& Harnden 1994). In\nfact, the X-ray and radio emission together outlines a nearly circular\nmorphology around \\psr. Clearly, the shell represents the blastwave of\n\\snr. The X-ray intensity distribution within the remnant appears\nrather patchy. While the southwest X-ray enhancement is a good tracer\nof the radio and optical emission peaks, there is no general\ncorrelation between fainter radio and X-ray features.\n\nThe superb spatial resolution of the \\Chandra\\ observation further\nallows for a close-up of the immediate vicinity of \\psr\\ (Fig.~$2b$).\nThe presence of a diffuse plerion-like nebula around the pulsar is\napparent. To decompose the nebula emission from the pulsar\ncontribution, we conducted phase-resolved image analysis. This enables\nus to estimate the local PSF based on the pulsed, point-like emission\nfrom the pulsar and to quantify the extended, unpulsed nebula\nradiation.\n\nFirst, we must determine the pulse period at the current epoch. We\nconstructed a periodigram around a narrow range of periods centered on\nthe expected period $\\pm 0.1$ ms, sampled in increments of $0.05(P^2/T)$,\nwere $T$ is the observation duration, and $P$ is the test\nperiod. For each trial period, we folded photons extracted from a\n1\\farcs0 aperture centered on the bootstrapped pulsar position (see\nbelow) into 20 phase bins and computed the $\\chi^2$ of the resultant\nprofile. We find a highly significant signal ($> 56 \\sigma$) at $P =\n50.508132(6)$ ms at Epoch 51421.630741 MJD; the uncertainty is\nestimated according to the method of Leahy (1987). We have assumed a\nperiod derivative of $\\dot P = 4.789342 \\times 10^{-13}$ for the data\nepoch (Deeter et al. 1999). In Figure~$3$ we display the resultant\nlight-curve folded at the peak period which, as expected, is roughly\nsinusoidal and modulated with a $\\sim 40\\%$ pulse fraction (defined as\nthe amplitude divided by the mean).\n\nNext, we defined two regions in the phase space, on- and off-pulse, by\nselecting eight adjacent phase bins corresponding to the peak and\ntrough of the pulse profile. The on-pulse image with the off-pulse\nimage subtracted is presented in Figure~$4b$. This image\nreproduced the expected PSF with no evidence of asymmetric deviations,\nas might be caused by poor aspect reconstruction, like that typically\nfound for \\rosat\\ images. Figure~$5$ presents average radial intensity\ndistributions around the centroid of the point-like source.\n\nBy subtracting the normalized pulsar image (Fig.~$4b$), we are able to\nconstruct an image of the nebula emission (Fig.~$4c$) alone. The\nsubtracted image is scaled to compensated for both the relative phase\ncoverage and for a 21\\% unpulsed emission contribution, estimated by\nminimize a pointlike contribution at the pulsar position of the nebula\nimage. As shown in Figure~$4c$, the extended emission is distinctly\ndifferent from the pointlike image of the pulsed emission from the\npulsar. The primarily feature is the NE-SW elongated feature, which is\nmorphologically symmetric relative to the pulsar and extends about\n$\\sim 2\\farcs5$ on both sides of the pulsar. However, the observed\nemission on the SW side appears twice as strong compared to the NE\nside, with an average intensity of $\\sim 7.5 \\times 10^{-2}\n{\\rm~counts~s^{-1}~arcsec^{-2}}$. Because the central core of the\ndistribution is significantly brighter than the extended features and\nthe subtraction of the pulsar contribution is somewhat arbitrary, the\nexact intensity distribution is uncertain.\n\nThere is also marginal evidence for a jet-like feature emanating from\nthe pulsar. This emission, most apparent in the NW and extending about\n$3^{\\prime\\prime}$, is nearly perpendicular to the NE-SW elongated\nnebula and is slightly bent toward North. The integrated emission of\nthe jet-like feature is roughly $\\sim 3.1 \\times 10^{-2}\n{\\rm~counts~s^{-1}}$. The configuration of the jet feature relative to\nthe nebula is remarkably similar to that of the Crab nebula as seen by\nROSAT and which is now clearly resolved with Chandra (see Chandra\npublicity photo).\n\nIn short, the X-ray emission can be decomposed into three major\nmorphological components: a point-like source, the surrounding nebula\nwhich shows evidence for a jet feature, and a patchy supernova remnant\nshell.\n\n\\begin{deluxetable}{lcc}\n\\tablewidth{0pt}\n\\tablecaption{HRC Spatial Components of \\snr\n\\label{tbl-1}}\n\\tablehead{\n\\colhead{Component$^a$} & \\colhead{Count Rate$^b$} & \\colhead{Size and Shape}\n}\n\\startdata\nPulsar$^c$ & & \\nl\n\\quad pulsed & 0.14 & point-like \\nl\n\\quad unpulsed & 0.18 & '' \\nl\nNebula & 0.8 & $5^{\\prime\\prime} \\times 3^{\\prime\\prime}$ NE-SW \\nl\nJet & 0.03 & $3^{\\prime\\prime}$ long SE-NW \\nl\nSNR Shell & 0.2 & $\\sim 1^{\\prime}$ diameter\\nl\n\\enddata\n\\tablenotetext{a}{See \\S 3; $^b$Count/s; $^c$X-ray emission\nfrom a $2^{\\prime\\prime}$ radius aperture around the pulsar.}\n\\end{deluxetable}\n\n\\section {Discussions}\n\n\tA comparison between the X-ray-emitting nebula around \\psr\\\nand the Crab nebula (see Chandra publicity photo\\footnote{Available at\n\\hbox{\\tt http://xrtpub.harvard.edu/photo/0052/0052\\_hand.html}}) is\nvery informative. The Crab nebula image shows a torus of\nX-ray-emitting loops, which most likely represents shocked pulsar wind\nmaterials consisting of magnetic waves and ultra-relativistic\nparticles. Also clear are the two jets of X-ray-emitting material\nemanating from the Crab pulsar, in the direction perpendicular to the\nmajor axis of the torus. We speculate that the nebula around \\psr\\ has\na similar structure. In fact, at the spatial resolution of Chandra at\nthe LMC, the size, morphology, and surface intensity of the two\nnebulae are all remarkably similar (Fig. $2b$).\n\n\tAssuming a power law spectrum for the X-ray emission from the\n\\snr\\ nebula of photon index 2.0 and N$_H = 4 \\times 10^{21}\n\\rm{cm}^2$ (Finley et al. 1993, Wang \\& Gotthelf 1998a), the\nconversion between the count rate and the energy flux in the standard\n1.0-10~keV band is $\\sim 1 \\times 10^{-10} {\\rm~ergs~s^{-1}~cm^{-2}\n/counts~s^{-1}}$. The corresponding total luminosity of the nebula is\n$\\sim 2.7 \\times 10^{37} {\\rm~ergs~s^{-1}}$, which is 13\\% of the\nspin-down energy of \\psr. The fraction is again similar to that\nof the Crab.\n\t\n\tN157B (PSR J0537$-$6910) is the only other LMC SNR with a\ndetected pulsar (16~ms) and also shows both an extended (resolved by\n\\rosat\\ HRI), non-thermal nebula and a partial X-ray-emitting shell\n(Wang \\& Gotthelf 1998a; 1998b). \n%This shell has a luminosity of $\\sim x \\times 10^{35} {\\rm~ergs~s^{-1}}$, \n%comparable to that of N158A's shell of $\\sim x \\times 10^{35} {\\rm~ergs~s^{-1}}$.\nThe upcoming \\chandra\\ observations\nwill make a detailed comparison between these two young Crab-like \nSNRs possible. \n\n\\acknowledgements\n\nWe gratefully acknowledge the Chandra team for making available the\npublic data used herein. In particular we thank A. Rots and S. Murray\nfor kindly making available their beta software. We thank U. Hwang for\npointing out an instrumental artifact (``ghost image'') in the original\nHRC image of SNR B0540-69. We thank Dick Manchester for sending us the\nradio image and Fernando Camilo, David Helfand, and Jules Halpern for\ncarefully reading the manuscript. This work was funded in part by\nNASA LTSA grants NAG5-7935 (E.V.G.) and NAG5-6413 (Q.D.W.). This is\ncontribution \\#690 of the Columbia Astrophysics Laboratory.\n\n\\begin{references} \n\\reference{} Caraveo, P., Mignani, R., \\& Bignami, G. B. 1998, in Memorie \ndella Societa Astronomia Italiana, Vol. 69, p.1061\n\\reference{} Chanan, G. A., Helfand, D. J., \\& Reynolds, S. P. 1984 ApJ, 287, \nL23\n\\reference{} Clark, D. H., Tuohy, I. R., Dopita, M. A., Mathewson, D. S., \nLong, K. S., Szymkowiak, A. E., Culhane, J. L. 1982, ApJ, 255, 440\n\\reference{} Deeter, J. E., Nagase, F., Boynton, P. E. 1999, ApJ, 512, 300\n\\reference{} Finley, J. P., Oegelman, H., Hasinger, G., Truemper, J. 1993 ApJ, \n410, 323\n\\reference{} Jones, T. W. et al. 1998, PASP, 110, 125\n\\reference{} Leahy, D. A., 1987, A\\&A, 180, 275\n\\reference{} Manchester, R. N., Staveley-Smith, \\& Kesteven, M. J. 1993, ApJ, \n411, 756\n\\reference{} Murray, S. S., et al., 1997, SPIE, 3114, 11\n\\reference{} Seward, F., D., Harnden, Jr., F. R., \\& Helfand, D. J. 1984 ApJ, \n287, L19\n\\reference{} Seward, F. D., \\& Harnden, Jr., F. R. 1994, ApJ, 421, 581\n\\reference{} Wang, Q. D. \\& Gotthelf, E. V. 1998a, ApJ, 494, 623.\n\\reference{} Wang, Q. D. \\& Gotthelf, E. V. 1998b, ApJL, 509, 109\n\\reference{} Weisskopf, M. C. O'Dell, S. L., van Speybroeck, L. P. 1996, Proc. \nSPIE 2805, Multilayer and Gazing Incidence X-ray/EUV Optics III, 2.\n\\reference{} Weiler, K. W. \\&\\ Sramek, R. A. 1988, ARAA, 25, 295\n\n\\end{references}\n\n\\begin{figure} \n\\centerline{ {\\hfil\\hfil\n\\psfig{figure=psr0540_paper1_fig1_lanl.ps,height=3.0in,angle=90, clip=}\n\\hfil\\hfil} }\n\\caption{The overall X-ray and radio view of the region of SNR~0540-69\ncontaining the central 50 ms pulsar \\psr. The contours denote the\nChandra HRC X-ray intensity distribution; the levels are\n0.001, 0.005, 0.008, 0.013, 0.03, 0.1, 0.3, 1., 3, 10, and 30 counts s$^{-1}$\narcsec$^{-2}$. The greyscale map shows the 6 cm radio emission which\ntraces the approximately circular remnant. The radio map is from\nManchester et al. (1993) and has a beam size with half power width of\n$\\sim 5\"$.\n\\label{fig1}}\n\\end{figure}\n\n\\begin{figure} \n\\centerline{ {\\hfil\\hfil\n\\psfig{figure=psr0540_paper1_fig2_lanl.ps,height=3.0in,angle=270,clip=} \n\\hfil\\hfil} }\n\\caption{X-ray intensity distribution around the region containing the\n50 ms pulsar \\psr. Left Panel) the Chandra HRC broad energy-band image\ncentered on the pulsar. The image has been adaptively smoothed using\na minimum signal-to-noise of 6 ratio and the intensity scale chosen to\nhighlight the diffuse SNR emission surrounding the bright pulsar\nnebula, which is fully saturated in this image. The central box\ndelineates the region enlarged and displayed in the right panel. Right\nPanel) Close up image around the pulsar, displayed scaled by the\nsquare root of intensity. Insert) Crab nebula image, placed at the\ndistance of the LMC (assuming a distance to the Crab of 2 kpc) and\nblurred to the HRC resolution. Notice the similar size, shape, and\noverall brightness morphology compared to \\psr.\n\\label{fig2}}\n\\end{figure}\n\n\\begin{figure} \n\\centerline{ {\\hfil\\hfil\n\\psfig{figure=psr0540_paper1_fig3.ps,height=2.5in,angle=270,clip=}\n\\hfil\\hfil} }\n\\caption{HRC light curve ($0.4 - 10$ keV) for \\psr\\ folded at the\nephemeris given in the text. Two periods are shown for clarity. The two sets \nof vertical\nbars denote the two phase regions (on/off) used to isolate the nebula from the\npulsar emission. The light curve has been extracted from a $1^{\\prime\\prime}$\nradius aperture centered on the pulsar.\n\\label{fig3}}\n\\end{figure}\n\n\\bigskip\\bigskip\n\n\\begin{figure} \n\\centerline{ {\\hfil\\hfil\n\\psfig{figure=psr0540_paper1_fig4_lanl.ps,height=2.0in,angle=270, clip=}\n\\hfil\\hfil} }\n\\caption{Phase-subtracted X-ray intensity maps of \\psr. Left Panel)\nBefore phase-subtraction, image of the pulsar and nebula (all photons),\nsame as the right panel of figure 2. Middle Panel) the pulsar image\ncontaining the pulsed photons only. This is in excellent\nrepresentation of the HRC point-spread function, consistent with the\nground calibration. Right Panel) same region after subtracting the\npulsar's contribution to the total flux (see text for details) -- this\nprovides a good estimate of the nebula emission surrounding the\npulsar. The cross marks the pulsar's centroid. The three maps are\nidentically sized and linearly scaled in intensity.\n\\label{fig4}}\n\\end{figure}\n\n\\begin{figure} \n\\centerline{ {\\hfil\\hfil\n\\psfig{figure=psr0540_paper1_fig5.ps,height=2.5in,angle=270, clip=}\n\\hfil\\hfil} }\n\\caption{HRC radial intensity distributions around the point-like\nemission peak of \\psr. The pulsar radial profile (solid line) is\nconsistent with the HRC point-spread function. The nebula profile\n(dotted line) is significantly extended, the enhancement between\n$0.1-1.5^{\\prime\\prime}$ is due to the relatively bright SW nebula\nregion.\n\\label{fig5}}\n\\end{figure}\n\n\\end{document}\n\n\n\n"
}
] |
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astro-ph0002167
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A Study of the Populations of X-ray Sources in the Small Magellanic Cloud with ASCA
|
[
{
"author": "Jun~Yokogawa\\altaffilmark{1}"
},
{
"author": "Kensuke~Imanishi"
},
{
"author": "Masahiro~Tsujimoto"
},
{
"author": "Mamiko~Nishiuchi\\altaffilmark{1}"
},
{
"author": "and Katsuji~Koyama\\altaffilmark{2}"
}
] |
The Advanced Satellite for Cosmology and Astrophysics (ASCA) has made multiple observations of the Small Magellanic Cloud (SMC). X-ray mosaic images in the soft (0.7--2.0~keV) and hard (2.0--7.0~keV) bands are separately constructed, and the latter provides the first hard X-ray view of the SMC. We extract 39 sources from the two-band images with a criterion of $S/N>5$, and conduct timing and spectral analyses for all of these sources. Coherent pulsations are detected from 12 X-ray sources; five of which are new discoveries. Most of the 12 X-ray pulsars are found to exhibit long-term flux variabilities, hence they are likely to be X-ray binary pulsars (XBPs). On the other hand, we classify four supernova remnants (SNRs) as thermal SNRs, because their spectra exhibit emission lines from highly ionized atoms. We find that XBPs and thermal SNRs in the SMC can be clearly separated by their hardness ratio (the ratio of the count rate between the hard and soft bands). Using this empirical grouping, we find many XBP candidates in the SMC, although no pulsations have yet been detected from these sources. Possible implications on the star-formation history and evolution of the SMC are presented by a comparison of the source populations in the SMC and our Galaxy.
|
[
{
"name": "ms.tex",
"string": "%\\documentstyle[12pt,aasms4]{article}\n\\documentstyle[aas2pp4,psbox]{article}\n\\setlength{\\topmargin}{-2cm}\n\\setlength{\\textheight}{26cm}\n\n\n\\newcommand{\\ulumi}{~erg~s$^{-1}$}\n\\newcommand{\\uflux}{~erg~s$^{-1}$~cm$^{-2}$}\n\n\n\\slugcomment{Submitted to ApJ Suppl.}\n\\lefthead{J. Yokogawa et al.}\n\\righthead{Populations of the X-ray Sources in the SMC}\n\n\\begin{document}\n\\title{A Study of the Populations of X-ray Sources \nin the Small Magellanic Cloud with ASCA}\n\n\\author{Jun~Yokogawa\\altaffilmark{1}, Kensuke~Imanishi, \nMasahiro~Tsujimoto, Mamiko~Nishiuchi\\altaffilmark{1},\nand Katsuji~Koyama\\altaffilmark{2}}\n\\affil{Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan;\njun@cr.scphys.kyoto-u.ac.jp,\nkensuke@cr.scphys.kyoto-u.ac.jp, tsujimot@cr.scphys.kyoto-u.ac.jp,\nmamiko@cr.scphys.kyoto-u.ac.jp, koyama@cr.scphys.kyoto-u.ac.jp}\n\n\n\\author{Fumiaki~Nagase}\n\\affil{Institute of Space and Astronautical Science, Yoshinodai, Sagamihara, Kanagawa 229-8510, Japan; nagase@astro.isas.ac.jp}\n\n\\and\n\n\\author{Robin~H.~D.~Corbet}\n\\affil{Code 662, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, U.S.A.; Universities Space Research Association;\ncorbet@bastet.gsfc.nasa.gov}\n\n\\altaffiltext{1}{Research Fellow of the Japan Society for the Promotion of Science (JSPS)}\n\\altaffiltext{2}{CREST, Japan Science and Technology Corporation (JST), 4-1-8 Honmachi, Kawaguchi, Saitama, 332-0012, Japan}\n\n\n\\begin{abstract}\nThe Advanced Satellite for Cosmology and Astrophysics (ASCA) has made\nmultiple observations of the Small Magellanic Cloud (SMC).\n X-ray mosaic images in the soft (0.7--2.0~keV) and hard (2.0--7.0~keV)\nbands are separately constructed, and the latter provides the first\nhard X-ray view of the SMC.\n We extract 39 sources from the two-band images with a criterion of $S/N>5$,\nand conduct\ntiming and spectral analyses for all of these sources.\nCoherent pulsations are detected from 12 X-ray sources;\nfive of which are new discoveries.\nMost of the 12 X-ray pulsars\nare found to exhibit long-term flux variabilities,\nhence they are likely to be X-ray binary pulsars (XBPs).\nOn the other hand,\nwe classify\nfour supernova remnants (SNRs) as thermal SNRs,\nbecause their spectra exhibit emission lines\nfrom highly ionized atoms.\n We find that XBPs and thermal SNRs in the SMC\ncan be clearly separated by their hardness ratio\n(the ratio of the count rate between the hard and soft bands).\nUsing this empirical grouping, we find many XBP candidates\nin the SMC, although no pulsations have yet been\ndetected from these sources.\n Possible implications on the star-formation history and\nevolution of the SMC are presented by a\ncomparison of the source populations in the SMC and our Galaxy.\n\\end{abstract}\n\n\\keywords{galaxies: evolution --- galaxies: individual (SMC, LMC)\n--- galaxies: starburst --- pulsars: general --- X-rays: stars}\n\n\\section{Introduction}\n Bright X-ray sources such as supernova remnants (SNRs) and binaries\nwith a neutron star (NS) or a black hole component are `relics' of\nmassive stars and hence carry key information on the\nstar formation history, dynamics, and structure of their host galaxy.\n However, our knowledge of the populations of bright X-ray sources in our Galaxy\nis highly incomplete due to the Galactic absorption in\nthe low energy band,\nlarge angular size that must be observed,\nand limited information on the distance of the relevant\nobjects.\n\n\n The Small Magellanic Cloud (SMC), a satellite of\nour Galaxy, is the next nearest neighbor after the Large Magellanic Cloud (LMC).\nThe proximity\n(60~kpc is assumed in this paper; Mathewson 1985\\markcite{Mathewson1985a}),\nreasonable angular size\n($\\sim 3^\\circ \\times 3^\\circ$),\nand low interstellar absorption to the SMC are all favorable for an unbiased\nsurvey of the X-ray source populations in the entire galaxy.\nSurveys of soft X-ray sources (below $\\sim 2$~keV)\nhave been carried out with the Einstein and ROSAT satellites.\nThe most complete source catalogs are\npresented in Wang \\& Wu (1992, hereafter WW92\\markcite{Wang1992})\nand Kahabka et al. (1999, hereafter K99\\markcite{Kahabka1999}).\nK99 classified the sources detected by the ROSAT PSPC\n(Position Sensitive Proportional Counter),\nbased on two different hardness\nratios, together with spatial information.\nCowley et al. (1997)\\markcite{Cowley1997} and \nSchmidtke et al. (1999)\\markcite{Schmidtke1999}\nmade numerous observations of the SMC with the ROSAT HRI\n(High Resolution Imager),\nand determined accurate positions of X-ray sources.\nOptical observations made at CTIO\n(Cerro Tololo Interamerican Observatory) showed\nthat five of these X-ray sources have a massive star companion and\nhence are high mass X-ray binaries (HMXBs).\n\n\n Bright X-ray sources can be classified by their spectral and temporal\ncharacteristics. X-rays from young SNRs are either due to a shock\nheated plasma (in shell-like SNRs) which preferentially emits soft\n(below $\\sim 2$~keV) line-dominated X-rays, or due to the release\nof rotational energy from isolated NSs (X-ray pulsars associated with\nCrab-like SNRs) with hard and featureless spectra.\nUnlike SNRs, the other classes of X-ray sources emit time-variable\nX-rays. NSs with a low mass companion star (low mass X-ray binaries:\nLMXBs) have hard spectra and often exhibit X-ray bursts. Black hole\nbinaries (BHs) have bimodal behavior and show both\nhigh-soft and low-hard spectral\nstates.\nNSs with a high mass stellar companion\n(HMXBs) have even harder X-ray spectra\nand often exhibit long-term flux variations\nof a factor $\\gtrsim 10$--100.\nMany HMXBs also show coherent pulsations (X-ray binary pulsars; XBPs).\n Consequently,\nmost bright X-ray sources emit\ncopious hard X-rays (above $\\sim 2$ keV).\nHowever, due mainly to a lack of imaging capability\nin the hard X-ray band,\nno systematic survey of the populations of hard X-ray sources\nhad previously been made.\nThe Advanced Satellite for Cosmology and Astrophysics\n(ASCA; Tanaka, Inoue, \\& Holt 1993\\markcite{Tanaka1993})\nis equipped with wide-band X-ray imaging instruments and\nhence is optimized for an X-ray population study.\n\n In this paper, we report the results\nfrom multiple observations on the SMC with ASCA.\nThe observation fields and the method of data reduction are\npresented in \\S\\ref{sec:obs}.\nIn \\S\\ref{sec:result},\nwe extract X-ray sources detected above the 5-$\\sigma$ level\nfrom the observation fields,\nperform temporal and spectral analyses on all the sources,\nand categorize them into thermal SNRs and XBPs.\n\\S\\ref{sec:comments} gives details of\nindividual X-ray pulsars and SNRs.\nIn \\S\\ref{sec:dis}, we propose a simple and reliable\nsource classification method.\nWe clearly distinguish between thermal SNRs and XBPs\nwith this method, then\ndiscuss these X-ray source populations in the SMC.\nFinally, we summarize this study in \\S\\ref{sec:conc}.\n\n\n\\section{Observations and Data Reduction \\label{sec:obs}}\n ASCA\nhad observed the SMC 10 times by the end of 1998 and\nwe have used the data from eight of these observations which are\neither in the public archive or came from our own proposed observations.\nObservation dates, pointing directions and other relevant information\nare listed in\nTable \\ref{tab:obs}.\nMost of the optically bright portion and the Eastern Wing of\nthe SMC\nhas been covered.\nIn each observation, X-ray photons were collected with\nfour XRTs (X-Ray Telescopes) and detected separately with\nthe two GISs (Gas Imaging Spectrometers) and\nthe two SISs (Solid-state Imaging Spectrometers).\nDetails of these instruments are presented separately\nin Serlemitsos et al. (1995)\\markcite{Serlemitsos1995},\nOhashi et al. (1996)\\markcite{Ohashi1996}, \nand Burke et al. (1994)\\markcite{Burke1994}.\n\n\\placetable{tab:obs}\n\n\n\nWe first screened the X-ray data from both the GIS and SIS\nwith the normal criteria:\ni.e. we rejected the data obtained in the SAA (South Atlantic Anomaly),\nthose with a cut-off rigidity lower than\n4~GV,\nand those with an elevation angle lower than $5^\\circ$.\nWe then rejected the particle events in the GIS with a rise-time\ndiscrimination technique, and the SIS data obtained when the elevation\nangle from the bright earth was lower than $25^\\circ$.\n The effects of RDD (Residual Dark Distribution) in the SIS data\nwere corrected if the observation was carried out later than 1996\nwith the method given in\nDotani et al. (1997)\\markcite{Dotani1997}.\nAfter the screening, the\ntotal available exposure time of two GISs was $\\sim570$~ks.\n\n\nThe GIS is more suitable than the SIS for X-ray population studies,\nbecause of\nits larger field of view, larger effective area at high energy,\nand better time resolution.\nThis paper thus mainly utilizes the GIS data,\nexcept for particular objects which require\nhigh energy resolution and soft X-ray sensitivity.\n\n\n Photon events for individual X-ray sources were extracted from a circle of $3^\\prime$ radius,\nin which $\\sim 90$\\% of incident photons are contained\n(Serlemitsos et al. 1995\\markcite{Serlemitsos1995}),\nor an ellipse for sources located significantly off-axis\nbecause of the distortion of the point spread function of the ASCA XRTs.\nBackground data\nwere taken from a nearby off-source area for each source.\n In some source-crowded areas, we selected a smaller circle\nwith a radius $\\sim 1\\farcm5$--$2^\\prime$ to minimize\ncross talk from nearby sources.\n\n\n\\section{Analyses and Results \\label{sec:result}}\n\\subsection{X-ray Images \\label{subsec:image}}\nFigure \\ref{fig:smc} shows the\nmosaic X-ray images in the soft (0.7--2.0~keV)\nand hard (2.0--7.0~keV) bands constructed from the multiple observations\nand\nthe telescope vignetting,\nnon X-ray background and exposure differences have\nbeen corrected.\n Of the two observations centered on SMC X-1,\nonly one (observation C),\nwhen SMC X-1 was much dimmer,\nwas used.\nThe ASCA soft band image of the SMC is different from\nthose obtained with Einstein and ROSAT (WW92; K99),\nindicating that many discrete sources in the SMC\nare highly variable.\nThe hard band image is the first such image obtained\nfor the SMC\nand it is found to have significant differences from the soft band image.\n\n\n\\placefigure{fig:smc}\n\n\n\n\\subsection{Source Catalog \\label{subsec:cat}}\n\nX-ray sources were identified from the soft/hard band images\nfrom each observation,\nwith the criterion that the $S/N$ ratio should exceed 5-$\\sigma$\nin at least one of the two-band images.\nConsequently 39 sources were found and are listed\nin Table \\ref{tab:smccat}.\nThe separation angle $\\sim 2^\\prime$ between sources No.\\,4\nand No.\\,5\nis comparable to the half power radius of the XRT,\nhence we estimated the $S/N$ ratio in a circle\ncontaining both of them and found it exceed 5-$\\sigma$.\n Since No.\\,4 appeared to be prominent in the soft band\nwhile No.\\,5 was strong in the hard band, we are confident\nthat there really exist two separate soft (No.\\,4) and hard (No.\\,5) sources.\nThe $S/N$ ratio of No.\\,34 exceeds 5-$\\sigma$ in the hard band,\nwhile in the soft band it suffers severe contamination from No.\\,30.\n\n\n\n\nWe derived hardness ratios (HRs) for all the sources\nexcept for No.\\,4, No.\\,5, and No.\\,34,\nand cataloged them in Table \\ref{tab:smccat}.\nThe HR is defined as ${\\rm HR} = (H-S)/(H+S)$,\nwhere $H$ and $S$ are the background subtracted GIS count rates\nin the 2.0--7.0~keV and 0.7--2.0~keV bands respectively.\n\n\\placetable{tab:smccat}\n\\notetoeditor{Please place the first half of Table \\ref{tab:smccat} \non an even page and the second half on the next odd page, \nso that Table \\ref{tab:smccat} covers the two facing pages. } \n\n\n\\subsection{Timing Analysis \\label{sec:timing}}\n\n We performed an FFT (Fast Fourier Transform) analysis\non all the sources to search for coherent pulsations.\nWe used only high-bit rate data in order to utilize\nthe maximum time resolution (up to 62.5~ms)\nfor those sources with high count rates.\nOtherwise\nwe used high-bit and medium-bit data simultaneously\nto achieve better statistics\nat the sacrifice of the time resolution reduced to 0.5~s. \nWe detected coherent pulsations from 11 sources,\nfive of which are new discoveries from this study.\nWe show a power spectrum obtained from SMC X-1 (No.\\,38; in \nobservation A) in Figure \\ref{fig:psd} (a) as an example of \nunambiguous detection. \nOnly AX J0105$-$722 showed rather weak sign of pulsations \nas shown in Figure \\ref{fig:psd} (b). \n\n\\placefigure{fig:psd}\n\n\n\nFor the 11 sources from which pulsations were detected in the FFT analysis,\nwe performed an epoch folding search to determine\nmore precise pulse periods.\nIn addition,\nthe orbital Doppler effect was corrected for\nSMC X-1, using the ephemeris presented in Wojdowski et al. (1998)\\markcite{Wojdowski1998}.\nThese derived pulse periods are presented in Table \\ref{tab:pcat}.\n\n\\placetable{tab:pcat}\n\n\nWe found no coherent period in the FFT power spectra\nfrom three sources positionally coincident with known pulsars: \nXTE J0055$-$724 (No.\\,16), SMC X-1 (No.\\,38; in observation C),\nand RX J0052.1$-$7319 (No.\\,14).\nNevertheless, we tried the epoch folding search\\footnote{Since\nSMC X-1 was in the 0.6-day eclipse phase during observation C,\nwe only used the data from non-eclipse times. }. \nA weak peak was detected from source No.\\,16 \nnear the known period $\\sim 59$~s as shown in Figure \\ref{fig:efs}, \nwhich indicates that No.\\,16 is a counterpart of XTE J0055$-$724. \nThis period is, however, not referred in Table \\ref{tab:pcat}, \nsimply because this source was relatively dim, \nand any reliable period was not obtained.\n\n\n\n\\placefigure{fig:efs}\n\n\n We also searched for burst-like activity\nby using light curves binned with various time scales\nfrom $\\sim$1~second to $\\sim$1~hour.\nHowever, no bursts were found.\n\n\n\n\\subsection{Spectral Analysis \\label{sec:spec}}\n X-rays were detected from eight radio SNRs:\n0102$-$723 (No.\\,30), 0103$-$726 (No.\\,31), N19 (No.\\,1), N66 (No.\\,24),\nDEM S128\n(No.\\,32\\footnote{No.\\,32=DEM S128 (radio SNR)=AX J0105$-$722 (X-ray pulsar).}),\n0056$-$725 (No.\\,21), 0049$-$736 (No.\\,12), and\n0047$-$735 (No.\\,4\\footnote{Excluded from the spectral analysis\nbecause of contamination (see \\S\\ref{subsec:image}).}).\nBefore fitting the overall spectra,\nwe distinguished thermal SNRs from others.\nDirect evidence for a thermal spectrum is the presence of\nemission lines from highly ionized atoms.\nThe brightest SNR 0102$-$723 is already known to exhibit thermal X-ray\nemission\n(e.g. Hayashi et al. 1994\\markcite{Hayashi1994}), hence we examined whether or not\nthe spectra of the remaining SNRs show any emission lines.\n In order to obtain better energy resolution,\nwe extracted the SIS spectra of 0103$-$726, N19, and N66.\nThe other SNRs DEM S128, 0056$-$725, and 0049$-$736 were out of the SIS\nfields.\nSince the latter two were too faint for spectral fitting,\nwe only used the GIS spectrum of DEM S128.\n We fitted the spectra in a narrow energy band\n($\\sim 1.1$--3~keV)\nwith a bremsstrahlung continuum and three narrow Gaussian lines centered\nat 1.34~keV, 1.85~keV, and 2.46~keV\n(K$_\\alpha$ lines from He-like Mg, Si, and S), and we\nfound evidence of emission lines from three SNRs\n(0103$-$726, N19, and N66).\nWe thus regarded them as thermal SNRs,\nand fitted their SIS spectra with\nthin-thermal plasma models as described in \\S\\ref{subsec:snrs}.\nFor the other SNRs,\nwe adopted both a power-law model and\na thin-thermal plasma model (Raymond \\& Smith 1977\\markcite{Raymond1977}),\nwith interstellar absorption.\nSince their GIS spectra\\footnote{Only the GIS2 spectrum was used for 0049$-$736,\nbecause this SNR was detected in the proximity of the GIS3\ncalibration source.}\nhad poor photon statistics,\nwe fixed the global abundance to be\n0.2~solar,\ni.e. that of the interstellar matter in the SMC\n(Russell \\& Dopita 1992\\markcite{Russell1992}),\nwhen the thermal plasma model was applied.\nWe hereafter refer to this abundance value as ``the SMC abundance.''\n\n\n As summarized in Table \\ref{tab:pcat}, we detected 13 X-ray pulsars.\nIn addition, No.\\,22 and No.\\,13 are\npositionally coincident with\nRX J0058.2$-$7231 and RX J0051.9$-$7311,\nboth are HMXBs with a Be star companion\n(Cowley et al. 1997\\markcite{Cowley1997}; \nSchmidtke et al. 1999\\markcite{Schmidtke1999}).\nX-ray spectra of these classes are generally described by\nan absorbed power-law below $\\sim 10$~keV (e.g. Nagase 1989\\markcite{Nagase1989}) and\nhence we used this model for spectral fitting.\nSpectra of the other (unclassified) sources had poor statistics,\nhence it was not clear whether they are thermal or not.\nNevertheless, we also adopted the power-law model for them.\nWe used only GIS2 spectra of\nAX J0051$-$733 (No.\\,8),\nRX J0059.2$-$7138 (No.\\,25),\nSMC X-1 (in observation H),\nand RX J0051.9$-$7311,\nbecause RX J0059.2$-$7138\nwas detected only on the edge of GIS2 and\nthe other three were detected near the GIS3 calibration source.\nOn the other hand,\nonly the GIS3 spectrum of\nAX J0049$-$729 (No.\\,3; in observation G)\nwas used because\nit was detected near the calibration source of GIS2.\nIn other cases we added the spectra of GIS2 and GIS3 to obtain better statistics.\n\n The simple power-law model showed a soft excess for three sources:\nRX J0059.2$-$7138, XTE J0111.2$-$7317 (No.\\,37)\nand SMC X-1 (in each observation).\nIncluding blackbody emission as a soft component gave a better fit.\nSpectral parameters,\nfluxes and absorption-corrected luminosities in Table \\ref{tab:smccat}\nare derived from this two-component model for these sources.\n\n\n Model fitting for the spectra of the SNR 0047$-$735 (No.\\,4),\nthe X-ray pulsar AX J0049$-$732 (No.\\,5),\nand No.\\,34 was not performed because these are heavily contaminated\nby nearby sources (see \\S\\ref{subsec:cat}).\nSources No.\\,27, No.\\,28, and 1SAX J0103.2$-$7209 (No.\\,29)\nhave been observed more than once, and the\nspectral parameters were derived separately.\nSince the parameters are consistent between observations\nfor all three sources, we performed combined fitting\nfor the spectra of different observations.\nHowever,\nAX J0049$-$729 and\nSMC X-1, which have also been observed more than once,\nshowed large flux variability and different spectral parameters.\n The SNR 0102$-$723 (No.\\,30) has been detected twice in the GIS field\n(in observation B and D), but only once in the SIS field (B).\nSince this source is a line-dominated young SNR, we only used the SIS spectrum\nfor the spectral analysis (see \\S\\ref{subsec:snrs}).\n\n\n The derived spectral parameters: photon index $\\Gamma$ or temperature $kT$,\nand column density $N_{\\rm H}$, flux $F_{\\rm x}$,\nand absorption-corrected luminosity $L_{\\rm x}$\nare presented in Table \\ref{tab:smccat}.\n\n\n\\section{Comments on Specific Sources \\label{sec:comments}}\n\n\\subsection{SNRs \\label{subsec:snrs}}\n\nFigure \\ref{fig:specsnrs} gives the spectra of SNRs\nwith the best-fit model described below.\nThe relevant parameters are presented in Table\n\\ref{tab:smccat} and \\ref{tab:spec0103}.\n\n\\paragraph{No.\\,30: 0102$-$723}\n\nA detailed analysis of the SIS spectrum\nof this SNR was carried out by Hayashi et al. (1994)\\markcite{Hayashi1994}.\nWe adopted their model and determined\nits flux and absorption-corrected luminosity\nas in Table \\ref{tab:smccat}.\n\n\\paragraph{No.\\,31: 0103$-$726}\n\nWe first adopted an absorbed thin-thermal plasma model\n(Raymond \\& Smith 1977\\markcite{Raymond1977}), in which\nthe condition of collisional ionization equilibrium (CIE)\nis assumed.\nThe abundances of O, Ne, Mg, Si, and S were treated as free parameters,\nwhile those of the other elements were fixed to the SMC abundance.\nThe best-fit parameters and\nthe model spectrum are given in\nTable \\ref{tab:spec0103} and Figure \\ref{fig:specsnrs} (a), respectively.\nAlthough the CIE model could reproduce the line profile fairly well,\nit was statistically rejected with 99\\% confidence.\n\nWe then included the effects of non-equilibrium ionization (NEI)\nin the plasma model (Masai 1994\\markcite{Masai1994}).\nAn additional parameter is the ionization timescale\n$\\tau = nt $, where $n$ is the electron density and $t$\nis the elapsed time after the plasma has been heated.\nNote that the plasma is in the CIE condition when\n$\\tau$ is larger than $\\sim 10^{12}$~s~cm$^{-3}$.\nThe best-fit parameters and\nthe model spectrum are given in\nTable \\ref{tab:spec0103} and Figure \\ref{fig:specsnrs} (b), respectively.\nThis model was also statistically rejected with 99\\% confidence.\nThe larger $\\chi^2$ is due to the difference between\nthe CIE/NEI plasma codes.\nThe best-fit value of the ionization timescale\nindicates that the plasma of 0103$-$726 is in the NEI condition.\nHowever, the confidence contours shown in Figure \\ref{fig:0103contour} \nsuggest that we can not distinguish\nbetween a high temperature NEI plasma\nand a low temperature CIE plasma model.\n\n\n\\placetable{tab:spec0103}\n\n\n\n\\paragraph{No.\\,1: N19}\n\nWe adopted an absorbed thin-thermal CIE plasma model.\nWe set the abundances of Ne and Mg to be free,\nwhile those of the other elements were fixed to the SMC abundance.\nBest-fit values of the abundances are\n0.7 (0.3--1.8) for Ne and 1.0 (0.3--1.8) for Mg\n(hereafter, 90\\% confidence limits are given in parentheses,\nunless otherwise mentioned).\n\n\n\\paragraph{No.\\,24: N66}\n\nAn absorbed thin-thermal CIE plasma model,\nwhere the SMC abundance was assumed for all elements,\ncould well reproduce the SIS spectrum.\n\n\n\\paragraph{No.\\,12: 0049$-$736}\n\nAlthough both a thermal CIE model and\na power-law model could well describe the spectrum,\nwe adopted the thermal one\nbecause the derived temperature ($\\sim 0.7$~keV)\nis reasonable for an SNR.\nThis implies that 0049$-$736 may be a thermal SNR.\n\n\\paragraph{No.\\,21: 0056$-$725}\nSince a thermal CIE model yielded\nan unusually high temperature of $\\sim 20$ ($>4$)~keV,\nwe adopted a power-law model.\nIt may be implied that\nthe spectrum of 0056$-$725 really has a non-thermal origin.\n\n\n\\paragraph{No.\\,32: DEM S128}\nA thermal CIE model gave\na temperature of 3.2 (2.2--5.0)~keV,\nwhich may be reasonable if this SNR is very young.\nHowever, generally\nsuch a young SNR exhibits prominent emission lines\nwhich originate from shock-heated ejecta.\nThe fact that no emission line was identified\nprefers the power-law model,\nwhich is adopted in Figure \\ref{fig:specsnrs} (g) and Table \\ref{tab:smccat}.\nTherefore a non-thermal spectrum for DEM S128 is implied.\nIn addition, we have\ndetected evidence for coherent pulsations\nfrom this source (= AX J0105$-$722)\nas described in \\S\\ref{sec:timing}.\nThe nature of DEM S128 is discussed in \\S\\ref{subsec:dems128}.\n\n\n\\placefigure{fig:specsnrs}\n\\placefigure{fig:0103contour}\n\n\n\n\\subsection{X-ray Pulsars \\label{sec:pul}}\n\n In this subsection, pulse periods are presented with\nerrors\nof the last digits\nin parentheses. The spectra and energy-resolved pulse shapes\nare separately\npresented in Figures \\ref{fig:pulspec} and \\ref{fig:pullc}, respectively.\nWe suggest that 14 of the 16 pulsars in the SMC\nare X-ray binary pulsars (XBPs),\nbecause of their flux variability and,\nin some cases, existence of an optical counterpart.\n\n\n\\paragraph{No.\\,3: AX J0049$-$729}\nCoherent pulsations with a 74.8(4)~s period\nwere first detected with RXTE (Corbet et al. 1997a\\markcite{Corbet1997a})\nin the direction of SMC X-3.\nHowever, the positional uncertainty was very large ($\\sim 2^\\circ$).\nDuring this analysis,\nwe found that No.\\,3 (AX J0049$-$729) was pulsating with a 74.68(2)~s period\nand so determined its position\nmore accurately\n(Yokogawa \\& Koyama 1998a\\markcite{Yokogawa1998a}; \nYokogawa et al. 1999a\\markcite{Yokogawa1999a}).\nThe ROSAT counterpart of this pulsar, RX J0049.1$-$7250,\nprovides the most accurate position with a $\\pm 13''$ error circle\n(Kahabka \\& Pietsch 1998\\markcite{Kahabka1998}),\nin which one Be star has been discovered (Stevens et al. 1999\\markcite{Stevens1999}).\n\n\nThis pulsar has been included in 11 observation fields\nof Einstein, ROSAT, and ASCA.\nYokogawa et al. (1999a\\markcite{Yokogawa1999a})\nfound\na large flux variability by a factor $\\gtrsim 100$\nduring the 11 observations,\nthus we can conclude that\nAX J0049$-$729 is an XBP with a Be star companion.\n\n\n\n\\paragraph{No.\\,5: AX J0049$-$732}\nCoherent pulsations with a 9.1321(4)~s period\nfrom No.\\,5 (AX J0049$-$732) were first detected during this analysis\n(Imanishi, Yokogawa, \\& Koyama 1998\\markcite{Imanishi1998}),\nfrom the data in a circle with a 3$^\\prime$ radius\ncentered on AX J0049$-$732.\nHowever, as noted in \\S\\ref{subsec:cat},\nthe separation between AX J0049$-$732\nand source No.\\,4 (SNR 0047$-$735) is only $\\sim 2^\\prime$.\n Therefore, we also performed an FFT analysis on\nthe data in a circle with 3$^\\prime$ radius centered on the SNR,\nand detected no pulsations.\n Hence the pulsations can clearly be attributed\nto AX J0049$-$732.\n\n\n\nROSAT sources 1WGA J0049.4$-$7310\nand 1WGA J0049.1$-$7311 are in the error circle of AX J0049$-$732.\nWe took their ROSAT spectra from HEASARC archive system\nand fitted each of them with an absorbed power-law model.\nThe sum of their fluxes was determined to be\n$\\sim 4 \\times 10^{-14}$\\uflux\\ (0.3--2.0~keV).\nAs noted in \\S\\ref{subsec:cat},\nthe ASCA spectrum of AX J0049$-$732 was heavily contaminated\nby that of a soft source No.\\,4 (SNR 0047$-$735). \nHence an accurate estimation of its flux was difficult,\nespecially in the soft band.\nNevertheless,\nwe fitted the contaminated spectrum simply with\nan absorbed power-law model and\nthe flux was derived to be $\\sim 9 \\times 10^{-14}$\\uflux\\ (0.3--2.0~keV).\nFurther observations with\nbetter spatial resolution and photon statistics are needed\nto reveal the nature of AX J0049$-$732.\n\n\n\\paragraph{No.\\,8: AX J0051$-$733}\nCoherent pulsations with a 323.2(5)~s period\nfrom No.\\,8 (AX J0051$-$733) were first detected during this analysis\n(Yokogawa \\& Koyama 1998b\\markcite{Yokogawa1998b}).\nRX J0050.8$-$7316, the ROSAT HRI counterpart of AX J0051$-$733,\nhas a Be star in its error circle (Cowley et al. 1997\\markcite{Cowley1997}).\nIn addition, Imanishi et al. (1999)\\markcite{Imanishi1999}\ninvestigated all the \nobservation fields of Einstein and ROSAT that included AX J0051$-$733, and\nfound flux variations of a factor $\\gtrsim 10$.\nThese results indicate that\nAX J0051$-$733 is an XBP with a Be star companion.\n\n\n\n\n\n\\paragraph{No.\\,11: AX J0051$-$722}\nCoherent pulsations with a $\\sim92$~s period were first discovered\nwith an RXTE observation\non November 15, 1997 (Marshall et al. 1997\\markcite{Marshall1997}).\nA TOO (Target Of Opportunity) observation with ASCA on December 12 (observation G)\nrevealed that No.\\,11 was pulsating with 91.12(5)~s period\n(Corbet et al. 1997a\\markcite{Corbet1997a}).\nSince then,\nthis source has been detected in many RXTE/BeppoSAX/ASCA observations,\nand found to be fading and rebrightening\n(Lochner et al. 1998\\markcite{Lochner1998a};\nLochner 1998\\markcite{Lochner1998b}).\nTherefore it is certainly an XBP and\nthe orbital period is postulated to be 120~days\n(Israel et al. 1998\\markcite{Israel1998}).\n\n\nIn K99, RX J0051.3$-$7216 is identified as the ROSAT counterpart\nof AX J0051$-$722.\nHowever,\nit may be a misidentification\nbecause the separation between\nthe ROSAT position and ASCA position is $\\gtrsim 2^\\prime$,\nwhich is significantly larger than the positional uncertainty of ROSAT/ASCA.\n\n\n\n\n\\paragraph{No.\\,15: 1WGA J0053.8$-$7226}\nCorbet et al. (1997a)\\markcite{Corbet1997a} discovered\ncoherent pulsations with a period of 46.63(4)~s\nfrom No.\\,15 in observation G.\nA ROSAT variable source 1WGA J0053.8$-$7226\nand a Be star exist in its error circle\n(Buckley et al. 1997\\markcite{Buckley1997}),\nhence 1WGA J0053.8$-$7226 would be\nan XBP with a Be star companion.\n\n\n\\paragraph{No.\\,16: XTE J0055$-$724}\nAn RXTE observation on January 22, 1998 and\na BeppoSAX observation on January 28, 1998 revealed that\nXTE J0055$-$724=1SAX J0054.9$-$7226 was exhibiting\ncoherent pulsations with a 58.969(1)~s period\n(Marshall \\& Lochner 1998\\markcite{Marshall1998}; \nSantangelo et al. 1998\\markcite{Santangelo1998}).\nASCA source No.\\,16 was detected in the error circle\nin observation F.\nWe performed an epoch folding search and found a weak peak at $\\sim 59$~s \n(Figure \\ref{fig:efs}),\nhence No.\\,16 is the counterpart of XTE J0055$-$724.\n\n\n\nIsrael et al. (1999b)\\markcite{Israel1999b} investigated the ROSAT archival data,\nand found flux variability of a factor $> 30$.\nThey also determined the error circle with $10''$ accuracy\nwithin which a Be star was discovered by Stevens et al. (1999)\\markcite{Stevens1999}.\nXTE J0055$-$724 is thus an XBP with a Be star companion.\n\n\n\n\\paragraph{No.\\,20: AX J0058$-$7203}\nCoherent pulsations with a 280.4(4)~s period\nfrom No.\\,20 (AX J0058$-$7203) were first detected during this analysis\n(Yokogawa \\& Koyama 1998b\\markcite{Yokogawa1998b}).\nTsujimoto et al. (1999)\\markcite{Tsujimoto1999} investigated all \nthe Einstein and ROSAT \nobservation fields covering the position of AX J0058$-$7203.\nThey found flux variations with a factor $\\gtrsim 10$,\nwhich indicates that\nthis pulsar is an XBP.\n\n\n\n\\paragraph{No.\\,25: RX J0059.2$-$7138}\nThe transient source\nNo.\\,25 (RX J0059.2$-$7138) was serendipitously detected\nwith ROSAT and ASCA on the same day.\nCoherent pulsations with a 2.7632(2)~s period were detected from\nthe ROSAT data\n(Hughes 1994\\markcite{Hughes1994b}).\nWe detected the same period in the ASCA data and\nhence confirmed the ROSAT result.\nHughes (1994)\\markcite{Hughes1994b} proposed a possible optical counterpart\nin the error circle, which was later revealed to be a Be star\nby Southwell \\& Charles (1996)\\markcite{Southwell1996}.\nThese facts indicate that this source is a transient XBP with a\nBe star companion.\nA broad-band study of this source is presented by\nKohno, Yokogawa, \\& Koyama (2000)\\markcite{Kohno2000}, \nusing the ROSAT and ASCA data simultaneously.\n\n\n\n\\paragraph{No.\\,29: 1SAX J0103.2$-$7209}\nHughes \\& Smith (1994\\markcite{Hughes1994a}) and\nYe et al. (1995\\markcite{Ye1995})\nmade ROSAT HRI observations of\nthe shell-like radio SNR 0101$-$724.\nNo X-ray emission from the radio shell was found,\nwhile a point source\nRX J0103.2$-$7209\n(=1SAX J0103.2$-$7209)\nwas detected inside the SNR.\nIn addition, a Be star has been discovered in the error circle\nof RX J0103.2$-$7209.\n\n\nA BeppoSAX observation on July 27, 1998\ndiscovered coherent pulsations with a 345.2(1)~s period from 1SAX J0103.2$-$7209\n(Israel et al. 1998\\markcite{Israel1998}),\nhence this source could be classified as an XBP with a Be star companion.\nIts ASCA counterpart No.\\,29 (AX J0103$-$722) has been\nobserved three times,\nin observations B, D, and F.\nWe detected coherent pulsations with a 348.9(3)~s period\nin observation D,\nwhich had the best statistics\n(Yokogawa \\& Koyama 1998c\\markcite{Yokogawa1998c}).\nWe could not detect coherent pulsations from the data obtained\nin the other two observations, probably due to the limited statistics.\n\n\nThe ASCA flux was determined to be\n$\\sim 1.0 \\times 10^{-12}$\\uflux\\ (2--10~keV)\nin each observation.\nThis value is 3 times smaller than\nthe BeppoSAX flux\n($\\sim 3 \\times 10^{-12}$\\uflux; 2--10~keV).\nThis variability confirms the binary nature of the source.\n\n\n\n\n\\paragraph{No.\\,32: AX J0105$-$722 \\label{subsec:dems128}}\nThe separation between the two sources\nNo.\\,32=AX J0105$-$722 and No.\\,33 is\nonly $\\sim 3^\\prime$.\nUsing the data in an oval-shaped region\nwhich included both AX J0105$-$722 and No.\\,33\n(region 1 in Figure \\ref{fig:dems128reg}), we\ndetected coherent pulsations with a 3.34300~s period \nwith a marginal significance of $\\sim99.5$\\%\n(Yokogawa \\& Koyama 1998d\\markcite{Yokogawa1998d}; Figure \\ref{fig:psd} (b)).\n Then we separately searched for pulsations from the regions 2 and 3,\nshown in Figure \\ref{fig:dems128reg}.\nWe found weak evidence for the 3.34300~s period from region 2\n(which includes AX J0105$-$722),\nbut not from region 3,\nhence the pulsations are probably due to AX J0105$-$722.\n\n\n\\placefigure{fig:dems128reg}\n\n\n\nThe error circle of AX J0105$-$722 includes\na ROSAT source RX J0105.3$-$7210 and\nan Einstein source SMC53,\nboth of which were identified with a radio SNR DEM S128\n(Filipovi\\'{c} et al. 1998\\markcite{Filipovic1998};\nWW92\\markcite{Wang1992}).\nThe ASCA flux is\n$\\sim 2.9 \\times 10^{-13}$\\uflux\\ (0.3--2.4~keV) or\n$\\sim 3.3 \\times 10^{-13}$\\uflux\\ (0.3--3.5~keV).\nThese are comparable with fluxes of ROSAT or Einstein\n(the discrepancy is within a factor $\\sim 2$).\n\n\nThere are several possibilities for the nature of AX J0105$-$722.\nIts photon index ($\\sim 2.2$), relatively low luminosity\n($\\sim 10^{35}$\\ulumi\\ in 0.7--10.0~keV), and the association with an SNR\nare common with\nSNRs emitting synchrotron X-rays\n(e.g. SN1006 --- Koyama et al. 1995\\markcite{Koyama1995};\nRX J1713.7$-$3946 --- Koyama et al. 1997\\markcite{Koyama1997}),\nCrab-like SNRs, or\nSoft $\\gamma$-ray Repeaters\n(SGR1806$-$20 --- Kouveliotou et al. 1998\\markcite{Kouveliotou1998};\nSGR1900$+$14 --- Kouveliotou et al. 1999\\markcite{Kouveliotou1999}; \nMurakami et al. 1999\\markcite{Murakami1999}; \nHurley et al. 1999\\markcite{Hurley1999}).\nWhether AX J0105$-$722 is pulsating or not\nand, if it is pulsating, the pulse period and the period derivative\ncarry essential information\nthat would enable us to distinguish between\nthese possibilities.\nFurther observations with better photon statistics are needed.\n\n\n\n\\paragraph{No.\\,37: XTE J0111.2$-$7317}\nXTE J0111.2$-$7317 was serendipitously discovered with RXTE\nand CGRO (Compton Gamma-Ray Observatory),\nand coherent pulsations with a $\\sim 31$~s period were detected\n(Chakrabarty et al. 1998a\\markcite{Chakrabarty1998a};\nWilson et al. 1998\\markcite{Wilson1998}).\nSource No.\\,37 was detected in the ASCA TOO observation H\n(Chakrabarty et al. 1998b\\markcite{Chakrabarty1998b}).\nCoherent pulsations with a 30.9497(6)~s period were detected,\nhence No.\\,37 is certainly the counterpart of XTE J0111.2$-$7317.\n\n\nAs described in \\S\\ref{sec:spec},\nthis pulsar shows a soft X-ray excess above the simple power-law model.\nYokogawa et al. (1999b)\\markcite{Yokogawa1999b} conducted \na detailed phase-resolved spectroscopic study using both the GIS and SIS,\nand concluded that the soft excess is also pulsating with the same pulse\nphase and period.\n\n\n\n\n\\paragraph{No.\\,38: SMC X-1}\nSMC X-1 is a well known XBP, having a\nB-type supergiant as a companion\n(Bildsten et al. 1997\\markcite{Bildsten1997}).\nDuring observations A and H,\nrandom flux variations of a factor $\\sim 3$ were detected.\nIn observation C, it was in an eclipse as predicted by the ephemeris \n(Wojdowski et al. 1998\\markcite{Wojdowski1998}), \nalthough we found no clear pulsation of $\\sim 0.71$~s (pulse period of SMC X-1)\n\n\n\nSMC X-1 has been observed for a long time\nand its pulse period is monotonically decreasing\n(e.g. Nagase 1989\\markcite{Nagase1989};\nWojdowski et al. 1998\\markcite{Wojdowski1998};\nKahabka \\& Li 1999\\markcite{Kahabka1999b}),\nincluding the ASCA observation A.\nThe period in the observation H is first determined in this study,\nand is consistent with the monotonic decrease.\n\n\n\n\n\n\n\n\\paragraph{2E 0050.1$-$7247}\nCoherent pulsations with a 8.8816(2)~s period\nfrom 2E 0050.1$-$7247=RX J0051.8$-$7231 were discovered by\nIsrael et al. (1997\\markcite{Israel1997}).\nFlux variability of a factor 20 and\na Be star in the error circle were detected and\nhence this pulsar is an XBP with a Be star companion.\nAn ASCA observation (G)\ncovered the position of 2E 0050.1$-$7247.\nWe did not detect any positive excess above the background level\nfrom the position of this source.\nThe upper limit of its flux is estimated to be\n$\\sim 1 \\times 10^{-13}$\\uflux\\ (0.7--10.0~keV),\nassuming that the photon index is $\\sim 1$.\n\n\n\n\\paragraph{RX J0052.1$-$7319}\nCoherent pulsations with a 15.3~s period from RX J0052.1$-$7319\nwere discovered in ROSAT and CGRO observations in 1996\n(Lamb et al. 1999\\markcite{Lamb1999};\nKahabka 1999\\markcite{Kahabka1999a}).\nFlux variability is also reported, therefore\nRX J0052.1$-$7319 could be classified as an XBP.\n\nThe position of No.\\,14 coincides with that of RX J0052.1$-$7319.\nHowever, we detected no sign of coherent pulsations\nfrom either an FFT analysis or an epoch folding search.\nTherefore, it is not clear whether No.\\,14 is really\nthe counterpart of RX J0052.1$-$7319.\n\n\n\\paragraph{XTE J0054$-$720}\nCoherent pulsations were found from XTE J0054$-$720 with RXTE.\nIts pulse period and flux in the 2--10~keV band were\n169.30~s and $\\sim 6.0 \\times 10^{-11}$\\uflux\\\non December 17, 1997, and\n168.40~s and $\\sim 3.3 \\times 10^{-11}$\\uflux\\\non December 20, 1997,\nrespectively (Lochner et al. 1998\\markcite{Lochner1998a}).\nThe transient and fading behavior indicates that\nXTE J0054$-$720 is an XBP.\n\nA part of its error circle ($\\sim 10^\\prime$ radius) is\nincluded in the ASCA observations.\nOnly one source, No.\\,17, was detected in the error circle\nduring ASCA observation F,\nalthough coherent pulsations were not detected.\nThe flux of No.\\,17\n($\\sim 3.6 \\times 10^{-13}$\\uflux; 2--10~keV)\nis about 100 times smaller than that reported with RXTE.\nHowever, the ROSAT counterpart of No.\\,17, RX J0055.4$-$7210, is regarded as\na background source in Filipovi\\'{c} et al. (1998)\\markcite{Filipovic1998}.\n\nWe note that\nthe ROSAT source RX J0052.9$-$7158 is also in the error circle\nof XTE J0054$-$720\n(and out of our observation fields).\nIt was reported to have a large flux variability\nand a Be star companion (Cowley et al. 1997\\markcite{Cowley1997}),\nand hence may be the counterpart of XTE J0054$-$720.\n\n\n\n\n\n\\paragraph{RX J0117.6$-$7330}\nRX J0117.6$-$7330 was serendipitously discovered\nin a ROSAT PSPC observation on September 30--October 2, 1992\n(Clark, Remillard, \\& Woo 1996\\markcite{Clark1996}).\nThe luminosity was $2.3\\times10^{37}$\\ulumi\\\nbetween 0.2--2.5~keV at that time\n(Clark, Remillard, \\& Woo 1997\\markcite{Clark1997}),\nand was found to diminish by a factor of over 100 within one year.\nMacomb et al. (1999)\\markcite{Macomb1999}\ndiscovered coherent pulsations with a $\\sim 22.07$~s period\nfrom the same data,\nwith the aid of archival data obtained by BASTE onboard CGRO\nin the same epoch.\nStrong Balmer emission lines and IR excess were detected\nfrom the companion star in the error circle \n(Coe et al. 1998)\\markcite{Coe1998}, \nindicating that RX J0117.6$-$7330 is an XBP with a Be star companion.\n\nAlthough the position of RX J0117.6$-$7330 was covered in\nASCA observations A and C, no X-ray emission was detected.\nIt was difficult to estimate the upper limits of the flux\nbecause of the contamination from SMC~X-1\nlocated only $\\sim 5'$ away from RX J0117.6$-$7330.\n\n\n\\placefigure{fig:pulspec}\n\\placefigure{fig:pullc}\n\n\n\\section{Discussion \\label{sec:dis}}\n\n\\subsection{Classification by Hardness Ratio \\label{subsec:classification}}\n\n We have classified many of the SMC sources into\ntwo classes (XBPs and thermal SNRs), with the aid of\ntheir temporal/spectral properties and other information.\nSince the number of thermal SNRs is only four, \nmore samples of thermal SNRs are essential \nto make any statistical discussion with XBPs and thermal SNRs.\nX-ray sources in the LMC is suitable for the inclusion \nfor the reason described in the next subsection, \nthus we included \nXBPs and thermal SNRs in the LMC from all the available ASCA data\n(40 observations as of 1998).\nLMC X-4,\nEXO 053109$-$6609.2,\n1SAX J0544.1$-$710, and\nA0538$-$67\nhave been detected with ASCA,\nand are regarded as XBPs due to\ntheir long-term flux variability\nand optical counterparts \n(Bildsten et al. 1997\\markcite{Bildsten1997};\nBurderi et al. 1998\\markcite{Burderi1998};\nCusumano et al. 1998\\markcite{Cusumano1998};\nHaberl, Dennerl, \\& Pietsch 1995\\markcite{Haberl1995};\nCorbet et al. 1997b\\markcite{Corbet1997b}).\nAlthough we could not detect coherent pulsations from A0538$-$67,\nthis source is very likely to be an XBP\nwith a Be star companion (Corbet et al. 1997b\\markcite{Corbet1997b},\nand references therein).\nTen SNRs in the LMC,\nN103B, 0509$-$67.5, 0519$-$69.0,\nN23, N49, N63A, DEM71, N132D, 0453$-$68.5, and N49B,\nhave been found to exhibit emission lines from ionized atoms\n(Hughes et al. 1995\\markcite{Hughes1995};\nHayashi 1997\\markcite{Hayashi1997};\nHughes, Hayashi, \\& Koyama 1998\\markcite{Hughes1998}),\nhence are classified as thermal SNRs.\nIn addition, ASCA has observed the SNRs\nN44, N86, 0548$-$70.4, 0534$-$69.9, and 0543$-$68.9.\nWe analyzed their spectra to search for any emission lines\nas described in \\S\\ref{sec:spec},\nand consequently N44 and 0548$-$70.4 were classified as thermal SNRs.\nWe also included two other established classes:\nCrab-like SNRs\\footnote{In this section,\n``Crab-like SNR'' indicates a SNR associated with\na rotation-powered X-ray pulsar.}\n(0540$-$69 and N157B)\nand BHs (LMC X-1 and LMC X-3).\n\nWe derived HRs and fluxes of the four XBPs, 12 thermal SNRs,\ntwo Crab-like SNRs and two BHs in the LMC.\nTo estimate their fluxes,\nwe fitted the GIS spectra with simple models;\nan absorbed power-law model for\nXBPs, Crab-like SNRs, and BHs,\nwhile\nan absorbed thin-thermal CIE plasma model for thermal SNRs.\nIn the thermal plasma model,\nthe global abundance was fixed to that\nof the interstellar matter in the LMC,\n0.3~solar (Russell \\& Dopita 1992\\markcite{Russell1992};\nHayashi 1997\\markcite{Hayashi1997};\nHughes et al. 1998\\markcite{Hughes1998})\nfor simplicity.\nThe line profiles of some thermal SNRs\ncould not be reproduced by the simple thermal plasma model.\nHowever, the continuum shapes were well described and\nhence the derived fluxes are unlikely to have any large systematic error.\nTo estimate the error, we fitted the GIS spectra of\ntwo thermal SNRs in the SMC,\n0102$-$723 and 0103$-$726,\nwith the same simple model\nwhere the SMC abundance was assumed for all elements.\nThe best-fit models\nwell traced the continuum shapes,\nshowing the same discrepancy in the line profiles.\nDerived fluxes between 0.7--10.0~keV were\n$1.3 \\times 10^{-11}$\\uflux\\ (0102$-$723) and\n$1.1 \\times 10^{-12}$\\uflux\\ (0103$-$726),\nrespectively,\nwhile detailed analysis in \\S\\ref{subsec:snrs}\nyielded fluxes of\n$1.4 \\times 10^{-11}$\\uflux\\ (0102$-$723) and\n$1.1 \\times 10^{-12}$\\uflux\\ (0103$-$726),\nrespectively.\nTherefore the systematic flux error caused by the simple model\nis estimated to be $\\lesssim 10$\\%.\n\n\nIn Figure \\ref{fig:hr-lobs_smclmc_class_unid},\nHRs of the sources in these classes are plotted against the observed luminosity $L_{\\rm obs}$,\ndefined as $L_{\\rm obs} = F_{\\rm x} \\times 4\\pi d^2$,\nwhere $d$ is the distance to the SMC (60~kpc) or LMC (50~kpc).\nThe LMC samples (represented by filled symbols)\nlargely enhanced the number of thermal SNRs,\nand we found a clear split between XBPs and thermal SNRs.\nTherefore we can safely say that\nthe HRs of all the XBPs in the SMC and LMC\nfall in a narrow region of $0.2\\leq{\\rm HR}\\leq0.6$\n(``XBP region''),\nwhile those of all the thermal SNRs\nfall in a region of $-1.0\\leq{\\rm HR}\\leq-0.6$\n(``thermal SNR region'').\n\n\n\\placefigure{fig:hr-lobs_smclmc_class_unid}\n\n\n\\subsection{Validity of Our Classification Method}\n\n Source classification with HR has also been\ncarried out with ROSAT data (K99).\nThe common characteristic of the method of K99 and ours is\nthat the HR is defined independently of any model:\nonly the number of photons detected by ROSAT/ASCA detectors is used.\nHence their/our HR is\nan ``apparent hardness of the spectrum.''\nSuch a simple method is not valid for X-ray sources in our Galaxy,\nbecause soft X-rays are absorbed by interstellar matter\nwhich gives a dependence of the HR on source distance.\n\n To check this, we simulated HRs for simple spectra\neither of thin-thermal plasma with a temperature of 0.5~keV,\na typical value for a thermal SNR, or power-law with a\nphoton index of 1.0, a typical value for an XBP.\n When the absorption column density is $3\\times 10^{21}$~H~cm$^{-2}$,\nwhich roughly corresponds to a distance of 1~kpc, HRs are\n$-$0.89 and 0.36, for the thermal and power-law model, respectively.\n For a larger absorption column density of $8\\times 10^{22}$~H~cm$^{-2}$,\nwhich is equivalent to the Galactic center region,\nthe HR of the thermal model or the power-law model\nincreased to be 0.5 or 0.96, respectively.\n We therefore conclude that in our Galaxy\nthe HR values can have a large scatter even for the same class,\ndepending on the source distances.\nOn the other hand, according to HI observations made by Luks (1994), \nwe can safely assume that the interstellar absorption is rather uniform\ntowards the SMC and LMC with a scale down to $15'$ (HPBW). \nIn fact, HI column density derived by Luks (1994) was \n$\\sim 1 \\times 10^{20}$--$7 \\times 10^{21}$~H~cm$^{-2}$. \nWithin this $N_{\\rm H}$ range, the HR values vary very small:\nfrom $-$0.94 to $-$0.81 (thin-thermal spectra) or from 0.25 to 0.48 \n(power-law spectra). Thus we conclude that possible uncertainty of HR \ndue to the $N_{\\rm H}$ spatial variation is smaller than the width of \nthe XBP region and thermal SNR region, \nhence the present classification by HR value should be reliable \nfor X-ray sources in the Magellanic Clouds. \n\nOur proposed method is much more simple compared with that of K99;\nthe classification criteria in K99 require\ntwo hardness ratios and source extent, but\nour method needs only one hardness ratio.\n\n\\subsection{Candidate of XBPs and Thermal SNRs \\label{subsec:cand}}\n\n In the HR-luminosity plane (Figure \\ref{fig:hr-lobs_smclmc_class_unid}), \nno thermal SNR is found in the XBP region,\nnor vice versa. In addition, other classes (Crab-like SNRs and BHs)\nare not found in these two regions.\nHence we can safely select candidates for XBPs or for thermal SNRs\nusing HRs.\nAmong the unclassified sources, shown by squares\nin Figure \\ref{fig:hr-lobs_smclmc_class_unid},\nwe find eight XBP candidates and one thermal SNR candidate.\nNote that the number of candidates is tentative,\nbecause the HRs of low-flux sources have large errors ($\\sim 0.2$).\n We detected no pulsations from the eight XBP candidates,\npossibly due to their limited statistics (low fluxes).\n The thermal SNR candidate is the radio SNR 0049$-$736,\nwhich was not classified as thermal in \\S\\ref{sec:spec}\nbecause of the limited photon statistics.\nWe note that the other unclassified SNRs\nDEM S128 (No.\\,32) and 0056$-$725 (No.\\,21)\nare out of the thermal SNR region.\nThis fact confirms the possible non-thermal nature\ndescribed in \\S\\ref{subsec:snrs}.\n In addition, 0056$-$725 is an XBP candidate and\nhence X-rays from this source may be attributed to\nan (unresolved) XBP in the radio SNR 0056$-$725,\nas 1SAX J0103.2$-$7209 (No.\\,29).\n\n\n\\subsection{Source Populations in the SMC \\label{sec:pop}}\n\n As described in \\S\\ref{sec:pul} and \\S\\ref{subsec:cand},\nwe have 14 XBPs and eight candidates in the SMC.\n With a typical exposure time of 40 ksec for\nthe present SMC and LMC observation, we\ncan obtain reasonable photon statistics\nfor the sources brighter than\n$\\sim 1\\times10^{-12}$\\uflux\\ (0.7--10.0~keV),\nwhich corresponds to\n$\\sim 4\\times10^{35}$\\ulumi.\n Therefore our observations cover the luminosity ranges\nof typical HMXBs and LMXBs.\n\n Since most XBPs are HMXBs\n(e.g. Bildsten et al. 1997\\markcite{Bildsten1997}),\nwe assume all of the XBPs and the candidates to be HMXBs\nfor simplicity.\n In addition, at least 11 X-ray sources have been identified\nwith high mass stellar optical counterparts, even though\ncoherent pulsations have not been detected (summarized in Table \\ref{tab:hmxbcat}).\nAdding these, we can count\n33 HMXBs in the SMC.\nOn the other hand, about 70 HMXBs are listed in our Galaxy\n(van Paradijs 1995\\markcite{Paradijs1995};\nBildsten et al. 1997\\markcite{Bildsten1997};\nNagase 1999\\markcite{Nagase1999}).\n\n\\placetable{tab:hmxbcat}\n\n\n\nNo LMXB has ever been discovered in the SMC\nincluding in this work,\nwhile in our Galaxy, about 100 LMXBs have been found so far\n(van Paradijs 1995\\markcite{Paradijs1995}).\n\n\n The radio surveys of SNRs are more complete than those of X-rays at this moment,\nand 14 and 220 radio SNRs are cataloged in the SMC and our Galaxy,\nrespectively\n(Mathewson et al. 1983\\markcite{Mathewson1983};\nMathewson et al. 1984\\markcite{Mathewson1984};\nMathewson et al. 1985\\markcite{Mathewson1985b};\nFilipovi\\'{c} et al. 1998\\markcite{Filipovic1998};\nGreen 1998\\markcite{Green1998}).\nAmong them, no Crab-like SNR is known in the SMC, while seven are\nknown in our Galaxy (e.g. Nagase 1999\\markcite{Nagase1999};\nPavlov, Zavlin, \\& Tr\\\"{u}mper 1999\\markcite{Pavlov1999}).\nThe thermal SNR candidate defined in \\S\\ref{subsec:cand}\nis the radio SNR 0049$-$736, hence the number of SNRs in the SMC remains unchanged.\nIn our Galaxy, new X-ray SNRs have been found with ROSAT and ASCA, thus\nover 100 X-ray SNRs are expected to be cataloged in the near future\n(e.g. Aschenbach 1996\\markcite{Aschenbach1996}).\n\n The estimated numbers of these classes in the SMC and our Galaxy\nare summarized in Table \\ref{tab:pop}.\nSince the mass ratio of our Galaxy to the SMC is roughly 100,\nthe source numbers in the SMC should be multiplied by 100\nfor a simple comparison with our Galaxy.\nSince hard X-rays from HMXBs brighter than $\\sim 5\\times10^{35}$\\ulumi\\\ncan penetrate the interstellar gas through the entire Galaxy, we may neglect\nany selection effect caused by Galactic absorption.\nThus we conclude that number of HMXBs normalized by the galaxy\nmass is much higher in the SMC than in our Galaxy.\nAccordingly, we suspect that the SMC has been\nmore active than our Galaxy in massive star formation.\n\n\n\\placetable{tab:pop}\n\n\nThe number ratio of HMXBs to LMXBs exhibits\na striking difference as has already\nbeen pointed out by Schmidtke et al. (1999)\\markcite{Schmidtke1999}.\nOur results make this difference even larger,\nespecially when we include the HMXB candidates; 33/0 in the SMC and 70/100 in our Galaxy.\nLMXBs are generally considered to comprise an older population\nthan HMXBs, because of their properties such\nas spatial distribution outside\nactive star forming regions and weak magnetic fields\n(e.g. Lewin, van Paradijs, \\& Taam 1995\\markcite{Lewin1995}).\nAccordingly, the high ratio in the SMC implies\nrather recent star formation activity about several $10^{\\rm 6-7}$~yr ago.\n\n\nBoth Crab-like SNRs and HMXBs originate from massive stars:\nthe former from a single star, while the latter from a binary system.\nThe number ratios of these classes in our Galaxy (7/70)\nand that in the SMC (0/33) are largely different from each other\nin spite of the similar origin.\nThis may imply that the formation efficiency of massive binary stars\nrelative to that of single massive stars was much higher in the SMC than in our Galaxy.\n\n\\section{Conclusion \\label{sec:conc}}\n\n We have performed systematic analyses of X-ray sources in the SMC\nwith all the available data obtained with ASCA.\n\nAmong the 16 X-ray pulsars in the SMC,\nfive were newly discovered during our analyses.\nWe also confirmed the pulsations of another seven pulsars.\nWe regarded 14 pulsars out of the 16 as XBPs\nbecause of their flux variability\nand, for some sources, the existence of an optical counterpart.\n\nEight radio SNRs were detected.\nThe spectral analyses revealed that\nat least four SNRs exhibit the emission lines of ionized atoms,\nhence they are expected to be thermal SNRs.\nAnother two SNRs are possibly emitting non-thermal X-rays.\n\n\nWe established a simple and reliable method of\nsource classification using the hardness ratio (HR).\nXBPs fall in a range of $0.2\\leq {\\rm HR} \\leq0.6$,\nwhile thermal SNRs fall in a range of $-1\\leq {\\rm HR}\\leq -0.6$.\n With this method,\neight XBP candidates and one thermal SNR candidate\nare found.\n Normalized by the galaxy mass, HMXBs are found\nto be extremely populous in the SMC, compared with those in our Galaxy.\n An even more striking contrast between the two galaxies is the number ratio\nof HMXBs to LMXB; it is 33/0 in the SMC but is 70/100 in our Galaxy.\nThe lack of Crab-like SNRs in the SMC may indicate that the\nformation of single massive stars in the SMC was less active than\nthat of binary systems.\n\n\n\\acknowledgments\nThe authors express their thanks to all the members of the ASCA team. \nThis research has made use of data obtained through \nthe High Energy Astrophysics Science Archive Research Center Online Service,\nprovided by the NASA/Goddard Space Flight Center.\nJ.Y. and M.N. are financially supported by the Japan Society for\nthe Promotion of Science. \n\n\n\\begin{references}\n\\reference{Allen1993}\n Allen, W. 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H. 1998, \\iaucirc, 7048\n\\reference{Wojdowski1998}\n Wojdowski, P., Clark, G. W., Levine, A. M., Woo, J. W., \\& Zhang, S. N.\n 1998, \\apj, 502, 253\n\\reference{Ye1995}\n Ye, T., Amy, S. W., Wang, Q. D., Ball, L., \\& Dickel, J. 1995, \\mnras, 275, 1218\n\\reference{Yokogawa1998a} \n Yokogawa, J., \\& Koyama, K. 1998a, \\iaucirc, 6835\n\\reference{Yokogawa1998b}\n Yokogawa, J., \\& Koyama, K. 1998b, \\iaucirc, 6853\n\\reference{Yokogawa1998c}\n Yokogawa, J., \\& Koyama, K. 1998c, \\iaucirc, 7009\n\\reference{Yokogawa1998d}\n Yokogawa, J., \\& Koyama, K. 1998d, \\iaucirc, 7028\n\\reference{Yokogawa1999a}\n Yokogawa, J., Imanishi, K., Tsujimoto, M., Kohno, M., \\& Koyama, K.\n 1999a, \\pasj, 51, 547\n\\reference{Yokogawa1999b}\n Yokogawa, J., Paul, B., Ozaki, M., Nagase, F., Chakrabarty, D., \\&\n Takeshima, T.\n 1999b, \\apj, submitted\n\\end{references}\n\\onecolumn\n\n\\begin{table}\n\\caption{SMC Fields Observed with ASCA. \\label{tab:obs}}\n%\\dummytable\\label{tab:obs}\n\\end{table}\n\n\\begin{table}\n\\caption{First ASCA Catalog of X-ray Sources in the SMC.\n\\label{tab:smccat}}\n%\\dummytable\\label{tab:smccat}\n\\end{table}\n\n\\begin{table}\n\\caption{X-ray Pulsars in the SMC.\\label{tab:pcat}}\n%\\dummytable\\label{tab:pcat}\n\\end{table}\n\n\\begin{table}\n\\caption{Best-Fit Parameters of 0103$-$726 for the CIE or NEI Model.\n\\label{tab:spec0103}}\n%\\dummytable\\label{tab:spec0103}\n\\end{table}\n\n\\begin{table}\n\\caption{Non-Pulsating HMXBs in the SMC.\n\\label{tab:hmxbcat}}\n%\\dummytable\\label{tab:hmxbcat}\n\\end{table}\n\n\\begin{table}\n\\caption{X-ray Source Populations in the SMC and Our Galaxy.\n\\label{tab:pop}}\n%\\dummytable\\label{tab:pop}\n\\end{table}\n\n\\newpage\n\n\\begin{figure}\n\\psbox[xsize=0.47\\textwidth]{f1a.eps}\n\\psbox[xsize=0.47\\textwidth]{f1b.eps}\n\\caption{SMC mosaic contour images obtained with ASCA GIS in\nthe soft (a: 0.7--2.0~keV)\nand hard band (b: 2.0--7.0~keV),\noverlaid with\nthe equatorial coordinates (J2000).\nThe effects of non X-ray background,\ntelescope vignetting and\ndifference of exposure time between observations\nwere corrected.\nThe complex structure for sources near the edge of the detector fields is due\nto the point spread function of ASCA XRTs.\nContour levels are logarithmically\nspaced and highly saturated at XTE J0111.2$-$7317.\n\\label{fig:smc}\n}\n\\end{figure}\n\n\n\n\\begin{figure}\n\\psbox[xsize=0.47\\textwidth]{f2a.eps}\n\\psbox[xsize=0.47\\textwidth]{f2b.eps}\n\\caption{Power spectra of SMC X-1 in observation A (a) and AX J0105$-$722 (b), \nwhere data points larger than 5 are plotted. \nPulsations were detected unambiguously from most of pulsars like (a), \nwhile AX J0105$-$722 exhibited rather weak evidence as shown in (b). \n\\label{fig:psd}\n}\n\\end{figure}\n\n\\begin{figure}\n\\psbox[xsize=0.47\\textwidth]{f3.eps}\n\\caption{Periodigram of XTE J0055$-$724 around a known period $\\sim 59$~s.\n\\label{fig:efs}\n}\n\\end{figure}\n\n\n\n\\begin{figure}\n\\psbox[xsize=0.47\\textwidth]{f4a.eps}\n\\psbox[xsize=0.47\\textwidth]{f4b.eps}\n\\psbox[xsize=0.47\\textwidth]{f4c.eps}\n\\psbox[xsize=0.47\\textwidth]{f4d.eps}\n\\psbox[xsize=0.47\\textwidth]{f4e.eps}\n\\psbox[xsize=0.47\\textwidth]{f4f.eps}\n\\psbox[xsize=0.47\\textwidth]{f4g.eps}\n\\caption{Spectra of SNRs. \nThe upper panels show data points (crosses) and the best-fit model \n(solid line; see text), \nwhile the lower panels show residuals from the best-fit model. \n(a) 0103$-$726 with the CIE model; \n(b) 0103$-$726 with the NEI model; \n(c) N19; \n(d) N66; \n(e) 0049$-$736; \n(f) 0056$-$725; \n(g) DEM S128 (=AX J0105$-$722). \n\\label{fig:specsnrs}\n}\n\\end{figure}\n\n\\begin{figure}\n\\psbox[xsize=0.47\\textwidth]{f5.eps}\n\\caption{Confidence contours between $\\tau$ and $kT$ \nin the NEI model for 0103$-$726. \n\\label{fig:0103contour}\n}\n\\end{figure}\n\n\n\n\\begin{figure}\n\\psbox[xsize=0.47\\textwidth]{f6a.eps}\n\\psbox[xsize=0.47\\textwidth]{f6b.eps}\n\\caption{X-ray contours obtained by GIS overlaid with\nthe three regions from which event lists were extracted\nto search for coherent pulsations from AX J0105$-$722 (see text).\n\\label{fig:dems128reg}\n}\n\\end{figure}\n\n\n\\begin{figure}\n\\psbox[xsize=0.47\\textwidth]{f7a.eps}\n\\psbox[xsize=0.47\\textwidth]{f7b.eps}\n\n\\psbox[xsize=0.47\\textwidth]{f7c.eps}\n\\psbox[xsize=0.47\\textwidth]{f7d.eps}\n\n\\psbox[xsize=0.47\\textwidth]{f7e.eps}\n\\psbox[xsize=0.47\\textwidth]{f7f.eps}\n\n\\psbox[xsize=0.47\\textwidth]{f7g.eps}\n\\psbox[xsize=0.47\\textwidth]{f7h.eps}\n\\end{figure}\n\n\\begin{figure}\n\\psbox[xsize=0.47\\textwidth]{f7i.eps}\n\\psbox[xsize=0.47\\textwidth]{f7j.eps}\n\n\\psbox[xsize=0.47\\textwidth]{f7k.eps}\n\\psbox[xsize=0.47\\textwidth]{f7l.eps}\n\\caption{GIS spectra of X-ray pulsars. \nThe upper panels show data points (crosses) and the best-fit model \n(solid line; see text), \nwhile the lower panels show residuals from the best-fit model. \nSee Figure 4 (g) for AX J0105$-$722. \n(a) AX J0049$-$729 in observation E; \n(b) AX J0051$-$733; \n(c) AX J0051$-$722;\n(d) 1WGA J0053.8$-$7226;\n(e) XTE J0055$-$724; \n(f) AX J0058$-$7203; \n(g) RX J0059.2$-$7138; \n(h) 1SAX J0103.2$-$7209 (average of observations B, D, and F); \n(i) XTE J0111.2$-$7317; \n(j) SMC X-1 in observation A; \n(k) SMC X-1 in observation C; \n(l) SMC X-1 in observation H. \n\\label{fig:pulspec}\n}\n\\end{figure}\n\n\n\\begin{figure}\n\\psbox[xsize=0.47\\textwidth]{f8a.eps}\n\\psbox[xsize=0.47\\textwidth]{f8b.eps}\n\n\\psbox[xsize=0.47\\textwidth]{f8c.eps}\n\\psbox[xsize=0.47\\textwidth]{f8d.eps}\n\\end{figure}\n\n\\begin{figure}\n\\psbox[xsize=0.47\\textwidth]{f8e.eps}\n\\psbox[xsize=0.47\\textwidth]{f8f.eps}\n\n\\psbox[xsize=0.47\\textwidth]{f8g.eps}\n\\psbox[xsize=0.47\\textwidth]{f8h.eps}\n\\end{figure}\n\n\\begin{figure}\n\\psbox[xsize=0.47\\textwidth]{f8i.eps}\n\\psbox[xsize=0.47\\textwidth]{f8j.eps}\n\n\\psbox[xsize=0.47\\textwidth]{f8k.eps}\n\\caption{Folded light curves of X-ray pulsars in the\nsoft (0.7--2.0~keV; upper panel) and\nhard (2.0--7.0~keV; middle panel) band, in which \nthe vertical axes show the normalized count rates.\nThe lower panel shows the intensity ratio of\nthe hard band to the soft band.\n(a) AX J0049$-$729 in observation E; \n(b) AX J0051$-$733; \n(c) AX J0051$-$722;\n(d) 1WGA J0053.8$-$7226;\n(e) AX J0058$-$7203; \n(f) RX J0059.2$-$7138; \n(g) 1SAX J0103.2$-$7209 in observation D; \n(h) AX J0105$-$722; \n(i) XTE J0111.2$-$7317; \n(j) SMC X-1 in observation A; \n(k) SMC X-1 in observation H. \n\\label{fig:pullc}\n}\n\\end{figure}\n\n\n\\begin{figure}\n\\psbox[xsize=0.97\\textwidth]{f9.eps}\n\\caption{Plot of HR as a function of the observed luminosity\nin 0.7--10.0~keV.\nOpen/filled symbols represent the SMC/LMC sources.\nSymbols represent\nXBPs (stars), thermal SNRs (circles),\nCrab-like SNRs (crosses), BHs (asterisks),\nother radio SNRs (dotted circles),\nnon-pulsating HMXBs (triangles) and\nunclassified sources (squares), respectively.\nTypical error of HR of\nthe latter three classes is\n$\\sim 0.2$.\n No.\\,39 (Galactic star HD 8191) is omitted here. \nThe variable sources detected multiple times \nare marked with the source numbers \n(No.\\,3=AX J0049$-$729 and No.\\,38=SMC X-1).\nStars in parentheses are \npositionally coincident with known XBPs, \nfrom which we detected no coherent pulsations\n(AX J0049$-$729 and RX J0052.1$-$7319). \n\\label{fig:hr-lobs_smclmc_class_unid}\n}\n\\end{figure}\n\n\n\n\\end{document}\n"
}
] |
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astro-ph0002168
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The afterglows of gamma-ray bursts
|
[
{
"author": "S. R. Kulkarni$^*$"
},
{
"author": "E.~Berger$^*$"
},
{
"author": "J.~S.~Bloom$^*$"
},
{
"author": "F.~Chaffee$^\\P$"
},
{
"author": "A.~Diercks$^*$"
},
{
"author": "S.~G.~Djorgovski$^*$"
},
{
"author": "D. A. Frail$^{\\dagger}$"
},
{
"author": "T.~J.~Galama$^*$"
},
{
"author": "R.~W.~Goodrich$^\\P$ F.~A.~Harrison$^*$"
},
{
"author": "R.~Sari$^*$ \\&\\ S.~A.~Yost$^*$"
}
] |
Gamma-ray burst astronomy has undergone a revolution in the last three years, spurred by the discovery of fading long-wavelength counterparts. We now know that at least the long duration GRBs lie at cosmological distances with estimated electromagnetic energy release of $10^{51}$ -- $10^{53}$ erg, making these the brightest explosions in the Universe. In this article we review the current observational state, beginning with the statistics of X-ray, optical, and radio afterglow detections. We then discuss the insights these observations have given to the progenitor population, the energetics of the GRB events, and the physics of the afterglow emission. We focus particular attention on the evidence linking GRBs to the explosion of massive stars. Throughout, we identify remaining puzzles and uncertainties, and emphasize promising observational tools for addressing them. The imminent launch of {\em HETE-2} and the increasingly sophisticated and coordinated ground-based and space-based observations have primed this field for fantastic growth.
|
[
{
"name": "references.tex",
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},
{
"name": "review.tex",
"string": "%\\documentstyle[amsfonts,epsfig,portland]{aipproc}\n\\documentstyle[epsfig,longtable]{aipproc}\n\n\\def\\ale{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}\\hbox{$<$}}}}\n\\def\\age{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}\\hbox{$>$}}}}\n\n\\begin{document}\n\\title{The afterglows of gamma-ray bursts}\n\n\\author{S. R. Kulkarni$^*$, E.~Berger$^*$, J.~S.~Bloom$^*$, \n F.~Chaffee$^\\P$, \\\\\n A.~Diercks$^*$,\n S.~G.~Djorgovski$^*$, D. A. Frail$^{\\dagger}$,\n T.~J.~Galama$^*$, \n R.~W.~Goodrich$^\\P$ \n F.~A.~Harrison$^*$, R.~Sari$^*$ \\&\\ S.~A.~Yost$^*$}\n\n\\address{$^*$California Institute of Technology, Pasadena, CA 91125,\n USA\\\\\n$^\\dagger$National Radio Astronomy Observatory,\n Socorro, NM 87801, USA \\\\\n$^\\P$W. M. Keck Observatory, Kamuela, HI 96743, USA}\n\n%\\lefthead{LEFT head}\n%\\righthead{RIGHT head}\n\\maketitle\n\n%\\psdraft\n\n\\begin{abstract}\n Gamma-ray burst astronomy has undergone a revolution in the last\n three years, spurred by the discovery of fading long-wavelength\n counterparts. We now know that at least the long duration GRBs lie at\n cosmological distances with estimated electromagnetic energy release\n of $10^{51}$ -- $10^{53}$ erg, making these the brightest explosions\n in the Universe. In this article we review the current\n observational state, beginning with the statistics of X-ray,\n optical, and radio afterglow detections. We then discuss the\n insights these observations have given to the progenitor population,\n the energetics of the GRB events, and the physics of the afterglow\n emission. We focus particular attention on the evidence linking GRBs to\n the explosion of massive stars. Throughout, we identify remaining\n puzzles and uncertainties, and emphasize promising observational\n tools for addressing them. The imminent launch of {\\em HETE-2}\n and the increasingly sophisticated and coordinated\n ground-based and space-based\n observations have primed this field for fantastic growth.\n\n\\end{abstract}\n\n\n\\section{Introduction} \n\\label{sec:introduction}\n\nGRBs have mystified and fascinated astronomers since their discovery.\nTheir brilliance and their short time\nvariability clearly suggest a compact object\n(black hole or neutron star) origin. Three decades of high-energy\nobservations, culminating in the definitive measurements of\nCGRO/BATSE, determined the spatial distribution to be isotropic yet\ninhomogeneous, suggestive of an extragalactic population (see\n\\cite{fm95} for a review of the situation prior to the launch of the\nBeppoSAX mission). Further progress had to await the availability\nof GRB positions adequate for identification of counterparts at\nother wavelengths.\n\n\nIn the cosmological scenario, GRBs would have energy releases comparable\nto that of supernovae (SNe). Based on this analogy,\nPaczy\\'nsk \\&\\ Rhoads \\cite{pr93} and Katz \\cite{k94}\npredicted that the gamma-ray burst would be followed\nby long-lived but fading emission.\nThese papers motivated systematic searches\nfor radio afterglow, including our effort at the VLA \\cite{fk95}.\nThe broad-band nature of this\n``afterglow'' and its detectability was underscored in later work\n\\cite{mr97,v97}. \n\nUltimately, the detection of the predicted afterglow had to await\nlocalizations provided by the Italian-Dutch satellite, BeppoSAX\n\\cite{b+97}. The BeppoSAX Wide Field Camera (WFC) observes\nabout 3\\% of the sky, triggering on the low-energy (2 -- 30 keV)\nportion of the GRB spectrum, localizing events to $\\sim$ 5 -- 10\narcminutes. X-ray afterglow was first discovered by BeppoSAX in GRB~970228,\nafter the satellite was re-oriented (within\nabout 8 hours) to study the error circle of a WFC detection with the\n2 -- 10 keV X-ray concentrators. The detection of fading \nX-ray emission, combined with the high sensitivity and the\nability of the concentrators to\nrefine the position to the arcminute level, led to the subsequent discovery of\nlong lived emission at lower frequencies \\cite{c+97,JvP+97,f+97}.\n\nOptical spectroscopy of the afterglow of GRB 970508 led to\nthe definitive demonstration of the extragalactic nature of this GRB\n\\cite{mdk+97}. The precise positions provided by radio and/or optical\nafterglow observations have allowed for the identification of host\ngalaxies, found in almost every case. Not only has this provided\nfurther redshift determinations, but it has been useful in tying GRBs\nto star formation through measurements of the host star formation rate\n(e.g. \\cite{kdr+98,dkb+98}). HST with its exquisite resolution has been\ncritical in localizing GRBs within their host galaxies and thereby shed\nlight on their progenitors (e.g. \\cite{fpt+99,hh99,bod+99}).\nObservations of the radio afterglow have directly established the\nrelativistic nature of the GRB explosions \\cite{f+97} and provided\nevidence linking GRBs to dusty star-forming regions. Radio observations\nare excellent probes of the circumburst medium and the current evidence\nsuggests that the progenitors are massive stars with copious stellar\nwinds. The latest twist is an apparent connection of GRBs with SNe\n\\cite{bkd+99}. Separately, an important development is the possible\nassociation of a GRB with a nearby (40 Mpc) peculiar SN \\cite{gvv+98,kfw+98}.\n\n\\begin{figure}[htb] \n\\centerline{\\psfig{figure=980703-lcurve.ps,width=7.3cm}\\qquad\\qquad\\psfig{figure=970508-lcurve.ps,width=7.3cm,angle=0}}\n\\vspace{10pt}\n\\caption[]{\\small {\\it\n Left: The radio light curve of GRB 980703. This is a typical\n afterglow, a rise to a peak followed by a power law decay. The\n longer lifetime of the radio afterglow allows us to see both the\n rise and the fall of the afterglow emission. In contrast, at\n optical and X-ray emission, most of the times we see only the\n decaying portion of the light curve. Right: The radio light curve\n of GRB970508 \\cite{fwk00}. The wild fluctuations of the light\n curve in the first three weeks are chromatic. At later times, the\n fluctuations become broad-band and subdued. These fluctuations\n are a result of multi-path propagation of the radio waves in the\n Galactic interstellar medium. As the source expands (at\n superluminal speeds) the scintillation changes from diffractive to\n refractive scintillation. This is analogous to why stars twinkle\n but planets do not.\\label{fig:980703-970508}}}\n\\end{figure}\n\nIn this paper we review the primary advances resulting from afterglow\nstudies. \\S{II} discusses the statistics of detections to-date,\nincluding possible causes for the lack of radio and optical afterglows\nfrom some GRBs. In \\S{III} we review constraints on the nature of the\nprogenitor population(s), in particular evidence linking some classes\nof GRBs to SNe. \\S{IV} describes the status of current understanding\nof the physics of the afterglow emission. Here we compare\nobservations to predictions of the basic spherically-symmetric model,\nand describe complications arising from deviations from spherical\nsymmetry and non-uniform distribution of the circumburst medium. We\nconclude with speculations of the near and long-term advances in this\nfield (\\S{V}).\n\nWe point out that this review has two biases. First, given the\nconcentration of previous review articles on optical and X-ray\nobservations, we emphasize the unique contributions of radio afterglow\nmeasurements. Second, this article is intended to also provide a\nsummary of the efforts of the Caltech-NRAO-CARA GRB collaboration, and\ntherefore details our work in particular. This review is in response\nto review talks given at the 1999 Maryland October meeting (SRK) and\nthe 5th Huntsville GRB meeting (DAF and SRK).\n\n\n\\section{Statistics of Afterglow Detections}\n\\label{sec:statistics}\n\nAfterglow emission was first detected from GRB~970228, both at X-ray\n\\cite{c+97} and optical frequencies \\cite{JvP+97}, but not\nat radio wavelengths \\cite{fksw98}. The first radio afterglow\ndetection came following the localization of GRB 970508\n\\cite{f+97}. Figure~\\ref{fig:980703-970508} shows\ntwo examples of radio lightcurves. The radio afterglow of GRB 970508\nis famous for several reasons: it was the first radio detection, it\ngave the first direct demonstration of relativistic expansion, and it\nremains the longest-lived afterglow \\cite{fwk00}.\n\nAfterglow emission is now routinely detected across the\nelectromagnetic spectrum. BeppoSAX has been\njoined in studying the X-ray afterglows \nby the All Sky Monitor (ASM) aboard the X-ray Timing Explorer\n(XTE), the Japanese ASCA mission, and recently the Chandra X-ray\nobservatory (CXO). A veritable armada of\noptical facilities (ranging from 1-m class telescopes to the 10-m Keck\ntelescopes) routinely discover and study optical afterglows. \nThe HST has been primarily used to make exquisite images of \nthe host galaxies (see above) but in the near future we expect other uses\nsuch as UV spectroscopy and identification of underlying SNe.\nThe VLA\nhas led the detection in radio. However, other\ncentimeter-wavelength facilities (the Australia Telescope National\nFacility, Westerbork Synthesis Radio Telescope, the Ryle Telescope)\nand millimeter wavelengths (James Clerk Maxwell Telescope, the Owens\nValley Millimeter Array, IRAM and the Plateau de Bure Interferometer)\nare now regularly contributing to afterglow studies.\n\nFigure~\\ref{fig:venn} summarizes the statistics of afterglow\ndetections. In almost all cases, X-ray emission has been detected,\nestablishing the critical importance of prompt X-ray observations.\nOptical afterglow appears to be detected in about 2/3 of all\nwell-localized events if sufficiently deep optical images are taken\nrapidly (i.e. within a day or so of the burst). Radio afterglows are\ndetected in 40\\% of the cases -- far more often than usually assumed.\nWe refer the reader to the Frail {\\it et al.} \\cite{fkw+00} for a\ncomprehensive summary of the X-ray/optical/radio afterglow detection\nstatistics. The non-detections are, as discussed below,\nas interesting as\nthe detections.\n\n\\begin{figure}[ht!] \n\\centerline{\\epsfig{file=venn.ps,width=3.5in}}\n\\vspace{10pt}\n\\caption[]{\\small {\\it\n A Venn diagram showing the detection statistics for 26\n well-localized GRBs in the Northern and Southern hemispheres. Of\n the 23 GRBs for which X-ray afterglows have been detected to date,\n 10 have optical afterglows (XO + XOR) and 9 have radio\n afterglows (XR + XOR). In total there are 13 optical and/or radio\n afterglows with corresponding X-ray afterglows.\n\\label{fig:venn}}}\n\\end{figure}\n\n\\smallskip\n\\noindent{\\bf Radio Non-detection.}\nThe failure to find radio afterglow is most likely due to lack of\nsensitivity. The brightest radio afterglow to date is that from GRB\n991208 (Frail GCN\\footnote{GCN refers to the GRB Coordinates Network\nCircular Services. This network is maintained by S. Barthelmy at the\nGoddard Space Flight Center;\\\\ see {$\\rm\nhttp://lheawww.gsfc.nasa.gov/docs/gamcosray/legr/bacodine/gcn\\_main.html$}}\n451) with a peak flux of 2 mJy, a 60-$\\sigma$ detection (at centimeter\nwavelengths) whereas the weakest afterglow is typically around\n5$\\sigma$. In contrast, at optical and X-ray wavelengths, afterglow\nemission is routinely detected at hundreds of sigma. If the VLA were\nto be upgraded by a factor of 10 in sensitivity, then we predict\nthat radio afterglow emission would, like X-ray emission, be detected\nfrom most GRBs.\n\n\n\\smallskip\n\\noindent{\\bf Optical Non-detection.} Non-detection at optical wavelengths\nis more interesting, as it may result in some cases from extinction\nalong\nthe line of sight or within the source.\nBad weather as well as rapid fading of the afterglow has certainly\nhindered some optical searches, which, due to notification delays,\ntypically begin some hours after the event. Furthermore, low Galactic\nlatitude events may be obscured, or hidden in crowded foregrounds.\nHowever, in some cases deep searches have been performed with no\nsuccess. Here, non-detection likely results from \nextinction by dust in the burst host galaxy and/or absorption by the\nintergalactic medium. GRB 970828 \\cite{ggv+98} is one example, as is\nthe more dramatic case of GRB 980329. This burst was one of the brightest\nevents in the WFC\\cite{iaa+98}. Searches for optical afterglow\nemission failed to identify any counterpart. VLA \nobservations identified an unusual radio variable in the field\n\\cite{tfk+98}. Soon thereafter, a red afterglow and a bright IR\nafterglow were identified (Klose GCN 43, Larkin et al. GCN 44). Taylor\net al. \\cite{tfk+98} suggest that the GRB arose in a region with high\nextinction. Further optical and IR work on this interesting afterglow\ncan be found in\n\\cite{gcp+99}, \\cite{ppm+98}, and \\cite{rlm+99}.\n\nOptically dim ``red'' but bright IR afterglows\ncan also result from the GRB being located at high redshift. Intergalactic\nHI absorption will result in a wavelength cutoff below the Lyman\nlimit, $<912(1+z)$ \\AA, where $z$ is the redshift of the source. This\neffect was originally invoked to explain the faint R-band but bright\nIR emission from GRB 980329 \\cite{f99}. We now know, based on recent\nKeck observations, that the GRB host is blue, incompatible with a\nhigh-$z$ origin. Rather, it is more tenable that the host is a\ntypical star-forming galaxy with dusty star-forming regions, and that\nthe GRB occurred in one such region\\cite{tfk+98}. We are presently\ncarrying out IR spectroscopy of this host to determine the redshift\nand the star formation rate (SFR). While searching for ``R dropouts''\nmay in the future provide an effective method for finding high-redshift\nevents, it is clear that cross-calibrated multi-band photometry of\nhigher quality than currently exists will be required to make this\nuseful.\n\n\\smallskip\n\\noindent{\\bf X-ray Non-detection.}\nThe spectra of most GRB events clearly extend into the X-ray band, as\nestablished by {\\it GINGA} observations\\cite{sfmy98}. How the X-ray\nemission observed during the burst connects to the X-ray afterglow is\nuncertain, due to sensitivity limitations of wide-field monitors.\nX-ray afterglow emission appears to be ubiquitous. Observations\nof the X-ray afterglow are important for two reasons: (i) the\nobservations of the X-ray afterglow by sensitive imaging instruments\n(e.g. the concentrators aboard BeppoSAX) result in sufficiently\nprecise (arcminute) localization and (ii) a significant (perhaps even\na dominant) fraction of the explosion\nenergy appears to be radiated in this band. Of all the SAX\nbursts, GRB 970111 is peculiar for the absence of X-ray afterglow\n(admittedly the data were obtained about 17 hours after the burst)\n\\cite{fac+99}. In view of the critical role played by\nX-ray afterglow in localization of GRBs we \nregard this non-detection to be worthy of further\ninvestigation.\n\n\\begin{table*}\n\\caption[]{Basic Properties of Selected GRBs}\n\\begin{tabular}{ccccccl}\nGRB & $\\alpha$(J2000) &$\\delta$(J2000) & R$_{\\rm host}$ & S $\\times\n10^{-6}$ & $z$ & References\\tablenote{References to redshift\ndetermination.} \\\\\n\\omit& (h m s) & ($^{\\circ}~'~''$) & (mag) & (erg cm$^{-2}$) &\\omit & \\omit \\\\\n\\tableline\n970228 & 05 01 47 & +11 46.9 & 25.2\\tablenote{$V$-band magnitude from\n HST. All others are R magnitude in the Johnson system.}\n & 1.7 & 0.695 & Djorgovski et al. GCN 289\\\\\n970508 & 06 53 49 & +79 16.3 & 25.7 &\n 3.1 & 0.835 & \\cite{mdk+97,bdk+98}\\\\\n970828 & 18 08 32 & +59 18 52 & TBD &\n 74 & 0.957 & \\cite{dfk+2000}\\\\\n971214 & 11 56 26 & +65 12.0 & 25.6 & \n 11 & 3.418 & \\cite{kdr+98}\\\\\n980326 & 08 36 34 & $-$18 51.4 & $\\age 27.3$ & \n 1 & \\ldots & \\omit\\\\\n980329 & 07 02 38 & $+$38 50.7 & 25.4 & \n 50 & \\ldots & \\omit\\\\\n980519 & 21 22 21 & $+$77 15.7 & 26.2 & \n 25 & \\ldots & \\omit\\\\\n980613 & 10 17 58 & $+$71 27.4 & 24.5 & \n 1.7 & 1.096 & Djorgovski et al. GCN 189 \\\\\n980703 & 23 59 07 & $+$08 35.1 & 22.6 & \n 37 & 0.966 & \\cite{dkb+98}\\\\ \n981226 & 23 29 37 & $-$23 55 54 & $\\age 22$ & \n N.A. & \\ldots & \\omit\\\\\n990123 & 15 25 31 & +44 46 00 & 24.4 & \n 265 & 1.600 & \\cite{kdo+99} \\\\\n990510 & 13 38 07 & $-$80 29 49 & $\\age 28$ &\n 23 & 1.619 & Vreeswijk et al. GCN 324\\\\\n990712 & 22 31 53 & $-$73 24 29 & 21.78 & \n N.A.& 0.430 & Galama et al. GCN 388\\\\\n991208 &16 33 54 & +46 27 21 & $\\age 25$ &\n 100 & 0.706 & Dodonov et al. GCN 475\\\\\n991216 & 05 09 31 & +11 17 07 & 24.5 & \n 256 & 1.020 & Vreeswijk et al. GCN 496\\\\\n\\end{tabular}\n\\end{table*}\n\\smallskip\n\n\n\\section{The Nature of the Progenitors}\n\\label{sec:progenitors}\n\nIn almost all cases, a host galaxy has been identified at the location\nof the fading afterglow. GRB redshifts can be obtained either via\nabsorption spectroscopy (when the transient is bright) or by emission\nspectroscopy of the host galaxy. In Figure~\\ref{fig:redshift} and\nTable~1 we summarize the measured redshifts and host galaxy\nmagnitudes. \nWhile the distance scale debate is settled (at least for the class of\nlong duration GRBs, see below) \nwe remain relatively ignorant of the nature of the central\nengine. Currently popular GRB models fall into two categories: {(i)}\nthe coalescence of compact objects (neutron stars, black holes and\nwhite dwarfs\n\\cite{eic+89,ls74,moc93,npp92}) and {(ii)} the collapse of the central\niron core of a massive star to a spinning black hole, a ``collapsar''\n\\cite{woo93,mw99}. We now summarize the light shed on the progenitor\nproblem by afterglow studies.\n\n\\begin{figure}[ht!]\n\\centerline{\\epsfig{figure=newfig-z.ps,width=9.cm}}\n\\vspace{7pt}\n\\caption[]{\\small {\\it\n The isotropic gamma-ray energy distribution of GRBs with confirmed\n redshifts. Bursts indicated in black are those with\n spectroscopically confirmed emission lines from the host galaxies;\n bursts indicated by a shaded column (e.g. 990123) are those with\n absorption line redshifts. The relevant key absorption or emission\nfeatures are noted at the top of the figure.\n\\label{fig:redshift}}}\n\\end{figure}\n\n\\smallskip\n\\noindent{\\bf The Location of GRBs Within Hosts.}\nA fundamental insight into the nature of SNe came\nfrom their location with respect to other objects within the host\ngalaxy (specifically HII regions and spiral arms) and the morphology\nof the host galaxy itself (elliptical versus spiral). \nIn a similar manner, we are now making progress in understanding GRB\nprogenitors by measuring offsets with respect to other objects in the\nhost galaxies. The rather good coincidence of GRBs with host galaxies\nalready suggests that they are unlikely to be a halo population (as\nwould be expected in the coalescence scenario \\cite{bsp99}). \nOn the other hand,\nwith the possible exception of GRB~970508\\cite{pfb+99}, they are clearly not\nassociated with galactic nuclei (i.e. massive central black holes).\nTypical offsets of GRBs from the centroid of their host galaxies are\ncomparable to the\nhalf-light radii of field galaxies at comparable magnitudes,\nsuggesting that GRBs originate from stellar populations.\n\n\\smallskip\n\\noindent{\\bf Host Galaxies.}\nDemonstrating a direct link between GRBs and (massive) star formation\nis more difficult. On the whole, the population of identified hosts\nseems typical in comparison to field galaxies in the same redshift and\nmagnitude range. The hosts have average luminosities for field\ngalaxies, modulo corrections due to evolution. Their emission line\nfluxes and equivalent widths are also statistically\nindistinguishable \nfrom the normal field galaxy population. The observed star formation\nrates, derived from recombination line fluxes (mostly the [O II] \n3727$\\,\\AA$ \nline) and from the UV continuum flux range from less than $1\\,\nM_\\odot$ yr$^{-1}$ to several tens of $M_\\odot$ yr$^{-1}$ -- \ntypical of normal\ngalaxies at comparable redshifts (extinction corrections can increase\nthese numbers by a factor of a few, but similar corrections apply to\nthe comparison field galaxy population as well). It will probably be\nnecessary to have a sample of several tens of GRB hosts before a\ncorrelation of GRBs with the (massive) star formation rate can be\ntested statistically. \nHowever, below we point to several specific\nexamples which are suggestive of a link between GRBs and star-forming\nregions.\n\n\n\\smallskip\n\\noindent{\\bf Association with Starforming Regions.}\nThere is evidence showing that GRBs arise from \ndusty regions within their host galaxies. In this \nrespect, radio observations provide a unique tool for detecting\nevents in regions of high ambient density (as was the case for GRB\n980329). An even more extreme example is GRB 970828, where the host\nwas identified based {\\it solely} on the VLA discovery of a radio\nflare \\cite{dfk+2000}. Interestingly enough, this is the dustiest galaxy in\nthe sample of GRB hosts to-date.\n\nSecond, some GRBs appear to be located within identifiable\nstar-forming regions. An example is GRB~990123 \\cite{bod+99,ftm+99,hh99}.\nVLA observations of GRB 980703 \\cite{fbk+2000} are perhaps more\nconvincing. The radio observations can be sensibly interpreted by\nappealing to free-free absorption from a foreground HII region (which\nwould dwarf the Orion complex). If this interpretation is correct\nthen this would be strong evidence for a GRB being located within a\nstarburst region.\n\n%\\centerline{\\epsfig{figure=326lc.ps,width=5.cm}\\qquad\\qquad\n%\\epsfig{figure=228sfd.ps,width=5cm,angle=270}}\n%\\centerline{\\psfig{figure=326lc.ps,width=5.0cm}\\qquad\\qquad\n% \\psfig{figure=228sfd.ps,width=5.0cm,angle=270}}\n\\begin{figure}[ht!]\n\\centerline{\\psfig{figure=326lc.ps,width=7.0cm}}\n\\vspace{7pt}\n\\caption[]{\\small {\\it R-band light curve of GRB\\,980326 and the\n sum of an initial power-law decay plus Ic supernova light\n curve for redshifts ranging from $z = 0.50$ to\n $z=1.60$; from \\cite{bkd+99}. \n%Right: The broad-band spectrum of the OT of GRB\\,970228\n% at March 30.8, 1997 UT ($\\bullet$ and upper-limit arrow). Also\n% shown is the spectral flux distribution of SN\\,1998bw ($\\circ$)\n% redshifted to the redshift of GRB\\,970228 ($z = 0.695$). The\n% similarity of the spectral flux distributions is\n% remarkable \\cite{gal+99}.\n\\label{fig:SN-curves}} \\vspace{0.1cm}}\n\\end{figure}\n\n\\medskip\n\\noindent{\\bf The GRB--SN link.}\nIf GRBs arise from the collapse of a massive star, it is an\nunavoidable consequence that emission from the underlying supernova\nshould be superimposed on the afterglow. Bloom et al. \\cite{bkd+99}\nmay have made the first detection of a possible SN component\nin the GRB~980326\nlightcurve (Fig. \\ref{fig:SN-curves}). These authors noted that SNe,\nin contrast to afterglows, have distinctive temporal and spectral\nsignatures: rising to a maximum at $\\sim 20(1+z)$ days, with little\nemission blueward of about 4000\\,\\AA\\ in the restframe\n(and certainly blueward of\n3000\\,\\AA) owing to a multitude of resonance absorption lines. This\ndiscovery has led to other possible SN detections, most notably\nGRB\\,970228 \\cite{gal+99,rei99}.\n\nThe suggestion of a GRB--SN connection is an intriguing one but it has\nyet to be placed on a firm footing. Important questions are: (i) are\nall long-duration GRBs accompanied by SNe? (ii) if so, are these SNe\nof type Ib/c? Ground-based observations are possible in those cases\nwhere the afterglow decays rapidly (e.g. GRB 980326) or if high quality\noptical and IR observations exist (e.g. GRB 970228).\n\nWe need more examples to test the GRB--SN link.\nFuture progress will depend on a combination of ground and HST\nobservations. For relatively nearby GRBs especially those with \na rapidly decaying optical afterglow\nit would be attractive and\nfeasible to obtain the spectrum of the SN around the time when the\nflux from the SN peaks.\nA moderate quality\nspectrum with SN-like features would have the singular\nadvantage of definitively\nconfirming the SN interpretation (as opposed to alternatives involving\nre-radiation by dust \\cite{wd99}). However, for most GRBs, we expect\nHST observations to play a critical role. \nHST's widely recognized strengths in accurate photometry of\nsources embedded in galaxies\\cite{gkc+98} and photometric stability\nmake the detection of a faint SN against the optical afterglow and the\nhost galaxy possible.\n\n\n\\medskip\n\\noindent{\\bf Diversity of the Progenitor Population.}\nAs was the case with SNe, it is likely naive to think of a single\nprogenitor population. \nBelow, we discuss the\ntwo additional classes which show some promise:\nthe mysterious short duration GRBs\nand a possible class of low luminosity GRBs associated with SNe.\n\n\\begin{figure}[ht!]\n\\centerline{\\epsfig{figure=2pops.eps,width=9.cm}}\n\\vspace{7pt}\n\\caption[]{\\small {\\it\n Distribution of duration ($T_{90}$) vs. spectral hardness for\n BATSE bursts (diamonds) from the 4B catalogue. There is a clear\n suggestion of two groups of GRBs: short/hard and long/soft\n events. Events localized by BeppoSAX\n (solid squares) appear to belong to the long duration\n class.\\label{fig:bim}}}\n\\end{figure}\n\n\n\\smallskip\n\\noindent\n{\\em Short Events.} It has been known for some time that the\ndistribution of the duration of GRBs appears to be bimodal\n\\cite{fm95}; see Figure~\\ref{fig:bim}. Furthermore, these two groups\nmay have different spatial distributions \\cite{kc96b}, with the short\nbursts being detected out to smaller limiting redshifts. However, we\nknow very little about this class of GRBs since, as noted earlier, all\nbursts localized by BeppoSAX and RXTE thus far are of long duration\n(Figure \\ref{fig:bim}). Fortunately, improvements in BeppoSAX and the\nimminent launch of HETE-2 provide for the first time the opportunity to\nfollow-up short GRBs.\n\n\nThe short duration bursts are difficult to accommodate in the\ncollapsar model, given the long collapse time of the core. However,\nthey find a natural explanation in the coalescence models. How would\nthese bursts manifest themselves? Li \\&\\ Paczy\\`nski\n\\cite{lp98b} speculate that if the short-duration bursts result\nfrom NS--NS mergers then they may leave a bright, but short-lived\n($\\ale 1$ day) optical transient. Radio observations provide a\ncomplementary tool for determining the nature of the short duration\nbursts. The low ambient density would result in weak afterglows (since\nflux $\\propto \\rho^{1/2}$) which are potentially detectable. Radio\nobservations have additional advantages of a longer lived afterglow,\nimmunity from weather and freedom from the diurnal cycle.\n\n\\begin{figure}[t!]\n\\centerline{\\psfig{figure=sn1998bw.ps,width=7.0cm,angle=0}}\n\\vspace{7pt}\n\\caption[]{\\small {\\it Discovery image of SN 1998bw\\cite{gvv+98}.\nThe SN is the bright object (marked with an arrow) SW of the\nnucleus. Relative to typical SNe, this SN is more energetic and \nappears to have synthesized ten times more Nickel.\n\\label{fig:sn1998bw}}\n\\vspace{0.1cm}}\n\\end{figure}\n\n\n\\smallskip \n\\noindent{\\em Gamma-ray Bursts Associated with Supernovae.} Observers\nand theorists alike have been intrigued by the possibility that the\nbright supernova, SN~1998bw, discovered by Galama et al.\n\\cite{gvv+98} in the error circle of GRB 980425 \\cite{paa+99}, is\nassociated with the gamma-ray event (Figure~\\ref{fig:sn1998bw}). \nKulkarni et al. \\cite{kfw+98}\ndiscovered that the SN had an extremely bright radio counterpart; see\nFigure \\ref{fig:sn1998bw-lc}. We noted that the inferred brightness\ntemperature exceeded the inverse Compton catastrophe limit of $5\\times\n10^{11}$ K and to avoid rapid cooling we postulated the existence of a\nrelativistically expanding blastwave ($\\Gamma\\age 2$). This\nrelativistic shock is, of course, in addition to the usual\nsub-relativistic SN shock. This relativistic shock may have produced\nthe GRB at early times. (We note here that we disagree with the much\nlower energy estimates of \\cite{wl99}; our recent calculations using\nthe same assumptions as those made in \\cite{wl99} result in an energy\nestimate similar to that obtained earlier \\cite{kfw+98} from\nminimum-energy formulation).\nThe optical modeling of the\nlightcurve and the spectra show that GRB 980425 was especially\nenergetic \\cite{imn+98,wes99} with an energy release of $3\\times 10^{52}$\nerg and Nickel production of nearly nearly a solar mass.\n\nIf GRB~980425 is associated with 1998bw, then this type of event is\nrare among the SAX localizations. GRB 980425 is most certainly not a\ntypical GRB: the red-shift of SN 1998bw is 0.0085 and the $\\gamma$-ray\nenergy release in GRB 980425 is at least four orders of magnitude less\nthan in other cosmologically located GRBs. For this reason, most\nastronomers (especially those in the GRB field; see Wheeler's foray in\nexperimental sociology\\cite{w99}) do not believe the association\nbetween GRB 980425 and SN 1998bw. On the other hand, as evidenced by \nthe \nintense interest in and modeling of the radio and optical data of SN\n1998bw, this object is of considerable interest to the SN\ncommunity. Indeed, we \nbelieve that the proposed GRB--SN association controversy has\nmuddied the main issue: SN 1998bw is an interesting SN in its own\nright.\n\n\n\\begin{figure}[ht!]\n\\centerline{\\epsfig{figure=smlin_lc.ps,width=8.cm,angle=-90}}\n\\caption[] {\\small {\\it\n The radio light curve of SN 1998bw at four wavelengths\n \\cite{kfw+98}. The peak brightness temperature of SN 1998bw at\n early times is $10^{13}$ K, well in excess of the inverse Compton\n limit of $5\\times{10}^{11}$ K, and can be best understood if the\n radio emission originates from a relativistic shock ($\\Gamma\\age 2$).\n\\label{fig:sn1998bw-lc}}}\n\\end{figure}\n\nWhat is the true distinguishing feature of SN 1998bw that may connect\nit to a GRB event? Is it the large energy release, as suggested by\nseveral authors\\cite{imn+98,grs+99}? We argue that in fact it is the\nenergy {\\em coupled into relativistic ejecta} that most closely\nconnects SN 1998bw to a GRB. In a typical SN, about $10^{51}$ erg is\ncoupled to the envelope of the star (a small fraction of the total SN\nenergy release of $10^{53}$ erg). In a GRB, a similar amount of\nenergy ($10^{51}$--$10^{52}$~erg depending on the event)\nis coupled to a much smaller ejecta mass, resulting in relativistic\noutflow. For SN 1998bw, applying the minimum energy formulation\nto the radio observations we infer the relativistic shell\nto contain $\\sim 10^{50}$ erg. \nNot only is this uncharacteristic\nof a typical SN (there exists no evidence for relativistic ejecta in ordinary\nSN), but it is not dissimilar from the energy implied for GRB\noutflows. One could therefore envisage a continuum of physical\nphenomenon between SN 1998bw and cosmological GRBs provided we use the\nenergy in the relativistic ejecta as the basic underlying\nparameter and not the isotropic gamma-ray release.\n\n\\section{Afterglow: The Physics and Energetics of the Fireball}\n\\label{sec:afterglow}\n\nOne can consider a GRB to be like a SN explosion with a central source\nreleasing energy $E_0$ (comparable to the mechanical release of energy\nin an SN). This is the so-called fireball model.\nThe difference between an SN and a GRB is primarily in\nejecta mass: 1--10 $M_\\odot$ for SNe whereas only $10^{-5}\\,M_\\odot$\nfor GRBs. The evolution of a GRB is much faster than that of a SN due\nto two factors: the ejecta expand relativistically and, thanks to the\nsmaller ejecta mass, the optical depth is considerably smaller.\n\nAs the ejecta encounter ambient gas, two shocks are produced: a\nshort-lived reverse shock (traveling through the ejecta) and a\nlong-lived forward shock (propagating into the swept-up ambient gas).\nAfterglow emission is identified with emission from the forward shock.\nIn order to obtain significant afterglow emission, several conditions\nare necessary. (1) Rapid equipartition of electrons with the shocked\nprotons (which hold most of the energy). (2) Acceleration of electrons\nto a power law spectrum (particle Lorentz factor distribution,\n$dN/d\\gamma\\propto \\gamma^{-p}$). (3) Rapid growth of the magnetic field\nwith energy density in the range of $10^{-2}$ of that of the protons.\nUnder these circumstances, afterglow emission is dominated by\nsynchrotron emission of the accelerated particles; see\n\\cite{spn97,w97a}. The weakness of this model is the assumption of\ngrowth in the magnetic field strength to the high values noted above\n(R. Blandford, pers. comm.).\n\nThe theoretically expected afterglow spectrum is shown in\nFigure~\\ref{fig:sari}. Three key frequencies can be identified:\n$\\nu_a$, the synchrotron self-absorption\nfrequency; $\\nu_m$, the frequency of the electron with a minimum\nLorentz factor (corresponding to the thermal energy behind the shock)\nand $\\nu_c$, the cooling frequency. Electrons which radiate above\n$\\nu_c$ cool on timescales equal to the age of the shock. The\nevolution of these three frequencies is determined by the\nhydrodynamical evolution of the shock which in turn is affected by two\nprincipal factors: the environment of the GRB and the geometry of the\nexplosion.\n\n\\begin{figure}[!ht]\n\\centerline{\\epsfig{figure=sari.ps,width=8cm}}\n\\vspace{10pt}\n\\caption[]{\\small{\\it\n Broad-band spectrum ($f_\\nu$) of the afterglow from a spherical fireball\n with constant density (``ISM'' model; see text) and $\\rho\\propto\n r^{-2}$ medium (``wind'' model; see text). This is representative of the\n observed spectrum few days after the burst. Note the distinct\n evolution of $\\nu_{a}$ and $\\nu_c$ in the two\n models.\\label{fig:sari}}}\n\\end{figure}\n\n\\smallskip\\noindent\n{\\em The GRB environment.} The earliest afterglow models made the\nsimplifying assumption of expansion into a constant density\nmedium. This is an appropriate assumption should the GRB progenitor\nexplode into a typical location of the host galaxy. However, there is\nincreasing evidence tying GRBs to massive stars (see\n\\S\\ref{sec:progenitors}). It is well known that massive stars lose\nmatter throughout their lifetime and thus one expects the circumburst\nmedium to exhibit a density profile, $\\rho\\propto r^{-2}$ where $r$ is\nthe distance from the progenitor. Chevalier \\&\\ Li\n\\cite{cl99} refer to these two models as the ISM (interstellar medium)\nand the wind model respectively. As can be seen from\nFigure~\\ref{fig:sari} these two models give rise to rather different\nevolution of the three critical frequencies.\n\n\\smallskip\\noindent {\\em Geometry: Jets versus Spheres.} The\nhydrodynamics is also affected by the geometry of the explosion. Many\npowerful astrophysical sources have jet-like structure. There is\nevidence (from polarization observations) indicating asymmetric\nexpansion in SNe \\cite{w99}, so it is only reasonable to assume that\nGRB afterglows also have jet-like geometry as well. \nA clear determination of the\ngeometry is essential in order to infer the true energy of the\nexplosion. This is especially important for energetic bursts such as\nGRB 990123 whose isotropic energy release approaches $M_\\odot c^2$.\n%SRK to add something on wind model\n\nLet the opening angle of the jet be $\\theta_0$. As long as the bulk\nLorentz factor, $\\Gamma$, is larger than $\\theta_0^{-1}$, the evolution\nof the jet is exactly the same as that of a sphere (for an observer\nsituated on the jet axis). However, once $\\Gamma$ falls below\n$\\theta_0^{-1}$ then two effects become important. First, for a well\ndefined jet, the on-axis observer sees an edge and thus one expects to\nsee a break in the afterglow emission. Second, the lateral expansion\nof the jet (due to heated and shocked particles) will start affecting\nthe hydrodynamical explosion.\n\n\n\\smallskip\\noindent {\\bf Wind or ISM?} \nThe two key diagnostics to distinguish these two models are the\nevolution of the cooling frequency (see Figure~\\ref{fig:sari}) and the\nearly behavior of the radio emission. In the wind model, the radio\nemission rises rapidly (relative to the ISM model) and the synchrotron\nself-absorption frequency falls rapidly with time. \nBoth these result\nfrom the fact that the ambient density decreases with radius (and hence\nin time)\nin the wind model.\n\nUnfortunately, in general, the current data are not of sufficient\nquality to firmly distinguish the two models. For example in GRB\n980519, the same optical and X-ray data appear to be adequately\nexplained by the jet+ISM model \\cite{sph99} and the sphere+wind\nmodel \\cite{cl99}. Including the radio data tips the balance, but only\nslightly, in favor of the wind model \\cite{fks+2000}.\nIn our opinion, the best example for the\nwind model is that of GRB 980329 \\cite{fks+99}; see\nFigure~\\ref{fig:980329-990510}. This afterglow exhibits the two\nunique signatures of the wind model: high $\\nu_a$ and a rapid rise.\nGiven the importance of making the distinction between the wind and\nthe ISM model we urge early wide band radio observations (especially\nat high frequencies).\n\n\n\\begin{figure}[hb!]\n\\centerline{\\epsfig{figure=980329-radio.ps,width=7.cm}\\qquad\\qquad\n\\epsfig{figure=990510-fit.eps,width=7cm,angle=0}}\n\\vspace{10pt}\n\\caption[]{\\small {\\it Left: \n Radio afterglow of GRB 980329 \\cite{fks+99}. \nThe rapid rise of the centimeter\n flux and the high absorption frequency (signified by the\n considerable strength of the millimeter emission) offer\n good support for GRB 980329 expanding into a circumburst medium\n with density falling as inverse square distance. \n The lines represents a wind model based on \n X-ray, optical, IR, mm and cm data.\n Right:\n Observed and model radio light curves of GRB 990510 \\cite{hbf+99}.\n\tThe model predictions for the radio afterglow emission are\n\tdisplayed by the solid line (jet fireball model) and dotted\n\tline (spherical fireball model). The observed optical afterglow\n\temission is displayed by the dotted-dashed line; see text for\n\tmore details.\n\\label{fig:980329-990510}}} \n\\end{figure}\n\n\n\n\n\\smallskip\\noindent {\\bf Energetics.} Of all the physical\nparameters of the fireball, the most eagerly sought parameter is the\ntotal energy $E_0$. By analogy with supernovae, it is $E_0$ which sets\nthe GRB phenomenon apart from other astrophysical phenomena.\nClasses of GRBs may eventually be distinguished and ranked by their\nenergy budget; for example, long-duration events, short duration\nevents and supernova-GRBs (see \\S\\ref{sec:progenitors}). \n\nOne approach has been to use the isotropic $\\gamma$-ray energy as a\nmeasure of $E_0$; see Figure~\\ref{fig:redshift}. There are three well\nknown problems with such estimates. First, collimation of the ejecta\n(jets) will result in overestimation of the total energy release. For\nGRB 990510 where a good case for a jet has been established\n(Figure~\\ref{fig:980329-990510}), the standard isotropic energy\nestimate is probably a factor of 300 more than the true energy\n\\cite{hbf+99}. Second, even after accounting for a possible jet\ngeometry, the efficiency of converting the shock energy into gamma-ray\nemission is very uncertain. For example, some authors \\cite{k99}\nadvocate low efficiency ($\\sim 1\\%$) which would result in an enormous\nupward correction to the usual isotropic estimates. Third, the bulk\nLorentz factor is extremely high during the emission of $\\gamma$-rays\nand thus the estimates critically depend on assumption of the geometry\nand granularity \\cite{kp99} of the emitting region. In particular, if\nthe emission is from small blobs \\cite{kp99} then the inferred\nestimates are grossly in error.\n\nIn contrast to this highly uncertain situation, afterglows offer (in\nprinciple) more robust methods to evaluate $E_0$. In view of the\nimportance of determining $E_0$ we summarize the different methods of\ndetermining $E_0$ from afterglow observations. One approach is to fit\na ``snapshot'' broad-band afterglow spectrum (from radio to X-rays) to\nan afterglow model; this approach was pioneered by Wijers \\&\\ Galama\n\\cite{wg99}. The strength of this method is that the estimated $E_0$\nis, in principle, robust. Specifically, the estimate does not depend on\nthe usually unknown environmental factors (run of density). However,\nin practice, this method is very sensitive to the values of the\ncritical frequencies (Figure~\\ref{fig:sari}) which are usually not well\ndetermined. This difficulty explains the wildly differing estimates of $E_0$\nfor GRB 970508 \\cite{wg99,gps99}. Furthermore, this method uses\nmeasurements obtained at early times (when the afterglow at high\nfrequencies is bright) with the result that the true source geometry is\nhidden by relativistic beaming.\n\nA second approach is to model the light curves of the afterglow in a\ngiven band, specifically a radio band. The advantages of this method\nare the photometric stability of radio interferometers and the low\nLorentz factor at the epoch of the peak of the radio emission. The\ndisadvantages are two-fold: the sensitivity to the environmental\nparameters (density) and the assumption of the constancy of the\nmicrophysics parameters (electron and magnetic field \nequipartition factors). Application of this\napproach to GRB 980703 has resulted in seemingly accurate measures of\nthe fireball parameters \\cite{fbk+2000}.\n\n\nFreedman \\&\\ Waxman \\cite{fw99} take yet another approach, and\nestimate the energy release from late time X-ray observations. They\nshow that the X-ray flux is insensitive to the GRB environment, and\nobtain robust estimates of the fireball energy per unit solid angle:\nfrom $3\\times 10^{51}$ erg to $3\\times 10^{53}$ erg.\n\nWith all the above approaches, however, the possible collimation of the\nejecta in jets is still a major uncertainty. This can be addressed by\nobserving the evolution of the afterglow as the ``edge'' of the jet\nbecomes visible. In most cases no evidence for jets has been seen,\nwith the notable exceptions of GRB 990510 and possibly GRB 990123. In\naddition, a variety of statistical arguments (the absence of copious\nnumbers of ``orphan afterglows'')\\cite{gri99,gvb+99,rho97} suggests\nthat, on average, the collimation cannot be extreme, and that for most\nbursts the opening angle is not less than 0.1 radian. Thus the total\nenergy for most bursts may be reduced to the range of $10^{50}$ erg to\n$3\\times 10^{51}$ erg, but could easily be much higher in at least some\ncases.\n\nPossibly the best approach to determining the energetics, which\nminimizes uncertainties due both to collimation (jets) and to the\nenvironment is to model the afterglow after it becomes\nnon-relativistic. This method builds on the well established minimum\nenergy formulation and the self-similarity of the Sedov solution. Not\nonly are the ejecta truly non-relativistic, but they are also\nessentially spherical, as by this time jets will have had sufficient\ntime to have undergone significant lateral expansion.\nIndeed, we can justifiably call this ``fireball\ncalorimetry'' \\cite{fwk00}. Applying this technique to the long-lived\nafterglow of GRB 970508 (Figure~\\ref{fig:980703-970508}) led to the\nsurprising result that $E_0 \\sim 5\\times 10^{50}$ erg -- weaker than a\nstandard SN! This is an astonishing result. If true, this result would\nsuggest that it is not $E_0$ which is the prime distinction between\nGRBs and SNe but the ejecta mass. However, Chevalier \\&\\ Li\n\\cite{cl2000} interpret the same data in the wind framework and derive\nmuch larger $E_0$. Clearly, we need more well studied afterglows with\nsufficient observations to first distinguish the circumburst\nenvironment (wind versus ISM) and then radio observations over a\nsufficiently long baseline to undertake calorimetry. Nonetheless, one\nshould bear in mind that the current evidence for large energy release\nin GRBs is not as strong as is usually assumed.\n\n\\section{Epilogue and Future}\n\\label{sec:epilogue}\n\nClearly, the GRB field is evolving rapidly. Along what direction[s] will\nthis field proceed in the coming years? One way to anticipate the\nfuture is by considering analogies from the past. \n\nIn \\S\\ref{sec:progenitors} we already discussed the parallels\nbetween the SN field and the GRB field. Here we discuss the\nnumerous parallels with quasar astronomy.\nFirst\ndiscovered at radio wavelengths, we now study quasars across the\nelectromagnetic spectrum. Although still identified by their\ngamma-ray properties, we now recognize the tremendous value of\npan-chromatic GRB and afterglow studies. In both cases, there was\nconsiderable controversy about the distance scale. However, once this\nissue was settled, it became clear that quasars are the most energetic\nobjects (sustained power) whereas GRBs are the most brilliant. For\nboth, the ultimate energy appears to be related to black holes (albeit\nof different masses).\n\nThe raging issues in GRB astronomy today are the same that fueled\nquasar studies in the 60's: the spatial distribution, the extraction of\nenergy from the central engine, the transfer of energy from stellar\nscales to parsec scales, and the geometry of the relativistic outflow\n(sphere or jet). Astronomers took decades to unify the seemingly\ndiverse types of quasars, and to conclude that there are two types of\ncentral engines: radio loud and radio quiet. Likewise, there may well\nbe two types of GRB engines: rapidly and slowly spinning black holes\nemerging respectively from collapse of a rotating core of a massive\nstar or coalescence of compact objects and the collapse of a massive\nstar. This picture could potentially explain both the cosmologically\nlocated GRBs and SN 1998bw. Finally, we can project that in the\nfuture, GRBs may be used to probe distant galaxies, just as quasars are\nused today to study the IGM.\n\n\nThere is a feeling in the astronomical community (outside the GRB\ncommunity) that the GRB problem is ``solved''. The truth is that the\nGRB problem is now getting defined! We now summarize our view of the\nmajor issues and anticipated near term advances. In our opinion the\nmajor issues are Diversity, Progenitors and Energy Generation.\n\nAs discussed earlier, high energy observations suggest the\nexistence of two classes: short and long duration bursts. It is possible\nthat afterglow observations may demarcate additional classes. If\nso, one can contemplate that within a year (assuming abundant\nlocalizations by HETE-2) that we will have new GRB designations such\nas {\\it s}GRBs (GRBs with late time bump indicative of \nan underlying SN), {\\it w}GRBs (GRBs whose\nafterglow clearly indicates a wind circumburst medium shaped by stellar\nwinds), {\\it i}GRBs (GRBs which explode in the interstellar medium) and so\non. \n\nThe broad indications are that GRBs are associated with stars and most\nlikely massive stars. However, we know little beyond this. Comparing\nthe unbeamed GRB event rate of $1.8\\times 10^{-10}$ yr$^{-1}$\nMpc$^{-3}$ \\cite{schmidt99} with $3\\times 10^{-5}$ Type Ibc SN\nyr$^{-1}$ Mpc$^{-3}$ and $10^{-6}$ yr$^{-1}$ NS--NS merger Mpc$^{-3}$\n\\cite{lamb99} shows that GRBs events are extremely rare; here we note\nthat the present data do not support a collimation correction in excess of\n100. It will be quite some time before we will be in a position to\nidentify the conditions necessary for a star to die as a GRB.\n\nIt is our opinion that SN 1998bw is a major development in the field of\nstellar collapse. The association (or lack) with GRB 980425\nunfortunately has distracted our attention of this important\ndevelopment. The existence of a significant amount of mildly relativistic\nmaterial, $\\sim 10^{50}$ erg \\cite{kfw+98}, is fascinating and it is\nironic that none of the models can account for this inferred value\nwhereas most of the theoretical effort has gone into explaining the \ngamma-ray burst itself (especially considering the uncertain association\nof GRB 980425 with SN 1998bw). Clearly, SN\n1998bw is a rare event but we are convinced that more such events\nwill be found and\naccordingly have mounted a major campaign to identify these SNe. The\nrobust signatures of this class are high $T_B$ and prompt X-ray\nemission since these are necessary consequences of a relativistic\nejecta. We note that if these future events are as bright as SN 1998bw\nthen the energy in the relativistic ejecta can be directly measured by\nVLBI observations of the expanding radio shell.\n\n\nIt is vitally important to make quantitative progress in determining\nthe energy release in GRBs. As discussed in \\S\\ref{sec:afterglow}, firm\nestimates of the energy release require well sampled broad-band data\nat early times and densely sampled radio light curves out to late\ntimes. This will require a {\\it coordinated} approach and necessarily\ninvolve many observatories around the world and in space. The same\ndatasets will also help us understand a profound puzzle: if GRBs indeed\narise from the death of massive stars then why do we not see signatures\nfor a circumburst medium shaped by stellar winds in {\\it all} long\nduration GRBs? Even ardent supporters of the wind model\n\\cite{cl99,cl2000} concede that some GRBs (e.g. GRB 990123, 990510) are\ndue to a jet expanding into a constant density medium.\n\n\nWe now discuss the anticipated returns. True to our tradition as\nobservers, we order the discussion by wavelength regimes!\n\n\n\\smallskip\n\\noindent{\\em Radio Observations: Dusty galaxies, Circumstellar Edges\nand Reverse Shocks.} Perhaps the most exciting use of radio afterglow\nis in identifying dusty star-forming host galaxies. Such host galaxies\nare not readily seen at optical wavelengths. Currently, such galaxies\nare eagerly sought and studied at sub-millimeter wavelengths. However,\nthe sensitivity and localization of such galaxies by sub-millimeter\ntelescopes is poor. In contrast, GRB host galaxies are identified at\nthe sub-arcsecond level. The present radio afterglow detection rate of\n40\\% already places an upper limit on the amount of star-formation in\ndusty regions, viz. this rate is not larger than that measured from\noptical observations. This result is entirely independent of the\nconclusion based on studies in the sub-millimeter regime, or the \ndiffuse cosmic FIR background found in the COBE\ndata. However, the result does rely on two assumptions: (i) GRBs trace\nstar formation and (ii) the GRB explosion and its aftermath does not\nradically alter the ambient medium (i.e., with a prompt and complete\ndestruction of dust grains along the line of sight).\n\nRadio observations of SNe offer a probe of the distribution of the\ncircumstellar matter. A spectacular example is SN 1980K whose radio\nflux dropped 14 yrs after the explosion \\cite{mvw+98}. A progenitor\nstar which suffered mass loss with variation in the wind speed could\nexplain the observations. Indeed, one {\\it expects} significant radial\nstructure in the circumburst medium as the progenitor evolves from a\nblue star to a red supergiant and thence to possibly a blue supergiant\netc. If GRBs come from binary stars which undergo a phase\nof common envelope envolution\n\\cite{bllb99} then the structure would be even more complicated.\nThus radio observations have the potential (in fortunate circumstances)\nto give us insight into the mass loss history of the progenitor star[s].\n\nThe prompt optical emission from GRB 990123 \\cite{abb+99} has been\ninterpreted to arise from the reverse shock \\cite{sp99}. Far less\ndiscussed is the prompt radio emission -- a radio flare -- also seen\nfrom this burst \\cite{kfs+99}. Sari \\&\\ Piran \\cite{sp99}\nsuggest that the radio emission also originates from the reverse\nshock as the electrons cool. Observations related to the reverse\nshocks are important since it is only through these observations that\nwe have a chance of studying the elusive ejecta. We now have four\nsuch examples of radio flares \\cite{kf00} and this represents an order\nof magnitude better success rate than ROTSE+LOTIS. We urge theorists\nto pay attention to these new findings. \nMore to the point,\nradio observations appear to be fruitful for the study of reverse\nshocks, especially when combined with observations of the prompt\noptical emission. This bodes well for the coming years given the\nefforts underway to increase the sensitivity of ROTSE \\cite{abb+99}.\n\n\n\\smallskip\n\\noindent{\\em X-ray Observations: Diversity \\&\\ Progenitors.} \n{\\it GINGA} identified a number of X-ray rich GRBs. BeppoSAX has found\nseveral such examples with some bursts lacking significant gamma-ray\nemission -- the so-called X-ray flashes \\cite{heise99}.\nWe know very little about these X-ray transients. \nCould they be GRBs\nin a very dense environment (with red giant progenitors)? We need to take\nsuch transients more seriously and intensively followup on such\nbursts.\n\nAnother interesting finding from {\\it GINGA} was the discovery of\nprecursor soft X-ray emission \\cite{m+91}. There is no simple\nexplanation for this phenomenon in the current internal-external shock\nmodel. We suggest that the soft X-ray emission precursor is similar to\nthe UV breakout of ordinary SNe. This hypothesis can be confirmed or\nrejected by obtaining the redshift to such bursts.\n\nThe X-ray rich GRB 981226 \\cite{faa+2000,fkb+99} was marked with two additional\npeculiarities: a precursor emission and afterglow emission which is\nseemingly undetectable after about 12 hours but then rises rapidly\nbefore commencing decay. Above we alluded to the fact that massive\nstars do not have a single phase of mass loss but instead\nhave a veritable history of\nmass loss (from birth to death). The X-ray observations of GRB 981226\ncould be accounted for in a model in which the progenitor has first a red\nsupergiant wind followed by a blue supergiant wind.\n\n\n\n\\smallskip\n\\noindent{\\em Optical Observations: SN link, Short bursts \\&\\ Geometry.}\nThe GRB--SN connection is best probed by optical observations. The\nvalue of optical observations has already been demonstrated by the\ncurrent observations of GRB 980326 and 970228. Clearly, more\nobservations are needed to establish this link. Once this link is\nestablished then one can undertake detailed spectroscopic studies of the\nSN with\nlarge ground-based telescopes and photometric studies with HST.\n\nOffsets of GRBs and the morphology of the host galaxies will continue\nto be of great interest. Such observations will help us differentiate\nwhether some GRBs come from nuclear regions or always from\nstar-forming regions. Under the current paradigm, the discovery of\nGRBs coincident with elliptical galaxies would be a major surprise.\nOn the other hand, one expects short bursts to arise in the halo of their\ngalaxies and thus in this case no coincidence is expected. We expect\nHETE-2 to contribute significantly to these issues.\nFinally, polarization measurements offer a very convenient way to probe the\ngeometry of the emitting region as has already been demonstrated\nfrom the discovery of polarization in GRB 990510 (e.g. \\cite{lcg99,wvg+99}).\n\n\n\\smallskip\n\\noindent{\\em Acknowledgments.} {\\small Our research is supported by\nNASA and NSF. JSB holds a Fannie \\&\\ John Hertz Foundation Fellowship,\nAD holds a Millikan Postdoctoral Fellowship in Experimental Physics,\nTJG holds a Fairchild Foundation Postdoctoral Fellowship in Observational\nAstronomy and RS holds Fairchild Foundation Senior Fellowship in\nTheoretical Astrophysics.\n The VLA is a\nfacility of the National Science Foundation operated under cooperative\nagreement by Associated Universities, Inc. \nThe W. M. Keck Observatory is operated by the California Association\nfor Research in Astronomy, a scientific partnership among California\nInstitute of Technology, the University of California and the National\nAeronautics and Space Administration. It was made possible by the\ngenerous financial support of the W. M. Keck Foundation.}\n\n\n\\begin{references}\n\n\\input {references.tex}\n\n\\end{references}\n\\end{document}\n"
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{
"name": "astro-ph0002168.extracted_bib",
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J. et al.,\n astro-ph/9906346 (1999).\n\n\n\\bibitem{woo93}\nWoosley, S.~E., {\\em ApJ} {\\bf 405}, 273, (1993).\n\n\n\\bibitem{wes99}\nWoosley, S.~E., Eastman, R. G. \\& Schmidt, B. P.,\n{\\em ApJ} {\\bf 516}, 788 (1999).\n\n\n\n\n\n%\\documentstyle[amsfonts,epsfig,portland]{aipproc}\n\\documentstyle[epsfig,longtable]{aipproc}\n\n\\def\\ale{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}\\hbox{$<$}}}}\n\\def\\age{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}\\hbox{$>$}}}}\n\n\\begin{document}\n\\title{The afterglows of gamma-ray bursts}\n\n\\author{S. R. Kulkarni$^*$, E.~Berger$^*$, J.~S.~Bloom$^*$, \n F.~Chaffee$^\\P$, \\\\\n A.~Diercks$^*$,\n S.~G.~Djorgovski$^*$, D. A. Frail$^{\\dagger}$,\n T.~J.~Galama$^*$, \n R.~W.~Goodrich$^\\P$ \n F.~A.~Harrison$^*$, R.~Sari$^*$ \\&\\ S.~A.~Yost$^*$}\n\n\\address{$^*$California Institute of Technology, Pasadena, CA 91125,\n USA\\\\\n$^\\dagger$National Radio Astronomy Observatory,\n Socorro, NM 87801, USA \\\\\n$^\\P$W. M. Keck Observatory, Kamuela, HI 96743, USA}\n\n%\\lefthead{LEFT head}\n%\\righthead{RIGHT head}\n\\maketitle\n\n%\\psdraft\n\n\\begin{abstract}\n Gamma-ray burst astronomy has undergone a revolution in the last\n three years, spurred by the discovery of fading long-wavelength\n counterparts. We now know that at least the long duration GRBs lie at\n cosmological distances with estimated electromagnetic energy release\n of $10^{51}$ -- $10^{53}$ erg, making these the brightest explosions\n in the Universe. In this article we review the current\n observational state, beginning with the statistics of X-ray,\n optical, and radio afterglow detections. We then discuss the\n insights these observations have given to the progenitor population,\n the energetics of the GRB events, and the physics of the afterglow\n emission. We focus particular attention on the evidence linking GRBs to\n the explosion of massive stars. Throughout, we identify remaining\n puzzles and uncertainties, and emphasize promising observational\n tools for addressing them. The imminent launch of {\\em HETE-2}\n and the increasingly sophisticated and coordinated\n ground-based and space-based\n observations have primed this field for fantastic growth.\n\n"
}
] |
astro-ph0002169
|
The hard X-ray properties of the Seyfert nucleus in NGC 1365
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[
{
"author": "G. Risaliti\\inst{1}"
},
{
"author": "R. Maiolino\\inst{2}"
},
{
"author": "L. Bassani\\inst{3}"
}
] |
We present BeppoSAX observations of the Seyfert 1.8 galaxy NGC1365 in the 0.1--100 keV range. The source was 6 times brighter than during an ASCA observation 3 years earlier. The 4--10 keV flux is highly variable during the BeppoSAX observation, while the soft (0.1-4 keV) emission is constant within the errors. Both a cold and a warm reflector and a cold absorber are required to explain the observed spectrum. The comparison between ASCA and BeppoSAX spectra strongly suggests that the circumnuclear material has a more complex structure than a simple homogeneous torus, with quite different absorbing gas columns along different lines of sight. A broad iron K$_\alpha$ line is also present in the spectrum, with the peak energy significantly redshifted. This can be explained by means of a relativistic disk line model. Alternatively, a warm absorption Fe line system with N$_H \simeq 10^{23}$ cm$^{-2}$ could account for the observed line profile. \keywords{Galaxies: individual: NGC 1365 -- Galaxies: active -- Galaxies: Seyfert -- X-rays: galaxies}
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[
{
"name": "n1365.tex",
"string": "\\documentclass[dvips]{aa}\n\\usepackage[dvips]{graphics}\n\\voffset2truecm\n\\begin{document}\n\n\\title{The hard X-ray properties of the Seyfert nucleus in NGC 1365}\n\\titlerunning{The hard X-ray properties of NGC1365}\n\n\\author{G. Risaliti\\inst{1}, R. Maiolino\\inst{2},\nL. Bassani\\inst{3}}\n\\authorrunning{Risaliti et al.}\n\n\n\\institute{\nDipartimento di Astronomia e Scienza dello Spazio,\nUniversit\\`a di Firenze, Largo E. Fermi 5, I--50125 Firenze, Italy\n(risaliti@arcetri.astro.it)\n\\and\nOsservatorio Astrofisico di Arcetri, Largo E. Fermi 5,\nI--50125 Firenze, Italy (maiolino@arcetri.astro.it)\n\\and\nIstituto T.E.S.R.E., CNR, via Gobetti 101,\nI-40129 Bologna, Italy (bassani@tesre.bo.cnr.it)\n}\n\n\\offprints{G. Risaliti}\n\n\\date{}\n\n\\thesaurus{03(11.09.1; NGC 1365; 11.01.2; 11.19.1; 13.25.2}\n\n\\maketitle\n\n\\begin{abstract}\n\nWe present BeppoSAX observations of the Seyfert 1.8 galaxy NGC1365 in the\n0.1--100 keV range.\nThe source was 6 times brighter than during an ASCA observation \n3 years earlier. The 4--10 keV flux is highly variable during\nthe BeppoSAX observation, while the soft (0.1-4 keV) emission is\nconstant within the errors.\nBoth a cold and a warm reflector and a cold absorber are required to explain\nthe observed spectrum. The comparison between ASCA and BeppoSAX spectra\nstrongly suggests that the circumnuclear material has a more complex\nstructure than a simple homogeneous torus, with quite different absorbing\ngas columns along different lines of sight.\nA broad iron K$_\\alpha$ line is also present in the spectrum, with the peak\nenergy significantly redshifted. This can be explained by means of a\nrelativistic disk line model. Alternatively, a warm\nabsorption Fe line system with N$_H \\simeq 10^{23}$ cm$^{-2}$ could account\nfor the observed line profile.\n\\keywords{Galaxies: individual: NGC 1365 -- Galaxies: active -- Galaxies:\nSeyfert -- X-rays: galaxies}\n\\end{abstract}\n\n\n\\section{Introduction.}\nNGC 1365 is a barred spiral galaxy (Hubble type SB0) in the Fornax\ncluster that hosts an active nucleus whose optical spectrum shows weak\nbroad Balmer lines (Seyfert 1.8, Alloin et al. 1981)\n\nIn this paper we present the analysis of the spectrum of NGC 1365 in the\n0.1-100 keV spectral range obtained with \nthe BeppoSAX satellite (Boella et al. 1997).\n\nDuring the past ten years NGC 1365 has been\nobserved several times in the X-rays \nby ASCA (Iyomoto et al. 1997, hereafter I97)\nROSAT (Komossa \\& Schulz 1998) and Ginga (Awaki 1991).\nThe 1-10 keV continuum spectrum observed by ASCA in August 1994 and\nJanuary 1995\n(I97) is well reproduced by a flat powerlaw (photon index $\\Gamma$=0.8)\nand a thermal soft component. A strong emission feature is present\nat E$\\sim$6.4--7 keV, which can be fitted by a single\nbroad emission line with E=6.58 keV and equivalent width \nEW=2.1 keV or, alternatively, by two narrow lines with\nE=6.4 keV (neutral iron, EW=0.9 keV) and E=6.7 keV (highly ionized iron,\nEW=0.9 keV).\nBoth these spectral features and the lack of (short term)\nvariability suggested that the ASCA spectrum is dominated by a cold\nreflection component which is usually observed in most of the heavily\nabsorbed, Compton thick sources (Maiolino et al. 1998, hereafter M98)\nand generally ascribed to the reflection from the molecular torus expected\nby the unified model of AGNs (Antonucci 1993).\n\nThe ASCA--SIS and ROSAT--HRI data, obtained in 1994 and 1995, reveal also\nthe presence of a strong off-nuclear X-ray source characterized by a\nsteep powerlaw spectrum (photon index $\\Gamma$=1.7 in the 1-10\nkeV band) and by a strong variability on time-scales of months; during the ASCA observation in\n1995 this source was as bright as the Seyfert 2 nucleus with a flux of 0.9$\\times 10^{-12}$ erg\ncm $^{-2}$ s$^{-1}$.\nThe spatial resolution of the BeppoSAX instruments does not allow to\nseparate the contribution of this source from that of the nucleus. \nWe will \n discuss the possible contamination from this off-nuclear source further in\nSect. 2.\n\nIn the next section we present the results of the spectral and temporal\nanalysis of our data. In Sect. 3 we discuss \nthe BeppoSAX data and their differences with respect to the previous\nX-ray observations.\nWe assume a distance of 18.4 Mpc for NGC 1365, as\nestimated by Fabbiano et al. (1992),\nand in agreement with more recent Cepheid\nmeasurement (Madore et al. 1998).\n%\n\\section{Data analysis}\nNGC 1365 was observed by SAX in August 1997. The effective\non--source integration\ntime was 8900 seconds for the LECS instrument (0.1-10 keV), 30000\nseconds for the MECS (1.65-10.5 keV) and 14000 seconds for the PDS\n(15-200 keV).\nThe spectrum and the light curve of the LECS and MECS\nwere obtained from\nthe ``event files'' provided by the BeppoSAX SDC, using the standard software\nfor X-ray analysis FTOOLS 4.0. The PDS spectrum was obtained by the FOT\nfiles of the SAX observation, using the XAS code, a software developed\nspecifically for the reduction and analysis of the SAX data.\n\nWe adopted the standard data reduction for the BeppoSAX spectra\nas described, for instance, in M98. \nThe final spectrum was rebinned to contain at least 20 counts/bin, so that\na gaussian statistics can be used to fit\nthe models to the data.\\\\\n\n\\subsection{Spectral analysis}\n\nThe beam-size of the PDS\n($\\sim 1.3^{\\circ}$ FWHM) includes also the\nSeyfert 2 galaxy NGC1386, also observed by BeppoSAX (M98),\nthat should contribute significantly to the 20--100 keV flux measured for\nNGC1365 (probably up to 50\\%). This problem, along with other effects observed\nin the light curve (Sect.2.2), prevent us from using the\nPDS data to constrain the spectral properties of the source.\n\nThe best fit to the LECS and MECS data is obtained by means of\na multi-component model typical of Compton-thin sources (see M98 for\ndetails). The continuum emission is well reproduced by \na powerlaw of photon index $\\Gamma$=1.93 (which is typical for\nSeyfert 1 spectra), a photoelectric cut-off, corresponding to a column\ndensity of cold absorbing material N$_H\\sim4\\times 10^{23}$ cm$^{-2}$, and a\nsecond powerlaw that fits the soft excess which may be due to\nextended components (starburst or hot gas in the Narrow Line Region)\n or to the X-ray source resolved by ASCA and ROSAT. \nThe whole spectrum is also absorbed by a Galactic column density of\n$1.4\\times 10^{20}$cm$^{-2}$.\nIf the extended contribution is dominant,\nwe would expect that a Raymond--Smith\nmodel also fits well the soft data.\nUnfortunately the statistics of our data in the soft band is not high enough to \ndiscriminate\n between a powerlaw and a thermal spectrum: a Raymond-Smith model\nwith kT$=2^{+0.6}_{-0.4}$ gives\n a slightly worse fit ($\\Delta \\chi^2 =2$) than\nthe powerlaw, but still in agreement at a 90\\% confidence level.\n\nIn addition to these continuum components, a narrow emission line with E=6.257\nkeV\\footnote{E=6.29 keV rest frame.} \nis strongly requested by the fit ($\\Delta \\chi^2$=18). Note that the\nline width parameter was not frozen to zero, therefore the narrowness of\nthe line is a result of the fit. The line\nequivalent width is EW=330$^{+70}_{-130}$ eV with respect to the observed\ncontinuum (EW=190$^{+45}_{-75}$ eV with respect to the unabsorbed\npowerlaw component).\nFinally, with a second line at E=6.95 keV\\footnote{E=7.0 rest frame.}\n(corresponding to H-like iron) the fit is better at a level of\nconfidence higher than 90\\% ($\\Delta \\chi^2$ =2.9).\nWe note that the energy of the cold line is significantly lower than\nthe value of the neutral iron K$_\\alpha$ line, which is\nE=6.365 keV, when corrected for the redshift (the best fit with the line\nenergy frozen at E=6.365 is worse by $\\Delta \\chi^2$ =3.5). This issue\nwill be discussed further in Sect. 3.\n\nThe results of our fit are summarized in Table 1 and shown in Fig. 1.\\\\\nThe fit of the low--state spectrum is not statistically good ($\\chi^2=47$\nfor 38 degrees of freedom), but this is due to the lower\nsignal--to--noise of the data. As shown in Fig. 1, there\nare no significant continuum features that are not well fitted, while\nthe high\n$\\chi^2 / d.o.f.$ is due to the large scatter of the points in the\n2-4 keV and 8-10 keV bands.\n\n\\begin{figure}\n\\centerline{\n\\resizebox{\\hsize}{!}{\\includegraphics{n1365_all.ps}}}\n%\\epsfig{file=n1365_all.ps}}\n\\caption{{Data + model for NGC 1365 (upper panel), residuals (central\npanel) and model for the best fit of our data}}\n\\end{figure}\n\\begin{table}\n\\centerline{\\begin{tabular}{cccc}\n\\hline\nParameter&Best-fit value\\\\\n\\hline\n&\\\\\n\\multicolumn{2}{c}{\\bf Total Spectrum}\\\\\nPowerlaw 1 $\\Gamma$ & 1.93$^{+0.25}_{-0.15}$\\\\\nPowerlaw 1 norm. & 7.4$^{+1.2}_{-0.65} 10^{-3}$ Ph. cm$^{-2}$ s$^{-1}$\nkeV$^{-1}$\\\\\nN$_H$ & 4.0$^{+0.4}_{-0.5} \\times 10^{23}$ cm$^{-2}$\\\\\nPowerlaw 2 $\\Gamma$ & 2.46$^{+0.40}_{-0.30}$ \\\\\nPowerlaw 2 norm. 2 &6.8$^{+2.6}_{-2.1} 10^{-4}$ Ph. cm$^{-2}$\ns$^{-1}$ keV$^{-1}$\\\\\nGaussian 1 Energy & 6.257$^{+0.09}_{-0.09}$ keV\\\\\nGaussian 1 norm. & 3.4$^{+1.3}_{-1.4} 10^{-5}$ Ph. cm$^{-2}$\ns$^{-1}$\nkeV$^{-1}$ \\\\\nGaussian 1 EW & 330$^{+70}_{-130}$ eV \\\\\nGaussian 2 Energy & 6.95 keV (fixed)\\\\\nGaussian 2 norm. & 1.4$^{+1.1}_{-1.3} 10^{-5}$ Ph. cm$^{-2}$\ns$^{-1}$\nkeV$^{-1}$ \\\\\nGaussian 2 EW & 120$^{+100}_{-100}$ eV \\\\\nFlux 2-10 keV & 6.6$\\times 10^{-12}$ keV cm$^{-2}$ s$^{-1}$\\\\\n$\\chi^2$/d.o.f. & 67/67 \\\\\n\\hline\\\\\n\\multicolumn{2}{c}{\\bf Low state}\\\\\nNormalization 1 & 5.8$^{+0.4}_{-0.5} 10^{-3}$ Ph. cm$^{-2}$ s$^{-1}$\\\\\nFlux 2-10 keV & 5.0$\\times 10^{-12}$ keV cm$^{-2}$ s$^{-1}$\\\\\n$\\chi^2$/d.o.f. & 47/38\\\\ \n\\hline\\\\\n\\multicolumn{2}{c}{\\bf High state}\\\\\nNormalization 1 & 1.0$^{+0.1}_{-0.05} 10^{-2}$ Ph. cm$^{-2}$ s$^{-1}$\\\\\nFlux 2-10 keV & 8.2$\\times 10^{-12}$ keV cm$^{-2}$ s$^{-1}$\\\\\n$\\chi^2$/d.o.f. & 51.7/55 \\\\\n\\hline\n\\end{tabular}}\n\\caption{\\footnotesize{Best fit model for NGC 1365. Errors are quoted\nat 90\\% level of confidence, using a $\\chi^2$ statistics.\nThe model also\nincludes a Galactic absorbing column density of $1.4\\times 10^{20}$ cm$^{-2}$.\nThe normalization of the powerlaws is at 1 keV. }}\n\\end{table}\n%\n\\begin{figure}\n\\centerline{\n\\resizebox{\\hsize}{!}{\\includegraphics{time.ps}}}\n\\caption{{Upper panel:\nlight curve of the MECS (1.65-10.5 keV) observation of NGC\n1365. Lower panel: light curves in the hard (4-10.5 keV) and soft (1.65-4 keV)\nbands.}}\n\\end{figure}~\n\n\\subsection{Timing analysis}\n\nThe flux measured by BeppoSAX in the 2--10 keV band\nis 6.6$\\times 10^{-12}$ erg cm$^{-2}$ s$^{-1}$, about 6\ntimes higher than the flux measured by ASCA in 1994--1995, but\nsimilar to the flux of 4.8$\\times 10^{-11}$ erg cm$^{-2}$ s$^{-1}$\nmeasured by Ginga during manouvering operations prior to 1990 (Awaki\n1991).\n\nThe light curve of NGC 1365, obtained from the MECS data (1.65-10.5 keV),\nis plotted in Fig. 2.\nThe count rate varies by a factor of $\\sim$ 2 during our observation.\nThere is an indication of periodicity with period\nT$\\simeq$ 45000 s, but longer observations are required to test\nthis hypothesis.\n\nIn Fig. 2 we also plot the low and high energy part of the light curve\nseparately. These two curves clearly show that the observed variability \nis mostly due to the high energy part of the spectrum,\nwhile the emission in the soft part of the spectrum is\nroughly constant\\footnote{ This is also supported by the timing\nanalysis of the LECS data: in this case\nthe statistics is lower than in the MECS data,\nhowever the light curve is constant\nwithin the errors, likewise to the low--energy light curve of the MECS.}.\nComparing these results with the spectral model in Table 1, we\ncan conclude that the variability is due to the direct emission (above the\nphotoelectric cutoff) from the\ncentral source, while the reflected or diffuse component\n (or the off-nuclear component) does not appear to vary.\n\nWe extracted two spectra from our MECS and PDS data, by selecting\nthe time intervals in which the\ncount rate in the 2-10 keV band\nis respectively higher and lower than the average.\nThe measured fluxes in the 2-10 keV band are 8.2$(\\pm 0.3)\\times 10^{-12}$\nerg cm$^{-2}$ s$^{-1}$ in the high state and 5.0 $(\\pm 0.2)\\times 10^{-12}$\nerg\ncm$^{-2}$ s$^{-1}$ in the low state.\nThe LECS and MECS spectra ($\\sim$ 1-10 keV) of the\nhigh- and low-state spectra can be fitted by using the\nsame model used for the total spectrum and by accounting for the\nvariability with a variation of the normalization\nof the transmitted powerlaw (i.e. the one dominating above 4 keV), i.e.\nby ascribing the observed flux changes to intrinsic variability of the nuclear\nsource. The results of these two fits are summarized in Table 1 and in Fig. 3.\n\n\\begin{figure}[h]\n\\centerline{\n\\resizebox{\\hsize}{!}{\\includegraphics{var_1365.ps}}}\n\\caption{{Spectra of NGC 1365 in its high\nand low state (upper and lower panel respectively).\nThe models are obtained by a\nfit to the 2-10 keV spectrum (excluding the PDS points).}}\n\\end{figure}\n\nThe light curve of the PDS behaves differently.\nThe variations in the 15--35 keV band are anticorrelated with\nthe variations in the 4--10 keV (MECS) spectral band (Fig. 3).\nThere are two possible explanations for this anti-correlation.\nThe Compton, cold reflection is most effective at $\\sim 30$ keV, therefore\nthe anticorrelation could reflect a real delay between the innermost\nprimary source and the cold reprocessing material. However, this\nscenario would require a 30 keV reflection efficiency of at least 60\\% that is\nvery high, although not completely ruled out by models, depending on the\ngeometry of the reflector\n(eg. Ghisellini et al. 1994). Alternatively, the observed\nvariability at 30 keV could be ascribed to the other Sy2 (NGC1386) in the\nPDS beam.\nThese two interpretations are also supported by an analysis of Fig. 3, in which the\nmodels are obtained by fitting the MECS data only. The extrapolation of these models\nat higher energies fall short to account for the PDS data, in agreement with the\nhypothesis of a contamination by an extra source or by a delayed, reflected\ncomponent.\n\nThe fact that the softer part of the spectrum is almost constant indicates that\nthe off-nuclear source does not contribute to the observed variability.\nIndeed, the spectrum of the latter source is an unabsorbed power law\n(Komossa \\& Schulz 1998)\nand, therefore, its\ncontribution to the variability should be significant in\nthe soft band (1.65-4 keV) too, in contrast to what observed.\nThe strength of the variability (the luminosity varied by 1.3$\\times 10^{41}$\nerg s$^{-1}$) also indicates that the\ncontribution of the off--nuclear source is marginal. The highest\nknown state of this source is that observed by ASCA in 1995, when the total\nluminosity in the 2-10 keV band was $\\sim 4\\times 10^{40}$ erg s$^{-1}$,\nthat was already\nan exceptional value for a non-nuclear galactic source.\nMoreover, the measured flux of the soft component\nis at the same level of that measured by ASCA.\nTherefore, from both the spectral and time analysis we can reasonably \nassume that the emission of the off-nuclear source\nduring our observation was not significantly\n higher than during the ASCA observation.\n\n\\section{Discussion}\nWhen comparing our BeppoSAX (1997) data with the past ASCA (1994-95) data there are\ndifferences that are not trivial to explain.\n\na) In 1994 the spectrum of NGC 1365 was dominated by a (cold) reflected\ncomponent. The measured 2-10 keV flux was 1.1$\\times10^{-12}$ erg cm$^{-2}$\ns$^{-1}$. In 1997 we find a variable, direct component, absorbed by a\ncolumn density N$_H = 4.0\\times 10^{23}$ cm$^{-2}$, whose 2-10 keV flux\nis 6.6$\\times 10^{-12}$ erg cm$^{-2}$ s$^{-1}$, i.e. 6 times higher than in\n1994.\n\nb) In the ASCA spectrum two iron emission lines are present, one at\nE=6.4 keV (cold) and one at E=6.7 keV (warm).\nIn the SAX spectrum we also find evidence for a cold and a warm (E=7\nkeV) component of the\niron line, but the flux of the cold component is three\ntimes higher than in 1994, while the warm component remains constant\nwithin the statistical errors.\n\nc) The energy of the cold iron line in the SAX spectrum (6.29 keV rest frame)\nis lower than the expected value (6.4 keV).\nAs a consequence, the energy of the cold line in the SAX spectrum\nis also lower than the cold (fainter) line observed in 1994, that is\nconsistent with 6.4 keV.\\\\\n\nThe model we propose to explain these data is based on a\nmulti-component absorber/reflector, composed by a warm, ionized component\nin the sub-parsec scale, a cold molecular torus and \nanother warm diffuse component outside the\ntorus. Fig. 4 schematically shows the various components of the model along\nwith their contribution to the observed spectrum.\nIn the following we discuss in detail each of these components and\nspectral features.\n\n\\subsection{The cold absorber}\nA cold absorbing medium is requested to explain the photoelectric\ncutoff in the SAX spectrum, that is commonly observed in most obscured\nSeyfert galaxies (Bassani et al. 1999). This medium is generally identified with\nthe obscuring molecular torus expected by the unified model\n(Antonucci 1993).\n\n\\subsection{The cold iron line}\nThe cold iron line at 6.4 keV\nis thought to be emitted by the accretion disk and, in part,\nby the circumnuclear torus predicted by the unified model (see eg.\nGhisellini et al. 1994 and Matt et al. 1991).\nThere are two possible explanations for the observed redshift of the iron\nline to 6.29 keV in the BeppoSAX spectrum of NGC 1365:\na relativistic redshift (if the line is produced in the inner part\nof an accretion disk) or a resonant absorption line at E$\\simeq$6.6 keV\nthat shifts the center of the 6.4 keV line. We discuss in some detail each of these\ntwo models in the following.\n\n\\begin{description}\n\\item[{\\it Model 1.}]\nWe fitted the emission line with the standard DISKLINE model in the Xspec 10.0\ncode for spectral analysis.\nIn this model\nthe redshifted profile is due to the general relativistic\neffects and the Doppler broadening.\nAll the parameters of the model (the inner\nand outer radius of \nthe disk and the inclination angle) were left free, except for the line energy,\nwhich was frozen to E=6.365 keV (i.e. 6.4 keV rest frame). Details of the\nline fit are given in Table 2a. The other parameters of the model are the\nsame as in Table 1, and their best fit values are equal, within the\nerrors, to those in Table 1.\nThe fit with the relativistic disk line is worse than the one\nshown in Table 1, though it is still acceptable ($\\Delta \\chi^2=2$).\n\nWe note that the fit requires an angle between the disk axis and the line\nof sight lower than 30 degrees (at the 90\\% confidence level), i.e.\na disk oriented face-on. This geometry is not favored by the unified schemes,\nsince this object is characterized by an obscured nucleus (inferred both\nfrom the optical spectrum and from the X-ray absorption) and, therefore,\nthe torus and the accretion disk are expected to be oriented edge-on.\nHowever, a warped disk could solve this inconsistency. \n\n\\item[{\\it Model 2.}]\nWe now discuss the alternative model of the warm absorption Fe line.\nA warm absorber in the central region of an AGN has been observed in\nseveral Seyfert 1 galaxies\nwith a column density as high as several 10$^{23}$ cm$^{-2}$ \n(eg. Komossa \\& Greiner 1999).\nIf this absorber is in an ionization state between Fe XXIV and Fe XIV\nthen the\nresonant K$_\\alpha$ transition can be both in emission and in\nabsorption at E$\\approx$6.5--6.7 keV.\nMatt (1994) predicts a Fe K$_\\alpha$ resonant absorption line of EW of\n20-30 eV for an ionized absorber with N$_H\\simeq 10^{23}$\ncm$^{-2}$, temperature T$\\simeq 10^6 $ K, and a non-isotropic\nspatial distribution around the central source.\nThe equivalent width can be larger if the temperature is higher\n(T=10$^7$ K is an acceptable value for the region around the\naccretion disk) and if the velocity dispersion of the warm absorber is high,\nso that the broadening of the absorption line prevents its saturation.\nFor example, following Matt (1994),\nif we assume T=10$^7$ K and a turbulence of $\\sim$ 500\nkm s$^{-1}$ the EW of the absorption line can be $\\sim$ 100 eV.\nThe combination of the cold emission line and the warm absorption line,\nconvolved at the spectral resolution of BeppoSAX, could result\nin an emission line\nwhose center is apparently redshifted (Fig. 4).\nA more quantitative description of this model is given in the Appendix and\nin Table 2b. \n\n\\end{description}\n\n\\begin{table}\n\\centerline{\\begin{tabular}{ccc}\n\\hline\nParameter&Best-fit value\\\\\n\\hline\n&&\\\\\n\\multicolumn{2}{c}{\\bf a) Relativistic line model} \\\\\nLine energy & 6.365 (fixed)\\\\\nDisk inner radius & R$_{IN}> 6 R_g$\\\\\nDisk outer radius & unconstrained\\\\\nInclination angle & 18.4$^{+12}_{-18}$ deg\\\\\nLine EW & 400$^{+300}_{-200}$ eV\\\\\n$\\chi^2$/d.o.f. &69/67\\\\\n\\hline\n&&\\\\\n\\multicolumn{2}{c}{\\bf b) Absorption line model} \\\\\nEmission line Energy & 6.365 keV (fixed)&\\\\\nEmission line EW & 400$^{+120}_{-200}$ eV\\\\\nAbsorption line Energy & 6.63$^{+0.25}_{-0.20}$ keV\\\\\nAbsorption line EW & 80 eV (fixed)\\\\\n$\\chi^2$/d.o.f. &66.3/68\\\\\n\\hline\n\\end{tabular}}\n\\caption{\\footnotesize{Best fit parameters of the two models proposed to\nexplain the observed profile of the cold Fe emission lines, as discussed\nin Sect. 3.2.}}\n\\end{table}\n\n\\subsection{The long term variability}\n\nAs outlined above, the X-ray emission and spectrum\nof NGC 1365 is very different in\nthe two observations performed by ASCA and BeppoSAX. This behavior is\nreminiscent of another well known case of similar long term variation,\ni.e.\nNGC 4051 (Guainazzi et al. 1998).\n\nThe differences between\nthe ASCA (1994) and SAX (1997) spectra, and in particular the\nflux variation, can be explained in two scenarios: 1) a Compton thick cloud\n(i.e. with N$_H > 10^{24}$ cm$^{-2}$) obscured\nthe nucleus in 1994 by passing through our line of sight, thus\nmaking the 2--10 keV spectrum reflection dominated; alternatively 2)\nthe intrinsic emission of the active nucleus might have been\nquiescent (or much reduced) in that period. The latter\ncase would be indistinguishable from the pure-reflection scenario,\nbecause of the spectral similarity between a reflection spectrum and a\nCompton-thin spectrum with N$_H\\sim 4\\times10^{23}$ cm$^{-2}$ when the\nsignal-to-noise is low (M98), as it is the case for the ASCA spectrum.\nMoreover, in case 2) the observed emission\ncould be composed both by a direct and a reflected component. Also,\nit is unlikely that the direct emission dominates, because a) in\nthis case some variability on short time scales would be expected, while\nthe ASCA light curve is constant within the errors (I97); and b) the\nhigh equivalent width of the iron lines implies an highly efficient\nreflection. \n\n\nWe cannot easily\ndistinguish between hypothesis 1) and 2), because both cases predict a\nreflection dominated\nspectrum, which depends only on the structure of the reflecting\nmedium. However, a very interesting result, regardless of which of the two\nmodels applies, is that in both scenarios a high reflection efficiency is\nrequired:\nthe ASCA 2-10 keV flux is 5.2\\% of the SAX\nN$_H$--corrected flux, that is near to the maximum possible reflection\nefficiency,\naccording to theoretical models (Ghisellini\net al. 1994). According to these models the reflection efficiency is\nstrongly dependent on the column density of the reflecting material, and\nis negligible for N$_H < 10^{24}$ cm$^{-2}$. We therefore conclude that\nthe reflection is not due to the same obscuring medium responsible for the\nphotoelectric cutoff observed in the SAX spectrum that,\naccording to our fits, has a column density (N$_H = 4\\times 10^{23}$cm$^{-2}$)\nmuch lower than what required to provide an efficient Compton reflection.\nThere are two simple models\n that could explain this discrepancy:\n \\begin{itemize}\n \\item the torus could be composed by a large number of thick clouds and\n diffuse gas with lower density and relatively low column density.\n Assuming this geometry the reflection efficiency could be high, and the\n SAX observation could have been performed when none of the thick clouds was\n intersecting our line of sight. However we note that in this scenario the\n covering factor of the clouds must be high, in order to make the\n reflection efficiency high enough. On the other hand,\n NGC 1365 was in a Compton thin state in two out of the three past\n observations (the Ginga and BeppoSAX ones), suggesting that the covering\nfactor of the thick clouds cannot be too high.\n\n\\item Alternatively, the obscuring torus might be characterized by a stratified\nstructure, with a column density in excess of $10^{24}$cm$^{-2}$ on the\nequatorial plane and much lower on the edge, the latter being along our line of\nsight.\nThis possibility is in agreement with some models that ascribe the\nintermediate Seyfert classification to orientation\neffects.\n\\end{itemize}\n\n\\begin{figure}\n\\centerline{\n\\resizebox{\\hsize}{!}{\\includegraphics{model2.ps}}}\n%\\epsfig{file=model2.ps,height=16cm}\n\\caption{{Sketch illustrating the geometry of the absorbing/reprocessing\nmaterial that we propose to explain the observed spectral components.\nThe observed profile of the cold iron line (6.29 keV rest\nframe) can be reproduced by\nboth models 1) and 2).}}\n\\end{figure}\n\nFinally, we note that the presence of a warm absorber in the central\nregion of the nucleus, speculated in Sect.3.2,\ncould also provide an explanation to the low--flux spectrum\nmeasured by ASCA alternative to those discussed above:\na change in ionization state of the warm absorber could\nintroduce a much higher absorption that, henceforth, could be responsible\nfor the lower flux observed in the ASCA data.\nIndeed, if the warm absorber is located close to the central source, as\nrequired by our model, a decrease of the intrinsic luminosity could be\nfollowed, with a short time delay, by a decrease of the ionization state\nof the absorber and, as a consequence, by an increase of the absorption.\nHowever, this effect is unlikely to provide all the additional column\ndensity required from the ASCA data, basically for two reasons: 1) the\nN$_H$ required ($\\sim 10^{24}$ cm$^{-2}$) is much higher\nthan any previous measurement of warm absorbers\n(as stated also in the Appendix, typical values of\nN$_H$ for warm absorbers are several 10$^{22}$ cm$^{-2}$, with a few\ncases of measured N$_H > 10^{23}$ cm$^{-2}$); 2)if a warm absorber with\nN$_H\\sim 10^{24}$ cm$^{-2}$ is present, we expect to detect a deep iron\nabsorption edge in the BeppoSAX spectrum, that is not observed. The\nmaximum {\\it warm} N$_H$ for which the iron edge\nis not detectable over the noise\n(in excess to the Fe edge due to the cold absorber)\nis a few 10$^{23}$ cm$^{-2}$.\n\n\n\\subsection{The cold mirrors}\n Whatever is the reason of the lower flux during the ASCA\nobservation, the comparison of the iron emission lines in the SAX and\nASCA spectra provides interesting constraints on the geometry and on the\nefficiency of the reprocessing/ reflecting material.\nThe flux of the cold iron line in 1997 (SAX)\nis three times higher than in 1994 (ASCA), \nconfirming that the iron line is produced both by the obscuring torus and\nby the reflection on\nthe accretion disk: when the nuclear source\nis active (or visible)\n both components are detected, while when the nucleus is\ninactive (or obscured) only the component reflected by the torus is detected.\nIf we assume that in 1994 the nucleus was in a low state (that is the \nmost likely scenario, as discussed above) then we can constrain the size of\nthe torus that produces one-third of the cold iron line, by taking\nadvantage of reverberation limits. We do not have information about the\nperiod when the nucleus first faded before the ASCA observation. However,\nthe ASCA observation was obtained in two parts\nseparated by 6 months and the two spectra are nearly identical, this\nconstrains the size of the cold reflecting torus to be larger than\n6 light-months, i.e. $> 0.15$ pc, in agreement with other independent\nestimates (Antonucci 1993, Gallimore et al. 1997, Greenhill \\& Gwinn 1997).\n\n\\subsection{The warm mirror}\nThe warm iron line in AGNs is thought to be emitted by the\ncircumnuclear hot gas that is responsible for the reflection of the\n(polarized) broad lines, i.e. the so-called {\\it warm mirror} (Matt et\nal. 1996).\nTo check if the discrepancy between the warm line energies in the\nBeppoSAX and ASCA spectra is statistically significant, we retrieved and\nanalized the ASCA data from the ASCA public archive. We found that the\nbest fit energy of the warm line is E=6.85 keV (rest frame), and E=7 keV\nis still acceptable ($\\Delta \\chi^2=1$). The line fluxes are also\ncompatible within the errors. This analysis suggests that \nthe warm ionized reflector that produces this line\nhas not changed its state between tha ASCA (1994) and BeppoSAX (1997)\nobservations, and therefore should be\nlocated at a distance larger than 3 light years from the nucleus.\n\nNote that the warm reflector is physically distinct from the\nwarm absorber responsible for the putative iron absorption system discussed\nin Sect. 3.1, both because\nof the different ionization properties and different size. As discussed in\nSect. 3.1, the warm absorber\nmust have a ionization state between FeXIV and FeXXIV, while the warm mirror\nemits a line at 7 keV that corresponds to FeXXV. Moreover, the ionized\nabsorber must be located in the vicinity of the black hole (around the\naccretion disk?) so that turbulent velocity can broaden the absorption line\npreventing its saturation, while the warm reflector must be located on scales\nlarger than 1 pc, as discussed above.\n\n\n\\subsection{The short term variability}\nAs discussed in Sect. 2.2,\nthe emission observed by BeppoSAX is strongly variable in the 4-10 keV\nband. The light curve is very well fitted by a sinusoid with a period of\n$\\sim 45000 $ seconds. Even though our observation is too short to\njustify any claim of periodicity, recent studies on the periodicity of\nthe Seyfert nucleus in IRAS 18325-5926 (Iwasawa et al.\n1998) make this subject very interesting. Anyway, no conclusion can be\ndrawn without longer observations.\n\n\\section{Conclusions}\nWe presented new BeppoSAX data in the 0.1--100 keV range of the Seyfert 1.8\ngalaxy NGC1365.\nThe spectrum is characterized by a continuum absorbed by a cold gaseous\ncolumn density of $\\rm N_H = 4\\times 10^{23}$ cm$^{-2}$ and an iron K$\\alpha$\nemission complex that is well fitted by a cold component at 6.29 keV and\na warm component at 7 keV (rest frame). At energies below the absorption cutoff\n(E $<$ 4 keV) a soft excess is present.\n\nThe cold absorption is probably due to the obscuring torus predicted by unified\nmodel of AGNs. The continuum is strongly variable during the BeppoSAX\nobservation. The variability is mostly due to the hard component of the\nspectrum above the photoelectric cutoff (4--10 keV), while the soft component\n(1.65--4 keV) is essentially constant. The rapid variability very likely\nreflects variations of the central engine. Instead, the soft excess is\nprobably due to an extended component, either associated to starburst activity\nor to hot gas in the Narrow Line Region. \n\nThe BeppoSAX spectrum is 6 times brighter than during two ASCA observations\nof NGC~1365 taken about 3 years earlier. The latter spectra were characterized\nby a flat continuum, indicative of cold Compton reflection, very likely from\nthe circumnuclear torus.\n\nThe high reflection efficiency, deduced from the comparison of the ASCA\nand BeppoSAX spectra, requires a column density of the reflector much\nhigher than that measured in absorption. We conclude that the\ncircumnuclear medium is strongly inhomogeneous: the torus could contain\nCompton thick clouds or, alternatively, has a steep density gradient\nfrom the edge to the equatorial regions.\n\nThe fading of the direct emission during the ASCA\nobservations can be explained in two ways: the central\nengine was hidden by a Compton thick cloud or, most probably, the nucleus\nwas in an intrinsically low state. In the latter scenario, the temporal\nbehavior of the cold and the warm iron lines indicate that the cold reflecting\ntorus must be located at a distance larger than 0.15 pc, while the warm\nmirror must be located at a distance larger than 1 pc. Both the circumnuclear\ntorus and the accretion disk contribute to the emission of the cold Fe line,\nin a proportion of about 1:2 respectively.\n\nThe cold iron line is significantly redshifted with respect to its nominal\nvalue. More specifically we measure a line peak (rest frame) of\n6.29 keV, that is inconsistent with the nominal value of 6.4 keV\nat a significance level higher than 99\\%. A disk relativistic line can fit\nthe observed profile, though the fit is worse than the analytical fit. Also,\naccording to this fit the accretion disk must be oriented face on, that is\nan improbable geometry for an absorbed AGN like NGC 1365. Alternatively,\nwe propose that the shift of the cold iron line is caused by a warm absorber,\nalong the line of sight (with $\\rm N_{warm}\\approx 10^{23}$ cm$^{-2}$),\nthat introduces an absorption Fe line at 6.5--6.7 keV:\nthe combination of the cold emission line and the warm absorption line,\nconvolved with the spectral resolution of BeppoSAX, results in an emission line\nwhose center is apparently shifted at 6.29 keV. The spectral fit of the data\nwith this second model is significantly better with respect to the\nrelativistic disk line.\n\n\\begin{acknowledgements}\nWe thank the anonymous referee for useful comments.\nG.R. and R.M. acknowledge the partial financial support\nfrom the Italian Space Agency (ASI)\nthrough the grant ARS--99--15 and from the\nItalian Ministry for University\nand Research (MURST) through the grant Cofin98-02-32.\n\\end{acknowledgements}\n\n\\appendix\n\\section{Details on the warm absorber model for the iron line\nredshift}\n\nIn this Appendix we discuss more in detail the spectral fit and the\nimplications of the model of the warm iron absorption to explain the\nredshift of the cold iron line described in Sect. 3.3 (model 2).\n\nWe fit our BeppoSAX data with a model whose components are the\nsame as in Table 1, except for the ``cold'' iron line at E=6.257 keV that\nwas replaced with a narrow line with energy frozen at 6.365 keV (6.4 keV rest\nframe) and a\nnarrow absorption line with EW=80 eV and E$\\sim$6.6 keV. Details of the\nfit are given in Table 2b.\nThe best fit with this model\nis better than in the case of the relativistic line model at high\nstatistical confidence ($\\Delta \\chi^2$=2.7 with one {\\it additional}\ndegree of freedom).\nUnfortunately, the statistics is not high enough to study the low and\nthe high state separately in the framework of this model and, in particular,\nvariations of the absorption line between the low--state and the\nhigh--state: in both cases the best fit\nvalue for the iron emission line energy\nis lower than the canonical one, but the shift is significant only\nat a $\\Delta \\chi^2 \\sim 2$ level and therefore the absorption line\ncannot be well constrained.\n\nThe redshift of the\nFe line could be simply due to random\nfluctuations (the signal-to-noise in our spectrum\n is not very high). To check this possibility\nwe performed a simulation by means of the XSPEC 10 code\nby using a very high integration time and with the same parameters as above\n(without absorption).\nAfter convolving with the response\nmatrix of the MECS instrument, we fitted the simulated spectrum\nwith a\nsingle gaussian (in emission).\nThe best fit of the resulting spectrum is a gaussian at E=6.3 keV and EW=190\nkeV, in agreement with what\nobserved in\nNGC 1365 (after correction for the continuum cold absorption), thus\nconfirming that the combination of the emission and the absorption lines\nresults in a redshifted observed lines and that the effect is not due\nto the limited signal-to-noise.\n\nSummarizing, a possible scenario to explain the Fe line profile in the BeppoSAX\nspectrum is that a broad iron emission line is formed at\nthe surface of the central accretion disk (similarly to what is observed in\nseveral Sy1s) and then it is partially absorbed by a warm circumnuclear\ngas that causes an apparent redshift of the cold line centroid.\n\nAs discussed above, for the\nabsorption system to be effective in redshifting the centroid of the\ncold\nemission line the column density of the warm absorber must be\n$N_{\\rm warm} \\simeq 10^{23}$cm$^{-2}$ or higher. \nAlthough observed in some Sy1s,\ntypically warm absorbers have column densities significantly lower\n(Reynolds 1997).\nPossibly, as illustrated in Fig. 4,\nthe warm absorber is preferentially distributed in the equatorial plane\nof\nthe torus/disk system and, as a consequence, the edge--on lines of sight\n(as it is probably\nthe case for NGC1365) are characterized by higher column densities\nof the warm gas.\n\nThe warm absorption model is favored both because it fits better\nthe observed data and because the relativistic line model requires a\ngeometry\nthat is improbable for this object. However, the relativistic line model\ncannot be rejected.\n\n\\begin{thebibliography}{99}\n\\bibitem{a1}\nAlloin D., Edmunds M.G., Lindblad P.O., Pagel B.E.J., 1981, A\\&A 191, 377\n\\bibitem{a2}\nAntonucci R.R.J., 1993, ARA\\&A 31, 473\n\\bibitem{a2bis}\nAwaki H., Nagoya University, PH D thesis\n\\bibitem{a3}\nBassani L., Dadina M., Maiolino R., et al., 1999, ApJS, 121, 473\n\\bibitem{a4}\nBoella G., Butler R. C., Perola G. C., et al., 1997, A\\&AS 122, 299\n\\bibitem{a5}\nFabbiano G., Kim D.W., Trincheri G., 1992, ApJS 80,531\n\\bibitem{a6}\nGallimore J.F., Baum S.A., O'Dea C.P., 1997, Nat 388, 852\n\\bibitem{a7}\nGhisellini G., Haardt F., Matt G., 1994, MNRAS 267, 743\n\\bibitem{a8}\nGreenhill L.J., Gwinn C.R., 1997, Ap\\&SS 248, 261\n\\bibitem{a9}\nGuainazzi M., Nicastro F., Fiore F., et al., 1998, MNRAS 301 L1\n\\bibitem{a10}\nIwasawa K., Fabian A. C., Brandt W. N., et al., 1998, MNRAS 295, L25\n\\bibitem{a11}\nIyomoto N., Makishima K., Fukazawa Y., et al., 1997, PASJ 48, 425 (I97)\n\\bibitem{a12}\nKomossa S., Greiner J., 1999, Proceedings of ``High Energy Processes in\nAccreting Black Holes'',\n J. Poutanen, R. Svensson (eds), ASP Conf. Ser., 228. \n(astro-ph 9810105)\n\\bibitem{a13}\nKomossa S., Schulz H., 1998, A\\&A 339, 345.\n\\bibitem{a13bis}\nMadore B. F., Freedman W. L., Silbermann N., et al., 1998, Nat 395, 47\n\\bibitem{a14}\nMaiolino R., Salvati M., Bassani L., et al., 1998, A\\&A 338, 781 (M98)\n\\bibitem{a15}\nMatt G., 1994, MNRAS 267, L17\n\\bibitem{a16}\nMatt G., Perola G. C., Piro L., 1991, A\\&A 247, 25\n\\bibitem{a17}\nMatt G., Brandt W. N., Fabian A.C. 1996, MNRAS 280, 823\n\\bibitem{a19}\nReynolds C.S., 1997, MNRAS, 286, 513\n\\bibitem{a20}\n\\end{thebibliography}\n\n\\end{document}\n\n--------------FECDD77F533B87B55566F5FB--\n\n\n"
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"name": "astro-ph0002169.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{a1}\nAlloin D., Edmunds M.G., Lindblad P.O., Pagel B.E.J., 1981, A\\&A 191, 377\n\\bibitem{a2}\nAntonucci R.R.J., 1993, ARA\\&A 31, 473\n\\bibitem{a2bis}\nAwaki H., Nagoya University, PH D thesis\n\\bibitem{a3}\nBassani L., Dadina M., Maiolino R., et al., 1999, ApJS, 121, 473\n\\bibitem{a4}\nBoella G., Butler R. C., Perola G. C., et al., 1997, A\\&AS 122, 299\n\\bibitem{a5}\nFabbiano G., Kim D.W., Trincheri G., 1992, ApJS 80,531\n\\bibitem{a6}\nGallimore J.F., Baum S.A., O'Dea C.P., 1997, Nat 388, 852\n\\bibitem{a7}\nGhisellini G., Haardt F., Matt G., 1994, MNRAS 267, 743\n\\bibitem{a8}\nGreenhill L.J., Gwinn C.R., 1997, Ap\\&SS 248, 261\n\\bibitem{a9}\nGuainazzi M., Nicastro F., Fiore F., et al., 1998, MNRAS 301 L1\n\\bibitem{a10}\nIwasawa K., Fabian A. C., Brandt W. N., et al., 1998, MNRAS 295, L25\n\\bibitem{a11}\nIyomoto N., Makishima K., Fukazawa Y., et al., 1997, PASJ 48, 425 (I97)\n\\bibitem{a12}\nKomossa S., Greiner J., 1999, Proceedings of ``High Energy Processes in\nAccreting Black Holes'',\n J. Poutanen, R. Svensson (eds), ASP Conf. Ser., 228. \n(astro-ph 9810105)\n\\bibitem{a13}\nKomossa S., Schulz H., 1998, A\\&A 339, 345.\n\\bibitem{a13bis}\nMadore B. F., Freedman W. L., Silbermann N., et al., 1998, Nat 395, 47\n\\bibitem{a14}\nMaiolino R., Salvati M., Bassani L., et al., 1998, A\\&A 338, 781 (M98)\n\\bibitem{a15}\nMatt G., 1994, MNRAS 267, L17\n\\bibitem{a16}\nMatt G., Perola G. C., Piro L., 1991, A\\&A 247, 25\n\\bibitem{a17}\nMatt G., Brandt W. N., Fabian A.C. 1996, MNRAS 280, 823\n\\bibitem{a19}\nReynolds C.S., 1997, MNRAS, 286, 513\n\\bibitem{a20}\n\\end{thebibliography}"
}
] |
astro-ph0002170
|
Measuring the Nonlinear Biasing Function\\ from a Galaxy Redshift Survey
|
[
{
"author": "Yair Sigad\\altaffilmark{1}"
},
{
"author": "Enzo Branchini\\altaffilmark{2}"
},
{
"author": "\\& Avishai Dekel\\altaffilmark{1}"
}
] |
We present a simple method for evaluating the nonlinear biasing function of galaxies from a redshift survey. The nonlinear biasing is characterized by the conditional mean of the galaxy density fluctuation given the underlying mass density fluctuation $\coav$, or by the associated parameters of mean biasing $\bh$ and nonlinearity $\bt$ (following Dekel \& Lahav 1999). Using the distribution of galaxies in cosmological simulations, at smoothing of a few Mpc, we find that $\coav$ can be recovered to a good accuracy from the cumulative distribution functions of galaxies and mass, $\cg(\delg)$ and $\cm(\delm)$, despite the biasing scatter. Then, using a suite of simulations of different cosmological models, we demonstrate that $\cm(\delm)$ can be approximated in the mildly nonlinear regime by a cumulative log-normal distribution of $1+\delm$ with a single parameter $\sigm$, with deviations that are small compared to the difference between $\cg$ and $\cm$. Finally, we show how the nonlinear biasing function can be obtained with adequate accuracy directly from the observed $\cg$ in redshift space. Thus, the biasing function can be obtained from counts in cells once the rms mass fluctuation at the appropriate scale is assumed a priori. The relative biasing function between different galaxy types is measurable in a similar way. The main source of error is sparse sampling, which requires that the mean galaxy separation be smaller than the smoothing scale. Once applied to redshift surveys such as PSC$z$, 2dF, SDSS, or DEEP, the biasing function can provide valuable constraints on galaxy formation and structure evolution.
|
[
{
"name": "cpdf.tex",
"string": "\\documentstyle[12pt,aaspp4,flushrt]{article}\n%\n%-------------------------------------\n% DEFINITIONS\n\\overfullrule 0pt\n%\\input psfig\n\\def\\fig #1, #2, #3 {\n \\smallskip\n \\centerline{\\psfig{figure=#1,height=#2 in,width=#3 in}} }\n\\def\\capt{\\small \\baselineskip 12pt }\n\n\\def\\eq#1{(\\ref{eq:#1})}\n\\def\\equ#1{equation~(\\ref{eq:#1})}\n\\def\\eqd#1{eq.~[\\ref{eq:#1}]}\n\\def\\se#1{\\S\\ref{sec:#1}}\n\\def\\Figu#1{Figure~\\ref{fig:#1}}\n\\def\\Fig#1{Fig.~\\ref{fig:#1}}\n\\def\\figg#1{figure~\\ref{fig:#1}}\n\n\\def\\cl{\\centerline}\n\\def\\\\{\\hfill\\break}\n\\def\\no{\\noindent}\n\\def\\etal{{\\it et al.\\ }}\n\\def\\rms{{\\it rms\\ }}\n\\def\\cf{{\\it cf. }}\n\\def\\eg{{e.g.}}\n\\def\\ie{{i.e.}}\n\n\\def\\vev#1{\\langle#1\\rangle}\n\\def\\av{\\vev}\n\\def\\vevbig#1{\\left\\langle#1\\right\\rangle}\n\\def\\la{\\langle}\n\\def\\ra{\\rangle}\n\\def\\be{\\begin{equation}}\n\\def\\ee{\\end{equation}}\n\\newcommand{\\brr}{\\begin{array}}\n\\newcommand{\\err}{\\end{array}}\n\n\\def\\ifm#1{\\relax\\ifmmode#1\\else$\\mathsurround=0pt #1$\\fi}\n\\def\\kms{\\ifmmode\\,{\\rm km}\\,{\\rm s}^{-1}\\else km$\\,$s$^{-1}$\\fi} \n\\def\\hmpc{\\,\\ifm{h^{-1}}{\\rm Mpc}}\n\\def\\dd{d}\n\\def\\d{{\\rm d}}\n\\def\\pa {\\partial}\n\\def\\msolar{M_{\\odot}}\n\\def\\hmsun{h^{-1}\\msolar}\n\n\\def\\ltsima{$\\; \\buildrel < \\over \\sim \\;$}\n\\def\\lsim{\\lower.5ex\\hbox{\\ltsima}}\n\\def\\gtsima{$\\; \\buildrel > \\over \\sim \\;$}\n\\def\\gsim{\\lower.5ex\\hbox{\\gtsima}}\n \n%Bold face and vectors:\n\\def\\pmb#1{\\setbox0=\\hbox{#1}%\n \\kern-.025em\\copy0\\kern-\\wd0\n \\kern.05em\\copy0\\kern-\\wd0\n \\kern-.025em\\raise.0433em\\box0}\n%\n\\def\\vv{\\pmb{$v$}}\n\\def\\vx{\\pmb{$x$}}\n\\def\\vr{\\pmb{$r$}}\n\\def\\vk{\\pmb{$k$}}\n\\def\\vnabla{\\pmb{$\\nabla$}}\n\\def\\div{\\vnabla\\!\\cdot\\!}\n\\def\\rot{\\vnabla\\!\\times\\!}\n\\def\\divv{\\div\\vv}\n\\def\\rotv{\\rot\\vv}\n\n\n\\def\\ssize{\\tiny}\n\\def\\betai{\\beta_{\\ssize I}}\n\\def\\bi{b_{\\ssize I}}\n\\def\\om{\\Omega_{\\rm m}}\n\\def\\ol{\\Omega_\\Lambda}\n\\def\\bh{\\hat{b}}\n\\def\\bt{\\tilde{b}}\n\n%LOCAL:\n\\def\\bha{\\hat{b}_{\\rm a}}\n\\def\\bta{\\tilde{b}_{\\rm a}}\n\\def\\sigb{\\sigma_{\\rm b}}\n\\def\\delg{\\delta_{\\rm g}}\n\\def\\delgz{\\delta_{\\rm g,z}}\n\\def\\delmz{\\delta_{\\rm z}}\n\\def\\delhz{\\delta_{\\rm g,z}}\n\\def\\delo{\\delta_{\\rm obs}}\n\\def\\dellnz{\\delta_{\\rm ln,z}}\n\\def\\delgone{\\delta_{\\rm g_1}}\n\\def\\delgtwo{\\delta_{\\rm g_2}}\n\\def\\delm{\\delta}\n\\def\\del{\\delta}\n\\def\\delh{\\delta_{\\rm g}}\n\\def\\coav{\\langle\\delg \\vert\\delm\\rangle}\n\\def\\coavh{\\langle\\delg \\vert\\delm\\rangle}\n\\def\\sigm{\\sigma}\n\\def\\sig{\\sigma}\n\\def\\sigmz{\\sigma_{\\rm z}}\n\\def\\sigg{\\sigma_{\\rm g}}\n\\def\\sigh{\\sigma_{\\rm g}}\n\\def\\cg{C_{\\rm g}}\n\\def\\cgz{C_{\\rm g,z}}\n\\def\\chz{C_{\\rm g,z}}\n\\def\\cgone{C_{\\rm g_1}}\n\\def\\cgtwo{C_{\\rm g_2}}\n\\def\\cm{C}\n\\def\\cmz{C_{\\rm z}}\n\\def\\ch{C_{\\rm g}}\n\\def\\pln{P_{\\rm ln}}\n\\def\\cln{C_{\\rm ln}}\n\\def\\clnz{C_{\\rm ln,z}}\n\\def\\clnm{C_{\\rm ln}(\\delta ; \\sigm)}\n\\def\\clng{C_{\\rm ln}(\\delta ; \\sigg)}\n\\def\\clnh{C_{\\rm ln}(\\delta ; \\sigh)}\n\\def\\neff{N_{\\rm eff}}\n\\def\\volbox{V_{\\rm box}}\n\\def\\vwin{V_{\\rm win}}\n\n%----------------------------------------------------------\n\n\n\\begin{document}\n%YS9 \\hfill\\today\n\\medskip\n\\baselineskip 14pt \n\n\\title{Measuring the Nonlinear Biasing Function\\\\\n from a Galaxy Redshift Survey}\n \n\\author{Yair Sigad\\altaffilmark{1}, \nEnzo Branchini\\altaffilmark{2},\n\\& Avishai Dekel\\altaffilmark{1} }\n\n\\altaffiltext{1}{Racah Institute of Physics, The Hebrew University,\nJerusalem 91904, Israel}\n\\altaffiltext{2}{Kapteyn Institute, University of Groningen,\nLandleven 12, 9700 AV, Groningen, The Netherlands}\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{abstract}\n\n\nWe present a simple method for evaluating the nonlinear biasing function of \ngalaxies from a redshift survey. The nonlinear biasing is characterized by \nthe conditional mean of the galaxy density fluctuation given the underlying \nmass density fluctuation $\\coav$, or by the associated parameters of mean \nbiasing $\\bh$ and nonlinearity $\\bt$ (following Dekel \\& Lahav 1999). Using \nthe distribution of galaxies in cosmological simulations, at smoothing of a \nfew Mpc, we find that $\\coav$ can be recovered to a good accuracy from the \ncumulative distribution functions of galaxies and mass, $\\cg(\\delg)$ and \n$\\cm(\\delm)$, despite the biasing scatter.\nThen, using a suite of simulations of different cosmological models, we \ndemonstrate that $\\cm(\\delm)$ can be approximated in the mildly nonlinear \nregime by a cumulative log-normal distribution of $1+\\delm$ with a single \nparameter $\\sigm$, with deviations that are small compared to the difference \nbetween $\\cg$ and $\\cm$.\nFinally, we show how the nonlinear biasing function can be \nobtained with adequate accuracy directly from the observed $\\cg$ in redshift \nspace. Thus, the biasing function can be obtained from counts in cells once the\nrms mass fluctuation at the appropriate scale is assumed a priori. The relative\nbiasing function between different galaxy types is measurable in a similar way.\nThe main source of error is sparse sampling, which requires that the mean \ngalaxy separation be smaller than the smoothing scale. Once applied to redshift\nsurveys such as PSC$z$, 2dF, SDSS, or DEEP, the biasing function can\nprovide valuable \nconstraints on galaxy formation and structure evolution.\n\n\\end{abstract}\n\n\\subjectheadings{cosmology: theory --- cosmology: observation ---\ndark matter --- galaxies: distances and redshifts --- \ngalaxies: formation --- galaxies: clustering ---\nlarge-scale structure of universe}\n\n\\vfill\\eject\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{INTRODUCTION}\n\\label{sec:intro}\n\nThe fact that galaxies of different types cluster differently \n(\\eg, Dressler 1980; Lahav, Nemiroff \\& Piran 1990; Santiago \\& Strauss 1992; \nLoveday \\etal 1995; Hermit \\etal 1996; Guzzo \\etal 1997) \nindicates that the galaxy distribution is in general biased compared \nto the underlying mass distribution. \nCosmological simulations confirm that halos and galaxies \nmust be biased (\\eg, Cen \\& Ostriker 1992; Kauffmann, Nusser \\&\nSteinmetz 1997; Blanton \\etal 1999; Somerville \\etal 2000).\nThe biasing becomes even more pronounced at high redshift,\nas predicted by theory (\\eg, Kaiser 1986; Davis \\etal 1985;\nBardeen \\etal 1986; Dekel \\& Rees 1987; Mo \\& White 1996; \nBagla 1998; Jing \\& Suto 1998; Wechsler \\etal 1998), \nand confirmed by the strong clustering of galaxies observed\nat $z\\sim 3$ (Steidel \\etal 1996; 1998).\nKnowing the biasing scheme is crucial for extracting dynamical\ninformation and cosmological constants from the observed galaxy distribution,\nand may also be very useful for understanding the process and history\nof galaxy formation.\n \nThe simplest possible biasing model relating the density fluctuation\nfields of matter and galaxies, $\\delm$ and $\\delg$,\nis the deterministic and linear\nrelation, $\\delg(\\vx)=b\\,\\delta(\\vx)$, where $b$ is a constant linear\nbiasing parameter. However, this is at best a crude approximation,\nbecause it is not self-consistent (\\eg, it does not prevent $\\delg$ from\nbecoming smaller than $-1$ when $b>1$) and is not preserved in time.\nAt any given time, scale and galaxy type, the biasing is expected in general \nto be nonlinear, i.e., $b$ should vary as a function of $\\delta$.\nThe nonlinearity of dark-matter halo biasing (as well as its dependence \non scale, mass and time) is approximated fairly well by the model of \nMo \\& White (1996), based on the extended Press-Schechter formalism \n(Bond \\etal 1991).\nImproved approximations have been proposed by \nJing (1998), Catelan \\etal (1998), Sheth \\& Tormen (1999) and Porciani\n\\etal (1999). \nIt is quantified further for halos and galaxies \nusing cosmological $N$-body simulations with semi-analytic\ngalaxy formation (\\eg, Somerville \\etal 2000).\n%\nThe biasing is also expected, in general, to be stochastic, in the sense that\na range of values of $\\delg$ is possible for any given value of $\\delm$.\nFor example, if the biasing is nonlinear on one scale, \nit should be different \nand non-deterministic on any other scale.\nThe origin of the scatter is shot noise as well as the influence\nof physical quantities other than mass density (\\eg, velocity\ndispersion, \n%dimensionality of local deformation, \nthe dimensionality of the local deformation tensor which affects \nthe shape of the collapsing object,\netc.) on the efficiency\nof galaxy formation.\n\nDekel \\& Lahav (1999) have proposed a general formalism\nfor galaxy biasing, that separates nonlinearity and stochasticity in a\nnatural way. The density fields are treated as random fields, and the\nbiasing is fully characterized by the conditional probability distribution \nfunction $P(\\delg\\vert\\delm)$.\nThe constant linear biasing factor $b$ is replaced by a mean {\\it biasing\nfunction}, \n\\be\n\\coav\\equiv b(\\delm)\\,\\delm ,\n\\label{eq:cond_def}\n\\ee\nwhich can in principle take a wide range of functional forms,\nrestricted by definition to have $\\av{\\delg}=0$ and $\\coav\\geq -1$ \nfor any $\\delm$.\nThe stochasticity is expressed by the higher moments about this mean, \nsuch as the conditional variance\n\\be\n\\sigb ^2(\\del) \\equiv \\av{\\epsilon^2 |\\delm} /\\sigma^2 ,\n\\quad \\epsilon \\equiv \\delg-\\av{\\delg|\\delm} \\ ,\n\\ee\nscaled for convenience by the variance of mass fluctuations, \n$\\sigma^2\\equiv\\av{\\delm^2}$.\n%\nTo second order, the biasing function $b(\\del)$ can be characterized \nby two parameters: the moments $\\bh$ and $\\bt$, \n\\be\n\\bh \\equiv\\ \\av{b(\\del)\\, \\del^2} /\\sig^2\n\\quad {\\rm and} \\quad\n\\bt^2 \\equiv\\ \\av{b^2(\\del)\\, \\del^2} /\\sig^2 \\ .\n\\ee\nThe parameter $\\bh$ is the natural extension of the linear biasing\nparameter, measuring the slope of the linear regression of $\\delg$ on\n$\\delm$, and $\\bt/\\bh$ is a useful measure of non-linearity.\nThe stochasticity is characterized independently by a third parameter,\n$\\sigb ^2 \\equiv \\av{\\epsilon^2}/\\sig^2$.\nAs has been partly explored by Dekel \\& Lahav (1999),\nthese parameters should enter any nonlinear analysis aimed at extracting \nthe cosmological density parameter $\\Omega$ from a galaxy redshift survey, \nand are therefore important to measure.\n\nIn this paper we propose a simple method to measure the biasing function\n$b(\\delta)$ and the associated parameters $\\bh$ and $\\bt$ from observed\ndata that are either already available, such as the PSC$z$ redshift \nsurvey (Saunders \\etal 2000), or that will soon become available, \nsuch as the redshift surveys of 2dF (Colless 1999) and SDSS \n(\\eg, Loveday \\etal 1998)\nand high-redshift surveys such as DEEP (Davis \\& Faber 1999).\n%\nAlternative methods have been proposed to measure the \nbiasing function, using the cumulant correlators of the observed \ndistribution of galaxies in redshift surveys (Szapudi 1998)\nor their bispectrum (Matarrese, Verde, Heavens 1997, Verde \\etal 1998).\n\nWe first show in \\se{CDF}, using halos and galaxies in $N$-body simulations,\nthat the difference between the cumulative\ndistribution functions (CDFs) of galaxies and mass can be straightforwardly\ntranslated into $\\coav$ despite the scatter in the biasing scheme.\nThen, in \\se{rob}, we demonstrate that for our purpose,\n$\\cm(\\delm)$ is insensitive to the cosmological model and can be \napproximated robustly by a cumulative log-normal distribution.\nThis means that we do not need to observe $\\cm(\\delta)$, which is hard to\ndo; we only need to measure $\\cg(\\delg)$ and, independently,\nthe rms value $\\sigm$ of the mass fluctuations on the same scale. \nIn \\se{redshift}, \nwe slightly modify the method to account for redshift-space distortions,\nand use mock galaxy catalogs from N-body simulations to evaluate the\nassociated errors.\nFinally, in \\se{errors}, we estimate the errors due to the sparse\nsampling and finite volume. \nThe method and its applications to existing and future data are\ndiscussed in \\se{conc}.\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{BIASING FUNCTION FROM DISTRIBUTION FUNCTIONS}\n\\label{sec:CDF}\n\nLet $\\cg(\\delg)$ and $\\cm(\\delm)$ be the cumulative distribution\nfunctions of the density fluctuations of galaxies and mass respectively\n(at a given smoothing window).\nHad the biasing relation been deterministic and monotonic, it could have\nbeen determined straightforwardly from the difference between these CDFs\nat given percentiles,\n\\be\n\\delg(\\del) = \\cg^{-1} [\\cm(\\del)] \\ , \n\\label{eq:cc}\n\\ee\nwhere $\\cg^{-1}$ is the inverse function of $\\cg$.$\\,$\\footnote{A similar \nrelation has been used by Narayanan \\& Weinberg (1998) for ``debiasing\" \nthe galaxy density field for the purpose of dynamical reconstruction.}\nIn the presence of scatter in the biasing scheme, strict monotonicity is\nviolated, but it is possible that $\\cg^{-1} [\\cm(\\del)]$ is still\na good approximation for $\\coav$, \n%which {\\it is} likely to be monotonic. \nas long as the latter is monotonic.\\footnote{The absence of spiral\ngalaxies in the centers of rich clusters may result in a non-monotonic\nbiasing function for this type of galaxies at small smoothing scales,\nas hinted in Blanton \\etal (1999). However, using the simulations\ndescribed in this section, \nSomerville \\etal (2000) do not find non-monotonicity for late \ntype galaxies at $8\\hmpc$ smoothing, as used in \\Figu{cc_rel}\nbelow.}\nThe validity of this approximation is addressed in the present section.\n\nWe use two cosmological $N$-body simulations in which \nboth halos and galaxies were identified (Kauffmann \\etal 1999).\nThe cosmological models are $\\tau$CDM (with $\\om=1$ and $h=0.5$)\nand $\\Lambda$CDM (with $\\om=0.3$, $\\ol=0.7$ and $h=0.7$).\n$N=256^3$ particles were simulated in a periodic box of comoving size $85$ and \n$141\\hmpc$ respectively (corresponding to a mass resolution of\n$1.0\\cdot 10^{10}h^{-1}M_{\\odot}$ and $1.4\\cdot 10^{10}h^{-1}M_{\\odot}$).\nThe simulations were run\nusing a parallel adaptive P$^3$M code kindly made available by\nthe Virgo Consortium (see Jenkins \\etal 1998) as part of the\n``GIF'' collaboration between the HU Jerusalem and the MPA Munich.\nThe present epoch is defined by a linear rms density fluctuation in\na top-hat sphere of radius $8\\hmpc$ of\n$\\sigma_8=0.6$ in the $\\tau$CDM simulation and $\\sigma_8=0.9$ in the\n$\\Lambda$CDM simulation. \nDark-matter halos were identified at densely sampled time steps using a\nfriends-of-friends algorithm.\nGalaxies were identified inside these halos by applying in retrospect\nsemi-analytic models (SAMs) of galaxy formation (Kauffmann \\etal 1999).\nThe SAMs simulate the important physical processes of galaxy formation\nsuch as gas cooling, star formation and supernovae feedback. \nAt different times in the redshift range 0 to 3, \nwe select halos by mass and galaxies by luminosity or type.\n%\nWe then compute density fields by applying top-hat smoothing with radii\nin the range $5-15\\hmpc$. We report detailed results for the case\nof $8\\hmpc$ smoothing, and refer to the scale dependence in several places.\n\n\\begin{figure} [t!]\n%1\n\\vspace{11.0truecm}\n{\\special{psfile=\"fig1.ps\" angle=-90\n hscale=60.0 vscale=60.0 hoffset=-5 voffset=350}}\n%vspace - space between line above plot and caption\n%hoffset - moves plot sideways (larger value moves right)\n%voffset - moves plot up & down (larger value moves up)\n\\caption{\\capt\nCDFs and the biasing function at different redshifts\nfor $\\tau$CDM halos with $M> 10^{12}h^{-1}\\msolar$ and TH8 smoothing. \n{\\it Top panels}: the matter $\\cm(\\del)$ (solid) and the halo $\\ch(\\delh)$ \n(dashed). Also shown is a log-normal distribution (dotted), largely hidden \nbehind the exact mass distribution. \n{\\it Bottom Panels}: $\\delh(\\vx)$ versus $\\del(\\vx)$ at grid points\nwithin the simulation box.\nThe true mean biasing function $\\coavh$ is marked by the filled circles\nwith error bars. Shown in comparison (solid line) is the approximation\nobtained by \\equ{cc} from the CDFs and the corresponding $1\\sigma$ error \nrange (dotted).\n}\n\\label{fig:cc_h}\n\\end{figure}\n\nThe figures of this section illustrate the success of the\napproximation, \\equ{cc}, in several different cases based on the\n$\\tau$CDM simulation, with top-hat smoothing of radius $8\\hmpc$\n(hereafter TH8, or TH$X$ for radius $X\\hmpc$), \nand at different redshifts.\n\\Figu{cc_h} refers to halos of mass $> 10^{12}h^{-1}\\msolar$ \n($>100$ particles).\nOn the top we show the cumulative distributions of halos and underlying \nmass fluctuations, $\\ch(\\delh)$ and $\\cm(\\del)$\n(our notation does not distinguish between halos and galaxies).\nThe errors in $\\ch$ are computed from 20 bootstrap simulations \nof the halo field. The errors in $\\cm$, estimated in the same way, \nare smaller by an order of magnitude and are therefore not shown. \nThe bottom panels show a point-by-point comparison of the TH8 fields \nof $\\delh(\\vx)$ and $\\del(\\vx)$ at points randomly chosen (1:8)\nfrom a uniform grid of spacing $2.64\\hmpc$ within the simulation box.\nThe true mean biasing function $\\coavh$ \nis marked by the filled circles with attached error bars. \nIt is computed by a local linear regression of $\\delh$ on $\\delta$ within \neach bin of $\\delta$, adopting the value of the fitted line at the \ncenter of the bin (only every other bin is shown).\nShown in comparison (solid line) is the approximation for $\\coavh$ obtained by \n\\equ{cc} from the CDFs, and the corresponding $1\\sigma$ error range based\non the bootstrap realizations (dotted lines).\n\nAs can be seen in \\Figu{cc_h}, the approximation is excellent over most\nof the $\\delta$ range --- the deviation at $z$=0 is within the\n$1\\sigma$ errors \nup to $\\delta \\sim 1.4$ (corresponding to $\\sim 97\\%$ of the volume). \nSystematic deviations show up at higher $\\delta$ values, where the \nscatter becomes larger and the mean biasing function flatter,\nmaking the deviations from monotonicity larger.\n%\nIn order to quantify the quality of the approximation, we average \nthe residuals (scaled by $\\sigg$):\n\\be\n\\Delta = {{1}\\over{N_{\\rm bins} \\sigg^2}}\n\\sum_{\\delm-{\\rm bins}}^{N_{\\rm bins}} {[\\delg(\\delm) - \\coav]^2} \\ ,\n\\label{eq:delta}\n\\ee\nwhere $\\delg(\\delm)$ is obtained via \\equ{cc}.\nWe exclude the poorly recovered high-density tail by\nlimiting the summation to those $N_{\\rm bins}$ bins of $\\delm$ for which\n$\\cm(\\delm)<0.99$ and $\\cg(\\delg)<0.99$.\n%\nThe values of $\\Delta$ in the various cases studied, including\nhalos and galaxies in $\\tau$CDM and $\\Lambda$CDM at different redshifts,\nare listed in Table~1.\nFor example, for the halos shown in \\Figu{cc_h} at $z=0$\nwe obtain $\\Delta = 0.08$, indicating that the typical error in\nthe approximation $\\delh(\\delm)$ is small compared to the actual scatter \n$\\sigh$ in the halo density field. \n\nA complementary approach for quantifying the quality of the approximation\nis by testing how well it recovers the values of the\nmoments of the biasing function, $\\bh$ and $\\bt$. In Table~1 we present \nthe values of these moments for the different cases, as computed directly \nfrom the simulation and as approximated by $\\delg(\\delm)$ \n(denoted by a subscript ``a\"). \nThese biasing parameters are computed based on 99.9\\% of the volume,\nexcluding the\nvery highest density peaks, where the error is \nlarge\n(The only exception is at $z$=3, where we use only 99\\% of the volume\nbecause the errors are even larger).\nFor the halos shown in \\Figu{cc_h} at $z=0$,\nwe see that $\\bh$ and $\\bt$ are recovered with errors of \n1\\% and 3\\% respectively.\n\n\n\\begin{figure} [b!]\n%2\n\\vspace{11.0truecm}\n{\\special{psfile=\"fig2.ps\" angle=-90\n hscale=60.0 vscale=60.0 hoffset=-5 voffset=350}}\n%vspace - space between line above plot and caption\n%hoffset - moves plot sideways (larger value moves right)\n%voffset - moves plot up & down (larger value moves up)\n\\caption{\\capt\nSame as \\Figu{cc_h}, but for bright galaxies of $M_{\\rm B}< -21$ rather than\nmassive halos.\n}\n\\label{fig:cc_g}\n\\end{figure}\n\n\nThe middle panels of \\Figu{cc_h} refer to $z=1$, where $\\bh\\simeq 2.2$.\nThe approximation of \\equ{cc} holds well in this case \nup to $\\delm\\sim 0.7$, which corresponds to \n$\\sim 98\\%$ of the volume. \nThe approximation remains good despite the large scatter (compared\nto the $z=0$ case) because the steepness of the biasing function\nhelps maintaining reasonable monotonicity. The goodness of the\nrecovery of the biasing function, with $\\Delta = 0.07$,\nis similar to the $z=0$ case. The parameters $\\bh$\nand $\\bt$ are recovered with an accuracy of $\\sim 5\\%$ (Table~1).\n%\nThe right panels of \\Figu{cc_h} demonstrate that the approximation is \nvalid even at $z$=3, where the biasing is extremely strong, $\\bh\\simeq 6.6$. \nThe recovery of the biasing function is still good, $\\Delta = 0.20$, \nand its moments are approximated to within $\\sim 2\\%$.\n \nThe halo biasing function in the $\\Lambda$CDM cosmology is recovered,\nin general, with similar success, as can be seen in the top part \nof Table~1. \nNote that in this case the recovery actually improves at higher redshift. \nThis reflects the fact that in $\\Lambda$CDM the halo biasing scatter becomes \nsmaller at higher redshift (see Somerville \\etal 2000, Fig. 17).\nIt results from the \nsmaller shot noise due to the higher abundance of high-redshift halos \nin $\\Lambda$CDM compared to $\\tau$CDM.\n\n\n% Galaxies\n\n\\Figu{cc_g} is analogous to \\Figu{cc_h}, but now for bright galaxies of \n$M_{\\rm B}-5\\log h < -19.5$. The recovery is again\nquantified in Table~1; it is quite similar to the case of halos.\nThe typical error is $\\Delta\\leq 0.08$,\nand the biasing parameters are recovered with an error of a couple to\na few percent.\n\n\nThe performance of our method has been tested for smoothing scales\nin the range $5-15\\hmpc$. \nFor the $\\tau$CDM model, we find that the quality of the approximation\nis practically independent of scale throughout this range; \nthe relative error in the biasing parameters is at the level of a few \npercent, and $\\Delta$ is in the range 0.1 to 0.2, rather similar to the \nvalues quoted in Table~1 for TH8 smoothing. \nOn the other hand, for $\\Lambda$CDM we do find that the performance\nimproves with increasing smoothing scale.\nWith TH15 at $z=0$, for halos (or galaxies),\nthe errors in the biasing parameters reduce to below 3\\% (1\\%),\nand $\\Delta=0.07$ (0.04), while for TH5 smoothing these errors\nare about 4 times larger.\nThis difference between the two models can be attributed to a \ndifference in the scale dependence of the biasing scatter \n(Somerville \\etal 2000, Figure 16), which translates to an error\nin our method via increased deviations from monotonicity.\n\n\n% Relative Biasing\nBefore we proceed with the biasing relative to the underlying mass,\nwe note that the {\\it relative~} biasing function of two\ndifferent galaxy types, $\\av{\\delgtwo | \\delgone}$, can be directly \nobservable from a redshift survey.\nAgain, for a deterministic and monotonic biasing process one has\n\\be\n\\delgtwo (\\delgone ) = \\cgtwo^{-1}[\\cgone(\\delgone )] \\ ,\n\\label{eq:cc12}\n\\ee\nand when biasing scatter is present, the question is to what extent\n\\equ{cc12} provides a valid approximation for the true relative\nbiasing function.\n\n\n\\begin{figure} [t!]\n%1\n\\vspace{9.truecm}\n{\\special{psfile=\"fig3.ps\" angle=0\nhscale=60.0 vscale=60.0 hoffset=50 voffset=-125}}\n\\caption{\\capt\nThe relative biasing of early versus late type galaxies, at $z$=0,\nfor $\\tau$CDM (right panels) and $\\Lambda$CDM (left panels).\nThe symbols are as in \\Figu{cc_h}. \n}\n\\label{fig:cc_rel}\n\\end{figure}\n\n\\Figu{cc_rel} shows the\nrelative biasing function of ``early'' and ``late'' type galaxies\nin the two cosmological models, at $z=0$ and with TH8 smoothing.\nThese galaxy types are distinguished in the SAM $N$-body simulations\naccording to the ratio of bulge to total luminosity in the V band being\nlarger or smaller than 0.4 respectively. \nThe large scatter in the relative biasing, due to errors in the two \ndensity fields, is reduced by including all the galaxies, without applying \na luminosity cut.\n\nAs can be seen in the last three columns of Table~1, the quality of the \nrecovery of the relative biasing function is not as good as in\nthe case of the absolute biasing of galaxies or halos.\nThe values of $\\Delta$ range from 0.2 to 0.56, compared to\n0.08 to 0.16 in the former cases. This is expected, because in the\ncase of relative \nbiasing the two density fields contribute to the stochasticity\nor deviation from monotonicity \n(see also the important role of sampling \nerrors in the recovery of the biasing function, \\S4.2).\nThe moments of the relative biasing function are recovered \nwith better than 15\\% accuracy at $z\\leq 1$, and to $\\sim$25\\%\naccuracy at $z=3$, in both cosmologies. In calculating the moments,\nunlike in \\Figu{cc_rel}, a luminosity cut has been applied:\n$M_{\\rm B}-5\\log h < -19.5$, \nand 99\\% of the volume was used.\nThe fact that the $\\Delta$ values are still significantly smaller than\nunity and the errors in the biasing parameters are not larger than 25\\%\nindicate that our method is capable of yielding meaningful estimates\nof the relative biasing function.\nIn both cosmologies, the relative biasing is almost scale independent\nin the range 5 -- 15 $\\hmpc$, as is the quality of the reconstruction.\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{THE MASS CDF: ROBUST AND LOGNORMAL}\n\\label{sec:rob}\n\n%Direct recovery of the biasing field is nontrivial.\nLarge redshift surveys provide a rich body of data for mapping \nthe galaxy density field in extended regions of space and computing \nits CDF with adequate accuracy. However, direct mapping of the {\\it mass}\ndensity field is much harder. For example, POTENT reconstruction from \npeculiar velocities \n(Dekel, Bertschinger \\& Faber 1990; Dekel \\etal 1999; Dekel 2000) \nyields the mass distribution in our local cosmological neighborhood\n(even out to $\\sim 100\\hmpc$), which in principle enables direct \nmapping of the local biasing field. However, the sparse and noisy data \nlimit the mass reconstruction to low resolution ($\\sim 10\\hmpc$)\ncompared to the volume sampled, which introduces \nlarge cosmic scatter in the mass CDF. \nNew accurate data nearby, based on SBF distances (Tonry \\etal 1997)\ndo enable a promising resolution of a few Mpc (see Dekel 2000), but \nlimited to inside the local sphere of radius $\\sim 30\\hmpc$.\n\nWhat makes the method proposed here feasible is the fact that the mass\nCDF is only weakly sensitive to variations in the cosmological scenario \nwithin the range of models that are currently considered as viable\nmodels for the formation of large-scale structure (\\eg, Primack 1998,\nBahcall \\etal 1999).\nIt has been proposed that the mass PDF can be well approximated by a\nlog-normal distribution in $\\rho/\\bar\\rho=1+\\delta$\n(\\eg, Coles \\& Jones 1991; Kofman \\etal 1994),\nand it has since been argued that this approximation becomes poor \nfor certain power spectra and at the tails of the distribution\n(Bernardeau 1994; Bernardeau \\& Kofman 1995).\nIn this section, we investigate the robustness of $\\cm(\\del)$ for our\npurpose here, namely, in comparison with the typical difference between \nthe CDFs of galaxies and mass (\\ie, the mean biasing function) which we are\ntrying to approximate.\n\nWe use for this purpose a suite of $N$-body simulations of six different \ncosmological models. In addition to the two high-resolution simulations \nof $\\tau$CDM and $\\Lambda$CDM used in the previous section, \nwe have simulated three random realizations of each of the three following\nmodels (all using a Hubble constant of $h=0.5$): \nstandard CDM (SCDM; $\\om=1$ with spectral index $n=1$), \nan extreme open CDM (OCDM; $\\om=0.2$, $n=1$),\nand an extreme tilted CDM (TCDM; $\\om=1$, $n=0.6$).\nThese simulations were run by Ganon \\etal (2000, in preparation) using\na PM code (by Bertschinger \\& Gelb 1991), \nwith $128^3$ particles in a $256\\hmpc$ box.\nThe present epoch is defined in these simulations by a linear fluctuation \namplitude of $\\sigma_8=1.0$.\nA similar simulation was run using a constrained realization (CR) of the\nlocal universe based on the galaxy density in the IRAS 1.2Jy redshift survey \nunder the assumption of no biasing (Kolatt \\etal 1996), \nwith $\\om=1$ and the present defined in this case by $\\sigma_8=0.7$.\n\n\\Figu{lognormal} (left) shows for the different models the deviations \n$\\Delta \\cm(\\delta)$ of the mass CDFs, smoothed TH8, from a cumulative\nlog-normal distribution with the same $\\sigma$. \n% \nThe log-normal probability density is \n\\def\\trho{\\tilde\\rho}\n\\be\n\\pln(\\delta) = {1\\over \\trho} {1\\over \\sqrt{2\\pi} s}\n \\ \\exp \\left[-{ (\\ln\\trho-m)^2 \\over 2s^2} \\right] \\ ,\n\\label{eq:logn}\n\\ee\nwhere\n\\be\n\\trho=1+\\delta \\ , \\quad\nm=-0.5 \\ln(1+\\sigma^2) \\ , \\quad \ns^2=\\ln(1+\\sigma^2) \\quad {\\rm and} \\quad\n\\sigma^2 = \\av{\\delta^2} \\ .\n\\ee\nThe cumulative log-normal distribution is obtained by integration,\n\\be\n\\cln(\\delta) = {\\rm erf} \\left[ {\\ln\\trho - m \\over s} \\right] \\ ,\n\\label{eq:cln}\n\\ee\nwhere\n\\be\n{\\rm erf}(x) \\equiv {1\\over \\sqrt{2\\pi}} \\int_{-\\infty}^x \n e^{-t^2/2} \\dd t \\ .\n\\ee\nFor the cases of OCDM, TCDM and SCDM, the CDF \nis obtained from the three simulations of each model put together.\nThe errors are similar in the different cases; \nwe therefore plot representative error bars only for the $\\tau$CDM case. \n \nIn all the realizations that had random Gaussian initial conditions, \nthe deviation from lognormality is less than 2\\%. The constrained \nrealization shows somewhat larger deviations, but even in this case they\nnever exceed 5\\%. These deviations are indeed smaller than the\ntypical differences between $\\ch(\\delm)$ and $\\cm(\\delm)$, \nwhich are on the order of 10\\% (see \\Figu{cc_h}).\n\n\n\n\\begin{figure} [t!]\n%1\n\\vspace{7.7truecm}\n{\\special{psfile=\"fig4.ps\" angle=-90\n hscale=55.0 vscale=55.0 hoffset=0 voffset=275}}\n\\caption{\\capt\nRobustness of the mass CDF to cosmological models.\n{\\it Left}: The deviation $\\Delta C$ of the CDFs from a cumulative \nlog-normal distribution, for various CDM cosmologies at $z=0$: \n%\n$\\tau$CDM (solid); \n$\\Lambda$CDM (long-dashed); OCDM (dot-dashed); TCDM (dashed); \nSCDM (dotted); and CR (dot-long-dashed). \n%\n{\\it Right}: The approximation $\\delh(\\delm)$ based on the exact\n$\\cm({\\delm})$ (solid curve, with dotted lines marking 1-$\\sigma$ errors), \nversus the one based on the approximation $\\cm({\\delm})=\\cln(\\delm)$ instead \n(dashed curve). They lie almost on top of each other.\nThe true mean biasing function $\\coavh$ is shown for comparison\n(points with error bars).\nAll are for halos with $M>10^{12}\\hmsun$ in the $\\tau$CDM simulation.\n}\n\\label{fig:lognormal}\n\\end{figure}\n\nIn order to evaluate how important the contribution of $\\Delta C$ is \nto the error in the recovery of $\\coavh$, we compare in the right \npanel of \\Figu{lognormal} the true $\\coavh$ in the $\\tau$CDM simulation\nwith two approximations $\\delh(\\delm)$ based on \\equ{cc}, \none using the true matter CDF and the other replacing it with a \ncumulative log-normal distribution of the same $\\sigm$. The results of\nthe two approximations are very similar; the differences between them\nseem to be much smaller than the differences between each of them and the\ntrue biasing function $\\coavh$.\n%\nWe can conclude that for the purpose of recovering the biasing function, \nfor the range of \nGaussian \ncosmological models considered, $\\cln$ is a good approximation for $\\cm$. \n\nThe proximity of $\\cm$ and $\\cln$ could have been alternatively evaluated by\nthe Kolmogorov-Smirnov (KS) statistic, $D={\\rm max}\\{\\vert\\Delta C\\vert\\}$.\nFor computing the KS significance $q(D)$, we estimate the effective\nnumber of ``independent\" points by $\\neff=\\volbox/\\vwin$, where $\\volbox$ \nis the volume of the simulation box and $\\vwin$ is the effective volume of\nthe smoothing window. A value of $q\\simeq 1$ ($D\\ll 1$) corresponds to a \ngood match, and $q\\ll 1$ ($D \\simeq 1$) to a poor match.\n%\nFor our $\\tau$CDM simulation, with TH8 smoothing at $z=0$ and 1,\nwe obtain $D\\simeq 0.01$ and $q>0.9999$, confirming that $\\cln$ is a\ngood fit. However, for the larger SCDM and OCDM simulations, although\n$D$ is still only $\\simeq 0.015$, the corresponding $q$ values are at the\nlevel of only a few percent. \nFor TCDM and CR, where $D$ is 0.016 and 0.052 respectively, the values\nof $q$ drop to the level of a fraction of a percent, and the discrepancy\nseems large. This KS test indicates that the log-normal approximation \nis not always perfect for general purpose, as has been argued in \nthe literature. However, our direct tests reported above demonstrate\nthat the use of the log-normal approximation is adequate \nfor the recovery of the mean biasing function in all these cases.\n\n%Cg not expected to be ln\nWe comment in passing that\nwhile the mass CDF is well approximated for our purpose by a log-normal \ndistribution, the shape of the halo (or galaxy) CDF is usually far from \na log-normal shape. This is implied by \\equ{cc}, from which it follows that\n$\\cg (\\delg )= \\cm [\\delg ^{-1}(\\delg)]$.\nOne does not expect to recover a log-normal distribution from a\ngeneral functional form for $\\delg ^{-1}$.\nIn particular, the linear biasing model, which seems to be an acceptable\napproximation in some cases with large smoothing (\\eg, IRAS 1.2Jy galaxies \nat 12$\\hmpc$ Gaussian smoothing; Sigad \\etal 1998), \nleads to a $\\cg (\\delg)$ that is far from log-normal.\nTrying to evaluate the difference between $\\ch$ and a log-normal\ndistribution using the KS statistic, we obtain for the halos in the $\\tau$CDM\nsimulation, with TH8 smoothing, both at $z=0$ and 1,\n$D\\simeq 0.08$ and $q\\simeq 0.05$, namely a poor fit compared to the\n$q\\simeq 1$ of $\\cm$ vs $\\cln$.\nSimilar conclusions are valid for galaxies.\n\nOur method for measuring the nonlinear biasing function requires \nan assumed value of $\\sigm$. Since $\\sigm$ is known only to a limited\naccuracy (\\se{conc}), we should check the robustness of our results to\nerrors in $\\sigm$. We repeated the reconstruction described in \\se{CDF},\nboth for halos and for galaxies,\nwith perturbed values of $\\sigm$ in a range $\\pm 20\\%$ about the\ntrue value of the simulation.\nNot surprisingly, we find that the analog of the linear biasing\nparameter, $\\bh$, varies roughly in proportion to $\\sigm^{-1}$. \nWe also find that $\\bt$ varies in a similar way, such that the\nratio $\\bt/\\bh$, which is the natural measure of nonlinear biasing\n(Dekel \\& Lahav 1999), is a very weak function of $\\sigm$, \nroughly $\\bt/\\bh \\propto \\sigm^{0.15}$. This test indicates that\nour method provides a robust measure of the nonlinearity in the biasing\nscheme, that is to a large extent decoupled from the uncertainty in the\nlinear biasing parameter.\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{REDSHIFT DISTORTIONS}\n\\label{sec:redshift}\n\nThe densities as measured in redshift space (z-space)\nare in general different from the real-space (r-space)\ndensities addressed so far, because the radial peculiar velocities \ndistort the volume elements along the lines of sight.\n%\nOne approach to deal with redshift distortions is to start by recovering \nthe full galaxy density field in r-space, \nusing the linear or a mildly-nonlinear approximation to gravitational\ninstability (e.g., Yahil \\etal 1991; Strauss \\etal 1992;\nFisher \\etal 1995; Sigad \\etal 1998), \nand then compute the biasing function in r-space as outlined above.\nThe accuracy of such a procedure would be limited by the approximation\nused for nonlinear gravity.\nAnother difficulty with this approach is that it requires one to assume a\npriori a specific \nbiasing scheme, already in the force calculation that enters the \ntransformation from z-space to r-space, while this biasing scheme is \nthe very unknown we are after; this would\nrequire a nontrivial iterative procedure. \n\nThe alternative we propose here is to actually use the z-space\nCDF, $\\cgz(\\delgz)$, as provided directly from counts in cells of \ngalaxies in a redshift survey.\nIf the redshift distortions affect the densities of galaxies and mass\nin a similar way, then one may expect the biasing function in z-space to \nbe similar to the one in real space, \n\\be\n\\av{\\delgz | \\delmz\\!=\\!\\delm} = \\av{\\delg | \\delm} \\ .\n\\label{eq:bf_zr}\n\\ee\nIf we only had a robust functional form for the mass CDF in\nz-space, $\\cmz(\\delmz)$, then we could compute the desired biasing\nfunction all in z-space, using \\equ{cc} but with the analogous z-space\nquantities. We thus need to test the validity of \\equ{bf_zr}, and come up\nwith a useful approximation for $\\cmz(\\delmz)$.\n\n\n\\begin{figure} [t!]\n%1\n\\vspace{8.0truecm}\n{\\special{psfile=\"fig5.ps\" angle=-90\nhscale=60.0 vscale=60.0 hoffset=-5 voffset=300}}\n\\caption{\\capt\nBiasing functions in z-space (dashed) versus r-space (solid).\nThe biasing functions are derived from the corresponding TH8 CDFs of\nhalos and mass in the $\\tau$CDM simulation at $z=0$.\nShown are halos of $M> 10^{12}h^{-1}\\msolar$ (left) and\n$M> 5\\cdot 10^{12}h^{-1}\\msolar$ (right).\n}\n\\label{fig:bias_z1}\n\\end{figure}\n\n\\Figu{bias_z1} illustrates the accuracy of \\equ{bf_zr}.\nIt compares the biasing functions in z-space and r-space,\nas derived via \\equ{cc} and its z-space analog from the corresponding \nCDFs of halos and mass in the $\\tau$CDM simulation with TH8 smoothing.\nThe two curves are remarkably similar for $\\delm < 0.6-0.8$, \nroughly out to the 1-sigma rms fluctuation value. \nThis is roughly the range where the biasing scatter is reasonably small\nand our basic method is applicable (\\se{CDF}, \\Figu{cc_h}).\nThe curves deviate gradually as $\\delm$ increases, partly due to stronger\n``fingers of god'' effects at high densities. The deviation is somewhat\nweaker for larger-mass halos\n(perhaps due to a lower velocity dispersion for more massive objects\nas a result of dynamical friction). \n\n\nThe direction of the deviation from \\equ{bf_zr}, as seen in \\Figu{bias_z1},\ncan be obtained by applying linear theory of redshift distortions\nto the case of linear biasing in r-space, $\\delg = b \\delm$.\nIn linear theory, the density fluctuations in r-space and z-space \nare related via $\\delmz=\\delm [1+f(\\om)\\mu^2]$, where\n$f(\\om) \\simeq \\om^{0.6}$ \n(with a negligible dependence on $\\ol$,\nsee Lahav \\etal 1991) and $\\mu$ is the\ncosine of the angle between the galaxy velocity vector and the line of sight.\nIf the galaxies obey the continuity equation, then $\\delgz-\\delg=\\delmz-\\delm$,\nwhich implies the following biasing relation in z-space:\n\\be\n\\delgz = {b+f(\\om)\\mu^2 \\over 1+f(\\om)\\mu^2} \\, \\delmz \\ .\n% =b_z\\delmz$.\n\\ee\nAveraging over all possible directions and assuming\n$\\om=1$, we find that the linear biasing parameter in z-space \nis predicted to be $b_z=(3b+2)/5$ for the case shown in \\Figu{bias_z1}.\nThis indicates that the linear biasing\nparameter tends to be closer to unity in z-space than in r-space.\nBased on our empirical tests of \\equ{bf_zr}, we learn that the\nnonlinear effects (of biasing and gravity) conspire to make \\equ{bf_zr}\na better approximation than implied by the linear approximation.\n\nNote that while the results of \\Figu{bias_z1} based on our high-resolution \n$\\tau$CDM simulation are quite accurate in the way they treat halos, they may\nsuffer from significant cosmic variance due to the relatively small \nvolume sampled, where the presence (or absence) of a few ``fingers of god\" \ncould strongly affect the biasing function in the high-$\\delm$ regime.\nTo test the validity of \\equ{bf_zr} with reduced cosmic variance,\nwe appeal to yet another set of N-body simulations (by Cole \\etal 1997)\nwhich cover a much larger volume but with lower resolution.\nThese simulations followed the evolution of $N=192^3$ particles in \na periodic box of comoving side $L=345.6 \\hmpc$ \nusing an Adaptive P$^3$M code. The cosmological models are $\\Lambda$CDM \n($\\om=0.3$, $\\ol=0.7$, $h=0.65$, cluster-normalized to $\\sigma_8=1.05$)\nand $\\tau$CDM ($\\Omega=1$, $h=0.25$, cluster-normalized to $\\sigma_8=0.55$).\nNine mock catalogs were extracted from each of the parent simulations,\neach containing $\\sim 5 \\cdot 10^5$ particles in a box of $L=200 \\hmpc$. \nThe partial overlap between the catalog volumes is thus about $50\\%$.\nThe central ``observer\" was chosen to mimic certain properties of the \nLocal Group environment (see Branchini \\etal 1999).\n%\nSince the resolution of these large simulations is inadequate for a\ndetailed halo identification based on many simulated particles in each halo, \nwe identify individual particles as galaxies using a Monte-Carlo procedure\nin which the galaxies are chosen to make a random realization of an \nassumed nonlinear biasing function. Here we adopt the biasing \nfunction proposed by Dekel \\& Lahav (1999) to fit the simulated \nresults of Somerville \\etal (2000):\n\\be\n\\delg(\\delta)= \\left\\{ \\brr{ll}\n (1 + b_0)(1 + \\delta)^{b_{\\rm neg}} -1 & \\delta \\le 0 \\\\\n b_{\\rm pos}\\delta + b_0 & \\delta > 0\n \\err \\right\\} ,\n\\label{eq:nlbias}\n\\end{equation}\nwith $b_{\\rm neg}=2$ and $b_{\\rm pos}=1$.\nThe mass density field is obtained with a Gaussian smoothing of\nradius $5\\hmpc$ at the points of a $128^3$ cubic grid inside a box\nof size $200\\hmpc$.\nGalaxy densities are obtained at the grid points based on\n\\equ{nlbias}, and then interpolated to the galaxy positions as defined\nby the selected particles.\nGiven the appropriate probability distributions $P(\\delta)$,\nthe value of $b_0$ is determined for each choice of the parameters\n$b_{\\rm neg}$ and $b_{\\rm pos}$ such that $\\langle \\delg \\rangle =0$ \nas required by definition.\nWe obtain $b_0=0.26$ and $b_0=0.19$ for the models of $\\Lambda$CDM\nand $\\tau$CDM respectively.\n\n\n\n\\begin{figure}[t!]\n%1\n\\vspace{11.0truecm}\n{\\special{psfile=\"fig6.ps\" angle=0\nhscale=60.0 vscale=60.0 hoffset=50 voffset=-100}}\n\\caption{\\capt\nCDFs and biasing functions in r-space versus z-space, averaged over mock\ncatalogs that were extracted from the large $\\Lambda$CDM simulation,\nwith TH8 smoothing. \nTop: CDFs in r-space (left) and z-space (right), \nfor mass (solid) and for galaxies (dashed). \nShown in comparison is $\\clnz$ with the $\\sigmz$ of the matter (dotted).\nBottom left: the biasing functions as derived from\nthe CDFs in r-space (long-dash) and z-space (short-dash); they are\nvery similar. Also shown is the biasing function derived\nin z-space assuming $\\clnz$ with $\\sigmz$ obtained using \\equ{sigmz}\n(dotted line).\nBottom right: absolute value of the difference between the \nbiasing functions: $\\delgz(\\delmz\\!=\\!\\delm)-\\delg(\\delm)$ (dashed)\nand $\\dellnz(\\delmz\\!=\\!\\delm)-\\delg(\\delm)$ (dotted).\n}\n\\label{fig:rz_cole}\n\\end{figure}\n\n\n\\Figu{rz_cole} compares the CDFs and associated biasing functions \nin r-space and z-space, averaged over nine mock catalog from the large-box\n$\\Lambda$CDM simulation.\nThe z-space biasing function is indeed almost indistinguishable from the\nr-space one (bottom panels); the differences are typically on the order of a \ncouple of percents.\nThe results for $\\tau$CDM are similar.\n\nIn order to quantify this difference further, we define a statistic\nanalogous to \n\\equ{delta}:\n\\be\n\\Delta = {{1}\\over{N_{\\rm bins} \\sigg^2}}\n\\sum_{\\delm-{\\rm bins}} {[\\delgz(\\delmz\\!=\\!\\delm) - \\delg(\\delm)]^2} \\ ,\n\\label{eq:delta2}\n\\ee\nin which the first and second terms are the biasing functions as derived from\nthe CDFs in z-space and r-space respectively.\nThe summation is over bins with $\\delta < \\delta_{\\rm max}$, such that\n$\\approx 99\\%$ of the volume is accounted for.\nWe also compute the two moments of the observed biasing function \n$\\bh_{\\rm obs}$ and $\\bt_{\\rm obs}$.\nThese three quantities, averaged over the mock catalogs, \nare listed in Table~2 (second column). Their deviation from the\n``true'' values (Table~2, first column)\nis the systematic error. The quoted errors refer to the 1$\\sigma$\nscatter about the mean; they represent the random errors. \nThe results are listed for the two models, $\\Lambda$CDM and $\\tau$CDM. \n%\nWe conclude that the biasing function and its moments, as computed \nfrom the z-space CDFs, resemble those computed from the r-space \nCDFs to within 2\\%. \n%\nNote that the Monte Carlo procedure\nwe use to generate mock catalogs artificially reduces the amount of \nclustering and over-smoothes the density fields for dark and luminous \nparticles. The net effect is to decrease the biasing \nmoments by $\\sim 7\\%$, relative to the values implied by the biasing\nscheme, \\equ{nlbias}.\nHowever, this bias does not affect the present \nanalysis for which ``true'' values are obtained from the mock catalogs\nthemselves \nand not from \\equ{nlbias}.\n\nOur next task is to come up with a robust CDF for the mass in z-space.\nWe try the same log-normal distribution that was found robust for\nour purpose in r-space (\\se{rob}), but with a proper rms in\nz-space, $\\sigmz$.\nBased on the linear approximation for Gaussian fields in the small-angle\nlimit (Kaiser 1987), we express $\\sigmz$ in terms of $\\sigm$\nand $\\om$ of the cosmological model by:\n\\be\n\\sigmz= \\left[1 +{2\\over3}f(\\om) + {1\\over5}f^2(\\om)\\right]^{\\onehalf} \\,\\sigm.\n\\label{eq:sigmz}\n\\ee\n%where $f(\\om) \\simeq \\om^{0.6}$ (with a negligible dependence on $\\ol$,\n%see Lahav \\etal 1991).\n%\nWe thus approximate the z-space biasing function by $\\dellnz(\\delmz)$,\nas derived from the z-space CDFs but where the mass CDF is replaced by\na cumulative log-normal distribution function $\\clnz$ (\\eqd{cln}) \nwith standard deviation $\\sigmz$ (\\eqd{sigmz}).\nThe resultant biasing function, averaged over the mock catalogs,\nis displayed in the bottom panels of \\Figu{rz_cole}.\nWe see that for $\\Lambda$CDM the differences between \n$\\dellnz(\\delmz\\!=\\!\\delm)$ and $\\delg(\\delm)$ are at at the level \nof a few percent. For $\\tau$CDM they are only a bit larger; they\nexceed 10\\% but only near $\\delm \\sim 2$, at the tail of the distribution.\nThe error in the biasing function $\\Delta$ defined in analogy to \\equ{delta2},\nand the biasing moments, are listed in Table~2 (third column, marked\n``z-space ln\"). \nThe systematic error $\\Delta$ is still well below 2\\%, \nbut the biasing parameters are systematically underestimated by \n4\\% and 7\\% in $\\Lambda$CDM and $\\tau$CDM respectively. \n\nOverall, it seems that our straightforward method deals with redshift\ndistortions fairly well, without any a priori assumption about the\nbiasing scheme.\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{SAMPLING ERRORS}\n\\label{sec:errors}\n\nThe accuracy of the derivation of the galaxy PDF is limited by two \nobservational factors: the finite volume sampled and the mean density \nof galaxies in the sample.\\footnote{The additional edge effects can be greatly \nminimized by using a volume-limited sample and a proper choice of cell \ncoverage (see Szapudi \\& Colombi 1996).}\n \nIn principle, the limited volume is responsible for cosmic variance\ndue to the fact that the long-wavelength fluctuations in the real\nuniverse are not\nfairly represented in the sampled volume. This is not of major concern\nfor us here because (a) it is expected to introduce only a random error,\nand (b) as long as the biasing is local, the effects of long waves\non the PDFs of galaxies and mass are expected to be correlated, making the\nlocal biasing function representative of the universal function\ndespite the relatively small sampling volume.\n\nMore important is the {\\it shot noise} introduced by the combination of\nvolume and sampling density effects. For a given cell size (or smoothing\nlength), the error can be divided into the error in the count within each cell\nand the error due to the finite number of cells in the sample volume.\nThese shot-noise sources may introduce both random and systematic errors.\nWe evaluate them by computing the mean and standard deviation\nover a suite of mock catalogs in which we vary either the volume\nor the sampling density for a fixed smoothing scale.\n\n\\begin{figure}[b!]\n%1\n\\vspace{11.0truecm}\n{\\special{psfile=\"fig7.ps\" angle=-90\n hscale=60.0 vscale=60.0 hoffset=-5 voffset=350}}\n\\caption{\\capt\nSampling errors due to finite volume (top) and sparse sampling\n(bottom), for fixed \nTH8 smoothing, estimated from the large $\\Lambda$CDM simulation.\nShown are the CDFs in real space (left), the derived biasing function\n(middle), and the error in it (right).\nThe mass CDF is marked by a solid line, and galaxy CDFs by broken lines.\nTop: volumes of $\\neff=3700$ and 600 are marked by long-dashed and \ndotted lines respectively.\nBottom: samples of galaxy separation $l=2.5, 8,$ and $10 \\hmpc$ are marked \nby long-dashed, short-dashed, and dotted lines respectively.\n}\n\\label{fig:errors}\n\\end{figure}\n\nWith TH8 smoothing, our mock catalogs from the large $\\Lambda$CDM\nsimulation contain $\\neff \\sim 3700$ independent cells.\nHowever, the currently available redshift surveys allow\nan analysis in a much smaller volume. For example, a volume-limited\nsubsample from the PSC$z$ catalog (Saunders \\etal 2000),\nthat is cut at a distance where the average galaxy separation\nis $l=8\\hmpc$ (i.e., on the order of our smoothing scale),\ncontains only $\\sim 600$ independent cells. \nWe therefore estimate the error associated with\nreducing the sampled volume such that $\\neff\\sim 600$ in each mock catalog.\nWe select from the simulation 9 such non-overlapping sub-volumes,\nwhile keeping the sampling density and smoothing length fixed.\nThe results for $\\Lambda$CDM, averaged over the mock catalogs, are\nshown in the upper \npanels of \\Figu{errors}, and the results for the two cosmological models are\nsummarized in Table~2 (column 4).\nWe find no significant systematic errors due to the\nvolume effect in a sample like PSC$z$ and with $\\sim 8\\hmpc$ smoothing\n(except in the very high-$\\delm$ tail for $\\tau$CDM).\nThe corresponding random errors in the biasing parameters are $5\\%$\nand $6\\%$ for $\\Lambda$CDM and $\\tau$CDM respectively.\n\nThe sampling density can be parameterized by the mean galaxy separation, $l$. \nIn our large simulation $l=2.5 \\hmpc$, much smaller than the smoothing \nlength of $8\\hmpc$, but in real samples $l$ could be on the order of the \nsmoothing length. To test the effect of sampling density, we produce 9\nmock catalogs in which galaxies are sub-sampled at random from the \noriginal catalog such that the mean separation is $l=$ 6, 8, or $10 \\hmpc$,\nwhile the smoothing length and large volume are kept fixed with\n$\\neff\\sim 3700$. \nThe results for $\\Lambda$CDM are shown in the bottom panels of \\Figu{errors},\nand for the two models in Table~2 (columns 5-7).\nWe see that the sparse sampling artificially enhances both positive\nand negative density fluctuations, which enlarges the width of the\ngalaxy PDF. This results in a steeper biasing function.\nFor $\\Lambda$CDM, the effect becomes noticeable only when $l \\geq 8\\hmpc$,\nwhere the systematic error in the biasing parameters is of order 10\\%\nand larger, \nand $\\Delta$ is of order a few percent.\nFor $\\tau$CDM the sampling-density effect is noticeable already for $l\n\\sim 6\\hmpc$, \nwith the error reaching $30-50\\%$ at $\\l \\sim 10\\hmpc$.\n%\nA plausible explanation for why the sparse sampling is more damaging in the \n$\\tau$CDM model is that the clustering in this model is weaker ($\\sigma_8$ is \nsmaller to match the cluster abundance which constrains $\\sigma_8\n\\Omega^{0.5}$), \nand therefore the high-density regions are poorly sampled by galaxies.\n\nIn summary: the main source of error in our analysis is the sparse sampling. \nFor recovering the biasing function with TH8 smoothing, the mean separation \nshould be $\\leq 8\\hmpc$.\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{CONCLUSION}\n\\label{sec:conc}\n \nWe propose a simple prescription for recovering the mean\nnonlinear biasing function from a large redshift survey. \nThe biasing function is defined by $b(\\delm)\\,\\delm = \\av{\\delg | \\delm}$,\nand is characterized to second order by two parameters, \n$\\bh$ and $\\bt$, measuring the mean biasing and its nonlinearity\nrespectively. The method is applied at a given cosmology, time, object \ntype and smoothing scale, and involves one parameter that should \nbe assumed a priori --- the rms mass density fluctuation $\\sigma$ \non the relevant scale. \n\nThe main steps of the algorithm are as follows:\n\\begin{enumerate}\n\\item \nObtain the observed cumulative distribution function in redshift space \n$\\cgz(\\delgz)$, by counts in cells or with window smoothing at a \ncertain smoothing length. \n\\item\nAssume a value for $\\sigm$ on that scale and for \nthe cosmological density parameter $\\om$,\nand approximate the mass CDF in redshift space by $\\clnz(\\delmz;\\sigmz)$, the\ncumulative log-normal distribution (\\eqd{cln}), with the width $\\sigmz$ derived\nfrom $\\sigm$ and $\\om$ by \\equ{sigmz}.\n\\item \nDerive the mean biasing function by \n\\be\n\\delg (\\delm\\!=\\!\\delmz) \\simeq\n\\delgz (\\delmz ) = \\cgz^{-1} [\\clnz(\\delmz;\\sigmz)] \\ \\ . \n\\ee \n\\end{enumerate}\n\nWe first showed that the mean biasing function, at TH8 smoothing,\ncan be derived with reasonable accuracy from the r-space CDFs of \ngalaxies (or halos) and mass, despite the biasing scatter. \nWe then demonstrated that for a wide range of CDM cosmologies\nthe mass CDF can be properly approximated for this \npurpose by a log-normal distribution of the same width $\\sigm$. \nNext we showed that the biasing functions in z-space and r-space \nare very similar, and that the z-space mass CDF can also be approximated by\na log-normal distribution, with a width derived from $\\sigm$ via \\equ{sigmz}.\nThis allows us to apply the method directly to the observed CDF \nin a redshift survey.\nThe errors in the recovered biasing function and its moments, \nin an ideal case of dense sampling in a large volume, are \nat the level of a few percent.\n\nIn any realistic galaxy survey the limited volume and discrete sampling\nintroduce further random and systematic errors.\nFor a survey like the PSC$z$ survey, the main source of error is the sampling\ndensity; the error does not exceed $\\sim 10\\%$ as long as the mean observed\ngalaxy separation \nis kept smaller than the smoothing radius.\nWe are currently in the process of applying this method to the PSC$z$\nsurvey (E. Branchini, \\etal 2000, in preparation), where a more\nspecific error \nanalysis will be carried out. \nThe sampling errors are expected to be significantly smaller\nfor the upcoming 2dF and SDSS redshift surveys.\n\nIn \\se{CDF} we showed that our method works well both for halos and\nfor galaxies, on scales 5 to 15$\\hmpc$, and in the redshift range \n$0\\leq z \\leq 3$ over which the biasing is expected to change drastically.\nWe obtain a similar accuracy when we vary the cosmological model, \nthe mass of the halos in the comparison, or \ngalaxy properties such as morphological type and luminosity.\nThe approximation $\\delg(\\delta)$ is \nconsistent (the deviation is less than 1-$\\sigma$) with the true average\nbiasing function $\\coav$ \nover a wide range of $\\delm$ values, which covers 98 -- 99\\%\nof the volume, depending on redshift and the type of biased objects. \nThis allows us to estimate the moments of the biasing function to\nwithin a few percent (see Table~1).\nThe moments of the biasing function are derived from 99.9\\% of the\nvolume (99\\% at $z$=3 and for relative biasing). \n\nThe method requires as external parameters the rms mass-density\nfluctuation $\\sigm$ and the cosmological parameter $\\om$.\nThese can be obtained by joint analyses of constraints from\nseveral observational data sets, such as \nthe cluster abundance (\\eg, Eke \\etal 1998), \npeculiar velocities (\\eg, Dekel \\& Rees 1994; Zaroubi \\etal 1997; \nFreudling \\etal 1999), \nCMB anisotropies (\\eg, de Bernardis \\etal 1999),\nand type Ia supernovae (Riess \\etal 1998; Perlmutter \\etal 1999).\nExamples for such joint analyses are Bahcall \\etal (1999)\nand Bridle \\etal (1999).\n\nThe method is clearly applicable at $z\\simeq0$ with available redshift surveys\nand especially with those that will become available in the near\nfuture, 2dF and SDSS.\nIn the future, this method may become applicable at higher redshifts as well,\nwhere the biasing plays an even more important role.\nWith the accumulation of Lyman-break galaxies at $z\\sim 3$, it may soon become\nfeasible to reconstruct their PDF by counts in cells, and our\nmethod will allow a recovery of the biasing function at this early\nepoch, with consequences on galaxy formation and on the evolution of\nstructure. \n\nWe have concentrated here on smoothing scales relevant to galaxy biasing, \nbut the method may also be applicable for the biasing of galaxy clusters,\non scales of a few tens of Mpc.\nThe biasing scatter may be larger for clusters because of their sparse\nsampling, but the larger mean biasing parameter for clusters may help\nin regaining the required monotonicity for \\equ{cc} to provide a valid\napproximation to the mean biasing function.\nThe mass PDF has been checked to be properly approximated by a \nlog-normal distribution at smoothing scales in the range 20 to $40\\hmpc$,\nusing simulations of the standard CDM and Cold+Hot DM models\n(Borgani \\etal 1995). The errors due to sparse sampling would require\na smoothing scale at the high end of this range.\n\nIn a large redshift survey which distinguishes between object types,\none can measure the {\\it relative} biasing function between two object \ntypes by applying \\equ{cc12} in redshift space, using the \nobserved CDFs for the two types without appealing to the underlying\nmass distribution at all. The upcoming large redshift surveys \n2dF and SDSS, and the DEEP survey at $z\\sim 1$, are indeed expected to\nprovide adequate samples of different galaxy types. \nCompared with the predictions of simulations and semi-analytic modeling \nof galaxy formation\n(\\eg, Kauffmann \\etal 1999; Benson \\etal 1998; Baugh \\etal 1999; \nSomerville \\& Primack 1999), the measured relative biasing function\ncan provide \nvaluable constraints on the formation of galaxies and the evolution\nof structure.\n\nWhile implementing the method outlined above for measuring the mean nonlinear\nbiasing function using current and future redshift surveys,\nthe next challenge is to devise a practical method for measuring the \nbiasing scatter about the mean.\n\n%-----------------------------\n\\acknowledgments{We thank S. Cole, A. Eldar, G. Ganon, T. Kolatt, \nR. Somerville and our collaborators in the GIF team,\nJ.M. Colberg, A. Diaferio, G. Kauffmann, and S.D.M. 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P., 1991,\nApJ, 372, 3 \n\n\\reference{z} Zaroubi, S., Zehavi, I., Dekel, A., Hoffman, Y., \\& Kolatt,\nT. 1997, ApJ, 486, 21\n\n\\end{references}\n\n\\vfill\\eject\n\n%%%%%%%%%%%%%% TABLES %%%%%%%%%%%%%%%% Tables %%%%%%%%%%%%%%\n\n\n\\bigskip\\bigskip\n\\cl{\n\\begin{tabular}{cccccccccccc}\n\\multicolumn{12}{l}{ {\\bf Table 1:} Recovery of the\nbiasing function from the CDFs} \\\\\n\\hline\\hline\n\\multicolumn{12}{c}{$\\Lambda $CDM}\\\\\n%\\hline\n & \\multicolumn{3}{c}{halos vs. mass} & &\n\\multicolumn{3}{c}{galaxies vs. mass} & &\n\\multicolumn{3}{c}{early vs. late type} \\\\\n& $z$=0 & $z$=1 & $z$=3 && $z$=0 & $z$=1 & $z$=3 && $z$=0 & $z$=1 &$z$=3\\\\\n$\\bh$ &0.67 &1.21 &2.98 &&0.89 &1.31 &2.38 &&1.11 &1.32&1.28\\\\\n$\\bha$ &0.58 &1.25 &2.86 &&0.80 &1.32 &2.25 &&1.20 &1.38&1.49\\\\\n$\\bt$ &0.74 &1.24 &3.04 &&0.91 &1.31 &2.40 &&1.13 &1.34&1.30\\\\\n$\\bta$ &0.75 &1.31 &3.08 &&0.90 &1.36 &2.38 &&1.35 &1.52&1.64\\\\\n$\\Delta$ &0.16 &0.14 &0.11 &&0.08 &0.08 &0.08 &&0.55 &0.38&0.56\\\\\n\\hline\n\\multicolumn{12}{c}{$\\tau$CDM}\\\\\n%\\hline\n & \\multicolumn{3}{c}{halos vs. mass} & &\n\\multicolumn{3}{c}{galaxies vs. mass} & &\n\\multicolumn{3}{c}{early vs. late type} \\\\\n& $z$=0 & $z$=1 & $z$=3 && $z$=0 & $z$=1 & $z$=3 && $z$=0 & $z$=1 &$z$=3\\\\\n$\\bh$ &0.90 &2.18 &6.62 &&0.93 &1.71 &4.44 &&1.17 &1.34 &1.27\\\\\n$\\bha$ &0.89 &2.28 &6.75 &&0.93 &1.75 &4.32 &&1.18 &1.39 &1.50\\\\\n$\\bt$ &0.93 &2.20 &7.85 &&0.95 &1.71 &4.62 &&1.18 &1.35 &1.31\\\\\n$\\bta$ &0.96 &2.30 &8.00 &&0.98 &1.76 &4.63 &&1.26 &1.46 &1.65\\\\\n$\\Delta$ &0.08 &0.07 &0.20 &&0.08 &0.04 &0.08 &&0.22 &0.20 &0.54\\\\\n\\hline\\hline\n\\end{tabular}\n}\n%\\bigskip\\bigskip\n\n\n\\bigskip\\bigskip\\bigskip\\bigskip\n\\cl{\n\\begin{tabular}{cccccccccc}\n\\multicolumn{8}{l}{ {\\bf Table 2:}\nRedshift distortions and sampling errors in the biasing function } \\\\\n\\hline\\hline\n\\multicolumn{8}{c}{$\\Lambda $CDM}\\\\\n%\\hline\n & True & z-space & z-space ln & Volume & $l=6^a$ & $l=8^a$ & $l=10^a$ \\\\\n$\\bh$ &1.13\n&$1.12 \\pm 0.006$\n&$1.09 \\pm 0.02$\n&$1.12 \\pm 0.05$\n&$1.17 \\pm 0.05$\n&$1.23 \\pm 0.04$\n&$1.31 \\pm 0.06$ \\\\\n$\\bt$ &1.14\n&$1.12 \\pm 0.006$\n&$1.10 \\pm 0.02$\n&$1.13 \\pm 0.05$\n&$1.17 \\pm 0.05$\n&$1.24 \\pm 0.04$\n&$1.32 \\pm 0.06$ \\\\\n$\\Delta$ & --- \n&$0.001 \\pm 0.001$\n&$0.002 \\pm 0.001$\n&$0.005 \\pm 0.006$\n&$0.006 \\pm 0.006$\n&$0.016 \\pm 0.010$\n&$0.049 \\pm 0.028$ \\\\\n\\hline\n\\multicolumn{8}{c}{$\\tau $CDM}\\\\\n%\\hline\n & True & z-space & z-space ln & Volume & $l=6^a$ & $l=8^a$ & $l=10^a$ \\\\\n$\\bh$ &1.188\n&$1.18 \\pm 0.002$\n&$1.11 \\pm 0.02$\n&$1.21 \\pm 0.06$\n&$1.35 \\pm 0.07$\n&$1.55 \\pm 0.07$\n&$1.80 \\pm 0.07$ \\\\\n$\\bt$ &1.192\n&$1.18 \\pm 0.002$\n&$1.11 \\pm 0.02$\n&$1.21 \\pm 0.06$\n&$1.36 \\pm 0.07$\n&$1.55 \\pm 0.07$\n&$1.81 \\pm 0.07$ \\\\\n$\\Delta$ & --- \n&$0.002 \\pm 0.0003$\n&$0.016 \\pm 0.011$\n&$0.072 \\pm 0.063$\n&$0.177 \\pm 0.178$\n&$0.563 \\pm 0.368$\n&$1.505 \\pm 0.564$ \\\\\n\\hline\\hline\n\\multicolumn{8}{l}{$^a$ in units of $\\hmpc$ }\n\\end{tabular}\n}\n\n\n\n\n\\end{document}\n\n\n"
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The calculations in Thomas-Fermi approximation show that in a gravitational field each cell of ultra dense matter inside celestial bodies obtains a very small positive electric charge. A celestial body is electrically neutral as a whole, because the negative electric charge exists at its surface. The positive volume charge is very small, on the order of magnitude it equals to $10^{-18}e$ per atom only. But it is sufficient to explain the occurrence of magnetic fields of the celestial bodies and the existence of a discrete spectrum of steady-state values of masses of planets, stars, and pulsars.
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"string": "\n\\documentstyle[epsfig,12pt]{article}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\begin{document}\n Submitted to \"Foundation of Physics\"\n\\bigskip\n\\begin{center}\n\n{\\bf\n\\title \"Astrophysical Effects Related to Gravity-Induced Electric Polarization of Matter.}\n\n\\bigskip\n\\author \"B.V.Vasiliev\n\\bigskip\n\nInstitute in Physical and Technical Problems,Dubna,Russia,141980\n\\bigskip\n\n$e-mail: vasiliev@main1.jinr.ru$\n\\end{center}\n\n\\bigskip\n\\begin{abstract}\nThe calculations in Thomas-Fermi approximation show that in a\ngravitational field each cell of ultra dense matter inside\ncelestial bodies obtains a very small positive electric charge. A\ncelestial body is electrically neutral as a whole, because the\nnegative electric charge exists at its surface. The positive\nvolume charge is very small, on the order of magnitude it equals\nto $10^{-18}e$ per atom only. But it is sufficient to explain the\noccurrence of magnetic fields of the celestial bodies and the\nexistence of a discrete spectrum of steady-state values of masses\nof planets, stars, and pulsars.\n\\end{abstract}\n\n\\bigskip\nPACS: 64.30.+i; 95.30.-k; 97.10.-q\n\n\\clearpage\n\n\\section{Introduction}\nAccording to the conventional point of view, gravity does not\ninduce any electric polarization in the interior of celestial\nbodies and electric forces are never considered in the balance of\nmatter of celestial bodies. Moreover, it is generally assumed that\nthe electric interaction plays practically no role in\nastrophysics. It is a consequence of the comprehension that the\nappreciable electric polarization cannot arise in metals and other\nnonsegneto- and nonpiro-electric materials. It is entirely correct\nfor all substances under action of small pressure. But, thus, one\ncan disregard the fact that ultrahigh pressure transmutes all\nsubstances into plasma state and radically changes the properties\nof substance. In ultradense plasma, there is a different additional\nmechanism of the gravity-induced electric polarization.\n\nIn a large celestial body, consisting of ultradense plasma, this\ngravity-induced electric polarization (GIEP) can be rather great\nand can play a determining role in the formation of a number of\nfeatures of the structure of a celestial body and its properties.\n\nFirst of all, it concerns the following three problems, the\nstatement and the solution of which change drastically:\n\n- the distribution of pressure and density of matter inside a\ncelestial body;\n\n- the generation of a magnetic field by celestial bodies;\n\n- the formation of a spectrum of steady-state values of masses of\ncelestial bodies.\n\nAs a consequence, these features of the structure can influence\nthe evolution of stars.\n\n\n\n\n\\section{The gravity-induced electric polarization in conducting matter}\nThe action of gravity on metals has often been a topic of\ndiscussion before \\cite{1}-\\cite{6}. The basic result of these\nresearches is reduced to the statement that inside\na metal gravity induces an electric field with an intensity\n\n\\begin{equation}\n\\bf{E}\\simeq\\frac{m_{i}\\bf{g}}{e},\\label{1010}\n\\end{equation}\n\nwhere $m_{i}$ is the mass of an ion,\n\n$\\bf{g}$ is gravity acceleration,\n\n$e$ is the electron charge.\n\nThis field is so small that it is not possible to measure it\nexperimentally. It is a direct consequence of the presence of an\nion lattice in a metal. This lattice is deformed by gravity and\nthen the electron gas adapts its density to this deformation. The\nresulting field becomes very small.\n\nUnder superhigh pressure, all substances transform into ultradense\nmatter usually named nuclear-electron plasma \\cite {7}. It occurs\nwhen external pressure enhances the density of matter several\ntimes \\cite{7,8}. Such values of pressure exist inside celestial\nbodies.\n\nIn nuclear-electron plasma the electrons form the degenerated\nFermi gas. At the same time, the positively charged ions form\ninside plasma a dense packing lattice \\cite{9},\\cite{10}. As\nusually accepted, this lattice may be replaced by a lattice of\nspherical cells of the same volume. The radius $r_{s}$ of such a\nspherical cell in plasma of the mass density $\\gamma$ is given by\n\n\n\\begin{equation}\n\\frac{4\\pi}{3}r_{s}^{3}=\\biggl(\\frac{\\gamma}{m_{i}}\\biggr)^{-1}=\n\\frac{Z}{n},\\label{1020}\n\\end{equation}\n\n\nwhere Z is the charge of the nucleus, $m_{i}=Am_{p}$ is the mass\nof the nucleus, A is the atomic number of the nucleus, $m_{p}$ is\nthe mass of a proton, and n is the electron number density\n\n\\begin{equation}\nn=\\frac{3Z}{4\\pi{r_{s}^{3}}}.\\label{1030}\n\\end{equation}\n\nThe equilibrium condition in matter is described by the constancy\nof its electrochemical potential \\cite{7}. In plasma, the direct\ninteraction between nuclei is absent, therefore the equilibrium in\na nuclear subsystem of plasma (at $T=0$) looks like\n\n\\begin {equation}\n\\mu_{i}=m_{i}\\psi+Ze\\varphi=const.\\label{1040}\n\\end {equation}\n\nHere $\\varphi$ is the potential of an electric field and $\\psi$ is\nthe potential of a gravitational field.\n\nThe direct action of gravitation on electrons can be neglected.\nTherefore, the equilibrium condition in the electron gas is\n\n\\begin {equation}\n\\mu_{e}=\\frac{p_{F}^{2}}{2m_{e}}-(e-\\delta{q})\\varphi=const,\\label{1050}\n\\end {equation}\n\nwhere $m_{e}$ is the mass of an electron and $p _ {F} $ is the\nFermi momentum.\n\nBy introducing the charge $\\delta {q}$, we take into account that\nthe charge of the electron cloud inside a cell can differ from\n$Ze$. A small number of electrons can stay at the surface of a\nplasma body where the electric potential is absent. It results\nthat the charge in a cell, subjected to the action of the electric\npotential, is effectively decreased on a small value $\\delta {q}$.\nIf the radius of a star $R_{0}$ is approximately ${10^{10}cm}$,\none can expect that this mechanism gives on the order of magnitude\n$\\frac{\\delta {q}}{e}\\simeq\\frac{r_{s}}{R_{0}}\\simeq{10^{-18}}$.\n\n\nThe electric polarization in plasma is a result of changing in\ndensity of both nuclear and electron gas subsystems. The\nelectrostatic potential of the arising field is determined by the\nGauss' law\n\n\n\\begin{equation}\n\\nabla^{2}\\varphi=\\frac{1}{r^{2}}\\frac{d}{dr}\\biggl[r^{2}\\frac{d}\n{dr}\\varphi\\biggr]= -4\\pi\\biggl[Ze\\delta(r)-en\\biggr],\\label{1060}\n\\end{equation}\n\nwhere the position of nuclei is described by the function\n$\\delta(r)$.\n\nAccording to the Thomas - Fermi method, $n$ is approximated by\n\n\\begin{equation}\nn=\\frac{8\\pi}{3h^{3}}p^{3}_{F}.\\label{1070}\n\\end{equation}\n\nWith this substitution, Eq.({\\ref{1060}}) is converted into a\nnonlinear differential equation for $\\varphi$, which for $r>0$ is\ngiven by\n\n\\begin{equation}\n\\frac{1}{r^{2}}\\frac{d}{dr}\\left(r^{2}\\frac{d}{dr}\\varphi(r)\\right)=\n4\\pi\\left[\\frac{8\\pi}{3h^{3}}\\right] \\left[2m_{e}(\\mu_{e}+(e-\n\\delta{q})\\varphi)\\right]^{3/2}.\\label{1080}\n\\end{equation}\n\n\nIt can be simplified by introducing the following variables\n\\cite{11}:\n\n\n\\begin{equation}\n\\mu_{e}+(e-\\delta{q})\\varphi=Ze^{2}{\\frac{u}{r}}\\label{1090}\n\\end{equation}\n\n\nand $r=ax$,\n\nwhere\n\n$a=\\{\\frac{9\\pi^{2}}{128Z}\\}^{1/3}a_{0}$\n\nwith $ a_{0}=\\frac{\\hbar^{2}}{m_{e}e^{2}}=$ Bohr radius.\n\n\nWith the account of Eq.({\\ref{1040}})\n\n\\begin{equation}\nZe^{2}{\\frac{u}{r}}= const\n-\\frac{m_{i}\\psi}{Z}-\\delta{q}\\varphi.\\label{1092}\n\\end{equation}\n\n\n\nThen Eq.({\\ref{1080}}) gives\n\n\\begin{equation}\n\\frac{d^{2}u}{dx^{2}}=\\frac{u^{3/2}}{x^{1/2}}.\\label{1100}\n\\end{equation}\n\nIn terms of u and x, the electron density within a cell is given\nby \\cite{11}\n\n\\begin{equation}\nn_{TF}=\\frac{8\\pi}{3h^{3}}p^{3}_{F}=\n\\frac{32Z^{2}}{9\\pi^{3}a^{3}_{0}}\n\\biggl(\\frac{u}{x}\\biggr)^{3/2}.\\label{1110}\n\\end{equation}\n\nUnder the influence of gravity, the charge of the electron gas in a\ncell becomes equal to\n\n\\begin{equation}\nQ_{e}=4\\pi{e}\\int^{r_{s}}_{0}n(r)r^{2}dr=\\frac{8\\pi{e}}{3h^{3}}\n\\biggl[2m_{e}\\frac{Ze^{2}}{a}\\biggr]^{3/2}4\\pi{a}^{3}\n\\int^{x_{s}}_{0}x^{2}dx\\biggl[\\frac{u}{x}\\biggr]^{3/2}.\\label{1140}\n\\end{equation}\n\nUsing Eq.({\\ref{1100}}), we obtain\n\n\n\\begin{equation}\nQ_{e}=Ze\\int^{x_{s}}_{0}xdx\\frac{d^{2}u}{dx^{2}}=\nZe\\int^{x_{s}}_{0}dx\\frac{d}{dx}\\biggl[x\\frac{du}{dx}-u\\biggr]=\nZe\\biggl[x_{s}\\frac{du}{dx}\\bigg|_{x_{s}}-u(x_{s})+u(0)\\biggr].\n\\label{1150}\n\\end{equation}\n\nAt $ r\\rightarrow0 $ the electric potential is due to the nucleus\nalone $ \\varphi{(r)} \\rightarrow\\frac {Ze} {r} $. It means that $\nu(0)\\rightarrow1 $ and each cell of plasma obtains a small charge\n\n\n\\begin{equation}\n\\delta{q}=Ze\\biggl[{x_{s}}\\frac{du}{dx}\\bigg|_{x_{s}}-u(x_{s})\\biggr]=\nZe{x_{s}}^2\\biggl[\\frac{d}{dx}\\biggl(\\frac{u}{x}\\biggr)\\biggr]_{x_{s}}.\n\\label{1160}\n\\end{equation}\n\nFor a cell placed in the point $\\bf{R}$ inside a star\n\n\\begin{equation}\n\\delta{q}=Zer_{s}^2\\biggl[\\frac{d}{d\\bf{R}}\n\\biggl(\\frac{u}{r}\\biggr)\\biggr]\\biggl[\\frac{d\\bf{R}}{dr_{s}}\\biggr].\n\\label{1170}\n\\end{equation}\n\nConsidering that the gravity acceleration\n$\\bf{g}=-\\frac{d\\psi}{d\\bf{R}}$ and the electric field intensity\n$\\bf{E}=-\\frac{d\\varphi}{d\\bf{R}}$\n\n\n\n\\begin{equation}\n\\frac{dr_{s}}{d\\bf{R}}=\\frac{r_{s}^2}{e}\\biggl[\\frac{\\frac{m_{i}}{Z}\\bf{g}\n+\\delta{q}\\bf{E}}{\\delta{q}}\\biggr].\\label{1180}\n\\end{equation}\n\nThis equation has the following solution\n\n\\begin{equation}\n\\frac{dr_{s}}{d\\bf{R}}=0\\label{1190}\n\\end{equation}\n\nand\n\n\\begin{equation}\n\\frac{m_{i}}{Z}\\bf{g}+\\delta{q}\\bf{E}=0.\\label{1200}\n\\end{equation}\n\nIn plasma, the equilibrium value of the electric field on nuclei\naccording to Eq.({\\ref{1040}}) is determined by Eq.({\\ref{1010}})\nas well as in a metal. But there is one more additional effect in\nplasma. Simultaneously with the supporting of nuclei in\nequilibrium, each cell obtains an extremely small positive\nelectric charge.\n\nAs $div{\\bf{g}}=-4\\pi{G}{n}m_{i}$ and\n$div{\\bf{E}}=4\\pi{n}\\delta{q}$, the gravity-induced electric\ncharge in a cell\n\n\\begin{equation}\n\\delta{q}=\\sqrt{G}\\frac{m_{i}}{Z}\\simeq{10^{-18}e},\\label{1210}\n\\end{equation}\n\nwhere $G$ is the gravity constant.\n\nHowever, because the sizes of bodies may be very large, the\nelectric field intensity may be very large as well\n\n\\begin{equation}\n\\bf{E}=\\frac{\\bf{g}}{\\sqrt{G}}.\\label{2050}\n\\end{equation}\n\nIn accordance with Eqs.({\\ref{1190}},{\\ref{1200}}), the action of\ngravity on matter is compensated by the electric force and the\ngradient of pressure is absent.\n\nThus, a celestial body is electrically neutral as a whole, because\nthe positive volume charge is concentrated inside the charged core\nand the negative electric charge exists on its surface and so one\ncan infer gravity-induced electric polarization of a body.\n\n\\section{Pressure distribution inside a celestial body.}\n\nAs at the surface of a celestial body pressure is absent, near\nthis surface there is always a stratum where plasma and\npolarization are absent. For the large stars, the size of this stratum\nis insignificant. But for a small planet it can comprise a\nsubstantial part of a planet, and thus, only a small relatively\ninternal region will be polarized. At the surface of this core,\nthe electric field intensity falls to zero. The jump in the\nelectric field intensity is accompanied on the surface of the core\nby the pressure jump $\\Delta p(R_{N})$(\\cite{12}-\\cite{13}). The\nimportant astrophysical consequence of the GIEP effect is the\nredistribution of the matter density inside a celestial body. In a\ncelestial body, consisting of matter with an atomic structure,\ndensity and pressure grow monotonously with depth. In a celestial\nbody, consisting of electron-nuclear plasma, the GIEP effect results\nin the fact that the pressure gradient inside the polarized core\nis absent and the matter density is constant. Pressure affecting the\nmatter inside this body is equal to the pressure jump at the\nsurface of the core\n\n\\begin{equation}\np=\\Delta p(R_{N})=\\frac{E(R_{N})^{2}}{8\\pi }=\\frac{2\\pi\n}{9}G\\gamma ^{2}R_{N}^{2}, \\label{3010}\n\\end{equation}\n\nwhere $\\gamma$ is the matter density in the core and R$_{N}$ is\nthe radius of the core.\n\nOne can say that this pressure jump is due to the existence of the\npolarization jump or, which is the same, the existence of the\nbonded surface charge, which is formed by electron pushed out from\nthe core and which makes the total charge of the celestial body\nequal to zero.\n\n\\section{Earth's structure.}\n\nIt is important, that the GIEP effect gives the possibility to\nconstruct the intrinsically self-consistent theory of the Earth\n\\cite{13}. Although it is rather a solution of a geophysical\nproblem than an astrophysical effect.\n\nEarlier models of the Earth assumed the existence of the\nmonotonous dependence of pressure inside the planet. The division\nof the Earth into the core and the mantle was explained by the\nfact that at the creation of the Earth, on its share a certain\namount of iron (and other heavy metals) and also a necessary\namount of stone were given out. The core consists of metals and\nthe mantle consists of stone. In these models, it was necessary to\nfit the parameters to get the densities of core and mantle and\ntheir sizes. It is not necessary to introduce any free parameters\ninto the Earth theory based on the GIEP effect. Assuming that the\nEarth consists of homogeneous matter, the division on core and\nmantle is explained by the existence of the pressure jump on the\nsurface of the core Eq.({\\ref{3010}}). The basic results of this\ntheory are reduced to the calculation of the following five values:\n\na) the radius of the Earth's core;\n\nb) the density of core matter;\n\nc) the density jump on the core-mantle boundary;\n\nd) the mass related to one electron of the Fermi gas in the core;\n\ne) the electric polarization of the core.\n\nTo express it in appropriate equations, one should substitute the\nfollowing four parameters (the gravitational constant $G$ is\nknown):\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics{ae-fig1.EPS}\n\\caption{The radial dependence of pressure and the matter density\ninside the Earth. The solid line is the calculated dependence of\nthe matter density; the dashed line is the density of the Earth\nobtained by measuring the propagation velocity of seismic waves.\nThe dash-dotted line is the calculated dependence of pressure\ninside the Earth over bulk module B=$1.3\\cdot 10^{12}$\ndyn/cm$^{2}$.} \\label{fig1}\n\\end{center}\n\\end{figure}\n\na) the mass of the Earth;\n\nb) the radius of the Earth;\n\nc) the matter density on the surface of the Earth;\n\nd) the bulk module of matter at the surface of the Earth.\n\nThus, other parameters can be obtained, for example, the pressure\ndistribution inside the Earth. The basic results of this theory are shown in\nFig.1.\n\n\n\n\nIn addition, from the obtained data it is possible to calculate the\nangular momentum of the Earth. This calculation gives the value of\n$0.339MR^2$. It is in agreement with the measured value of\n$0.331MR^2$ within several percent of the accuracy.\n\nIt is possible to calculate the magnetic moment of the Earth.\n\nApparently, using the appropriate data of other planets (the mass,\nthe size, and the properties of matter at the surface), it is\npossible to construct models of these planets. It can be made, if\nthese planets have electrically polarized cores and corresponding\nmagnetic fields.\n\n\n\n\\section{The gyromagnetic ratio of a celestial body}\n\nAnother astrophysical consequence of the GIEP effect is coupled\nby the rotation of celestial bodies about their axes. A celestial\nbody is electroneutral as a whole. The positive volume charge is\nconcentrated inside the core and the negative charge is located at\nthe surface of the core. When rotating, they move on different\nradii. As a result, all celestial bodies, when the GIEP effect\nis present, obtain magnetic moments\n\n \\begin{equation}\n \\mu=\\frac{2}{15}\\frac{4\\pi}{3c}\\rho\\Omega{R_{N}^{5}}.\\label{5010}\n \\end{equation}\n\n\nIf the size of the body is sufficiently large, the core radius\n$R_{N}$ does not differ significantly from its external radius R.\nFor this celestial body, the angular momentum of the core\ncoincides by the order of magnitude with the angular momentum of\nthe body as a whole\n\n \\begin{equation}\n L=\\frac{2}{5}M\\Omega{R}^{2}\\label{5020}\n \\end{equation}\n\nwhere $M=\\frac{4\\pi}{3}{\\gamma{R^{3}}}$ is the mass of a celestial\nbody and $\\Omega$ is the velocity of rotation.\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[5cm,14cm][17cm,2cm]{ae-fig2.EPS}\n\\vspace{11cm} \\caption{The observed values of the magnetic moments\nof celestial bodies vs. their angular momenta. On the ordinate,\nthe logarithm of the magnetic moment over $Gs\\cdot{cm^3}$ is\nplotted; on the abscissa the logarithm of the angular momentum\nover $erg\\cdot{s}$ is shown. The solid line illustrates\nEq.({\\ref{5030}}). The dash-dotted line is the fitting of the\nobserved values.} \\label{fig2}\n\\end{center}\n\\end{figure}\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[5cm,14cm][17cm,2cm]{ae-fig5.EPS}\n\\vspace{14cm} \\caption{The estimated values of the magnetic\nmoments of pulsars \\cite{19} vs. their angular momenta. Solid line\nis Eq.({\\ref{5030}}). The axes are as in Fig.2.} \\label{fig3}\n\\end{center}\n\\end{figure}\n\n Finally, the gyromagnetic ratios for these bodies should be close to\n the universal value\n\n \\begin{equation}\n \\frac{\\mu }{L}=\\frac{G^{1/2}}{3c}.\\label{5030}\n \\end{equation}\n\nThe values of $\\mu $(L) for all celestial bodies (for which they\nare known today) are shown in Fig.2. The data for planets are\ntaken from \\cite{14}, the data for stars are taken from \\cite{15},\nand for pulsars - from \\cite{16}.\n\n\nAs can be seen from the figure with the logarithmic accuracy, all\ncelestial bodies - stars, planets, and pulsars - really have the\ngyromagnetic ratio close to the universal\nvalue $\\frac{G^{1/2}}{3c}$. Only the data for the Moon fall out,\nbecause its size and inner pressure are too small to create an\nelectrically polarized core. The estimation of the magnetic moment of\nthe Earth within the frame of the theory mentioned above \\cite{13}\ngives $\\mu \\simeq 4\\cdot 10^{25}Gs\\cdot cm^{3}$. It is almost\nprecisely one half from the observed value of $8.05\\cdot\n10^{25}Gs\\cdot cm^{3}$. For some planets, the values of magnetic\nmoments are in a good agreement with Eq.({\\ref{5030}}) but they\nhave an opposite sign. Apparently, it means that the hydrodynamic\nmechanism also plays a certain role.\n\nFor the majority of pulsars, there are estimations of magnetic\nfields \\cite{19} obtained using a number of model assumptions\n\\cite{16}. It is impossible to consider these data as the data of\nmeasurements, but nevertheless, they also agree in certain way\nwith Eq.({\\ref{5030}}),(Fig.3)\n\n\n\\section{The masses of celestial bodies.}\n\nThe important astrophysical outcome of the GIEP effect is a\ndiscrete distribution of masses of celestial bodies. This spectrum\nis a result of the fact that electron-nuclear plasmas can exist in\nvarious states.\n\nThe equation of state of matter subjected to high pressure is\nusually described as a polytrope \\cite{7}:\n\n\\begin{equation}\np=C\\cdot \\gamma ^{1+\\frac{1}{k}}, \\label{6010}\n\\end{equation}\n\nwhere C is the dimensional constant,\n\nk is the polytropy.\n\n\\subsection{Nonrelativistic electron-nuclear plasma.}\n\nAt relatively small pressure, substances are transmuted into\nnonrelativistic electron-nuclear (or electron-ion) plasma. It is\npeculiar to conditions existing inside cores of planets. According\nto \\cite{7}, the state equation of the nonrelativistic\nelectron-nuclear plasma (characterized by the polytropy k=3/2) is\n\n\\begin{equation}\np_{(3/2)}=\\frac{\\left( 3\\pi ^{2}\\right) ^{2/3}\\hbar ^{2}\\gamma ^{5/3}}{%\n5m_{e}(\\beta\\cdot m_{p})^{5/3}}, \\label{6020}\n\\end{equation}\n\nwhere $\\beta\\cdot{m_{p}}$ is the mass of matter related to one\nelectron of the Fermi gas system and m$_{p}$ is the proton mass.\n\nIf the pressure inside a celestial body is formed by the GIEP\neffect and is determined by Eq.({\\ref{3010}}), than from\nEq.({\\ref{6020}}) for the nonrelativistic Fermi gas of electrons,\nwe obtain the steady-state value of mass for a core of planet\n\n\\begin{equation}\nM_{(3/2)}=C_{(3/2)}\\cdot \\left( \\frac{\\hbar\n^{2}}{Gm_{e}m_{p}}\\right) ^{3/2}\\cdot \\frac{\\gamma ^{1/2}}{\\beta\n^{5/2}m_{p}}, \\label{6030}\n\\end{equation}\n\nwhere C$_{(3/2)}=\\frac{54\\pi }{5}\\left( \\frac{\\pi }{10}\\right)\n^{1/2}\\simeq 19.$\n\nThe dependence of Eq.({\\ref{6030}}) is shown in Fig.4. Therefore,\nany planet (even consisting from pure hydrogen) should have a mass\nless than 10$^{31}g$ (if its density is approximately equal to $1\ng/cm^3$).\n\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[5cm,14cm][17cm,2cm]{ae-fig3.EPS}\n\\vspace{14cm}\n\\caption{The dependence of the core mass of planets\non $\\beta$ (Eq.({\\ref{6030}})) at $\\gamma =1g/cm^{3}$. On the\nordinate, the logarithm of mass (over $1 g$) is plotted.}\n\\label{fig4}\n\\end{center}\n\\end{figure}\n\n\nIn Fig.4 the masses of the planets of the Solar system are marked.\nThe mass of the Jupiter is $1.9\\cdot 10^{31}g$. It is close to the\nspecified limit. For the Jupiter Eq.({\\ref{6030}}) gives $\\beta\n\\simeq 2$. It is according to the data that the large planets have\nthe deuterium-helium composition. For other planets the mantle is\nnot small in comparison with their sizes. For this reason,\nEq.({\\ref{6030}}) can give an excessive estimation for other\nplanets.\n\n\\subsection{Relativistic electron-nuclear plasma.}\n\nWhen the pressure increases, the substances are transmuted into\nrelativistic electron-nuclear plasma (the polytropy k= 3). Its\nstate equation is \\cite{7}\n\n\\begin{equation}\np_{(3)}=\\frac{\\left( 3\\pi ^{2}\\right) ^{1/3}\\hbar c\\gamma ^{4/3}}{%\n4m_{p}^{4/3}\\beta ^{4/3}} \\label{6040}\n\\end{equation}\n\nIf this plasma is originated by the GIEP effect, then the\nsteady-state value of mass of a star consisting of it, according\nto Eqs.({\\ref{3010}},{\\ref{6040}}) is\n\n\\begin{equation}\nM_{(3)}=C_{(3)}\\cdot A_{\\star}^{3/2}\\cdot \\frac{m_{p}}{\\beta\n^{2}}, \\label{6050}\n\\end{equation}\n\nwhere the dimensionless constants are\n\n\\begin{equation}\nA_{\\star}=\\left( \\frac{\\hbar c}{Gm_{p}^{2}}\\right) =1.54\\cdot\n10^{38} \\label{6060}\n\\end{equation}\n\nand C$_{(3)}=\\left( 1.5^{5}\\pi \\right) ^{1/2}\\simeq 4.88.$\n\nBecause of the electric neutrality, one proton should be related to\nelectron of the Fermi gas of plasma. The existence of one neutron\nper proton is characteristic for a substance consisting of light\nnuclei. The quantity of neutrons grows approximately to 1.8 per\nproton for the heavy nuclei substance. Therefore, it is necessary\nto expect that inside stars $2<\\beta<2.8$.\n\nThe masses of stars can be measured with a considerable accuracy,\nif these stars compose a binary system. There are almost 200\ndouble stars which masses are known with the required accuracy\n\\cite{17}. Among these stars there are giants, dwarfs, and stars of\nthe main sequence. Their average masses are described by the\nequality\n\n\\begin{equation}\n\\langle M_{star}\\rangle =\\left( 1.36\\pm 0.05\\right) M_{\\odot },\n\\label{6070}\n\\end{equation}\n\nwhere $M_{\\odot }$ is the mass of the Sun.\n\nThe center of this distribution (Fig.5) corresponds to\nEq.({\\ref{6050}}) at $\\beta \\simeq 2.6$.\n\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[5cm,14cm][17cm,2cm]{ae-fig4c.EPS}\n\\vspace{11cm}\n\\caption{Mass distributions of stars and pulsars\nfrom the binary systems \\cite{17}-\\cite{18}. The curve shows\n$\\beta$ (Eq.({\\ref{6050}})).} \\label{fig5}\n\\end{center}\n\\end{figure}\n\n\n\\subsection{Ultrarelativistic electron-nuclear plasma.}\n\nFurther increase in pressure transmutes substances into\nultrarelativistic plasma. Then nuclear reactions of capture of\nelectrons by nuclei become favorable and the neutronization of\nmatter takes place. Equilibrium pressure of ultrarelativistic\nplasma does not depend on its density. It is formally\ncharacterized by the polytropy k=-1 and its state equation is\n\\cite{7}\n\n\\begin{equation}\np_{(-1)}=\\frac{\\Delta ^{4}}{12\\pi ^{2}\\left( \\hbar c\\right) ^{3}}.\n\\label{6080}\n\\end{equation}\n\nHere $\\Delta $ is the difference between the energy of the\ninitial nucleus and the energy of the daughter nucleus.\n\nThe equilibrium mass of a star, consisting of ultrarelativistic\nplasma, according to Eqs.({\\ref{3010}}),Eq.({\\ref{6080}}) is\n\n\\begin{equation}\nM_{(-1)}=C_{(-1)}\\left( \\frac{\\Delta ^{6}}{\\left( \\hbar c\\right)\n^{9/2}G^{3/2}\\gamma ^{2}}\\right) , \\label{6090}\n\\end{equation}\n\nwhere C$_{(-1)}=\\frac{1}{4\\pi ^{3}}\\left( \\frac{3}{2\\pi }%\n\\right) ^{1/2}\\simeq 6\\cdot 10^{-3}.$\n\nAccording to the astrophysical data a neutronization of matter\ntakes place at the density $\\gamma\\approx{10^{7}}\\frac{g}{cm^3}$.\nThus, Eq.({\\ref{6090}}) gives\n\n\\begin{equation}\nM_{(-1)}\\approx{8\\cdot{10^{32}}}g\\approx{0.4}M_{\\odot}.\\label{6100}\n\\end{equation}\n\nCertainly this result is the rough estimation on the order of\nmagnitude only, but it is in a satisfactory agreement with\nmeasurements of the astronomers related to masses of white dwarfs\nfrom double systems.\n\n\\subsection{Nonrelativistic neutron matter.}\n\nAt higher pressure, the substance is transmuted into a\nnonrelativistic neutron matter with a small impurity of protons\nand electrons \\cite{7}. The state equation of the nonrelativistic\nneutron matter will coincide with Eq.({\\ref{3010}}) with a\nreplacement of $m_{e}$ with $m_{p}$\n\n\n\\begin{equation}\np_{(3/2)}^{(n)}=\\frac{\\left( 3\\pi ^{2}\\right) ^{2/3}\\hbar ^{2}\\gamma ^{5/3}}{%\n5m_{p}^{8/3}\\beta ^{5/3}}. \\label{6110}\n\\end{equation}\n\nTogether with Eq.({\\ref{3010}}), it gives the equilibrium mass of\nthe nonrelativistic neutron star\n\n\\begin{equation}\nM_{(3/2)}^{(n)}=C_{(3/2)}\\left( \\frac{\\hbar ^{2}}{G}\\right) ^{3/2}\\frac{%\n\\gamma ^{1/2}}{m_{p}^{4}\\beta ^{5/2}}. \\label{6120}\n\\end{equation}\n\nAs the density $\\gamma \\simeq 4\\cdot 10^{13}g/cm^{3}$ and\n$\\beta=2.6$\n\n\\begin{equation}\nM_{(3/2)}^{(n)}\\simeq{0.05}M_{\\odot }.\\label{6130}\n\\end{equation}\n\nThe astronomers have not found such neutron stars.\n\n\\subsection{Relativistic neutron matter.}\n\nWith further increase in pressure, the neutron Fermi gas becomes a\nrelativistic one. Its state equation completely coincides with the\nstate equation of the relativistic Fermi gas of electrons\nEq.({\\ref{3010}})\n\n\\begin{equation}\np_{(3)}^{(n)}=\\frac{\\left( 3\\pi ^{2}\\right) ^{1/3}\\hbar c\\gamma ^{4/3}}{%\n4m_{p}^{4/3}\\beta ^{4/3}}. \\label{6140}\n\\end{equation}\n\nAs well as the masses of relativistic stars, the masses of\nrelativistic pulsars do not depend on their density and can be\ndirectly expressed through world constants\n\n\\begin{equation}\nM_{(3)}^{(n)}=C_{(3)}\\cdot A_{\\star}^{3/2}\\cdot \\frac{m_{p}}{\\beta\n^{2}} \\label{6150}\n\\end{equation}\n\n(at $\\beta =1$ for the pure neutron Fermi gas).\n\nAs it is specified in \\cite{7}, at this density of matter it\nis necessary to take into account nuclear forces and the presence\ninside nuclear matter except neutrons also of protons, $\\pi\n^{-}$mesons, and electrons. It can be made using $\\beta $ as a\nparameter of the correction.\n\nThe mass of the neutron star can be measured with a considerable\naccuracy if it enters into a binary system. The astronomers have\nfound 16 radio-pulsars \\cite{18} and 7 X-pulsars \\cite{16} in\nbinary systems. They all are located in a very narrow mass\ninterval (Fig.5)\n\n\\begin{equation}\n\\langle M_{pulsar}\\rangle =(1.38\\pm 0.03)M_{\\odot }. \\label{6160}\n\\end{equation}\n\nThe center of this distribution corresponds to Eq.({\\ref{6150}})\nwith the correction parameter $\\beta \\simeq 2.6$ just as for\nrelativistic stars. Thus, we come to the conclusion that\nEq.({\\ref{6150}}) on the order of magnitude correctly describes\nthe results of astronomical observations.\n\n\\section{Conclusion.}\n\nIt is expedient to underline the basic obtained results in\nsummary.\n\n1. The developed theory defines a concept of the steady-state\nvalues of masses of celestial bodies related to their equations of\nstate and gives the possibility to calculate these values.\n\n2. It gives the new way for the determination of the substance\ndensity distribution inside celestial bodies. According to early\nmodels, it was supposed that density of a substance inside celestial\nbodies grows more or less monotonically with depth and at the\ncentre of a star, the density has the greatest value and even a\nblack hole may exist there. According to the developed theory,\nthe density of a substance inside a star is constant.\n\n3. It is interesting to emphasize that the \"biography\" of such a\nstar appears much poorer than in the Chandrasecar model.\n\nThere cannot exist a black hole inside a star, and it should not\ncollapse with a temperature decrease. All the considered effects are\nbased on an equilibrium of the Fermi system. Temperature does not\ninfluence the parameters of relativistic plasma. Therefore, a star\nwith a mass close to the steady-state value (Eq.({\\ref{6050}})) is\nin a stable equilibrium not depending on temperature. The existing\nstars should retain the stability at any (even at zero)\ntemperature. Therefore, a collapse of the already existing stars\napparently is impossible. The instability of a star can arise with\nburning out of light nuclei - deuterium and helium - and with a\nrelated increasing of $\\beta$. This growth leads to the reduction\nof a steady-state value of mass (Eq.({\\ref{6050}})) and, probably,\nto the distraction of the stars wiht masses more than the\nsteady-state value.\n\n4. The developed theory determines the simple and essential\nmechanism of generation of the magnetic field by celestial bodies.\nAll early models tried to solve the basic problem - to calculate\nthe magnetic field of a celestial body. Such a statement of the basic\nproblem of planetary and stellar magnetism is unacceptable at present.\nSpace flights and a development of astronomy discovered a remarkable\nand earlier unknown fact: the magnetic moments of all celestial bodies\nare proportional to their angular momenta and the proportionality\ncoefficient is determined by the ratio of world constants. The\nexplanation of this phenomenon is the basic problem of planetary\nand stars magnetism nowadays. Early models cannot explain this\nphenomenon. The developed theory used for this explanation a\nstandard mechanism.\n\n5. It is possible to consider that now the predicted steady-state\nvalues of masses of celestial bodies and the predicted values of\ntheir magnetic moments are in a satisfactory agreement with the\ndata of observations. But it is tempting to obtain these\ndata to closer limit of accuracy. Two arrows in the upper part of Fig.5 mark\nmasses of stars consisting of extremely light and heavy nuclei.\nThese values are obtained from Eq.({\\ref{6050}}) without the use\nof any fitting parameters. In agreement wiht the developed theory,\nif stars have a \"usual\" chemical composition, there must be no\nstars outside of this interval (or these stars should be\nunstable). The histogram on Fig.5 is somewhat wider. It is\ninteresting to understand, whether there is a principal deviation\nfrom the developed theory or it is a result of measuring errors.\nFirst of all, it requires a more careful and precise measurement\nof masses of binary stars.\n\n\n%\\clearpage\n\n\n\\begin{thebibliography}{19}\n\n\\bibitem {1} Shiff L.I. and Barnhill M.V. - Phys. Rev.,1968,v.151,pp.1067-1071.\n\\bibitem {2} Dressler A.I. a.o. - Phys.Rev.,1968,v.168,pp.737-743.\n\\bibitem {3} Riegel T.J. - Phys. Rev.B,1970,v. 2,pp.825-828.\n\\bibitem {4} Kumar N. and Naddini R. - Phys. Rev. D.,1973,v.7,pp.1067-1071.\n\\bibitem {5} Leung M.C. et al. - Canad.Journ. of Phys.,1971,v.49,pp.2754-2767.\n\\bibitem {6} Leung M.C. - Nuovo Cimento,1972,v.76,pp.825-929.\n\\bibitem {7} Landau L.D. and Lifshits E.M. - Statistical Physics,1980, vol.1,3rd edition,Oxford:Pergamon.\n\\bibitem {8} Vasiliev B.V. and Luboshits V.L. - Physics-Uspekhi,1994,v.37,pp.345-351.\n\\bibitem {9} Kirzhnitz D.A. - JETP, 1960, v.38, pp.503-508.\n\\bibitem {10} Abrikosov A.A. - JETP, 1960, v.39, pp.1797-1805.\n\\bibitem {11} Leung Y.C. - Physics of Dense Matter, 1984, Science Press/World Scientific, Beijing and Singapure.\n\\bibitem {12} Vasiliev B.V. - Nuovo Cimento B,1997,v.112,pp.1361-1372.\n\\bibitem {13} Vasiliev B.V. - Nuovo Cimento B,1999,v.114,pp.291-300.\n\\bibitem {14} Sirag S.-P. - Nature,1979,v.275,pp.535-538.\n\\bibitem {15} Borra E.F. and Landstreet J.D. - The Astrophysical Journ, Suppl., 1980, v.42, 421-445.\n\\bibitem {16} Beskin V.S., Gurevich, A.V., Istomin Ya.N. - Physics of the Pulsar Magnetosphere, Cambridge University Press, 1993.\n\\bibitem {17} Heintz W.D. - Double stars,1978, Geoph. and Astroph.monographs, vol.15, D.Reidel Publ.Comp.\n\\bibitem {18} Thorsett S.E. and Chakrabarty D. - E-preprint: astro-ph/9803260, 1998, 35pp.\n\\bibitem {19} Taylor J.H., Manchester R.N., Lyne A.G., Camilo F., Catalog of 706 pulsars,\n 1995, pulsar.prinston.edu\n\n\\end{thebibliography}\n\n\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002171.extracted_bib",
"string": "\\begin{thebibliography}{19}\n\n\\bibitem {1} Shiff L.I. and Barnhill M.V. - Phys. Rev.,1968,v.151,pp.1067-1071.\n\\bibitem {2} Dressler A.I. a.o. - Phys.Rev.,1968,v.168,pp.737-743.\n\\bibitem {3} Riegel T.J. - Phys. Rev.B,1970,v. 2,pp.825-828.\n\\bibitem {4} Kumar N. and Naddini R. - Phys. Rev. D.,1973,v.7,pp.1067-1071.\n\\bibitem {5} Leung M.C. et al. - Canad.Journ. of Phys.,1971,v.49,pp.2754-2767.\n\\bibitem {6} Leung M.C. - Nuovo Cimento,1972,v.76,pp.825-929.\n\\bibitem {7} Landau L.D. and Lifshits E.M. - Statistical Physics,1980, vol.1,3rd edition,Oxford:Pergamon.\n\\bibitem {8} Vasiliev B.V. and Luboshits V.L. - Physics-Uspekhi,1994,v.37,pp.345-351.\n\\bibitem {9} Kirzhnitz D.A. - JETP, 1960, v.38, pp.503-508.\n\\bibitem {10} Abrikosov A.A. - JETP, 1960, v.39, pp.1797-1805.\n\\bibitem {11} Leung Y.C. - Physics of Dense Matter, 1984, Science Press/World Scientific, Beijing and Singapure.\n\\bibitem {12} Vasiliev B.V. - Nuovo Cimento B,1997,v.112,pp.1361-1372.\n\\bibitem {13} Vasiliev B.V. - Nuovo Cimento B,1999,v.114,pp.291-300.\n\\bibitem {14} Sirag S.-P. - Nature,1979,v.275,pp.535-538.\n\\bibitem {15} Borra E.F. and Landstreet J.D. - The Astrophysical Journ, Suppl., 1980, v.42, 421-445.\n\\bibitem {16} Beskin V.S., Gurevich, A.V., Istomin Ya.N. - Physics of the Pulsar Magnetosphere, Cambridge University Press, 1993.\n\\bibitem {17} Heintz W.D. - Double stars,1978, Geoph. and Astroph.monographs, vol.15, D.Reidel Publ.Comp.\n\\bibitem {18} Thorsett S.E. and Chakrabarty D. - E-preprint: astro-ph/9803260, 1998, 35pp.\n\\bibitem {19} Taylor J.H., Manchester R.N., Lyne A.G., Camilo F., Catalog of 706 pulsars,\n 1995, pulsar.prinston.edu\n\n\\end{thebibliography}"
}
] |
astro-ph0002172
|
A wavelet analysis of QSO spectra
|
[
{
"author": "Tom Theuns and Saleem Zaroubi"
},
{
"author": "Max-Planck Institut f\\\"ur Astrophysik"
},
{
"author": "Postfach 123"
},
{
"author": "85740 Garching"
},
{
"author": "Germany"
}
] |
The temperature of the intergalactic medium (IGM) is an important factor in determining the line-widths of the absorption lines in the \lya forest. We present a method to characterise the line-widths distribution using a decomposition of a \lya spectrum in terms of discrete wavelets. Such wavelets form an orthogonal basis so the decomposition is unique. We demonstrate using hydrodynamic simulations that the mean and dispersion of the wavelet amplitudes is strongly correlated with both the temperature of the absorbing gas and its dependence on the gas density. Since wavelets are also localised in space, we are able to analyse the temperature distribution as a function of position along the spectrum. We illustrate how this method could be used to identify fluctuations in the IGM temperature which might result from late reionization or local effects.
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[
{
"name": "ma80.tex",
"string": "%MNSAMPLE.TEX specimen article 11.12.92\n%\\documentstyly[onecolumn,graphics]{TN}\n\\documentstyle[graphics]{mn}\n%\\documentstyle[referee]{mn}\n\\newcommand{\\kms}{{km s$^{-1}$}}\n\\newcommand{\\smk}{{km$^{-1}$ s}}\n\\newcommand{\\K} {\\rm K}\n\\newcommand{\\centm}{{cm$^{-2}$}}\n\\newcommand{\\etal}{{et al.}~}\n\\newcommand{\\done}{\\delta^{(1)}}\n\\newcommand{\\de}{\\delta}\n\\newcommand{\\p}{\\partial}\n\\newcommand{\\f}{\\frac}\n\\newcommand{\\lam}{\\lambda}\n\\newcommand{\\Lam}{\\Lambda}\n\\newcommand{\\ap}{\\approx}\n\\newcommand{\\eps}{\\epsilon}\n\\newcommand{\\Om}{\\Omega}\n\\newcommand{\\w}{\\omega}\n\\newcommand{\\s}{\\sigma}\n\\newcommand{\\al}{\\alpha}\n\\newcommand{\\fde}{\\tilde{\\delta}}\n\\newcommand{\\fpsi}{\\tilde{\\psi}}\n\\newcommand{\\fphi}{\\tilde{\\phi}}\n\\newcommand{\\fv}{\\tilde{v}}\n\\newcommand{\\fJ}{\\tilde{J}}\n\\newcommand{\\fW}{\\widetilde{W}}\n\\newcommand{\\fT}{\\widetilde{T}}\n\\newcommand{\\ftau}{\\tilde{\\tau}}\n\\newcommand{\\bfx}{{\\bf x}}\n\\newcommand{\\bfr}{{\\bf r}}\n\\newcommand{\\bfs}{{\\bf s}}\n\\newcommand{\\bfz}{{\\bf z}}\n\\newcommand{\\bfy}{{\\bf y}}\n\\newcommand{\\bfk}{{\\bf k}}\n\\newcommand{\\bfv}{{\\bf v}}\n\\newcommand{\\bfq}{{\\bf q}}\n\\newcommand{\\bfg}{{\\bf g}}\n\\newcommand{\\bfp}{{\\bf p}}\n\\newcommand{\\bft}{{\\bf t}}\n\\newcommand{\\bfu}{{\\bf u}}\n\\newcommand{\\bfL}{{\\bf L}}\n\\newcommand{\\bfS}{{\\bf S}}\n\\newcommand{\\bfT}{{\\bf T}}\n\\newcommand{\\vr}{{\\varrho}}\n\\newcommand{\\vphi}{{\\varphi}}\n\\newcommand{\\hvphi}{{\\hat\\varphi}}\n\\newcommand{\\fvphi}{\\tilde{\\varphi}}\n\\newcommand{\\calA}{{\\cal A}}\n\\newcommand{\\calB}{{\\cal B}}\n\\newcommand{\\calC}{{\\cal C}}\n\\newcommand{\\calD}{{\\cal D}}\n\\newcommand{\\calE}{{\\cal E}}\n\\newcommand{\\calF}{{\\cal F}}\n\\newcommand{\\calG}{{\\cal G}}\n\\newcommand{\\calI}{{\\cal I}}\n\\newcommand{\\calJ}{{\\cal J}}\n\\newcommand{\\calL}{{\\cal L}}\n\\newcommand{\\calK}{{\\cal K}}\n\\newcommand{\\calM}{{\\cal M}}\n\\newcommand{\\calS}{{\\cal S}}\n\\newcommand{\\calH}{{\\cal H}}\n\\newcommand{\\calP}{{\\cal P}}\n\\newcommand{\\calT}{{\\cal T}}\n\\newcommand{\\calV}{{\\cal V}}\n\\newcommand{\\bc}{\\begin{center}}\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\ec}{\\end{center}}\n\\newcommand{\\lan}{\\langle}\n\\newcommand{\\ran}{\\rangle}\n%some notations\n\\newcommand{\\E}[1]{{\\times 10^{#1}}}\n\\newcommand{\\Mpc}{\\rm Mpc}\n\\newcommand{\\grad}{\\nabla}\n\\newcommand{\\apm}{{\\sc {APMSPH }}}\n\\newcommand{\\hydra}{{\\sc{HYDRA }}}\n\\newcommand{\\tree}{{\\sc{TREESPH }}}\n\\newcommand{\\cmbfast}{{\\sc {CMBFAST }}}\n\\newcommand{\\vpfit}{{\\sc {VPFIT}}}\n\\newcommand{\\autovp}{{\\sc {AUTOVP}}}\n\\newcommand{\\lya}{Ly$\\alpha$~}\n\\newcommand{\\eg}{{e.g.~}}\n\\newcommand{\\ie}{{i.e.~}}\n% ions\n% ions\n\\renewcommand{\\H}{{\\mbox{${\\rm H{\\sc i}~}$}}}\n\\newcommand{\\Hp}{{\\mbox{${\\rm H{\\sc ii}~}$}}}\n\\newcommand{\\He}{{\\mbox{${\\rm He{\\sc i}~}$}}}\n\\newcommand{\\Hep}{{\\mbox{${\\rm He{\\sc ii}~}$}}}\n\\newcommand{\\Hepp}{{\\mbox{${\\rm He{\\sc iii}~}$}}}\n\\newcommand{\\h} {{\\rm H{\\sc i}}}\n\\newcommand{\\hp} {{\\rm H{\\sc ii}}}\n\\newcommand{\\he} {{\\rm He{\\sc i}}}\n\\newcommand{\\hep} {{\\rm He{\\sc ii}}}\n\\newcommand{\\hepp} {{\\rm He{\\sc iii}}}\n\\newcommand{\\NHI}{\\mbox{$N_{\\rm H{\\sc i}}$}}\n%\n\\newcommand{\\sig}{\\sigma_{_{\\!{\\!G}}}}\n\\newcommand{\\lra}{{\\leftrightarrow}}\n%\n\\newcommand{\\ltsima}{\\mbox{$\\; \\buildrel < \\over \\sim \\;$}}\n%\\def \\ltsima{$\\; \\buildrel < \\over \\sim \\;$}\n\\def \\simlt{\\lower.5ex\\hbox{\\ltsima}} % < over ~\n%\\def \\gtsima{$\\; \\buildrel > \\over \\sim \\;$}\n\\def \\gtsima{\\mbox{$\\; \\buildrel > \\over \\sim \\;$}}\n\\def \\simgt{\\lower.5ex\\hbox{\\gtsima}} % > over ~\n\\newcommand{\\ls}{\\mathrel{\\mathchoice{\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr<\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr<\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr<\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr<\\cr\\sim\\cr}}}}}\n%\tsome backspaces\n\\newcommand{\\bbbb}{{\\!\\!\\!\\!}}\n%\n\\title[Wavelet analysis of QSO spectra] \n{A wavelet analysis of QSO spectra}\n\\author[Theuns \\& Zaroubi]{Tom Theuns and Saleem Zaroubi\\\\\nMax-Planck Institut f\\\"ur Astrophysik, Postfach 123, 85740 Garching, Germany}\n\n\\begin{document}\n\\maketitle\n\n\\begin{abstract}\nThe temperature of the intergalactic medium (IGM) is an important\nfactor in determining the line-widths of the absorption lines in the\n\\lya forest. We present a method to characterise the line-widths\ndistribution using a decomposition of a \\lya spectrum in terms of\ndiscrete wavelets. Such wavelets form an orthogonal basis so the\ndecomposition is unique. We demonstrate using hydrodynamic simulations\nthat the mean and dispersion of the wavelet amplitudes is strongly\ncorrelated with both the temperature of the absorbing gas and its\ndependence on the gas density. Since wavelets are also localised in\nspace, we are able to analyse the temperature distribution as a\nfunction of position along the spectrum. We illustrate how this method\ncould be used to identify fluctuations in the IGM temperature which\nmight result from late reionization or local effects.\n\\end{abstract}\n\n\\begin{keywords}\ncosmology: theory -- intergalactic medium -- hydrodynamics --\nlarge-scale structure of universe -- quasars: absorption lines\n\\end{keywords}\n\n\\section{Introduction}\nResonant absorption by neutral hydrogen in the intergalactic medium\nalong the line of sight to a distant quasar is responsible for the many\nabsorption lines seen in the \\lya forest, blueward of the quasar's \\lya\nemission line (Bahcall \\& Salpeter 1965, Gunn \\& Peterson 1965; see\nRauch 1998 for a review). The general properties of these \\lya\nabsorption lines are remarkably well reproduced by hydrodynamic\nsimulations of cold dark matter (CDM) dominated cosmologies (Cen \\etal\n1994, Zhang, Anninos \\& Norman 1995, Miralda-Escud\\'e \\etal 1996,\nHernquist \\etal 1996, Wadsley \\& Bond 1996, Zhang \\etal 1997, Theuns\n\\etal 1998).\n\nOn large scales where pressure is unimportant, gas traces the dark\nmatter and the \\lya spectrum can be used to infer the underlying\ndensity perturbations in the dark matter (Croft \\etal 1997, Nusser \\&\nHaehnelt 1999). On small scales however, pressure gradients oppose the\ninfall of gas into small potential wells (Jeans smoothing), leaving the\nabsorber more extended in space than the underlying dark matter. The\nwidth of the absorption line is then determined by residual Hubble\nexpansion across the absorber (Hernquist \\etal 1996), Jeans smoothing\nand thermal broadening. Theuns, Schaye \\& Haehnelt (2000) analysed\nvarious line broadening mechanisms and demonstrated the importance of\nthe gas temperature in controlling the line-widths.\n\nThe strong dependence of the small-scale properties of the \\lya forest\non the temperature of the gas allows one to reconstruct the thermal\nevolution of the IGM. The gas temperature is set by the balance between\nadiabatic cooling caused by expansion and photo-heating by the\nUV-background. This introduces a tight relation between density and\ntemperature, $T=T_0(\\rho/\\langle\\rho\\rangle)^{\\gamma-1}$ (Hui \\& Gnedin\n1997). The parameters $T_0$ and $\\gamma$ of this \\lq equation of\nstate\\rq~ are very sensitive to the reionization {\\em history} of the\nIGM (Haehnelt \\& Steinmetz 1998). This is because thermal time scales\nare long in the low density IGM probed by the \\lya forest, hence that\ngas retains a memory about the past history of the ionising\nbackground. Consequently, the \\lya forest provides us with a fossil\nrecord of the history of reionization, which can be explored by\nunravelling its thermal history as deduced from the \\lya forest.\n\nSchaye \\etal (1999, see also Ricotti, Gnedin \\& Shull 2000) developed\nand tested a method to infer $T_0$ and $\\gamma$ based on the\nline-widths of the absorption lines. Applying this method to high\nresolution QSO spectra for a range of redshifts, they found (Schaye\n\\etal 2000) that the temperature $T_0$ decreases with decreasing\nredshift as expected, however, there is a large increase in $T_0$ round\n$z=3$, together with a decrease in the value of $\\gamma$. They\nattributed this change in the equation of state to late reionization of\nhelium II. They also noted that the temperature at higher redshifts is\nstill fairly high, which might be an indication that we are approaching\nthe epoch of hydrogen reionization.\n\nThe method of Schaye \\etal to characterise line-widths is based on\nVoigt profile fitting of absorption lines (Webb 1987, Carswell \\etal\n1987). The rationale behind fitting absorption lines with a Voigt\nprofile is partly historical, and stems from earlier theoretical models\nin which the forest was produced by a set of \\lya \\lq clouds\\rq~. The\nline-width of these absorbers was assumed to be set by thermal and \\lq\nturbulent\\rq~ broadening, which would produce a Voigt profile, and line\nblending was responsible for the lines with large deviations from the\nVoigt profile. In the new paradigm of the \\lya forest absorption in the\ngeneral IGM is responsible for lines, and there is no a priori reason\nto expect lines to have the Voigt shape.\n\nIn this paper we discuss a different method of characterising\nline-widths, based on discrete wavelets (see e.g. Press et al. 1992 for\nan introduction and further references). Wavelets provide an orthogonal\nbasis for a unique decomposition of a signal (the spectrum) in terms of\nlocalised functions with a finite bandwidth. Thus they are a compromise\nbetween characterising a signal in terms of its individual pixel values\nand in terms of Fourier modes. In the first case, the characterisation\nhas no information on correlations between different pixels (no\nfrequency information) but perfect positional information. A Fourier\ndecomposition, on the other hand, has perfect frequency information but\nno positional information. The analysis of a spectrum in terms of\nwavelets has the advantage that one can study the clustering of lines\n(\\lq positional information\\rq), as a function of their widths (\\lq\nfrequency information\\rq).\n\nThe usage of wavelets to analyse QSO spectra was pioneered by Pando \\&\nFang (1996, 1998), who used a wavelet analysis of \\lya absorption lines\nto describe the clustering of those lines. The wavelet analysis\ndetected large scale structure in the \\lya forest, which had proved\ndifficult using more traditional methods. In contrast to Pando \\& Fang,\nwe will use wavelets to analyse the absorption spectrum directly,\nthereby eliminating the somewhat subjective step of first decomposing\nthe continuous spectrum in absorption lines. The advantage of this new\nmethod is that it allows us to objectively characterise the typical\nwidth of absorption features as a function of position along the\nspectrum\\footnote{We will usually refer to absorption features as \\lq\nlines\\rq, but this is just a convenient name for what the eye picks\nout. The wavelet decomposition itself is unique and has no prejudice as\nto what should be considered a line.}.\n\nWe will show using hydrodynamic simulations that the probability\ndistribution of wavelet amplitudes can be used to characterise the\nequation of state of the absorbing medium, in terms of the temperature\nat the mean density, $T_0$, and the slope, $\\gamma$, of the\ntemperature-density relation. In addition we use the fact that wavelets\nare localised in position along the spectrum, thereby allowing us to\ndetect spatial variations in $T_0$ and/or $\\gamma$, which might be\npresent as a result of late helium II reionization or local effects.\n\nThis paper is organised as follows. In Section~\\ref{sect:setup} we\nfirst give a brief description of the generation of mock spectra from\nour simulations and illustrate the decomposition of the spectra in\ndiscrete wavelets. The statistics of the wavelet amplitudes for\ndifferent simulations is discussed in Section~\\ref{sect:analysis} and\nthe results are summarised in Section~\\ref{sect:conclusions}. Recently,\nMeiksin (2000) discussed indepently the application of wavelets to QSO\nspectra.\n\n\n\\section{Wavelet analysis of mock spectra}\n\\label{sect:setup}\n\\subsection{Mock spectra}\n\\label{sect:mock}\nWe use the L1 simulation described before in Theuns \\etal\n(2000). Briefly, this is a simulation of a flat, vacuum energy\ndominated cold dark matter model with matter density $\\Omega_m=0.3$,\nbaryon fraction $\\Omega_b h^2=0.019$ and Hubble constant $H_0=65$ km\ns$^{-1}$ Mpc$^{-1}$. Density fluctuations in this model are normalised\nto the abundance of galaxy clusters (Eke \\etal 1996) and we have used\n\\cmbfast (Seljak \\& Zaldarriaga 1996) to compute the appropriate linear\ntransfer function. The IGM in this model is photo-ionised and\nphoto-heated by the UV-background from QSOs, as computed by Haardt \\&\nMadau (1996).\n\nWe simulated this cosmological model with a modified version of the\n\\hydra simulation code (Couchman \\etal 1995), which combines\nhierarchical P3M gravity (Couchman 1991) with smoothed particle\nhydrodynamics (SPH, Lucy 1977, Gingold \\& Monaghan 1977). We simulate a\nperiodic, cubic box of size 7.7 co-moving Mpc using 128$^3$ particles\nof each species, which gives us sufficient resolution to compute\nline-widths reliably (Theuns \\etal 1998). To investigate other effects,\nwe also make use of simulations of a model with the same numerical\nresolution, cosmology and thermal history, but with a smaller box size\n(3.8 Mpc), and a set of simulations with a smaller normalisation\n$\\sigma_8=0.775$ and $\\sigma_8=0.4$.\n\nIn the analysis stage, we impose a particular equation of state on the\ngas at low overdensities ($\\rho/\\langle\\rho\\rangle < 20$) of the form\n$T=T_0 (\\rho/\\langle\\rho\\rangle)^{\\gamma-1}$, varying the values of\n$T_0$ and $\\gamma$. We then compute mock spectra that mimick the actual\nobserved HIRES spectrum of the $z_{\\rm em}=3.0$ QSO 1107+485, discussed\nby Rauch et al. (1997), using the following procedure. We divide the\nobserved spectrum in three redshifts bins, $z=2.5-2.625$,\n$z=2.625-2.875$ and $z=2.875-3$ and scale the mean absorption of the\nsimulations at $z=2.5$, $z=2.75$ and $z=3$ to the corresponding\nobserved value. The simulated spectra are resampled to the observed\nresolution, and convolved with a Gaussian to mimick instrumental\nbroadening. We have analysed the noise statistics of the QSO 1107\nspectrum as a function of flux, and add noise with these properties to\nthe simulated spectra. By randomly combining individual sight lines\nthrough the simulation volume, we generate a single long spectrum of\nlength 37 492 km s$^{-1}$. Velocity $v$ is related to redshift $z$ via\n$v\\equiv c\\left[log_e(1+z)-log_e(1+z_1)\\right]$, where $c$ is the speed\nof light, $z$ is redshift and $z_1$ is the redshift where \\lya starts\nto be confused with Ly$\\beta$ for QSO 1107. In order to perform the\nwavelet analysis, we resample the spectrum to $2^{15}$=32768 pixels,\nequally spaced in velocity. In what follows, we will refer to a\nsimulation with a particular equation of state by giving $T_0/10^4$K\nand $\\gamma$, so the model $(1.5,5/3)$ has the imposed equation of\nstate $T=1.5\\times 10^4\\,(\\rho/\\langle\\rho\\rangle)^{2/3}$. We will\npresent results for four equations of state, using $T_0=1.5$ and\n$2.2\\times 10^4$K and $\\gamma=1$ and 5/3.\n\n\\subsection{Wavelets}\n\\label{sect:wavelets}\n\\begin{figure*}\n\\setlength{\\unitlength}{1cm} \\centering\n\\begin{picture}(17,9)\n\\put(-1, -14.5){\\special{psfile=wltdecomp.ps hscale=100 vscale=100}}\n\\end{picture}\n\\caption{Example of a Daubechies 20 wavelet decomposition of a mock\n\\lya spectrum at $z\\sim 3$. Panel (a): Flux $F$ as a function of\nvelocity $v$ for a mock spectrum of QSO 1107. Panel (b): decomposition\nof $F$ in terms of wavelets with resolutions $2^{i-15}\\times V$ for\n$i=9\\cdots 12$ (from $18.3$ to 146.4 km s$^{-1}$) . Panel (c):\nindividual wavelets that make up the curve in (b), for $i=9$ (top\ncurve) to $i=12$ (bottom curve), off-set vertically for clarity. The\nresolution corresponding to each wavelet is indicated on the right\naxis. Most lines are detected in all shown wavelet resolutions, but\nonly narrow lines are strongly detected at the highest resolution\n$i=9$.}\n\\label{fig:wltdecomp}\n\\end{figure*}\n\n\\begin{figure*}\n\\setlength{\\unitlength}{1cm}\n\\centering\n\\begin{picture}(17,9)\n\\put(-1, -14.5){\\special{psfile=exmp.ps hscale=100 vscale=100}}\n\\end{picture}\n\\caption{Wavelet decomposition of a simulated spectrum at $z\\sim 3$\n(panel a) into the wavelet with resolution $i=9$ ($18.3$ km s$^{-1}$),\nwhose amplitude $A$ is shown in panel (b). The rms amplitude $\\langle\nA(9,1000)^2\\rangle$, box-car smoothed over 1000 km s$^{-1}$ is shown in\npanel (c) (full line). The simulated spectrum was made by combining\nmock spectra from two models with different values of $T_0$ ($1.5\\times\n10^4$ and $2.2\\times 10^4$K) but the same value of $\\gamma=5/3$, in\nstretches of length 6000 km s$^{-1}$. The temperature of this mixed\nmodel is shown as the dashed line in panel (c) (right axis). There is a\nstrong correlation between the rms wavelet amplitude and the\ntemperature of the absorbing gas, with $\\langle A^2\\rangle$ on average\nmuch larger for the cold parts of the spectrum, where $T_0=1.5\\times\n10^4$K, than in the hotter parts where $T_0=2.2\\times 10^4$K.}\n\\label{fig:exmp}\n\\end{figure*}\n\nThe decomposition of a mock spectrum in terms of discrete wavelets is\nunique, once a particular wavelet basis has been chosen. Here we will\nuse the Daubechies 20 wavelet (Daubechies 1988; see e.g. Press et\nal. 1992 for a general discussion on wavelets, and an example of the\nDaubechies 20 wavelet). Just as fast Fourier transforms, (discrete)\nwavelets come in powers of two, but unlike Fourier modes, a given\nwavelet has finite bandwidth and hence corresponds to a range of\nfrequencies. Nevertheless we will refer to a wavelet of a particular\n\\lq resolution\\rq, for example quoting its full width at half\nmaximum. The simulated spectrum has a length of $V=$37492 km s$^{-1}$\nand the wavelet resolutions correspond to $2^{i-15}\\times V$. Here we\nwill use the exponent $i$ to refer to wavelets of a particular\nresolution, e.g. $i=9$ corresponds to a wavelet of width 18.3 km\ns$^{-1}$. Analysing a signal in terms of the amplitudes of wavelets\nwith different resolutions was pioneered in a different context by\nMallat (1989).\n\nAn example of a wavelet decomposition of a simulated spectrum is shown\nin Figure~\\ref{fig:wltdecomp}. Using wavelets with only four\nresolutions ($i=9-12$) already gives a relatively good description of\nthe strong absorption features in the spectrum. Note how every line in\nthe top panel is \\lq detected\\rq~ on most resolution levels, indicating\nthat each individual absorption line is also made-up of a range of\nfrequencies. This is of course because these lines are relatively well\napproximated by Voigt profiles, which also have extended\nbandwidth. However, some lines are only weakly detected in the $i=9$\nnarrow wavelet, while some of the narrower lines lead to large\namplitudes at this high resolution. It is this feature, namely that\nsome narrow lines are picked-up strongly by the narrow wavelets while\nthe broader lines are not, that allows us to characterise objectively\nthe typical line-widths of absorption lines.\n\nFor a smaller value $T_0$ of the IGM temperature, there will be a\nlarger fraction of narrow lines in the absorption spectrum. For a given\npixel at velocity $v$ in the spectrum, let\n\\begin{equation}\n{\\cal A}(v;i,W) \\equiv \\int_{v-W/2}^{v+W/2} A(v;i)^2\ndv/W \n\\end{equation}\ndenote the mean rms amplitude of the wavelet at resolution $i$, box-car\nsmoothed over a window of size $W$ (km s$^{-1}$). We will usually drop\nthe indices $i$ and $v$ in what follows, and assume $i=9$ unless stated\notherwise. For a spectrum with a larger fraction of narrow lines,\n${\\cal A}$ will be larger on average, hence we can in principle use the\nstatistics of ${\\cal A}$ as a measure of $T_0$, once the relation\nbetween them is calibrated with simulations.\n\nIn addition to this mean trend, ${\\cal A}$ will fluctuate along the\nspectrum, due to (random) fluctuations in the strengths of lines. Here\nwe give an example showing that averaging $A^2$ over a relatively short\nstretch of spectrum is already enough to distinguish between models\nwith different $T_0$. This suggests it might be possible to detect {\\em\nfluctuations} in $T_0$ (and $\\gamma$), which might be a relic of a\nrecent epoch of reionization or local effects. We will present a more\ndetailed analysis of how this can be done below and restrict ourselves\nhere to a typical example illustrated in Figure~\\ref{fig:exmp}. To make\nthe shown spectrum, we have combined spectra of the $(1.5,5/3)$ model\non scales of 6000 km s$^{-1}$ with spectra of the 30 per cent hotter\nmodel $(2.2,5/3)$, into one long spectrum of length $V$. (In what\nfollows, we will refer to this model as the mixed-temperature model.)\nThe rms amplitude ${\\cal A}(v;9,1000)$ of the $i=9$ (18.3 km s$^{-1}$)\nwavelet, smoothed on 1000 km s$^{-1}$, is sufficiently different\nbetween these two equations of state that stretches of the colder model\ncan readily be distinguished from the hotter one as regions with larger\n${\\cal A}$.\n\nIn this example, both models have been scaled independently to have the\nsame mean optical depth, corresponding to the observed value for QSO\n1107. In reality, regions of higher temperature would tend to have\nsmaller optical depth because of the $T^{-0.7}$ temperature dependence\nof the recombination coefficient. This would tend to decrease the\namplitude of the wavelets in the hotter regions even more, making it\n{\\em easier} to distinguish between hot and cold regions.\n \n\\section{Wavelet statistics}\n\\label{sect:analysis}\n\\subsection{measuring the equation of state}\n\\begin{figure}\n\\setlength{\\unitlength}{1cm} \\centering\n\\begin{picture}(7,9)\n\\put(-2.4, -4){\\special{psfile=fig3a.ps hscale=60 vscale=60}}\n\\end{picture}\n\\caption{Cumulative fraction $\\bar C(< {\\cal A})$ of pixels, where the\nmean rms wavelet amplitude ${\\cal A}\\equiv \\langle A(9,500)^2\\rangle$\nof the $i=9$ wavelet, box-car smoothed over a window of size $W=500$ km\ns$^{-1}$, is less than some value, averaged over 100 spectra. The\ndifferent curves refer to different equations of state, as labelled in\nthe figure. Squares refer to the mixed-temperature model, obtained from\ncombining spectra of model $(1.5,5/3)$ with those of model $(2.2,5/3)$,\nin stretches of length 6000 km s$^{-1}$. Models with smaller $T_0$ and\nshallower equation of state have a larger fraction of pixels with large\nvalues of ${\\cal A}$. The mixed-temperature model differs from the\ncorresponding single temperature models.}\n\\label{fig:av500}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\centering\n\\begin{picture}(7,9)\n\\put(-2.5, -4){\\special{psfile=fig3b.ps hscale=60 vscale=60}}\n\\end{picture}\n\\caption{Same as Figure~\\ref{fig:av500}, but for a large smoothing\nscale $W=2000$ km s$^{-1}$.}\n\\label{fig:av2000}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\centering\n\\begin{picture}(7,9)\n\\put(-2.5, -4){\\special{psfile=fig4a.ps hscale=60 vscale=60}}\n\\end{picture}\n\\caption{Cumulative probability distribution of the dispersion\n$\\sigma_{ij}^2\\equiv \\langle (\\bar C_i-C_j)^2\\rangle$ for a smoothing\nwindow $W=500$ km s$^{-1}$. The first model in the caption refers to\nthe model $i$ for which $\\bar C_i$ is the mean (over 100 spectra)\ncumulative distribution of ${\\cal A}$. The second model in the caption\nrefers to model $j$ with cumulative distribution $C_j$ for a single\nspectrum. $\\sigma_{ij}^2$ is a measure of the extent that model $j$\nresembles model $i$. For $j=i$, it characterises the dispersion of the\ncumulative distribution of model $i$ around its mean. The shown models\n(2.2,1) and (1.5,5/3) can both be distinguished easily from model\n(1.5,1) since $\\sigma_{ij}^2$ tends to be $\\ge 0.004$ for most\nrealisations of these models, whereas a realisation of model (1.5,1)\nrarely deviates from its mean to such a large extent.}\n\\label{fig:disp500}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\centering\n\\begin{picture}(7,9)\n\\put(-2.5, -4){\\special{psfile=ks.ps hscale=60 vscale=60}}\n\\end{picture}\n\\caption{Kolmogorov-Smirnov test whether a given realisation of model\n$j$ (second model in the legend) is drawn from the distribution of\nmodel $i$ (first model in the legend) for $i=(1.5,5/3)$ and $j=i$ (full\nline) and $j=(2.2,1)$ (dashed line).}\n\\label{fig:kstest}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\centering\n\\begin{picture}(7,9)\n\\put(-2.5, -4){\\special{psfile=fig5.ps hscale=60 vscale=60}}\n\\end{picture}\n\\caption{Same as Figure~\\ref{fig:disp500}, but for the\nmixed-temperature model and with $W=2000$ km s$^{-1}$. The\nmixed-temperature model resembles most strongly its cold constituent,\nyet can be distinguished from it at the $>$ 80 per cent confidence\nlevel.}\n\\label{fig:disp2000_mixed}\n\\end{figure}\n\nIn the previous section we showed that the rms amplitude of the $i=9$\nnarrow wavelet is strongly anti-correlated with the temperature of the\nabsorbing gas. Consequently we can characterise the temperature\ndistribution of the IGM over the spectrum using the corresponding\ndistribution of wavelet amplitudes. For each of 100 realisations of\nmodels with a specified equation of state, we have computed the\ncumulative distribution of ${\\cal A}$,\n\\begin{equation}\nC(< {\\cal A}) = \\int_0^{\\cal A} P({\\cal A}) d{\\cal A}\\,,\n\\end{equation}\nwhere $P({\\cal A})$ is the probability distribution of ${\\cal A}$, and\nwe plot the mean over 100 realisations, $\\bar C(< {\\cal A})$, in\nfigures~\\ref{fig:av500} and \\ref{fig:av2000} for $W=500$ and 2000 km\ns$^{-1}$, respectively.\n\nAs expected, the colder models are systematically shifted to larger\nvalues of ${\\cal A}$, since they contain a large number of narrow lines\nand consequently have larger values of ${\\cal A}$. Note, however, that\nthe dependence on the slope $\\gamma$ is also quite strong, but this may\nbe partly a consequence of using the mean density as the pivot point\naround which we change the slope. We have also superposed the\nmixed-temperature model, which stays close to the hot component for\nsmall values of ${\\cal A}$ before veering away to the locus of the cold\ncomponent for large values of the amplitude.\n\nHaving shown that the mean cumulative distribution $\\bar C({\\cal A})$\ndepends on the equation of state, we now want to characterise how well\ndifferent models can be distinguished from each other, based on a {\\em\nsingle} spectrum. Hence, we want to characterise to what extent the\ncumulative distribution $C_j({\\cal A})$ for a single spectrum of model\n$j$ differs from the mean, $\\bar C_i$, for model $i$. To this end, we\ncompute the dispersion\n\\begin{equation}\n\\sigma_{ij}^2 \\equiv \\int_0^\\infty (\\bar C_i({\\cal A})- C_j({\\cal\nA}))^2 d{\\cal A}\\,.\n\\end{equation}\nFor a single realisation of a spectrum of model $j$, $\\sigma_{ij}^2$ is\njust a number. In order to be able to distinguish between two models\n$i$ and $j$ based on a single spectrum, it is necessary that the\ndispersion $\\sigma_{ii}^2$ be much smaller than the mean difference\n$\\sigma_{ij}^2$ between the models.\n\nFigure~\\ref{fig:disp500} shows the cumulative probability distribution\n$C(>\\sigma_{ij}^2)$ for $W=500$ for three different equations of\nstate. The confidence level at which a single spectrum of the model\nwith equation of state say (1.5,5/3) (model $j$) can be distinguished\nfrom the model with equation of state (1.5,1) (model $i$) can be\ndirectly read-off from this figure. For example, in $> 95$ per cent of\ncases $\\sigma_{ij}^2 > 0.004$ for $i\\ne j$, whereas in only 2 per cent\nof cases, a model which really has the equation of state (1.5,1) will\ndiffer from the mean of this model to such a large extent.\n\nA more usual statistic to judge whether a single realisation of a model\nis drawn from a given probability distribution is the\nKolmogorov-Smirnov test, based on the maximum absolute difference\n$dC={\\rm max}|\\bar C_i({\\cal A}) - C_j({\\cal A})|$ between two\ncumulative distributions. The cumulative distribution of the\nKS-statistic is shown in figure~{\\ref{fig:kstest}}, where we compare it\nfor models (1.5,5/3) and (2.2,1), which resemble each other most in\nfigure~\\ref{fig:disp500}. For 20 (5) per cent of realisations of model\n(1.5,5/3), $dC>0.1$ ($dC>0.12$), and at this level of contamination, 60\n(40) per cent of models (2.2,1) have $dC$ larger than that.\n\nFinally, figure~\\ref{fig:disp2000_mixed} illustrates how well the\nmixed-temperature model can be distinguished from either the cold or\nthe hot model with $\\gamma=5/3$. This model is most likely mistaken\nwith the colder single temperature counterpart. In 70 (25) per cent of\ncases, the mixed model has $\\sigma_{ij}^2 > 0.004$ ($\\sigma_{ij}^2 >\n0.01)$. This happens for the cold model in only 10 (5) per cent of\nrealisations.\n\n\\subsection{other effects}\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\centering\n\\begin{picture}(7,9)\n\\put(-2.5, -4){\\special{psfile=fig7.ps hscale=60 vscale=60}}\n\\end{picture}\n\\caption{Same as figure~\\ref{fig:av2000} but for models with different\nvalues of the normalisation $\\sigma_8$, indicated in the legend. Models\nwith smaller $\\sigma_8$ resemble more clustered but hotter models, but\nthe effect is relatively weak for realistic values of $\\sigma_8$.}\n\\label{fig:sigma8}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\centering\n\\begin{picture}(7,9)\n\\put(-2.5, -4){\\special{psfile=fig6.ps hscale=60 vscale=60}}\n\\end{picture}\n\\caption{Cumulative distribution $C(< {\\cal A})$, for a smoothing scale\nof 500 km s$^{-1}$ (full lines) and 2000 km s$^{-1}$ (dashed lines),\nfor a simulation box of 3.8 Mpc (thin lines) and 7.7Mpc (thick lines),\nbut the same numerical resolution. As before, we have plotted $C(<\n{\\cal A})$ averaged over 100 random realizations of the particular\nmodel. The model shown is (1.5,5/3) and the spectra are scaled to a\nmean effective optical depth of 0.26 at $z=3$. The influence of missing\nlong wavelength perturbations on the wavelet statistic is small.}\n\\label{fig:boxsize}\n\\end{figure}\n\nAbsorption features are broader in models with a smaller amplitude of\nthe dark matter fluctuations (Theuns et al. 2000), thereby resembling\nmore clustered but hotter models. This may lead to a degeneracy between\n$T_0$ and $\\sigma_8$ (Bryan \\& Machacek 1999; note that Theuns, Schaye\n\\& Haehnelt (2000) showed that their Voigt profile analysis does not\nsuffer from such a degeneracy). For the statistic presented here, this\ndegeneracy is not very strong, as shown in figure~\\ref{fig:sigma8}. The\nmodel with $\\sigma_8=0.775$ does not differ much from its more\nclustered counterpart with $\\sigma_8=0.9$. Only for very low levels of\nclustering, $\\sigma_8=0.4$, is the effect important. All models have\nbeen scaled to a mean effective optical depth of 0.26 at a redshift\n$z=3$.\n\n\nFinally we have investigated the influence of the small box size in our\nnumerical simulations, and the result is shown in\nfigure~\\ref{fig:boxsize}. Lack of long wavelength perturbations\ndecreases the observed range in ${\\cal A}$, as expected, but the effect\nof this purely numerical artifact is relatively weak.\n\n\n\\section{Conclusions}\n\\label{sect:conclusions}\nClues to the thermal history of the Universe are hidden in the small\nscale structure of the \\lya forest. There are two reasons for\nthis. Firstly, the widths of absorption lines are very sensitive to the\ntemperature of gas, and secondly, thermal time scales are long in the\nlow-density IGM that is responsible for the \\lya forest. Since the\ntemperature of the photo-ionised IGM is determined by the evolution of\nthe ionising background, unravelling the thermal history will have the\nadded benefit of putting strong limits on the sources of UV light at\nhigh redshifts.\n\nWe have presented a new way of analysing the small scale structure of\nthe \\lya forest, based on the unique decomposition of a spectrum in\ndiscrete wavelets. We have shown that the rms amplitude $\\langle\nA^2\\rangle$ of narrow wavelets (18.3 km $^{-1}$) correlates strongly\nwith the temperature of the IGM, and also depends on the slope of the\nequation of state. We have quantified to what extent different models\ncan be distinguished, using statistics of $\\langle A^2\\rangle$\n\nOur mock spectra have been designed to mimick an observed spectrum of\nQSO 1107+485 as much as possible. In particular, we have imposed on our\nsimulated spectra the same large scale optical depth fluctuations as\nare observed in QSO 1107, making our mock spectra quite realistic. Even\nso, we can still easily distinguish between models that differ in\ntemperature by less than 30 per cent. We have quantified the dependence\nof these statistics on numerical artifacts (missing long wavelength\nperturbations due to the smallness of our simulation box) and on the\namplitude of the dark matter fluctuations ($\\sigma_8$).\n\nWavelets are also localised in space, making it possible to study $T_0$\nand $\\gamma$ as a function of position along the spectrum. We\ncharacterised the extent to which we can distinguish models with a\nsingle value of $T_0$ from a model with temperature fluctuations, as\nmight result from late reionization or local effects.\n\n\n\\section*{Acknowledgments}\nWe acknowledge simulating discussion with Martin Haehnelt, Michael\nRauch, Joop Schaye and Simon White, This work has been supported by the\n\\lq Formation and Evolution of Galaxies\\rq~ network set up by the\nEuropean Commission under contract ERB FMRX-CT96086 of its TMR\nprogramme. This research was conducted in cooperation with Silicon\nGraphics/Cray Research utilising the Origin 2000 super computer at\nDAMTP, Cambridge.\n\n\\begin{thebibliography}{}\n\\bibitem[\\protect\\citename{}]{} Bahcall J.N., Salpeter E.E., 1965, ApJ,\n142, 1677\n\n\\bibitem[\\protect\\citename{}]{} Bryan G., Machacek M.A., 1999, preprint\n(astro-ph/9906459)\n\n\\bibitem[\\protect\\citename{Carswell \\etal 1987}]{carswellwba87} \nCarswell R.F., Webb J.K., Baldwin J.A., Atwood B., 1987, ApJ, 319,\n709\n\n\\bibitem[\\protect\\citename{Cen \\etal 1994}]{cenor94} Cen R.,\nMiralda-Escud\\'e J., Ostriker J.P., Rauch M., 1994, ApJL, 437, L9\n\n\n\\bibitem[\\protect\\citename{Couchman 1991}]{Couchman91} Couchman\nH.M.P., 1991, ApJL, 368, L23\n\n\\bibitem[\\protect\\citename{Couchman, Thomas \\& Pearce\n1995}]{Couchman95} Couchman H.M.P., Thomas P.A., Pearce F.R., 1995,\nApJ, 452, 797\n\n\\bibitem[\\protect\\citename{}]{} Croft R., Weinberg D.H., Katz N.,\nHernquist L., 1997, ApJ, 488, 532\n\n\\bibitem[\\protect\\citename{}]{} Debauchies I., 1988, Communications on\nPure and Applied Mathematics, 41, 909\n\n\\bibitem[\\protect\\citename{}]{} Eke V.R., Cole S., Frenk C.S.,\n1996, MNRAS, 282, 263\n\n\\bibitem[\\protect\\citename{Gingold \\& Monaghan\n1977}]{GingoldMonaghan77} Gingold R.A., Monaghan J.J., 1977, MNRAS,\n181, 375\n\n\n\\bibitem[\\protect\\citename{}]{} Gunn J.E., Peterson B.A., 1965, ApJ,\n142, 1633\n\n\\bibitem[\\protect\\citename{Haardt \\& Madau 1996}]{HaardtMadau96}\nHaardt F., Madau P., 1996, ApJ, 461, 20\n\n\\bibitem[\\protect\\citename{}]{} Haehnelt M.G., Steinmetz M., 1998,\nMNRAS, 298, 21\n\n\\bibitem[\\protect\\citename{Hernquist \\etal 96}]{Hernquistetal96}\nHernquist L., Katz N., Weinberg D.H., Miralda-Escud\\'e J., 1996,\nApJL, 457, L51\n\n\\bibitem[\\protect\\citename{}]{} Hui L., Gnedin N.Y., 1997, MNRAS, 292, 27\n\n\n\\bibitem[\\protect\\citename{Lucy 1970}]{Lucy77} Lucy L.B., 1977, AJ,\n82, 1023\n\n\\bibitem[\\protect\\citename{}]{} Mallat S.G., 1989, IEEE Transaction on\npattern analysis and machine intelligence, 11(7), 674\n\n\\bibitem[] {} Meiksin A., 2000, preprint (astro-ph/0002148)\n\n\\bibitem[\\protect\\citename{}]{} Miralda-Escud\\'e J., Cen R.,\nOstriker J.P.,Rauch M., 1996, ApJ, 471, 582\n\n\n\\bibitem[\\protect\\citename{}]{} Nusser A., Haehnelt M., 1999, MNRAS,\n303, 179\n\n\n\\bibitem[\\protect\\citename{}]{} Press W.H., Teukolsky S.A., Vetterling\nW.T., Flannery B.P., 1992, Numerical Recipes, Cambridge University Press\n\n\\bibitem[\\protect\\citename{}]{} Rauch M., 1996, in Cold Gas at High\nRedshift, ed. M.N.Bremer, P.P. van der Werf, H.J.A. R\\\"ottgering,\nC.L.Carilli (Dordrecht:Kluwer), 137\n\n\\bibitem[\\protect\\citename{}]{} Rauch M., 1998, ARA\\& A, 36, 267\n\n\\bibitem[\\protect\\citename{}]{} Rauch M., Miralda-Escud\\'e, J., Sargent\nW.L.W., Barlow T.A., Weinberg D.H., Hernquist L., Katz N., Cen R.,\nOstriker J., 1997, ApJ, 489, 7\n\n\\bibitem[\\protect\\citename{}]{} Ricotti M., Gnedin N.Y., Shull J.M.,\n2000, ApJ in press (astro-ph/9906413)\n\n\\bibitem[]{} Pando J., Fang L.Z., 1996, ApJ, 459, 1\n\\bibitem[]{} Pando J., Fang L.Z., 1998, A\\& A, 340, 335\n\\bibitem[\\protect\\citename{}]{} Seljak U., Zaldarriaga M., 1996, ApJ,\n469, 437\n\n\\bibitem[\\protect\\citename{}]{} Schaye J., Theuns T., Leonard A.,\nEfstathiou G., 1999, MNRAS, 310, 57\n\n\n\\bibitem[\\protect\\citename{}]{} Schaye J., \\etal, 2000, submitted to\nMNRAS (astro-ph/9912432)\n\n\n\\bibitem[\\protect\\citename{}]{} Theuns T., Leonard A., Efstathiou G.,\nPearce F.R., Thomas P.A., 1998, MNRAS, 301, 478\n\n\n\\bibitem[\\protect\\citename{}]{} Theuns T., Schaye, J., Haehnelt, M.,\n2000, submitted to MNRAS (astro-ph/9908288)\n\n\\bibitem[\\protect\\citename{Wadsley \\& Bond 1996}]{wadsleyb96} Wadsley\nJ., Bond J.R, 1996, in \"Computational Astrophysics\", Proc. 12th\nKingston Conference, Halifax, Oct. 1996, ed. D. Clarke \\& M. West\n(PASP)\n\n\\bibitem[]{} Webb J.K., 1987, PhD thesis, Univ. Cambrdige\n\n\\bibitem[\\protect\\citename{}]{} Zhang Y., Anninos P., Norman M.L.,\n1995, ApJL, 453, L57\n\n\\bibitem[\\protect\\citename{}]{} Zhang Y., Anninos P., Norman M.L.,\nMeiksin, A., 1997, ApJ, 485, 496\n\n\\end{thebibliography}{}\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002172.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[\\protect\\citename{}]{} Bahcall J.N., Salpeter E.E., 1965, ApJ,\n142, 1677\n\n\\bibitem[\\protect\\citename{}]{} Bryan G., Machacek M.A., 1999, preprint\n(astro-ph/9906459)\n\n\\bibitem[\\protect\\citename{Carswell \\etal 1987}]{carswellwba87} \nCarswell R.F., Webb J.K., Baldwin J.A., Atwood B., 1987, ApJ, 319,\n709\n\n\\bibitem[\\protect\\citename{Cen \\etal 1994}]{cenor94} Cen R.,\nMiralda-Escud\\'e J., Ostriker J.P., Rauch M., 1994, ApJL, 437, L9\n\n\n\\bibitem[\\protect\\citename{Couchman 1991}]{Couchman91} Couchman\nH.M.P., 1991, ApJL, 368, L23\n\n\\bibitem[\\protect\\citename{Couchman, Thomas \\& Pearce\n1995}]{Couchman95} Couchman H.M.P., Thomas P.A., Pearce F.R., 1995,\nApJ, 452, 797\n\n\\bibitem[\\protect\\citename{}]{} Croft R., Weinberg D.H., Katz N.,\nHernquist L., 1997, ApJ, 488, 532\n\n\\bibitem[\\protect\\citename{}]{} Debauchies I., 1988, Communications on\nPure and Applied Mathematics, 41, 909\n\n\\bibitem[\\protect\\citename{}]{} Eke V.R., Cole S., Frenk C.S.,\n1996, MNRAS, 282, 263\n\n\\bibitem[\\protect\\citename{Gingold \\& Monaghan\n1977}]{GingoldMonaghan77} Gingold R.A., Monaghan J.J., 1977, MNRAS,\n181, 375\n\n\n\\bibitem[\\protect\\citename{}]{} Gunn J.E., Peterson B.A., 1965, ApJ,\n142, 1633\n\n\\bibitem[\\protect\\citename{Haardt \\& Madau 1996}]{HaardtMadau96}\nHaardt F., Madau P., 1996, ApJ, 461, 20\n\n\\bibitem[\\protect\\citename{}]{} Haehnelt M.G., Steinmetz M., 1998,\nMNRAS, 298, 21\n\n\\bibitem[\\protect\\citename{Hernquist \\etal 96}]{Hernquistetal96}\nHernquist L., Katz N., Weinberg D.H., Miralda-Escud\\'e J., 1996,\nApJL, 457, L51\n\n\\bibitem[\\protect\\citename{}]{} Hui L., Gnedin N.Y., 1997, MNRAS, 292, 27\n\n\n\\bibitem[\\protect\\citename{Lucy 1970}]{Lucy77} Lucy L.B., 1977, AJ,\n82, 1023\n\n\\bibitem[\\protect\\citename{}]{} Mallat S.G., 1989, IEEE Transaction on\npattern analysis and machine intelligence, 11(7), 674\n\n\\bibitem[] {} Meiksin A., 2000, preprint (astro-ph/0002148)\n\n\\bibitem[\\protect\\citename{}]{} Miralda-Escud\\'e J., Cen R.,\nOstriker J.P.,Rauch M., 1996, ApJ, 471, 582\n\n\n\\bibitem[\\protect\\citename{}]{} Nusser A., Haehnelt M., 1999, MNRAS,\n303, 179\n\n\n\\bibitem[\\protect\\citename{}]{} Press W.H., Teukolsky S.A., Vetterling\nW.T., Flannery B.P., 1992, Numerical Recipes, Cambridge University Press\n\n\\bibitem[\\protect\\citename{}]{} Rauch M., 1996, in Cold Gas at High\nRedshift, ed. M.N.Bremer, P.P. van der Werf, H.J.A. R\\\"ottgering,\nC.L.Carilli (Dordrecht:Kluwer), 137\n\n\\bibitem[\\protect\\citename{}]{} Rauch M., 1998, ARA\\& A, 36, 267\n\n\\bibitem[\\protect\\citename{}]{} Rauch M., Miralda-Escud\\'e, J., Sargent\nW.L.W., Barlow T.A., Weinberg D.H., Hernquist L., Katz N., Cen R.,\nOstriker J., 1997, ApJ, 489, 7\n\n\\bibitem[\\protect\\citename{}]{} Ricotti M., Gnedin N.Y., Shull J.M.,\n2000, ApJ in press (astro-ph/9906413)\n\n\\bibitem[]{} Pando J., Fang L.Z., 1996, ApJ, 459, 1\n\\bibitem[]{} Pando J., Fang L.Z., 1998, A\\& A, 340, 335\n\\bibitem[\\protect\\citename{}]{} Seljak U., Zaldarriaga M., 1996, ApJ,\n469, 437\n\n\\bibitem[\\protect\\citename{}]{} Schaye J., Theuns T., Leonard A.,\nEfstathiou G., 1999, MNRAS, 310, 57\n\n\n\\bibitem[\\protect\\citename{}]{} Schaye J., \\etal, 2000, submitted to\nMNRAS (astro-ph/9912432)\n\n\n\\bibitem[\\protect\\citename{}]{} Theuns T., Leonard A., Efstathiou G.,\nPearce F.R., Thomas P.A., 1998, MNRAS, 301, 478\n\n\n\\bibitem[\\protect\\citename{}]{} Theuns T., Schaye, J., Haehnelt, M.,\n2000, submitted to MNRAS (astro-ph/9908288)\n\n\\bibitem[\\protect\\citename{Wadsley \\& Bond 1996}]{wadsleyb96} Wadsley\nJ., Bond J.R, 1996, in \"Computational Astrophysics\", Proc. 12th\nKingston Conference, Halifax, Oct. 1996, ed. D. Clarke \\& M. West\n(PASP)\n\n\\bibitem[]{} Webb J.K., 1987, PhD thesis, Univ. Cambrdige\n\n\\bibitem[\\protect\\citename{}]{} Zhang Y., Anninos P., Norman M.L.,\n1995, ApJL, 453, L57\n\n\\bibitem[\\protect\\citename{}]{} Zhang Y., Anninos P., Norman M.L.,\nMeiksin, A., 1997, ApJ, 485, 496\n\n\\end{thebibliography}"
}
] |
astro-ph0002173
|
Radial Velocity Studies of Close Binary Stars.~III\footnote[1]{Based on the data obtained at the David Dunlap Observatory, University of Toronto.}
|
[
{
"author": "Slavek M. Rucinski"
},
{
"author": "Wenxian Lu"
},
{
"author": "Stefan W. Mochnacki"
}
] |
Radial velocity measurements and simple sine-curve fits to the orbital velocity variations are presented for the third set of ten contact binary systems: CN~And, HV~Aqr, AO~Cam, YY~CrB, FU~Dra, RZ~Dra, UX~Eri, RT~LMi, V753~Mon, OU~Ser. All systems but two are contact, double-line spectroscopic binaries with four of them (YY~CrB, FU~Dra, V753~Mon, OU~Ser) being the recent discoveries of the Hipparcos satellite project. The most interesting object is V753~Mon with the mass-ratio closest to unity among all contact systems ($q = 0.970 \pm 0.003$) and large total mass ($(M_1+M_2) sin^3i = 2.93 \pm 0.06$). Several of the studied systems are prime candidates for combined light and radial-velocity synthesis solutions.
|
[
{
"name": "pap_30w.tex",
"string": "% Draft of the WUMa-30 paper\n\n\\documentstyle[11pt,aaspp4]{article}\n%\\documentstyle[12pt,aasms4]{article} % manuscript format for publ\n\n\\begin{document}\n\n\\renewcommand{\\thefootnote}{\\fnsymbol{footnote}}\n\n\\title{Radial Velocity Studies of Close Binary \nStars.~III\\footnote[1]{Based on the data obtained at the David Dunlap \nObservatory, University of Toronto.}}\n\n\\renewcommand{\\thefootnote}{\\arabic{footnote}}\n\n\\author{Slavek M. Rucinski, Wenxian Lu, Stefan W. Mochnacki\\\\\ne-mail: {\\it rucinski@astro.utoronto.ca, lu@astro.utoronto.ca,\nmochnacki@astro.utoronto.ca}}\n\n\\affil{David Dunlap Observatory, University of Toronto \\\\\nP.O.Box 360, Richmond Hill, Ontario L4C~4Y6, Canada}\n\n\\centerline{\\today}\n\n\\begin{abstract}\nRadial velocity measurements and simple sine-curve fits to the orbital \nvelocity variations are presented for the third set of ten contact binary \nsystems: CN~And, HV~Aqr, AO~Cam, YY~CrB, FU~Dra, RZ~Dra, UX~Eri, \nRT~LMi, V753~Mon, OU~Ser. All systems but two are contact, double-line \nspectroscopic binaries with four of them \n(YY~CrB, FU~Dra, V753~Mon, OU~Ser) being the recent\ndiscoveries of the Hipparcos satellite project. \nThe most interesting object\nis V753~Mon with the mass-ratio closest to unity among all contact\nsystems ($q = 0.970 \\pm 0.003$) and large total mass \n($(M_1+M_2) sin^3i = 2.93 \\pm 0.06$). Several of the studied \nsystems are prime candidates for combined light and \nradial-velocity synthesis solutions.\n\\end{abstract}\n\n\\keywords{ stars: close binaries - stars: eclipsing binaries -- \nstars: variable stars}\n\n\\section{INTRODUCTION}\n\\label{sec1}\n\nThis paper is a continuation of the radial velocity studies of close \nbinary stars, \\cite{LR99} (Paper I) and \\cite{RL99} (Paper II).\nThe main goals and motivations are described in these papers.\nIn short, we attempt to obtain modern radial velocity data for\nclose binary systems which are accessible to the 1.8 meter class \ntelescopes at medium spectral resolution of about R = 10,000 -- 15,000. \nSelection of the objects is quasi-random in the sense that we\nstarted with shortest period contact binaries. The intention is\nto publish the results in groups of ten systems as soon as reasonable\norbital elements can be obtained from measurements evenly distributed \nin orbital phases. We are currently observing a few dozens of such systems.\nThe rate of progress may slow down, as we move into systems with\nprogressively longer periods. \n \nThis paper is structured in the same way as Papers~I and II in that it \nconsists of two tables containing the radial velocity \nmeasurements (Table~\\ref{tab1}) and \ntheir sine-curve solutions (Table~\\ref{tab2}) \nand of brief summaries of previous studies for individual systems. \nThe reader is referred to the previous papers for technical details \nof the program. In short, all observations described here were \nmade with the 1.88 meter telescope of the David \nDunlap Observatory (DDO) of the University of Toronto. The \nCassegrain spectrograph giving the scale of \n0.2 \\AA/pixel, or about 12 km/s/pixel, was used; \nthe pixel size of the CCD was 19~$\\mu$m. A relatively wide \nspectrograph slit of 300~$\\mu$m corresponded to the angular size on \nthe sky of 1.8 arcsec and the projected width of 4 pixels. \nThe spectra were centered at 5185 \\AA\\ with the spectral coverage of \n210 \\AA. The exposure times were typically 10 -- 15 minutes long.\n\nThe data in Table~\\ref{tab1} are organized in the same manner as \nin Paper~II. It provides information about the relation between \nthe spectroscopically observed epoch of the primary-eclipse T$_0$ \nand the recent photometric determinations in the form of the (O--C) \ndeviations for the number of elapsed periods E. It also contains, \nin the first column below the star name,\nour new spectral classifications of the program objects. The classification\nspectra, were obtained with a grating giving a dispersion of \n0.62 \\AA/pixel in the range 3850 -- 4450 \\AA. The program-star spectra \nwere ``interpolated'' between spectra of standard stars \nin terms of relative strengths of lines \nknown as reliable classification criteria.\n\nIn the radial-velocity solutions of the orbits, the data have \nbeen assigned weights on the basis of our ability to resolve the \ncomponents and to fit independent Gaussians to each of the \nbroadening-function peaks. Weight equal to zero in \nTable~\\ref{tab1} means that an observation was not used \nin our orbital solutions; however, these observations may be utilized in \ndetailed modeling of broadening functions, if such are \nundertaken for the available material. The full-weight points are \nmarked in the figures by filled symbols while \nhalf-weight points are marked \nby open symbols. Phases of the observations with zero weights are \nshown by short markers in the lower parts of the figures; they were \nusually obtained close to the phases of orbital conjunctions.\n\nAll systems discussed in this paper but one have been observed for\nradial velocities for the first time. The only exception is RZ~Dra\nfor which an SB1 orbit solution was obtained by \\cite{str46}.\nThe solutions presented in Table~\\ref{tab2} for \nthe four circular-orbit parameters, $\\gamma$, K$_1$, K$_2$ and T$_0$, \nhave been obtained iteratively, with fixed values of the orbital period. \nFirst, two independent least-squares solutions for \neach star were made using the same programs as described in Papers~I\namd II. Then, one combined solution for both amplitudes and the common \n$\\gamma$ was made with the fixed mean \nvalue of T$_0$. Next, differential corrections for $\\gamma$, \nK$_1$, K$_2$, and T$_0$ were determined, providing best \nvalues of the four parameters. These values are given in Table~\\ref{tab2}. \nThe corrections to $\\gamma$, K$_1$, K$_2$, and T$_0$ were finally \nsubject to a ``bootstrap'' process (several thousand \nsolutions with randomly drawn data with repetitions) to \nprovide the median values and ranges of the\nparameters. We have adopted them as measures of \nuncertainty of parameters in Table~\\ref{tab2}.\n\nThroughout the paper, when the errors are not written otherwise, we \nexpress standard mean errors in terms of the last quoted digits, \ne.g. the number 0.349(29) should be interpreted as $0.349 \\pm 0.029$. \n\n\\placetable{tab1}\n\n\\placetable{tab2}\n\n\\section{RESULTS FOR INDIVIDUAL SYSTEMS}\n\\label{sec2}\n\n\\subsection{CN And}\n\nThe variability of CN~And was discovered by \\cite{hof49}. Modern \nlight curves were presented by \\cite{kal83}, \\cite{raf85},\n\\cite{kes89} and \\cite{sam98}. The light curve is of the EB-type,\nwith unequally deep eclipses. From the eclipse timing, \nthere exists a clear indication of a\ncontinuous period decrease. We used the almost contemporary\nwith our observations determination of the primary eclipse time \n$T_0$ by \\cite{sam98}. The radial velocity curve\nof the secondary component (see Figure~\\ref{fig1})\nshows some asymmetry in the first half of the orbital period which \nmay explain why our $T_0$ is shifted by $-0.014$ day to earlier\nphases. From the radial-velocity point of view, the system\nlooks like a typical A-type contact binary, but it can be also\na very close semi-detached system.\n\nTwo groups of investigators attempted solutions of the light curves\nfor orbital parameters, disregarding lack of any information on\nthe spectroscopic mass-ratio. Our $q_{sp} = 0.39 \\pm 0.03$ differs\nrather drastically from these photometric estimates.\n\\cite{kal83} expected the mass-ratio to be within \n$0.55 < q_{ph} < 0.85$. \\cite{raf85} found the most \nlikely interval to be $0.5 < q_{ph} < 0.8$; \nthey saw indications of a strong contact. The matter\nof the contact or semi-detached nature of the system\nshould be re-visited in view of the \ndiscrepancy between our $q_{sp}$ and the previous\nestimates of $q_{ph}$. \n\nThe photometric data at maximum light were published by \\cite{kal83}:\n$V = 9.62$, $(B-V) = 0.45$. The system is apparently a moderately\nstrong X-ray source (\\cite{sha96}). \n\n\\placefigure{fig1}\n\n\\subsection{HV Aqr}\n\nVariability of HV~Aqr was discovered relatively recently \nby \\cite{hut92}. The type of variability was identified by\n\\cite{sch92} and a preliminary, but thorough study was\npresented by \\cite{rob92}. The system shows total\neclipses at the shallower of the two minima, so it is definitely\nan A-type one. This circumstance is important to our\nresults because both available \nephemerides of Schirmer and Robb do\nnot predict the primary minimum correctly and we are\nnot sure how our radial-velocity \nobservations relate to the photometric observations: Our $T_0$\nfalls at phase 0.47 for the former and at 0.70\nfor the latter. Probably the values of the orbital period\nare slightly incorrect for both ephemerides. We used\nthe period of 0.374460 day, following \\cite{sch92}; if\nthis is incorrect, then part of the scatter in our data\nmay be due to the incorrect phasing over the span of 450 days\nof our observations. \n\nThe mass-ratio of HV~Aqr is small, $q_{sp} = 0.145 \\pm 0.05$.\nIt agrees perfectly with the photometric solution of\n\\cite{rob92} of $q_{ph} = 0.146$ which confirms the validity\nof the photometric approach for totally eclipsing systems,\nin contrast with the typical lack of agreement\nfor partially eclipsing systems.\n\nOur spectral type of F5V agrees with the observed $(B-V)=0.63-0.78$\nfor a relatively large reddening of $E_{B-V}=0.08$\nexpected by \\cite{rob92}. The system is bright with $V = 9.80$,\nand is potentially one of the \nbest for a combined spectroscopic -- photometric solution.\n\n\\subsection{AO Cam}\n\nVariability of AO Cam was discovered by \\cite{hof66}. \\cite{mil82}\nanalyzed their photometric observations in a simplified way.\nSubsequent photometric solution by \\cite{eva85}\nand even the sophisticated work of \\cite{bar93} \ndid not bring much progress in view of the partial eclipses\nand total lack of any information on the mass-ratio. \\cite{bar93}\nstated that AO~Cam is definitely a W-type system; they \nestimated the photometric mass-ratio at $q_{ph}\n=1.71 \\pm 0.04$ or $1/q = 0.585$. This value is very different\nfrom our spectroscopic result, $q_{sp} = 0.413 \\pm 0.011$,\nbut we do confirm the W-type of the system.\n\nAO Cam does not have any $UBV$ data. Our spectral\nclassification is G0V. In view of its\nconsiderable brightness of $V = 9.50$ at maxima, \nit appears to be a somewhat neglected system. \n\nTo predict the moment of the primary eclipse $T_0$,\nwe used the ephemeride based on the period of \\cite{eva85}\nand the observations of the {\\it secondary eclipses\\/}\nby \\cite{fau86}. The (O--C) deviation is relatively small\nin spite of many orbital periods elapsed since Faulker's\nobservations.\n\n\\subsection{YY CrB}\n\nYY~CrB is one of the variable stars discovered by the Hipparcos\nsatellite mission (\\cite{hipp}). The only available \nlight curve comes from this satellite; \nthe star has not been studied in any other way.\nThere are no obvious indications of total eclipses, but\nthe coverage of eclipses is relatively poor so that\nit is possible that the minimum identified as the primary\nis not the deeper one. We used the primary minimum ephemeride of\nHipparcos and this results in a contact system of type A, that is with\nthe more massive and hotter component eclipsed at this minimum.\n\nThe system is bright, $V_{max} = 8.64$, and its Hipparcos parallax is\nrelatively large and well-determined, $p = 11.36 \\pm 0.85$\nmilli-arcsec (mas), giving a good estimate of the\nabsolute magnitude of the system, $M_V=3.92 \\pm 0.16$. With\n$(B-V) = 0.62 \\pm 0.02$ from the Hipparcos database, the\n$M_V(\\log P, B-V)$ calibration (\\cite{RD97}) gives \n$M_V^{cal}=3.88$ so that the agreement is perfect. Our \nspectral classification of F8V agrees with the $(B-V)$ color index.\n\nWith the very good parallax and the new radial velocity data,\nYY CrB is one of the systems which have a great \npotential of providing an excellent \ncombined photometric and spectroscopic solution.\n\n\\subsection{FU Dra}\n\nFU~Dra is another Hipparcos discovery. Again, we assumed the\nprimary eclipse identification and its ephemeride as in the \nHipparcos publication (\\cite{hipp}). With these assumptions, the system\nappears to belong to the W-type systems. The mass-ratio\nis somewhat small for such systems, $q_{sp} = 0.25 \\pm 0.03$.\n\nThe system is bright, $V_{max} = 10.55$, but its Hipparcos parallax\nis only moderately well determined, $p = 6.25 \\pm 1.09$ \nmas, resulting in the absolute magnitude $M_V=4.53 \\pm 0.38$.\nThe system was measured by the Hipparcos project\nto have a relatively large tangential motion,\n$\\mu_{RA} = -255.85 \\pm 1.18$ mas and $\\mu_{dec} = 16.61 \\pm 1.18$ mas.\nThe large proper motion had been noticed before (\\cite{lee84a}, \n\\cite{lee84b}), but the spatial velocity was then estimated \nassuming an uncertain spectroscopic parallax. Using the Hipparcos\ndata one obtains the two tangential components, $V_{RA} = -194$ \nkm~s$^{-1}$ and $V_{dec} = 13$ km~s$^{-1}$. The radial\nvelocity $\\gamma = -11$ km~s$^{-1}$ is moderate, so that only the\nRA component of the spatial tangential velocity is very large. \n\n\\placefigure{fig2}\n\n\\subsection{RZ Dra}\n\nRZ Dra has been frequently photometrically observed \nsince the discovery by \\cite{cer07}.\nThe most recent extensive analysis of the system was by \\cite{kre94}.\nIt utilized the only extant set of\nspectroscopic observations by \\cite{str46}\nwhich led to a detection of one, brighter component. \nOur data confirm the primary amplitude $K_1 = 100$ km~s$^{-1}$, \nbut we have been to also detect the secondary\ncomponent. The system consists of components considerably\ndiffering in the effective temperature, and thus is classified as\nan EB-type binary. Spectroscopically, one sees a more massive\ncomponent eclipsed at the deeper minimum so that it can be an\nAlgol semi-detached binary or an A-type contact system in poor\nthermal contact.\nThe analysis of \\cite{kre94} was made under the assumption \nof the semi-detached configuration. They found the \nphotometric mass-ratio\n$q_{ph} \\simeq 0.45$, but some solutions suggested $q_{ph}\n\\simeq 0.55$. Our relatively well defined solution for both\ncomponents gives $q_{sp} = 0.40 \\pm 0.04$. The same\ninvestigation of Kreiner et al.\\ \nprovided the starting value of $T_0$. In spite of\nindications that the period may be variable and that\nmany epochs elapsed since the study by Kreiner et al.,\nthe observed shift in the primary eclipse time is relatively \nsmall.\n\nThe spectral type that we observed, A6V, most probably applies to the\nprimary component which is much hotter than its companion (we\nhave not attempted to separate the spectra in terms of spectral types).\nThe Hipparcos parallax of the system, $p=1.81 \\pm 1.01$ mas,\nis too poor for an more extensive analysis of the absolute\nmagnitude of the system. RZ~Dra appears to\nbe a relatively short-period (0.55 day)\nsemi-detached Algol with both components accessible to\nspectroscopic observations.\n\n\\subsection{UX Eri}\n\nUX Eri is a contact binary which was extensively \nphotometrically observed since its discovery by \\cite{sol37}.\nThe first modern contact-model solutions which gave surprisingly\ngood agreement with our spectroscopic mass-ratio, $q_{sp}=0.37 \\pm 0.02$,\nwas presented by \\cite{mau72} almost quarter of a century ago;\nit utilized the light curve of \\cite{bin67} and\narrived at $q_{ph} = 0.42$. \n\nOur observations have been supplemented by four\nobservations obtained at the same time by Dr.\\ Hilmar\nDuerbeck at the European Southern Observatory with\na 1.52m telescope and a Cassegrain spectrograph. \nAs a starting point of our solution, \nwe used the moment of the primary minimum $T_0$ \nas predicted on the basis of observations \nby \\cite{AH98a} and \\cite{AH98b}; both took place actually\nslightly after our spectroscopic observations.\n\nUX Eri appears to be an A-type contact binary. \nThe $(B-V)$ color index is not available for this star\n(it has also not been measured by Hipparcos),\nso we have not been able to relate it to our spectral \nclassification of F9V.\nThe Hipparcos parallax $p=6.57 \\pm 2.84$ mas provides\na relatively poor estimate of the absolute magnitude \nfor the maximum brightness of $V_{max} = 10.59$:\n$M_V = 4.7 \\pm 0.9$.\n\n\\subsection{RT LMi}\n\nRT LMi was discovered as a variable star by \\cite{hof49}. The most recent\nanalysis from which we took the time of the primary eclipse $T_0$\nis by \\cite{nia94}. The system has been characterized in this study as \na W-type contact binary of spectral type G0V with photospheric \nspots. Our spectral classification is based on poor spectra,\nbut they indicate a slightly earlier spectral type, of approximately\nF7V. As \\cite{nia94}\npointed out, the minima were observed to be of almost equal depth.\nOur spectroscopic orbit gives an A-type so that the minimum selected\nby the authors as the primary corresponds to the eclipse of the\nmore massive component (the temporal shift is very small\nin spite of many elapsed epochs). The photometric solution of \\cite{nia94}\nassuming the W-type appears therefore to be invalid. \nThe system is otherwise quite an inconspicuous\ncontact binary. It lacks even most essential photometric data.\nThe Simbad database gives $V_{max} = 11.4$, but the source of this\nvalue is not cited.\n\n\\placefigure{fig3}\n\n\\subsection{V753 Mon}\n\nV753 Mon is a new discovery of the Hipparcos mission. It is probably\none of the most interesting new close binaries recently discovered.\nV753 Mon has not been studied before. The only published \nphotometric data come from the $uvby$ survey \nof \\cite{ols94} who found $(b-y) = 0.214 \\pm 0.008$,\n$m_1=0.160 \\pm 0.003$ and $c_1=0.693 \\pm 0.023$. The \n$(b-y)$ color index color corresponds\nto $(B-V) \\simeq 0.34$ or the spectral type F2V. Our spectral\nclassification is A8V which does not agree with these estimates\nand with $(B-V)=0.36$ in\nthe Hipparcos catalog, unless there is considerable reddening of\nabout $E_{B-V} \\simeq 0.12$. However, the early type would be\nin a better accord with the large masses indicated by the\nradial velocity solution (see below).\nThe brightness data in the Olsen measurements\nindicated quite appreciable variability, $V=8.46 \\pm 0.34$, but this\nindication has been apparently overlooked. The Hipparcos mission\ndatabase treats it as a new discovery.\n\nThe two features distinguish V753 Mon as a particularly interesting\nsystem: The mass-ratio close to unity and the large amplitudes of radial\nvelocity variations indicating a large total mass. The mass-ratio\n$q_{sp}=0.970 \\pm 0.009$ is the closest to unity of all \nknown contact binaries. Note that the currently largest\nmass ratios are $q=0.80$ for VZ~Psc (\\cite{hri95})\nand SW~Lac (\\cite{zha89}) and $q=0.84$ for OO~Aql\n(\\cite{hri89}).\nSince contact systems with $q \\simeq 1$ are not observed, but \nare expected to experience {\\it strong favorable \nobservational biases for their detection and ease in analysis\\/},\nit is generally thought that contact configurations avoid this\nparticular mass-ratio.\nThe summed amplitudes of the radial velocity variations \nfor V753~Mon give the\ntotal mass of the system, $(M_1+M_2) sin^3i = 2.93 \\pm 0.06$. \nThis is in perfect agreement with the expected masses of two\nmain-sequence stars of the spectral type F2V seen on an orbit\nexactly perpendicular to the plane of the sky. The light\nvariation is about 0.52 mag., in place of the expected\nabout 1.0 mag.\\ for a contact system with $q \\simeq 1$; \ntherefore, the total mass for $i<90^\\circ$ may turn \nout to be substantially larger. For the spectral type\nestimated by us the individual masses should be close \nto $1.7\\,M_\\odot$.\n\nOur radial velocity data show that\nwith the ephemeride based on the Hipparcos data, the system belongs\nto the W-type contact systems. Apparently, the eclipses are\nof almost the same depth, as expected for $q \\simeq 1$.\nHowever, the light curve from Hipparcos\nis poorly covered around the secondary minimum so that \nthe identification of the eclipses is uncertain. Obviously,\nthe distinction between A-type and W-type systems becomes\nimmaterial for $q \\rightarrow 1$. \n\nThe system is begging a new light curve and an extensive analysis,\nnot only because of the unusual properties, but also because it\nis bright, $V_{max}=8.34$, and has a moderately well determined\nHipparcos parallax: $p=5.23 \\pm 1.04$ resulting in\n$M_V = 1.93 \\pm 0.43$. This is in perfect agreement with\nthe $M_V(\\log P, B-V)$ calibration which gives $M_V^{cal} = 1.90$\nfor the assumed $(B-V)=0.34$. The agreement would not be that good\nif the color index is smaller, say 0.22, then one would obtain\n$M_V^{cal} = 1.54$ which is still within the uncertainty \nof the parallax. Further investigations of V753~Mon will therefore\ncontribute to the absolute-magnitude calibration which is\nrather moderately-well defined for contact binaries with periods\nlonger than about 0.5 day (\\cite{RD97}).\n\n\\subsection{OU Ser}\n\nOU~Ser is the fourth Hipparcos mission discovery in this group\nof systems. The light curve shows almost equally\ndeep minima. With the Hipparcos ephemeride, the system appears\nto be an A-type one with a small mass-ratio $q_{sp} = 0.173 \\pm 0.017$.\nOur spectral classification of the system indicates the spectral\ntype F9/G0V.\n\nThe distinguishing properties of OU~Ser in the Hipparcos database\nare its large proper motion and a well measured parallax.\nThe tangential components of the proper motion are $\\mu_{RA} =\n-387.5 \\pm 0.9$ mas and $\\mu{dec} = 2.8 \\pm 0.8$ mas. With the\nparallax of $p = 17.3 \\pm 1.0$ mas this translates into the\nspatial components $V_{RA} = -106$ km~s$^{-1}$ and \n$V_{dec} = 1$ km~s$^{-1}$. The mean radial velocity of the\nsystem is $\\gamma = -64.08 \\pm 0.41$ km~s$^{-1}$. Thus, the\nRA and the radial velocity components indicate a high-velocity\nstar.\n\nThe large proper motion of the star had been the reason for\ninclusion in the survey by \\cite{car94}. They noted also the\nbroad lines indicating short-period binarity and possibility\nof light variations. Their photometric data $V=8.27$,\n$(B-V)=0.62$ and $(U-B)=0.08$ agree with our spectral classification,\nF9/G0V. The $ubvy$ survey of \\cite{ols94} suggests a slightly\nlarger $(B-V) \\simeq 0.66$ on the basis of the $(b-y)=0.411 \n\\pm 0.003$, hence a spectral type around G1/2V. The difference\nin the classification may be due to the apparently low metallicity\nof the system as judged by its low index $m_1=0.168 \\pm 0.004$\n(provided this index is not confused by any chromospheric activity).\nthe other data of Olsen are $V=8.278 \\pm 0.005$ and $c_1 = 0.281\n\\pm 0.006$.\n\nAssuming $V_{max}=8.25$ and the parallax $p=17.3 \\pm 1.0$ \nmas, one obtains $M_V = 4.44 \\pm 0.12$. This again agrees very well\nwith the absolute magnitude derived from the \n$M_V(\\log P, B-V)$ calibration of \\cite{RD97}:\nFor $(B-V)=0.62$, $M_V^{cal} = 4.32$, \nwhile for $(B-V)=0.66$, $M_V^{cal}=4.46$.\n\nWith the excellent parallax data and its properties of a high\nvelocity star, OU~Ser deserves a combined photometric --\nspectroscopic solution.\n\n\\section{SUMMARY}\n\nThe paper brings radial velocity data for the third group of ten \nclose binary systems that we observed \nat the David Dunlap Observatory. All, but RZ~Dra (which\nhad SB1 radial velocity data), have never been\nobserved spectroscopically; all ten are binaries with \nboth components clearly detected so that they can be called SB2. \nAll systems, but CN~And and RZ~Dra, which may be very\nclose semi-detached systems, are contact binaries. \nWe describe special features of the individual systems in the\ndescriptions in Section~\\ref{sec2}. We note that again\nabout half of the system are A-type contact binaries; the likely\nreasons why we prefer them over the W-type systems in\nour randomly drawn sample are given in the Conclusions to Paper~II.\nWe also observed as EB2 systems two binaries, CN~And and RZ~Dra;\nthey are most probably semi-detached binaries.\n\nWe do not give the calculated\nvalues of $(M_1+M_2) \\sin^3i = 1.0385 \\times 10^{-7}\\,(K_1+K_2)^3\\,\nP({\\rm day})\\,M_\\odot$ because in most cases the\ninclination angles are either unknown or not trustworthy. However,\none case is very interesting here: The total mass of components\nof the system V753~Mon is very large, $M_1+M_2 > 2.93 M_\\odot$.\nSince {\\it too large velocity amplitudes\\/} are a rare phenomenon\nin the world of contact systems, this system requires special\nattention of the observers. The binary is also unique in having its\nmass-ratio exceptionally close to unity, $q_{sp}=0.970 \\pm 0.009$. \nTwo other systems discovered by the\nHipparcos mission are also very important and promise excellent\ncombined solutions, YY~CrB and OU~Ser. It is important that both\nare high-velocity stars and have excellent parallaxes. And, finally,\nthe recently discovered system HV~Aqr offers an excellent solution\nin view of the total, well-defined eclipses and very good radial\nvelocity data.\n\n\\acknowledgements\nThe authors would like to thank Jim Thomson for help with\nobservations and to Hilmar Duerbeck for a permission to use\nhis observations of UX~Eri.\n\nThe research has made use of the SIMBAD database, operated at the CDS, \nStrasbourg, France and accessible through the Canadian \nAstronomy Data Centre, which is operated by the Herzberg Institute of \nAstrophysics, National Research Council of Canada.\n\n\\begin{thebibliography}{}\n\\bibitem[Agerer \\& Huebscher 1998a] % UX Eri\n {AH98a} Inf.\\ Bull.\\ Var.\\ Stars, 4562\n\\bibitem[Agerer \\& Huebscher 1998b] % UX Eri\n {AH98b} Inf.\\ Bull.\\ Var.\\ Stars, 4606\n\\bibitem[Barone et al.\\ 1993] % AO Cam\n {bar93} Barone, F., Di Fioere, L., Milano, L.\\ \\&\n Russo, G. 1993, \\apj, 407, 237\n\\bibitem[Binnendijk 1967] % UX Eri\n {bin67} Binnendijk, L. 1967, \\aj, 72, 82\n\\bibitem[Carney et al.\\ 1994] % OU Ser\n {car94} Carney, B.W., Latham, D.W., Laird, J.B. \\& \n Aguilar, L.A. 1994, \\aj, 107, 2240\n\\bibitem[Ceraski 1907] % RZ Dra\n {cer07} Ceraski, W. 1907, Astr.\\ Nachr., 174, 265\n\\bibitem[ESA 1997]\n {hipp} European Space Agency. 1997. The Hipparcos and Tycho\n Catalogues (Paris: ESA), SP-1200\n\\bibitem[Evans et al.\\ 1985] % AO Cam\n {eva85} Evans III, E., Grossoehme, D.H.\\ \\& Moyer Jr., E.J.\n \\pasp, 97, 648\n\\bibitem[Faulkner 1986] % AO Cam\n {fau86} Falkner, D.R. 1986, \\pasp, 98, 690\n\\bibitem[Hoffmeister 1949] % CN And\n {hof49} Hoffmeister, C. 1949, Astr.\\ Nachr., 12, 1\n\\bibitem[Hoffmeister 1949b] % RT LMi\n {hof49b} Hoffmeister, C. 1949b, Astr.\\ Abhandl., 12, 1\n\\bibitem[Hoffmeister 1966] % AO Cam\n {hof66} Hoffmeister, C. 1966, Astr.\\ Nachr., 289, 1\n\\bibitem[Hrivnak 1989] % OO Aql\n {hri89} Hrivnak, B.J. 1989, \\apj, 340, 458\n\\bibitem[Hrivnak et al.\\ 1995] % VZ Psc\n {hri95} Hrivnak, B.J., Guinan, E.F. \\& Lu, W. 1995, \n \\apj, 455, 300\n\\bibitem[Hutton 1992] % HV Aqr\n {hut92} Hutton, R.G. 1992, Inf.\\ Bull.\\ Var.\\ Stars, 3723\n\\bibitem[Kaluzny 1983] % CN And\n {kal83} Kaluzny, J. 1983, Acta Astr., 33, 345\n\\bibitem[Keskin 1989] % CN And\n {kes89} Keskin, V. 1989, \\apss, 153, 191\n\\bibitem[Kreiner et al.\\ 1994] % RZ Dra\n {kre94} Kreiner, J.M., Pajdosz, G., Tremko, J. \\& Zola, S.\n 1994, \\aap, 285, 459\n\\bibitem[Lee 1984a] % FU Dra\n {lee84a} Lee, S.-G. 1984a, \\aj, 89, 702\n\\bibitem[Lee 1984b] % FU Dra\n {lee84b} Lee, S.-G. 1984b, \\aj, 89, 720\n\\bibitem[Lu \\& Rucinski 1999]\n {LR99} Lu, W. \\& Rucinski, S.M. 1999, \\aj, 118, 515 (Paper I)\n\\bibitem[Mauder 1972] % UX Eri\n {mau72} Mauder, H. 1972, \\aap, 17, 1\n\\bibitem[Milone et al.\\ 1982] % AO Cam\n {mil82} Milone, E.F., Piggott, D.H.\\ \\& Morris, S.L. \n \\jrasc, 76, 90\n\\bibitem[Niarchos et al.\\ 1994] % RT LMi\n {nia94} Niarchos, P.G., Hoffmann, M.\\ \\& Duerbeck, H.W.\n 1994, \\aaps, 103, 39\n\\bibitem[Olsen 1994] % V753 Mon\n {ols94} Olsen, E.H. 1994, \\aaps, 106, 257\n\\bibitem[Refert et al.\\ 1985] % CN And\n {raf85} Rafert, J.B., Markworth, N.L. \\& Michaels, E.J. 1985\n \\pasp, 97, 310\n\\bibitem[Robb 1992] % HV Aqr\n {rob92} Robb, R.M. 1992, Inf.\\ Bull.\\ Var.\\ Stars, 3798\n\\bibitem[Rucinski \\& Duerbeck 1997]\n {RD97} Rucinski, S.M. \\& Duerbeck, H.W. 1997, \n \\pasp, 109, 1340 % Hipparcos calibration\n\\bibitem[Rucinski \\& Lu 1999]\n {RL99} Rucinski, S.M. \\& Lu, W. 1999, \\aj, 118, 2451 (Paper II)\n\\bibitem[Samec et al.\\ 1998] % CN And\n {sam98} Samec, R.G., Laird, H., Mutzke, M. \\& Faulkner, D.R.\n Inf.\\ Bull.\\ Var.\\ Stars, 4616\n\\bibitem[Shaw et al.\\ 1996] % CN And\n {sha96} Shaw, J.S., Caillault, J., Schmitt, J.H.M.M. 1996,\n \\apj, 461, 951\n\\bibitem[Schirmer 1992] % HV Aqr\n {sch92} Shirmer, J. 1992, Inf.\\ Bull.\\ Var.\\ Stars, 3785\n\\bibitem[Soloviev 1937] % UX Eri\n {sol37} Soloviev, A. 1937, Tadjik Obs.\\ Circ., No.~27, 7\n\\bibitem[Struve 1946] % RZ Dra\n {str46} Struve, O. 1946, \\apj, 103, 76\n\\bibitem[Zhai \\& Lu 1989] % SW Lac\n {zha89} Zhai, D.S. \\& Lu, W.X. 1989, Acta Astr.\\ Sinica, 9, 208\n\\end{thebibliography}\n\n\\clearpage\n\n\\noindent\nCaptions to figures:\n\n\\bigskip\n\n\\figcaption[fig1_30w.ps] {\\label{fig1}\nRadial velocities of the systems CN~And, HV~Aqr, AO~Cam and YY~CrB\nare plotted in individual panels versus orbital phases. The thin lines \ngive the respective circular-orbit (sine-curve) fits to the radial velocities.\nNote that AO~Cam is a W-type system while the rest are A-type\nsystems. Short marks in the lower \nparts of the panels show phases of available \nobservations which were not used in the solutions because of the \nblending of lines. Open symbols in this and the next figure\nindicate observations given half-weights in the solutions. All\npanels have the same vertical scales.\n}\n\n\\figcaption[fig2_30w.ps] {\\label{fig2}\nRadial velocities of the systems FU~Dra, RZ~Dra, UX~Eri and RT~LMi. \n}\n\n\\figcaption[fig3_30w.ps] {\\label{fig3}\nRadial velocities of the systems V753~Mon and OU~Ser. While both of\nthese recently-discovered systems are very interesting, V753~Mon is\nexceptional in having a mass-ratio very close to unity in\nshowing very large radial-velocity amplitudes.\n}\n\n\n\n\\clearpage\n\n\\begin{table} % large table of individual observations\n\\dummytable \\label{tab1} % rucinski2tab1.tex\n\\end{table}\n \n\n\\begin{table} % summary of circular orbit determinations\n\\dummytable \\label{tab2} % rucinski2tab2.tex\n\\end{table}\n\n\\end{document}\n\n"
},
{
"name": "tab1_30w.tex",
"string": "\\documentstyle[aj_pt4]{article} % table format\n \n\\typeout{_\nFor mysterious reasons, this file gives errors related to\nsidehead. Just keep on pressing Ret while processing and the\nresult is OK. The problem disappears if the header is one-line,\nnot two lines long.\n_}\n\n\\begin{document}\n\\pagestyle{empty}\n\n\\begin{deluxetable}{ccrrrr}\n\\small\n%\\tablewidth{0pt}\n\\tablewidth{320pt}\n\\tablenum{1}\n\\tablecaption{DDO observations of the third group of ten close binary systems}\n\\tablehead{\n\\colhead{HJD--2,400,000} & \\colhead{Phase} & \n\\colhead{~V$_1$} & \\colhead{~~$\\Delta$V$_1$} &\n\\colhead{~V$_2$} & \\colhead{~~$\\Delta$V$_2$} \n% \\\\ % problem here?\n%\\colhead{2,400,000+} & \\colhead{} &\n%\\colhead{(km s$^{-1}$)} & \\colhead{(km s$^{-1}$)} & \n%\\colhead{(km s$^{-1}$)} & \\colhead{(km s$^{-1}$)}\n}\n\\startdata\n\\sidehead{\\bf CN And}\n50615.7873 & 0.3120 & $ -107.6$ & $ -1.8$ &\\phn 178.0 & $ -4.7$ \\nl\n50615.7986 & 0.3364 & $ -105.5$ & $ -5.7$ &\\phn 154.6 & $ -12.6$ \\nl\n50615.8112 & 0.3636 & $ -91.3$ & $ -0.3$ &\\phn 133.3 & $ -11.4$ \\nl\n50615.8222 & 0.3874 & $ -73.2$ &\\phn 8.6 &\\phn 92.0 & $ -28.9$ \\nl\n50615.8339 & 0.4127 & $ -52.5$ &\\phn 18.0 & \\nodata & \\nodata \\nl\n50631.8015 & 0.9154 &\\phn 40.6\\tablenotemark{a} \n&\\phn 21.1\\tablenotemark{a} & \\nodata & \\nodata \\nl\n50631.8122 & 0.9385 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50631.8250 & 0.9662 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50651.7711 & 0.0656 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50651.7821 & 0.0893 & $ -76.6$\\tablenotemark{a}\n & $ -5.1$\\tablenotemark{a} & \\nodata & \\nodata \\nl\n50651.7948 & 0.1168 & $ -80.4$ &\\phn 3.1 &\\phn 156.6 &\\phn 31.2 \\nl\n50651.8056 & 0.1401 & $ -91.2$ &\\phn 1.1 &\\phn 169.0 &\\phn 20.9 \\nl\n50651.8173 & 0.1654 & $ -98.1$ &\\phn 2.2 &\\phn 170.1 &\\phn 1.6 \\nl\n50651.8282 & 0.1889 & $ -106.1$ & $ -0.1$ &\\phn 184.7 &\\phn 1.5 \\nl\n50651.8416 & 0.2179 & $ -109.2$ &\\phn 1.4 &\\phn 195.0 &\\phn 0.1 \\nl\n50651.8525 & 0.2414 & $ -106.8$ &\\phn 5.5 &\\phn 198.0 & $ -1.2$ \\nl\n50651.8648 & 0.2680 & $ -103.4$ &\\phn 8.4 &\\phn 185.5 & $ -12.5$ \\nl\n50700.7094 & 0.8111 &\\phn 55.0 & $ -1.3$ & $ -250.5$ & $ -17.6$ \\nl\n50700.7206 & 0.8353 &\\phn 57.4 &\\phn 7.0 & $ -250.5$ & $ -32.7$ \\nl\n50700.7326 & 0.8612 &\\phn 51.4 &\\phn 9.3 & $ -225.6$ & $ -29.0$ \\nl\n50700.7433 & 0.8844 &\\phn 42.3 &\\phn 9.0 & $ -205.4$ & $ -31.5$ \\nl\n50708.7686 & 0.2254 & $ -103.2$ &\\phn 8.2 &\\phn 203.6 &\\phn 6.8 \\nl\n50708.7829 & 0.2563 & $ -102.4$ &\\phn 9.9 &\\phn 206.7 &\\phn 7.4 \\nl\n50708.7952 & 0.2828 & $ -118.6$ & $ -8.1$ &\\phn 191.7 & $ -3.0$ \\nl\n50709.7059 & 0.2507 & $ -113.3$ & $ -0.9$ &\\phn 186.1 & $ -13.4$ \\nl\n50709.7181 & 0.2770 & $ -109.7$ &\\phn 1.4 &\\phn 186.6 & $ -9.6$ \\nl\n50771.5187 & 0.8154 &\\phn 59.7 &\\phn 4.3 & $ -244.8$ & $ -14.2$ \\nl\n50771.5326 & 0.8454 &\\phn 49.9 &\\phn 2.5 & $ -213.8$ & $ -3.7$ \\nl\n50852.4794 & 0.7547 &\\phn 56.3 & $ -6.3$ & $ -262.5$ & $ -13.4$ \\nl\n50852.4904 & 0.7785 &\\phn 61.9 &\\phn 0.6 & $ -232.7$ &\\phn 12.9 \\nl\n50852.5032 & 0.8061 &\\phn 58.9 &\\phn 1.6 & $ -247.0$ & $ -11.6$ \\nl\n51080.6489 & 0.7818 &\\phn 60.4 & $ -0.5$ & $ -216.1$ &\\phn 28.6 \\nl\n51080.6597 & 0.8052 &\\phn 62.2 &\\phn 4.7 & $ -206.1$ &\\phn 29.8 \\nl\n51080.6718 & 0.8313 &\\phn 52.3 &\\phn 0.8 & $ -220.5$ &\\phn 0.1 \\nl\n51080.6826 & 0.8547 &\\phn 46.0 &\\phn 1.6 & $ -206.0$ & $ -3.6$ \\nl\n51080.6943 & 0.8799 &\\phn 34.3 & $ -0.8$ & $ -205.6$ & $ -27.1$ \\nl\n51080.7054 & 0.9039 &\\phn 31.5 &\\phn 6.7 & $ -180.5$ & $ -28.3$ \\nl\n51085.6730 & 0.6379 &\\phn 36.2 & $ -5.6$ & $ -208.0$ & $ -12.2$ \\nl\n51085.6842 & 0.6621 &\\phn 58.2 &\\phn 8.6 & $ -227.6$ & $ -11.8$ \\nl\n51085.6959 & 0.6874 &\\phn 58.3 &\\phn 2.3 & $ -225.1$ &\\phn 7.0 \\nl\n51085.7065 & 0.7103 &\\phn 61.5 &\\phn 1.6 & $ -239.8$ &\\phn 2.5 \\nl\n51085.7208 & 0.7412 &\\phn 67.1 &\\phn 4.6 & $ -228.5$ &\\phn 20.4 \\nl\n51085.7323 & 0.7660 &\\phn 59.0 & $ -3.2$ & $ -237.9$ &\\phn 10.2 \\nl\n51085.7460 & 0.7956 &\\phn 61.8 &\\phn 2.7 & $ -222.1$ &\\phn 18.0 \\nl\n51085.7573 & 0.8200 &\\phn 49.8 & $ -4.5$ & $ -193.6$ &\\phn 34.2 \\nl\n\\tablebreak\n\\sidehead{\\bf HV Aqr}\n50631.7429 & 0.1851 & $ -33.4$ &\\phn 9.3 &\\phn 264.9 & $ -0.7$ \\nl\n50785.5092 & 0.8199 &\\phn 31.9 & $ -2.7$ & $ -273.0$ & $ -3.7$ \\nl\n50785.5204 & 0.8498 &\\phn 31.0 &\\phn 0.4 & $ -252.4$ & $ -11.1$ \\nl\n51080.5304 & 0.6776 &\\phn 32.7 & $ -1.6$ & $ -270.5$ & $ -3.2$ \\nl\n51080.5416 & 0.7075 &\\phn 32.5 & $ -4.6$ & $ -278.6$ &\\phn 8.1 \\nl\n51080.5542 & 0.7411 &\\phn 37.0 & $ -1.6$ & $ -294.0$ &\\phn 2.7 \\nl\n51080.5650 & 0.7700 &\\phn 37.6 & $ -0.7$ & $ -297.5$ & $ -2.7$ \\nl\n51080.5768 & 0.8015 &\\phn 30.9 & $ -5.5$ & $ -271.9$ &\\phn 10.0 \\nl\n51080.5875 & 0.8301 &\\phn 34.3 &\\phn 0.9 & $ -263.6$ & $ -2.8$ \\nl\n51080.5992 & 0.8613 &\\phn 29.6 &\\phn 0.9 & $ -224.9$ &\\phn 3.3 \\nl\n51080.6099 & 0.8899 &\\phn 30.8 &\\phn 7.5 & $ -187.8$ &\\phn 3.1 \\nl\n51080.6216 & 0.9211 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n51080.6323 & 0.9497 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n51085.5773 & 0.1554 & $ -36.7$ &\\phn 2.2 &\\phn 237.8 & $ -1.5$ \\nl\n51085.5880 & 0.1840 & $ -44.5$ & $ -1.9$ &\\phn 279.6 &\\phn 14.9 \\nl\n51085.5998 & 0.2155 & $ -50.8$ & $ -5.6$ &\\phn 287.2 &\\phn 4.5 \\nl\n51085.6104 & 0.2438 & $ -53.3$ & $ -7.2$ &\\phn 288.3 & $ -1.1$ \\nl\n51085.6235 & 0.2788 & $ -44.7$ &\\phn 0.8 &\\phn 267.2 & $ -17.6$ \\nl\n51085.6342 & 0.3073 & $ -35.9$ &\\phn 7.6 &\\phn 281.9 &\\phn 11.2 \\nl\n51085.6459 & 0.3386 & $ -49.1$ & $ -9.3$ &\\phn 257.7 &\\phn 12.4 \\nl\n51085.6566 & 0.3672 & $ -42.7$ & $ -7.5$ &\\phn 206.0 & $ -7.6$ \\nl\n\\sidehead{\\bf AO Cam}\n50699.8482 & 0.0913 & $ -160.6$\\tablenotemark{a}\n & $ -11.5$\\tablenotemark{a} &\\phn 42.4 & $ -0.6$ \\nl\n50699.8589 & 0.1237 & $ -190.4$ & $ -1.5$ &\\phn 70.0 &\\phn 10.6 \\nl\n50699.8725 & 0.1649 & $ -233.5$ & $ -4.7$ &\\phn 84.2 &\\phn 8.3 \\nl\n50699.8832 & 0.1974 & $ -250.7$ & $ -0.6$ &\\phn 77.4 & $ -7.3$ \\nl\n50699.8952 & 0.2338 & $ -263.0$ & $ -0.6$ &\\phn 93.5 &\\phn 3.7 \\nl\n50850.4835 & 0.6933 &\\phn 216.3 & $ -5.3$ & $ -110.6$ & $ -0.4$ \\nl\n50850.4964 & 0.7324 &\\phn 236.8 &\\phn 1.0 & $ -111.6$ &\\phn 4.5 \\nl\n50850.5111 & 0.7770 &\\phn 234.7 &\\phn 1.0 & $ -110.6$ &\\phn 4.6 \\nl\n50850.5244 & 0.8173 &\\phn 216.0 &\\phn 0.7 & $ -106.9$ &\\phn 0.7 \\nl\n50850.5387 & 0.8607 &\\phn 182.7 &\\phn 3.5 & $ -89.1$ &\\phn 3.6 \\nl\n50850.6490 & 0.1950 & $ -257.0$ & $ -8.1$ &\\phn 82.8 & $ -1.4$ \\nl\n50850.6629 & 0.2371 & $ -260.9$ &\\phn 2.0 &\\phn 89.6 & $ -0.4$ \\nl\n50850.6770 & 0.2799 & $ -255.4$ &\\phn 3.9 &\\phn 80.4 & $ -8.1$ \\nl\n50850.6889 & 0.3159 & $ -244.1$ & $ -1.6$ &\\phn 79.6 & $ -2.0$ \\nl\n50850.7030 & 0.3587 & $ -201.3$ &\\phn 6.2 &\\phn 74.0 &\\phn 6.9 \\nl\n50850.7158 & 0.3975 & $ -170.3$ & $ -6.7$ &\\phn 50.7 &\\phn 1.7 \\nl\n50850.7303 & 0.4414 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50852.5208 & 0.8687 &\\phn 182.3 &\\phn 11.5 & $ -88.2$ &\\phn 1.0 \\nl\n50852.5294 & 0.8948 &\\phn 159.0\\tablenotemark{a}\n &\\phn 18.4\\tablenotemark{a} & $ -72.1$ &\\phn 4.6 \\nl\n50852.5394 & 0.9251 & \\nodata & \\nodata & $ -55.0$\\tablenotemark{a}\n &\\phn 5.1\\tablenotemark{a} \\nl\n51220.6274 & 0.6645 &\\phn 203.6 &\\phn 1.6 & $ -97.0$ &\\phn 5.1 \\nl\n51220.6382 & 0.6972 &\\phn 218.5 & $ -5.2$ & $ -123.1$ & $ -12.1$ \\nl\n51220.6499 & 0.7327 &\\phn 233.8 & $ -2.1$ & $ -120.5$ & $ -4.4$ \\nl\n51220.6606 & 0.7651 &\\phn 228.6 & $ -7.6$ & $ -107.3$ &\\phn 8.9 \\nl\n51220.6735 & 0.8042 &\\phn 218.9 & $ -4.0$ & $ -114.2$ & $ -3.5$ \\nl\n51220.6845 & 0.8376 &\\phn 195.9 & $ -4.5$ & $ -106.9$ & $ -5.5$ \\nl\n\\tablebreak\n\\sidehead{\\bf YY CrB}\n50948.6816 & 0.9077 &\\phn 50.8 &\\phn 18.1 & $ -149.6$ &\\phn 8.3 \\nl\n50948.6888 & 0.9268 &\\phn 42.5 &\\phn 16.9 & $ -123.6$ &\\phn 5.1 \\nl\n50948.6960 & 0.9460 &\\phn 42.6 &\\phn 24.5 & $ -114.7$ & $ -16.9$ \\nl\n50948.7122 & 0.9890 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50948.7202 & 0.0102 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50948.7277 & 0.0302 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50949.6499 & 0.4791 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50949.6571 & 0.4983 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50949.6643 & 0.5174 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50951.6721 & 0.8493 &\\phn 57.3 &\\phn 6.6 & $ -232.6$ & $ -0.8$ \\nl\n50951.6797 & 0.8694 &\\phn 60.4 &\\phn 15.2 & $ -187.5$ &\\phn 21.8 \\nl\n50951.6872 & 0.8894 &\\phn 42.4 &\\phn 3.4 & $ -195.0$ & $ -11.2$ \\nl\n50951.6959 & 0.9125 &\\phn 46.7 &\\phn 15.7 & $ -152.4$ & $ -1.5$ \\nl\n50951.7066 & 0.9409 &\\phn 42.2 &\\phn 22.1 & $ -139.6$ & $ -33.4$ \\nl\n50960.7595 & 0.9816 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50960.7676 & 0.0031 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50960.7751 & 0.0230 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50960.7834 & 0.0451 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50960.7907 & 0.0645 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50960.7979 & 0.0836 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50960.8066 & 0.1067 & $ -55.3$ & $ -8.4$ &\\phn 183.1 &\\phn 13.8 \\nl\n50960.8138 & 0.1258 & $ -60.1$ & $ -7.1$ &\\phn 209.1 &\\phn 14.8 \\nl\n50960.8210 & 0.1449 & $ -64.8$ & $ -6.4$ &\\phn 217.5 &\\phn 1.0 \\nl\n50960.8290 & 0.1662 & $ -65.5$ & $ -2.1$ &\\phn 234.3 & $ -3.0$ \\nl\n50960.8362 & 0.1853 & $ -67.6$ & $ -0.5$ &\\phn 255.0 &\\phn 2.5 \\nl\n50960.8434 & 0.2044 & $ -71.9$ & $ -2.0$ &\\phn 257.4 & $ -6.5$ \\nl\n50960.8514 & 0.2257 & $ -68.2$ &\\phn 3.7 &\\phn 270.6 & $ -1.4$ \\nl\n50961.6013 & 0.2171 & $ -71.2$ &\\phn 0.0 &\\phn 269.9 &\\phn 0.6 \\nl\n50961.6088 & 0.2370 & $ -67.8$ &\\phn 4.6 &\\phn 274.2 & $ -0.1$ \\nl\n50961.6160 & 0.2561 & $ -75.8$ & $ -3.2$ &\\phn 265.5 & $ -9.6$ \\nl\n50961.6249 & 0.2797 & $ -67.9$ &\\phn 3.6 &\\phn 262.9 & $ -7.5$ \\nl\n50961.6321 & 0.2989 & $ -63.9$ &\\phn 5.6 &\\phn 264.0 &\\phn 1.8 \\nl\n50961.6393 & 0.3180 & $ -64.5$ &\\phn 2.0 &\\phn 240.2 & $ -9.9$ \\nl\n50961.6476 & 0.3400 & $ -65.3$ & $ -3.2$ &\\phn 233.2 &\\phn 1.5 \\nl\n50961.6549 & 0.3594 & $ -55.6$ &\\phn 1.6 &\\phn 218.9 &\\phn 7.2 \\nl\n50961.6620 & 0.3783 & $ -54.2$ & $ -2.5$ &\\phn 191.7 &\\phn 2.5 \\nl\n50961.6704 & 0.4006 & $ -48.3$ & $ -3.9$ &\\phn 166.4 &\\phn 7.3 \\nl\n50961.6776 & 0.4197 & $ -41.5$ & $ -4.0$ &\\phn 135.8 &\\phn 5.1 \\nl\n50961.7762 & 0.6815 &\\phn 49.2 & $ -8.1$ & $ -271.4$ & $ -12.5$ \\nl\n50961.7834 & 0.7007 &\\phn 53.3 & $ -6.9$ & $ -277.7$ & $ -6.6$ \\nl\n50961.7906 & 0.7198 &\\phn 56.4 & $ -5.9$ & $ -280.0$ & $ -0.6$ \\nl\n50961.7994 & 0.7431 &\\phn 49.7 & $ -13.7$ & $ -294.2$ & $ -10.0$ \\nl\n50961.8066 & 0.7623 &\\phn 53.5 & $ -9.8$ & $ -287.8$ & $ -4.2$ \\nl\n50961.8138 & 0.7814 &\\phn 53.2 & $ -9.0$ & $ -278.5$ &\\phn 0.5 \\nl\n50961.8228 & 0.8053 &\\phn 51.6 & $ -7.8$ & $ -269.4$ & $ -1.7$ \\nl\n50961.8300 & 0.8244 &\\phn 54.4 & $ -1.8$ & $ -254.2$ &\\phn 0.2 \\nl\n50961.8372 & 0.8435 &\\phn 57.4 &\\phn 5.3 & $ -235.1$ &\\phn 2.4 \\nl\n\\tablebreak\n\\sidehead{\\bf FU Dra}\n50853.7375 & 0.1173 & $ -208.4$ & $ -8.3$ &\\phn 40.0 &\\phn 4.1 \\nl\n50853.7475 & 0.1499 & $ -228.6$ &\\phn 9.8 &\\phn 56.4 &\\phn 10.9 \\nl\n50853.7583 & 0.1851 & $ -269.6$ & $ -0.5$ &\\phn 48.7 & $ -4.5$ \\nl\n50853.7679 & 0.2164 & $ -294.7$ & $ -8.8$ &\\phn 47.4 & $ -10.0$ \\nl\n50853.7792 & 0.2532 & $ -284.4$ &\\phn 7.7 &\\phn 55.1 & $ -3.9$ \\nl\n50853.7889 & 0.2849 & $ -288.6$ & $ -3.2$ &\\phn 52.8 & $ -4.5$ \\nl\n50853.8002 & 0.3217 & $ -263.3$ &\\phn 0.8 &\\phn 58.4 &\\phn 6.4 \\nl\n50853.8868 & 0.6040 &\\phn 170.7 &\\phn 11.3 & $ -53.1$ &\\phn 1.1 \\nl\n50853.8978 & 0.6399 &\\phn 201.4 & $ -3.4$ & $ -73.7$ & $ -8.1$ \\nl\n50853.9104 & 0.6810 &\\phn 240.3 & $ -3.1$ & $ -77.9$ & $ -2.6$ \\nl\n50853.9204 & 0.7136 &\\phn 266.9 &\\phn 4.8 & $ -80.9$ & $ -1.0$ \\nl\n50853.9311 & 0.7485 &\\phn 268.3 & $ -1.1$ & $ -80.2$ &\\phn 1.6 \\nl\n50853.9409 & 0.7804 &\\phn 271.0 &\\phn 6.7 & $ -72.9$ &\\phn 7.6 \\nl\n50853.9521 & 0.8169 &\\phn 257.7 &\\phn 12.8 & $ -72.9$ &\\phn 2.7 \\nl\n50858.8237 & 0.6999 &\\phn 255.2 & $ -0.4$ & $ -71.6$ &\\phn 6.7 \\nl\n50858.8238 & 0.7003 &\\phn 241.0 & $ -14.8$ & $ -90.7$ & $ -12.3$ \\nl\n50858.8482 & 0.7798 &\\phn 268.2 &\\phn 3.7 & $ -79.2$ &\\phn 1.3 \\nl\n50858.8595 & 0.8167 &\\phn 227.4 & $ -17.7$ & $ -90.9$ & $ -15.2$ \\nl\n50860.8036 & 0.1551 & $ -240.6$ &\\phn 3.0 &\\phn 52.8 &\\phn 6.0 \\nl\n50860.8313 & 0.2454 & $ -277.0$ &\\phn 15.0 &\\phn 54.9 & $ -4.1$ \\nl\n50860.8582 & 0.3331 & $ -263.0$ & $ -8.2$ &\\phn 42.7 & $ -6.9$ \\nl\n50860.8882 & 0.4309 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50896.8648 & 0.7262 &\\phn 274.1 &\\phn 7.9 & $ -66.3$ &\\phn 14.7 \\nl\n50880.9355 & 0.7916 &\\phn 265.5 &\\phn 5.7 & $ -89.0$ & $ -9.6$ \\nl\n\\sidehead{\\bf RZ Dra}\n50610.8110 & 0.2287 & $ -74.3$ &\\phn 11.0 &\\phn 239.2 & $ -13.8$ \\nl\n50610.8229 & 0.2503 & $ -90.6$ & $ -4.4$ &\\phn 258.0 &\\phn 2.8 \\nl\n50610.8360 & 0.2741 & $ -74.6$ &\\phn 10.5 &\\phn 251.2 & $ -1.2$ \\nl\n50645.6647 & 0.4983 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50645.6794 & 0.5250 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50645.6954 & 0.5540 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50700.5321 & 0.0986 & $ -53.3$\\tablenotemark{a} \n & $ -7.8$\\tablenotemark{a} & \\nodata & \\nodata \\nl\n50700.5464 & 0.1245 & $ -51.2$ &\\phn 6.4 &\\phn 184.8 &\\phn 1.8 \\nl\n50700.5620 & 0.1528 & $ -61.4$ &\\phn 7.3 &\\phn 209.1 & $ -1.9$ \\nl\n50700.5764 & 0.1790 & $ -80.1$ & $ -3.4$ &\\phn 212.5 & $ -18.7$ \\nl\n50700.5917 & 0.2068 & $ -70.0$ &\\phn 12.6 &\\phn 243.3 & $ -2.9$ \\nl\n50700.6059 & 0.2325 & $ -78.1$ &\\phn 7.5 &\\phn 248.4 & $ -5.3$ \\nl\n50700.6217 & 0.2612 & $ -84.8$ &\\phn 1.1 &\\phn 255.8 &\\phn 1.3 \\nl\n50700.6368 & 0.2886 & $ -92.1$ & $ -8.8$ &\\phn 226.6 & $ -21.4$ \\nl\n50700.6539 & 0.3197 & $ -74.7$ &\\phn 2.3 &\\phn 229.5 & $ -2.6$ \\nl\n50700.6686 & 0.3464 & $ -73.6$ & $ -4.6$ &\\phn 231.4 &\\phn 19.7 \\nl\n50700.6854 & 0.3768 & $ -53.4$ &\\phn 3.6 &\\phn 216.4 &\\phn 34.9 \\nl\n50708.5343 & 0.6249 &\\phn 71.8 & $ -7.3$ & $ -187.3$ & $ -25.2$ \\nl\n50708.5485 & 0.6507 &\\phn 95.9 &\\phn 6.6 & $ -213.7$ & $ -26.0$ \\nl\n50708.5644 & 0.6795 &\\phn 89.2 & $ -9.0$ & $ -169.8$ &\\phn 40.4 \\nl\n50708.5787 & 0.7055 &\\phn 96.9 & $ -6.9$ & $ -232.7$ & $ -8.4$ \\nl\n50708.5940 & 0.7333 &\\phn 114.0 &\\phn 7.0 & $ -229.8$ &\\phn 2.6 \\nl\n50708.6083 & 0.7592 &\\phn 108.9 &\\phn 1.5 & $ -189.6$ &\\phn 43.8 \\nl\n50708.6242 & 0.7881 &\\phn 100.6 & $ -4.2$ & $ -214.4$ &\\phn 12.4 \\nl\n50708.6389 & 0.8148 &\\phn 118.3 &\\phn 18.7 & $ -223.0$ & $ -9.2$ \\nl\n50708.6519 & 0.8384 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n51326.6143 & 0.6196 &\\phn 69.6 & $ -7.2$ & $ -180.9$ & $ -24.6$ \\nl\n51326.6267 & 0.6421 &\\phn 73.9 & $ -12.2$ & $ -226.0$ & $ -46.2$ \\nl\n51326.6401 & 0.6665 &\\phn 94.0 & $ -0.5$ & $ -218.2$ & $ -17.3$ \\nl\n51326.6543 & 0.6922 &\\phn 99.7 & $ -1.5$ & $ -216.8$ &\\phn 1.1 \\nl\n51326.6675 & 0.7162 &\\phn 108.1 &\\phn 2.7 & $ -233.0$ & $ -4.7$ \\nl\n51326.6798 & 0.7385 &\\phn 112.9 &\\phn 5.6 & $ -230.2$ &\\phn 3.0 \\nl\n51326.6918 & 0.7603 &\\phn 108.2 &\\phn 0.9 & $ -244.2$ & $ -10.9$ \\nl\n51326.7049 & 0.7841 &\\phn 120.5 &\\phn 15.2 & $ -231.5$ & $ -3.3$ \\nl\n51326.7174 & 0.8068 &\\phn 102.7 &\\phn 1.3 & $ -201.8$ &\\phn 16.6 \\nl\n51326.7318 & 0.8329 &\\phn 109.8 &\\phn 15.1 & $ -221.1$ & $ -19.7$ \\nl\n51326.7437 & 0.8545 &\\phn 99.9 &\\phn 12.5 & $ -186.4$ & $ -3.5$ \\nl\n51459.5493 & 0.9353 &\\phn 71.3\\tablenotemark{a} \n &\\phn 22.3\\tablenotemark{a} & \\nodata & \\nodata \\nl\n%\\tablebreak\n\\sidehead{\\bf UX Eri}\n50414.6722 & 0.7633 &\\phn 110.2 &\\phn 6.0 & $ -241.0$ & $ -8.9$ \\nl\n50414.6808 & 0.7826 &\\phn 112.6 &\\phn 10.0 & $ -220.5$ &\\phn 7.3 \\nl\n50415.5345\\tablenotemark{b} & 0.6998 &\\phn 107.6 \n&\\phn 7.6 & $ -208.1$ &\\phn 12.8 \\nl\n50416.6548\\tablenotemark{b} & 0.2158 & $ -78.0$ \n& $ -1.1$ &\\phn 245.0 & $ -7.9$ \\nl\n50417.6084\\tablenotemark{b} & 0.3574 & $ -55.6$ \n&\\phn 3.3 &\\phn 209.4 &\\phn 4.7 \\nl\n50418.7036\\tablenotemark{b} & 0.8169 &\\phn 94.9 \n& $ -1.6$ & $ -204.8$ &\\phn 6.8 \\nl\n50470.4851 & 0.1069 & $ -46.6$ & $ -2.3$ &\\phn 188.7 &\\phn 22.9 \\nl\n50470.4957 & 0.1308 & $ -58.2$ & $ -3.8$ &\\phn 206.2 &\\phn 13.5 \\nl\n50470.5084 & 0.1593 & $ -66.6$ & $ -2.1$ &\\phn 217.5 & $ -2.2$ \\nl\n50470.5198 & 0.1849 & $ -76.2$ & $ -4.8$ &\\phn 242.1 &\\phn 3.8 \\nl\n50470.5325 & 0.2134 & $ -83.7$ & $ -7.1$ &\\phn 250.9 & $ -1.2$ \\nl\n50470.5432 & 0.2374 & $ -79.1$ & $ -0.4$ &\\phn 259.8 &\\phn 2.0 \\nl\n50700.7652 & 0.2661 & $ -93.6$ & $ -15.1$ &\\phn 247.7 & $ -9.6$ \\nl\n50700.7794 & 0.2980 & $ -70.2$ &\\phn 4.6 &\\phn 246.6 & $ -0.9$ \\nl\n50700.7947 & 0.3323 & $ -69.8$ & $ -2.8$ &\\phn 226.7 &\\phn 0.3 \\nl\n50700.8089 & 0.3642 & $ -52.2$ &\\phn 4.1 &\\phn 208.4 &\\phn 10.5 \\nl\n50700.8251 & 0.4006 & $ -43.0$ & $ -2.1$ &\\phn 180.4\\tablenotemark{a}\n &\\phn 23.9\\tablenotemark{a} \\nl\n50709.8225 & 0.6068 &\\phn 61.8 & $ -8.0$ & $ -159.0$\\tablenotemark{a}\n & $ -19.0$\\tablenotemark{a} \\nl\n50709.8353 & 0.6356 &\\phn 89.9 &\\phn 8.1 & $ -175.7$ & $ -3.6$ \\nl\n50854.5324 & 0.5938 &\\phn 54.5 & $ -9.3$ & $ -146.2$\\tablenotemark{a}\n & $ -22.3$\\tablenotemark{a} \\nl\n50854.5454 & 0.6230 &\\phn 80.9 &\\phn 4.0 & $ -161.9$ & $ -3.1$ \\nl\n50854.5584 & 0.6522 &\\phn 73.5 & $ -14.3$ & $ -175.6$ &\\phn 12.4 \\nl\n51229.4903 & 0.6679 &\\phn 83.1 & $ -9.5$ & $ -187.5$ &\\phn 13.5 \\nl\n51229.5010 & 0.6919 &\\phn 92.6 & $ -5.9$ & $ -205.9$ &\\phn 10.9 \\nl\n51229.5128 & 0.7184 &\\phn 96.9 & $ -5.8$ & $ -226.9$ &\\phn 1.3 \\nl\n51229.5237 & 0.7429 &\\phn 100.5 & $ -4.0$ & $ -231.6$ &\\phn 1.1 \\nl\n51229.5361 & 0.7708 &\\phn 95.8 & $ -8.0$ & $ -240.6$ & $ -9.7$ \\nl\n51229.5468 & 0.7948 &\\phn 96.3 & $ -4.6$ & $ -230.6$ & $ -7.3$ \\nl\n\\sidehead{\\bf RT LMi}\n51254.5913 & 0.6163 &\\phn 44.1 & $ -9.3$ & $ -206.1$ & $ -22.1$ \\nl\n51254.6031 & 0.6478 &\\phn 64.7 & $ -1.4$ & $ -234.4$ & $ -15.7$ \\nl\n51254.6169 & 0.6846 &\\phn 66.4 & $ -10.7$ & $ -257.2$ & $ -8.4$ \\nl\n51254.6287 & 0.7161 &\\phn 91.2 &\\phn 8.3 & $ -238.4$ &\\phn 26.2 \\nl\n51254.6408 & 0.7484 &\\phn 96.9 &\\phn 11.9 & $ -241.3$ &\\phn 29.2 \\nl\n51254.6549 & 0.7860 &\\phn 68.7 & $ -13.9$ & $ -266.7$ & $ -2.8$ \\nl\n51254.6668 & 0.8177 &\\phn 81.4 &\\phn 4.9 & $ -247.6$ & $ -0.3$ \\nl\n51254.6796 & 0.8519 &\\phn 76.9 &\\phn 10.7 & $ -222.2$ & $ -3.2$ \\nl\n51254.6916 & 0.8839 &\\phn 58.9 &\\phn 5.6 & $ -187.3$ & $ -3.6$ \\nl\n51261.5672 & 0.2228 & $ -102.7$ &\\phn 1.5 &\\phn 246.0 & $ -0.1$ \\nl\n51261.5790 & 0.2543 & $ -111.6$ & $ -6.0$ &\\phn 255.9 &\\phn 6.1 \\nl\n51261.5919 & 0.2887 & $ -95.5$ &\\phn 7.3 &\\phn 249.7 &\\phn 7.5 \\nl\n51261.6038 & 0.3204 & $ -91.5$ &\\phn 5.0 &\\phn 213.5 & $ -11.3$ \\nl\n51261.7384 & 0.6794 &\\phn 70.8 & $ -5.0$ & $ -264.1$ & $ -18.8$ \\nl\n51261.7507 & 0.7122 &\\phn 90.7 &\\phn 8.3 & $ -232.4$ &\\phn 30.8 \\nl\n51261.7638 & 0.7472 &\\phn 80.2 & $ -4.8$ & $ -281.1$ & $ -10.7$ \\nl\n51261.7761 & 0.7800 &\\phn 77.6 & $ -5.8$ & $ -275.1$ & $ -9.2$ \\nl\n51267.5473 & 0.1732 & $ -100.9$ & $ -6.1$ &\\phn 206.2 & $ -14.0$ \\nl\n51267.5584 & 0.2028 & $ -100.1$ &\\phn 1.4 &\\phn 262.7 &\\phn 24.2 \\nl\n51267.5749 & 0.2468 & $ -112.0$ & $ -6.4$ &\\phn 238.2 & $ -11.6$ \\nl\n51267.5892 & 0.2850 & $ -100.0$ &\\phn 3.3 &\\phn 232.6 & $ -11.0$ \\nl\n51267.6009 & 0.3162 & $ -101.2$ & $ -3.7$ &\\phn 220.8 & $ -6.9$ \\nl\n51267.6145 & 0.3525 & $ -81.2$ &\\phn 5.4 &\\phn 199.8 &\\phn 2.0 \\nl\n51267.6252 & 0.3810 & $ -74.6$ &\\phn 0.5 &\\phn 193.4 &\\phn 26.8 \\nl\n51267.6382 & 0.4157 & $ -74.1$\\tablenotemark{a} \n & $ -15.6$\\tablenotemark{a} & \\nodata & \\nodata \\nl\n51267.6494 & 0.4456 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n51267.6608 & 0.4760 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n\\sidehead{\\bf V753 Mon}\n50852.6964 & 0.6378 &\\phn 163.6 & $ -9.1$ & $ -103.6$ & $ -12.1$ \\nl\n50852.7109 & 0.6593 &\\phn 178.6 & $ -8.2$ & $ -112.7$ & $ -7.5$ \\nl\n50852.7409 & 0.7036 &\\phn 207.5 &\\phn 0.3 & $ -124.7$ &\\phn 0.3 \\nl\n50852.7497 & 0.7166 &\\phn 204.1 & $ -6.7$ & $ -126.9$ &\\phn 1.5 \\nl\n50852.7593 & 0.7308 &\\phn 210.3 & $ -3.1$ & $ -126.0$ &\\phn 4.9 \\nl\n50852.7681 & 0.7437 &\\phn 216.9 &\\phn 2.4 & $ -123.7$ &\\phn 8.3 \\nl\n50854.5887 & 0.4328 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50854.5984 & 0.4471 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50858.5422 & 0.2721 & $ -127.3$ &\\phn 8.5 &\\phn 219.6 &\\phn 11.9 \\nl\n50858.5518 & 0.2863 & $ -124.9$ &\\phn 8.0 &\\phn 206.3 &\\phn 1.4 \\nl\n50858.5631 & 0.3030 & $ -123.0$ &\\phn 4.8 &\\phn 205.8 &\\phn 5.8 \\nl\n50858.5715 & 0.3154 & $ -117.6$ &\\phn 5.2 &\\phn 207.1 &\\phn 12.0 \\nl\n50884.5606 & 0.7012 &\\phn 200.9 & $ -5.5$ & $ -123.0$ &\\phn 1.2 \\nl\n50884.5718 & 0.7177 &\\phn 202.4 & $ -8.7$ & $ -126.7$ &\\phn 2.0 \\nl\n50884.5857 & 0.7383 &\\phn 214.9 &\\phn 0.7 & $ -122.7$ &\\phn 9.0 \\nl\n50884.5980 & 0.7564 &\\phn 214.7 &\\phn 0.2 & $ -126.3$ &\\phn 5.7 \\nl\n51232.5375 & 0.6624 &\\phn 192.6 &\\phn 4.0 & $ -112.6$ & $ -5.7$ \\nl\n51232.5481 & 0.6781 &\\phn 193.8 & $ -3.2$ & $ -118.9$ & $ -3.9$ \\nl\n51232.5600 & 0.6956 &\\phn 204.6 &\\phn 0.1 & $ -124.3$ & $ -2.0$ \\nl\n51232.5716 & 0.7128 &\\phn 206.8 & $ -3.1$ & $ -126.1$ &\\phn 1.4 \\nl\n51232.5856 & 0.7334 &\\phn 213.8 &\\phn 0.1 & $ -131.6$ & $ -0.4$ \\nl\n51232.5971 & 0.7504 &\\phn 212.5 & $ -2.2$ & $ -129.7$ &\\phn 2.5 \\nl\n51232.6111 & 0.7711 &\\phn 213.7 &\\phn 0.6 & $ -130.5$ &\\phn 0.2 \\nl\n51232.6226 & 0.7881 &\\phn 208.1 & $ -1.5$ & $ -125.1$ &\\phn 2.2 \\nl\n51232.6370 & 0.8094 &\\phn 207.1 &\\phn 4.5 & $ -119.3$ &\\phn 1.1 \\nl\n51232.6476 & 0.8250 &\\phn 200.0 &\\phn 4.5 & $ -112.3$ &\\phn 1.3 \\nl\n51232.6601 & 0.8435 &\\phn 193.4 &\\phn 8.3 & $ -99.0$ &\\phn 4.6 \\nl\n51232.6707 & 0.8591 &\\phn 181.2 &\\phn 6.3 & $ -93.4$ &\\phn 0.2 \\nl\n51232.6840 & 0.8788 &\\phn 168.4 &\\phn 8.3 & $ -77.5$ &\\phn 1.8 \\nl\n51232.6949 & 0.8949 &\\phn 158.4 &\\phn 11.8 & $ -64.0$ &\\phn 2.2 \\nl\n51281.5742 & 0.0895 & $ -80.9$\\tablenotemark{a}\n & $ -25.6$\\tablenotemark{a} &\\phn 123.3 & $ -6.3$ \\nl\n51281.5856 & 0.1063 & $ -92.4$ & $ -21.9$ &\\phn 134.6 & $ -9.8$ \\nl\n51281.5972 & 0.1235 & $ -99.8$ & $ -15.1$ &\\phn 151.1 & $ -7.1$ \\nl\n51513.8070 & 0.0969 & $ -92.5$\\tablenotemark{a}\n & $ -30.4$\\tablenotemark{a} &\\phn 126.7 & $ -9.5$ \\nl\n51513.8180 & 0.1131 & $ -103.2$ & $ -26.9$ &\\phn 140.3 & $ -9.7$ \\nl\n51513.8304 & 0.1315 & $ -109.1$ & $ -18.2$ &\\phn 159.6 & $ -4.5$ \\nl\n51513.8412 & 0.1474 & $ -110.6$ & $ -8.5$ &\\phn 174.3 & $ -0.8$ \\nl\n51513.8536 & 0.1657 & $ -123.4$ & $ -10.0$ &\\phn 184.1 & $ -1.9$ \\nl\n51513.8647 & 0.1821 & $ -124.2$ & $ -2.5$ &\\phn 190.0 & $ -4.0$ \\nl\n51513.8779 & 0.2016 & $ -126.9$ &\\phn 2.5 &\\phn 200.3 & $ -1.2$ \\nl\n51513.8887 & 0.2176 & $ -130.5$ &\\phn 3.3 &\\phn 204.4 & $ -1.4$ \\nl\n51513.9011 & 0.2359 & $ -133.6$ &\\phn 3.2 &\\phn 205.2 & $ -3.5$ \\nl\n51513.9118 & 0.2517 & $ -133.4$ &\\phn 4.1 &\\phn 208.4 & $ -0.9$ \\nl\n51513.9238 & 0.2694 & $ -128.8$ &\\phn 7.4 &\\phn 206.8 & $ -1.3$ \\nl\n51513.9346 & 0.2854 & $ -123.6$ &\\phn 9.6 &\\phn 207.2 &\\phn 2.1 \\nl\n51524.7788 & 0.3022 & $ -116.4$ &\\phn 11.7 &\\phn 202.9 &\\phn 2.7 \\nl\n51524.7912 & 0.3205 & $ -116.4$ &\\phn 4.1 &\\phn 198.1 &\\phn 5.3 \\nl\n51524.8062 & 0.3427 & $ -103.1$ &\\phn 5.4 &\\phn 187.5 &\\phn 6.3 \\nl\n51524.8169 & 0.3585 & $ -99.0$ & $ -0.9$ &\\phn 170.1 & $ -1.1$ \\nl\n51524.8289 & 0.3762 & $ -82.3$ &\\phn 2.7 &\\phn 174.9 &\\phn 16.5 \\nl\n51524.8397 & 0.3922 & $ -73.0$ & $ -1.2$ &\\phn 163.9 &\\phn 18.3 \\nl\n\\sidehead{\\bf OU Ser}\n50852.8082 & 0.2676 & $ -108.4$ & $ -4.0$ &\\phn 163.1 & $ -5.6$ \\nl\n50852.8133 & 0.2848 & $ -109.9$ & $ -6.2$ &\\phn 162.1 & $ -2.5$ \\nl\n50852.8184 & 0.3020 & $ -103.6$ & $ -1.1$ &\\phn 159.1 &\\phn 1.3 \\nl\n50852.8251 & 0.3246 & $ -106.1$ & $ -5.8$ &\\phn 145.1 &\\phn 0.2 \\nl\n50852.8302 & 0.3417 & $ -98.1$ &\\phn 0.0 &\\phn 130.8 & $ -1.5$ \\nl\n50852.8354 & 0.3593 & $ -97.0$ & $ -1.5$ &\\phn 118.3 &\\phn 1.2 \\nl\n50852.8417 & 0.3805 & $ -89.4$ &\\phn 2.4 &\\phn 101.1 &\\phn 5.4 \\nl\n50852.8472 & 0.3990 & $ -91.3$ & $ -3.2$ &\\phn 82.4 &\\phn 7.6 \\nl\n50852.8525 & 0.4169 & $ -91.2$ & $ -6.9$ & \\nodata & \\nodata \\nl\n50852.8586 & 0.4374 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50852.8638 & 0.4550 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50852.8690 & 0.4725 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50852.8757 & 0.4951 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50852.8809 & 0.5126 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50852.8860 & 0.5298 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50852.8926 & 0.5520 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50852.8978 & 0.5695 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50852.9030 & 0.5871 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50852.9090 & 0.6073 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50852.9143 & 0.6251 & $ -47.6$ & $ -12.2$ & $ -243.8$ & $ -13.9$ \\nl\n50852.9196 & 0.6430 & $ -37.0$ & $ -4.7$ & $ -248.1$ & $ -0.8$ \\nl\n50852.9273 & 0.6689 & $ -34.2$ & $ -5.6$ & $ -275.6$ & $ -7.0$ \\nl\n50852.9324 & 0.6861 & $ -28.8$ & $ -2.1$ & $ -279.3$ &\\phn 0.4 \\nl\n50852.9375 & 0.7033 & $ -29.1$ & $ -3.9$ & $ -291.7$ & $ -3.4$ \\nl\n50852.9436 & 0.7239 & $ -25.7$ & $ -1.7$ & $ -293.4$ &\\phn 1.8 \\nl\n50852.9486 & 0.7407 & $ -25.7$ & $ -2.1$ & $ -292.8$ &\\phn 5.1 \\nl\n50852.9537 & 0.7579 & $ -26.0$ & $ -2.5$ & $ -294.7$ &\\phn 3.3 \\nl\n50852.9597 & 0.7781 & $ -24.5$ & $ -0.4$ & $ -293.9$ &\\phn 0.8 \\nl\n50852.9648 & 0.7953 & $ -26.1$ & $ -1.0$ & $ -287.5$ &\\phn 1.4 \\nl\n50852.9699 & 0.8125 & $ -27.1$ & $ -0.5$ & $ -280.8$ & $ -0.3$ \\nl\n50852.9765 & 0.8347 & $ -26.2$ &\\phn 2.9 & $ -263.5$ &\\phn 2.4 \\nl\n50852.9817 & 0.8523 & $ -26.7$ &\\phn 4.9 & $ -252.2$ & $ -0.6$ \\nl\n50852.9868 & 0.8694 & $ -31.6$ &\\phn 2.8 & $ -233.4$ &\\phn 2.0 \\nl\n50858.8758 & 0.7135 & $ -26.4$ & $ -1.9$ & $ -291.0$ &\\phn 1.2 \\nl\n50858.8817 & 0.7334 & $ -28.6$ & $ -4.9$ & $ -299.8$ & $ -2.8$ \\nl\n50858.8878 & 0.7539 & $ -28.6$ & $ -5.1$ & $ -297.1$ &\\phn 1.1 \\nl\n50858.8945 & 0.7765 & $ -21.4$ &\\phn 2.6 & $ -291.2$ &\\phn 3.9 \\nl\n50858.9011 & 0.7987 & $ -27.7$ & $ -2.3$ & $ -291.1$ & $ -3.7$ \\nl\n50858.9077 & 0.8210 & $ -32.6$ & $ -5.1$ & $ -276.0$ & $ -0.6$ \\nl\n50858.9151 & 0.8459 & $ -30.8$ & $ -0.2$ & $ -265.3$ & $ -8.2$ \\nl\n50858.9216 & 0.8678 & $ -27.0$ &\\phn 7.1 & $ -236.7$ &\\phn 0.3 \\nl\n50858.9279 & 0.8890 & $ -36.4$ &\\phn 1.6 & $ -210.4$ &\\phn 4.1 \\nl\n50896.9083 & 0.8709 & $ -32.8$ &\\phn 1.8 & $ -230.0$ &\\phn 3.9 \\nl\n50896.9155 & 0.8951 & $ -26.3$ &\\phn 12.9 & $ -202.3$ &\\phn 5.2 \\nl\n50896.9231 & 0.9208 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50896.9320 & 0.9507 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50896.9392 & 0.9750 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50930.8318 & 0.1823 & $ -102.4$ & $ -1.3$ &\\phn 148.1 & $ -1.2$ \\nl\n50930.8380 & 0.2032 & $ -97.7$ &\\phn 5.2 &\\phn 160.2 &\\phn 0.1 \\nl\n50930.8442 & 0.2240 & $ -103.7$ &\\phn 0.4 &\\phn 164.4 & $ -2.6$ \\nl\n50930.8520 & 0.2503 & $ -106.1$ & $ -1.4$ &\\phn 173.0 &\\phn 2.8 \\nl\n50930.8583 & 0.2716 & $ -105.0$ & $ -0.7$ &\\phn 161.0 & $ -7.0$ \\nl\n50930.8647 & 0.2931 & $ -99.6$ &\\phn 3.6 &\\phn 165.5 &\\phn 3.9 \\nl\n50930.8720 & 0.3177 & $ -102.9$ & $ -1.8$ &\\phn 152.3 &\\phn 3.0 \\nl\n50930.8778 & 0.3373 & $ -92.5$ &\\phn 6.2 &\\phn 140.9 &\\phn 5.1 \\nl\n50930.8840 & 0.3582 & $ -93.8$ &\\phn 1.9 &\\phn 123.1 &\\phn 5.0 \\nl\n50930.8909 & 0.3814 & $ -94.2$ & $ -2.6$ &\\phn 104.0 &\\phn 9.3 \\nl\n50930.8968 & 0.4013 & $ -91.2$ & $ -3.5$ & \\nodata & \\nodata \\nl\n50930.9024 & 0.4202 & $ -84.7$ & $ -1.1$ & \\nodata & \\nodata \\nl\n50940.8035 & 0.7837 & $ -20.9$ &\\phn 3.5 & $ -289.3$ &\\phn 3.8 \\nl\n50940.8098 & 0.8049 & $ -29.8$ & $ -3.9$ & $ -280.1$ &\\phn 4.4 \\nl\n50940.8184 & 0.8339 & $ -24.2$ &\\phn 4.8 & $ -259.7$ &\\phn 6.8 \\nl\n50949.7573 & 0.9552 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50949.7632 & 0.9750 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50949.7691 & 0.9949 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50949.7750 & 0.0148 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50949.7823 & 0.0394 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50949.7884 & 0.0600 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50949.7942 & 0.0795 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50949.7999 & 0.0987 & \\nodata & \\nodata & \\nodata & \\nodata \\nl\n50949.8065 & 0.1210 & $ -90.5$ &\\phn 1.5 &\\phn 98.3 &\\phn 1.0 \\nl\n50949.8124 & 0.1408 & $ -95.5$ & $ -0.0$ &\\phn 122.1 &\\phn 4.9 \\nl\n50949.8182 & 0.1604 & $ -100.2$ & $ -1.8$ &\\phn 137.7 &\\phn 3.7 \\nl\n50949.8250 & 0.1833 & $ -101.1$ &\\phn 0.1 &\\phn 150.2 &\\phn 0.3 \\nl\n50949.8308 & 0.2028 & $ -103.9$ & $ -1.0$ &\\phn 159.7 & $ -0.2$ \\nl\n50949.8367 & 0.2227 & $ -106.4$ & $ -2.3$ &\\phn 161.2 & $ -5.5$ \\nl\n\\tablenotetext{a}{The data which have been given half\nweight in the orbital solutions.}\n\\tablenotetext{b}{The data for UX~Eri kindly provided by\nDr.\\ H.\\ Duerbeck.}\n\\tablecomments{Velocities are expressed in km~s$^{-1}$. \nObservations leading to entirely unseparable \nbroadening- and correlation-function peaks \nare marked by the ``no-data'' symbol (\\nodata); these observations\nmay be eventually used in more extensive modeling of broadening\nfunctions.} \n\\enddata\n\\end{deluxetable}\n\\end{document}\n"
},
{
"name": "tab2_30w.tex",
"string": "% print in landscape: dvips -t landscape tab2_30w\n\n\\documentstyle[aj_pt4]{article} % Table 2\n\n\\begin{document}\n\\pagestyle{empty}\n\n\\begin{deluxetable}{lclrrrccc}\n\\small\n\\tablecolumns{9}\n%\\tablewidth{670pt}\n\\tablewidth{0pt}\n\\tablenum{2}\n\\tablecaption{Spectroscopic orbital elements of the third\nten of close binary systems}\n\\tablehead{\n \\colhead{Name} & % 1\n \\colhead{Type} & % 1a\n \\colhead{Other} & % 2\n \\colhead{$\\gamma$} & % 3\n \\colhead{K$_1$} & % 4\n \\colhead{$\\epsilon_1$} & % 5\n \\colhead{T$_0$ -- 2,400,000} & % 6\n \\colhead{P (days)} & % 7\n \\colhead{q =} \\nl % 8\n \\colhead{Sp.\\ type} & % 1\n \\colhead{} & % 1a\n \\colhead{names} & % 2\n \\colhead{} & % 3\n \\colhead{K$_2$} & % 4\n \\colhead{$\\epsilon_2$} & % 5\n \\colhead{(O--C) and [E]} & % 6 \n \\colhead{assumed} & % 7 \n \\colhead{$m_2/m_1$} % 8\n}\n% format template\n% name & type & HD/BD & gamma & K1 &\n% errV1 & T0-2,400,000 & P & q \\nl\n% sp & & BD/Hip & & K2 &\n% errV2 & O-C, [E] & & \\nl\n\\startdata\nCN~And & A/EB & BD$+39^\\circ 59$ & $-24.86$(1.45) & 87.53(1.11) & \n 6.10 & 50850.2790(22) & 0.462793 & 0.390(33) \\nl\n ~~~F5V& & & & 224.35(2.84) &\n 18.03 & $-0.0137$ [327] & & \\nl % OK\nHV~Aqr & A & BD$-3^\\circ 5183$ & $-3.77$(1.25) & 42.41(1.44) &\n 4.83 & 50859.3453(8) & 0.374460 & 0.145(50) \\nl\n~~~F5V & & & & 293.35(2.11) &\n 11.46 & \\nodata \\tablenotemark{a} & & \\nl\nAO~Cam & W & BD$+52^\\circ 826$ & $-13.17$(0.83) & 250.50(1.05) &\n 6.47 & 50960.1131(5) & 0.329905 & 2.420(11) \\nl\n~~~G0V & & & & 103.51(1.28) &\n 5.50 & $-0.0121$ [13732] & & 1/q=0.413 \\nl\nYY~CrB & A & HD~141990 & $-4.58$(1.02) & 68.07(1.54) &\n 7.79 & 50955.8711(6) & 0.376565 & 0.243(23) \\nl\n~~~F8V & & HIP~77598 & & 279.85(1.55) &\n 14.13 & $-0.0053$ [6521] & & \\nl\nFU~Dra & W & & $-11.38$(1.14) & 280.76(2.09) &\n 8.68 & 50866.2777(8) & 0.306718 & 3.989(30) \\nl\n~~~F8V & & HIP~76272 & & 70.38(1.84) &\n 7.51 & $-0.0086$ [7714] & & 1/q=0.251 \\nl \nRZ~Dra & A/EB & & 10.68(1.76) & 96.85(1.72) &\n 7.53 & 51035.4103(28) & 0.550876 & 0.396(37) \\nl\n~~~A6V & & HIP~90092 & & 244.47(3.54) &\n22.22 & $-0.0165$ [39186] & & \\nl\nUX~Eri & A & BD$-7^\\circ 553$ & 12.79(1.09) & 91.75(1.55) &\n 6.81& 50416.5587(14) & 0.445279 & 0.371(21) \\nl\n~~~F9V & & HIP~14699 & & 245.76(1.86) &\n 10.09 & $+0.0030$ [$-78$] & & \\nl\nRT~LMi & A & & $-10.30$(1.74) & 95.34(1.67) &\n 7.28 & 51261.1008(16) & 0.374918 & 0.366(38) \\nl\n~~~F7V:& & & & 260.17(3.59) &\n 15.68 & $-0.0016$ [41056] & & \\nl\nV753~Mon & W & HD~54975 & 38.58(0.83) & 176.07(0.97) &\n 8.84 & 51188.0809(15) & 0.677049 & 1.031(9) \\nl\n~~~A8V & & HIP~34684 & & 170.76(0.97) &\n 6.80 & $-0.0249$ [3970] & & 1/q=0.970 \\nl\nOU~Ser & A& HD~136924 & $-64.08(0.41)$ & 40.59(0.59) &\n 3.80 & 50901.9916(3) & 0.296764 & 0.173(17) \\nl\n~~~F9/G0V& & HIP~75269 & & 234.24(0.69) &\n 5.97 & +0.0026 [8093] & & \\nl\n\\tablenotetext{a}{The two available ephemerides for moments of\nprimary minima of HV~Aqr give discordant results and do not provide a clear\nguidance to which eclipse our $T_0$ applies. It has been\nassumed that the system is A-type on the basis of the light curve\ndata; see the text.}\n\\tablecomments{The convention of naming the\ncomponents is that the subscript 1 designates\nthe component which is eclipsed at the\ndeeper minimum and is therefore the hotter one. \nThe standard errors of the circular \nsolutions in the table are expressed in units of last decimal places \nquoted; they are given in parantheses after each value. \nFor example, the last table entry for $q$, 0.173(17) should be \ninterpretted as $0.173 \\pm 0.017$. \nThe average radial velocities ($\\gamma$), the \nvelocity amplitudes (K$_i$) and the standard unit-weight \nerrors of the solutions ($\\epsilon$) are expressed \nin km~s$^{-1}$. The calculated moments of primary minima\nare given by $T_0$ while their (O--C) deviations (in days) \nhave been calculated from the most \nrecent available ephemerides, as given in the text,\nusing the assumed periods and the number of epochs given by [E].}\n\\enddata\n\\end{deluxetable}\n\n\\end{document}\n\n \n\n"
}
] |
[
{
"name": "astro-ph0002173.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[Agerer \\& Huebscher 1998a] % UX Eri\n {AH98a} Inf.\\ Bull.\\ Var.\\ Stars, 4562\n\\bibitem[Agerer \\& Huebscher 1998b] % UX Eri\n {AH98b} Inf.\\ Bull.\\ Var.\\ Stars, 4606\n\\bibitem[Barone et al.\\ 1993] % AO Cam\n {bar93} Barone, F., Di Fioere, L., Milano, L.\\ \\&\n Russo, G. 1993, \\apj, 407, 237\n\\bibitem[Binnendijk 1967] % UX Eri\n {bin67} Binnendijk, L. 1967, \\aj, 72, 82\n\\bibitem[Carney et al.\\ 1994] % OU Ser\n {car94} Carney, B.W., Latham, D.W., Laird, J.B. \\& \n Aguilar, L.A. 1994, \\aj, 107, 2240\n\\bibitem[Ceraski 1907] % RZ Dra\n {cer07} Ceraski, W. 1907, Astr.\\ Nachr., 174, 265\n\\bibitem[ESA 1997]\n {hipp} European Space Agency. 1997. The Hipparcos and Tycho\n Catalogues (Paris: ESA), SP-1200\n\\bibitem[Evans et al.\\ 1985] % AO Cam\n {eva85} Evans III, E., Grossoehme, D.H.\\ \\& Moyer Jr., E.J.\n \\pasp, 97, 648\n\\bibitem[Faulkner 1986] % AO Cam\n {fau86} Falkner, D.R. 1986, \\pasp, 98, 690\n\\bibitem[Hoffmeister 1949] % CN And\n {hof49} Hoffmeister, C. 1949, Astr.\\ Nachr., 12, 1\n\\bibitem[Hoffmeister 1949b] % RT LMi\n {hof49b} Hoffmeister, C. 1949b, Astr.\\ Abhandl., 12, 1\n\\bibitem[Hoffmeister 1966] % AO Cam\n {hof66} Hoffmeister, C. 1966, Astr.\\ Nachr., 289, 1\n\\bibitem[Hrivnak 1989] % OO Aql\n {hri89} Hrivnak, B.J. 1989, \\apj, 340, 458\n\\bibitem[Hrivnak et al.\\ 1995] % VZ Psc\n {hri95} Hrivnak, B.J., Guinan, E.F. \\& Lu, W. 1995, \n \\apj, 455, 300\n\\bibitem[Hutton 1992] % HV Aqr\n {hut92} Hutton, R.G. 1992, Inf.\\ Bull.\\ Var.\\ Stars, 3723\n\\bibitem[Kaluzny 1983] % CN And\n {kal83} Kaluzny, J. 1983, Acta Astr., 33, 345\n\\bibitem[Keskin 1989] % CN And\n {kes89} Keskin, V. 1989, \\apss, 153, 191\n\\bibitem[Kreiner et al.\\ 1994] % RZ Dra\n {kre94} Kreiner, J.M., Pajdosz, G., Tremko, J. \\& Zola, S.\n 1994, \\aap, 285, 459\n\\bibitem[Lee 1984a] % FU Dra\n {lee84a} Lee, S.-G. 1984a, \\aj, 89, 702\n\\bibitem[Lee 1984b] % FU Dra\n {lee84b} Lee, S.-G. 1984b, \\aj, 89, 720\n\\bibitem[Lu \\& Rucinski 1999]\n {LR99} Lu, W. \\& Rucinski, S.M. 1999, \\aj, 118, 515 (Paper I)\n\\bibitem[Mauder 1972] % UX Eri\n {mau72} Mauder, H. 1972, \\aap, 17, 1\n\\bibitem[Milone et al.\\ 1982] % AO Cam\n {mil82} Milone, E.F., Piggott, D.H.\\ \\& Morris, S.L. \n \\jrasc, 76, 90\n\\bibitem[Niarchos et al.\\ 1994] % RT LMi\n {nia94} Niarchos, P.G., Hoffmann, M.\\ \\& Duerbeck, H.W.\n 1994, \\aaps, 103, 39\n\\bibitem[Olsen 1994] % V753 Mon\n {ols94} Olsen, E.H. 1994, \\aaps, 106, 257\n\\bibitem[Refert et al.\\ 1985] % CN And\n {raf85} Rafert, J.B., Markworth, N.L. \\& Michaels, E.J. 1985\n \\pasp, 97, 310\n\\bibitem[Robb 1992] % HV Aqr\n {rob92} Robb, R.M. 1992, Inf.\\ Bull.\\ Var.\\ Stars, 3798\n\\bibitem[Rucinski \\& Duerbeck 1997]\n {RD97} Rucinski, S.M. \\& Duerbeck, H.W. 1997, \n \\pasp, 109, 1340 % Hipparcos calibration\n\\bibitem[Rucinski \\& Lu 1999]\n {RL99} Rucinski, S.M. \\& Lu, W. 1999, \\aj, 118, 2451 (Paper II)\n\\bibitem[Samec et al.\\ 1998] % CN And\n {sam98} Samec, R.G., Laird, H., Mutzke, M. \\& Faulkner, D.R.\n Inf.\\ Bull.\\ Var.\\ Stars, 4616\n\\bibitem[Shaw et al.\\ 1996] % CN And\n {sha96} Shaw, J.S., Caillault, J., Schmitt, J.H.M.M. 1996,\n \\apj, 461, 951\n\\bibitem[Schirmer 1992] % HV Aqr\n {sch92} Shirmer, J. 1992, Inf.\\ Bull.\\ Var.\\ Stars, 3785\n\\bibitem[Soloviev 1937] % UX Eri\n {sol37} Soloviev, A. 1937, Tadjik Obs.\\ Circ., No.~27, 7\n\\bibitem[Struve 1946] % RZ Dra\n {str46} Struve, O. 1946, \\apj, 103, 76\n\\bibitem[Zhai \\& Lu 1989] % SW Lac\n {zha89} Zhai, D.S. \\& Lu, W.X. 1989, Acta Astr.\\ Sinica, 9, 208\n\\end{thebibliography}"
}
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astro-ph0002174
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[
{
"name": "haloes3.tex",
"string": "%&latex209\n\\documentstyle[psfig,12pt]{article}\n\\textwidth 16.0cm \n\\textheight 23.0cm\n\\parindent 1.0cm\n\\topmargin 0in\n\\oddsidemargin 0in\n\\newcommand{\\eg}{{\\sl e.g.}}\n\\newcommand{\\ie}{{\\sl i.e.}}\n\\newcommand{\\cf}{{\\sl c.f.}}\n\\newcommand{\\etal}{{\\sl et al.}}\n\\newcommand{\\etc}{{\\sl et c.}}\n\\newcommand{\\rtidal}{$\\Re_{tidal}$}\n\\newcommand{\\oiiir}{$L_{[OIII]}$ vs. P$_{tot}$}\n\\newcommand{\\oiir}{$L_{[OII]}$ vs. P$_{tot}$}\n\\newcommand{\\ltae}{\\raisebox{-0.6ex}{$\\,\\stackrel\n{\\raisebox{-.2ex}{$\\textstyle <$}}{\\sim}\\,$}}\n\\newcommand{\\gtae}{\\raisebox{-0.6ex}{$\\,\\stackrel\n{\\raisebox{-.2ex}{$\\textstyle >$}}{\\sim}\\,$}}\n\\bf\n\n\\begin{document}\n\\noindent\n{\\Large\\bf The large-scale distribution of warm ionized gas around\nnearby radio galaxies with jet-cloud interactions}\n\\vglue 0.5cm\\noindent\n{\\bf C.N. Tadhunter$^{1}$, M. Villar-Martin$^{1,2}$, R. Morganti$^{3}$,\nJ. Bland-Hawthorn$^{4}$ \\&\nD. Axon$^{5}$}\n\\vglue 0.5cm\\noindent\n{\\small $^{1}$ Department of Physics, University of Sheffield, Sheffield S3 7RH, UK \\\\\n$^{2}$ Institude d'Astrophysique, 98bis Boulevard Arago, F-75014, Paris, France \\\\\n$^{3}$ NFRA, PO Box 2, 7990 AA Dwingeloo, The Netherlands \\\\\n$^{4}$ Anglo-Australian Observatory, PO Box, 296 Epping, NSW 2121, Australia \\\\\n$^{5}$ Division of Physics and Astronomy, Department of Physical Sciences,\nUniversity of Hertfordshire, College Lane, Hatfield, Herts AL10 9AB, UK }\n\n\\vglue 0.5cm\\noindent\n{\\bf Abstract} Deep, narrow-band H$\\alpha$ observations taken with\nthe TAURUS Tunable Filter (TTF) on the 4.2m WHT telescope\nare presented for two nearby radio\ngalaxies with strong jet-cloud interactions.\nAlthough the brightest emission\nline components are closely aligned with the radio jets --- providing\nnearby examples of the ``alignment effect'' most commonly observed\nin high redshift ($z > 0.5$) radio galaxies --- lower surface brightness\nemission line structures are detected at large distances (10's of kpc) from\nthe radio jet axis. These latter\nstructures cannot be reconciled with anisotropic illumination\nof the ISM by obscured quasar-like sources, since parts of the \nstructures lie outside any plausible quasar ionization cones. Rather, the\ndistribution of the emission lines around the fringes of the extended\nradio lobes suggests that the gas is ionized either by direct interaction with\nthe radio components, or by the diffuse photoionizing radiation fields \nproduced in the shocks generated in such interactions. These observations\nserve to emphasise that the ionizing effects of the radio components can\nextend far from the radio jet axes, and that deep emission line imaging\nobservations are required to reveal the true distribution of warm gas\nin the host galaxies. We expect future deep imaging observations to \nreveal similar structures perpendicular to the radio axes in the high-z radio galaxies.\n\n\\section{Introduction}\nPowerful radio galaxies are frequently associated with extended emission line\nnebulosities which extend on radial scales of 5 --- 100 kpc from the nuclei\nof the host early-type galaxies (Hansen \\etal\\ 1987, Baum \\etal\\ 1988).\nThe morphological and kinematical properties of these\nnebulae provide important clues to the origins of\nthe gas, and the origins of the activity as a whole. The study of such gas is, for example, important for our understanding of the building of galaxy disks \nand bulges by infall since their epoch of formation.\nTherefore, it is crucial to\ndetermine the extent to which the observed emission line properties reflect\nthe intrinsic distribution of the warm gas in the haloes of the host galaxies,\nand the extent to which they reflect the effects of the nuclear activity and\ninteractions with the extended radio sources. \n \nIn most low redshift ($z < 0.2$) radio galaxies the optical emission line regions are broadly distributed in angle around the nuclei of\nthe host galaxies, the correlations between the optical\nand radio structural axes are weak, and \nthe gas kinematics are often quiescent, with line\nwidths and velocity shifts consistent in most cases with gravitational\nmotions in the host early-type galaxies (Tadhunter, Fosbury\n\\& Quinn 1989; Baum, Heckman \\& van Breugel 1990). \nHowever, optical observations\nreveal a dramatic change in the properties of the nebulosities as the\nredshift and radio power increase: the emission line kinematics become \nmore disturbed (compare Tadhunter \\etal\\ 1989 with McCarthy, Baum \\&\nSpinrad 1996) \nand the optical/UV structures become more closely aligned with the radio \naxes of the host galaxies (McCarthy \\etal\\ 1987,\nMcCarthy \\& van Breugel 1989). The most recent high resolution HST images \nof $z \\sim 1$ radio galaxies show that\nthe structures are not only closely\naligned with the radio axes, but they are also highly collimated, with\na jet-like\nappearance (Best et al. 1996). \n%In high redshift ($z > 0.5$) radio galaxies \n%both the emission line and the UV continuum structures are closely\n%aligned with the radio axes (McCarthy \\etal\\ 1987). \nThe nature of the ``alignment effect'' is\na key issue for our general understanding of powerful radio galaxies, of particular relevance to the use of radio sources as probes of the high redshift universe.\n\nOf the many models which have been proposed to explain the alignment effect, the\ntwo which have received the most attention are the {\\it anisotropic illumination}\nand the {\\it jet-cloud interaction}\\footnote{We use ``jet-cloud interaction''\nas a generic term to describe interactions between the warm ISM\nand the radio-emitting components, which could include the radio lobes\nand hot-spots, as well as the radio jets.} models. \n\nIn the case of anisotropic illumination it is proposed that\nthe gaseous haloes of the host galaxies are illuminated by the broad\nradiation\ncones of the quasars hidden in the cores of the galaxies (\\eg\\ Barthel\n1989), with the emission lines resulting from photoionization of the ambient ISM by the EUV radiation in the cones (\\eg\\ Fosbury 1989), and the extended optical/UV\ncontinuum comprising a combination of the nebular continuum emitted by the warm\nemission line clouds (Dickson \\etal\\ 1995) and scattered quasar light \n(Tadhunter \\etal\\ 1988, Fabian 1989). The alignment of the obscuring tori perpendicular to the collimation axes of the plasma jets then leads to a \nnatural alignment of the extended nebulosities with the radio axes. The best\nevidence to support the anisotropic illumination model is provided by\npolarimetric observations of powerful radio galaxies at all redshifts\nwhich show evidence for high UV polarization and scattered quasar features\n(\\eg\\ Tadhunter \\etal\\, 1992, Young \\etal\\ 1996, Dey \\& Spinrad 1996, Cimatti \\etal\\ 1996, Cimatti\n\\etal\\ 1997, Ogle \\etal\\ 1997).\nIt would be difficult to explain these polarimetric results in terms of\nany mechanism other than scattering of the anisotropic radiation\nfield of an illuminating quasar or AGN. However, despite the success\nof the illumination model at explaining the polarization properties, a \nsigificant fraction of radio galaxies --- comprising $\\sim$30 -- 50\\% of radio\ngalaxies at $z\\sim1$, and a smaller proportion of lower redshifts --- are dominated by jet-like UV emission line structures,\nwhich are more\nhighly collimated than would be expected on the basis of the\n45 -- 60$^{\\circ}$ opening half-angle illumination cones\npredicted by the unified schemes for powerful radio galaxies\n(Barthel 1989, Lawrence 1991). Moreover,\nthe highly disturbed emission line kinematics\nobserved in many high-z sources are also difficult to reconcile with\nquasar illumination of the undisturbed ambient ISM of the host galaxies. \n \n\nJet-cloud interactions \nhave the potential to explain many of the\nfeatures of powerful radio galaxies which cannot be explained in terms\nanisotropic quasar illumination. Although the jet-cloud interactions\nare likely to be complex, at the very least the clouds will be compressed,\nionized and accelerated as they enter the shocks driven through\nthe ISM by the jets. Therefore, jet-cloud interactions provide a promising\nexplanation for the high-surface-brightness and extreme emission line kinematics\nof the structures aligned along the radio axes of high-z sources. \n%The clouds\n%involved in such interactions will have their line emission enhanced\n%by three mechanisms: (a) direct shock ionization or ionization by photons\n%generated in the hot post-shock gas (Sutherland \\etal\\ 1995, \n%Dopita \\& Sutherland 1997), (b) photoionization by the\n%narrow blazar beams associated with the relativistic jets (\\eg\\ Padovani\n%\\& Urry 1992), and (c) an increase in the covering factors\n%of the warm clouds as they are flattened and shredded by their interaction with %the hot post-shock wind (Klein, McKee \\& Collela 1994, Clark 1996, Bremer, %Fabian \\& Crawford 1997).\n%Note that the latter mechanism will lead to an enhancement\n%of the line flux regardless of whether the ionizing photons are generated by\n%the hot, post-shock gas or by a central quasar. In this model\n%much of the UV continuum associated with the aligned structures can be %explained in terms of the nebular continuum\n%mitted by the warm, shocked clouds (Dickson \\etal\\ 1995) and/or the\n%AGN light scattered by dust in the clouds shredded by the jet-induced\n%shocks (Bremer \\etal\\\n%1997). More controversially, it has also been proposed that\n%the UV continuum emission is associated with bursts of star formation triggered\n%by the compression effect of the shocks driven by the jets\n%(\\eg\\ Rees 1989, de Young 1989).\nIndeed, recent spectroscopic observations of jet-cloud interactions in \nlow redshift\nradio galaxies provide clear observational evidence for the acceleration and ionization of warm clouds by the jet-induced shocks (\\eg\\ Clark \\etal\\ 1998, Villar-Martin \\etal\\ 1999). Moreover, theoretical modelling work\nhas demonstrated that jet-induced shocks are a viable,\nif not unique,\nmechanism for producing the emission line spectra of radio galaxies\n(\\eg\\ Dopita \\& Sutherland 1998). \n\nIt is clear that no single mechanism can explain the emission line\nproperties of radio galaxies over the full range of redshift and radio\npower; some combination of AGN illumination and jet-cloud interactions is required, with the jet-cloud interactions becoming increasingly important\nas the redshift and/or radio power increases. However, a major problem with\nsuch a combined model is that, \nwhile the polarimetric results demonstrate that quasar illumination is \nimportant in many high redshift sources, the extended structures are often\ndominated by highly collimated jet-like structures, with no\nsign of the broad cone-like emission line distributions predicted\nby the unified schemes for powerful radio galaxies. \n\nHow do we explain this\ndearth of broad cones in the objects with the\nmost highly collimated structures? Possibilities include the following.\n\\begin{itemize}\n\\item {\\bf The gas structures are intrinsically aligned along the radio\naxes of the high redshift sources}, so that the emission \nline nebulae reflect the true \ndistribution of warm/cool gas, rather than the ionization patterns\ninduced by the jets or illuminating AGN. \nFor example, West (1994)\nhas proposed that a general alignment of the gas structures along the\nradio axis may be a natural consequence of the formation of giant elliptical\ngalaxies in a heirarchical galaxy formation scenario, although it is\nnot clear that the structures formed in this way would be quite as\nhighly collimated as those observed in the high-z radio galaxies. \n\\item {\\bf The nuclei of the host galaxies do not contain powerful\nquasars}, and the ionization of the extended gas is dominated by the jets: either by direct jet/cloud interactions, or by illumination by the\nrelativistically-beamed jet radiation. This scenario is supported\nby the discovery at low redshifts of a class of powerful radio galaxies with weak, low ionization nuclear\nemission line regions (see Laing 1994, Tadhunter \\etal\\ 1998). \nHowever, at least some high-z radio galaxies with highly\ncollimated UV structures show direct evidence for powerful quasar\nnuclei in the form of scattered quasar features in their polarized\nspectra, so this explanation cannot hold in every case. \n\\item {\\bf The broad-cone radiation of the buried quasars does\nnot escape from the nuclear regions of the host galaxies}, because\nof the absorbing effects of circum-nuclear gas. In this case the ionization of the\nextended gas in the aligned structures is likely to be dominated by jet-cloud interactions, but quasar or beamed jet radiation may also contribute along\nthe jet axis,\nif the jets punch a hole in the obscuring material. Direct evidence for\nrequisite obscuring material in the central regions is provided by the relatively high occurrence rate of \nassociated CIV and Ly$\\alpha$ absorption line systems in the UV\nspectra of radio-loud\nquasars \n(\\eg\\ Anderson \\etal\\ 1987, Wills \\etal\\ 1995), the relatively\nred SEDs of steep spectrum radio quasars (Baker 1997), and the detection of\nsignificant BLR reddening in a substantial fraction of nearby\nbroad-line radio galaxies (\\eg\\ Osterbrock, Koski \\& Miller 1995, Hill\n\\etal\\, 1996).\n\\item {\\bf The dearth of broad ionization cones in the high-z sources\nis a consequence of an observational selection effect:} most of the \nexisting emission line\nimages of the high-z sources have been taken in the light of the\nlow ionization [OII]$\\lambda$3727 line which is emitted particularly strongly\nby the jet-induced shocks (\\eg\\ Clark \\etal\\ 1997, 1998), \nbut is relatively weak in the more highly ionized\nquasar illumination cones. Thus, given that the \npublished ground-based images of the high-z objects are relatively\nshallow and have a low spatial resolution, while the published HST images have a higher\nresolution but are insensitive to low surface brightness structures,\nthe existing images are likely to be biased in\nfavour of the high-surface-brightness shocked structures along the radio axes. In this\ncase, we would expect deep emission images to reveal gaseous structures outside\nthe main high surface brightness structures aligned along the radio axes. \nIf the gas away from the radio axis is predominantly photoionized by quasars\nhidden in the cores of the galaxies we would expect the extended low surface\nbrightness structures to have a broad distribution, \nconsistent with quasar illumination. Detection of such\nemission line morphologies in the objects with the most highly\ncollimated structures would lead to a reconciliation between the anisotropic\nillumination and jet-cloud interaction models, thereby resolving the outstanding uncertainties surrounding the nature of the alignment effect.\n\\end{itemize}\nIn order to test the latter possibility\nit is important to obtain deep emission line imaging observations for the objects with closely aligned radio and optical structures.\nWe report here pilot observations of two intermediate-redshift radio galaxies\n--- 3C171 ($z=0.2381$) and 3C277.3($z=0.08579$) --- which are nearby prototypes\nof the high-z radio galaxies, in the sense that they show high surface \nbrightness emission line structures which are closely aligned along their radio\naxes. The results challenge some commonly-held assumptions about the\nionization of the extended gaseous haloes around powerful radio galaxies.\n\n\\section{Observations}\n\nEmission line and continuum observations of\n3C171 and 3C277.3(Coma A)\nwere taken using the Taurus Tunable Filter (TTF) on the\n4.2m WHT telescope at the La Palma Observatory on the night of the \n27th January 1998. A log of the observations is presented in \nTable 1, while a\nfull description of the TTF is given in Bland-Hawthorn \\& Jones (1998a,b). Use of the\nf/2 camera of TAURUS with the Tek5 CCD resulted in a pixel scale of 0.56\narcseconds per pixel; and\nthe seeing conditions were subarcsecond for the observations reported here.\nThe faintest structures visible in the images for both objects have\nan H$\\alpha$ surface brightness of $\\sim1\\times10^{-17}$ erg cm$^{-2}$ \ns$^{-1}$ arcsec$^{-2}$.\n\nBecause of ghosting effects in the flat field images, no flat fielding of the\ndata was attempted. However, comparisons between images taken with different\nfilters and/or with the objects placed in different positions on the detector,\ndemonstrate that the ghost images of stars and galaxies in the field do not contaminate the images of the main\ntarget objects described below.\n \nThe reduction of the images consisted of \nbias subtraction, atmospheric extinction correction, flux calibration,\nsky subtraction and registration. From the comparison \nbetween the measurements of the flux calibration standard stars\ntaken at various times during the run it is estimated\nthat the absolute flux calibration is accurate to within $\\pm$30\\%, and\nthe H$\\alpha$ emission line fluxes agree at this level with the long-slit\nspectroscopy measurements in Clark (1996). For the\nemission line images, the TTF was tuned to the wavelength of H$\\alpha$ shifted to the redshift of the emission lines in the nuclear regions of the galaxies.\nHowever, velocity structure in the haloes of the host galaxies may result in\nthe emission lines in the extended structures not being exactly centred in the\nTTF bandpass, which has a Lorentzian shape. We estimate that, at maximum, this\nwill result in the fluxes being underestimated by a factor of two for components\nwith extreme $\\pm$600 km/s shifts, but this will not affect our main conclusions\nwhich are based largely on the emission line structures, rather than the\nemission line fluxes.\n\nIn order the facilitate comparison between the radio and optical structures, radio images were obtained for both sources. The radio and optical\nimages were registered by matching the positions of the core radio sources \nwith the positions of the continuum\ncentroids in the optical continuum images, with the pixel scale and rotation\nof the optical images calibrated using the known positions of stars in the CCD\nfields.\n\nThe radio image of Coma A was made using data taken with the VLA A-array\nconfiguration at 1.4 GHz (20cm). This gives a resolution for the final image \nof 1.14x1.13 arcseconds in p.a. -72.\nThe data, which were extracted from the VLA archive, were originally \npresented and discussed in great detail by van Breugel \\etal\\ (1985). We\ntherefore refer to that paper for all the radio information about Coma A.\n\nThe radio image of 3C171 was kindly provided by K. Blundell. The image \nwas made with the VLA at 8~GHz with a resolution of 1.3 arcsec FWHM.\nMore information about the radio characteristics of this source can be found in Blundell\n(1996).\n\n \n\\section{Results}\n\\subsection{3C277.3 (Coma A)}\n\nPrevious spectroscopic and imaging observations of 3C277.3 by\nvan Breugel \\etal\\ (1985) and Clark (1996) show the presence\nof a series of high surface brightness structures along the\nradio axis. These include: a high ionization emission line region\nassociated with knots in radio jet some 6 arcseconds to the \nsouth east of the nucleus; an enhancement in the emission line \nflux close to the hotspot in the northern radio lobe; and an emission\nline arc which partially circumscribes the northern radio hotspot.\nAlthough the kinematic and ionization evidence for a jet-cloud\ninteraction in this source is less clear than in some other radio\ngalaxies (\\eg\\ 3C171: see below) --- the ionization state is relatively\nhigh and the emission lines relatively narrow --- van Breugel\n\\etal\\ (1985) found evidence for a jump in the emission line radial velocities\nacross the northern radio lobe, while Clark (1996) noted that the ionization\nhas a minimum, and the electron temperature a peak, at the position of the\nnorthern radio hotspot. Note that there is no clear evidence for a powerful\nquasar nucleus in this source: the nuclear regions show no evidence\nfor scattered quasar light, and the nuclear emission line region has a \nrelatively low luminosity and ionization state compared with the brightest\nextended emission line regions along the radio axis.\n\nOur deep H$\\alpha$ images (Figure 1a) show that the emission line regions\nalong the radio axis\nform part of a spectacular system of interlocking emission line arcs and filaments, which\nextend almost as far perpendicular as parallel\nto the radio axis. Of particular interest is the fact that the brightest\narc structure wraps a full 180$^{\\circ}$ around the nucleus, with enhancements\nin the emission line surface brightness where the arc intercepts the radio\naxis to the north and south of the nucleus. The spatially integrated\nH$\\alpha$\nfluxes of the bright knots along the radio axis (including the nucleus),\nthe extended low surface brightness filaments, and the nebula as a whole\nare $2.5\\times10^{-14}$, $1.6\\times10^{-14}$ and $4.1\\times10^{-14}$ erg \ns$^{-1}$ cm$^{-2}$ respectively. For our adopted cosmology\\footnote{$H_0 = 50 km s^{-1} kpc^{-1}$ and $q_0 = 0.0$ assumed throughout.} \nthe corresponding H$\\alpha$ emission line\nluminosities are $8.6\\times10^{41}$, $5.6\\times10^{41}$ and $1.42\\times10^{42}$\nerg s$^{-1}$ respectively. \n\nThe fact that the main arc and filament structures are not visible, or\nare considerably fainter, in the\nintermediate-band\ncontinuum image (Figure 1b) --- which is at least as sensitive to continuum structures\nas the narrow-band H$\\alpha$ image --- demonstrates that they are predominantly\nemission line structures. However, \na number of faint galaxies and continuum structures are detected within\n100 kpc of the nucleus of Coma A, and at least some of these continuum structures (highlighted by arrows in the figure) are intimately associated with the\nextended H$\\alpha$ filamentary structures.\n\nOverall, the Coma A system has the appearance of an interacting group of\ngalaxies: the H$\\alpha$ filaments bear a marked resemblance to \nthe HI tails detected in 21cm radio observations\nof interacting groups (\\eg\\ the M81 group: Yun \\etal\\ 1994); and it is\nplausible that the faint continuum\nstructures represent the debris of interactions/mergers between the\ndominant giant elliptical galaxy and less massive galaxies in the same group.\nThe X-ray luminosity of Coma A ($L_{0.5-3kev} < 8.1\\times10^{42}$ erg s$^{-1}$:\nFabbiano \\etal\\ 1984) is also consistent with a group environment. \n\nFigure 2 shows an overlay of the emission line image and the 6cm radio map. \nThis reveals a striking match between the emission line\nand radio structures. As well as the high surface brightness features along\nthe radio axis, the brightest arc to the north of the nucleus closely\nfollows the outer edge of northern radio lobe. The emission line \nstructures appear to bound the radio structures: the brighter\nemission line features have a similar radial and lateral extent to the radio\nfeatures. It is notable, however, that fainter, more diffuse emission line structures\nare detected well outside the radio lobes on the\nnorthern and eastern sides of the galaxy.\n\nThe detection of arc structures circumscribing radio lobes is not\nwithout precedent: the intermediate redshift radio galaxies PKS2250-41 (Clark \\etal\\ 1998,\nVillar-Martin \\etal\\ 1999), 3C435A (Rocca-Volmerange \\etal\\ 1994) and PKS1932-46\n(Villar-Martin \\etal\\ 1998), the high redshift radio galaxies 3C280\n(McCarthy \\etal\\ 1995) and 3C368 (Best \\etal\\ 1996), and the central\nelliptical galaxy in the cooling flow cluster A2597 (Keokemoer \\etal\\ 1999),\nall show evidence for arcs associated with radio lobes. In many of these\ncases there is also spectroscopic evidence that the emission line gas extends beyond the radio lobes.\n\n%We further note that the emission line morphology of Coma A shows a striking %resemblence\n%to that seen in the gas surrounding the radio lobes of the dominant\n%elliptical galaxy at the centre of the colling flow cluster A2597 \n%(Koekemoer et al 1999, preprint). Not only is the northern lobe of A2597\n%circumscibed by an emission line arc, but there are optical filaments\n%which extend well beyond its southern lobe (see their figure 2).\n%Furthermore Keokemoer et al also report the exisitence of numerous\n%blue continuum sources, which one might liken to the 'faint galaxies'\n%seen in our images, which they argue are star-forming knots created by\n%a jet-cloud interaction.\n\n\n\\subsection{3C171}\n\n3C171 is another example of an object in which high surface brightness emission\nline structures are closely aligned along the axis of the radio jets\n(Heckman \\etal\\ 1984, Baum \\etal\\ 1988). The \nspectroscopic evidence for a jet-cloud interaction in this source is strong:\nthe emission line kinematics along the radio axis are highly disturbed; and the the general\nline ratios and ionization minima coincident with the radio hotspots to the\neast and west of the nucleus provide strong evidence that the emission line\ngas has been compressed and ionized by jet-induced shocks\n(Clark \\etal\\ 1998). A further\npossible consequence of the jet-cloud interactions is the highly disturbed \nradio structure, with the radio lobes showing a greater\nextent perpendicular- than parallel to the jet axis, giving\nan overall H-shaped appearance (Heckman \\etal\\ 1984, Blundell 1996). \n\nOur deep H$\\alpha$ and continuum images of this source are shown in Figure 3, while an overlay of the optical emission line image and\nthe radio map is presented in Figure 4. From the continuum-subtracted H$\\alpha$\nimage we measure spatially integrated emission line fluxes of\n$2.12\\times10^{-14}$, $6.2\\times10^{-16}$ and $2.63\\times10^{-14}$ \nerg s$^{-1}$ cm$^{-2}$ \nrespectively for\nthe high surface brightness structures aligned along the radio axis\n(including the nucleus), the\nfaint filament to the north, and the nebula as a whole. The corresponding\nH$\\alpha$ emission line luminosities are $6.6\\times10^{42}$, \n$1.9\\times10^{41}$ and $8.1\\times10^{42}$ erg s$^{-1}$ respectively.\n \n \nAlthough the emission line structures in 3C171 are\nclearly different in detail from those detected in Coma A, there are important\ngeneral similarities. Most notably, as in Coma A, the highest surface brightness emission line\nfeatures are closely aligned along the radio axis, yet lower surface brightness\nstructures are also detected in the direction perpendicular to the radio axis. The emission line structures have a similar radial extent in the\ndirections perpendicular and parallel to the radio axis. Away from the\nradio axis, the most striking emission line feature is the filament \nwhich extends 9 arcseconds (45 kpc)\nnorth of the nucleus. This feature lies along the\nfringes of the western radio lobe, just as the arc to the north of the nucleus\nin Coma A skirts the outer edge of the northern radio lobe in that object.\nA further similarity with Coma A is that, in the radio axis direction, the\nradio structures are confined within the emission line structures, which have\na similar radial extent. We also find evidence\nfor emission line gas that is not clearly associated with radio structures: \nthe faint, diffuse\nH$\\alpha$ emission to the south \neast of the nucleus lies well to the south of the extended eastern radio\nlobe. However, 3C171 is different from Coma A in the sense that\nthe radio lobes extend further than the emission line structures in the\ndirection perpendicular to the radio axis on the northern side of the galaxy.\n\n\n\\section{Discussion}\n\nThe main aim of the deep emission line imaging\nobservations\nwas to attempt to detect the broad emission line cones outside the main\naligned structures, and thereby reconcile the AGN illumination and jet-cloud\ninteractions models. The unified schemes predict illumination \ncones with opening \nhalf-angles\nof 45-60$^{\\circ}$. Although the extended emission line nebulosities in low \nredshift radio galaxies\nrarely show the sharp-edged cone structures observed in some Seyfert galaxies\n(\\eg\\ Pogge 1988, Tadhunter \\& Tsvetanov 1989), the emission \nline distributions are generally consistent with broad cone illumination\nof an inhomogeneous ISM \n(Hansen \\etal\\ 1987, Baum \\etal\\ 1989, Fosbury 1989). The detection of similar\nemission line distributions in 3C171 and\nComa A would support the idea that the extended ionized haloes are photoionized\nby quasars hidden in the cores of the galaxies.\n\nThe deep imaging observations presented in this paper have confounded our\nexpectations in the sense that, while they do show extended \nof emission line gas well away from the radio axis, the emission line\ndistribution cannot be reconciled with any plausible ionization cone model.\nNot only do some of the features wrap through a full 180$^{\\circ}$ in position angle around the nucleus of Coma A, but there are\nno sharp boundaries in the surface brightness of the structures, corresponding\nto the edges of an ionization cone. It is possible for the emission line \ndistributions to appear broader than the nominal 45-60$^{\\circ}$ cones\npredicted by the unified schemes if the cone axes are tilted towards\nthe observer. However, in order to explain the emission line distributions\nin 3C171 and Coma A in this way, the cones would have to be tilted to such\nan extent that the observer's line of sight would lie within the cone\nand we would see the illuminating AGN directly. Clearly this is not the case,\nand it appears highly unlikely that the extended filaments away from\nthe radio axis are\nphotoionized by a central source of ionizing photons. \n\nThe most plausible alternative to quasar illumination is ionization by the\nshocks associated with the expanding radio jets and lobes. The emission lines\ncould be produced as the warm clouds cool behind the shock fronts or, alternatively, as a consequence of photoionization of precursor clouds by\nthe ionizing photons produced in the cooling, shocked gas. In either case we would \nexpect\na close morphological association between the radio and optical \nstructures, just\nas we observe in 3C171 and Coma A. By adapting equation 4.4 of Dopita and Sutherland (1996), and assuming a shock speed through the warm clouds of\n200 km s$^{-1}$, we estimate that the rate of flow of warm ISM through the\nshocks would have to be at least 1.9$\\times$10$^4$ M$_{\\odot}$ yr$^{-1}$\nfor 3C171, and 3.2$\\times$10$^3$ M$_{\\odot}$ yr$^{-1}$ for Coma A, in\norder for the emission line luminosities of the\nnebulae as a whole to be produced entirely by shock ionization. Energetically,\nthe shock ionization mechanism appears to be feasible in the sense that\nthe total emission line luminosities of the sources\nare $<$10\\% of\nthe bulk powers of the radio jets (Clark 1996, Clark \\etal\\ 1998)\\footnote{In order to derive this result we have scaled the\nresults of Clark (1996), who considered only the emission line components\nalong the radio axis, to the total emission line fluxes for the nebulae\nas a whole, as derived from our H$\\alpha$ images.}. \n\n\n%One interpretation of the emission line images is that the \n%ionization of the extended gas is entirely\n%ominated by the effects of radio-plasma-induced shocks. In this scenario \n%the radio structures\n%interact with pre-existing warm/cool gas structures in the haloes\n%of the galaxies, with enhancements in the emission line surface\n%brightness at the sites of the strongest interaction. For this\n%scenario to work the ionization effect of the jets and hotspots would\n%have to be stronger than that of the radio lobes, in order to explain\n%the higher surface brightness of the structures along the radio axes. For %example, it is possible that the shocks induced by the jets and hotspots\n%are faster\n%than those induced by the more slowly expanding lobes. Because the ionizing\n%energy of the shocks rises rapidly with shock speed, this would naturally\n%explain the higher surface brigtnesses of the structures along\n%the radio axis.\n\nHowever, it is not possible to rule out some\ncontribution to the ionization of the extended structures\nby a central photoionizing source. As discussed in the\nintroduction, some radio sources with relativistic jets\nmay not have powerful quasar nuclei. If this is the case, the narrow\nbeams of radiation emitted by the jets could contribute to the ionization of the structures along\nthe radio axis,\nalthough the ionization of the more extended filamentary structures would\ncontinue to be be dominated by interactions with the rdaio lobes.\n\nOne further possibility is that the structures are photoionized by young\nstars associated with the filaments. This is supported by\nthe presence of faint continuum structures associated with the H$\\alpha$\nfilaments (see Figure 1(c)), and the spectroscopic detection of excess UV continuum emission to the\nnorth and south of the nucleus along the radio axis above the level expected\nfor the nebular continuum emitted by the warm gas\n(Clark 1996). Without further information\non the nature and spectrum of the extended continuum structures it is difficult\nto test this model at the present time.\n\nAn open question for both 3C171 and Coma A is the extent to which the structures\nreflect the true distributions of ionized gas in the haloes of the host galaxies,\nand the extent to which the structures are distorted by their interaction\nwith the radio components. It is possible for shock fronts to sweep up material\ninto shell-like structures. However, given that the clouds are likely to be destroyed by hydrodynamical interactions\nwith the fast, hot wind behind the shock fronts within\na few shock crossing times (\\eg\\ Klein, McKeee \\& Collella 1994), \nand given also the presence of\ndiffuse H$\\alpha$ emission well away from the radio structures in\nboth Coma A and 3C171, \nit seems more plausible that these \nrepresent pre-existing gas structures. Cloud destruction by\nshocks may also lead to a relative absence of warm gas in \nthe lobes, further enhancing the shell-like appearance of the emission\nline structures.\nIn the \ncase of Coma A it is likely that we are seeing\nthe results of interactions between between the radio-emitting\ncomponents and the gaseous remnants of mergers/interactions in a group\nof galaxies. \n%A similar scenario has been proposed for the higher redshift\n%radio galaxy PKS2250-41, which also shows an emission line arc circumscribing\n%the radio lobes (Clark \\etal\\ 1998).\n\nClearly, detailed measurements of the kinematics, \nline ratios, and continuum spectra of\nthe filamentary structures are required in order to resolve\nthe outstanding issues concerning the physical state, ionization\nand origins of the warm gas.\n\n\n \n\\section{Implications for high redshift radio galaxies}\n\nOur observations demonstrate the presence of extended gaseous structures\nwell away from the high-surface-brightness structures aligned along\nthe radio axes in two nearby radio\ngalaxies. Given that Coma A and 3C171 are similar to the high redshift\nradio galaxies in the sense that they show high-surface-brightness emission line\nstructures closely aligned along their radio axes, as well as evidence\nfor disturbed emission line kinematics, it seems likely that similar extended \ngaseous structures also exist in the high-z sources. In this case, the highly\ncollimated\nstructures visible in the existing images of some $z \\sim 1$ \n3C radio sources may reflect more the ionization pattern induced by the radio jets than the\ntrue distribution of warm/cool gas in the host galaxies. \n\nNote, however, that 3C171 and Coma A\nhave radio and emission line luminosities that are an order of magnitude\nlower than 3C radio galaxies at $z \\sim 1$. Furthermore, the radio lobes in\n3C171 and Coma A extend further in the direction perpendicular to the radio\njets than is typical in high redshift 3C radio sources. \nTherefore, it is difficult to predict the detectability of the extended low surface brightness\nstructures in the high-z radio galaxies ($z > 1$) based on a straightforward extrapolation of the properties of 3C171 and Coma A. \nGiven the smaller lateral extents of the radio lobes in the \nhigh-z sources, the ionization effects associated with the lobes may be less\neffective at large distances from the radio axes in such objects. In\naddition, the structures in the high-z sources will\nbe \nsubject to $(1+z)^{-4}$ cosmological surface brightness dimming which\nwill make them more difficult to detect relative to nearby sources for\nsimilar intrinsic brightness levels. However, set against this is the\nfact that, in contrast to \nComa A and 3C171, there exists good polarimetric evidence that many \nof the high-z\nradio galaxies contain powerful quasars hidden in their cores. Provided\nthat the ionizing photons in the broad ionization cones can\nescape the nuclear regions (but see discussion in introduction),\nillumination by the quasar cones will enhance the surface\nbrightnesses of the extended structures and render them more easily\ndetectable.\n\nThe extended low surface brightness structures may already have been\ndetected spectroscopically in at least one high-z source: deep, long-slit\nKeck spectra taken along the radio axis\nof 3C368 ($z = 1.135$) by Stockton, Ridgway \\& Kellogg (1996) show the presence of a faint emission \nline region well\noutside the main high surface brightness emission line\nregions closer to the nucleus. The relatively\nnarrow lines and high ionization state measured in this\nfaint, low-surface-brightness region are consistent\nwith quasar illumination of the undisturbed ambient medium of the host galaxy.\n\nSome encouragement may also be drawn from the detection of large Ly$\\alpha$\nhaloes around radio galaxies at $z > 2$ (\\eg\\ Adam et al. 1997). Although the Ly$\\alpha$ in these\nhaloes may not be formed by direct photoionization by an AGN, but rather\nby resonant scattering of Ly alpha photons produced in the \nextended regions around\nthe nuclei (Villar-Martin \\etal\\ 1996), these observations at least demonstrate the presence of \nextensive haloes of cool ISM surrounding the host galaxies of some of the highest\nredshift radio galaxies. \n\nThus, we\nexpect future deep emission line imaging of $z \\sim 1$ radio galaxies to reveal\nthe true distribution of the extended ionized gas in the host galaxies, and to provide clues to the origins of the gas and the evolution of the host galaxies.\n\n\\section{Conclusions}\n\nDeep emission line imaging observations of two nearby examples of \nthe radio-optical alignment effect have revealed extensive low-surface-brightness emission line structures well away from the radio\naxes, thus demonstrating that the intrinsic distribution of warm gas is more\nextensive than previosly suspected. \n\nThe general distribution of the gaseous structures is imcompatible with\nthe standard quasar illumination picture, while their association with\nthe extended radio structures provides clear evidence that they are interacting\nwith the radio lobes, hotspots and jets. These may be objects in which\nthe ionization of the extended emission line regions is entirely dominated by shocks\ninduced by interactions between the radio plasma and the ISM.\n\nIt is often assumed that broad distribution of ionized gas observed\nin low redshift radio galaxies without clear signs of jet-cloud\ninteractions imply illumination by the broad ionization\ncones of quasars hidden in the cores of the galaxies. These new observations\nsuggest that this may not always be the case, and that the lobes as well as\nthe jets may have a significant ionizing effect.\n\\vglue 0.5cm\\noindent\n{\\bf Acknowledgments.} The Willian Herschel Telescope is operated on\nthe island of La Palma by the Isaac Newton Group in the Spanish\nObservatorio del Roches de los Muchachos of the Instituto de Astrofisica\nde Canarias. We thank Katherine Blundell for allowing us\nto use to her radio image of 3C171. 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Como Conf. 1988, BL Lac\nObjects, Springer-Verlag, Berlin, p.79\n\n\\item Tadhunter, C.N., Fosbury, R.A.E., Quinn, P., 1989, MNRAS, 240, 255\n\n\\item Tadhunter, C., Scarrott, S., Draper, P., Rolph, C., 1992, MNRAS, 256, 53p\n\n\\item Tadhunter, C.N., Tsvetanov, Z., 1989, Nat, 341, 422\n\n\\item Tadhunter, C.N., Morganti, R., Robinson, A., Dickson, R., Villar-Martin,\nM., Fosbury, R.A.E., 1997, MNRAS, submitted.\n\n\\item Villar-Martin, Binette, Fosbury, 1996, A\\&A, 312, 751\n\n\\item Villar-Martin, M., Tadhunter, C.N., Morganti, R., Clark, N., Killeen, N.,\nAxon, D., 1998, A\\&A, 332, 479\n\n\\item Villar-Martin, M., Tadhunter, C.N., Morganti, R., Axon, D., 1999,\nMNRAS, 307, 24\n\n\n\\item van Breugel, W., Miley, G., Heckman, T., Butcher, H., Bridle, A., 1985,\nApJ, 290, 496\n\n \n\\item West, M.J., 1994, MNRAS, 268, 79\n\n\\item Wills, B.J., Thompson, K.L., Han, M., Netzer, H., Wills, D., Baldwin, J.A.,\nFerland, G.J., Browne, I.W.A., Brotherton, M.S., ApJ, 447, 139\n\n\\item Young, S., Hough, J.H., Efstathiou, A., Wills, B.J., Axon, D.J., Bailey,\nJ.A., Ward, M.J., 1996, MNRAS, 279, L72\n\n\\item Yun, M.S., Ho, P.T.P., Lp, K.Y., 1994, Nat, 272, 530\n\\end{description}\n\n\\clearpage\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{lccccl}\nObject &Blocking Filter(\\AA) &Etalon(\\AA) &Exposure Time(s) &Seeing('') &Comments \\\\\n &$\\lambda_c$/$\\Delta \\lambda$ &$\\lambda_c$/$\\Delta \\lambda$ \n& &FWHM & \\\\ \\\\\n3C171 &8140/330 &8124/28 &1800 &0.95 &H$\\alpha +$Continuum \\\\\n&8570/400 &--- &900 &0.95 &Continuum \\\\\n3C277.3 &7070/260 &7124/19 &2$\\times$900 &0.98 &H$\\alpha +$Continuum \\\\\n&7580/280 &--- &900 &0.98 &Continuum \\\\\n\\end{tabular}\n\\caption{Details of the TTF imaging observations for 3C171\nand 3C277.3. The second and third columns give the central wavelengths/bandwidths for the blocking filters and the etalon respectively.}\n\\end{center}\n\\end{table}\n\\newpage\\noindent\n\\begin{figure}\n\\psfig{figure=coma1ac.ps,width=15cm}\n\\caption{TTF images of Coma A (3C277.3): (a) H$\\alpha+$continuum; (b) pure H$\\alpha$; (c) continuum ($\\lambda_c =$7580\\AA\\,). In the continuum image\nthe arrows point to faint continuum features associated with the extended\nH$\\alpha$ filamentary structures, the ``G'' symbols indicate galaxies, while\nthe ``S'' symbol indicates a faint star (unresolved in HST images).\n}\n\\end{figure}\n\\begin{figure}\n\\psfig{figure=coma1c.ps,width=15cm}\n\\caption{Overlay of the H$\\alpha+$continuum image for Coma A (greyscale) \nwith the\n6cm radio map of van Breugel \\etal\\, (1985) (contours).\n}\n\\end{figure}\n\n\n\\begin{figure}\n\\psfig{figure=3c171bc.ps,width=15cm}\n\\caption{TTF images of 3C171: (a) H$\\alpha+$continuum; (b) pure H$\\alpha$; (c) continuum ($\\lambda_c =$8570\\AA\\,). The symbols have the same meaning as in \nFigure 1.\n}\n\\end{figure}\n\\begin{figure}\n\\psfig{figure=ha3c171-radioc.ps,width=15cm}\n\\caption{Overlay of the H$\\alpha$ image for 3C171 (greyscale) \nwith the\n6cm radio map of Blundell(1996) (contours).\n}\n\\end{figure}\n\n\n\\end{document} \n"
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astro-ph0002175
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Finite-Correlation-Time Effects in the Kinematic Dynamo Problem
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Most of the theoretical results on the kinematic amplification of small-scale magnetic fluctuations by turbulence have been confined to the model of white-noise-like ($\delta$-correlated in time) advecting turbulent velocity field. In this work, the statistics of the passive magnetic field in the diffusion-free regime are considered for the case when the advecting flow is finite-time correlated. A new method is developed that allows one to systematically construct the correlation-time expansion for statistical characteristics of the field such as its probability density function or the complete set of its moments. The expansion is valid provided the velocity correlation time is smaller than the characteristic growth time of the magnetic fluctuations. This expansion is carried out up to first order in the general case of a $d$-dimensional arbitrarily compressible advecting flow. The growth rates for all moments of the magnetic-field strength are derived. The effect of the first-order corrections due to the finite correlation time is to reduce these growth rates. It is shown that introducing a finite correlation time leads to the loss of the small-scale statistical universality, which was present in the limit of the $\delta$-correlated velocity field. Namely, the shape of the velocity time-correlation profile and the large-scale spatial structure of the flow become important. The latter is a new effect, that implies, in particular, that the approximation of a locally-linear shear flow does not fully capture the effect of nonvanishing correlation time. Physical applications of this theory include the small-scale kinematic dynamo in the interstellar medium and protogalactic plasmas.
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"string": "\\documentstyle[psfig,epsf,aps]{revtex}\n%include \"eucal\" for a version of \\mathcal font \n%\\usepackage{amsbsy,amsmath,amssymb,cyrillic,psfig,epsf}\n\n%\\oddsidemargin0in\n%\\evensidemargin0in\n%\\textwidth6.5in\n%\\topmargin-0.6in \n%\\textheight9.15in\n\n%\\renewcommand{\\baselinestretch}{1.0}\n\n\\title{Finite-Correlation-Time Effects in the Kinematic Dynamo Problem}\n\\author{Alexander~A.~Schekochihin\\thanks{Present address: \nBlackett Laboratory, Imperial College, \nPrince Consort Rd, London~SW7~2BZ,~U.K.;\nelectronic mail: sure@pppl.gov} \nand Russell~M.~Kulsrud\\thanks{Electronic mail: \nrkulsrud@astro.princeton.edu}\\\\\n{\\em Princeton University, P.~O.~Box~451, Princeton, New Jersey 08543}}\n\\date{19 April 2001}\n\n\\def\\chapref#1{Chapter~\\ref{#1}}\n\\def\\Chapref#1{Chapter~\\ref{#1}}\n\\def\\ssecref#1{Sec.~\\ref{#1}}\n\\def\\Secref#1{Section~\\ref{#1}}\n\\def\\secref#1{Sec.~\\ref{#1}}\n\\def\\apref#1{Appendix~\\ref{#1}}\n\\def\\Apref#1{Appendix~\\ref{#1}}\n\\def\\exref#1{(\\ref{#1})}\n\\def\\Exref#1{(\\ref{#1})}\n\\def\\eqref#1{Eq.~(\\ref{#1})}\n\\def\\Eqref#1{Equation~(\\ref{#1})}\n\\def\\figref#1{Fig.~\\ref{#1}}\n\\def\\Figref#1{Figure~\\ref{#1}}\n\\def\\tabref#1{Table~\\ref{#1}}\n\\def\\Tabref#1{Table~\\ref{#1}}\n\\def\\refref#1{Ref.~\\citenum{#1}}\n\\def\\Refref#1{Reference~\\citenum{#1}}\n\n\n\n%----------------------Defs for cyrillic script-----------------------\n\\def\\ikr{\\u i}\n\\def\\tvzn{\\cdprime}\n\\def\\mzn{\\cprime}\n\\def\\ts{t\\-s}\n\\def\\eob{e1}\n\\def\\Eob{E1}\n%---------------------------------------------------------------------\n\n\\def\\etal{{\\it et al.~}}\n\n\\def\\where{\\quad{\\rm where}\\quad}\n\\def\\const{{\\rm 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t}\n\\def\\intdd{\\int{\\rm d}^d}\n\\def\\unity{{\\bf 1}}\n\\def\\tr{{\\,\\rm tr\\,}}\n\\def\\vb{{\\bf b}}\n\n%-----------------------------------------------------------------------\n\n\n\\def\\vx{{\\bf x}}\n\\def\\vy{{\\bf y}}\n\\def\\vk{{\\bf k}}\n\\def\\vu{{\\bf u}}\n\\def\\vB{{\\bf B}}\n\\def\\vF{{\\bf F}}\n\n\\def\\kpar{k_{\\parallel}}\n\\def\\lpar{\\ell_{\\parallel}}\n\\def\\gpar{\\gamma_{\\parallel}}\n\\def\\dpar{\\nabla_{\\parallel}}\n\n\\def\\E{{\\cal E}}\n\n\\def\\tcorr{\\tau_{\\rm c}}\n\\def\\teddy{\\tau_{\\rm eddy}}\n\\def\\urms{u_{\\rm rms}}\n\\def\\ueddy{u_{\\rm eddy}}\n\\def\\vth{v_{\\rm th}}\n\\def\\lmfpi{\\ell_{{\\rm mfp}i}}\n\\def\\lmfpn{\\ell_{{\\rm mfp}n}}\n\\def\\kres{k_{*}}\n\\def\\Re{{\\rm Re}}\n\\def\\Rm{{\\rm R}_m}\n\\def\\Pr{{\\rm Pr}}\n\n\\def\\virg{,\\quad}\n\n% -------------------------JAK's macros:---------------------------------\n\\def\\vlp{\\mathopen{\\boldsymbol{(}}} % bold left parenthesis\n\\def\\vrp{\\mathclose{\\boldsymbol{)}}} % bold right parenthesis\n\\def\\VVlp{\\mathopen{\\boldsymbol{\\Biggl(}}} % bold Bigg left parenthesis\n\\def\\VVrp{\\mathopen{\\boldsymbol{\\Biggr)}}} % bold Bigg right parenthesis\n%------------------------------------------------------------------------\n\\def\\Vlp{\\mathopen{\\boldsymbol{\\Bigl(}}} % bold Big left parenthesis\n\\def\\Vrp{\\mathopen{\\boldsymbol{\\Bigr)}}} % bold Big right parenthesis\n\n\n\\begin{document}\n\n\n\\maketitle\n\n\\vskip5mm\n\n\\centerline{\\tt Published in \nPhysics of Plasmas, vol.~8, pp.~4937-4953 (November 2001)} \n\n\\vskip5mm\n\n\\begin{abstract}\n\nMost of the theoretical results on the kinematic amplification of \nsmall-scale magnetic fluctuations by turbulence have been confined \nto the model of white-noise-like ($\\delta$-correlated in time) \nadvecting turbulent velocity field. \nIn this work, \nthe statistics of the passive magnetic field in the diffusion-free \nregime are considered for the case when the advecting flow \nis finite-time correlated. \nA new method is developed that allows one to systematically construct \nthe correlation-time expansion for statistical characteristics \nof the field such as its probability density function or \nthe complete set of its moments. The expansion is valid \nprovided the velocity correlation time is smaller than \nthe characteristic growth time of the magnetic fluctuations. \nThis expansion is carried out up to first order \nin the general case of a $d$-dimensional arbitrarily \ncompressible advecting flow. The growth rates for all moments \nof the magnetic-field strength are derived. The effect of \nthe first-order corrections due to the finite correlation time \nis to reduce these growth rates. It is shown that \nintroducing a finite correlation time leads to the loss of\nthe small-scale statistical universality, which was present \nin the limit of the $\\delta$-correlated velocity field. \nNamely, the shape of the velocity time-correlation profile \nand the large-scale spatial structure of the flow \nbecome important. The latter is a new effect, that implies, \nin particular, that the approximation of a locally-linear \nshear flow does not fully capture the effect of \nnonvanishing correlation time. \nPhysical applications of this theory include the small-scale \nkinematic dynamo in the interstellar medium and protogalactic \nplasmas. \n\n\\end{abstract}\n\n\n\n\n\n\n\\section{Introduction}\n\n\nThe study of the statistics of magnetic fluctuations excited by a random \nGaussian white-noise-like advecting velocity field, was pioneered by \nKazantsev~\\cite{Kazantsev}, and, in more recent times, has generated \na considerable amount of research (see, e.~g., Ref.~\\cite{Almighty_Chance} \nand references therein, as well as Refs.~\\cite{KA,Gruzinov_Cowley_Sudan,Vergassola,Rogachevskii_Kleeorin,Chertkov_etal_dynamo,BS_metric,AAS_thesis,SBK_review}). \nWhile much attention has concentrated on \nresistive dynamo problems, most often for very large magnetic Prandtl \nnumbers, \nit is well known that the fundamental Zeldovich's, \nor ``stretch--twist--fold,'' \nmechanism of the magnetic-energy amplification (the so-called \n``fast dynamo'') is active regardless of the presence of \nthe resistive (diffusive) regularization~\\cite{Vainshtein_Zeldovich}. \nIf the initial seed magnetic field is concentrated on the scales \nof the same order as the characteristic scales of the advecting \nvelocity, the stretching and folding of the magnetic-field \nlines by the random flow\nleads to an exponential growth of the magnetic \nfluctuations at scales that decrease exponentially fast, \nuntil the diffusive scales are \nreached~\\cite{Batchelor_vort_analog,KA,AAS_thesis,SBK_review}. \nThis scenario is common in astrophysical applications such as \nthe turbulence in the interstellar medium or in \nthe protogalaxy where the Prandtl number ranges from~$10^{14}$ \nto~$10^{22}$, giving rise to~7 to~11 decades of small (subviscous) \nscales available to the magnetic \nfluctuations~\\cite{KA,Kulsrud_etal_proto,SBK_review}. \nIn fact, the initial diffusion-free regime may well be the only one \npractically important in such applications as far as the kinematic \napproximation is concerned, since the nonlinear saturation effects \nare likely to set in before the diffusion scales \nare reached~\\cite{Kulsrud_lecture}. \nOn the fundamental physical level, the diffusion-free regime, \nin which the magnetic-field lines are fully frozen into the flow, \nexhibits most clearly the underlying symmetry properties \nof the passive advection~\\cite{BS_metric}. \n\nWith a few notable exceptions (such as Refs.~\\cite{DMSR_mean_field,MRS_dynamo_theorem,Gruzinov_Cowley_Sudan,Chertkov_etal_dynamo}), \nthe dominant approach in the existing \nliterature on the turbulent kinematic dynamo problem \nhas been to study the statistics of passive magnetic fields advected \nby a flow $\\vxi(t,\\vx)$ whose two-time correlation \nfunction is approximated by a $\\delta$ function, \n$\\<\\vxi(t)\\vxi(t')\\>\\propto\\delta(t-t')$. This white-noise property of \nthe velocity greatly simplifies matters: the evolution equations \nfor such statistical quantities as the correlation functions and \nprobability density function of the magnetic field can be derived \nin closed form and yield themselves to exact solution. \n\nIn this paper, we relax the white-noise assumption and explore \nthe effects that arise when a finite-time correlated velocity \nfield is introduced. This immediately raises the level \nof difficulty associated with solving the statistical \nproblem. Within the theoretical framework adopted here, \nthe difficulty can be described in the following terms. \nIn the zero-correlation-time approximation, \none essentially has to deal with only one closed differential equation that \nfully determines the desired statistics. Allowing for a finite \nvelocity correlation time leads to an infinite number of interlinked\nintegro-differential equations involving time-history integrals. \nThese equations form an infinite open hierarchy that formally \nconstitutes the exact description of \nthe problem (these matters are explained in more detail \nin~\\ssecref{KT_method_hierarchy}).\nSolving this hierarchy in its entirety without additional assumptions \nappears to be an impossible task. \nThe most obvious way to make progress is clearly to try \na perturbative approach, i.e., to consider the kinematic dynamo \nproblem with an advecting field \nwhose correlation time is short, but finite. \nIf the correlation time~$\\tcorr$ is assumed to be small, one can \nexpect to be able \nto construct an expansion in the powers of~$\\tcorr$ (in what follows, \nwe will frequently refer to it as {\\em the $\\tau$~expansion})\nand calculate corrections to the growth rates of the moments \nof the magnetic field. This is the program that we undertake here. \n\nWe consider the one-point statistics of the passive magnetic field \nin the diffusion-free regime. \nIn this context, the infinite hierarchy we have mentioned \nabove interrelates the one-point probability density function~(PDF)\nof the magnetic field and an infinite set of response functionals. \nThese are averaged multiple functional derivatives of \nthe magnetic field with respect to the velocity field and its \ngradients. \nWe develop a {\\em functional expansion method} that allows us \nto calculate successive terms in the $\\tau$~expansion \nand derive in a closed form \na Fokker--Planck equation for the one-point~PDF of the magnetic field. \nWe limit ourselves to advancing \nthe expansion one order beyond the zero-correlation-time \napproximation. The result is a set of corrections to the growth \nrates of all moments of the magnetic field. These corrections \nare negative, so the growth rates are reduced. \n \nThe expansion is carried out assuming \nthat the velocity correlation time is small and keeping \nthe time integral of the velocity correlation \nfunction fixed. The latter constraint ensures that the dynamo \ngrowth rate remains finite when the correlation time vanishes. \nAn alternative way, which is sometimes deemed preferable on physical \ngrounds (see, e.g, Ref.~\\cite{Kinney_etal_2D}), \nis to fix the total energy of the velocity field. \nSince a $\\delta$-correlated velocity field must necessarily \npossess infinite energy, fixing the energy at a finite value \nleads to vanishing of the growth rates when~$\\tcorr=0$.\nThe {\\em relative} ordering of the terms in \nthe expansion is, however, the same, regardless of what \nis kept fixed, so the technical side of the expansion method \nis unaffected. \n\nOur expansion technique \nwill be given detailed treatment in the body of this paper. \nHere, let us rather discuss the finite-correlation-time effects \nthat can be distilled on the basis of our approach.\nAs it turns out, a number of new interesting phenomena \nmanifest themselves already at the level of \nthe short-but-finite-correlation-time approximation. \n\nIn the case of the $\\delta$-correlated advecting flow, \nthe one-point statistics of the passive magnetic field are \n{\\em universal} in the sense that they only depend on \none small-scale property of the velocity: \nthe time integral of the one-point correlation tensor of its gradients, \n$\\int\\diff t\\<\\nabla\\vxi(t)\\nabla\\vxi(0)\\>$. \nThe essential novelty in the case of finite correlation time \nis that this small-scale universality is lost on two accounts. \n\nFirst, the $\\tau$~expansion exhibits a sensitive dependence \non the specific shape of the time-correlation profile of the \nvelocity field (in recent literature, this was first explicitly \npointed out by Boldyrev~\\cite{Boldyrev_tcorr}; \nsee also Refs.~\\cite{vanKampen,vanKampen_review}). \nNamely, multiple time integrals of products \nof velocity correlation functions enter the expressions for \nthe expansion coefficients. Choosing different correlation \nprofiles leads to order-one changes in the values of these \ncoefficients. The root of this nonuniversality lies in the topology \nof the vertex-correction diagrams that contribute to the \norders higher than the zeroth in \nthe $\\tau$~expansion (see~\\ssecref{tau_discussion}).\n\nSecond, the first-order terms of the $\\tau$~expansion \nfeature a part that arises from the {\\em fourth-order} \nderivatives of the velocity correlation function, i.e., from \nthe second derivatives of the velocity field. In the one-point statistical \napproach, this is the first manifestation \nof the more general tendency that introducing finite correlation times \nbrings into play the large-scale structure of the velocity field. \nA related effect is the loss of Galilean invariance due to \nthe fact that the expansion terms also depend on the actual {\\em energy} \nof the velocity field, i.e., on the rms value of the sweeping velocity.\nIndeed, now that the trajectories of the fluid elements have a ``memory'' \nof themselves, which extends approximately one~$\\tcorr$ back in time, \nwe should naturally expect that there will appear \nan effective ``correlation length'' \nof the velocity (in what regards the one-point statistics of the fields \nit advects) approximately equal to~$\\xi\\tcorr$. Therefore, the one-point \nstatistics of the passive fields now depend not only on \nthe instantaneous velocity difference between two fluid particles \nthat meet at a given time (i.e., the velocity gradient at a point), \nbut also on the velocity that swept them into place and on \nthe variation of the velocity gradient over the correlation length. \nThis appearance of first-order corrections due to the second derivatives \nof the flow is a new effect, which indicates, in particular, \nthat the customary approximation used in the Batchelor \nregime, where the advecting velocity is assumed to be locally \nlinear~\\cite{Batchelor,ZRMS_linear}, is only justified for \nthe $\\delta$-correlated-in-time advecting fields. \n\nSuch are the main qualitative consequences of introducing \na finite-time-correlated velocity field into the kinematic dynamo \nproblem (or, in general, any passive-advection model). \nA few words are in order as to the quantitative \nimpact of a finite correlation time on the dynamo action. \nAs we have already mentioned, the effect of the first-order \ncorrections is to reduce the growth rates of all moments of \nthe magnetic field. Besides the nonuniversal dependence \non the spatial and temporal structure of the velocity \ncorrelation function, the reduction depends in a universally \ncalculable way on the usual set of parameters: \nthe order of the moment, the dimension of space, \nand the degree of compressibility of the flow. \nThe overall magnitude of this reductive effect is measured \nby the expansion parameter, which is of the order \nof~$\\tcorr\\gamma$, where $\\gamma$~is the growth rate of \nthe magnetic energy. It is not hard \nto demonstrate (see~\\ssecref{growth_rates_expanded}) \nthat~$\\tcorr\\gamma d\\sim(\\tcorr/\\teddy)^2$, where \n$\\teddy$~is the ``eddy-turnover'' time of the advecting \nturbulent velocity field and $d$~is the dimension of space. \nIn a standard Kolmogorov-type turbulence setting, one would, of course, \nexpect any such approximation to be valid at best marginally, since \n$\\tcorr \\sim \\teddy$. Astrophysical plasmas offer more \nvariety in this respect, as their driving forces (typically supernova \nexplosions) can, in fact, decorrelate faster than the turbulent eddies \nturn over~\\cite{Almighty_Chance}. In any event, \nthe small-$\\tcorr$ expansion does not offer much \nmore than qualitative, or, at best, semiquantitative, \ninformation about the way the dynamo action is modified \nby the finiteness of the correlation time. It is, of course, \nclear that introducing a finite correlation time cannot \naltogether suppress the fast-dynamo \nmechanism~\\cite{MRS_dynamo_theorem,Chertkov_etal_dynamo}. \nOn the other hand, \nour conclusion that some reduction of the growth rate should be \nexpected, is corroborated by numerical \nevidence~\\cite{Chandran_tcorr,Kinney_etal_2D,Chou} \nthat suggests a reduction of about~40\\% to~50\\%. \nIn fact, in~\\secref{sec_one_eddy}, we offer a semiquantitative \nevaluation of the finite-$\\tcorr$ correction to the growth rate \nwhich yields a reduction of approximately~40\\% in the three-dimensional \ncase and for~$\\tcorr\\sim\\teddy$. Of course, this is at best \njust an indication of the well-behaved character of our \nexpansion, rather than a truly solid quantitative confirmation of~it. \n\nThe literature on the $\\tau$~expansion and finite-correlation-time \neffects is not extensive. \nKliatskin and Tatarskii~\\cite{Kliatskin_Tatarskii} were the first \nto propose the hierarchy of equations for the response functionals \nas a starting point for a method of successive approximations \nas applied to the description of waves propagating in a medium \nwith random inhomogeneities. Vainshtein~\\cite{Vainshtein_KT} \napplied this method to the mean-field \nkinematic dynamo theory. The Kliatskin--Tatarskii method \nand its relation to our functional expansion method are discussed \nat the end of~\\ssecref{KT_method_exp}. \nVan~Kampen~\\cite{vanKampen} and Terwiel~\\cite{Terwiel} developed \nthe so-called cumulant expansion method; van~Kampen's review \narticle~\\cite{vanKampen_review} \nalso contains a good critical survey of other $\\tau$-expansion \nschemes predating his work. \nHis method was later \napplied in the kinematic-dynamo context by Knobloch~\\cite{Knobloch} \nand Chandran~\\cite{Chandran_tcorr}. Their treatment was Lagrangian and \ndid not include any effects due to the explicit spatial dependence \nin the induction equation. Consequently, the nonuniversality of \nthe $\\tau$~expansion with respect to the spatial structure of \nthe velocity correlator was not captured. \nThe van~Kampen method is discussed in detail in~\\ssecref{VK_method}.\nParallel to our development of the functional expansion method, \nBoldyrev~\\cite{Boldyrev_tcorr} proposed a $\\tau$-expansion \nmethod that was based on the exact \nsolution of the induction equation in the Lagrangian frame \nand offered a way to calculate the second moment of the magnetic \nfield that elicited the nonuniversal character of \nthe $\\tau$~expansion with respect to both temporal and spatial \nproperties of the velocity correlation tensor. \nMolchanov, Ruzmaikin, and Sokoloff~\\cite{MRS_dynamo_theorem} \nconsidered the statistics of the kinematic dynamo in \na renovating flow using the formalism of infinite products \nof random matrices. \n(See also~Ref.~\\cite{DMSR_mean_field} for the treatment \nof the kinematic mean-field dynamo in a renovating flow.) \nA version of their approach was later advanced \nby Gruzinov, Cowley, and Sudan~\\cite{Gruzinov_Cowley_Sudan}. \nConsiderable progress was achieved in a nonperturbative way by \nChertkov {\\em et al.}~\\cite{Chertkov_etal_scalar2D}, \nwho studied the passive-scalar problem in two dimensions for arbitrary \nvelocity correlation times. However, their method only works in \nthe two-dimensional case. \n \nThus, while we now seem to have a fairly good understanding of \nthe structure of the $\\tau$~expansion and such qualitative \nfeatures as the loss of the small-scale universality, \nan adequate nonperturbative theory of the kinematic dynamo \nand passive advection in finite-time-correlated turbulent velocity \nfields remains an open problem. \n\nThis paper is organized in the following way. \nIn~\\secref{sec_tau_exp}, our functional expansion method \nis systematically developed on the example of the simplest \navailable passive-advection problem: that of the Lagrangian \npassive vector in an incompressible flow. In this model, \nno explicit spatial dependence is present. \nIn~\\ssecref{KT_method_hierarchy}, \\ssecref{KT_method_Mark}, \nand~\\ssecref{KT_method_exp}, \nwe present a functional formalism that allows one to systematically \nconstruct successive terms in the $\\tau$-expanded \nFokker--Planck equation. \nThe dependence of the expansion coefficients on the \nspecific functional form of the velocity time correlation\nprofile emerges.\nThe expansion is carried out up to the first order in~$\\tcorr$.\nIn~\\ssecref{VK_method}, our method is compared with \nthe van~Kampen cumulant expansion method~\\cite{vanKampen}. \nWe ascertain that results obtained via the van~Kampen method \nare consistent with ours. \nFinally, in~\\ssecref{tau_discussion}, we discuss the underlying \nstructure of the $\\tau$~expansion in diagrammatic terms. \nIn~\\secref{sec_KT_dynamo}, the general arbitrarily compressible \nspace-dependent dynamo problem is solved with the aid \nof the functional expansion. At this level, the nonuniversality \nwith respect to the spatial structure of the velocity correlations, \nas well as the loss of Galilean invariance, become evident. \nIn~\\ssecref{hierarchy}, we explain \nthe emergence of an infinite hierarchy of equations for the characteristic \nfunction and various averaged response functionals of the magnetic field \nin the passive dynamo problem with finite-time-correlated advecting flow. \nThe hierarchy is advanced up to the emergence of the second-order \nresponse functions.\nIn~\\ssecref{tau_expansion}, we construct the $\\tau$~expansion \nup to first order in the correlation time, which leads to a closed equation \nfor the characteristic function of the magnetic field. \nIn~\\ssecref{Fokker_Planck_tcorr}, we derive the Fokker--Planck \nequation for the one-point~PDF of the magnetic-field strength \nvalid to first order in the correlation time. The distribution \nis lognormal. \nIn~\\ssecref{growth_rates_expanded}, we calculate the rates of \ngrowth of all moments of the magnetic field with (negative) first-order \ncorrections. \nFinally, in~\\secref{sec_one_eddy}, \nwe give a semiquantitative argument \nthat relates the expansion parameter to the ratio of \nthe correlation and eddy-turnover times of the velocity field. \nWe also evaluate the finite-$\\tcorr$ reduction of the magnetic-energy \ngrowth rate in a model incompressible turbulence consisting of \neddies of a fixed size. \nIn~\\Apref{ap_k_space}, we provide the basic relations that \nallow one to express the results we have obtained in the configuration \nspace in terms of the spectral characteristics of the velocity field. \nSome of the more cumbersome technical details of the $\\tau$~expansion \nare exiled to~\\Apref{ap_response2}. \n\n\n\n\\section{The Gaussian Functional Expansion Formalism}\n\\label{sec_tau_exp}\n\n\nIn this Section, we explain the Gaussian functional method \nfor constructing the short-correlation-time expansion for \npassive~advection problems. \nWorking out such expansions for specific problems \noften involves a fair amount of algebra, \nwhich tends to obscure the otherwise transparent \nideas behind them. \nIn an attempt at the maximum possible clarity of exposition, \nwe first consider a model that, \nwhile preserving most of the essential features of the \npassive-advection problems, offers much greater technical simplicity. \nNamely, let us consider the following stochastic equation \nin $d$~dimensions:\n\\bea\n\\label{model_B}\n\\dt B^i = \\sigma^i_k B^k.\n\\eea\nAll the fields involved explicitly depend on time only. \nThe specific initial distribution of~$B^i$ is not important \nfor the derivation or the validity of the results below. \nSpatial isotropy is always assumed. \nThe matrix field~$\\sigma^i_k(t)$ is Gaussian with zero mean \nand a given two-point correlation tensor:\n\\bea\n\\label{model_sigma}\n\\bigl<\\sigma^i_k(t)\\sigma^j_l(t')\\bigr> = T^{ij}_{kl}\\kappa(t-t'),\n\\qquad\\qquad\\\\\n\\nonumber\nT^{ij}_{kl} = \\delta^{ij}\\delta_{kl} + a\\bigl(\\delta^i_k\\delta^j_l \n+ \\delta^i_l\\delta^j_k\\bigr),\\qquad a = -1/(d+1).\n\\eea\nThese equations can be interpreted to describe the evolution of \na passive magnetic field in a Lagrangian frame, where \nthe Lagrangian advecting velocity field is Gaussian \nand incompressible, and the tensor~$\\sigma^i_k$ is its gradient matrix. \nIn the more general context of the theory of passive advection, \nequations~\\exref{model_B} and~\\exref{model_sigma} model the stochastic \ndynamics of a vector connecting two Lagrangian tracer particles in \nan ideal fluid.\n\nWe assume that the temporal correlation function~$\\kappa(t-t')$ \nof~$\\sigma^i_k(t)$ has a certain characteristic width~$\\tcorr$, \ni.e., the field~$\\sigma^i_k(t)$ possesses a correlation time~$\\tcorr$.\nOur task in this section is to construct an expansion \nof the statistics of~$B^i(t)$ in powers of~$\\tcorr$, which is \nassumed to be small. The limit~$\\tcorr\\to0$ \nought to be taken in such a way that the time integral of the \ncorrelation function is kept constant:\n\\bea\n\\label{kbar_const}\n\\int_0^\\infty\\diff\\tau\\,\\kappa(\\tau) = {\\kbar\\over2} = {\\rm const}\n\\quad{\\rm and}\\quad\\tcorr\\kbar \\ll 1.\n\\eea\nThe white-noise limit of zero correlation time is realized \nby setting~$\\kappa(\\tau)=\\kbar\\delta(\\tau)$. \n\nThe first step in our averaging scheme is to define \nthe characteristic function of the field~$B^i(t)$,\n\\bea\n\\label{model_Z}\nZ(t;\\mu) = \\bigl<\\tZ(t;\\mu)\\bigr> \n= \\bigl<\\exp\\bigl[i\\mu_i B^i(t)\\bigr]\\bigr>.\n\\eea\nHere and in what follows, the overtildes designate unaveraged \nrandom functions. Upon differentiating~$\\tZ(t;\\mu)$ with respect \nto time and making use of~\\eqref{model_B}, we obtain a new stochastic \nequation:\n\\bea\n\\label{model_eq_Ztilde}\n\\dt\\tZ = \\sigma^i_k\\mu_i{\\d\\over\\d\\mu_k}\\,\\tZ \n= \\L^k_i\\sigma^i_k\\tZ,\n\\eea \nwhere the auxiliary operator~$\\L^k_i$ has been introduced \nfor the sake of notational compactness. \n\nOur objective now is to learn how to obtain a closed equation \nfor the averaged characteristic function~$Z(t;\\mu)$, i.e., \nhow to average~\\eqref{model_eq_Ztilde} when~$\\sigma^i_k$ has \na nonzero correlation time. The inverse Fourier transform \n(with respect to~$\\mu_i$) of the resulting equation \nwill be the Fokker--Planck equation for the PDF~$P(t;\\vB)$ of \nthe passive field~$B^i$. \n\n\n\n\\subsection{The Hierarchy of Response Functions}\n\\label{KT_method_hierarchy}\n\nWe start the construction of the functional expansion \nby developing an exact formalism that describes \nthe one-point statistics of the field~$B^i(t)$. \nLet us average both sides of~\\eqref{model_eq_Ztilde} \nand ``split'' the mixed average that arises on the right-hand \nside with the aid of the well-known \nFurutsu--Novikov (or ``Gaussian-integration'') \nformula~\\cite{Furutsu,Novikov}:\n\\bea\n\\label{model_eq_Z}\n\\dt Z(t) = \\L^k_i\\bigl<\\sigma^i_k(t)\\tZ(t)\\bigr> \n= \\L^k_i T^{i\\b}_{k\\a}\\int_0^t\\diff t'\\,\\kappa(t-t')G^\\a_\\b(t|t'),\n\\eea\nwhere we have suppressed the~$\\mu$'s in the arguments, \nused the formula~\\exref{model_sigma} for the second-order \ncorrelation tensor of~$\\sigma^i_k(t)$, and introduced \nthe {\\em averaged first-order response function:} \n\\bea\n\\label{def_G1}\nG^\\a_\\b(t|t') = \\bigl<\\tG^\\a_\\b(t|t')\\bigr> = \n\\biggl<{\\delta\\tZ(t)\\over\\delta\\sigma^\\b_\\a(t')}\\biggr>.\n\\eea\nThis function is subject to the causality constraint: \n$G^\\a_\\b(t|t')=0$ if~$t'>t$ [hence the upper integration limit \nin~\\eqref{model_eq_Z}]. \nIntegrating~\\eqref{model_eq_Ztilde} from~$0$ to~$t$, taking \nthe functional derivative~$\\delta/\\delta\\sigma^\\b_\\a(t')$ of \nboth sides, averaging, setting~$t'=t$, and taking causality into \naccount, we~get\n\\bea\n\\label{G1_tt}\nG^\\a_\\b(t|t) = \\L^\\a_\\b Z(t).\n\\eea\nWe have thus obtained the equal-time form of~$G^\\a_\\b(t|t')$.\nIn order to determine the response function at~$t'<t$, \nwe simply take the functional derivative~$\\delta/\\delta\\sigma^\\b_\\a(t')$ \nof both sides of~\\eqref{model_eq_Ztilde} and find that \neach element of the unaveraged tensor~$\\tG^\\a_\\b(t|t')$ \nsatisfies an equation identical in form to~\\eqref{model_eq_Ztilde}. \nUpon averaging this, we obtain an evolution equation \nfor~$G^\\a_\\b(t|t')$ subject to the initial condition~\\exref{G1_tt} \nat~$t=t'$:\n\\bea\n\\label{G1_eq}\n\\dt G^\\a_\\b(t|t') = \\L^l_j\\bigl<\\sigma^j_l(t)\\tG^\\a_\\b(t|t')\\bigr>.\n\\eea\nThis equation can now be handled in the same fashion \nas~\\eqref{model_eq_Ztilde}, the average on the right-hand side \nsplit via the Furutsu--Novikov formula in terms of the correlation \ntensor of~$\\sigma^j_l(t)$ and the appropriately defined \nsecond-order averaged response \nfunction~$G^{\\a_1\\a_2}_{\\b_1\\b_2}(t|t_1,t_2)$. \nAt equal times, the latter can be expressed in terms of~$G^\\a_\\b(t|t')$ \njust as~$G^\\a_\\b(t|t)$ was expressed in terms of~$Z(t)$. \nAt different times, we obtain the evolution equation \nfor~$G^{\\a_1\\a_2}_{\\b_1\\b_2}(t|t_1,t_2)$ by taking the functional \nderivative of the equation for~$\\tG^\\a_\\b(t|t')$ and averaging. \n\nAn infinite linked hierarchy can be constructed by further \niterating this procedure and introducing response functions \nof ascending orders. Let us give the general form of this \nhierarchy. Define the {\\em $n$th-order averaged response function:} \n\\bea\n\\label{def_Gn}\nG^{\\a_1\\dots\\a_n}_{\\b_1\\dots\\b_n}(t|t_1,\\dots,t_n) = \n\\biggl<{\\delta\\tZ(t)\\over\\delta\\sigma^{\\b_1}_{\\a_1}(t_1)\\dots\n\\delta\\sigma^{\\b_n}_{\\a_n}(t_n)}\\biggr>.\n\\eea\nThis function has two essential properties: \n(i) it is causal: $G^{\\a_1\\dots\\a_n}_{\\b_1\\dots\\b_n}(t|t_1\\dots t_n)=0$\nif any~$t_i>t$; (ii) it remains invariant under all \nsimultaneous permutations of the times $t_1,\\dots,t_n$ \nand indices $\\a_1,\\dots,\\a_n$, $\\b_1,\\dots,\\b_n$, \nwhich correspond to changes of the order of functional \ndifferentiation in the definition~\\exref{def_Gn}.\nThe $n$th-order response function satisfies the following \nrecursive relations: if~$t_1,\\dots,t_n<t$,\n\\bea\n\\label{Gn_eq}\n\\dt G^{\\a_1\\dots\\a_n}_{\\b_1\\dots\\b_n}(t|t_1\\dots t_n) = \n\\L^k_i T^{i\\b_{n+1}}_{k\\a_{n+1}}\\int_0^t\\diff t_{n+1}\\,\\kappa(t-t_{n+1})\nG^{\\a_1\\dots\\a_{n+1}}_{\\b_1\\dots\\b_{n+1}}(t|t_1\\dots t_{n+1});\n\\eea\nif, say, $t_n=t$ and $t_1,\\dots,t_{n-1}\\le t_n$, \n\\bea\n\\label{Gn_tt}\nG^{\\a_1\\dots\\a_{n-1}\\a_n}_{\\b_1\\dots\\b_{n-1}\\b_n}(t|t_1\\dots t_{n-1},t) = \n\\L^{\\a_n}_{\\b_n} \nG^{\\a_1\\dots\\a_{n-1}}_{\\b_1\\dots\\b_{n-1}}(t|t_1\\dots t_{n-1}).\n\\eea\nThe hierarchy is ``forward'' at different times \nand ``backward'' at equal times. \nThe characteristic function~$Z(t)$ is formally treated \nas the zeroth-order response function. \n\n\n\n\n\\subsection{The White-Noise Approximation}\n\\label{KT_method_Mark}\n\nThe white-noise approximation is obtained by \nsetting~$\\kappa(t-t')=\\kbar\\delta(t-t')$. We are then left \nwith just~\\eqref{model_eq_Z}, where the time history \nintegral reduces to~${1\\over2}\\kbar G^\\a_\\b(t|t)$, which is substituted \nfrom~\\eqref{G1_tt}. This produces a closed evolution \nequation for~$Z(t)$. The Fourier transform of it is\nthe Fokker--Planck equation for the~PDF of~$B^i$ at time~$t$\nin the $\\delta$-correlated regime:\n\\bea\n\\label{FPEq_delta}\n\\dt P(t) = {\\kbar\\over2}\\,T^{i\\b}_{k\\a} \\L^k_i \\L^\\a_\\b P(t) \n= {\\kbar\\over2}\\,\\LL P(t).\n\\eea\nIn order to be not overly burdened by notation, \nwe typically use the same symbol for denoting an operator \nin the Fourier space of the~$\\mu$'s and its analog in the configuration \nspace of the~$B$'s. This should lead to no confusion, as \nthe context will always be clear. Thus, \n\\bea\n\\L^k_i = \\mu_i{\\d\\over\\d\\mu_k} = - {\\d\\over\\d B^i} B^k \n= - \\(\\delta^k_i + B^k{\\d\\over\\d B^i}\\). \n\\eea\nDue to isotropy, the probability density function~$P$ depends \non the absolute value~$B=|\\vB|$ only.\nThe operator~$\\LL$ in~\\eqref{FPEq_delta} can therefore \nbe written in the following isotropic form:\n\\bea\n\\label{def_L_iso}\n\\LL = T^{i\\b}_{k\\a} \\L^k_i \\L^\\a_\\b = \n{d-1\\over d+1}\\[B^2{\\d^2\\over\\d B^2} + (d+1)B{\\d\\over\\d B}\\],\n\\eea \nwhich turns~\\eqref{FPEq_delta} into the familiar \nFokker--Planck equation for the one-point~PDF of the \nmagnetic field in the kinematic $\\delta$-correlated \ndynamo problem taken for the incompressible \nflow~\\cite{BS_metric,AAS_thesis}. \nThe resulting distribution is lognormal and the moments of~$B$~satisfy \n\\bea\n\\label{expected_outcome}\n\\dt\\<B^n\\> = \n{1\\over2}\\,{d-1\\over d+1}\\,n\\(n+d\\)\\kbar\\<B^n\\>.\n\\eea\nThis is the expected outcome, because, \nas was shown in Ref.~\\cite{BS_metric},\nthe Lagrangian and Eulerian statistics are the same \nfor the $\\delta$-correlated incompressible flow. \n\nThus, the solution in the $\\delta$-correlated limit is quite \nelementary. Things become much more complicated once the \nwhite-noise assumption is relaxed and a nonzero, however small, \nvelocity correlation time is introduced.\n\n\n\n\n\n\n\\subsection{The Recursive Expan\\-sion}\n\\label{KT_method_exp}\n\nIn order to construct an expansion in small correlation time, \nit is convenient to combine the equations~\\exref{Gn_eq} \nand~\\exref{Gn_tt} into one recursive integral relation \nthat expresses the $n$th-order response function in terms \nof its immediate precursor and its immediate successor:\n\\bea\n\\nonumber\nG^{\\a_1\\dots\\a_n}_{\\b_1\\dots\\b_n}(t|t_1\\dots t_n) =\n\\L^{\\a_n}_{\\b_n} \nG^{\\a_1\\dots\\a_{n-1}}_{\\b_1\\dots\\b_{n-1}}(t_n|t_1\\dots t_{n-1})\n\\qquad\\qquad\\qquad\\qquad\\\\ \n\\label{Gn_rec_rln}\n+\\,\\,\\L^k_i T^{i\\b_{n+1}}_{k\\a_{n+1}}\n\\int_{t_n}^t\\diff t'\\int_0^{t'}\\diff t_{n+1}\\,\\kappa(t'-t_{n+1})\nG^{\\a_1\\dots\\a_{n+1}}_{\\b_1\\dots\\b_{n+1}}(t'|t_1\\dots t_{n+1}).\n\\eea \nThe above relation is exact and \nvalid for $t_1,\\dots,t_{n-1} \\le t_n \\le t$.\nDue to the permutation symmetry of the response functions, \nthis does not limit the generality. \nThe desired expansion is constructed \nby repeated application of the formula~\\exref{Gn_rec_rln}.\n\nLet us substitute the formula~\\exref{Gn_rec_rln} with~$n=1$ \nfor the first-order response function into the right-hand side \nof~\\eqref{model_eq_Z}:\n\\bea\n\\nonumber\n\\dt Z(t) = \\LL\\int_0^t\\diff t_1\\,\\kappa(t-t_1)Z(t_1)\n\\qquad\\qquad\\qquad\\qquad\\\\ \n+\\,\\,T^{i\\b_1}_{k\\a_1} T^{m\\b_2}_{n\\a_2} \\L^k_i \\L^n_m\n\\int_0^t\\diff t_1 \\int_{t_1}^t\\diff t' \\int_0^{t'}\\diff t_2\\, \n\\kappa(t-t_1)\\kappa(t'-t_2) \nG^{\\a_1\\a_2}_{\\b_1\\b_2}(t'|t_1,t_2),\n\\label{Z_via_G2}\n\\eea \nwhere the operator~$\\LL$ is defined in~\\exref{def_L_iso}.\nWe now use the formula~\\exref{Gn_rec_rln} to express \nthe second-order response function on the right-hand side \nof the above equation: for~$t_2>t_1$, we have\n\\bea\n\\nonumber\nG^{\\a_1\\a_2}_{\\b_1\\b_2}(t'|t_1,t_2) = \n\\L^{\\a_2}_{\\b_2} G^{\\a_1}_{\\b_1}(t_2|t_1)\n\\qquad\\qquad\\qquad\\\\\n+\\,\\,\\L^q_p T^{p\\b_3}_{q\\a_3}\n\\int_{t_2}^{t'}\\diff t'' \\int_0^{t''}\\diff t_3\\,\\kappa(t''-t_3)\nG^{\\a_1\\a_2\\a_3}_{\\b_1\\b_2\\b_3}(t''|t_1,t_2,t_3), \n\\label{G2_rec}\n\\eea\nwhile for~$t_2<t_1$ we flip the variables, $t_1\\leftrightarrow t_2$,\nto make sure that the first-order response function on the right-hand \nside do not vanish: \n\\bea\n\\nonumber\nG^{\\a_1\\a_2}_{\\b_1\\b_2}(t'|t_1,t_2) = \n\\L^{\\a_1}_{\\b_1} G^{\\a_2}_{\\b_2}(t_1|t_2)\n\\qquad\\qquad\\qquad\\\\\n+\\,\\,\\L^q_p T^{p\\b_3}_{q\\a_3}\n\\int_{t_1}^{t'}\\diff t'' \\int_0^{t''}\\diff t_3\\,\\kappa(t''-t_3)\nG^{\\a_2\\a_1\\a_3}_{\\b_2\\b_1\\b_3}(t''|t_2,t_1,t_3). \n\\label{G2_rec_flip}\n\\eea\nThe recursion relation~\\exref{Gn_rec_rln} is now applied \nto the first-order response functions in \nthe formulas~\\exref{G2_rec} and~\\exref{G2_rec_flip}:\n\\bea\n\\label{G1_rec}\nG^{\\a_1}_{\\b_1}(t_2|t_1) = \\L^{\\a_1}_{\\b_1}Z(t_1)\n+ \\L^q_p T^{p\\b_3}_{q\\a_3}\n\\int_{t_1}^{t_2}\\diff t'' \\int_0^{t''}\\diff t_3\\,\\kappa(t''-t_3)\nG^{\\a_1\\a_3}_{\\b_1\\b_3}(t''|t_1,t_3),\\\\\n\\label{G1_rec_flip}\nG^{\\a_2}_{\\b_2}(t_1|t_2) = \\L^{\\a_2}_{\\b_2}Z(t_2)\n+ \\L^q_p T^{p\\b_3}_{q\\a_3}\n\\int_{t_2}^{t_1}\\diff t'' \\int_0^{t''}\\diff t_3\\,\\kappa(t''-t_3)\nG^{\\a_2\\a_3}_{\\b_2\\b_3}(t''|t_2,t_3).\\,\n\\eea\nAll this must be substituted into~\\eqref{Z_via_G2}:\n\\bea\n\\nonumber\n\\dt Z(t) &=& \\LL\\int_0^t\\diff t_1\\,\\kappa(t-t_1)Z(t_1)\\\\\n\\nonumber\n&+& T^{i\\b_1}_{k\\a_1}T^{m\\b_2}_{n\\a_2}\n\\L^k_i\\L^n_m\\L^{\\a_1}_{\\b_1}\\L^{\\a_2}_{\\b_2}\n\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t'\\int_0^{t_1}\\diff t_2\\,\n\\kappa(t-t_1)\\kappa(t'-t_2)Z(t_2)\\\\\n\\nonumber\n&+& T^{i\\b_1}_{k\\a_1}T^{m\\b_2}_{n\\a_2}\n\\L^k_i\\L^n_m\\L^{\\a_2}_{\\b_2}\\L^{\\a_1}_{\\b_1}\n\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t'\\int_{t_1}^{t'}\\diff t_2\\,\n\\kappa(t-t_1)\\kappa(t'-t_2)Z(t_1)\\\\\n&+& R(t),\n\\label{Z_with_R}\n\\eea \nwhere the remainder~$R(t)$ contains the assembled terms \nthat involve quintuple time integrals. \n\nSo far, all the manipulations we have carried out have been exact. \nIt is now not hard to perceive the emerging contours of \nthe small-$\\tcorr$ expansion. Since the time-correlation \nfunction~$\\kappa(t-t')$ is a profile of width~$\\sim\\tcorr$, \nthe area under which is constant and equal to~$\\kbar$, \nthe triple time integrals in~\\eqref{Z_with_R} are of \nthe order of~$\\tcorr\\kbar^2$, while the quintuple time \nintegrals absorbed into~$R(t)$ are of the order of~$\\tcorr^2\\kbar^3$. \nFurther application of the recursion formula~\\exref{Gn_rec_rln} \nto the second- and third-order response functions \nin the equations~\\exref{G2_rec}--\\exref{G1_rec_flip} \nleads to the appearance of more multiple time integrals \nof the time-correlation function~$\\kappa(t-t')$. \nThese integrals are of orders~$\\tcorr^2\\kbar^3$, \n$\\tcorr^3\\kbar^4$,~etc. \nWe would only like to keep terms up to first order in the \ncorrelation time. The remainder term~$R(t)$ in~\\eqref{Z_with_R}\ncan therefore be dropped.\\\\ \n\n{\\em Remark on the physics of the $\\tau$~expansion.} \nThe above argument is based on the stipulation made \nat the beginning of this Section that the $\\tau$~expansion \nmust be carried out keeping the integral of the velocity \ntime correlation function constant [formula~\\exref{kbar_const}]. \nThis requirement is natural because it leads to finite \ndynamo growth rates in the limit of zero correlation \ntime [see~\\ssecref{KT_method_Mark}, \\eqref{expected_outcome}]. \nHowever, it is also acceptable to institute an alternative, \narguably more physical, requirement that the {\\em total energy} \nof the velocity field (i.e., the rms velocity) \nremain constant (as, e.g, in the numerics of Ref.~\\cite{Kinney_etal_2D}). \nQuantitatively, this means that~$\\kappa(0)$, \nrather than~$\\int_0^\\infty\\diff\\tau\\,\\kappa(\\tau)$, \nis kept fixed. \nUnder this constraint, the terms that \nwe have previously estimated to be of orders~$\\kbar$, \n$\\tcorr\\kbar^2$, $\\tcorr^2\\kbar^3$,~etc., and hence, $\\kbar$ being \nconstant, to represent the zeroth, first, second,~etc.~orders of the \n$\\tau$~expansion, should now be reevaluated as follows. \nSince $\\kbar\\sim\\tcorr\\kappa(0)$, these terms are \nof orders~$\\tcorr\\kappa(0)$, $\\tcorr^3\\kappa(0)^2$, \n$\\tcorr^5\\kappa(0)^3$,~etc., and therefore constitute \nthe first, third, fifth,~etc.~orders of the expansion. \nThe shortcoming of this approach is that the dynamo growth \nrates vanish when~$\\tcorr=0$, so formally there is no \nnontrivial zero-correlation-time limit. \nWith $\\kbar=\\const$, this problem was avoided because the energy \nwas formally infinite when~$\\tcorr=0$ (a $\\delta$-correlated \nvelocity field cannot have a finite energy).\nIn any event, we see that, since the difference between \nkeeping~$\\kbar$ and~$\\kappa(0)$ constant\ndoes not affect the relative magnitudes \nof the terms in the expansion, our expansion scheme remains \nvalid in both cases. Let us therefore proceed with our construction.\\\\\n \nThe dependence of the right-hand side of~\\eqref{Z_with_R} \non the ``past'' values of~$Z$ (i.e., on its values at times \npreceding~$t$) can also be resolved in the framework of \nthe small-$\\tcorr$ expansion. Formally integrating~\\eqref{Z_with_R}, \nwe get, at times~$t_1<t$, \n\\bea\nZ(t_1) = Z(t) - \\LL\\int_{t_1}^{t}\\diff t'\\int_0^{t'}\\diff t_2\\,\n\\kappa(t'-t_2)Z(t_2) + \\cdots\n\\eea \nUpon substituting this onto the right-hand side of~\\eqref{Z_with_R} \nand again discarding all the terms of orders higher than \nthe first in~$\\tcorr$, we~get\n\\bea\n\\nonumber\n\\dt Z(t) &=& \\LL\\int_0^t\\diff t_1\\,\\kappa(t-t_1)Z(t)\\\\\n\\nonumber\n&-& \\LL^2\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t'\\int_0^{t'}\\diff t_2\\,\n\\kappa(t-t_1)\\kappa(t'-t_2)Z(t)\\\\\n\\nonumber\n&+& (\\LL^2-\\LL_1)\n\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t'\\int_0^{t_1}\\diff t_2\\,\n\\kappa(t-t_1)\\kappa(t'-t_2)Z(t)\\\\\n&+& (\\LL^2-\\LL_2)\n\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t'\\int_{t_1}^{t'}\\diff t_2\\,\n\\kappa(t-t_1)\\kappa(t'-t_2)Z(t).\n\\label{Z_expanded}\n\\eea \nWe have introduced the following two operators:\n\\bea\n\\label{def_L1}\n\\LL_1 &=& \\L^k_i T^{i\\b_1}_{k\\a_1} \\bigl[\\L^{\\a_1}_{\\b_1},\\L^n_m\\bigr] \nT^{m\\b_2}_{n\\a_2}\\L^{\\a_2}_{\\b_2} \n= {d^2\\over d+1}\\,\\LL,\\\\\n\\label{def_L2}\n\\LL_2 &=& \\L^k_i T^{i\\b_1}_{k\\a_1} \\bigl[\\L^{\\a_1}_{\\b_1},\\LL\\bigr] \n= 2d\\LL,\n\\eea\nwhere the square brackets denote commutators. \nWe see that the terms in~\\eqref{Z_expanded} that contain~$\\LL^2$ \ncancel out, and only those terms remain that are due to \nthe non-self-commuting nature of the operator~$\\L^k_i$. \n\nFinally, we inverse-Fourier transform~\\eqref{Z_expanded} \ninto the $\\vB$~space and take the long-time limit, $t\\gg\\tcorr$. \nThe following Fokker--Planck equation with constant coefficients \nresults:\n\\bea\n\\label{model_FPEq_1}\n\\dt P = {\\kbar\\over2}\\[1 - \\tcorr\\kbar d\n\\({1\\over2}{d\\over d+1}\\,K_1 + K_2\\)\\] \\LL P,\n\\eea \nwhere the coefficients, \n\\bea\n\\label{def_K1}\nK_1 &=& {4\\over\\tcorr\\kbar^2}\\lim_{t\\to\\infty}\n\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t_2\\int_0^{t_1}\\diff t_3\\,\n\\kappa(t-t_1)\\kappa(t_2-t_3),\\\\\n\\label{def_K2}\nK_2 &=& {4\\over\\tcorr\\kbar^2}\\lim_{t\\to\\infty}\n\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t_2\\int_{t_1}^{t_2}\\diff t_3\\,\n\\kappa(t-t_1)\\kappa(t_2-t_3),\n\\eea\nare constants that depend on the particular shape of \nthe time-correlation function~$\\kappa(t-t')$. \nThus, the $\\tau$~expansion is {\\em nonuniversal} in the sense \nthat the specific choice of the functional form of \nthe small-time regularization directly affects the values \nof the expansion coefficients (cf.~Ref.~\\cite{Boldyrev_tcorr}). \nAs an example, let us give the values of the coefficients~$K_1$ \nand~$K_2$ for two popular choices of~$\\kappa(t-t')$: \n\\bea\n\\kappa(t-t') = \n{\\kbar\\over2\\tcorr}\\,\\exp\\bigl[-|t-t'|/\\tcorr\\bigr]\n&\\Longrightarrow& K_1 = K_2 = 0.5\\\\\n\\kappa(t-t') = \n{\\kbar\\over\\sqrt{\\pi}\\tcorr}\\,\\exp\\bigl[-(t-t')^2/\\tcorr^2\\bigr]\n&\\Longrightarrow& K_1 \\approx 0.33, \\quad K_2 \\approx 0.23.\n\\eea\n\nIn \\secref{sec_KT_dynamo}, we will apply the method we have \npresented above to the more realistic general compressible kinematic \ndynamo problem in the Eulerian frame.\\\\\n\n{\\em Remark on the Kliatskin--Tatarskii method.}\nThe Gaussian hierarchy given by the equations~\\exref{Gn_eq} \nand~\\exref{Gn_tt} and based on repeated application of the \nFurutsu--Novikov formula was proposed by Kliatskin and \nTatarskii~\\cite{Kliatskin_Tatarskii} as a basis for constructing \nsuccessive-approximation solutions of the problem of light propagation \nin a medium with randomly distributed inhomogeneities. \nTheir method in its original form was carried over to the mean-field \ndynamo theory with finite-time-correlated velocity field \nby Vainshtein~\\cite{Vainshtein_KT}. \nThe method we have outlined in this section, while also \nbased on the response-function hierarchy~\\exref{Gn_eq}--\\exref{Gn_tt}, \ndiffers substantially from that developed and applied \nby these authors. Their successive-approximation scheme \nconsisted essentially in writing out the first $n$~equations \nin the hierarchy~\\exref{Gn_eq}--\\exref{Gn_tt} and then truncating \nit at the $n$th step by replacing~$\\kappa(t-t_{n+1})$ by \n$\\kbar\\delta(t-t_{n+1})$ \nin the equation for the $n$th-order response function. \nThis gave a closed system of equations that could be solved. \nCarried out in the first order, such a procedure would \ncorrespond to setting~$\\kappa(t'-t_2)=\\kbar\\delta(t'-t_2)$ \nin~\\eqref{Z_via_G2} and \nconsequently~$\\kappa(t_2-t_3)=\\kbar\\delta(t_2-t_3)$ \nin the expressions~\\exref{def_K1} and~\\exref{def_K2} \nfor the coefficients~$K_1$ and~$K_2$. Such a substitution \nleads to~$K_1=0$ \nand~$K_2=(2/\\tcorr\\kbar)\\int_0^\\infty\\diff\\tau\\,\\tau\\kappa(\\tau)$, \nwhich is incorrect. \nThe reason for this discrepancy is that, in the time integrals \ninvolving multiple products of the correlation \nfunctions~$\\kappa(t-t_1)$, $\\kappa(t_2-t_3)$, etc., \nthe latter cannot be approximated by $\\delta$~functions plus \nfirst-order corrections even in the small-$\\tcorr$ limit. \n\n\n\n\\subsection{Comparison with the Van Kampen Cumulant Expansion Method}\n\\label{VK_method}\n\nThe evolution equation~$\\exref{model_eq_Ztilde}$ \nfor the ``unaveraged characteristic function''~$\\tZ(t;\\mu)$ \nis a stochastic linear differential equation whose form agrees \nexactly with that of the general such equation considered by \nvan~Kampen~\\cite{vanKampen,vanKampen_review} \nand simultaneously by Terwiel~\\cite{Terwiel}:\n\\bea\n\\dt\\tZ(t) = \\A(t)\\tZ(t),\n\\eea \nwhere, in our case, $\\A(t) = \\L^k_i\\sigma^i_k(t)$.\nIn his work, van~Kampen developed a formalism that allowed one \nto construct successive terms in the short-correlation-time \nexpansion of~$Z=\\langle\\tZ\\rangle$ in terms of the cumulants \nof the operator~$\\A$. Terwiel's projection-operator method \nwas shown by its author to be equivalent to that of van~Kampen. \n\nLet us see what happens if the passive-advection \nproblem given by~\\eqref{model_B}, or, equivalently, \nby~\\eqref{model_eq_Ztilde} is subjected to van~Kampen's \nexpansion algorithm. The latter proceeds as follows.\n\nStart by writing the formal solution \nof~\\eqref{model_eq_Ztilde} in terms of the time-ordered \nexponential:\n\\bea\n\\nonumber\n\\tZ(t) = \\l\\lceil\\exp\\int_0^t\\diff t'\\A(t')\\r\\rceil \\tZ(0)\n\\qquad\\qquad\\qquad\\qquad\\\\\n=\\,\\[1+ \\int_0^t\\diff t_1\\,\\A(t_1) + \n\\int_0^t\\diff t_1\\int_0^{t_1}\\diff t_2\\,\\A(t_1)\\A(t_2) + \n\\cdots\\]\\tZ(0).\n\\eea\nThis solution is averaged assuming that the initial \ndistribution of~$\\tZ$ is independent of the statistics of~$\\A$:\n\\bea\n\\nonumber\nZ(t) = \\biggl[1 + \n\\int_0^t\\diff t_1\\int_0^{t_1}\\diff t_2\\,\n\\bigl<\\A(t_1)\\A(t_2)\\bigr>\\biggr.\n\\qquad\\qquad\\qquad\\qquad\\\\ \n+\\,\\biggl.\\int_0^t\\diff t_1\\int_0^{t_1}\\diff t_2\n\\int_0^{t_2}\\diff t_3\\int_0^{t_3}\\diff t_4\\,\n\\bigl<\\A(t_1)\\A(t_2)\\A(t_3)\\A(t_4)\\bigr> + \\cdots\\biggr]Z(0).\n\\label{Z_via_Z0}\n\\eea \nHere all the odd-order averages have vanished \n(recall that~$\\A = \\L^k_i\\sigma^i_k$).\nThe closed equation for~$Z(t)$ is now obtained as follows. \nFirst, the formal solution~\\exref{Z_via_Z0} is differentiated \nwith respect to time:\n\\bea\n\\nonumber\n\\dt Z(t) = \\biggl[ \n\\int_0^t\\diff t_1\\,\\bigl<\\A(t)\\A(t_1)\\bigr>\\biggr.\n\\qquad\\qquad\\qquad\\qquad\\\\ \n\\biggl.+\\,\\int_0^t\\diff t_1\\int_0^{t_1}\\diff t_2\\int_0^{t_2}\\diff t_3\\,\n\\bigl<\\A(t)\\A(t_1)\\A(t_2)\\A(t_3)\\bigr> + \\cdots\\biggr]Z(0).\n\\label{dtZ_via_Z0}\n\\eea\nSecond, $Z(0)$~is expressed in terms of~$Z(t)$ by formally \ninverting the operator series on the right-hand side of~\\eqref{Z_via_Z0}, \nwhereupon $Z(0)$~is substituted into~\\eqref{dtZ_via_Z0}. \nKeeping only the terms that contain up to three time integrations, \nas we did in the previous section, we~get\n\\bea\n\\nonumber\n\\dt Z(t) &=& \\biggl[ \n\\int_0^t\\diff t_1\\,\\bigl<\\A(t)\\A(t_1)\\bigr>\\biggr.\\\\\n\\nonumber\n&+&\\int_0^t\\diff t_1\\int_0^{t_1}\\diff t_2\\int_0^{t_2}\\diff t_3\\,\n\\bigl<\\A(t)\\A(t_1)\\A(t_2)\\A(t_3)\\bigr>\\\\\n&-&\\biggl.\\int_0^t\\diff t_1\\int_0^t\\diff t_2\\int_0^{t_2}\\diff t_3\\,\n\\bigl<\\A(t)\\A(t_1)\\bigr>\\bigl<\\A(t_2)\\A(t_3)\\bigr> + \\cdots\\biggr] Z(t).\n\\label{Z_eq_A}\n\\eea\nThe quadruple average in the above expression splits into \nthree products of second-order averages in the usual Gaussian way. \nSince \n\\bea\n\\label{A_avg_2}\n\\bigl<\\A(t)\\A(t_1)\\bigr> = \\kappa(t-t_1)\\,T^{ij}_{kl}\\L^k_i\\L^l_j \n= \\kappa(t-t_1)\\,\\LL,\n\\eea\nwe have\n\\bea\n\\nonumber\n\\bigl<\\A(t)\\A(t_1)\\A(t_2)\\A(t_3)\\bigr> \n&=& \\kappa(t-t_1)\\kappa(t_2-t_3)\\, \nT^{ij}_{kl} T^{mn}_{pq}\\L^k_i\\L^l_j\\L^p_m\\L^q_n\\\\ \n\\nonumber\n&+&\\kappa(t-t_2)\\kappa(t_1-t_3)\\, \nT^{im}_{kp} T^{jn}_{lq}\\L^k_i\\L^l_j\\L^p_m\\L^q_n\\\\ \n\\nonumber\n&+&\\kappa(t-t_3)\\kappa(t_1-t_2)\\, \nT^{in}_{kq} T^{jm}_{lp}\\L^k_i\\L^l_j\\L^p_m\\L^q_n\\\\\n\\nonumber\n&=& \\kappa(t-t_1)\\kappa(t_2-t_3)\\,\\LL^2\\\\\n\\nonumber\n&+& \\kappa(t-t_2)\\kappa(t_1-t_3)\\,\\bigl(\\LL^2 - \\LL_1\\bigr)\\\\\n&+& \\kappa(t-t_3)\\kappa(t_1-t_2)\\,\\bigl(\\LL^2 - \\LL_2\\bigr),\n\\label{A_avg_4}\\\\\n\\bigl<\\A(t)\\A(t_1)\\bigr>\\bigl<\\A(t_2)\\A(t_3)\\bigr> \n&=& \\kappa(t-t_1)\\kappa(t_2-t_3)\\,\\LL^2. \n\\label{A_avg_22}\n\\eea \nThe operators~$\\LL$, $\\LL_1$, and~$\\LL_2$ are the same as those \nin the previous section [see definitions~\\exref{def_L_iso}, \n\\exref{def_L1}, and~\\exref{def_L2}].\nThe averages~\\exref{A_avg_2}, \\exref{A_avg_4}, and~\\exref{A_avg_22} \nare now substituted into~\\eqref{Z_eq_A}. \nThe triple time integrals can be argued to represent \n(all of the) first-order terms in the small-$\\tcorr$ expansion \nin the same way as it was done in~\\ssecref{KT_method_exp}. \nIn the limit~$t\\gg\\tcorr$, the coefficients in~\\eqref{Z_eq_A} \ndo not depend on time. The resulting Fokker--Planck equation \nfor the PDF~$P(t;B)$ \n[which is the inverse Fourier transform of~$Z(t;\\mu)$]\nobtained by the van~Kampen method and analogous \nto~\\eqref{model_FPEq_1} is then\n\\bea\n\\label{FPEq_vKampen}\n\\dt P = {\\kbar\\over2}\\[1 - \\tcorr\\kbar d\n\\({1\\over2}{d\\over d+1}\\,C_1 + C_2\\) \n- {1\\over2}\\,\\tcorr\\kbar\\bigl(C_0-C_1-C_2\\bigr)\\LL\\] \\LL P,\n\\eea\nwhere the coefficients~$C_0$, $C_1$, and~$C_2$, that depend \non the shape function~$\\kappa(t-t')$, are as follows:\n\\bea\n\\label{def_C0}\nC_0 &=& {4\\over\\tcorr\\kbar^2}\\lim_{t\\to\\infty}\n\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t_2\\int_0^{t_2}\\diff t_3\\,\n\\kappa(t-t_1)\\kappa(t_2-t_3),\\\\\n\\label{def_C1}\nC_1 &=& {4\\over\\tcorr\\kbar^2}\\lim_{t\\to\\infty}\n\\int_0^t\\diff t_1\\int_0^{t_1}\\diff t_2\\int_0^{t_2}\\diff t_3\\,\n\\kappa(t-t_2)\\kappa(t_1-t_3),\\\\\n\\label{def_C2}\nC_2 &=& {4\\over\\tcorr\\kbar^2}\\lim_{t\\to\\infty}\n\\int_0^t\\diff t_1\\int_0^{t_1}\\diff t_2\\int_0^{t_2}\\diff t_3\\,\n\\kappa(t-t_3)\\kappa(t_1-t_2).\n\\eea\nBy comparing the definition of~$C_0$ with those of \nthe coefficients~$K_1$ and~$K_2$ in~\\ssecref{KT_method_exp} \n[see formulas~\\exref{def_K1} and~\\exref{def_K2}], \nwe immediately establish that $C_0=K_1+K_2$. \nFurthermore, it is also not hard to ascertain \nthat~$C_1=K_1$ and~$C_2=K_2$. Therefore, the last term \nin~\\eqref{FPEq_vKampen} vanishes, and the first-order \nFokker--Planck equations~\\exref{model_FPEq_1} and~\\exref{FPEq_vKampen} \nare identical.\nThus, the results obtained via the van~Kampen method \nare consistent with ours.\nUnlike the van~Kampen method, \nhowever, our method does not involve any nontrivial operator \nalgebra and is therefore better suited for a wide variety of applications. \nIn particular, the stochastic equations containing spatial \nderivatives (such as the convective derivatives present in all Eulerian \npassive-advection problems) can be handled without much \nadditional difficulty (this will be done in detail for the full \nkinematic dynamo problem in~\\secref{sec_KT_dynamo}).\n\n\n\n\n\n\n\n\\subsection{Discussion: The Vertex Corrections}\n\\label{tau_discussion}\n\nWhile the particular methods one employs to obtain the successive \nterms in the $\\tau$~expansion may vary and depend on one's taste \nand the specific demands of the stochastic problem at hand, \nthe underlying structure of the $\\tau$~expansion remains the same \nand is rooted in the common properties of all turbulence closure \nproblems (see, e.g.,~Ref.~\\cite{Krommes_review}). As we have stated \nin general terms in the introduction to this paper, and \nas was clear from our construction of the response-function formalism \nin~\\ssecref{KT_method_hierarchy}--\\ssecref{KT_method_exp} \nor of van~Kampen's explicit series solution~\\exref{Z_via_Z0} \nin~\\ssecref{VK_method}, \naveraged solutions of stochastic equations such \nas~\\eqref{model_eq_Ztilde} can be represented in terms \nof infinite sums of multiple time-history integrals containing \nproducts of time-correlation functions~$\\kappa(t_i-t_j)$ in \nthe integrands. This summation can be visualized in terms \nof Feynman-style diagrams. The $n$-point \ndiagrams represent the terms containing $n$~time-history \nintegrations. As an example, \\figref{fig_diagrams} lists the three \npossible four-point diagrams. \n\nIt was noted by Kazantsev~\\cite{Kazantsev} (see also \nRef.~\\cite{Vainshtein_Zeldovich}) \nthat the white-noise approximation corresponds to the partial \nsummation of all ladder-type diagrams such as the four-point \none shown in \\figref{fig_diagrams}(a).\nThe distinctive property of these diagrams is that the pairs \nof points $t_i$,~$t_j$ \nat which the time-correlation functions in the integrands \nof the time-history integrals are taken, can be fused without \ninterfering with each other. No essential information is therefore \nlost when the time-correlation functions~$\\kappa(t_i-t_j)$ are \napproximated by $\\delta$~functions. However, in all orders of \nthe $\\tau$~expansion but the zeroth, diagrams with more \ntangled topology appear: e.g., in the first order, these are the \ndiagrams~\\ref{fig_diagrams}(b) and~\\ref{fig_diagrams}(c)]. \nSuch diagrams are \noften referred to as the vertex corrections. Fusing points in \nthese diagrams leads to the loss of terms that cannot \nbe neglected~\\cite{fnote_KT_fusing_pts}.\n%\\footnote{See the remark on the Kliatskin--Tatraskii \n%method at the end of~\\ssecref{KT_method_exp}. The reason for \n%the discrepancy between their method and ours is rooted precisely \n%in such illegitimate fusing of points.} \nThis is the context in which \nthe emerging nonuniversality with respect to the shape of the \ntime-correlation profile should be viewed. \n\nIn this paper, we restrict our consideration to the first-order \nterms in the $\\tau$~expansion. The relevant diagrams are \nthe four-point ones shown in~\\figref{fig_diagrams}. \nThe diagrams~\\ref{fig_diagrams}(b) and~\\ref{fig_diagrams}(c) give \nrise to the coefficients~$C_1$ and~$C_2$, respectively \n[see~\\eqref{FPEq_vKampen} and formulas~\\exref{def_C1} \nand~\\exref{def_C2}]. Upon changing variables $t_1\\leftrightarrow t_2$ \nin the diagram~\\ref{fig_diagrams}(b) and \n$t_1\\rightarrow t_2$, $t_2\\rightarrow t_3$, $t_3\\rightarrow t_1$ \nin the diagram~\\ref{fig_diagrams}(c), we see that these diagrams \nequally well correspond to the coefficients~$K_1$ and~$K_2$ \n[\\eqref{model_FPEq_1} and formulas~\\exref{def_K1} \nand~\\exref{def_K2}]. \n\n\\begin{figure} \n\\centerline{\\psfig{file=diagrams.eps}}\n\\vskip0.25in\n\\caption{\\small The three possible fourth-order diagrams. \nThe times~$t_1$, $t_2$, $t_3$ are integration variables \nand may float along the axis, but their positions relative \nto each other and to the time~$t$ are determined by the limits \nof integration and therefore preserved. \nA dashed line connecting any two times~$t_i$ and~$t_j$ \nrepresents the time-correlation function~$\\kappa(t_i-t_j)$ \nin the integrand of a triple time-history integral.}\n\\label{fig_diagrams}\n\\end{figure}\n\n\n\n\\section{The Functional Expansion for the Kinematic Dynamo \nin a Finite-Time-Correlated Velocity Field}\n\\label{sec_KT_dynamo}\n\n\nIn this Section, we use the functional expansion method \ndeveloped in~\\secref{sec_tau_exp} to construct the $\\tau$~expansion \nfor the general diffusion-free\nkinematic dynamo problem in the Eulerian frame \nwith an arbitrarily compressible velocity field. \n\nThrough the convective derivative, an explicit spatial \ndependence is now present in the problem. This leads \nto the appearance of the new effect advertised in the Introduction: \nwhile the zeroth-order terms \nin the expansion only depend on the one-point correlation \nproperties of the velocity gradients, \nthe first-order terms also depend on \nthe {\\em energy} of the advecting velocity field and on the one-point \ncorrelation function of its {\\em second} derivatives. \nThe former represents the loss of Galilean invariance, the latter \nthe loss of the small-scale universality and the advent of the \nsensitive dependence of the statistics on the large-scale \nstructure of the velocity correlations. \n\nIn this Section, all statistics are {\\em Eulerian.} \nFor the questions regarding the transformation of PDF's of passive \nfields from the Eulerian to the Lagrangian frame, we address the reader \nto Ref.~\\cite{BS_metric}, \nas well as to Ref.~\\cite{Boldyrev_tcorr}, \nwhere the $\\tau$~expansion is treated as a problem in stochastic \ncalculus and Lagrangian statistics are discussed. \n\n\n\n\n\\subsection{The Gaussian Hierarchy}\n\\label{hierarchy}\n\nThe magnetic field passively advected by the \nvelocity field~$\\xi^i(t,\\vx)$ evolves according to \nthe Hertz induction equation (formally in $d$~dimensions):\n\\bea\n\\label{ind_eq}\n\\dt B^i = - \\xi^k B^i_{,k} + \\xi^i_{,k} B^k - \\xi^k_{,k} B^i,\n\\eea\nwhere $\\xi^i_{,k}=\\d\\xi^i/\\d x^k$, $B^i_{,k}=\\d B^i/\\d x^k$, and \nthe Einstein summation convention is used throughout. \nLet the advecting velocity field $\\xi^i(t,\\vx)$ be a homogeneous \nand isotropic \nGaussian random field whose statistics are defined by its \nsecond-order correlation tensor: \n\\bea\n\\bigl<\\xi^i(t,\\vx)\\xi^j(t',\\vx')\\bigr> = \\kappa^{ij}(t-t',\\vx-\\vx'),\n\\eea\nwhere, as a function of the time separation~$t-t'$, \nthe correlator~$\\kappa^{ij}$ is \nassumed to have a finite width~$\\tcorr$, which we will call \n{\\em the velocity correlation time.} \nAs we will only study the one-point statistics of the magnetic field, \nall relevant information about the velocity correlation properties \nis contained in the Taylor expansion of~$\\kappa^{ij}$ \naround the origin:\n\\bea\n\\nonumber\n\\kappa^{ij}(\\tau,\\vy)\\,\\,=\\,\\,\\kappa_0(\\tau)\\delta^{ij} \n&-& {1\\over 2}\\,\\kappa_2(\\tau)\\bigl[y^2\\delta^{ij} + 2a y^iy^j\\bigr]\\\\\n\\label{xi_024} \n&+&{1\\over 4}\\,\\kappa_4(\\tau)y^2\\bigl[y^2\\delta^{ij} + 2b y^iy^j\\bigr] \n+ \\cdots,\n\\eea \nas~$y\\to0$. \nHere~$a$ and~$b$ are the compressibility parameters. \nBetween the purely incompressible and the purely irrotational cases, \nthey vary in the intervals\n\\bea\n-{1\\over d+1}\\le a \\le 1, \\qquad -{2\\over d+3}\\le b \\le 2.\n\\eea\nWe should like to mention here that the choice of the coefficients \nof the small-scale expansion~\\exref{xi_024} of the velocity correlation \ntensor is, strictly speaking, not entirely unconstrained. \nAs~$\\kappa^{ij}(\\tau,\\vy)$ is a {\\em correlation function}, \nit must be an inverse Fourier transform of a proper correlation \nfunction in the Fourier space~\\cite{Monin_Yaglom}. \nIn~\\Apref{ap_k_space}, we give the expressions for \nthe coefficients of the expansion~\\exref{xi_024} \nin terms of the spectral characteristics of the velocity field. \nWe further note that, while $a$~and $b$~can certainly \nbe functions of~$\\tau$, \nwe will not overly shrink the limits of physical generality by \nassuming that they are either constant or slowly-varying functions \nof time, i.e.~that they do not change appreciably over one correlation \ntime. \n\nIn order to determine the one-point statistics of the magnetic field, \nwe follow the standard procedure~\\cite{Polyakov} and introduce the \ncharacteristic function of~$B^i(t,\\vx)$ at an arbitrary fixed spatial \npoint~$\\vx$:\n\\bea\nZ(t;\\mu) = \\bigl<\\tZ(t,\\vx;\\mu)\\bigr> \n= \\bigl<\\exp\\bigl[i\\mu_i B^i(t,\\vx)\\bigr]\\bigr>. \n\\eea\nAs usual, the angle brackets denote ensemble \naverages and the overtildes mark unaveraged quantities. \nThe function~$Z$ is the Fourier transform of the~PDF of the vector \nelements~$B^i$. Due to spatial homogeneity,\n$Z$~does not depend on the point~$\\vx$, where~$B^i(t,\\vx)$ is taken. \nUpon differentiating~$\\tZ$ with respect to time and using~\\eqref{ind_eq}, \nwe get\n\\bea\n\\label{Ztilde_eq}\n\\dt\\tZ = -\\xi^k\\tZ_{,k}\n+ \\xi^i_{,k}\\mu_i{\\d\\over\\d\\mu_k}\\tZ \n- \\xi^k_{,k}\\mu_l{\\d\\over\\d\\mu_l}\\tZ \n= -\\xi^k\\tZ_{,k} + \\L^k_i\\,\\xi^i_{,k}\\tZ,\n\\eea\nwhere, for the sake of future convenience, we introduce \nthe operator\n\\bea\n\\label{def_Lambda}\n\\L^k_i = \\mu_i{\\d\\over\\d\\mu_k} - \\delta^k_i\\mu_l{\\d\\over\\d\\mu_l},\n\\eea\nwhich will turn up repeatedly in this calculation.\n\nIn order to obtain an evolution equation for the characteristic \nfunction~$Z(t;\\mu)$ of the random magnetic field, \nwe average both sides of~\\eqref{Ztilde_eq}. \nSince, due to the homogeneity of the problem,\n$\\langle\\xi^k\\tZ_{,k}\\rangle = - \\langle\\xi^k_{,k}\\tZ\\rangle$, \nwe may write the equation for~$Z(t;\\mu)$ in the following form:\n\\bea\n\\nonumber\n\\dt Z(t) = \\bigl(\\delta^k_i + \\L^k_i\\bigr)\n\\bigl<\\xi^i_{,k}(t,\\vx)\\tZ(t,\\vx)\\bigr>\n\\qquad\\qquad\\qquad\\\\ \n= -\\bigl(\\delta^k_i + \\L^k_i\\bigr)\n\\int_0^t\\diff t_1\\intx_1\\,\n\\kappa^{i\\b_1}_{,k\\a_1}(t-t_1,\\vx-\\vx_1)\nG^{\\a_1}_{\\b_1}(t,\\vx|t_1,\\vx_1),\n\\label{Z_eq}\n\\eea\nwhere the mixed average on the right-hand side has been ``split''\nwith the aid of the Furutsu--Novikov (``Gaussian-integration'') \nformula~\\cite{Furutsu,Novikov}, \nand the $\\mu$~dependence in the arguments has been suppressed \nfor the sake of notational compactness.\nWe have introduced the first-order averaged response function \nof the following species:\n\\bea \nG^{\\a_1}_{\\b_1}(t,\\vx|t_1,\\vx_1) = \n\\bigl<\\tG^{\\a_1}_{\\b_1}(t,\\vx|t_1,\\vx_1)\\bigr>\n= \\<{\\delta\\tZ(t,\\vx)\\over\\delta\\xi^{\\b_1}_{,\\a_1}(t_1,\\vx_1)}\\>. \n\\eea\nAs a response function, $G^{\\a_1}_{\\b_1}$~satisfies the causality \nconstraint:~$G^{\\a_1}_{\\b_1}(t,\\vx|t_1,\\vx_1) = 0$ for~$t_1>t$.\nThe same-time form of~$G^{\\a_1}_{\\b_1}$ can be obtained in terms \nof the characteristic function~$Z(t)$:\nintegrating~\\eqref{Ztilde_eq} from~$0$ to~$t_1$, taking the functional \nderivative~$\\delta/\\delta\\xi^{\\b_1}_{,\\a_1}(t',\\vx_1)$, \naveraging, setting~$t'=t_1$, and taking causality into account, \nwe~get \n\\bea\n\\label{G_same}\nG^{\\a_1}_{\\b_1}(t_1,\\vx|t_1,\\vx_1) = \n\\delta(\\vx-\\vx_1)\\,\\L^{\\a_1}_{\\b_1} Z(t_1).\n\\eea\nIn order to find~$G^{\\a_1}_{\\b_1}(t,\\vx|t_1,\\vx_1)$ at $t>t_1$, \nwe take the functional derivative~$\\delta/\\delta\\xi^{\\b_1}_{,\\a_1}(t',\\vx')$ \nof both sides of~\\eqref{Ztilde_eq} and establish that each element of \nthe unaveraged tensor~$\\tG^{\\a_1}_{\\b_1}$ satisfies \nan equation identical in form to~\\eqref{Ztilde_eq}: \n\\bea\n\\label{Gtilde_eq}\n\\dt\\tG^{\\a_1}_{\\b_1}(t,\\vx|t_1,\\vx_1) = \n- \\xi^m(t,\\vx)\\tG^{\\a_1}_{\\b_1,m}(t,\\vx|t_1,\\vx_1)\n+ \\L^n_m\\xi^m_{,n}(t,\\vx)\\tG^{\\a_1}_{\\b_1}(t,\\vx|t_1,\\vx_1).\n\\eea\nSubscripts such as ``$_{,m}$'' in the above equation mean, in accordance \nwith the usual notation, the partial differentiation with respect \nto~$x^m$, viz.,~$\\d/\\d x^m$.\n\nWe must now average~\\eqref{Gtilde_eq} in its turn, to obtain an evolution \nequation for~$G^{\\a_1}_{\\b_1}(t,\\vx|t_1,\\vx_1)$ at $t>t_1$. \nUsing the initial condition~\\exref{G_same}, let us write \nthis evolution equation in the integral form valid for all~$t\\ge t_1$:\n\\bea\n\\nonumber\nG^{\\a_1}_{\\b_1}(t,\\vx|t_1,\\vx_1) = \n\\delta(\\vx-\\vx_1)\\,\\L^{\\a_1}_{\\b_1} Z(t_1)\\, \n\\qquad\\qquad\\qquad\\\\ \n%\\nonumber\n%-\\,\\int_{t_1}^t\\diff t' \n%\\[\\bigl<\\xi^m(t',\\vx)\\tG^{\\a_1}_{\\b_1,m}(t',\\vx|t_1,\\vx_1)\\bigr>\n%- \\L^n_m\\bigr<\\xi^m_{,n}(t',\\vx)\\tG^{\\a_1}_{\\b_1}(t',\\vx|t_1,\\vx_1)\\bigl>\\]\\\\\n%= \\delta(\\vx-\\vx_1)\\,\\L^{\\a_1}_{\\b_1} Z(t_1)\\\\\n\\nonumber \n- \\int_{t_1}^t\\diff t'\\int_0^{t'}\\diff t_2\\intx_2\n\\Bigl[\\kappa^{m\\b_2}(t'-t_2,\\vx-\\vx_2) \nG^{\\a_1}_{\\b_1\\b_2,m}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2)\\Bigr.\\\\\n+\\,\\Bigl.\\kappa^{m\\b_2}_{,n\\a_2}(t'-t_2,\\vx-\\vx_2) \nG^{\\a_1\\a_2}_{\\b_1\\b_2}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2)\\Bigr],\n\\qquad\\qquad \n\\label{G_eq}\n\\eea\nwhere the mixed averages have again been ``split'' \nby the Furutsu--Novikov formula, at the price of introducing \ntwo new second-order response functions:\n\\bea\nG^{\\a_1}_{\\b_1\\b_2}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2) \n&=& \\<\\delta^2\\tZ(t',\\vx)\\over\n\\delta\\xi^{\\b_1}_{,\\a_1}(t_1,\\vx_1)\\delta\\xi^{\\b_2}(t_2,\\vx_2)\\>,\\\\\nG^{\\a_1\\a_2}_{\\b_1\\b_2}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2)\n&=& \\<\\delta^2\\tZ(t',\\vx)\\over\n\\delta\\xi^{\\b_1}_{,\\a_1}(t_1,\\vx_1)\\delta\\xi^{\\b_2}_{,\\a_2}(t_2,\\vx_2)\\>.\n\\eea\n\nIn the same way that the equal-time first-order response function \nwas expressed in terms of~$Z(t)$ [\\eqref{G_same}],\nthe second-order response functions\nat~$t'=t_1$ or~$t'=t_2$ can be expressed \nin terms of~$G^{\\a_2}_{\\b_2}(t_1,\\vx|t_2,\\vx_2)$ \nor~$G^{\\a_1}_{\\b_1}(t_2,\\vx|t_1,\\vx_1)$, respectively. \nBecause of causality, \nthe former representation would be valid provided~$t_1\\ge t_2$, \nthe latter in the opposite case~$t_2\\ge t_1$. \nAt other times, $t_1,t_2\\le t'$, the functions \n$G^{\\a_1}_{\\b_1\\b_2}$ and $G^{\\a_1\\a_2}_{\\b_1\\b_2}$ \nsatisfy integral equations analogous to~\\eqref{G_eq}, \nwhere third-order response functions make their appearance.\nAn infinite open hierarchy can thus be obtained by further iterating this \nprocedure and introducing response functions of ascending orders. \nThis hierarchy constitutes the exact description of the \nstatistics of the kinematic dynamo problem with arbitrary \nvelocity correlation time.\n\n\n\n\\subsection{The $\\tau$ Expansion}\n\\label{tau_expansion}\n\nThe expansion in small correlation time must be \ncarried out in such a way that the time integral of the \nvelocity correlator~$\\kappa^{ij}(\\tau,\\vy)$ remains \nconstant.\n%\\footnote{Alternatively, one may rather choose \n%to fix~$\\kappa^{ij}(0,0)$, the total energy of the velocity field.\n%In this case, the expansion terms that are zeroth- and first-order \n%in~$\\tcorr$ in the method advanced below, must be reinterpreted \n%as first- and third-order terms respectively. The change is \n%purely interpretational and does not affect the results. \n%The main disadvantage of the expansion with constant energy \n%is that the dynamo growth rates vanish in the zero-correlation-time \n%limit, for a $\\delta$-correlated velocity field cannot have \n%a finite energy.}\nSince $\\kappa^{ij}(\\tau,\\vy)$~has \na finite (small) width~$\\tcorr$, we can conclude \nthat the double time integral on the right-hand side of~\\eqref{G_eq} \nmust be of first order in the correlation time~$\\tcorr$. \nAs we are only interested in constructing the $\\tau$~expansion \nup to first order, it is now sufficient to calculate the second-order \nresponse functions $G^{\\a_1}_{\\b_1\\b_2}$ and $G^{\\a_1\\a_2}_{\\b_1\\b_2}$ \nwith zeroth-order precision. \n\nWe have already mentioned that recursive relations completely \nanalogous to the relation~\\exref{G_eq} can be derived for the second-order \nresponse functions. The latter are thereby expressed as their \nequal-time values plus double time integrals of the same sort \nas that which appeared on the right-hand side of~\\eqref{G_eq}.\nThese time integrals are first order in the correlation time \nand can therefore be neglected. The equal-time \nvalues of the second-order response functions are obtained \nby formally integrating~\\eqref{Ztilde_eq}, taking functional \nderivatives of it, averaging, and using causality. \nThe second-order response functions are thus expressed \nto zeroth order in terms of the first-order ones. \nThese latter can by the same token be replaced by their \nequal-time values, which only contain the characteristic \nfunction~$Z(t)$. The resulting expressions, valid to zeroth order, \nmust be substituted into the first-order term (the double time \nintegral) in~\\eqref{G_eq}. All these manipulations, which require \na fair amount of algebra, are relegated to~\\apref{ap_response2}.\nHere we simply give the resulting expression for the \nfirst-order response function, valid to first order in~$\\tcorr$: \n\\bea\n\\nonumber\nG^{\\a_1}_{\\b_1}(t,\\vx|t_1,\\vx_1) = \n\\delta(\\vx-\\vx_1)\\biggl[\\L^{\\a_1}_{\\b_1} Z(t_1)\\biggr.\n\\qquad\\qquad\\qquad\\\\ \n\\nonumber\n-\\,\\,\\int_{t_1}^t\\diff t'\\int_0^{t_1}\\diff t_2\\,\n\\kappa^{m\\b_2}_{,n\\a_2}(t'-t_2,0)\n\\bigl(\\delta^n_m + L^n_m\\bigr)\\L^{\\a_1}_{\\b_1}\\L^{\\a_2}_{\\b_2} Z(t_2)\\qquad\\\\\n\\nonumber\n-\\,\\,\\int_{t_1}^t\\diff t'\\int_{t_1}^{t'}\\diff t_2\\,\n\\kappa^{m\\b_2}_{,n\\a_2}(t'-t_2,0)\n\\bigl(\\delta^n_m + L^n_m\\bigr)\\L^{\\a_2}_{\\b_2}\\L^{\\a_1}_{\\b_1} Z(t_1)\\qquad\\\\\n\\nonumber\n\\biggl.+\\,\\,\\int_{t_1}^t\\diff t'\\int_0^{t_1}\\diff t_2\\,\n\\kappa^{\\a_1\\b_2}_{,\\b_1\\a_2}(t'-t_2,0)\\,\n\\L^{\\a_2}_{\\b_2} Z(t_2)\\biggr]\\qquad\\qquad\\\\\n+\\,\\,{\\d^2\\delta(\\vx-\\vx_1)\\over\\d x^m\\d x^n}\n\\int_{t_1}^t\\diff t'\\int_{t_1}^{t'}\\diff t_2\\,\n\\kappa^{mn}(t'-t_2,0)\\,\\L^{\\a_1}_{\\b_1} Z(t_1) + {\\cal O}(\\tcorr^2).\n\\label{G_eq_1}\n\\eea\n\nThis expression must now be substituted into the time-history \nintegral on the right-hand side of~\\eqref{Z_eq}. \nThis gives a closed integro-differential equation for the \ncharacteristic function~$Z(t)$. However, the dependence on \nthe past values of~$Z$ is spurious and can be resolved \nto first order in~$\\tcorr$. Indeed, we can formally \nintegrate~\\eqref{Z_eq} from~$t_1$ to~$t$ and, using the \nzeroth-order value of the first-order response function [the first \nterm in the formula~\\exref{G_eq_1}],~get\n\\bea\n\\label{Z_eq_1}\nZ(t_1) = Z(t) + \n\\bigl(\\delta^n_m + \\L^n_m\\bigr)\n\\int_{t_1}^t\\diff t'\\int_0^{t'}\\diff t_2\\,\n\\kappa^{m\\b_2}_{,n\\a_2}(t'-t_2,0)\\,\n\\L^{\\a_2}_{\\b_2} Z(t_2) + {\\cal O}(\\tcorr^2).\n\\eea\nThe double time integral in this equation is of first order in~$\\tcorr$, \nas usual. \n\nUpon assembling the equations~\\exref{Z_eq}, \\exref{G_eq_1}, \nand~\\exref{Z_eq_1}, we finally arrive at the following closed partial \ndifferential equation for~$Z(t)$:\n\\bea\n\\nonumber\n\\dt Z(t) = -\\int_0^t\\diff t_1\\,\n\\kappa^{i\\b_1}_{,k\\a_1}(t-t_1,0)\n\\bigl(\\delta^k_i + \\L^k_i\\bigr)\\L^{\\a_1}_{\\b_1} Z(t)\n\\qquad\\qquad\\qquad\\\\\n\\nonumber\n-\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t'\\int_0^{t_1}\\diff t_2\\,\n\\kappa^{i\\b_1}_{,k\\a_1}(t-t_1,0)\n\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad\\\\\n\\nonumber\n\\times\\,\\kappa^{m\\b_2}_{,n\\a_2}(t'-t_2,0)\n\\bigl(\\delta^k_i + \\L^k_i\\bigr)\n\\bigl[\\L^{\\a_1}_{\\b_1},\\L^n_m\\bigr]\\L^{\\a_2}_{\\b_2} Z(t)\\qquad\\\\\n\\nonumber\n-\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t'\\int_{t_1}^{t'}\\diff t_2\\,\n\\kappa^{i\\b_1}_{,k\\a_1}(t-t_1,0)\n\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad\\\\\n\\nonumber\n\\times\\,\\kappa^{m\\b_2}_{,n\\a_2}(t'-t_2,0)\n\\bigl(\\delta^k_i + \\L^k_i\\bigr)\n\\bigl[\\L^{\\a_1}_{\\b_1},\\bigl(\\delta^n_m + \\L^n_m\\bigr)\n\\L^{\\a_2}_{\\b_2}\\bigr]Z(t)\\qquad\\\\\n\\nonumber\n-\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t'\\int_0^{t_1}\\diff t_2\\,\n\\kappa^{i\\b_1}_{,k\\a_1}(t-t_1,0)\\kappa^{\\a_1\\b_2}_{,\\b_1\\a_2}(t'-t_2,0)\n\\bigl(\\delta^k_i + \\L^k_i\\bigr)\\L^{\\a_2}_{\\b_2} Z(t)\\qquad\\\\\n-\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t'\\int_{t_1}^{t'}\\diff t_2\\,\n\\kappa^{i\\b_1}_{,k\\a_1mn}(t-t_1,0)\\kappa^{mn}(t'-t_2,0)\n\\bigl(\\delta^k_i + \\L^k_i\\bigr)\\L^{\\a_1}_{\\b_1} Z(t).\n\\quad\\,\\,\\,\n\\label{Z_eq_closed}\n\\eea \nThe square brackets denote commutators.\n\nNote that, besides the second derivatives of the velocity correlation \ntensor, the first-order terms contain the fourth ones, as well \nas the undifferentiated tensor itself [in the last term \nin~\\eqref{Z_eq_closed}]. The latter implies the loss of Galilean \ninvariance, the former the loss of small-scale universality in the \nsense that the large-scale structure of the velocity correlator \nstarts to play a role. This effect could not have been captured \nif the velocity field had been assumed to be purely a combination \nof the instantaneous velocity at a given point and a linear shear.\n\n\n\n\n\\subsection{The Fokker--Planck Equation}\n\\label{Fokker_Planck_tcorr}\n\nIn order to obtain the Fokker--Planck equation for the PDF of \nthe magnetic field, we must inverse-Fourier transform~\\eqref{Z_eq_closed} \nback to $\\vB$~dependence. The inverse Fourier transform of~$Z(t;\\mu)$\nis the one-point PDF~$P(t;\\vB)$. \nWe will continue using the symbol~$\\L^k_i$ to denote \nthe counterpart of the operator~$\\L^k_i$ in the $\\vB$~space: \n\\bea\n\\label{Lambda_Bspace}\n\\L^k_i = (d-1)\\,\\delta^k_i - B^k{\\d\\over\\d B^i} \n+ \\delta^k_i B^l{\\d\\over\\d B^l}.\n\\eea \nDue to the isotropy of the problem, the PDF~$P(t;\\vB)$ will in fact \nbe a scalar function of the field strength~$B$ only. Thus, all \nthe operators that appear on the right-hand side of the $\\vB$-space\ncounterpart of~\\eqref{Z_eq_closed} must, after they are convolved \nwith the velocity correlation tensors, be expressible in terms \nof~$B$.\nLet us use the Taylor expansion~\\exref{xi_024} of the velocity correlator \nto calculate the tensor convolutions in~\\eqref{Z_eq_closed}. \nWe have\n\\bea\n\\kappa^{ij}(\\tau,0) &=& \\kappa_0(\\tau)\\,\\delta^{ij},\\\\\n\\kappa^{ij}_{,kl}(\\tau,0) &=& \n-\\kappa_2(\\tau)\\bigl[\\delta^{ij}\\delta_{kl} + \na\\,\\bigl(\\delta^i_k\\delta^j_l + \\delta^i_l\\delta^j_k\\bigr)\\bigr] \n= -\\kappa_2(\\tau)\\,T^{ij}_{kl},\\\\\n\\nonumber\n\\kappa^{ij}_{,klmm}(\\tau,0) &=&\n\\kappa_4(\\tau)\\bigl[2\\,(d+2+b)\\,\\delta^{ij}\\delta_{kl} + \n(d+4)\\,b\\,\\bigl(\\delta^i_k\\delta^j_l + \n\\delta^i_l\\delta^j_k\\bigr)\\bigr]\\\\\n&=& \\kappa_4(\\tau)\\,U^{ij}_{kl}.\n\\eea\nA number of second-order differential operators (with respect to~$B$)\narise in~\\eqref{Z_eq_closed}. In the zeroth-order term, \nwe have\n\\bea\n\\label{deff_LL}\n\\LL = T^{i\\b_1}_{k\\a_1}\\bigl(\\delta^k_i + \\L^k_i\\bigr)\\L^{\\a_1}_{\\b_1} \n= {d-1\\over d+1}\\,\\biggl(B{\\d\\over\\d B} + d\\biggr)\n\\Biggl(\\(1+\\igamma\\) B{\\d\\over\\d B} + (d+1)\\igamma\\Biggr);\n\\eea\ntwo operators appearing in the first-order terms result from \nthe non-self-commuting nature of the operator~$\\L^k_i$ \n[see the second and the third terms \nin~\\eqref{Z_eq_closed}]~\\cite{fnote_operators}:\n%\\footnote{These operators are \n%the generalized versions of the operators~$\\LL_1$ and~$\\LL_2$ \n%of~\\ssecref{KT_method_exp}.}\n\\bea\n\\nonumber\n\\LL_1 &=& T^{i\\b_1}_{k\\a_1} T^{m\\b_2}_{n\\a_2}\n\\bigl(\\delta^k_i + \\L^k_i\\bigr) \n\\bigl[\\L^{\\a_1}_{\\b_1},\\L^n_m\\bigr]\\L^{\\a_2}_{\\b_2}\\\\\n\\label{deff_LL1}\n&=& {d^2(d-1)\\over(d+1)^2}\\,\\biggl(B{\\d\\over\\d B} + d\\biggr)\n\\biggl(1+{\\igamma\\over d^2}\\biggr)^2 B{\\d\\over\\d B},\\\\\n\\nonumber\n\\LL_2 &=& \nT^{i\\b_1}_{k\\a_1} T^{m\\b_2}_{n\\a_2}\n\\bigl(\\delta^k_i + \\L^k_i\\bigr)\n\\bigl[\\L^{\\a_1}_{\\b_1},\\bigl(\\delta^n_m+\\L^n_m\\bigr)\\L^{\\a_2}_{\\b_2}\\bigr] =\nT^{i\\b_1}_{k\\a_1}\\bigl(\\delta^k_i + \\L^k_i\\bigr)\n\\bigl[\\L^{\\a_1}_{\\b_1},\\LL\\bigr]\\\\\n\\label{deff_LL2}\n&=& {2d(d-1)\\over d+1}\\,\\biggl(B{\\d\\over\\d B} + d\\biggr)\n\\biggl(1+{\\igamma\\over d^2}\\biggr) B{\\d\\over\\d B};\n\\qquad\n\\eea\nand, finally, there are two other operators due \nto the presence of the convective term (i.e., explicit spatial \ndependence) in the induction equation \n[see the fourth and the fifth terms in~\\eqref{Z_eq_closed}]:\n\\bea \n\\nonumber\n\\MM_1 &=& T^{i\\b_1}_{k\\a_1} T^{\\a_1\\b_2}_{\\b_1\\a_2}\n\\bigl(\\delta^k_i + \\L^k_i\\bigr)\\L^{\\a_2}_{\\b_2}\\,=\\, \n{d(d-1)\\over(d+1)^2}\\,\\biggl(B{\\d\\over\\d B} + d\\biggr)\\\\\n&&\\qquad\\times\n\\Biggl[\\(1 + {2\\igamma\\over d^2} + {d(d+1)-1\\over d^3}\\,\\igamma^2\\)\nB{\\d\\over\\d B} + {(d+1)^2\\over d^2}\\,\\igamma\\Biggr],\\quad\n\\label{deff_MM1}\\\\\n\\nonumber\n\\MM_2 &=& U^{i\\b_1}_{k\\a_1}\n\\bigl(\\delta^k_i + \\L^k_i\\bigr)\\L^{\\a_1}_{\\b_1}\\,=\\,\n{2(d-1)(d+4)\\over d+3}\\,\\biggl(B{\\d\\over\\d B} + d\\biggr)\\\\\n&&\\qquad\\times\n\\Biggl[\\(1 + {d^2+4d+2\\over2d(d+4)}\\,\\zeta\\)B{\\d\\over\\d B} \n+ {(d+2)(d+3)\\over2(d+4)}\\,\\zeta\\Biggr].\n\\label{deff_MM2}\n\\eea\nIn all of the above, $\\igamma = d\\bigl[1+(d+1)a\\bigr]$ and \n$\\zeta = d\\bigl[2+(d+3)b\\bigr]$ are compressibility \nparameters that vanish in the case of incompressible flow.\nIn this latter case, the operators defined above simplify \nconsiderably: \n\\bea\n\\LL_1 = {d^2\\over d+1}\\,\\LL, &\\quad & \n\\LL_2 = 2d\\,\\LL,\\\\\n\\MM_1 = {d\\over d+1}\\,\\LL, &\\quad & \n\\MM_2 = {2(d+1)(d+4)\\over d+3}\\,\\LL.\n\\eea\n\nIf we take the long-time limit, i.e.,~$t\\gg\\tcorr$, \nthe coefficients in~\\eqref{Z_eq_closed} do not depend on time~$t$.\nWe can now use the inverse Fourier transform of~\\eqref{Z_eq_closed} \ntaken in this limit \nand the isotropic operators listed above to assemble \nthe Fokker--Planck equation for the~PDF of the magnetic field.\nThis equation contains the desired corrections that are of first order \nin the velocity correlation time~$\\tcorr$ and represent \nthe first available manifestation of the finite-correlation-time \neffects. We have\n\\bea\n\\label{FPEq_expanded}\n\\dt P = {\\kbar_2\\over2}\n\\(\\LL - {1\\over2}\\,\\tcorr\\kbar_2\\bigl[K_1\\bigl(\\LL_1+\\MM_1\\bigr) + K_2\\LL_2 \n+ \\tK_2\\MM_2\\bigr]\\)P,\n\\eea \nwhere the overall dimensional factor is \n\\bea\n\\label{deff_kbar2}\n\\kbar_2 = 2\\int_0^\\infty\\diff\\tau\\,\\kappa_2(\\tau),\n\\eea\nand the coefficients~\\cite{fnote_coeffs},\n%\\footnote{The coefficients~$K_1$ and~$K_2$ \n%are essentially the same as their namesakes that appeared \n%in~\\ssecref{KT_method_exp} (with~$\\kbar$ replaced by~$\\kbar_2$). \n%The coefficient~$\\tK_2$ would be proportional to~$K_2$ \n%if we assumed that the time correlation properties of the velocity \n%correlator~$\\kappa^{ij}(\\tau,\\vy)$ were embodied in a single \n%scalar function, so that \n%$\\kappa_0(\\tau)\\propto\\kappa_2(\\tau)$ and \n%$\\kappa_4(\\tau)\\propto\\kappa_2(\\tau)$.} \n\\bea\n\\label{deff_K1}\nK_1 &=& {4\\over\\tcorr\\kbar_2^2}\\lim_{t\\to\\infty}\n\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t_2\\int_0^{t_1}\\diff t_3\\,\n\\kappa_2(t-t_1)\\kappa_2(t_2-t_3),\\\\\n\\label{deff_K2}\nK_2 &=& {4\\over\\tcorr\\kbar_2^2}\\lim_{t\\to\\infty}\n\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t_2\\int_{t_1}^{t_2}\\diff t_3\\,\n\\kappa_2(t-t_1)\\kappa_2(t_2-t_3),\\\\\n\\label{deff_tK2}\n\\tK_2 &=& {4\\over\\tcorr\\kbar_2^2}\\lim_{t\\to\\infty}\n\\int_0^t\\diff t_1\\int_{t_1}^t\\diff t_2\\int_{t_1}^{t_2}\\diff t_3\\,\n\\kappa_4(t-t_1)\\kappa_0(t_2-t_3),\n\\eea\nare constants that depend on the particular shapes of \nthe time-correlation functions~$\\kappa_0(\\tau)$, $\\kappa_2(\\tau)$, \nand~$\\kappa_4(\\tau)$. Such sensitive dependence is a new feature \nand represents a loss of universality with respect to the specific \ntime-correlation profiles (cf.~Ref.~\\cite{Boldyrev_tcorr}). \nAs we have pointed out in~\\ssecref{tau_expansion}, \nthe universality with respect to the functional form of \nthe velocity correlator in space is also lost (this effect \nis incorporated into the coefficient~$\\tK_2$). \n\nLet us also list the much more compact form that the Fokker--Planck \nequation~\\exref{FPEq_expanded} assumes in the case of an incompressible \nvelocity field:\n\\bea\n\\label{FPEq_expanded_inc}\n\\dt P = {\\kbar_2\\over2}\n\\[1 - \\tcorr\\kbar_2 d\\({1\\over2}\\,K_1 + K_2 \n+ {(d+1)(d+4)\\over d(d+3)}\\,\\tK_2\\)\\] \\LL P.\n\\eea\nHere it is especially manifest that the true expansion \nparameter in the problem is~$\\tcorr\\kbar_2 d$. \nThis is a general statement that holds regardless of the \ndegree of compressibility, as can be readily verified \nby counting powers of~$d$ in the general expressions for \nthe operators~$\\LL$, $\\LL_1$, $\\LL_2$, $\\MM_1$, and~$\\MM_2$ \n[formulas~\\exref{deff_LL}--\\exref{deff_MM2}].\n\nIt is evident that the distribution resulting \nfrom~\\eqref{FPEq_expanded} is lognormal, which is a well-known fact \nin the kinematic-dynamo and passive-advection theory. \nSince we are interested in \nthe quantitative description of the fast-dynamo effect, we will \nnow proceed to calculate the growth rates of the moments of \nthe magnetic field. \n\n\n\n\n\\subsection{The Dynamo Growth Rates}\n\\label{growth_rates_expanded}\n\nThe evolution of all moments of~$B$ can be determined \nfrom~\\eqref{FPEq_expanded}. \nThe $n$th moment is calculated according to\n\\bea\n\\label{def_Bn}\n\\<B^n\\> = {2\\pi^{d/2}\\over\\Gamma(d/2)}\\int_0^\\infty{\\rm d}B\\,B^{n+d-1}P(t;B).\n\\eea\n%where $S_d=2\\pi^{d/2}/\\Gamma(d/2)$ is the area of $d$-dimensional unit sphere.\nUpon multiplying both sides of~\\eqref{FPEq_expanded} by~$B^{d+n-1}$ and \nintegrating over~$B$, we find that~$\\<B^n\\>$ satisfies:\n\\bea\n\\nonumber\n\\dt\\<B^n\\> &=& \\gamma(n)\\<B^n\\>\\\\\n\\label{Bn_eq} \n&=& {\\kbar_2\\over2}\\Bigl\\{\\Gamma(n) - \n\\tcorr\\kbar_2 d\\bigl[K_1\\Gamma_1(n) + K_2\\Gamma_2(n) \n+ \\tK_2\\tGamma_2(n)\\bigr]\\Bigr\\}\\<B^n\\>,\n\\eea\nwhere the nondimensionalized zeroth-order growth rates \nare (cf.~Ref.~\\cite{BS_metric}) \n\\bea\n\\label{Gamma0}\n\\Gamma(n) = {d-1\\over d+1}\\,n\\bigl[n+d + (n-1)\\igamma\\bigr],\n\\eea \nand the universal parts of the \n(negative) first-order corrections arising from the second- and \nfourth-order terms in the velocity correlator~\\exref{xi_024} are\n\\bea\n\\label{Gamma1}\n\\Gamma_1(n) &=& {1\\over2}\\,{d-1\\over d+1}\\,n\n\\[\\(n+d\\)\\(1+{2\\igamma\\over d^2}\\) + \\(n-1\\)\\,{\\igamma^2\\over d^2}\\],\\\\\n\\label{Gamma2}\n\\Gamma_2(n) &=& {d-1\\over d+1}\\,n\\(n+d\\)\\(1+{\\igamma\\over d^2}\\),\\\\\n\\label{tGamma2}\n\\tGamma_2(n) &=& {(d-1)(d+4)\\over d(d+3)}\\,n\n\\[n+d + {n\\over2}\\({d^2+4d+2\\over d(d+4)}-1\\)\\zeta\\].\n\\eea \nWe observe that, for $n=0$, \n$\\Gamma=\\Gamma_1=\\Gamma_2=\\tGamma_2=0$. This simply means that \nboth zeroth- and first-order terms in the $\\tau$~expansion \npreserve the normalization of the~PDF, i.e., our expansion \nis {\\em conservative,} as it should be. \n\nIn the incompressible flow, the total growth rate \nof the $n$th moment can be written in a more compact form:\n\\bea\n\\label{gamma_iso}\n\\gamma(n) = {\\kbar_2\\over2}\\,{d-1\\over d+1}\\,n(n+d)\n\\l[1 - \\tcorr\\kbar_2 d\\({1\\over2}\\,K_1 + K_2 \n+ {(d+1)(d+4)\\over d(d+3)}\\,\\tK_2\\)\\].\n\\eea\n\nWe see that the corrections to the growth rates \nof the magnetic-field moments are negative, so the growth \nrates are reduced. The amount of reduction depends on \na variety of factors including the dimension of space, \nthe order of the moment, the degree of compressibility, \nthe functional form of \nthe velocity correlator in time and space, and, of course, \nthe velocity correlation time. \nLet us note that our general results derived for an arbitrarily \ncompressible velocity field reveal no qualitatively essential \neffect of compressibility on the behavior of the first-order \nfinite-correlation-time corrections to the dynamo growth rates \nin the diffusion-free regime. \nCompressibility of the flow simply leads to additive (and positive) \ncorrections to the incompressible values of~$\\Gamma(n)$, \n$\\Gamma_1(n)$, $\\Gamma_2(n)$, and~$\\tGamma_2(n)$. Quantitatively, \nthese corrections may affect the exact conditions for the \nbreak-down of the first-order approximation. For more discussion \nof the compressibility effects in the kinematic dynamo \n(with a $\\delta$-correlated velocity field), we address \nthe reader to Refs.~\\cite{Rogachevskii_Kleeorin,BS_metric,SCMM_folding}. \n\nWe remind the reader that here we have studied magnetic fluctuations \n{\\em in the diffusion-free regime} and therefore dropped the term \nin the induction equation that is responsible for the resistive \nregularization. Such an approach is justified for plasmas with \nvery large magnetic Prandtl numbers (e.g., the ISM or the prototogalaxy) \nand applies to the initial stage of the small-scale dynamo \nthat lasts for a time of order~$t\\sim\\log\\Pr$ that elapses \nbefore the magnetic fluctuations reach resistive \nscales~\\cite{Kulsrud_lecture,SBK_review}. After that, or \nif the Prandtl number is of order unity or small (as is, e.g., \nthe case for the Sun), resistive effects must be taken into account. \nIn this case, the calculation of the moments of the \nmagnetic field via the Fokker--Planck equation for its~PDF \nas presented in this Section does not apply because of the \nclosure problem associated with the diffusion term \n[the equations for~$\\tZ(t,\\vx;\\mu)$ and~$Z(t;\\mu)$ do not close]. \nHowever, the general $\\tau$-expansion method proposed in this paper \ncan, in principle, be applied to multipoint correlators \nof the magnetic field, for which treating the diffusive case \npresents no conceptual difficulty. One-point moments can then \nbe obtained by fusing the points at which the multipoint \ncorrelators are taken~(cf.~Refs.~\\cite{Frisch_etal,fnote_diff_result}). \nAlthough it is the diffusive case that is studied in most \nnumerical simulations, where $\\Pr$ rarely exceeds~$100$, \nit is not necessarily the most relevant \none in the context of the (proto)galactic dynamo, \nfor which $\\Pr\\sim10^{14}\\div 10^{22}$. Indeed, as we already \npointed out in the Introduction, the initial (proto)galactic \nseed field may well be strong enough for the kinematic \napproximation to break down while the dynamo is still in \nthe diffusion-free stage~\\cite{Kulsrud_lecture}. \nIf this is the case, the effect of magnetic diffusion \nmust be studied in conjunction with nonlinear saturation \nof the magnetic fluctuations~\\cite{Kinney_etal_2D}. \n\n\n\\section{A Physical Example: The One-Eddy Model} \n\\label{sec_one_eddy}\n\n%Let us now present a qualitative argument on the nature \n%of the expansion parameter that has emerged. We already pointed \n%out in~\\ssecref{tau_expansion} that the true expansion parameter \n%in the problem was~$\\tcorr\\kbar_2 d$. This was also manifest in \n%formulas~\\exref{Bn_eq} and~\\exref{gamma_iso}. \n%Let us see now what this means in physical terms. \n\nIn real astrophysical environments, such as the interstellar medium \nand the protogalactic plasmas, the magnetic fields are \nacted upon by a Kolmogorov-like turbulence with a fully developed \ninertial range about three decades wide ($\\Re\\sim 10^4$). \nWhile the velocities of the turbulent eddies excited by the \nKolmogorov cascade decrease with the scale of the eddy, \nthe velocity gradients increase (see, e.g.,~Ref.~\\cite{Frisch_book}). \nTherefore, the dominant role in the process of amplification of\nthe small-scale magnetic fluctuations is played by the smallest \neddies. With this circumstance \nin mind, one often considers, for modeling purposes, a synthetic \nincompressible turbulent velocity field consisting of eddies \nall of which have the same fixed size but random isotropic \norientation (for detailed discussions of the galactic and protogalactic \ndynamo, we refer the reader \nto~Refs.~\\cite{KA,Kulsrud_etal_proto,Kulsrud_lecture,SBK_review}). \nIn this Section, we will present a brief discussion of the implications \nof the $\\tau$-expansion theory developed in~\\secref{sec_KT_dynamo} \nfor such a model problem, which will \nhenceforth be referred to as the {\\em one-eddy model}. \n\nThe velocity field in the one-eddy model is specified as follows:\n\\bea\n\\xi^i(t,\\vx) &=& \\intk e^{i\\vk\\cdot\\vx}\\xi^i(t,\\vk), \n\\eea\nwhere the Fourier modes~$\\xi^i(t,\\vk)$ are random variables \nthat satisfy \n\\bea\n\\bigl<\\xi^i(t,\\vk)\\xi^j(t',\\vk')\\bigr> &=& (2\\pi)^d\\delta(\\vk+\\vk') \n\\(\\delta^{ij} - {k_i k_j\\over k^2}\\)\\delta(k-k_0)\\kappa(t-t'). \n\\eea\nIn this case, $\\kappa_2(\\tau)\\propto\\kappa(\\tau)$, and, upon using \nthe relations listed in~\\Apref{ap_k_space}, we~get \n\\bea\n\\label{kappa0_kappa2}\n\\kappa_0(\\tau) &=& {1\\over k_0^2}\\,{(d-1)(d+2)\\over d+1}\\,\\kappa_2(\\tau),\\\\\n\\label{kappa4_kappa2}\n\\kappa_4(\\tau) &=& k_0^2\\,{d+3\\over2(d+4)(d+1)}\\,\\kappa_2(\\tau). \n\\eea\nLet us specify a plausible velocity time-correlation profile:\n\\bea\n\\label{kappa2_OU}\n\\kappa_2(\\tau) = {\\kbar_2\\over2\\tcorr}\\,\n\\exp\\(-{|\\tau|\\over\\tcorr}\\).\n\\eea\nFor this correlation function, which corresponds, for example, \nto the well-known Ornstein--Uhlenbeck random process \n(see, e.g.,~Ref.~\\cite{Almighty_Chance}), \nthe coefficients of the $\\tau$~expansion~\\exref{gamma_iso} \nare~$K_1=K_2=1/2$. \nThe relations~\\exref{kappa0_kappa2} and~\\exref{kappa4_kappa2} \nprovide the value of~$\\tK_2$: \n\\bea\n\\label{tK2_k}\n\\tK_2 = {(d-1)(d+2)(d+3)\\over2(d+1)^2(d+4)}\\,K_2. \n\\eea\n\nLet us define the ``eddy-turnover'' time~$\\teddy\\sim(k_0\\xi)^{-1}$ \nof such a velocity field according to the following relation: \n\\bea\n\\label{deff_teddy_k} \n{1\\over\\teddy^2} = k_0^2\\,{1\\over\\tcorr} \n\\int_{-\\infty}^{+\\infty}\\diff\\tau\\,\\kappa^{ii}(\\tau,\\vy=0) \n= k_0^2\\,d\\,{\\kbar_0\\over\\tcorr} \n= {d(d-1)(d+2)\\over d+1}\\,{\\kbar_2\\over\\tcorr}, \n\\eea \nwhere we have used~\\eqref{kappa0_kappa2} to express \n$\\kbar_0$ in terms of~$\\kbar_2$. \nNote that the same expression is obtained if \n$\\teddy\\sim(\\nabla\\vxi:\\nabla\\vxi)^{-1/2}$~is \nformally defined in terms of the velocity gradients \n(without recourse to the one-eddy model):\n\\bea\n\\label{deff_teddy_x}\n{1\\over\\teddy^2} = {1\\over\\tcorr}\n\\int_{-\\infty}^{+\\infty}\\diff\\tau\\,|\\kappa^{ii}_{,jj}(\\tau,\\vy=0)|\n= {d(d-1)(d+2)\\over d+1}\\,{\\kbar_2\\over\\tcorr}.\n\\eea\nWe recall that the zeroth-order growth rate~$\\gamma_0$ of the \nmagnetic-fluctuation energy~$\\<B^2\\>$ is~[see formula~\\exref{gamma_iso}] \n\\bea\n\\label{deff_gamma} \n\\gamma_0 = {(d-1)(d+2)\\over d+1}\\,\\kbar_2.\n\\eea \nFormulas~\\exref{deff_teddy_k} and~\\exref{deff_gamma} then imply \n\\bea\n\\label{small_param}\n\\({\\tcorr\\over\\teddy}\\)^2 = \\tcorr\\gamma_0 d \n= {(d-1)(d+2)\\over d+1}\\,\\tcorr\\kbar_2 d.\n\\eea\nWe have established a correspondence between the small \nparameter that has arisen in our expansion of the dynamo \ngrowth rates and the ``physical'' small parameter, which is\nthe ratio of the correlation and eddy-turnover times. \nOf course, the above expression hinges on \nthe definitions~\\exref{deff_teddy_k} or~\\exref{deff_teddy_x} of~$\\teddy$. \nA simple physical argument can be made in favor of these definitions \nand the resulting formula~\\exref{small_param}. \nNamely, let us observe that when~$\\tcorr\\sim\\teddy$ the eddy \nonly stretches the magnetic field line in one of the~$d$ \navailable directions during one turnover time, \nwhence~$\\tcorr\\gamma \\sim 1/d$. The same estimate follows \nfrom the formula~\\exref{small_param}.\n\nLet us now evaluate the first-order correction to the growth rate \nof the magnetic energy. In the one-eddy model, one gets, upon using \nformulas~\\exref{gamma_iso} and~\\exref{tK2_k} and taking~$K_1=K_2=1/2$ \nfor the Ornstein--Uhlenbeck time-correlation profile~\\exref{kappa2_OU}, \n\\bea\n\\label{exp_gamma}\n\\gamma = \\gamma(2) = \\gamma_0\\bigl(1 - C_d\\tcorr\\gamma_0 d\\bigr), \n\\qquad C_d = {2d(d+1)-1\\over2d(d-1)(d+2)}. \n\\eea\nWe note that in three dimensions, $C_d=23/60\\simeq 40\\%$. \nWhen~$\\tcorr\\sim\\teddy$, we have $\\tcorr\\gamma_0 d\\sim 1$, \nand the resulting growth-rate reduction of~$\\sim40\\%$ is in \na good qualitative agreement with the available numerical \nresults~\\cite{Chandran_tcorr,Kinney_etal_2D,Chou}. Of course, \nas we have already stressed in the Introduction, our \n$\\tau$~expansion is not designed for the case of~$\\tcorr\\sim\\teddy$, \nso the fact that it gives a fairly reasonable prediction should not be \nconsidered as an adequate quantitative corroboration \nof our theory. At best, one might conclude that the \nfirst-order expansion is well behaved for not-too-small values \nof the expansion parameter. \n\nLet us emphasize, however, that \nsuch a well-behaved expression has resulted from a number \nof essentially arbitrary (albeit physically reasonable) \nspecifications of the parameters involved in the $\\tau$~expansion. \nOne of the most physically important points that we have tried \nto make in this work is, in fact, that the inclusion of \nfinite-correlation-time effects leads to {\\em nonuniversal} \nstatistics, so the quantitative predictions of the theory \ncan and will change appreciably if such factors as \nthe shapes of the time-correlation profiles are changed. \nNamely, one would obtain expressions of the form~\\exref{exp_gamma} \nwith different values of the coefficient~$C_d$. \nFor sufficiently large values of~$\\tcorr\\gamma_0 d$, \nthe validity of the expansion~\\exref{exp_gamma} will break down, \nand the expression in the brackets may even become negative. \nHowever, the following heuristic argument can be envisioned \nin this context. \n\nLet us recall that the finite-correlation-time effect \nwas due to the presence of time-history integrals such as \nthose that appear in the equations~\\exref{Z_eq}, \n\\exref{G_eq}, and~\\exref{G_eq_1}. \nThe first-order corrections in the Fokker--Planck \nequation~\\exref{FPEq_expanded} arose from systematically \napproximating the time evolution of the statistical quantities \n[response functions and characteristic function~$Z(t;\\mu)$] \nthat entered these time-history integrals. \nThe corrected (``true'') value of~$\\gamma$ represents, \nin a rough way, the rate at which these quantities change. \nIt would appear then that a better estimate of~$\\gamma$ \nwould be obtained if~$\\gamma_0$ in the first-order term in \nthe brackets in~\\eqref{exp_gamma} were replaced with \nthe corrected value~$\\gamma$. With this caveat, we would \nfind~that~\\cite{fnote_Pade}\n%\\footnote{Formally speaking, this formula \n%represents the $(0,1)$-term of the Pad\\'e series \n%corresponding to the $\\tau$~expansion. Whether the Pad\\'e \n%summation method applied to the $\\tau$~expansion results in \n%a good convergent approximation of the finite-correlation-time \n%effect is unclear.} \n\\bea\n\\gamma = {\\gamma_0\\over 1 + C_d\\tcorr\\gamma_0 d}. \n\\eea\nTo first order, this formula is equally accurate as~\\eqref{exp_gamma}. \nHowever, it better represents the fact that, \nas $\\tcorr\\gamma_0 d$~increases, the corrected value of \nof the growth rate should be expected to saturate~\\cite{Kinney_etal_2D}. \nOf course, such considerations cannot substitute for an adequate \nnonperturbative theory of the passive advection and kinematic dynamo \nin finite-time-correlated flows, which remains an open problem. \n\n\n\\section*{Acknowledgments}\n\nThe authors would like thank S.~A.~Boldyrev \nfor extensive and very fruitful \ndiscussions of the physics and the formalism of \nthe finite-time-correlated kinematic dynamo problem. \nBoth the substance and the style of the presentation \nhave benefited from suggestions made by J.~A.~Krommes who \nread an earlier manuscript of this work. \nWe are also grateful to G.~Falkovich, V.~Lebedev, S.~Cowley, \nand the anonymous referee for several useful comments. \n\nThis work was supported by the \nU.~S.~Department of Energy under Contract~No.~DE-AC02-76-CHO-3073.\n\n\n\n\n\n\\appendix\n\n\n\n\\section{Small-Scale-Expansion Coefficients of the Velocity Correlation \nTensor in Terms of Velocity Spectra} \n\\label{ap_k_space}\n\nIn this Appendix, we list the basic formulas that relate the coefficients \nof the small-scale expansion~\\exref{xi_024} of the velocity correlation \ntensor to the spectral characteristics of the velocity field. \nThese relations allow one to apply the results on the small-$\\tcorr$ \nexpansion obtained in~\\secref{sec_KT_dynamo} to velocity fields \nthat are specified in the Fourier, rather than configuration, space. \nThey also provide a set of consistency constraints that must be respected \nwhen the specific functional forms of~$\\kappa_0(\\tau)$, $\\kappa_2(\\tau)$, \nand~$\\kappa_4(\\tau)$ are chosen. \n\nLet the advecting velocity field be given as a sum of spatial \nFourier modes, \n\\bea\n\\label{FT_inverse}\n\\xi^i(t,\\vx) &=& \\intk e^{i\\vk\\cdot\\vx}\\xi^i(t,\\vk).\n\\eea\nand let the Fourier coefficients~$\\xi^i(t,\\vk)$ be random variables \nthat satisfy \n\\bea\n\\label{kappa_k}\n\\bigl<\\xi^i(t,\\vk)\\xi^j(t',\\vk')\\bigr> &=& (2\\pi)^d\\delta(\\vk+\\vk') \n\\[\\kappa(k,t-t')\\delta^{ij} + \\tkappa(k,t-t')\\,{k_i k_j\\over k^2}\\].\n\\eea\nFor the incompressible flows,~$\\tkappa(k,\\tau)=-\\kappa(k,\\tau)$; \nfor the irrotational ones,~$\\kappa(k,\\tau)=0$. \nThe coefficients of the expansion~\\exref{xi_024} can then be expressed \nas follows:\n\\bea\n\\label{kappa0_k}\n\\kappa_0(\\tau) &=& {1\\over d}\\intk \\bigl[d\\kappa(k,\\tau) + \n\\tkappa(k,\\tau)\\bigr],\\\\\n\\kappa_2(\\tau) &=& {1\\over d(d+2)}\\intk k^{2}\\bigl[(d+2)\\kappa(k,\\tau) + \n\\tkappa(k,\\tau)\\bigr],\\\\\n\\kappa_4(\\tau) &=& {1\\over 2d(d+2)(d+4)}\\intk k^4\\bigl[(d+4)\\kappa(k,\\tau) + \n\\tkappa(k,\\tau)\\bigr],\\\\\na(\\tau) &=& \\kappa_2(\\tau)^{-1}{1\\over d(d+2)}\\intk k^{2}\\tkappa(k,\\tau),\\\\ \n\\label{b_k}\nb(\\tau) &=& \\kappa_4(\\tau)^{-1}{1\\over d(d+2)(d+4)}\\intk k^{4}\\tkappa(k,\\tau),\n\\eea \nwhere the $\\vk$-space integrations of radial functions can, of course, \nbe written more explicitly~as \n\\bea\n\\intk = \\Idk k^{d-1}, \\qquad S_d={2\\pi^{d/2}\\over \\Gamma(d/2)}.\n\\eea\nThe derivation of the above relations is straightforward and \nbased on the expressions for the correlation functions \nof isotropic fields in configuration space in terms of their spectra. \nFor the 3-D~case, these expressions can be found in~Ref.~\\cite{Monin_Yaglom}. \nA detailed derivation of the formulas~\\exref{kappa0_k}-\\exref{b_k} \nfor the $d$-dimensional case is also given in \nAppendix~A of~Ref.~\\cite{SBK_review}. \n\n\n\\section{Second-Order Response Functions}\n\\label{ap_response2}\n\nIn this Appendix, we provide the zeroth-order expressions \nfor the second-order response functions that we used \nin~\\ssecref{tau_expansion}. They are all derived in the same \nfashion: \\eqref{Ztilde_eq}~is formally integrated, functional \nderivatives of it are taken with respect to the velocity \nfield~$\\xi^i$ or its gradients~$\\xi^i_{,k}$ at the appropriate \nmoments, the result is averaged, and the causality property \nof the response functions is used. Here we simply list \nthe results. \n\nWhen~$t_2\\ge t_1$, we have, {\\em to zeroth order in the correlation \ntime~$\\tcorr$,}\n\\bea\n\\nonumber\nG^{\\a_1}_{\\b_1\\b_2}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2) = \nG^{\\a_1}_{\\b_1\\b_2}(t_2,\\vx|t_1,\\vx_1;t_2,\\vx_2)\n\\qquad\\qquad\\\\\n= -\\delta(\\vx-\\vx_2) G^{\\a_1}_{\\b_1,\\b_2}(t_2,\\vx|t_1,\\vx_1) \n+ \\[{\\d\\over\\d x^n}\\,\\delta(\\vx-\\vx_2)\\]\\L^n_{\\b_2}\nG^{\\a_1}_{\\b_1}(t_2,\\vx|t_1,\\vx_1),\n\\label{Ga1b1b2}\\\\\n\\nonumber\nG^{\\a_1\\a_2}_{\\b_1\\b_2}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2) = \nG^{\\a_1\\a_2}_{\\b_1\\b_2}(t_2,\\vx|t_1,\\vx_1;t_2,\\vx_2) \n\\qquad\\qquad\\\\\n= -\\Delta^{\\a_2}(\\vx-\\vx_2) G^{\\a_1}_{\\b_1,\\b_2}(t_2,\\vx|t_1,\\vx_1) \n+ \\delta(\\vx-\\vx_2)\\L^{\\a_2}_{\\b_2}\nG^{\\a_1}_{\\b_1}(t_2,\\vx|t_1,\\vx_1),\n\\label{Ga1a2b1b2}\n\\eea \nwhere we have introduced the following notation: by definition, \n\\bea\n{\\delta\\xi^m(t,\\vx)\\over\\delta\\xi^{\\b_2}_{,\\a_2}(t_2,\\vx_2)} = \n\\delta^m_{\\b_2}\\delta(t-t_2)\\Delta^{\\a_2}(\\vx-\\vx_2).\n\\eea\nThe function~$\\Delta^{\\a_2}(\\vx-\\vx_2)$ is nonrandom and has the following \nproperty, which will be all that we need to know \nabout~it:\n\\bea\n{\\d\\over\\d x^n}\\,\\Delta^{\\a_2}(\\vx-\\vx_2) = \n\\delta^{\\a_2}_n\\delta(\\vx-\\vx_2).\n\\eea\n\nWhen~$t_1>t_2$, the expressions~\\exref{Ga1b1b2} and~\\exref{Ga1a2b1b2}\nvanish by causality, so we have to flip the order of functional \ndifferentiation:\n\\bea\n\\nonumber\nG^{\\a_1}_{\\b_1\\b_2}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2) = \nG^{\\ \\ \\a_1}_{\\b_2\\b_1}(t_1,\\vx|t_2,\\vx_2;t_1,\\vx_1) \n\\qquad\\qquad\\\\\n= -\\Delta^{\\a_1}(\\vx-\\vx_1) G_{\\b_2,\\b_1}(t_1,\\vx|t_2,\\vx_2) \n+ \\delta(\\vx-\\vx_1)\\L^{\\a_1}_{\\b_1}\nG_{\\b_2}(t_1,\\vx|t_2,\\vx_2),\n\\label{Ga1b2b1}\\\\\n\\nonumber\nG^{\\a_1\\a_2}_{\\b_1\\b_2}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2) = \nG^{\\a_2\\a_1}_{\\b_2\\b_1}(t_1,\\vx|t_2,\\vx_2;t_1,\\vx_1) \n\\qquad\\qquad\\\\\n= -\\Delta^{\\a_1}(\\vx-\\vx_1) G^{\\a_2}_{\\b_2,\\b_1}(t_1,\\vx|t_2,\\vx_2) \n+ \\delta(\\vx-\\vx_1)\\L^{\\a_1}_{\\b_1}\nG^{\\a_2}_{\\b_2}(t_1,\\vx|t_2,\\vx_2).\n\\label{Ga2a1b2b1}\n\\eea\nIn~\\eqref{Ga1b2b1}, the following obvious notation was used:\n\\bea\nG^{\\ \\ \\a_1}_{\\b_2\\b_1}(t_1,\\vx|t_2,\\vx_2;t_1,\\vx_1) \n= \\<\\delta^2\\tZ(t_1,\\vx)\\over\n\\delta\\xi^{\\b_2}(t_2,\\vx_2)\\delta\\xi^{\\b_1}_{,\\a_1}(t_1,\\vx_1)\\>,\n\\eea\nand a new first-order response function appeared:\n\\bea\nG_{\\b_2}(t_1,\\vx|t_2,\\vx_2) \n= \\<{\\delta\\tZ(t_1,\\vx)\\over\\delta\\xi^{\\b_2}(t_2,\\vx_2)}\\>.\n\\eea\nThe equal-time form of this function is\n\\bea\n\\label{Gb2_same}\nG_{\\b_2}(t_2,\\vx|t_2,\\vx_2) \n= \\[{\\d\\over\\d x^n}\\,\\delta(\\vx-\\vx_2)\\]\\L^n_{\\b_2} Z(t_2). \n\\eea\n\nThe first-order response functions that appear in \nthe formulas~\\exref{Ga1b1b2}, \\exref{Ga1a2b1b2}, \\exref{Ga1b2b1}, \nand~\\exref{Ga2a1b2b1} can be written as their equal-time \nvalues~\\exref{G_same} and~\\exref{Gb2_same} plus first-order terms. \nTo zeroth order, we have therefore: for~$t_2\\ge t_1$,\n\\bea\n\\nonumber\nG^{\\a_1}_{\\b_1\\b_2}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2) &=& \n-\\[{\\d\\over\\d x^{\\b_2}}\\,\\delta(\\vx-\\vx_1)\\]\\delta(\\vx-\\vx_2) \n\\L^{\\a_1}_{\\b_1} Z(t_1)\\\\\n&+& \\delta(\\vx-\\vx_1)\\[{\\d\\over\\d x^n}\\,\\delta(\\vx-\\vx_2)\\]\n\\L^n_{\\b_2}\\L^{\\a_1}_{\\b_1} Z(t_1),\\\\\n\\nonumber\nG^{\\a_1\\a_2}_{\\b_1\\b_2}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2) &=& \n-\\[{\\d\\over\\d x^{\\b_2}}\\,\\delta(\\vx-\\vx_1)\\]\\Delta^{\\a_2}(\\vx-\\vx_2)\n\\L^{\\a_1}_{\\b_1} Z(t_1)\\\\ \n&+& \\delta(\\vx-\\vx_1)\\delta(\\vx-\\vx_2)\n\\L^{\\a_2}_{\\b_2}\\L^{\\a_1}_{\\b_1} Z(t_1);\n\\eea\nfor~$t_1\\ge t_2$,\n\\bea\n\\nonumber\nG^{\\a_1}_{\\b_1\\b_2}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2) &=& \n-\\Delta^{\\a_1}(\\vx-\\vx_1)\\[{\\d^2\\over\\d x^{\\b_1}\\d x^n}\\,\\delta(\\vx-\\vx_2)\\] \n\\L^n_{\\b_2} Z(t_2)\\\\\n&+& \\delta(\\vx-\\vx_1)\\[{\\d\\over\\d x^n}\\,\\delta(\\vx-\\vx_2)\\]\n\\L^{\\a_1}_{\\b_1}\\L^n_{\\b_2} Z(t_2),\\\\\n\\nonumber\nG^{\\a_1\\a_2}_{\\b_1\\b_2}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2) &=& \n-\\Delta^{\\a_1}(\\vx-\\vx_1)\\[{\\d\\over\\d x^{\\b_1}}\\,\\delta(\\vx-\\vx_2)\\] \n\\L^{\\a_2}_{\\b_2} Z(t_2)\\\\\n&+& \\delta(\\vx-\\vx_1)\\delta(\\vx-\\vx_2)\n\\L^{\\a_1}_{\\b_1}\\L^{\\a_2}_{\\b_2} Z(t_2).\n\\eea\n\nThese expressions must be substituted into~\\eqref{G_eq}.\nThe volume integrals with respect to~$\\vx_2$ can be done, \ntaking into account the extremely useful fact that all \nodd spatial derivatives of the velocity \ncorrelator~$\\kappa^{ij}(\\tau,\\vy)$ vanish at \nthe origin (at~$\\vy=0$).\nThe results are: for~$t_2\\ge t_1$,\n\\bea\n\\nonumber\n\\intx_2\\,\\kappa^{m\\b_2}(t'-t_2,\\vx-\\vx_2)\nG^{\\a_1}_{\\b_1\\b_2,m}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2)\\qquad\\qquad\\\\ \n=\\,\\[-{\\d^2\\delta(\\vx-\\vx_1)\\over\\d x^{\\b_2}\\d x^m}\\,\n\\kappa^{m\\b_2}(t'-t_2,0) \n+ \\delta(\\vx-\\vx_1)\\,\n\\kappa^{m\\b_2}_{,mn}(t'-t_2,0)\\,\n\\L^n_{\\b_2}\\]\\L^{\\a_1}_{\\b_1} Z(t_1),\\\\\n\\nonumber\n\\intx_2\\,\\kappa^{m\\b_2}_{,n\\a_2}(t'-t_2,\\vx-\\vx_2)\nG^{\\a_1\\a_2}_{\\b_1\\b_2}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2)\\qquad\\qquad\\\\\n=\\,\\delta(\\vx-\\vx_1)\\,\n\\kappa^{m\\b_2}_{,n\\a_2}(t'-t_2,0)\\,\\L^n_m\n\\L^{\\a_2}_{\\b_2}\\L^{\\a_1}_{\\b_1} Z(t_1);\\qquad\\qquad\\qquad\n\\eea\nfor~$t_1\\ge t_2$,\n\\bea\n\\nonumber\n\\intx_2\\,\\kappa^{m\\b_2}(t'-t_2,\\vx-\\vx_2)\nG^{\\a_1}_{\\b_1\\b_2,m}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2)\\qquad\\qquad\\\\\n=\\,\\delta(\\vx-\\vx_1)\n\\[-\\kappa^{\\a_1\\b_2}_{,\\b_1n}(t'-t_2,0) \n+ \\kappa^{m\\b_2}_{,mn}(t'-t_2,0)\\,\n\\L^{\\a_1}_{\\b_1}\\]\\L^n_{\\b_2} Z(t_2),\\qquad\\\\ \n\\nonumber\n\\intx_2\\,\\kappa^{m\\b_2}_{,n\\a_2}(t'-t_2,\\vx-\\vx_2)\nG^{\\a_1\\a_2}_{\\b_1\\b_2}(t',\\vx|t_1,\\vx_1;t_2,\\vx_2)\\qquad\\qquad\\\\ \n=\\,\\delta(\\vx-\\vx_1)\\,\n\\kappa^{m\\b_2}_{,n\\a_2}(t'-t_2,0)\\,\\L^n_m\n\\L^{\\a_1}_{\\b_1}\\L^{\\a_2}_{\\b_2} Z(t_2).\\qquad\\qquad\\qquad \n\\eea\nWith the aid of these expressions and~\\eqref{G_eq}, one \nobtains~\\eqref{G_eq_1} of~\\ssecref{tau_expansion}.\n\n\n\n\n\n\n\\begin{thebibliography}{99}\n\n\\bibitem{Kazantsev}\nA.~P.~Kazantsev, \n``Enhancement of a magnetic field by a conducting fluid,\"\nSov. Phys. JETP~{\\bf 26}, 1031~(1968).\n\n\\bibitem{Almighty_Chance}\nYa.~B.~Zeldovich, A.~A.~Ruzmaikin, and D.~D.~Sokoloff, \n{\\it The Almighty Chance} (World Scientific, London,~1990).\n\n\\bibitem{KA} \nR.~M.~Kulsrud and S.~W.~Anderson, \n``The spectrum of random magnetic fields in the mean field dynamo \ntheory of the galactic magnetic field,\" \nAstrophys.~J.~{\\bf 396}, 606~(1992).\n\n\\bibitem{Gruzinov_Cowley_Sudan}\nA.~Gruzinov, S.~Cowley, and R.~Sudan, \n``Small-scale-field dynamo,''\nPhys. Rev. Lett.~{\\bf 77}, 4342~(1996).\n\n\\bibitem{Vergassola}\nM.~Vergassola, \n``Anomalous scaling for passively advected magnetic fields,''\nPhys. Rev.~E~{\\bf 53}, R3021~(1996).\n\n\\bibitem{Rogachevskii_Kleeorin}\nI.~Rogachevskii and N.~Kleeorin, \n``Intermittency and anomalous scaling for magnetic fluctuations,''\nPhys. Rev.~E~{\\bf 56}, 417~(1997).\n\n\\bibitem{Chertkov_etal_dynamo}\nM.~Chertkov, G.~Falkovich, I.~Kolokolov, and M.~Vergassola, \n``Small-scale turbulent dynamo,''\nPhys.~Rev.~Lett.~{\\bf 83}, 4065~(1999).\n\n\\bibitem{BS_metric} \nS.~A.~Boldyrev and A.~A.~Schekochihin, \n``Geometric properties of passive random advection,''\n%chao-dyn/9907034 (1999); \nPhys.~Rev.~E~{\\bf 62}, 545~(2000).\n\n\\bibitem{AAS_thesis}\nA.~A.~Schekochihin, \n{\\em Statistical Theory of Small-Scale Turbulent Astrophysical Dynamos}\n(Ph.~D.~Thesis, Princeton University,~2001).\n\n\\bibitem{SBK_review}\nA.~A.~Schekochihin, S.~A.~Boldyrev, and R.~M.~Kulsrud,\n``Spectra and growth rates of fluctuating magnetic fields \nin the kinematic dynamo theory with large magnetic Prandtl numbers,''\nhttp://xxx.lanl.gov, preprint~No.~astro-ph/0103333~(2001); \nsubmitted to Astrophys.~J.\n\n\\bibitem{Vainshtein_Zeldovich}\nS.~I.~Vainshtein and Ya.~B.~Zeldovich,\n``Origin of magnetic fields in astrophysics,''\nSov.~Phys.~Usp.~{\\bf 15}, 159~(1972).\n\n\\bibitem{Batchelor_vort_analog}\nG.~K.~Batchelor, \n``On the spontaneous magnetic field in a conducting liquid \nin turbulent motion,''\nProc. R.~Soc. London, Ser.~A~{\\bf 201}, 405~(1950).\n\n\\bibitem{Kulsrud_etal_proto}\nR.~M.~Kulsrud, R.~Cen, J.~P.~Ostriker, and D.~Ryu, \n``The protogalactic origin for cosmic magnetic fields,''\nAstrophys.~J.~{\\bf 480}, 481~(1997).\n\n\\bibitem{Kulsrud_lecture}\nR.~M.~Kulsrud,\n``The origin of galactic magnetic fields,''\nin: B.~Coppi, A.~Ferrari, and E.~Sindoni, Eds., \n{\\em Proceedings of the International School of Physics \n``Enrico Fermi,''} Course~CXLII \n(IOS Press, Amsterdam,~2000). \n\n\\bibitem{DMSR_mean_field}\nP.~Dittrich, S.~A.~Molchanov, D.~D.~Sokoloff, and A.~A.~Ruzmaikin,\n``Mean magnetic field in renovating random flow,''\nAstron. Nachr.~{\\bf 305}, 119~(1984).\n\n\\bibitem{MRS_dynamo_theorem}\nS.~A.~Molchanov, A.~A.~Ruzmaikin, and D.~D.~Sokoloff, \n``A dynamo theorem,''\nGeophys. Astrophys. Fluid Dyn.~{\\bf 30}, 241~(1984).\n\n\\bibitem{Kinney_etal_2D}\nR.~M.~Kinney, B.~Chandran, S.~Cowley, and J.~C.~McWilliams, \n``Magnetic field growth and saturation in plasmas with large \nmagnetic Prandtl number. I.~The two-dimensional case,''\nAstrophys.~J.~{\\bf 545}, 907~(2000). \n\n\\bibitem{Boldyrev_tcorr}\nS.~A.~Boldyrev, \n``On Batchelor passive advection by a finite-time correlated \nrandom velocity field,'' \nhttp://xxx.lanl.gov, preprint~No.~astro-ph/0006267~(2000); \nsubmitted to Astrophys.~J. \n\n\\bibitem{vanKampen}\nN.~G.~van~Kampen, \n``A cumulant expansion for stochastic linear differential equations.~I,''\nPhysica~{\\bf 74}, 215 (1974); \n``A cumulant expansion for stochastic linear differential equations.~II,''\nPhysica~{\\bf 74}, 239~(1974).\n\n\\bibitem{vanKampen_review}\nN.~G.~van~Kampen,\n``Stochastic differential equations,''\nPhys.~Rep.~{\\bf 24}, 171~(1976).\n\n\\bibitem{Batchelor}\nG.~K.~Batchelor, \n``Small-scale variation of convected quantities \nlike temperature in turbulent fluid,\" \nJ.~Fluid Mech.~{\\bf 5}, 113~(1959).\n\n\\bibitem{ZRMS_linear}\nYa.~B.~Zeldovich, A.~A.~Ruzmaikin, S.~A.~Molchanov, and D.~D.~Sokoloff,\n``Kinematic dynamo problem in a linear velocity field,''\nJ.~Fluid Mech.~{\\bf 144}, 1~(1984).\n\n\\bibitem{Chandran_tcorr}\nB.~D.~G.~Chandran, \n``The effects of velocity correlation times on the turbulent \namplification of magnetic energy,''\nAstrophys.~J.~{\\bf 482}, 156~(1997).\n\n\\bibitem{Chou}\nH.~Chou,\n``Numerical analysis of magnetic field amplification \nby turbulence,''\nAstrophys.~J.~{\\bf 556}, 1038~(2001). \n\n\\bibitem{Kliatskin_Tatarskii}\nV.~I.~Kliatskin and V.~I.~Tatarskii,\n``A new method of successive approximations in the problem of the \npropagation of waves in a medium having random large-scale \ninhomogeneities,'' \nIzv. Vyssh. Uchebn. Zaved., Radiofiz.~{\\bf 14}, 1400~(1971). \n\n\\bibitem{Vainshtein_KT}\nS.~I.~Vainshtein,\n``Theory of a turbulent dynamo,'' \nIzv. Vyssh. Uchebn. Zaved., Radiofiz.~{\\bf 21}, 1803~(1978).\n\n\\bibitem{Terwiel}\nR.~H.~Terwiel, \n``Projection operator method applied to stochastic linear \ndifferential equations,''\nPhysica~{\\bf 74}, 248~(1974).\n\n\\bibitem{Knobloch}\nE.~Knobloch, \n``The root-mean-square magnetic field in turbulent diffusion,''\nAstrophys.~J.~{\\bf 220}, 330~(1978).\n\n\\bibitem{Chertkov_etal_scalar2D}\nM.~Chertkov, G.~Falkovich, I.~Kolokolov, and V.~Lebedev, \n``Statistics of a passive scalar advected by a large-scale two-dimensional \nvelocity field: Analytic solution,'' \nPhys. Rev.~E~{\\bf 51}, 5609~(1995).\n\n\\bibitem{Furutsu}\nK.~Furutsu, \n``On the statistical theory of electromagnetic waves \nin a fluctuating medium.~(I),''\nJ.~Res. Natl. Bur. Stand.~{\\bf 67D}, 303~(1963).\n\n\\bibitem{Novikov}\nE.~A.~Novikov, \n``Functionals and the random-force method in turbulence theory,''\nSov. Phys.~JETP~{\\bf 20}, 1290~(1965).\n\n\\bibitem{Krommes_review}\nJ.~A.~Krommes, \n``Fundamental statistical descriptions of plasma turbulence \nin magnetic fields,''\nto appear in Phys.~Rep.~(2001).\n\n\\bibitem{fnote_KT_fusing_pts}\nSee the remark on the Kliatskin--Tatraskii \nmethod at the end of~\\ssecref{KT_method_exp}. The reason for \nthe discrepancy between their method and ours is rooted precisely \nin such illegitimate fusing of points.\n\n\\bibitem{Monin_Yaglom}\nA.~S.~Monin and A.~M.~Yaglom, \n{\\em Statistical Fluid Mechanics: Mechanics of Turbulence,} Volume~II \n(MIT Press, Cambridge, MA,~1975).\n\n\\bibitem{Polyakov}\nA.~M.~Polyakov,\n``Turbulence without pressure,'' \nPhys. Rev.~E~{\\bf 52}, 6183~(1995).\n\n\\bibitem{fnote_operators} \nThese operators are \nthe generalized versions of the operators~$\\LL_1$ and~$\\LL_2$ \nof~\\ssecref{KT_method_exp}.\n\n\\bibitem{fnote_coeffs}\nThe coefficients~$K_1$ and~$K_2$ \nare essentially the same as their namesakes that appeared \nin~\\ssecref{KT_method_exp} (with~$\\kbar$ replaced by~$\\kbar_2$). \nThe coefficient~$\\tK_2$ would be proportional to~$K_2$ \nif we assumed that the time-correlation properties of the velocity \ncorrelator~$\\kappa^{ij}(\\tau,\\vy)$ were embodied in a single \nscalar function, so that \n$\\kappa_0(\\tau)\\propto\\kappa_2(\\tau)$ and \n$\\kappa_4(\\tau)\\propto\\kappa_2(\\tau)$. \n\n\\bibitem{SCMM_folding}\nA.~Schekochihin, S.~Cowley, J.~Maron, and L.~Malyshkin, \n``Structure of small-scale magnetic fields in the kinematic \ndynamo theory,'' \nhttp://xxx.lanl.gov, preprint~No.~astro-ph/0105322~(2001); \nto be published in Phys.~Rev.~E. \n\n\\bibitem{Frisch_etal}\nU.~Frisch, A.~Mazzino, and M.~Vergassola, \n``Intermittency in passive scalar advection,''\nPhys.~Rev.~Lett.~{\\bf 80}, 5532~(1998);\nU.~Frisch, A.~Mazzino, A.~Noullez, and M.~Vergassola, \n``Lagrangian method for multiple correlations in passive scalar advection,''\nPhys.~Fluids~{\\bf 11}, 2178~(1999).\n\n\\bibitem{fnote_diff_result}\nFor the $\\delta$-correlated incompressible 3-D~velocity field, \nthe growth rates of~$\\langle B^n\\rangle$ in the kinematic \nregime with diffusion [the diffusive counterpart \nof~\\eqref{expected_outcome}] were recently obtained by \nChertkov {\\em et al.}~\\cite{Chertkov_etal_dynamo} \n(subject to the additional assumption that the magnetic \nexcitation stays at scales smaller than the velocity scale). \nThe growth rate of the magnetic energy~$\\langle B^2\\rangle$ \nin this regime has been known for a long \ntime~\\cite{Kazantsev,Almighty_Chance,KA,Gruzinov_Cowley_Sudan,SBK_review}.\nArbitrarily small magnetic diffusivity~$\\eta$ gives a finite correction \nto the growth rates because it stops the spreading \nof magnetic fluctuations towards ever-smaller scales --- \nthe process that substantially contributes to the growth \nof the magnetic energy and the higher moments. \nMathematically, this means that the limits~$t\\to\\infty$\nand~$\\eta\\to 0$ cannot be interchanged, a common occurrence \nin the theory of turbulence. \n\n\\bibitem{Frisch_book}\nU.~Frisch, \n{\\em Turbulence: The Legacy of A.~N.~Kolmogorov} \n(Cambridge University Press, Cambridge,~1995). \n\n\\bibitem{fnote_Pade}\nFormally speaking, this formula \nrepresents the $(0,1)$-term of the Pad\\'e series \ncorresponding to the $\\tau$~expansion. Whether the Pad\\'e \nsummation method applied to the $\\tau$~expansion results in \na good convergent approximation of the finite-correlation-time \neffect is an issue that will not be investigated here. \n\n\\end{thebibliography}\n\n\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002175.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{Kazantsev}\nA.~P.~Kazantsev, \n``Enhancement of a magnetic field by a conducting fluid,\"\nSov. Phys. JETP~{\\bf 26}, 1031~(1968).\n\n\\bibitem{Almighty_Chance}\nYa.~B.~Zeldovich, A.~A.~Ruzmaikin, and D.~D.~Sokoloff, \n{\\it The Almighty Chance} (World Scientific, London,~1990).\n\n\\bibitem{KA} \nR.~M.~Kulsrud and S.~W.~Anderson, \n``The spectrum of random magnetic fields in the mean field dynamo \ntheory of the galactic magnetic field,\" \nAstrophys.~J.~{\\bf 396}, 606~(1992).\n\n\\bibitem{Gruzinov_Cowley_Sudan}\nA.~Gruzinov, S.~Cowley, and R.~Sudan, \n``Small-scale-field dynamo,''\nPhys. Rev. Lett.~{\\bf 77}, 4342~(1996).\n\n\\bibitem{Vergassola}\nM.~Vergassola, \n``Anomalous scaling for passively advected magnetic fields,''\nPhys. Rev.~E~{\\bf 53}, R3021~(1996).\n\n\\bibitem{Rogachevskii_Kleeorin}\nI.~Rogachevskii and N.~Kleeorin, \n``Intermittency and anomalous scaling for magnetic fluctuations,''\nPhys. Rev.~E~{\\bf 56}, 417~(1997).\n\n\\bibitem{Chertkov_etal_dynamo}\nM.~Chertkov, G.~Falkovich, I.~Kolokolov, and M.~Vergassola, \n``Small-scale turbulent dynamo,''\nPhys.~Rev.~Lett.~{\\bf 83}, 4065~(1999).\n\n\\bibitem{BS_metric} \nS.~A.~Boldyrev and A.~A.~Schekochihin, \n``Geometric properties of passive random advection,''\n%chao-dyn/9907034 (1999); \nPhys.~Rev.~E~{\\bf 62}, 545~(2000).\n\n\\bibitem{AAS_thesis}\nA.~A.~Schekochihin, \n{\\em Statistical Theory of Small-Scale Turbulent Astrophysical Dynamos}\n(Ph.~D.~Thesis, Princeton University,~2001).\n\n\\bibitem{SBK_review}\nA.~A.~Schekochihin, S.~A.~Boldyrev, and R.~M.~Kulsrud,\n``Spectra and growth rates of fluctuating magnetic fields \nin the kinematic dynamo theory with large magnetic Prandtl numbers,''\nhttp://xxx.lanl.gov, preprint~No.~astro-ph/0103333~(2001); \nsubmitted to Astrophys.~J.\n\n\\bibitem{Vainshtein_Zeldovich}\nS.~I.~Vainshtein and Ya.~B.~Zeldovich,\n``Origin of magnetic fields in astrophysics,''\nSov.~Phys.~Usp.~{\\bf 15}, 159~(1972).\n\n\\bibitem{Batchelor_vort_analog}\nG.~K.~Batchelor, \n``On the spontaneous magnetic field in a conducting liquid \nin turbulent motion,''\nProc. R.~Soc. London, Ser.~A~{\\bf 201}, 405~(1950).\n\n\\bibitem{Kulsrud_etal_proto}\nR.~M.~Kulsrud, R.~Cen, J.~P.~Ostriker, and D.~Ryu, \n``The protogalactic origin for cosmic magnetic fields,''\nAstrophys.~J.~{\\bf 480}, 481~(1997).\n\n\\bibitem{Kulsrud_lecture}\nR.~M.~Kulsrud,\n``The origin of galactic magnetic fields,''\nin: B.~Coppi, A.~Ferrari, and E.~Sindoni, Eds., \n{\\em Proceedings of the International School of Physics \n``Enrico Fermi,''} Course~CXLII \n(IOS Press, Amsterdam,~2000). \n\n\\bibitem{DMSR_mean_field}\nP.~Dittrich, S.~A.~Molchanov, D.~D.~Sokoloff, and A.~A.~Ruzmaikin,\n``Mean magnetic field in renovating random flow,''\nAstron. Nachr.~{\\bf 305}, 119~(1984).\n\n\\bibitem{MRS_dynamo_theorem}\nS.~A.~Molchanov, A.~A.~Ruzmaikin, and D.~D.~Sokoloff, \n``A dynamo theorem,''\nGeophys. Astrophys. Fluid Dyn.~{\\bf 30}, 241~(1984).\n\n\\bibitem{Kinney_etal_2D}\nR.~M.~Kinney, B.~Chandran, S.~Cowley, and J.~C.~McWilliams, \n``Magnetic field growth and saturation in plasmas with large \nmagnetic Prandtl number. I.~The two-dimensional case,''\nAstrophys.~J.~{\\bf 545}, 907~(2000). \n\n\\bibitem{Boldyrev_tcorr}\nS.~A.~Boldyrev, \n``On Batchelor passive advection by a finite-time correlated \nrandom velocity field,'' \nhttp://xxx.lanl.gov, preprint~No.~astro-ph/0006267~(2000); \nsubmitted to Astrophys.~J. \n\n\\bibitem{vanKampen}\nN.~G.~van~Kampen, \n``A cumulant expansion for stochastic linear differential equations.~I,''\nPhysica~{\\bf 74}, 215 (1974); \n``A cumulant expansion for stochastic linear differential equations.~II,''\nPhysica~{\\bf 74}, 239~(1974).\n\n\\bibitem{vanKampen_review}\nN.~G.~van~Kampen,\n``Stochastic differential equations,''\nPhys.~Rep.~{\\bf 24}, 171~(1976).\n\n\\bibitem{Batchelor}\nG.~K.~Batchelor, \n``Small-scale variation of convected quantities \nlike temperature in turbulent fluid,\" \nJ.~Fluid Mech.~{\\bf 5}, 113~(1959).\n\n\\bibitem{ZRMS_linear}\nYa.~B.~Zeldovich, A.~A.~Ruzmaikin, S.~A.~Molchanov, and D.~D.~Sokoloff,\n``Kinematic dynamo problem in a linear velocity field,''\nJ.~Fluid Mech.~{\\bf 144}, 1~(1984).\n\n\\bibitem{Chandran_tcorr}\nB.~D.~G.~Chandran, \n``The effects of velocity correlation times on the turbulent \namplification of magnetic energy,''\nAstrophys.~J.~{\\bf 482}, 156~(1997).\n\n\\bibitem{Chou}\nH.~Chou,\n``Numerical analysis of magnetic field amplification \nby turbulence,''\nAstrophys.~J.~{\\bf 556}, 1038~(2001). \n\n\\bibitem{Kliatskin_Tatarskii}\nV.~I.~Kliatskin and V.~I.~Tatarskii,\n``A new method of successive approximations in the problem of the \npropagation of waves in a medium having random large-scale \ninhomogeneities,'' \nIzv. Vyssh. Uchebn. Zaved., Radiofiz.~{\\bf 14}, 1400~(1971). \n\n\\bibitem{Vainshtein_KT}\nS.~I.~Vainshtein,\n``Theory of a turbulent dynamo,'' \nIzv. Vyssh. Uchebn. Zaved., Radiofiz.~{\\bf 21}, 1803~(1978).\n\n\\bibitem{Terwiel}\nR.~H.~Terwiel, \n``Projection operator method applied to stochastic linear \ndifferential equations,''\nPhysica~{\\bf 74}, 248~(1974).\n\n\\bibitem{Knobloch}\nE.~Knobloch, \n``The root-mean-square magnetic field in turbulent diffusion,''\nAstrophys.~J.~{\\bf 220}, 330~(1978).\n\n\\bibitem{Chertkov_etal_scalar2D}\nM.~Chertkov, G.~Falkovich, I.~Kolokolov, and V.~Lebedev, \n``Statistics of a passive scalar advected by a large-scale two-dimensional \nvelocity field: Analytic solution,'' \nPhys. Rev.~E~{\\bf 51}, 5609~(1995).\n\n\\bibitem{Furutsu}\nK.~Furutsu, \n``On the statistical theory of electromagnetic waves \nin a fluctuating medium.~(I),''\nJ.~Res. Natl. Bur. Stand.~{\\bf 67D}, 303~(1963).\n\n\\bibitem{Novikov}\nE.~A.~Novikov, \n``Functionals and the random-force method in turbulence theory,''\nSov. Phys.~JETP~{\\bf 20}, 1290~(1965).\n\n\\bibitem{Krommes_review}\nJ.~A.~Krommes, \n``Fundamental statistical descriptions of plasma turbulence \nin magnetic fields,''\nto appear in Phys.~Rep.~(2001).\n\n\\bibitem{fnote_KT_fusing_pts}\nSee the remark on the Kliatskin--Tatraskii \nmethod at the end of~\\ssecref{KT_method_exp}. The reason for \nthe discrepancy between their method and ours is rooted precisely \nin such illegitimate fusing of points.\n\n\\bibitem{Monin_Yaglom}\nA.~S.~Monin and A.~M.~Yaglom, \n{\\em Statistical Fluid Mechanics: Mechanics of Turbulence,} Volume~II \n(MIT Press, Cambridge, MA,~1975).\n\n\\bibitem{Polyakov}\nA.~M.~Polyakov,\n``Turbulence without pressure,'' \nPhys. Rev.~E~{\\bf 52}, 6183~(1995).\n\n\\bibitem{fnote_operators} \nThese operators are \nthe generalized versions of the operators~$\\LL_1$ and~$\\LL_2$ \nof~\\ssecref{KT_method_exp}.\n\n\\bibitem{fnote_coeffs}\nThe coefficients~$K_1$ and~$K_2$ \nare essentially the same as their namesakes that appeared \nin~\\ssecref{KT_method_exp} (with~$\\kbar$ replaced by~$\\kbar_2$). \nThe coefficient~$\\tK_2$ would be proportional to~$K_2$ \nif we assumed that the time-correlation properties of the velocity \ncorrelator~$\\kappa^{ij}(\\tau,\\vy)$ were embodied in a single \nscalar function, so that \n$\\kappa_0(\\tau)\\propto\\kappa_2(\\tau)$ and \n$\\kappa_4(\\tau)\\propto\\kappa_2(\\tau)$. \n\n\\bibitem{SCMM_folding}\nA.~Schekochihin, S.~Cowley, J.~Maron, and L.~Malyshkin, \n``Structure of small-scale magnetic fields in the kinematic \ndynamo theory,'' \nhttp://xxx.lanl.gov, preprint~No.~astro-ph/0105322~(2001); \nto be published in Phys.~Rev.~E. \n\n\\bibitem{Frisch_etal}\nU.~Frisch, A.~Mazzino, and M.~Vergassola, \n``Intermittency in passive scalar advection,''\nPhys.~Rev.~Lett.~{\\bf 80}, 5532~(1998);\nU.~Frisch, A.~Mazzino, A.~Noullez, and M.~Vergassola, \n``Lagrangian method for multiple correlations in passive scalar advection,''\nPhys.~Fluids~{\\bf 11}, 2178~(1999).\n\n\\bibitem{fnote_diff_result}\nFor the $\\delta$-correlated incompressible 3-D~velocity field, \nthe growth rates of~$\\langle B^n\\rangle$ in the kinematic \nregime with diffusion [the diffusive counterpart \nof~\\eqref{expected_outcome}] were recently obtained by \nChertkov {\\em et al.}~\\cite{Chertkov_etal_dynamo} \n(subject to the additional assumption that the magnetic \nexcitation stays at scales smaller than the velocity scale). \nThe growth rate of the magnetic energy~$\\langle B^2\\rangle$ \nin this regime has been known for a long \ntime~\\cite{Kazantsev,Almighty_Chance,KA,Gruzinov_Cowley_Sudan,SBK_review}.\nArbitrarily small magnetic diffusivity~$\\eta$ gives a finite correction \nto the growth rates because it stops the spreading \nof magnetic fluctuations towards ever-smaller scales --- \nthe process that substantially contributes to the growth \nof the magnetic energy and the higher moments. \nMathematically, this means that the limits~$t\\to\\infty$\nand~$\\eta\\to 0$ cannot be interchanged, a common occurrence \nin the theory of turbulence. \n\n\\bibitem{Frisch_book}\nU.~Frisch, \n{\\em Turbulence: The Legacy of A.~N.~Kolmogorov} \n(Cambridge University Press, Cambridge,~1995). \n\n\\bibitem{fnote_Pade}\nFormally speaking, this formula \nrepresents the $(0,1)$-term of the Pad\\'e series \ncorresponding to the $\\tau$~expansion. Whether the Pad\\'e \nsummation method applied to the $\\tau$~expansion results in \na good convergent approximation of the finite-correlation-time \neffect is an issue that will not be investigated here. \n\n\\end{thebibliography}"
}
] |
astro-ph0002176
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An eigenfunction method for particle acceleration at ultra-relativistic shocks
|
[
{
"author": "Axel W. Guthmann$^*$"
},
{
"author": "John G. Kirk$^*$"
},
{
"author": "Yves A. Gallant${^{\\dagger, \\ddagger}}$ and Abraham Achterberg$^{\\ddagger}$"
}
] |
We adapt and modify the eigenfunction method of computing the power-law spectrum of particles accelerated at a relativistic shock front via the first-order Fermi process \cite{aguthmann:kirkschneider87} to apply to shocks of arbitrarily high Lorentz factor. The power-law index of accelerated particles undergoing isotropic small-angle scattering at an ultrarelativistic, unmagnetized shock is found to be $s=4.23\pm0.2$ (where $s=d\ln f/ d\ln p$, with $f$ the Lorentz-invariant phase-space density and $p$ the momentum), in agreement with the results of Monte-Carlo simulations. We present results for shocks in plasmas with different equations of state and for Lorentz factors ranging from 5 to infinity.
|
[
{
"name": "TP-26.tex",
"string": "\\documentstyle[epsf]{aipproc}\n\\begin{document}\n\\title{An eigenfunction method for particle acceleration at ultra-relativistic shocks}\n\n\\author{Axel W. Guthmann$^*$, John G. Kirk$^*$,\nYves A. Gallant${^{\\dagger, \\ddagger}}$ and Abraham Achterberg$^{\\ddagger}$}\n\\address{$^*$Max-Planck-Institut f\\\"ur Kernphysik, Postfach 103980 ,\nD-69029 Heidelberg, Germany \\thanks{homepage: http://www.mpi-hd.mpg.de/theory/}\\\\\n$^{\\dagger}$ Astronomical Institute, Utrecht University, P.O. Box 80000, 3508 TA Utrecht,\n Netherlands\\\\\n$^{\\ddagger}$ Dublin Institute for Advanced Studies, 5 Merrion Square, Dublin 2, Ireland\\\\}\n%\\lefthead{LEFT head}\n%\\righthead{RIGHT head}\n\\maketitle\n\n\n\\begin{abstract}\nWe adapt and modify the eigenfunction method of computing the power-law spectrum\nof particles accelerated at a relativistic shock front via the\nfirst-order Fermi process\n\\cite{aguthmann:kirkschneider87}\n to apply to shocks of arbitrarily high Lorentz\nfactor. The power-law index of accelerated particles undergoing\nisotropic small-angle scattering at an ultrarelativistic, unmagnetized \nshock is found to be $s=4.23\\pm0.2$ (where $s=d\\ln f/ d\\ln p$, \nwith $f$ the Lorentz-invariant phase-space density and $p$ the\nmomentum), in agreement with the results of Monte-Carlo simulations. \nWe present results for\nshocks in plasmas with different equations of state and for Lorentz \nfactors ranging from 5 to infinity. \n\n\\end{abstract}\n\n%\\section*{Introduction}\n\\section*{The method}\nWe study a stationary shock front in the $x-y-$plane. The accelerated\nparticles are assumed to be test-particles without influence on the\ndynamics of the plasma or the jump conditions at the\nshock-front. The plasma flows\nalong the $z$-axis, with constant velocities $u_{-}$ \nin the upstream ($z<0$) region and $u_{+}$ downstream ($z>0$), the \nvelocities are related by the Rankine-Hugoniot jump conditions.\n\nTest-particles are injected into the acceleration process and their interaction with the\nplasma flow is assumed to give rise to diffusion in the angle $\\cos^{-1}\\mu$ between a particle's\n velocity and the shock normal. In the frame of the shock front this leads to\na stationary transport equation valid for the local plasma rest frame and given in mixed coordinates\nas \\cite{aguthmann:kirkschneider87}\n\\begin{equation}\\label{E:aguthmann:1}\n \\Gamma(u+\\mu)\\frac{\\partial f}{\\partial\n z}=\\frac{\\partial}{\\partial \\mu}\n D_{\\mu \\mu}(1-\\mu^{2})\\frac{\\partial f}{\\partial \\mu}\n\\end{equation}\nwhere the plasma speed $u$ is measured in units of the speed of light,\n$\\Gamma=\\left(1-u^{2}\\right)^{-1/2}$ is the Lorentz-factor,\n$f(p,\\mu,z)$ is the (Lorentz invariant)\nphase-space density as a function of the particle \nmomentum $p$, direction $\\mu$\nand position. $p$ and $\\mu$ are measured in the\nlocal rest frame of the plasma, whereas $z$ is measured in the rest frame of \nthe shock front.\n\nEquation (\\ref{E:aguthmann:1}) is\nsolved using the separation {\\it Ansatz} \n \\cite{aguthmann:kirkschneider87}\n\\begin{equation}\\label{E:aguthmann:2} \n f(p,u,\\mu,x)=\\sum_{i=-\\infty}^{+\\infty}g_i(p)Q_i(\\mu,u)\\exp\\left(\\Lambda_iz\n/\\Gamma\\right),\n\\end{equation}\nvalid in each half-plane \nwith $\\Lambda_i$ and $Q_i$ the eigenvalues and\neigenfunctions of the equation \n\\begin{equation}\n\\label{E:aguthmann:3}\n\\left\\{ \\frac{\\partial}{\\partial \\mu} \\left[\n D_{\\mu\\mu}\\frac{\\partial}{\\partial \\mu} \\right]-\\Lambda_i(u+\\mu) \\right\\} \nQ_i(\\mu,u)=0 \n\\end{equation}\nThe momentum distribution of particles with energy far above the injection energy range \n-- those in which we are interested -- takes the shape of a power-law $g_i(p)\\propto p^{-s}$ with a power-law index $s$,\nsince there is no preferred momentum scale in this range.\n\nMatching the expansion (\\ref{E:aguthmann:2}) across the shock front \naccording to Liouville's Theorem and\nimposing physically realistic boundary conditions up and downstream\nleads to a nonlinear algebraic equation for the power law index $s$.\n\nIn \\cite{aguthmann:kirkschneider87} and \\cite{aguthmann:heavensdrury88} \nonly the eigenfunctions with $i<0$ were used and the method \nwas applied to mildly relativistic shock speeds ($\\Gamma_-\\le5$).\nHere, we use the eigenfunctions with $i>0$ and \ncalculate them directly with a \nnumerical scheme. In the limit $u_-\\rightarrow1$ an analytic \nexpression is available \\cite{aguthmann:kirkschneider89}. \nFour eigenfunctions ($i=1,3,5,7$) are shown in Fig.~\\ref{f:aguthmann:1}A \nas functions of the cosine $\\mu_{\\rm s}=(\\mu+u)/(1+\\mu u)$ \nof the angle between the particle direction and the shock normal, \nmeasured in the shock rest frame.\nFor $i>1$ they are oscillatory for $-1 < \\mu_{\\rm s} < 0$ and for all $i>0$ \nfall off monotonically in the\nrange $0<\\mu_{\\rm s}<1$.\n\\begin{figure}\n\\centerline{\\epsfxsize=7.5cm\\epsffile{TP-26-fig01.eps}\\epsfxsize=7.5 cm\\epsffile{TP-26-fig02.eps}}\n\\caption{A) (left) The eigenfunctions $Q_i$ for $i=1,3,5,7$ for $\\Gamma_-=223$,\nas a function of the \n(cosine of the) angle between the particle speed and the \nshock normal, measured\nin the shock frame, for a relativistic gas.\nB) (right) The power-law index $s$ for relativistic gas with isotropic \n(solid, 2nd from top) and anisotropic \n(dashed-dotted, top) scattering operator and \nfor a strong shock in a gas of adiabatic index $4/3$, with \nisotropic (dashed, 4th from top) and \nanisotropic (dotted, 3rd from top) scattering\n}\n\\protect\\label{f:aguthmann:1}\n\\end{figure}\n\n\\section*{Results}\nThe index $s$ of the momentum spectra of the \naccelerated particles in different cases are shown in \nFig.~\\ref{f:aguthmann:1}B. The jump conditions investigated are those \nfor a relativistic gas both up and downstream:\n$u_-u_+=1/3$\\label{S:aguthmann:1} and\nfor a strong shock in a medium with adiabatic index $4/3$ \\cite{aguthmann:kirkduffy99}.\n \nAlso we investigate two \ndifferent scattering operators, $D_{\\mu\\mu 1}=1-\\mu^2$ (isotropic small/angle\nscattering)\nand $D_{\\mu\\mu 2}=(1-\\mu^2)\\times(\\mu^2+0.01)^{1/3}$\ncorresponding to scattering in weak Kolmogorov turbulence, together with \na rough prescription for avoiding the lack of scattering at $\\mu=0$ \\cite{aguthmann:heavensdrury88}. \nFor high upstream Lorentz-factors \nthe power-law index settles at a value around $4.23$ for all equations of state,\nwhich is reproduced in the limiting case $u_-\\rightarrow1$. \nThe scattering operator has only a minor effect.\n\n\\section*{Summary}\nThese results are in agreement with \nthe asymptotic Monte-Carlo results of Gallant et al.\n\\cite{aguthmann:gallant} and those of Bednarz \\& Ostrowski\n\\cite{aguthmann:bednarz} for $\\Gamma_-\\approx200$.\nAnisotropic scattering, which has not been treated by Monte-Carlo simulations, \nleads to a slight steeping in the power-law spectrum,\n because fewer particles are able to cross the region $\\mu \\approx 0$\n and return to the shock.\nFrom observations of GRB afterglows, Galama et al. \n\\cite{aguthmann:galama} and Waxman \\cite{aguthmann:waxmann}\nhave found synchrotron spectral indices \ncorresponding to $s\\approx4.25$, \nimplying that the particles could \nindeed have been accelerated by the first order Fermi mechanism operating at\nan ultrarelativistic shock front.\n\n\\subsection*{ }\nThis work was supported by the European Commission under the TMR programme, contract number ERBFMRX-CT98-0168\n\n\\begin{references}\n\\bibitem{aguthmann:bednarz} Bednarz, J., Ostrowski, M., {\\it Phys. Rev. Lett.} {\\bf 80},\n 3911 (1998).\n\\bibitem{aguthmann:galama} Galama, T. et al., {\\it Astrophysical Journal} {\\bf 500},\n L101 (1998).\n\\bibitem{aguthmann:gallant} Gallant, Y.A., Achterberg, A., Kirk, J.G., {\\it Astron. Astrophys. \nSuppl. Ser.} {\\bf 138}, 549 (1999)\n\\bibitem{aguthmann:heavensdrury88}Heavens, A.F., Drury L.O'C.,\n{\\it MNRAS} {\\bf 235}, 997 (1988)\n\\bibitem{aguthmann:kirkduffy99} Kirk, J.G., Duffy, P., {\\it Journal of Physics G: Nucl. Part. Phys.}\n{\\bf 25}, R163 (1999)\n\\bibitem{aguthmann:kirkschneider87}Kirk, J.G., Schneider, P., {\\it Astrophysical \nJournal} {\\bf 315}, 425 (1987).\n\\bibitem{aguthmann:kirkschneider89}Kirk, J.G., Schneider, P., {\\it Astronomy \\& Astrophysics} \n{\\bf 225}, 559 (1989)\n\\bibitem{aguthmann:waxmann} Waxmann, E., {\\it Astrophysical Journal} {\\bf 485}, L5 (1997).\n\\end{references}\n \n\\end{document}\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002176.extracted_bib",
"string": "\\bibitem{aguthmann:bednarz} Bednarz, J., Ostrowski, M., {\\it Phys. Rev. Lett.} {\\bf 80},\n 3911 (1998).\n\n\\bibitem{aguthmann:galama} Galama, T. et al., {\\it Astrophysical Journal} {\\bf 500},\n L101 (1998).\n\n\\bibitem{aguthmann:gallant} Gallant, Y.A., Achterberg, A., Kirk, J.G., {\\it Astron. Astrophys. \nSuppl. Ser.} {\\bf 138}, 549 (1999)\n\n\\bibitem{aguthmann:heavensdrury88}Heavens, A.F., Drury L.O'C.,\n{\\it MNRAS} {\\bf 235}, 997 (1988)\n\n\\bibitem{aguthmann:kirkduffy99} Kirk, J.G., Duffy, P., {\\it Journal of Physics G: Nucl. Part. Phys.}\n{\\bf 25}, R163 (1999)\n\n\\bibitem{aguthmann:kirkschneider87}Kirk, J.G., Schneider, P., {\\it Astrophysical \nJournal} {\\bf 315}, 425 (1987).\n\n\\bibitem{aguthmann:kirkschneider89}Kirk, J.G., Schneider, P., {\\it Astronomy \\& Astrophysics} \n{\\bf 225}, 559 (1989)\n\n\\bibitem{aguthmann:waxmann} Waxmann, E., {\\it Astrophysical Journal} {\\bf 485}, L5 (1997).\n"
}
] |
astro-ph0002177
|
[] |
[
{
"name": "paper.tex",
"string": "\\documentclass[psfig,11pt]{article}\n\\usepackage{graphics}\n\\newcommand {\\msol}{\\mbox{M$_{\\odot}$}}\n\\newcommand{\\mhtwo} {\\hbox{$M_{{\\rm H}_2}$}}\n\\newcommand{\\mhi} {\\hbox{$M_{\\rm HI}$}}\n\\newcommand{\\lo} {\\hbox{${\\rm L}_{\\odot}$}}\n\\newcommand{\\lsol} {\\hbox{${\\rm L}_{\\odot}$}}\n\\newcommand{\\lb} {\\hbox{$L_{\\rm B}$}}\n\\newcommand{\\lfir} {\\hbox{$L_{\\rm FIR}$}}\n\\newcommand{\\lco} {\\hbox{$L_{\\rm CO}$}}\n\\newcommand{\\ratioo} {N({\\rm H}_2) / I_{\\rm CO}}\n\\newcommand{\\kms} {{\\rm \\, km \\, s^{-1}}}\n\\newcommand{\\K} {{\\rm \\, K}}\n\\def \\ergs{{\\rm \\, erg \\, s^{-1}}}\n\\def \\MHI{M_{\\rm HI}}\n\\def \\Mo{{\\rm \\, M_\\odot}}\n\\def\\ga{\\lower.5ex\\hbox{$\\; \\buildrel > \\over \\sim \\;$}}\n\\def\\la{\\lower.5ex\\hbox{$\\; \\buildrel < \\over \\sim \\;$}}\n\\oddsidemargin=5mm\n\\textwidth=16cm\n\\topmargin=-15mm\n\\textheight=23cm\n\\baselineskip=7mm\n\\begin{document}\n\n{\\Large Formation of Molecular Gas in the debris of violent \nGalaxy Interactions} \\\\\n\nJonathan~Braine, Observatoire de Bordeaux, UMR 5804, CNRS/INSU, B.P. 89, \n F-33270 Floirac, France \\\\\n\nUte Lisenfeld, Institut de Radioastronomie Millim\\'etrique, Avenida \nDivina Pastora 7, NC18012 Granada, Spain \\\\\n\nPierre-Alain Duc, Institute of Astronomy, Madingley Rd., Cambridge, CB30HA, \nUK and \\\\\nCNRS and CEA/DSM/DAPNIA Service d'astrophysique, Saclay,\n91191 Gif sur Yvette cedex, France\\\\\n\nSt\\'ephane Leon, ASIAA, Academia Sinica, P.O. Box 1-87, Nanking, Taipei 115, Taiwan\n\n\\bigskip\\bigskip\n\n\\baselineskip=7mm\n\n{\\bf In many gravitational interactions between galaxies, gas and stars that\nhave been torn from either or both of the precursor galaxies can collect in\n'tidal tails'. Star formation begins anew in these regions to produce 'tidal\ndwarf galaxies' \\cite{Mirabel92} \\cite{Duc94a} \\cite{Duc97b} \n\\cite{Duc98b}, giving insight into the process of galaxy formation through\nthe well-defined timescale of the interaction. \nBut tracking the star formation process has proved to be\ndifficult: the tidal dwarf galaxies with young stars showed no evidence of the\nmolecular gas out of which new stars form \\cite{Brouillet92} \\cite{Walter99}\n\\cite{Smith94} \\cite{Smith99}. Here we report the\ndiscovery of molecular gas (carbon monoxide emission) in two tidal dwarf\ngalaxies. In both cases, the molecular gas peaks at the same location as the\nmaximum in atomic-hydrogen density, unlike most gas-rich galaxies. We infer\nfrom this that the molecular gas formed from the HI, rather than being torn\nin molecular form from the interacting galaxies. Star formation in the tidal\ndwarfs appears to mimic that process in normal spiral galaxies\nlike our own.}\n\n\\bigskip\n\nTidal Dwarf Galaxies (TDGs) \nare gas-rich irregular galaxies made out of stellar and gaseous \nmaterial pulled out by tidal forces from the disks of the colliding \nparent galaxies into the intergalactic medium \\cite{Zwicky56} \n\\cite{Schweizer78} \\cite{Hibbard96} \\cite{Ducrev}.\nThey are found at the ends of long tidal tails, sometimes \n100 kpc from the nuclei of their progenitors, and host active \nstar-forming regions. TDGs contain two main stellar components:\nyoung stars recently formed by collapse of expelled atomic \nhydrogen (HI) clouds, and an older \nstellar population, at least 1 Gyr old, originally part of the disk of\nthe parent galaxies. Their overall gaseous and stellar\nproperties range between those of classical dwarf irregular and blue compact\ndwarf galaxies, with the exception of their metallicity which is higher --\ntypical of the outer disk of a spiral \\cite{Ducrev}. \nWhether a large fraction of dwarf galaxies were formed through tidal \nencounters in the early universe when spiral galaxies were more \ngaseous and less metal rich and collisions more frequent is an open \nquestion and one of the drivers to study \nTDGs. One way to answer this question is the dark matter content\nof dwarf galaxies. Observations of ordinary dwarf \ngalaxies show that a lot of dark matter, or mass that is in some sotofar \ninvisible form, is necessary to account for their rotation \nvelocities. Numerical simulations of gravitational\ninteractions indicate that TDGs should have very little dark matter \n\\cite{Barnes92} if the dark matter is, as currently believed, in form of \na large halo and not in, say, a rotating disk.\nThus, {\\it if} TDGs are found to possess the same dark matter \nproperties as other dwarf galaxies then powerful constraints are\nplaced on the form of dark matter.\nIf TDGs do {\\it not} contain dark matter as ordinary dwarf galaxies,\nthen tidal interactions cannot be the principal formation mechanism\nfor these small galaxies nor can dark matter be part of galactic disks. \n\n%Because TDGs currently forming out of metal-enriched spirals are \n%intrinsically metal rich \\cite{Duc98b}, Carbon Monoxide (CO) should \n%be more easily detectable than in classical metal poor dwarfs. CO\n%provides the best tracer of the mass and kinematics of the dense\n%gas from which stars form so TDGs are very attractive targets.\n%Curiously, previous attempts to detect CO emission towards TDGs\n%failed \\cite{Smith94} \\cite{Smith99}.\n\nThe observations were carried out with the 30meter telescope operated by the\nInstitut de Radioastronomie Millim\\'etrique (IRAM) on Pico Veleta, Spain\nin June of 1999. \nCarbon Monoxide (CO) emission is detected in the Southern TDG in Arp~105 \n(Figure 1 ; hereafter A105S) and \nmain TDG in Arp~245 (Figure 2; hereafter A245N)\nin both the ground state CO($J=1-0$) and \nthe CO($J=2-1$) transitions. Small maps were made of both sources\nto localise the CO emission with respect to the atomic hydrogen\n(HI), ionized gas (H$\\alpha$), and optical continuum \\cite{Duc97b}\n\\cite{Duc99b}. \nThe central (0,0) CO(1--0) spectra are shown in Fig. 3 along\nwith the HI spectra at the same positions with a similar beamsize.\nThe CO(1--0) luminosities and derived H$_2$ mass estimates (see Table 1)\nof A105S and A245N are far above those of other dwarf galaxies \n\\cite{Taylor98}. Despite the different environments,\nthe star formation efficiency, defined as the rate of star formation\nper mass of molecular gas, is quite close to that observed in the \nMilky Way and other spiral galaxies \\cite{Kennicutt98}.\n\nSmall CO maps have been made consisting of six positions\ntowards A105S and four positions towards A245N. In both cases,\nthe CO peaks at the HI column density maximum and the dynamics of \nthe atomic and molecular components are virtually identical (Figure 3).\nIn spiral galaxies, on the other hand, HI and \nCO have very different distributions (see {\\it e.g.} \\cite{Guelin93}\n\\cite{Braine4414a}), showing that the molecular gas \nthat we have found in the TDGs has not simply been torn off the parent \ngalaxies together with the HI but has formed {\\it in situ}.\nAlthough the calculations \nwere performed for post-shock gas, an estimate of the molecule \nformation time is $t \\sim n^{-1}$Gyr \\cite{Hollenbach89} where $n$ \nis the density of the atomic medium in particles cm$^{-3}$.\nNumerical simulations of Arp~245 \\cite{Duc99b} yield an age of \nabout 100 Myr for A245N and a\nrough age estimate for A105S can be obtained by dividing the \nprojected distance to the spiral by the relative radial velocity, \nyielding about 200 Myr \\cite{Duc97b}, sufficient for H$_2$ formation \nin standard atomic hydrogen clouds ($\\overline{n} \\sim 10$cm$^{-3}$).\nThe dust on which the H$_2$ forms is captured from the parent\ngalaxies and present in the atomic gas \\cite{Neininger96} \\cite{Dumke97}\n\\cite{Braine3079}. {\\it The molecular gas has formed \ninside the HI clouds and star formation is proceeding in a standard \nway from the molecular gas.}\n\nOur observations show that the molecular gas is an important \ncomponent in the visible mass budget of TDGs, between $\\sim 20$\\% and\n$\\ga 50$\\% of the atomic hydrogen mass (see Table 1).\nThe fact that we detect large\nquantities of molecular gas and that we have every reason to \nbelieve that this gas is the result of conversion from HI into \nH$_2$ indicates that the central regions of these objects should be\ngravitationally bound. If the HI were dense enough pre-encounter then\nCO would form and be routinely detected beyond R$_{25}$ (the optical \nradius) in galactic disks, like HI -- it is not \\cite{Guelin93}\n\\cite{Neininger96} \\cite{Dumke97} \\cite{sage}. \nWhile it was clear that TDGs are kinematically decoupled from their\nparent galaxies, prior to these data, the evidence that TDGs were\nbound was morphological -- the accumulation of matter at the tips\nof the tidal tails and the presence of star forming regions. \nAlthough higher angular resolution is necessary,\nthis conclusion provides firmer ground for the calculation of the \ndynamical mass, which relies on the assumption \nthat the object is gravitationally bound and in equilibrium, and\nthus for the determination of dark matter which\nby definition is detected as discrepancy between the velocities expected \nbased on the mass of what we see directly and those observed. \n\n\\bibliographystyle{unsrt}\n\\bibliography{tdg_nature}\n\n\\newpage\n\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{lll}\n & A105S & A245N \\\\\n\\hline\n\\smallskip \nRA(J2000) & 11 11 13.5 & 09 45 44.1 \\\\\n\\smallskip \nDec(J2000)& +28 41 20 & -14 17 28 \\\\\n\\smallskip \nHI velocity (LSR)& $cz=8890 \\kms$ & $cz=2175 \\kms$ \\\\\n\\smallskip \nadopted distance & 115 Mpc & 31 Mpc \\\\\n\\smallskip \n$L_{\\rm H\\alpha}$ & $1 - 2 \\times 10^{40}\\ergs$ & $7 \\times 10^{39}\\ergs$ \\\\\n\\smallskip \nM$_{\\rm B}$, L$_{\\rm B}$/L$_{\\rm B}\\odot$ &-16.9, $9 \\times 10^8$\n & -17.25, $1.2 \\times 10^9$ \\\\\n\\smallskip \nB -- V & 0.3 & 0.55 \\\\\n%12+[O/H] & 8.4 & 8.6 \\\\\n\\smallskip \n$\\MHI$ & $5 \\times 10^8\\Mo$ & $9 \\times 10^8\\Mo$\\\\\n%CO(1--0) & 111.9514 GHz & 114.4409 GHz \\\\\n%CO(2--1) & 223.8985 GHz & 228.8775 GHz \\\\\n\\hline\n\\smallskip \n%$L_{\\rm CO} (\\K\\kms$pc$^2$) & $\\ge 5 \\times 10^7$ & $\\ge 3 \\times 10^7$\\\\\n%\\smallskip \n\\mhtwo (\\msol) & $\\ge 2.2 \\times 10^8$ & $\\ge 1.4 \\times 10^8$ \\\\\n\\end{tabular}\n\\caption[]{{\\baselineskip=7mm\nProperties of the Arp~105 and Arp~245 Tidal Dwarf Galaxies.\nThe data are from \n\\cite{Duc94a} \\cite{Duc97b} for A105S and \\cite{Duc99b} for A245N.\nPosition is (0,0) of CO map and velocity is zero of spectra (Fig. 3).\n%CO(1--0) luminosities are the result of the observations presented here and \n%likely represent a lower limit because weaker, undetected, CO emission \n%may be present at other positions. \nM$_{\\rm B}$ and L$_{\\rm B}$ include\na correction for galactic absorption of 0.3 magnitudes for A245N. \nA105S is at high galactic latitude so no correction is applied.\nThe molecular gas mass is estimated using a $\\ratioo$ factor \nof 2 $\\times 10^{20} \\K\\kms$cm$^{-2}$ and likely represents a lower limit \nbecause weaker, undetected, CO emission may be present at other positions. \nWe have included the mass of Helium in the molecular clouds.\nRelative to the velocities of the TDGs, the spiral and elliptical in the \nArp~105 system have velocities of -130 and -400 km/s. In Arp~245, the\nvelocities of the spirals NGC 2992 and NGC 2993 are 155 and 245 km/s \nwith respect to the TDG.\n}}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{llllll}\n\\hline\nSource & offset & I$_{\\rm CO}$ & rms & vel. & $\\Delta$V$_{\\rm fwhm}$ \\\\\n\\smallskip \n & ($\\delta$RA,$\\delta$Dec) & K km/s & mK & km/s & km/s\\\\\n\\hline\nA105S & (0,0) & 0.3$\\pm.05$ & 2.5 & 19$\\pm6$ &38$\\pm10$ \\\\\n\\smallskip \n & & 0.2$\\pm.05$ & 3.5 &16$\\pm5$ & 25$\\pm10$ \\\\\n\\smallskip \nA105S & (10,0) &0.1$\\pm.05$ & 3 & 59$\\pm6$ & 19$\\pm10$ \\\\\n\\smallskip \nA105S & (-10,0) &0.15$\\pm.05$ & 2.8 & -4$\\pm5$ & 22$\\pm13$ \\\\\n\\smallskip \nA105S & other &0.15$\\pm.05$ & 2.5 & 15$\\pm6$ & 15$\\pm8$ \\\\\n%A105S & (-5.3,25) & $0.5\\pm.1$ & 4 \\\\\n% & & $1.5\\pm.1$ & 12 \\\\\n\\smallskip \nA245N & (0,0) & $1.3\\pm.1$ & 4.9 &-32$\\pm4$ &48$\\pm10$ \\\\\n\\smallskip \n& & $2.0\\pm.5$& 18 &-32$\\pm10$ &66$\\pm20$ \\\\\n\\smallskip \nA245N & (3,14) & $0.6\\pm.15$ & 7 &-33$\\pm10$ &47$\\pm15$ \\\\\n%& & $1\\pm.5$ & 26 \\\\\n\\smallskip \nA245N & (0,-10) & $0.9\\pm.15$ & 7.6 &-27$\\pm7$ &44$\\pm14$ \\\\\n%& & $1.3\\pm.5$ & 29 \\\\\n\\smallskip \nA245N & (0,-20) & $0.5\\pm.2$ & 9.5 &-27$\\pm12$ &32$\\pm15$ \\\\\n\\end{tabular}\n\\caption[]{\n{\\baselineskip=7mm \nMolecular gas in Tidal Dwarf Galaxies.\nThe CO observations presented here provide the first detections \nof molecular gas in TDGs.\nThe offset is in arcseconds with respect to the position given \nin Table 1 and the red circle in Figures 1 and 2. I$_{\\rm CO}$\nis the flux of the CO line expressed in Kelvin km/s.\nThe lines without source and offset are the CO(2--1) \nobservations of the preceding source and position. Noise levels (rms) \nare given for channel widths of 2~MHz in the CO(1--0) line and\n2.5~MHz in the CO(2--1) line. \n%The molecular gas mass is calculated as in Table 1 for each position. \nThe velocity of the line center is with respect to the HI velocity \ngiven in Table 1. Note that the ``detections''\nof the off-center A105S positions are uncertain so the velocities\nand line widths may be meaningless. \nThe spectra for each position were averaged, a continuum level was \nthen subtracted such that the average flux outside the line\nwindow is zero, and resulting spectra were smoothed to yield the\nresults presented in Fig. 3 and Table 2.\nNo baselines other than the continuum level are subtracted from the data.\nThe A105S ``other'' position\nrepresents the average of the spectra for the (0,5) (0,-5) and (0,-10)\npositions. Taken individually, these points were not detected and \nyield 3$\\sigma$ limits of I$_{\\rm CO} \\la 0.3$K km/s. \nThe CO emission from A105S is consistent with a near-punctual\nsource, much like for the optical and HI. \nThe angular resolutions are respectively \n22$''$ and 11$''$; beam efficiencies are 0.72 and 0.48.\n}} \n\\end{center}\n\\end{table}\n\n\\clearpage\n\n\\pagebreak\n\n\\newpage\n\n\\begin{figure}\n%\\resizebox{\\hsize}{!}{\\rotatebox{270}{\\includegraphics{A105_nature.ps}}}\n\\caption {{\\baselineskip=7mm\nThe Southern Tidal Dwarf Galaxy (blow-up) in the interacting system \nArp~105 (NGC 3561 \\cite{arpatlas}; ``the Guitar''). \nHI emission contours are superposed on a blow-up \nof a V band image of A105S \\cite{Duc97b}.\nThe frame is 4.4$'$ x 5.9$'$; North is up and East to the left.\nRed circle is (0,0) position of CO observations\nand represents the FWHM (22$''$) of the CO(1--0) beam.\nThe Arp~105 system \\cite{Duc94a} \\cite{Duc97b}\nis an interaction between a spiral and an elliptical\nwhich has generated an HI-rich extended TDG at the end of the Northern\ntidal tail and a more compact TDG at the tip of the Southern tail\nfrom the spiral. Arp~105~South (A105S) \ncontains roughly 5 $10^8$ \\msol\\ of HI and strong H$\\alpha$ emission,\ncorresponding to a star formation rate of $\\sim 0.2$\\msol/yr.\nNonetheless, stellar synthesis models \\cite{Fritze98}\nof A105S indicate that the stellar mass is dominated by the old \nspiral disk population while the luminosity comes in majority from stars \nformed {\\it in situ}. \n }}\n\\end{figure}\n\n\\begin{figure}\n%\\resizebox{\\hsize}{!}{\\rotatebox{270}{\\includegraphics{A245_nature.ps}}}\n\\caption {{\\baselineskip=7mm\nThe Tidal Dwarf Galaxy (blow-up) in the interacting system \nArp~245 (NGC~2992/3 \\cite{arpatlas}). \nHI emission contours are superposed on a \nblow-up of a V band image of A105S \\cite{Duc99b}. %\\cite{Duc99a}\nThe frame is 5.8$'$ x 7.4$'$; North is up and East to the left.\nRed circle is (0,0) position of CO observations\nand represents the FWHM (22$''$) of the CO(1--0) beam.\nArp~245 is an interaction between two spirals. The TDG, A245N,\nhas been formed in the tidal tail which stems from NGC~2992 and\ncontains nearly twice as much HI as A105S but slightly weaker\nH$\\alpha$ emission. The old stellar population is more prominent \nin A245N than in A105S \\cite{Duc99b}.\nThe physical size and total HI mass of Arp~245 are smaller than \nin Arp~105.} }\n\\end{figure}\n\n\\begin{figure}\n%\\resizebox{\\hsize}{!}{\\rotatebox{270}{\\includegraphics{co_hi_spec.ps}}}\n\\caption {{\\baselineskip=7mm\nCO(1--0) and HI spectra of the (0,0) position of A105S (left) and\nA245N (right). \nThe velocities and line widths of the CO and HI emission are very similar.\nTowards the very compact TDG A105S, the CO emission is not resolved. \nThe CO emission in A245N is extended with detections in {\\it at least}\n3 of 4 observed points. The H$\\alpha$ emission in A245N \\cite{Duc99b}\ndecreases substantially towards the (0,-10) offset position while \nthe HI \\cite{Duc99b} and CO (see Table 2) are still strong.\nIn contrast, the H$\\alpha$ emission towards the (3,14) position is\ncomparable to the center whereas the CO and HI have decreased \nsignificantly.\nThe temperature scale (main beam) is in milliKelvins and \nvelocities in km/s. HI intensity is in arbitrary units.} }\n\\end{figure}\n\n\\end{document}\n\n\\newpage\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\rotatebox{270}{\\includegraphics{A105_nature.ps}}}\n\\end{figure}\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\rotatebox{270}{\\includegraphics{A245_nature.ps}}}\n\\end{figure}\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\rotatebox{270}{\\includegraphics{co_hi_spec.ps}}}\n\\end{figure}\n\n\\end{document}\n\n"
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"name": "paper.bbl",
"string": "\\begin{thebibliography}{10}\n\n\\bibitem{Mirabel92}\nI.~F. Mirabel, H.~Dottori, and D.~Lutz.\n\\newblock Genesis of a dwarf galaxy from the debris of the {A}ntennae.\n\\newblock {\\em Astron. Astrophys.}, 256:L19--23, 1992.\n\n\\bibitem{Duc94a}\nP.-A. Duc and I.~F. Mirabel.\n\\newblock Recycled galaxies in the colliding system {A}rp 105.\n\\newblock {\\em Astron. Astrophys.}, 289:83--93, 1994.\n\n\\bibitem{Duc97b}\nP.-A. Duc, E.~Brinks, J.~E. Wink, and I.~F. Mirabel.\n\\newblock Gas segregation in the interacting system {A}rp 105.\n\\newblock {\\em Astron. Astrophys.}, 326:537--553, 1997.\n\n\\bibitem{Duc98b}\nP.-A. {Duc} and I.~F. {Mirabel}.\n\\newblock Young tidal dwarf galaxies around the gas-rich disturbed lenticular\n {NGC} 5291.\n\\newblock {\\em Astron. Astrophys.}, 333:813--826, 1998.\n\n\\bibitem{Brouillet92}\nN.~Brouillet, C.~Henkel, and A.~Baudry.\n\\newblock Detection of an intergalactic molecular complex?\n\\newblock {\\em Astron. Astrophys.}, 262:L5--8, 1992.\n\n\\bibitem{Walter99}\nF.~{Walter} and A.~{Heithausen}.\n\\newblock The discovery of a molecular complex in the tidal arms near {NGC}\n 3077.\n\\newblock {\\em Astrophys. J. Lett.}, 519:L69--72, 1999.\n\n\\bibitem{Smith94}\nB.~J. Smith and J.~L. Higdon.\n\\newblock A search for {CO}(1-0) emission from the tidal structures of\n interacting and merging galaxies.\n\\newblock {\\em Astron. J.}, 108:837--843, 1994.\n\n\\bibitem{Smith99}\nB.~J. {Smith}, C.~{Struck}, J.~D.~P. {Kenney}, and S.~{Jogee}.\n\\newblock The {M}olecule-rich tail of the peculiar galaxy {NGC} 2782 ({A}rp\n 215).\n\\newblock {\\em Astron. J.}, 117:1237--1248, 1999.\n\n\\bibitem{Zwicky56}\nF.~Zwicky.\n\\newblock Multiple galaxies.\n\\newblock {\\em Erg. d. exakt. Naturwiss. Bd.}, XXIX. S.:344, 1956.\n\n\\bibitem{Schweizer78}\nF.~Schweizer.\n\\newblock Galaxies with long tails.\n\\newblock In E.M. Berkhuijsen and R.~Wielebinski, editors, {\\em Structure and\n Properties of Nearby Galaxies}, page 279. Dordrecht, D. Reidel Publishing\n Co., 1978.\n\n\\bibitem{Hibbard96}\nJ.~E. {Hibbard} and J.~H. {van Gorkom}.\n\\newblock H{I}, {HII}, and {R}-{B}and {O}bservations of a {G}alactic {M}erger\n {S}equence.\n\\newblock {\\em Astron. J.}, 111:655--695, 1996.\n\n\\bibitem{Ducrev}\nP.-A. {Duc} and I.~F. {Mirabel}.\n\\newblock Tidal dwarf galaxies.\n\\newblock In J.~Barnes \\&~D. Sanders, editor, {\\em IAU Symposium186, Galaxy\n Interactions at Low and High Redshift}, page~61. Kluwer: Dordrecht, 1997.\n\n\\bibitem{Barnes92}\nJ.~E. Barnes and L.~Hernquist.\n\\newblock Formation of dwarf galaxies in tidal tails.\n\\newblock {\\em Nature}, 360:715--717, 1992.\n\n\\bibitem{Duc99b}\nP.-A. {Duc}, E.~{Brinks}, V.~{Springel}, B.~{Pichardo}, P.~{Weilbacher}, and\n I.~F. {Mirabel}.\n\\newblock The interacting system {NGC}~2992/3 ({A}rp~245).\n\\newblock {\\em Astron. J. submitted}, 1999.\n\n\\bibitem{Taylor98}\nC.~L. {Taylor}, H.A. {Kobulnicky}, and E.~D. {Skillman}.\n\\newblock C{O} {E}mission in {L}ow-{L}uminosity, {HI}-rich {G}alaxies.\n\\newblock {\\em Astron. J.}, 116:2746--2756, 1998.\n\n\\bibitem{Kennicutt98}\nJr. {Kennicutt}, Robert~C.\n\\newblock Star formation in galaxies along the hubble sequence.\n\\newblock {\\em Ann. Rev. Astron. Astrophys.}, 36:189--232, 1998.\n\n\\bibitem{Guelin93}\nM.~{Gu\\'elin}, R.~{Zylka}, P.~G. {Mezger}, C.~G.~T. {Haslam}, E.~{Kreysa},\n R.~{Lemke}, and A.~W. {Sievers}.\n\\newblock 1.3 mm emission in the disk of {NGC} 891: {E}vidence of cold dust.\n\\newblock {\\em Astron. Astrophys.}, 279:L37--L40, November 1993.\n\n\\bibitem{Braine4414a}\nJ.~{Braine}, F.~{Combes}, and W.~{Van Driel}.\n\\newblock N{GC} 4414: {A} flocculent galaxy with a high gas surface density.\n\\newblock {\\em Astron. Astrophys.}, 280:451--467, December 1993.\n\n\\bibitem{Hollenbach89}\nD.~{Hollenbach} and C.~F. {MCKee}.\n\\newblock Molecule formation and infrared emission in fast interstellar shocks.\n {III} - results for {J} shocks in molecular clouds.\n\\newblock {\\em Astrophys. J.}, 342:306--336, July 1989.\n\n\\bibitem{Neininger96}\nN.~{Neininger}, M.~{Gu\\'elin}, S.~{Garcia-Burillo}, R.~{Zylka}, and\n R.~{Wielebinski}.\n\\newblock Cold dust and molecular line emission in {NGC} 4565.\n\\newblock {\\em Astron. Astrophys.}, 310:725--736, June 1996.\n\n\\bibitem{Dumke97}\nM.~{Dumke}, J.~{Braine}, M.~{Krause}, R.~{Zylka}, R.~{Wielebinski}, and\n M.~{Gu\\'elin}.\n\\newblock The interstellar medium in the edge-on galaxy {NGC} 5907. {C}old dust\n and molecular line emission.\n\\newblock {\\em Astron. Astrophys.}, 325:124--134, September 1997.\n\n\\bibitem{Braine3079}\nJ.~{Braine}, M.~{Gu\\'elin}, M.~{Dumke}, N.~{Brouillet}, F.~{Herpin}, and\n R.~{Wielebinski}.\n\\newblock Gas and dust in the active spiral galaxy {NGC} 3079.\n\\newblock {\\em Astron. Astrophys.}, 326:963--975, 1997.\n\n\\bibitem{sage}\nL.~J. {Sage}.\n\\newblock The properties and origins of molecular gas in the lenticular\n galaxies {NGC} 404, 4710 and 5195.\n\\newblock {\\em Astron. Astrophys.}, 239:125--136, November 1990.\n\n\\bibitem{arpatlas}\nH.~{Arp}.\n\\newblock Atlas of peculiar galaxies.\n\\newblock {\\em Astrophys. J. Supp. Ser.}, 14:1--20, 1966.\n\n\\bibitem{Fritze98}\nU.~Fritze-v.Alvensleben and P.-A. Duc.\n\\newblock Tidal dwarf galaxies: Their present state and future evolution.\n\\newblock In {\\em The Magellanic Clouds and other Dwarf Galaxies, eds. J. M.\n Braun, T. Richtler Proceedings of Workshop of the Graduiertenkolleg\n Bonn-Bochum, Bad Honnef (Jan. 18-22, 1998)}, 1998.\n\n\\end{thebibliography}\n"
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astro-ph0002178
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There have been great and rapid progresses in the field of $\gamma$-ray bursts (denoted as GRBs) since BeppoSAX and other telescopes discovered their afterglows in 1997. Here, we will first give a brief review on the observational facts of GRBs and direct understanding from these facts, which lead to the standard fireball model. The dynamical evolution of the fireball is discussed, especially a generic model is proposed to describe the whole dynamical evolution of GRB remnant from highly radiative to adiabatic, and from ultra-relativistic to non-relativistic phase. Then, Various deviations from the standard model are discussed to give new information about GRBs and their environment. In order to relax the energy crisis, the beaming effects and their possible observational evidences are also discussed in GRB's radiations.
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"name": "astro-ph0002178.tex",
"string": "\\documentstyle[11pt]{article}\n\\parskip=1mm\n\\parindent=8mm\n\\textwidth=165mm\n\\textheight=235mm\n\\topmargin=-20mm\n\\oddsidemargin=0mm\n%\\mathindent=0mm\n\n\n\\begin{document}\n\n\\baselineskip=4.5mm\n\n\\vspace*{25mm}\n\\begin{center}\n{\\bf \\Huge What do $\\gamma$-ray bursts look like?}\\footnote[1]{\\em Invited \ntalk, to appear in the Proceedings of the 1999 Pacific Rim Conference on \nStellar Astrophysics.}\n\\end{center}\n\\vspace{5mm}\n\\begin{center}\n{\\large \\bf T. Lu}\n\n\\vspace{2mm}\n{\\small Department of Astronomy, Nanjing University, Nanjing 210093, China}\n\\end{center}\n\n\\begin{abstract}\nThere have been great and rapid progresses in the field of $\\gamma$-ray\nbursts \n(denoted as GRBs) since BeppoSAX and other telescopes discovered their \nafterglows in 1997.\nHere, we will first give a brief review on the observational facts of \nGRBs and direct understanding from these facts, which lead to the standard \nfireball model. The dynamical evolution of the fireball is discussed,\nespecially\na generic model is proposed to describe the whole dynamical \nevolution of GRB remnant from highly radiative to adiabatic, and from \nultra-relativistic to non-relativistic phase. Then, Various deviations from\nthe \nstandard model are discussed to give new \ninformation about GRBs and their environment. In order to relax the energy\ncrisis, \nthe beaming effects and their possible observational evidences are also \ndiscussed in GRB's radiations. \n\\end{abstract}\n \n{\\bf Keywords:} $\\gamma$ ray: bursts - shock waves - ISM: jets and outflows\n\n\\section{Introduction} \n\n$\\gamma$-ray burst (or shortly, GRB) is an astronomical phenomenon of short \nduration enhancement of $\\gamma$-rays from cosmic space. It was discovered \nby R.W. Klebesadel et al. in 1967 and published in 1973. There have been more \nthan 2000 GRBs discovered now. If there are appropriate satellites in the\nsky, \npeople could discover one or two GRBs everyday in average. However, they \nare still among the most mysterious astronomical \nobjects even at present time (M\\'{e}sz\\'{a}ros 1999; Piran 1999a). The\ndifficulty encountered in this field lies in that GRBs occur at random,\npeople \ncan not prepare to observe\nin advance, they are too short in duration to be studied in detail, they were \nobserved only in $\\gamma$-ray band which has very low precision in\nlocalization \nand could not be identified or associated with other objects of known\ndistances. \nWithout the \nknowledge of distances, no serious studies could be made in astrophysics.\n\nIn early 1997, the Italian-Dutch Satellite, BeppoSAX, brought the great\nbreak-through by rapid and accurate GRB localization and thus provided a \nsmall arcmin (or even smaller) error box. With so small an error box, \nit identified an X-ray counter-part (now known as X-ray afterglow) \nof GRB970228 even 8 hours after the $\\gamma$-ray trigger (Costa et al. 1997). \nSeveral hours later, its optical afterglow was also observed \n(Groot et al. 1997; van Paradijs et al. 1997).\nSince then, BeppoSAX has observed more than 20 GRBs, of which almost all \nexhibited X-ray afterglows. Based on the precise localization, many \ntelescopes observed about a dozen optical afterglows and about ten radio \nafterglows. Up to now, people have observed host galaxies of more than \nten GRBs with large red-shifts, showing them definitely at cosmological \ndistances. These great discoveries lead to rapid developments. A lot of \nquestions have now been clarified. However, compared with GRB itself,\nafterglow \nappears to be simpler and has been known much better. In contrast, the GRB \nitself, especially its energy source and origin, still keeps to be mysterious.\n\nThe main observational facts of GRBs are as follows (Piran 1999a):\n\n \n{\\bf Temporal properties:}\n The GRB duration ($T$) is very short, usually only a \nfew seconds or tens of seconds, or occasionally as long as a few tens of\nminutes\nor as short as a few milli-seconds. Their time profiles are diverse, some\nmay be \nsimply shaped, others complicated, multi-peaked. There seems to be a roughly \nbimodal distribution of long bursts of $T \\geq 2$ s and short bursts \nof $T \\leq 2$ s. The time scales of variability \n($\\delta T$), especially their rising time, may be as short as only\nmilli-seconds or \neven sub-milli-seconds. Typically, $\\delta T \\sim 10^{-2} T$.\n\n{\\bf Spectral properties:}\nThe photon energy radiated in GRB is typically in the range of tens \nkeV to a few MeV. However, high energy tail up to GeV or even higher than\n10 GeV \ndoes exist. The spectra are definitely non-thermal and can usually be fitted \nby power law $N(E)dE \\propto E^{-\\alpha} dE$ (or break power law) with \nindex $\\alpha$ within about $1.8$ to $2.0$. The $\\gamma$-ray fluences \nare typically in the range of $(0.1 - 10) \\times 10^{-6}$ ergs/cm$^{2}$.\n\n{\\bf Spatial distribution:} After the launch of the CGRO (Compton Gamma-Ray \nObservatory) Satellite in 1991, the Burst and Transient Source Experiment\n(BATSE) \nshowed clearly that the spatial \ndistribution of GRB sources is highly isotropic with almost zero dipole and\nquadrupole components (Meegan et al. 1992). This distribution favors GRBs\nat cosmological \ndistances at least statistically. However, GRBs at extended dark halo of our \nGalaxy could also explain this feature. This led to a great debate between \nGalactic origin and cosmological origin. \n\n{\\bf Afterglows:} Afterglows are counterparts of GRBs at wave bands other\nthan \n$\\gamma$-rays, may be in X-ray, optical, or even radio bands. They are\nvariable, \ntypically decaying according to power laws: $F_{\\nu} \\propto t^{-\\alpha}$ \n($\\nu=$ X, optical, ......) with $\\alpha = 1.1 - 1.6$ for X-ray, $\\alpha \n= 1.1 - 2.1$ for optical band. X-ray afterglows can last days or even weeks; \noptical afterglows and radio afterglows months. The most important discovery \nis that many \nafterglows show their host galaxies being definitely at cosmological\ndistances \n(with large red-shifts up to $Z=3.4$ or even 5). Thus, the debate is \nsettled down, GRBs are at cosmological distances, they should be the most \nenergetic events ever known since the Big Bang.\n\n\\section{The Standard Fireball Shock Model}\n\n{\\bf Stellar level event:} The variability time scale is usually very\nshort. Let \n$\\delta T \\sim {\\rm ms}$, then, the space scale of the initial source, \n$R_{\\rm i} <c\\delta T \\sim 3 \\times 10^{2} {\\rm km}$. Hence, even for black\nhole, \nconsidering $R = 2{\\rm G}M/c^{2}$, we have \n$M \\leq \\frac{{\\rm c}^{3}\\delta T}{2{\\rm G}} \\sim 10^{2}$~M$_{\\odot}$. If the \nburster is not a black hole, its mass should be much smaller. Thus, we can\nconclude \nthat the GRB should be \n{\\bf a stellar phenomenon} and the burster should be {\\bf a compact \nstellar object} which may be related with neutron star (or strange star) or \nstellar black hole. \n\n{\\bf Fireball:} From the measured fluence $F$ and the measured distance $D$, \nif emission is \nisotropic, we can calculate the total radiated energy to be $E_{0} = F(4\\pi \nD^{2})\\approx 10^{51}(F/(10^{-6}{\\rm ergs/cm}^{2}))(D/(3{\\rm Gpc}))^{2}$.\nThus, \nvery large energy ($10^{51}$ ergs) is initially contained in a small volume\nof \n$(4/3)\\pi R_{i}^{3} \\sim 1 \\times 10^{23}$ cm$^{3}$. This should be\ninevitably \na fireball, of which the optical depth for \n$\\gamma \\gamma \\longrightarrow {\\rm e}^{+} {\\rm e}^{-}$,\n$\\tau_{\\gamma\\gamma}$, \nis very large. Consider a typical burst with an observed fluence \n$F$, at a distance $D$, with a temporal variability time scale \n$\\delta T$, its average optical depth can be written as: \n\\begin{equation}\n\\tau_{\\gamma\\gamma} = \\frac{f_{\\rm p} \\sigma_{\\rm T} F D^{2}}{R_{\\rm i}^{2}\nm_{\\rm e} c^2}\n\\sim 10^{17} f_{\\rm p}\n\\bigg(\\frac{F}{10^{-6} {\\rm ergs/cm^2}}\\bigg)\n\\bigg(\\frac{D}{3~{\\rm Gpc}}\\bigg)^2\n\\bigg(\\frac{\\delta T}{1~{\\rm ms}}\\bigg)^{-2}, \n\\end{equation}\nwhere $f_{\\rm p}$ denotes the fraction of photon pairs \nsatisfying $\\sqrt{E_1 E_2} > $m$_{\\rm e}$ c$^2$. \n\nFor so large an optical depth, there seem to appear two serious difficulties. \nFirst, the radiation in an optically thick case should be thermal, while \nthe observed radiation is definitely non-thermal. Second, high energy \nphotons should be easily converted into ${\\rm e}^{+} {\\rm e}^{-}$ pairs, \nwhile the observed high energy tail indicates that \nthis convertion has not happened. However, it is very interesting to note \nthat just such a large optical depth paves the way to solve both of them.\n\n{\\bf Compactness problem:} In fact, the luminosity of the thermal \nradiation, according to the \nStefan-Boltzmann law, should be proportional to the surface of the \nfireball which is initially so small that the thermal radiation can not \nbe observed. However, just due to the large optical depth, the radiation \npressure should be very high and could accelerate the fireball expansion \nto become ultra-relativistic with a large Lorentz factor $\\gamma$. After \nexpanding to a large enough distance, it may be getting optically thin.\nAt this time, the non-thermal $\\gamma$-ray bursts can be observed. Does \nsuch a large distance contradict the compactness relation \n$R_{\\rm i} \\le {\\rm c} \\delta T$ compared with the \nmilli-second variabilities? To answer this question, let us first \nnote that this relation holds only for non-relativistic (rest) \nobject with $R_{\\rm i}$ denoting its space scale. For an\nultra-relativistically \nexpanding fireball, the compactness relation should be relaxed to \n\\begin{equation}\nR_{\\rm e} \\le \\gamma^{2} {\\rm c} \\delta T,\n\\end{equation}\nhere $R_{\\rm e}$ is the space scale of the expanding fireball with Lorentz \nfactor $\\gamma$. Considering two photons we observed at two different times \napart by $\\delta T$, as the emitting region is moving towards the observer \nwith a Lorentz factor $\\gamma \\gg 1$, the second photon\nshould be emitted at a far nearer place than the first one. This gives \neffectively short time variabilities and leads to the additional factor \n$\\gamma^{2}$ appearing in the above compactness relation.\n\nThe factor $f_{\\rm p}$ in the optical depth $\\tau_{\\gamma\\gamma}$ also \nsensitively depends on the ultra-relativistic expansion of the fireball. \nAs for this case, the observed photons are blue-shifted, in the comoving \nframe, their energy \nshould be lower by a factor of $\\gamma$, and fewer photons will have \nsufficient energy to produce pairs. This gives a factor depending \non spectral index $\\alpha$, namely a factor of $\\gamma^{2\\alpha}$ in \n$\\tau_{\\gamma\\gamma}$. \n\n{\\bf Ultra-relativistic expansion:} Therefore, the optical \ndepth $\\tau_{\\gamma\\gamma}$ will decrease by a \nfactor of $\\gamma^{4+2\\alpha}$ \nfor the ultra-relativistically expanding fireball (Goodman 1986; \nPaczy\\'{n}ski 1986; Piran 1999a; Krolik \\& Pier 1991):\n\\begin{equation}\n\\tau_{\\gamma\\gamma} =\n{f_{\\rm p} \\over \\gamma ^{2 \\alpha}} {{\\sigma_{\\rm T} F D^2} \n \\over {R_{\\rm e}^2 {\\rm m}_{\\rm e} {\\rm c}^2}}\n\\approx {10^{17} \\over \\gamma ^{(4+2\\alpha)}}\nf_{\\rm p}\n\\bigg({ F \\over 10^{-6} {\\rm ergs/cm^2}} \\bigg)\n\\bigg({ D \\over 3~{\\rm Gpc}}\\bigg)^2\n\\bigg({ \\delta T \\over 1~{\\rm ms}} \\bigg)^{-2}.\n\\end{equation}\nNote, the spectral index $\\alpha$ is approximately 2, we will have \n$\\tau_{\\gamma\\gamma} < 1$ for $\\gamma > 10^{17/(4+2\\alpha)} \\sim 10^{2}$. \nThus, in order for the fireball to become optically thin, as required by \nthe observed non-thermal spectra of $\\gamma$-ray bursts, its expanding \nspeed should be ultra-relativistic with Lorentz factor \n\\[\\gamma > \\sim 10^{2}.\\]\nThis is a very important character for GRBs, which \nlimits the baryonic mass contained in the fireball seriously. If the initial\nenergy is $E_{0}$, then the baryonic mass $M$ should be less than \n\\begin{equation}\nE_{0}/({\\rm c}^{2}\\gamma) \\le 10^{-5}{\\rm M}_{\\odot} (E_{0} / (2\\times\n10^{51} {\\rm ergs})),\n\\end{equation}\notherwise, the initial energy can not be converted to the kinetic energy of \nthe bulk motion of baryons with such a high Lorentz factor. Most models\nrelated \nwith neutron stars contain baryonic mass much higher than this limit. This is \nthe famous problem named as ``baryon contamination''.\n\nIt is worthwhile to note that this very condition $\\gamma > \\sim 10^{2}$ can\nalso explain the existence of the high energy tail in the GRB spectra, as the \nobserved high energy\nphotons should be only low energy photons in the frame of emitting region,\nthey\nare not energetic enough to be converted into ${\\rm e}^{+}{\\rm e}^{-}$ pairs.\n\n{\\bf Internal-external shock:} What is the radiation mechanism in the\nfireball \nmodel? The fireball \nexpansion has successfully made a conversion of the initial internal energy \ninto the bulk kinetic energy of the expanding ejecta. However, this is the \nkinetic energy of the associated protons, not the photons. We should have \nanother mechanism to produce radiation, otherwise, even after the fireball \nbecoming optically thin, the $\\gamma$-ray bursts can not be observed. \nFortunately, the shocks described below can do such a job. \n\nThe fireball can be regarded as roughly homogeneous in its local rest frame, \nbut due to the Lorentz contraction, it looks like a shell (ejecta) with \nwidth of the initial size of the fireball. As the shell collides with \ninter-stellar medium (ISM), shocks will be \nproduced (Rees \\& M\\'{e}sz\\'{a}ros 1992; Katz, J., 1994; \nSari \\& Piran 1995; Mitra 1998). This is usually \ncalled as external shocks. Relativistic electrons that have been \naccelerated in the relativistic shocks will usually emit synchrotron \nradiation. As the amount of swept-up interstellar matter getting larger \nand larger, the shell will be decelerated and radiation of longer wave \nlength will be emitted. Thus, an external shock can produce only smoothly \nvarying time-dependent emission, not the spiky multi-peaked structure \nfound in many GRBs. If the central energy source is not completely \nimpulsive, but works intermittently, it can produce many shells (or \nmany fireballs) with different Lorentz factors. Late but faster shells \ncan catch up and collide with early slower ones, and then, shocks \n(internal shocks) thus produced will lead to the observed bursting \n$\\gamma$-ray emission (Rees \\& M\\'{e}sz\\'{a}ros 1994; \nPaczy\\'{n}ski \\& Xu 1994). This \nis the so called external-internal shock model, \ninternal shocks give rise to $\\gamma$-ray bursts and external shocks to \nafterglows. The internal shocks can only convert a part of their energies \nto the $\\gamma$-ray bursts, other part remains later to interact with the \ninterstellar medium and lead to afterglows. Typically, the GRB is produced \nat a large distance of about 10$^{13}$ cm to the center, such a large \ndistance is allowed according to the relaxed compactness relation \n$R_{\\rm e} \\le \\gamma^{2} {\\rm c} \\delta T$, while its afterglows are\nproduced at \nabout 10$^{16}$ cm or even much farther. This internal-external shock \nscenario, under the simplified assumptions of uniform \nenvironment with typical ISM number density of $n \\sim 1 {\\rm cm^{-3}}$, \nisotropic emission of synchrotron radiation and only impulsive energy \ninjection, is known as the standard model. \n\n{\\bf Spectra of afterglows:} The instantaneous spectra of afterglows,\naccording \nto this model, can be \nwritten as $F_{\\nu} \\propto \\nu^{\\beta}$, with different $\\beta$ for \ndifferent range of frequency $\\nu$ (Sari et al. 1998; Piran 1999b). Let \n$\\nu_{sa}$ be the self absorption frequency, for which the optical depth \n$\\tau(\\nu_{sa})=1$. For $\\nu < \\nu_{sa}$, we have the Wien's law: \n$\\beta=2$. For $\\nu_{sa} < \\nu < \\min~(\\nu_{\\rm m},\\nu_{\\rm c})$, we \ncan use the low energy synchrotron tail, $\\beta=-1/3$. Here \n$\\nu_{\\rm m}$ is the synchrotron frequency of an electron with \ncharacteristic energy, $\\nu_{\\rm c}$ is the cooling frequency, namely \nthe synchrotron frequency of an electron that cools during the local \nhydrodynamic time scale. For frequency within $\\nu_{\\rm m}$ and \n$\\nu_{\\rm c}$, we have $\\beta = -1/2$ for fast cooling \n($\\nu_{\\rm c} < \\nu_{\\rm m}$) and $\\beta=-(p-1)/2$ for slow cooling \n($\\nu_{\\rm m} < \\nu_{\\rm c}$). For $\\nu > \\max(\\nu_{\\rm m},\\nu_{\\rm c})$, \nwe have $-p/2$. Here, $p$ is the spectral index of the emitting \nelectrons: $N(E)\\propto E^{-p}$.\n\n\\section{Dynamical Evolution of the Fireball}\n\nDuring the $\\gamma$-ray bursting phase and the early stage of afterglows,\nthe fireball expansion is initially ultra-relativistic and highly \nradiative, but finally it would be getting into non-relativistic and\nadiabatic, \na unified dynamical evolution should match all these phases. In fact, the \ninitial ultra-relativistic phase has been well described by some simple\nscaling \nlaws (M\\'{e}sz\\'{a}ros \\& Rees 1997a; Vietri 1997; Waxman 1997; Wijers et\nal. 1997), \nwhile the final \nnon-relativistic and adiabatic phase should obey the Sedov (1969) rule, \nwhich has well been studied in Newtonian approximation. The key equation\n(Blandford \\& McKee 1976; Chiang \\& Dermer 1999) is\n\\begin{equation}\n\\frac{{\\rm d}\\gamma}{{\\rm d}m} = -\\frac{\\gamma^{2}-1}{M},\n\\end{equation}\nhere $m$ denotes the rest mass of the swept-up medium, $\\gamma$ the bulk\nLorentz \nfactor, and $M$ the total mass in the co-moving frame including internal\nenergy $U$. \nThis equation was originally derived under the ultra-relativistic\ncondition. The \nwidely accepted results derived under this equation are correct for \nultra-relativistic expansion. Accidentally, these results are also suitable\nfor the \nnon-relativistic and radiative case. However, for the non-relativistic and \nadiabatic case, they will lead to wrong result ``$v \\propto R^{-3}$'' ($v$\nis the \nvelocity), while the correct Sedov result should be ``$v \\propto R^{-3/2}$'', \nas first pointed out by Huang, Dai and Lu (1999a,b).\n\nIt has been proved (Huang, Dai \\& Lu 1999a,b) that in the general case, \nthe above equation should be replaced by \n\\begin{equation}\n\\frac{{\\rm d}\\gamma}{{\\rm d}m} = -\\frac{\\gamma^{2}-1}{M_{ej} + \\epsilon m \n+ 2(1-\\epsilon)\\gamma m},\n\\end{equation}\nhere $M_{ej}$ is the mass ejected from GRB central engine, $\\epsilon$ is the \nradiated fraction of the shock generated thermal energy in the co-moving \nframe. The above equation will lead to correct results for all cases \nincluding the Sedov limit. This generic model is suitable for both \nultra-relativistic and non-relativistic, and both radiative and adiabatic \nfireballs. As proved by Huang et al. (1998a,b), Wei \\& Lu (1998a) and \nDai et al. (1999a), \nonly several days after the burst, a fireball will usually become \nnon-relativistic and adiabatic, while the afterglows can last some months, \nthe above generic model is really useful and important.\n\n\\section{Comparison and Association of GRB with SN}\n\nSupernova was known as the most energetic phenomenon at the stellar level. \nSN explosion is the final violent event in the stellar evolution. \nDynamically, it can also be described as a fireball, which however expands \nnon-relativistically. After the SN explosion, there is usually a remnant\nwhich \ncan shine for more than thousands of years and be well described\ndynamically by \nSedov model (Sedov 1969).\n\nGRB is also a phenomenon at the stellar level. However, it is much more \nenergetic and much more violent than SN explosion! It has been proved to \nbe described \nas a fireball, which expands ultra-relativistically. The GRB may also leave\na remnant which shines for months now known as afterglow. \n\nTheir comparison is given in Table I:\n\\begin{center}\n\\begin{tabular}{|l|l|l|}\n\\multicolumn{3}{c}{Table I} \\\\ \\hline\n & GRBs & SNs \\\\ \\hline\n {\\bf Burst} & {\\bf Bursting $\\gamma$-rays} & {\\bf SN explosion} \\\\\n\\hline \n Energy up to & 10$^{54}$ ergs & $10^{51}$ ergs \\\\\n Time Scale & 10 sec & Months \\\\\n Profile & irregular & smooth \\\\\n Wave Band & $\\gamma$-ray & Optical \\\\ \\hline\n{\\bf Relic} & {\\bf Afterglow} & {\\bf Remnant} \\\\ \\hline\nTime Scale & Months & 10$^{3}$ Years \\\\\nWave Band & Multi-band & Multi-band \\\\ \\hline\n{\\bf Understanding} & & \\\\ \\hline\nFireball Expansion & Ultra-relativistic & Non-relativistic \\\\\nMechanism & ??? & Stellar Core Collapse \\\\\nKey Process & ??? & Neutrino process \\\\ \\hline\n\\end{tabular}\n\\end{center}\n\nIn April 1998, a SN 1998bw was found to be in the 8' error circle of the X-ray\nafterglow of GRB 980425 (Galama et al. 1998; Kulkarni et al. 1998). However, \nits host galaxy is at a red-shift z=0.0085 (Tinney et al. 1998), indicating a \ndistance of 38 Mpc (for $H_{0} = 65$ km s$^{-1}$ Mpc$^{-1}$), which leads the \nenergy of the GRB to be too low, only about \n$5 \\times 10^{47}$ ergs, 4 orders of magnitude lower than normal GRB. \n\nLater, in the light curves of GRB 980326 (Bloom et al. 1999; \nCastro-Tirado \\& Gorosabel 1999b) and GRB 970228 (Reichart 1999; \nGalama et al. 1999b), some evidence related with SN was found. This is \na very important question worth while to study further (see e.g. Wheeler \n1999). These two violent phenomena, GRB and SN, might be closely related. \nThey might be just two steps of one single event (Woosley et al. 1999; \nCheng \\& Dai 1999; Wang et al. 1999b; Dai 1999d). It is interesting to \nnote that the first step might provide a low baryon environment for \nthe second step to produce GRB. Such a kind of models can give a way \nto avoid the baryon contamination.\n\n\\section{Inner Engine and Energetics}\n\nThere have been a lot of models proposed to explain the central engine of\nGRBs \n(see e.g. Castro-Tirado 1999a; Piran 1999a; Cheng \\& Dai 1996; \nDai \\& Lu 1998b). \nAll these objects are related with compact stars such as neutron star (NS), \nstrange star (SS), black hole (BH) etc. For example, binary mergers (NS-NS, \nNS-BH, ...), massive star collapsing, phase transitions (NS to SS) and others \nhave been proposed. To build a successful model for central engine, the most \ndifficult task is to solve the baryon contamination. There seem to be three \nkinds of ways: 1) based on BH, which can swallow baryons; 2) based on SS, of \nwhich baryons are only contained in its crust with mass less than \n$10^{-5}$ M$_{\\odot}$; 3) based on the two-step process pointed out in \nabove section.\n\nA system of a central BH with a debris torus rotating round it may form after \ncompact star merging or massive star collapsing. In this system, two kinds of \nenergies can be used: the rotational energy of the BH and the gravitational \nenergy of the torus. The rotational energy of the BH can be extracted via the \nB-Z (Blandford \\& Znajek 1977) mechanism (M\\'{e}sz\\'{a}ros \\& Rees 1997b;\nPaczy\\'{n}ski 1998). For \na maximally rotating BH, its rotational energy can be extracted up to 29\\% of \nthe BH rest mass, while the gravitational binding energy of the torus can be \nextracted up to 42\\% of the torus rest mass. Lee, Wijers and Brown (1999) \nrecently studied the possibility to use these mechanisms in producing GRB. \n\nThe phase transition from neutron star to strange star can release huge\nenergy \nto account for GRB. As an estimate, we can reasonably assume that about 20-30 \nMeV is released per baryon during the phase transition. Total energy released \nthis way can be up to about $(4-6) \\times 10^{52}$ ergs. Strange star is the \nstellar object in the quark level. Whether it exists or not is a fundamental \nphysical/astrophysical problem. Its main part is a quark core with large \nstrangeness (known as strange core). There could be a thin crust with mass of \nonly about $\\sim (10^{-6} - 10^{-5})$M$_{\\odot}$ (Alcock et al. 1986; Huang\n\\& Lu \n1997a,b; Lu 1997; Cheng et al. 1998), all baryons are contained in the crust. \nIt is interesting to note that this baryonic mass is low enough to\navoid the baryon contamination. Klu\\'{z}niak and Ruderman (1998) proposed \ndifferentially rotating neutron stars as an origin of GRBs. Dai and Lu\n(1998b) \nused this mechanism to the case of differentially rotating strange stars and \nproposed a possible model for GRB without baryon contamination.\n\n\\section{New Information Implied by the Deviations from the Standard Model}\n\nThe standard model described above is rather successful in that its physical \npicture is very clear, it gives results very simple, and observations on GRB\nafterglows support it at least qualitatively but generally. However, various \nquantitative deviations have been found. They indicate that the \nsimplifications made in the standard model should be improved. These \ndeviations may reveal important new information, such as non-uniform \nenvironment, additional energy injection, beaming effects of radiation \nand others.\n\n{\\bf Wind environment effects:} Dai and Lu (1998c) analysed the afterglows \nof GRB970616 and others. They \nstudied the general case of $n \\propto R^{-k}$ for the non-uniform\nenvironment \ndensity (here $n$ is the number density of the environment medium) and \nfound that the X-ray afterglow of GRB970616 can well be fitted by $k = 2$, \nand pointed out that this non-uniformity may be due to the existence of \na stellar wind. After the detailed studies by Chevalier \\& Li (1999a,b), the \nstellar wind model has become widely interested. People are aware that it may \ncontain many implications about the pregenitors of GRBs and provide\nstrong support to their massive star origin.\n\n{\\bf Additional energy injection:} The optical afterglows of GRB 970228 and \nGRB 970508 had some complexities, \nshowing down-up-down variation in their light curves. These features can be \nexplained by long time scale energy injection from their central engines \n(Dai \\& Lu 1998a,b; Rees \\& M\\'{e}sz\\'{a}ros 1998; Panaitescu et al. 1998). \nFor example, a milli-second pulsar with \nsuper-strong magnetic field can be produced at birth of GRB. As the \nfireball expands, the central pulsar can continuously \nsupply energy through magnetic dipole radiation. Initially, the energy \nsupply is small enough, the afterglow shows declining. As it becomes \nimportant, the afterglow shows rising. However, the magnetic dipole \nradiation should itself attenuate later. Thus, the down-up-down shape \nwould appear naturally. Dai and Lu (1999c) analysed GRB 980519, 990510 \nand 980326, and obtained the results agreeing well with observations.\n\n{\\bf Additional radiations:} Though the synchrotron radiation is \nusually thought to be the main radiation mechanism, \nhowever, under some circumstances, the inverse Compton scattering may play an \nimportant role in the emission spectrum, and this may influence the temporal \nproperties of GRB afterglows (Wei \\& Lu 1998a,b).\n\nLater data in the afterglows of GRB 970228 (Reichart 1999; \nGalama et al. 1999b) and 980326 (Bloom et al. 1999; Castro-Tirado \\& \nGorosabel 1999b) may show the deviations as additional contributions\nfrom supernovae.\n\n{\\bf Beaming effects:} \nGRB 990123 has been found very strong in its \n$\\gamma$-ray emission, and the red \nshift of its host galaxy is very large (z=1.6) (Kulkarni et al. 1999a; \nGalama et al. 1999a; Akerlof et al. 1999; Castro-Tirado, et al. 1999a; \nHjorth, et al. 1999; Andersen, et al. 1999). If its radiation is isotropic, \nthe radiation energy only in $\\gamma$-rays is already as high as \n$E_{\\gamma} \\sim 3.4 \\times 10^{54}$ ergs, closely equals two solar rest \nenergy ($E_{\\gamma} \\approx 2{\\rm M}_{\\odot}$c$^{2}$)! As the typical mass\nof the \nstellar object is in the order of $\\sim 1 {\\rm M}_{\\odot}$, while the\nradiation \nefficiency for the total energy converting into the $\\gamma$-ray emission \nis usually very low, such a high emission energy is very difficult to \nunderstand (Wang, Dai \\& Lu 1999a).\n\nA natural way to relax the energy crisis is to assume that the radiation of\nGRB \nis beaming, rather than isotropic. Denote the jet angle as $\\Omega$, \nthen the radiation energy $E$ will be reduced to $E\\Omega/4\\pi$. At the\nsame time, \nthe estimated burst rate should increase by a factor of $4\\pi/\\Omega$. Are \nthere any observational evidences for the jet in GRB and its afterglow? \nPugliese et al. (1999), Rhoads (1997, 1999), Sari et al. (1999) and \nWei \\& Lu (1999a,b) have discussed this question. \nKulkarni et al. (1999b) observed that two days after the burst, the\ndecaying was \ngetting more steepening, appearing as a break in the light curve of GRB\n990123, \nand they regarded this as the evidence for jet. Recently, Huang et al.\n(1999c) \ncalculated the influences of various parameters on the jetted emission of\nGRB, \nshowed that a break in the light curve may appear in the case of narrow jet\nand \nfor small electron energy fraction and small magnetic energy fraction. \n\n{\\bf Dense environment effects:} However, Dai and Lu (1999b) \npointed out that a shock undergoing the transition from a relativistic\nphase to \na non-relativistic phase may also show a break in the light curve, if there\nare \ndense media and/or clouds in the way, this break may happen earlier. This\nmodel \ncould also give an explanation for the observed steepening. Recently, \nWang et al. (1999c) proved that the dense environment model can also \nexplain well the radio afterglow of GRB 980519 (Frail et al. 1999). Thus, we \nshould study the break appearing in the light curve further to take both \nbeaming and dense environment effects into account. \n\n\\section{Conclusion}\n\nThe standard internal-external shock model, which is built under many \nsimplifications, has been proved to be well fitted by \nobservations qualitatively but generally. Based on the success of this \nmodel, it should be very important to study the deviations from the \nstandard model, which indicate that the simplifications should be \nrelaxed in some aspects. Hence, the deviations contain \nimportant new information and have been a fruitful research area. \n\nIn contrast to the rapid progress in understanding the nature of \nafterglows, GRB itself has not yet been clear. However, this is a very \nimportant problem. 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Lu (LU, Tan)\nDepartment of Astronomy\nNanjing University\nNanjing 210093\nP.R. China\nTel. 86-25-3592507\n"
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"name": "tangle9.tex",
"string": "%&latex209\n\\documentstyle[psfig,12pt]{article}\n\\textwidth 16.0cm \n\\textheight 23.0cm\n\\parindent 1.0cm\n\\topmargin 0in\n\\oddsidemargin 0in\n\\newcommand{\\eg}{{\\sl e.g.}}\n\\newcommand{\\ie}{{\\sl i.e.}}\n\\newcommand{\\cf}{{\\sl c.f.}}\n\\newcommand{\\etal}{{\\sl et al.}}\n\\newcommand{\\etc}{{\\sl et c.}}\n\\newcommand{\\rtidal}{$\\Re_{tidal}$}\n\\newcommand{\\oiiir}{$L_{[OIII]}$ vs. P$_{tot}$}\n\\newcommand{\\oiir}{$L_{[OII]}$ vs. P$_{tot}$}\n\\newcommand{\\ltae}{\\raisebox{-0.6ex}{$\\,\\stackrel\n{\\raisebox{-.2ex}{$\\textstyle <$}}{\\sim}\\,$}}\n\\newcommand{\\gtae}{\\raisebox{-0.6ex}{$\\,\\stackrel\n{\\raisebox{-.2ex}{$\\textstyle >$}}{\\sim}\\,$}}\n\n\n\\begin{document}\n\\noindent\n{\\Large\\bf Highly polarized structures in the near-nuclear regions \nof Cygnus~A: intrinsic anisotropy within the cones?}\n\\vglue 0.5cm\\noindent\n{\\bf C.N. Tadhunter$^{1}$, W. Sparks$^{2}$, D.J. Axon$^{3}$, L. Bergeron$^{2}$,\nN.J. Jackson$^{4}$, C. Packham$^{5}$, J.H. Hough$^{3}$, A. Robinson$^{3}$, \nS. Young$^{3}$}\n\\vglue 0.5cm\\noindent\n{\\small $^{1}$Department of Physics, University of Sheffield, Sheffield S3 7RH, UK \\\\\n$^{2}$Space Telescope Science Institute, 3700 San Martin Drive, Baltimore,\nMD 21218, USA \\\\\n$^{3}$Division of Physics and Astronomy, Department of Physical Sciences,\nUniversity of Hertfordshire, College Lane, Hatfield, Herts AL10 9AB, UK \\\\\n$^{4}$Nuffield Radio Astronomy Laboratory, Jodrell Bank, University\nof Manchester, UK \\\\\n$^{5}$Isaac Newton Group, Sea Level Office, Apartado de Correos,\n321, 38780 Santa Cruz de La Palma, Islas Canarias, Spain}\n\\vglue 0.5cm\\noindent\n{\\bf Abstract.}\nWe present near-IR imaging polarimetry observations of the nucleus of Cygnus~A,\ntaken with the NICMOS camera of the HST at a wavelength of 2.0$\\mu$m.\nThese maps reveal a highly collimated region of polarized emission\nstraddling the nucleus and extending to a radius of 1.2 arcseconds. Remarkably,\nthis feature coincides with one, but only one, limb of the edge-brightened\nbicone structure seen in the total intensity image. The\nhigh degree ($P_k \\sim 25$\\%) and orientation of the extended polarization feature are\nconsistent with a scattering origin. Most plausibly,\nthe detection of polarization along only one limb of the bicone is a consequence\nof {\\it intrinsic anisotropy} of the near-IR continuum within the radiation cones, with the direction of maximum intensity of the near-IR radiation field\nsignificantly displaced from the direction of the radio axis.\nThe unresolved nuclear core source\nis also highly polarized ($P_k > 28$\\%), with a position \nangle close to the perpendicular\nto the radio axis. Given that this high degree\nof nuclear polarization can only be explained\nin terms of dichroic extinction if the dichroic mechanism is\nunusually efficient in Cygnus~A, it is more likely that the nuclear\npolarization is due to the scattering of nuclear light in an unresolved\nscattering region close to the AGN. In this case, the flux of the core\nsource in the K-band is dominated by scattered rather than transmitted quasar light, and\nprevious extinction estimates based on K-band photometry of the core \nsubstantially underestimate the true nuclear extinction.\n\n\\section{Introduction}\n\nAs yet, little is known about the structure of the inner regions of\npowerful radio galaxies and the impact of the activity on \ncircumnuclear regions.\nThe high resolution and sensitivity afforded by\nimaging observations using the Hubble Space Telescope (HST) has revealed\na wealth of complex structures in such objects, with dust lanes, jets\nand large regions of scattered emission from hidden nuclei. One of\nthe key targets in studies which aim to elucidate the interplay between active\nnuclei and their host galaxies, and between galactic activity of\ndifferent types, is the archetypal powerful radio galaxy Cygnus~A\n(see Carilli \\& Barthel 1996 for a review).\n%As part of a detailed ongoing study\n%of this object, \n%here we present\n%infrared imaging polarization\n%observations centered at $\\approx 2.0\\mu$m,\n%obtained for Cygnus~A using the\n%Near Infrared Camera and MultiObject Spectrometer (NICMOS) on-board HST.\n\nHST infrared imaging observations of Cygnus~A by Tadhunter \\etal\\ (1999) \nrevealed an edge-brightened \nbi-conical \nstructure centred on the nuclear point source, which is\nstrikingly similar to those observed around young stellar objects. The \nedge-brightening of this structure provides evidence that the bicone \nis defined as much by outflows in the nuclear regions \nas by the polar diagram of the illuminating quasar radiation field.\nThe HST observations also show an unresolved nuclear source at 2.0 and 2.25$\\mu$m. However, from the imaging observations alone it is unclear\nwhether this unresolved source represents the highly extinguished quasar nucleus\nseen directly through the obscuring torus, or emission from a \nless-highly-extinguished extended region around the nucleus. \n%A further\n%implication of the NICMOS images is that not all of the anisotropy in the %nuclear\n%radiation field is caused by extinction on a scale $<$100 pc in the torus; some %of the \n%anisotropy must \n%be generated by absorption and \n%scattering in the dust lane on a 1kpc scale.\n\nNear-IR polarization observations have the potential to remove the uncertainties surrounding\nthe nature of the unresolved nuclear sources and, in addition, to provide \nfurther important\ninformation about the obscuration and anisotropy in the near-nuclear regions\nof powerful radio galaxies. Previous ground-based polarimetric\nobservations of Cygnus~A by \nPackham \\etal\\ (1998) demonstrate that the nuclear regions are highly polarized\nin the K-band, with a measured polarization of $P_k \\sim 4$\\% for\na 1 arcsecond diameter aperture centred on the compact IR nucleus. However, the \nresolution of the ground-based observations is insufficient to resolve the\nstructures and determine the polarization mechanism unambiguously.\nIn this letter we present new diffraction-limited infrared imaging \npolarimetry observations\nof Cygnus~A made with the Near Infrared Imaging Camera and Multi-Object\nSpectrometer (NICMOS: MacKenty \\etal\\ 1997) on the HST. \nThese observations resolve the polarized structures, and raise new\nquestions about the nature of the anisotropy in the near-nuclear regions\nof this key source.\n\n\n\n\\section{Observations and data reduction}\n\nNICMOS Camera 2 `long wavelength' infrared imaging polarization observations were taken December 1997 and August 1998, giving a pixel scale of 0.075 arcseconds and\na total field of 19.4$\\times$19.4 arcseconds. \nThe NICMOS polarizers are self-contained spectral elements, with the three long\nwavelength polarizers effective from $\\lambda \\approx 1.9$---$2.1\\mu$m, resulting\nin an effective central wavelength of $\\approx 2.0\\mu$m\n(MacKenty \\etal\\ 1997).\nThe polarizers are oriented at approximately 60$^{\\circ}$ intervals and have\ncharacteristics as presented by Hines (1998).\nEach exposure\nconsisted of a number of non-destructive reads of the detector which were\noptimally combined in the reduction software to remove cosmic rays.\nRegular chops were made to offset fields in order to\nfacilitate accurate background subtraction. \nThe total integration time was 2400 seconds per polarizer.\n\nThe reduction of the data used standard IRAF/STSDAS pipeline processing\ntogether with pedestal removal as given by\nvan de Marel (1998).\nThe three final, clean polarization images were combined following the\nprescription of Sparks \\& Axon (1999), using the pipeline produced\nvariance data. The output data comprised a set of images containing\neach of the Stokes parameters $I, Q, U$, their variances and covariances,\na debiassed estimate of the polarization intensity and polarization\ndegree using the method of Serkowski (1958), and also position angle and\nuncertainty estimates on each of those images, as described in detail\nin Sparks \\& Axon (1999).\n\nThe two epochs of observation were acquired with different instrumental\norientation, and were analysed independently to provide a robust check\non our estimated uncertainties and on the possibility of systematic errors.\nA variety of spatial resolutions were used, from full \ndiffraction-limited NICMOS resolution down to $\\approx 1$ arcsec \nby smoothing the\ninput three images prior to polarization analysis.\nBoth epochs were fully consistent within the estimated statistical errors,\nimplying that there are no significant sources of systematic uncertainty.\nMeasurements of several Galactic stars in the field of Cygnus~A give 2.0$\\mu$m\npolarizations of $P_{2.0\\mu m} < 2.0$\\% for 5 pixel diameter apertures. This\ncan be regarded as an upper limit on the level of systematic error in estimates\nof P. The typical statistical uncertainties for the most highly polarized\nregions measured in our full resolution images are $\\pm$1.5\\% for $P$, and $\\pm$3$^{\\circ}$\nfor the polarization angle.\nIn the following, we will present the data for the December\n1997 observations only, since these have a higher S/N \nas a consequence of longer exposure\ntimes.\n\n \n\n\n\\section{Results}\n\n\nFigure 1 shows the first epoch polarization results.\nAs expected, the total intensity image (Stokes $I$) is very similar\nto the direct images published previously by Tadhunter \\etal\\ (1999).\nIn particular, it shows\nan apparent edge-brightened, reasonably symmetric, bi-conical structure centred on the nucleus\nwith an \nopening\nangle of 116 degrees and whose axis is closely aligned \nwith the large scale radio\njet.\n\nThe image of polarized intensity, however, reveals\nintriguing differences compared to total intensity.\nThe only regions of strongly polarized\nemission (apart from the nucleus discussed below) are confined\nto a quasi-linear structure running along the NW-SE limb of the\nbi-conical structure. This feature shows approximate reflection symmetry\nabout the nucleus, as opposed to the axial symmetry about the\nradio axis in the total\nintensity image.\nThe brightness ratio of the two limbs of the cone to the east\nof the nucleus is approximately\n2:1 in total intensity image, while in polarized intensity image it is\n$>$12:1. Note that the polarization structure\nvisible in our 2.0$\\mu$m image is strikingly different from that of\nthe optical V- and B-band polarization images (Tadhunter \\etal\\ 1990, \nOgle \\etal\\ 1997), in which the\npolarized emission appears uniformly distributed across the\nkpc-scale ionization cones and shows no clear preference for the\nNW-SE limb of the bi-cone. \n\nTypical {\\it measured} degrees of polarization\nare in excess of $10$\\%\\, up to a maximum of $\\approx$25\\%\nin the polarized region to the south east of the nucleus. However, \nthese measures underestimate the true degree of {\\it intrinsic}\npolarization in the extended structures, because starlight from the host\ngalaxy makes a substantial contribution to the total flux. For example, using\nthe azimuthal intensity profile measured in annulus with inner radius 4 pixels\nand outer radius 12 pixels,\nwe estimate that the diffuse starlight from the host galaxy contributes\n50 - 70\\% of the total flux in the south east arm of the bicone. Assuming that\nthe starlight is unpolarized, the degree of intrinsic polarization in\nthe south east arm is $P_{2.0\\mu m}^{intr} \\sim$50 -- 70\\%. Such high degrees of measured\nand intrinsic IR polarization are unprecedented in observations of active galaxies\nin which the synchrotron emitting jets are not observed directly at infrared\nwavelengths. \n%\n% Is this last sentence true?? \n%\n\n\n%Particularly the linear feature to the SE of the nucleus, is highly\n%polarized at a level of several tens of percent. Thus it is likely that the bi-cone \n%represents an illuminated structure --- an inner reflection nebulosity. \n%Further support for the idea \n%that\n%the bicone is dominated by reflected continuum light at infrared wavelengths is provided by \n%the\n%fact that the structure is visible in filters (e.g. F160W) which do not suffer substantial\n%emission line contamination. \n%In addition to the reflected nuclear light, it is likely that there\n%is a significant contribution to the bi-cone\n%emission from Pa$\\alpha$ emitted by\n%photoionized regions in the illuminated structures (Pa$\\alpha$ falls within the bandpass\n%of the polarization filters).\n\n\\subsection{The nucleus}\n\nThe nuclear point source, discussed in detail by Tadhunter \\etal\\ (1999),\nis also highly polarized. In the polarized intensity image the main nuclear\ncomponent\nappears unresolved ($FWHM = 2.24$ pixels) and its position agrees\nwith that of the nucleus in the total intensity image to within 0.5 pixels (0.04 arcseconds).\nThus, it appears likely that the bulk of the polarization is associated with the compact\nnucleus rather than a more extended region around the nucleus. The core\ndoes, however, show a faint entension to the NW in the polarized intensity image.\nThis extension is aligned with the larger scale polarization\nstructures, and its polarization E-vector is close to perpendicular to the radius vector from the nucleus.\n\nFrom our full resolution polarization images, the measured\ndegree of polarization at the peak flux of the nuclear point \nsource is $P_{2.0\\mu m}^{m} \\sim 20$\\%.\nHowever, spurious polarization can arise because of small mis-alignments between\nthe polarization images, especially in the nuclear regions where\nthere are sharp gradients in the light distribution. To guard against such effects\nwe have smoothed the polarization data using a 5$\\times$5 pixel boxcar filter\n(0.375$\\times$0.375 arcseconds) and re-measured the polarization in the nuclear regions. As expected, the measured degree of polarization in the nucleus in the smoothed image\nis less ($P_{2.0\\mu m}^{m}\\sim10$\\%) than in the full resolution image, because of the greater degree of contamination\nby unpolarized starlight and extended structures around the nucleus. In order\nto determine the intrinsic polarization of the point source it is\nnecessary to first determine the \nproportion of flux contributed by the point source to the total flux in\nthe nuclear regions. Experiments involving the\nsubtraction of a Tiny Tim generated point spread function (Krist \\& Hook 1997)\nsuggest that an upper limit on the \nfractional contribution of the nucleus to the total flux in a 5$\\times$5 pixel\npixel box centred on the nucleus is\n$f_{nuc} < 35$\\%. Thus,\nassuming that {\\it all} the polarization in the near-nuclear regions is due to the unresolved\ncompact core, and that the remainder of the light is unpolarized, the intrinsic\npolarization of the unresolved core source is $P_{2.0\\mu m}^{intr} = P_{2.0\\mu m}^{m}/f_{nuc} > 28$\\%. \n\n\nThe position angle of polarization E-vector of the \ncore source measured in our full resolution polarization\nmap ($PA = 201 \\pm 3$), is close to perpendicular to the\nradio jet axis ($PA = 105 \\pm 5$). This is similar to the situation\nseen in other AGN, and in particular Cen~A, where, towards longer wavelengths\nand smaller apertures, the infrared polarization becomes more and more closely\nperpendicular to the radio jet (Bailey \\etal\\ 1986).\n\n\\section{Discussion}\n\n\\subsection{The nature of the unresolved core source}\n\nA major motivation for the HST observations was to investigate the nature of the\ncompact core source and the cause of the relatively large polarization\nmeasured in the core by Packham \\etal\\ (1998). The explanation\nfavoured by Packham \\etal\\ is that the\ncompact core source represents transmitted quasar light, \nwhile the high polarization\nis due to dichroic absorption by aligned dust grains in the central \nobscuring torus. Because the\ndichroic mechanism is relatively inefficient, a high polarization implies a large\nextinction: from observations of Galactic stars it is known\nthat {\\it at least} 55 magnitudes of visual extinction\nis required to produce a K-band polarization of 28\\%\nfor optimum grain alignment (Jones 1989). More typically, the correlation\nbetween K-band polarization and extinction deduced for Galactic stars\nby Jones (1989) implies that an extinction of $A_v \\sim 350$ magnitudes\nwould be required for $P_k = 28$\\%. \nFor comparison, an upper limit on the K-band extinction in\nCygnus A, estimated by comparing\nthe 2.25$\\mu$m core flux with mid-IR and X-ray fluxes, is\n$A_v < 94$ magnitudes (see Tadhunter\n\\etal\\ 1999 for details). Thus, the dichroic mechanism is only\nfeasible if\nthe efficiency of the mechanism in Cygnus A is greater than it is along most\nlines of sight in our Galaxy. Such enhanced efficiency\ncannot be entirely ruled out, given that the Galactic dichroic\npolarization involves a randomly oriented magnetic field component, whereas the magnetic fields in the central obscuring regions of AGN may be more coherent.\nIn this context it is notable that near- and mid-IR polarization measurements of the central regions of the nearby\nSeyfert galaxy NGC1068 provide evidence for\na greater dichroic efficiency than predicted by the Jones (1989) correlation,\nwith $P_k = 5$\\% produced by $A_v \\sim$20 -- 40 magnitudes (Lumsden et al.\n1999). However, even the greater dichroic efficiency deduced for NGC1068 \nwould not be sufficient to produce the high \npolarization measured in \nthe core of Cygnus A if $A_v < 94$ magnitudes. \n%If\n%correct, this mechanism would imply \n%the presence of an ordered magnetic field in the near-nuclear\n%regions of Cygnus~A, with the field direction\n%predominantly in the plane of the obscuring torus.\n\nThe efficiency problem might be resolved if the extinction to the core source in\nthe K-band is higher than the $A_v < 94$ estimated on the basis of comparisons of the K-band flux with the mid-IR and X-ray fluxes. Indeed,\nsubstantially higher extinctions have been deduced for Cygnus A, both from \nmodelling the X-ray spectrum of the core\n($A_v = 170\\pm30$: Ueno \\etal\\ 1994) and from comparisons between \nhard-X-ray continuum, [OIII] emission line and mid-infrared continuum \nfluxes ($A_v = 143\\pm35$: Ward 1996, Simpson 1995). If such high extinctions also apply to the quasar nucleus in the K-band, the low efficiency of\nthe dichroic mechanism would be less of a problem. However, for any reasonable quasar SED, the\ncontribution of such a highly obscured quasar nucleus to the flux and the \npolarization of the {\\it detected} 2.0$\\mu$m core source would \nbe negligible (i.e. we would not expect to detect the quasar nucleus directly\nin the K-band).\nThus, it is more likely that the relatively low extinction deduced\nfrom the K-band flux measurements reflects contamination of the K-band core by emission from a less-highly-obscured \nregion, which is close enough to the central AGN to remain unresolved\nat the resolution of our HST observations. Although it has been proposed that\nthe contaminating radiation in the K-band may include hot dust emission and/or line emission\nfrom quasar-illuminated regions close to the nucleus\n(e.g. Stockton \\& Ridgway 1996), such emission would have a low intrinsic polarization, and a large dichroic efficiency would still be required \nin order to produce the polarization of this component by dichroism.\n\n%Given the problems with the dichroic polarization mechanism it is important\n%to consider alternative explanations for the high polarization of the core. \nThe most plausible alternative to dichroic extinction \nis that the K-band core source\nrepresents scattered- rather than transmitted quasar light. In this case,\nthe polarization is a consequence of scattering in an unresolved region\nclose to the illuminating quasar; we do not detect the quasar nucleus\ndirectly in the K-band; and previous extinction estimates based on the K-band\nfluxes substantially underestimate the true nuclear extinction. Note\nthat the presence\nof such a scattered component\nwould resolve the discrepancy between the extinction estimates based on\nK-band flux measurements, and those based on fluxes measured at other wavelengths.\n\n\n%We can use our observations to place constraints on the properties of the\n%putative scattering region. For isotropic scattering --- a reasonable\n%approximation if the scatterers are electrons or small dust\n%particles --- the scattered flux \n%measured by the observer ($F_{obs}$) is related to the direct (illuminating)\n%flux from the AGN ($F_{dir}$) by the following equation:\n%$F_{obs} = F_{dir} 10^{-A_k/2.5} f (\\Omega_{sc}/4\\pi)$\n%where $A_k$ is the K-band extinction of the scattering region in magnitudes,\n%$\\Omega_{sc}$ is the solid angle subtended by the scattering region as viewed\n%from the illuminating AGN, and $f$ is the fraction of photons along a particlar %line of sight from the AGN\n%that is scattered in the scattering region. By comparing the %2.0$-$2.25$\\micron$m\n%flux ratio measured from our NICMOS\n%data with a standard near-IR quasar SED ($F_{\\nu} \\propto nu^{-1.5}$ ref??},\n%we determine an extinction of $A_k = 3.9$ for the unresolved\n%scattering region. A limit on $F_{dir}$ can be obtained from\n%the hard X-ray flux of Cygnus~A and consideration of quasar SEDs. From an %examination of the SEDs for radio-loud quasars\n%presented in Elvis \\etal\\ (1994) we determine the following conservative upper %limit: $F_{2.0$\\micron$m} < F_{1kev}\\times5\\times10^5$ W Hz$^{-1}$.\n%Combining this with the hard-X-ray flux of\n%the core of Cygnus~A from Uneo \\etal\\ (1984) we obtain\n%$F_{dir} < 4.4\\times10^{-27)$ W Hz$^{-1}$. Finally, substituting this limit \n%into equation 1, with the\n%estimated K-band extinction and the measured 2.0$\\micron$m core flux we\n%obtain the following limit on the product of the scattering depth and\n%the fraction of sky covered by the scattering region:\n%$ f (\\Omega_{sc}/4\\pi)$ f > 1.7\\times10^{-3}$. Assuming that we see \n%scattered light from one side of the nucleus only, the maximum covering factor\n%for the scattering region corresponds to complete coverage of one of ionization\n%cones, or $(\\Omega_{sc}/4\\pi) = 0.21$, for the 55$^{\\circ} opening half-angle\n%cones in Cygnus~A (\\eg\\ Tadhunter \\etal\\ 1994). For this fractional coverage \n%the scattering depth is \n%$f > 8\\times10^{-3}$. Conversely, the minimum sky coverage for an optically\n%thick ($f = 1.0$) scattering region is $(\\Omega_{sc}/4\\pi) = %1.7\\times10^{-3}$. \n\n\n%What is the nature of the putative near-nuclear scattering region? Given the\n%alignment of the polarization perpendicular to the radio axis it seems likely\n%that the scattering material is distributed closer to the poles than to the walls of the %obscuring torus.\n%One possibility is that the scattering takes\n%place in the region responsible for the associated UV absorption line\n%systems which are common in radio-loud quasars (\\eg\\ Anderson \\etal\\ 1987).\n%However, the associated absorption line systems, which may be linked to the %X-ray\n%``warm absorber'' phenomenon, have maximum ionized\n%column densities of $\\sim5\\times10^{22}$\n%cm$^{-2}$, corresponding to a Thompson electron scattering\n%depths of $f\\sim3.5\\times10^{-2}$. Unless there is significant dust\n%associated with the scattering/absorbing region, such a small scattering\n%depth implies a large fractional coverage of the cone by the scattering %material. \n%ost plausibly, the scattering takes place in a region intermediate\n%in scale between\n%the pc-scale BLR and the kpc-scale extended narrow line region,\n%perhaps in the ``inner narrow\n%line region'' which emits the broad [SVI], [SXI], [FeVII] and\n%[OIII] emission lines detected in optical/IR spectra of the core\n%(Ward \\etal\\ 1991, Tadhunter \\etal\\ 1994, \n%Stockton \\& Ridgway 1996).\n\nFinally, we must also consider the possibility that the core polarization is \ndue to synchrotron radiation associated with the pc-scale\njet visible in VLBI radio images (Krichbaum \\etal\\ 1996). \nAlthough the {\\it integrated} polarization \nof the radio core is small even at high radio frequencies ($P_{22GHz} < 5$\\%:\nDreher 1979), we\ncannot entirely rule out the possibility that we are observing a highly polarized sub-component of\nthe jet which suffers a relatively low extinction, or alternatively\nthat the radio core source as a whole suffers large Faraday depolarization at radio\nwavelengths, and would appear more highly polarized at infrared wavelengths. \nPolarization observations at sub-mm wavelengths\nwill be required to investigate this latter possibility.\n\n%The edge-brightened bi-polar structure is strikingly similar to the structures\n%observed around young stellar objects (YSOs: \\eg\\\n%Velusamy \\& Langer 1998), which led Tadhunter \\etal\\ (1999)\n%to propose that outflows driven by the central quasar\n%hollow out funnels on opposite sides of the nucleus in the kpc-scale disk \n%responsible for the dust lane; the lateral expansion of the outflows\n%lead to a density enhancement in the walls of the funnel\n%and the structures are\n%illuminated by the anisotropic radiation field of the quasar. \n%The opening angles of the illumination cones produced by the pc-scale\n%torus surrounding the quasar must be larger than the opening angles of the funnel \n%structures produced by the outflows. \n\n\\subsection{The extended polarization structures}\n\nAn intriguing feature of our HST observations is the high degree of polarization measured\nalong, and only along, the NW-SE limb of the bicone. The\norientation of the polarization measured along the limb is consistent with the scattering\nof light from a compact illuminating source in the nucleus,\nwhile the high degree\nof polarization is consistent with the edge-brightened bi-cone\ngeometry of Tadhunter \\etal\\ (1999), in the\nsense that the scattering angle for the edge-brightened region will\nbe close to the optimal 90$^\\circ$ required for maximal polarization.\nHowever, the fact that the polarization is measured along only one\nlimb is difficult to reconcile with the simplest bicone model\nin which the illuminating IR radiation field is azimuthally isotropic, and the\nscattering medium is uniformly distributed around the walls of the funnels\nhollowed out by the circum-nuclear outflows. In this simplest model\nboth limbs would be highly polarized in the direction\nperpendicular to the radius vector of the source, and this is clearly\ninconsistent with the observations.\n\nOur observation require that one or more of the assumptions implicit in the simple model must be relaxed.\nIn general terms this requires either invoking specific matter distributions\nwithin the cone and/or an anisotropic illumination pattern of the central source \nitself.\n\nPerhaps the simplest way of reconciling the polarization characteristics \nwith the bi-cone geometry is to adjust the relative \nimportance of scattering and intrinsic emmission with azimuth around the cone,\nso that one limb of the cone is dominated by scattered radiation, while the\nother is predominatly intrinsic radiation. \n%In order to explain the\n%differences between the optical and IR polarization images in this\n%way, the scattering material would need be close to optically thick\n%to the optical continuum in all \n%directions around the walls of the cones, but only present a substantial\n%optical depth to the near-IR continuum in direction corresponding to the\n%NW-SE limb of the bi-cone. This wavelength dependence\n%would in turn imply that the scattering medium is dust rather than electrons.\nSince the band-pass of the \nNICMOS polarizers contains the Paschen alpha line, this provides an obvious potential\nsource of the diluting radiation for the unpolarized regions. \n%Other possibilites include thermal radiation\n%from hot dust and star formation. \nUnfortunately there is no obvious reason why such an asymmetry should exist. \nFurthermore, direct images with the F222M filter show that there is no radical\nchange in the relative brightness of the two limbs of the eastern cone between\n2.0$\\mu$m and 2.25$\\mu$m. This is an \nargument against the Paschen alpha model for the intrinsic\nemission, since the F222M filter admits no emission lines as\nstrong as Paschen alpha.\n%\n%\n% \n%\n%While star formation might be triggered by an expanding shock \n%wave surrounding the jet, there seem no obvious way to suppress the \n%star-froamtion on the polarized limb,\n%and the symmetry in total flux would have to be coincidental. \n% \n% To radiate significantly at 2.0 microns the dust would have to be\n% very hot, and it seems unlikely that such high temperatures\n% could be produced at such large distances from the nucleus --- most\n% models of hot dust place the the dust on a pc rather than kpc scale.\n% I also find the star formation idea rather unlikely. So I have \n% left both of these possibilities out (given the lack of space).....Clive\n%\n%\n%\n% JIM/TIM How much bigger does the mass density of dust have to be for\n% multiple scattering to provide the explanation?\n% Isn't multiple scattering a non-starter in the sense that the this\n% would imply that the scattering medium is optically thick at IR wavelengths? In this\n% case, if it's dust scattering, then the dust lane as a whole would be optically\n% thick in the IR and we wouldn't see through to the nuclear regions! --- Clive\n%\n%\n%Other alternatives are equally unpalatable. For example one could effectively\n%depolarise one limb if the optical scattering depth was large enough so that\n%multiple scattering was important. Cancelling the polarization by the intriduction of a second \n%source of polarization e.g. dichroic absorption via transmittion through aligned grains requires\n%a conspiratorily magnetic field geometry and high optical depths.....Clive\n% \n\n\nAn alternative possibility\nis that the NW-SE limb is brighter because the near-IR\nradiation field of the illuminating AGN is more intense in that direction (i.e. the illuminating\nradiation field is azimuthally anisotropic within the cones). In this\ncase, the clear difference in structure\nbetween the optical and \nnear-IR reflection nebulae suggests that the sources of illumination\nat the two wavelengths are different: while the source of the shorter wavelength\ncontinuum must produce a radiation field which is azimuthally isotropic within\ncones defined by the obscuring torus, the source of illumination \nat the longer wavelengths is required to display\nconsiderable degree of azimuthal anisotropy. \nThe near-IR continuum source must also have a relatively red spectrum, in order\nto avoid producing similar structures at optical and infrared wavelengths. \nThe near-IR anisotropy might arise in the following ways.\n\\begin{enumerate}\n\\item {\\bf Beamed radiation from the inner radio jet.} The near-IR continuum \nis emitted by a \ncomponent of the inner synchrotron jet which has a direction\nof bulk relativistic motion siginificantly\ndisplaced from the axis of the large-scale radio jet, such that\nthe radiation is beamed towards the NW-SE limb of the bicone. However, given\nthe remarkable degree of collimation, and the lack of bending, observed in the Cygnus~A\njet on scales betweem 1pc and 100kpc,\na major difficulty\nwith this model is that the the jet would have to bend through a large angle on\na scale smaller than $\\sim$1pc (the resolution of the VLBI maps), whilst retaining\nthe rotational symmetry in the jet structure about the nucleus. A further requirement\nof this model is that, if\nthe inner jet is precessing, the precession timescale must be greater than the light\ntravel time ($\\sim$5000 years) across the bicone structure.\n\\item {\\bf Anisotropic hot dust emission.} The near-IR continuum is emitted by hot dust in the inner regions of the galaxy,\nwith a larger projected area of the emitting region visible from one limb of the bicone\nthan from the other. For example, if the near-IR radiation is emitted by dust in a warped disk close\nto the central AGN --- perhaps an outer part of the accretion disk --- the warp could be\noriented such that the NW-SE limb has an almost face-on view of the emitting region, whereas the\nthe NE-SW limb has a more oblique view. There is already direct observational evidence for\na warped outer accretion disk in at least one active galaxy\n(Miyoshi \\etal\\ 1995). Given that\nthis mechanism would produce a relatively mild, broad-beam anisotropy,\nan optically thick torus on scales larger than the hot dust emitting region would\nstill be required in order to\nproduce the sharp-edges to the illuminated bicone structure.\n\\end{enumerate} \n%The beaming idea draws some support from\n%the fact that some infrared nebulae associated\n%YSOs in our Galaxy\n%show a similar morphologies in polarized light, and these features have\n%explained in terms of scattering of a highly collimated beams of radiation\n%(e.g. the Chamealeon nebula: ref??)\nNote that\nregardless of how any anisotropy in the IR radiation field might be produced,\nsuch anisotropy would not by itself explain the nature of the unpolarized\nemission along the SW-NE limb of the bicone, and the lack of variation\nin the brightness\nratio of the two limbs of the eastern cone between 2.0$\\mu$m\nand 2.25$\\mu$m. It may also\nbe difficult to reconcile the anisotropic illumination model\nwith the polarization properties of the unresolved\ncore source: if the core polarization is due to scattering, the orientation\nof the core polarization vector implies that a substantial flux of illuminating\nphotons must escape at large angles to the NW-SE limb of the bicone.\n\n\nWe expect future spectropolarimetry observations to resolve the uncertainties concerning\nthe origin of the near-IR polarization structures in Cygnus~A.\nFor example, in the case of the anisotropic illumination mechanisms considered above, the anisotropy\nis in the {\\it continuum} flux rather than the broad lines\nassociated with the AGN. Thus, if this model is correct, \nthe broad lines will be relatively weak or\nabsent in the polarized spectrum of the extended structures.\nIn contrast, for a non-uniform distribution of scattering material but\nisotropic illumination within the cones, the broad lines and continuum will be \nscattered equally, and the equivalent widths of the broad lines in the polarized\nspectrum should fall within the\nthe range measured for steep spectrum radio quasars. \n\n \n\n%A more radical explanation might be that the innner morphology is not a true \n%bi-cone but, for example, originates as a projection of a warped disk.\n%In this picture the polarized limb is formed by illumination of the inner parts of\n%the disk\n%much closer to the nucleus than the unpolarised limb, which is seen because\n%of the boosting provided by forward unpolarized scattering. \n%\n% But what about the forward scattered component from the inner ring? (this\n% should be bright and not just concentrated in the nucleus) Also, unless the\n% material is distributed in just two rings, which just happen to be at the\n% correct inclination to be viewed edge-on, what about the scattered light from\n% all the rings at other angles in the warped disk structure?....Clive\n%\n\n%\n% Another radical suggestion: suppose that the walls of the funnel emit H2 molecular\n% emission, with the molecular emission excited by some mechanism other than direct illumination\n% by the AGN. Suppose also that the radiation field is anisotropic, with a maximum intensity\n% in the direction of the NW-SE limb (see above). Thehe molecules might be dissociated\n% along this limb, and there would be no diluting molecular H2 emission, whereas along the\n% other limb the molecules could remain intact and give unpolarized intrinsic emission.\n% Note that H2 lines of similar strength contribute to both 2.0 and 2.25 bands.\n% \n\n\n\\section{Conclusions and Future Work}\n\nOur NICMOS polarimetry observations of Cygnus~A have demonstrated the existence of\na compact reflection nebula around the hidden core, but one whose polarization\nproperties are inconsistent with the simplest illumination model suggested by the\nimaging data. \nThe predominantly axial symmetry of the total intensity imaging is\nreplaced by axial asymmetry and reflection symmetry about the nucleus in polarized light.\n% But it's not quite reflection symmetry.....Clive\n\nWe have discussed several mechanisms to explain the near-IR polarization structures. \nWhile none of these is entirely satisfactory, it is clear that the near-IR polarization\nproperties have the potential to provide key information about the geometries of\nthe central emitting regions in AGN, and the near-IR continuum emission mechanism(s).\nIn this context, it will be interesting in future to make similar \nobservations of a large sample of powerful radio galaxies in order to determine whether the\nextraordinary IR polarization properties of Cygnus~A are a common feature\nof the general population of such objects. \n\\newpage\\noindent\n{\\bf Acknowledgments.} \nBased on Observations made with the ESA/NASA {\\it Hubble Space Telescope}, \nobtained at the Space Telescope Science Institute, which is operated by the\nAssociation of Universities for Research in Astronomy, Inc., under NASA contract\nNAS5-26555. We thank the referee --- Stuart Lumsden --- for useful comments. A. Robinson acknowledges support from the Royal Society.\n\\vglue 1.0cm\\noindent\n{\\bf References}\n\\begin{description}\n%\\reference{arnaud87}Arnaud, K.A., Johnstone, R.M., Fabian, A.C., \n%Crawford, C.S., \n%Nulsen, P.E.J., Shafer, R.A., Mushotsky, R.F., 1987, MNRAS, 227, 241\n\n%\\reference{baade54}Baade W., Minkowski R., 1954, ApJ, 119, 215\n\n%\\reference{baker97} Baker J.C., 1997, MNRAS, 286, 23\n\n\\item Bailey, J.A., Sparks, W.B., Hough, J.H., Axon, D.J., 1986,\nNat, 332, 150\n\n%\\reference{barthel89}Barthel P.D., 1989, ApJ, 336, 606\n\n\\item Carilli C., Barthel, P.D., 1996, A\\&ARev, 7, 1\n\n%Djorgovski S., Weir, N., Matthews, K., Graham, J.R., 1991, ApJ, 372, L67\n\n\\item Dreher, J.W., 1979, ApJ, 230, 687\n\n\\item Hines, D.C., 1998, NICMOS \\& VLT, ESO Workshop and \nConference Proceedings, 55, Wolfram Freudling and Richard Hook (eds), p63\n\n\n%\\reference{jackson98}Jackson N., Tadhunter, C., Sparks, B., 1998, MNRAS, in %press\n\n\\item Jones, T.J., 1989, ApJ, 346, 728\n\n\\item Krichbaum, T.P., Alef, W., Witzel, A., 1996, in Cygnus~A --- Study of a \nRadio Galaxy, ed. C.L. Carilli \\& D.E., Harris (Cambridge: \nCambridge University Press), 93.\n\n\\item Krist J.E., Hook, R., 1997, TinyTim User Guide, Version 4.4 (Baltimore:STScI)\n\n\n%\\reference{kulkarni98}\n%Kulkarni V.P., Calzetti, D., Bergeron, L., Rieke, M., Axon, D., \n%Skinner, C., Colina, L., Sparks, W., Daou, D., Gilmore, D.,\n%Holfeltz, S., MacKenty, J., Noll, K., Ritchie, C., Schneider, G., \n%Schultz, A., Storrs, A., Suchkov, A., Thompson, R., 1998, ApJ, 492, L121\n\n%\\reference{lawrence91}Lawrence A., 1991, MNRAS, 252, 586\n\n\\item Lumsden, S.L., Moore, T.J.T., Smith, C., \nFujiyoshi, T., Bland-Hawthorn, J., \nWard, M.J., 1999, MNRAS, 303, 209\n\n\\item MacKenty J.W., \\etal\\, 1997, NICMOS Instrument Handbook, Version 2.0\n(Baltimore: STScI)\n\n\\item Miyoshi, M., Moran, J., Herrnstein, J., Greenhill, L., \nNakai, N., Diamond, P., Inoue, M., 1995, Nature, 373, 127\n\n\\item \nOgle P.M., Cohen, M.H., Miller, J.S., Tran, H.D., Fosbury, R.A.E.,\nGoodrich, R.W., 1997, ApJ, 482, L37\n\n%\\reference{osterbrock76}\n%Osterbrock, D.E., Koski, A.T., Phillips. M.M., 1976, ApJ, 206, 898\n\n\\item Packham, C., Hough, J.H., Young, S., \nChrysostomou, A., Bailey, J.A., Axon, D.J., Ward, M.J., 1996,\nMNRAS, 278, 406\n\n\\item\nPackham, C., Young, S., Hough, J.H., Tadhunter, C.N., Axon., 1998,\nMNRAS, 297, 939\n\n%\\reference{simpson95}Simpson C., 1995, DPhil thesis, University of Oxford\n\n%\\reference{simpson94}Simpson C., Ward, M., Kotilainen, J., 1994, MNRAS, 271, 247\n\n%\\reference{schreier98}\n%Schreier, E.J., Marconi, A., Axon, D.J., Caon, N., Machetto, D., \n%Capetti, A., Hough, J.H., Young, S., Packham, C., 1998, ApJ, \n\n\\item Serkowski, 1958, Acta.Astron., 8, 135\n\n\\item Sparks, W.B., Axon, D.J., 1999, PASP, in press\n \n\\item\nStockton A., Ridgway S.E., Lilly, S., 1994, AJ, 108, 414\n\n\\item\nStockton, A., Ridgway, S.E., 1996, in Cygnus~A --- Study of a \nRadio Galaxy, ed. C.L. Carilli \\& D.E., Harris (Cambridge: \nCambridge University Press), 1 \n\n\\item\nTadhunter C.N., Scarrott S.M., Rolph C.D., 1990, MNRAS, 246, 163 \n\n%\\reference{tadhunter91}Tadhunter C.N., 1991, MNRAS, 251, 46p\n \n\\item Tadhunter C.N., Metz, S., Robinson, A., 1994, MNRAS, 268, 989 \n\n\\item Tadhunter C.N., Packham, C., Axon, D.J., Jackson, N.J.,\nHough, J.H., Robinson, A., Young, S., Sparks, W., 1999, ApJ, 512, L91 \n\n\\item\nUeno S., Katsuji K., Minoru N., Yamauchi S., Ward M.J., 1994, ApJ, 431, L1\n\n%\\reference{velusamy98}\n%Velusamy T., Langer, W.D., 1998, Nat, 392, 685 \n\n\\item\nWard M.J., Blanco P.R., Wilson A.S., Nishida M., 1991, ApJ, 382, 115\n\n\\item\nWard M.J., 1996, in Cygnus~A --- Study of a Radio Galaxy, ed. C.L. Carilli\n\\& D.E., Harris (Cambridge: Cambridge University Press), 43\n\n\\item van der Marel, R., 1998: \nhttp://sol.stsci.edu/~marel/software.html\n\n\\end{description}\n\\newpage\\noindent\n{\\bf Figure 1}. Infrared (2.0$\\mu$m) polarization images of Cygnus~A. \nTop left -- \ntotal intensity (Stokes I) at full resolution; top right -- polarization degree at full resolution; bottom left --\npolarized intensity at full resolution; and bottom right -- polarization vectors plotted\non a contour map of the polarized intensity image derived from the data smoothed with\na 5$\\times$5 pixel box filter, with length of vectors proportional to the percentage polarization.\nThe line segment in the intensity image shows the direction of the radio axis. At the \nredshift of Cygnus~A, 1.0 arcsecond corresponds to 1.0 kpc for \n$H_0 = 75$ km s$^{-1}$ Mpc$^{-1}$ and $q_0 = 0.0$.\n\n\n\\begin{figure}\n\\psfig{figure=pol3c.ps,width=15cm}\n\\end{figure}\n\n\n\\end{document} \n \n \n\n"
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astro-ph0002180
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An Empirical Test and Calibration of \hii\/ Region Diagnostics
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[
{
"author": "Robert C. Kennicutt"
},
{
"author": "Jr."
},
{
"author": "\\altaffilmark{1,2}\\ Fabio Bresolin"
},
{
"author": "\\altaffilmark{3,4}\\ Howard French"
},
{
"author": "\\altaffilmark{5,6}\\ Pierre Martin\\altaffilmark{7}"
}
] |
We present spectrophotometry in the 3600--9700 \AA\ region for a sample of 39 \hii\ regions in the Galaxy and Magellanic Clouds, for which independent information is available on the spectral types and effective temperatures of the ionizing stars. The spectra have been used to evaluate nebular diagnostics of stellar temperature, metal abundance, and ionization parameter, and compare the observed behavior of the line indices with predictions of nebular photoionization models. We observe a strong degeneracy between forbidden-line sequences produced by changes in stellar \teff\/ and metal abundance, which severely complicates the application of many forbidden-line diagnostics to extragalactic \hii\ regions. Our data confirm however that the Edmunds \& Pagel [\ion{O}{2}]$+$[\ion{O}{3}] abundance index and the V\'{\i}lchez \& Pagel \etap\ index provide more robust diagnostics of metal abundance and stellar effective temperature, respectively. A comparison of the fractional helium ionization of the \hii\ regions with stellar temperature confirms the reliability of the spectral type vs \teff\/ calibration for the relevant temperature range \teff\ $\le$ 38000 K. We use empirical relations between the nebular hardness indices and \teff\/ to reinvestigate the case for systematic variations in the stellar effective temperatures and the upper IMFs of massive stars in extragalactic \hii\ regions. The data are consistent with a significant softening of the ionizing spectra (consistent with cooler stellar temperatures) with increasing metal abundance, especially for $Z \le$ \zsun. However unresolved degeneracies between $Z$ and \teff\ still complicate the interpretation of this result.
|
[
{
"name": "ms.tex",
"string": "%\\documentstyle[12pt,aasms4,amssym]{article}\n\\documentstyle[11pt,aaspp4,flushrt]{article}\n\n\\begin{document}\n\n%\\newcommand{\\sp}{\\mbox {S$^+$}}\n\\newcommand{\\spp}{\\mbox {S$^{++}$}}\n\\newcommand{\\op}{\\mbox {O$^+$}}\n\\newcommand{\\opp}{\\mbox {O$^{++}$}}\n\\newcommand{\\teff}{\\mbox {$T_{\\!\\!\\em eff}$}}\n\\newcommand{\\tstar}{\\mbox {$T_*$}}\n\\newcommand{\\qh}{\\mbox {$Q_{H^0}$}}\n\\newcommand{\\x}{\\mbox {$R_{23}$}}\n\\newcommand{\\stt}{\\mbox {$S_{23}$}}\n\\newcommand{\\etap}{$\\eta^\\prime$}\n\\newcommand{\\ariii}{\\mbox {[Ar III]\\thinspace $\\lambda$7135}}\n\\newcommand{\\sii}{\\mbox {[S II]\\thinspace $\\lambda\\lambda$6716,\\thinspace 6731}}\n\\newcommand{\\oii}{\\mbox {[O II]\\thinspace $\\lambda$3727}}\n\\newcommand{\\siii}{\\mbox {[S III]\\thinspace $\\lambda\\lambda$9069,\\thinspace 9532}}\n\\newcommand{\\oiii}{\\mbox {[O III]\\thinspace $\\lambda\\lambda$4959,\\thinspace 5007}}\n\\newcommand{\\nii}{\\mbox {[N II]\\thinspace $\\lambda\\lambda$6548,\\thinspace 6583}}\n\\newcommand{\\neiii}{\\mbox {[Ne III]\\thinspace $\\lambda$3869}}\n\\newcommand{\\msun}{\\mbox {${\\rm M_\\odot}$}}\n\\newcommand{\\zsun}{\\mbox {${\\rm Z_{\\odot}}$}}\n\\newcommand{\\lsun}{\\mbox {${\\rm L_\\odot}$}}\n\\newcommand{\\angs}{\\mbox{~\\AA}}\n%\\newcommand{\\line}{\\mbox {$\\lambda$}}\n\\newcommand{\\lines}{\\mbox {$\\lambda\\lambda$}}\n\\newcommand{\\hii}{H\\thinspace II}\n\\newcommand{\\ew}{EW(H$\\beta$)}\n\\newcommand{\\halpha}{H$\\alpha$} \n\\newcommand{\\ha}{\\mbox {H$\\alpha$}}\n\\newcommand{\\hbeta}{H$\\beta$}\n\\newcommand{\\hgamma}{H$\\gamma$}\n\\newcommand{\\hb}{\\mbox {H$\\beta$}}\n\\newcommand{\\cf}{cf.\\/\\ } \n\\newcommand{\\eg}{e.g.\\/}\n\\newcommand{\\ie}{i.e.\\/\\ } \n\\newcommand{\\etal}{et\\thinspace al.\\ } % et al.\n\n%\\received{} %\\accepted{} %\\journalid{}{} %\\articleid{}{}\n%\\slugcomment{}\n\n\\lefthead{Kennicutt, Bresolin, French & Martin} \n\\righthead{HII region diagnostics}\n\n\\title{An Empirical Test and Calibration of \\hii\\/ Region Diagnostics}\n\n\\author{Robert C. Kennicutt, Jr.,\\altaffilmark{1,2}\\ \nFabio Bresolin,\\altaffilmark{3,4}\\ \nHoward French,\\altaffilmark{5,6}\\ \nPierre Martin\\altaffilmark{7}\n}\n\\altaffiltext{1}{Steward Observatory, \nUniversity of Arizona, Tucson, AZ 85721}\n\n\\altaffiltext{2}{Visiting Astronomer, Cerro Tololo Interamerican \nObservatory, National Optical Astronomical Observatories, which are\noperated by AURA, Inc., under contract with the National Science \nFoundation.}\n\n\\altaffiltext{3}{European Southern Observatory, \nKarl-Schwarzschild-Str. 2, D-85748 Garching b. M\\\"{u}nchen, Germany}\n\n\\altaffiltext{4}{Present address: Institut fur Physik und Astronomie, \nScheinerstr. 1, D-81679, Munich, Germany}\n\n\n\\altaffiltext{5}{Department of Astronomy, University of \nMinnesota, 116 Church Street SE, Minneapolis, MN 55455}\n\n\\altaffiltext{6}{Honeywell Technology Center, 3660 Technology Drive,\nMinneapolis, MN 55418}\n\n\\altaffiltext{7}{CFHT, P.O. Box 1597, Kamuela, HI 96743}\n\n\n\\begin{abstract} \n\nWe present spectrophotometry in the 3600--9700 \\AA\\ region for a\nsample of 39 \\hii\\ regions in the Galaxy and Magellanic Clouds,\nfor which independent information is available on the spectral\ntypes and effective temperatures of the ionizing stars. The\nspectra have been used to evaluate nebular diagnostics\nof stellar temperature, metal abundance, and ionization parameter,\nand compare the observed behavior of the line indices with predictions\nof nebular photoionization models. We observe a strong degeneracy\nbetween forbidden-line sequences produced by changes in stellar \\teff\\/\nand metal abundance, which severely complicates the application of\nmany forbidden-line diagnostics to extragalactic \\hii\\ regions. Our\ndata confirm however that the Edmunds \\& Pagel [\\ion{O}{2}]$+$[\\ion{O}{3}]\nabundance index and the V\\'{\\i}lchez \\& Pagel \\etap\\ index provide\nmore robust diagnostics\nof metal abundance and stellar effective temperature, respectively.\nA comparison of the fractional helium ionization of the \\hii\\ regions\nwith stellar temperature confirms the reliability of the spectral\ntype vs \\teff\\/ calibration for the relevant temperature range\n\\teff\\ $\\le$ 38000 K. We use empirical relations between the nebular\nhardness indices and \\teff\\/ to reinvestigate the case for systematic\nvariations in the stellar effective temperatures and the upper IMFs of \nmassive stars in extragalactic \\hii\\ regions. The data are consistent\nwith a significant softening of the ionizing spectra (consistent with\ncooler stellar temperatures) with increasing metal abundance, especially\nfor $Z \\le$ \\zsun. However unresolved degeneracies between $Z$ and \\teff\\ \nstill complicate the interpretation of this result.\n\n\\end{abstract}\n\n\\keywords{galaxies: ISM --- galaxies: star clusters --- HII regions}\n\n% -------------------------------------------------------------------------\n\\section{INTRODUCTION}\n\nOver the past 15 years high-quality emission-line spectra have been obtained\nfor hundreds of \\hii\\ regions in nearby spiral and irregular galaxies. The\nprimary use of these data has been to study the chemical composition\npatterns in galactic disks (e.g., McCall, Rybski, \\& Shields 1985, \nVila-Costas \\& Edmunds 1992, Zaritsky, Kennicutt, \\& Huchra 1994, Dinerstein \n1996). However with the availability of state-of-the-art photoionization codes\nsuch as {\\sc cloudy} (Ferland \\etal 1998), combined with stellar population \nsynthesis codes for young clusters (e.g., Leitherer \\& Heckman 1995,\nLeitherer et al. 1999), \\hii\\ region spectra are being applied increasingly\nto measure the ages and initial mass functions (IMFs) of the ionizing\nstar clusters (e.g., V\\'{\\i}lchez \\& Pagel 1988, Shields 1990, Stasi\\'nska\n\\& Leitherer 1996, Bresolin, Kennicutt, \\& Garnett 1999, hereafter BKG). \nSimilar techniques have been applied to model the infrared emission-line \nspectra of IR-luminous starbursts, and the results have been interpreted as \nevidence for an anomalous IMF in these objects (e.g., Rieke et al. 1993).\n\nA basic limitation in this approach is its reliance on a long chain of \ntheoretical inputs: stellar evolution models as functions of stellar\nmass, chemical composition and mass-loss rates; stellar atmosphere models\nas functions of effective temperature, surface gravity, chemical composition,\nand mass-loss properties, and photoionization models for the surrounding\n\\hii\\ region. The derived nebular abundances tend to be insensitive \nto the details of these models, but the inferred properties of the ionizing\nstars are sensitive to the model inputs at every step in the chain.\nThe problem is especially acute when using \\hii\\ region or starburst \nspectra to constrain\nthe effective temperatures and IMFs of the ionizing stars (e.g., Mathis 1985,\nMcCall et al.~1985, V\\'{\\i}lchez \\& Pagel 1988, BKG).\nMost studies show evidence for a systematic softening of the\nionizing continuum of \\hii\\ regions with increasing metal abundance, but\nthe absolute range in stellar effective temperatures is highly model \ndependent, and the case for a systematic variation in the upper \nIMF is shaky at best (BKG and references therein).\n\nAnother approach, which can circumvent many of these difficulties,\nis to test the nebular diagnostics empirically, by obtaining spectra\nfor nearby \\hii\\ regions which are ionized by stars of known spectral type. \nThis makes it possible to anchor the nebular indicators of stellar\ntemperature directly to the stellar spectral classification system.\nFurthermore, by modeling these \\hii\\ regions with the same methods that are \napplied to extragalactic regions one can directly assess the reliability\nof the model-based approach.\n\nThis empirical approach was first explored by Chopinet \\&\nLortet-Zuckermann (1976) and Kaler (1978) to calibrate the \n[\\ion{O}{3}]$\\lambda$5007/\\hbeta\\ ratio as an indicator of stellar\neffective temperature. For studies of extragalactic \\hii\\ regions \nand starbursts a more robust hardness index than [\\ion{O}{3}]/\\hbeta\\ \nis desirable, because the excitation of [\\ion{O}{3}] varies locally within\n\\hii\\ regions, and it is sensitive to other physical parameters \n(e.g., metal abundance, ionization parameter, dust) which can vary\nsystematically in galaxies (e.g., Kennicutt 1984, Shields 1990).\nOther hardness indices have been developed for extragalactic applications\n(e.g., V\\'{\\i}lchez \\& Pagel 1988), but their reliability has not been tested \nempirically. \n\nIn this paper we report the results of a spectrophotometric study \nof 39 \\hii\\ regions in the Galaxy, the LMC, and the SMC, which is aimed at \nproviding an empirical foundation for nebular-based measurements of the stellar\nionizing continuum and IMF in galaxies. We use the spectra to evaluate\nseveral nebular diagnostics of massive stellar populations, and to\ncompare the known properties of the stars in these regions with\nthose inferred from photoionization modeling.\nOur study is mainly motivated by applications to stellar \ntemperatures and IMFs, but the approach is more generally applicable to \nspectral modeling of extragalactic \\hii\\ regions and starbursts.\nThis paper is complementary in approach to a recent analysis of Oey\net al. (2000), which has addressed many of these same questions using\ndetailed point-by-point observations of 4 \\hii\\ regions in the LMC.\n\nThe remainder of this paper is organized as follows. \nThe \\hii\\/ region sample and the observations are\ndescribed in \\S~2 and \\S~3, respectively. In \\S~4 we analyze \nthe behavior of the principal diagnostic line ratios and investigate\nseveral commonly applied abundance and spectral hardness indicators.\nIn \\S~5 we apply the empirical calibration to constrain the range of\nstellar effective temperature and upper IMF in galactic disks.\n\n\n\\section{\\hii\\/ REGION SAMPLE AND PROPERTIES}\n\nSince the first prerequisite for this work is knowledge of the exciting\nstars in the calibrating \\hii\\ regions, the ideal approach is to \nobserve small Galactic \\hii\\ regions ionized by single stars (or a few stars)\nof known spectral type. Such ``calibrating\" objects comprise approximately\nhalf of our sample, while the remaining objects,\nionized by larger OB associations or clusters, provide the link to\nthe brighter class of \\hii\\ regions observed in external galaxies.\n\nThe calibrating \\hii\\ regions were selected to span the maximum available \nrange in stellar spectral type and effective temperature. \nPreference was given to nebulae with \nangular diameters that fit within the length of the spectrograph slit\n(3\\arcmin\\ $-$ 6\\arcmin), and to regions with low to moderate extinction,\nwith $E(B-V) < 2$ mag in most cases.\nMost of our sample was drawn from the northern survey \nof small Galactic \\hii\\ regions defined by Hunter \\& Massey (1990; =HM90),\nand the southern sample of \\hii\\ regions studied by Shaver et al.~(1983)\nin their abundance survey of the Milky Way.\nIdentifications and spectral types for the ionizing stars were taken\ndirectly from HM90 for the northern sample, and from a variety of published\nsources for the southern objects. Most of the latter \nderive from classification work in the 1970's by Georgelin and \ncollaborators (e.g., Georgelin, Georgelin, \\& Roux 1973, Chopinet,\nGeorgelin, \\& Lortet-Zuckermann 1973).\nTable 1 lists the main properties of the \\hii\\ regions in our sample,\nincluding the sources of the stellar spectral types and oxygen abundances.\nColumn 8 indicates the observatory used to obtain the spectra, and\nasterisks denote objects in the calibrating subsample.\n\nIt is relatively easy to compile an adequate sample of small \\hii\\ regions\nionized by single stars of type O6V and later (\\teff\\ $\\le$ 42000).\nHowever this becomes nearly impossible for hotter O stars, because\nsuch stars almost always form in rich OB associations along with \nnumerous later-type stars. The contribution of the cooler\nstars to the ionizing continuum can be significant, and this composite \nionization needs to be taken into account in the determination of \\teff.\nWe observed several of these large Galactic \\hii\\/ regions, \nincluding M8, M16, M17, the Rosette nebula (S275), the Carina nebula,\nand the giant \\hii\\ region NGC~3603. We used the most recent studies of\ntheir stellar contents, including near-infrared observations in many cases,\nto identify all of the principal ionizing stars. \nIn order to extend our coverage to even higher stellar \ntemperatures, we also observed four \\hii\\ regions ionized by early-type \nWolf-Rayet stars, the Galactic regions RCW~5 = NGC~2359 (WN4), RCW~48 = \nNGC~3199 (WN5), and the LMC regions DEM~174 (WN4p) and DEM~231 (WN3). \n\nThe remainder of our sample consists of much larger \\hii\\ regions\nlocated in the LMC and SMC. Most of these objects are physically\ndistinct from the smaller Galactic \\hii\\ regions, being ionized by\nmuch more populous OB associations, and as such are less suitable for \nour empirical calibration of nebular diagnostics. However these\nobjects are directly analagous to the more distant extragalactic \\hii\\ regions,\nand their stellar contents have been cataloged by various authors\n(Table 1), so we can analyze them on the same basis as the\nsmaller Galactic \\hii\\ regions.\n\nTo assign a stellar effective temperature to the \\hii\\/ regions we have\nadopted the spectral type--\\teff\\/ calibration by Vacca, Garmany and\nShull (1996), together with the stellar ionizing fluxes predicted by\nSchaerer \\& de Koter (1997). The resulting temperatures and luminosities\nare listed in columns 4 and 5 of Table 1. In the case of an ensemble of \nhot stars, a mean temperature was derived by summing the He$^0$ and \nH$^0$ ionizing fluxes of all of the stars, and calculating the \neffective temperature of a class V \nstar having the same $Q_1/Q_0$ ratio (He$^0$ to H$^0$ total ionizing\nflux ratio). Effective temperatures for the W-R stars were estimated\nusing the semi-empirical calibration of Esteban et al. (1993).\nMore detailed information on the stellar contents\nof the individual \\hii\\ regions is given in the Appendix.\n\nOxygen abundances, expressed as 12+$\\log$(O/H), are given in column 6, and\ntheir sources are indicated in column 7. When abundances were \nunavailable in the literature and could not be measured directly from\nour spectra, we estimated the abundance using the empirical indicator\n\\x=([O~III]\\lines4959,5007+[O~II]\\lines3726,3729)/\\hbeta\\/ (Pagel \\etal\n1979), as calibrated by Edmunds and Pagel (1984). These estimates are\nlisted in parentheses in Table 1. The accuracy of the \\x-based abundances\nis of order $\\pm$0.2 dex, but this is sufficient for our purposes.\n\nFigure~1 shows the range of stellar temperatures and oxygen abundances\nfor the \\hii\\ regions in our sample. Squares and round points denote \ncalibrating and non-calibrating \\hii\\ regions with\ndirect (electron temperature based) abundance measurements, respectively.\nOpen triangles indicate those regions with empirical (\\x) abundance\nestimates. The \\hii\\ regions cover a stellar temperature range of\n32000 $-$ 48000 K, with the Wolf-Rayet nebulae extending to 67000 K.\nThe 28 Galactic \\hii\\/ regions span a range of O/H abundances of\n$-0.5 \\le [O/H] \\le 0.0$ (assuming \n12+$\\log$(O/H)$_\\odot$ = 8.9), while the 9 LMC regions cluster around\n[O/H] $\\simeq$ $-$0.4, and the single SMC region (N66 = NGC~346) \nhas [O/H] = $-$0.7. \n\nThe range of abundances in the sample is important for the interpretation\nwhich follows, because changes in metal abundance can mimic many of the \ntrends in nebular spectra that are produced by changes in stellar \ntemperature or IMF. For lack of a better prescription we have adopted a \nsingle conversion of spectral type to \\teff\\/ in our analysis, independent\nof abundance, and this conceivably could introduce some coupling between\nthe two parameters (\\S~4.3). Fortunately, Fig.~1 shows that $Z/Z_\\odot$ \nand \\teff\\ are largely decoupled from each other in our sample, and this\nshould allow us to separate their effects on the nebular spectra.\n%There is a slight tendency for the \\hii\\ regions with the\n%coolest ionizing stars to be more metal-rich than the mean for the\n%sample. This is mainly due to a selection effect, reflecting the fact\n%that most cataloged late-type stars are located relatively near to the\n%Sun in the Galaxy. \n\n\\section{OBSERVATIONS AND DATA REDUCTION}\n\nOur data consist of spectrophotometry covering the wavelength range \n3600--9700 \\AA. The extended coverage to\nthe near-infrared includes the \\siii\\/ doublet,\nwhich when combined with measurements of \\sii, \\oii, and \\oiii\\/\nprovides a robust measure of the hardness \nof the ionizing stellar continuum (Mathis 1985, V\\'{\\i}lchez \\& Pagel 1988).\n\n\\subsection{Steward Observatory Data}\n\nSpectra of the northern sample of Galactic \\hii\\/ regions were\nobtained in 1993 Oct and 1995 Jun with the B\\&C CCD spectrograph\non the Bok telescope, equipped \nwith a thinned Loral 800$\\times$1200 element CCD detector. Two grating\nsettings were used to cover the full spectral range. \nA 400 g~mm$^{-1}$ grating blazed at 4800 \\AA\\ provided coverage of the \n3600--6900~\\AA\\ region, hereafter denoted as the ``blue\"\nspectra. A second set of ``red\" spectra were obtained \nwith a 400 g~mm$^{-1}$ grating blazed at 7500 \\AA\\ to cover the\n6400--9700 \\AA\\ region. \nA slit width of 2\\farcs5 provided a spectral resolution \nof 8 \\AA\\ FWHM. The full spatial coverage of a spectrum \nwas 3\\farcm5, with a single pixel on the detector projecting \nto 0\\farcs83 on the sky. Spectra of NGC~7538 and NGC~7635 were obtained in\nin 1988 Nov using the same spectrograph but with a 800$\\times$800 element \nTexas Instruments CCD detector. The same setup was used for the red spectra,\nbut the blue spectra were obtained with a 600 g~mm$^{-1}$ grating\nblazed at 3570 \\AA, to cover the region between 3700--5100 \\AA.\n\nFigure~2 shows images of the \\hii\\ regions, with the slit\npositions superimposed. Most of the images were taken from the Digitized\nSky Surveys\\footnotemark. The \\hii\\ regions were observed at a fixed position \nextending E--W through the\ncenter of the nebula (but offset from bright stars to avoid\ncontamination of the spectrum), and also in a drift scanned mode, where\nthe image of the \\hii\\/ region was trailed across the slit to provide\nan integrated spectrum. Comparison of the fixed and scanned spectra \n(integrated over the length of the slit in both instances) reveals\nsurprisingly small differences in the main diagnostic line ratios, \nindicating that the fixed pointings provide a representative sampling\nof the nebula. This is illustrated in Figure~3, \nwhich compares the behavior of [\\ion{O}{3}]/\\hbeta\\ vs [\\ion{N}{2}]/\\halpha\\\nand [\\ion{S}{2}]/\\halpha\\ for the two sets of spectra, with each pair of\nobservations connected. Most of the \ndifferences follow the trajectories expected from changes in the nebular\nionization parameter. We have chosen to analyze the fixed position data, \nin order to take advantage of their higher signal/noise,\nand to maintain consistency with the CTIO data, which were \ntaken as fixed pointings. The only exception is the very large \n\\hii\\ region M8 (S25), which shows a large inconsistency between fixed\nand scanned spectra, presumably because the former is \nis strongly influenced by local variations in ionization \nstructure. In that case we use the drift scanned spectrum, which \nsamples a region of 10\\arcmin\\ $\\times$ 3\\arcmin\\ (EW $\\times$ NS),\ncentered on the position listed in Table 1 (see Fig.~2d). \n\n\\footnotetext{The Digitized Sky Surveys were produced at the \nSpace Telescope Science Institute under U.S. Government grant NAG W-2166.\nThe images of these surveys were based on photographic data obtained\nusing the Oschin Schmidt Telescope at Palomar Mountain and the\nUK Schmidt Telescope. The plates were processed into the present\ndigital form with the permission of these institutions.}\n\nExposure times of 300$-$1200 sec were chosen to provide accurate \nspectrophotometry of the bright diagnostic lines (S/N $>$ 20 in most cases). \nThe fainter auroral lines such as \n[\\ion{O}{3}]\\thinspace $\\lambda$4363 were not a target of this study, and\nin many cases they were too weak in our spectra to be useful.\nThe spectrophotometric flux calibration was determined using \nstandard stars from Massey et al. (1988) for the blue\nspectra, and stars from Oke \\& Gunn (1983) for the red spectra. \nThe observations were made with 2\\farcs5 and 4\\farcs5 wide slits, oriented\nto limit errors from atmospheric dispersion effects to $<$0.05 mag across\nthe wavelength range. \n\n\\subsection{CTIO Data}\n\nThe southern Galactic \\hii\\/ regions and all of the LMC and SMC \n\\hii\\ regions were observed in 1987 Jan, 1987 Dec, and 1988 Jan\nusing the CTIO 1.0 m and 1.5 m telescopes.\nAt the time that these observations were made a blue-sensitive CCD\ndetector was not available, so the blue spectra were obtained \nwith a 2D FRUTTI photon counting detector system on the 1.0 m Cassegrain\nspectrograph. The instrument was configured\nwith a 600 g~mm$^{-1}$ grating blazed at 5000 \\AA\\ and WG-360 blocking\nfilter, which provided coverage of 3600--7000 \\AA\\ and a resolution of \n6 \\AA\\ FWHM when used with an 8\\arcsec\\ $\\times$ 6\\arcmin\\ slit.\nAll observations were made with the slit oriented E--W at a fixed position,\nusually centered 10\\arcsec\\ south of the central star. Due to the limited \ndynamic range of the 2D FRUTTI detector, observations of bright \nregions were made with neutral density filters, and\nexposure times for most objects were 900--1800 sec, largely independent \nof surface brightness. Standard stars from Stone \\& \nBaldwin (1983) were observed with a 12\\arcsec\\ wide slit for flux calibration.\n\nRed spectra were obtained with the Cassegrain spectrograph on \nthe CTIO 1.5 m telescope, equipped with an unthinned 385$\\times$576\nGEC CCD detector. Two grating settings were used for most of the \nobjects. A 158 g~mm$^{-1}$ grating blazed at 8000 \\AA\\ in first \norder and a OG-550 blocking filter provided complete coverage of the\n5730--10200 \\AA\\ region, with a resolution of approximately 20 \\AA\\ FWHM\nwhen used with a 6\\arcsec\\ $\\times$ 6\\arcmin\\ slit. \nA second set of spectra were obtained\nusing a 600 g~mm$^{-1}$ grating blazed at 6750 \\AA, to cover the\nregion 5650--6850 \\AA\\ at 5 \\AA\\ resolution, again with a 6\\arcsec\\ slit.\nThe low-resolution spectra were used primarily to measure the diagnostic\nlines longward of 7000 \\AA\\ (mainly \\siii\\ and \\ariii), while the \nhigher-resolution spectra provided the best measurements of the \\nii, \\sii,\nand \\ion{He}{1} $\\lambda$6678 lines. Exposure times ranged from 120 to 1800 \nsec. Standard stars from Stone and Baldwin (1983) and Baldwin \\& Stone \n(1984) were observed with a 12\\arcsec\\ slit. \n\nIn order to investigate the local variation in the nebular diagnostic indices\nwithin individual \\hii\\ regions, we obtained spectra at additional positions\nin the Carina and 30 Doradus \\hii\\ regions, as shown in Figures 2c and \n2g, respectively. The observations of 30 Dor include a series of five \npositions extending E--W a total of 24\\arcmin\\ through the center of the \\hii\\\nregion. We also obtained red spectra only at 22 other positions in 30 Dor and \n12 positions in the Orion nebula, to match previous observations at \n3700--7200 \\AA\\ by Mathis, Chu, \\& Peterson (1985) and Peimbert \\& \nTorres-Peimbert (1977), respectively. Charts showing the positions of these\nmeasurements can be found in the original papers. The red spectra were\nused to extend the wavelength coverage of the published measurements to the \n\\siii\\ lines. We used the overlapping coverage of the \\halpha, \n[\\ion{N}{2}], and [\\ion{S}{2}] lines to firmly tie in the \n[\\ion{S}{3}] fluxes, and confirm that the identical regions were observed. \n\n\\subsection{Data Reduction and Calibration}\\label{reduction}\n\nThe spectra were reduced using the two-dimensional spectrum reduction\npackage in IRAF\\footnotemark, following conventional procedures.\nWe limit the discussion here to reductions and tests that were \nunique to this data set. Spatial distortions in the long-slit spectra were \nremoved using comparison lamp exposures. The distortions were\nconsiderable in the 2D FRUTTI data, and data within 5--10\\%\\\nof the slit edges were excluded in subsequent reductions.\nThe 2D FRUTTI spectra were checked for deadtime effects in the bright lines,\nusing short exposures obtained with darker neutral filters, and by \ncomparing the observed \\oiii\\ doublet ratio (the strongest feature in most\nraw spectra) to its theoretical value. Deadtime effects were present in only\na small fraction of the spectra, and in such cases the \n[\\ion{O}{3}]\\thinspace $\\lambda$5007 line was discarded, \nand the scaled flux of [\\ion{O}{3}]\\thinspace $\\lambda$4959 was used instead.\nSimilar checks were carried out with multiple neutral density\nfilters on the standard stars, and measurements with any hint of a\nsaturation problem were discarded.\n\n\\footnotetext{IRAF is \ndistributed by the National Optical Astronomical Observatories, which\nare operated by AURA Inc., under contract with the National Science\nFoundation.} \n\nCalibration of the red CCD spectra in the \\siii\\ region also required special\ncare, due to the presence of unresolved telluric water absorption lines, \nTo maximize the reliability of the [\\ion{S}{3}] measurements we made frequent\nobservations of subdwarf standard stars located at the same airmass as the \n\\hii\\/ regions, and used a high-order spline fit to the stellar spectra\nto remove the absorption on\nwavelength scales of $>$50 \\AA\\ (exclusive of the regions around the\nPaschen emission lines, which are influenced by absorption lines in the\nstandard stars). The reliability of this procedure was\nconfirmed by the degree of consistency of the observed \\siii\\ doublet ratios\nwith its theoretical value (2.44), and by the shapes of the \ncalibrated continuum spectra in the \\hii\\ regions themselves.\n%These tests indicate that the total [\\ion{S}{3}] doublet flux should be\n%accurate at the 10--20\\%\\ level for most objects.\nAs a conservative measure we attach a mean uncertainty of \n$\\pm$20\\%\\ to the summed \\siii\\ fluxes.\n\nThe overall precision of the spectrophotometry was determined from \ncomparisons of multiple observations of the same objects, intercomparison\nof the blue and red spectra in the overlapping wavelength regions, and from\nthe measured ratios of the [\\ion{O}{3}] and [\\ion{S}{3}] doublets.\nThe typical uncertainties for strong lines range from $\\pm$5\\%\\ or better for \nthe Bok CCD spectrophotometry (excluding the [\\ion{S}{3}]\nlines) to $\\pm$10\\%\\ for the CTIO blue spectra (2D FRUTTI) and \n$\\pm$20\\%\\ for the [\\ion{S}{3}] fluxes and the CTIO [\\ion{O}{2}] fluxes.\nExternal comparisons with published sources such as Dufour (1975), Shaver et\nal. (1983), Mathis et al. (1985), and Hunter (1992) show consistency to the \ndegree that is expected given the measuring errors above and differences in\npositions and aperture sizes. The only exception is a tendency for the\n\\ion{He}{1}\\ $\\lambda$5876 fluxes measured at CTIO (2D FRUTTI) to be \nsignificantly lower than those from published sources, and consequently \nwe attach more weight to the \\ion{He}{1}\\ $\\lambda$6678 (CCD) data in these \nobjects. \n\n\\subsection{Emission-Line Measurements}\\label{spectra}\n\n%Since a main goal of our analysis is to compare the observed\n%spectra of the \\hii\\/ regions with the integrated spectra\n%of model \\hii\\/ regions, \nA one-dimensional spectrum of each region was extracted \nby summing over the radial extent of the \\hii\\ region on the slit.\nWhenever possible a background sky measured from the outer parts of the slit\nwas subtracted, but when the \\hii\\ region filled the slit the sky\nwas included and subtracted in the fitting of each line flux\n(after confirming the absence of sky line contamination). \nAnalysis of the extracted 1D spectra followed standard\nprocedures. Line fluxes were measured by a direct integration\nof the line profile, with subtraction of a linearly interpolated \ncontinuum, using either the SPLOT task in IRAF or our own software.\nThe flux scales of the blue and red spectra were tied together using the \nsum of the \\halpha\\ and \\nii\\ lines. \n\nReddening corrections were derived from the Balmer decrement\n(\\halpha, \\hbeta, \\hgamma), the theoretical Balmer line\nratios as calculated by Hummer \\& Storey (1987), and the average\ninterstellar reddening curve from Cardelli, Clayton, \\& Mathis (1989). \nWhen measured electron \ntemperatures and densities were available, either from the literature or from \nour spectra, they were used to determine the theoretical Balmer\ndecrement; otherwise a temperature of 10000 K and density of 100 cm$^{-1}$\nwere assumed.\n\nTable 2 lists the reddening-corrected line fluxes for the principal\ndiagnostic lines, as well as the logarithmic extinction at \\hbeta\\ (column 2).\nAll fluxes are normalized to $f(H\\beta) = 100$. For \\hii\\ regions with\nmultiple measurements we have listed the fluxes for a single representative\nposition. Complete line lists,\nincluding the fainter lines and the multiple position measurements are\navailable from the authors upon request.\n\n\\section{ANALYSIS}\n\nBefore we specifically address the nebular diagnostics of abundance\nand stellar temperature, it is instructive to examine the behavior\nof the \\hii\\ region spectra using the well-known diagnostic diagrams of\nBaldwin, Phillips, \\& Terlevich (1981), \nand compare them to the spectra of more distant and luminous extragalactic\n\\hii\\ regions. \n\nTo aid in the physical interpretation of these diagnostic\ndiagrams, we have computed a set of {\\sc cloudy} nebular models\n(Ferland et al.~1998), using non-LTE stellar atmosphere models by the Munich\ngroup (Pauldrach \\etal 1998) as the source of ionizing photons, as\ndescribed in BKG. These will be used later to \ncompare the stellar effective temperatures from nebular model fitting\nto the actual effective temperatures of the exciting stars. However in\nthis section the main use of the models will be to illustrate how \nchanges in metal abundance, stellar temperature, or ionization parameter\naffect the various line ratios.\n\n\\subsection{Diagnostic Diagrams and Ionization Parameter}\n\nFigure 4 shows two of the most commonly used diagnostic diagrams for\nextragalactic \\hii\\ regions and AGNs, with the excitation ratio \n[\\ion{O}{3}]$\\lambda5007$/H$\\beta$ plotted against \n[\\ion{N}{2}]$\\lambda$6583/H$\\alpha$ and \\sii/\\halpha.\nHere and in the following figures we have subdivided the sample:\nsolid squares mark the calibrating Galactic \\hii\\ regions ionized\nby one (or a few) OB stars; open squares correspond to the more\nluminous Galactic \\hii\\ regions ionized by associations of OB stars\nwith a range of spectral types; open circles denote the LMC and SMC\nregions, and open stars indicate the four nebular ionized by early-type\nW-R stars. For comparison we have plotted with small triangles the same line \nratios for a large sample of extragalactic \\hii\\ regions in Sa--Im galaxies, \nfrom BKG.\n\nExtragalactic \\hii\\ regions show a tight spectral sequence in both\nof these diagrams (McCall, Rybski, \\& Shields 1985, Kennicutt \\& Garnett\n1996), which often is interpreted as evidence that giant \\hii\\ regions\nare predominantly radiation bounded objects (McCall et al. 1985).\nFigure 4 shows that the much smaller Galactic \\hii\\ regions also\nlie on this same sequence. The correspondence is especially tight\nin the case of [\\ion{O}{3}]/\\hbeta\\ vs [\\ion{N}{2}]/\\halpha, where the\nsequences are virtually indistinguishable. The WR nebulae lie\nwell above the sequence, which reflects the very high effective\ntemperatures of these stars (\\teff\\ $\\ge$ 55000 K). The LMC \\hii\\ regions \nshow a slight tendency toward weaker [\\ion{N}{2}] emission, which probably\nreflects the anomalous N/O ratio in this galaxy (Garnett 1999).\n\nIn extragalactic \\hii\\ regions the tight spectral sequences (Fig.~4)\nare mainly interpreted as being abundance sequences (e.g., Searle 1971, \nShields \\& Searle 1978, Pagel \\& Edmunds 1978, McCall et al.~1985).\nHowever in our sample the primary variable\nalong the sequence is not abundance but stellar temperature. This\nis shown in Figure 5, which again shows the [\\ion{O}{3}]/\\hbeta\\ vs \n[\\ion{N}{2}]/\\halpha\\ relation, but this time with the points coded\nby stellar temperature (left) and by oxygen abundance (right). \nAlthough both parameters clearly influence the position of \\hii\\ regions\nalong the sequence, variations in \\teff\\/ clearly dominate in this sample.\nThe virtual indistinguishability between this \\teff\\/ sequence\nwith the extragalactic ``abundance\" sequence illustrates \nthe degeneracy between temperature and abundance\n(and to some degree ionization parameter) in this type of diagnostic\ndiagram. In hindsight this may help to explain why it has proven\nso difficult to disentagle variations in ionization temperature and\nIMF from abundance variations in extragalactic \\hii\\ regions.\n\nThe correspondence between the Galactic and extragalactic sequences\nis much poorer for [\\ion{O}{3}]/\\hbeta\\\nvs [\\ion{S}{2}]/\\halpha, with the small Galactic \\hii\\ regions showing\nsystematically weaker [\\ion{S}{2}] emission (Fig.~4). A comparison with the\ndriftscanned spectra in Fig.~3 shows that this is partly due to the \nspatial undersampling of our slit spectra, but the remainder of the \ndifference appears to be a systematic difference in mean ionization parameter\nbetween the two samples. This is quantified in Figure 6, which \nplots the ionization-sensitive ratio \\sii/\\siii\\ as a function of \\teff\\ \nof the ionizing stars (same symbols as Fig.~4). The \nThe [\\ion{S}{2}]/[\\ion{S}{3}] ratio is commonly used as a diagnostic of the \nnebular ionization parameter $U$ (D\\'{\\i}az et al. 1991), defined in this case\nas the ratio of ionizing photon to electron densities. It can be expressed as:\n\\begin{equation}\nU = {{Q_{H^0}} \\over {4 \\pi {R_S}^2 n c}}\n\\end{equation}\nwhere $Q_{H^0}$ is the ionizing luminosity of the stars (photons per sec), \n$R_S$ is the Str\\\"omgren radius of the \\hii\\ region, $n$ is the \nelectron density, and $c$ is the speed of light. Superimposed on\nFig.~6 are photoionization models for values of \n$\\log U$ between $-$1.5 and $-$4.0 (see BKG for details). \nMost of the regions studied here lie in the range of $-3.5 \\le \\log U \n\\le -1.5$, whereas most bright extragalactic \\hii\\ regions lie in a \nnarrower range with $-3.5 \\le \\log U \\le -2.5$ (BKG). The difference\nprimarily reflects the larger aperture sizes in extragalactic studies\n(typically hundreds of parsecs in projected diameter). This\ndifference is not large enough to affect the comparison of\n$U$-insensitive indices such as the abundance parameter \\x\\ and the\nnebular hardness parameter \\etap\\ (\\S 4.3), but it may need to be\ntaken into account when applying more ionization-sensitive indices\nsuch as [\\ion{O}{3}]/\\hbeta, [\\ion{Ne}{3}]/\\hbeta, or \n[\\ion{O}{3}]/[\\ion{N}{2}] (below).\n\n\\subsection{Abundance Indices}\n\nThe backbone of the extragalactic abundance scale rests on direct\nelectron temperature based measurements, but in metal-rich \\hii\\ regions the \ntemperature-sensitive auroral lines are unobservable, and most abundance\ninformation in that regime is based on ``empirical\" excitation indices \nsuch as \\x\\ (Pagel\net al.~1979) or [\\ion{O}{3}]$\\lambda$5007/[\\ion{N}{2}]$\\lambda$6583 \n(Alloin et al.~1979).\n%and \\stt\\ $\\equiv$ (\\sii\\ $+$ \\siii )/\\hbeta\\ \n%(D\\'{\\i}az \\& P\\'erez-Montero 1999). \nOur data are not of sufficient quality to improve on \nthe existing calibrations of these indices, but \nwe can use our spatially resolved observations of \n30 Dor, Carina, and Orion to investigate the robustness of the empirical\nabundance indices. Do spectra of different regions in the same object\nyield consistent abundances? \n\nAs a test of the \\x\\ index, the left panel of Figure 7 shows the relation \nbetween \\oiii/\\hbeta\\ and \\oii/\\hbeta\\ (with linear scales) for the multiple\npositions in 30 Dor (open stars), Carina (triangles), and Orion \n(open circles). The 30 Dor data include spectra from Mathis et al.~(1985)\nand the Orion data are all from Peimbert \\& Torres-Peimbert (1977).\nAll three \\hii\\ regions show a very large range of excitation across\nthe regions sampled, with both [\\ion{O}{3}]/\\hbeta\\ and [\\ion{O}{2}]/\\hbeta\\\nvarying by factors of 2--5. However the sum of the line fluxes (\\x) is\nrelatively constant, as shown by the diagonal lines in Fig. 7,\nThe constancy of \\x\\\nis especially impressive in 30 Doradus and Carina, where the dispersion\nin \\x\\ transforms to a full range of $<$0.1 dex in O/H. The \\x\\ index\nis less well-behaved in Orion, though the range in abundances about\nthe mean value is no larger than the calibration uncertainty of the method.\nOur results confirm a similar test applied to \nthe giant \\hii\\ region NGC~604 in M33 (Diaz et al.~1987),\nand suggest that even spatially undersampled observations of local \n\\hii\\ regions may be useful for calibrating \\x.\n\nV\\'{\\i}lchez \\& Esteban (1996) and D\\'{\\i}az \\& P\\'erez-Montero (1999) \nhave explored the use of the sum of the [\\ion{S}{2}] and [\\ion{S}{3}]\nforbidden-line strengths, \\stt\\ $\\equiv$ (\\sii\\ $+$ \\siii )/\\hbeta\\\nas an empirical abundance index, in analogy to \\x. The main advantage\nof this index over \\x\\ is its monotonic behavior as a function of oxygen\nabundance, and its insensitivity to the global degree of ionization of\nthe nebula, at least for giant extragalactic \\hii\\ regions. The right\npanel of Fig.~7 shows the behavior of this index for the multiple \nposition observations of 30 Dor, Carina, and Orion. In contrast to \n\\x\\ (left panel), the \\stt\\ values show much more scatter and nearly complete\noverlap between the three \\hii\\ regions. This probably is due to a \ncombination of observational error in the \\siii\\ measurements and\nlarge local variations in \\sii/\\hbeta, which forms preferentially at\nthe ionization interfaces and in shocks. The \\stt\\ ratio (and hence\nthe inferred metal abundance) also varies systematically across the nebulae, \nespecially in 30 Dor, where the data span the full range of\nradius in the \\hii\\ region. This suggests that \\stt\\ should\nonly be applied to global spectra of \\hii\\ regions, which sample a \nrepresentative fraction of the S$^{++}$ and S$^+$ emitting volumes.\nDespite the considerable scatter in \\stt\\ within each \\hii\\ region,\nthe corresponding dispersion in inferred metal abundances \nis only slightly larger than for \\x, due to the relatively\nweak $Z$-dependence of \\stt\\ in this excitation range, if the calibration of \nD\\'{\\i}az \\& P\\'erez-Montero (1999) is used. \n\nFigure 8 shows a similar test of the [\\ion{O}{3}]/[\\ion{N}{2}] empirical\nabundance parameter. We would expect this ionization-sensitive index\nto show a larger dispersion within individual \\hii\\ regions, and this\nis borne out in Fig. 8. The index shows a dispersion of $\\ge$1 dex in all\nthree \\hii\\ regions, and the \ninferred abundance values overlap between the objects. The horizontal lines\nindicate the corresponding oxygen abundances in terms of $12 + \\log O/H$,\nusing the calibration of Dutil \\& Roy (1999); the inferred abundances\nshow dispersions of $\\pm0.2 - 0.3$ dex in a given \\hii\\\nregion, about 2--3 times larger than for \\x. The relevance of these\nresults for extragalactic applications is unclear, however. Comparisons of \noxygen abundances derived from [\\ion{O}{3}]/[\\ion{N}{2}] and \\x\\ have\ntended to show excellent agreement across a wide range of excitation\n(Ryder 1995, Roy \\& Walsh 1997), and indeed the former abundances show\na lower scatter, which suggests that the \n[\\ion{O}{3}]/\\ion{N}{2}] method can be reliable for luminous \\hii\\ regions\nwhere the spectrophotometric aperture encloses most of the emitting\nvolume. However it is also possible that the apparent consistency of\nthe [\\ion{O}{3}/\\ion{N}{2}] abundances is the result of a relatively\nnarrow range of ionization parameters and other nebular properties within\nthe samples that have been studied to date, and that this consistency\ncould break down when applied to samples \nof \\hii\\ regions with systematically different aperture sampling, ionization\nstructure, or other nebular properties. \n\n\\subsection{Diagnostics of Stellar Temperature and IMF}\n\nEmission-line spectra of \\hii\\ regions and starbursts are being applied\nincreasingly to constrain the ages and IMFs in the exciting star clusters\n(e.g., Stasi\\'nska \\& Leitherer 1996, Garcia-Vargas et al. 1997, BKG,\nGarnett 2000, and references therein). These applications rely on the ability \nto use nebular ionization models to characterize the shape and\nhardness of the ionizing continuum shortward of the Lyman break. \nIn this section we use the sample of calibrating \\hii\\ regions to\ndirectly assess several hardness parameters, ranging from robust\nindices such as the ionized He fraction to crude but commonly used\nindices such as the [\\ion{O}{3}]/\\hbeta\\ ratio. \n\n\\subsubsection{He Recombination Lines}\n\nThe fractional ionization of He provides a robust measure of stellar\ntemperature, following methods established originally by Zanstra (1927).\nMost of the helium in \nnormal \\hii\\ regions is either neutral or singly ionized,\nso the relevant diagnostics are the ratios of the \\ion{He}{1}\\ and\n\\ion{H}{1}\\ recombination lines. Figure 9 shows the line ratios\n\\ion{He}{1}~$\\lambda$5876/\\hbeta\\ and \\ion{He}{1}~$\\lambda$6678/\\halpha\\ \nplotted as functions of stellar temperature. Superimposed are the \nmodel relations, based on the stellar atmosphere models of BKG and\nassuming Case B recombination following Osterbrock (1989). Models\nare plotted for abundances of 1.0 \\zsun\\ (solid lines) and 0.2 \\zsun\\\n(dashed lines), and for ionization parameter $\\log U$ of $-$1.5 \n(upper) and $-$4.0 (lower). Given the relatively narrow range of $U$\nin our sample the ionization parameter dependence is unimportant, but\nthe range of abundance in the sample has some effect on the observed\nline ratios (both via line blanketing in the ultraviolet and the He\nabundance). The symbols \ndifferentiate between calibrating single-star regions, and larger\nGalactic and Magellanic Cloud \\hii\\ regions, following Figure 4. The\nmodel lines represent the mean He ionization over the entire nebula, so for\nthe \\hii\\ regions with partial He ionization we only considered\nobjects for which we had full or representative spatial coverage of\nthe nebula.\n\nFigure 9 shows an excellent agreement between the observed levels\nof He ionization and the model predictions, especially for \n\\ion{He}{1}~$\\lambda$6678/\\halpha\\ where our data are the best\nand reddening errors are minimal. The most discrepant regions are\nS275, where our spatial coverage is very incomplete, and S162 (NGC~7635),\nwhich is ionized by an O6.5\\thinspace IIIf star. The latter is the only \\hii\\ \nregion in our sample which is predominantly ionized by a giant star,\nbut it is unclear whether the discrepancy for this object is coincidental \nor indicative of a general problem with the low-gravity stellar models.\nOtherwise the data show that the \\ion{He}{1}\\ lines provide an excellent\nmeasure of stellar temperature. Unfortunately this method is only\nsensitive when nebular He is partially ionized (35000 K $\\le$ \\teff\\ \n$\\le$ 39000 K). Most extragalactic \\hii\\ regions \nshow nearly complete ionization of helium (\\teff\\ $\\ge$ 40000~K), but the\n\\ion{He}{1}\\ lines do provide important constraints on the ionizing spectrum\nin the innermost metal-rich disks of spirals, where many other hardness\nindices break down (BKG). Moreover, Fig.~9 provides independent \nconfirmation of the reliability of the Vacca et al. (1996) effective \ntemperature scale, at least for \nluminosity class V stars in the \\teff\\ = 34000 $-$ 39000 K range. \n\n\\subsubsection{Forbidden-Line Excitation Indices}\n\nThe simplest and crudest indicators of stellar temperature are based\non single forbidden-line ionization indices, such as [\\ion{O}{3}]/\\hbeta\\\n(Chopinet \\& Lortet-Zuckermann 1976, Kaler 1978, Copetti, Pastoriza, \\&\nDottori 1985, 1986), or analogous infrared\nindices such as [\\ion{O}{3}]\\thinspace 88 $\\mu$m/H\\thinspace 53$\\alpha$ \nor [\\ion{N}{3}]\\thinspace 57 $\\mu$m/H\\thinspace 53$\\alpha$ (Puxley et al.\n1989). Figure 10 shows the dependence of \\oiii/\\hbeta\\ on stellar\ntemperature, again with the \\hii\\ regions subdivided as in Figure 4.\nThis measure of the excitation shows a tight correlation with\n\\teff\\ (for this sample of \\hii\\ regions), confirming the good\ncorrelations seen previously by Chopinet \\& Lortet-Zuckermann (1976), \nKaler (1978), and Hunter (1992). A roughly linear, increasing trend\ntrend in [\\ion{O}{3}]/\\hbeta\\ with \\teff\\ is expected, because the\nnebular volume containing double-ionized oxygen increases with the\nhigher ionizing flux emitted by earlier spectral type stars\n(Stasi\\'{n}ska 1978). The observed correlation has a remarkably linear\nform, extending to the WR stars with temperatures of nearly 70000 K.\nThe adopted \\teff\\ scale for the WR stars (Esteban et al.~1993) is \npartly based on nebular modeling, however, so \nstrictly speaking the empirical relation in Fig. 10 only applies for\n\\teff\\ $\\le$ 50000~K.\n\nDespite the tightness of the correlation in Figure 10, the [\\ion{O}{3}]/\\hbeta\\\nratio must be applied with considerable caution to extragalactic \n\\hii\\ regions and starbursts, because the ratio is sensitive to \nother variables such as ionization parameter and metal abundance. \nThis is illustrated by the four model sequences in Fig. 10, plotted for \noxygen abundances of 0.2 $Z_\\odot$ and 1.0 $Z_\\odot$ and \n$\\log U$ = $-$2.0 and $-$4.0 (with \\teff\\/ varying along each sequence). \nThe best fitting\nmodels correspond to typical ionization parameters of $\\log U \\sim -2.5$\nand $Z/Z_\\odot \\sim 0.5 - 1$, consistent with the measured values from \nFig.~5 and Table 1, respectively. However the same excitation vs \\teff\\\nrelation may not apply in \nexternal galaxies, where both $Z/Z_\\odot$ and $\\log$U may be shifted\nrelative to the typical values in this sample.\n\nWe have also investigated the behavior of two other ionization indices\nwhich have been suggested as hardness indicators, \\ariii/\\halpha\\\nand \\neiii/\\oii. Both are plotted against stellar temperature in\nFigure 11. The figure also shows the temperature dependence of \n\\oiii/\\hbeta, but plotted this time with a logarithmic scale to\nprovide a direct comparison with the other two indices. The behavior of\n[\\ion{Ar}{3}]/\\halpha\\ is qualitatively similar to that seen for \n[\\ion{O}{3}]/\\hbeta, but with a larger scatter and shallower slope \nabove \\teff $\\sim$ 38000 K. This is not surprising because the lower\nionization potential for Ar$^+$ (27.6 eV vs 35.1 eV for O$^+$) \nis close to the He$^+$ edge at 24.6 eV. Furthermore the excitation\nof [\\ion{Ar}{3}] is sensitive to the ionization parameter and abundance\nin the same way as [\\ion{O}{3}], so it provides a poor substitute \nfor the much more robust He$^+$/H$^+$ index discussed earlier.\n\nThe bottom panel of Fig. 11 shows the temperature dependence of the\nhybrid forbidden-line ratio \\neiii/\\oii. Ali et al.~(1991) have shown\nthat this ratio provides a valuable index for deriving ionization\ncorrection factors in nebular abundance measurements.\nFigure 11 shows a strong monotonic dependence of [\\ion{Ne}{3}]/[\\ion{O}{2}] \non \\teff, which reflects the 41.1 eV ionization potential of Ne$^+$, but\nthe large scatter in the relation limits its usefulness as a stellar \nthermometer. The weakness of the [\\ion{Ne}{3}] line in metal-rich \n\\hii\\ regions also limits its value for extragalactic applications. \nA similar plot of [\\ion{Ne}{3}]/\\hbeta\\ shows a nearly\nidentical scatter, so variations on [\\ion{O}{2}] excitation are\nnot responsible for this dispersion. Our result is somewhat surprising\nin light of the relatively robust behavior of [\\ion{Ne}{3}]/\\hbeta] in \nthe recent analysis of Oey et al. (2000). Of all of the forbidden-line\nratios that are accessible at visible wavelengths, the familiar\n[\\ion{O}{3}]/\\hbeta\\ index appears to be the most useful stellar\ntemperature indicator, though this sensitivity is accompanied by \nstrong dependences on many other nebular properties.\n\n\\subsubsection{Composite Ionization Indices: \\etap}\n\nThe well-known sensitivity of excitation indices such as \n[\\ion{O}{3}]/\\hbeta\\ to nebular ionization structure and abundance\nled Mathis (1985) and V\\'{\\i}lchez \\& Pagel (1988) to investigate\nthe use of composite indices based on the ionization of more than\none element, in an effort to find a more robust UV hardness indicator.\nThe advent of CCD spectrographs has made the \\siii\\ doublet accessible,\nand with it the possibility of using the $O^{+}/O^{++}$ and \n$S^+/S^{++}$ to contrain \\teff\\ independently of metal abundance\nand ionization parameter. A convenient hardness index is the \nparameter \\etap\\ introduced by V\\'{\\i}lchez \\& Pagel (1988):\n\\begin{equation}\n\\eta\\prime = \\frac{[O\\thinspace II]\\lambda\\lambda3726,3729 / \\oiii}{\\sii / \\siii } .\n\\end{equation}\n\n\\noindent\nThe robustness of \\etap\\ can be tested directly by plotting the behavior\nof [\\ion{O}{2}]/[\\ion{O}{3}] vs [\\ion{S}{2}]/[\\ion{S}{3}] for 30 Doradus, \nOrion, and Carina, where\nwe have spectra at multiple positions. This is shown in Figure 12a,\nalong with a series of nebular models from BKG. \nConstant \\teff\\/ lines are drawn at $Z = 0.5~Z_\\odot$ for\n\\teff\\ = 50000, 45000, 40000, and 35000~K (left to right). \nAlong each line the ionization\nparameter varies from $\\log U=-1.5$ (bottom) to $\\log U=-4.0$ (top).\nThe dashed lines show the effects of changing metal\nabundance between $Z = 0.2~Z_\\odot$ (left) and 1.0 $Z_\\odot$ (right,\nindicated by small dots), for the same\nrange of stellar temperatures and a fixed ionization parameter \n$\\log U=-2.5$. For further details on the models see BKG.\n\nFor 40000~K $\\le$ \\teff\\ $\\le$ 50000~K the lines of constant stellar\ntemperature have a slope of near unity in this diagram (i.e. constant \\etap),\ndemonstrating the robustness of \\etap\\ against changes in ionization\nparameter, at least in the models. More impressive yet is the \ndistribution of the observed line ratios at the various positions\nin 30 Doradus (open stars) and Orion (open circles), which fall on\nlines of nearly constant \\etap, over ranges of nearly an order of magnitude\nin [\\ion{O}{2}]/[\\ion{O}{3}] or [\\ion{S}{2}/[\\ion{S}{3}].\nThe observations of Carina (triangles)\nshow a large scatter in \\etap, and we suspect that this dispersion is real,\nreflecting the influence of ionization from stars\nwith different temperatures across this complex region. However \nOey et al. (2000) have also found that \\etap\\ shows a larger point-to-point\nvariation in their sample of 4 LMC shell \\hii\\ regions, and this may\nsuggest limits to the range of spatial scales and nebular properties\nwhere \\etap\\ provides a reliable measure of ionizing stellar temperature.\n\nAlthough the spectra of 30 Dor and Orion are consistent with a nearly\nconstant value of \\etap\\ (and hence \\teff), Fig.~12a shows a systematic \noffset between the effective temperatures implied by the models\n($\\sim$39000 K and 37000--38000 K respectively), and those estimated from\nthe stellar contents of the regions ($\\sim$48500 K and 40000 K respectively).\nFigure 12b shows the same diagram for the other \\hii\\ regions in the \nsample (a nebular model for \\teff\\ = 30000 K is added), and a similar offset\nin the stellar temperature scales is apparent, if one compares with the\nactual \\teff\\ values in Table 1. The \\hii\\ regions ionized by cooler stars\n(\\teff\\ $<$ 37000 K) seem to show better agreement with the models.\nNevertheless the general consistency between the nebular and spectroscopic \ntemperatures is encouraging, confirming and extending earlier results\nby Mathis \\& Rosa (1991).\n\nFigure~12 impressively demonstrates the robustness of \\etap\\ against \nsystematic variations in $U$, but the models plotted in the figure\nsuggest a significant dependence of \\etap\\ on metal abundance. The\ndashed lines show the effects of changing $Z$ from 0.2 \\zsun\\ (left)\nto 1.0 \\zsun\\ (right). The $Z$-dependence is relatively weak for\nhotter stars (\\teff\\ $\\ge$ 40000 K) and low abundances ($Z \\le 0.5$ \\zsun), \nbut becomes large for cooler stars, where the effects of abundance and stellar\ntemperature become virtually degenerate, and \\etap\\ itself\nbecomes nearly degenerate with [\\ion{O}{2}/\\ion{O}{3}] and [\\ion{O}{3}]/\\hbeta.\nInspection of the models suggests that two physical effects contribute\nto this abundance sensitivity, increased stellar metal line blanketing in the \nultraviolet, which softens the ionizing spectrum at a given effective \ntemperature, and the increasing dominance of nebular cooling (especially\nO$^{++}$) over ionization structure in determining the relative forbidden-line\nstrengths at high abundance (Shields \\& Searle 1978, Oey \\& Kennicutt 1993,\nStasinska \\& Leitherer 1996). Thus it is important to confirm\nthe \\etap-derived stellar temperatures for low-excitation nebulae with those\nderived from more robust hardness indices, such as the He recombination lines.\n\nThe degeneracy between abundance and stellar temperature in model spectra\nhas hampered previous model-based studies of the metallicity dependence of the \nstellar temperatures and IMFs of extragalactic \\hii\\ regions (e.g., BKG).\nHowever the data presented in this paper allow to test the correlation between \n\\etap\\ and \\teff\\ empirically, independently of the nebular models.\nThe results are shown in Figure 13; the points show the measured values of\n$\\log$ \\etap\\ and \\teff, subdivided as in Fig.~4, while the three lines show \nthe nebular model relations for 0.2, 0.5, and 1.0 $Z_\\odot$ ($\\log U = -2.5$\nin all three cases). The \\hii\\ regions span a range of roughly 2 dex in\n$\\log$ \\etap\\ (S237, with no detected [\\ion{O}{3}] emission, is not plotted),\nand the index shows a monotonic dependence on stellar temperature, albeit\nwith a considerable scatter. The general\nshape of the $\\log \\eta\\prime$ vs \\teff\\ relation is consistent with that\npredicted by the nebular models; the hatched line shows a quadratic \nfit to the observed \\hii\\ regions (excluding the WR nebulae, where the\ntemperature calibration is uncertain), and its general shape is in\ngood agreement with the model relations for the relevant abundance \nrange of $\\sim$0.4--1.0 \\zsun. \n\nIn contrast to the behavior of our nebular models, our \\hii\\ region data \nshow no evidence for a strong $Z$-dependence of the \\etap\\ vs \\teff\\\nrelation. In particular, there is no evidence in Fig.~13 for a systematic \nshift between the LMC \\hii\\ regions\nand the more metal-rich (on average) Galactic \\hii\\ regions, or likewise\nfor any difference between the most metal-rich and metal-poor Galactic\n\\hii\\ regions. Within the considerable scatter the trends seen in Fig.~13\nare independent of abundance. The singular exception of the \nSMC \\hii\\ region N66, which is the most metal-poor region in the sample,\nbut the \\teff\\ value of this region almost certainly is underestimated,\ndue to the presence of the luminous WR star HD 5980 (see the appendix).\n\nWe cannot explain why the observed\nbehavior of \\etap\\ appears to be more robust than the models would predict,\nbut we can speculate on the possible reasons. As pointed out earlier,\nour empirical estimates of \\teff\\ for the \\hii\\ regions are based on\nstellar spectral classifications, using a single, metallicity-independent\nspectral type vs \\teff\\ calibration (Vacca et al. 1996).\nWe believe that this procedure is justified, because the stellar types\nare predominantly assigned on the basis of H, He$^0$, and He$^+$ \nabsorption line strengths, which ought be robust against metallicity effects.\nHowever the stellar atmosphere grids which are used in the nebular\nmodels do show considerable changes in ultraviolet line blanketing with\nincreasing metal abundance, and this may alter the \nionization temperature at a given fixed effective temperature, in a way\nthat would not be reflected in the assigned spectral types of \nthe stars. Stated in another way, although we have calibrated \\etap\\\nin terms of stellar effective temperatures in Figure 13, the \nionization temperatures that are derived from \\etap\\ may not \nnecessarily coincide with \\teff\\ for abundances that differ substantially\nfrom the local Galactic value. We return to this point in \\S 5.\n\nIn summary, our data suggest that \\etap\\ offers the prospect of estimating \nthe characteristic \nstellar temperatures of the ionizing associations in \\hii\\ regions,\nover a relatively large temperature range ($33000 K \\le\nT_{eff} < 50000 K$), and on a calibration that is directly tied\nto the stellar spectral classification system, independent of the\nnebular model chain. However two important limitations of \\etap\\ must\nbe recognized before the results in Fig.~13 are applied indiscriminantly to\n\\hii\\ regions in external galaxies. First, the scatter in the $\\log$ \\etap\\ \nvs \\teff\\\nrelation is considerable, amounting to an rms uncertainty of $\\pm$3000 K\nfor any individual region. Second, photoionization models suggest that \nabundance effects may introduce systematic shifts of a comparable\nmagnitude in the derived effective temperatures, though the observations\nof the calibrating \\hii\\ regions do not show evidence for shifts of\nthis magnitude.\n\n\\section{Application to Extragalactic \\hii\\ Regions}\n\nIn this section we briefly apply the empirical relations between nebular\nhardness properties and stellar temperature from the previous section\nto the sample of extragalactic \\hii\\ regions studied by BKG.\nThe BKG data are well suited to our purposes because they span a\nlarge range of metal abundance and spiral galaxy type, and they are\nbased on spectra covering the 3600--9700 \\AA\\ range, so we can apply\nall of the hardness indices discussed earlier, including \\etap. Our\napproach is complementary to the model-based studies of V\\'{\\i}lchez \\&\nPagel (1988), Stasi\\'nska \\& Leitherer (1996), and BKG.\n\nWe begin by using the empirical fit to the $\\log$ \\etap\\ vs \\teff\\ relation\nin Fig.~13 (hatched line) to derive stellar temperatures for the BKG\nextragalactic \\hii\\ regions with reliable measurements of \\etap.\nFitting a quadratic function to the \ncalibrating Galactic \\hii\\ regions (solid squares) yields:\n\\begin{equation}\nT_{eff} = 50819 - 16485 x + 3778 x^2 \n\\end{equation}\nwhere $x \\equiv \\log$ \\etap. Although this relation is based solely on\nthe smaller calibrating \\hii\\ regions, where the \\teff\\ values are the\nmost reliable, using the entire sample does not change the resulting\nrelation significantly. Equation (3) is given primarily so readers\ncan reproduce and check the results described below; in view of the\ncaveats discussed in the previous section we {\\it strongly} advise\nagainst applying this relation generally to extragalactic regions, \nleast of all to luminous starbursts, where the physical conditions may differ\nsubstantially from those of the calibrating \\hii\\ regions.\n\nWith these caveats firmly in mind, the top panel of Figure 14 shows the \ncharacteristic stellar temperatures \\tstar\\ and oxygen abundance for \nthe BKG sample. We have deliberately avoided referring to these\nas effective temperatures, to emphasize that these are ionization\ntemperatures which may not coincide precisely with \\teff\\ outside\nthe calibrated abundance range. The abundances \nhave been derived using the \\x\\ empirical method following the calibration of\nEdmunds \\& Pagel (1984), and should be reliable to within\n$\\pm$0.2 dex for $Z \\le$ \\zsun, but less accurate at higher abundances.\nHowever this accuracy is sufficient for testing for general trends in \\tstar\\ \nwith metallicity. The values of \\tstar\\ inferred from equation (3)\nshow a large scatter, consistent with the large scatter observed\nin the calibrating sample (Fig.~13), combined with \nany real scatter in \\tstar\\ at fixed abundance, due to variations\nin age and other properties of the ionizing star clusters. \nThe large dispersion in Fig. 14a underscores the dangers of applying \n\\etap\\ or any other forbidden-line hardness parameter to an individual\n\\hii\\ region. Nevertheless the general behavior of \\tstar\\ \nshould be meaningful.\n\nThe top panel of Fig.~14 shows a clear trend in stellar temperature, with the \ntypical \\teff\\/ decreasing from $\\sim$55000 K at 0.2 $Z_\\odot$ \n($12 + \\log O/H = 8.2$)to $\\sim$40000 K above solar abundance \n($12 + \\log O/H = 8.9$). This trend is in excellent agreement with the\nmodel-based results of BKG, except for a temperature offset of \nabout 5000 K; BKG esitmated a \\teff\\/ range of 50000 K to 35000 K\nover the same abundance range. In both cases note that most of the \\teff\\/\nchange is restricted to abundances below solar.\n\nThe measured \\ion{He}{1}\\ line strengths in the BKG spectra provide another\nempirical constraint on the stellar temperatures in metal-rich \\hii\\ regions.\nUnfortunately the He lines are only useful for regions ionized by stars\nwith \\teff\\ $\\le$ 38000 K, when one allows for observational uncertainties\nin the He line fluxes and the dependences on abundance and ionization \nparameter. Nevertheless we can at least test the consistency of the\n\\etap\\ and He$^+$/He$^0$ temperature scales for the most metal-rich\nregions ($12 + \\log O/H > 9.0$). The crosses in Fig.~14 \nshow the values of \\teff\\ that are implied by the observed \n\\ion{He}{1}\\thinspace $\\lambda$5876/\\hbeta\\ ratios and the models\nshown in Fig.~9 (the \\ion{He}{1}\\thinspace $\\lambda$6678 line is\nusually too faint to provide reliable constraints on \\teff), with\nwith arrows indicating objects for which the He recombination lines only\nset lower limits on \\teff. The \\ion{He}{1}\\ data confirm the general\ntrend toward lower \\tstar\\ for $Z >$ \\zsun, but with \\tstar\\ $\\sim \n38000 - 39000$ K at the highest abundances, about 2000 K cooler than given\nby \\etap. This comparison provides a good illustration of how two different\nhardness indices can provide complementary constraints on the stellar\npopulations in the \\hii\\ regions. \n\nAs an additional consistency check on these results, the bottom panel of \nFig.~14 shows the same relation, but in this case with the \\tstar\\ values \nderived from the average of the \\etap\\ vs \\teff\\ calibration (Fig.~13\nand eq. [3]), and the relation between [\\ion{O}{3}]/\\hbeta\\ and \\teff\\\nfrom Fig.~10). The latter is known to be sensitive\nto ionization parameter and to metal abundance itself, but surprisingly\nit yields values of \\tstar\\ that are close to those derived from \\etap.\nThis comparison yields a somewhat lower \\tstar\\ values at high abundance,\nwhich are in better agreement with the values derived from the \\ion{He}{1}\\\nrecombination lines. However because of the susceptibility of \n[\\ion{O}{3}]/\\hbeta\\ to dependences on parameters other than \\teff\\\nwe do not apply this diagnostic further. We suspect that the general\nconsistency of the results here are due to the fact that mean abundances\nand ionization parameters of the calibrating \\hii\\ region samples are\ntypical of the extragalactic \\hii\\ regions in the BKG sample, but this\ndoes {\\it not} imply that the abundance dependence of \\tstar\\ implied by\nthe [\\ion{O}{3}] excitation is necessarily robust by any means.\n\nIn summary the empirically-based stellar temperature indices show\nevidence for a systematic decrease in mean stellar temperature\nwith increasing metal abundance, which appears to qualitatively confirm\nprevious results based on nebular model fitting (V\\'ilchez \\& Pagel\n1988, BKG). Several physical effects\ncan contribute to this softening of the ionizing continuum with \nincreasing metallicity: increased line blanketing at constant \\teff,\na shift in \\teff\\ at constant stellar mass, and/or a change in the \nupper mass limit to the IMF. The models of Stas\\'inska \\& Leitherer\n(1996) suggest that changes in atmospheric blanketing and stellar\nevolution can account for most of the changes, and our results do\nnot contradict this conclusion. We refer the reader to that\npaper and to BKG for a more\ncomplete discussion of the implications of these changes in \\teff.\n\n\\section{CONCLUSIONS}\n\nIn conclusion, we have presented a set of empirical diagnostic line\nratios, calibrated against the effective temperature of the exciting\nstars. Our results provide a stronger empirical foundation for many\nof the most widely used nebular diagnostics (e.g., \\x, \\etap), and \nthey show much better agreement between observations and models than\noften was seen in earlier generations of stellar atmosphere and nebular\nphotoionization models (cf., Mathis 1985, V\\'ilchez \\& Pagel 1988).\nThe empirical relations presented here should be useful in many \ninvestigations of the\nstellar populations of extragalactic \\hii\\/ regions, where very limited\ninformation is available on the exciting stars, and where an \nestimate of the nebular-based effective temperature is needed, \neven with a restricted wavelength coverage.\n\nWe close by reemphasizing the exploratory nature of this study,\nand pointing out the most urgently needed improvements before \none can reliably extract quantitative constraints on the stellar\ncontents and IMFs of star forming regions from nebular spectra.\nOn the empirical side, this approach can be much improved if \naccurate ($T_e$-based) metal abundances are obtained for all of the calibrating\n\\hii\\ regions (or their exciting stars), and the effects of effective\ntemperature, metal abundance, and nebular geometry are accounted for\nexplicitly in the analysis. Oey et al. (2000) have demonstrated the\nvalue of obtaining high signal/noise point-by-point measurements of\nindividual \\hii\\ regions, and applying this approach to a larger sample\nof objects would provide a major improvement over our exploratory \nanalysis. On the theoretical side, more self-consistent\nstellar models for the relevant range of abundances, temperatures, and\ngravities are the most crucial inputs. This would also allow for a \nconsistent treatment of stellar and nebular abundances in the photoionization\ncalculations. We hope that these initial results may stimulate\nfurther progress in these areas.\n\n\\acknowledgements\n\nIt is a pleasure to thank A.~Pauldrach, R.-P. Kudritzki, and T.~Hoffmann\nfor sharing their unpublished stellar atmosphere models, and S.~Oey\nfor a preliminary version of her paper and many discussions about this work. \nThis research was supported in part by the National Science Foundation\nthrough grants AST-9421145 and AST-9900789. \n\n\\bigskip\n\n\\appendix\n\n\\centerline{\\bf APPENDIX}\n\n\\centerline{\\bf EXPLANATORY NOTES ON INDIVIDUAL H\\thinspace II REGIONS}\n\n\\bigskip\n\n\\noindent\nS257: The spectral type adopted is the one predicted by HM90 on the\nbasis of the observed total nebular ionizing flux.\n\n\\noindent\nS275 (Rosette): The ionizing cluster is NGC~2244; earliest spectral\ntype is O4 V((f)); a total of 9 stars earlier than B0.5 has been\nincluded in the computation of \\teff.\n\n\\noindent\nRCW 5 (NGC 2359): A Wolf-Rayet (WN 4) ring nebula. Esteban \\etal (1993) \nderive \\teff=67$\\pm$11 $\\times 10^4K$. Given the uncertainties in the\ntreatment of WR star atmospheres, this object, together with RCW~48,\nis included to observe the trends in the nebular diagnostics at very\nhigh \\teff\\/ values.\n\n\\noindent\nRCW 16: Walborn (1982) gives two early-type stars in NGC 2467, HD\n64568 (O3 V((f*))) and HD 64315 (O6 Vn).\n\n\\noindent\nRCW 48 (NGC 3199): The second Wolf-Rayet (WN 5) ring nebula in our sample,\nwith \\teff=57$\\pm$14 $\\times 10^4K$ (Esteban \\etal 1993).\n\n\\noindent\nRCW 53 (Carina): A total of 36 early-type stars in Tr14 and Tr16 has\nbeen considered, excluding $\\eta$ Carinae and one WR star (HD 93162).\n\n\\noindent\nRCW 57 (NGC~3603): Drissen \\etal (1995) identify 11 O-type stars and 3 WN6 stars\nwhich account for at least 80\\% of the ionization of the nebula. The\ntemperature derived here does not include the WN6 stars, which according\nto Esteban et al. (1993) have \\teff $\\le$ 42000 K.\n\n\\noindent\nS49 (M16): 20 early-type stars\n\n\\noindent\nS45 (M17): 12 early-type stars classified from optical and $K$-band\nspectroscopy by Hanson, Howarth \\& Conti (1997).\n\n\\noindent\nS100: The spectral type adopted is the one predicted by HM90 on the\nbasis of the observed total nebular ionizing flux.\n\n\\noindent\nS158 (NGC 7538): Ionizing star is CGO 654, with spectral type O7V,\nfrom Crampton, Georgelin, \\& Georgelin (1978).\n\n\\noindent\nS162 (NGC 7635): Ionizing star is BD+60 2522, with spectral type O6.5 IIIf,\nfrom Conti \\& Alschuler (1971). Classified as O6.5 IIIef by Conti \\&\nLeep (1974). \n\n\\noindent\nN11B: We have assumed that the stellar association LH10 is responsible \nfor the ionization (26 ionizing stars).\n\n\\noindent\nN44: The slit was centered on N44B, ionized by LH 47/48.\n\n\\noindent\nN51D: We have included the 40 early-type stars classified by Oey \\&\nSmedley (1998) in LH 51 and LH 54.\n\n\\noindent\nN144: Garmany, Massey \\& Parker (1994) list 32 ionizing stars in LH\n58. The 3 WR stars were not included.\n\n\\noindent\n30 Dor: We have included the 64 early-type stars in R136 listed by\nMassey \\& Hunter (1998), excluding the WR stars.\n\n\\noindent\nN70: The ionizing cluster is LH 114, studied by Oey (1996).\n\n\\noindent\nN180: The ionizing cluster has been assumed to be LH 117, studied by\nMassey \\etal (1989a).\n\n\\noindent\nN66 (SMC): The temperature we derived is based on the stellar census\nof Massey et al. (1989). 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M., \\& Pagel, B. E. J. 1988, \\mnras, 231,257\n\n%\\reference{} V\\'{\\i}lchez, J. M., Pagel, B. E. J., D\\'{\\i}az, A. I., Terlevich, E., \\& Edmunds, M. G. 1988, \\mnras, 235, 633\n\n\\reference{} V\\'{\\i}lchez, J. M., \\& Esteban, C. 1996, \\mnras, 280, 720\n\n\\reference{} Walborn, N.R. 1982, \\aj, 87, 1300\n\n\\reference{} Walborn, N.R. 1987, \\aj, 93, 868\n\n\\reference{} Zanstra, H. 1927, \\apj, 65, 50\n\n\\reference{} Zaritsky, D., Kennicutt, R. C., \\& Huchra, J. P. 1994, \\apj, 420, 87\n\n\\end{references}\n\n\\newpage\n\\centerline{\\bf FIGURE LEGENDS}\n\n\\bigskip\n\n\\figcaption{Distribution of oxygen abundances and ionization-weighted stellar\ntemperatures for the \\hii\\ region sample. Open squares denote nebulae\nwith direct abundance determinations based on electron temperature\nmeasurements. Filled triangles denote \\hii\\ regions with empirical\n(R$_{23}$) abundance estimates.}\n\n\\figcaption{Charts showing the locations of the long-slit spectrophotometric\nmeasurements. In all cases north is at the top and east is to the left.\nThe box in M8 (Fig. 2d) indicates the region covered by the drift scan.}\n\n\\figcaption{Diagnostic diagrams showing the differences between the fixed\npointing spectra (solid points) and the drift scans (open points) for\nthe northern sample of Galactic \\hii\\ regions.}\n\n\\figcaption{Comparison of spectral properties of the Galactic calibrating\n\\hii\\ regions (solid squares), large Galactic \\hii\\ regions (open squares),\nLMC and SMC \\hii\\ regions (open circles), and WR nebulae (open stars).\nThe small triangles show for comparison the spectral sequence for\nextragalactic \\hii\\ regions in a large sample of galaxies from BKG.}\n\n\\figcaption{Relation between [\\ion{O}{3}]/\\hbeta\\ and [\\ion{N}{2}]/\\halpha\\ for\nthe \\hii\\ regions in this sample, subdivided by stellar effective\ntemperature (left) and by nebular oxygen abundance (right).}\n\n\\figcaption{The [S II]\\lines6716,6731/[S III]\\lines9069,9532 vs\n\\teff\\/ diagram for the \\hii\\ regions. The symbol coding is the same\nas in Fig. 4. The continuous lines show\nnebular models at 0.2 $Z_\\odot$, for a variety of ionization\nparameter values $\\log U$ (as labelled). The dotted lines refer to solar\nabundance models at $\\log U=-2.0, -2.5$ and $-3.0$.}\n\n\\figcaption{(Left): Relation between [\\ion{O}{3}]/\\hbeta\\ and \n[\\ion{O}{2}]/\\hbeta\\\nfor subregions observed in 30 Doradus (open stars), Carina (solid triangles),\nand Orion (open circles). The dashed lines show constant values of the\nempirical abundance parameter \\x. Note the relative constancy of \\x\\\nacross the 30 Dor and Carina, despite the large local variations in\nexcitation. (Right): Corresponding relation between [\\ion{S}{3}]/\\hbeta\\ and\n[\\ion{S}{2}]/\\hbeta\\ line ratios. Diagonal lines show constant values\nof the abundance index \\stt .}\n\n\\figcaption{Relation between [\\ion{O}{3}]/\\hbeta\\ and the extragalactic \\hii\\\nregion empirical abundance index [\\ion{O}{3}]/[\\ion{N}{2}], for subregions\nobserved in 30 Doradus (open stars), Carina (solid triangles), and Orion (open\ncircles). The dashed horizontal lines show values of constant oxygen\nabundance, using the calibration of Dutil \\& Roy (1999).}\n\n\\figcaption{Dependence of nebular \\ion{He}{1}\\ recombination line strengths\n(relative to Balmer lines) as a function of stellar effective temperature,\nas measured by \\ion{He}{1}\\thinspace $\\lambda$5876 (top) and\n\\ion{He}{1}\\thinspace $\\lambda$6678 (bottom). Both ratios are approximately\nproportional to the fraction ionization of He in the nebula. Symbols\nare coded as in Fig. 4. The lines\nshow the relations expected from stellar atmosphere and nebular\nphotoionization models for different abundances, as described in the text.}\n\n\\figcaption{Correlation between excitation index [\\ion{O}{3}]/\\hbeta\\ and\nstellar effective temperature, with symbols coded as in Fig. 4. The\nfour sets of lines show photoionization model sequences for oxygen\nabundances of 0.2 and 1.0 $Z_\\odot$ and ionization parameters\n$\\log U = -2.0$ and $-4.0$.}\n\n\\figcaption{Dependences of three nebular excitation indices on stellar\neffective temperatures. The symbols are coded as in Figs. 4 and 10.}\n\n\\figcaption{Relationship between ionization-sensitive forbidden-line ratios\n[\\ion{S}{2}]/[\\ion{S}{3}] and [\\ion{O}{2}]/[\\ion{O}{3}].\n(a) Spatially resolved observations of the 30 Doradus nebula (open circles),\nthe Orion nebula (solid squares), and the Carina nebula (open triangles).\nThe solid lines show photoionization model sequences for stellar\ntemperatures of 50000 K, 45000 K, 40000 K, and 35000 K (left to right).\n(b) The same line ratios for the full sample of \\hii\\ regions, with\nsymbols coded as in Fig. 4. Solid lines show the same model sequences,\nwith the addition of a 30000 K model (far right). Dashed lines show\nthe effects of increasing the metal abundance, as discussed in the text.}\n\n\\figcaption{Dependence of the ionization hardness parameter \\etap\\\n(eq. [2]) and stellar effective for the \\hii\\ regions in this sample,\nwith symbols coded as in Fig. 4. The lines show photoionization model\nsequences for oxygen abundances of 0.2, 0.5, and 1.0 $Z_\\odot$.\nThe hatched line shows a quadratic empirical fit to the data.}\n\n\\figcaption{The top panel shows the relationship between mean stellar\ntemperature inferred from the \\etap\\ parameter (eqs. [2, 3]) and\nnebular oxygen abundances, for the BKG sample of extragalactic\n\\hii\\ regions. The middle panel shows the stellar temperatures\nderived from an average of \\etap\\ and [\\ion{O}{3}]/\\hbeta, as\ndescribed in the text. Crosses in both panels show values of \\tstar\\\nderived from \\ion{He}{1} $\\lambda$5876/\\hbeta. Arrows indicate\nlower limits to \\tstar, corresponding to full He ionization.}\n\n%\\end{document}\n\n%------------------ TABLES ------------------------------------------\n%\\begin{table}\n\\input{table1}\n%\\dummytable\\label{sample.table}\n%\\end{table}\n\\input{table2}\n\n\\end{document}\n%------------------ FIGURES ------------------------------------------\n\\newpage\n\n%\\epsscale{1.2}\n\n%FIG. 1\n\\begin{figure}\n\\plotfiddle{FIG1.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n\\caption{Distribution of oxygen abundances and ionization-weighted stellar\ntemperatures for the \\hii\\ region sample. Open squares denote nebulae\nwith direct abundance determinations based on electron temperature\nmeasurements. Filled triangles denote \\hii\\ regions with empirical\n(R$_{23}$) abundance estimates.\n\\label{oh.vs.teff}} \n\\end{figure}\n\n%FIG. 2\n\\newpage\n\\begin{figure}\n\\plotfiddle{FIG2.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n\\caption{Charts showing the locations of the long-slit spectrophotometric\nmeasurements. In all cases north is at the top and east is to the left.\nThe box in M8 (Fig. 2d) indicates the region covered by the drift scan used.\n\\label{fc}} \n\\end{figure}\n\n%FIG. 3\n\\newpage\n\\begin{figure}\n\\plotfiddle{FIG3.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n\\caption{Diagnostic diagrams showing the differences between the fixed\npointing spectra (solid points) and the drift scans (open points) for \nthe northern sample of Galactic \\hii\\ regions.\n\\label{drift}} \n\\end{figure}\n\n%FIG. 4\n\\newpage\n\\begin{figure}\n\\plotfiddle{FIG4.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n\\caption{Comparison of spectral properties of the Galactic calibrating\n\\hii\\ regions (solid squares), large Galactic \\hii\\ regions (open squares),\nLMC and SMC \\hii\\ regions (open circles), and WR nebulae (open stars).\nThe small triangles show for comparison the spectral sequence for \nextragalactic \\hii\\ regions in a large sample of galaxies from BKG.} \n\\end{figure}\n\n%FIG. 5\n\\newpage\n\\begin{figure}\n\\plotfiddle{FIG5.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n\\caption{The [S II]\\lines6716,6731/[S III]\\lines9069,9532 vs \n\\teff\\/ diagram for the \\hii\\ regions. The symbol coding is the same\nas in Fig. 4. The continuous lines show\nnebular models at 0.2 $Z_\\odot$, for a variety of ionization\nparameter values $\\log U$ (as labelled). The dotted lines refer to solar\nabundance models at $\\log U=-2.0, -2.5$ and $-3.0$.}\n\\end{figure}\n\n%FIG. 6\n\\newpage\n\\begin{figure}\n\\plotfiddle{FIG6.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n\\caption{Relation between [\\ion{O}{3}]/\\hbeta\\ and [\\ion{N}{2}]/\\halpha\\ for\nthe \\hii\\ regions in this sample, subdivided by stellar effective \ntemperature (left) and by nebular oxygen abundance (right).} \n\\end{figure}\n\n%FIG. 7\n\\newpage\n\\begin{figure}\n\\plotfiddle{FIG7.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n\\caption{Relation between [\\ion{O}{3}]/\\hbeta\\ and [\\ion{O}{2}]/\\hbeta\\\nfor subregions observed in 30 Doradus (open stars), Carina (solid triangles),\nand Orion (open circles). The dashed lines show constant values of the\nempirical abundance parameter \\x. Note the relative constancy of \\x\\\nacross the 30 Dor and Carina, despite the large local variations in \nexcitation.} \n\\end{figure}\n\n%FIG. 8\n\\newpage\n\\begin{figure}\n\\plotfiddle{FIG8.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n\\caption{Relation between [\\ion{O}{3}]/\\hbeta\\ and the extragalactic \\hii\\\nregion empirical abundance index [\\ion{O}{3}]/[\\ion{N}{2}], for subregions \nobserved in 30 Doradus (open stars), Carina (solid triangles), and Orion (open \ncircles). The dashed horizontal lines show values of constant oxygen\nabundance, using the calibration of Dutil \\& Roy (1999).}\n\\end{figure}\n\n%FIG. 9\n\\newpage\n\\begin{figure}\n\\plotfiddle{FIG9.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n\\caption{Dependence of nebular \\ion{He}{1}\\ recombination line strengths \n(relative to Balmer lines) as a function of stellar effective temperature, \nas measured by \\ion{He}{1}\\thinspace $\\lambda$5876 (top) and \n\\ion{He}{1}\\thinspace $\\lambda$6678 (bottom). Both ratios are approximately\nproportional to the fraction ionization of He in the nebula. Symbols\nare coded as in Fig. 4. The lines\nshow the relations expected from stellar atmosphere and nebular \nphotoionization models for different abundances, as described in the text.}\n\\end{figure}\n\n%FIG. 10\n\\newpage\n\\begin{figure}\n\\plotfiddle{FIG10.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n\\caption{Correlation between excitation index [\\ion{O}{3}]/\\hbeta\\ and\nstellar effective temperature, with symbols coded as in Fig. 4. The \nfour sets of lines show photoionization model sequences for oxygen\nabundances of 0.2 and 1.0 $Z_\\odot$ and ionization parameters \n$\\log U = -2.0$ and $-4.0$.} \n\\end{figure}\n\n%FIG. 11\n\\newpage\n\\begin{figure}\n\\plotfiddle{FIG11.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n\\caption{Dependences of three nebular excitation indices on stellar\neffective temperatures. The symbols are coded as in Figs. 4 and 10.}\n\\end{figure}\n\n%FIG. 12\n\\newpage\n\\begin{figure}\n\\figurenum{12}\n\\plotfiddle{FIG12a.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n\\caption{Relationship between ionization-sensitive forbidden-line ratios \n[\\ion{S}{2}]/[\\ion{S}{3}] and [\\ion{O}{2}]/[\\ion{O}{3}].\n(a) Spatically resolved observations of the 30 Doradus nebula (open circles),\nthe Orion nebula (solid squares), and the Carina nebula (open triangles).\nThe solid lines show photoionization model sequences for stellar \ntemperatures of 50000 K, 45000 K, 40000 K, and 35000 K (left to right).\n(b) The same line ratios for the full sample of \\hii\\ regions, with\nsymbols coded as in Fig. 4. Solid lines show the same model sequences,\nwith the addition of a 30000 K model (far right). Dashed lines show\nthe effects of increasing the metal abundance, as discussed in the text.}\n\\end{figure}\n\n%FIG. 12b\n\\newpage\n\\begin{figure}\n\\figurenum{12b}\n\\plotfiddle{FIG12b.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n%\\caption{} \n\\end{figure}\n\n%FIG. 13\n\\newpage\n\\begin{figure}\n\\figurenum{13}\n\\plotfiddle{FIG13.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n\\caption{Dependence of the ionization hardness parameter \\etap\\ \n(eq. [2]) and stellar effective for the \\hii\\ regions in this sample,\nwith symbols coded as in Fig. 4. The lines show photoionization model\nsequences for oxygen abundances of 0.2 and 1.0 $Z_\\odot$.} \n\\end{figure}\n\n%FIG. 14\n\\newpage\n\\begin{figure}\n\\figurenum{14}\n\\plotfiddle{FIG14.ps}{15cm}{0}{100}{100}{-320}{-270}\n\\vspace{3cm}\n\\caption{The top panel shows the relationship between mean stellar\ntemperature inferred from the \\etap\\ parameter (eqs. [2, 3]) and\nnebular oxygen abundances, for the BKG sample of extragalactic\n\\hii\\ regions. The middle panel shows the stellar temperatures\nderived from the \\ion{He}{1}\\thinspace $\\lambda$5876/\\hbeta\\ ratios\nin the same \\hii\\ regions. Arrows denote lower limits to the \nstellar temperature for nebulae with full ionization of He.}\n\\end{figure}\n\n%FIG. 15\n%\\newpage\n%\\begin{figure}\n%\\figurenum{15}\n%\\plotfiddle{paper_theory.ps}{15cm}{0}{100}{100}{-320}{-270}\n%\\vspace{3cm}\n%\\caption{} \n%\\end{figure}\n\n\n\\end{document}\n\n\n"
},
{
"name": "table1.tex",
"string": "%\\documentstyle[apjpt4]{article}\n%\\pagestyle{empty}\n%\\begin{document}\n\n\\begin{deluxetable}{lcccccccl}\n\\scriptsize\n\\tablecolumns{9}\n%\\tablewidth{0pt}\n\\tablenum{1}\n\\tablecaption{H~II region sample\\label{sample.table}}\n\\tablehead{\n\\colhead{H II Region} \t\t& \n\\colhead{RA (2000)}\t\t\t&\n\\colhead{DEC (2000)} \t\t&\n\\colhead{T$_*$}\t\t\t\t&\n\\colhead{log Q$_0$}\t\t\t&\n\\colhead{12+log(O/H)}\t\t\t&\n\\colhead{Ref.}\t\t\t\t&\n\\colhead{Tel.}\t\t\t&\n\\colhead{Other ID}\t\t\\\\\n\\colhead{(1)}\t&\n\\colhead{(2)}\t&\n\\colhead{(3)}\t&\n\\colhead{(4)}\t&\n\\colhead{(5)}\t&\n\\colhead{(6)}\t&\n\\colhead{(7)}\t&\n\\colhead{(8)}\t&\n\\colhead{(9)}}\n\\startdata \n\\cutinhead{Galaxy}\nS212 * & 04 40 36 & \\phantom{-}50 27 46\t& 40600\t& 49.07 & (8.5) & 1 & Bok &\t\t\t\\nl\nS237 * & 05 31 27 & \\phantom{-}34 14 58\t& 32900\t& 48.21 & (8.9) & 1 & Bok &\t\t\t\\nl\nM42 * \t & 05 35 17 & -05 23 28 \t\t& 40100 & 49.11 & 8.76 & 2,a & CTIO\t& Orion, NGC 1976\t\t\t\\nl\nS255 * & 06 12 54 & \\phantom{-}17 59 23\t& 33300\t& 48.02 & 8.32 & 1,b & CTIO & IC 2162\t\t\\nl\t\nS257 * & 06 12 48 & \\phantom{-}18 00 00\t& 34100\t& 48.37 & 8.26 & 1,b & Bok &\t\t\t\\nl\nS271 * & 06 14 59 & \\phantom{-}12 20 16\t& 33300\t& 48.02 & (8.9) & 1 & Bok & \t\t\t\\nl\nS275 & 06 31 40 & \\phantom{-}04 57 48\t& 42600\t& 49.83 & 8.20 & 3,b & CTIO & Rosette neb.\t\\nl\nS288 * & 07 08 37 & -04 18 48\t\t\t& 35900\t& 48.46 & (8.7) & 1 & Bok & \t\t\t\\nl\nRCW 6 * & 07 09 54 & -18 30 21\t\t\t& 42700\t& 49.29 & 8.79 & 4,b & CTIO & S301\t\t\\nl\nRCW 5 & 07 18 30 & -13 13 48\t\t\t& 67000\t& 48.90 & 8.48 & 5,b & CTIO & NGC 2359, S298\t\\nl\nRCW 8 * & 07 30 04 & -18 32 13\t\t\t& 33300\t& 48.32 & 8.67 & 1,b & CTIO & S305\t\t\\nl\nS307 * & 07 35 33 & -18 45 34\t\t\t& 33300\t& 48.02 & (8.8) & 1 & Bok & \t\t\\nl\nRCW 16 * & 07 52 19 & -26 26 30\t\t\t& 48700\t& 49.95 & 8.56 & 6,b & CTIO & NGC 2467, S311\t\\nl\nRCW 34 * & 08 56 28 & -43 05 46\t\t\t& 37200\t& 48.64 & 8.90 & 7,b & CTIO & \t\t\t\\nl\nRCW 40 * & 09 02 21 & -48 41 55\t\t\t& 38400\t& 48.80 & 8.99 & 8,b &\tCTIO & \t\t\\nl\nRCW 48 & 10 16 33 & -57 56 02\t\t\t& 57000\t& 49.57 & 8.85 & 5,b & CTIO & NGC 3199\t\\nl\nRCW 53 & 10 44 19 & -59 53 21 \t\t& 45700\t& 50.91 & 8.49 & 9,b & CTIO & Carina neb., NGC 3372 \\nl\nNGC 3603 & 11 15 09 & -61 16 17\t\t\t& 48900\t& 50.77 & 8.51 & 10,b & CTIO & RCW 57\t\t\\nl\nRCW 62 & 11 38 20 & -63 22 22\t\t\t& 41700\t& 50.06 & 8.54 & 11,b & CTIO & $\\lambda$ Cen\t\\nl\nM8 & 18 03 37 & -24 23 12\t\t\t& 41000\t& 49.05 & 8.74 & 12,c & Bok & NGC 6523, S25, Lagoon \t\\nl\nM16 & 18 18 48 & -13 47 00\t\t\t& 40500\t& 50.21 & 8.76 & 13,d & Bok & NGC 6611, S49, Eagle \t\\nl\nM17 & 18 20 26 & -16 10 36\t\t\t& 45600\t& 50.37 & 8.81 & 14,a & Bok & NGC 6618, S45, Omega\t\\nl\nS99 * & 20 00 54 & \\phantom{-}33 29 48 \t& 38400\t& 48.80 & (8.7) & 1 & Bok & \\nl\nS100 * & 20 01 44 & \\phantom{-}33 31 14 \t& 46100\t& 49.82 & (8.4) & 1 & Bok & \t\t\t\\nl\nS148 * & 22 56 09 & \\phantom{-}58 30 00 \t& 33300\t& 48.02 & (8.9) & 1 & Bok &\t\t\t\\nl\nS152 * & 22 58 40 & \\phantom{-}58 47 01\t& 35900\t& 48.46 & (8.7) & 1 & Bok & \t\t\t\\nl\nS156 * & 23 05 59 & \\phantom{-}60 15 01\t& 40300\t& 49.28 & (8.7) & 1 & Bok & IC 1470\t\t\\nl\nS158 *\t & 23 13 46 & \\phantom{-}61 28 21 & 41000 & 49.05 & 8.34 & 8,e & Bok & NGC 7538 \\nl\nS162 * & 23 20 44 & \\phantom{-}61 11 41 & 41250 & 49.47 & 8.66 & 2,e & Bok & NGC 7635, Bubble \\nl\n\\cutinhead{LMC}\nN11B & 04 54 49 & -66 25 36\t\t\t& 45100\t& 50.81 & 8.49 & 15,b & CTIO & DEM 34 \t\t\\nl\nN44 & 05 22 06 & -67 55 00\t\t\t& 40800\t& 50.53 & 8.56 & 16,b & CTIO & DEM 152 \t\t\\nl\nN138D,B & 05 24 23 & -68 31 48 \t\t& 67000 & \\nodata & 8.50 & b & CTIO & DEM 174\t\t\t\\nl\nN51D & 05 26 14 & -67 30 18\t\t\t& 39700\t& 50.46 & 8.48 & 17,b & CTIO & DEM 192\t\t\\nl\nN144 & 05 26 33 & -68 51 48\t\t\t& 41100\t& 50.43 & 8.51 & 18,b & CTIO & DEM 199\t\t\\nl\nN57C & 05 33 10 & -67 42 48 \t\t& 67000 & \\nodata & 8.56 & b & CTIO & NGC 2020, DEM 231\t\\nl\n30 Dor & 05 38 42 & -69 06 03\t\t\t& 48500\t& 51.63 & 8.41 & 19,d &\tCTIO &\t\t\\nl\nN70 & 05 43 21 & -67 50 48\t\t\t& 45300\t& 50.31 & 8.60 & 20,b & CTIO & DEM 301\t\t\\nl\nN180 & 05 48 14 & -70 02 00\t\t\t& 45600\t& 50.48 & 8.41 & 21,b & CTIO & DEM 322\t\t\\nl\n\\cutinhead{SMC}\nN66 & 00 59 18 & -72 10 48 \t\t& 41900\t& 50.72 & 8.22 & 22,d & CTIO & NGC 346\t\t\\nl\n\\enddata\n\\scriptsize\n\\tablerefs{Sources of spectral types: 1. Hunter \\& Massey 1990; 2. Conti \\& Alschuler 1971;\n3. Massey etal 1995; 4. Lahulla 1987; \n5. Esteban etal 1993; 6. Walborn 1982; 7. Heydari-Malayeri 1988; \n8. Georgelin etal 1973; 9. Massey \\& Johnson 1993; 10. Drissen etal 1995;\n11. Walborn 1987; 12. Lada etal 1976; 13. Hillenbrand etal 1993; \n14. Hanson etal 1997; 15. Parker etal 1992; 16. Oey \\& Massey 1995;\n17. Oey \\& Smedley 1998; 18. Garmany etal 1994; 19. Massey \\& Hunter 1998;\n20. Oey 1996; 21. Massey etal 1989a; 22. Massey etal 1989b.\\newline\nSources of abundances: a. Peimbert etal 1993; b. This paper;\nc. Melnick etal 1989; d. Shaver etal 1983; e. Talent \\& Dufour 1979.\n}\n\\end{deluxetable}\n%\\end{document}\n\n\n\n\n\n\n"
},
{
"name": "table2.tex",
"string": "%\\documentstyle[apjpt4]{article}\n%\\pagestyle{empty}\n%\\begin{document}\n\n\\begin{deluxetable}{lcccccccccc}\n\\scriptsize\n\\tablecolumns{11}\n\\tablewidth{0pt}\n\\tablenum{2}\n\\tablecaption{Reddening-corrected line fluxes}\n\n\\tablehead{\n\\colhead{HII Region} \t& \n\\colhead{c}\t\t\t&\n\\colhead{[O II]} \t\t&\n\\colhead{[Ne III]}\t\t&\n\\colhead{[O III]}\t \t&\n\\colhead{He I} \t\t&\n\\colhead{[N II]} \t\t&\n\\colhead{He I}\t\t\t&\n\\colhead{[S II]} \t\t&\n\\colhead{[Ar III]}\t\t&\n\\colhead{[S III]} \t\t\\\\\n%\\cline{2-3} \\\\[-3mm]\n\\colhead{} \t\t\t&\n\\colhead{}\t\t\t&\n\\colhead{3727} \t\t\t&\n\\colhead{3869}\t\t\t&\n\\colhead{4959+5007} \t\t&\n\\colhead{5876} \t\t\t&\n\\colhead{6548+6583} \t\t&\n\\colhead{6678}\t\t\t&\n\\colhead{6716+6731} \t\t&\n\\colhead{7135}\t\t\t&\n\\colhead{9069+9532}\t\t\\\\\n\\colhead{(1)}\t&\n\\colhead{(2)}\t&\n\\colhead{(3)}\t&\n\\colhead{(4)}\t&\n\\colhead{(5)}\t&\n\\colhead{(6)}\t&\n\\colhead{(7)}\t&\n\\colhead{(8)}\t&\n\\colhead{(9)}\t&\n\\colhead{(10)}\t&\n\\colhead{(11)}}\n\\startdata \n% object c 3727 3869 4959+5007 5876 6548+6583 6678 6717+6731 7135 9069+9532\nS212 & 1.25 & 332 & 0 & 249 & 13 & 68 & 4 & 30 & 123 & 87 \\nl\nS237 & 0.99 & 305 & 3 & 0 & 0 & 160 & 0 & 69 & 0 & 54 \\nl\nM42 & 0.44 & 182 & 8 & 263 & 11 & 92 & 3 & 14 & 10 & 118 \\nl\nS255 & 1.53 & 407 & 10 & 20 & 5 & 152 & 1 & 64 & 4 & 73 \\nl\nS257 & 0.88 & 208 & 0 & 22 & 5 & 125 & 2 & 58 & 4 & 79 \\nl\nS271 & 1.29 & 319 & 0 & 8 & 2 & 140 & 2 & 48 & 3 & 29 \\nl\nS275 & 1.03 & 182 & 5 & 203 & 11 & 41 & 2 & 22 & 8 & 68 \\nl\nS288 & 1.09 & 291 & 14 & 171 & 10 & 77 & 2 & 20 & 7 & 94 \\nl\nRCW 6 & 0.79 & 278 & 5 & 186 & 13 & 94 & 4 & 50 & 11 & 189 \\nl\nRCW 5 & 1.14 & 346 & 137 & 1431 & 16 & 85 & 7 & 75 & 27 & 259 \\nl\nRCW 8 & 1.83 & 423 & 0 & 7 & 3 & 144 & 1 & 53 & 1 & 86 \\nl\nS307 & 1.42 & 300 & 0 & 43 & 6 & 129 & 1 & 39 & 4 & 90 \\nl\nRCW 16 & 0.67 & 180 & 16 & 384 & 12 & 40 & 4 & 15 & 13 & 194 \\nl\nRCW 34 & 1.91 & 250 & 10 & 122 & 11 & 103 & 4 & 31 & 0 & 185 \\nl\nRCW 40 & 1.30 & 380 & 0 & 64 & 10 & 152 & 5 & 43 & 11 & 163 \\nl\nRCW 48 & 1.67 & 241 & 56 & 783 & 10 & 83 & 4 & 47 & 20 & 188 \\nl\nRCW 53 & 0.87 & 405 & 10 & 210 & 10 & 102 & 4 & 32 & 12 & 126 \\nl\nNGC 3603 & 2.80 & 172 & 47 & 584 & 12 & 27 & 5 & 6 & 19 & 163 \\nl\nRCW 62 & 1.02 & 293 & 3 & 147 & 10 & 60 & 4 & 13 & 10 & 118 \\nl\nM8 & 0.64 & 249 & 4 & 147 & 11 & 132 & 3 & 18 & 12 & 135 \\nl\nM16 & 0.89 & 212 & 3 & 118 & 12 & 128 & 3 & 30 & 10 & 89 \\nl\nM17 & 1.24 & 132 & 20 & 437 & 14 & 53 & 4 & 13 & 16 & 121 \\nl\nS99 & 1.84 & 194 & 6 & 230 & 14 & 56 & 4 & 22 & 11 & 118 \\nl\nS100 & 1.99 & 101 & 32 & 560 & 16 & 31 & 5 & 9 & 16 & 138 \\nl\nS148 & 1.28 & 317 & 0 & 10 & 5 & 187 & 1 & 60 & 10 & 189 \\nl\nS152 & 1.59 & 325 & 0 & 113 & 11 & 118 & 3 & 28 & 11 & 146 \\nl\nS156 & 1.43 & 297 & 2 & 121 & 12 & 121 & 4 & 25 & 13 & 148 \\nl\nS158\t & 1.70 & 168 & 15 & 403 & \\nodata & 38 & 3 & 16 & 13 & 120 \\nl\nS162\t & 0.77 & 226 & 2 & 172 & \\nodata & 98 & 2 & 21 & 9.4 & 160 \\nl\nN11B & 0.39 & 310 & 19 & 406 & 11 & 25 & 4 & 22 & 11 & 103 \\nl\nN44 & 0.22 & 413 & 12 & 297 & 8 & 36 & 3 & 44 & 9 & 110 \\nl\nN138D,B & 0.25 & 299 & 69 & 1048 & 13 & 19 & 0 & 52 & 19 & 169 \\nl\nN51D & 0.37 & 470 & 8 & 242 & 12 & 26 & 3 & 40 & 7 & 75 \\nl\nN144 & 0.30 & 293 & 26 & 419 & 9 & 26 & 4 & 33 & 11. & 113 \\nl\nN57C\t & 0.28 & 226 & 58 & 891 & 14 & 27 & 4 & 47 & 14 & 109 \\nl\n30 Dor & 0.62 & 245 & 40 & 569 & 11 & 15 & 4 & 19 & 11 & 110 \\nl\nN70 & 0.25 & 478 & 13 & 243 & 12 & 36 & 3 & 75 & 11 & 82 \\nl\nN180 & 0.38 & 328 & 20 & 373 & 11 & 25 & 4 & 28 & 9 & 86 \\nl\nN66 & 0.28 & 122 & 49 & 752 & 9 & 6 & 3 & 14 & 9 & 58 \\nl\n\\enddata\n\\end{deluxetable}\n%\\end{document}\n"
}
] |
[] |
astro-ph0002181
|
Statistical properties of SGR 1806-20 bursts
|
[
{
"author": "Ersin {G\\\"o\\u{g}\\\"u\\c{s}}\\altaffilmark{1,3}"
},
{
"author": "Peter M. Woods\\altaffilmark{1,3}"
},
{
"author": "Chryssa Kouveliotou\\altaffilmark{2,3}"
},
{
"author": "Jan van Paradijs\\altaffilmark{1,4}"
},
{
"author": "Michael S. Briggs\\altaffilmark{1,3}"
},
{
"author": "Robert C. Duncan\\altaffilmark{5}"
},
{
"author": "Christopher Thompson\\altaffilmark{6}"
}
] |
We present statistics of SGR 1806-20 bursts, combining 290 events detected with RXTE/PCA, 111 events detected with BATSE and 134 events detected with ICE. We find that the fluence distribution of bursts observed with each instrument are well described by power laws with indices 1.43, 1.76 and 1.67, respectively. The distribution of time intervals between successive bursts from SGR 1806-20 is described by a lognormal function with a peak at 103 s. There is no correlation between the burst intensity and either the waiting times till the next burst or the time elapsed since the previous burst. In all these statistical properties, SGR 1806-20 bursts resemble a self-organized critical system, similar to earthquakes and solar flares. Our results thus support the hypothesis that the energy source for SGR bursts is crustquakes due to the evolving, strong magnetic field of the neutron star, rather than any accretion or nuclear power.
|
[
{
"name": "web_sub.tex",
"string": "\\documentstyle[aaspp4]{article}\n\n\\begin{document}\n\n\\title{Statistical properties of SGR 1806-20 bursts}\n\n\\author{Ersin {G\\\"o\\u{g}\\\"u\\c{s}}\\altaffilmark{1,3}, \nPeter M. Woods\\altaffilmark{1,3}, Chryssa Kouveliotou\\altaffilmark{2,3},\nJan van Paradijs\\altaffilmark{1,4}, Michael S. Briggs\\altaffilmark{1,3},\nRobert C. Duncan\\altaffilmark{5}, Christopher Thompson\\altaffilmark{6}}\n\n\\altaffiltext{1}{Department of Physics, University of Alabama in Huntsville,\n Huntsville, AL 35899} \n\\altaffiltext{2}{Universities Space Research Association}\n\\altaffiltext{3}{NASA Marshall Space Flight Center, SD-50, Huntsville, AL\n35812}\n\\altaffiltext{4}{Astronomical Institute ``Anton Pannekoek'', University of\n Amsterdam, 403 Kruislaan, 1098 SJ Amsterdam, NL} \n\\altaffiltext{5}{Department of Astronomy, University of Texas, RLM 15.308, \n Austin, TX 78712-1083}\n\\altaffiltext{6}{Department of Physics and Astronomy, University of North\n Carolina, Philips Hall, Chapel Hill, NC, 27599-3255}\n\n\\authoremail{Ersin.Gogus@msfc.nasa.gov}\n\n\\begin{abstract}\n\nWe present statistics of SGR 1806-20 bursts, combining\n290 events detected with \nRXTE/PCA, 111 events detected with BATSE and 134 events detected with ICE. \nWe find that the fluence distribution of bursts \nobserved with each instrument \nare well described \nby power laws with indices 1.43, 1.76 and 1.67, respectively.\nThe distribution of time intervals between successive bursts from \nSGR 1806-20 is described by a lognormal function with a peak at 103 s. \nThere is no \ncorrelation between the burst intensity \nand either the waiting times till the next burst or the time elapsed\nsince the previous burst. \nIn all these statistical properties, SGR 1806-20 bursts resemble \na self-organized critical system, similar to earthquakes \nand solar flares. \nOur results thus support the hypothesis that the energy source for SGR bursts \nis crustquakes due to the evolving, strong magnetic field of the neutron star, \nrather than any accretion or nuclear power.\n\n\\end{abstract}\n\n\\keywords{gamma rays: bursts -- stars: individual (SGR 1806-20) --\nX-rays: bursts }\n\n\\section{Introduction}\n\n\nSoft gamma repeaters (SGR) are a rare class of objects \ncharacterized by their repetitive emission of low energy gamma-ray bursts. \nSGR bursts last $\\sim$ 0.1 s and their spectra are usually well\ndescribed by an optically thin thermal bremsstrahlung (OTTB) model with \nkT $\\sim$ 20--40 keV. Three of the four known SGRs are\nassociated with slowly rotating (P$_{\\rm spin}$ $\\sim$ ~5--8 s; \nMazets et al. 1979, Kouveliotou et al. 1998, Hurley et al. 1999), \nultra-strongly magnetized ($B \\gtrsim 10^{14}$ Gauss; \nKouveliotou et al. 1998, Kouveliotou et al. 1999a) neutron stars\npositioned within or near young supernova remnants. \nFor a review of the burst and persistent emission properties of SGRs, \nsee Kouveliotou (1999b) and Hurley (2000).\n\nCheng et al. (1996) \\markcite{cheng96} reported similarities\nbetween particular statistical properties of a sample of 111 SGR 1806-20 bursts\n(observed with the International Cometary Explorer, ICE, between 1979 and 1984) \nand\nearthquakes. They noted that the distribution of the event energies of both \nphenomena follow a\npower law, dN $\\propto$ E$^{-\\gamma}$~dE, with index, $\\gamma$ $\\sim$\n1.6. Furthermore, they found that the cumulative waiting times between \nsuccessive SGR \nbursts and earthquakes are similar.\nLaros et al. (1987) noted that the distribution of waiting times between \nsuccessive SGR 1806-20 bursts follow a lognormal function, which was also seen \nbetween micro-glitches of the Vela pulsar\n(Hurley et al. 1994). Using the same data set, Palmer (1999) showed that, \nsimilar to\nearthquakes, some SGR 1806-20 bursts may originate from relaxation systems. \n{G\\\"o\\u{g}\\\"u\\c{s}} et al. (1999) studied a set of 1024 bursts from SGR\n1900+14;\n187 bursts were detected with the Burst and Transient Source Experiment (BATSE)\naboard the Compton Gamma Ray Observatory (CGRO)\nand 837 bursts were detected with the Proportional Counter Array (PCA)\non the Rossi X-ray Timing Explorer (RXTE)\nduring an active period of the source in 1998. \nWe found that their fluence distribution is consistent \nwith a power law of index $\\gamma$ = 1.66 over 4 orders of magnitude.\nThe distribution of waiting times between \nsuccessive bursts also follows a lognormal function, which peaks at \n$\\sim$ 49 s. \nWe discussed the idea that SGRs, like earthquakes and solar flares, \nare manifestations\nof self-organized critical systems (Bak, Tang \\& Wiesenfeld 1988).\nAll of these results are consistent with\nthe idea that SGR bursts are caused by starquakes,\nwhich are the result of a fracture of the crust of a magnetically-powered \nneutron star, \nor ``magnetar\" (Duncan \\& Thompson 1992\\markcite{dt92}; Thompson and Duncan\n1995\\markcite{td95}, 1996\\markcite{td96}).\n\nSGR 1806-20 exhibited sporadic bursting activity from the launch of BATSE \n(in April 1991) until November 1993 (Kouveliotou et al. ~1994\\markcite{kou94}).\nIn October 1996, the source entered a burst active phase. \nThe reactivation initiated a series \nof pointed observations with the RXTE/PCA over a period of two weeks.\nThese observations led to the discovery of 7.47 s pulsations from SGR 1806-20\nand confirmed its nature as a magnetar (Kouveliotou et al. 1998). \nIn these two weeks RXTE/PCA recorded a total of 290 bursts\\setcounter{footnote}{6}\n\\footnote{Examples of RXTE/PCA observations of SGR 1806-20 can be\nseen at {\\tt http://gammaray.msfc.nasa.gov/batse/sgr/sgr1806/}}.\nIn the BATSE data, SGR 1806-20 burst activity was persistent but variable from\nOctober 1996 up to October 1999 with a total of 116 recorded bursts.\nIn this {\\it Letter}, we present a comprehensive study of the statistical \nproperties of SGR 1806-20 by combining several data bases. Sections 2, 3 and 4\ndescribe the CGRO/BATSE, RXTE/PCA and ICE observations, respectively. \nOur results are\npresented in Section 5 and discussed in Section 6.\n\n\n\\section{BATSE Observations} \n\nIn our analysis we\nhave used DISCriminator Large Area detector (DISCLA) data with coarse \nenergy resolution (4\nchannels covering energies from 25 keV to $\\sim$2 MeV), Spectroscopy \nTime-Tagged Event (STTE) data and\nSpectroscopy High Energy Resolution Burst (SHERB) data with fine energy\nbinning (256 channels covering energies from 15 keV to $\\sim$10 MeV) \nfrom the Spectroscopy Detectors. \nA detailed description of BATSE instrumentation\nand data types can be found in Fishman et al.~(1989)\\markcite{fish89}.\n\nBATSE triggered on 74 bursts between September 1993 and\nJune 1999. For 32 of the brightest events, STTE or SHERB data\nwith detailed spectral information were obtained. \nThe background subtracted spectra were fit to optically-thin thermal\nbremsstrahlung\n(OTTB) and power law models. The OTTB model, F(E)$\\propto$ \nE$^{-1}$$\\exp$($-$E/kT), provided suitable fits \n(0.76 $<$ $\\chi^{2}_\\nu$ $<$ 1.36) to all \nspectra, with temperatures ranging between 18 and 43 keV. The\npower law model failed to fit most of the spectra. The weighted mean of the\nOTTB temperatures for this sample of 32 events is $20.8 \\pm 0.2$ keV.\n\nTo increase our burst sample we performed an off-line search for untriggered \nBATSE events from SGR 1806-20 using a method explained in detail by \nWoods et al. (1999a).\nFigure 1 shows the overall BATSE burst activity history of SGR 1806-20.\nWe limited our search during active phases of the source.\nWe found, in addition to the 74 triggered events, \n42 untriggered bursts during the time intervals 1993 September 13 -- \n1993 November 20 and 1995 September 7 -- 1999 October 26.\nOf these 116 events, \n111 events (triggered and untriggered) had DISCLA data and were sufficiently \nintense to allow spectral fitting. \nBecause of the long DISCLA data integration time (1.024 s) compared to\ntypical SGR burst durations ($\\sim$ 0.1 s), we could estimate only the \nfluence for each event. We fit the background-subtracted source spectrum to an \nOTTB model with a fixed kT of 20.8 keV, a reasonable choice considering the \nfairly narrow kT distribution of the triggered bursts derived above.\nWe find that the burst fluences \nrange between $1.4 \\times 10^{-8}$ and\n$4.3 \\times 10^{-6}$ ergs cm$^{-2}$. For a distance to SGR\n1806-20 of 14.5 kpc (Corbel et al.~1997)\\markcite{cor97}, and assuming\nisotropic emission, the corresponding \nenergy range is $3.5 \\times 10^{38}$ -- $1.1 \\times 10^{41}$ ergs.\nIn comparison, the energies of SGR 1900+14 bursts seen with BATSE\nrange between $1.1 \\times 10^{38}$ -- $1.5 \\times 10^{41}$ ergs \n({G\\\"o\\u{g}\\\"u\\c{s}} et al. ~1999) and those of SGR 1627-41 between\n$8.0 \\times 10^{37}$ -- $5.5 \\times 10^{41}$ ergs (Woods et al. 1999b).\n\n\\section{RXTE Observations}\n\nWe performed 13 pointed observations of SGR 1806-20 with the RXTE/PCA,\nfor a total effective exposure time of $\\sim$ 141 ks between 1996 November 5 \nand 18. We searched PCA Standard 1 data (2-60 keV) with 0.125 s time resolution \nfor bursts using the following procedure.\nFor each 0.125 s bin, we estimated a background count rate by \nfitting a first order polynomial\nto 5 s of data before and after each bin with a 3 s gap between the bin\nsearched and the background intervals.\nBins with count rates exceeding 125 counts/0.125 s were assumed to \ninclude burst emission and were excluded from the background intervals. \nA burst was defined as any continuous set of bins with count rates \nabove 5.5 $\\sigma$ of the estimated background.\nFor the typical PCA count rate of 12 $-$ 18 counts/0.125 s in this energy\nband, 5.5 $\\sigma$ level corresponds to $\\sim$ 20 $-$ 25 counts in a 0.125 s \nbin.\nWe found 290 events and measured the count fluence of each burst by simply \nintegrating the background-subtracted counts over the bins covering the event.\n\nTo compare the integrated count fluences obtained with the PCA to the\nBATSE fluences, we determined a conversion factor between the two as follows. \nFirst, we searched for bursts observed with both\ninstruments and found 8 such events (5 of which had triggered BATSE). \nAssuming a constant OTTB model as described in Section 2, we estimated the\nfluence of these bursts.\nWe then computed the\nratio of the BATSE fluence to the PCA counts of each common event.\nThese ratios fall within a fairly narrow range \n($3.5 \\times 10^{-12}$ and $8.1 \\times 10^{-12}$ ergs\ncm$^{-2}$counts$^{-1}$).\nTheir weighted mean is $5.5 \\times 10^{-12}$ ergs cm$^{-2}$counts$^{-1}$\nwith a standard deviation, $\\sigma$ = $1.3 \\times 10^{-12}$ ergs cm$^{-2}$\ncounts$^{-1}$.\nThe mean is very close to the one estimated for SGR 1900+14 \n({G\\\"o\\u{g}\\\"u\\c{s}} et al. ~1999) and consistent with the idea that SGR bursts \nhave a similar spectral shape. \nUsing this conversion factor, we find that the\nfluences of the PCA bursts range from $1.2 \\times 10^{-10}$ to \n$1.9 \\times 10^{-7}$ ergs cm$^{-2}$ and the burst energies range from $3.0 \n\\times 10^{36}$ to $4.9 \\times 10^{39}$ ergs.\n\n\n\\section{ICE Observations}\n\nFrom 1978 to 1986 the Los Alamos GRB detector on board ICE satellite \n(Anderson et al. 1978) almost continuously observed \nthe Galactic center region within which SGR\n1806-20 is located. It detected\n134 bursts\nfrom the source between 1979 January 7 and 1984 June 8 (Laros et al. ~1987,\n~1990; Ulmer et al. ~1993). Combining observational details given \nby Ulmer et al. (1993) and energy spectral information obtained by OTTB fits \nto bursts (at energies E $>$ 30 keV)\ngiven by Fenimore et al. (1994) and Atteia et al. (1987),\nwe estimate that the ICE burst fluences range form \n$1.5 \\times 10^{-8}$ to $6.5 \\times 10^{-6}$ ergs cm$^{-2}$ and \ntheir corresponding isotropic energies are between $3.6 \\times 10^{38}$ and \n$1.6 \\times 10^{41}$ ergs.\n\n\n\\section{Statistical Data Analysis and Results}\n\nFrom the previous 3 sections, we clearly see that the BATSE and ICE detection\nsensitivities are quite similar, with PCA extending the logN$-$logP distribution\nto lower values. We now combine all data bases to a common set,\nenabling several statistical analyses. \n\n{\\it{(i) Burst fluence distributions :}}~~\nTo eliminate systematic effects \ndue to low count statistics or binning,\nwe have employed the maximum likelihood technique to fit the unbinned\nburst fluences. A power law fit to 92 BATSE fluence values between \n$5.0 \\times10^{-8}$ and $4.3 \\times 10^{-6}$ ergs cm$^{-2}$ yields a power\nlaw exponent, $\\gamma$ = $1.76 \\pm 0.17$ (68$\\%$ confidence level). \nBursts with fluences below $5.0 \\times10^{-8}$ ergs cm$^{-2}$ were excluded\nto avoid undersampling effects due to lower detection efficiency.\nFigure 2 shows the BATSE fluences binned into equally spaced logarithmic \nsteps (filled circles).\nSimilarly, we fit the 266 PCA fluence values between\n$1.7 \\times 10^{-10}$ and $1.9 \\times 10^{-7}$ ergs cm$^{-2}$ \nto a power law model \nand obtain a best fit exponent value of 1.43 $\\pm$ 0.06 (see Fig 2,\ndiamonds for PCA).\nFinally, the 113 ICE fluences between $1.8 \\times 10^{-7}$ and $6.5 \\times \n10^{-6}$ ergs cm$^{-2}$ yield $\\gamma$ = 1.67 $\\pm$ 0.15 (see Fig 2 squares for\nICE).\nWe find that the power law indices obtained for BATSE and \nICE agree well with each other, while the index obtained from \nPCA is marginally lower.\n\nWe fit the ICE fluences to a power law $\\times$ exponential \nmodel and to a broken power law model to search for \nevidence of a turnover claimed by Cheng et al. (1996).\nNeither model provides a statistically significant improvement \nover a single power law fit.\nIt is important to note that there is no evidence of a high energy cut-off\nor a break in the energy distribution (see Fig 2). \n\n\n{\\it{(ii) Waiting times distribution:}}~~ \nTo measure the waiting times between successive SGR 1806-20 bursts,\nwe identified 22 RXTE observation windows containing two or more bursts without\nany gaps. We\nthen determined 262 recurrence interval times $\\Delta$T (i.e. time difference\nbetween successive bursts).\nFigure 3 shows a histogram of the $\\Delta$Ts, which range from\n0.25 to 1655 s.\nWe have fit the ($\\Delta$T)-distribution to a lognormal function and found\na peak at $\\sim$ 97 s (with $\\sigma \\sim$ 3.6). \nThis fit does not include waiting times less than 3 s to avoid contribution of\ndouble peaked events in which the second peak appears shortly \n($\\sim$ 0.25$-$3 s) after the first one.\nTo correct for biases due to the RXTE observation window ($\\sim$ 3000 s),\nwe performed extensive numerical simulations and found that the intrinsic\npeak of the distribution should be at $\\sim$ 103 s.\nNote that the observation windows with no bursts may represent \na long-waiting-time tail which is additional to the lognormal distribution.\n\nTo investigate the relation between the waiting time till the next\nburst ($\\Delta$$T^{+}$) and the intensity of each burst, we divided the 290 \nevents sample into 6 intensity intervals, each of which contains\napproximately 50 events. We fit the $\\Delta$$T^{+}$-distribution \nalso to a lognormal distribution and determined each peak\nmean-{$\\Delta$$T^{+}$} (which range from 82 s to 148 s) and \nthe mean counts for each of the 6 groups. \nWe show in Figure 4 (a) that there is no\ncorrelation between $\\Delta$$T^{+}$ and the total burst counts (the Spearman\nrank-order correlation coefficient, $\\rho$ = $-$0.2 with a probability that\nthis correlation occurs in a random data set, P = 0.70). \nSimilarly, we investigated the relation between the elapsed times since the\nprevious burst ($\\Delta$$T^{-}$) and the intensity of the bursts.\nWe find that mean-$\\Delta$$T^{-}$ extends from 77 s to 120 s. \nFigure 4 (b) shows that there is also no correlation between \nmean-{$\\Delta$$T^{-}$} and the burst counts ($\\rho$ = $0.4$, P = 0.46). \n\n\n\\section{Discussion}\n\nThe fluence distributions of the SGR 1806-20 bursts seen with ICE and \nBATSE\nare well described by single power laws with indices 1.67 $\\pm$ 0.15 and \n1.76 $\\pm$\n0.17, respectively, while RXTE bursts have an index of 1.43 $\\pm$ 0.06.\nThese indices are similar to those found for SGR 1900+14 \n(1.66, {G\\\"o\\u{g}\\\"u\\c{s}} et al. 1999) and SGR 1627-41 (1.62, \nWoods et al. 1999b).\nThe ICE and BATSE values are consistent with one another, over nearly the same\nenergy range but at different epochs. This suggests that SGR event fluence \ndistributions\nmay not vary greatly in time, therefore, we combine the ICE and BATSE values to \ncalculate a ``high-energy'' \nindex, $\\gamma$ = 1.71 $\\pm$ 0.11. \nThe difference between the ``low-energy'' (RXTE) index and the ``high-energy''\nindex is insignificant ($\\sim$ 2.3 $\\sigma$); more ``high-energy'' data are\nneeded to determine whether there is a break in the distribution.\n\nPower law energy distributions have also been found for earthquakes with \n$\\gamma$ = 1.4 to 1.8 (Gutenberg \\& Richter 1956; Chen et al. 1991; \nLay \\& Wallace 1995), \nand solar flares, $\\gamma$ = 1.53 to 1.73 (Crosby et al. 1993, Lu et al.\n1993).\nThis is a typical behavior seen in self-organized critical systems. \nThe concept of\nself-organized criticality (Bak, Tang \\& Wiesenfeld 1988) states that \nsub-systems\nself-organize due to some driving force to a critical state at which a slight\nperturbation can cause a chain reaction of any size within the system. \nSGR power law fluence distributions, along with a lognormal waiting time \ndistribution \nsupport the idea that systems responsible for SGR bursts are in a\nstate of self-organized criticality. \nWe believe that in SGRs, the critical systems are neutron star crusts\nstrained by evolving magnetic stresses (cf. Thompson \\& Duncan ~1995).\n\nCheng et al. (1996) suggested that there is a high energy cut-off in the\ncumulative energy distribution of SGR 1806-20 bursts seen by ICE. In a\ncumulative energy distribution, the values of neighboring points are correlated,\nconsequently, judging the significance of apparent deviations is very difficult.\nFor these reasons we used a maximum likelihood fitting technique and displayed\nthe differential energy distributions (e.g Fig.2). We find no evidence for a\nhigh-energy cut-off in the ICE data of SGR 1806-20 up to burst energies\n$\\sim 10^{41}$ ergs.\nIt should be noted, however,\nthat a high energy cut-off or turnover must exist because otherwise the total \nenergy diverges.\n\nThe distribution of waiting times of SGR 1806-20 bursts observed with RXTE\nis well described by a lognormal function, similar to that found by Hurley et\nal. (1994) for the bursts seen with ICE. The waiting times of the RXTE events \nare on\naverage shorter than the ones observed with ICE, maybe due to different burst\nactive phase of the source or to instrumental sensitivity (the PCA is \nmore\nsensitive to weaker bursts than ICE, and the system displayed plenty of weaker\nbursts as well as strong ones in 1996), or combination of both. \nRecently G\\\"o\\u{g}\\\"u\\c{s} et al. (1999) showed that the recurrence time \ndistribution of SGR\n1900+14 bursts observed with RXTE is also a lognormal function which peaks at\n$\\sim$ 49 s. \nThe lack of any correlation between\nthe intensity and the waiting time until the next burst\nagrees well with the results of ICE observations of SGR 1806-20 (Laros et\nal. 1987). This behavior, also seen in SGR 1900+14 (G\\\"o\\u{g}\\\"u\\c{s} et al. \n1999) confirms\nthat the physical mechanism responsible for SGR bursts is different from systems\nwhere accretion-powered outbursts take place (e.g. the Rapid Burster, \nLewin et al. 1976, and the Bursting Pulsar, Kouveliotou et al. 1996)\n\nThe burst activity of SGR 1806-20 over the last three years is considerably \ndifferent from that of SGR 1900+14. After a long period with almost no bursts, \nBATSE recorded 200 bursts from SGR 1900+14 between 1998 May and 1999 January,\nwith a remarkably low activity thereafter.\nOn the other hand, after SGR 1806-20 reactivated in 1996, it\ncontinued bursting on a lower rate, with 18 bursts in 1997, 32 in 1998\nand 18 in 1999 through October. \nThe latest RXTE observations of SGR 1806-20 in 1999 August revealed \nthat smaller scale bursts are still occurring occasionally in this system,\nwhereas contemporaneous RXTE observations of SGR 1900+14 do not show \nburst activity of any size.\nThis continuation of burst activity may prevent \nthe deposition of very large amounts of stress in the crust. \nTherefore, in SGR 1806-20 it may be\nless likely to expect, in the near future, a giant flare from this source,\nas the ones seen on 1979 March 5 from SGR 0526-66 (Mazetz et al. 1979)\nand on 1998 August 27 from SGR 1900+14 (Hurley et al. 1999).\n\n\n\\acknowledgments\n\nWe are grateful to the referee, Dr. David Palmer for his very constructive \ncomments. \nWe acknowledge support from NASA grant NAG5-3674 (E.G., J.v.P.)\nthe cooperative agreement NCC 8-65 (P.M.W.); \nNASA grants NAG5-7787 and NAG5-7849 (C.K.);\nTexas Advanced\nResearch Project grant ARP-028 and NASA grant NAG5-8381 (R.C.D.). \n\n\n\\begin{references}\n\n\\reference{and78} Anderson, K.A., et al. 1978, IEEE Trans. Geosci.\nElectron., GE-16, 157\n\\reference{att87} Atteia, J.-L., et al. 1987, \\apjl, 320, L105\n\\reference{bak88} Bak, P., Tang, C. \\& Wiesenfeld, K., 1988, \\pra, 38,\n364\n\\reference{chen91} Chen, K., Bak, P. \\& Obukhov, S.P., 1991, \\pra, 43,\n625\n\\reference{cheng95} Cheng, B., et al. 1996, \\nat, 382, 518\n\\reference{cor97} Corbel, S., et al. 1997, \\apj, 478, 624\n\\reference{cros93} Crosby, N.B., et al. 1993, \\solphys, 143, 275\n\\reference{dt92} Duncan, R.C. \\& Thompson C. 1992 \\apjl, 392, L9\n\\reference{fen94} Fenimore, E.E., Laros, J.G. \\& Ulmer, A. 1994, \\apj, 432, 742\n\\reference{fish89} Fishman, G.J., et al. 1989, Compton Observatory Science\nWorkshop, ed. W.N. Johnson, NASA Conference Publication, 2 \n\\reference{go99)} {G\\\"o\\u{g}\\\"u\\c{s}}, E., et al. 1999, \\apjl, 526, L93\n\\reference{gr56} Gutenberg, B. \\& Richter, C.F. 1956, Bull. Seis. Soc.\nAm., 46, 105\n\\reference{gr65} Gutenberg, B. \\& Richter, C.F. 1965, Seismicity of the\nEarth and Associated phenomena (New York: Hafner)\n\\reference{hur99} Hurley, K., et al. 1999, \\nat, 397, 41\n\\reference{hur00} Hurley, K., et al. 2000, in the Proc. of 5th Huntsville GRB\nSymposium, in press\n\\reference{hur94} Hurley, K.J., et al. 1994, \\aap, 288, L49\n\\reference{kou94} Kouveliotou, C., et al. 1994, \\nat, 362, 728\n\\reference{kou96} Kouveliotou, C., et al. 1996, \\nat, 397, 799\n\\reference{kou98} Kouveliotou, C., et al. 1998, \\nat, 393, 235\n\\reference{kou99} Kouveliotou, C., et al. 1999a, \\apjl, 510, L115\n\\reference{kou99} Kouveliotou, C., 1999b, Proc. Natl. Acad. Sci., 96, 5351\n\\reference{lar87} Laros, J.G., et al. 1987, \\apjl, 320, L111\n\\reference{lar90} Laros, J.G., et al. 1990, 21st Int. Cosmic-Ray Conf., 1, 68\n\\reference{lay95} Lay, T. \\& Wallace, T., eds. 1995, Modern Global Seismology,\n(San Diego: Academic), p.376\n\\reference{lew76} Lewin, W.H.G, et al., 1976, \\apj, 207, L95\n\\reference{lu93} Lu, E.T., et al., 1993, \\apj, 412, 841\n\\reference{maz79} Mazetz, E.P., et al. 1979, Nature, 282, 581\n\\reference{pa99} Palmer, D.M., 1999, \\apjl, 512, L113\n\\reference{td95} Thompson, C. \\& Duncan, R.C. 1995, \\mnras, 275, 255\n\\reference{td96} Thompson, C. \\& Duncan, R.C. 1996, \\apj, 473, 322\n\\reference{ulm93} Ulmer, A., er al. 1993, \\apj, 418, 395\n\\reference{wo99a} Woods, P., et al. 1999a, \\apjl, 524, L55\n\\reference{wo99b} Woods, P., et al. 1999b, \\apjl, 519, L139\n\n\\end{references}\n\n\\newpage\n\n\n\\begin{figure}[h]\n\\plotone{gogus_figure-1.ps}\n\\caption{Plot of activity history of SGR 1806-20 as seen with BATSE.\nShaded\nregions denote the time intervals within which the off-line untriggered\nburst\nsearch was not performed. The filled parts illustrate the events within\neach time\nbin which led to an on-board trigger.}\n\\label{onebarrel}\n\\end{figure}\n\n\n\\newpage\n\n\\begin{figure}[h]\n\\plotone{gogus_figure-2.ps}\n\\caption{Differential fluence distributions of SGR 1806-20 bursts as seen\nby\nRXTE (diamonds), BATSE (filled circles) and ICE (squares). The lines are\nobtained fitting a power law model with the maximum likelihood technique.\nThe solid lines show the intervals used in the fit and the dashed lines\nare the extrapolations of each model.}\n\\label{onebarrel}\n\\end{figure}\n\n\n\\newpage\n\n\n\\begin{figure}[h]\n\\plotone{gogus_figure-3.ps}\n\\caption{Histogram of the waiting times, $\\Delta$T, between successive RXTE PCA\nbursts from SGR 1806-20. The line shows the best fit lognormal function.\nThe solid portion of the line indicates the data used in the fit. The excess\nof short intervals above the model is due to the double peaked events as\nexplained in the text.}\n\\label{onebarrel}\n\\end{figure}\n\n\n%\\newpage\n\n\\begin{figure}[h]\n\\plotone{gogus_figure-4.ps}\n\\caption{(a) Plot of lognormal mean waiting times till the next burst\n($\\Delta$$T^{+}$)\nvs mean total counts. No correlation is seen ($\\rho$ = $-$0.2, P=0.70);\n(b) The plot of lognormal mean elapsed\ntimes since the previous burst ($\\Delta$$T^{-}$) vs mean counts\ndoes not show any correlation either ($\\rho$ = 0.4, P=0.46).} \n\\label{onebarrel}\n\\end{figure}\n\n\n\n\\end{document}\n\n"
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astro-ph0002182
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Stellar Evolution and Large Extra Dimensions
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[
{
"author": "S. Cassisi $^1$"
},
{
"author": "V. Castellani $^2$"
},
{
"author": "S. Degl'Innocenti $^2$"
},
{
"author": "G. Fiorentini $^3$ and B. Ricci $^3$"
}
] |
We discuss in detail the information on large extra dimensions which can be derived in the framework of stellar evolution theory and observation. The main effect of large extra dimensions arises from the production of the Kaluza-Klein (KK) excitations of the graviton. The KK-graviton and matter interactions are of gravitational strength, so the KK states never become thermalized and always freely escape. In this paper we first pay attention to the sun. Production of KK gravitons is incompatible with helioseismic constraints unless the $4+n$ dimensional Planck mass $M_s$ exceeds $300$ Gev/c$^2$. Next we show that stellar structures in their advanced phase of H burning evolution put much more severe constraints, $M_s > 3-4$ TeV/c$^2$, improving on current laboratory lower limits.
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"name": "artg.tex",
"string": "\\documentstyle[preprint,tighten,aps]{revtex}\n%\n%\n%%%%%%%%%%DEFINITIONS%%%%%%%%%%%%%%%%\n\n\\def\\lapprox{\\mathrel{\\mathop\n {\\hbox{\\lower0.5ex\\hbox{$\\sim$}\\kern-0.8em\\lower-0.7ex\\hbox{$<$}}}}}\n\\def\\gapprox{\\mathrel{\\mathop\n {\\hbox{\\lower0.5ex\\hbox{$\\sim$}\\kern-0.8em\\lower-0.7ex\\hbox{$>$}}}}}\n\n\n\\begin{document}\n\\author{ S. Cassisi $^1$, V. Castellani $^2$,\n S. Degl'Innocenti $^2$, G. Fiorentini $^3$ and\n\tB. Ricci $^3$}\n\n\\address{\n $^{1}$ Osservatorio Astronomico di Collurania, via Maggini10,\n I-64100 Teramo, Italy.\\\\\n $^{2}$ Dipartimento di Fisica dell'Universit\\`a di Pisa and\n Istituto Nazionale di Fisica Nucleare, Sezione di Pisa,\n\tvia Livornese 582/A, S. Piero a Grado, 56100 Pisa.\\\\\n $^{3}$ Dipartimento di Fisica dell'Universit\\`a di Ferrara and\n Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara,\n via Paradiso 12, I-44100 Ferrara, Italy .\n}\n\n\n\\preprint{\\vbox{\\noindent\n% \\hfill hep-ph/9904nnn\\\\\n \\null\\hfill INFNFE-02-00}}\n\n\\title{Stellar Evolution and Large Extra Dimensions}\n\n\n\\date{February 2000}\n\n \\maketitle\n\n\n\\begin{abstract}\n\nWe discuss in detail the information on large extra dimensions\nwhich can be derived in the framework of stellar evolution theory\nand observation. \nThe main effect of large extra dimensions arises from\nthe production of the Kaluza-Klein (KK) excitations of\nthe graviton. \nThe KK-graviton and matter interactions are of gravitational\nstrength, so the KK states never become thermalized and always \nfreely escape.\nIn this paper we first pay attention to the sun.\nProduction of KK gravitons is \nincompatible with helioseismic constraints unless \nthe $4+n$ dimensional Planck mass $M_s$ exceeds\n$300$ Gev/c$^2$.\nNext we show that stellar structures\nin their advanced phase of H burning evolution put much more severe\nconstraints, $M_s > 3-4$ TeV/c$^2$, improving on\ncurrent laboratory lower limits. \n\n\\end{abstract}\n\n\\section {Introduction}\n\nRecently there has been a revived interest in the physics of\nextra-spatial dimensions.\nIn order to provide a framework of solving the hierarchy problem,\nin refs. \\cite{Arkani98a,Antoniadis98,Arkani98b}, \nthe fundamental Planck scale - where gravity becomes comparable\nin strength with the other interactions -\nwas taken to be near the weak scale. The observed \nweakness of gravity at long distances is due to the\npresence of $n$ new spatial dimensions, with size $R$\nwhich are large compared to the\nelectroweak scale. The relation between the Planck mass\nin $4$ dimensions \n($M_{Pl}= \\sqrt{\\hbar c/G_N}=1.2 \\, 10^{19}$GeV/c$^2$)\nand that in $4+n$ dimensions ($M_s$) is\n\\begin{equation}\n\\label{eq1}\nR^n= (\\hbar/c)^n M_{Pl}^2 / (M_s^{n+2} \\, \\Omega_n)\n\\end{equation}\nwhere $\\Omega_n$ is the volume of the n-dimensional\nsphere with unit radius.\nLaboratory limits, essentially from LEP II \\cite{Lep} give a lower\nbound on $M_s$ of about 1 TeV/c$^2$.\nThe choice $M_s \\sim 1$ TeV/c$^2$ yields $R \\sim 10^{32/n -17}$ cm.\nThe case $n=1$ gives $R\\simeq 10^{15}$cm which is \nexcluded since it would modify newtonian gravitation at\nsolar system distances. Already for $n=2$ one has $R\\simeq 1$mm\nwhich is the distance where our present\nexperimental measurement of gravitational forces stops,\nand one needs information from different sources.\n\nIn this context, one should remind that in last decades the improved \nknowledge of several physical mechanisms has \nallowed astrophysicists to produce stellar models with a significant degree of \nreliability. As a matter of fact, current stellar models nicely \nreproduce the large variety of stellar structures populating the sky, passing also \nsome subtle tests as the ones recently provided by seismologic investigations of \nour sun. Such a success has already opened the way of using stellar structures as a \nnatural laboratory to test the space allowed for new physics, i.e., to investigate \nthe allowed modifications of the current physical scenario \\cite{Raffeltlibro}. \nThis looks as a \nquite relevant opportunity, bearing in mind that a stellar structure is governed \nby the whole ensemble of physical laws investigated in terrestrial laboratories \nand that these stellar structures, in varying their mass and ages, experience a \nrange of physical situations not yet reached in current laboratory experiments. \nOn this basis, the ``stellar laboratory\" has already provided relevant \nconstraints on several physical ingredient as, e.g., the existence of Weak \nInteracting Massive Particles \\cite{Rood89,SF88} or the neutrino \nmagnetic moments \\cite{Raffelt90,Castellani93}.\n\n\nAstrophysical constraints on large extra dimensions have\nbeen discussed in \\cite{Arkani98b} and \nin \\cite{Barger99}. \nThe main effect of large extra dimensions arises from\nthe production of the Kaluza-Klein (KK) excitations of\nthe graviton. The KK-graviton and matter interactions are of gravitational\nstrength, so the KK states never become thermalized and always \nfreely escape. The associated energy loss (through photon-photon annihilation, \nelectron-positron annihilation,\ngravi-Compton-Primakoff scattering, gravi-bremsstrahlung,\nnucleon-nucleon bremsstrahlung) \nhave been calculated in \\cite{Barger99} and observational constraints on $M_s$\nhave been derived from simple considerations on \nthe energetics of sun, red giants and supernovae.\n\nIn this paper we discuss in more detail the information on large\nextra dimensions\nwhich can be derived in the framework of stellar evolution theory\nand observation. \nThe first part is devoted to the study of the \nsun, which represents a privileged laboratory in view of the\nrichness and accuracy of available data.\nIn particular we shall consider the following topics:\\\\\ni)As well known there is a remarkable agreement\nbetween the predictions of the Standard Solar Model (SSM) and the results\nof helioseismic observations, see e.g. \\cite{eliosnoi,nutel99,Bahcall99}.\nProduction of KK gravitons provides a new energy loss, which \nwill become incompatible with helioseismic constraints if \nthe $4+n$ dimensional Planck mass $M_s$ is sufficiently low.\nIn this way we shall determine lower limits \non $M_s$ from helioseismic observations.\\\\\nii)Despite its several successes, the standard solar model presents\nus with some puzzles, e.g. the deficit of solar neutrinos, see e.g. \\cite{valencia97}, \nthe depletion of the photospheric lithium abundance,\nsee e.g. \\cite{litio}, and - perhaps - an underestimate \nof the sound speed just\nbelow the convective envelope, see e.g. \\cite{nutel99,Bahcall98}. \nCould it be that the new physics of KK-graviton \nproduction accounts for some of these anomalies?\n\nIn addition, the efficiency of KK-graviton energy loss \n appears strongly dependent on the temperature. This\nsuggests to consider stars\nexperiencing internal temperatures much larger than in the sun and which, in \nturn, are particularly sensitive to the efficiency of cooling \nmechanisms. In this way the investigation will be extended to red giants structures, which\nwill provide a much more stringent limit on $M_s$.\n\nIn section \\ref{first} we give a first look at \nKK-graviton production in the sun, determining the order of magnitude of\nthe acceptable $M_s$ and presenting the structure of solar\nmodels where the new energy loss is relevant.\nIn section \\ref{helio} we shall determine the helioseismic\nconstraints on $M_s$, from data on the photospheric \nhelium abundance and on sound speed in the energy production\nregion. The effect of KK-graviton production\non the ``solar puzzles'' mentioned\nabove is discussed in sect. \\ref{puzzle}.\nSect. \\ref{rg} will be devoted to red giant stars.\n\nOur conclusions are summarized at the end of the paper,\nwhereas in the appendix we collect the relevant formulas \nfor the energy losses.\n\n\\section{A first look at the effects of KK-graviton production in the sun}\n\\label{first}\n\nIt is interesting to compare the energy loss \ndue to KK-graviton production with the energy production from the pp\nchain at the center of the sun. The values of density, temperature \nand chemical composition derived from the SSM of \\cite{Bahcall98}\nare presented in Table \\ref{tabssm}. The results of other SSM calculations\nare similar, see e.g. \\cite{report}.\nEnergy loss and production rates, computed according \nto the results of Appendix A, are compared in Table \\ref{tabepsi}.\nThe most important contribution always comes from the photon-photon\nannihilation. \n\nOne expects that the solar solar structure would be drastically\nmodified if the energy loss due to \nKK-gravitons becomes comparable with the nuclear energy production\nrate. In this way one can derive the following lower limits on $M_s$:\n\\begin{equation}\n\\label{ms2}\nn=2 \\,: \\quad M_s> 140 \\, GeV/c^2\n\\end{equation}\n\\begin{equation}\n\\label{ms3}\nn=3 \\,: \\quad M_s> 3.5 \\, GeV/c^2\n\\end{equation}\nThis result which is essentially the same as that in ref. \\cite{Barger99}\nsuggests that we concentrate on the $n=2$ case only.\nSo far we assumed just a rough knowledge of the solar structure. \nOne can expect that\nmore detailed information, as that provided by helioseismology, \nprovide more stringent constraints.\n\nTo understand in more detail the effect of KK-graviton production\nwe have built solar models which include this additional\nenergy loss. The energy generation subroutine was modified so as to include\nthe KK-graviton loss and the stellar evolution code FRANEC \\cite{Ciacio}\nwas run by varying the three free parameters of the model (initial\nhelium abundance $Y_{in}$, initial metal abundance $Z_{in}$\nand mixing length $\\alpha$) until\nit provides a solar structure \n(i.e. it reproduces the observed solar luminosity, radius\nand photospheric metal abundance at the solar age).\n\nAs an example, we present here the case $M_s=0.2$ TeV/c$^2$.\nThe main differences with respect to our SSM are depicted\nin Table \\ref{tab02} and Fig. \\ref{fig02}.\nSeveral features can be easily understood by observing\nthat the solar model with KK-graviton production has to\nproduce, now and in the past, a higher amount \nof nuclear energy, in order to compensate \nfor the additional energy loss.\n \nMore hydrogen has been burnt into helium, and \nthe initial helium abundance has to be reduced with \nrespect to the SSM (otherwise one would get \na stellar structure which, being too much helium rich,\nwould be presently overluminous). Consequently,\nthe present photospheric helium abundance $Y_{ph}$\nis decreased with respect to the SSM prediction.\n\nNevertheless, the central helium abundance is still\nsomehow larger than in SSM and more energy is being\nproduced in order to compensate for the KK-graviton losses.\nThis is achieved with a somehow larger central temperature.\n\nIn the solar core, both temperature and ``mean molecular\nweight'' are thus higher than in the SSM, so that one cannot\na priori decide for the behaviour of the sound speed.\nIn fact Fig. \\ref{fig02} shows a decrease near the center and a\nsignificant increase near $R=0.2 R_\\odot$, i.e. in a region where\nhelioseismic determinations are still very accurate.\n\nThese observations will be useful for determining the \nrelevant observables which are sensitive to $M_s$ and which\ncan be constrained by means of helioseismology.\n\nIn Fig. \\ref{figepsi} we also compare the nuclear energy production rate\nwith the losses due to KK-gravitons. The results are consistent\nwith the qualitative energetics analysis discussed above. \n\n\n\\section{Helioseismic constraints on $ M_s$}\n\\label{helio}\n\nHelioseismology provides detailed information on several solar properties. \nIn particular, the sound speed profile and the photospheric helium \nabundance $Y_{ph}$ are determined with high accuracy.\nIn ref. \\cite{eliosnoi} it was estimated that the isothermal sound\n speed squared, $u= P/\\rho $ at distance\n$R=0.2 R_\\odot $ is determined with an accuracy of about \n $\\Delta u/u \\approx 1\\cdot 10^{-3}$,\n\\begin{equation}\n\\label{equ02}\nu_{0.2}^{\\odot}=(1.238 \\pm 0.001)\\cdot 10^ {15} \\, cm^2/s^2\n\\end{equation}\n%\nThis uncertainty, defined as the ``statistical'' \\cite{eliosnoi}\n or ``one sigma'' error \\cite{valencia97},\n was obtained \n by taking into account all possible contributions \n arising from: i) measurement errors, ii) the inversion method\nand iii) the choice of the reference model\n (the recent analysis of \\cite{Bahcall99} confirms the estimate\n of \\cite{eliosnoi} for each contribution to the uncertainty). \n These estimated errors were added in quadrature.\nWith a similar attitude the uncertainty of \n$Y_{ph}$ was estimated:\n\\begin{equation}\n\\label{eqyph}\n Y_{ph}^{\\odot}=0.249\\pm0.003\n\\end{equation}\n \nRecent accurate standard solar model calculations \nare successful in reproducing sound speed in the energy production\nregion as well as the photospheric helium abundance, \ntheir predictions being quite close to the central helioseismic\nestimates, see e.g. \\cite{Bahcall98,eliosnoi}. \nOn the other hand, as discussed in the previous section, \n both quantities are sensitive \nto the energy loss due to KK-graviton production \n For this reason, we concentrate here on \n$Y_{ph}$ and on the value of \n$u$ at $R=0.2 R_\\odot$ {hereafter $u_{0.2}$. \n\nWe have built a series of solar models with $M_s$ \nin the range of few hundred GeV/c$^2$ in order to determine the\ndependence of both observables on $M_s$, see Figs. \\ref{figdelta} \nand \\ref{figpiano}. \nFor each observable $Q$ the results have been parametrized in the form\n\\begin{equation}\n\\label{eqfit}\n Q(M_s) =Q_{SSM} ( 1 + (m/M_s)^\\alpha)\\quad ,\n\\end{equation}\nwith the results for the parameters $ m $ and $\\alpha$ shown \nin Table \\ref{tabalfa}. By requiring that the differences\nin the calculated observables do not exceed the helioseismic uncertainty, \nwe get the following lower bounds on $M_s$:\\\\\n\n\\noindent\n-from $Y_{ph}$ : $M_s > 0.23$ TeV/c$^2$\\\\\n\n\\noindent\n-from $u_{0.2}$ : $M_s > 0.31$ TeV/c$^2$\\\\\n\nThese bounds are stronger that that of Eq. (\\ref{ms2}), which\nwas obtained by using crude energetical considerations. \nHowever, the accuracy of helioseismic method has yielded an improvement\nof just a factor of two.\nIn fact, KK-graviton energy loss rate $\\epsilon_{KK}$ depends\non high powers of $M_s$, so that drastic changements of \n $\\epsilon_{KK}$ result from just tiny modifications of $M_s$.\n\n\n\n\\section{Extra-dimensions and the puzzles of the SSM}\n\\label{puzzle}\n\nAs well known, in front of its several successes,\n the standard solar model presents us with some puzzles: \n\n\\noindent\ni) The signals measured by all solar neutrinos experiments are \nsystematically lower than those predicted \nby SSMs, an effect which is now \ncommonly ascribed to\n neutrino oscillations.\n\n\\noindent\nii) The observed photospheric lithium abundance is \n a factor of hundred smaller than the meteoritic value\n\\cite{litio}. \nLithium is being continuosly mixed in the convective \nenvelope, however -according to the SSM - it should not be \ndestroyed by nuclear reactions since even at the bottom of the\n convective zone the temperature is not high enough to burn it. \nThis signals some deficiency of the standard solar model, \nwhich is built in a one dimensional approximation and neglects rotation, \nsee \\cite{RVCD}.\n\n\\noindent\niii) The helioseismically determined sound speed just below \nthe convective envelope is somehow smaller\n(by 0.4\\%) with respect to the predictions of the most \nrecent and accurate SSM calculations, see e.g. \\cite{nutel99,Bahcall98}.\n\n\nIt is thus natural to ask what is the effect of the hypothetical \nlarge extra dimensions on these items.\n{\\footnote \n{We recall that in \\cite{Smirnov} conversion of electron neutrinos to \nthe light fermions propagating in the bulk of $4+n$ dimensions has been\nconsidered as a solution of the solar neutrino problem.}}\n\nConcerning solar neutrinos, the answer is already contained in the \nprevious discussion. When KK-graviton production is effective,\n the central temperature increases and consequently the\n production of Beryllium and Boron neutrinos\nis increased, see Table \\ref{tab02}. KK-graviton production would \nthus make the neutrino puzzle even more serious.\nAt the bottom of the convective zone the temperature\n would be even smaller than that predicted by SSM, see Table \\ref{tab02}, \nso that there is no help in lithium burning. Sound speed\n just below the convective enevelope is practically unchanged\n with respect the SSM,\nso that the disagreement cannot be affected.\n\nIn short, KK graviton production would provide no cure to the SSM puzzles.\n\n\\section{Red giants and KK-gravitons}\n\\label{rg}\n\n\nA glance at the current evolutionary scenario easily indicates low-mass Red \nGiant Branch (RGB) stars as good candidates for \ninvestigating the effects of KK-graviton production.\nAs a matter of fact a RGB star reaches internal temperatures of the order of \n$10^8$ K. \nMoreover, the structure of RGB stars is quite sensitive\n to the cooling mechanisms which regulate the \nsize of the He core at the He ignition.\nThe size of He core in turn governs several \nobservational quantities both in these RGB structures as well as in the \nsubsequent phase of central He burning (Horizontal Branch, HB) stars. \nWe will follow this approach discussing the effect of KK-graviton cooling on \nthe evolution of suitable RGB structures. Comparison of theoretical predictions \nwith available experimental (i.e. observational) data will allow to put more \nstringent constraints on the minimal $4+n$ dimensional Planck mass $M_s$.\n\nTo perform our investigation we used our latest version of the FRANEC\nevolutionary code \\cite{Ciacio} to predict the observational\nproperties of stellar models with different metallicities but with a\ncommon age of the order of 10 Gyr, thus adequate for RGB stars\nactually evolving in galactic globular stellar clusters (GCs). In\norder to make more clear to the reader the following discussion, in\nFig. \\ref{fighr} we show the typical Hertzprung-Russel diagram for a\ngalactic GC (upper panel) and the corresponding theoretical one (lower\npanel) as obtained by using the prescriptions provided by our own\ncomputations. The most relevant evolutionary phases and observational\nfeatures are clearly marked. The diagram represents the locus of stars\nfor a given chemical composition and age but different masses. As the\nmass increases, the star moves from the Main Sequence location (H\ncentral burning phase) to the RGB (H shell burning phase) till\nreaching a maximum luminosity where the central He ignition occurs\n(RGB tip), driving the structure to the central He burning (Horizontal\nBranch) phase.\n\nNumerical experiments disclose that a stronger cooling has a little effect on \nthe morphology of the diagram depicted in Fig. \\ref{fighr}, but severe consequences on \nthe internal structure of the star. Fig. \\ref{figtro}\n shows the predicted time dependence\nof the central temperature-- density relation for selected values of $M_s$ and $n=2$. \nAs expected, one finds that by increasing $M_s$\nthe efficiency of the extra-cooling decreases.\n Above $M_s \\simeq 5$ TeV/c$^2$ the effects on the \nevolutionary history of the stellar structure vanish. Even a quick inspection of\ndata in Fig. \\ref{figtro} reveals that the assumption $M_s\\sim 1.5$ TeV/c$^2$\n(i.e. already above the current accelerator lower limit for $M_s$) is deeply affecting\n the structure so that one expects\nstrong observational consequences. As a matter of fact, by exploring the case \n$M_s$=1 TeV/c$^2$ (the previous lower limit) one finds that RGB stars would fail to ignite \nHelium, running against the well-established evidence of Helium burning star in \ngalactic GCs. Fig. \\ref{figtro} shows that increasing the cooling for each given central \ndensity the central temperature is lower, as expected. According to well known \nprescriptions of the stellar evolutionary theory, one can thus easily predict that \nthe end of the RGB phase -- i.e. the central He ignition -- will be delayed and the mass of the \nHe core at this stage will be larger.\n\nTo discuss this point in some detail, we show in Fig. \\ref{figmc} the\nHe core mass at the central He ignition (RGB tip) for selected\nassumptions about the value of $M_s$ and n=2. As shown in the same\nFig. \\ref{figmc} in order to cover the range of metallicity (Z)\nspanned by the galactic GCs, computations have been performed for a\n$0.8M_\\odot$ star with Z=0.0002 and for $1M_\\odot$ star with Z=0.02.\n\n\nTo constrain the value of $M_s$ one has now to discuss theoretical results in terms \nof observable quantities. In this context one finds that the extra-cooling is \ngoverning two main observational parameters: i) the luminosity \nof the RGB tip, ii) the luminosity of He burning HB stars. In both cases the stronger the \nextra-cooling the larger is the predicted luminosity.\n\nIn this paper, we focus our attention on the first parameter only.\nSeveral papers have already remarked the good agreement\nbetween observations and \nstandard model theoretical predictions \\cite{DA90,SC98}. Such good agreement is shown \nalso in Fig. \\ref{figtip}\n where we report luminosity (in bolometric absolute magnitudes) \nof the brightest observed RGB star in clusters with different metallicities \\cite{Fro83,Fer20}\nas compared with theoretical predictions for the canonical scenario \n($M_s \\rightarrow \\infty$). According to the discussions given in several papers \n(see e.g. \\cite{CDL,SC98}) the theoretical predictions should represent within \nabout 0.1 mag. the {\\em {upper envelope}} of the observed star luminosity, and this is\nprecisely \nwhat one finds in Fig. \\ref{figtip}. However, the same figure shows that \nfor finite value of $M_s$\n theoretical predictions move toward larger luminosity, in \ndisagreement with observations. \n\nBy inspection of data in Fig. \\ref{figtip} one can conclude conservatively that values of \n$Ms \\leq$ 3 TeV/c$^2$ are definitively ruled out by the observational tests, whereas a \nlower limit of 4 TeV/c$^2$ appears reasonably acceptable. \nThus this detailed evolutionary investigation has improved the crude \nestimate of ref \\cite{Barger99} $M_s \\gapprox 2 $ TeV/c$^2$.\n\n\n\n\n\\section{Concluding remarks}\n\nWe summarize here the main points of this paper:\\\\\n\n\\noindent \ni)Helioseismic constraints on the sound speed in the\n energy production region and on the photospheric helium\nabundance rule out values of the $4+2$ dimensional \nPlanck mass below $M_s= 0.3$ TeV/c$^2$. \n\n\n\\noindent\nii)The introduction of additional energy loss due to \nKK-graviton production cannot be a cure to the puzzles posed by \nSSM calculations. In particular, the predicted neutrino\nsignals would be even larger than those of the SSM.\n \n\\noindent\niii)Observational constraints\nfor Red Giant stars evolving in galactic globulars imply \n$M_s > 3-4$ TeV/c$^2$. This bound is stronger than\nthat provided by accelerator, thus \nindicating how useful it is, and hopefully it will be, the synergetic use\nof terrestrial and stellar laboratories.\n\n\n\n\\acknowledgments\n\n\nWe are extremely grateful to Z. Berezhiani, D. Comelli and F. Villante\nfor discussions. This work is co-financed by the\n Ministero dell'Universit\\`a e della Ricerca Scientifica e\nTecnologica (MURST) within the ``Astroparticle Physics'' project.\n\n\n\\appendix\n\n\\section{Star energy-loss via KK-gravitons}\n\nThe energy loss rate per unit mass \ndue to escaping KK gravitons has been calculated in\n\\cite{Barger99}. Three processes are important\nfor KK-graviton production\nin the sun and in the red giants.\nThe relevant formulas \nare collected below, in natural units as well as in units\nmore useful for implementation in a stellar evolution code.\nFor a comparison, the energy production rate per unit mass\ndue to the pp-chain is also parametrized.\n\n\n\\subsubsection{Photon photon annihilation to KK gravitons: \n$\\gamma+\\gamma \\rightarrow grav$}\n\nWhen $n$ extra dimensions are effective, the Newtonian\ninteraction potential [ $ V \\sim 1/(M_{pl}^2 r) $]is modified to\n$V \\sim 1/(M_s^{n+2} r^{1+n})$, so that the coupling of each particle\nto the gravitational field is proportional to $ 1/M_s^{1+n/2}$\nand KK-graviton \nproduction cross sections are proportional to the square\nof this quantity. \nA thermal photon gas is uniquely specified\nby its temperature T and fundamental physical constants\n$(\\hbar, c$ and $K_B$) so that dimensional considerations\nfix the dependence of the energy loss rate per unit volume $Q_{\\gamma}$.\nIn natural units, this has dimension of [Energy]$^5$, so that\none has $ Q_{\\gamma}= A_{\\gamma}(n) M_s^{-n-2}T^{n+7}$ where\n$A_{\\gamma}(n)$ are numerical coefficients given in eq. (7) of \n\\cite{Barger99}. The energy loss rate per unit mass is obtained by\ndividing Q by the mass density $\\rho$. When temperature\nis in expressed in Kelvin degress, density in g/cm$^3$ and\n$M_s$ in TeV/c$^2$, the energy loss $\\epsilon_{\\gamma}$ in erg/g/s\nis thus:\n\\begin{equation}\n\\label{eqeg1}\nn=2 \\quad \\epsilon_{\\gamma}= 7.25 \\, \\cdot 10^{-66} \\frac{T^9} {\\rho M_s^4}\n\\end{equation}\n\\begin{equation}\n\\label{eqeg2}\nn=3 \\quad \\epsilon_{\\gamma}= 4.42 \\, \\cdot 10^{-82} \\frac{T^{10}} {\\rho M_s^5}\n\\end{equation}\n\n\n\\subsubsection{Gravi-compton Primakoff scattering:\n$\\gamma +e \\rightarrow e+grav$}\n\n\nThe expression for the energy loss is in this case:\n\\begin{equation}\n\\epsilon_{GCP}= B(n) \\frac{\\alpha}{m_e} \\frac{n_e}{\\rho}\n \\frac{T^{n+5}} {M_s^{n+2}}\n\\end{equation}\nwhere the numerical coefficients $B(n)$ are found in eq. 15\nof \\cite{Barger99}, $m_e (n_e)$ is the\nelectron mass (numerical density). The dependence on \n$M_s$ is easily understood from the previous considerations,\n$\\alpha$ comes in from \nelectro-magnetic coupling of the electron\nand the factor $n_e/\\rho$ clearly expresses the proportionality\nto the electron number per unit mass. \nDimensional analysis\nis not sufficient to fully specify the dependence on\ntemperature due to the presence of another\nmass scale, $m_e$, which is relevant \nfor non-relativistic electrons, see \\cite{Arkani98b}.\nIn the same units as in eq. (\\ref{eqeg1},\\ref{eqeg2}):\n\\begin{equation}\n\\label{eqgcp1}\nn=2 \\quad \\epsilon_{GCP}= 1.69 \\, \\cdot 10^{-78} \\frac{T^7 n_e} {\\rho M_s^4}\n\\end{equation}\n\\begin{equation}\n\\label{eqgcp2}\nn=3 \\quad \\epsilon_{GCP}= 5.60 \\, \\cdot 10^{-94} \\frac{T^{8}n_e} {\\rho M_s^5}\n\\end{equation}\n\n\n\\subsubsection{Gravi-Bremsstrahlung: $e+Z \\rightarrow e+Z+grav$}\n\nThe energy loss is now:\n\\begin{equation}\n\\epsilon_{GB}= C(n) \\alpha^2 \\frac{n_e}{\\rho}\n \\frac{T^{n+1}} {M_s^{n+2}} \\Sigma_j n_j Z_j^2\n\\end{equation}\nwhere $n_j$ is the number density of nuclei with atomic\nnumber $Z_j$ and the numerical factors $C(n)$\nare given in eq. (21) of \\cite{Barger99}.\nIn the same units of eqs. (\\ref{eqeg1},\\ref{eqeg2}) one has:\n\\begin{equation}\n\\label{eqgb1}\nn=2\\,: \\quad \\epsilon_{GB}= 5.86 \\, \\cdot 10^{-75} \\frac{T^3 n_e} {\\rho M_s^4}\n\\Sigma_j n_j Z_j^2 \n\\end{equation}\n\\begin{equation}\n\\label{eqgb2}\nn=3\\,: \\quad \\epsilon_{GB}= 9.74 \\, \\cdot 10^{-91} \\frac{T^{4}n_e} {\\rho M_s^5}\n\\Sigma_j n_j Z_j^2 \n\\end{equation}\n\n~\\\\\n\nThe total energy loss due to KK-graviton production is\n\\begin{equation}\n\\epsilon_{KK}=\\epsilon_{\\gamma} + \\epsilon_{GCP} + \\epsilon_{GB}\n\\end{equation}\n\n~\\\\\n\nIt is useful to compare the above energy losses with the \ne.m. energy production rate per unit mass from the pp-chain.\nThe slowest reaction of the chain is the $p+p\\rightarrow d+e^+ +\\nu_e$\nwhich in the temperature region of interest for the sun, has a rate \n$<\\sigma v>_{pp}= A T^{3.83}$, with $A=4.398 \\,\\cdot 10^{-71}$ cm$^3$/s and $T$\nis expressed in Kelvin.\nThe energy production rate per unit mass through the ppI termination of the\npp-chain is:\n\\begin{equation}\n\\label{epsipp}\n\\epsilon_{ppI}= \\frac{1}{4} \\rho \\frac{X^2}{m_H^2} Q_{em} <\\sigma v>_{pp}\n\\end{equation}\nwhere $Q_{em}=26.1$ MeV is the average e.m. energy released in the \n$4p+2e^- \\rightarrow ^4He+2\\nu_e$, $X $ is the H-mass fraction\nand $m_H$ is the hydrogen mass. In the same units as in Eq. \n(\\ref{eqeg1}) one has:\n\\begin{equation}\n\\epsilon_{ppI}= 2.97 \\, \\cdot 10^{-27} X^2 \\rho T^{3.83}\n\\end{equation}\nAs well known the ppI branch is the main energy source in the Sun. \nEverywhere it gives the strongest contribution to the energy production\nrate: \n\\begin{equation}\n\\label{epsinuc}\n\\epsilon_{nuc}= \\epsilon_{ppI}+\\epsilon_{ppII}+\\epsilon_{ppIII}+\\epsilon_{CNO} \\, .\n\\end{equation}\n\n\n\n\n\\begin{thebibliography}{99}\n\n\\bibitem{Arkani98a}N. Arkani-Hamed, S. Dimopoulos and G. Dvali,\nPhys. Lett. B 429 (1998) 263.\n\n\\bibitem{Antoniadis98} I. Antoniadis,\nN. Arkani-Hamed, S. Dimopoulos and G. Dvali,\nPhys. Lett. B 436 (1998) 257.\n\n\\bibitem{Arkani98b} \tN. Arkani-Hamed, S. Dimopoulos and G. Dvali,\nPhys. Rev. D59 (1999) 086004.\n\n\\bibitem{Lep}For a review see e.g.\nG.F. Giudice, hep-ph/9912279, to appear in the Proceeding\nof the XIX International Symposium on Lepton and Photon Interactions at\nHigh Energies, Stanford University, August 1999, \nhttp://lp99.slac.stanford.edu/; V. Ruhlmann-Kleider, ibidem.\n\n\\bibitem{Raffeltlibro}\nG. Raffelt, ``Stars as laboratories for fundamental physics'', The University Chicago\nPress, Chicago 1996.\n\n\\bibitem{Rood89} R. Rood and A.Renzini, Proc. 3rd ESO-Cern Symposium\n\"Astronomy, Cosmology and Fundamental Physics\", M.Caffo, R.Fanti, G.Giacomelli\nand A.Renzini eds., p.287. (1989)\n\n\\bibitem{SF88}\nD.N. Spergel and J. Faulkner, Ap. J. Letter 331 (1988) 21\n\n\\bibitem{Raffelt90} G.Raffelt, Ap. J. 365 (1990) 559.\n\n\\bibitem{Castellani93} V.Castellani and S.Degl'Innocenti, Ap. J. 402 (1993) 574.\n\n\\bibitem{Barger99} V. Barger et al. hep-ph/9905474v2 (1999)\n\n\\bibitem{eliosnoi}\nS. Degl'Innocenti, W. Dziembowski, G. Fiorentini and B. Ricci,\nAstr. Phys. 7 (1997) 77.\n\n\\bibitem{nutel99} G. Fiorentini and B. Ricci, Proceeeding of the\nInternational Workshop ``Neutrino Telescopes '99'',M.B. Ceolin ed,\n Venice 1999, astro-ph/9905341.\n\n\\bibitem{Bahcall99}S.Basu, M. H. Pinsonneault and J. N. Bahcall, \nastro-ph/9909247, to appear on Ap. J. (2000).\n\n\n\\bibitem{valencia97} G.Fiorentini and B.Ricci, ``Beyond the Standard\nModel: from theory to experiment'', World Scientific, Singapore 1999,\nastro-ph/980118. \n\n\\bibitem{litio}N. Grevesse and A. Noels, \nin ``Origin and Evolution of the Elements'',\neds. N. Prantzos, E. Vangion-Flam and M. Cass\\'e , Cambridge University Press,\nCambridge 1993.\n%, Astron. Astroph. 242 (1991) 488.\n\n\n\\bibitem{Bahcall98} J.N. Bahcall, S. Basu and M.H. Pinsonneault,\nPhys. Lett. B. 433 (1998) 1. (BP98)\n\n\n\\bibitem{report}V. Castellani, S. Degl'Innocenti, G. Fiorentini, M. Lissia and B. Ricci, Phy. Rep. 281 (1997) 309.\n\n\n\\bibitem{Ciacio}F. Ciacio, S. Degl'Innocenti and B. Ricci,\nAstron. Astroph. Suppl. Ser. 123 (1997) 449.\n\n\\bibitem{RVCD}\n O.~Richard, S. Vauclair, C. Charbonnel and W. A. Dziembowski,\n Astron. Astroph. 312 (1996) 1000.\n\n\\bibitem{Smirnov} \nG. Dvali and A. Y. Smirnov, hep-ph/9904211 (1999)\n\n\n\\bibitem{DA90}\nG.S. Da Costa and T.E. Armandroff, Astron. J. 100 (1990) 162\n\n\\bibitem{SC98}\nM. Salaris and. S. Cassisi, Monthly Not. Royal Astron. Soc. \n298 (1998) 166\n\n\\bibitem{CDL}\nV. Castellani, S. Degl'Innocenti and V. Luridiana, \nAstron. Astroph. 272 (1993) 442\n\n\\bibitem{Fro83}\nJ.A. Frogel, J.G. Cohen, S.E. Persson, Ap. J. 275 (1983) 773\n\n\\bibitem{Fer20}\nF.R. Ferraro, P. Montegriffo, L. Origlia and F. Fusi Pecci,\nESO preprint N. 1355, December 1999.\n\n%\\bibitem{bordo2} A. S. Brun et al. Ap. J. 525 (1999) 1032.\n\n%\\bibitem{BP95}J.N. Bahcall and M.H. Pinsonneault,\n% Rev. Mod. Phys. 67 (1995) 781.\n\n\n\n\\end{thebibliography}\n\n\n%%%%%%%%%%%%%%%%%%%%%%TABLE %%%%%%%%%%%%%%%%%%%\n\n\\begin{table}\n\\caption{ Physical and chemical \nproperties of the solar center, according to the\nSSM of [16].}\n\\begin{tabular}{lc}\n$T$[K]\t\t& $1.569 \\,\\cdot 10^7$\\\\\n$\\rho$ [g/cm$^3$]\t& 152\\\\\n$X$\t\t& 0.33867\\\\\n$Y$\t\t& 0.64014\\\\\n$\\Sigma_j \\frac{X_j}{A_j} Z_j^2 $ & 1.06\n\\end{tabular}\n\\label{tabssm}\n\\end{table}\n \n\\begin{table}\n\\caption{KK-energy loss and production\nrates calculated at the solar center (see Appendix for definitions).\nRates are in erg/g/s and the\n $4+n$ dimensional Planck mass $M_s$ is in TeV/c$^2$.}\n\\begin{tabular}{lcc}\n\t\t & $n=2$\t & $n=3$ \\\\\n$\\epsilon_\\gamma$ & $2.75\\,\\cdot 10^{-3}M_s^{-4}$ & $2.63\\, \\cdot 10^{-12}M_s^{-5}$\\\\\n$\\epsilon_{GB}$ & $1.59\\, \\cdot 10^{-4}M_s^{-4}$ & $8.26\\, \\cdot 10^{-13}M_s^{-5}$\\\\\n$\\epsilon_{GCP}$ & $8.82\\, \\cdot 10^{-4}M_s^{-4}$ & $2.29\\, \\cdot 10^{-12}M_s^{-5}$\\\\\n$\\epsilon_{KK}$ & $3.79\\, \\cdot 10^{-3}M_s^{-4}$ & $5.75\\, \\cdot 10^{-12}M_s^{-5}$\\\\\n\\hline\n$\\epsilon_{ppI}$ & $10.5$ & $10.5$ \n\\end{tabular}\n\\label{tabepsi}\n\\end{table}\n\n\n\\begin{table}\n\\caption{Fractional differences, (model-SSM)/SSM, between the calculated \nproperties of a solar model with $M_s=0.2$ TeV/c$^2$ ($n=2$)\nand the SSM.}\n\\begin{tabular}{lc}\ninitial composition & \\\\\n$Y_{in}$ & -2.3\\%\\\\\n$Z_{in}$ & +0.88\\%\\\\\n\\hline\nconvective envelope & \\\\\n$Y_{ph}$ &-2.5\\%\\\\\n$R_{b}$ &+0.08\\%\\\\\n$T_b$ &-0.72\\%\\\\\n%$u_b$ & -0.27\\% ....!!!! Attenzione....\\\\\n\\hline\nsolar center & \\\\\n$X_c$ &-5.6\\%\\\\\n$Y_c$ &+3.0\\%\\\\\n$T_c$ &+1.7\\%\\\\\n\\hline\nneutrino fluxes & \\\\\n$Be$ & +24\\%\\\\\n$B $ & +52\\%\n\\end{tabular}\n\\label{tab02}\n\\end{table}\n\n\n\\begin{table}\n\\caption{ The best fit parameters for Eq. \\ref{eqfit}.}\n\\begin{tabular}{lcc}\n & $m$[GeV/c$^2$] & $\\alpha$\\\\\n$u_{0.2}$ & 60 & 4.3 \\\\\n$Y_{ph}$ & 80 & 4.1 \\\\\n\\end{tabular}\n\\label{tabalfa}\n\\end{table}\n\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%% FIGURE %%%%%%%%%%%%%%%%%%%%\n\n\n\n\n\\begin{figure}\n\\caption{Fractional variation with respect to the SSM prediction,\n(model-SSM)/SSM, of the squared \nisothermal sound speed $u(r)=P/\\rho$ in the solar model\n with $M_s=0.2$ TeV/c$^2$ and $n=2$. The shaded area corresponds to the \n``$1 \\sigma$'' or statistical helioseismic uncertainty, see [6].}\n\\label{fig02}\n\\end{figure}\n\n\n\\begin{figure}\n\\caption{Energy losses due to KK-graviton production along the\nsolar structure of the model\nwith $M_s=0.2$ TeV/c$^2$ and $n=2$.\n Dashed line corresponds to the photon-photon annihilation,\ndash-dotted line to gravi-Compton-Primakoff effects, dotted line to \ngravi-bremsstrahlung process. For a comparison also the nuclear\nenergy production (full line) is shown.}\n\\label{figepsi}\n\\end{figure}\n\n\\begin{figure}\n\\caption{Fractional variation with respect to the SSM predictions of the\nquantities $Y_{ph}$ (diamonds) and $u_{0.2}$ (squares) in the solar models \n with different values of $M_s$.}\n\\label{figdelta}\n\\end{figure}\n\n\n\\begin{figure}\n\\caption{The photospheric helium abundance $Y_{ph}$ and the value of \n$u=P/\\rho$ at $R=0.2 R_\\odot$: a) as constrained by helioseismology, see\nEqs. (\\ref{eqyph},\\ref{equ02}); b) as modified\nby models with the indicated value of $M_s$, in TeV/c$^2$).}\n\\label{figpiano}\n\\end{figure}\n\n\n\n\\begin{figure}\n\\caption {Upper panel: typical observational Hertzprung-Russel diagram\nfor a galactic GC. Lower panel: the corresponding theoretical\nHertzprung-Russel diagram. The most relevant evolutionary phases are\nshown.}\n\\label{fighr}\n\\end{figure} \n\n\\begin{figure}\n\\caption{Time behaviour\nof the central temperature -- density relation for a solar model from the Main sequence\nto the ignition of central He burning as predicted by present evolutionary calculations\nfor the canonical case (std) and for the labelled values of $M_s$ and $n=2$.}\n\\label{figtro}\n\\end{figure}\n\n\n\\begin{figure}\n\\caption{The mass, in solar units, of the He core at the central He ignition (RGB tip)\n as a function of $M_s$ for n=2. In order to cover the range of metallicity (Z)\nspanned by the galactic GCs, computations have been performed for a\n$0.8M_\\odot$ star with Z=0.0002 and for $1M_\\odot$ star with Z=0.02.}\n\\label{figmc}\n\\end{figure}\n\n\\begin{figure}\n\\caption{Luminosity (in bolometric absolute magnitudes) \nof the brightest observed RGB star (RGB tip) in clusters with different metallicities\n ([M/H] = Log(M/H)$_{\\rm star}$ - Log(M/H)$_{\\odot}$, where M is fractional abundance\nby mass of all the elements heavier than Helium) [24,25]\n%\\cite{Fro83,Fer20}\n as compared with theoretical predictions for the canonical scenario (std)\nand for models with energy losses due to KK-gravitons with the labelled values\nof $M_s$ and $n=2$.}\n\\label{figtip}\n\\end{figure}\n\n\n\n\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"
}
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[
{
"name": "astro-ph0002182.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{Arkani98a}N. Arkani-Hamed, S. Dimopoulos and G. Dvali,\nPhys. Lett. B 429 (1998) 263.\n\n\\bibitem{Antoniadis98} I. Antoniadis,\nN. Arkani-Hamed, S. Dimopoulos and G. Dvali,\nPhys. Lett. B 436 (1998) 257.\n\n\\bibitem{Arkani98b} \tN. Arkani-Hamed, S. Dimopoulos and G. Dvali,\nPhys. Rev. D59 (1999) 086004.\n\n\\bibitem{Lep}For a review see e.g.\nG.F. Giudice, hep-ph/9912279, to appear in the Proceeding\nof the XIX International Symposium on Lepton and Photon Interactions at\nHigh Energies, Stanford University, August 1999, \nhttp://lp99.slac.stanford.edu/; V. Ruhlmann-Kleider, ibidem.\n\n\\bibitem{Raffeltlibro}\nG. Raffelt, ``Stars as laboratories for fundamental physics'', The University Chicago\nPress, Chicago 1996.\n\n\\bibitem{Rood89} R. Rood and A.Renzini, Proc. 3rd ESO-Cern Symposium\n\"Astronomy, Cosmology and Fundamental Physics\", M.Caffo, R.Fanti, G.Giacomelli\nand A.Renzini eds., p.287. (1989)\n\n\\bibitem{SF88}\nD.N. Spergel and J. Faulkner, Ap. J. Letter 331 (1988) 21\n\n\\bibitem{Raffelt90} G.Raffelt, Ap. J. 365 (1990) 559.\n\n\\bibitem{Castellani93} V.Castellani and S.Degl'Innocenti, Ap. J. 402 (1993) 574.\n\n\\bibitem{Barger99} V. Barger et al. hep-ph/9905474v2 (1999)\n\n\\bibitem{eliosnoi}\nS. Degl'Innocenti, W. Dziembowski, G. Fiorentini and B. Ricci,\nAstr. Phys. 7 (1997) 77.\n\n\\bibitem{nutel99} G. Fiorentini and B. Ricci, Proceeeding of the\nInternational Workshop ``Neutrino Telescopes '99'',M.B. Ceolin ed,\n Venice 1999, astro-ph/9905341.\n\n\\bibitem{Bahcall99}S.Basu, M. H. Pinsonneault and J. N. Bahcall, \nastro-ph/9909247, to appear on Ap. J. (2000).\n\n\n\\bibitem{valencia97} G.Fiorentini and B.Ricci, ``Beyond the Standard\nModel: from theory to experiment'', World Scientific, Singapore 1999,\nastro-ph/980118. \n\n\\bibitem{litio}N. Grevesse and A. Noels, \nin ``Origin and Evolution of the Elements'',\neds. N. Prantzos, E. Vangion-Flam and M. Cass\\'e , Cambridge University Press,\nCambridge 1993.\n%, Astron. Astroph. 242 (1991) 488.\n\n\n\\bibitem{Bahcall98} J.N. Bahcall, S. Basu and M.H. Pinsonneault,\nPhys. Lett. B. 433 (1998) 1. (BP98)\n\n\n\\bibitem{report}V. Castellani, S. Degl'Innocenti, G. Fiorentini, M. Lissia and B. Ricci, Phy. Rep. 281 (1997) 309.\n\n\n\\bibitem{Ciacio}F. Ciacio, S. Degl'Innocenti and B. Ricci,\nAstron. Astroph. Suppl. Ser. 123 (1997) 449.\n\n\\bibitem{RVCD}\n O.~Richard, S. Vauclair, C. Charbonnel and W. A. Dziembowski,\n Astron. Astroph. 312 (1996) 1000.\n\n\\bibitem{Smirnov} \nG. Dvali and A. Y. Smirnov, hep-ph/9904211 (1999)\n\n\n\\bibitem{DA90}\nG.S. Da Costa and T.E. Armandroff, Astron. J. 100 (1990) 162\n\n\\bibitem{SC98}\nM. Salaris and. S. Cassisi, Monthly Not. Royal Astron. Soc. \n298 (1998) 166\n\n\\bibitem{CDL}\nV. Castellani, S. Degl'Innocenti and V. Luridiana, \nAstron. Astroph. 272 (1993) 442\n\n\\bibitem{Fro83}\nJ.A. Frogel, J.G. Cohen, S.E. Persson, Ap. J. 275 (1983) 773\n\n\\bibitem{Fer20}\nF.R. Ferraro, P. Montegriffo, L. Origlia and F. Fusi Pecci,\nESO preprint N. 1355, December 1999.\n\n%\\bibitem{bordo2} A. S. Brun et al. Ap. J. 525 (1999) 1032.\n\n%\\bibitem{BP95}J.N. Bahcall and M.H. Pinsonneault,\n% Rev. Mod. Phys. 67 (1995) 781.\n\n\n\n\\end{thebibliography}"
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astro-ph0002183
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The Asiago-ESO/RASS QSO Survey. I. \\ The Catalog and the Local QSO Luminosity Function \altaffilmark{*}
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[
{
"author": "A. Grazian"
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This paper presents the first results of a survey for bright quasars ($V < 14.5$ and $R<15.4$) covering the North Hemisphere at galactic latitudes $|b|>30$. The photometric database is derived from the GSC and USNO catalogs. Quasars are identified on the basis of their X-ray emission measured in the ROSAT All Sky Survey. The surface density of quasars brighter than 15.5 mag turns out to be $10 \pm 2 \cdot 10^{-3} deg^{-2}$, about 3 times higher than that estimated by the PG survey. The quasar optical Luminosity Function (LF) at $0.04 < z \le 0.3$ is computed and shown to be consistent with a Luminosity Dependent Luminosity Evolution of the type derived by La Franca and Cristiani (1997) in the range $0.3 < z \le 2.2$. The predictions of semi-analytical models of hierarchical structure formation agree remarkably well with the present observations.
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"name": "Grazian.tex",
"string": "% paper1.tex, RASS\n% SAMPLE2.TEX -- AASTeX macro package tutorial paper.\n\n% The first item in a LaTeX file must be a \\documentstyle command to\n% declare the overall style of the paper. The \\documentstyle lines\n% that are relevant for the AASTeX macros are shown; one is uncommented out\n% so that the file can be processed.\n\n\\documentstyle[12pt,aasms4]{article}\n%\\documentstyle[11pt,aaspp4]{article}\n%\\documentstyle[aas2pp4]{article}\n\n% The eqsecnum style changes the way equations are numbered. Normally,\n% equations are just numbered sequentially through the entire paper.\n% If eqsecnum appears in the \\documentstyle command, equation numbers will\n% be sequential through each section, and will be formatted \"(sec-eqn)\",\n% where sec is the current section number and eqn is the number of the\n% equation within that section. The eqsecnum option can be used with\n% any substyle.\n\n%\\documentstyle[11pt,eqsecnum,aaspp4]{article}\n\n% Authors are permitted to use the fonts provided by the American Mathematical\n% Society, if they are available to them on their local system. These fonts\n% are not part of the AASTeX macro package or the regular TeX distribution.\n\n%\\documentstyle[12pt,amssym,aasms4]{article}\n\n% Here's some slug-line data. The receipt and acceptance dates will be \n% filled in by the editorial staff with the appropriate dates. Rules will \n% appear on the title page of the manuscript until these are uncommented \n% out by the editorial staff.\n\n%\\received{4 August 1988}\n%\\accepted{23 September 1988}\n%\\journalid{337}{15 January 1989}\n%\\articleid{11}{14}\n\n\\slugcomment{submitted to the Astronomical Journal \\today}\n\n% Authors may supply running head information, if they wish to do so, although\n% this may be modified by the editorial offices. The left head contains a\n% list of authors, usually three allowed---otherwise use et al. The right\n% head is a modified title of up to roughly 44 characters. Running heads\n% are not printed.\n\n\\lefthead{Grazian et al.}\n\\righthead{The Asiago-ESO/RASS QSO Survey}\n\n% This is the end of the \"preamble\". Now we wish to start with the\n% real material for the paper, which we indicate with \\begin{document}.\n% Following the \\begin{document} command is the front matter for the\n% paper, viz., the title, author and address data, the abstract, and\n% any keywords or subject headings that are relevant.\n\n\\begin{document}\n\n\\title{The Asiago-ESO/RASS QSO Survey. I. \\\\\nThe Catalog and the Local QSO Luminosity Function \\altaffilmark{*}}\n\n\\author{A. Grazian}\n\\affil{Astronomy Department, University of Padua, I-35122 Padua, Italy}\n\n\\author{S. Cristiani \\altaffilmark{1}}\n\\affil{European Southern Observatory, ST European Coordinating\nFacility, D-85748 Garching bei M\\\"unchen, Germany}\n\n\\author{V. D'Odorico}\n\\affil{SISSA, I-34013 Trieste, Italy} \n\n\\author{A. Omizzolo}\n\\affil{Vatican Observatory}\n\n\\and\n\n\\author{A. Pizzella}\n\\affil{European Southern Observatory, Casilla 19001, Santiago 19,\nChile and Astronomy Department, University of Padua, I-35122 Padua, Italy}\n\n% Notice that each of these authors has alternate affiliations, which\n% are identified by the \\altaffilmark after each name. The actual alternate\n% affiliation information is typeset in footnotes at the bottom of the\n% first page, and the text itself is specified in \\altaffiltext commands.\n% There is a separate \\altaffiltext for each alternate affiliation\n% indicated above.\n\n\\altaffiltext{1}{On leave from the Astronomy Department, University of Padua.}\n\\altaffilmark{*}{Based on material collected with the ESO-La Silla, Asiago, NOAO and\nVATT telescopes}\n\n% The abstract environment prints out the receipt and acceptance dates\n% if they are relevant for the journal style. For the aasms style, they\n% will print out as horizontal rules for the editorial staff to type\n% on, so long as the author does not include \\received and \\accepted\n% commands. This should not be done, since \\received and \\accepted dates\n% are not known to the author.\n\n\\begin{abstract}\nThis paper presents the first results of a survey for bright quasars\n($V < 14.5$ and $R<15.4$) covering the North Hemisphere at galactic\nlatitudes $|b|>30$.\nThe photometric database is derived from the GSC and USNO\ncatalogs. Quasars are identified on the basis of their X-ray emission\nmeasured in the ROSAT All Sky Survey. The surface density of quasars\nbrighter than 15.5 mag turns out to be $10 \\pm 2 \\cdot 10^{-3} deg^{-2}$, \nabout 3 times higher than that estimated by the PG survey. \nThe quasar optical Luminosity Function (LF) \nat $0.04 < z \\le 0.3$ is computed and shown to be consistent with a\nLuminosity Dependent Luminosity Evolution of the type derived \nby La Franca and Cristiani (1997) in the range $0.3 < z \\le 2.2$.\nThe predictions of semi-analytical models of\nhierarchical structure formation agree remarkably well\nwith the present observations.\n\\end{abstract}\n\n% The different journals have different requirements for keywords. The\n% keywords.apj file, found on aas.org in the pubs/aastex-misc directory, \n% contains a list of keywords used with the ApJ and Letters. These are \n% usually assigned by the editor, but authors may include them in their \n% manuscripts if they wish. \n\n\\keywords{clusters: quasars, general}\n%\\keywords{globular clusters,peanut clusters,bosons,bozos}\n\n% That's it for the front matter. On to the main body of the paper.\n% We'll only put in tutorial remarks at the beginning of each section\n% so you can see entire sections together.\n\n% In the first two sections, you should notice the use of the LaTeX \\cite\n% command to identify citations. The citations are tied to the\n% reference list via symbolic KEYs. We have chosen the first three\n% characters of the first author's name plus the last two numeral of the\n% year of publication. The corresponding reference has a \\bibitem\n% command in the reference list below.\n%\n% Please see the AASTeX manual for a more complete discussion on how to make\n% \\cite-\\bibitem work for you. \n\\section{Introduction}\n\nQuasar surveys provide basic information for the understanding of a\nnumber of astrophysical, cosmological and cosmogonical issues:\nthe formation and\nevolution of galactic structures, the physics of the AGN phenomenon,\nthe UV and X-ray backgrounds.\n\nThe general behaviour of the QSO optical luminosity function (OLF)\nis well established in the redshift\ninterval $0.3<z<2.2$ for which color techniques provide reliable selection\ncriteria (see \\cite{HS:90,boyle92,HF94}, for a review of the subject).\nA pure luminosity evolution (PLE) appears to reasonably describe tha data\nin the interval $0.6<z<2.2$. \nIn the range $0.3<z<0.6$ the OLF appears to be flatter than observed\nat higher redshifts (\\cite{pippa92}), requiring a luminosity dependent\nluminosity evolution (LDLE, \\cite{lf97} LC97). \nThis departure from a PLE provides an interesting clue for the\nphysical interpretation of the QSO evolving population\n(\\cite{caval97}, LC97).\nThe present observational evidence, however, relies on a relatively\nsmall number of objects: in the $0.3<z<0.6$ range for $M_B<-25$, $32$\nQSOs are observed by LC97 instead of the\n$19$ expected from the best-fit PLE model. Analogous results by\nK\\\"ohler et al. (1997) and Goldschmidt and Miller (1998) are likewise\nbased on very small samples.\n\nTo provide a statistically solid basis for the LDLE\npattern and to investigate whether such a trend\npersists (and possibly becomes more evident) at redshifts lower than\n0.3, we decided to carry out a new large-area survey of quasars at\nbright optical fluxes.\nA typical apparent magnitude for a $M_B = -24$ QSO at $z\\sim 0.1$ is\nin fact $B \\sim 14.5$ and the surface density of these objects,\naccording to previous surveys (e.g. the BQS, \\cite{SeG83}),\nis expected to be less than $10^{-3}$ per sq.deg., requiring an efficient\nselection criterion and the coverage of a significant fraction \nof the whole sky in order to collect a meaningful sample.\n\nIn Sect.2 we describe the photometric database from which optical\nfluxes have been derived, in Sect.3 the criteria followed to select\nthe candidates, in Sect.4 the spectroscopic follow-up, in Sect.5 the\nderived quasar counts and the optical luminosity function and in\nSect.6 a few consequences for model scenarios.\n\n\\section{The Photometric Database}\n\nA number of photometric catalogues are available in the literature,\ncovering a substantial fraction of the celestial sphere down to the\noptical magnitudes of interest for the present survey.\nWe have chosen the {\\em USNO} (\\cite{mone96}), {\\em GSC} (\\cite{lask88})\nand the {\\em DSS} (\\cite{http1}).\n\nTo test the accuracy of the photometric calibration of these\ncatalogues, we have used as a comparison in the Northern sky\nthe photometric standards of Landolt (1992).\n% (\\cite{land92})\nIn the Southern hemisphere we have used 446 standards\nderived from the input catalog used to calibrate the photometric\nmaterial of the Homogeneous Bright Quasar Survey (HBQS, \\cite{SC95}).\nFrom both samples only relatively bright (12.5$\\leq$$V$$\\leq$16.0) and\nnot too red $(B-R)$$\\leq$+1.0 stars have been chosen in order to match\nthe characteristics of the quasars searched for in this survey.\n\nWe finally defined three flux-limited samples adopting as photometric\nreference: \n\\begin{enumerate} \n\\item {in the Northern hemisphere objects with $11.0 < V_{GSC} \\le 14.5$ in\nthe GSC catalog. The relation between the $V_{GSC}$ band and\nthe corresponding Johnson $V$ turned out to be:\n\\begin{equation}\nV_{GSC}=V-0.21\n\\end{equation}\nwith $\\sigma_{V}=0.27$ $mag$. 7 ($4\\%$) of the 183 Landolt stars \nused for this comparison were not found in the GSC catalog.\n}\n\\item{in the Northern hemisphere objects from the USNO catalog with\n$13.5 < R_{USNO} \\le 15.4$.\nThe relation between the $R_{USNO}$ band and\nthe corresponding Johnson-Kron-Cousins $R$ turned out to be:\n\\begin{equation}\nR_{USNO}=R_{JKC}+0.096\n\\end{equation}\nwith $\\sigma_{R_{USNO}}=0.267$ $mag$.\nNo correlation between the residuals of $R_{USNO}-R_{JKC}$ and the\ncolor $(B-R)_{JKC}$ has been found. According to Monet et al. (1996),\nthe internal magnitude estimators for stars in the USNO catalog are\nprobably accurate to something like 0.15 magnitudes over the range\n$R_{USNO}=12$ $mag$ to $R_{USNO}=19$ $mag$, but the systematic error\narising from the plate-to-plate differences is at least 0.25\nmagnitudes in the Northern hemisphere, consistent with our estimates.\n}\n\\item {\nin the Southern hemisphere we have derived\n$B_J$ magnitudes from the Digitized Sky Survey (DSS). Small scans \n(``postage stamps'' of $2' \\times 2'$) of each object\nof interest and of 20-50 surrounding objects with known GSC $B_J$\nmagnitudes were extracted from the DSS. The magnitude of the object of \ninterest was then calibrated against the GSC objects.\nIn this way a $\\sigma_{B_J}$ of $0.10$ $mag$ was obtained in the interval\n$12.0 < B_J <15.5$.\n}\n\\end{enumerate} \n\n\\section{The Selection of the Sample}\n\n\\subsection{The ROSAT All Sky Survey}\nIn order to pick out the bright quasars from the overwhelming number\nof stars in the same magnitude range, an efficient selection criterion is\nrequired. A convenient possibility is offered \nby the X-ray emission, which is a key signature of the AGN phenomenon.\n\nThe ROSAT All Sky Survey (hereafter RASS, \\cite{vog92})\nwas carried out\nduring the period July 1990/February 1991 with the PSPC and has produced\na photometric database in the Soft-X (0.1-2.4 KeV). This shallow survey\ncovers almost the entire sky at a bright level ($10^{-13}$ erg \ncm$^{-2}$ sec$^{-1}$) and initially contained 60000 sources.\nA more evolved reduction analysis, SASS-II, has produced\nthe RASS Bright Source Catalogue (RASS-BSC, \\cite{vog99}),\na sample of\n18811 X-ray sources at a limiting flux level of 0.05 $cps$\\footnote{$cps$ is\nthe 'counts per second' of a source and is a measure of the flux, when a\nprecise X-soft spectrum is considered. For $F(\\nu)\\propto\n\\nu^{-1}$ 0.05 $cps$ correspond to $10^{-13}$ erg s$^{-1}$ cm$^{-2}$.\n}\nall over the sky.\n\nThe main constituents of the RASS catalogue are AGNs and peculiar\nstars (CV, M stars, K stars, WDs, X-ray binaries and coronally active\nstars), but there are also cluster of galaxies, BL Lacs, SN remnants,\nneutron stars and normal galaxies (or starbursts). A convenient way\nto distinguish/isolate AGNs is the comparative analysis of their\nsoft-X/optical properties (\\cite{hasing98}).\n\nWe have cross-correlated the RASS catalogue with the photometric\ndatabases described in the previous section for sources at galactic\nlatitudes $|b|\\ge 30$ deg and with a RASS-BSC exposure time $\\ge 300$\ns, i.e. $flux\\ge$ 0.05 $cps$. \nSources classified as extended in the RASS have been disregarded,\nwhile no selection based on optical morphology was applied.\nWe have looked for optical objects in\nthe range $11.0 < V_{GSC} \\le 14.5$ and $13.5 < R_{USNO} \\le 15.4$\naround the RASS sources, adopting a matching radius three times the\nRMS positional uncertainty of each entry in the RASS catalog\n(typically $3 \\times 12''$). In this way very few (of the order of\n$0.1 \\%$) true identifications in the desired optical range are\nmissed. Misidentifications, i.e. ``X-ray quiet'' AGN in the desired\noptical magnitude range falling by chance in the RASS error-box, are\nalso possible, but extremely unlikely, given the low surface density\nof these bright AGN and are in any case irrelevant for the present\nwork, which aims at the definition of the local {\\it optical} QSO LF.\n\nThe resulting catalogue covers 8164 square degrees in the North and\n5855 square degrees in the South.\n\n\\subsection{ The $\\alpha_{ox}$ distribution of quasars and the\nSelection Criteria}\n\nFor each source the $\\alpha_{ox}$ index was computed as\n$\\alpha_{ox}= -0.408 \\log cps -0.163 R +3.65$\nor\n$\\alpha_{ox}= -0.428 \\log cps -0.171 V +3.84$\nor \n$\\alpha_{ox}= -0.483 \\log cps -0.193 B_J +4.20$.\n\nTo obtain an estimate of the intrinsic distribution of the\n$\\alpha_{ox}$ of quasars we have plotted the observed $B$, $V$ or $R$\nmagnitudes vs. the $\\log cps$ for the $0.04< z \\le 0.3$ quasars listed\nin the $8^{th}$ edition\nof the V\\'eron catalog (VV98, 1998).\nFig.~1 shows the result for northern QSOs and $R$ magnitudes.\n%\n\\placefigure{fig1}\n%\nIn this diagram the locus $\\alpha_{ox} = {\\rm const}$ is represented\nby a straight diagonal line. \n``X-ray quiet'' objects, i.e. with a flux$\\le 0.05 cps$ to the left\nof the vertical continuous line, are missed in the RASS.\nIf we assume that the intrinsic distribution of the $\\alpha_{ox}$ is\nnot a function of the apparent luminosity (\\cite{yuan:98}), selecting\nobjects with $\\alpha_{ox} < \\alpha_{max}$ (i.e. ``X-ray loud'') and\noptically brighter than a convenient limit will\nprovide a sample with a degree of incompleteness that is not a\nfunction of the apparent magnitude. For example, in the case of the\nUSNO database the limit in $R$ turns out to be $R < (3.65\n-\\alpha_{max}-0.408 \\log cps_{min}) /0.163 = 25.64 - 6.13\n\\alpha_{max}$. If we adopt (see Fig.~1) an $\\alpha_{max}=1.7$ at magnitudes\nbrighter than $R=15.4$ only the objects with $\\alpha_{ox} >\n\\alpha_{max}$ will be missed.\n\nTab.~1 lists the interval of optical magnitudes and the\ncorresponding limit on $\\alpha_{ox}$ chosen for the USNO, GSC and DSS\nsub-samples. The last column shows the degree of completeness\nestimated on the basis of the fraction of quasars of the VV98 found with the\nadopted criterion.\n%\n\\placetable{tbl-1}\n%\nExamining the properties of the VV98 quasars in terms of the various\nRASS parameters, we have found two further\nempirical criteria, based on the hardness ratios $HR1$ and $HR2$\n(\\cite{vog99}), to increase the effectiveness of the selection\nwithout affecting its completeness:\n\\begin{enumerate}\n\\item{\n$-0.9\\le HR1 \\le 0.9 $, where $HR1$,\nthe hardness ratio 1 is defined as $(A-B)/(A+B)$, \nwith the ROSAT-PSPC count\nrates A in the hard band (0.5 $\\div$ 2.0 keV) and B in the soft band (0.1\n$\\div$ 0.4 keV).}\n\\item{\n$-0.6\\leq HR2\\leq +0.8$, where $HR2$,\nthe hardness ratio 2, is defined as $(C-D)/(C+D)$, \nwith the ROSAT-PSPC count\nrates C in the hard band (0.9 $\\div$ 2.0 keV) and D in the soft band (0.5\n$\\div$ 0.9 keV).}\n\\end{enumerate}\n\n\\section{Spectroscopic Follow-up}\n\nIn the following we concentrate our discussion on the sample of\nNorthern objects, for which the follow-up spectroscopy is more\nadvanced. The Southern sample will be described elsewhere. The list\nof the quasar candidates and the results of the spectroscopy \nare reported in Tab.~2. \nIt should be noted that Tab.~2 cannot be considered a list of\noptical identifications of X-ray sources. The cross-correlation\nprocedure defined in the previous section aims at finding optical\nobjects in a desired magnitude range around X-ray sources. In some\ncases an entry in Tab.~2 may exist even if the true identification of\nthe X-ray source is another (typically fainter) optical object. For\nexample, even if the optical counterpart of the RASS source\nJ013624.3+205712 is known to be the QSO 3C47.0, with $V\\simeq 18.1$\nand $z=0.425$, in Tab.~2 we list an object of $R_{USNO}=14.7$\nwhich happens to fulfill the criteria of the cross-correlation.\n%\n\\placetable{tbl-2a}\n%\nThe follow-up observations of the QSO candidates have been carried out at\nthe 1.8m telescope in Asiago with a Boller and Chivens Spectrograph or\nwith the Asiago Faint Object Spectrograph and Camera (AFOSC),\nat the 1.5m ESO, 1.5m Danish and NTT telescopes in La Silla\nwith a Boller and Chivens Spectrograph, DFOSC and EMMI respectively and\nwith the 90'' telescope at Kitt Peak.\nThe resolution of the spectra ranges between 10 and 30 \\AA. \n\nThe reduction process used the standard MIDAS facilities \n(Banse et al., 1983) available at the Padua Department of Astronomy and at \nESO Garching.\nThe raw data were sky-subtracted and corrected for pixel-to-pixel sensitivity\nvariations by division with a suitably normalized exposure of the spectrum of\nan incandescent source (flat-field). Wavelength calibration was carried out by\ncomparison with exposures of He-Ar, He, Ar and Ne lamps. Relative flux\ncalibration was carried out by observations of spectrophotometric\nstandard stars (Oke, 1990). \n\nThe identification classes are: $AGN$ = emission-line object,\nirrespective of the line width; $STAR$ = star; $GAL$ = galaxy; $BL$ = BL Lac \nobject. Identifications as BL Lac or Galaxy have been taken from the\n NASA/IPAC Extragalactic Database (NED).\nUncertain identifications and redshifts are indicated with a\ncolon ($:$). \n\nIn order to test the reliability of our selection, additional\ncandidates, selected with less restrictive criteria than those reported\nin the previous section, were observed. They are\nreported in Tab.~3.\nThe spectra of the AGNs found during the follow-up spectroscopy are shown in\nFig.~2.\n%\n\\placetable{tbl-3}\n\\placefigure{fig2}\n%\n\\section{First Results}\n\nThe spectroscopic observations of the Northern sample are still\nincomplete: only 45$\\%$ of the candidates have been identified.\nDifferent areas of the sky, in particular different strips in right\nascension, have been observed down to different magnitude limits.\nTables 4-5 list the extension of the area covered with a complete\nspectroscopic follow up as a function of the limiting magnitude.\n\nIn the following computations we have adopted for the Northern sample\nthe ``effective areas'' listed in Tabs.\n~4-5, which take into account the\nincompleteness factors estimated in the previous sections.\n%\n\\placetable{tbl-4}\n\\placetable{tbl-5}\n%\n\\subsection{Quasar Counts}\n\nFig.~3 shows the LogN-LogS relation of QSOs brighter than $M_B = -23$\nmag\n\\footnote{In the present\npaper the K-corrections are computed on the basis of the composite spectrum of\nCristiani and Vio (1990), galactic extinction is taken into account\naccording to Burstein and Heiles (1982). The values $q_0 = 0.5$, and\n$H_0=50$~Km/s/Mpc are adopted throughout.} \nwith $z \\ge 0.04$, for the USNO and GSC subsamples\ntogether. The LogN-LogS has been computed with the $\\sum 1/Area_{max}$\nmethod, a convenient approach when the various sub-areas have very different\nmagnitude limits. \n\n\\placefigure{fig3}\n\nThe LogN-LogS relation found in the present survey is consistent with\na single power-law distribution with the slope $0.67$ reported by\nK\\\"ohler et al. (1997) for QSOs with 0.07$\\le z\\le$2.2, with a\nslightly higher normalization: if we fix $\\beta = 0.67$ in a $\\log N =\n\\beta B+k$ relation, we find $k=-12.15^{+0.17}_{-0.19}$. If we\nrestrict our sample to $z>0.07$ we find $k=-12.2\\pm 0.2$, in agreement\nwith the normalization, $k=-12.4$, of K\\\"ohler et\nal. (1997).\n\nA comparison with the Palomar Bright Quasar Survey (BQS, \\cite{SeG83})\nshows that at $B \\sim 15.5$ the cumulative BQS counts are about a\nfactor 3 lower. This confirms previous findings by Goldschmidt et\nal.(1992), LC97, K\\\"ohler et al. (1997). \\placetable{tbl-counts}\n \n\\subsection{The QSO Luminosity Function at $0.04< z\\le 0.3$}\n\nA preliminary, cursory analysis of the QSO optical LF has been carried\nout on the basis of the present sample. A more detailed discussion\nof the complete spectroscopic database will be developed elsewhere \n(Grazian and Cristiani, in preparation). To compute the LF at $0.04<\nz\\le 0.3$ we have used the generalized $1/V_{max}$ ``coherent''\nestimator (\\cite{avni:80}) in a slightly modified version which tries\nto estimate in an unbiased manner the volume-luminosity space\n``available'' to each object (cf. the method of Page \\& Carrera, 1999)\nand takes into account the evolution of the LF within the redshift\ninterval. Errors were estimated from Poisson statistics\n(\\cite{gehrels:86}). The data values of the LF at $0.04 < z \\le 0.3$\nare given in Tab.~\\ref{tbl-LF}. \n%\n\\placetable{tbl-LF}\n%\nFigures 4a and 4b show the comparison of the newly derived QSO LF at\n$0.04< z\\le 0.3$ with data at higher redshift, up to $z=2.2$\n(LC97), and with a PLE and an LDLE parameterization,\nrespectively.\nThe points in the range $0.04 < z \\le 0.3$ are the result of the\npresent survey, \nthe data in the other redshift ranges are derived from LC97.\nNo effort has been made in the derivation of the LF at $0.04 < z \\le\n0.3$ to subtract off the luminosity of the host galaxy.\n%\n\\placefigure{fig4}\n%\nThe PLE parameterization is the global best fit to the QSO \nLF derived in the interval $0.3 < z < 2.2$ by LC97 (Model B), \nwho found it to be inconsistent with\nthe data at $0.3<z<0.6$ at a $3 \\sigma$ level.\nThe present result confirms and strengthens the conclusion of LC97:\nif we compare the prediction of the Model B PLE of LC97 in the range\n$0.04< z\\le 0.3$, a $\\chi^2 \\simeq 14$ for the 5 data points of\nTab.~\\ref{tbl-LF} is derived, corresponding to a formal probability of\n$1.9 \\%$. \n\nFig.~4b shows that an LDLE parameterization of the type of Model C of\nLC97 can reproduce the data in a much more satisfactory way. \nThe best agreement with the data from $z=0.04$ to $z=2$ is obtained,\nassuming the functional form (LC97)\n\\begin{equation}\n\\label{eq:LDLE}\n\\Phi (M_B,z) = { {\\Phi^\\ast} \\over { 10^{0.4[M_B-M_B^*(z)](\\alpha + 1)} +\n10^{0.4[M_B-M_B^*(z)](\\beta + 1)} } } \\\\\n\\end{equation}\nwith\n\\begin{equation}\nM_B^*(z) = M^*_B(z=2)-2.5 k \\log [(1+z)/3]\n\\end{equation}\nand\n\\begin{eqnarray}\nfor~M_B \\leq M_B^*(z)&:&~ k = k_1 + k_2 [M_B-M_B^*(z)]e^{-z/{.40}} \\\\\n\\nonumber for~M_B > M_B^*(z)&:&~ k = k_1 \n\\end{eqnarray}\nwhere $\\alpha$ and $\\beta$ correspond to the faint-end and bright-end\nslopes of the optical LF, respectively and $M^*_B(z=2)$ is the\nmagnitude of the break in the double power-law shape of the LF at $z=2$.\nThe actual values adopted in the LDLE parameterization are:\n$ {\\Phi^\\ast}= 9.8\\times 10^{-7} mag^{-1} Mpc^{-3},\n~M^*_B(z=2)=-26.3,\n~k_1=3.33,\n~k_2=0.37,\n~\\alpha = -1.45, \n~\\beta = -3.76 $, providing a $\\chi^2$ probability $\\simeq 58 \\%$ \nin the range $0.04 < z \\le 0.3$ when compared to the 5 data points of\nTab.~\\ref{tbl-LF}.\n\\section{Discussion}\nFranceschini et al. (1994) and La Franca et al. (1995) have shown that\nthe QSO emission in the soft-X and at visible wavelengths scales\nlinearly. A confirmation of the constant ratio $L_X/L_O$ and\nindependence both from $L_O$ and from $z$ comes from Yuan et al. (1998).\nBoyle et al. (1994) derived a XLF comparable to the QSO OLF known at\nthat epoch with an evolutionary rate $L_X(z)=L_X(0)(1+z)^{3.25}$,\nsimilar to the optical one. These works favor a scenario in which\nessentially the same QSO population is observed, both in the soft-X\nand in the optical. In this way the flattening of the OLF observed in\nthe present survey should be reflected in a flattening in the\ncorresponding soft-X LF. Indeed Miyaji et al. (1999) show that the\nbright part of the 0.5-2 keV LF flattens with decreasing redshift from\na value $1+\\beta \\simeq 3.5$ at $0.4 < z < 0.8$ to $1+\\beta \\simeq\n2.6$ at $0.015 < z < 0.2$, which is similar to what we observe in the\noptical: $1+\\beta \\simeq 3.7$ at $0.6 < z < 1.0$ and $1+\\beta \\simeq\n3.1$ at $0.04 < z \\le 0.3$.\n\nThe decline of the space density of quasars from a peak around\nredshift 2 to the present epoch has been modeled by several authors in \nthe framework of hierarchical theories of structure formation\n(\\cite{cattaneo:99,HM:99,KH:99,MSD:99}). In particular Kauffmann and\nHaehnelt (1999, KH99) have attempted to reproduce quantitatively the\nevolution of the quasar number density incorporating a scheme for the\ngrowth of massive black holes (MBHs) into semi-analytical models following\nthe evolution of galaxies in CDM-dominated scenarios.\nTogether with the decrease in the merging rates and in the amount of\ngas available to fuel the MBHs, which are built-in features of the\nsemi-analytic models, KH99 assume an increase of the timescale for gas \naccretion in order to reproduce the steep decline in the number\ndensity of quasars from $z \\sim 2$ to $z=0$. Other authors have\nfollowed similar recipes assuming a decreasing mass accretion\n(\\cite{HM:99}), or a decreasing efficiency of the accretion\n(\\cite{cattaneo:99}), or a delayed quasar activity with respect to the \ndynamical formation of the halos with a longer delay for smaller halos\n(\\cite{MSD:99}). \n\nAs can be seen from Fig.~17 of KH99, the semi-analytical models have\ndifficulties in reproducing the steep decrease of\nthe QSO density at low redshift that is commonly measured (\\cite{HS:90}).\nThe most promising scenario is a $\\Lambda$CDM, in which the accretion\ntimescale, $t_{\\rm acc}$, is assumed to vary in the same way as the\nhost galaxy dynamical time ($t_{\\rm acc} \\propto [0.7 +\n0.3(1+z)^3]^{-1/2}$). This model is able to reproduce\nthe evolution of the galaxy LF and of the cold gas content of\ngalaxies, but is apparently predicting a too slow quasar decline.\nThe present data significantly reduce this disagreement in the\nsense that the higher quasar space density measured in\nour survey corresponds fairly well to the $\\Lambda$CDM semi-analytical\npredictions, as shown in Fig.~\\ref{semi_anal}.\n%\n\\placefigure{semi_anal}\n%\n\\acknowledgments\nIt is a pleasure to thank A. Wicenec for his invaluable help with the\nphotometric database and F.La Franca, M. Haehnelt and G.Kauffmann for\nenlightening discussions. We are indebted to Mira and Philippe V\\'eron\nwhose indications helped us to improve significantly the accuracy of\nthe identifications. We would also like to thank an anonymous referee\nfor several useful comments which improved the paper. AG acknowledges\nthe generous hospitality of ESO during two visits to Garching. This\nwork is based on photographic data obtained using The UK Schmidt\nTelescope. The UK Schmidt Telescope was operated by the Royal\nObservatory Edinburgh, with funding from the UK Science and\nEngineering Research Council, until 1988 June, and thereafter by the\nAnglo-Australian Observatory. Original plate material is copyright (c)\nof the Royal Observatory Edinburgh and the Anglo-Australian\nObservatory. The plates were processed into the present compressed\ndigital form with their permission. The Digitized Sky Survey was\nproduced at the Space Telescope Science Institute under US Government\ngrant NAG W-2166. The NASA/IPAC Extragalactic Database (NED) is\noperated by the Jet Propulsion Laboratory, California Institute of\nTechnology, under contract with the National Aeronautics and Space\nAdministration.\n\\clearpage\n \n\\begin{deluxetable}{lcccc}\n%\\tablewidth{33pc}\n\\tablewidth{400pt}\n\\tablecaption{Selection Criteria and Completeness}\n\\tablehead{\n\\colhead{Sub-sample} &\n\\colhead{Magnitude Interval} &\n\\colhead{$\\alpha_{ox}$} &\n\\colhead{Completeness} &\n\\colhead{Completeness} \\\\\n\\colhead{} &\n\\colhead{} &\n\\colhead{max} &\n\\colhead{$N_{found}/N_{VV98}$} &\n\\colhead{ \\% }\n}\n\\startdata\nUSNO & $13.5 < R~ < 15.4 $ & 1.7 & 24/36 & 68 \\nl\nGSC & $12.5 < V~ < 14.5 $ & 1.9 & 5/8 & 63 \\nl\nDSS & $12.6 < B_J < 15.2 $ & 1.9 & 8/9 & 89 \\nl\n\\label{tbl-1}\n\\enddata\n\\end{deluxetable}\n\\clearpage\n%%\n\\begin{deluxetable}{lrrrrrc}\n\\tablenum{2}\n\\tablewidth{0pt}\n\\tablecaption{THE USNO SAMPLE}\n\\tablehead{\n\\colhead{Name (1RXS)} & \\colhead{R.A.} \t&\n\\colhead{Declination} & \\colhead{$R_{USNO}$} & \\colhead{$V_{GSC}$} &\n\\colhead{$z$} & \\colhead{Type}}\n\\startdata\n J000150.9+111705 & 00 01 50.6 & +11 16 47.6 & 15.10 & & 0.158 & AGN \\nl \n J001031.3+105832 & 00 10 31.0 & +10 58 29.6 & 13.60 & 14.66 & 0.089 & AGN \\nl \n J002337.1+044220 & 00 23 37.2 &\t+4 42 22.3 & 14.30 & 15.13 & 0.081 & AGN \\nl \n J002811.6+310342 & 00 28 10.8 & +31 03 47.8 & 15.30 & & 0.500 & AGN \\nl \n J002913.9+131605 & 00 29 13.7 & +13 16 03.6 & 15.30 & 15.23 & 0.142 & AGN\\nl \n J004240.8+301742 & 00 42 41.6 & +30 17 43.9 & 14.40 & &\t &\t \\nl \n J005154.8+172552 & 00 51 54.8 & +17 25 58.4 & 15.30 & & 0.064 & AGN \\nl \n J013556.7+231605 & 01 35 58.5 & +23 15 56.5 & 15.20 & &\t &\t \\nl \n J013624.3+205712 & 01 36 25.3 & +20 56 49.6 & 14.70 & & & \\nl\n J014239.9+000514 & 01 42 38.4 &\t+0 05 14.9 & 15.30 & &\t &\t \\nl \n J015242.1+010040 & 01 52 41.9 &\t+1 00 25.1 & 14.40 & 13.57 & 0.230 & GAL\\nl \n J015524.9+022818 & 01 55 24.9 &\t+2 28 16.2 & 15.10 & & & \\nl \n J015546.4+071902 & 01 55 46.4 &\t+7 19 03.8 & 15.40 & &\t &\t \\nl \n J015935.1+104707 & 01 59 34.9 & +10 46 46.7 & 15.20 & &\t &\t \\nl \n J075704.9+583245 & 07 57 06.2 & +58 32 58.7 & 14.50 & 14.48 & & \\nl \n J080132.3+473618 & 08 01 32.0 & +47 36 15.8 & 15.20 & & 0.158 & AGN \\nl\n J080525.8+753424 & 08 05 23.7 & +75 34 34.7 & 15.30 & 14.40 & & \\nl \n J080534.6+543132 & 08 05 34.8 & +54 31 30.3 & 14.90 & &\t &\t \\nl \n J080649.5+751853 & 08 06 48.3 & +75 18 30.7 & 15.10 & &\t &\t \\nl \n J080938.9+754851 & 08 09 39.8 & +75 48 55.1 & 14.20 & & 0.094 & AGN \\nl \n J080949.2+521855 & 08 09 49.2 & +52 18 58.2 & 14.50 & 14.84 & 0.138 & BL \\nl \n J081059.0+760245 & 08 10 58.6 & +76 02 42.5 & 14.20 & 14.59 & 0.100 & AGN \\nl \n J081228.3+623627 & 08 12 28.2 & +62 36 23.3 & 14.50 & 14.15 &\t &\t \\nl \n J083045.0+340527 & 08 30 45.4 & +34 05 31.6 & 15.30 & & 0.063 & AGN \\nl \n J083121.0+483148 & 08 31 22.3 & +48 32 13.9 & 15.10 & 15.13 &\t &\t \\nl \n J083821.6+483800 & 08 38 22.0 & +48 38 01.7 & 14.80 & 14.63 &\t &\t \\nl \n J084255.9+292752 & 08 42 56.0 & +29 27 26.2 & 15.40 & & 0.193 & GAL\\nl\n J084445.2+765313 & 08 44 45.3 & +76 53 09.3 & 13.90 & 15.72 & 0.131 & AGN \\nl \n J084658.3+704452 & 08 47 05.7 & +70 44 41.1 & 15.20 & 14.62 &\t &\t \\nl \n J085343.5+574846 & 08 53 44.1 & +57 48 41.3 & 15.00 & & 0.000 & STAR \\nl\n J085358.8+770054 & 08 53 59.4 & +77 00 54.6 & 15.40 & &\t &\t \\nl \n J085823.0+520533 & 08 58 24.2 & +52 05 40.7 & 15.10 & &\t &\t \\nl \n J085902.0+484611 & 08 59 02.9 & +48 46 09.0 & 14.30 & 14.99 & 0.083 & AGN \\nl \n J090020.1+503143 & 09 00 19.1 & +50 31 40.5 & 15.10 & 14.91 &\t &\t \\nl \n J090038.4+411409 & 09 00 38.5 & +41 13 55.9 & 15.10 & &\t &\t \\nl \n J090808.7+500912 & 09 08 08.8 & +50 09 20.0 & 15.10 & &\t &\t \\nl \n J090950.6+184956 & 09 09 50.6 & +18 49 47.6 & 15.30 & &\t &\t \\nl \n J091010.2+481317 & 09 10 10.0 & +48 13 41.4 & 14.30 & & 0.118 & AGN \\nl \n J091254.7+793731 & 09 12 49.4 & +79 37 51.8 & 14.70 & 15.59 &\t &\t \\nl \n J091552.3+090056 & 09 15 51.8 &\t+9 00 50.9 & 14.50 & 12.99 & 0.000 & STAR \\nl\n J091651.8+523829 & 09 16 52.0 & +52 38 27.9 & 15.30 & & 0.190 & BL\\nl\n J091904.6+732334 & 09 19 08.8 & +73 23 59.2 & 15.30 & &\t &\t \\nl \n J091954.9+552120 & 09 19 55.3 & +55 21 36.6 & 14.90 & & 0.123 & AGN \\nl \n J092246.4+512046 & 09 22 48.0 & +51 20 45.9 & 14.40 & 14.80 & & \\nl \n J092916.4+501344 & 09 29 15.7 & +50 14 15.7 & 15.20 & 13.78 & & \\nl\n J093047.9+404446 & 09 30 47.8 & +40 44 41.3 & 15.30 & &\t &\t \\nl \n J093355.6+141932 & 09 33 55.9 & +14 19 19.9 & 15.40 & &\t &\t \\nl \n J093427.2+745123 & 09 34 28.4 & +74 51 19.9 & 14.20 & &\t &\t \\nl \n J093701.0+010548 & 09 37 01.0 &\t+1 05 43.0 & 13.60 & 13.87 & 0.051 & AGN \\nl \n J093942.8+560247 & 09 39 43.8 & +56 02 30.6 & 14.10 & & 0.116 & AGN \\nl \n J094617.2+025505 & 09 46 16.9 &\t+2 54 58.7 & 15.10 & &\t &\t \\nl \n J094653.0+132000 & 09 46 52.6 & +13 19 53.6 & 15.20 & & & \\nl \n J094713.2+762317 & 09 47 16.7 & +76 23 28.2 & 15.00 & 14.79 & & \\nl \n J095104.2+192531 & 09 51 03.5 & +19 25 32.1 & 15.30 & &\t &\t \\nl \n J095406.7+212250 & 09 54 08.1 & +21 22 25.5 & 14.90 & &\t &\t \\nl \n J095652.4+411524 & 09 56 52.3 & +41 15 22.3 & 15.40 & 15.00 & & \\nl \n J095708.1+243319 & 09 57 07.2 & +24 33 15.6 & 14.50 & &\t &\t \\nl \n J100050.9+315555 & 10 00 52.1 & +31 56 03.3 & 15.20 & &\t &\t \\nl \n J100121.5+555351 & 10 01 20.8 & +55 53 52.8 & 14.80 & & 1.414 & AGN\\nl\n J100335.1+444422 & 10 03 35.0 & +44 44 39.6 & 15.20 & &\t &\t \\nl \n J100505.4+562426 & 10 05 06.1 & +56 24 29.3 & 14.80 & &\t &\t \\nl \n J100659.7+673249 & 10 07 00.8 & +67 32 46.8 & 14.00 & 14.69 &\t &\t \\nl \n J100851.6+541451 & 10 08 54.7 & +54 14 45.9 & 15.40 & &\t &\t \\nl\n J100947.3+523442 & 10 09 48.5 & +52 34 51.2 & 15.20 & & & \\nl\n J101238.4+101722 & 10 12 38.5 & +10 17 18.8 & 14.80 & &\t &\t \\nl \n J101303.2+355131 & 10 13 03.2 & +35 51 23.3 & 14.60 & 15.26 & 0.070 & AGN \\nl \n J101504.3+492604 & 10 15 04.1 & +49 25 59.9 & 15.20 & & 0.200 & BL \\nl\n J101624.0+333827 & 10 16 22.9 & +33 38 17.0 & 14.10 & &\t &\t \\nl \n J101645.9+421024 & 10 16 45.1 & +42 10 25.1 & 13.90 & & 0.054 & AGN \\nl \n J101702.4+390256 & 10 17 03.6 & +39 02 49.4 & 14.30 & & 0.206 & GAL\\nl \n J101716.7+051145 & 10 17 16.8 &\t+5 11 49.5 & 15.00 & &\t &\t \\nl \n J101906.8+231846 & 10 19 06.7 & +23 18 37.0 & 15.20 & &\t &\t \\nl \n J102236.0+301753 & 10 22 37.4 & +30 17 49.8 & 14.50 & 14.71 &\t &\t \\nl \n J102258.8+202252 & 10 22 58.2 & +20 22 37.5 & 15.10 & & 0.129 & GAL \\nl\n J102338.5+523356 & 10 23 39.6 & +52 33 49.4 & 15.20 & &\t &\t \\nl \n J102531.2+514039 & 10 25 31.2 & +51 40 34.7 & 13.60 & & 0.045 & AGN \\nl \n J102836.6+630255 & 10 28 37.2 & +63 02 48.2 & 15.00 & &\t &\t \\nl \n J102915.4+572402 & 10 29 14.8 & +57 23 53.1 & 15.30 & & 0.186 & AGN\\nl\n J102946.7+401914 & 10 29 46.8 & +40 19 13.6 & 14.70 & 15.07 & & \\nl \n J103134.2+284711 & 10 31 34.3 & +28 47 00.6 & 15.20 & & 0.060 & AGN \\nl \n J103244.5+391331 & 10 32 44.2 & +39 13 22.6 & 15.30 & &\t &\t \\nl \n J103422.3+605316 & 10 34 24.9 & +60 53 11.5 & 15.40 & &\t &\t \\nl \n J103439.8+281755 & 10 34 39.9 & +28 17 41.6 & 14.80 & &\t &\t \\nl \n J104043.6+330057 & 10 40 44.0 & +33 00 59.5 & 14.90 & & 0.081 & AGN \\nl \n J104303.0+005423 & 10 43 02.5 &\t+0 54 17.9 & 14.80 & & & \\nl \n J104346.6+223006 & 10 43 47.0 & +22 29 57.4 & 14.60 & &\t &\t \\nl \n J104427.6+271813 & 10 44 27.7 & +27 18 05.4 & 14.00 & &\t &\t \\nl \n J104427.6+271813 & 10 44 27.7 & +27 18 05.4 & 14.00 & &\t &\t \\nl \n J104819.1+521837 & 10 48 18.0 & +52 18 30.3 & 14.70 & &\t &\t \\nl \n J104926.1+245134 & 10 49 25.5 & +24 51 23.0 & 14.70 & &\t &\t \\nl \n J105037.1+801204 & 10 50 35.6 & +80 11 50.7 & 14.90 & 14.85 &\t &\t \\nl \n J105124.8+382053 & 10 51 24.5 & +38 20 46.7 & 15.20 & &\t &\t \\nl \n J105143.8+335936 & 10 51 43.8 & +33 59 26.5 & 15.10 & & 0.167 & AGN \\nl \n J105151.0+213739 & 10 51 51.0 & +21 37 25.9 & 14.20 & &\t &\t \\nl \n J105214.2+055514 & 10 52 15.3 &\t+5 55 08.2 & 15.00 & 13.96 &\t &\t \\nl \n J105355.0+661209 & 10 53 55.7 & +66 12 01.8 & 15.30 & &\t &\t \\nl \n J105444.4+483145 & 10 54 44.7 & +48 31 38.8 & 15.40 & & 0.286 & AGN \\nl \n J105519.1+402739 & 10 55 19.5 & +40 27 16.6 & 15.20 & & 0.120 & AGN \\nl \n J105837.5+562816 & 10 58 37.7 & +56 28 11.4 & 14.10 & & 0.144 & BL \\nl\n J110237.0+724633 & 11 02 38.3 & +72 46 20.7 & 15.10 & & & \\nl \n J110412.4+765859 & 11 04 13.8 & +76 58 58.2 & 15.40 & & 0.313 & AGN \\nl \n J110537.4+585128 & 11 05 37.6 & +58 51 20.7 & 15.20 & &\t &\t \\nl \n J110748.8+710538 & 11 07 52.2 & +71 06 01.4 & 14.40 & 14.75 &\t &\t \\nl \n J110831.9+695129 & 11 08 26.9 & +69 51 41.7 & 15.00 & &\t &\t \\nl \n J111011.4+011333 & 11 10 12.1 &\t+1 13 27.2 & 14.50 & 15.06 &\t &\t \\nl \n J111422.6+582318 & 11 14 21.9 & +58 23 19.0 & 14.70 & & 0.206 & GAL\\nl \n J111830.0+402557 & 11 18 30.4 & +40 25 54.5 & 14.40 & & 0.154 & AGN \\nl \n J111907.1+413018 & 11 19 07.6 & +41 30 03.0 & 15.40 & &\t &\t \\nl \n J112034.0+100821 & 11 20 34.2 & +10 08 04.5 & 15.20 & &\t &\t \\nl \n J112147.3+114420 & 11 21 47.1 & +11 44 18.2 & 13.50 & 14.48 & 0.050 & AGN \\nl \n J112349.2+723002 & 11 23 51.8 & +72 30 08.4 & 15.00 & 15.09 &\t &\t \\nl \n J112842.9+633559 & 11 28 41.6 & +63 35 50.5 & 15.40 & &\t &\t \\nl \n J112850.7+231036 & 11 28 51.1 & +23 10 37.0 & 15.40 & &\t &\t \\nl \n J112854.0+210630 & 11 28 55.2 & +21 06 30.9 & 15.30 & &\t &\t \\nl \n J113109.0+263212 & 11 31 09.3 & +26 32 07.8 & 15.40 & &\t &\t \\nl \n J113302.0+184655 & 11 33 02.0 & +18 47 32.8 & 15.20 & &\t &\t \\nl \n J113313.3+500837 & 11 33 12.7 & +50 08 56.6 & 15.00 & & 0.310 & GAL\\nl \n J113630.9+673708 & 11 36 30.1 & +67 37 04.0 & 15.40 & & 0.135 & BL\\nl \n J113737.4+103931 & 11 37 38.1 & +10 39 30.2 & 15.30 & &\t &\t \\nl \n J113826.8+032210 & 11 38 27.1 &\t+3 22 09.9 & 14.90 & &\t &\t \\nl \n J113849.7+574245 & 11 38 49.6 & +57 42 43.9 & 13.60 & & 0.115 & AGN \\nl \n J114009.0+030727 & 11 40 08.7 &\t+3 07 11.0 & 15.30 & &\t &\t \\nl \n J114106.1+024110 & 11 41 05.7 &\t+2 41 16.3 & 15.10 & &\t &\t \\nl \n J114247.5+215717 & 11 42 45.8 & +21 57 22.4 & 15.30 & 13.25 &\t &\t \\nl \n J114509.2+381326 & 11 45 09.9 & +38 13 29.1 & 15.40 & &\t &\t \\nl \n J114509.3+304724 & 11 45 10.3 & +30 47 16.7 & 14.30 & & 0.059 & AGN \\nl \n J114606.1+035959 & 11 46 06.2 &\t+3 59 55.2 & 14.60 & &\t &\t \\nl \n J114755.3+090235 & 11 47 55.0 &\t+9 02 28.6 & 14.50 & &\t &\t \\nl \n J115137.3+561341 & 11 51 38.1 & +56 13 30.8 & 15.10 & &\t &\t \\nl \n J115553.6+732416 & 11 55 54.2 & +73 23 44.7 & 15.00 & 15.65 &\t &\t \\nl \n J115719.0+333645 & 11 57 17.4 & +33 36 39.9 & 15.10 & & 0.213 & GAL\\nl\n J115746.9+412642 & 11 57 46.1 & +41 26 37.4 & 14.40 & &\t &\t \\nl \n J120333.4+022939 & 12 03 32.9 &\t+2 29 34.5 & 14.40 & 13.88 & 0.077 & AGN \\nl \n J120547.8+584828 & 12 05 48.9 & +58 48 30.0 & 15.20 & &\t &\t \\nl \n J120954.9+062806 & 12 09 54.6 &\t+6 28 13.3 & 14.40 & &\t &\t \\nl \n J121104.0+700536 & 12 11 03.9 & +70 05 31.3 & 14.00 & 14.59 &\t &\t \\nl \n J121157.1+055800 & 12 11 57.5 &\t+5 58 00.9 & 14.10 & &\t &\t \\nl \n J121217.1+280356 & 12 12 16.2 & +28 04 07.4 & 15.40 & & 0.167 & AGN \\nl \n J121417.7+140312 & 12 14 17.7 & +14 03 12.6 & 13.90 & 13.96 & 0.081 & AGN \\nl \n J121510.9+073205 & 12 15 10.9 &\t+7 32 03.8 & 15.40 & & 0.136 & BL\\nl \n J121752.1+300705 & 12 17 52.0 & +30 06 59.9 & 14.40 & & 0.237 & BL\\nl \n J122044.5+690533 & 12 20 47.9 & +69 05 37.7 & 15.00 & &\t * & GAL \\nl\n J122144.4+751848 & 12 21 44.0 & +75 18 38.5 & 14.80 & 14.37 & 0.070 & GAL\\nl \n J122523.1+042128 & 12 25 22.9 &\t+4 21 18.6 & 14.10 & & & \\nl \n J122623.7+372657 & 12 26 23.3 & +37 27 01.3 & 15.40 & &\t &\t \\nl \n J122635.9+455933 & 12 26 36.9 & +45 59 40.4 & 15.10 & &\t &\t \\nl \n J122745.1+084147 & 12 27 44.8 &\t+8 41 49.8 & 13.60 & & 0.084 & AGN \\nl \n J122859.5+272527 & 12 29 00.3 & +27 25 21.4 & 15.10 & &\t &\t \\nl \n J123132.5+641420 & 12 31 31.3 & +64 14 17.5 & 15.00 & & 0.170 & BL\\nl \n J123154.6+323248 & 12 31 55.1 & +32 32 40.8 & 14.40 & &\t &\t \\nl \n J123235.8+060315 & 12 32 35.8 &\t+6 03 09.7 & 15.10 & &\t &\t \\nl \n J123325.8+093119 & 12 33 25.8 &\t+9 31 23.0 & 14.10 & & 0.415 & AGN \\nl \n J123658.8+631111 & 12 36 58.7 & +63 11 12.9 & 15.20 & & & GAL\\nl\n J123942.4+342453 & 12 39 42.5 & +34 24 55.7 & 15.20 & &\t &\t \\nl \n J124129.4+372206 & 12 41 29.4 & +37 22 01.7 & 13.90 & & 0.063 & AGN \\nl \n J124141.2+344032 & 12 41 39.9 & +34 40 17.6 & 14.60 & 14.96 &\t& \\nl\n J124211.3+331703 & 12 42 10.6 & +33 17 02.2 & 14.10 & 14.98 & 0.044 & AGN \\nl \n J124306.2+421233 & 12 43 07.1 & +42 12 31.1 & 15.30 & &\t &\t \\nl \n J124306.5+353859 & 12 43 04.2 & +35 39 16.8 & 14.90 & 15.23 & & \\nl \n J124324.2+271645 & 12 43 24.7 & +27 16 48.6 & 14.70 & & & GAL\\nl\n J124339.6+700517 & 12 43 39.3 & +70 05 29.9 & 14.70 & 15.68 & & \\nl \n J124701.3+442325 & 12 47 00.1 & +44 23 13.7 & 15.30 & &\t &\t \\nl \n J124717.2+481240 & 12 47 16.3 & +48 12 39.6 & 15.30 & &\t &\t \\nl \n J124818.9+582031 & 12 48 18.7 & +58 20 28.8 & 14.50 & &\t & BL\\nl\n J125005.7+263118 & 12 50 05.7 & +26 31 07.3 & 15.20 & & 2.043 & AGN \\nl \n J125422.6+793618 & 12 54 23.1 & +79 36 12.8 & 15.20 & &\t &\t \\nl \n J125801.0+470237 & 12 57 59.4 & +47 02 01.3 & 14.80 & &\t &\t \\nl \n J125830.1+652121 & 12 58 27.8 & +65 21 30.7 & 15.40 & & & \\nl \n J125851.4+235532 & 12 58 51.4 & +23 55 26.6 & 13.90 & & 0.071 & AGN \\nl \n J130052.9+564101 & 13 00 50.7 & +56 40 51.1 & 15.40 & &\t &\t \\nl \n J130258.8+162423 & 13 02 58.8 & +16 24 27.7 & 14.90 & 15.09 & 0.067 & AGN \\nl \n J130425.4+333512 & 13 04 27.2 & +33 35 13.0 & 14.40 & & 0.188 & GAL\\nl\n J130803.0+035124 & 13 08 03.1 &\t+3 51 14.1 & 15.10 & &\t &\t \\nl \n J130947.1+081949 & 13 09 47.0 &\t+8 19 48.9 & 14.80 & & 0.155 & AGN \\nl \n J131218.0+351524 & 13 12 17.7 & +35 15 20.3 & 14.70 & & 0.184 & AGN \\nl \n J131334.0+725914 & 13 13 32.0 & +72 59 10.9 & 15.20 & & 0.112 & AGN \\nl \n J131349.6+365357 & 13 13 49.0 & +36 53 57.7 & 15.40 & &\t &\t \\nl \n J131414.6+412347 & 13 14 18.3 & +41 24 30.1 & 15.30 & &\t &\t \\nl \n J131432.5+122706 & 13 14 32.7 & +12 27 17.9 & 14.70 & &\t &\t \\nl \n J131451.5+421819 & 13 14 51.5 & +42 18 19.1 & 14.80 & &\t &\t \\nl \n J131555.1+212508 & 13 15 55.1 & +21 25 21.5 & 15.00 & &\t &\t \\nl \n J131750.4+601047 & 13 17 50.3 & +60 10 40.6 & 15.30 & &\t &\t \\nl \n J132025.1+690018 & 13 20 24.6 & +69 00 12.4 & 15.40 & & 0.067 & AGN \\nl\n J132042.4+601526 & 13 20 45.3 & +60 15 16.2 & 14.00 & & & \\nl \n J132314.2+463132 & 13 23 14.9 & +46 31 21.8 & 15.00 & & 0.143 & AGN \\nl \n J132400.2+573918 & 13 24 00.8 & +57 39 16.1 & 13.90 & & 0.115 & BL\\nl\n J132434.9+475802 & 13 24 35.5 & +47 58 00.7 & 15.10 & &\t &\t \\nl \n J132602.2+601206 & 13 26 02.3 & +60 11 59.4 & 15.10 & &\t &\t \\nl \n J132632.2+792850 & 13 26 32.3 & +79 28 51.7 & 15.00 & & & \\nl \n J132847.3+503808 & 13 28 48.5 & +50 37 53.5 & 15.30 & &\t &\t \\nl \n J132908.3+295018 & 13 29 08.8 & +29 50 23.9 & 15.40 & & 0.047 & AGN \\nl \n J132943.8+315338 & 13 29 43.6 & +31 53 36.3 & 14.60 & & 0.090 & AGN \\nl \n J133434.3+575019 & 13 34 35.3 & +57 50 15.3 & 15.00 & &\t &\t \\nl \n J133439.6+171748 & 13 34 37.3 & +17 17 49.4 & 15.30 & &\t &\t \\nl \n J133608.2+755041 & 13 36 09.8 & +75 50 34.9 & 15.20 & 15.28 &\t &\t \\nl \n J133718.8+242306 & 13 37 18.7 & +24 23 02.9 & 14.30 & 14.26 & 0.107 & AGN \\nl \n J133826.6+321252 & 13 38 26.9 & +32 12 51.9 & 15.20 & &\t &\t \\nl \n J133908.5+115855 & 13 39 08.5 & +11 58 53.5 & 15.30 & &\t &\t \\nl \n J133938.5+183055 & 13 39 37.8 & +18 30 59.4 & 15.10 & &\t &\t \\nl \n J134021.4+274100 & 13 40 21.9 & +27 41 26.8 & 14.20 & 14.19 & & \\nl \n J134210.9+564219 & 13 42 10.1 & +56 42 10.9 & 14.60 & & 0.040 & AGN \\nl \n J134335.3+413839 & 13 43 35.7 & +41 38 24.3 & 14.70 & 14.60 &\t &\t \\nl \n J134356.7+253845 & 13 43 56.7 & +25 38 46.9 & 14.10 & 15.09 & & \\nl \n J134357.3+271252 & 13 43 57.4 & +27 12 40.9 & 15.40 & & 0.077 & AGN \\nl \n J134453.1+000525 & 13 44 52.9 &\t+0 05 19.7 & 14.80 & 15.51 &\t &\t \\nl \n J134607.5+293814 & 13 46 08.1 & +29 38 10.5 & 14.10 & & 0.076 & AGN \\nl \n J135022.2+094007 & 13 50 22.1 &\t+9 40 10.7 & 14.00 & &\t &\t \\nl \n J135022.2+094007 & 13 50 22.1 &\t+9 40 10.7 & 14.00 & &\t &\t \\nl \n J135143.8+242420 & 13 51 43.9 & +24 24 21.5 & 14.90 & &\t &\t \\nl \n J135436.0+180523 & 13 54 35.6 & +18 05 17.2 & 15.30 & & 0.152 & AGN \\nl \n J135553.3+383427 & 13 55 53.5 & +38 34 29.1 & 15.00 & & 0.051 & AGN \\nl \n J135821.2+360356 & 13 58 24.5 & +36 03 47.7 & 15.00 & 15.36 &\t &\t \\nl \n J140310.5+375810 & 14 03 08.8 & +37 58 27.6 & 15.20 & &\t &\t \\nl \n J140519.6+020008 & 14 05 19.4 &\t+2 00 05.2 & 14.80 & & 0.000 & STAR\\nl \n J140606.1+580045 & 14 06 04.8 & +58 00 41.3 & 15.30 & &\t &\t \\nl \n J140622.2+222350 & 14 06 21.9 & +22 23 46.7 & 15.10 & & 0.098 & AGN \\nl \n J140924.1+261827 & 14 09 23.9 & +26 18 21.3 & 15.40 & & 0.940 & AGN \\nl \n J141336.8+702954 & 14 13 36.7 & +70 29 50.4 & 14.30 & & 0.107 & AGN \\nl \n J141342.6+433938 & 14 13 43.7 & +43 39 44.1 & 14.70 & & 0.089 & GAL \\nl\n J141346.6+263246 & 14 13 45.3 & +26 33 03.1 & 15.00 & 14.85 &\t &\t \\nl \n J141700.5+445556 & 14 17 00.8 & +44 56 06.0 & 14.70 & 15.17 & 0.114 & AGN \\nl \n J141756.8+254329 & 14 17 56.7 & +25 43 24.7 & 15.30 & & 0.237 & BL \\nl\n J141758.8+360749 & 14 17 58.0 & +36 08 10.5 & 15.20 & &\t &\t \\nl \n J141901.9+280942 & 14 19 01.9 & +28 09 41.7 & 14.80 & &\t &\t \\nl \n J142058.6+262450 & 14 20 56.1 & +26 24 22.5 & 15.40 & 14.95 &\t &\t \\nl \n J142107.1+253818 & 14 21 07.6 & +25 38 20.8 & 15.40 & & 1.050 & AGN \\nl \n J142129.8+474719 & 14 21 29.8 & +47 47 24.7 & 14.30 & 14.62 & 0.072 & AGN \\nl \n J142313.4+505537 & 14 23 14.3 & +50 55 38.1 & 15.20 & & 0.274 & AGN \\nl \n J142425.2+595254 & 14 24 24.1 & +59 53 00.7 & 15.10 & 14.18 &\t &\t \\nl \n J142630.6+390348 & 14 26 30.7 & +39 03 43.5 & 13.50 & &\t &\t \\nl \n J142700.5+234803 & 14 27 00.4 & +23 48 00.1 & 14.80 & &\t & BL\\nl\n J142725.3+194954 & 14 27 25.0 & +19 49 52.3 & 14.00 & 15.60 & 0.131 & AGN \\nl \n J142906.7+011708 & 14 29 06.5 &\t+1 17 05.0 & 13.60 & 13.21 & 0.086 & AGN \\nl \n J142924.3+451826 & 14 29 25.0 & +45 18 31.6 & 15.10 & &\t &\t \\nl \n J143308.8+232650 & 14 33 08.4 & +23 26 31.1 & 15.10 & &\t &\t \\nl \n J143445.8+332814 & 14 34 45.3 & +33 28 19.8 & 14.70 & &\t &\t \\nl \n J144034.4+242255 & 14 40 34.3 & +24 22 50.4 & 15.30 & &\t &\t \\nl \n J144248.5+120042 & 14 42 48.2 & +12 00 40.4 & 14.60 & & 0.162 & BL\\nl\n J144645.8+403510 & 14 46 45.9 & +40 35 05.8 & 15.10 & & 0.267 & AGN \\nl \n J144754.0+283323 & 14 47 54.2 & +28 33 23.7 & 15.40 & &\t &\t \\nl \n J144825.6+355955 & 14 48 25.0 & +35 59 46.4 & 15.00 & & 0.111 & AGN \\nl \n J145307.6+255438 & 14 53 08.0 & +25 54 32.8 & 15.40 & &\t &\t \\nl \n J145307.8+215333 & 14 53 08.3 & +21 53 38.5 & 15.10 & &\t &\t \\nl \n J145559.0+492158 & 14 55 59.5 & +49 21 52.3 & 15.40 & &\t &\t \\nl \n J145729.4+083356 & 14 57 29.0 &\t+8 34 22.6 & 15.00 & & 0.167 & AGN \\nl \n J145843.1+213614 & 14 58 42.7 & +21 36 10.0 & 15.30 & & 0.062 & AGN \\nl \n J150023.0+763644 & 15 00 22.3 & +76 36 37.7 & 14.70 & 15.14 &\t &\t \\nl \n J150124.1+302638 & 15 01 24.2 & +30 26 33.2 & 15.30 & &\t &\t \\nl \n J150317.5+681011 & 15 03 16.3 & +68 10 05.7 & 15.00 & & & \\nl \n J150332.0+295026 & 15 03 32.1 & +29 50 23.9 & 14.80 & &\t &\t \\nl \n J150506.8+435002 & 15 05 07.3 & +43 50 05.1 & 15.00 & &\t &\t \\nl \n J150752.3+515116 & 15 07 52.6 & +51 51 11.1 & 15.40 & &\t &\t \\nl \n J151040.8+333515 & 15 10 41.1 & +33 35 05.4 & 15.30 & &\t &\t \\nl \n J151105.3+525128 & 15 11 06.0 & +52 51 26.8 & 15.00 & &\t &\t \\nl \n J151447.0+351348 & 15 14 46.9 & +35 13 48.6 & 14.80 & &\t &\t \\nl \n J151634.5+205847 & 15 16 34.5 & +20 58 37.4 & 14.90 & &\t &\t \\nl \n J151845.3+061340 & 15 18 45.7 &\t+6 13 55.8 & 14.40 & & 0.102 & AGN \\nl \n J151921.7+590823 & 15 19 21.6 & +59 08 23.6 & 14.40 & 15.09 & 0.078 & AGN \\nl \n J152558.6+181423 & 15 25 58.5 & +18 14 15.6 & 15.00 & &\t &\t \\nl \n J152806.5+132337 & 15 28 06.9 & +13 23 50.3 & 15.20 & &\t &\t \\nl \n J152912.9+381226 & 15 29 14.0 & +38 13 06.0 & 15.00 & 15.06 & 0.000 & STAR\\nl \n J153140.9+201927 & 15 31 41.3 & +20 19 30.1 & 15.30 & &\t &\t \\nl \n J153202.3+301631 & 15 32 02.2 & +30 16 28.6 & 13.50 & 15.30 & 0.064 & BL\\nl\n J153718.8+084355 & 15 37 20.5 &\t+8 44 08.7 & 15.20 & &\t &\t \\nl \n J153935.2+473545 & 15 39 34.9 & +47 35 53.1 & 15.00 & 14.87 & & \\nl \n J154236.8+581153 & 15 42 36.9 & +58 11 45.0 & 13.90 & 14.07 &\t &\t \\nl \n J154508.1+170935 & 15 45 07.5 & +17 09 50.4 & 14.70 & & 0.045 & AGN \\nl \n J154732.3+102446 & 15 47 32.2 & +10 24 51.2 & 15.40 & &\t &\t \\nl \n J154751.7+025538 & 15 47 51.9 &\t+2 55 50.8 & 14.70 & & 0.098 & AGN \\nl \n J154814.6+450040 & 15 48 14.7 & +45 00 27.8 & 14.90 & &\t &\t \\nl \n J155023.8+281125 & 15 50 24.0 & +28 11 17.2 & 15.20 & &\t &\t \\nl \n J155041.6+413915 & 15 50 39.0 & +41 39 29.9 & 15.30 & &\t &\t \\nl \n J155411.8+241415 & 15 54 10.9 & +24 14 40.5 & 15.40 & &\t &\t \\nl \n J155444.6+082202 & 15 54 44.6 &\t+8 22 21.6 & 15.40 & & 0.119 & AGN \\nl \n J155543.2+111114 & 15 55 43.0 & +11 11 24.1 & 14.30 & 13.81 & 0.360 & BL\\nl\n J155643.0+294838 & 15 56 42.8 & +29 48 47.5 & 13.90 & 14.63 & 0.087 & AGN \\nl \n J155745.0+353020 & 15 57 42.3 & +35 30 29.9 & 13.90 & &\t &\t \\nl \n J155818.7+255118 & 15 58 18.8 & +25 51 24.4 & 15.30 & & 0.070 & AGN \\nl \n J160529.2+720852 & 16 05 26.0 & +72 08 36.3 & 15.20 & &\t &\t \\nl \n J160740.7+254106 & 16 07 40.2 & +25 41 12.6 & 13.80 & 13.87 &\t &\t \\nl \n J161047.7+330329 & 16 10 47.8 & +33 03 37.7 & 14.10 & & 0.097 & AGN \\nl \n J161413.0+260412 & 16 14 13.2 & +26 04 15.9 & 15.10 & & 0.131 & AGN \\nl \n J161601.3+323222 & 16 16 01.8 & +32 32 28.8 & 15.10 & & 0.118 & AGN \\nl \n J161711.4+063816 & 16 17 10.5 &\t+6 38 43.0 & 15.20 & & 0.092 & AGN \\nl \n J161804.5+672409 & 16 18 03.8 & +67 23 50.0 & 15.00 & &\t &\t \\nl \n J161809.2+361951 & 16 18 09.4 & +36 19 57.8 & 13.80 & & 0.034 & AGN \\nl \n J161814.2+293828 & 16 18 14.0 & +29 38 08.9 & 15.30 & &\t &\t \\nl \n J162011.5+172413 & 16 20 11.3 & +17 24 27.5 & 15.20 & & 0.114 & AGN \\nl \n J162100.4+254547 & 16 21 00.3 & +25 46 03.3 & 14.70 & &\t &\t \\nl \n J162114.3+181936 & 16 21 14.4 & +18 19 49.9 & 15.20 & & 0.125 & AGN \\nl \n J162348.2+402948 & 16 23 48.2 & +40 29 59.0 & 15.00 & &\t &\t \\nl \n J162355.9+370018 & 16 23 56.4 & +37 00 44.9 & 15.30 & &\t &\t \\nl \n J162456.7+755457 & 16 24 56.5 & +75 54 55.8 & 13.70 & & 0.200 & AGN \\nl \n J162607.6+335902 & 16 26 07.2 & +33 59 15.0 & 14.80 & & 0.204 & AGN \\nl \n J163116.3+095545 & 16 31 16.0 &\t+9 55 57.9 & 15.00 & & 0.092 & AGN \\nl \n J163323.3+471848 & 16 33 23.5 & +47 19 00.1 & 14.60 & & 0.116 & AGN \\nl \n J163338.4+371311 & 16 33 38.7 & +37 13 14.8 & 14.70 & & & \\nl \n J163509.5+343956 & 16 35 09.2 & +34 40 03.4 & 15.40 & &\t &\t \\nl \n J163523.2+545304 & 16 35 23.2 & +54 53 00.3 & 15.00 & &\t &\t \\nl \n J164443.2+261909 & 16 44 44.1 & +26 19 04.6 & 15.20 & & & \\nl \n J164550.2+792129 & 16 45 49.5 & +79 21 28.6 & 14.90 & &\t &\t \\nl \n J164625.8+392922 & 16 46 26.0 & +39 29 32.2 & 14.60 & & 0.100 & AGN \\nl \n J164735.4+495001 & 16 47 34.8 & +49 49 59.8 & 14.60 & & 0.047 & AGN \\nl \n J164801.1+295650 & 16 48 00.8 & +29 56 57.4 & 14.30 & & 0.101 & AGN \\nl \n J165141.2+721824 & 16 51 39.6 & +72 18 42.7 & 15.40 & &\t &\t \\nl \n J165253.7+400927 & 16 52 56.6 & +40 08 43.1 & 15.00 & &\t &\t \\nl \n J170328.3+614114 & 17 03 28.9 & +61 41 10.1 & 14.70 & &\t &\t \\nl \n J170425.2+333145 & 17 04 22.4 & +33 31 40.3 & 14.90 & 13.46 &\t &\t \\nl \n J170535.1+334011 & 17 05 34.9 & +33 40 12.3 & 14.90 & &\t &\t \\nl \n J171013.2+334410 & 17 10 13.5 & +33 44 03.6 & 14.80 & & 0.208 & AGN \\nl \n J171322.8+325631 & 17 13 22.6 & +32 56 28.8 & 14.50 & & 0.100 & AGN \\nl \n J171410.8+575826 & 17 14 11.5 & +57 58 33.5 & 14.90 & & 0.092 & AGN \\nl \n J171601.3+311215 & 17 16 01.9 & +31 12 13.5 & 14.40 & 15.48 & 0.111 & AGN \\nl \n J171935.9+424518 & 17 19 33.9 & +42 45 22.5 & 15.00 & &\t &\t \\nl \n J172320.5+341756 & 17 23 20.8 & +34 17 57.8 & 14.50 & & 0.206 & AGN\\nl \n J172609.3+743103 & 17 26 08.3 & +74 31 03.4 & 14.60 & & 0.052 & AGN \\nl \n J172855.8+515654 & 17 28 54.6 & +51 56 49.2 & 14.90 & 14.21 & & \\nl \n J173114.5+323250 & 17 31 15.2 & +32 32 58.4 & 13.90 & 14.05 & & \\nl \n J174025.8+514942 & 17 40 25.7 & +51 49 42.4 & 14.50 & & & \\nl \n J174815.0+582333 & 17 48 15.3 & +58 23 35.5 & 15.00 & &\t &\t \\nl \n J174839.6+530240 & 17 48 37.6 & +53 02 45.4 & 15.40 & &\t &\t \\nl \n J214923.8+092921 & 21 49 23.7 &\t+9 28 47.3 & 15.30 & &\t &\t \\nl \n J215912.7+095247 & 21 59 12.3 &\t+9 52 43.4 & 14.90 & & 0.101 & AGN \\nl \n J222602.8+172245 & 22 26 02.2 & +17 22 47.0 & 15.40 & & & \\nl \n J224939.6+110016 & 22 49 39.6 & +11 00 29.2 & 14.80 & & 0.084 & AGN \\nl \n J225207.7+145448 & 22 52 08.1 & +14 54 49.6 & 14.80 & & 0.130 & AGN \\nl \n J225636.8+052522 & 22 56 36.5 &\t+5 25 17.2 & 14.90 & & 0.066 & AGN \\nl \n J225932.9+245505 & 22 59 32.9 & +24 55 05.6 & 13.50 & 15.07 & 0.034 & AGN \\nl \n J231357.3+144424 & 23 13 56.3 & +14 43 53.5 & 14.90 & &\t &\t \\nl \n J231517.5+182825 & 23 15 17.1 & +18 28 14.4 & 15.00 & & 0.104 & AGN \\nl \n J232339.1+090842 & 23 23 39.0 & +9 08 50.6 & 14.80 & & 0.068 & AGN \\nl \n J233606.6+241555 & 23 36 06.1 & +24 15 58.3 & 14.50 & & 0.039 & AGN \\nl \n J233641.8+235526 & 23 36 42.2 & +23 55 29.0 & 14.20 & & 0.127 & GAL\\nl\n J233739.8+001604 & 23 37 40.7 &\t+0 16 35.3 & 14.90 & & & \\nl\n J234031.5+102934 & 23 40 31.0 & +10 29 39.0 & 14.70 & &\t &\t \\nl \n J234339.0+024445 & 23 43 39.8 &\t+2 45 03.9 & 15.40 & & 0.091 & AGN \\nl \n J235257.1+032008 & 23 52 58.0 &\t+3 20 17.3 & 14.30 & & 0.086 & AGN \\nl \n J235754.3+132418 & 23 57 53.8 & +13 24 09.6 & 15.30 & &\t &\t \\nl \n\\enddata\n\\label{tbl-2a}\n\\end{deluxetable}\n\n% GSC\n\\begin{deluxetable}{lrrrrc}\n\\tablenum{2}\n\\clearpage\n\\tablewidth{0pt}\n\\tablecaption{THE GSC SAMPLE}\n\\tablehead{\n\\colhead{Name (1RXS)} & \\colhead{R.A.} \t&\n\\colhead{Declination} & \\colhead{$V_{GSC}$} &\n\\colhead{$z$} & \\colhead{Type}} \n\\startdata\n J000350.4+020340 & 00 03 49.7 &\t+2 03 58.9 & 13.28 & & \\nl\n J001219.0+100602 & 00 12 19.3 & +10 06 45.8 & 14.02 & \t & \t \\nl\n J003633.7+254513 & 00 36 32.4 & +25 45 18.2 & 14.32 & \t & \t \\nl\n J004400.0+313729 & 00 44 00.0 & +31 37 04.3 & 14.42 & \t & \t \\nl\n J004719.4+144215 & 00 47 19.4 & +14 42 11.8 & 14.00 & 0.039 & AGN \\nl\n J004931.6+112832 & 00 49 32.0 & +11 28 26.0 & 14.37 & 0.275 & AGN \\nl\n J005017.9+083734 & 00 50 17.4 &\t+8 37 35.3 & 14.31 & \t & \t \\nl\n J005029.2+112902 & 00 50 27.9 & +11 29 10.9 & 14.37 & 0.000 & STAR\\nl\n J005351.3+221222 & 00 53 50.9 & +22 12 13.7 & 14.38 & \t & \t \\nl\n J005953.3+314934 & 00 59 53.3 & +31 49 37.4 & 13.74 & 0.015 & AGN \\nl\n J010014.0+055200 & 01 00 14.1 &\t+5 51 54.8 & 14.00 & \t & \t \\nl\n J011125.4+152625 & 01 11 24.8 & +15 26 26.8 & 13.59 & \t & \t \\nl\n J011704.2+000025 & 01 17 03.6 &\t+0 00 27.0 & 14.50 & 0.040 & AGN \\nl\n J012732.9+191043 & 01 27 32.5 & +19 10 43.8 & 11.80 & 0.017 & AGN \\nl\n J015240.2+014718 & 01 52 39.6 &\t+1 47 16.8 & 13.92 & 0.080 & BL\\nl\n J015242.1+010040 & 01 52 41.9 & +1 00 25.1 & 13.57 & 0.230 & GAL\\nl\n J020026.7+024012 & 02 00 26.3 &\t+2 40 09.9 & 12.77 & 0.078 & AGN\\nl\n J024920.8+191813 & 02 49 20.7 & +19 18 14.2 & 14.18 & 0.031 & AGN\\nl\n J025153.2+222735 & 02 51 53.7 & +22 27 35.7 & 12.40 & 0.000 & STAR\\nl\n J075704.9+583245 & 07 57 06.2 & +58 32 58.7 & 14.48 & 0.168 & AGN\\nl\n J080525.8+753424 & 08 05 23.7 & +75 34 34.7 & 14.40 & & \\nl\n J081228.3+623627 & 08 12 28.2 & +62 36 23.3 & 14.15 & \t & \t \\nl\n J081517.8+460429 & 08 15 16.9 & +46 04 30.7 & 14.24 & \t & \t \\nl\n J081917.9+642943 & 08 19 17.6 & +64 29 40.0 & 14.40 & 0.039 & AGN \\nl\n J082407.3+613612 & 08 24 11.3 & +61 36 11.3 & 14.01 & & \\nl\n J083137.6+192339 & 08 31 38.3 & +19 23 45.2 & 11.43 & \t & \t \\nl\n J083811.0+245336 & 08 38 10.9 & +24 53 42.4 & 12.80 & \t & \t \\nl\n J084456.2+425826 & 08 44 56.6 & +42 58 35.1 & 14.40 & \t & \t \\nl\n J084602.9+830757 & 08 46 17.9 & +83 07 43.5 & 14.47 & \t & \t \\nl\n J084742.5+344506 & 08 47 42.5 & +34 45 03.8 & 13.64 & 0.064 & AGN \\nl\n J090008.1+743419 & 09 00 03.7 & +74 34 26.4 & 14.37 & \t & \t \\nl\n J091230.8+155531 & 09 12 31.0 & +15 55 24.3 & 13.42 & \t & \t \\nl\n J091552.3+090056 & 09 15 51.8 &\t+9 00 50.9 & 12.99 & 0.000 & STAR \\nl \n J091826.2+161825 & 09 18 26.0 & +16 18 19.2 & 13.21 & 0.030 & AGN \\nl\n J092030.8+013544 & 09 20 31.1 &\t+1 35 37.1 & 14.14 & \t & \t \\nl\n J092108.2+480201 & 09 21 11.3 & +48 01 59.2 & 13.84 & \t & \t \\nl\n J092343.0+225437 & 09 23 43.0 & +22 54 32.7 & 13.43 & & \\nl\n J092512.3+521716 & 09 25 13.0 & +52 17 11.4 & 13.66 & 0.036 & AGN \\nl\n J092603.6+124406 & 09 26 03.3 & +12 44 03.3 & 13.71 & 0.028 & AGN \\nl\n J092702.8+390221 & 09 27 04.0 & +39 02 17.8 & 13.59 & & \\nl\n J092705.7+374157 & 09 27 03.0 & +37 42 05.5 & 14.12 & \t & \\nl\n J093701.0+010548 & 09 37 01.0 &\t+1 05 43.0 & 13.87 & 0.051 & AGN \\nl\n J093900.4+253008 & 09 39 00.4 & +25 30 14.6 & 14.41 & \t & \t \\nl\n J094204.0+234106 & 09 42 04.8 & +23 41 06.5 & 14.15 & 0.021 & GAL\\nl\n J094432.8+573544 & 09 44 04.7 & +57 33 28.1 & 14.13 & \t & \t \\nl\n J094851.0+153901 & 09 48 50.2 & +15 38 34.6 & 14.25 & \t & \t \\nl\n J095340.4+014154 & 09 53 41.3 &\t+1 42 01.7 & 13.98 & \t & \t \\nl\n J095624.5+064803 & 09 56 23.8 &\t+6 48 01.6 & 14.34 & \t & \t \\nl\n J095919.3+435033 & 09 59 19.2 & +43 50 35.4 & 13.57 & \t & \t \\nl\n J100446.0+144651 & 10 04 47.6 & +14 46 45.2 & 14.23 & 0.082 & AGN \\nl\n J100641.5+213955 & 10 06 43.6 & +21 39 27.7 & 14.50 & \t & \t \\nl\n J101218.6+631133 & 10 12 21.6 & +63 11 32.1 & 14.21 & \t & \t \\nl\n J101718.0+291439 & 10 17 18.3 & +29 14 33.8 & 13.96 & 0.048 & AGN\\nl\n J101912.1+635802 & 10 19 12.6 & +63 58 02.2 & 13.69 & 0.041 & AGN\\nl\n J102334.6+443346 & 10 23 35.0 & +44 33 41.5 & 13.86 & \t & \t \\nl\n J102407.0+273130 & 10 24 06.7 & +27 31 22.7 & 14.22 & \t & \t \\nl\n J102611.1+523755 & 10 26 06.2 & +52 37 56.3 & 13.99 & & \\nl\n J104038.7+373233 & 10 40 39.0 & +37 32 31.3 & 13.36 & \t & \t \\nl\n J104333.4+010109 & 10 43 32.8 &\t+1 01 08.6 & 13.99 & 0.072 & AGN \\nl\n J104439.4+384541 & 10 44 39.1 & +38 45 34.8 & 14.48 & 0.036 & GAL\\nl\n J105121.3+360728 & 10 51 21.3 & +36 07 27.4 & 13.31 & \t & \t \\nl\n J105214.2+055514 & 10 52 15.3 &\t+5 55 08.2 & 13.96 & \t & \t \\nl\n J105328.5+053052 & 10 53 29.7 &\t+5 30 30.2 & 13.92 & \t & \t \\nl\n J105340.7+525310 & 10 53 41.2 & +52 53 01.7 & 14.25 & \t & \t \\nl\n J110159.1+572316 & 11 02 00.1 & +57 22 50.3 & 14.43 & \t & \t \\nl\n J110310.2+363911 & 11 03 10.7 & +36 39 06.3 & 13.41 & \t & \t \\nl\n J110321.2+133759 & 11 03 21.8 & +13 37 52.4 & 12.90 & \t & \t \\nl\n J110455.7+433421 & 11 04 56.0 & +43 34 03.0 & 14.29 & \t & \t \\nl\n J110943.6+214519 & 11 09 41.1 & +21 44 24.2 & 14.33 & 0.032 & GAL\\nl\n J111300.1+102518 & 11 13 00.2 & +10 25 12.3 & 14.29 & \t & \t \\nl\n J111349.5+093518 & 11 13 49.7 &\t+9 35 10.9 & 12.42 & 0.029 & AGN \\nl\n J112147.3+114420 & 11 21 47.1 & +11 44 18.2 & 14.48 & 0.050 & AGN \\nl\n J112150.8+405147 & 11 21 51.2 & +40 51 46.4 & 13.97 & \t & \t \\nl\n J112315.6+193610 & 11 23 14.6 & +19 35 25.5 & 14.13 & \t & \t \\nl\n J112536.7+542243 & 11 25 36.1 & +54 22 56.9 & 14.33 & 0.021 & AGN\\nl\n J114116.2+215624 & 11 41 16.2 & +21 56 21.1 & 13.25 & 0.063 & AGN\\nl\n J114516.1+794054 & 11 45 16.1 & +79 40 52.6 & 13.50 & 0.065 & AGN\\nl\n J114738.0+050119 & 11 47 37.4 &\t+5 01 09.3 & 12.09 & \t & \t \\nl\n J114741.4+001524 & 11 47 41.7 &\t+0 15 24.1 & 14.23 & & \\nl\n J115658.6+241523 & 11 56 55.8 & +24 15 35.2 & 13.55 & 0.142 & GAL\\nl\n J120333.4+022939 & 12 03 32.9 &\t+2 29 34.5 & 13.88 & 0.077 & AGN\\nl\n J120829.9+132752 & 12 08 29.8 & +13 28 06.0 & 13.31 & \t & \t \\nl\n J121417.7+140312 & 12 14 17.7 & +14 03 12.6 & 13.96 & 0.081 & AGN\\nl\n J121607.4+504926 & 12 16 07.0 & +50 49 30.2 & 14.25 & 0.031 & AGN\\nl\n J121900.7+110727 & 12 18 59.8 & +11 07 53.9 & 13.53 & \t & \t \\nl\n J121920.9+063838 & 12 19 21.5 &\t+6 38 43.9 & 13.22 & & \\nl\n J122005.9+650552 & 12 20 10.3 & +65 05 55.2 & 14.34 & \t & \t \\nl\n J122144.4+751848 & 12 21 44.0 & +75 18 38.5 & 14.37 & 0.070 & AGN\\nl\n J122147.1+015637 & 12 21 46.6 &\t+1 56 35.3 & 13.76 & \t & \t \\nl\n J122306.6+103722 & 12 23 06.7 & +10 37 16.8 & 12.25 & 0.026 & GAL\\nl\n J122324.4+024040 & 12 23 24.2 &\t+2 40 44.9 & 12.81 & 0.023 & AGN\\nl\n J122512.5+321354 & 12 25 13.1 & +32 14 00.9 & 14.38 & 0.061 & AGN\\nl\n J122906.5+020311 & 12 29 06.7 &\t+2 03 08.1 & 12.26 & 0.158 & AGN\\nl\n J123014.2+251805 & 12 30 14.2 & +25 18 05.9 & 14.49 & 0.135 & BL\\nl\n J123055.5+315207 & 12 30 55.8 & +31 52 16.1 & 14.19 & \t & \t \\nl\n J123203.6+200930 & 12 32 03.6 & +20 09 29.6 & 12.87 & 0.064 & AGN\\nl\n J123415.2+481306 & 12 34 16.0 & +48 13 06.9 & 14.31 & \t & \t \\nl\n J123651.1+453907 & 12 36 51.2 & +45 39 04.4 & 13.59 & 0.290 & AGN\\nl\n J123658.6+455341 & 12 36 57.0 & +45 53 26.0 & 14.41 & & \\nl\n J124147.5+564506 & 12 41 46.7 & +56 45 13.5 & 13.13 & \t & \t \\nl\n J124312.5+362743 & 12 43 12.7 & +36 27 43.8 & 11.42 & \t & \t \\nl\n J124955.0+102312 & 12 49 54.5 & +10 23 08.3 & 14.03 & \t & \t \\nl\n J125731.7+354313 & 12 57 32.7 & +35 43 19.9 & 14.19 & & \\nl\n J130934.9+285908 & 13 09 36.1 & +28 59 15.0 & 13.95 & \t & \t \\nl\n J131957.2+523533 & 13 19 58.8 & +52 35 27.7 & 13.49 & \t & \t \\nl\n J132016.3+330828 & 13 20 14.7 & +33 08 36.1 & 13.17 & 0.036 & GAL\\nl\n J133451.1+374616 & 13 34 51.9 & +37 46 20.7 & 13.83 & \t & \t \\nl\n J133718.8+242306 & 13 37 18.7 & +24 23 02.9 & 14.26 & 0.107 & AGN\\nl\n J133752.7+204634 & 13 37 50.9 & +20 46 39.8 & 14.20 & \t & \t \\nl\n J134021.4+274100 & 13 40 21.9 & +27 41 26.8 & 14.19 & & \\nl\n J134952.7+020446 & 13 49 52.8 &\t+2 04 44.3 & 13.32 & & \\nl\n J135119.8+033722 & 13 51 20.2 &\t+3 37 16.4 & 13.77 & \t & \t \\nl\n J135304.8+691832 & 13 53 03.4 & +69 18 29.5 & 12.92 & \t & \t \\nl\n J135420.2+325547 & 13 54 20.0 & +32 55 47.9 & 12.78 & 0.026 & AGN\\nl\n J140226.8+054103 & 14 02 26.3 &\t+5 40 51.8 & 13.26 & \t & \t \\nl\n J141722.1+452544 & 14 17 21.9 & +45 25 46.7 & 13.94 & \t & \t \\nl\n J141759.6+250817 & 14 17 59.2 & +25 08 13.2 & 11.02 & & \\nl\n J141802.6+800710 & 14 17 59.3 & +80 07 02.2 & 14.19 & \t & \t \\nl\n J142425.2+595254 & 14 24 24.1 & +59 53 00.7 & 14.18 & \t & \t \\nl\n J142906.7+011708 & 14 29 06.5 &\t+1 17 05.0 & 13.21 & 0.086 & AGN\\nl\n J143104.8+281716 & 14 31 04.8 & +28 17 14.8 & 13.43 & 0.046 & AGN\\nl\n J143452.3+483938 & 14 34 52.4 & +48 39 42.6 & 13.38 & \t & \t \\nl\n J143729.6+412842 & 14 37 29.9 & +41 28 35.2 & 13.70 & \t & \t \\nl\n J144713.2+570205 & 14 47 13.0 & +57 01 56.7 & 13.97 & \t & \t \\nl\n J150401.5+102620 & 15 04 01.2 & +10 26 16.2 & 14.19 & 0.036 & AGN\\nl\n J150406.7+485856 & 15 04 07.1 & +48 58 55.1 & 14.05 & \t & \t \\nl\n J150724.6+433356 & 15 07 23.5 & +43 33 51.6 & 13.64 & \t & \t \\nl\n J150950.2+415540 & 15 09 49.7 & +41 55 38.8 & 14.29 & \t & \t \\nl\n J151750.8+050615 & 15 17 51.7 & +5 06 27.4 & 13.98 & 0.039 & AGN\\nl\n J151837.9+404506 & 15 18 38.9 & +40 45 00.0 & 14.19 & & \\nl\n J153345.9+690037 & 15 33 44.7 & +69 00 34.0 & 13.73 & \t & \t \\nl\n J153412.6+625902 & 15 34 13.2 & +62 58 57.7 & 13.76 & \t & \t \\nl\n J153522.9+600515 & 15 35 24.5 & +60 05 15.3 & 13.17 & \t & \t \\nl\n J153552.0+575404 & 15 35 52.4 & +57 54 08.5 & 13.91 & 0.030 & AGN\\nl\n J153704.2+374830 & 15 37 04.0 & +37 48 26.9 & 13.43 & \t & \t \\nl\n J153944.2+275113 & 15 39 43.9 & +27 50 58.1 & 13.74 & \t & \t \\nl\n J154236.8+581153 & 15 42 36.9 & +58 11 45.0 & 14.07 & \t & \t \\nl\n J154348.9+401343 & 15 43 50.5 & +40 13 41.6 & 13.05 & \t & \t \\nl\n J154532.3+420500 & 15 45 34.7 & +42 05 07.2 & 13.87 & \t & \t \\nl\n J155305.9+445749 & 15 53 05.1 & +44 57 39.9 & 14.16 & \t & \t \\nl\n J155532.2+351207 & 15 55 32.7 & +35 11 54.8 & 13.41 & \t & \t \\nl\n J155543.2+111114 & 15 55 43.0 & +11 11 24.1 & 13.81 & 0.360 & BL\\nl\n J155625.4+090311 & 15 56 26.0 & +9 03 19.2 & 14.47 & 0.042 & AGN\\nl\n J155703.2+635029 & 15 57 03.3 & +63 50 27.4 & 14.01 & 0.030 & AGN\\nl\n J155721.3+445902 & 15 57 22.6 & +44 58 54.3 & 14.16 & \t & \t \\nl\n J155909.5+350144 & 15 59 09.7 & +35 01 47.3 & 14.14 & 0.031 & AGN\\nl\n J160740.7+254106 & 16 07 40.2 & +25 41 12.6 & 13.87 & \t & \t \\nl\n J161004.4+671030 & 16 10 04.0 & +67 10 25.9 & 13.67 & 0.067 & BL\\nl\n J161124.8+585106 & 16 11 24.6 & +58 51 01.3 & 14.24 & 0.032 & AGN\\nl\n J161301.5+371656 & 16 13 01.7 & +37 17 15.2 & 14.37 & 0.070 & AGN\\nl\n J161801.9+775230 & 16 17 59.8 & +77 52 34.5 & 13.55 & \t & \t \\nl\n J161951.7+405834 & 16 19 51.3 & +40 58 47.5 & 14.31 & & \\nl\n J162013.1+400858 & 16 20 12.7 & +40 09 05.7 & 14.18 & \t & \t \\nl\n J162409.7+260421 & 16 24 09.3 & +26 04 31.4 & 14.03 & 0.040 & AGN\\nl\n J162552.9+434654 & 16 25 53.3 & +43 46 51.9 & 13.70 & & \\nl\n J162903.6+361911 & 16 29 05.3 & +36 18 58.7 & 14.45 & 0.000 & STAR\\nl\n J163056.3+361848 & 16 30 56.1 & +36 18 48.5 & 14.45 & \t & \t \\nl\n J165057.5+222653 & 16 50 57.8 & +22 26 47.8 & 14.29 & \t & \t \\nl\n J165352.6+394538 & 16 53 52.2 & +39 45 36.3 & 11.27 & 0.033 & BL\\nl\n J165551.7+214559 & 16 55 51.4 & +21 46 01.2 & 13.79 & \t & \t \\nl\n J171227.2+355256 & 17 12 28.5 & +35 53 02.1 & 13.73 & 0.027 & AGN\\nl\n J171959.4+241202 & 17 19 59.7 & +24 12 07.6 & 14.08 & \t & \t \\nl\n J172855.8+515654 & 17 28 54.6 & +51 56 49.2 & 14.21 & & \\nl\n J173114.5+323250 & 17 31 15.2 & +32 32 58.4 & 14.05 & \t & \t \\nl\n J174700.3+683626 & 17 46 59.8 & +68 36 36.1 & 13.78 & 0.063 & GAL\\nl\n J174702.0+493803 & 17 47 03.0 & +49 38 19.3 & 14.20 & \t & \t \\nl\n J213740.3+013711 & 21 37 39.9 & +1 37 16.4 & 13.35 & \t & \t \\nl\n J222408.1+172903 & 22 24 08.1 & +17 28 47.4 & 14.42 & \t & \t \\nl\n J225314.2+040957 & 22 53 11.9 & +4 10 36.1 & 14.35 & & \\nl\n J225453.7+241449 & 22 54 55.1 & +24 14 45.5 & 14.18 & \t & \t \\nl\n J230315.7+085226 & 23 03 15.6 & +8 52 26.9 & 11.05 & 0.016 & AGN\\nl\n J230706.6+163153 & 23 07 05.3 & +16 32 27.1 & 13.78 & \t & \t \\nl\n J231341.0+140113 & 23 13 40.5 & +14 01 15.6 & 13.86 & 0.041 & AGN\\nl\n J233413.9+073637 & 23 34 13.9 &\t+7 37 01.2 & 13.86 & \t & \t \\nl\n J234106.5+093805 & 23 41 06.6 &\t+9 38 09.1 & 14.38 & \t & \t \\nl\n J234728.8+242743 & 23 47 28.8 & +24 27 45.8 & 13.65 & \t & \t \\nl\n J234953.5+242754 & 23 49 53.3 & +24 27 51.6 & 13.65 & \t & \t \\nl\n J235122.7+234417 & 23 51 21.5 & +23 44 24.4 & 14.02 & \t & \t \\nl\n\\enddata\n\\label{tbl-2b}\n\\end{deluxetable}\n\\clearpage\n%\n\\begin{deluxetable}{lrrrrc}\n\\tablenum{3}\n\\tablewidth{0pt}\n\\tablecaption{Other Spectroscopic Identifications}\n\\tablehead{\n\\colhead{Name (1RXS)} & \\colhead{R.A.} &\n\\colhead{Declination} & \\colhead{$B_{J}$} &\n\\colhead{$z$} & \\colhead{Type}}\n\\startdata\nJ000011.9+052318 & 00 00 11.80 & +05 23 17.3 & 16.40 & 0.039 & AGN\\nl\nJ000637.1+434223 & 00 06 36.60 & +43 42 28.3 & 14.80 & 0.166 & AGN\\nl\nJ000805.6+145027 & 00 08 05.70 & +14 50 23.3 & 14.50 & 0.043 & AGN\\nl\nJ001409.9+304928 & 00 14 01.00 & +30 49 24.3 & 18.20 &:0.000 & STAR\\nl\nJ004649.4+152741 & 00 46 50.00 & +15 27 52.6 & 16.10 &:0.078 & AGN\\nl\nJ005050.6+353645 & 00 50 50.80 & +35 36 42.2 & 14.60 & 0.056 & AGN\\nl\nJ005346.9+223209 & 00 53 46.20 & +22 32 22.5 & 15.80 & 0.148 & AGN\\nl\nJ011205.2+224452 & 01 12 05.80 & +22 44 38.6 & 15.80 & 0.000 & STAR\\nl\nJ020012.5+130317 & 02 00 13.90 & +13 03 13.1 & 16.20 & 0.000 & STAR\\nl\nJ130710.9+394540 & 13 07 11.50 & +39 45 33.1 & 15.40 & 0.076 & AGN\\nl\nJ144240.3+262330 & 14 42 40.80 & +26 23 32.4 & 16.40 &:0.110 & AGN\\nl\nJ151601.5+020055 & 15 16 01.40 & +2 00 59.8 & 16.80 & 0.105 & AGN\\nl\n%%%% J170033.1+355309 & 17 00 33.30 & +35 52 56.0 & 15.80 &:0.192 & AGN\\nl\nJ170320.4+373731 & 17 03 20.10 & +37 37 23.8 & 16.20 & * & AGN\\nl\nJ171235.5+245037 & 17 12 35.80 & +24 50 26.8 & 17.50 & * & AGN\\nl\nJ221832.8+192527 & 22 18 31.30 & +19 25 42.8 & 14.40 & 0.000 & STAR\\nl\nJ232841.4+224853 & 23 28 42.90 & +22 49 43.7 & 15.20 & 0.000 & STAR\\nl\nJ234114.9+142820 & 23 41 15.90 & +14 28 43.7 & 16.80 & 0.000 & STAR\\nl\nJ235959.1+083355 & 23 59 59.30 & +8 33 54.1 & 15.40 & 0.083 & AGN\\nl\n\\label{tbl-3}\n\\enddata\n\\end{deluxetable}\n%\n\\clearpage\n%\n\\begin{deluxetable}{lrrcr}\n\\tablenum{4}\n\\tablewidth{0pt}\n\\tablecaption{The USNO Spectroscopic Follow-up ($0 < \\delta < 90$)}\n\\tablehead{\n\\colhead{$R_{min}$} & \\colhead{$R_{max}$} &\n\\colhead{$AR_{min}$} & \\colhead{$AR_{max}$} &\n\\colhead{$AREA$} }\n\\startdata\n% USNO\n13.50 & 15.40 & 00.00 & 01.00 & 315.250 \\nl \n13.50 & 14.55 & 01.00 & 06.00 & 662.000 \\nl \n13.50 & 15.40 & 06.00 & 08.00 & 32.750 \\nl \n13.50 & 14.40 & 08.00 & 09.00 & 366.750 \\nl \n13.50 & 14.40 & 09.00 & 10.00 & 732.750 \\nl \n13.50 & 13.90 & 10.00 & 11.00 & 688.000 \\nl \n13.50 & 14.40 & 11.00 & 12.00 & 652.750 \\nl \n13.50 & 13.90 & 12.00 & 13.00 & 727.566 \\nl \n13.50 & 14.60 & 13.00 & 14.00 & 758.042 \\nl \n13.50 & 14.60 & 14.00 & 15.00 & 781.193 \\nl \n13.50 & 13.70 & 15.00 & 16.00 & 730.482 \\nl \n13.50 & 14.60 & 16.00 & 17.00 & 780.750 \\nl \n13.50 & 14.60 & 17.00 & 18.00 & 388.000 \\nl \n13.50 & 14.90 & 18.00 & 22.00 & 93.500 \\nl \n13.50 & 14.50 & 22.00 & 24.00 & 454.750 \\nl \n\\label{tbl-4}\n\\enddata\n\\end{deluxetable}\n\n\\begin{deluxetable}{lrrcr}\n\\tablenum{5}\n\\tablewidth{0pt}\n\\tablecaption{The GSC Spectroscopic Follow-up ($0 < \\delta < 90$)}\n\\tablehead{\n\\colhead{$V_{min}$} & \\colhead{$V_{max}$} &\n\\colhead{$AR_{min}$} & \\colhead{$AR_{max}$} &\n\\colhead{$AREA$} }\n\\startdata\n% GSC\n11.00 & 14.00 & 00.00 & 02.00 & 646.250 \\nl\n11.00 & 14.50 & 02.00 & 04.00 & 298.000 \\nl\n11.00 & 14.50 & 04.00 & 06.00 & 32.750 \\nl\n11.00 & 13.50 & 06.00 & 08.00 & 32.750 \\nl\n13.20 & 14.10 & 08.00 & 09.00 & 366.750 \\nl\n11.00 & 13.75 & 09.00 & 10.00 & 732.750 \\nl\n13.96 & 14.10 & 10.00 & 11.00 & 688.000 \\nl\n13.45 & 13.75 & 11.00 & 12.00 & 652.750 \\nl\n11.85 & 13.00 & 12.00 & 13.00 & 727.566 \\nl\n11.00 & 13.35 & 13.00 & 14.00 & 758.042 \\nl\n11.00 & 13.25 & 14.00 & 15.00 & 781.193 \\nl\n13.80 & 14.05 & 15.00 & 16.00 & 730.482 \\nl\n11.00 & 13.75 & 16.00 & 18.00 &1168.750 \\nl\n11.00 & 14.50 & 18.00 & 20.00 & 000.000 \\nl\n11.00 & 14.50 & 20.00 & 22.00 & 935.000 \\nl\n11.00 & 13.50 & 22.00 & 24.00 & 454.750 \\nl\n\\label{tbl-5}\n\\enddata\n\\end{deluxetable}\n\\clearpage\n\n\\begin{deluxetable}{cccc}\n\\tablenum{6}\n\\tablewidth{0pt}\n\\tablecaption{The Differential QSO Counts}\n\\tablehead{\n\\colhead{ $B$ interval } & \\colhead{$<B>$} &\n\\colhead{ N } & \\colhead{$\\log{\\rm surf.den.}$}\\\\\n & & & $mag^{-1} deg^{-2}$\n}\n\\startdata\n12.5-13.5 & 13.0 & ~3 & -3.34 \\nl\n13.5-14.5 & 14.2 & 19 & -2.69 \\nl\n14.5-15.5 & 14.8 & 24 & -2.04 \\nl\n\\label{tbl-counts}\n\\enddata\n\\end{deluxetable}\n\\clearpage\n%\n\\begin{deluxetable}{cccc}\n\\tablenum{7}\n\\tablewidth{0pt}\n\\tablecaption{The QSO Luminosity Function at $0.04 < z < 0.3$}\n\\tablehead{\n\\colhead{ $M_B$ interval } & \\colhead{$<M_B>$} &\n\\colhead{ N } & \\colhead{$\\log {\\rm LF}$}\\\\\n & & & $Mpc^{-3} mag^{-1}$\n}\n\\startdata\n-21.5 -22.5 & -22.04 & ~3 & -6.05 \\nl\n-22.5 -23.5 & -23.31 & ~9 & -6.84 \\nl\n-23.5 -24.5 & -24.10 & 23 & -6.89 \\nl\n-24.5 -25.5 & -25.10 & 11 & -7.75 \\nl\n-25.5 -28.5 & -26.72 & ~2 & -9.35 \\nl\n\\label{tbl-LF}\n\\enddata\n\\end{deluxetable}\n\\clearpage\n\\normalsize\n\n% Now comes the reference list. In this document, we used \\cite to call\n% out citations, so we must use \\bibitem in the reference list, which\n% means we use the LaTeX thebibliography environment. Please note that\n% \\begin{thebibliography} is followed by a null argument. If you forget\n% this, mayhem ensues, and LaTeX will say \"Perhaps a missing item?\" when\n% you run it. Do not call us, do not send mail when this happens. Put\n% the silly {} after the \\begin{thebibliography}.\n%\n% Each reference has a \\bibitem command to define the citation format\n% to be placed in the text (in []) and the symbolic tag used for \n% cross referencing (in {}).\n%\n% See sample1.tex, or the AASTeX guide, for an alternative to the \\cite-\n% \\bibitem command.\n\n\\begin{thebibliography}{}\n\\bibitem[Avni \\& Bahcall, 1980]{avni:80}\nAvni, Y., \\& Bahcall, J. N. 1980, ApJ, 235, 694\n\\bibitem[Banse et al. 1983]{MIDAS} \nBanse, K., Crane, P., Ounnas, C. \\& Ponz, D., 1983. In: Proc. of\nDECUS, Zurich, p.\\ 87\n\\bibitem[Bessel 1990]{bess90} Bessel, M. S. 1990, \\aaps, 83, 357.\n\\bibitem[Boyle 1992]{boyle92}\nBoyle B.J., 1992, in \"Texas/ESO-CERN Symposium on Relativistic\nAstrophysics, Cosmology and Particle Physics\", ed(s) Barrow J.D.,\nMestel L. and Thomas P., Ann. N.Y. Acad. of Sci., 647, 14\n\\bibitem[Burstein \\& Heiles 1982]{bur:hei}\n\tBurstein, D., Heiles, C. 1982, AJ, 87, 1165\n\\bibitem[Cattaneo 1999]{cattaneo:99}\nCattaneo, A. astro-ph/9907335 \n\\bibitem[Cavaliere et al. 1997]{caval97} Cavaliere, A., Perri, M., \nVittorini, V. 1997, Mem.S.A.It., 68, 27\n\\bibitem[Cristiani \\& Vio (1990)]{cri:vio}\n\tCristiani, S., Vio, R. 1990, A\\&A, 227, 385\n\\bibitem[Cristiani et al. 1995]{SC95}\nCristiani, S., La Franca, F., Andreani, P., Gemmo, A., Goldschmidt, P.,\nMiller, L., Vio, R., Barbieri, C., Bodini, L., Iovino, A., Lazzarin, M.,\nClowes, R.G., MacGillivray, H., Gouiffes, C., Lissandrini, C., Savage,\nA. 1995, A\\&AS, 112, 347\n\\bibitem[Digitized Sky Survey]{http1} The Digitized Sky Survey\n{\\it http://arch-http.hq.eso.org/dss/dss}\n\\bibitem[Franceschini et al. 1994]{franceschini94}\nFranceschini, A., La Franca, F., Cristiani, S., Martin-Mirones,\nJ.M. 1994, MNRAS, 269, 683\n\\bibitem[Gehrels, 1986]{gehrels:86}\nGehrels, N. 1986, \\apj, 303, 346\n\\bibitem[Goldschmidt et al. 1992]{pippa92} Goldschmidt, P., Miller,\nL., La Franca, F., Cristiani, S. 1992, MNRAS, 256, 65p \n\\bibitem[Goldschmidt and Miller 1998]{pippa98} Goldschmidt, P., Miller,\nL. 1998, MNRAS, 293, 107\n\\bibitem[Haiman and Menou 1999]{HM:99}\nHaiman, Z., Menou, K. astro-ph/9810426\n\\bibitem[Hartwick and Schade 1990]{HS:90} \nHartwick, F.D.A., Schade, D. 1990, ARA\\&A, 28, 437 \n\\bibitem[Hasinger et al.\\ 1998] {hasing98}\nHasinger, G., Burg, R., Giacconi, R., Schmidt, M., Tr\\\"umper, J.,\nZamorani, G. 1998, A\\&A, 329, 482\n\\bibitem[Hewett and Foltz 1994]{HF94} \nHewett, P.C., Foltz, C.B. 1994, PASP, 106, 113 \n\\bibitem{} \nHewett, P.C., Foltz, C.B., Chaffee, F.H. 1993, \\apj, 406, L43 \n\\bibitem[Kauffmann and Haehnelt]{KH:99}\nKauffmann, G., Haehnelt, M. astro-ph/9906493\n\\bibitem[K\\\"ohler et al. 1997]{HES97} \nK\\\"ohler, T., Groote, D., Reimers, D., Wisotzki, L. 1997, A\\&A,\n325, 502\n\\bibitem[La Franca et al, 1995]{lf95}\nLa Franca, F., Franceschini, A., Cristiani, S., Vio, R.\n1995, A\\&A, 299, 19\n\\bibitem[La Franca and Cristiani, 1997]{lf97}\nLa Franca, F., Cristiani, S. 1997, AJ, 113, 1517\n\\bibitem[Landolt 1992]{land92} Landolt, A.U. 1992, AJ, 104, 340.\n\\bibitem[Lasker et al.\\ 1988]{lask88} Lasker, B. M., Sturch, C. R.\net al. 1988, \\apjs, 68, 1.\n\\bibitem[Miyaji et al., 1999]{miyaji:99}\nMiyaji, T., Hasinger, G., Schmidt, M. astro-ph/9910410\n\\bibitem[Monaco et al. 1999]{MSD:99}\nMonaco, P., Salucci, P., Danese, L. astro-ph/9907095 \n\\bibitem[Monet et al.\\ 1996]{mone96} Monet, D. \\aaps, 188, 5404.\n\\bibitem[Oke, 1990]{stand}\nOke, J.B. 1990, \\aj, 99, 1621.\n\\bibitem[Page \\& Carrera, 1999]{page99}\nPage, M.J., Carrera, F.J. astro-ph/9909434 \n\\bibitem[Schmidt \\& Green\\ 1983]{SeG83} Schmidt, M., Green, R. F. \n1983, ApJ, 269, 352\n\\bibitem[V\\'eron and V\\'eron 1998]{veron98}\nV\\'eron, M.P., V\\'eron, P., 1998, A Catalogue of Quasars and Active\nNuclei, 1998, ESO Scientific report No. 18.\n\\bibitem[Voges 1992]{vog92} Voges, W., 1992 In ESA, Environment\nObservation and Climate Modelling Through International Space Projects. Space\nSciences with Particular Emphasis on High-Energy Astrophysics p 9-19\n\\bibitem[Voges et al.\\ 1999]{vog99}\nVoges, W., Aschenbach, B., Boller, T.,\nBrauninger, H., Briel, U., Burkert, W., Dennerl, K., Englhauser, J.,\nGruber, R., Haberl, F., Hartner, G., Hasinger, G.,\nPfeffermann, E., Pietsch, W., Predehl, P., Rosso, C., Schmidt, J. H. M. M.,\nTr\\\"umper, J., Zimmermann, H.-U. astro-ph/9909315\n\\bibitem[Yuan, Siebert and Brinkmann, 1998]{yuan:98}\nYuan, W., Siebert, J., Brinkmann, W. 1998, A\\&A, 334, 498\n\\end{thebibliography}\n\\clearpage\n%\n\\begin{figure}\n\\plotone{Grazian.fig1.ps}\n\\caption{The incompleteness in the present selection of quasar\ncandidates is due to objects not found in the RASS catalogue (with a\nflux $\\le 0.05$ cps, on the left of the vertical continuous line) and\nto the ones with $\\alpha_{ox}\\ge 1.7$ (on the left of the dashed line).\n\\label{fig1}}\n\\end{figure}\n\n\\begin{figure}\n\\plotone{Grazian.fig2a.ps}\n\\caption{a) - The spectra of the AGN confirmed with the follow-up\nspectroscopy}\n\\end{figure}\n\\begin{figure}\n\\figurenum{2}\n\\plotone{Grazian.fig2b.ps}\n\\caption{b) - The spectra of the AGN confirmed with the follow-up spectroscopy \n\\label{fig2}}\n\\end{figure}\n%\n\\begin{figure}\n\\plotone{Grazian.fig3.ps}\n\\caption{The LogN-LogS relation of QSOs. Open squares refer to the\npresent sample and are QSOs with $z \\ge 0.04$. A correction of -0.037\nto the values of Col.~4 in Tab.~6 has been applied to account for the\nBennet bias. The continuous straight line is the relation found by\nK\\\"ohler et al. (1997) for QSOs with 0.07$\\le z\\le$2.2. The filled\ncircle is the point derived from the PG Survey.\n\\label{fig3}}\n\\end{figure}\n%\n\\begin{figure}\n\\plotone{Grazian.fig4a.ps}\n\\caption{a) - The luminosity function of QSOs compared with a\nparameterization of Pure Luminosity Evolution (see text). The points\nin the range $0.04 < z \\le 0.3$ are the result of the present survey, the\nremaining data are derived from LC97.}\n\\end{figure}\n%\n\\begin{figure}\n\\figurenum{4}\n\\plotone{Grazian.fig4b.ps}\n\\caption{b) - The luminosity function of QSOs compared with a\nparameterization of Luminosity Dependent\nLuminosity Evolution.\n\\label{fig4}}\n\\end{figure}\n%\n\\begin{figure}\n\\figurenum{5}\n\\plotone{Grazian.fig5.ps}\n\\caption{The continuous line represents the evolution of the space density of\nquasars with $M_B < -24$ predicted by the $\\Lambda$CDM model described in the\ntext (KH99). \nFilled circles are data from the present work, filled triangles are\nderived from LC97 and\nopen squares show data from Hartwick \\& Schade (1990).\n\\label{semi_anal}}\n\\end{figure}\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002183.extracted_bib",
"string": "\\begin{thebibliography} is followed by a null argument. If you forget\n% this, mayhem ensues, and LaTeX will say \"Perhaps a missing item?\" when\n% you run it. Do not call us, do not send mail when this happens. Put\n% the silly {} after the \\begin{thebibliography}.\n%\n% Each reference has a \\bibitem command to define the citation format\n% to be placed in the text (in []) and the symbolic tag used for \n% cross referencing (in {}).\n%\n% See sample1.tex, or the AASTeX guide, for an alternative to the \\cite-\n% \\bibitem command.\n\n\\begin{thebibliography}{}\n\\bibitem[Avni \\& Bahcall, 1980]{avni:80}\nAvni, Y., \\& Bahcall, J. N. 1980, ApJ, 235, 694\n\\bibitem[Banse et al. 1983]{MIDAS} \nBanse, K., Crane, P., Ounnas, C. \\& Ponz, D., 1983. In: Proc. of\nDECUS, Zurich, p.\\ 87\n\\bibitem[Bessel 1990]{bess90} Bessel, M. S. 1990, \\aaps, 83, 357.\n\\bibitem[Boyle 1992]{boyle92}\nBoyle B.J., 1992, in \"Texas/ESO-CERN Symposium on Relativistic\nAstrophysics, Cosmology and Particle Physics\", ed(s) Barrow J.D.,\nMestel L. and Thomas P., Ann. N.Y. Acad. of Sci., 647, 14\n\\bibitem[Burstein \\& Heiles 1982]{bur:hei}\n\tBurstein, D., Heiles, C. 1982, AJ, 87, 1165\n\\bibitem[Cattaneo 1999]{cattaneo:99}\nCattaneo, A. astro-ph/9907335 \n\\bibitem[Cavaliere et al. 1997]{caval97} Cavaliere, A., Perri, M., \nVittorini, V. 1997, Mem.S.A.It., 68, 27\n\\bibitem[Cristiani \\& Vio (1990)]{cri:vio}\n\tCristiani, S., Vio, R. 1990, A\\&A, 227, 385\n\\bibitem[Cristiani et al. 1995]{SC95}\nCristiani, S., La Franca, F., Andreani, P., Gemmo, A., Goldschmidt, P.,\nMiller, L., Vio, R., Barbieri, C., Bodini, L., Iovino, A., Lazzarin, M.,\nClowes, R.G., MacGillivray, H., Gouiffes, C., Lissandrini, C., Savage,\nA. 1995, A\\&AS, 112, 347\n\\bibitem[Digitized Sky Survey]{http1} The Digitized Sky Survey\n{\\it http://arch-http.hq.eso.org/dss/dss}\n\\bibitem[Franceschini et al. 1994]{franceschini94}\nFranceschini, A., La Franca, F., Cristiani, S., Martin-Mirones,\nJ.M. 1994, MNRAS, 269, 683\n\\bibitem[Gehrels, 1986]{gehrels:86}\nGehrels, N. 1986, \\apj, 303, 346\n\\bibitem[Goldschmidt et al. 1992]{pippa92} Goldschmidt, P., Miller,\nL., La Franca, F., Cristiani, S. 1992, MNRAS, 256, 65p \n\\bibitem[Goldschmidt and Miller 1998]{pippa98} Goldschmidt, P., Miller,\nL. 1998, MNRAS, 293, 107\n\\bibitem[Haiman and Menou 1999]{HM:99}\nHaiman, Z., Menou, K. astro-ph/9810426\n\\bibitem[Hartwick and Schade 1990]{HS:90} \nHartwick, F.D.A., Schade, D. 1990, ARA\\&A, 28, 437 \n\\bibitem[Hasinger et al.\\ 1998] {hasing98}\nHasinger, G., Burg, R., Giacconi, R., Schmidt, M., Tr\\\"umper, J.,\nZamorani, G. 1998, A\\&A, 329, 482\n\\bibitem[Hewett and Foltz 1994]{HF94} \nHewett, P.C., Foltz, C.B. 1994, PASP, 106, 113 \n\\bibitem{} \nHewett, P.C., Foltz, C.B., Chaffee, F.H. 1993, \\apj, 406, L43 \n\\bibitem[Kauffmann and Haehnelt]{KH:99}\nKauffmann, G., Haehnelt, M. astro-ph/9906493\n\\bibitem[K\\\"ohler et al. 1997]{HES97} \nK\\\"ohler, T., Groote, D., Reimers, D., Wisotzki, L. 1997, A\\&A,\n325, 502\n\\bibitem[La Franca et al, 1995]{lf95}\nLa Franca, F., Franceschini, A., Cristiani, S., Vio, R.\n1995, A\\&A, 299, 19\n\\bibitem[La Franca and Cristiani, 1997]{lf97}\nLa Franca, F., Cristiani, S. 1997, AJ, 113, 1517\n\\bibitem[Landolt 1992]{land92} Landolt, A.U. 1992, AJ, 104, 340.\n\\bibitem[Lasker et al.\\ 1988]{lask88} Lasker, B. M., Sturch, C. R.\net al. 1988, \\apjs, 68, 1.\n\\bibitem[Miyaji et al., 1999]{miyaji:99}\nMiyaji, T., Hasinger, G., Schmidt, M. astro-ph/9910410\n\\bibitem[Monaco et al. 1999]{MSD:99}\nMonaco, P., Salucci, P., Danese, L. astro-ph/9907095 \n\\bibitem[Monet et al.\\ 1996]{mone96} Monet, D. \\aaps, 188, 5404.\n\\bibitem[Oke, 1990]{stand}\nOke, J.B. 1990, \\aj, 99, 1621.\n\\bibitem[Page \\& Carrera, 1999]{page99}\nPage, M.J., Carrera, F.J. astro-ph/9909434 \n\\bibitem[Schmidt \\& Green\\ 1983]{SeG83} Schmidt, M., Green, R. F. \n1983, ApJ, 269, 352\n\\bibitem[V\\'eron and V\\'eron 1998]{veron98}\nV\\'eron, M.P., V\\'eron, P., 1998, A Catalogue of Quasars and Active\nNuclei, 1998, ESO Scientific report No. 18.\n\\bibitem[Voges 1992]{vog92} Voges, W., 1992 In ESA, Environment\nObservation and Climate Modelling Through International Space Projects. Space\nSciences with Particular Emphasis on High-Energy Astrophysics p 9-19\n\\bibitem[Voges et al.\\ 1999]{vog99}\nVoges, W., Aschenbach, B., Boller, T.,\nBrauninger, H., Briel, U., Burkert, W., Dennerl, K., Englhauser, J.,\nGruber, R., Haberl, F., Hartner, G., Hasinger, G.,\nPfeffermann, E., Pietsch, W., Predehl, P., Rosso, C., Schmidt, J. H. M. M.,\nTr\\\"umper, J., Zimmermann, H.-U. astro-ph/9909315\n\\bibitem[Yuan, Siebert and Brinkmann, 1998]{yuan:98}\nYuan, W., Siebert, J., Brinkmann, W. 1998, A\\&A, 334, 498\n\\end{thebibliography}"
}
] |
astro-ph0002185
|
Cluster Selection and the Evolution of Brightest Cluster Galaxies
|
[
{
"author": "D. J. Burke\\altaffilmark{1,2,5}"
},
{
"author": "C. A. Collins\\altaffilmark{1,5}"
},
{
"author": "R. G. Mann\\altaffilmark{3,4,5}"
}
] |
The K-band Hubble diagram of Brightest Cluster Galaxies (BCGs) is presented for a large, \xray\ selected cluster sample extending out to $z = 0.8$. The controversy over the degree of BCG evolution is shown to be due to sample selection, since the BCG luminosity depends upon the cluster environment. Selecting only the most \xray\ luminous clusters produces a BCG sample which shows, under the assumption of an Einstein-de Sitter cosmology, significantly less mass growth than that predicted by current \semianalytic\ galaxy formation models, and significant evidence of any growth only if the dominant stellar population of the BCGs formed relatively recently ($z \leq 2.6$).
|
[
{
"name": "ms.tex",
"string": "%%\n%% accepted, 02/03/00\n%%\n\n\\documentstyle[emulateapj]{article}\n%\\documentstyle[aas2pp4]{article}\n%%\\documentclass[preprint2]{aastex}\n\n\\slugcomment{Accepted for publication in ApJ Letters}\n\\lefthead{Burke et al.}\n\\righthead{BCG Evolution and Cluster Selection}\n\n%%\n%% Personal definitions\n%%\n\n\\newcommand{\\ho}[1]{{\\rm H$_0 = #1$~km\\,\\persec\\,\\permpc}}\n\n%%\n%% Sample info\n%%\n\\newcommand{\\lx}{\\mbox{$L_{x}$}}\n\n\\newcommand{\\lmineds}{2.3}\n\n\\newcommand{\\nclus}{76} \n\\newcommand{\\abscal}{0.05}\n\n\\newcommand{\\ltsim}{\\lesssim}\n\\newcommand{\\gtsim}{\\gtrsim}\n\n\\newcommand{\\zf}{\\mbox{$z_f$}}\n\n\\newcommand{\\persec}{\\mbox{s$^{-1}$}}\n\\newcommand{\\permpc}{\\mbox{Mpc$^{-1}$}}\n\\newcommand{\\lumin}{\\mbox{erg \\persec}}\n\n%% English/US spelling\n\\newcommand{\\centre}{center}\n\\newcommand{\\colour}{color}\n\\newcommand{\\favoured}{favored}\n\\newcommand{\\behaviour}{behavior}\n\\newcommand{\\programmes}{programs}\n\n%% hyphenation\n\\newcommand{\\semianalytic}{semi-analytic}\n\\newcommand{\\semianalytical}{semi-analytical}\n\\newcommand{\\xray}{X-ray}\n\n%% punctuation\n\\newcommand{\\eg}{\\mbox{e.g.}}\n\\newcommand{\\etal}{\\mbox{et al.}}\n\n%% papers\n\\newcommand{\\cmfirst}{Collins \\& Mann~\\markcite{cm98}(1998; hereafter CM98)}\n\\newcommand{\\pcmmain}{\\protect\\markcite{cm98}CM98}\n\\newcommand{\\cmmain}{\\markcite{cm98}CM98}\n\n\\newcommand{\\abkfirst}{Arag\\'{o}n-Salamanca, Baugh \\& Kauffmann \\markcite{abk98}(1998; hereafter ABK98)}\n\\newcommand{\\pabkmain}{\\protect\\markcite{abk98}ABK98}\n\\newcommand{\\abkmain}{\\markcite{abk98}ABK98}\n\n\\newcommand{\\deprop}{De Propris \\etal~\\markcite{depropris99}(1999)}\n\\newcommand{\\depropbracket}{De Propris \\etal~\\markcite{depropris99}1999}\n\n\\newcommand{\\lynam}{Lynam \\etal~\\markcite{pdl99}(1999)}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{document}\n\n\\title{Cluster Selection and the Evolution of Brightest Cluster Galaxies}\n\n\\author{\nD. J. Burke\\altaffilmark{1,2,5},\nC. A. Collins\\altaffilmark{1,5},\nR. G. Mann\\altaffilmark{3,4,5}}\n\n\\altaffiltext{1}{Astrophysics Research Institute, Liverpool John Moores University,\n12 Quays House, Egerton Wharf, Birkenhead, CH41 1LD, UK}\n\\altaffiltext{2}{Institute for Astronomy, University of Hawaii,\n2680 Woodlawn Drive, Honolulu, HI 96822}\n\\altaffiltext{3}{Astrophysics Group, Blackett Laboratory, \nImperial College, Prince Consort Road, London, SW7 2AZ, UK}\n\\altaffiltext{4}{Institute for Astronomy, University of Edinburgh, \nRoyal Observatory, Blackford Hill, Edinburgh, EH9 3NJ, UK}\n\\altaffiltext{5}{Visiting Astronomer at the \nNASA Infrared Telescope\nFacility, which is operated by the University of\nHawaii under contract from the National Aeronautics\nand Space Administration.}\n%%\\email{burke@ifa.hawaii.edu,cac@astro.livjm.ac.uk}\n%%\\email{rgm@roe.ac.uk}\n\n%% Abstract\n\\begin{abstract}\nThe K-band Hubble diagram of Brightest Cluster Galaxies (BCGs) is presented\nfor a large, \\xray\\ selected cluster sample extending out to $z = 0.8$.\nThe controversy over the degree of BCG evolution is shown to be due to\nsample selection,\nsince the BCG luminosity depends upon the cluster environment.\nSelecting only the most \\xray\\ luminous clusters produces a BCG sample \nwhich \nshows, under the assumption of an Einstein-de Sitter cosmology, \nsignificantly less mass growth than that predicted by current \n\\semianalytic\\ galaxy formation models, and significant evidence of \nany growth only if the\ndominant stellar population of the BCGs formed relatively recently ($z \\leq 2.6$).\n\n\\end{abstract}\n\n\\keywords{Galaxies: clusters: general --- galaxies: elliptical and lenticular, \ncD --- galaxies: evolution --- galaxies: formation}\n\n\\section{INTRODUCTION}\n\\label{intro}\n\nThe majority of stars in giant ellipticals \nfound in the cores of rich galaxy clusters are old;\nphotometric and spectroscopic studies of cluster galaxies out to\n$z \\approx 1$ suggest a formation redshift, \\zf, greater than 2,\nwith little variation within a cluster, \nand that secondary bursts of star formation account for\na small fraction of the stellar mass\n(\\eg\\ \nArag\\'{o}n-Salamanca \\etal~\\markcite{aecc93}1993;\nEllis \\etal~\\markcite{ellis97}1997;\nStanford, Eisenhardt \\& Dickinson~\\markcite{sed98}1998;\nvan Dokkum \\etal~\\markcite{vd98}1998;\nPoggianti \\etal~\\markcite{morphs99}1999).\n\nHowever, to understand the process of galaxy formation it is necessary to\nknow where the stars were formed as well as when.\nIn the traditional view of early-type galaxy formation---a\n``monolithic'' collapse at high redshift \n(\\eg\\ Eggen, Lynden-Bell \\& Sandage~\\markcite{els62}1962;\nLarson~\\markcite{larson69}1969)---all the stars\nwere formed in situ, in direct contrast to the merger-driven\ngrowth of galaxies predicted by \n\\semianalytical\\ models for hierarchical cosmologies, such as CDM\n(\\eg\\ Kauffmann \\& White~\\markcite{kw93}1993;\nBaugh, Cole \\& Frenk~\\markcite{bcf96}1996).\nSince the ages of the stars are similar in both scenarios,\nit is the change in mass with look-back time that\nseparates the two \npictures\nobservationally.\nThe current data are inconclusive;\nfor example,\nthe hierarchical models are \\favoured\\ by the enhanced\nmerger fraction seen in the $z=0.8$ cluster MS1054.4-0321\n(van Dokkum \\etal~\\markcite{v99}1999), whilst\n\\deprop\\ show \nno evidence for mass evolution of bright ellipticals in clusters\nout to $z \\approx 1$.\nIn general it is difficult to follow the evolutionary history of \nellipticals since selection methods can seriously bias the samples,\nc.f. the discussions of progenitor bias in van Dokkum \\& Franx~\\markcite{vf96}(1996),\nthe effect of preferential selection of the most massive objects at\neach epoch in Kauffmann \\& Charlot~\\markcite{kc98}(1998),\nand the use of \\colour\\ selection in Jimenez \\etal~\\markcite{jimenez99}(1999).\n\nOne approach to minimising such problems is to study the evolution of \na particular class of ellipticals---brightest cluster galaxies (BCGs)---because\nof their unique location, close to the \\centre\\ of the cluster's\npotential well.\nBCGs do not appear to be drawn from the same luminosity function\nas other cluster galaxies (\\eg\\ Dressler~\\markcite{dressler78}1978), \nwhich suggests that they have a distinct formation history.\nKnowledge of BCG evolution can therefore provide different\nconstraints on galaxy formation models to studies\nof the general cluster population.\n\nThe K-band Hubble diagram for BCGs has recently been extended\nto $z \\approx 1$ by \nboth \\cmfirst\\ and \n\\abkfirst: these\nobservations provide the opportunity to measure the luminosity\nevolution of BCGs since evolutionary and pass-band \ncorrections are insensitive to the recent star-formation history of\na galaxy at near-IR wavelengths (\\eg\\ Bershady~\\markcite{bershady95}1995;\nMadau, Pozzetti, \\& Dickinson~\\markcite{madau98}1998).\nThe conclusions drawn are contradictory,\ndespite the use of the same cosmology and a common assumption that\nthe stellar populations of BCGs are old and passively evolving;\n\\cmmain\\ assert that the stellar populations of BCGs in the most massive clusters\nhave not grown significantly since $z \\approx 1$,\nwhilst \\abkmain\\ argue that their results are in good agreement with \nthe mass increase of BCGs---by a factor of four in an\nEinstein-de Sitter cosmology---predicted by \n\\semianalytical\\ \nmodels over the same redshift range.\nThe two samples have almost no overlap---\\cmmain\\ having used\nan \\xray\\ selected cluster catalogue whilst\n\\abkmain\\ used a heterogeneous compilation that was mainly optically selected---and\nit is the aim of the present work to show that the results\ncan be reconciled by considering the properties of the \nclusters in the two samples.\nSection~\\ref{data} describes the BCG sample used---\nan extension of that of \\cmmain---and\nthe reduction methods employed, whilst\nsection~\\ref{results} presents the results of the analysis\nand a comparison to those of \\abkmain.\nThroughout this letter\nan Einstein-de Sitter cosmology with \\ho{50} is assumed,\nand \\xray\\ luminosities (\\lx) are quoted for the 0.3--3.5~keV pass band.\n\n\\section{DATA}\n\\label{data}\n\n\\subsection{Sample}\n\\label{data:sample}\n\nThe data presented here comprise K-band observations of \\nclus\\ BCGs.\nThis sample, which incorporates that of \\cmmain,\nspans a redshift range of 0.05 to 0.83, and is drawn from the following\n\\xray\\ selected cluster catalogues:\nthe Einstein EMSS (Gioia \\& Luppino \\markcite{gl94}1994; \nNichol \\etal\\ \\markcite{n97}1997; Henry \\markcite{h99}1999),\nthe Southern and Bright SHARC catalogues \n(Burke \\etal\\ \\markcite{b97}1997; \nRomer \\etal\\ \\markcite{bsharc}2000),\nand the ROSAT NEP Survey (Henry \\etal\\ \\markcite{nep97}1997).\n\\xray\\ selection is to be preferred, since both \\xray\\ luminosity and \n\\xray\\ temperature should be more closely related to cluster\nmass than optical richness.\n\nThe \\xray\\ luminosity-redshift coverage of the cluster sample is shown\nby the circles in Figure~1. \nThe additional symbols show those clusters from \\abkmain\\ with a \nmeasured \\xray\\ flux or upper limit,\nexcept for Cl~2155+0334 (also known as Cl~2157+0347), which\nhas been removed because photometric and\nspectroscopic observations show no evidence for a cluster\n(Thimm \\& Belloni~\\markcite{tb94}1994; Oke, Postman \\& \nLubin~\\markcite{opl98}1998), and Cl~0016+16, since it is in both samples.\nThe difference in \\xray\\ luminosity coverage at $z > 0.5$\nfor the two samples is striking;\nthe implications of this are discussed in section~\\ref{results}.\n\n\\vspace{2mm}\n\\begin{center}\n%\n%%\\plotfiddle{fig1.eps}{2in}{-90}{32}{32}{-120}{180}\n\\plotfiddle{fig1.eps}{2in}{-90}{32}{32}{-120}{190}\n%\n\\begin{minipage}{8.75cm}\n\\small\\parindent=3.5mm\n{\\sc Fig.}~1.---Cluster \\xray\\ luminosity as a function of redshift.\nThe circles indicate the BCG sample presented here; \nopen for clusters used \nin \\pcmmain\\ and filled for the new observations.\nClusters from \\pabkmain\\ with measured \\xray\\ fluxes are shown\nas plus ($+$) symbols and the arrow ($\\uparrow$) symbol \nrepresents the $3\\sigma$ upper limit for Cl~1603+4329.\nThe dashed line, at $\\lx = \\lmineds \\times 10^{44}$~\\lumin, \nshows the luminosity used by\n\\pcmmain\\ to separate their sample into high- and low-\\lx\\ clusters.\n%\n\\par\n\\end{minipage}\n%\n\\end{center}\n\\vspace{3mm}\n\nThe K-band BCG observations were made using the IRCAM3 and UFTI cameras on the\nUKIRT and NSFCAM on the IRTF, with some of the\ndata being provided by the service \\programmes\\ of both telescopes.\nIRCAM3 and NSFCAM are 256x256 pixel InSb devices with a field of\nview close to 70\\arcsec\\ by 70\\arcsec\\ (the IRCAM3 and NSFCAM\npixel scales are 0.281 and 0.3~\\arcsec\\,pixel$^{-1}$\nrespectively), and UFTI is a 1024x1024 pixel HgCdTe array with\na pixel scale of 0.091~\\arcsec\\,pixel$^{-1}$,\ngiving a field of view of 92\\arcsec\\ by 92\\arcsec.\nThe observing strategy is the same as presented in \\cmmain:\nthe BCGs were imaged using a jitter pattern and\nseparate sky exposures were taken \nfor those objects which filled the field of view.\n\n\\subsection{Reduction}\n\\label{data:reduction}\n\nThe data reduction system improves upon that presented in \n\\cmmain, and incorporates elements from the methods described\nin Stanford, Eisenhardt \\& Dickinson~\\markcite{sed95}(1995) \nand Hall, Green \\& Owen~\\markcite{hall98}(1998).\nAn outline is presented below as the method \nwill be fully described in a later paper.\n\nThe individual frames were masked for bad pixels, dark subtracted\nand divided by the exposure time.\nA flat field image was created by median combination of the \nobject images---or separate sky exposures if these were available---and\napplied to the object frames. \nMasking of cosmic ray events was performed \non the flattened images before they were mosaiced together,\nwhich completed the processing of those objects with sky exposures.\nOtherwise the mosaic---which is substantially deeper than \nthe individual exposures---was used to create an object mask,\nwhich was then applied to the individual images before they were\nmedian-combined to form a flat.\nThe flattened exposures were then processed as above to create the\nfinal image.\n\nObservations of stars from the UKIRT faint standards \nlist (Casali \\& Hawarden~\\markcite{ukirt-fs}1992)\nwere used to calibrate the photometry onto the UKIRT system\nassuming an extinction of 0.088 mag airmass$^{-1}$, \nthe median value for K-band observations at Mauna Kea.\nComparisons of the results from repeat observations, both\nwithin and between observing runs, show that the magnitudes\nagree to \\abscal\\ mag.\n\nAperture magnitudes were measured using a 50~kpc diameter aperture\nand have been corrected for Galactic absorption using the\nmaps of Schlegel, Finkbeiner, \\& Davis~\\markcite{schlegel98}(1998):\nthe correction is small, mostly being less than 0.05~mag, but\nreaching 0.1~mag in several cases.\nThe position of the aperture was chosen so as to maximise the \nflux contained within it whilst remaining close to the \\centre\\ of\nthe cluster \\xray\\ emission.\nThose pixels contaminated by stars and obvious non-cluster\ngalaxies were excluded from the calculation, being replaced by values \nchosen from regions at the same distance from the aperture \\centre.\nNo attempt has been made to remove flux due to other cluster galaxies\nfalling within the aperture, and so the results are\ndirectly comparable to those of \\abkmain.\n\n\\section{RESULTS}\n\\label{results}\n\nThe K-band Hubble diagram for the two BCG samples is shown in \nFigure~2. The lines show model predictions\ncalculated using the GISSEL96 code (Bruzual \\& Charlot \\markcite{bc}1993),\nfor a solar-metallicity stellar population with a Salpeter initial mass function:\nthe solid line indicates a no-evolution model for a 10~Gyr old\nstellar population, whereas the other lines are for stellar populations \nwhich form in an instantaneous burst of star formation at a single \nepoch---$\\zf = 2$ for the dashed line and $\\zf = 5$ for the dotted line---and then \nevolve passively.\nThe models have been normalised to match the low-redshift, X-ray selected, \nBCG sample of \\lynam, following the method used in \\abkmain, \nassuming a growth curve, $d\\,\\log{L}$/$d\\,\\log{r}$, of 0.7\nfor the aperture corrections and a \\colour\\ of $R-K = 2.6$.\n\n%%\\begin{figure*}[b]\n%%\\plotone{fig2.eps}\n%%\\caption[fig2.eps]{\n%%Magnitude-redshift relation for brightest cluster galaxies\n%%in the observed K band.\n%%Filled and open symbols represent those \n%%BCGs in high- and low-\\lx\\ clusters respectively; the\n%%division is as in Figure~\\ref{fig:z-lx}.\n%%The circles in the top panel indicate the sample presented here,\n%%whilst the squares are for the BCGs in the\n%%two $z=1.3$ clusters from Rosati \\etal~\\protect\\markcite{rosati99}(1999),\n%%where the magnitudes have been measured within 50~kpc diameter apertures\n%%(P. Rosati~1999, private communication).\n%%The bottom panel shows the sample of \\pabkmain, where \n%%the crosses are for those clusters without a measured \\xray\\ flux.\n%%The no-evolution prediction, assuming a 10~Gyr old\n%%stellar population, is shown by the solid line;\n%%passive-evolution models, in which the stars form at a single\n%%epoch, are shown as dashed ($\\zf = 2$)\n%%and dotted ($\\zf = 5$) lines.\n%%\\label{fig:z-mk}}\n%%\\end{figure*}\n\n\\vspace{2mm}\n\\begin{center}\n%\n%\\plotone{fig2.eps}\n\\plotfiddle{fig2.eps}{4.2in}{0}{42}{42}{-120}{-10}\n%\n\\begin{minipage}{8.75cm}\n\\small\\parindent=3.5mm\n{\\sc Fig.}~2.---Magnitude-redshift relation for brightest cluster galaxies\nin the observed K band.\nFilled and open symbols represent those \nBCGs in high- and low-\\lx\\ clusters respectively; the\ndivision is as in Figure~1.\nThe circles in the top panel indicate the sample presented here,\nwhilst the squares are for the BCGs in the\ntwo $z=1.3$ clusters from Rosati \\etal~\\protect\\markcite{rosati99}(1999),\nwhere the magnitudes have been measured within 50~kpc diameter apertures\n(P. Rosati~1999, private communication).\nThe bottom panel shows the sample of \\pabkmain, where \nthe crosses are for those clusters without a measured \\xray\\ flux.\nThe no-evolution prediction, assuming a 10~Gyr old\nstellar population, is shown by the solid line;\npassive-evolution models, in which the stars form at a single\nepoch, are shown as dashed ($\\zf = 2$)\nand dotted ($\\zf = 5$) lines.\n%\n\\par\n\\end{minipage}\n%\n\\end{center}\n\\vspace{3mm}\n\nThe result remains qualitatively the same as Figure~6 of \\cmmain; BCGs\nin high-\\lx\\ clusters form a homogeneous population which is\nbrighter, and has a smaller scatter, than that of low-\\lx\\ clusters.\nThis can be more clearly seen in Figure~3,\nwhich shows the scatter around the model predictions\nas a function of cluster \\xray\\ luminosity.\nIt is this relationship between BCG and cluster properties that leads\nto the contradictory conclusions of \\cmmain\\ and \\abkmain:\nout of the eleven $z > 0.5$ clusters in the latter sample, nine have\n\\xray\\ flux measurements or upper limits, with all but two of these having\na low \\xray\\ luminosity (Figure~1).\nIt is unsurprising that these clusters are not similar\nto rich, local clusters, as they\nwere discovered on the basis of their optical properties\n(\\eg\\ Castander \\etal~\\markcite{castander94}1994;\nHolden \\etal~\\markcite{holden97}1997).\nThe squares in Figure~2 represent the \nBCGs in the two $z = 1.3$ clusters discussed by\nRosati \\etal~\\markcite{rosati99}(1999): the high-\\lx\\ cluster (solid square)\nwas discovered by means of its \\xray\\ emission,\nwhereas the low-\\lx\\ cluster (open square) was detected by its galaxy population. \nAlthough based on only two points, this suggests that the correlation \nwith environment holds at this redshift. \n\n%%\\begin{figure*}[b]\n%%\\plotone{fig3.eps}\n%%\\caption[fig3.eps]{\n%%Residuals about the model predictions, defined as \n%%$\\Delta m_k = m_{\\rm BCG} - m_{\\rm model}$, as a function of \n%%cluster \\xray\\ luminosity.\n%%The BCGs presented here are shown as circles, the\n%%sample of \\pabkmain\\ is shown as in Figure~\\ref{fig:z-lx},\n%%and the squares represent the two clusters from \n%%Rosati \\etal~\\protect\\markcite{rosati99}(1999).\n%%The three panels are for the models shown in\n%%Figure~\\ref{fig:z-mk}:\n%%a) no-evolution model for a 10~Gyr old stellar population,\n%%b) formation at a redshift of 2 followed by passive evolution,\n%%and \n%%c) as for b) but with a formation redshift of 5.\n%%\\label{fig:lx-dmk}}\n%%\\end{figure*}\n\nThe \\semianalytic\\ models discussed in \\abkmain\\ predict a factor of \n$\\sim $4--5 increase in the stellar masses of BCGs in\nmassive clusters since $z=1$, for an Einstein-de Sitter universe.\nTo test whether the data presented here supports this level of evolution, \na correlation between redshift and the BCG residuals\n($\\Delta m_k$, \\eg\\ Figure~4)\nhas been sought.\nPassive-evolution models with $\\zf=2$ and $\\zf=5$ have been used to\ncalculate the residuals---since they provide a conservative range for the \nformation epoch of massive cluster ellipticals \n(\\eg\\ Ellis \\etal~\\markcite{ellis97}1997)---and\nseparate fits made to the high- and low-\\lx\\ cluster subsamples.\nSince the form of any evolution is unknown a priori, a non-parametric\nrank-order statistic---Kendall's $\\tau$---was used; it also has the advantage that\nit is insensitive to the choice of normalisation adopted for the Bruzual\n\\& Charlot models.\nAll save one of the fits showed no significant ($>3\\sigma$) evidence for\nevolution; the exception, at a significance of $3.6\\sigma$, was the\nhigh-\\lx\\ subsample with $\\zf=2$.\nTo find the maximum formation epoch that is still compatible with \nevolution of the high-\\lx\\ subsample, \\zf\\ was increased \nfrom 2 until the correlation significance dropped below $3\\sigma$.\nEvolution is found only if the stars formed recently ($\\zf \\leq 2.6$).\n\n\\vspace{2mm}\n\\begin{center}\n%\n%%\\plotone{fig3.eps}\n%\\plotfiddle{fig3.eps}{4.5in}{0}{45}{45}{-130}{-10}\n\\plotfiddle{fig3.eps}{4.1in}{0}{42}{42}{-120}{-10}\n%\n\\begin{minipage}{8.75cm}\n\\small\\parindent=3.5mm\n{\\sc Fig.}~3.---Residuals about the model predictions, defined as \n$\\Delta m_k = m_{\\rm BCG} - m_{\\rm model}$, as a function of \ncluster \\xray\\ luminosity.\nThe BCGs presented here are shown as circles, the\nsample of \\pabkmain\\ is shown as in Figure~1,\nand the squares represent the two clusters from \nRosati \\etal~\\protect\\markcite{rosati99}(1999).\nThe three panels are for the models shown in\nFigure~2:\na) no-evolution model for a 10~Gyr old stellar population,\nb) formation at a redshift of 2 followed by passive evolution,\nand \nc) as for b) but with a formation redshift of 5.\n%\n\\par\n\\end{minipage}\n%\n\\end{center}\n\\vspace{3mm}\n\n%%\\begin{figure*}[b]\n%%\\plotfiddle{fig4.eps}{2in}{-90}{32}{32}{-120}{180}\n%%\\caption[fig4.eps]{\n%%Residuals about the $\\zf=5$ model for the X-ray selected BCG sample.\n%%Filled and open symbols indicate BCGs in high- and low-\\lx\\\n%%clusters respectively.\n%%The lines show the expected locus of the residuals for the three\n%%models shown in Figure~\\ref{fig:z-mk}.\n%%\\label{fig:lz-dmk}}\n%%\\end{figure*}\n\n\\vspace{2mm}\n\\begin{center}\n%\n%\\plotfiddle{fig4.eps}{2in}{-90}{32}{32}{-120}{180}\n\\plotfiddle{fig4.eps}{2.1in}{-90}{32}{32}{-120}{190}\n%\n\\begin{minipage}{8.75cm}\n\\small\\parindent=3.5mm\n{\\sc Fig.}~4.---Residuals about the $\\zf=5$ model for the X-ray selected BCG sample.\nFilled and open symbols indicate BCGs in high- and low-\\lx\\\nclusters respectively.\nThe lines show the expected locus of the residuals for the three\nmodels shown in Figure~2.\n%\n\\par\n\\end{minipage}\n%\n\\end{center}\n\\vspace{3mm}\n\nTo quantify the amount of evolution allowed by the data, the same\nparametric form as employed by\n\\abkmain---namely $M(z) = M(0) \\times (1+z)^\\gamma$---was used to estimate \nthe growth in the stellar mass content of BCGs. \nFitting for both $\\gamma$ and $M(0)$ indicates that, in the\nhigh-\\lx\\ sample \n(which best approximates the cluster selection adopted for\nthe \\semianalytic\\ models), \nthe typical BCG mass has increased by a factor\nof $1.9\\pm0.3$ (for $\\zf=2$) or $1.3\\pm0.2$ ($\\zf=5$) \nbetween $z=1$ and the present.\nThese growth factors are substantially lower than either \nthe factor of $\\sim$4--5 predicted by the \\semianalytic\\ models,\nor the measured values of 4.6 ($\\zf=2$) and 3.2 ($\\zf=5$),\nof \\abkmain.\nThe growth factor can also be estimated by fitting for $\\gamma$ alone if one\nassumes a low-redshift normalisation for the model predictions.\nHowever, this currently involves applying a \\colour-correction\nto low-redshift optical BCG data,\nwhich introduces further uncertainty: \napplying a single $R-K$ correction to the \\xray-selected\nsample of \\lynam\\ changes the measured growth factor \nof the high-\\lx\\ sample by less than 20\\%,\nwhilst using the normalisation adopted by \\abkmain---based\non an optically-selected sample---increases the\ngrowth factor by 50\\%.\nK-band observations of the \\lynam\\ \nsample are being obtained to circumvent this problem in future\nwork.\n\n\\section{CONCLUSION}\n\\label{conclusion}\n\nThe K-band luminosities of BCGs are correlated with their environment:\nclusters with a high \\xray\\ luminosity contain\nBCGs which are brighter, and have a smaller scatter, \nthan those BCGs in clusters with a low \\xray\\ luminosity.\nThe BCG evolution seen by \\abkmain\\ has been shown to be\nan artifact of a selection bias in their cluster sample;\nat high redshifts, their clusters are systematically less \\xray\\ luminous\nthan their low-redshift \nsample, and so their BCGs are systematically fainter.\n\nUnder the assumption of an Einstein-de Sitter universe,\nnon-parametric tests show that the only significant evidence for\nBCG mass evolution over the range $0.05 \\leq z \\leq 0.83$\noccurs when the dominant stellar population formed\nrelatively recently ($\\zf \\leq 2.6$).\nUsing the same parametric form as \\abkmain, the masses of BCGs \nin high-\\lx\\ clusters are found to have, at most, doubled since $z=1$,\ncompared to the factor of $\\sim 4$ increase predicted, for BCGs in\nmassive clusters, by the \\semianalytic\\ models discussed\nby \\abkmain.\n\n\\acknowledgements\n\nDJB acknowledges support from PPARC grant \nGR/L21402\nand SAO contract SV4-64008\nand RGM that from \nPPARC at Imperial College and Edinburgh.\nDJB would like to thank\nPeter Draper, Tim Hawarden, and Sandy Leggett for useful discussions.\nWe thank the referee, Alfonso Arag\\'{o}n-Salamanca, for\nuseful comments that improved the paper,\nthe service \\programmes\\ of both UKIRT and IRTF for obtaining\nsome of the data presented here,\nand Piero Rosati and collaborators for providing aperture\nmagnitudes for the two Lynx clusters.\nThe United Kingdom Infrared Telescope is operated by the \nJoint Astronomy Centre on behalf of the U.K. Particle Physics and \nAstronomy Research Council.\n\n%%\\clearpage\n\n\\begin{references}\n%%\n\\reference{abk98}\nArag\\'{o}n-Salamanca, A., Baugh, C. M., \\& Kauffmann, G. 1998, \\mnras, 297, 427 (ABK98)\n%%\n\\reference{aecc93}\nArag\\'{o}n-Salamanca, A., Ellis, R. S., Couch, W. J., Carter, D. 1993, \\mnras, 262, 764\n%%\n\\reference{bcf96}\nBaugh, C. M., Cole, S., \\& Frenk, C. S. 1996, \\mnras, 282, L27\n%%\n\\reference{bershady95}\nBershady, M. A. 1995, \\aj, 109, 87\n%%\n\\reference{bc}\nBruzual A., G. \\& Charlot, S. 1993, \\apj, 405, 538 \n%%\n\\reference{b97}\nBurke, D. J., Collins, C. A., Sharples, R. M., Romer, A. K., Holden, B. P.,\n\\& Nichol, R. C. 1997, \\apjl, 488, L83\n%%\n\\reference{cm98}\nCollins, C. A., \\& Mann, R. G. 1998, \\mnras, 297, 128 (CM98)\n%%\n\\reference{ukirt-fs}\nCasali, M. M., \\& Hawarden, T. G. 1992, \nThe JCMT-UKIRT Newsletter, No. 3, 33\n%%\n\\reference{castander94}\nCastander, F. J., Ellis, R. S., Frenk, C. S., Dressler, A., \n\\& Gunn, J. E. 1994, \\apjl, 424, L79 \n%%\n\\reference{depropris99}\nDe Propris, R., Stanford, S. A., Eisenhardt, P. R., Dickinson, M.,\n\\& Elston, R. 1999, \\aj, 118, 719\n%%\n\\reference{dressler78}\nDressler, A. 1978, \\apj, 222, 23\n%%\n\\reference{els62}\nEggen, O. J., Lynden-Bell, D., \\& Sandage, A. R. 1962, \\apj, 136, 748\n%%\n\\reference{ellis97}\nEllis, R.S., Smail, I., Dressler, A., Couch, W.J., Oemler, A., Butcher, H., \\&\nSharples, R.M., 1997, \\apj, 483, 582\n%%\n\\reference{gl-94}\nGioia, I. M., \\& Luppino, G. A. 1994, \\apjs, 94, 583\n%%\n\\reference{hall98}\nHall, P. B., Green, R. F., \\& Cohen, M. 1998, \\apjs, 119, 1 \n%%\n\\reference{h97}\nHenry, J. P., et al. 1997, \\aj, 114, 1293 \n%%\n\\reference{h99}\nHenry, J. P. 1999, \\apj, submitted\n%%\n\\reference{holden97}\nHolden, B. P., Romer, A. K., Nichol, R. C., \\& Ulmer, M. P. 1997, \\aj, 114, 1701 \n%%\n\\reference{jimenez99}\nJimenez, R., Friaca, A., Dunlop, J., Terlevich, R., Peacock, J.,\n\\& Nolan, L. 1999, \\mnras, 305, L16\n%%\n\\reference{kc98}\nKauffmann, G., \\& Charlot, S. 1998, \\mnras, 294, 705\n%%\n\\reference{kw93}\nKauffmann, G., \\& White, S. D. M. 1993, \\mnras, 264, 201\n%%\n\\reference{larson69}\nLarson, R. B. 1969, \\mnras, 145, 405\n%%\n\\reference{pdl99}\nLynam, P. D., Collins, C. A., James, P. A., B\\\"{o}hringer, H., \\&\nNeumann, D. M. 1999, preprint (astro-ph/9908348)\n%%\n\\reference{madau98}\nMadau, P., Pozzetti, L., \\& Dickinson, M. E. 1998, \\apj, 498, 106\n%%\n\\reference{n97}\nNichol, R. C., Holden, B. P., Romer, A. K., Ulmer, M. P.,\nBurke, D. J., \\& Collins, C. A. 1997, \\apj, 481, 644\n%%\n\\reference{opl98}\nOke, J. B., Postman, M., \\& Lubin, L. M. 1998, \\aj, 116, 549 \n%%\n\\reference{morphs99}\nPoggianti, B. M., Smail, I., Dressler, A., Couch, W. J., Barger, A. J., \nButcher, H., Ellis, R. S., \\& Oemler, A., Jr. 1999, \\apj, 518, 576 \n%%\n\\reference{bsharc}\nRomer, A. K., et al. 2000, \\apjs, in print\n%%\n\\reference{rosati99}\nRosati, P., Stanford, S. A., Eisenhardt, P. R., Elston, R., Spinrad, H., \nStern, D., \\& Dey, A. 1999, \\aj, 118, 76 \n%%\n\\reference{schlegel98}\nSchlegel, D., Finkbeiner, D., \\& Davis, M. 1998, \\apj, 500, 525\n%%\n\\reference{sed95}\nStanford, S. A., Eisenhardt, P. R., \\& Dickinson, M. 1995, \\apj, 450, 512 \n%%\t\t\t\t\t\t \n\\reference{sed98}\t\t\t\t \nStanford, S. A., Eisenhardt, P. R., \\& Dickinson, M. 1998, \\apj, 492, 461\n%%\n\\reference{tb94}\nThimm, G. J., \\& Belloni, P. 1994, \\aap, 289, L27 \n%%\n\\reference{v96}\nvan Dokkum, P. G., \\& Franx, M., 1996, \\mnras, 281, 985\n%%\n\\reference{vf98}\nvan Dokkum, P. G., Franx, M., Kelson, D. D., \\& Illingworth, G. D. 1998,\n\\apjl, 504, L17\n%%\n\\reference{v99}\nvan Dokkum, P. G., Franx, M., Fabricant, D., Kelson, D. D., \\& Illingworth, G. D. 1999,\n\\apjl, 520, L95\n%%\n\\end{references}\n\n\\end{document}\n"
}
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astro-ph0002186
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The Extreme Compact Starburst in MRK 273
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"author": "C.L. Carilli and G.B. Taylor"
}
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Images of neutral Hydrogen 21cm absorption and radio continuum emission at 1.4 GHz from Mrk 273 were made using the Very Long Baseline Array and Very Large Array. These images reveal a gas disk associated with the northern nuclear region with a diameter of 0.5$''$ (370 pc), at an inclination angle of 53$^o$. The radio continuum emission is composed of a diffuse component plus a number of compact sources. This morphology resembles those of nearby, lower luminosity starburst galaxies. These images provide strong support for the hypothesis that the luminosity of the northern source is dominated by an extreme compact starburst. The HI 21cm absorption shows an east-west gradient in velocity of 450 km s$^{-1}$ across 0.3$''$ (220 pc), implying an enclosed mass of 2$\times$10$^{9}$ M$_\odot$, comparable to the molecular gas mass. The brightest of the compact sources may indicate radio emission from an active nucleus (AGN), but this source contributes only 3.8$\%$ to the total flux density of the northern nuclear region. The HI 21cm absorption toward the southeast radio nucleus suggests infall at 200 km s$^{-1}$ on scales $\le$ 40 pc, and the southwest near IR nucleus is not detected in high resolution radio continuum images.
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{
"name": "MRK273.tex",
"string": "% SAMPLE2.TEX -- AASTeX macro package tutorial paper.\n \n\\documentstyle[12pt,aasms4,psfig]{article}\n \n\\slugcomment{to appear in Astrophysical Journal (letters)}\n \n\\begin{document}\n\n\\title{The Extreme Compact Starburst in MRK 273}\n \n\\author{C.L. Carilli and G.B. Taylor}\n\\affil{NRAO, P.O. Box O, Socorro, NM, 87801, USA \\\\}\n\\authoremail{ccarilli@nrao.edu}\n \n\\begin{abstract}\n\nImages of neutral Hydrogen 21cm absorption and radio continuum\nemission at 1.4 GHz from Mrk 273 were made using the Very Long\nBaseline Array and Very Large Array. These images reveal a gas disk\nassociated with the northern nuclear region with a diameter of 0.5$''$\n(370 pc), at an inclination angle of 53$^o$. The radio continuum\nemission is composed of a diffuse component plus a number of compact\nsources. This morphology resembles those of nearby, lower luminosity\nstarburst galaxies. These images provide strong support for the\nhypothesis that the luminosity of the northern source is dominated by\nan extreme compact starburst. The HI 21cm absorption shows an\neast-west gradient in velocity of 450 km s$^{-1}$ across 0.3$''$ (220\npc), implying an enclosed mass of 2$\\times$10$^{9}$ M$_\\odot$,\ncomparable to the molecular gas mass. The brightest of the compact\nsources may indicate radio emission from an active nucleus (AGN), but\nthis source contributes only 3.8$\\%$ to the total flux density of the\nnorthern nuclear region. The HI 21cm absorption toward the \nsoutheast radio\nnucleus suggests infall at 200 km s$^{-1}$ on scales\n$\\le$ 40 pc, and the southwest near IR nucleus is not detected in high\nresolution radio continuum images. \n\n\\end{abstract}\n \n\\keywords{ galaxies:starburst, \nseyferts, active, ISM, individual:Mrk 273 - quasars:absorption lines -\nradio lines: galaxies - supernovae} \n\n\\section {Introduction}\n\nLuminous infrared galaxies are the most numerous sources\nwith luminosities $\\ge$ 10$^{11}$ L$_\\odot$ in the nearby \nuniverse (Sanders and Mirabel 1996). The bulk of\nthe luminosity from these sources is infrared emission from warm dust.\nA critical question concerning\nthese sources is whether the dust is heated by an active nucleus, or \na starburst? Recent studies using near IR spectroscopy suggest that\nthe dominant dust heating mechanism in most luminous infrared galaxies\n(80$\\%$) is star formation (Genzel et al. 1998), although AGN heating\nmay become significant \nfor the highest luminosity sources\n($\\ge$ 10$^{12.3}$ L$_\\odot$;\nVeilleux et al. 1999). \nThis question has taken on new significance \ndue to the recent discovery of a population of luminous infrared galaxies\nat high redshift seen in deep sub-millimeter and millimeter imaging\nsurveys. If these high $z$ sources are starbursts, then they may\ndominate the \ncosmic star formation rate at $z > 2$ (Smail, Ivison, and Blain 1997, \nBarger et al. 1998, Hughes et al. 1998, Blain et\nal. 1999, Eales et al. 1999, Bertoldi et\nal. 1999).\n\nThe most direct evidence to date of a dominant starburst in \na luminous infrared galaxy is the discovery of a population of radio\nsupernovae in the nuclear regions of Arp 220 by Smith et al. (1998)\nusing high resolution imaging at 1.4 GHz. \nRadio observations are unique \nin this regard, since they are unobscured by dust and\nallow for imaging with mas resolution. We have begun a program of\nimaging the radio continuum emission and HI 21cm absorption in\nluminous infrared galaxies using the Very Long Baseline Array and \nthe Very Large Array at resolutions ranging from 1 to\n100 mas. Results on the Seyfert 1 galaxy Mrk 231\nhave been presented in Carilli, Wrobel, and Ulvestad (1998), \nTaylor et al. (1999), and Ulvestad, Carilli, and Wrobel (1998). \nThose data revealed the presence of an AGN driven\nradio-jet source on pc-scales at the center of \na (possibly star forming)\ngas disk with a diameter of a few hundred pc, \nwith about half the radio continuum emission coming from\nthe disk. \n\nIn this letter we present the results on Mrk 273 at z = 0.0377.\nMrk 273 has an infrared luminosity of $\\rm L_{FIR} = 1.3\n\\times 10^{12} L_\\odot$ (as defined in Condon 1992), where we assume \nH$_o$ = 75 km s$^{-1}$ Mpc$^{-1}$. The optical galaxy has been\nclassifed as a Seyfert 2, LINER, and both (Baan et al. 1998, \nColina, Arribas, and Borne 1999, Goldader et al. 1995), and it has a disturbed\nmorphology on kpc-scales, with \ntidal tails indicating a merger event within the last 10$^{8}$ years\n(Knapen et al. 1998). Near IR spectroscopy reveals strong PAH\nfeatures indicative of a starburst, but also high ionization lines\nindicative of an AGN (Genzel et al. 1998, Lutz et al. 1998). The\nX-ray emission also presents a mixed picture, with evidence for a\nhighly absorbed hard component,\nbut possible Fe L emission at 0.8 keV indicating cool (0.4 keV) gas\n(Iwasawa 1999). Broad absorption in the HI 21cm line and OH megamaser\nemission have also been detected in Mrk 273 (Baan, Haschick, and \nSchmelz 1985, Schmelz, Baan, and Haschick 1988).\n\nThe nuclear regions in Mrk 273 on sub-arcsecond scales are complex,\nwith a double nucleus on a scale of 2$''$ seen in the near IR\n(Knapen et al. 1998, Majewski et al. 1993, Armus et al. 1990), \nand in the radio continuum\n(Ulvestad and Wilson 1984, Condon et al. 1991, Knapen et\nal. 1998, Coles et al. 1999). The most peculiar aspect of \nMrk 273 is that only one of the nuclei (the northern source) is seen\nin both the radio continuum and the near IR. The southeast nucleus is\ndetected in the radio continuum, but is very faint in the near IR,\nalthough there may be a faint blue `star cluster' at this position\n(Scoville et al. 2000). The southwest nucleus is seen in the near IR,\nbut shows only very weak, extended radio continuum emission (Knapen et\nal. 1998). High resolution near IR imaging with the HST shows that\nboth the north and southwest IR peaks \nare redder than the surrounding galaxy, and that\nthe northern nucleus is redder than the southwestern nucleus (Scoville et \nal. 2000). \n\nImaging of CO emission from Mrk 273 shows a peak at the northern\nnucleus, with faint extended emission on scales of a few arcseconds\n(Downes and Solomon 1998). Downes and Solomon derive a molecular gas\nmass of $1 \\times 10^{9}$ M$_\\odot$ for the northern nucleus, and find\nthat the CO is most likely in a disk with size $< 0.6''$. From these\ndata they conclude that the northern nucleus of Mrk 273 is an\nextreme compact starburst, with an IR\nluminosity of $6 \\times 10^{11}$ L$_\\odot$ emitted from a region $<$\n400 pc in diameter. This conclusion is supported by the \n0.2$''$ resolution images of the HI 21cm absorption presented in Coles et\nal. (1999), which reveal a velocity \ngradient along the major axis of the northern nucleus.\n\nIn this letter we present high resolution\nimaging (10 mas to 50 mas) of the HI 21cm absorption\nand radio continuum emission from Mrk 273. These data\nconfirm the existence of a rotating gas disk with a diameter of\n350 pc, and reveal a population of compact sources,\npossibly composed of luminous radio supernovae and/or nested radio\nsupernova remnants.\n\n\\section{Observations}\n\nObservations of Mrk 273 were made on May 31 and June 6, 1999 \nwith the Very Long Baseline Array (VLBA), including the\nphased Very Large Array (VLA) as an\nelement in the very long baseline array. The pass band was \ncentered at the frequency of the neutral hydrogen 21cm line \nat a heliocentric redshift of: z = 0.0377, or cz = 11300 km\ns$^{-1}$. The total bandwidth was 16 MHz, using two orthogonal\npolarizations, 256 spectral channels, and 2 bit correlation.\nThe total on-source observing time was 13.4 hrs.\n\nData reduction was performed using the Astronomical Image Processing\nSystem (AIPS) and AIPS++. Standard {\\sl a priori} gain calibration\nwas performed using the measured gains and system temperatures of each\nantenna. The compact radio source J1337+550 was observed every 5 minutes,\nand this source was used to determine the initial fringe rates and\ndelays. The source 3C 345 was used to calibrate the\nfrequency dependent gains (band pass calibration). The source J1400+621\nwas used to check the absolute gain calibration. \nThe results showed agreement of observed and\nexpected flux densities to within 3$\\%$.\n\nAfter application of the delay and rate solutions, and band pass\ncalibration, a continuum data set for Mrk 273 was generated by\naveraging off-line channels. This continuum data set was then used for\nthe hybrid imaging process, which involves iterative imaging and\nself-calibration of the antenna-based complex gains (Walker 1985). The\nfinal iteration involved both phase and amplitude calibration with a 3\nminute averaging time for phases and 15 minutes for amplitudes. The\nself-calibration solutions were applied to the spectral line data\nset. The spectral line data were then analyzed at various spatial and\nspectral resolutions by tapering the visibility data, and by smoothing\nin frequency. The continuum emission was subtracted from the spectral\nline visibility data using UVLIN. Images of the line and continuum\ndata were deconvolved using the Clark `CLEAN' algorithm as implemented\nin IMAGR. For the radio continuum images we also employed the\nmulti-resolution CLEAN algorithm as implemented in AIPS++ (Holdaway\nand Cornwell 1999). Results were consistent for all image\nreconstruction algorithms, and we present the naturally weighted\nClark CLEAN continuum images in the analysis below.\nThe full resolution of the naturally weighted images is \n10 mas. We also present images at 50 mas resolution made using\na Gaussian taper of the visibilities. \n\n\\section{Results and Analysis}\n\nThe 1.368 GHz continuum image of Mrk 273 at 50 mas resolution is displayed in\nFigure 1. The image shows that the northern nucleus is \nextended, with a major axis of 0.5$''$ and a minor axis of\n0.3$''$. The region shows two peaks separated by 0.11$''$. \nWe designate the western peak N1 and the eastern peak N2.\nThese two peaks can also be seen in near IR images of Mrk 273\n(Knapen et al. 1998). \nThe total flux density from this region is 86$\\pm$9 mJy.\nThe southeastern source, which we designate SE, \nis also extended over about 0.3$''$, \nwith a total flux density of 40$\\pm$4 mJy. \n\nFigure 2 shows the 1.368 GHz\ncontinuum images of the northern and southeastern \nnuclei of Mrk 273 at 10 mas resolution. The northern source\nis highly resolved, consisting of a diffuse component extending over\n0.5$''$, punctuated by a number of compact sources. Table 1 lists the\npositions and surface brightnesses\nat 10 mas resolution of the six sources with surface brightnesses\n$\\ge$ 0.5 mJy beam$^{-1}$. \nPositions are relative to the peak surface brightness, corresponding\nto N1. The nominal position of N1 in Figure 2 is (J2000):\n$13^h 44^m 42.119^s$, $55^o 53' 13.48''$, based on \nphase-referencing observations using the celestial calibrator \nJ1337+550 with a 5 minute cycle time. Note that the minimum error in\nthe absolute astrometry is 12 mas, as set by the uncertainty in the \ncalibrator source position (see Wilkinson et al. 1998 \nand references therein). The true error after phase transfer is likely \nto be significantly higher than this (Fomalont 1995, Beasley and\nConway 1995).\n\nGiven the incomplete Fourier spacing \ncoverage for VLBI imaging, in particular for short spacings, \nit is possible that the CLEAN algorithm has generated spurious\npoint sources when trying to deconvolve extended emission \nregions. Conversely, we cannot rule-out the possibility that\nthe extended emission is composed \nof mostly faint point sources. The use of multiresolution CLEAN\nmitigates these problems, and the sources listed in Table 1\nall reproduce with essentially the same surface brightnesses\nfor images made with the Clark CLEAN, multi-resolution CLEAN,\nand for images made with different visibility weighting schemes.\nThe brightness temperatures of these sources\nare all $\\ge 3 \\times 10^6$ K, indicating non-thermal emission. \nThe southeastern nucleus is also resolved, with high surface brightness \nemission occuring over a scale of 50 mas. \nWe set a 4$\\sigma$ limit of 0.14 mJy\nto any compact radio source associated with the southwestern\npeak (large cross in Figure 1) seen at near IR wavelengths \n(Knapen et al. 1998).\n\nSpectra of the HI 21cm absorption toward SE, and N1 and N2,\nat 50 mas resolution\nare shown in Figure 3. The spectrum of SE shows\na double peaked profile, with the two lines separated by \n400 km s$^{-1}$, each with a Full Width at Half Maximum (FWHM)\nof about 280 km s$^{-1}$. \nThere is marginal evidence that each component has\nvelocity sub-structure, but the SNR of these data are insufficient\nto make a firm conclusion on this point. \nThe peak optical depth of each line is about 0.12$\\pm$0.02, and the \nimplied HI column density in each component is then: N(HI) = \n6.4$\\pm$1.1 $\\times$10$^{19}$ $\\times$ $T_s$ cm$^{-2}$, \nwhere $T_s$ is the HI spin temperature in K.\n\nAn interesting comparison is made with the MERLIN absorption spectra\nat 0.2$''$ resolution toward the SE component (Coles et al. 1999).\nAt this resolution, MERLIN detects 19 mJy of continuum emission, and\nshows a 3 mJy absorption line at about 11200 km s$^{-1}$, and weaker\nabsorption of about 1 mJy at 11400 km s$^{-1}$. The VLBA data\nshow a peak continuum surface brightness of 10 mJy beam$^{-1}$ at 50 mas\nresolution, and absorption line depths of \n1 mJy at both velocities. This suggests that the\nabsorption at 11200 km s$^{-1}$ is due to extended gas covering \nboth the compact and extended continuum emitting regions, while the 11400\nkm s$^{-1}$ absorption is due to a small cloud ($\\le$ 40 pc) covering\nonly the high surface brightness continuum emission. Assuming 11200 km\ns$^{-1}$ indicates the systemic velocity of the gas at that \nlocation in the galaxy disk (Coles et al. 1999),\nthen the higher velocity system would be infalling at 200 km\ns$^{-1}$.\n\nThe spectrum of N2 shows a relatively narrow absorption line, with a\nFWHM = 160 km s$^{-1}$, a peak optical depth of 0.59$\\pm$0.06, and an\nHI column density of $1.8\\pm0.2 \\times 10^{20}$ $\\times$ $T_s$\ncm$^{-2}$. The spectrum of N1 shows a broad, flat absorption profile\nwith FWHM = 540 km s$^{-1}$, with optical depths ranging from\n0.1 and 0.4$\\pm$0.04 across the line profile. \nAgain, there is marginal evidence for a few\nnarrower, higher optical depth components. The total HI column density is\n$1.8 \\pm 0.3 \\times 10^{20} \\times T_s$ cm$^{-2}$. The velocity\nrange of the HI absorption toward N1 is comparable to that seen for\nthe OH megamaser emission (Baan, Haschick, and Schmeltz 1985,\nStavely-Smith et al. 1987).\n\nFigure 4 shows the position-velocity (P-V) diagram for the HI 21cm\nabsorption along the major axis of the northern nucleus. There is a\nvelocity gradient from east to west of about 450 km s$^{-1}$ across\n300 mas, plus an apparent flattening of the velocity distribution to\nlarger radii. The P-V distribution is confused somewhat by the broad\nabsorption seen toward N1 (at position --90 mas in Figure 4). The\neast-west velocity gradient of the HI absorption across the northern\nsource is consistent with results from MERLIN HI 21cm \nimaging at 0.2$''$ resolution (Coles et al. 1999), and\nwith the velocity field derived from CO emission\nobservations at 0.6$''$ resolution (Downes and Solomon 1998).\n\n\\section{Discussion}\n\nThe most significant result from our high resolution radio continuum\nimaging of Mrk 273 is that the emission from the\nnorthern nucleus extends over a region of $0.3'' \\times 0.5''$\n(220$\\times$370 pc), punctuated by a number of compact sources with\nflux densities between 0.5 and 3 mJy. This morphology resembles those\nof the starburst nuclei of NGC 253 and M82 (Ulvestad and Antonnuci\n1997, Muxlow et al. 1994), on a similar spatial scale. However, the\ntotal radio luminosity is an order magnitude larger in Mrk 273. The\nphysical conditions in this region are extreme, with a minimum\npressure of 10$^{-9}$ dynes cm$^{-2}$, and corresponding magnetic\nfields of 100 $\\mu$G.\n\nThe 1.4 GHz radio continuum emission from nuclear starburst galaxies\nis thought to be primarily synchrotron radiation from relativistic\nelectrons spiraling in interstellar magnetic fields, with the\nelectrons being accelerated in supernova remnant shocks (Condon 1992,\nDuric 1988). The compact sources are then individual supernovae or\nsupernova remnants, while the diffuse emission is thought to be from\nelectrons that have diffused away from the supernova remnant\nshocks. Our high resolution images provide strong support for the\nhypothesis of Downes and Solomon (1998) that the northern nucleus of\nMrk 273 is an extreme compact starburst, with a massive star formation\nrate of 60 M$_\\odot$ year$^{-1}$, as derived from the radio continuum\nluminosity (Condon 1992), and occuring in a region of only 370 pc\ndiameter. From their detailed analysis of the CO emission from Mrk\n273, Downes and Solomon (1998) propose that the star formation occurs\nin a disk with scale height of 21 pc and a total gas mass of $1 \\times\n10^9$ M$_\\odot$.\n\nThe nature of the weak, compact radio continuum sources in Mrk 273 is\nnot clear, but given the similarity in morphology with the starburst\nnuclei in M82 and NGC 253, it is likely that these sources are a\ncombination of nested supernova remnants and/or luminous radio\nsupernovae. These sources have radio spectral luminosities $\\ge\n10^{28}$ ergs s$^{-1}$ Hz$^{-1}$ at 1.4 GHz, which is an order of\nmagnitude higher than the brightest radio supernovae remnants seen in\nM82 (Muxlow et al. 1994), and are comparable in luminousity to the\nrare class of extreme luminosity radio supernovae characterized by SNe\n1986J (Rupen et al. 1987) and 1979C (Weiler and Sramek 1988). A\nsubstantial population of such luminous supernovae has been discovered\nin the starburst nucleus of Arp 220 by Smith et al. (1998), who\nsuggest that the high luminosities of those supernovae may indicate a\ndenser local environment relative to typical supernovae, by a factor 3\nor so (Chevalier 1984). If the compact sources in Mrk 273 are nested\nsupernova remnants, then it would require 10 or more of the most\nluminous M82-type supernova remnants in regions less than 7 pc in\nsize. Future high resolution imaging of Mrk 273 is required to\nclarify the nature of these compact sources.\n \n%Smith et al. derive a star formation rate for Arp 220 from the\n%number of observed supernovae, assuming a nominal 1/e lifetime of\n%10 years for the sources, and assuming that the only supernovae\n%that exist are the luminous ones. \n\nIt is possible that the brightest of the compact sources, coincident \nwith N1, indicates the presence of a weak radio AGN. Supporting evidence\nfor this conclusion is the broad HI absorption line observed toward\nN1. This component contributes only 3.8$\\%$ to the total \nradio luminosity at 1.4 GHz of the northern nuclear regions. \n\nFrom flattening of the radio spectrum between 1.6 and 5 GHz, Knapen et\nal. (1998) suggested that there may be a dominant, synchrotron\nself-absorbed radio-loud AGN in the northern nucleus of Mrk 273. The\nimages presented herein clearly preclude this hypothesis. We feel a\nmore likely explanation for the low frequency flattening is free-free\nabsorption. We are currently analyzing images with\nsub-arcsecond resolution between 327 MHz and 22 GHz in order to\ndetermine the origin of this low frequency flattening.\n\nThe gas disk hypothesis for the northern nucleus of Mrk 273 is\nsupported by the observed velocity gradient in the HI 21cm absorption\nalong the major axis. The rotational velocity at a radius of 220 pc\nis 280 km s$^{-1}$, assuming an inclination angle of 53$^o$. Assuming\nKeplerian rotation, the enclosed mass inside this radius is then\n2$\\times$10$^{9}$ M$_\\odot$, comparable to the molecular\ngas mass observed on this scale.\n\nOverall, these data support the idea that the dominant energy source\nin the northern nuclear region\nin Mrk 273 is a starburst and not an AGN.\nHowever, the presence of an AGN somewhere in the inner 2$''$\nof Mrk 273 is still suggested, based on \nthe high ionization near IR lines (Genzel et al. 1998),\nthe (possible) hard X-ray component (Iwasawa 1999), and\nthe Seyfert II optical spectrum, although Condon et al. (1991)\nargue that a Seyfert II spectrum is not necessarily a conclusive AGN\nindicator. It is possible that the AGN\nis located at either the SE radio nucleus, or the SW near IR\nnucleus. \n\nThe SE radio nucleus presents a number of peculiarities, the\nmost important of which is the weakness of the near IR emission\n(Knapen et al. 1998, Scoville et al. 2000). Knapen et al. (1998)\nsuggested that this source may simply be the chance projection of a\nbackground radio source. However, the probability of a chance\nprojection of a 40 mJy source within 1$''$ of the northern nucleus is\nonly $4\\times10^{-7}$ (Langston et al. 1990, Richards et al. 1999).\nThis low probability, and the fact that we see evidence for gas infall\ninto the SE nucleus in the HI 21cm absorption images, \neffectively preclude the background source\nhypothesis. The radio morphology is consistent with an amorphous jet,\nor a very compact starburst, although the lack of CO emission from\nthis region argues for an AGN. \nOne possible cause for the lack of\nnear IR emission is that the active region is still obscured at 2.2\n$\\mu$m. The HI 21cm absorption column density is \n6.4$\\pm$1.1 $\\times$10$^{22}$ $\\times$ ($\\rm {T_s}\\over{10^3 K}$) cm$^{-2}$,\nwhile the absorption column derived from \nthe hard X-ray spectrum may be as large as $4 \\times\n10^{23}$ cm$^{-2}$, depending on the X-ray powerlaw index.\nUsing the HI 21cm column leads to A$_v$ = \n$40 \\times ({\\rm {T_s}\\over{10^3 K}})$, assuming a Galactic\ndust-to-gas \nratio. This is comparable the extinction responsible for the\nobscuration in the near IR of the AGN in the powerful radio galaxy\nCygnus A (Ward 1996). Imaging at wavelengths of \n10 $\\mu$m or longer, with\nsub-arcsecond resolution, is required to address this interesting\nquestion.\n\nWe do not detect any high surface brightness radio emission associated\nwith the SW near IR nucleus. This could simply mean that \nthis region harbours a radio quiet AGN.\nAn alternative posibility is that this is\na star forming region in which the \nstar formation is very recent, commencing less than\n10$^6$ years ago, such that a substantial population of radio \nsupernovae and supernova remnants have not yet had time to develop.\n\n\\vskip 0.2truein \n\nWe thank J. Wrobel, J. Ulvestad, and K. Menten for useful discussions\nand comments. \nThis research made use of the NASA/IPAC Extragalactic Data Base (NED)\nwhich is operated by the Jet propulsion Lab, Caltech, under contract\nwith NASA. The VLA and VLBA are operated by the \nNational Radio Astronomy Observatory, which is a facility of\nthe National Science Foundation operated under cooperative \nagreement by Associated Universities, Inc. CLC acknowledges support from\nthe Alexander von Humboldt Society, and the Max Planck Institute for\nRadio Astronomy.\n\n\\newpage\n\n\\centerline{\\bf References}\n\nArmus, L., Heckman, T.M., and Miley, G.K. 1990,\nApJ, 364, 471\n\nBaan, W.A., Haschick, A.D., and Schmelz, J.T\n1985, ApJ (letters), 298, 51\n\nBaan, W.A., Salzer, J.J., and Lewinter, R.D. 1998, ApJ, \n509, 633\n\nBeasley, A.J. and Conway, J.E. 1995, in {\\sl Very Long Baseline\nInterferometry}, eds. J. Zensus, P. Diamond, and P. Napier, p. 327\n\nBertoldi, F. et al. 1999, A\\&A (letters), in preparation\n\nBlain, A., Smail, I., Ivison, R.J., \\& Kneib,\nJ.-P. 1999, MNRAS, 302, 623\n\nChevalier, R.A. 1984, ApJ (letters), 285, 63\n\nColes, G.H., Pedlar, A., Holloway, A.J., and Mundell, C.G. 1999,\nMNRAS, 310, 1033\n\nColina, L., Arribas, S., and Borne, K.D. 1999, ApJ (letters), 527, 13\n\nCondon, J.J. 1992, ARAA, 30, 575\n\nCondon, J.J., Huang, Z.P., Yin, Q.F., and Thuan, T.X. 1991, ApJ 378, 65\n\nDownes, D. and Solomon, P. 1998, ApJ, 507, 615\n\nDuric, Neb 1988, Space Science Reviews, 48, 73\n\nIwasawa, K. 1999, MNRAS, 302, 961\n\nEales, S., et al. 1999, ApJ, 515, 518\n\nFomalont, E. 1995, in {\\sl Very Long Baseline\nInterferometry}, eds. J. Zensus, P. Diamond, and P. Napier, p. 363\n\nGenzel, R. et al. 1998, ApJ, 498, 579\n\nGoldader, J.D., Joseph, R.D., Doyon, R., and Sanders, D.B. 1995,\nApJ, 444, 97\n\nHoldaway, M. and Cornwell, T. 1999, in preparation\n\nHughes, D. et al. 1998, Nature, 394, 341\n\nKnapen, J.H. et al. 1998, ApJ (letters), 490, 29\n\nLangston, G.I., Conner, S.R., Heflin, M.B., Lehar, J., and Burke,\nB.F. 1990, ApJ, 353, 34\n\nLutz, D., Spoon, H.W., Rigopoulou, D., Moorwood, A.F., and Genzel, R. 1998,\nApJ (letters), 505, 103\n\nMajewski, S.R., Hereld, M., Koo, D.C., Illingworth, G.D., \nand Heckman, T.M. 1993, ApJ, 402, 125\n\nMuxlow, T.W., Pedlar, A., Wilkinson, P.N., Axon, D.J., Sanders,\nE.M., and de Bruyn, A.G. 1994, MNRAS, 266, 455\n\nRichards, E. 1999, ApJ, in press\n\nRupen, M.P., van Gorkom, J.H., Knapp, G.R., Gunn, J.E., and Schneider, D.P. \n1987, AJ, 94, 61\n\nSanders, D.B. and Mirabel, I.F. 1996, ARAA, 34, 749\n\nSchmelz, J.T., Baan, W.A., and Haschick, A.D. 1988, ApJ, 329, 142\n\nScoville, N.Z. et al. 2000, AJ, in press (astroph 9912246)\n\nSmail, I., Ivison, R., \\& Blain, A. 1997, ApJ\n(letters), 490, 5\n\nSmith, H.E., Lonsdale, C.J., Lonsdale, C.J., and Diamond, P.J. 1998,\nApJ (letters), 493, 17\n\nStavely-Smith, L., Cohen, R.J., Chapman, J.M., Pointon, L., \nand Unger, S.W. 1987, MNRAS, 226, 689\n\nTaylor, G.B., Silver, C.S., Ulvestad, J.S., and Carilli,\nC.L. 1999, ApJ, 519, 185\n\nUlvestad, J.S., Wrobel, J.M., and Carilli, C.L. 1999,\nApJ, 516, 127\n\nUlvestad, J.S. and Antonucci, R.J. 1997, ApJ, 488, 621\n\nUlvestad, J.S. and Wilson, A.S. 1984, ApJ, 278, 544\n\nVeilleux, S., Sanders, D.B., and Kim, D.-C. 1999, ApJ, 522, 113\n\nWalker, R.C. 1985, in {Aperture Synthesis in Radio Astronomy}, eds. \nR. Perley, F. Schwab, and A. Bridle (NRAO: Green Bank), p. 189\n\nWard, M.J. 1996, in {\\sl Cygnus A}, eds. C. Carilli and D. Harris,\n(Cambridge University Press), p. 43\n\nWeiler, K.W. and Sramek, R.A. 1988, ARAA, 26, 295\n\nWilkinson, P.N., Browne, I.W.A., Patnaik, A.R., Wrobel, J.M., and\nSorathia, B. 1998, MNRAS, 300, 790\n\n\\newpage\n\\begin{deluxetable}{cc}\n\\footnotesize\n\\tablecaption{Compact Sources in Mrk 273}\n\\tablewidth{0pt}\n\\tablehead{\n\\colhead{Surface Brightness} & \\colhead{Relative Position} \\nl\n\\colhead{mJy beam$^{-1}$} & \\colhead{mas} \\nl\n}\n\\startdata\n3.07 & 0 ~~~ 0 \\nl\n0.91 & 85E, 37N \\nl\n0.76 & 75E, 14N \\nl\n0.55 & 26E, 16S \\nl\n0.53 & 110E, 33N \\nl\n0.51 & 47W, 39S \\nl\n\\enddata\n\\end{deluxetable}\n\n\\newpage\n\n\\centerline{Figure Captions}\n\n\\noindent Figure 1 -- An image of Mrk 273 at 1.368 GHz at 50 mas \n(37 pc) resolution.The contour levels are \na geometric progression in the square root of\ntwo, hence every two contours implies a factor two rise in \nsurface brightness. The first contour level is 0.25 mJy beam$^{-1}$.\nThe peak surface brightness is 10 mJy beam$^{-1}$ and the off-source\nrms is 85$\\mu$Jy beam$^{-1}$. \nThe reference position (0,0) corresponds to (J2000):\n$13^h 44^m 42.142^s$, $55^o 53' 13.15''$, based on \nphase-referencing observations using the celestial calibrator \nJ1337+550 with a 5 minute cycle time. The cross in the SW corner\nindicates the position of the SW near IR nucleus. \n\n%The total flux density in the nortern source\n%is 86 mJy while that in the southeast source is 40 mJy.\n\n\\noindent Figure 2a -- An image of the northern nuclear regions of\nMrk 273 at 1.368 GHz at 10 mas (7.3 pc) resolution.\nThe contours are linear with an increment of 0.1 mJy beam$^{-1}$, \nstarting at 0.1 mJy beam$^{-1}$.\nThe peak surface brightness is 3.05 mJy beam$^{-1}$\nand the off-source rms is 36 $\\mu$Jy beam$^{-1}$. \n\n\\noindent Figure 2b -- The same as Figure 2A, but now for the \nsoutheastern nuclear regions. The peak surface brightness is \n1.35 mJy beam$^{-1}$.\n\n\\noindent Figure 3 -- The HI 21cm absorption spectra toward Mrk 273\nfrom images at 50 mas resolution. \nFigure 3a is the spectrum of N1. The peak surface brightness\nof 7.8 mJy beam$^{-1}$ has been subtracted.\nFigure 3b is the spectrum of N2. The peak surface brightness\nof 6.7 mJy beam$^{-1}$ has been subtracted.\nBoth these spectra have a velocity resolution of 29 km s$^{-1}$.\nFigure 3c is the spectrum of SE at\na velocity resolution of 58 km s$^{-1}$.\nThe peak surface brightness\nof 10 mJy beam$^{-1}$ has been subtracted. \nThe zero point on the velocity scale corresponds to \na heliocentric velocity of 11300 km s$^{-1}$ in all spectra.\n\n\\noindent Figure 4 -- The position-velocity plot for the HI 21cm absorption\nacross the major axis of the northern nucleus of Mrk 273 at a spatial\nresolution of 50 mas (37 pc) and a velocity resolution of 60 km s$^{-1}$. The\ncontour levels (in absoption) are: 0.4, 0.8, 1.2, 1.6, 2.0, 2.4, 2.8\nmJy beam$^{-1}$. The position of continuum component N1 corresponds\nto --90 mas, while N2 corresponds to +20 mas. The zero point on the\nvelocity scale corresponds to a heliocentric velocity of 11300 km\ns$^{-1}$ in all spectra.\n\n\\vfill\\eject \n\n\n% ADD FOR FIGURES ----------------\n\\begin{figure}\n\\psfig{figure=Fig1.ps,width=6in}\n\\caption{ }\n\\end{figure}\n\n\\vfill\\eject \n\n\\begin{figure}\n\\psfig{figure=Fig2a.ps,width=6in}\n\\caption{ }\n\\end{figure}\n\n\\vfill\\eject \n\n\\begin{figure}\n\\psfig{figure=Fig2b.ps,width=6in}\n\\end{figure}\n\n\\vfill\\eject \n\n\\begin{figure}\n\\psfig{figure=N1.PS,width=3in}\n%\\hspace*{0in}\n\\psfig{figure=N2.PS,width=3in}\n%\\hspace*{2in}\n\\psfig{figure=S1.PS,width=3in}\n\\caption{ }\n\\end{figure}\n\n\\vfill\\eject \n\n\\begin{figure}\n\\psfig{figure=Fig4.ps,width=6in}\n\\caption{ }\n\\end{figure}\n\n\\vfill\\eject \n\n\\end{document}\n\n\n\n%If the 5 compact sources are indeed\n%radio supernovae, then \n%assuming a $\\rm 1\\over e$ lifetime of 10 years for the \n%sources (Sramek and Weiler 1988), leads to \n%a lower limit to the supernovae\n%rate of order 0.5 year$^{-1}$. The implied lower limit to\n%the massive star formation rate is then ?? \n%limit to the massive star formation rate of\n%?? M$_\\odot$ year$^{-1}$ (Condon 1992). \n\n%From flattening of the radio spectrum between 1.6and 5 GHz, Knapen et\n%al. (1998) suggested that there may be a dominant, synchrotron\n%self-absorbed radio-loud AGN in the northern nucleus of Mrk 273. The\n%images presented herein clearly preclude this hypothesis. We feel a\n%more likely explanation for the low frequency flattening is free-free\n%absorption. The implied emission measure is then 5$\\times$10$^6$ pc\n%cm$^{-6}$, requiring a thermal electron density of 300 cm$^{-3}$ for\n%T$_e$ = 10$^4$ K and assuming a pathlength through the disk of 50\n%pc. The ionized gas pressure would then be 10$^{-9}$ dynes cm$^{-2}$,\n%which is comparable to the minimum energy pressure derived from the\n%radio sychrotron emission. We are currently analyzing images with\n%sub-arcsecond resolution between 327 MHz and 22 GHz in order to\n%determine the origin of this low frequency flattening.\n\n\n\n \n"
}
] |
[] |
astro-ph0002187
|
Eclipse maps of spiral shocks in the accretion disc of IP~Pegasi in outburst
|
[
{
"author": "Raymundo Baptista$^1$"
},
{
"author": "E. Harlaftis$^2$ and D. Steeghs$^{3,4}$"
},
{
"author": "$^1$ Departamento de F\\'\\i sica"
},
{
"author": "Universidade Federal de Santa Catarina"
},
{
"author": "Campus Trindade"
},
{
"author": "88040-900"
},
{
"author": "Florian\\'opolis - SC"
},
{
"author": "Brazil"
},
{
"author": "Observatory of Athens"
},
{
"author": "Lofos Koufou"
},
{
"author": "P.\\ Penteli"
},
{
"author": "Athens"
},
{
"author": "152 36"
},
{
"author": "Greece"
},
{
"author": "$^3$ School of Physics \\& Astronomy"
},
{
"author": "Andrews"
},
{
"author": "North Haugh"
},
{
"author": "St.\\"
},
{
"author": "Fife"
},
{
"author": "KY16 9SS"
},
{
"author": "Scotland"
},
{
"author": "$^4$ Physics \\& Astronomy"
},
{
"author": "Highfield"
},
{
"author": "Southampton"
},
{
"author": "SO17 1BJ"
},
{
"author": "UK"
}
] |
Eclipse lightcurves of the dwarf nova IP Peg during the November 1996 outburst are analysed with eclipse mapping techniques to constrain the location and investigate the spatial structure of the spiral shocks observed in the Doppler tomograms (Harlaftis et~al. 1999). Eclipse maps in the blue continuum and in the C\,III+N\,III $\lambda 4650$ emission line show two asymmetric arcs of $\sim 90$ degrees in azimuth and extending from intermediate to the outer disc regions ($R\simeq 0.2 - 0.6\; R_{L1}$, where $R_{L1}$ is the distance from disc centre to the inner Lagrangian point) which are interpreted as being the spiral shocks seen in the Doppler tomograms. The He\,II $\lambda 4686$ eclipse map also shows two asymmetric arcs diluted by a central brightness source. The central source probably corresponds to the low-velocity component seen in the Doppler tomogram and is understood in terms of gas outflow in a wind emanating from the inner parts of the disc. We estimate that the spirals contribute about 16 and 30 per cent of the total line flux, respectively, for the He\,II and C\,III+N\,III lines. Comparison between the Doppler and eclipse maps reveal that the Keplerian velocities derived from the radial position of the shocks are systematically larger than those inferred from the Doppler tomography indicating that the gas in the spiral shocks has sub-Keplerian velocities. We undertake simulations with the aim to investigate the effect of artifacts on the image reconstruction of the spiral structures.
|
[
{
"name": "ippeg.tex",
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Baptista et~al.]\n {Raymundo Baptista$^1$, E. Harlaftis$^2$ and D. Steeghs$^{3,4}$ \\\\\n $^1$ Departamento de F\\'\\i sica, Universidade Federal de Santa Catarina,\n Campus Trindade, 88040-900, Florian\\'opolis - SC, Brazil, \\\\\n ~ email: bap@fsc.ufsc.br \\\\\n $^2$ Astronomical Institute, Observatory of Athens, Lofos Koufou,\n P.\\ Penteli, Athens, 152 36, Greece, email: ehh@astro.noa.gr \\\\\n $^3$ School of Physics \\& Astronomy, University of St.\\,Andrews,\n North Haugh, St.\\,Andrews, Fife, KY16 9SS, Scotland \\\\\n $^4$ Physics \\& Astronomy, University of Southampton, Highfield,\n Southampton, SO17 1BJ, UK, email: ds@astro.soton.ac.uk }\n\\date{Accepted for publication at Monthly Notices of the Royal Astronomical\n\t\tSociety}\n\n\\pagerange{1--7}\n\\pubyear{2000}\n\n\\begin{document}\n\n\\label{firstpage}\n\n\\maketitle\n\n\\begin{abstract}\n\nEclipse lightcurves of the dwarf nova IP Peg during the November\n1996 outburst are analysed with eclipse mapping techniques to \nconstrain the location and investigate the spatial structure of the\nspiral shocks observed in the Doppler tomograms (Harlaftis et~al. 1999).\nEclipse maps in the blue continuum and in the C\\,III+N\\,III\n$\\lambda 4650$ emission line show two asymmetric arcs of $\\sim 90$\ndegrees in azimuth and extending from intermediate to the outer disc\nregions ($R\\simeq 0.2 - 0.6\\; R_{L1}$, where $R_{L1}$ is the distance\nfrom disc centre to the inner Lagrangian point) which are interpreted \nas being the spiral shocks seen in the Doppler tomograms.\nThe He\\,II $\\lambda 4686$ eclipse map also shows two asymmetric arcs\ndiluted by a central brightness source.\nThe central source probably corresponds to the low-velocity\ncomponent seen in the Doppler tomogram and is understood in terms\nof gas outflow in a wind emanating from the inner parts of the disc.\nWe estimate that the spirals contribute about 16 and 30 per cent of\nthe total line flux, respectively, for the He\\,II and C\\,III+N\\,III lines.\nComparison between the Doppler and eclipse maps reveal that the \nKeplerian velocities derived from the radial position of the shocks are systematically larger than those inferred from the Doppler tomography\nindicating that the gas in the spiral shocks has sub-Keplerian velocities.\nWe undertake simulations with the aim to investigate the effect of\nartifacts on the image reconstruction of the spiral structures.\n\n\\end{abstract}\n\n\\begin{keywords}\nbinaries: close -- novae, cataclysmic variables -- eclipses -- \naccretion, accretion discs -- stars: individual: (IP\\,Pegasi).\n\\end{keywords}\n\n\\section{Introduction}\n\nAccretion discs are widespread in astrophysical environments, from\nsheltering the birth of stars to providing the energetics for the most\nviolent phenomena such as relativistic jets.\nDespite its general importance and although considerable\neffort both in observation and theory has been invested over the past\ndecade, the structure and underlying physics of accretion discs remains\npoorly understood. One of the major unsolved problems concerns the\nnature of the anomalous viscosity mechanism responsible for the\ninward spiraling of the disc material (Frank, King \\& Raine 1992).\n\nBest prospects for progress in understanding accretion discs physics\nare possibly found in mass-exchanging binaries such as Cataclysmic\nVariables (CVs). In these close binaries mass is fed to a non-magnetic\n($B\\simlt 10^{5}$ G) white dwarf via an accretion disc by a Roche lobe\nfilling companion star (the secondary). The sub-class of \n{\\em dwarf novae} comprises low-mass transfer CVs which show recurrent\noutbursts of 2--5 magnitudes on timescales of months either due to an\ninstability in the mass transfer from the secondary or due to a thermal\ninstability in the accretion disc which switches the disc from a low \nto a high-viscosity regime (Warner 1995 and references therein).\n\nSpiral shocks have been advocated by various researchers as a possible\nmechanism for transport of angular momentum in accretion discs (Savonije,\nPapaloizou \\& Lin 1994) and may be the key, together with magnetic\nviscosity (Hawley, Balbus \\& Winters, 1999), in understanding the\nviscosity mechanism.\nThe recent discovery of spiral shocks in the accretion disc of the\ndwarf novae IP~Pegasi in outburst -- from Doppler tomography of emission\nlines (Steeghs, Harlaftis \\& Horne 1997, 1998; Harlaftis et~al. 1999) \n-- confirmed the results of hydrodynamical simulations (Armitage \\& Murray\n1998, Stehle 1999).\nThe spiral shocks are produced in the outer regions of the disc by the\ntides raised by the secondary star. During the outburst the disc expands\nand its outer parts feel more effectively the gravitational attraction\nof the secondary star leading to the formation of spiral arms.\n\nHere we report on the eclipse mapping analysis of the data obtained by\nHarlaftis et al. (1999; see there for observations and data reduction).\nOur goal is to confirm the existence, constrain the location and to\ninvestigate the spatial structure of the spiral shocks observed in\nthe Doppler tomograms. Section\\,\\ref{dados} presents the data and\ngives details of the analysis procedures. In section\\,\\ref{sim} we\npresent a set of simulations with the eclipse mapping method aimed to\nclarify the interpretation of the results of section\\,\\ref{results} in\nterms of real spiral shocks. A summary of our findings is given in \nsection\\,\\ref{fim}.\n\n\n\\section{Data Analysis} \\label{dados}\n\n\\subsection{Lightcurves}\n\nA time-series of high-resolution, optical spectrophotometry \n($\\Delta\\lambda= 4354-4747$ \\AA, velocity dispersion of $27\\; km\\,s^{-1}$\nper pixel) covering one eclipse of IP Peg was obtained during the third\nday of the November 1996 outburst. The reader is referred to Harlaftis \net~al. (1999) for a detailed description of the dataset and of the\nreduction procedures.\nLightcurves were extracted for the blue continuum ($4365-4440$ \\AA)\nand for the C\\,III+N\\,III $\\lambda 4650$ (Bowen blend) and He\\,II $\\lambda\n4686$ lines and phase folded according to the sinusoidal ephemeris of \nWolf et~al. (1993),\n\\begin{equation}\nT_{\\rm mid}({\\rm HJD}) = 2\\,445\\,615.4156 + 0.158\\,206\\,16 \\; E + (O-C) \n\\end{equation}\nwhere \n$$(O-C) = 1.0903 \\times 10^{-3} \\; \\sin \\left[ 2\\,\\pi\\;\n\\frac{E-10258}{10850.88} \\right] \\;\\; . $$\nThe line lightcurves were continuum subtracted and, therefore,\ncorrespond to {\\em net} line emission.\nThe three lightcurves are shown in Fig.\\,\\ref{fig1} as gray open squares. \n\nThe C\\,III+N\\,III lightcurve shows a peculiar double-stepped eclipse\nshape revealing the presence of two asymmetric brightness sources\ndisplaced from disc centre. Although less pronounced,\nthe same morphology can also be seen in the continuum lightcurve.\nThe shape of the He\\,II eclipse is more symmetrical than that of\nthe other passbands but mid-eclipse occurs earlier with respect to the\ncontinuum eclipse, indicating that the line surface distribution is \nalso asymmetric.\n\nThe continuum and He\\,II lightcurves show a conspicuous orbital\nmodulation with maximum at phase $\\phi \\simeq -0.15$ cycle and minimum\nat $\\phi \\simeq +0.15$ cycle. This is not seen in the C\\,III+N\\,III \nlightcurve although an increase in flux is clearly visible after phase\n$\\phi= +0.22$ cycle. For any reasonable mass ratio, $q<1$ [$q$=0.5 \nfor IP~Peg, Wood \\& Crawford (1986)], the shadow\nof the secondary star covers regions outside the primary lobe for\norbital phases $|\\phi|> 0.2$ cycle. Therefore, it is hard to explain\nthe observed modulation in terms of occultation by the secondary star\nunless the eclipsed source lies outside the primary lobe. \nThereafter, we assign the orbital modulation to gas obscuration by the\nspiral arm seen at maximum between phases 0.0-0.25 cycle (see section\\,\\ref{results}).\n\nOut-of-eclipse brightness changes are not accounted for by the eclipse\nmapping method, which assumes that all variations in the eclipse lightcurve\nare due to the changing occultation of the emitting region by the\nsecondary star (but see Bobinger et~al. 1996 for an example of how to\ninclude orbital modulations in the eclipse mapping scheme). Orbital\nvariations were therefore removed from the lightcurves by fitting a\nspline function to the phases outside eclipse, dividing the lightcurve\nby the fitted spline, and scaling the result to the spline function\nvalue at phase zero. This procedure removes orbital modulations with\nonly minor effects on the eclipse shape itself.\nThe corrected lightcurves are shown in Fig.\\,\\ref{fig1} as filled\ncircles. For the purpose of eclipse mapping analysis the lightcurves\nwere limited to the phase range ($-0.18,+0.28$) since data outside\nof eclipse is basically used to set the out-of-eclipse level and\nflickering in this phase range serves to add unnecessary noise to the fit. \n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FIGURE 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\subsection{Eclipse maps}\n\nThe eclipse mapping method is an inversion technique that uses \nthe information contained in the shape of the eclipse to recover\nthe surface brightness distribution of the eclipsed accretion disc.\nThe reader is referred to Horne (1985), Rutten et al. (1992) and \nBaptista \\& Steiner (1993) for the details of the method.\n\nAs our eclipse map we adopted a grid of $51 \\times 51$ pixels\ncentered on the primary star with side 2~R$_{\\rm L1}$, where\nR$_{\\rm L1}$ is the distance from the disk center to the inner\nLagrangian point.\nThe eclipse geometry is controled by a pair of $q$ and $i$ values.\nThe mass ratio $q$ defines the shape and the relative size of the\nRoche lobes. The inclination $i$ determines the shape and extent of\nthe shadow of the secondary star as projected onto the orbital plane.\nWe obtained reconstructions for two sets of parameter, ($q=0.5 \\; , \\;\ni=81\\degr$) (Wood \\& Crawford 1986) and ($q=0.58 \\; , \\; i=79.5\\degr$)\n(Marsh 1988), which correspond to an eclipse width of the disc\ncentre of $\\Delta\\phi= 0.086$ (Wood \\& Crawford 1986;\nMarsh \\& Horne 1990). These combination of parameters ensure that\nthe white dwarf is at the center of the map. There is no perceptible\ndifference in eclipse maps obtained with either geometry. Hence, for\nthe remainder of the paper we will refer to and show the results for \n($q=0.5 \\; , \\; i=81\\degr$).\n\nThe lightcurves were analyzed with eclipse mapping techniques to solve\nfor a map of the disc brightness distribution and for the flux of an\nadditional uneclipsed component in each passband. The uneclipsed component\naccounts for all light that is not contained in the eclipse map in the\norbital plane (i.e., light from the secondary star and/or a vertically\nextended disc wind). The reader is referred to Rutten et~al. (1992) and\nBaptista, Steiner \\& Horne (1996) for a detailed description of and \ntests with the uneclipsed component. For the reconstructions we adopted\nthe default of limited azimuthal smearing of Rutten et~al. (1992), which\nis better suited for recovering asymmetric structures than the original\ndefault of full azimuthal smearing (see Baptista et~al. 1996).\n\nLightcurves, fitted models and grayscale plots of the resulting eclipse\nmaps are shown in Fig.\\,\\ref{fig2} and will be discussed in detail in \nsection\\,\\ref{results}.\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FIGURE 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\section{Eclipse mapping simulations} \\label{sim}\n\nWe performed various simulations with asymmetric sources in order\n(i) to investigate how the presence of spiral structures in the\naccretion disc affects the shape of the eclipse lightcurve, and\n(ii) to evaluate the ability of the eclipse mapping method to \nreconstruct these structures in the eclipse maps. \n\nFor the simulations we adopted the geometry of IP Peg ($q=0.5$ and $i=81\n\\degr$) and constructed lightcurves with the same signal to noise ratio\nand orbital phases of the real data of section\\,\\ref{dados}. \nFigure\\,\\ref{fig3} shows the results of the simulations.\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FIGURE 3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nAsymmetric compact sources (model \\#1) result in eclipse lightcurves with\nrapid brightness changes at ingress/egress phases. The azimuthal smearing\neffect characteristic of the eclipse mapping method is responsible for the\ndistortion which makes the compact sources appear `blurred' in azimuth.\nNevertheless, their radial and azimuthal locations are satisfactory \nrecovered.\n\nBrightness distributions with spiral structures (models \\#2 to \\#4) result\nin eclipse shapes with characteristic `bulges', whose extension and location\nin phase reflect the orientation and radial extent of the spiral arms.\nDue to the azimuthal smearing effect these structures are reproduced in\nthe form of asymmetric arcs, whose maximum brightness and radial position\nyield information about the orientation, position and radial extent of\nthe original spiral arms. The adition of a symmetric brightness\nsource (i.e., centred in the eclipse map, model \\#5) can dilute the\npresence of spiral arms. In this case the eclipse shape is smoother\nand more symmetric in comparison with those of models \\#2-4 and the\nasymmetric arcs are less clearly visible in the eclipse map, mixing\nwith the brightness distribution of the central source.\n\nThese simulations show that the eclipse mapping method is able to\nreproduce asymmetric light sources such as spiral arms (provided the\nasymmetric sources are properly eclipsed) and that the asymmetric\nstructures seen in the eclipse maps of Fig.\\,\\ref{fig2} are not caused\nby artifacts of the method. Models \\#3 to \\#5 are the relevant ones for\nthe purpose of comparing the results of the simulations with those\nfrom the IP~Peg data (Fig.\\,\\ref{fig2}). The morphology of the \ncontinuum and C\\,III+N\\,III lightcurves is similar to that of models\n\\#3 and \\#4, while the He\\,II lightcurve resembles that of model \\#5.\n\n\n\\section{Results} \\label{results}\n\nData and model lightcurves are shown in the left panels of Fig.\\,\\ref{fig2}.\nHorizontal dashed lines indicate the uneclipsed component in each case.\nThe uneclipsed component corresponds to about 12, 1 and 1 per cent of the\ntotal flux, respectively for the continuum, C\\,III+N\\,III and He\\,II curves.\nWhile a non-negligible fraction of the light in the continuum \nprobably arises from an emitting region outside of the orbital plane \n(possibly a disk wind), the net He\\,II and C\\,III+N\\,III emission mostly\narises from (or close to) the orbital plane.\n\nThe middle panels of Fig.\\,\\ref{fig2} show eclipse maps in a logarithmic\ngrayscale. The maps in the right panels show the asymmetric part of the\nmaps in the middle panels and are obtained by calculating and subtracting\nazimuthally-averaged intensities at each radius.\n\nThe continuum and C\\,III+N\\,III lightcurves display bulges similar to\nthat of the lightcurves of models \\#3 and \\#4 (Section 3) and result in\neclipse maps with two clearly visible asymmetric arcs, which are\ninterpreted as being the spiral shocks seen in the Doppler tomograms\nof Harlaftis et~al. (1999). In comparison with the models of\nFig.\\,\\ref{fig3}, the orientation of the arcs suggests that the spirals\nare aligned in a direction perpendicular to the major axis of the binary\n(models \\#3 and \\#4). The arcs show an azimuthal extent of $\\sim 90\\degr$\nand extend from the intermediate to the outer disc regions ($R\\simeq\n0.2-0.6\\;R_{\\rm L1}$). Therefore, the outer radius of the spirals is\nof the same order of the disc outburst radius ($R_d \\simeq 0.34\\;a \\simeq\n0.6\\;R_{L1}$) inferred by Wood et~al. (1989). The eclipse maps show no\nevidence of the bright spot at disc rim and no enhanced emission along\nthe gas stream trajectory.\n\nThe azimuthal location of the arcs is consistent with the results\nfrom hydrodynamical simulations and from the Doppler tomography.\nThe arc in the upper left quadrant of the eclipse map (hereafter\narc 1) corresponds to the spiral arm whose maximum occurs at phases\n0.5--0.75 while the arc in the lower right quadrant (arc 2) corresponds\nto the spiral arm seen at maximum intensity at phases 0.0--0.25\n(orbital phases increases clockwise in the eclipse maps of \nFig.\\,\\ref{fig2} and phase zero coincides with the inner lagrangian\npoint L1). The arcs are not symmetrical with respect to the centre of\nthe disc. In C\\,III+N\\,III, arc 2 is further away from disc centre\nthan arc 1 -- in agreement with the Doppler tomography, which indicates\nsmaller velocities for the spiral arm 2 ($\\simeq 550\\; km\\, s^{-1}$)\nthan for the spiral arm 1 ($\\simeq 700\\; km\\, s^{-1}$).\n\nThe lightcurve of He\\,II is quite symmetrical with less pronounced\nbulges than in C\\,III+N\\,III, resulting in an eclipse map consisting\nof a symmetrical, centred brightness distribution and asymmetric arcs\nat different distances from disc centre. The outermost arc (arc 2) is\nmore easily seen in the eclipse map, while the emission from the \ninnermost arc (arc 1) is blendend with that of the central source.\nNevertheless, arc 1 is clearly seen in the asymmetric part of the He\\,II\nmap show in the right panel of Fig.\\,\\ref{fig2}. The symmetrical emission\ncomponent is probably related to the low-velocity component seen in He\\,II\nDoppler tomograms and is suggested to be due to gas outflow in a wind\nemanating from the inner parts of the disc (see also Marsh and Horne, 1990;\nfor an alternative interpretation, slingshot prominence from the secondary\nstar, see Steeghs et~al. 1996). The He\\,II arcs contribute about 16 per\ncent of the total flux of the eclipse map -- in good agreement with the\nresults from the Doppler tomography, which indicate that the spirals\ncontribute $\\simeq 15$ per cent of the total He\\,II emission (Harlaftis \net~al. 1999). In comparison, the arcs in the C\\,III+N\\,III and continuum\nmaps contribute, respectively, about 30 and 13 per cent of the total flux.\n\nWe quantify the properties of the asymmetric arcs by dividing the eclipse\nmap in azimuthal slices (i.e., `slices of pizza') and computing the\ndistance at which the intensity is maximum for each azimuth. This\nexercice allows to trace the distribution in radius and azimuth of the\nspiral structures. The results are plotted in Fig.\\,\\ref{fig4} as a\nfunction of orbital phase. The diagrams for He\\,II were computed from its\nasymmetric map and are noisier than those for C\\,III+N\\,III because most\n($\\simeq 84$ per cent) of the flux in the eclipse map is subtracted with\nthe symmetric component. The two spiral shocks are clearly visible in the\nintensity diagrams, as well as their distinct locations with respect to \ndisc centre. In He\\,II the outer spiral (arc2) is brighter than the inner\nspiral (arc1), in line with the results of Harlaftis et~al. (1999), while\nin C\\,III+N\\,III arc 1 is brighter than arc 2. The middle panels give\nthe radial position of the maximum intensity as a function of binary\nphase. For C\\,III+N\\,III, the maximum intensity along arc 1 lies at a\nconstant distance of $\\simeq 0.28\\; R_{L1}$ from disc centre while the\nmaximum intensity of arc 2 occurs at $\\simeq 0.55\\; R_{L1}$.\nThe numbers are similar for He\\,II.\n\nWe computed equivalent Keplerian velocities for each radius assuming\n$M_1= 1.0 \\pm 0.1 \\; M_\\odot$ e $R_{\\rm L1}= 0.81\\; R_\\odot$ (Marsh \\&\nHorne 1990). The results are plotted in the upper panel of Fig.\\,\\ref{fig4}.\nGray lines show the corresponding uncertainties at the 1-$\\sigma$ limit. \nFor comparison, the results from the C\\,III+N\\,III and He\\,II Doppler\ntomograms (Harlaftis et~al. 1999; see their fig.\\,4 for the He\\,II\ndiagram) are shown as dashed lines. Since the C\\,III+N\\,III Doppler map\nis much noisier and blurred than the He\\,II Doppler map, the corresponding\ndiagram is noisier and less reliable than the He\\,II diagram on the right\npanel. We obtain velocities in the range $850-1050 \\; km\\, s^{-1}$ for\nthe spiral 1 compared to the observed $400-770\\; km\\,s^{-1}$ and in the\nrange $650-800\\; km\\,s^{-1}$ for the spiral 2 compared to the observed\n$400-550 \\; km\\,s^{-1}$ (observed values from Harlaftis et~al. 1999). \nThe Keplerian velocities calculated from the\nradial position of the shocks are systematically larger than those\ninferred from the Doppler tomography, suggesting that the gas in the\nspiral shocks has sub-Keplerian velocities. This is in line with the\nresults of the hydrodynamical simulations of Steeghs \\& Stehle (1999,\nsee their fig.\\,5), which predicts velocities lower than Keplerian (by as\nmuch as 15 per cent) in the outer disc near the spirals.\n\nWe remark that with the white dwarf mass and Roche lobe radius of IP~Peg\nthe Keplerian velocity at the largest possible disc radius ($R\\simeq 0.85\\;\nR_{\\rm L1}$) is about $530 \\; km\\,s^{-1}$. Therefore, if the observed\nvelocities of Harlaftis et~al. (1999) do reflect Keplerian motions, \nthen the emitting gas should be at the border and even outside the\nprimary lobe.\n\nOccultation of light from the inner disc regions by the spirals might\nproduce the out of eclipse variations seen in Fig.\\,\\ref{fig1}. This is\nexpected since the spiral waves are also vertically extended. From the\nazimuthal position of the spirals in the eclipse map, the maximum\noccultation (i.e., the minimum of the orbital modulation) should occur\nwhen the spirals are seen face on, at orbital phases $\\simeq -0.3$ and\n$\\simeq +0.15$ cycle, in agreement with the modulations seen in\nFig.\\,\\ref{fig1}.\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FIGURE 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\section{Conclusions} \\label{fim}\n\nWe analyzed eclipse lightcurves of the dwarf novae IP Peg during\nthe November 1996 outburst in order to confirm the existence, \nconstrain the location and investigate the spatial structure of the\nspiral shocks observed in the Doppler tomograms.\nOur mais results can be summarized as follows:\n\n\\begin{itemize}\n\\item Eclipse maps in the blue continuum and in the C\\,III+N\\,III\nemission line reveal two asymmetric arcs at different azimuth and\nradius from disc centre which are consistent with the spiral shocks\nseen in the Doppler tomograms. The arcs show an azimuthal extent of\n$\\sim 90\\degr$ and extend from the intermediate to the outer disc \nregions ($R\\simeq 0.2 - 0.6\\; R_{L1}$). \nThe outer radius of the spirals is of the same order of the disc \noutburst radius ($R_{d}\\simeq 0.34\\;a\\simeq 0.6\\; R_{L1}$).\n\n\\item The He\\,II eclipse map is composed of a central brightness source\nplus asymmetric arcs at different distances from disc centre. \nThe symmetric component probably corresponds to the low-velocity\ncomponent seen in He\\,II Doppler tomograms and is understood in terms\nof gas outflow in a wind emanating from the inner parts of the disc.\n\n\\item The spirals contribute about 16 and 30 per cent of the total line\nflux, respectively, for the He\\,II and C\\,III+N\\,III lines, and 13 per\ncent in the continuum. \n\n\\item The Keplerian velocities derived from the radial position of the\nshocks are systematically larger than those inferred from the Doppler\ntomography, indicating that the gas in the spiral shocks has\nsub-Keplerian velocities.\n\n\\end{itemize}\n\n\n\\section*{Acknowledgments}\n\nWe thank an anonymous referee for helpful discussions and comments.\nThis work was partially supported by the PRONEX/Brazil program through the\nresearch grant FAURGS/FINEP 7697.1003.00. RB acknowledges financial \nsupport from CNPq/Brazil through grant no. 300\\,354/96-7.\nETH was supported by the TMR contract ERBFMBICT960971 of the European\nUnion. \n\n\\begin{thebibliography}{99}\n\n\\bibitem {1} Armitage P. J., Murray J. R., 1998. MNRAS, 297, L81\n\\bibitem {3} Baptista R., Steiner J. E., 1993. A\\&A, 277, 331\n\\bibitem {4} Baptista R., Steiner J. E., Horne K., 1996. MNRAS, 282, 99\n\\bibitem {5} Bobinger A., Horne K., Mantel K. H., Wolf S., 1997. A\\&A, 327, 1023\n\\bibitem {7} Frank J., King A. R., Raine D. J., 1992. Accretion Power in\n\t\tAstrophysics - 2nd edition, Cambridge University Press, Cambridge\n\\bibitem {9} Harlaftis E. T., Steeghs D., Horne K., Mart\\'\\i n E., Magazz\\'u\n\t\tA., 1999. MNRAS, in press \n\\bibitem {11} Horne K., 1985. MNRAS, 213, 129\n\\bibitem {13} Marsh T. R., 1988. MNRAS, 231, 1117\n\\bibitem {15} Marsh T. R., Horne K., 1990. ApJ, 349, 593 \n\\bibitem {17} Rutten R. G. M., van Paradijs J., Tinbergen J., 1992. A\\&A,\n\t\t260, 213\n\\bibitem {19} Savonije G. J., Papaloizou J., Lin C., 1994. MNRAS, 268, 13\n\\bibitem {20} Steeghs D., Horne K., Marsh T. R., Donati J. F., 1996. MNRAS,\n\t\t281, 626\n\\bibitem {21} Steeghs D., Harlaftis E. T., Horne K., 1997. MNRAS, 290, L28\n\\bibitem {22} Steeghs D., Harlaftis E. T., Horne K., 1998. MNRAS, 296, 463\n\\bibitem {23} Steeghs D., Stehle R., 1999. MNRAS, 307, 99\n\\bibitem {24} Stehle R., 1999. MNRAS, 304, 687\n\\bibitem {25} Warner B., 1995. Cataclysmic Variable Stars, Cambridge\n\t\tAstrophysics Series 28, Cambridge University Press, Cambridge\n\\bibitem {26} Wolf S., et al., 1993. A\\&A, 273, 160\n\\bibitem {27} Wood J. H., Crawford C. S., 1986. MNRAS, 222, 645\n\\bibitem {28} Wood J. H., et~al., 1989. MNRAS, 239, 809\n\n\\end{thebibliography}\n\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FIGURE 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure*}\n%\\centerline{\\psfig{figure=ipfig1.ps,width=11cm,rheight=13cm}}\n \\caption{ Original lightcurves (gray open squares), fitted splines\n\t(gray dashed lines) and corrected lightcurves (black filled squares),\n\tfor the continuum, C\\,III+N\\,III and He\\,II data. Vertical dotted\n\tlines mark the ingress/egress phases of the white dwarf for an\n\tassumed eclipse width of $\\Delta\\phi=0.086$ cycle (Wood \\& Crawford\n\t1986) and horizontal dotted lines mark the reference (mid-eclipse)\n\tflux level of the spline fit. }\n \\label{fig1}\n\\end{figure*}\n\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FIGURE 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure*}\n%\\centerline{\\psfig{figure=ipfig2.ps,width=11cm,rheight=13cm}}\n \\caption{ Left: Data (dots with error bars) and model (solid lines)\n\tlightcurves of IP Peg at outburst maximum for the continuum,\n\tC\\,III+N\\,III $\\lambda 4650$ and He\\,II $\\lambda 4686$ lines.\n\tHorizontal dashed lines indicate the uneclipsed component in each\n\tcase. Middle: eclipse maps in a logarithmic grayscale. Right:\n\tthe eclipse maps of the middle panel after subtracting their\n\tsymmetric part; these diagrams emphasize the asymmetric structures.\n\tBrighter regions are indicated in black; fainter regions in white.\n\tA cross mark the center of the disc; dotted lines show the Roche \n\tlobe and the gas stream trajectory; dotted circles mark disc radii\n\tof $R=0.2$ and $0.6\\;R_{L1}$; the secondary is to the right \n\tof each map and the stars rotate counterclockwise. }\n\\label{fig2}\n\\end{figure*}\n\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FIGURE 3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure*}\n\\centerline{\\psfig{figure=ipfig3.ps,width=14.5cm,rheight=17.5cm}}\n\\caption{ Simulations with asymmetric brightness distributions.\n\tPanels in the center show different synthetic images in logarithmic\n\tgrayscale. Panels in the left show noise-added lightcurves derived \n\tfrom these brightness distributions (dots) and the fitted models \n\t(solid lines). Vertical dotted lines mark the ingress/egress phases\n\tof the center of the disc. The dashed curve in the lower panel\n\tillustrates the contribution from the spiral arms to the eclipse\n\tshape of model \\#5. Panels on the right show the corresponding\n\teclipse maps in the same logarithmic grayscale as in the middle panel.\n\tThe notation is the same as in Fig.\\,\\ref{fig2}. }\n\\label{fig3}\n\\end{figure*}\n\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FIGURE 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure*}\n%\\centerline{\\psfig{figure=ipfig4.ps,angle=-90,width=15cm,rheight=11cm}}\n \\caption{ The dependency with binary phase of the maximum intensity,\n\tradius and corresponding Keplerian velocity at maximum intensity,\n\tas derived from the C\\,III+N\\,III and He\\,II eclipse maps. The\n\tvelocities were computed assuming $M_1= 1.0\\pm 0.1\\; M_\\odot$ and\n\t$R_{L1}= 0.81\\; R_\\odot$ (Marsh \\& Horne 1990) and the intensities\n\tare plotted in an arbitrary scale. Gray lines show the uncertainties \n\tin the velocity at the 1-$\\sigma$ limit. The dependency of velocity\n\twith orbital phase as derived from the C\\,III+N\\,III and He\\,II Doppler\n\ttomograms (Harlaftis et al. 1999; see their fig.4) are shown as dashed\n\tlines for comparison. The location of the spiral arms are indicated by\n\thorizontal bars with labels 1 (inner spiral) and 2 (outer spiral). }\n \\label{fig4}\n\\end{figure*}\n\n\\bsp\n\\end{document}\n"
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{
"name": "astro-ph0002187.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem {1} Armitage P. J., Murray J. R., 1998. MNRAS, 297, L81\n\\bibitem {3} Baptista R., Steiner J. E., 1993. A\\&A, 277, 331\n\\bibitem {4} Baptista R., Steiner J. E., Horne K., 1996. MNRAS, 282, 99\n\\bibitem {5} Bobinger A., Horne K., Mantel K. H., Wolf S., 1997. A\\&A, 327, 1023\n\\bibitem {7} Frank J., King A. R., Raine D. J., 1992. Accretion Power in\n\t\tAstrophysics - 2nd edition, Cambridge University Press, Cambridge\n\\bibitem {9} Harlaftis E. T., Steeghs D., Horne K., Mart\\'\\i n E., Magazz\\'u\n\t\tA., 1999. MNRAS, in press \n\\bibitem {11} Horne K., 1985. MNRAS, 213, 129\n\\bibitem {13} Marsh T. R., 1988. MNRAS, 231, 1117\n\\bibitem {15} Marsh T. R., Horne K., 1990. ApJ, 349, 593 \n\\bibitem {17} Rutten R. G. M., van Paradijs J., Tinbergen J., 1992. A\\&A,\n\t\t260, 213\n\\bibitem {19} Savonije G. J., Papaloizou J., Lin C., 1994. MNRAS, 268, 13\n\\bibitem {20} Steeghs D., Horne K., Marsh T. R., Donati J. F., 1996. MNRAS,\n\t\t281, 626\n\\bibitem {21} Steeghs D., Harlaftis E. T., Horne K., 1997. MNRAS, 290, L28\n\\bibitem {22} Steeghs D., Harlaftis E. T., Horne K., 1998. MNRAS, 296, 463\n\\bibitem {23} Steeghs D., Stehle R., 1999. MNRAS, 307, 99\n\\bibitem {24} Stehle R., 1999. MNRAS, 304, 687\n\\bibitem {25} Warner B., 1995. Cataclysmic Variable Stars, Cambridge\n\t\tAstrophysics Series 28, Cambridge University Press, Cambridge\n\\bibitem {26} Wolf S., et al., 1993. A\\&A, 273, 160\n\\bibitem {27} Wood J. H., Crawford C. S., 1986. MNRAS, 222, 645\n\\bibitem {28} Wood J. H., et~al., 1989. MNRAS, 239, 809\n\n\\end{thebibliography}"
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astro-ph0002188
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The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. To clarify (but not resolve) this ambiguity, a toy model of an eternally inflating universe is introduced. Vilenkin's proposal for avoiding these problems is also discussed, as is the question of whether it is meaningful to discuss probabilities for unrepeatable measurements.
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"name": "ahg-prit.tex",
"string": "%RE: ``Inflationary Models and Connections to Particle Physics,''\n% write-up of talk given at the Pritzker Symposium on the Status\n% of Inflationary Cosmology, Chicago, Illinois, January 29-31,\n% 1999. To appear in the proceedings. Final draft, 1/17/00.|\n\n\\documentstyle[12pt,epsf]{article}\n\n\\textheight 8.9in \\textwidth 6.5in \\oddsidemargin 0in \n\\topmargin -37pt % Corresponds to 1 inch margin at top\n\n\\newcommand{\\beq}{\\begin{equation}}\n\\newcommand{\\eeq}{\\end{equation}}\n\n% The following macro causes equations to be numbered by section:\n\\renewcommand{\\theequation}{\\arabic{section}.\\arabic{equation}}\n% In addition, the macro\n% \\setcounter{equation}{0}\n% must be added after each \\section{} command.\n\n% The following macro causes the Section headings to be printed\n% Roman numerals, rather than Arabic numerals:\n\\renewcommand{\\thesection}{\\Roman{section}.}\n\n% The following macro causes the footnotes to be indicated by\n% symbols such as asterisks and daggers, rather than numbers.\n\\renewcommand{\\thefootnote}{\\fnsymbol{footnote}}\n\n% The following macro mimics Latex's \\subsection command, but\n% uses no subsection number:\n\\newcommand{\\subhead}[1]{\\goodbreak \\vskip 3.25ex plus\n 1ex minus 0.2ex \\noindent {\\large \\bf\n #1}\\par\\nobreak \\vskip 1.5ex plus 0.2ex}\n\n% The following macros define some special symbols used in this\n% manuscript:\n% Less than or approximately equal to:\n \\def\\lta{\\mathrel{\\vcenter{\\vbox{\\offinterlineskip \\hbox{$<$}\n \\vskip 0.2 pt \\hbox{$\\sim$}}}}}\n% tot (used for subscripts):\n \\def\\tot{{\\rm tot}}\n\n\\begin{document}\n\n\\begin{titlepage}\n\n\\setcounter{footnote}{1}\n\\setcounter{page}{1}\n\n\\vbox{}\n\\flushright{MIT-CTP-2947, astro-ph/0002188}\n\\vskip 1.5 truein\n\\begin{center}\n{\\Large \\bf Inflationary Models\\\\}\n\\medskip\n{\\Large \\bf and\\\\}\n\\medskip\n{\\Large \\bf Connections to Particle\nPhysics\\footnote{Talk given at the {\\it Pritzker Symposium on the\nStatus of Inflationary Cosmology}, Chicago, Illinois, January 29\n-- 31, 1999. To appear in the proceedings.}\\\\}\n\\bigskip \\bigskip\n{\\bf Alan H. Guth\\footnote{This work is supported in part by\nfunds provided by the U.S. Department of Energy (D.O.E.) under\ncooperative research agreement \\#DF-FC02-94ER40818, and in part\nby funds provided by NM Rothschild \\& Sons Ltd and by the\nEPSRC.}\\\\}\n\\medskip\n{\\small \\it Center for Theoretical Physics\\\\}\n{\\small \\it Laboratory for Nuclear Science and\nDepartment of Physics\\\\}\n{\\small \\it Massachusetts Institute of Technology,\nCambridge, Massachusetts\\ \\ 02139\\ \\ \\ U.S.A.\\footnote{Present\naddress.}\\\\ and \\\\\nIsaac Newton Institute for Mathematical Sciences, \\\\\nClarkson Road, Cambridge CB3 0EH, UK\\\\}\n\\bigskip\n{\\tt guth@ctp.mit.edu\\\\}\n\\bigskip \\bigskip\n\\end{center}\n\n\\begin{abstract}\nThe basic workings of inflationary models are summarized, along\nwith the arguments that strongly suggest that our universe is the\nproduct of inflation. The mechanisms that lead to eternal\ninflation in both new and chaotic models are described. Although\nthe infinity of pocket universes produced by eternal inflation\nare unobservable, it is argued that eternal inflation has real\nconsequences in terms of the way that predictions are extracted\nfrom theoretical models. The ambiguities in defining\nprobabilities in eternally inflating spacetimes are reviewed,\nwith emphasis on the youngness paradox that results from a\nsynchronous gauge regularization technique. To clarify (but not\nresolve) this ambiguity, a toy model of an eternally inflating\nuniverse is introduced. Vilenkin's proposal for avoiding these\nproblems is also discussed, as is the question of whether it is\nmeaningful to discuss probabilities for unrepeatable\nmeasurements.\n\\end{abstract}\n\n\\end{titlepage}\n\n\\setcounter{footnote}{0}\n\n% Section I:\n\\section{Introduction}\n\\setcounter{equation}{0}\n\nThere are many fascinating issues associated with eternal\ninflation, which will be the main subject of this talk. You have\ncertainly heard other people talk about eternal inflation, but I\nfeel that the topic is important enough so that you should hear\nabout it in some accent other than Russian. I will begin by\nsummarizing the basics of inflation, including a discussion of\nhow inflation works, and why many of us believe that our universe\nalmost certainly evolved through some form of inflation. This\nmaterial is certainly not new, but I think it is an appropriate\nintroduction to any volume that focuses on inflationary\ncosmology. Then I will move on to discuss eternal inflation,\nfirst explaining how it works. I will then argue the eternal\ninflation has important implications, and raises important\nquestions, which should not be dismissed as being merely\nmetaphysical.\n\n% Section II:\n\\section{How Does Inflation Work?}\n\\setcounter{equation}{0}\n\nIn this section I will review the basics of how inflation works,\nfocusing on the earliest working forms of inflation---{\\it new\ninflation} \\cite{Linde1, Albrecht-Steinhardt1} and {\\it chaotic\ninflation} \\cite{chaotic}. While more complicated possibilities\n(e.g. hybrid inflation \\cite{hyb1,hyb2,hyb3,hyb4,hyb5} and\nsupernatural inflation \\cite{RSG}) appear very plausible, the\nbasic scenarios of new and chaotic inflation will be sufficient\nto illustrate the physical effects that I want to discuss in this\narticle. \n\nThe key property of the laws of physics that makes inflation\npossible is the existence of states of matter that have a high\nenergy density which cannot be rapidly lowered. In the original\nversion of the inflationary theory \\cite{Guth1}, the proposed\nstate was a scalar field in a local minimum of its potential\nenergy function.\\footnote{A similar proposal was advanced by\nStarobinsky \\cite{Starobinsky}, in which the high energy density\nstate was achieved by curved space corrections to the\nenergy-momentum tensor of a scalar field.} Such a state is\ncalled a {\\it false vacuum}, since the state temporarily acts\nas if it were the state of lowest possible energy density. \nClassically this state would be completely stable, because there\nwould be no energy available to allow the scalar field to cross\nthe potential energy barrier that separates it from states of\nlower energy. Quantum mechanically, however, the state would\ndecay by tunneling \\cite{Coleman}. Initially it was hoped that\nthis tunneling process could successfully end inflation, but it\nwas soon found that the randomness of false vacuum decay would\nproduce catastrophically large inhomogeneities \\cite{Guth1, HMS,\nGuthWeinberg}. \n\nThis ``graceful exit'' problem was solved by the invention of the\nnew inflationary universe model \\cite{Linde1,\nAlbrecht-Steinhardt1}, which achieved all the successes that had\nbeen hoped for in the context of the original version. In this\ntheory inflation is driven by a scalar field perched on a plateau\nof the potential energy diagram, as shown in Fig.~\\ref{newinf}. \nSuch a scalar field is generically called the {\\it inflaton}. If\nthe plateau is flat enough, such a state can be stable enough for\nsuccessful inflation. Soon afterwards Linde showed that the\ninflaton potential need not have either a local minimum or a\ngentle plateau; in chaotic inflation \\cite{chaotic}, the\ninflaton potential can be as simple as\n\\beq\n V(\\phi)={1 \\over 2} m^2 \\phi^2, \n \\label{eq:2.1}\n\\eeq\nprovided that $\\phi$ begins at such a large value that it takes a\nlong time for it to relax. For simplicity of language, I will\nstretch the meaning of the phrase ``false vacuum'' to include all\nof these cases; that is, I will use the phrase to denote any\nstate with a high energy density that cannot be rapidly\ndecreased. While inflation was originally developed in the\ncontext of grand unified theories, the only real requirement on\nthe particle physics is the existence of a false vacuum state.\n\n% htbp = Here, Top, Bottom, Page of floats; Default = tbp\n\\begin{figure}[ht]\n\\epsfxsize=201pt % Reduced 69.4%\n\\centerline{\\epsfbox{newinf2.eps}}\n\\caption{Generic form of the potential for the new inflationary\nscenario.} \n\\label{newinf}\n\\end{figure}\n\n\\subhead{The New Inflationary Scenario:}\n\nSuppose that the energy density of a state is approximately equal\nto a constant value $\\rho_f$. Then, if a region filled with this\nstate of matter expanded by an amount $dV$, its energy would have\nto increase by\n\\beq\n d U = \\rho_f \\, d V \\ . \n \\label{eq:2.2}\n\\eeq\nSomething would have to supply that energy. Work would have to\nbe done to cause the region to expand, which implies that the\nregion has a negative pressure, which pulls back against whatever\nis causing the region to expand. The work done by this negative\npressure $p_f$ is given by the elementary formula\n\\beq\n dW = - p_f \\, d V \\ .\n \\label{eq:2.3}\n\\eeq\nEquating the work with the change in energy, one finds\n\\beq\n p_f = - \\rho_f \\ . \n \\label{eq:2.4}\n\\eeq\nIt is this negative pressure which is the driving force behind\ninflation. When one puts this negative pressure into Einstein's\nequations to find out its gravitational effect, one finds that it\nleads to a repulsion, causing such a region to undergo\nexponential expansion. If the region can be approximated as\nisotropic and homogeneous, this result can be seen from the\nstandard Friedmann-Robertson-Walker (FRW) equations:\n\\beq\n {d^2 a \\over d t^2} = - {4 \\pi \\over 3} G ( \\rho + 3 p ) a \\ \n = { 8 \\pi \\over 3 } G \\rho_f a \\ .\n \\label{eq:2.5}\n\\eeq\nwhere $a(t)$ is the scale factor, $G$ is Newton's constant, and\nwe adopt units for which $\\hbar = c = 1$. For late times the\ngrowing solution to this equation has the form\n\\beq\n a(t) \\propto e^{\\chi t} \\ , \\hbox{ where } \\chi = \\sqrt{{8 \\pi\n \\over 3} G \\rho_f } \\ .\n \\label{eq:2.6}\n\\eeq\nOf course inflationary theorists prefer not to assume that the\nuniverse began homogeneously and isotropically, but there is\nconsiderable evidence for the ``cosmological no-hair conjecture''\n\\cite{Jensen-Stein-Schabes}, which implies that a wide class of\ninitial states will approach this exponentially expanding\nsolution. \n\nSo the basic scenario of new inflation begins by assuming\nthat at least some patch of the early universe was in this\npeculiar false vacuum state. In the original papers\n\\cite{Linde1, Albrecht-Steinhardt1} this initial\ncondition was motivated by the fact that, in many quantum field\ntheories, the false vacuum resulted naturally from the\nsupercooling of an initially hot state in thermal equilibrium. \nIt was soon found, however, that quantum fluctuations in the\nrolling inflaton field give rise to density perturbations in the\nuniverse \\cite{Starobinsky2, GuthPi, Hawking1, BST, BFM}, and\nthat these density perturbations would be much larger than\nobserved unless the inflaton field is very weakly coupled. For\nsuch weak coupling there would be no time for an initially\nnonthermal state to reach thermal equilibrium. Nonetheless,\nsince thermal equilibrium describes a probability distribution in\nwhich all states of a given energy are weighted equally, the fact\nthat thermal equilibrium leads to a false vacuum implies that\nfalse vacuum-like states are not uncommon. Thus, even in the\nabsence of thermal equilibrium, even if the universe started in a\nhighly chaotic initial state, it seems reasonable to simply\nassume that some small patches of the early universe settled into\nthe false vacuum state, as was suggested for example in\n\\cite{Guth-RS}. The idea that one should consider small\npatches of the early universe with arbitrary initial\nconfigurations of scalar fields was later emphasized by Linde\n\\cite{chaotic} in the context of chaotic inflation. Linde\npointed out that even highly improbable initial patches could be\nimportant if they inflated, since the exponential expansion could\nstill cause such patches to dominate the volume of the universe. \nOne might hope that eventually a full theory of quantum origins\nwould allow us to calculate the probability of regions settling\ninto the false vacuum, but I will argue in Sec.~V that, in the\ncontext of eternal inflation, this probability is quite\nirrelevant.\n \nOnce a region of false vacuum materializes, the physics of the\nsubsequent evolution seems rather clear-cut. The gravitational\nrepulsion caused by the negative pressure will drive the region\ninto a period of exponential expansion. If the energy density of\nthe false vacuum is at the grand unified theory scale ($\\rho_f\n\\approx (2 \\times 10^{16}\\ \\hbox{GeV})^4)$, Eq.~(\\ref{eq:2.6})\nshows that the time constant $\\chi^{-1}$ of the exponential\nexpansion would be about $10^{-38}$ sec. For inflation to\nachieve its goals, this patch has to expand exponentially for at\nleast 60 e-foldings. Then, because this state is only\nmetastable---the inflaton field is perched on top of the hill of\nthe potential energy diagram of Fig.~\\ref{newinf}---eventually\nthis state will decay. The inflaton field will roll off the\nhill, ending inflation. And when it does, the energy density\nthat has been locked in the inflaton field is released. Because\nof the coupling of the inflaton to other fields, that energy\nbecomes thermalized to produce a hot soup of particles, which is\nexactly what had always been taken as the starting point of the\nstandard big bang theory before inflation was introduced. From\nhere on the scenario joins onto the standard big bang\ndescription. The role of inflation is to replace the postulates\nof the standard big bang theory with dynamically generated\ninitial conditions.\n\nThe inflationary mechanism produces an entire universe starting\nfrom essentially nothing, so one needs to answer the question of\nwhere the energy of the universe came from. The answer is that\nit came from the gravitational field. I am not saying that the\ncolossal energy of the universe was stored from the beginning in\nthe gravitational field. Rather, the crucial point is that the energy\ndensity of the gravitational field is literally negative---a\nstatement which is true both in Newtonian gravity and in general\nrelativity. So, as more and more positive energy materialized\nin the form of an ever-growing region filled with a\nhigh-energy scalar field, more and more negative energy \nmaterialized in the form of an expanding region filled with a\ngravitational field. So the total energy remained very small, and\ncould in fact be exactly zero. There is nothing known that\nplaces any limit on the amount of inflation that can occur while\nthe total energy remains exactly zero.\\footnote{In Newtonian\nmechanics the energy density of a gravitational field is\nunambiguously negative; it can be derived by the same methods\nused for the Coulomb field, but the force law has the opposite\nsign. In general relativity there is no coordinate-invariant way\nof expressing the energy in a space that is not asymptotically\nflat, so many experts prefer to say that the total energy is\nundefined. Either way, there is agreement that inflation is\nconsistent with the general relativistic description of energy\nconservation.}\n\n\\subhead{Chaotic Inflation:}\n\nChaotic inflation \\cite{chaotic} can occur in the context of a\nmuch more general class of potential energy functions. In\nparticular, even a potential energy function as simple as\nEq.~(\\ref{eq:2.1}), describing a scalar field with a mass and no\ninteraction, is sufficient to describe chaotic inflation. \nChaotic inflation is illustrated in Fig.~\\ref{chaoticinf}. In\nthis case there is no state that bears any obvious resemblance to\nthe false vacuum of new inflation. Instead the scenario works by\nsupposing that chaotic conditions in the early universe produced\none or more patches in which the inflaton field $\\phi$ was at\nsome high value $\\phi = \\phi_0$ on the potential energy curve. \nInflation occurs as the inflaton field rolls down the hill. As\nlong as the initial value $\\phi_0$ is sufficiently high on the\ncurve, there will be sufficient inflation to solve all the\nproblems that inflation is intended to solve. \n\n\\begin{figure}[ht]\n\\epsfxsize=275pt % Reduced 69.4%\n\\centerline{\\epsfbox{eipot1.eps}}\n\\caption{Generic form of the potential for the chaotic inflationary\nscenario.} \n\\label{chaoticinf}\n\\end{figure}\n\nThe equations describing chaotic inflation can be written simply,\nprovided that we assume that the universe is already flat enough\nso that we do not need to include a curvature term. The field\nequation for the inflaton field in the expanding universe is\n\\beq\n \\ddot \\phi + 3 H \\dot \\phi = - {\\partial V \\over \\partial\n \\phi } \\ ,\n \\label{eq:2.7}\n\\eeq\nwhere the overdot denotes a derivative with respect to time $t$,\nand $H$ is the time-dependent Hubble parameter given by\n\\beq\n H^2 = {8 \\pi \\over 3} G V \\ .\n \\label{eq:2.8}\n\\eeq\nFor the toy-model potential energy of Eq.~(\\ref{eq:2.1}), these\nequations have a very simple solution:\n\\beq\n \\phi = \\phi_0 - {m \\over \\sqrt{12 \\pi G}} \\, t \\ .\n \\label{eq:2.9}\n\\eeq\nOne can then calculate the number $N$ of inflationary e-foldings,\nwhich is given by\n\\beq\n N = \\int_{\\phi = \\phi_0}^{\\phi = 0} H(t) \\, dt = 2 \\pi G\n \\phi_0^2 \\ .\n \\label{eq:2.10}\n\\eeq\nIn this free-field model $N$ depends only on $\\phi_0$ and not on the\ninflaton mass $m$. Thus the number of e-foldings will exceed 60\nprovided that\n\\beq\n \\phi_0 > \\sqrt{60 \\over 2 \\pi} \\, M_{\\rm P} \\approx 3.1 M_{\\rm\n P} \\ , \\label{eq:2.11}\n\\eeq\nwhere $M_{\\rm P} \\equiv 1/\\sqrt{G} = 1.22 \\times 10^{19}$ GeV is\nthe Planck mass. Although the value of the scalar field is\nlarger than $M_{\\rm P}$, the energy density can be low compared\nto the Planck scale: \n\\beq\n \\rho_0 = {1 \\over 2} m^2 \\phi_0^2 > {60 \\over 4 \\pi} M_{\\rm P}^2 m^2\n \\ .\n \\label{eq:2.12}\n\\eeq\nFor example, if $m = 10^{16}$ GeV, then the potential energy\ndensity is only $3 \\times 10^{-6}\\, M_{\\rm P}^4$. Since it is\npresumably the energy density that is relevant to gravity, one\ndoes not expect this situation to lead to strong quantum gravity\neffects.\n\n% Section III:\n\\section{Evidence for Inflation}\n\\setcounter{equation}{0}\n\nThe arguments in favor of inflation are pretty much the same no\nmatter which form of inflation we are discussing. In my opinion,\nthe evidence that our universe is the result of some form of\ninflation is very solid. Since the term {\\it inflation}\nencompasses a wide range of detailed theories, it is hard to\nimagine any alternative. Let me review the basic arguments.\n\n\\subhead{1) The universe is big}\n\nFirst of all, we know that the universe is incredibly large. The\nvisible part of it contains about $10^{90}$ particles. It is\neasy, however, to take this fact for granted: of course the\nuniverse is big, it's the whole universe! In ``standard''\nFriedmann-Robertson-Walker cosmology, without inflation, one\nsimply postulates that about $10^{90}$ or more particles were\nhere from the start. If, however, we try to imagine a theory\ndescribing the origin of the universe, it would have to somehow\noutput this number of $10^{90}$ or more. That is a very big\nnumber, and it is hard to imagine it ever coming out of a\ncalculation in which the input consists only geometrical\nquantities, quantities associated with simple dynamics, and\nfactors of 2 and $\\pi$. In the inflationary model, the huge\nnumber of particles is explained naturally by the exponential\nexpansion, which reduces the problem to explaining 60 or 70\ne-foldings of inflation. In fact, it is easy to construct\nunderlying particle theories that will give far more than 70\ne-foldings, suggesting that the observed universe is only a tiny\nspeck within the universe as a whole.\n\n\\subhead{2) The Hubble expansion}\n\nThe Hubble expansion is also easy to take for granted, since it\nis so familiar. In standard FRW cosmology, the Hubble expansion\nis part of the list of postulates that define the initial\nconditions. But inflation offers an explanation of how the\nHubble expansion began. The repulsive gravity associated with\nthe false vacuum is exactly the kind of force needed to propel\nthe universe into a pattern of motion in which any two particles\nare moving apart with a velocity proportional to their\nseparation.\n\n\\subhead{3) Homogeneity and isotropy}\n\nThe degree of uniformity in the universe is startling. Through\ncareful measurements of the cosmic background radiation, we know\nthat the intensity of this radiation is the same in all\ndirections to an accuracy of 1 part in 100,000. To get some\nfeeling for how high this precision is, we can imagine a marble\nthat is spherical to this accuracy. The surface of the\nmarble would have to be shaped with a tolerance of about 1,000\nangstroms, a quarter of the wavelength of light. \n\nAlthough precision lenses can be ground to quarter-wavelength\naccuracy, we would nonetheless be shocked if we ever dug up a\nstone from the ground that was round to this extraordinary\naccuracy. If such a stone were somehow found, I am confident\nthat we would not accept an explanation of its origin which\nsimply proposed that the stone started out perfectly round. \nSimilarly, in the current era, I do not think it makes sense to\nconsider any theory of cosmogenesis that cannot offer some\nexplanation of how the universe became so incredibly isotropic. \n\nThe uniformity of the cosmic background radiation implies that\nthe observed universe had become uniform in temperature by about\n300,000 years after the big bang, when the universe cooled enough\nso that the opaque plasma neutralized into a transparent gas. In\nstandard FRW cosmology, the uniformity could be established by\nthis time only if signals could propagate 100 times faster than\nlight, which is not possible. In inflationary cosmology,\nhowever, the uniformity can be created initially on microscopic\nscales, by normal thermal-equilibrium processes. Then inflation\ntakes over and stretches the regions of uniformity to become\nlarge enough to encompass the observed universe.\n\n\\subhead{4) The flatness problem}\n\nI find the flatness problem particularly impressive, because the\nnumbers that it leads to are so extraordinary. The problem\nconcerns the value of the ratio\n\\beq\n \\Omega_\\tot \\equiv {\\rho_\\tot \\over \\rho_c} \\ ,\n \\label{eq:3.1}\n\\eeq\nwhere $\\rho_\\tot$ is the average total mass density of the\nuniverse and $\\rho_c = 3 H^2 / 8 \\pi G$ is the critical density,\nthe density that would make the universe spatially flat. \n($\\rho_\\tot$ includes any vacuum energy $\\rho_{\\rm vac} =\n\\Lambda/ 8 \\pi G$ associated with the cosmological constant\n$\\Lambda$, if it is nonzero.)\n\nThe present value of $\\Omega_\\tot$ satisfies\n\\beq\n 0.1 \\lta \\Omega_{\\tot,0} \\lta 2 \\ ,\n \\label{eq:3.2}\n\\eeq\nbut the precise value is not known. Despite the breadth of this\nrange, the value of $\\Omega_\\tot$ at early times is highly\nconstrained, since $\\Omega_\\tot=1$ is an unstable equilibrium\npoint of the standard model evolution. If $\\Omega_\\tot$ was ever\n{\\it exactly} equal to one, it would remain so forever. However,\nif $\\Omega_\\tot$ differed slightly from 1 in the early universe,\nthat difference---whether positive or negative---would be\namplified with time. In particular, the FRW equations imply that\n$\\Omega_\\tot - 1$ grows as\n\\beq\n \\Omega_\\tot - 1 \\propto \\cases{t &(during the\n radiation-dominated era)\\cr \n t^{2/3} &(during the matter-dominated era)\\ .\\cr}\n \\label{eq:3.3}\n\\eeq\nAt $t=1$ sec, for example, Dicke and Peebles \\cite{dicke} pointed\nout that $\\Omega_\\tot$ must have equaled one to an accuracy of\none part in $10^{15}$. Classical cosmology provides no\nexplanation for this fact---it is simply assumed as part of the\ninitial conditions. In the context of modern particle theory,\nwhere we try to push things all the way back to the Planck time,\n$10^{-43}$ sec, the problem becomes even more extreme. At this\ntime $\\Omega_\\tot$ must have equaled one to 58 decimal places!\n\nWhile this extraordinary flatness of the early universe has no\nexplanation in classical FRW cosmology, it is a natural\nprediction for inflationary cosmology. During the inflationary\nperiod, instead of $\\Omega_\\tot$ being driven away from 1 as\ndescribed by Eq.~(\\ref{eq:3.3}), $\\Omega_\\tot$ is driven towards\n1, with exponential swiftness:\n\\beq\n \\Omega_\\tot - 1 \\propto e^{-2 H_{\\rm inf} t} \\ ,\n \\label{eq:3.4}\n\\eeq\nwhere $H_{\\rm inf}$ is the Hubble parameter during inflation. \nThus, as long as there is enough inflation, $\\Omega_\\tot$ can\nstart at almost any value, and it will be driven to unity by the\nexponential expansion. \n\n\\subhead{5) Absence of magnetic monopoles}\n\nAll grand unified theories predict that there should be, in the\nspectrum of possible particles, extremely massive magnetic\nmonopoles. By combining grand unified theories\nwith classical cosmology without inflation, Preskill\n\\cite{preskill} found that magnetic monopoles would be produced\nso copiously that they would outweigh everything else in the\nuniverse by a factor of about $10^{12}$. A mass density this\nlarge would cause the inferred age of the universe to drop to\nabout 30,000 years! In inflationary models, the monopoles can be\neliminated simply by arranging the parameters so that inflation\ntakes place after (or during) monopole production, so the\nmonopole density is diluted to a completely negligible level.\n\n\\subhead{6) Anisotropy of the cosmic background radiation}\n\nThe process of inflation smooths the universe essentially\ncompletely, but quantum fluctuations of the inflaton field can\ngenerate density fluctuations as inflation ends. Generically\nthese are adiabatic Gaussian fluctuations with a nearly\nscale-invariant spectrum \\cite{Starobinsky2, GuthPi, Hawking1,\nBST, BFM}. New data is arriving quickly, but so far the\nobservations are in excellent agreement with the predictions of\nthe simplest inflationary models. For a review, see for example\nBond and Jaffe \\cite{bond-jaffe}, who find that the combined data\ngive a slope of the primordial power spectrum within 5\\% of the\npreferred scale-invariant value.\n\n\n% Section IV:\n\\section{Eternal Inflation: Mechanisms}\n\\setcounter{equation}{0}\n\nHaving discussed the mechanisms and the motivation for inflation\nitself, I now wish to move on the main issue that I want to\nstress in this article---eternal inflation, the questions that it\ncan answer, and the questions that it raises. In this section I\nwill discuss the mechanisms that make eternal inflation possible,\nleaving the other issues for the following sections. I will\ndiscuss eternal inflation first in the context of new inflation,\nand then in the context of chaotic inflation, where it is more\nsubtle. \n\n\\subhead{Eternal New Inflation:}\n\nThe eternal nature of new inflation was first discovered by\nSteinhardt \\cite{steinhardt-nuffield} and Vilenkin\n\\cite{vilenkin-eternal} in 1983. Although the false vacuum is a\nmetastable state, the decay of the false vacuum is an exponential\nprocess, very much like the decay of any radioactive or unstable\nsubstance. The probability of finding the inflaton field at the\ntop of the plateau in its potential energy diagram does not fall\nsharply to zero, but instead trails off exponentially with time\n\\cite{guth-pi2}. However, unlike a normal radioactive substance\nsuch as radium, the false vacuum exponentially expands at the\nsame time that it decays. In fact, in any successful inflationary\nmodel the rate of exponential expansion is always much faster\nthan the rate of exponential decay. Therefore, even though the\nfalse vacuum is decaying, it never disappears, and in fact the\ntotal volume of the false vacuum, once inflation starts,\ncontinues to grow exponentially with time, ad infinitum. \n\n\\begin{figure}[ht]\n\\centerline{\\epsfbox{eternpr.eps}}\n\\caption{A schematic illustration of eternal inflation.} \n\\label{eternalline}\n\\end{figure}\n\nFig.~\\ref{eternalline} shows a schematic diagram of an eternally\ninflating universe. The top bar indicates a region of false\nvacuum. The evolution of this region is shown by the successive\nbars moving downward, except that I could not show the expansion\nand still fit all the bars on the page. So the region is shown\nas having a fixed size in comoving coordinates, while the scale\nfactor, which is not shown, increases from each bar to the next. \nAs a concrete example, suppose that the scale factor for each bar\nis three times larger than for the previous bar. If we follow\nthe region of false vacuum indicated by the top bar as it evolves\ninto the second bar, in about one third of the region the scalar\nfield rolls down the hill of the potential energy diagram,\nprecipitating a local big bang that will evolve into something\nthat will eventually appear to its inhabitants as a universe. \nThis local big bang region is shown in gray and labeled\n``Universe.'' Meanwhile, however, the space has expanded so much\nthat each of the two remaining regions of false vacuum is the\nsame size as the starting region. Thus, if we follow the region\nfor another time interval of the same duration, each of these\nregions of false vacuum will break up, with about one third of\neach evolving into a local universe, as shown on the third bar\nfrom the top. Now there are four remaining regions of false\nvacuum, and again each is as large as the starting region. This\nprocess will repeat itself literally forever, producing a kind of\na fractal structure to the universe, resulting in an infinite\nnumber of the local universes shown in gray. These local\nuniverses are often called {\\it bubble universes,} but that\nterminology conveys the unfortunate connotation that the local\nuniverses are spherical. While bubbles formed in first-order\nphase transitions are round \\cite{coleman-deluccia}, the local\nuniverses formed in eternal new inflation are generally very\nirregular, as can be seen for example in the two-dimensional\nsimulation by Vanchurin, Vilenkin, and Winitzki in Fig.~2 of\nRef.~\\cite{vvw}. I therefore prefer to call them {\\it pocket\nuniverses,} to try to avoid the suggestion that they are round.\n\nThe diagram in Fig.~\\ref{eternalline} is of course an\nidealization. The real universe is three dimensional, while the\ndiagram illustrates a schematic one-dimensional universe. It is\nalso important that the decay of the false vacuum is really a\nrandom process, while I constructed the diagram to show a very\nsystematic decay, because it is easier to draw and to think\nabout. When these inaccuracies are corrected, we are still left\nwith a scenario in which inflation leads asymptotically to a\nfractal structure \\cite{aryal-vilenkin} in which the universe as\na whole is populated by pocket universes on arbitrarily small\ncomoving scales. Of course this fractal structure is entirely on\ndistance scales much too large to be observed, so we cannot\nexpect astronomers to actually find it. Nonetheless, one does\nhave to think about the fractal structure if one wants to\nunderstand the very large scale structure of the spacetime\nproduced by inflation. \n\nMost important of all is the simple statement that once inflation\nbegins, it produces not just one universe, but an infinite\nnumber of universes. \n\n\\subhead{Eternal Chaotic Inflation:}\n\nThe eternal nature of new inflation depends crucially on the\nscalar field lingering at the top of the plateau of\nFig.~\\ref{newinf}. Since the potential function for chaotic\ninflation, Fig.~\\ref{chaoticinf}, has no plateau, it does not\nseem likely that eternal inflation can happen in this context. \nNonetheless, Andrei Linde \\cite{linde-eternal} showed in 1986\nthat chaotic inflation can also be eternal. \n\nThe key to eternal chaotic inflation is the role of quantum\nfluctuations, which is very significant in all inflationary\nmodels. Quantum fluctuations are invariably important on very\nsmall scales, and with inflation these very small scales are\nrapidly stretched to become macroscopic and even astronomical. \nThus the quantum fluctuations of the inflaton field can have very\nnoticeable effects.\n\n\\begin{figure}[ht]\n\\epsfxsize=275pt % Reduced 69.4%\n\\centerline{\\epsfbox{eipot2.eps}}\n\\caption{Evolution of the inflaton field during eternal chaotic\ninflation.} \n\\label{chaotic-eternal}\n\\end{figure}\n\nWhen the mass of the scalar field is small compared to the Hubble\nparameter $H$, these quantum evolution of the scalar field is\naccurately described as a random walk. It is useful to divide\nspace into regions of physical size $H^{-1}$, and to discuss the\naverage value of the scalar field $\\phi$ within a given region. \nIn a time $H^{-1}$, the quantum fluctuations cause the scalar\nfield to undergo a random Gaussian jump of zero mean and a\nroot-mean-squared magnitude\n\\cite{random-vil-ford,random-linde,Starobinsky2,random-starobinsky}\ngiven by\n\\beq\n \\Delta \\phi_{\\rm qu} = {H \\over 2 \\pi} \\ .\n \\label{eq:4.1}\n\\eeq\nThis random quantum jump is superimposed on the classical motion,\nas indicated in Fig.~(\\ref{chaotic-eternal}).\n\nTo illustrate how eternal inflation happens in the simplest\ncontext, let us consider again the free scalar field described by\nthe potential function of Eq.~(\\ref{eq:2.1}). We consider a\nregion of physical radius $H^{-1}$, in which the field has an\naverage value $\\phi$. Using Eq.~(\\ref{eq:2.9}) along with\nEqs.~(\\ref{eq:2.8}) and (\\ref{eq:2.1}), one finds that the\nmagnitude of the classical change that the field will undergo in\na time $H^{-1}$ is given in by\n\\beq\n \\Delta \\phi_{\\rm cl} = {M_{\\rm P} m \\over \\sqrt{12 \\pi}} \\, H^{-1} =\n {1 \\over 4 \\pi} {M_{\\rm P}^2 \\over \\phi} \\ .\n \\label{eq:4.2}\n\\eeq\nLet $\\phi^*$ denote the value of $\\phi$ which is\nlarge enough so that\n\\beq\n \\Delta \\phi_{\\rm qu} (\\phi^*) = \\Delta \\phi_{\\rm cl}(\\phi^*) \\ ,\n \\label{eq:4.3}\n\\eeq\nwhich implies that\n\\beq\n \\phi^* = \\left( {3 \\over 16 \\pi} \\right)^{1/4} {M_{\\rm P}^{3/2} \\over\n m^{1/2}} \\ .\n \\label{eq:4.4}\n\\eeq\n\nNow consider what happens to a region for which the initial\naverage value of $\\phi$ is equal to $\\phi^*$. In a time interval\n$H^{-1}$, the volume of the region will increase by $e^3 \\approx\n20$. At the end of the time interval we can divide the original\nregion into 20 regions of the same volume as the original, and in\neach region the average scalar field can be written as\n\\beq\n \\phi = \\phi^* + \\Delta \\phi_{\\rm cl} + \\delta \\phi \\ ,\n \\label{eq:4.5}\n\\eeq\nwhere $\\delta \\phi$ denotes the random quantum jump, which is\ndrawn from a Gaussian probability distribution with standard\ndeviation $\\Delta \\phi_{\\rm qu} = \\Delta \\phi_{\\rm cl}$. \nGaussian statistics imply that there is a 15.9\\% chance that a\nGaussian random variable will exceed its mean by more than one\nstandard deviation, and therefore there is a 15.9\\% chance that\nthe net change in $\\phi$ will be positive. Since there are now\n20 regions of the original volume, on average the value of $\\phi$\nwill exceed the original value in 3.2 of these regions. Thus the\nvolume for which $\\phi \\ge \\phi^*$ does not (on average)\ndecrease, but instead increases by more than a factor of 3. \nSince this argument can be repeated, the expectation value of the\nvolume for which $\\phi \\ge \\phi^*$ increases exponentially with\ntime. Typically, therefore, inflation never ends, but instead\nthe volume of the inflating region grows exponentially without\nbound. The minimum field value for eternal inflation is a little\nbelow $\\phi^*$, since a volume increase by a factor of 3.2 is\nmore than necessary---any factor greater than one would be\nsufficient. A short calculation shows that the minimal value for\neternal inflation is $0.78 \\phi^*$.\n\nWhile the value of $\\phi^*$ is larger than Planck scale, again we\nfind that this is not true of the energy density:\n\\beq\n V(\\phi^*) = {1 \\over 2} m^2 \\phi^{*2} = \\sqrt{3 \\over 64 \\pi}\n \\, m M_{\\rm P}^3 \\ ,\n \\label{eq:4.6}\n\\eeq\nwhich for $m = 10^{16}$ GeV gives an energy density of $1 \\times\n10^{-4} \\, M_{\\rm P}^4$. \n\nIf one carries out the same analysis with a potential function\n\\beq\n V(\\phi) = {1 \\over 4} \\lambda \\phi^4 \\ ,\n \\label{eq:4.7}\n\\eeq\none finds \\cite{linde-book} that\n\\beq\n \\phi^* = \\left( 3 \\over 2 \\pi \\lambda \\right)^{1/6} M_{\\rm P} \\ ,\n \\label{eq:4.8}\n\\eeq\nand\n\\beq\n V(\\phi^*) = \\left( 3 \\over 16 \\pi \\right)^{2/3} \\lambda^{1/3}\n M_{\\rm P}^4 \\ .\n \\label{eq:4.9}\n\\eeq\nSince $\\lambda$ must be very small in any case so that\ndensity perturbations are not too large, one finds again that\neternal inflation is predicted to happen at an energy density well\nbelow the Planck scale.\n\n% Section V:\n\\section{Eternal Inflation: Implications}\n\\setcounter{equation}{0}\n\\label{implications}\n\nWhen I told Rocky Kolb that I was going to be talking about\neternal inflation, he said, ``That's OK, we can talk about\nphysics later.'' So that's the point I'd like to address here. \nIn spite of the fact that the other universes created by eternal\ninflation are too remote to imagine observing directly, I still\nbelieve that eternal inflation has real consequences in terms of\nthe way we extract predictions from theoretical models. \nSpecifically, there are four consequences of eternal inflation\nthat I will highlight.\n \n\\subhead{1) Unobservability of initial conditions}\n\nFirst, eternal inflation implies that all hypotheses about the\nultimate initial conditions for the universe---such as the\nHartle-Hawking \\cite{hartle-hawking} no boundary proposal, the\ntunneling proposals by Vilenkin \\cite{tunnel-vilenkin} or Linde\n\\cite{tunnel-linde}, or the more recent Hawking-Turok instanton\n\\cite{hawking-turok}---become totally divorced from observation.\nThat is, one would expect that if inflation is to continue\narbitrarily far into the future with the production of an\ninfinite number of pocket universes, then the statistical\nproperties of the inflating region should approach a steady state\nwhich is independent of the initial conditions. Unfortunately,\nattempts to quantitatively study this steady state are severely\nlimited by several factors. First, there are ambiguities in\ndefining probabilities, which will be discussed later. In\naddition, the steady state properties seem to depend strongly on\nsuper-Planckian physics which we do not understand. That is, the\nsame quantum fluctuations that make eternal chaotic inflation\npossible tend to drive the scalar field further and further up\nthe potential energy curve, so attempts to quantify the steady\nstate probability distribution \\cite{LLM,GBLinde} require the\nimposition of some kind of a boundary condition at large $\\phi$. \nAlthough these problems remain unsolved, I still believe that it\nis reasonable to assume that in the course of its perpetual\nevolution, an eternally inflating universe would lose all memory\nof the state in which it started.\n\nAlthough the ultimate origin of the universe would become\nunobservable, I would not expect that the question of how the\nuniverse began would lose its interest. While eternally\ninflating universes continue forever once they start, they are\npresumably not eternal into the past. (The word {\\it eternal} is\ntherefore not technically correct---it would be more precise to\ncall this scenario {\\it semi-eternal} or {\\it future-eternal}.) \nWhile the issue is not completely settled, it appears likely that\neternally inflating universes must necessarily have a beginning. \nBorde and Vilenkin \\cite{borde-vilenkin} have shown, provided\nthat certain conditions are met, that spacetimes which are\nfuture-eternal must have an initial singularity, in the sense\nthat they cannot be past null geodesically complete. The proof,\nhowever, requires the weak energy condition, which is classically\nvalid but quantum-mechanically violated \\cite{borde-vilenkin2}. \nIn any case, I am not aware of any viable model without a\nbeginning, and certainly nothing that we know can rule out the\npossibility of a beginning. The possibility of a quantum origin\nof the universe is very attractive, and will no doubt be a\nsubject of interest for some time. Eternal inflation, however,\nseems to imply that the entire study will have to be conducted\nwith literally no input from observation. \n\n\\subhead{2) Irrelevance of initial probability}\n\nA second consequence of eternal inflation is that the\nprobability of the onset of inflation becomes totally\nirrelevant, provided that the probability is not identically zero.\nVarious authors in the past have argued that one type of\ninflation is more plausible than another, because the initial\nconditions that it requires appear more likely to have occurred. \nIn the context of eternal inflation, however, such arguments have\nno significance.\n\nTo illustrate the insignificance of the probability of the onset\nof inflation, I will use a numerical example. We will imagine\ncomparing two different versions of inflation, which I will call\nType A and Type B\\relax. They are both eternally inflating---but\nType A will have a higher probability of starting, while Type B\nwill be a little faster in its exponential expansion rate. Since\nI am trying to show that the higher starting probability of Type\nA is irrelevant, I will choose my numbers to be extremely\ngenerous to Type A\\relax. First, we must choose a number for how\nmuch more probable it is for Type A inflation to begin, relative\nto type B\\relax. A googol, $10^{100}$, is usually considered a\nlarge number---it is some 20 orders of magnitude larger than the\ntotal number of baryons in the visible universe. But I will be\nmore generous: I will assume that Type A inflation is more likely\nto start than type B inflation by a factor of $10^{1,000,000}$. \nType B inflation, however, expands just a little bit faster, say\nby 0.001\\%. We need to choose a time constant for the\nexponential expansion, which I will take to be a typical grand\nunified theory scale, $\\tau = 10^{-37}$ sec. ($\\tau$ represents\nthe time constant for the overall expansion factor, which takes\ninto account both the inflationary expansion and the exponential\ndecay of the false vacuum.) Finally, we need to choose a length\nof time to let the system evolve. In principle this time\ninterval is infinite (the inflation is eternal into the future),\nbut to be conservative we will watch the system for only one\nsecond.\n\nWe imagine setting up a statistical ensemble of universes at\n$t=0$, with an expectation value for the volume of Type A\ninflation exceeding that of Type B inflation by $10^{1,000,000}$. \nFor brevity, let the term ``weight'' to refer to the ensemble\nexpectation value of the volume. Thus, the weights of Type A\ninflation and Type B inflation will begin with the ratio\n\\beq\n \\left.{W_B \\over W_A}\\right|_{t=0} = 10^{-1,000,000} \\ .\n \\label{eq:5.1}\n\\eeq\nAfter one second of evolution, the expansion factors for Type A\nand Type B inflation will be\n\\begin{eqnarray}\n \\label{eq:5.2}\n Z_A & = & e^{t/\\tau} = e^{10^{37}} \\\\\n \\label{eq:5.3}\n Z_B & = & e^{1.00001\\,t/\\tau} = e^{0.00001\\,t/\\tau} Z_A\n \\nonumber \\\\\n & = & e^{10^{32}} Z_A \\approx 10^{4.3 \\times 10^{31}} Z_A \n \\ .\n\\end{eqnarray}\nThe weights at the end of one second are proportional to these\nexpansion factors, so\n\\beq\n \\left.{W_B \\over W_A}\\right|_{t=1\\ \\rm sec} = 10^{\\left(4.3\n \\times 10^{31} - 1,000,000\\right)} \\ .\n \\label{eq:5.4}\n\\eeq\nThus, the initial ratio of $10^{1,000,000}$ is vastly superseded\nby the difference in exponential expansion factors. In fact, we\nwould have to calculate the exponent of Eq.~(\\ref{eq:5.4}) to an\naccuracy of 25 significant figures to be able to barely detect\nthe effect of the initial factor of $10^{1,000,000}$. \n\nOne might criticize the above argument for being naive, as the\nconcept of time was invoked without any discussion of how the\nequal-time hypersurfaces are to be chosen. I do not know a\ndecisive answer to this objection; as I will discuss later, there\nare unresolved questions concerning the calculation of\nprobabilities in eternally inflating spacetimes. Nonetheless,\ngiven that there is actually an infinity of time available, it is\nseems reasonable to believe that the form of inflation that\nexpands the fastest will always dominate over the slower forms by\nan infinite factor.\n\nA corollary to this argument is that new inflation is not dead. \nWhile the initial conditions necessary for new inflation cannot\nbe justified on the basis of thermal equilibrium, as proposed in\nthe original papers \\cite{Linde1,Albrecht-Steinhardt1}, in the\ncontext of eternal inflation it is sufficient to conclude that\nthe probability for the required initial conditions is nonzero. \nSince the resulting scenario does not depend on the words that\nare used to justify the initial state, the standard treatment of\nnew inflation remains valid.\n\n\\subhead{3) Inevitability of eternal inflation}\n\nThird, I'd like to claim that, since it appears that a universe\nis in principle capable of eternally reproducing, it is hard to\nbelieve that any other description can make sense at all. To\nclarify this point, let me raise the analogy of rabbits. We all\nknow that rabbits can reproduce---in fact, they reproduce like\nrabbits. Suppose that you went out into the woods and found a\nrabbit that had characteristics indicating that it did not belong\nto any known rabbit species. Then you would have to theorize\nabout how the rabbit originated. You might entertain the notion\nthat the rabbit was created by some unique, mysterious, cosmic\nevent that you hope to someday understand better. Or you could\nassume that the rabbit was created by the process of rabbit\nreproduction that we all know so well. I think that we would all\nconsider the latter possibility to be far more plausible. So, I\nclaim that once we become convinced that universes can reproduce\nlike rabbits, then the situations are similar. When we notice\nthat there is a universe and ask how it originated, the same\ninferences that we made for the rabbit question should apply to\nthis one.\n\n\\subhead{4) Possibility of restoring the uniqueness of\ntheoretical predictions}\n\nA fourth consequence of eternal inflation is the possibility that\nit offers to rescue the predictive power of theoretical physics. \nAll the indications suggest that string theory or M theory\ndescribes an elegantly unique theoretical structure, but\nnonetheless it seem unlikely that the theory possesses a unique\nvacuum. Since predictions will ultimately depend on the\nproperties of the vacuum, the predictive power of string/M theory\nmay be limited. Eternal inflation, however, provides a hope that\nthis problem can be remedied. Even if many types of vacua are\nequally stable, it may turn out that a unique state produces the\nmaximum possible rate of inflation. If so, then this state will\ndominate the universe, even if its expansion rate is only\ninfinitesimally larger than the other possibilities. Thus,\neternal inflation might allow physicists to extract unique\npredictions, in spite of the multiplicity of stable vacua.\n\n% Section VI:\n\\section{Difficulties in Calculating Probabilities}\n\\setcounter{equation}{0}\n\nIn an eternally inflating universe, anything that can happen will\nhappen; in fact, it will happen an infinite number of times. Thus,\nthe question of what is possible becomes trivial---anything is\npossible, unless it violates some absolute conservation law. To\nextract predictions from the theory, we must therefore learn to\ndistinguish the probable from the improbable.\n\nHowever, as soon as one attempts to define probabilities in an\neternally inflating spacetime, one discovers ambiguities. Since\nan eternally inflating universe produces an infinite number of\npocket universes, the sample space is infinite. The fraction of\nuniverses with any particular property is given by the\nmeaningless ratio of infinity divided by infinity. To obtain a\nwell-defined answer, one needs to invoke some method of\nregularization. The most straightforward form of regularization\nconsists of truncating the space to a finite subspace, and then\ntaking a limit in which the subspace becomes larger and larger.\n\nTo understand the nature of the problem, it is useful to think\nabout the integers as a model system with an infinite number of\nentities. We can ask, for example, what fraction of the integers\nare odd. Most people would presumably say that the answer is\n$1/2$, since the integers alternate between odd and even. That\nis, if the string of integers is truncated after the $N$th, then\nthe fraction of odd integers in the string is exactly $1/2$ if\n$N$ is even, and is $(N+1)/2N$ if $N$ is odd. In any case, the\nfraction approaches $1/2$ as $N$ approaches infinity.\n\nHowever, the ambiguity of the answer can be seen if one imagines\nother orderings for the integers. One could, if one wished,\norder the integers as \n\\beq\n 1,3,\\ 2,\\ 5,7,\\ 4,\\ 9,11,\\ 6\\ ,\\ldots, \n \\label{eq:6.1}\n\\eeq\nalways writing two odd integers followed by one even integer. \nThis series includes each integer exactly once, just like the\nusual sequence ($1,2,3,4, \\ldots$). The integers are just\narranged in an unusual order. However, if we truncate the\nsequence shown in Eq.~(\\ref{eq:6.1}) after the $N$th entry, and\nthen take the limit $N \\to \\infty$, we would conclude that 2/3 of\nthe integers are odd. Thus, we see that probabilities can\ndepend nontrivially on the method of regularization that is used.\n\nIn the case of eternally inflating spacetimes, one might consider\na regularization defined by ordering the pocket universes in the\nsequence in which they form, and then truncating after the $N$th. \nHowever, each pocket universe fills its own future light cone, so\nno pocket universe forms in the future light cone of another. \nAny two pocket universes are spacelike separated from each other,\nso different observers can disagree about which formed first. \nOne can arbitrarily choose equal-time surfaces that foliate the\nspacetime, and then truncate at some value of $t$, but this\nrecipe is far from unique. In practice, different ways of\nchoosing equal-time surfaces give different results. \n\n% Section VII\n\\section{The Youngness Paradox}\n\\setcounter{equation}{0}\n\nIf one chooses a regularization in the most naive way, one is led\nto a set of very peculiar results which I call the {\\it youngness\nparadox.} \n\nSpecifically, suppose that one constructs a Robertson-Walker\ncoordinate system while the model universe is still in the false\nvacuum (de Sitter) phase, before any pocket universes have\nformed. One can then propagate this coordinate system forward\nwith a synchronous gauge condition,\\footnote{By a synchronous\ngauge condition, I mean that each equal-time hypersurface is\nobtained by propagating every point on the previous hypersurface\nby a fixed infinitesimal time interval $\\Delta t$ in the\ndirection normal to the hypersurface.} and one can define\nprobabilities by truncating at a fixed value $t_f$ of the\nsynchronous time coordinate $t$. That is, the probability of any\nparticular property can be taken to be proportional to the volume\non the $t = t_f$ hypersurface which has that property. This\nmethod of defining probabilities was studied in detail by Linde,\nLinde, and Mezhlumian, in a paper with the memorable title ``Do\nwe live in the center of the world?'' \\cite{center-world}. I\nwill refer to probabilities defined in this way as synchronous\ngauge probabilities.\n\nThe youngness paradox is caused by the fact that the volume of\nfalse vacuum is growing exponentially with time with an\nextraordinarily short time constant, in the vicinity of\n$10^{-37}$ sec. Since the rate at which pocket universes form is\nproportional to the volume of false vacuum, this rate is\nincreasing exponentially with the same time constant. That means\nthat in each second the number of pocket universes that exist is\nmultiplied by a factor of $\\exp\\left\\{10^{37}\\right\\}$. At any\ngiven time, therefore, almost all of the pocket universes that\nexist are universes that formed very very recently, within the\nlast several time constants. The population of pocket universes\nis therefore an incredibly youth-dominated society, in which the\nmature universes are vastly outnumbered by universes that have\njust barely begun to evolve. Although a mature universe has a\nlarger volume then a young one, this multiplicative factor is of\nlittle importance, since in synchronous coordinates the volume no\nlonger grows exponentially once the pocket universe forms.\n\nProbability calculations in this youth-dominated ensemble lead to\npeculiar results, as discussed in Ref.~\\cite{center-world}. These\nauthors considered the expected behavior of the mass density in\nour vicinity, concluding that we should find ourselves very near\nthe center of a spherical low-density region. Here I would like\nto discuss a less physical but simpler question, just to\nillustrate the paradoxes associated with synchronous gauge\nprobabilities. Specifically, I will consider the question: ``Are\nthere any other civilizations in the visible universe that are\nmore advanced than ours?''. Intuitively I would not expect\ninflation to make any predictions about this question, but I will\nargue that the synchronous gauge probability distribution\nstrongly implies that there is no civilization in the visible\nuniverse more advanced than we are.\n\nSuppose that we have reached some level of advancement, and\nsuppose that $t_{\\rm min}$ represents the minimum amount of time\nneeded for a civilization as advanced as we are to evolve,\nstarting from the moment of the decay of the false vacuum---the\nstart of the big bang. The reader might object on the grounds\nthat there are many possible measures of advancement, but I would\nrespond by inviting the reader to pick any measure she chooses;\nthe argument that I am about to give should apply to all of them. \nThe reader might alternatively claim that there is no sharp\nminimum $t_{\\rm min}$, but instead we should describe the problem\nin terms of a function which gives the probability that, for any\ngiven region within a pocket universe of the size of our visible\nuniverse, a civilization as advanced as we are would develop by\ntime $t$. I believe, however, that the introduction of such a\nprobability distribution would merely complicate the argument,\nwithout changing the result. So, for simplicity of discussion, I\nwill assume that there is some sharply defined minimum time\n$t_{\\rm min}$ required for a civilization as advanced as ours to\ndevelop.\n\nSince we exist, our pocket universe must have an age $t_0$\nsatisfying \n\\beq\n t_0 \\ge t_{\\rm min} \\ . \n \\label{eq:7.1}\n\\eeq\nSuppose, however, that there is some civilization\nin our visible universe that is more advanced than we are, let us\nsay by 1 second. In that case Eq.~(\\ref{eq:7.1}) is not\nsufficient, but instead the age of our pocket universe would have\nto satisfy\n\\beq\n t_0 \\ge t_{\\rm min} + 1 \\hbox{\\ second}\\ . \n \\label{eq:7.2}\n\\eeq\nHowever, in the synchronous gauge probability distribution,\nuniverses that satisfy Eq.~(\\ref{eq:7.2}) are outnumbered by\nuniverses that satisfy Eq.~(\\ref{eq:7.1}) by a factor of\napproximately $\\exp\\left\\{10^{37}\\right\\}$. Thus, if we know\nonly that we are living in a pocket universe that satisfies\nEq.~(\\ref{eq:7.1}), the probability that it also satisfies\nEq.~(\\ref{eq:7.2}) is approximately\n$\\exp\\left\\{-10^{37}\\right\\}$. We would conclude, therefore,\nthat it is extraordinarily improbable that there is a\ncivilization in our visible universe that is at least 1 second\nmore advanced than we are.\n\nPerhaps this argument explains why SETI has not found any signals\nfrom alien civilizations, but I find it more plausible that it is\nmerely a symptom that the synchronous gauge probability\ndistribution is not the right one.\n\n% Section VIII\n\\section{Toy Model of Eternal Inflation}\n\\setcounter{equation}{0}\n\nThe conceptual issue involved in the youngness paradox can\nperhaps be clarified by considering a toy model of a highly\nsimplified eternally inflating universe. Suppose that the\nuniverse as a whole can be labeled with a global time variable\n$t$, and that it consists of a countably infinite set of pocket\nuniverses, each of which is labeled by an index $i$. For\nsimplicity, we let each pocket universe have zero spatial\ndimensions, so a spacetime point is fully specified by the time\n$t$ and the index $i$ which indicates the pocket universe in\nwhich it is located. We assume that each pocket universe $i$\nforms at some time $t_i = n_i \\tau$, where $n_i$ is an integer and\n$\\tau$ is a fixed time constant characterizing the entire\nuniverse. Let the number of pocket universes that form at time\n$t = n \\tau$ be equal to $2^n$, for each nonnegative integer $n$. \nAssume that each pocket universe exists for a time $T \\gg \\tau$,\nand then disappears, and that within each pocket universe the\ninterval from the time of formation to disappearance is uniformly\npopulated with ``sentient beings.'' Within each pocket universe\nwe can define a relative time, $t_{\\rm rel} \\equiv t - t_i$,\nwhich measures the amount of time since the formation of the\npocket universe. \n\nThe difficult question, then, is the following: At what relative\ntime $t_{\\rm rel}$ does a {\\it typical} sentient being live? If\none answers this question by truncating the spacetime by the\ncriterion\n\\beq\n t \\le t_c \\ , \n \\label{eq:8.1}\n\\eeq\nfor some cut-off time $t_c = n_c \\tau$, then one finds that most\nof the pocket universes in the truncated spacetime formed within\nthe past few time constants. As $t_c \\to \\infty$, the mean value\nof $t_{\\rm rel}$ approaches $\\tau$. This method is analogous to\nthe synchronous gauge cut-off discussed above. If, however, one\ntruncates the spacetime by including all pocket universes for\nwhich the time of formation\n\\beq\n t_i \\le t_c \\ , \n \\label{eq:8.2}\n\\eeq\nthen the mean value of $t_{\\rm rel}$ is equal to $T/2$ for any\n$t_c$. The truncation method of Eq.~(\\ref{eq:8.1}) leads to the\nyoungness paradox, in which the probability sample is strongly\ndominated by universes that are extremely young, while the\ntruncation method of Eq.~(\\ref{eq:8.2}) does not.\n\nAt this point, I have to admit that I do not understand how to\nresolve the ambiguities associated with this toy model. It is\nconceivable that there is no meaningful method of regularization,\nand that $t_{\\rm rel}$ is somehow not susceptible to\nprobabilistic predictions. It is also conceivable that there is\nsomething wrong with either the truncation (\\ref{eq:8.1}) or\n(\\ref{eq:8.2}) or both, and that a correct analysis would lead to\na unique probability calculation. It is also conceivable that\nthe regularization has to be specified as part of the theory, so\nthat the truncations (\\ref{eq:8.1}) and (\\ref{eq:8.2}) represent\ntwo distinct theories, each of which is logically consistent.\n\n% Section IX\n\\section{An Alternative Probability Prescription}\n\\setcounter{equation}{0}\n\nSince the probability measure depends on the method used to\nregulate the infinite spacetime of eternal inflation, we are not\nforced to accept the consequences of the synchronous gauge\nprobabilities. A very attractive alternative has been proposed\nby Vilenkin \\cite{vilenkin-proposal}, and developed further by\nVanchurin, Vilenkin, and Winitzki \\cite{vvw}. This procedure is,\nroughly speaking, analogous to the truncation of\nEq.~(\\ref{eq:8.2}). \n\nThe key idea of the Vilenkin proposal is to define probabilities\nwithin a single pocket universe (which he describes more\nprecisely as a connected, thermalized domain). Thus, unlike the\nsynchronous gauge method, there is no comparison between old\npocket universes and young ones. To justify this approach it is\ncrucial to recognize that each pocket universe is infinite, even\nif one starts the model with a finite region of de Sitter space. \nThe infinite volume arises in the same way as it does for the\nspecial case of Coleman-de Luccia bubbles\n\\cite{coleman-deluccia}, the interior of which are open\nRobertson-Walker universes. From the outside one often describes\nsuch bubbles in a coordinate system in which they are finite at\nany fixed time, but in which they grow without bound. On the\ninside, however, the natural coordinate system is the one that\nreflects the intrinsic homogeneity, in which the space is\ninfinite at any given time. The infinity of time, as seen from\nthe outside, becomes an infinity of spatial extent as seen on the\ninside. Thus, at least for continuously variable parameters, a\nsingle pocket universe provides an infinite sample space which\ncan be used to define probabilities. The second key idea of\nVilenkin's method is to use the inflaton field itself as the time\nvariable, rather than the synchronous time variable discussed in\nthe previous section.\n\nThis approach can be used, for example, to discuss the\nprobability distribution for $\\Omega$ in open inflationary\nmodels, or to discuss the probability distribution for some\narbitrary field that has a flat potential energy function. If,\nhowever, the vacuum has a discrete parameter which is homogeneous\nwithin each pocket universe, but which takes on different values\nin different pocket universes, then this method does not apply. \n\n\\begin{figure}[ht]\n\\centerline{\\epsfbox{vilsp2.eps}}\n\\caption{A schematic picture of a pocket universe, illustrating\nVilenkin's proposal for the calculation of probabilities.} \n\\label{vilenkin-space}\n\\end{figure}\n\nThe proposal can be described in terms of\nFig.~\\ref{vilenkin-space}. We suppose that the theory includes\nan inflaton field $\\phi$ of the new inflation type, and some set\nof fields $\\chi_i$ which have flat potentials. The goal is to\nfind the probability distribution for the fields $\\chi_i$. We\nassume that the evolution of the inflaton $\\phi$ can be divided\ninto three regimes, as shown on the figure. $\\phi < \\phi_1$\ndescribes the eternally inflating regime, in which the evolution\nis governed by quantum diffusion. For $\\phi_1 < \\phi < \\phi_{\\rm\nend}$, the evolution is described classically in a slow-roll\napproximation, so that $\\dot \\phi \\equiv {\\rm d} \\phi / {\\rm d}\nt$ can be expressed as a function of $\\phi$. For $\\phi >\n\\phi_{\\rm end}$ inflation is over, and the $\\phi$ field no longer\nplays an important role in the evolution. The $\\chi_i$ fields\nare assumed to have a finite range of values, such as angular\nvariables, so that a flat probability distribution is\nnormalizable. They are assumed to have a flat potential energy\nfunction for $\\phi > \\phi_{\\rm end}$, so that they could settle\nat any value. They are also assumed to have a flat potential\nenergy function for $\\phi < \\phi_1$, although they might interact\nwith $\\phi$ during the slow-roll regime, however, so that they\ncan affect the rate of inflation. \n\nSince the potential for the $\\chi_i$ is flat for $\\phi < \\phi_1$,\nwe can assume that they begin with a flat probability\ndistribution $P_0(\\chi_i) \\equiv P(\\chi_i, \\phi_1)$ on the $\\phi\n= \\phi_1$ hypersurface. If the kinetic energy function for the\n$\\chi_i$ is of the standard form, we take $P_0(\\chi_i) = const$. \nIf, however, the kinetic energy is nonstandard,\n\\beq\n {\\cal L}_{\\rm kinetic} = g^{ij}(\\chi) \\partial_\\mu \\chi_i\n \\partial^\\mu \\chi_j \\ ,\n \\label{eq:9.1}\n\\eeq\nas is plausible for a field described in angular variables, then\nthe initial probability distribution is assumed to take the\nreparameterization-invariant form\n\\beq\n P_0(\\chi_i) \\propto \\sqrt{ \\det g} \\ .\n \\label{eq:9.2}\n\\eeq\nDuring the slow-roll era, it is assumed that the $\\chi_i$ fields\nevolve classically, so one can calculate the number of e-folds of\ninflation $N(\\chi_i)$ as a function of the final value of the\n$\\chi_i$ (i.e., the value of $\\chi_i$ on the $\\phi = \\phi_{\\rm\nend}$ hypersurface). One can also calculate the final values\n$\\chi_i$ in terms of the initial values $\\chi_i^0$ (i.e., the\nvalue of $\\chi_i$ on the $\\phi=\\phi_1$ hypersurface). One then\nassumes that the probability density is enhanced by the volume\ninflation factor $e^{3 N (\\chi_i)}$. The evolution from\n$\\chi_i^0$ to $\\chi_i$ results in a Jacobian factor. The\n(unnormalized) final probability distribution is thus given by\n\\beq\n P(\\chi_i, \\phi_{\\rm end}) = P_0(\\chi_i^0) e^{3 N (\\chi_i)} \\,\n \\det {\\partial \\chi_j^0 \\over \\partial \\chi_k} \\ .\n \\label{eq:9.3}\n\\eeq\nAlternatively, if the evolution of the $\\chi_i$ during the\nslow-roll era is subject to quantum fluctuations, Ref.~\\cite{vvw}\nshows how to write a Fokker-Planck equation which is equivalent\nto averaging the result of Eq.~(\\ref{eq:9.3}) over a collection of\npaths that result from interactions with a noise term.\n\nThe Vilenkin proposal sidesteps the youngness paradox by defining\nprobabilities by the comparison of volumes within one pocket\nuniverse. The youngness paradox, in contrast, arose when one\nconsidered a probability ensemble of all pocket universes at a\nfixed value of the synchronous gauge time coordinate---an\nensemble that is overwhelmingly dominated by very young pocket\nuniverses.\n\nThe proposal has the drawback, however, that it cannot be used to\ncompare the probabilities of discretely different alternatives. \nFurthermore, although the results of this method seem\nreasonable, I do not at this point find them compelling. That\nis, it is not clear what principles of physics or probability\ntheory ensure that this particular method of regularizing the\nspacetime is the one that leads to correct predictions. Perhaps\nthere is no way to answer this question, so we may be forced to\naccept this proposal, or something similar to it, as a postulate.\n\n% Section X\n\\section{Probabilities with only one universe?}\n\nIn discussing a probabilistic approach to cosmology, we need to\nknow whether it makes sense to talk about a probability\ndistribution for a cosmic parameter such as $\\Omega$, for which\nwe have only one example to measure. I have certainly heard more\nthan one physicist say that he or she doesn't think that one can\nmeaningfully talk about probabilities for an experiment that can\nbe done only once. The notion that probability requires\nrepetition is very widespread, and I am sure that it is\nincorporated into many books about probability theory. \nNonetheless, I would like to argue that repetition is not at all\nnecessary to make use of probability theory. Instead, I will\nargue that probability is meaningful whenever one has a {\\it\nstrong} probabilistic prediction, by which I mean a prediction\nthat the probability for some discernible event is either very\nclose to zero or very close to one.\n\nThus, if a cosmological theory predicts a probability\ndistribution for $\\Omega$ which is reasonably flat, then there is\nno strong prediction, and the implications of the theory for\n$\\Omega$ do not provide a way of testing the theory. However, if\nthe theory predicts that the probability of $\\Omega$ lying\noutside the range of 0.99 to 1.01 is $10^{-6}$, then I would\nclaim that the prediction is meaningful and can be used to test\nthe theory.\n\nMy point of view can be explained most easily by considering coin\nflips. If a flip of an unbiased coin is repeated 20 times, the\nprobability of getting 20 successive heads is a very small\nnumber, about $10^{-6}$. This is an example of what I call a\nstrong prediction. Many common examples of strong predictions\ninvolve repetition. However, if 20 unbiased coins are flipped\nsimultaneously in a single experiment, the probability that all\nwill come up heads is identical, about $10^{-6}$. Since the\nprobability of these two results---20 successive heads or 20\nsimultaneous heads---are both equally small, I would draw the\nobvious conclusion that we should be equally surprised if either\nresult occurred. It does not matter that the first result\ninvolved repetition, while the second did not. Some might argue\nthat the 20 simultaneous coin flips involved the replication of\nidentical experiments, even if they were not performed in\nsuccession, so I will take the analogy one step further. Suppose\nwe constructed a roulette wheel that was so finely ruled that\nthe probability of the ball landing on 0 was only $10^{-6}$. \nAgain, we should be just as surprised if this result occurred as\nwe would be if 20 successive coins landed heads.\n\nSimilarly, if our cosmological theory predicted that the\nprobability of $\\Omega$ lying outside the range of 0.99 to 1.01\nis $10^{-6}$, we should be just as surprised if this outcome\noccurred as we would be if 20 consecutive coins came up heads. \nIn both cases, we would have good cause to question the\nassumptions that went into calculating the prediction.\n\n% Section X\n\\section{Conclusion}\n\\setcounter{equation}{0}\n\nIn this paper I have summarized the workings of inflation, and\nthe arguments that strongly suggest that our universe is the\nproduct of inflation. I argued that inflation can explain the \nsize, the Hubble expansion, the homogeneity, the isotropy, and the\nflatness of our universe, as well as the absence of magnetic\nmonopoles, and even the characteristics of the nonuniformities. \nThe detailed observations of the cosmic background radiation\nanisotropies continue to fall in line with inflationary\nexpectations, and the evidence for an accelerating universe fits\nwell with the inflationary preference for a flat universe.\n\nNext I turned to the question of eternal inflation, claiming\nthat essentially all inflationary models are eternal. In my opinion\nthis makes inflation very robust: if it starts anywhere,\nat any time in all of eternity, it produces an infinite number of\npocket universes. Eternal inflation has the very attractive\nfeature, from my point of view, that it offers the possibility of\nallowing unique predictions even if the underlying string theory\ndoes not have a unique vacuum. I have also emphasized, however,\nthat there are important problems in understanding the\nimplications of eternal inflation. First, there is the problem\nthat we do not know how to treat the situation in which the\nscalar field climbs upward to the Planck energy scale. Second,\nthe definition of probabilities in an eternally inflating\nspacetime is not yet a closed issue, although important progress\nhas been made. And third, I might add that the entire present\napproach is at best semiclassical. A better treatment may not be\npossible until we have a much better handle on quantum gravity,\nbut eventually this issue will have to be faced.\n\n\\section*{Acknowledgments}\n\nThe author particularly thanks Andrei Linde, Alexander Vilenkin,\nNeil Turok, and other participants in the Isaac Newton Institute\nprogramme {\\it Structure Formation in the Universe} for very\nhelpful conversations. This work is supported in part by funds\nprovided by the U.S. Department of Energy (D.O.E.) under\ncooperative research agreement \\#DF-FC02-94ER40818, and in part\nby funds provided by NM Rothschild \\& Sons Ltd and by the EPSRC.\n\n% Macros that control the format for all references:\n\\newcommand{\\jf}{\\it} % Journal name font\n\\newcommand{\\jt}{\\/} % Journal name spacing correction\n % Replace by {} if Journal name font is not italics\n\\newcommand{\\VPY}[3]{{\\bf #1}, #2 (#3)} % Volume Page Year\n\\newcommand{\\ispace}{\\thinspace} % Space between multiple initials\n\n% Macro to implement the \\. command for spacing \\ispace between initials\n% LaTeX uses \\.{o} for an o with an overdot, but I want to use \\. for\n% periods separating multiple initials. Use \\U{o} for an o with an \n% overdot:\n\\let\\U=\\.\n\\def\\.{.\\nobreak\\ispace\\ignorespaces}\n\n% Macros for individual journal names:\n\\newcommand{\\IJMODPHYS}[3]{{\\jf Int. J. Mod. Phys.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\JETP}[3]{{\\jf JETP Lett.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\MPL}[3]{{\\jf Mod. Phys. Lett.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\NC}[3]{{\\jf Nuovo Cim.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\NP}[3]{{\\jf Nucl. Phys.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\PHYREP}[3]{{\\jf Phys. Rept.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\PL}[3]{{\\jf Phys. Lett.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\PRD}[3]{{\\jf Phys. Rev. D\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\PRL}[3]{{\\jf Phys. Rev. Lett.\\jt} \\VPY{#1}{#2}{#3}}\n\\newcommand{\\PTRSLA}[3]{{\\jf Phil. Trans. R. Soc. Lond.\\jt\\ A}\n\\VPY{#1}{#2}{#3}}\n\\newcommand{\\ZhETF}[3]{{\\jf Zh. Eksp. Teor. Fiz.\\jt} \\VPY{#1}{#2}{#3}}\n\n\\begin{thebibliography}{99}\n\n\\bibitem{Linde1}\nA\\.D.~Linde, \\PL{108B}{389--393}{1982}.\n% A New Inflationary Universe Scenario: A Possible Solution of the\n% Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole\n% Problems\n\n\\bibitem{Albrecht-Steinhardt1}\nA.~Albrecht and P\\.J.~Steinhardt, \\PRL{48}{1220--1223}{1982}.\n% Cosmology for Grand Unified Theories with Radiatively Induced\n% Symmetry Breaking\n\n\\bibitem{chaotic}\nA\\.D.~Linde, \\ZhETF{38}{149--151}{1983} [\\JETP{38}{176--179}{1983}];\n% Chaotic inflating universe\nA\\.D.~Linde, \\PL{129B}{177--181}{1983}.\n% Chaotic inflation\n\n\\bibitem{hyb1} \nA\\.D.~Linde, \\PL{B259}{38--47}{1991}.\n% Axions in Inflationary Cosmology\n\n\\bibitem{hyb2}\nA\\.R.~Liddle and D\\.H.~Lyth, \\PHYREP{231}{1--105}{1993},\nastro-ph/9303019.\n% The Cold Dark Matter Density Perturbation\n\n\\bibitem{hyb3}\nA\\.D.~Linde, \\PRD{49}{748--754}{1994}, astro-ph/9307002.\n% Hybrid Inflation\n\n\\bibitem{hyb4}\nE\\.J.~Copeland, A\\.R.~Liddle, D\\.H.~Lyth, E\\.D.~Stewart, and\nD.~Wands, \\PRD{49}{6410-6433}{1994}, astro-ph/9401011.\n% False Vacuum Inflation with Einstein Gravity\n\n\\bibitem{hyb5}\nE.~Stewart, \\PL{B345}{414--415}{1995}, astro-ph/9407040.\n% Mutated Hybrid Inflation\n\n\\bibitem{RSG}\nL.~Randall, M.~Solja\\v{c}i\\'{c}, and A\\.H.~Guth,\n\\NP{B472}{377--408}{1996}, hep-ph/9512439; also hep-ph/9601296.\n% Supernatural Inflation: Inflation from Supersymmetry\n% with No (Very) Small Parameters\n% Supernatural Inflation (hep-ph/9601296).\n\n\\bibitem{Guth1}\nA\\.H.~Guth, \\PRD{23}{347--356}{1981}.\n% The Inflationary Universe: A Possible Solution to the Horizon\n% and Flatness Problems\n\n\\bibitem{Starobinsky}\nA\\.A.~Starobinsky, \\ZhETF{30}{719}{1979} [\\JETP{30}{682}{1979}];\nA\\.A.~Starobinsky, \\PL{91B}{99--102}{1980}.\n% A New Type of Isotropic Cosmological Models without Singularity\n% (yes, that really is ``Models''; reprinted in Abbott & Pi)\n\n\\bibitem{Coleman}\nS.~Coleman, \\PRD{15}{2929--2936}{1977} [see errata\n\\VPY{16}{1248}{1977}];\n% The Fate of the False Vacuum. 1. Semiclassical Theory\nC\\.G.~Callan and S.~Coleman,\n\\PRD{16}{1762--1768}{1977}.\n% The Fate of the False Vacuum. 2. First Quantum Corrections\n\n\\bibitem{HMS}\nS\\.W.~Hawking, I\\.G.~Moss, and J\\.M.~Stewart,\n\\PRD{26}{2681--2693}{1982}.\n% Bubble Collisions in the Very Early Universe\n\n\\bibitem{GuthWeinberg}\nA\\.H.~Guth and E\\.J.~Weinberg, \\NP{B212}{321--364}{1983}.\n% Could the Universe Have Recovered from a Slow First Order Phase\n% Transition?\n\n\\bibitem{Jensen-Stein-Schabes}\nL\\.G. Jensen and J\\.A. Stein-Schabes, \\PRD{35}{1146--1150}{1987},\nand references therein.\n% Is inflation natural?\n% Lars Gerhard Jensen and Jaime A. Stein-Schabes \n\n\\bibitem{Starobinsky2}\nA\\.A.~Starobinsky, \\PL{117B}{175--178}{1982}.\n% Dynamics of phase transition in the new inflationary universe\n% scenario and generation of perturbations\n\n\\bibitem{GuthPi}\nA\\.H.~Guth and S.-Y.~Pi, \\PRL{49}{1110--1113}{1982}.\n% Fluctuations in the new inflationary universe\n\n\\bibitem{Hawking1}\nS\\.W.~Hawking, \\PL{115B}{295--297}{1982}.\n% The development of irregularities in a single bubble\n% inflationary universe\n\n\\bibitem{BST}\nJ\\.M.~Bardeen, P\\.J.~Steinhardt, and M\\.S.~Turner,\n\\PRD{28}{679--693}{1983}.\n% Spontaneous creation of almost scale-free density perturbations\n% in an inflationary universe\n\n\\bibitem{BFM}\nFor a modern review, see\nV\\.F.~Mukhanov, H\\.A.~Feldman, and R\\.H.~Brandenberger,\n\\PHYREP{215}{203--333}{1992}.\n% Theory of Cosmological Perturbations\n\n\\bibitem{Guth-RS}\nA\\.H.~Guth, \\PTRSLA{307}{141--148}{1982}.\n% Phase transitions in the embryo universe\n\n\\bibitem{dicke}\nR\\.H.~Dicke and P\\.J\\.E.~Peebles, in {\\bf General\nRelativity: An Einstein Centenary Survey}, eds: S\\.W.~Hawking and\nW.~Israel (Cambridge University Press, 1979).\n\n\\bibitem{preskill}\nJ\\.P.~Preskill, \\PRL{43}{1365--1368}{1979}.\n% Cosmological production of superheavy magnetic monopoles\n\n\\bibitem{bond-jaffe}\nJ\\.R.~Bond and A\\.H.~Jaffe, talk given at Royal Society Meeting\non {\\bf The Development of Large Scale Structure in the\nUniverse,} London, England, 25-26 Mar 1998, submitted to {\\jf\nPhil. Trans. Roy. Soc. Lond. A}, astro-ph/9809043.\n\n\\bibitem{steinhardt-nuffield}\nP\\.J. Steinhardt, in {\\bf The Very Early Universe}, Proceedings\nof the Nuffield Workshop, Cambridge, 21 June -- 9 July, 1982,\neds: G\\.W.~Gibbons, S\\.W.~Hawking, and S\\.T\\.C.~Siklos (Cambridge\nUniversity Press, 1983), pp. 251--266.\n% Natural Inflation\n\n\\bibitem{vilenkin-eternal}\nA.~Vilenkin, \\PRD{27}{2848--2855}{1983}.\n% The Birth of Inflationary Universes.\n\n\\bibitem{guth-pi2}\nA\\.H.~Guth and S.-Y.~Pi, \\PRD{32}{1899--1920}{1985}.\n% Quantum Mechanics of the Scalar Field in the New Inflationary\n% Universe\n\n\\bibitem{coleman-deluccia}\nS.~Coleman \\& F.~De~Luccia, \\PRD{21}{3305--3315}{1980}.\n% Gravitational effects on and of vacuum decay\n\n\\bibitem{vvw}\nV.~Vanchurin, A.~Vilenkin, \\& S.~Winitzki, gr-qc/9905097.\n% Predictability crisis in inflationary cosmology and its\n% resolution\n\n\\bibitem{aryal-vilenkin}\nM.~Aryal and A.~Vilenkin, \\PL{199B}{351--357}{1987}.\n% The Fractal Dimension of Inflationary Universe.\n% Mukunda Aryal\n\n\\bibitem{linde-eternal}\nA\\.D.~Linde, \\MPL{A1}{81}{1986};\n% Eternal Chaotic Inflation\nA\\.D.~Linde, \\PL{175B}{395--400}{1986};\n% Eternally Existing Selfreproducing Chaotic Inflationary Universe\nA\\.S.~Goncharov, A\\.D.~Linde, and V\\.F.~Mukhanov,\n\\IJMODPHYS{A2}{561--591}{1987}.\n% The Global Structure of the Inflationary Universe.\n\n\\bibitem{random-vil-ford}\nA.~Vilenkin and L\\.H.~Ford, \\PRD{26}{1231--1241}{1982}.\n% Gravitational Effects Upon Cosmological Phase Transitions.\n\n\\bibitem{random-linde}\nA\\.D.~Linde, \\PL{B116}{335}{1982}.\n% Scalar Field Fluctuations in Expanding Universe and the New\n% Inflationary Universe Scenario.\n\n\\bibitem{random-starobinsky}\nA.~Starobinsky, in {\\bf Field Theory, Quantum Gravity and\nStrings}, eds: H.J. de Vega \\& N. S\\'anchez, {\\jf Lecture Notes\nin Physics\\jt} (Springer Verlag) Vol.~246, pp.~107--126 (1986).\n\n\\bibitem{linde-book}\nSee for example A\\.D.~Linde, {\\bf Particle Physics and\nInflationary Cosmology} (Harwood Academic Publishers, Chur,\nSwitzerland, 1990) Secs.~1.7--1.8.\n\n\\bibitem{hartle-hawking}\nJ\\.B.~Hartle \\& S\\.W.~Hawking, \\PRD{28}{2960--2975}{1983}.\n% Wave Function of the Universe\n\n\\bibitem{tunnel-vilenkin}\nA.~Vilenkin, \\PRD{30}{509--511}{1984};\n% Quantum Creation of Universes\nA.~Vilenkin, \\PRD{33}{3560--3569}{1986};\n% Boundary Conditions in Quantum Cosmology\nA.~Vilenkin, gr-qc/9812027, to be published in {\\bf Proceedings\nof COSMO 98}, Monterey, CA, 15-20 November, 1998.\n% The Quantum Cosmology Debate\n\n\\bibitem{tunnel-linde}\nA\\.D. Linde, \\NC{39}{401--405}{1984};\n% Quantum Creation of the Inflationary Universe\nA\\.D. Linde, \\PRD{58}{083514}{1998}, gr-qc/9802038.\n% Quantum Creation of an Open Inflationary Universe\n\n\\bibitem{hawking-turok}\nS\\.W.~Hawking \\& N\\.G.~Turok, \\PL{B425}{25--32}{1998}, hep-th/9802030.\n% Open Inflation Without False Vacua.\n\n\\bibitem{LLM}\nA.~Linde, D.~Linde, \\& A.~Mezhlumian, \\PRD{49}{1783--1826}{1994},\ngr-qc/9306035.\n% From the Big Bang Theory to the Theory of a Stationary\n% Universe\n\n\\bibitem{GBLinde}\nJ.~Garcia-Bellido \\& A.~Linde, \\PRD{51}{429--443}{1995},\nhep-th/9408023.\n% Stationarity of Inflation and Predictions of Quantum Cosmology\n\n\\bibitem{borde-vilenkin}\nA.~Borde \\& A.~Vilenkin, \\PRL{72}{3305--3309}{1994}, gr-qc/9312022.\n% Eternal inflation and the initial singularity\n\n\\bibitem{borde-vilenkin2}\nA.~Borde \\& A.~Vilenkin, \\PRD{56}{717--723}{1997}, gr-qc/9702019.\n% Violations of the Weak Energy Condition in Inflating\n% Space-Times.\n\n\\bibitem{center-world}\nA.~Linde, D.~Linde, \\& A.~Mezhlumian, \\PL{B345}{203--210}{1995},\nhep-th/9411111.\n\n\\bibitem{vilenkin-proposal}\nA.~Vilenkin, \\PRL{81}{5501--5504}{1998}, hep-th/9806185.\n% Unambiguous Probabilities in an Eternally Inflating Universe\n\n\\end{thebibliography}\n\n\\end{document}\n"
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{
"name": "astro-ph0002188.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{Linde1}\nA\\.D.~Linde, \\PL{108B}{389--393}{1982}.\n% A New Inflationary Universe Scenario: A Possible Solution of the\n% Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole\n% Problems\n\n\\bibitem{Albrecht-Steinhardt1}\nA.~Albrecht and P\\.J.~Steinhardt, \\PRL{48}{1220--1223}{1982}.\n% Cosmology for Grand Unified Theories with Radiatively Induced\n% Symmetry Breaking\n\n\\bibitem{chaotic}\nA\\.D.~Linde, \\ZhETF{38}{149--151}{1983} [\\JETP{38}{176--179}{1983}];\n% Chaotic inflating universe\nA\\.D.~Linde, \\PL{129B}{177--181}{1983}.\n% Chaotic inflation\n\n\\bibitem{hyb1} \nA\\.D.~Linde, \\PL{B259}{38--47}{1991}.\n% Axions in Inflationary Cosmology\n\n\\bibitem{hyb2}\nA\\.R.~Liddle and D\\.H.~Lyth, \\PHYREP{231}{1--105}{1993},\nastro-ph/9303019.\n% The Cold Dark Matter Density Perturbation\n\n\\bibitem{hyb3}\nA\\.D.~Linde, \\PRD{49}{748--754}{1994}, astro-ph/9307002.\n% Hybrid Inflation\n\n\\bibitem{hyb4}\nE\\.J.~Copeland, A\\.R.~Liddle, D\\.H.~Lyth, E\\.D.~Stewart, and\nD.~Wands, \\PRD{49}{6410-6433}{1994}, astro-ph/9401011.\n% False Vacuum Inflation with Einstein Gravity\n\n\\bibitem{hyb5}\nE.~Stewart, \\PL{B345}{414--415}{1995}, astro-ph/9407040.\n% Mutated Hybrid Inflation\n\n\\bibitem{RSG}\nL.~Randall, M.~Solja\\v{c}i\\'{c}, and A\\.H.~Guth,\n\\NP{B472}{377--408}{1996}, hep-ph/9512439; also hep-ph/9601296.\n% Supernatural Inflation: Inflation from Supersymmetry\n% with No (Very) Small Parameters\n% Supernatural Inflation (hep-ph/9601296).\n\n\\bibitem{Guth1}\nA\\.H.~Guth, \\PRD{23}{347--356}{1981}.\n% The Inflationary Universe: A Possible Solution to the Horizon\n% and Flatness Problems\n\n\\bibitem{Starobinsky}\nA\\.A.~Starobinsky, \\ZhETF{30}{719}{1979} [\\JETP{30}{682}{1979}];\nA\\.A.~Starobinsky, \\PL{91B}{99--102}{1980}.\n% A New Type of Isotropic Cosmological Models without Singularity\n% (yes, that really is ``Models''; reprinted in Abbott & Pi)\n\n\\bibitem{Coleman}\nS.~Coleman, \\PRD{15}{2929--2936}{1977} [see errata\n\\VPY{16}{1248}{1977}];\n% The Fate of the False Vacuum. 1. Semiclassical Theory\nC\\.G.~Callan and S.~Coleman,\n\\PRD{16}{1762--1768}{1977}.\n% The Fate of the False Vacuum. 2. First Quantum Corrections\n\n\\bibitem{HMS}\nS\\.W.~Hawking, I\\.G.~Moss, and J\\.M.~Stewart,\n\\PRD{26}{2681--2693}{1982}.\n% Bubble Collisions in the Very Early Universe\n\n\\bibitem{GuthWeinberg}\nA\\.H.~Guth and E\\.J.~Weinberg, \\NP{B212}{321--364}{1983}.\n% Could the Universe Have Recovered from a Slow First Order Phase\n% Transition?\n\n\\bibitem{Jensen-Stein-Schabes}\nL\\.G. Jensen and J\\.A. Stein-Schabes, \\PRD{35}{1146--1150}{1987},\nand references therein.\n% Is inflation natural?\n% Lars Gerhard Jensen and Jaime A. Stein-Schabes \n\n\\bibitem{Starobinsky2}\nA\\.A.~Starobinsky, \\PL{117B}{175--178}{1982}.\n% Dynamics of phase transition in the new inflationary universe\n% scenario and generation of perturbations\n\n\\bibitem{GuthPi}\nA\\.H.~Guth and S.-Y.~Pi, \\PRL{49}{1110--1113}{1982}.\n% Fluctuations in the new inflationary universe\n\n\\bibitem{Hawking1}\nS\\.W.~Hawking, \\PL{115B}{295--297}{1982}.\n% The development of irregularities in a single bubble\n% inflationary universe\n\n\\bibitem{BST}\nJ\\.M.~Bardeen, P\\.J.~Steinhardt, and M\\.S.~Turner,\n\\PRD{28}{679--693}{1983}.\n% Spontaneous creation of almost scale-free density perturbations\n% in an inflationary universe\n\n\\bibitem{BFM}\nFor a modern review, see\nV\\.F.~Mukhanov, H\\.A.~Feldman, and R\\.H.~Brandenberger,\n\\PHYREP{215}{203--333}{1992}.\n% Theory of Cosmological Perturbations\n\n\\bibitem{Guth-RS}\nA\\.H.~Guth, \\PTRSLA{307}{141--148}{1982}.\n% Phase transitions in the embryo universe\n\n\\bibitem{dicke}\nR\\.H.~Dicke and P\\.J\\.E.~Peebles, in {\\bf General\nRelativity: An Einstein Centenary Survey}, eds: S\\.W.~Hawking and\nW.~Israel (Cambridge University Press, 1979).\n\n\\bibitem{preskill}\nJ\\.P.~Preskill, \\PRL{43}{1365--1368}{1979}.\n% Cosmological production of superheavy magnetic monopoles\n\n\\bibitem{bond-jaffe}\nJ\\.R.~Bond and A\\.H.~Jaffe, talk given at Royal Society Meeting\non {\\bf The Development of Large Scale Structure in the\nUniverse,} London, England, 25-26 Mar 1998, submitted to {\\jf\nPhil. Trans. Roy. Soc. Lond. A}, astro-ph/9809043.\n\n\\bibitem{steinhardt-nuffield}\nP\\.J. Steinhardt, in {\\bf The Very Early Universe}, Proceedings\nof the Nuffield Workshop, Cambridge, 21 June -- 9 July, 1982,\neds: G\\.W.~Gibbons, S\\.W.~Hawking, and S\\.T\\.C.~Siklos (Cambridge\nUniversity Press, 1983), pp. 251--266.\n% Natural Inflation\n\n\\bibitem{vilenkin-eternal}\nA.~Vilenkin, \\PRD{27}{2848--2855}{1983}.\n% The Birth of Inflationary Universes.\n\n\\bibitem{guth-pi2}\nA\\.H.~Guth and S.-Y.~Pi, \\PRD{32}{1899--1920}{1985}.\n% Quantum Mechanics of the Scalar Field in the New Inflationary\n% Universe\n\n\\bibitem{coleman-deluccia}\nS.~Coleman \\& F.~De~Luccia, \\PRD{21}{3305--3315}{1980}.\n% Gravitational effects on and of vacuum decay\n\n\\bibitem{vvw}\nV.~Vanchurin, A.~Vilenkin, \\& S.~Winitzki, gr-qc/9905097.\n% Predictability crisis in inflationary cosmology and its\n% resolution\n\n\\bibitem{aryal-vilenkin}\nM.~Aryal and A.~Vilenkin, \\PL{199B}{351--357}{1987}.\n% The Fractal Dimension of Inflationary Universe.\n% Mukunda Aryal\n\n\\bibitem{linde-eternal}\nA\\.D.~Linde, \\MPL{A1}{81}{1986};\n% Eternal Chaotic Inflation\nA\\.D.~Linde, \\PL{175B}{395--400}{1986};\n% Eternally Existing Selfreproducing Chaotic Inflationary Universe\nA\\.S.~Goncharov, A\\.D.~Linde, and V\\.F.~Mukhanov,\n\\IJMODPHYS{A2}{561--591}{1987}.\n% The Global Structure of the Inflationary Universe.\n\n\\bibitem{random-vil-ford}\nA.~Vilenkin and L\\.H.~Ford, \\PRD{26}{1231--1241}{1982}.\n% Gravitational Effects Upon Cosmological Phase Transitions.\n\n\\bibitem{random-linde}\nA\\.D.~Linde, \\PL{B116}{335}{1982}.\n% Scalar Field Fluctuations in Expanding Universe and the New\n% Inflationary Universe Scenario.\n\n\\bibitem{random-starobinsky}\nA.~Starobinsky, in {\\bf Field Theory, Quantum Gravity and\nStrings}, eds: H.J. de Vega \\& N. S\\'anchez, {\\jf Lecture Notes\nin Physics\\jt} (Springer Verlag) Vol.~246, pp.~107--126 (1986).\n\n\\bibitem{linde-book}\nSee for example A\\.D.~Linde, {\\bf Particle Physics and\nInflationary Cosmology} (Harwood Academic Publishers, Chur,\nSwitzerland, 1990) Secs.~1.7--1.8.\n\n\\bibitem{hartle-hawking}\nJ\\.B.~Hartle \\& S\\.W.~Hawking, \\PRD{28}{2960--2975}{1983}.\n% Wave Function of the Universe\n\n\\bibitem{tunnel-vilenkin}\nA.~Vilenkin, \\PRD{30}{509--511}{1984};\n% Quantum Creation of Universes\nA.~Vilenkin, \\PRD{33}{3560--3569}{1986};\n% Boundary Conditions in Quantum Cosmology\nA.~Vilenkin, gr-qc/9812027, to be published in {\\bf Proceedings\nof COSMO 98}, Monterey, CA, 15-20 November, 1998.\n% The Quantum Cosmology Debate\n\n\\bibitem{tunnel-linde}\nA\\.D. Linde, \\NC{39}{401--405}{1984};\n% Quantum Creation of the Inflationary Universe\nA\\.D. Linde, \\PRD{58}{083514}{1998}, gr-qc/9802038.\n% Quantum Creation of an Open Inflationary Universe\n\n\\bibitem{hawking-turok}\nS\\.W.~Hawking \\& N\\.G.~Turok, \\PL{B425}{25--32}{1998}, hep-th/9802030.\n% Open Inflation Without False Vacua.\n\n\\bibitem{LLM}\nA.~Linde, D.~Linde, \\& A.~Mezhlumian, \\PRD{49}{1783--1826}{1994},\ngr-qc/9306035.\n% From the Big Bang Theory to the Theory of a Stationary\n% Universe\n\n\\bibitem{GBLinde}\nJ.~Garcia-Bellido \\& A.~Linde, \\PRD{51}{429--443}{1995},\nhep-th/9408023.\n% Stationarity of Inflation and Predictions of Quantum Cosmology\n\n\\bibitem{borde-vilenkin}\nA.~Borde \\& A.~Vilenkin, \\PRL{72}{3305--3309}{1994}, gr-qc/9312022.\n% Eternal inflation and the initial singularity\n\n\\bibitem{borde-vilenkin2}\nA.~Borde \\& A.~Vilenkin, \\PRD{56}{717--723}{1997}, gr-qc/9702019.\n% Violations of the Weak Energy Condition in Inflating\n% Space-Times.\n\n\\bibitem{center-world}\nA.~Linde, D.~Linde, \\& A.~Mezhlumian, \\PL{B345}{203--210}{1995},\nhep-th/9411111.\n\n\\bibitem{vilenkin-proposal}\nA.~Vilenkin, \\PRL{81}{5501--5504}{1998}, hep-th/9806185.\n% Unambiguous Probabilities in an Eternally Inflating Universe\n\n\\end{thebibliography}"
}
] |
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astro-ph0002189
|
Spatially-resolved spectra of the accretion disc of the novalike UU Aquarii
|
[
{
"author": "Raymundo Baptista$^1$"
},
{
"author": "C. Silveira$^1$"
},
{
"author": "J.E. Steiner$^2$ and Keith Horne$^3$"
},
{
"author": "% and Knox Long$^4$"
},
{
"author": "$^1$ Departamento de F\\'\\i sica"
},
{
"author": "Universidade Federal de Santa Catarina"
},
{
"author": "Campus Trindade"
},
{
"author": "88040-900"
},
{
"author": "Florian\\'opolis - SC"
},
{
"author": "Brazil"
},
{
"author": "$^2$ Laborat\\'orio Nacional de Astrof\\'\\i sica-LNA/CNPq"
},
{
"author": "CP 21"
},
{
"author": "37500-000"
},
{
"author": "Itajub\\'a"
},
{
"author": "$^3$ School of Physics \\& Astronomy"
},
{
"author": "Andrews"
},
{
"author": "North Haugh"
},
{
"author": "St.\\"
},
{
"author": "Fife"
},
{
"author": "KY16 9SS"
},
{
"author": "Scotland"
},
{
"author": "3700 San Martin Drive"
},
{
"author": "Baltimore"
},
{
"author": "% MD 21218"
},
{
"author": "USA"
}
] |
Time-resolved spectroscopy of the novalike variable UU Aquarii is analyzed with eclipse mapping techniques to produce spatially resolved spectra of its accretion disc and gas stream as a function of distance from disc centre in the range 3600-6900 \AA. The spatially-resolved spectra show that the continuum emission becomes progressively fainter and redder for increasing disc radius -- reflecting the radial temperature gradient -- and reveal that the H\,I and He\,I lines appear as deep, narrow absorption features in the inner disc regions transitioning to emission with P Cyg profiles for intermediate and large disc radii. The spectrum of the uneclipsed component has strong H\,I and He\,I emission lines plus a Balmer jump in emission and is explained as optically thin emission from a vertically extended disc chromosphere + wind. Most of the line emission probably arises from the wind. The spatially-resolved spectra also suggest the existence of gas stream ``disk-skimming'' overflow in UU~Aqr, which can be seen down to $R\simeq 0.2\; R_{L1}$. The comparison of our eclipse maps with those of Baptista, Steiner \& Horne (1996) suggests that the asymmetric structure in the outer disc previously identified as the bright spot may be the signature of an elliptical disc similar to those possibly present in SU~UMa stars during superoutbursts.
|
[
{
"name": "uu3.tex",
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Baptista et~al.]\n\t{Raymundo Baptista$^1$, C. Silveira$^1$, J.E. Steiner$^2$\n\tand Keith Horne$^3$ \\\\\n%\tand Knox Long$^4$ \\\\\n\t$^1$ Departamento de F\\'\\i sica, Universidade Federal de Santa Catarina,\n Campus Trindade, 88040-900, Florian\\'opolis - SC, Brazil, \\\\\n ~ email: bap@fsc.ufsc.br, silveira@fsc.ufsc.br \\\\\n\t$^2$ Laborat\\'orio Nacional de Astrof\\'\\i sica-LNA/CNPq, CP 21, 37500-000,\n\tItajub\\'a, Brazil, email: steiner@lna.br \\\\\n\t$^3$ School of Physics \\& Astronomy, University of St.\\,Andrews,\n\tNorth Haugh, St.\\,Andrews, Fife, KY16 9SS, Scotland, \\\\\n ~ email: kdh1@st-and.ac.uk \\\\\n% $^4$ Space Telescope Science Institute, 3700 San Martin Drive, Baltimore,\n% MD 21218, USA, email: long@stsci.edu \n\t}\n\\date{Accepted for publication at Monthly Notices of the Royal Astronomical\n\t\tSociety}\n\n\\pagerange{1-13}\n\\pubyear{2000}\n\n\\begin{document}\n\n\\maketitle\n\n\\begin{abstract}\n\nTime-resolved spectroscopy of the novalike variable UU Aquarii is analyzed\nwith eclipse mapping techniques to produce spatially resolved spectra\nof its accretion disc and gas stream as a function of distance from disc\ncentre in the range 3600-6900 \\AA. The spatially-resolved spectra show\nthat the continuum emission becomes progressively fainter and redder for\nincreasing disc radius -- reflecting the radial temperature gradient --\nand reveal that the H\\,I and He\\,I lines appear as deep, narrow absorption\nfeatures in the inner disc regions transitioning to emission with P Cyg\nprofiles for intermediate and large disc radii. The spectrum of the\nuneclipsed component has strong H\\,I and He\\,I emission lines plus a Balmer\njump in emission and is explained as optically thin emission from a\nvertically extended disc chromosphere + wind. \nMost of the line emission probably arises from the wind.\nThe spatially-resolved spectra also suggest the existence of gas stream \n``disk-skimming'' overflow in UU~Aqr, which can be seen down to\n$R\\simeq 0.2\\; R_{L1}$. The comparison of our eclipse maps with those \nof Baptista, Steiner \\& Horne (1996) suggests that the asymmetric structure \nin the outer disc previously identified as the bright spot may be the \nsignature of an elliptical disc similar to those possibly present in \nSU~UMa stars during superoutbursts.\n\n\\end{abstract}\n\n\\begin{keywords}\nbinaries: close -- novae, cataclysmic variables -- eclipses -- accretion\ndiscs -- stars: individual: (UU Aquarii).\n\\end{keywords}\n\n\n\\section{Introduction}\n\nThe standard picture of a novalike system is that of a close binary in\nwhich a late type star fills its Roche lobe and transfers matter to a\ncompanion white dwarf via an accretion disc. A bright spot is expected \nto form where the gas stream from the donor star hits the edge of the\naccretion disc.\n\nThe SW Sex stars (Thorstensen et~al. 1991) form a sub-class of the\nnovalikes with orbital periods in the range 3-4 hs that do not seem to\nfit within the above standard picture, displaying a range of peculiarities:\n(1) single peaked asymmetric emission lines showing little eclipse, \n(2) large ($\\sim 70\\degr$) phase shifts between photometric and\nspectroscopic conjunction, \n(3) orbital phase-dependent absorption in the Balmer lines,\n(4) Doppler tomograms bright in the lower-left quadrant with small\nor no sign of disc emission, and\n(5) v-shaped continuum eclipses implying in flat radial temperature \nprofiles in the inner disc (e.g., Warner 1995 and references therein).\nEarlier proposals to explain the phenomenon include accretion disc winds\n(Honeycutt, Schlegel \\& Kaitchuck 1986), magnetic white dwarfs\ndisrupting the inner disc (Williams 1989), and gas stream overflow\n(Hellier \\& Robinson 1994). The two most recent models proposed to\nexplain the phenomenology of the SW Sex stars are the disc-anchored\nmagnetic propeller (Horne 1999) and a combination of stream overflow\n+ disc winds (Hellier 1999).\n\nUU~Aqr is an eclipsing novalike (P$_{\\rm orb}= 3.9$\\,hr) whose \nspectrum is dominated by single-peaked strong Balmer and He\\,I emission\nlines (e.g., Downes \\& Keyes 1988). H$\\alpha$ spectroscopy revealed\nthat the line profile is highly asymmetric and phase-dependent \nand that the spectroscopic conjunction lags mid-eclipse\nby $\\sim 0.15$ cycle (Haefner 1989; Diaz \\& Steiner 1991).\nThe lack of the rotational disturbance typical of emitting accretion\ndiscs during eclipse in H$\\beta$ led Hessman (1990) to the suggestion\nthat the emission lines have a non-disc origin.\n\nBaptista, Steiner \\& Cieslinski (1994; hereafter BSC94) derived a\nphotometric model for the binary with $q= 0.30$, M$_1 = 0.67\\:\n{\\rm M}_{\\odot}$, an inclination of $i= 78$ degrees.\nFrom the analysis of mid-eclipse fluxes they suggested that the Balmer\nlines are formed in an extended region only partially occulted during\neclipse, possibly in a wind emanating from the inner disc.\nThey also found that UU Aqr presents long-term brightness variations of\nlow amplitude ($\\simeq 0.3$ mags) on timescales of years.\n\nThe eclipse mapping study of Baptista, Steiner \\& Horne (1996;\nthereafter BSH96) indicates that the inner disc of UU Aqr is\noptically thick, resulting in a distance estimate of 200 pc.\nTemperatures in the disc range from $\\sim 6000$\\,K in the outer \nregions to $\\sim 16000$\\,K near the white dwarf at disc centre.\nThe radial temperature profiles in the high state follow the\nT$\\:\\propto R^{-3/4}$ law in the outer and intermediate disc regions\nbut flattens off in the inner disc, leading to mass accretion rates\nof $10^{-9.2}\\:{\\rm M_{\\odot}\\,yr}^{-1}$ at $R= 0.1\\: R_{\\rm L1}$\nand $10^{-8.8}\\:{\\rm M_{\\odot}\\,yr}^{-1}$ at $R= 0.3\\: R_{\\rm L1}$\n($R_{\\rm L1}$ is the distance from disc centre to the inner Lagrangian\npoint). Together with other characteristics, this led BSH96 to suggest\nthat UU Aqr was an SW Sex star.\nThe comparison of eclipse maps of the low and high states revealed that\nthe differences are due to changes in the structure of the outer parts\nof the disc, the most noticeable effect being the appearance of a\nconspicuous red, bright structure at disc rim, which the authors\nidentified with the bright spot.\n\nAccording to BSH96, the \\.{M} of UU Aqr is barely above the critical\nlimit for disc instability to set in. Warner (1997) noted that the\nouter disc temperature is only 6000 K and remarked that small variations\nin \\.{M} could lead to dwarf novae type outbursts.\nHoneycutt, Robertson \\& Turner (1998) performed a long-term photometric\nmonitoring of UU Aqr which confirmed the high and low brightness states\nof BSC94 and revealed the existence of small amplitude ($\\simlt 1.0$ mag)\nbrightness variations on timescales of a few days, which they called\n`stunted outbursts'.\n\nThe detailed spectroscopic study of Hoard et~al. (1998) reinforced the\nclassification of UU Aqr as an SW Sex star.\nThey found evidences for the presence of a bright spot at the impact site\nof the gas stream with the edge of the disc, and a non-axisymmetric,\nvertically and azimuthally extended absorbing structure in the disc.\nThey proposed an explanation for the absorbing structure as well as for\nthe other spectroscopic features of UU Aqr in terms of the explosive\nimpact of the accretion stream with the disc.\nOptical and ultraviolet spectroscopy by Kaitchuck et~al. (1998)\nshows a secondary eclipse at phase 0.4 in the optical and Balmer lines\n(but not in the UV continuum or lines) which they suggested may be\ncaused by an occultation of the bright spot and stream region by material\nsuspended above the inner disc.\n\nIn this paper we report on the analysis of time-resolved spectroscopy\nof UU Aqr with multi-wavelength eclipse mapping techniques to derive \nspatially-resolved spectra of the accretion flow in this binary.\nSection~\\ref{data} describes the observations and data reduction procedures,\nwhile section~\\ref{analise} describes the analysis of the light curves with\neclipse mapping techniques.\nSection~\\ref{resultados} presents eclipse maps at selected wavelengths,\nthe radial intensity and brightness temperature distributions,\nspatially resolved spectra of the accretion disc and gas stream as well\nas the spectrum of the uneclipsed component.\nThe results are discussed in section~\\ref{discussao} and summarized in section~\\ref{conclusao}.\n\n\n\\section{Observations} \\label{data}\n\nTime-resolved spectroscopy covering 5 eclipses of UU~Aqr was obtained\nwith the 2.1-m telescope at the Kitt Peak National Observatory (KPNO) on\nJuly-August 1993 in the spectral range 3500--6900 \\AA\\ (spectral\nresolution of $\\Delta\\lambda= 1.5$ \\AA\\ pixel$^{-1}$).\nThe observations consist of 5 sets of $\\simeq 100$ short exposure\n($\\Delta t=30s$) spectra at a time resolution of 50\\,s. A close comparison\nstar (star C1 of BSC94) was included in the slit to allow correction of sky\ntransparency variations and slit losses. The observations (summarized in\nTable~\\ref{tab1}) were performed under good (cloud-free) sky conditions and\nat small to moderate air masses ($X \\leq 1.4$) except for run 1, which\nstarted while the object was still at a reasonably high zenith angle\n($X= 2.2$).\n%\n% ############################### TABLE 1 #################################\n\\begin{table*}\n \\centering\n \\begin{minipage}{120mm}\n \\caption{Journal of the observations.}\n \\label{tab1}\n\\begin{tabular}{@{}lccccccc@{}}\n~~Date & Run & \\multicolumn{2}{c}{UT} & No. of & Spectral & Cycle &\nPhase range \\\\ [-0.5ex]\n~(1993) && start & end & spectra & range (\\AA) & number & (cycle) \\\\ [1ex]\n22 July & 1 & 05:56 & 07:33 & 105 & 3564.0--6766.5 & 17389 & $-0.20,+0.21$ \\\\\n27 July & 2 & 07:59 & 09:40 & 111 & 3601.6--6805.5 & 17420 & $-0.11,+0.32$ \\\\\n13 August & 3 & 07:52 & 09:25 & 101 & 3646.5--6850.5 & 17524 & $-0.22,+0.17$ \\\\ \n15 August & 4 & 07:01 & 08:37 & 106 & 3649.5--6853.5 & 17536 & $-0.20,+0.20$ \\\\\n16 August & 5 & 06:18 & 08:18 & 110 & 3649.5--6853.5 & 17542 & $-0.27,+0.24$ \\\\ \n\\end{tabular}\n\\end{minipage}\n\\end{table*}\n% #########################################################################\n\n\nThe data were bias-subtracted and corrected for flat-field and slit\nillumination effects using standard {\\sc iraf} procedures.\n1-D spectra of both variable and comparison star were extracted\nwith the optimal extraction algorithm of Horne (1986). \nThe individual spectra were checked for the presence of possible cosmic\nrays and, when appropriate, were corrected by interpolation from the\nneighboring wavelengths. Arc-lamp observations were used to calibrate the\nwavelength scale (accuracy of 0.15 \\AA). Observations of the standard spectrophotometric stars\nBD+28\\,4211 and G191\\,B2B (Massey et~al. 1988) were used to derive the\ninstrumental sensitivity function and to flux calibrate the set of extracted\nspectra on each night. Error bars were computed taking into account the photon\ncount noise and the sensitivity response of the instrument.\n\nThe reduced spectra were combined to produce trailed spectrograms of the\nvariable and the comparison star for each night. The display of the trailed\nspectrograms of the comparison star shows that there were non negligible sky\ntransparency variations and/or time-dependent slit losses along the runs.\nWe defined a reference spectrum of the comparison star by computing an average\nof 40 spectra on night 5 corresponding to the time for which the star was\nclosest to zenith.\nWe normalized the spectrograms of the comparison star by dividing each\nspectrum by the reference spectrum. A 2-D cubic spline fit was used to\nproduce a smoothed version of the normalized spectrograms.\nThe sky transparency variations and variable slit losses were corrected\nby dividing the spectrogram of the variable by the smoothed, normalized\nspectrogram of the comparison star on each night (a procedure analogous\nto the flat-field correction).\nThe reference spectrum is consistent with the UBVRI photometry of star C1\n(BSC94) at the 1-$\\sigma$ level. Therefore, the absolute photometric accuracy\nof these observations should be better than 10 per cent.\n\nFig.\\,\\ref{fig1} shows average out-of-eclipse and mid-eclipse spectra of\nUU~Aqr on 1995 August 13. The spectra are dominated by strong single-peaked\nBalmer emission lines but also show He\\,I lines and the blend of\nC\\,III, N\\,III and He\\,II lines at $\\sim 4650$ \\AA. The emission lines\nhave asymmetrical shapes, the red side of the line being stronger --\nin accordance with the results of Hessman (1990) and Diaz \\& Steiner (1991).\nThe He\\,I lines and the higher energy Balmer lines show a possible double\npeak structure suggesting either classical double-peaked emission from a\nhighly inclined disc or single peaked emission with a central absorption\ncomponent. While the continuum is reduced by a factor\n$\\simeq 3$ during eclipse, the emission lines\nsuffer a much smaller reduction in flux suggesting that they possibly\narise from a vertically-extended source larger than the accretion disc\n(responsible for the continuum emission), in accordance with inferences\ndrawn by BSC94.\n%\n% ############################## FIGURE 1 #################################\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig01.ps,angle=-90,width=10.5cm,rheight=7.5cm}}\n\\caption{Average out-of-eclipse (black, phase range $-0.22$ to $-0.06$ cycle)\nand mid-eclipse (light gray, phase range $-0.025$ to 0.025 cycle) spectra of\nUU~Aqr on 1995 August 13. Major emission features are indicated by vertical\ndotted lines.}\n\\label{fig1}\n\\end{figure}\n\n\nFig.\\,\\ref{fig2} shows lightcurves of the 5 runs in the broad band $5000-\n6500$ \\AA. The gap in run 5 is due to\nan interruption of the observations to check the telescope focus.\nThe lightcurves have similar eclipse shapes and out of eclipse flux levels,\nwith variations at the level of $\\simlt 20$\\ per cent between the runs.\nIndications that the observations were performed while UU~Aqr was in its\nhigh brightness state come from the eclipse shape and average out of eclipse\nflux level. The latter suggests that the object was even slightly brighter\nthan the typical high brightness state of BSC94.\nThese remarks are in agreement with the historical lightcurve of Honeycutt\net~al. (1998, see their fig.\\,1), which shows that UU~Aqr reached a maximum\nof its long-term average brightness level during 1993, the epoch of our\nobservations. The spectral range of the lightcurves in Fig.\\,1 corresponds\nroughly to the $V$ band.\nThe average out of eclipse level of all runs yields an approximate mean\nmagnitude of $V= 13.2 \\pm 0.2$ mag, consistent with the value drawn from\nthe lightcurve of Honeycutt et~al. (1998), of $V= 13.4 \\pm 0.6$ mag.\n%\n% ############################## FIGURE 2 #################################\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig02.ps,width=10cm,rheight=12cm}}\n\\caption{Broad band lightcurves of the UU Aqr dataset. The curves are\nprogressively displaced upwards by 20 mJy for visualization purposes.\nHorizontal lines at mid-eclipse show the true zero level in each case.}\n\\label{fig2}\n\\end{figure}\n\n\n\\section{Data analysis} \\label{analise}\n\n\\subsection{Light curve construction}\n\nThe spectra were divided into 226 passbands of 15 \\AA\\ in the continuum and\nfainter lines, and $\\simeq 500\\; km\\,s^{-1}$ across the most prominent lines.\nFor each passband a lightcurve was extracted by computing the average flux\non the corresponding wavelength range and phase folding the resulting data\naccording to the ephemeris of BSC94. A phase correction of $-0.003$ cycle was\nfurther applied to the data to make the centre of the white dwarf eclipse\ncoincident with phase zero. For those passbands including emission lines\nthe light curves comprise the total flux at the corresponding bin with\nno subtraction of a possible underlying continuum contribution.\n\nSince the dataset correspond to the same brightness level it was possible\nto combine the lightcurves of all runs to produce average lightcurves for\neach passband. This is helpful to increase the signal-to-noise ratio of the\nlightcurves and to reduce the influence of flickering in the eclipse shape.\nFor each passband, we first normalized the individual lightcurves by\nfitting a spline function to the phases outside eclipse and dividing the\nlightcurve by the fitted spline. The normalized lightcurves were combined by\nseparating the data into phase bins of 0.0038~cycle and computing the median\nfor each bin. The median of the absolute deviations with respect to the\nmedian is taken as the corresponding uncertainty.\nThe resulting lightcurve is scaled back to flux units by multiplying the\ncombined lightcurve by the median flux of the spline functions at phase zero.\nThis procedure removes orbital variations outside eclipse with\nonly minor effects on the eclipse shape itself.\n\n\n\\subsection{Eclipse mapping}\n\\label{mem}\n\nThe eclipse mapping method was used to solve for a map of the disc\nbrightness distribution and for the flux of an additional uneclipsed\ncomponent in each passband. For the details of the method the reader\nis referred to Horne (1985, 1993), Baptista \\& Steiner (1993) and\nRutten et al. (1994).\n\nFor our analysis we adopted the same eclipse map of BSH96, a $51 \\times 51$\npixel grid centred on the primary star with side $2 \\:R_{L1}$ where\n$R_{L1}$ is the distance from the disc centre to the inner Lagrangian point.\nThis choice provides maps with a nominal spatial resolution of $0.039 \\:\nR_{L1}$, comparable to the expected size of the white dwarf in UU~Aqr\n($\\simeq 0.032\\: R_{L1}$). The eclipse geometry is specified by the mass\nratio $q$ and the inclination $i$. We adopted the parameters of BSC94,\n$i= 78\\degr$ and $q=0.3$.\nThe specific intensities in the eclipse map were computed assuming\nR$_{L1}= 0.74 \\; R_\\odot$ (BSC94) and a distance of 200 pc (BSH96).\n\nThe statistical uncertainties of the eclipse maps were estimated with a\nMonte Carlo procedure (e.g., Rutten et al. 1992; Baptista et~al. 1995).\nFor a given narrow-band lightcurve a set of 10 artificial lightcurves is\ngenerated, in which the data points are independently and randomly\nvaried according to a Gaussian distribution with standard deviation\nequal to the uncertainty at that point. The lightcurves are fitted\nwith the eclipse mapping algorithm to produce a set of randomized\neclipse maps. These are combined to produce an average map and a map\nof the residuals with respect to the average, which yields the statistical\nuncertainty at each pixel.\nThe uncertainties obtained with this procedure will be used when\nestimating the errors in the derived radial temperature and intensity\nprofiles as well as in the spatially-resolved spectra.\n\nAverage light curves, fitted models, and eclipse maps at selected passbands\nare show in Figs.\\,\\ref{fig3} and \\ref{fig4}. These will be discussed in\ndetail in section\\,\\ref{resultados}.\n\n\n\\section{Results} \\label{resultados}\n\n\\subsection{Accretion disc structure}\n\\label{estrutura}\n\nIn this section we compare eclipse maps at selected passbands in order\nto study the structure of the accretion disc at different wavelengths.\n\nFig.\\,\\ref{fig3} shows lightcurves (left panels) and eclipse maps (right\npanels) of 4 selected continuum passbands close to the Johnson-Cousins\nUBVR effective wavelengths in order to allow a comparison with\nthe results of BSH96.\nDashed horizontal lines depict the uneclipsed component in each case.\nThe continuum lightcurves show a deep eclipse with a slightly asymmetric\negress shoulder which is more pronounced for longer wavelengths.\nThis results in eclipse maps with brightness distributions concentrated\ntowards disc centre and asymmetric structures in the trailing quadrant of\nthe disc closest to the secondary star (the upper right quadrant in the\neclipse maps of Fig.\\,\\ref{fig3}).\nThe uneclipsed component at $\\lambda 3657$ is perceptibly \nlarger than at $\\lambda 4411$, suggesting that the Balmer jump is\nin emission and that the uneclipsed light has an important contribution\nfrom optically thin gas. This is in line with previous results by\nBSC94 and BSH96.\nThe eclipse shapes and out of eclipse levels resemble those\nof the high brightness state observed by BSH96, although with a less\npronounced asymmetry at eclipse egress. Accordingly, the eclipse maps\nclearly lack the noticeable asymmetric structure at disc edge which was\nthe main characteristic of the high state (BSH96, see their Fig.\\,3).\nWe will return to this point in section\\,\\ref{discussao}.\n%\n% ############################## FIGURE 3 #################################\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig03.ps,width=11cm,rheight=13.5cm}}\n\\caption{ Lightcurves (left) and eclipse maps (right) at selected continuum\n\tpassbands. Data lightcurves are shown as gray dots with error bars and\n\tthe fitted models appear as solid black lines. A horizontal dashed line\n\tdepicts the uneclipsed component in each case. Labels indicate the\n\tcentral wavelength of each passband. Eclipse maps are shown to the right\n\tin a logarithmic grayscale: dark regions are brighter; white corresponds\n\tto $\\log I_\\nu= -6.5$, and black to $\\log I_\\nu= -3.1$. Dotted curves\n\tshow the projection of the primary Roche lobe onto the orbital plane\n\tand the theoretical gas stream trajectory; the secondary star is to the\n\tright of each panel and the stars rotate counter-clockwise. }\n\\label{fig3}\n\\end{figure}\n\nFig.\\,\\ref{fig4} shows lightcurves and eclipse maps for the line centre\npassbands of H$\\alpha$, H$\\beta$, H$\\gamma$ and He\\,I $\\lambda$5876.\nWe remark that the line lightcurves include the total flux at the \ncorresponding wavelength range with no subtraction of an interpolated\ncontinuum. The eclipses are shallow, leading to brightness distributions\nwhich are flatter than those of the continuum. \nSimilar to the continuum maps, the asymmetry in the egress shoulder is\nmore pronounced for the lines at longer wavelengths.\nThe uneclipsed components are considerably larger than in the continuum,\nindicating that the uneclipsed spectrum has strong Balmer and He\\,I\nemission lines.\nThe large error bars of the H$\\alpha$ centre lightcurve is due not to\nlow signal-to-noise ratio but to the variability of the eclipse shape at\nthis wavelength. This effect is also seen, although to a lesser extent,\nin H$\\beta$ and H$\\gamma$.\n%\n% ############################## FIGURE 4 #################################\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig04.ps,width=11cm,rheight=13.5cm}}\n\\caption{ Lightcurves (left) and eclipse maps (right) for the H$\\alpha$,\n\tH$\\beta$, H$\\gamma$ and He\\,I $\\lambda 5876$ line centre passbands.\n\tThe notation and logarithmic grayscale are the same as in\n\tfigure\\,\\ref{fig3}. }\n\\label{fig4}\n\\end{figure}\n\n\nFig.\\,\\ref{fig5} shows (Doppler) velocity-resolved lightcurves (left) and\neclipse maps (right) across the H$\\beta$ line.\nThere is marginal evidence of rotational disturbance: the minimum of the\nblue bin lightcurve ($- 494 \\; km \\;s^{-1}$) is slightly displaced towards \nnegative phases while that of the red bin lightcurve ($+ 494 \\; km \\;s^{-1}$)\nis correspondingly displaced towards positive phases, suggesting that the\nline emitting gas rotates in the prograde sense.\nHowever, the eclipse maps in the symmetric velocity bins do not show the\nmirror symmetry (over the line joining both stars) expected for line\nemission from a Keplerian disc around the white dwarf.\nEqually remarkable are the facts that the lightcurve in the red bin has a\nmuch larger out-of-eclipse flux than its blue counterpart and that the\ncorresponding eclipse map is perceptibly brighter than that of the blue\nbin anywhere. A similar behaviour is found in the other lines for which\nvelocity-resolved maps were obtained.\nThis cannot be attributed to the underlying continuum since the\ninterpolated continuum has essentially a constant level across each line.\nIt seems clear that most of the line emission does not arise from a\ndisc in Keplerian rotation.\n%\n% ############################## FIGURE 5 #################################\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig05.ps,width=10cm,rheight=12.2cm}}\n\\caption{ H$\\beta$ velocity-resolved lightcurves (left) and eclipse maps\n\t(right) at velocities of $-494,\\; 0,\\; {\\rm and}\\; +494\t\\;km \\;s^{-1}$.\n\tThe notation and logarithmic grayscale are the same as in\n\tfigure\\,\\ref{fig3}. }\n\\label{fig5}\n\\end{figure}\n\n\n\\subsection{Radial temperature distribution and mass accretion rate estimate}\n\nThe simplest way of testing theoretical disc models is to convert the\nintensities in the eclipse maps to blackbody brightness temperatures,\nwhich can then be compared to the radial run of the effective temperature\npredicted by steady state, optically thick disc models. However, as\ndiscussed by Baptista et~al. (1998), a relation between the effective\ntemperature and a monochromatic brightness temperature is non-trivial,\nand can only be properly obtained by constructing self-consistent models\nof the vertical structure of the disc. Therefore, our analysis here\nis meant as preliminary, and should be complemented by detailed disc\nspectrum modeling in a future paper.\n\nFig.\\,\\ref{fig6} shows brightness temperature radial distributions for\nthe continuum maps of Fig.\\,\\ref{fig3} in a logarithmic scale.\nEach temperature shown is the blackbody brightness temperature that\nreproduces the observed surface brightness at the corresponding pixel\nassuming a distance of 200~pc to UU~Aqr (BSH96). Steady-state disc models\nfor mass accretion rates of $10^{-8.5}$, $10^{-9}$, $10^{-9.5}$ and\n$10^{-10}\\; M_\\odot \\; yr^{-1}$ are plotted as dotted lines for comparison.\nThese models assume M$_1= 0.67 \\; M_\\odot$ and $R_1= 0.012 \\; R_\\odot$\n(BSC94).\n\nThe distributions resemble those obtained by BSH96 for the high brightness\nstate of UU Aqr, closely following the $T\\propto R^{-3/4}$ law for steady\naccretion in the intermediate and outer disc regions ($R \\geq 0.2\\; \nR_{\\rm L1}$) but displaying a noticeable flattening in the inner disc\n($R < 0.1\\; R_{\\rm L1}$).\nTemperatures range from $\\sim 18000$ K in the inner disc to 6000 K in the\nouter disc regions, leading to inferred mass accretion rates of \\.{M}=\n$10^{-9.0 \\pm 0.3}\\; M_\\odot \\, yr^{-1}$ at $R= 0.1\\; R_{\\rm L1}$ and\n$10^{-8.7 \\pm 0.2} \\; M_\\odot \\, yr^{-1}$ at $R= 0.3\\; R_{\\rm L1}$ --- in\ngood agreement with the results of BSH96 for the high brightness state.\nThe quoted errors on \\.{M} account for the statistical uncertainties in the\neclipse maps, obtained from the Monte Carlo procedure described in\nsection\\,\\ref{mem}, and the scatter in the temperatures of maps at\ndifferent wavelengths.\nThe eclipse map at $\\lambda 3657$ leads to temperatures which are\nsystematically higher than those of the other continuum maps of Fig.\\,3,\nin an example of the limitations of using brightness temperatures to\nestimate the mass accretion rate. This difference reflects the fact that\nthe Balmer jump appears in emission for the intermediate and outer disc\nregions, as will be seen in section\\,\\ref{spectra}.\n%\n% ############################## FIGURE 6 #################################\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig06.ps,angle=-90,width=11cm,rheight=7.5cm}}\n\\caption{ Brightness temperature radial distributions of the UU Aqr accretion\n\tdisc for the continuum maps of figure\\,\\ref{fig3}, calculated assuming\n\ta distance of 200 pc to the system (BSH96). Dotted lines correspond to\n\tsteady-state disc models for mass accretion rates of \\.{M}$= 10^{-8.5}$,\n\t$10^{-9}$, $10^{-9.5}$ and $10^{-10}\\; M_\\odot \\; yr^{-1}$, assuming\n\tM$_1= 0.67 \\; M_\\odot$ and $R_1= 0.012 \\; R_\\odot$ (BSC94). Abscissae\n\tare in units of the distance from disc centre to the inner Lagrangian\n\tpoint (R$_{\\rm L1}$). }\n\\label{fig6}\n\\end{figure}\n\n\n\\subsection{Radial line intensity distributions}\n\nLeft panel in Fig.\\,\\ref{fig7} shows radial intensity distributions for\nthe most prominent lines (solid) and adjacent continuum (dotted) in a\nlogarithmic scale. The line distributions were obtained from the average\nof all eclipse maps across the line region, while the continuum\ndistributions were obtained from the average of eclipse maps on\nboth sides of each line. \nNet line emission distributions were computed by subtracting the\ndistributions of the adjacent continuum from those of the lines,\nand are shown in the right panel.\nIn the external map regions ($R \\simgt 0.7\\; R_{\\rm L1}$) the intensities\nof both line and continuum drop by a factor $\\sim 10^3$ with respect\nto the inner disc regions, making the computation of the net emission\nquite noisy and unreliable.\nH$\\alpha$ is seen in emission (intensities larger than those at the\nadjacent continuum) at all disc radii and up to $R \\simeq 0.6\\; R_{\\rm L1}$. \nThe other lines are in absorption in the inner disc and transition to\nemission at intermediate ($R \\sim 0.2\\; R_{\\rm L1}$) disc radius.\nThis behaviour is noticeably different from that observed at the low\nbrightness state, where H$\\alpha$ is seen in emission in the inner disc\nand disappears into the continuum for $R \\simeq 0.3\\; R_{\\rm L1}$ (BSH96).\nThis result suggests that the line emission region increases in size\nfrom the low to the high brightness state, possibly in response to changes\nin mass accretion rate.\nThe transition from absorption to emission occurs at larger disc radii for\nlines of higher excitation. This can be explained, for the Balmer lines,\nby the increase in continuum emission at the inner disc for shorter\nwavelengths.\n%\n% ############################## FIGURE 7 #################################\n%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig07.ps,width=10cm,rheight=12cm}}\n\\caption{ Radial line intensity profiles for the most prominent lines,\n\tcalculated assuming a distance of 200 pc to the system (BSH96). \n\tAbscissae are in units of the distance from disc centre to the inner\n\tLagrangian point (R$_{\\rm L1}$). Right panels show net line emission \n\tradial distributions. Dotted lines depict the slope of the expected\n\trelation $I \\propto R^{-1.5}$. }\n\\label{fig7}\n\\end{figure}\n\nA set of dotted lines in the right panel indicate the slope of the empirical\nradial dependency of the line emissivity in accretion discs, $I \\propto\nR^{-1.5}$, as inferred from Doppler Tomography by assuming a Keplerian\ndistribution of velocities for the emitting gas (Marsh et al. 1990).\nFor H$\\gamma$ and He\\,I $\\lambda$5876, the net emission occurs for a narrow range of radii making a comparison with the empirical law difficult.\nThe derived radial distributions for H$\\alpha$ and H$\\beta$ are clearly\ndifferent from the empirical $I \\propto R^{-1.5}$ law; in particular,\nthe H$\\alpha$ distribution is flat at inner and intermediate disc radii\n($R <0.3\\; R_{\\rm L1}$).\nThis remark suggests that the line emitting regions on the disc surface\nare not in Keplerian orbits or that a substantial fraction of the emission\nlines does not arise from the accretion disc, in line with the inferences\ndrawn by the comparison of velocity-resolved eclipse maps in\nsection\\,\\ref{estrutura}.\nThe latter hypothesis is consistent with the significant uneclipsed\ncomponents inferred for the Balmer and He\\,I lines (section\n\\,\\ref{uneclipsed}).\n\n\n\\subsection{Spatially resolved spectra}\n\\label{spectra}\n\nEach of the eclipse maps yields spatially-resolved information about\nthe emitting region on a specific wavelength range. By combining all\nnarrow-band eclipse maps we are able to isolate the spectrum of the\neclipsed region at any desired position (e.g., Rutten et~al. 1994;\nBaptista et~al. 1998).\n\nTo investigate the possible influence of the gas stream on the disc\nemission and motivated by the observed asymmetries in the eclipse maps\nshown in section\\,\\ref{estrutura}, we divided the disc into two major\nazimuthal regions to extract spatially-resolved spectra: the gas stream\nregion (upper right quadrant in the eclipse maps of Figs.\\,3 and 4) and\nthe disc region (the remaining 3/4 of the eclipse map). \nFor each of these regions, we divided the maps into a set of 6 concentric\nannuli centred on the white dwarf of width $0.1\\: R_{L1}$ and with radius increasing in steps of $0.1\\: R_{L1}$.\nEach spectrum is obtained by averaging the intensity of all pixels\ninside the corresponding annulus and the statistical uncertainties\naffecting the average intensities are estimated with the Monte Carlo\nprocedure described in section\\,\\ref{mem}.\n\n\n\\subsubsection{Disc spectra}\n\\label{disc}\n\nFig.\\,\\ref{fig8} shows spatially-resolved spectra of the disc region in\na logarithmic scale. The inner annular region is at the top and each\nspectrum is at its true intensity level. The spectrum of the uneclipsed\ncomponent is shown in the lower panel and will be discussed in detail in\nsection\\,\\ref{uneclipsed}.\n%\n% ############################## FIGURE 8 #################################\n%\n\\begin{figure*}\n\\centerline{\\psfig{figure=xfig08.ps,angle=-90,width=21cm,rheight=15cm}}\n\t\\caption{ Spatially resolved spectra of the UU Aqr accretion disc.\n\tThe spectra were computed for a set of concentric annular sections\n\t(radius range indicated on the right, in units of $R_{L1}$).\n\tThe lower panel shows the spectrum of the uneclipsed light.\n\tThe most prominent line transitions are indicated by vertical dotted\n\tlines. Error bars were derived via Monte Carlo simulations with the\n\teclipse lightcurves. }\n\\label{fig8}\n\\end{figure*}\n%\nThe spectrum of the inner disc is characterized by a blue and bright\ncontinuum filled with deep and narrow absorption lines. The continuum\nemission becomes progressively fainter and redder for increasing disc radius\nwhile the lines transition from absorption to emission showing clear P~Cygni\nprofiles on all lines mapped at higher spectral resolution. The Balmer jump\nappears in absorption in the inner disc and weakly in emission in the\nintermediate and outer disc regions suggesting that the outer disc in\nUU~Aqr is optically thin. The change in the slope and intensity\nof the continuum with increasing disc radius reflects the temperature\ngradient in the accretion disc, with the effective temperature decreasing\noutwards.\n\nThe spatially resolved spectra of the disc are plotted in\nFig.\\,\\ref{fig9} as a function of velocity for the H$\\alpha$, H$\\beta$\nand H$\\gamma$ regions. Vertical dotted lines mark line centre and the\nmaximum blueshift/redshift velocity expected for gas in Keplerian\norbits around a $0.67 M_\\odot$ white dwarf as seen from an inclination of\n$i=78\\degr$ ($v \\sin i= 3200 \\;km \\;s^{-1}$) [BSC94].\n%\t\n% ############################## FIGURE 9 #################################\n%\n\\begin{figure}[h]\n\\centerline{\\psfig{figure=xfig09.ps,width=9.5cm,rheight=11cm}}\n\t\\caption{ Spatially resolved spectra in the H$\\alpha$, H$\\beta$ and\n\tH$\\gamma$ regions as a function of velocity. The notation is the same\n\tas in figure\\,\\ref{fig8}. Dotted vertical lines mark line centre and\n\tthe maximum blueshift/redshift velocity expected for gas in Keplerian\n\torbits around a $0.67 M_\\odot$ white dwarf seen at an inclination of\n\t$i=78\\degr$ ($v \\sin i= 3200 \\;km \\;s^{-1}$). }\n\\label{fig9}\n\\end{figure}\n% \nThe absorption lines at disc centre are perceptibly narrower than expected\nfor emission from either the white dwarf atmosphere or from disc gas in\nKeplerian orbits around the white dwarf. The discrepancy increases if the\nlarger mass estimates of Diaz \\& Steiner (1991) and Kaitchuck et~al (1998)\nare assumed for the white dwarf. Moreover, the absorption lines at disc\ncentre are deep, while lines produced in a white dwarf atmosphere or\ninnermost disc regions should be broad and shallow. The width of the lines\nindicate a velocity dispersion of $\\simeq 1500 \\;km \\;s^{-1}$ for the line\nemitting region in the line of sight to the disc centre and higher\nvelocities ($\\sim 2000 \\;km \\;s^{-1}$) for the gas in the outer disc at\n$R \\simeq 0.5\\; R_{\\rm L1}$.\nThis is in clear disagreement with the expected behaviour of line emission\nfrom gas in a Keplerian disc and provide additional evidence that these\nlines do not arise from the disc atmosphere.\nOn the other hand, the lines at intermediate and outer disc regions\n($R \\simgt 0.2\\; R_{\\rm L1}$) show clear P~Cygni profiles indicating origin\nin an outflowing gas, probably the disc wind.\n\nWe note that the H$\\alpha$ line shows a redshifted ($v \\sim 1800 \\;km\\;\ns^{-1}$) absorption component in spectra of the outer disc regions ($R >\n0.3\\; R_{L1}$). Comparison of disc spectra at different azimuths shows\nthat this absorption is produced in the front side of the disc, but an\norigin in the gas stream can possibly be ruled out since the absorption\ncomponent is seen with similar strengths in the leading and trailing\n(the one containing the gas stream) quadrants.\nThe interpretation of this feature is not straightforward and deserves a\nbit of caution, since it is not clearly seen in any other line and also\nbecause the surface brightness in the corresponding disc region is only\na few percent of the intensities in the inner disc.\n\n\n\\subsubsection{The uneclipsed spectrum}\n\\label{uneclipsed}\n\nThe spectrum of the uneclipsed light (lower panel of Fig.\\,\\ref{fig8})\nshow prominent Balmer and He\\,I emission lines. The Balmer jump is clearly\nin emission and the optical continuum rises towards longer wavelengths\nsuggesting that the Paschen jump is also in emission. These results\nare consistent with the findings of BSH96 and indicate that the uneclipsed\nlight has an important contribution from optically thin gas from outside\nthe orbital plane. The Balmer lines mapped at higher spectral resolution\nshow broad asymmetric profiles, with line peaks displaced to the red\nside and wings extending up to $\\simeq 1500 \\;km \\;s^{-1}$. The observed\nasymmetry is consistent with that previously seen in the integrated spectra\nof Diaz \\& Steiner (1991) and Hessman (1990) and is similar to that\nobserved in the resonant ultraviolet lines of UX~UMa, where the uneclipsed\ncomponent was attributed to emission in a vertically-extended disc wind\n(Baptista et~al. 1995; 1998; Knigge \\& Drew 1997).\n\nThe fractional contribution of the uneclipsed component to the total flux\nwas obtained by dividing the flux of the uneclipsed light by the average\nout of eclipse level at each passband. The result is shown in \nFig.\\,\\ref{fig10}. The fractional contribution of the uneclipsed light\nis very significant for the optical emission lines, reaching 40-60\\ per cent\nat the Balmer lines and 20-40\\ per cent at the He\\,I lines, and decreases\nsteadily along the Balmer series. \nThe difference in fractional contribution between the Balmer\nand He\\,I lines and among the Balmer lines indicates the existence of\na vertical temperature gradient in the material above/below the disc,\nwith the He\\,I lines (which require higher excitation energies)\nbeing produced closer to the orbital plane. In any case, a substantial \nfraction of the light at these lines does not arise from the orbital\nplane and is not occulted during eclipse.\nThe uneclipsed component gives significant contribution also to the\ncontinuum emission. About 20\\ per cent of the flux at the Balmer continuum\nand similar fraction of the continuum emission at the red end\nof the spectrum arise from regions outside the orbital plane.\n%\t\n% ############################# FIGURE 10 #################################\n%\n\\begin{figure}[h]\n\\centerline{\\psfig{figure=xfig11.ps,angle=-90,width=10cm,rheight=7.5cm}}\n\t\\caption{ Fractional contribution of the uneclipsed component to\n\tthe total flux as a function of wavelength. The values were obtained\n\tby dividing the flux of the uneclipsed component by the average out\n\tof eclipse level for each passband. }\n\\label{fig10}\n\\end{figure}\n\n\n\\subsubsection{The gas stream region}\n\\label{stream}\n\nFig.\\,\\ref{fig11} shows the ratio between the spectrum of the gas stream\nregion and the disc region at same radius as a function of radius.\nA dotted line marks the unity level for each panel. \nThe comparison shows that the spectrum of the gas stream is noticeably\ndifferent from the disc spectrum in the outer disc regions (where one\nexpects a bright spot to form due to the shock between the inflowing\nstream and the outer disc rim), but also reveals systematic differences\nbetween stream and disc spectra in a range of radii. In all cases,\nthe stream emission is stronger than that of the adjacent disc.\n%\t\n% ############################# FIGURE 11 #################################\n%\n\\begin{figure*}\n\\centerline{\\psfig{figure=xfig10.ps,width=14cm,rheight=17cm}}\n\t\\caption{ Ratio of the gas stream spectrum and the disc spectrum \n\tfor the same set of annular regions of figure\\,\\ref{fig8}. Dashed\n\tlines mark the unity level for each panel. The notation is the same\n\tas in fig.\\,\\ref{fig8}.}\n\\label{fig11}\n\\end{figure*}\n\nThis result suggests that the material in the gas stream continues to flow\ndownstream beyond the bright spot position. In this regard, there are three\npotential cases: (1) stream overflow that arcs high above/below the disc\nuntil it hits the disc surface again at a downstream position closer to \nthe white dwarf (hereafter called the ``classical stream overflow''); \n(2) stream overflow that continuously skims the disc surface (hereafter\ncalled the ``disc-skimming overflow''); and (3) the stream drills into the\ndisc at the impact site (hereafter named the ``disc stream penetration'').\nThe latter case seems physically unrealistic and is not supported by hydrodynamic calculations of stream-disc interaction (Armitage \\& Livio\n1996, 1998). \nThe fact that there is enhanced emission in the stream region extending\nall the way from the outer disc down to $R\\simeq 0.2\\; R_{L1}$ argues in\nfavor of an interpretation in terms of disc-skimming overflow instead of\nthe classical stream overflow -- as has been suggested to explain the\nbehaviour of SW~Sex stars (Hellier \\& Robinson 1994; Hellier 1996) --\nsince the latter would produce enhanced emission only at the position of\nthe two spots, at the initial impact site in the outer disc edge and at\nthe re-impact site much closer to disc centre (Lubow 1989).\n\nThe spectrum of the ratio becomes redder for decreasing disc radius,\npossibly a combination of the disc emission becoming bluer as one moves\ninwards and the gas stream emission becoming redder while its energy is\ncontinuously lost in the shock with disc material along the inward stream\ntrajectory.\nThis is reminiscent of what was seen in ultraviolet eclipse observations\nof the dwarf novae IP~Peg in quiescence, which revealed a compact blue\nbright spot with an extended red tail (Baptista et~al. 1993). \n\n\n\\section{Discussion} \\label{discussao}\n\nIn this section we present and discuss some possible interpretations for\nthe results of section\\,\\ref{resultados} in the context of the current\nmodels for the SW Sex stars.\n\n\\subsection{Where do the lines come from?}\n\nIn previous sections we have accumulated evidences that the behaviour\nof the UU Aqr lines in its high state is not consistent with emission\nin a disc atmosphere, namely: \n(i) negligible rotational disturbance, (ii) no mirror symmetry between\neclipse maps in symmetric velocity bins; (iii) H$\\alpha$ line emission\ndistribution much flatter than the empirical $I \\propto R^{-1.5}$ law;\n(iv) significant uneclipsed components, and (v) presence of P~Cygni\nprofiles in the disc spectra at intermediate and large disc radii.\nIf the lines do not arise in the disc atmosphere, where do they come from?\n\nThe most compelling interpretation is that the lines are produced in a\ndisc chromosphere + wind. This region is hot, dense, opaque and has low\nexpansion velocities close to the orbital plane in order to produce the\nobserved deep, narrow absorption lines in the line of sight to the inner\ndisc. Most of the high excitation lines are produced close to the disc\nplane. The density and temperature decrease with height above/below the\ndisc as the outflowing gas spreads over an increasing surface area.\nOptically thin emission from this extended region is\nprobably responsible for the Balmer jump (and lines) in emission observed\nin the uneclipsed spectrum. Support in favor of this scenario comes from\nthe recent detailed modeling of the C\\,{\\sc IV} wind line of eclipsing\nnova-likes by Schlosman, Vitello \\& Mauche (1996) and Knigge \\& Drew\n(1997). Their results suggest the existence of a relatively dense ($n_e\n\\sim 4 \\times 10^{12}$~cm$^{-3}$) and vertically extended chromosphere\nbetween the disc surface and the fast-moving parts of the wind, which\ncould produce significant amounts of optically thin emission.\nAt orbital phases around eclipse, gas outflowing in the direction of the\nsecondary star will be seen along the line of sight to the bright underlying\naccretion disc as blueshifted absorption features, while gas expelled in\nthe direction away from the secondary star should contribute with\nredshifted emission.\n\nWe tested this scenario by \ncomparing spatially resolved spectra of the disc lune closest to the\nsecondary star (the right hemisphere of the disc in the eclipse maps of\nFig.\\,\\ref{fig3}, hereafter called the ``front'' side) and of the disc\nlune farthest away from the secondary star (the left hemisphere of the\ndisc in Fig.\\,\\ref{fig3}, hereafter called the ``back'' side). \nFor this purpose, we defined two opposite azimuthal disc regions of width\n$30\\degr$ along the major axis of the binary, and extracted spatially\nresolved spectra for the same set of annuli as above. These spatially\nresolved spectra are noisier than those of Figs.\\,\\ref{fig8} and\n\\ref{fig9} because in this case the average intensity of each annulus\nis computed from a significantly smaller number of pixels. The results\nare shown in Fig.\\,\\ref{fig9A} for the H$\\beta$ and H$\\gamma$ regions\nand are consistent with our interpretation:\nThe blueshifted absorption component is seen mainly in the front side of\nthe disc while the redshifted emission is generally more prominent in\nspectra of the back side of the disc.\nThe fact that the blueshifted absorption can still be seen projected along\nthe line of sight at the outer regions of the disc favours a more spherical\nor equatorial geometry for the outflowing gas instead of a highly collimated,\npolar jet.\n%\t\n% ############################## FIGURE 12 ################################\n%\n\\begin{figure}\n\\vspace*{7cm}\n%\\centerline{\\psfig{figure=xfig12.ps,angle=-90,width=10.5cm,rheight=7cm}}\n\t\\caption{ Comparison of spatially resolved spectra of the front and\n\tback side of the disc (see text) in the H$\\beta$ and H$\\gamma$ regions.\n\tThe notation is the same as in figure\\,\\ref{fig9}. For clarity, only\n\tthe H$\\gamma$ spectra of two annuli are shown. }\n\\label{fig9A}\n\\end{figure}\n\nThe chromosphere + disc wind interpretation satisfactorily accounts for all\nthe features listed above and also gives a plausible explanation for \n(1) the distinct semi-amplitude of the radial velocity $K$ and systemic\nvelocity $\\gamma$ as inferred from different emission lines and \n(2) the time dependent $K$ and $\\gamma$ values (Hoard et~al. 1998). \nThe centroid of lines of different excitation level will occur at different\nlocations in the primary lobe and will sample different velocities \nalong the line of sight. With respect to (2), \nthe comparison of the H$\\alpha$ map of BSH96 (which corresponds to the low\nbrightness state) with that of Fig.\\,\\ref{fig4} (the high state) reveals\nthat in the latter the emission extends over a much larger region of the\nprimary lobe with a pronounced asymmetry in the stream region,\nsuggesting that the wind emission is variable in time and is intimately\nconnected with the mass accretion rate. \nThis remark gives additional support to the suggestion\nby Hoard et~al. (1998) that the observed time dependence of the $K$ and\n$\\gamma$ velocities might be due to variability of a wind component\nin UU Aqr.\n\nAn alternative possibility is to consider the deep absorption lines\nseen towards the line of sight to the disc centre as being produced by\nabsorption in a vertically extended disc rim. Although this scenario\naccounts for the narrow absorption lines,\nit is not able to explain the large velocities inferred from the line\nwidth for intermediate and large disc radius nor the P~Cygni profiles.\nFurthermore, it should result in a perceptible front-back asymmetry in\nthe disc surface brightness (namely, the back side of the disc should be\nbrighter) which is not seen in the eclipse maps.\n\nRecently, Horne (1999) proposed that most of the features of the SW Sex\nstars could be explained in terms of a disc-anchored magnetic propeller,\nin which energy and angular momentum are extracted from the magnetic field\nof the inner disc regions to fling part of the material in the gas stream\nout of the binary towards the back side of the disc. \nAlthough this model is able to explain many of the observed features of\nUU Aqr, it can only account for the observed P Cygni profiles if the gas\ntrapped by the inner disc magnetic field is expelled in all directions\nand not only towards the back of the disc.\nWe note that, in this case, there is no significant difference between\nthe propeller and the disc wind models and, in fact, the former could\npossibly work as the underlying physical mechanism driving the latter.\n\nIf disk-skimming overflow does occur, we might expect that \ndissipation of energy in the collision between the gas stream and the\ndisc material gives rise to a bulge extending along the stream trajectory\nover and under the disc. This bulge will appear in front of the\nchromosphere + wind line emitting region at the inner disc when seen\nalong the line of sight at orbital phases 0.5-0.9.\nThis may explain the phase-dependent absorption lines, observed from\nphases 0.5-0.9 and with maximum at phase $\\sim 0.8$ (Heafner 1989;\nHoard et~al. 1998). The enhanced line emission along the gas stream\n(see Fig.\\,\\ref{fig4}) is possibly responsible for the phase offset\nbetween photometric and spectroscopic conjunction\n(Diaz \\& Steiner 1991; Hoard et~al. 1998). \n\nIn summary, the picture which emerges from our results is consistent\nwith the results from the Doppler tomography and the model proposed\nfor UU Aqr by Hoard et~al. (1998).\n\n\n\\subsection{Where has the bright spot gone?}\n\nAlthough our observations correspond to the high brightness state of\nUU Aqr, our eclipse maps do not show the conspicuous asymmetric structure\nseen in the high state eclipse maps of BSH96 and which was interpreted\nas being the bright spot.\nThe explanation for the `disappearance' of the bright spot may be\nconnected with the stunted outbursts found by Honeycutt et~al. (1998).\n\nBSH96 pointed out that the inferred accretion rate of UU Aqr\nis close to the critical mass accretion rate for disc instability\nto occur and remarked that the long-term lightcurves of accretion\ndiscs with mass transfer rates near their critical limit might display\nlow-amplitude ($\\simlt 1.0$ mag) outbursts caused by thermal\ninstabilities in the outer disc regions (e.g., Lin, Papaloizou \\&\nFaulkner 1985). In this case the outburst is restricted to the outer\n1/3 of the disc extent while the inner disc remains in a high viscosity,\nsteady state.\nHoneycutt et~al (1998) suggested that such dwarf-nova type instabilities\ncould be an explanation for the stunted outbursts of UU Aqr if a\nmechanism can be identified to make the amplitudes appear small. \nWe note that the observed low amplitudes can be easily accounted for\nby the reduced contrast of the light from the outbursting outer\nregions -- where the efficiency in transforming gravitational potential\nenergy in radiation is relatively low -- in comparison to the bright,\noptically thick and steady inner disc.\n\nIf the observed stunted outbursts of UU Aqr are caused by thermal\ninstabilities in its outer disc, the disc radius is expected to\nincrease during the outburst and will eventually reach the 3:1 tidal\nresonance radius leading to an elliptical precessing disc reminiscent\nof what possibly happens in SU UMa stars in superoutburst\n(e.g., Warner 1995 and references therein). \nWe suggest that the azimuthally elongated structure seen in the\neclipse maps of BSH96 is the signature of such an elliptical disc\nand not the bright spot. Following this line of reasoning, this\nstructure should not be present when the disc radius is smaller than\nthe tidal resonance radius. Support for this interpretation comes from\nthe comparison of disc radius in the high state eclipse maps of BSH96\nand our eclipse maps. \nFrom BSH96 data we estimate a disc radius of $R_d \\simeq 0.7 \\; \nR_{\\rm L1}$, comparable to the 3:1 tidal resonance radius for a\nmass ratio of $q=0.3$. Our eclipse maps lead to a smaller value of\n$R_d = 0.65 \\; R_{\\rm L1}$. Therefore, we suggest that UU Aqr was in an \noccasional superhumper state during the high brightness state observations\nof BSC94.\n\nIn the model of Hoard et~al. (1998), after the explosive impact of the\nhigh \\.{M} accretion stream with the edge of the disc, the incomming gas \nforms an optically thick absorbing bulge on the disc that either follows \nroughly the stream trajectory or runs along the rim of the disc, producing\nthe absorption features seen at phases 0.4-0.9. It may alternatively be\npossible that the structure seen in the eclipse maps of BSH96 is the\nsignature of such post-impact stream material running along the edge of\nthe disc. In this scenario, the azimuthally extended bulge would be present\nor not depending on the (variable) mass accretion rate and the resulting\norbital hump would remain fixed in phase.\n\nIt would be interesting (although outside the scope of this paper) to\nreanalize the data of BSC94 to see if the orbital hump present in the high\nstate precesses in phase in a similar manner as superhumps in superoutbursts\n(supporting the elliptical disc scenario) or if its maximum occurs always\nat the same orbital phase range about 0.8 - 0.9 cycle (favouring the\npost-impact bulge scenario).\n\n\n\\section{Conclusions} \\label{conclusao}\n\nWe used time-resolved spectroscopy to study the structure and spectra\nof the accretion disc and gas stream of the novalike UU~Aquarii in\nthe optical range. The main results of this analysis can be summarized\nas follows:\n\n\\begin{itemize}\n\n\\item The spectrum of the inner disc shows a blue continuum filled with deep,\nnarrow absorption lines which transition to emission with clear P~Cygni\nprofiles at intermediate and large radii ($R\\simgt 0.2 \\; R_{L1}$).\n\n\\item The spectrum of the uneclipsed light has strong H\\,I and He\\,I\nemission lines and a Balmer jump in emission indicating a significant\ncontribution from optically thin regions outside the orbital plane.\n\n\\item Velocity-resolved eclipse maps and spectra indicate that most\nof the line emission probably arises in a vertically-extended disc\nchromosphere + wind.\n\n\\item Differences in fractional contribution among emission lines suggests\na vertical temperature gradient in the material above/below the disc.\n\n\\item The comparison of the spectrum of the gas stream region and the\ndisc region at the same radius as a function of radius gives evidence \nof gas stream disc-skimming overflow down to $R\\simeq 0.2\\; R_{L1}$.\nThis may explain the phase-dependent absorption in emission lines.\n\n\\item The comparison of our eclipse maps with those of BSH96 suggests that\nthe asymmetric structure in the outer disc previously identified as\nthe bright spot may be the signature of an elliptical precessing disc\nsimilar to those possibly present in SU UMa stars during superoutbursts.\n\n\\end{itemize}\n\n\n\\section*{Acknowledgments}\n\nWe gratefully acknowledge the director of KPNO for granting telescope time\nfor this project at the Summer Queue Program, Tod Boroson and the team\nof observers at KPNO for their kind effort in collecting the data, \nKnox Long and the director of STScI for financial support through\nthe Director Discretionary fund, Susan Keener for helping with the data\nreduction at STScI, and an anonymous referee for valuable comments and\nsuggestions that helped to improve the presentation of the results.\nRB acknowledges financial support from CNPq/Brazil through grant no. 300\\,354/96-7. 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"name": "astro-ph0002189.extracted_bib",
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astro-ph0002190
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Constraining the Lifetime of Quasars from their Spatial Clustering
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[
{
"author": "Zolt\\'an Haiman\\altaffilmark{1}"
}
] |
The lifetime of the luminous phase of quasars is constrained by current observations to be $10^{6} \lsim t_Q \lsim 10^8$ years, but is otherwise unkown. We model the quasar luminosity function in detail in the optical and X--ray bands using the Press--Schechter formalism, and show that the expected clustering of quasars depends strongly on their assumed lifetime $t_Q$. %within this range. %If quasars are short lived, their duty cycle is small, and they %must reside in abundant, low--mass dark matter halos. Conversely, if quasars %live longer, they must be hosted by rarer, more massive and more strongly %clustered halos. We quantify the resulting dependence of clustering on the We quantify this dependence, and find that existing measurements of the correlation length of quasars are consistent with the range $10^{6} \lsim t_Q \lsim 10^8$. We then show that future measurements of the power spectrum of quasars out to $z\sim 3$, from the 2dF or Sloan Digital Sky Survey, can significantly improve this constraint, and in principle allow a precise determination of $t_Q$. We estimate the systematic errors introduced by uncertainties in the modeling of the quasar-halo relationship, as well as by the possible existence of obscured quasars.
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[
{
"name": "msrev.tex",
"string": "%\\documentstyle[aasms4]{article}\n\\documentstyle[emulateapj]{article}\n\n\n\\def\\gsim{\\;\\rlap{\\lower 2.5pt\n \\hbox{$\\sim$}}\\raise 1.5pt\\hbox{$>$}\\;}\n\\def\\lsim{\\;\\rlap{\\lower 2.5pt\n \\hbox{$\\sim$}}\\raise 1.5pt\\hbox{$<$}\\;}\n\\def\\msun{{\\rm\\,M_\\odot}}\n\\def\\yr{{\\rm\\,yr}}\n\\def\\au{{\\rm\\,AU}}\n\\def\\del{{\\partial}}\n\\def\\gm{{\\rm\\,g}}\n\\def\\cm{{\\rm\\,cm}}\n\\def\\sec{{\\rm\\,s}}\n\\def\\erg{{\\rm\\,erg}}\n\\def\\kev{{\\rm\\,keV}}\n\\def\\ev{{\\rm\\,eV}}\n\\def\\K{{\\rm\\,K}}\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\def\\lta{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar''218$}}\n \\raise 2.0pt\\hbox{$\\mathchar''13C$}}}\n\\def\\gta{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar''218$}}\n \\raise 2.0pt\\hbox{$\\mathchar''13E$}}}\n\\newcommand{\\beq}{\\begin{equation}}\n\\newcommand{\\eeq}{\\end{equation}}\n\n\\lefthead{HAIMAN \\& HUI}\n\\righthead{QSO CLUSTERING}\n\n\\begin{document}\n\\title{Constraining the Lifetime of Quasars from their Spatial Clustering}\n\\author{Zolt\\'an Haiman\\altaffilmark{1}}\n\\affil{Princeton University Observatory, Princeton, NJ 08544, USA \\\\email: zoltan@astro.princeton.edu}\n\\and\n\\author{Lam Hui}\n\\affil{Institute for Advanced Study, Olden Lane, Princeton, NJ 08544, USA \\\\\nemail: lhui@ias.edu}\n\n\\altaffiltext{1}{Hubble Fellow}\n\n\\vspace{0.75\\baselineskip}\n\\submitted{ApJ, in press (submitted on Feb. 8. 2000)}\n\n\\begin{abstract}\n\nThe lifetime of the luminous phase of quasars is constrained by current\nobservations to be $10^{6} \\lsim t_Q \\lsim 10^8$ years, but is otherwise\nunkown. We model the quasar luminosity function in detail in the optical and\nX--ray bands using the Press--Schechter formalism, and show that the expected\nclustering of quasars depends strongly on their assumed lifetime $t_Q$.\n%within this range.\n%If quasars are short lived, their duty cycle is small, and they\n%must reside in abundant, low--mass dark matter halos. Conversely, if quasars\n%live longer, they must be hosted by rarer, more massive and more strongly\n%clustered halos. We quantify the resulting dependence of clustering on the\nWe quantify this dependence, and find that existing measurements of the\ncorrelation length of quasars are consistent with the range $10^{6} \\lsim t_Q\n\\lsim 10^8$. We then show that future measurements of the power spectrum of\nquasars out to $z\\sim 3$, from the 2dF or Sloan Digital Sky Survey, can\nsignificantly improve this constraint, and in principle allow a precise\ndetermination of $t_Q$. We estimate the systematic errors introduced by\nuncertainties in the modeling of the quasar-halo relationship, as well as by\nthe possible existence of obscured quasars.\n\\end{abstract}\n\n\\keywords{cosmology: theory -- cosmology: observation -- quasars: formation -- large scale structure}\n\n\\section{Introduction}\n\\label{section:introduction}\n\nA long outstanding problem in cosmology is the synchronized evolution of the\nquasar population over the redshift range $0\\lsim z\\lsim 5$. Observations in\nthe optical (Pei 1995) and radio (Shaver et al. 1994) show a pronounced peak in\nthe abundance of bright quasars at $z\\approx 2.5$; recent X--ray observations\n(Miyaji et al. 2000) confirm the rapid rise from $z=0$ towards $z\\approx 2$,\nbut have not shown evidence for a decline at still higher redshifts.\nIndividual quasars are widely understood to consist of supermassive black holes\n(BHs) powered by accretion (Lynden-Bell 1967; Rees 1984). A plausible\ntimescale for quasar activity is then the Eddington time, $4\\times10^7$\n($\\epsilon$/0.1) yr, the e-folding time for the growth of a BH accreting mass\nat a rate $\\dot M$, while shining at the Eddington luminosity with a radiative\nefficiency of $L=L_{\\rm Edd}=\\epsilon\\dot M c^2$. The lifetime $t_Q$ of the\nluminous phase of quasars can be estimated directly, by considering the space\ndensity of quasars and galaxies. At $z\\sim 2$, the ratio $n_Q/n_G \\sim 3\\times\n10^{-3}$ implies the reassuringly close value of $t_Q\\sim t_{\\rm Hub}\nn_Q/n_G\\sim 10^7$ yr (Blandford 1999 and references therein). These lifetimes\nare significantly shorter than the Hubble time, suggesting that the quasar\npopulation evolves on cosmic time--scales by some mechanism other than local\naccretion physics near the BH.\n\nIt is tempting to identify quasars with halos condensing in a cold dark matter\n(CDM) dominated universe, as the halo population naturally evolves on cosmic\ntime--scales (Efstathiou \\& Rees 1988; Haiman \\& Loeb 1998; Kauffmann \\&\nHaehnelt 2000). Furthermore, quasars reside in a subset of all galaxies, while\nthe redshift--evolution of the galaxy population as a whole (qualitatively\nsimilar to that of bright quasars) has been successfully described by\nassociating galaxies with dark halos (e.g. Lacey \\& Cole 1993; Kauffmann \\&\nWhite 1993). A further link between galaxies and quasars comes from the recent\ndetection, and measurements of the masses of massive BHs at the centers of\nnearby galaxies (Magorrian et al. 1998; van der Marel 1999).\n\nThese arguments suggest that the evolution of the quasar population can indeed\nbe described by ``semi--analytic'' models, associating quasars with dark matter\nhalos. In this type of modeling, the quasar lifetime plays an important role.\nThe quasar phase in a single halo could last longer ($t_{\\rm Q}\\sim10^8$yr),\nwith correspondingly small $M_{\\rm bh}/M_{\\rm halo}$ ratios, or last shorter\n($t_{\\rm Q}\\sim10^6$yr), with larger BH formation efficiencies (Haiman \\& Loeb\n1998; Haehnelt et al. 1998). Note that although recent studies have\nestablished a correlation between the bulge mass $M_{\\rm bulge}$ and BH mass\n$M_{\\rm bh}$, this correlation leaves a considerable uncertainty in the\nrelation between $M_{\\rm bh}$ and the mass $M_{\\rm halo}$ of its host halo. If\nthe initial density fluctuations are Gaussian with a CDM power spectrum, the\nclustering of collapsed halos is a function of their mass -- rarer, more\nmassive halos cluster more strongly (Kaiser 1984; Mo \\& White 1996). Hence,\nmeasurements of quasar clustering are a potentially useful probe of both BH\nformation efficiencies and quasar lifetimes (La Franca et al. 1998, Haehnelt et\nal. 1998).\n\nIn this paper, we assess the feasibility of breaking the above degeneracy, and\ninferring quasar lifetimes, from the statistics of clustering that will be\navailable from the Sloan Digital Sky Survey (SDSS, Gunn \\& Weinberg 1995) and\nAnglo-Australian Telescope Two-Degree-Field (2dF, Boyle et al. 1999). Previous\nworks (e.g. Stephens et al. 1997; Sabbey et al. 1999) have yielded estimates\nsuggesting that quasars are clustered more strongly than galaxies. However, the\ncurrent uncertainties are large, especially at higher redshifts, where\nclustering has been found to decrease (Iovino \\& Shaver 1988; Iovino et\nal. 1991), to stay constant (Andreani \\& Cristiani 1992; Croom \\& Shanks 1996),\nor to increase with redshift (La Franca et al. 1998). As a result, no strong\nconstraints on the life--time can be obtained yet. The key advance of\nforthcoming surveys over previous efforts is two--fold. Because of their sheer\nsize, i.e. the large number of quasars covering a large fraction of the sky,\nboth shot--noise and sample variance can be beaten down, significantly reducing\nthe statistical uncertainties. Furthermore, the large sample-size will\neliminate the need to combine data from different surveys with different\nselection criteria, hence allowing cleaner interpretation.\n\nRecent measurements of the local massive black hole density have stimulated\ndiscussions of a radiative efficiency which is much lower than the usual $\\sim\n0.1$ (e.g. Haehnelt et al. 1999). A convincing constraint on the lifetime of\nquasars could be therefore highly interesting, as this might have implications\nfor the local accretion physics near the BH.\n\nThis paper is organized as follows. In \\S~\\ref{section:models}, we summarize\nour models for the quasar luminosity function, and in\n\\S~\\ref{section:clustering} we compute the quasar correlation function in these\nmodels. In \\S~\\ref{section:present}, we compare the model predictions with\npresently available data, and in \\S~\\ref{section:future} we assess the ability\nof future optical redshift surveys to discriminate between the various models.\nIn \\S~\\ref{section:xray}, we repeat our analysis in the soft X--ray band, and\nexamine the contribution of quasars to the X-ray background, and its\nauto--correlation. In \\S~\\ref{section:discussion}, we address some of the\ncaveats arising from our assumptions, and in \\S~\\ref{section:conclusions} we\nsummarize our conclusions and the implications of this work.\n\n\\section{Models for the Quasar Luminosity Function}\n\\label{section:models}\n\nIn this section, we briefly summarize our model for the luminosity function\n(LF) of quasars, based on associating quasar BHs with dark halos. Our\ntreatment is similar to previous works (Haiman \\& Loeb 1998; Haehnelt et\nal. 1998), although differs in some of the details. A more extensive treatment\nis provided in the Appendix. The main assumption is that there is, on average,\na direct monotonic relation between halo mass $M_{\\rm halo}$ and average quasar\nluminosity $L_{M,z}$, which we parameterize using the simple\npower--law ansatz:\n\n\\beq \\bar L_{M,z}= x_0(z) M_{\\rm halo} \\left(\\frac{M_{\\rm\nhalo}}{M_0}\\right)^{\\alpha(z)}.\n\\label{eq:params00}\n\\eeq\n\nHere $x_0(z)$ and $\\alpha(z)$ are ``free functions'', whose values are found by\nthe requirement that the resulting luminosity function agrees with\nobservations. As explained in the Appendix, our model has one free parameter,\nthe lifetime $t_Q$, which uniquely determines $x_0(z)$ and $\\alpha(z)$ in any\ngiven background cosmology. We assume the background cosmology to be either\nflat ($\\Lambda$CDM) with $(\\Omega_\\Lambda,\\Omega_{\\rm m},h,\\sigma_{\\rm\n8h^{-1}},n)=(0.7,0.3,0.65,1.0,1.0)$ or open (OCDM) with\n$(\\Omega_\\Lambda,\\Omega_{\\rm m},h,\\sigma_{\\rm\n8h^{-1}},n)=(0,0.3,0.65,0.82,1.3)$. In LCDM, we find $(-\\log[x_0/{\\rm L_\\odot\nM_\\odot^{-1}}],\\alpha) \\approx (1,0.4)$ and $\\approx (-0.2, -0.1)$ for\nlifetimes of $t_Q=10^{8}$ and $t_Q=10^{6.5}$yr, respectively. Similarly, in\nOCDM, we find $(-\\log[x_0/{\\rm L_\\odot M_\\odot^{-1}}],\\alpha) \\approx (1,0.25)$\nand $\\approx (-0.2, -0.25)$ for these two lifetimes.\n\nIn Figure~\\ref{fig:LFfits}, we demonstrate the agreement between the LF\ncomputed in our models with the observational data at two different redshifts,\n$z=2$ and $z=3$. For reference, the upper labels in this figure show the\napparent magnitudes in the SDSS $g^\\prime$ band, assuming that the intrinsic\nquasar spectrum is the same as the mean spectrum in the Elvis et al. (1994)\nquasar sample. The photometric detection threshold\\footnote{See\nhttp://www.sdss.org/science/tech\\_summary.html.} of SDSS is $g^\\prime \\approx\n22.6$, corresponding to a BH mass of $\\approx 10^{8} {\\rm M_\\odot}$ at $z=3$\nand a three times smaller mass at $z=2$. As the figure shows, the overall\nquality of the fits is excellent; for reference, the dashed lines show the\nad--hoc empirical fitting formulae from Pei (1995). Similarly accurate match\nto the quasar LF is achieved at different redshifts, and in the models assuming\nan OCDM cosmology. Figure~\\ref{fig:LFfits} shows, in particular, that the fits\nobtained from the power--law ansatz adopting either a short (solid lines) or a\nlong (dotted lines) lifetime are nearly indistinguishable; hence modeling the\nLF by itself does not constrain the quasar lifetime within the limits\n$10^{6.5}$ yr $\\lsim t_Q \\lsim 10^8$ yr.\n\nBefore considering constraints on the lifetime from clustering, it is useful to\npoint out that estimates for both upper and lower limits on $t_Q$ follow from\nthe observed luminosity function alone.\n\n{\\it Lower limit on $t_Q$.} A halo of mass $M_{\\rm halo}$ is unlikely to harbor\na BH more massive than $\\approx 6\\times10^{-3} (\\Omega_{b}/\\Omega_{0}) M_{\\rm\nhalo} = 6\\times 10^{-4} M_{\\rm halo}$, where $\\approx 6\\times10^{-3}$ is the\nratio $M_{\\rm bh}/M_{\\rm bulge}$ found in nearby galaxies (Magorrian et\nal. 1998) because $M_{\\rm bulge}$ cannot be larger than\n$(\\Omega_{b}/\\Omega_{0}) M_{\\rm halo}$. This maximal BH could at best emit\n$\\approx 10\\%$ of the Eddington luminosity in the B--band, implying $L/M_{\\rm\nhalo} \\lsim 3~{\\rm L_\\odot/M_\\odot}$. We find (cf. Fig.~\\ref{fig:params}) that\nour short lifetime model with $t_Q=10^{6.5}$ yr nearly reaches this limit;\nmodels with shorter lifetimes would require unrealistically large $L/M_{\\rm\nhalo}$ ratios.\n\n{\\it Upper limit on $t_Q$.} Long lifetimes, on the other hand, require the\nratio $L/M_{\\rm halo}$ to be small; this can lead to unrealistically large halo\nmasses. The brightest quasars detected at redshifts $z\\approx 2-3$ have\nluminosities as large as $L\\approx 10^{14} {\\rm L_\\odot}$ (Pei 1995). We find\n(cf. Fig.~\\ref{fig:params}) that in order to avoid the host halo masses of\nthese bright quasars to exceed $\\sim 10^{15}~{\\rm M_\\odot}$, the lifetime\ncannot be longer than $\\sim 10^8$ yr. An alternative, standard argument goes as\nfollows. The black hole mass grows during the quasar phase as $e^{t_Q/t_E}$\nwhere $t_E = 4\\times10^7 (\\epsilon/0.1)$ yr is the Eddington time. Assuming a\nconservative initial black hole mass of $1 M_{\\odot}$, a lifetime longer than\n$10^9$ yr would give final black hole masses that are unacceptably large.\n\n\\vspace{2\\baselineskip}\n\n\\section{The Clustering of Quasars}\n\\label{section:clustering}\n\nAs demonstrated in the previous section, equally good fits can be obtained to\nthe luminosity function of quasars, assuming either a short or a long lifetime,\nand a power-law dependence of the mean quasar luminosity on the halo mass $\\bar\nL\\propto M^\\alpha$. In this section, we derive the clustering of quasars in\nour models, and demonstrate that they depend significantly on the assumed\nlifetime.\n\nThe halos are a biased tracer of the underlying mass distribution, customarily\nexpressed by $P_{\\rm halo} (k) = b^2 P(k)$ where $P_{\\rm halo}$ and $P$ are the\nhalo and mass power spectra as a function of wavenumber $k$. The bias parameter\nfor halos of a given mass $M$ at a given redshift $z$ is given by (Mo \\& White\n1996)\n\n\\beq\nb(M,z)= 1 + \\frac{1}{\\delta_c}\\left[\n\\left(\\frac{\\delta_c}{\\sigma(M)D(z)}\\right)^2-1\\right],\n\\label{eq:biasM}\n\\eeq\n\nwhere $D(z)$ is the linear growth function, $\\sigma(M)$ is the r.m.s. mass\nfluctuation on mass--scale $M$ (using the power spectrum of Eisenstein \\& Hu\n1999), and $\\delta_c\\approx 1.68$ is the usual critical overdensity in the\nPress--Schechter formalism (see Jing 1999 and Sheth \\& Tormen 1999 for more\naccurate expressions for $b(M,z)$ for low $M$, which we find not to affect our\nresults here). The bias associated with quasars with luminosity $L$ in our\nmodels is given by averaging over halos of different masses associated with\nthis luminosity. Following equation \\ref{eq:matchdiff}, we obtain\n\n\\begin{eqnarray}\nb(L,z) = && \\hspace{-0.5cm}\\left[\\frac{d\\phi}{dL}(L,z)\\right]^{-1} \\times\n\\int_0^\\infty dM \\frac{dN}{dM}(M,z) \\\\\n\\nonumber && b(M,z) \\frac{dg}{dL}(L,\\bar L_{M,z}) f_{\\rm on}(M,z).\n\\label{eq:biasL}\n\\end{eqnarray}\n\nWe show in Figure~\\ref{fig:bias} the resulting bias parameter $b(L,z)$ in the\nmodels corresponding to Figure~\\ref{fig:LFfits}, with short and long lifetimes,\nand at redshifts $z=2$ and 3. As expected, quasars are more highly biased in\nthe long lifetime model, by a ratio $b$(long)/$b$(short)$\\gsim 2$. In the\n$\\Lambda$CDM case, at the detection threshold of SDSS, we find\n$b$(long)$\\approx 3$ at $z=3$ and $b$(long)$\\approx2$ at $z=2$. Bright quasars\nwith $g^\\prime=17$ are predicted to have a bias at $z=3$ as large as $b=10$.\nFor reference, we also show in this figure the bias parameters obtained in the\nOCDM cosmology, which are significantly lower than in the $\\Lambda$CDM case.\nThe number of quasars observed at a fixed flux implies an intrinsically larger\nnumber of sources if OCDM is assumed, because the volume per unit redshift and\nsolid angle in an open universe is smaller. This lowers the corresponding halo\nmass and therefore the bias.\n\n\\section{Comparison with Available Data}\n\\label{section:present}\n\nAs emphasized in \\S~\\ref{section:introduction}, the presently available data\nleave considerable uncertainties in the clustering of quasars. Nevertheless, it\nis interesting to contrast the results of the previous section with preliminary\nresults from the already relatively large, homogeneous sample of high--redshift\nquasars in the 2dF survey (Boyle et al. 2000). Our predictions are obtained by\nrelating the apparent magnitude limit to a minimum absolute luminosity at a\ngiven redshift: $\\log [L_{\\rm min}(z)/L_{B,\\odot}] = 0.4[5.48- B + 5\\log(d_{\\rm\nL}(z)/{\\rm pc})-5]$. This relation assumes no K--correction, justified by the\nnearly flat quasar spectra ($\\nu F_\\nu = $ const) at the relevant wavelengths\n(e.g. Elvis et al. 1994; Pei 1995). In our model, the correlation length $r_0$\nis given implicitly by\n\n\\beq\n\\xi_q(r_0)\\equiv \\bar b^2(z) D^2(z) \\xi_m(r_0) = 1,\n\\label{eq:xiq}\n\\eeq\n\nwhere $\\xi_m(r)$ is the usual dark matter correlation function, and $\\bar b(z)$\nis the value of the bias parameter $b(L,z)$ as determined in the previous\nsection, but now averaged over all quasars with magnitudes brighter than the\ndetection limit,\n\n\\beq\n\\bar b(z) = \\left[\\int_{L_{\\rm min}(z)}^\\infty dL \\frac{d\\phi}{dL} \\right]^{-1}\n\\int_{L_{\\rm min}(z)}^\\infty dL \\frac{d\\phi}{dL} b(L,z).\n\\label{eq:bave}\n\\eeq\n\nIn Figure~\\ref{fig:r0} we show the resulting correlation lengths in the long\nand short lifetime models. Also shown is a preliminary data--point with\n1$\\sigma$ error--bars from the 2dF survey, based on $\\approx$3000 quasars with\napparent magnitudes $B < 20.85$ (Croom et al. 1999). The upper panel shows the\nresults in our fiducial $\\Lambda$CDM model with predictions for this magnitude\ncut. The published results for $r_0$ are cosmology dependent, and we have\nsimply converted them for our cosmological models by taking the corresponding\naverage of the redshift-distance and angular-diameter-distance -- this crude\ntreatment is adequate given the large measurement errors. Our models\ngenerically predict a gradual increase of the correlation length with redshift\n(``positive evolution''). The clustering is dominated by the faintest quasars\nnear the threshold luminosity; as a result, the fixed magnitude-cut of\n$B=20.85$ corresponds to more massive, and more highly clustered halos at\nhigher redshifts. There are two additional effects that determine the\nredshift--evolution of clustering: (1) quasars of a fixed luminosity are more\nabundant towards high--$z$, requiring smaller halo masses to match their number\ndensity, and (2) halos with a fixed mass are more highly clustered towards\nhigh-$z$. We find, however, that these effects are less important than the\nincrease in $M_{\\rm halo}$ caused by fixing the apparent magnitude threshold,\nwhich gives rise to the overall positive evolution.\n\nThe clustering in the long--lifetime model is stronger, and evolves more\nrapidly than in the short--lifetime case. As we can see, the present\nmeasurement error-bars are large -- the whole range of life-times from\n$10^{6.5}$ to $10^8$ yr is broadly consistent with the data, to within $\\sim 2\n\\sigma$. For the $\\Lambda$CDM model, the 2dF data-point is consistent with a\nlifetime of around $10^{7.7 \\pm 0.8}$ yr; in the OCDM model the lifetime is\nsomewhat higher, $10^{8 \\pm 0.8}$ yr. It is worth emphasizing here that the\nconstraints on lifetime from clustering depends on the underlying cosmological\nparameters one assumes, which future large scale structure measurements (from\ne.g. the microwave background, galaxy surveys and the Lyman--$\\alpha$ forest)\nwill hopefully pin down to the accuracy required here.\n\nLastly, we note that observational results on $r_0$ are commonly obtained by a\nfit to the two-point correlation of the form $\\xi (r) =\n(r/r_0)^{-\\gamma}$. Since $r_0$ is the correlation length where the correlation\nis unity, we expect our formalism to begin to fail on such a scale, because\nneither linear fluctuation growth nor linear biasing holds. On the other hand,\nit is also unclear whether $r_0$ as presently measured from a 2-parameter fit\nto the still rather noisy observed two-point correlation necessarily\ncorresponds to the true correlation length. While our crude comparison with\nexisting data in Figure~\\ref{fig:r0} suffices given the large measurement\nerrors, superior data in the near future demand a more refined treatment, which\nis the subject of the next section.\n\n\\section{Expectations from the SDSS and 2dF}\n\\label{section:future}\n\nAlthough existing quasar clustering measurements still allow a wide range of\nquasar lifetimes, and do not provide tight constraints on our models,\nforthcoming large quasar samples from SDSS or the complete 2dF survey are\nideally suited for this purpose. Here we estimate the statistical uncertainties\non the derived lifetimes, using the three--dimensional quasar power spectrum\n$P_Q(k)$ derived from these surveys.\n\nThe variance of the power spectrum is computed by\n\n\\beq \n\\langle \\delta P_{\\rm Q}^2 (k) \\rangle = n_k^{-1} [\\bar b^2 P(k) + \\bar n]^2,\n\\label{eq:variance}\n\\eeq \n\nwhere the large scale fluctuations are assumed to be Gaussian, $n_k$ is the\nnumber of independent modes, $\\bar n$ is the mean number density of observed\nquasars, $P_Q(k) = \\bar b^2 P(k)$ is the quasar power spectrum and $P(k)$ is\nthe mass power spectrum (Feldman, Kaiser \\& Peacock 1994). For a survey of\nvolume $V$, and a $k$-bin of size $\\Delta k$, we use $n_k = k^2 \\Delta k V / 4\n\\pi^2$. The fractional variance is therefore $n_k^{-1} \\{1 + 1/[\\bar n \\bar b\nP(k)]\\}^2$. In terms of minimizing this error, increasing the luminosity cut of\na survey has the advantage of raising the bias $\\bar b$, but has the\ndisadvantage of decreasing the abundance $\\bar n$. In practice, $\\bar b$\nchanges relatively slowly with mass (slower than $\\bar b\\propto M$) whereas\n$\\bar n$ varies with mass much more rapidly ($\\bar n \\sim 1/M$, or steeper if\n$M>M_\\star$). As a result, we find that for our purpose of determining the\nclustering and the quasar lifetime, it is better to include more (fainter)\nquasars.\n\nThe power spectrum $P_Q(k)$ of quasars in $\\Lambda$CDM is shown in\nFigure~\\ref{fig:sdsslcdm} at two different redshifts near the peak of the\ncomoving quasar abundance, $z=2$ and $z=3$. We assume that redshift slices are\ntaken centered at each redshift with a width of $\\Delta z = 0.5$ (which enters\ninto the volume $V$ above). Results are shown in the long and short lifetime\nmodels, together with the expected $1\\sigma$ error bars from SDSS (crosses).\nAlso shown in the lower panel are the expected error bars from 2dF (open\nsquares), which are slightly larger because of the smaller volume (for SDSS, we\nassume an angular coverage of $\\pi$ steradians, and for 2dF, an area of $0.23$\nsteradians). We do not show error bars for 2dF beyond $k \\sim 0.01 {\\, \\rm\nMpc/h}$ because larger scales would likely be affected by the survey window.\nWe also only show scales where the mass power spectrum and biasing are believed\nto be linear.\n\nAs these figures show, the long and short $t_Q$ models are easily\ndistinguishable with the expected uncertainties both from the SDSS and the 2dF\ndata, out to a scale of $\\sim 100$Mpc. The measurement errors at different\nscales are independent (under the Gaussian assumption), and hence, when\ncombined, give powerful constraints e.g. formally, even models with lifetimes\ndiffering by a few percent can be distinguished with high confidence using the\nSDSS. However, systematic errors due to the theoretical modeling are expected\nto be important at this level, which we will discuss in \\S\n\\ref{section:discussion}.\n\nIn Figure~\\ref{fig:sdsslcdm}, we have used the magnitude cuts for spectroscopy,\ni.e. $B=20.85$ for 2dF and $B=20.4$ ($g^\\prime\\approx 19$) for SDSS. If\nphotometric redshifts of quasars are sufficiently accurate, the magnitude cuts\ncan be pushed fainter, further decreasing the error-bars -- although it is\nlikely that the photometric redshift errors will be large enough that one can\nonly measure the clustering in projection, in some well-defined redshift-bin\npicked out using color information. Color selection of $z > 3$ quasars has\nalready proven to be highly effective (Fan et al. 1999); a high redshift sample\ncan give valuable information on the evolution of the quasar clustering (see\nFig. \\ref{fig:r0}).\n\n\\section{Quasar Clustering in X-ray}\n\\label{section:xray}\n\nBoth the luminosity function (e.g. Miyaji et al. 2000), and the clustering of\nquasars (e.g. Carrera et al. 1998) has been studied in the X--ray band,\nanalogously to the optical observations described above. At present, the\naccuracy of both quantities are inferior to that in the optical. Nevertheless,\nit is interesting to consider the clustering of quasars in the X--ray regime,\nbecause (1) applying the exercise outlined above to a different wavelength band\nprovides a useful consistency check on our results, (2) observations with the\n{\\it Chandra X--ray Observatory (CXO)} and {\\it XMM} can potentially\\footnote{\nsee http://asc.harvard.edu and http://xmm.vilspa.esa.es, respectively} probe\nquasars at redshifts higher than currently reached in the optical, and (3)\nX-ray observations are free from complications due to dust extinction, although\nother forms of obscuration are possible (see \\S \\ref {section:discussion}). In\naddition, we will consider here the auto--correlation of the soft X--ray\nbackground (XRB) as another potential probe of quasar clustering and lifetime.\n\nThe formalism we presented in \\S~\\ref{section:models} and\n\\S~\\ref{section:clustering} is quite general, and we here apply it to the soft\nX--ray luminosity function (XRLF) from Miyaji et al. (2000). The details of\nthe fitting procedure are given in the Appendix. In analogy with the optical\ncase, we find that the clustering of X-ray selected quasars depends strongly on\nthe lifetime. As an example, including all quasars whose observed flux is\nabove $3 \\times 10^{-14} {\\, \\rm erg \\, cm^{-2}\\, s^{-1}}$, we find the\ncorrelation length at $z=2$ to be $\\approx 4h^{-1}$Mpc in the short lifetime,\nand $\\approx 11h^{-1}$Mpc in the long lifetime case ($\\Lambda$CDM). Current\ndata probes the clustering of X-ray quasars only at low redshifts ($z\\lsim 1$,\nsee Carrera et al. 1998), where our models suffer from significant\nuncertainties due to the subhalo problem discussed in \\S\n\\ref{section:discussion}. Constraints at $z\\gsim 2$ could be available in the\nfuture from {\\it CXO} and {\\it XMM}, provided that a large area of the sky is\nsurveyed at the improved sensitivities of these instruments.\n\nWe next focus on the quasar contribution to the soft X--ray background and its\nauto--correlation, which as we will see is dominated by quasar contributions at\nsomewhat higher redshifts. The mean comoving emissivity at energy $E$ from all\nquasars at redshift $z$, typically in units of ${\\rm keV \\, cm^{-3} \\, s^{-1}\n\\, sr^{-1}}$, is given in our models by\n\n\\beq\n\\bar j(E,z) = \\frac{1}{4\\pi} \\int_0^\\infty dL \\frac{d\\phi}{dL} L_X(E,L),\n\\label{eq:jxray}\n\\eeq where $L_X(E,L)$ is the luminosity (in ${\\rm keV \\, s^{-1} \\, keV^{-1}}$)\nat the energy $E$ of a quasar whose luminosity at $(1+z)$ keV is $L$. We have\nused the mean spectrum of Elvis et al. (1994) to include a small K--correction\nwhen computing the background at observed energies $E\\ne 1$keV. The mean\nbackground is the integral of the emissivity over redshift,\n\n\\begin{equation}\n\\bar I(E) = \\int_0^\\infty \\frac{d\\chi}{(1+z)} \\bar j(E_z,\\chi),\n\\label{eq:xrb}\n\\end{equation}\nwhere $\\bar I$ is typically given in units of ${\\rm keV \\, cm^{-2} \\, s^{-1} \\,\nsr^{-1} \\, keV^{-1}}$, $E_z = E (1+z)$, and $\\chi$ is the comoving distance\nalong the line of sight.\n\nIf $\\delta(z)$ is the mass fluctuation at some position at redshift $z$, then\nthe fluctuation of the emissivity at the same position and redshift is given by\n$b_X(z) \\delta(z) \\bar j(E_z, z)$, where we have defined the X-ray\nemission--weighted bias $\\bar b_X(z)$ as\n\n\\beq\n\\bar b_X(z) = \\frac{1}{\\bar j(E_z,z)} \n\\frac{1}{4\\pi} \\int_0^\\infty dL \\frac{d\\phi}{dL} L_X(E_z,L) b_X(L,z).\n\\label{eq:biasx}\n\\eeq\n\nFor simplicity, we compute the auto--correlation $w_\\theta$ of the XRB using\nthe Limber approximation, together with the small angle approximation, as:\n\n\\begin{eqnarray}\n\\label{eq:Clwtheta}\nC_\\ell(E) &=& {\\bar I(E)}^{-2} \\int \\frac{d\\chi}{r_\\chi^2}\nW^2(E_\\chi,\\chi) P_0(\\ell/r_\\chi) \\\\ \n\\nonumber w_\\theta(E) &=& \n\\int {\\ell d\\ell \\over 2\\pi} C_\\ell(E) J_0 (\\ell \\theta),\n\\end{eqnarray}\n\nwhere $C_\\ell$ is the angular power spectrum, $J_0$ is the zeroth order Bessel\nfunction, $P_0(\\ell/r_\\chi)$ is the linear mass power spectrum today, $r_\\chi$\nis the angular diameter distance ($=\\chi$ for a flat universe), and\n$W(E_\\chi,\\chi) = \\bar j(E_z,z) \\bar b_X(z) D(z)/(1+z)$. When the power\nspectrum is measured in practice, shot-noise has to be subtracted or should be\nincluded in the theoretical prediction, whereas the same is not necessary for\nthe angular correlation except at zero-lag.\n\nOur models predicts the correct mean background spectrum $\\bar I(E)$, computed\nfrom equation~\\ref{eq:xrb}, at $E=1$ keV. We have included all quasars down to\nthe observed 1 keV flux of $2\\times10^{-17}~{\\rm erg~cm^{-2}~s^{-1}}$, i.e. we\nused our models to extrapolate the XRLF to two orders of magnitude fainter than\nthe ROSAT detection threshold for discrete sources (Hasinger \\& Zamorani 1997),\nto make up the remaining $\\sim 50\\%$ of the XRB at 1keV. Our models predict a\nfaint--end slope that is steeper than the Miyaji et al. (2000) fitting\nformulae, allowing faint quasars to contribute half of the background. The\nemissivities peak at $z\\approx 2$, coinciding with the peak of the XRLF,\nimplying that our model produces most of the XRB, as well as its\nauto--correlation signal at $z\\approx 2$. Note that the known contribution\nfrom nearby galaxy clusters is $\\sim 10\\%$ (Gilli et al. 1999), which we ignore\nhere.\n\nIn Figure \\ref{fig:xrb}, we show our predictions for the two point angular\ncorrelation $w_\\theta$ of the XRB from quasars at 1 keV. Most measurements at\nthe soft X-ray bands have yielded only upper limits, which are consistent with\nour predictions (e.g. variance at $\\lsim 0.12$ at a scale of $10$ arcmin. and\n$E = 0.9 - 2$keV, from Carrera et al. 1998; see also references therein).\nSoltan et al. (1999) obtained angular correlations significantly higher than\nprevious results (dashed curve), which, taken at face value, would imply quasar\nlifetimes $t_Q \\gg 10^8$ yr. However, the results of Soltan et al. (1999)\ncould be partially explained by galactic contamination (Barcons et\nal. 2000). We therefore view this measurement as an upper limit, which is\nconsistent with models using both lifetimes we considered. Figure \\ref{fig:xrb}\nshows that $w_\\theta$ predicted in the long and short lifetime models differ by\na factor of $\\sim 2$ on angular scales of 0.1-1 degrees, offering another\npotential probe of quasar lifetimes, provided that $w_\\theta$ can be measured\nmore accurately in the future, and that the contribution to the clustering\nsignal from nearby non-quasar sources (e.g. clusters) is small or can be\nsubtracted out. Finally, we note that there have been detections of of\nclustering on several-degree-scales at the hard X-ray bands ($2 - 10$ keV) from\nthe HEAO satellite (Treyer et al. 1998) -- while a prediction for such energies\nwould be interesting (see also Lahav et al. 1997), it would require an\nextrapolation of the X-ray spectrum, since we normalize by fitting to the\nsoft-Xray luminosity function.\n\n\\section{Further Considerations}\n\\label{section:discussion}\n\nWe have shown above that the quasar lifetime could be measured to high\nprecision, using the soon available large samples of quasars at $z\\lsim 3$;\neither from the 2dF or the SDSS survey. This precision, however, reflects only\nthe statistical errors in the simple model we have adopted for relating quasars\nto dark matter halos. The main hindrance in determining the quasar lifetime\nwill likely be systematic errors; here we discuss how several potential\ncomplications could affect the derived lifetime.\n\n\\vspace{\\baselineskip} {\\em Obscured sources.} Considerations of the hard\nX--ray background have led several authors to suggest the presence of a large\npopulation of ``absorbed'' quasars, necessary to fit the hard slope and overall\namplitude of the background. Although not a unique explanation for the XRB,\nthis would imply that the true number of quasars near the faint end of both the\noptical and soft X--ray LF is $\\sim10$ times larger than what is observed; 90\\%\nbeing undetected due to large absorbing columns of dust in the optical, and\nneutral hydrogen in the soft X--rays (see, e.g. Gilli et al. 1999). Unless the\noptically bright and dust--obscured phases occur within the same object (Fabian\n\\& Iwasawa 1999), this increase would have a direct effect on our results,\nsince we would then need to adjust our fitting parameters to match a $\\sim10$\ntimes higher quasar abundance. We find that this is easily achieved by leaving\n$x_0$ and $\\alpha$ unchanged, and instead raising the lifetime from $10^{6.5}$\nto $10^{7.5}$ yr in the short lifetime model, and from $10^{8}$ to $10^{8.6}$\nyr in the long lifetime model. In the latter case, a 10-fold increase in the\nduty cycle requires only an increase in $t_Q$ by a factor of $\\approx 4$, owing\nto the shape of the age distribution $dp_a/dt$ (Lacey \\& Cole 1993). Our\nresults would then hold as before, but they would describe the two cases of\n$t_Q=10^{7.5}$ and $10^{8.6}$ yr. Interestingly, this scenario would imply\nthat the quasar lifetime could not be shorter than $t_Q\\approx10^{7.5}$ yr,\nsimply based on the abundance of quasars (cf. \\S~\\ref{section:models}). Future\ninfrared and hard X-ray observations should help constrain the abundance of\nobscured sources, and reduce this systematic uncertainty.\n\n\\vspace{\\baselineskip} {\\em Multiple BH's in a single halo.} A possibility\nthat could modify the simple picture adopted above is that a single halo might\nhost several quasar black holes. A massive (e.g. $10^{14}~{\\rm M_\\odot}$) halo\ncorresponds to a cluster of galaxies; while the Press--Schechter formalism\ncounts this halo as a single object. If quasar activity is triggered by\ngalaxy--galaxy mergers, a massive Press-Schechter halo, known to contain\nseveral galaxies, could equally well host several quasars (e.g. Cavaliere \\&\nVittorini 1998). There is some observational evidence of perhaps merger driven\ndouble quasar activity (Owen et al. 1985; Comins \\& Owen 1991). One could\ntherefore envision that quasars reside in the sub--halos of massive ``parent''\nhalos -- a scenario that would modify the predicted clustering. To address\nthese issues in detail, one needs to know the mass--function of sub--halos\nwithin a given parent halo, as well as the rate at which they merge and turn\non. In principle, this information can be extracted from Monte Carlo\nrealizations of the formation history of halos in the extended Press--Schechter\nformalism (i.e. the so called merger tree) together with some estimate of the\ntime-scale for mergers of sub--halos based on, for instance, dynamical friction\n(e.g. Kauffmann \\& Haehnelt 2000). Here, we consider two toy models that we\nhope can bracket the plausible range of clustering predictions.\n\nTo simplify matters, we ignore the scatter in $L$--$M$ in the following\ndiscussion. Suppose one is interested in quasars of a luminosity $L$ at\nredshift $z_0$, which correspond to Press-Schechter halos of mass $M_0$ in our\nformalism as laid out in \\S \\ref{section:models}. This choice of $M_0$ matches\nthe abundance of quasars, expressed approximately as $L(d\\Phi/dL)\\approx\nM_0[dN(M_0, z_0)/dM_0] (t_Q/t_{\\rm Hub})$ (the merger, or activation rate of\nhalos is approximated as $\\sim t_{\\rm Hub}^{-1}$, where $t_{\\rm Hub}$ is the\nHubble time), and implies the bias $b_0(L)\\approx b(M_0,z_0)$.\n\nIn model A, we suppose the Press-Schechter halos are identified at some earlier\nredshift $z_1$ -- these would be sub--halos of those Press-Schechter halos\nidentified at $z_0$. Quasars of luminosity $L$ now correspond to sub--halos of\nmass $M_1$. The abundance of these sub-halos is given by the Press-Schechter\nmass function $dN(M_1, z_1)/dM_1$, which is related to the mass function at\n$z_0$ by $dN(M_1, z_1)/dM_1 = \\int_{M_1}^\\infty dM [dN(M, z_0)/dM] [d{\\cal\nN}(M_1, z_1 | M, z_0) / dM_1]$ where $dM_1 \\times d{\\cal N}(M_1, z_1 | M, z_0)\n/ dM_1$ is the average number of $M_1 \\pm dM_1/2$ sub--halos within parent\nhalos of mass $M$, given by (e.g. Sheth \\& Lemson 1999)\n\n\\begin{eqnarray}\n\\label{eq:condPS}\n&& d{\\cal N}(M_1, z_1 | M, z_0) / dM_1 = \\\\ \\nonumber\n&& \\quad \\quad {M\\over M_1} {1\\over \\sqrt{2\\pi}} \n{{\\delta_1 - \\delta_0}\\over {[\\sigma^2 (M_1) - \\sigma^2 (M)]^{3/2}}} \\\\ \\nonumber\n&& \\quad \\quad\n{\\, \\rm exp} \\left\\{ -{(\\delta_1 - \\delta_0)^2 \\over {2[\\sigma^2 (M_1)-\\sigma^2 (M)]}}\\right\\}\n{d \\sigma^2 (M_1) \\over dM_1},\n\\end{eqnarray}\n\nwhere $\\delta_1 = \\delta_c/D(z_1)$ and $\\delta_0 = \\delta_c/D(z_0)$ (see\neq. \\ref{eq:biasM}).\n\nTo match the abundance of quasars at luminosity $L$, we impose the condition\nthat $M_1 [dN(M_1, z_1)/dM_1] \\approx$ $M_0[dN(M_0, z_0)/dM_0]$ , which\ndetermines $M_1$ given $z_1$, $M_0$ and $z_0$. The bias of the quasars is no\nlonger $b_0 (L) \\approx b(M_0, z_0)$, but is instead given by\n\n\\begin{eqnarray}\n\\label{eq:beff}\n&& b_{\\rm eff}^A (L,z_1) = \\left[{dN(M_1, z_1) \\over dM_1}\\right]^{-1} \\\\ \\nonumber \n&& \\quad \\int_{M_1}^\\infty dM {dN(M, z_0) \\over dM} {d{\\cal N}\n(M_1, z_1 | M, z_0) \\over dM_1} b(M, z_0).\n\\end{eqnarray}\n\nWe show in Fig. \\ref{fig:comparebiasPS} the ratio of $b_{\\rm eff}^A (L,z_1)/b_0\n(L)$ as a function of $z_1$, for $z_0 = 3$ and $z_0 = 2$ respectively, and for\na range of masses $M_0$ which are representative of the halos that dominate our\nclustering signal in previous discussions. It is interesting how the bias\n$b_{\\rm eff}^A (L,z_1)$ is not necessarily larger than our original bias $b_0\n(L)$, despite the fact that the bias of sub--halos should be boosted by their\ntaking residence in bigger halos. This is because the relevant masses here\n(e.g. $M_0$) are generally large, and we find that the number of halos of mass\n$M_0$ at $z_1$ is always {\\it smaller} than the number of halos of the same\nmass at $z_0 < z_1$. Hence, to match the observed abundance of quasars at the\nsame $L$, $M_1$ must be chosen to be smaller than $M_0$. As\nFig. \\ref{fig:comparebiasPS} shows, this could, in some cases, more than\ncompensate the increase in clustering due to massive parent halos. Because of\nthese two opposing effects, the bias does not change by more than about $50 \\%$\neven if one considers $z_1$ as high as $10$. This translates into a factor of\n$\\sim 2$ uncertainty in our predictions for the quasar power spectrum. Our\nclustering predictions for the short and long lifetime models differ by about a\nfactor of $\\sim 5$, implying that the lifetime can still be usefully\nconstrained at $z\\gsim 2$. As we can see from Fig. \\ref{fig:comparebiasPS}, at\nlower redshifts, or equivalently lower $M_0/M_\\star$, our predictions for the\nquasar power spectrum should be more uncertain.\n\nOne might imagine modifying the above model by allowing mergers to take place\npreferentially in massive parents, and therefore boosting the predicted bias.\nIn model B, we adopt a more general procedure of matching the observed quasar\nabundance by $L (d\\Phi/dL) = M_1 \\int_{M_1}^\\infty dM [dN(M, z_0)/dM] [d{\\cal\nN}(M_1, z_1 | M, z_0) / dM_1]$ $(t_Q/t_{\\rm Hub}) f(M_1, M) $ where\n$(t_Q/t_{\\rm Hub}) f(M_1, M)$ is the probability that an $M_1$ sub--halo\nresiding within a parent halo of $M_0$ harbors an active quasar of luminosity\n$L$. It is conceivable that $f$ increases with the parent mass $M_0$ -- a more\nmassive parent might encourage more quasar activity by having a higher fraction\nof mergers or collisions. The following heuristic argument shows that one\nmight expect $[d{\\cal N}(M_1, z_1 | M, z_0) / dM_1] f(M_1, M)$ to scale\napproximately as $\\sim M^{4/3}$. Let $N_h$ be the number of sub--halos inside a\nparent halo of mass $M$. The rate of collisions is given by $N_h^2 v_h \\sigma_h\n/R^3$ where $v_h$ is the velocity of the sub--halos, $\\sigma_h$ is their\ncross-section and $R^3$ is the volume of the parent halo. Using $N_h \\propto M$\n(which can be obtained from eq. \\ref{eq:condPS} in the large $M$ limit), $v_h\n\\propto \\sqrt{M/R}$ (virial theorem) and $R^3 \\propto M$ (fixed overdensity of\n$\\sim 200$ at the redshift of formation), the rate of collisions scales with\nthe parent mass as $M^{4/3}$, if one ignores the possibility that $\\sigma_h$\nmight depend on the parent mass as well. A similar scaling of $M^{1.3}$ has\nbeen observed in simulations of the star-burst model for Lyman-break objects\n(Kolatt et al. 1999, Weschler et al. 1999).\n\nTo model the enhanced rate of collisions inside massive parent halos, we can\nsimply modify model A by using $f(M_1, M) = (M/M_1)^{1/3}$. The effective\nbias is given by\n\n\\begin{eqnarray}\n&& b_{\\rm eff}^B (L,z_1) = \\\\ \\nonumber\n&& \\left[\\int_{M_1}^\\infty dM {dN(M, z_0) \\over dM} {d{\\cal N}\n(M_1, z_1 | M, z_0) \\over dM_1} \\left({M\\over M_1}\n\\right)^{1\\over 3} \\right]^{-1} \\\\ \\nonumber &&\n\\times\\int_{M_1}^\\infty dM {dN(M, z_0) \\over dM} {d{\\cal N}\n(M_1, z_1 | M, z_0) \\over dM_1} \\left({M \\over M_1}\\right)^{1\\over 3} \nb(M,z_0).\n\\label{eq:beffB}\n\\end{eqnarray}\n\nWe find that the above prescription does not significantly alter our\nconclusions following from model A: the $M^{1/3}$ enhancement of the activation\nrate inside massive parent halos turns out to be relatively shallow, and\ntranslate to a small effect in the bias. Finally, we note that $z_1$ above\ncould in principle depend on $M_0$ and $M_1$, a possibility that would require\nfurther modeling and is not pursued here.\n\n\\vspace{\\baselineskip} {\\em Galaxies without BH's.} Another possibility that\ncould modify our picture is that only a fraction $f<1$ of the halos harbor\nBH's; the duty cycle could then reflect this fraction, rather than the lifetime\nof quasars. Although there is evidence (e.g. Magorrian et al. 1998) that most\n{\\it nearby} galaxies harbor a central BH, this is not necessarily the case at\nredshifts $z=2-3$: the fraction $f$ of galaxies hosting BH's at $z=2-3$ could,\nin principle have merged with the fraction $1-f$ of galaxies without BH's,\nsatisfying the local constraint.\n\nUsing the extended Press--Schechter formalism (Lacey \\& Cole 1993), one can\ncompute the rate of mergers between halos of various masses. On galaxy--mass\nscales, the merger rates at $z=2-3$ are comparable to the reciprocal of the\nHubble time (cf. Fig. 5 in Haiman \\& Menou 2000), implying that a typical\ngalaxy did not go through numerous major mergers between $z=2-3$ and $z=0$,\ni.e. that the fraction $f$ cannot be significantly less than unity at $z=2-3$.\nA more detailed consideration of this issue is beyond the scope of this paper;\nwe simply note that the lifetimes derived here scale approximately as $1/f$,\nwhere $f$ is likely of order unity.\n\n\\vspace{\\baselineskip} {\\em Larger scatter in $L/M$.} The scatter $\\sigma$ we\nassumed around the mean relation between quasar luminosity and halo mass is\nmotivated by the scatter found empirically for the $M_{\\rm bh}-M_{\\rm bulge}$\nrelation (Magorrian et al. 1998). It is interesting to consider the\nsensitivity of our conclusions to an increased $\\sigma$. In general, scatter\nraises the number of quasars predicted by our models, by an amount that depends\non the slope of the underlying mass function $dN/dM$. As a result, increasing\n$\\sigma$ raises, and flattens the predicted LF. We find that an increase of\n$\\sigma$ from 0.5 to 1 (an additional order of magnitude of scatter) can be\ncompensated by a steeper $\\bar L_M$ relation, typically replacing $\\alpha$ with\n$\\approx \\alpha-0.5$. As a result of the increase in $\\sigma$, quasars with a\nfixed $L$ are, on average, associated with larger, and more highly biased\nhalos.\n\nNevertheless, we find that the mean bias $\\bar b$ of all sources above a fixed\nflux (cf. eq.~\\ref{eq:bave}), and therefore the correlation length $r_0$, is\nunchanged by the increased scatter (at the level of $\\sim 3\\%$). The reason\nfor the insensitivity of $r_0$ to the amplitude of the scatter can be\nunderstood as follows. The mean bias $\\bar b$ of all sources with $L>L_{\\rm\nmin}$ is dominated by the bias $b(L)$ of sources near the threshold $L_{\\rm\nmin}$. The latter is obtained by averaging $b(M)$ over halos of different\nmasses (cf. eq.~\\ref{eq:biasL}), and it is dominated by the bias of the\nsmallest halos within the width of the scatter, i.e. of halos with mass $M_{\\rm\nmin} \\approx \\bar M / 10^\\sigma$, where $\\bar M$ defines the mean relation\nbetween $L_{\\rm min}$ and halo mass i.e. $L_{\\rm min}$ = $\\bar L(\\bar M)$, and\n$\\sigma$ quantifies the scatter (see eq. \\ref{eq:scatter}). As mentioned\nbefore, increasing the scatter makes the luminosity function flatter, which\nmeans to match the observed abundance of halos at a fixed luminosity $L_{\\rm\nmin}$, one has to choose a higher $\\bar M$. In other words, $\\bar M$ scales up\nwith the scatter, and it turns out to scale up approximately as $10^\\sigma$,\nmaking $M_{\\rm min}$ and hence the effective bias roughly independent of\nscatter.\n\nWe note that the relation between quasar luminosity and halo mass can, in\nprinciple be derived from observations, by measuring $M_{\\rm halo}$ for the\nhosts of quasars (e.g. by weak lensing, or by finding test particles around\nquasars, such as nearby satellite galaxies).\n\n\\vspace{\\baselineskip} {\\em Mass and redshift dependent lifetime.} In all of\nthe above, we have assumed that the quasar lifetime is a single parameter,\nindependent of the halo mass. This is not unreasonable if the Eddington time,\nthe timescale for the growth of black hole mass, is indeed the relevant\ntime--scale, $4\\times10^7$ ($\\epsilon$/0.1) yr. Implicit in such reasoning is\nthat the active phase of the quasar is coincident with the phase where the\nblack hole gains most of its mass. This is not the only possibility; see\nHaehnelt et al. (1999) for more discussions. One can attempt to explore how\n$t_Q$ depends on halo mass by applying our method to quasars grouped into\ndifferent absolute luminosity ranges, but the intrinsic scatter in the\nmass-luminosity relation should be kept in mind. We emphasize, however, since\nwe fit the luminosity function and clustering data at the same redshift, there\nis no need within our formalism to assume a redshift independent lifetime. In\nfact, performing our exercise as a function of redshift could give interesting\nconstraints on how $t_Q$ evolves with redshift.\n\n\\section{Conclusions}\n\\label{section:conclusions}\n\nIn this paper, we have modeled the quasar luminosity function in detail in the\noptical and X--ray bands using the Press--Schechter formalism. The lifetime of\nquasars $t_Q$ enters into our analysis through the duty--cycle of quasars, and\nwe find that matching the observed quasar LF to dark matter halos yields the\nconstraint $10^6 \\lsim t_Q \\lsim 10^8$ yr: smaller lifetimes would imply overly\nmassive BH's, while longer lifetimes would necessitate overly massive halos.\nThis range reassuringly brackets the Eddington timescale of $4\\times10^7$\n($\\epsilon$/0.1) yr.\n\nThe main conclusion of this paper is that the lifetime (and hence $\\epsilon$,\nif the Eddington time is the relevant timescale for quasar activity) can be\nfurther constrained within this range using the clustering of quasars: for\nquasars with a fixed luminosity, longer $t_Q$ implies larger host halo masses,\nand higher bias. We find that as a result, the correlation length $r_0$ varies\nstrongly with the assumed lifetime. Preliminary data from the 2dF survey\nalready sets mild constraints on the lifetime. Depending on the assumed\ncosmology, we find $t_Q=10^{7.7\\pm 0.8}$ yr ($\\Lambda$CDM) or $t_Q=10^{8\\pm\n0.8}$ yr (OCDM) to within $1\\sigma$ statistical uncertainty. These values are\nalso found to satisfy upper limits on the auto--correlation function of the\nsoft X--ray background.\n\nForthcoming large quasar samples from SDSS or the complete 2dF survey are\nideally suited for a study of quasar clustering, and they can, in principle\nconstrain the quasar lifetime to high accuracy, with small statistical\nerrors. We expect the modeling of the quasar--halo relation, as well as the\npossible presence of obscured quasars, to be the dominant sources of systematic\nuncertainty. Not discussed in depth in this paper is the possibility of using\nhigher moments (such as skewness), which our models also make definite\npredictions for, and will be considered in a future publication. Remarkably,\nour best determination of the lifetime of quasars might come from the\nstatistics of high--redshift quasars, rather than the study of individual\nobjects.\n\n\\acknowledgments \n\nNear the completion of this work, we became aware of a similar, independent\nstudy by P. Martini \\& D. Weinberg. We thank M. Haehnelt, K. Menou,\nE. Quataert, U-L. Pen., U. Seljak, R. Sheth and D. Spergel for useful\ndiscussions, T. Miyaji for his advice on the X--ray luminosity function, and\nT. Shanks and S. Croom for discussions on the 2dF survey. 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We adopt the\nparameterization of the observational LF in the optical B band, given in the\nredshift range $0<z\\lsim 4$ by Pei (1995). We assume the background cosmology\nto be either flat ($\\Lambda$CDM) with $(\\Omega_\\Lambda,\\Omega_{\\rm\nm},h,\\sigma_{\\rm 8h^{-1}},n)=(0.7,0.3,0.65,1.0,1.0)$ or open (OCDM) with\n$(\\Omega_\\Lambda,\\Omega_{\\rm m},h,\\sigma_{\\rm\n8h^{-1}},n)=(0,0.3,0.65,0.82,1.3)$. The LF quoted by Pei (1995) is scaled\nappropriately with cosmology by keeping $(d\\phi/dL) dV d_{\\rm L}^2$=const,\nwhere $dV$ is the volume element, and $d_{\\rm L}$ is the luminosity distance),\nso that $(d\\phi/dL)dL$ is the comoving abundance in ${\\rm Mpc^{-3}}$ of quasars\nwith B--band luminosity $L$ (in solar units $L_{B,\\odot}$). The comoving\nabundance $dN/dM(M,z)$ of dark halos is assumed to follow the Press--Schechter\n(1974) formalism. We assume that each halo harbors a single quasar that turns\non when the halo forms, i.e. triggered by merger (e.g. Percival \\& Miller\n1999), and shines for a fixed lifetime $t_Q$ (relaxing these assumptions is\ndiscussed below in section~\\ref{section:discussion}). The duty--cycle $f_{\\rm\non}$ of halos with mass $M$ at redshift $z$, is then given by the fraction of\nthese halos younger than $t_Q$. The distribution of ages $dp_a/dt(M,z,t)$ for\nhalos of mass $M$ existing at redshift $z$ is obtained using the extended\nPress-Schechter formalism, which assumes that the halo formed at the epoch when\nit acquired half of its present mass (Lacey \\& Cole 1993). The duty--cycle,\nwhich is the probability that a dark matter halo of a given mass harbors an\nactive quasar, is simply\n\n\\beq\nf_{\\rm on}(M,z)=\\int_0^{t_Q} dt \\frac{dp_a}{dt}(M,z,t).\n\\label{eq:duty}\n\\eeq\n\nA model in which the quasar turns on/off more gradually (as expected if the\nmass of the BH grows significantly during the luminous quasar phase) is\nequivalent to one having additional scatter in the ratio $L/M$, which is\ndiscussed in \\S~\\ref{section:discussion}. We next relate the quasar luminosity\nto the mass of its host halo. We define $dp/dL(M,L,z)$ to be the probability\nthat a halo of mass $M$ at redshift $z$ hosts a quasar with luminosity $L$, and\nexpress this quantity as\n\n\\beq\n\\frac{dp}{dL}(L,M,z) = \\frac{dg}{dL}(L,\\bar L_{M,z}) f_{\\rm on}(M,z).\n\\label{eq:pdiff}\n\\eeq\n\nHere $dg/dL(L,\\bar L_{M,z})$ is the probability distribution of luminosities\nassociated with the subset of halos of mass $M$ harboring a live quasar\n(normalized to $\\int_0^\\infty dL dg/dL=1$), and $\\bar L_{M,z}$ is the mean\nquasar luminosity for these halos. In the limit of a perfect intrinsic\ncorrelation, we would have $dg/dL(L,\\bar L_{M,z})=\\delta(L-\\bar L_{M,z})$; more\nrealistically, this correlation will have non--negligible scatter. Lacking an\na--priori theory for this scatter, we here simply assume that it follows the\nsame functional form as the scatter found empirically for the $M_{\\rm\nbh}-M_{\\rm bulge}$ relation (Magorrian et al. 1998), and we set\n\n\\beq\n\\frac{dg}{dL}(L,\\bar L_M) \\propto \\exp(-(\\log L/\\bar L_{M,z})^2/2\\sigma^2).\n\\label{eq:scatter}\n\\eeq\n\nFor reference, we note that the empirical scatter between $M_{\\rm bh}$ and\n$M_{\\rm bulge}$ gives $\\sigma\\sim0.5$, it is not yet clear, however, what\nfraction of this scatter is intrinsic vs. instrumental (van der Marel\n1999). One might expect the scatter in the $L$--$M_{\\rm halo}$ relation not to\nbe significantly larger, since (i) for a sufficiently high fueling rate, the\nluminosity $L$ corresponding to $M_{\\rm bh}$ is likely to always be near the\nEddington limit, and (ii) at least for disk galaxies, the bulge luminosity\ncorrelates well with the total luminosity $L_{\\rm tot}$ ($\\sigma\\sim0.5$, see\ne.g. Andredakis \\& Sanders 1994); $L_{\\rm tot}$ is tightly correlated with the\nvelocity dispersion $\\sigma_v$ through the Tully-Fisher relation\n(e.g. Raychaudhury et al. 1997) as is the total halo mass to $\\sigma_v$\n(Eisenstein \\& Loeb 1996). Nevertheless, in \\S~\\ref{section:discussion} below\nwe will investigate the consequences of an increased scatter. We note that an\nextension of the models presented here, by following the merger histories of\nhalos and their BH's can, in principle, be used to estimate the scatter in\n$L/M_{\\rm halo}$. Cattaneao, Haehnelt \\& Rees (1998) have used this approach\nto fit the observed relation $M_{\\rm bh}/M_{\\rm bulge}$, including its scatter.\n\nUnder the above assumptions, the cumulative probability that a halo of mass $M$\nhosts a quasar with luminosity equal to or greater than $L$ is given by\n\n\\beq\np(L,M,z)=f_{\\rm on}(M,z) \\int_L^\\infty dL \\frac{dg}{dL}(L,\\bar L_{M,z}),\n\\label{eq:pcum}\n\\eeq\n\nand matching the observed cumulative quasar LF requires\n\n\\beq\n\\int_L^\\infty dL \\frac{d\\phi}{dL}(L,z)\n = \\int_0^\\infty dM \\frac{dN}{dM}(M,z) p(L,M,z),\n\\label{eq:matchcum}\n\\eeq\n\nor alternatively, matching the differential LF gives\n\n\\beq\n\\frac{d\\phi}{dL}(L,z) = \\int_0^\\infty dM \\frac{dN}{dM}(M,z) \n\\frac{dg}{dL}(L,\\bar L_{M,z}) f_{\\rm on}(M,z).\n\\label{eq:matchdiff}\n\\eeq\n\nEquation \\ref{eq:matchcum} or \\ref{eq:matchdiff}, together with equations\n\\ref{eq:duty}, \\ref{eq:scatter}, and \\ref{eq:pcum} implicitly determines the\nfunction $\\bar L_{M,z}$, once the quasar lifetime $t_Q$ and magnitude of\nscatter $\\sigma$ are specified. In general, these equations would need to be\nsolved iteratively. In practice, we have found that sufficiently accurate\nsolutions (given the error bars on the observational LF in Pei 1995;\ncf. Fig.~\\ref{fig:LFfits}) can be found by using the simple power--law ansatz:\n\n\n\\beq\n\\bar L_{M,z}= x_0(z) M_{\\rm halo} \n \\left(\\frac{M_{\\rm halo}}{M_0}\\right)^{\\alpha(z)},\n\\label{eq:params}\n\\eeq\n\nwhere the coefficients $x_0(z)$ and $\\alpha(z)$ depend on $t_Q$, $\\sigma$, and\nthe underlying cosmology (Haiman \\& Loeb 1998; Haehnelt et al. 1998). In\nsummary, assuming a fixed scatter $\\sigma$, our model has only one free\nparameter, the quasar lifetime $t_Q$.\n\nWe emphasize that our parameterization in equation \\ref{eq:params} is purely\nphenomenological -- it gives us a convenient way to relate the quasar\nluminosity to the host halo mass ($\\bar L_{M,z}$). In reality, the quasar\nluminosity likely depends on the details of its immediate physical environment\n(e.g. gas supply, magnetic fields, angular momentum distribution, etc.), in\naddition to the halo mass. Our description includes these possibilities only\nin allowing a non--negligible scatter around the mean relation $\\bar L_{M,z}$.\nThe rationale behind this choice is that the average properties of the physical\nenvironment should ultimately be governed by the halo mass (or circular\nvelocity), as expected within the picture of structure formation via\nhierarchical clustering.\n\nA useful check on the physical implications of equation \\ref{eq:params} is\nobtained by assuming that the luminosity $\\bar L_{M,z}$ is produced by a BH of\nmass $M_{\\rm bh}$, shining at the Eddington limit $L_{\\rm Edd}=(4\\pi G \\mu m_p\nc/ \\sigma_{T}) M_{\\rm bh}$. In the mean spectrum of a sample of quasars with\ndetections from radio to X--ray bands (Elvis et al. 1994), $\\approx 7\\%$ of the\nbolometric luminosity is emitted in the rest--frame $B$ band, resulting in\n$L=0.07 L_{\\rm Edd} = 5\\times 10^3 {\\rm L_{B,\\odot} (M_{\\rm bh}/M_\\odot})$.\nEquation \\ref{eq:params} then translates into a relation between the mass of a\nBH and its host halo,\n\n\\beq\n\\bar M_{\\rm bh} = 10^{-3.7} x_0(z) M_{\\rm halo} \n \\left(\\frac{M_{\\rm halo}}{M_0}\\right)^{\\alpha(z)}.\n\\label{eq:params-bh}\n\\eeq\n\nAs an example, Haehnelt et al. (1999) argue that the central BH mass is\ndetermined by a radiative feedback from the central BH that would unbind the\ndisk in a dynamical time. Their derived scaling corresponds to $\\alpha=2/3$ and\n$x_0\\propto (1+z)^{5/2}$, not far from what we find for the long--lifetime case\n(cf. Figure~\\ref{fig:params} and discussion below).\n\nIn Figure~\\ref{fig:params}, we show the values of the parameters $x_0(z)$ and\n$\\alpha(z)$ obtained in our models when two different quasar lifetimes are\nassumed, $t_Q=10^{6.5}$ (solid curves) and $t_Q=10^8$ yr (dotted curves). The\nfilled dots show the parameters in $\\Lambda$CDM, and the empty dots in the OCDM\ncosmology. We have set the arbitrary constant $M_0=10^{12}~{\\rm M_\\odot}$ in\nboth cases. Note that $t_Q$ determines both $\\alpha$ and $x_0$, and therefore\nthe values of $\\alpha$ and $x_0$ are correlated. In general, the fitting\nparameters show little evolution in the range $2<z<4$, around the peak of the\nquasar LF. According to equation \\ref{eq:params-bh}, the corresponding BH\nmasses in, e.g. a $10^{12} {\\rm M_\\odot}$ halo at $2<z<4$ are $M_{\\rm\nbh}\\approx 4\\times 10^{-4} M_{\\rm halo}= 4\\times10^8{\\rm M_\\odot} $ and $M_{\\rm\nbh}\\approx 2\\times 10^{-5} M_{\\rm halo}= 2\\times10^7{\\rm M_\\odot}$ in the short\nand long lifetime models, respectively.\n\nThe fitting procedure described above can be repeated in the X--ray bands. We\ntherefore fit the XRLF using equation~\\ref{eq:params} analogously to the\noptical case, except $\\bar L_{M,z}$ now denotes the X--ray luminosity at 1 keV,\nquoted in units of ${\\rm erg~s^{-1}}$. Note that the XRLF in Miyaji et\nal. (2000) is quoted a function of luminosity at observed 1 keV, i.e. no\nK--correction is applied (alternatively, the XRLF can be interpreted as the\nrest--frame luminosity function of sources with an average intrinsic photon\nindex of 2). Figure~\\ref{fig:paramsx} show the resulting fitting parameters\n$x_0$ and $\\alpha$ in the $\\Lambda$CDM cosmology, analogous to those shown in\nFigure~\\ref{fig:paramsx} for the optical case. It is apparent that both\nparameters have a somewhat behavior different from that in the optical. This\nreflects the fact that the mean quasar spectrum must evolve with redshift, or\nat least is black-hole/halo mass dependent: if every quasar had the same\nspectrum, or at least a similar X--ray/optical flux ratio, the fitting\nparameters derived from the optical and X--ray LF would differ only by a\nconstant in $x_0$. For our purpose of deriving clustering, it is sufficient to\ntreat $x_0$ and $\\alpha$ as phenomenological fitting parameters, and we do not\naddress the physical reason for the apparent spectral evolution (see Haiman \\&\nMenou for a brief discussion).\n\nIt is important to note that the simple power-law ansatz in\nequation~\\ref{eq:params} with the parameters shown in Figure~\\ref{fig:paramsx}\nadequately fits only the faint end of the XRLF. In the optical case, the\nentire range of observed luminosities is well matched by our models\n(cf. Fig~\\ref{fig:LFfits}). In comparison, the well--fitted range in X--rays\ntypically extends from the detection threshold to up to 2-3 orders of magnitude\nin luminosity (i.e. typically upto $\\sim 3\\times 10^{45}~{\\rm erg~s^{-1}}$),\ndepending on redshift, and our models underestimate the abundance of still\nbrighter quasars. One might then consider searching for a different ansatz to\nreplace equation~\\ref{eq:params} that fits the entire range of the observed\nLF. However, we have verified that the rare quasars with these high\nluminosities would contribute negligibly both to the clustering signals, or the\nXRB investigated here. Therefore, we did not consider further improvements over\nequation~\\ref{eq:params}, since this would not change our results.\n\n\n%########################## figure 1 ########################################\n\\clearpage\n\\newpage\n\\begin{figure}[t]\n\\special{psfile=fig1.eps hoffset=25 voffset=-400 hscale=70 vscale=70}\n\\vspace*{4.5in}\n\\caption{Fits to the quasar luminosity function at redshifts $z=2$ and 3 in our\nmodels, with two different quasar lifetimes $t_Q=10^{6.5}$ (solid curves)\nand $t_Q=10^8$ yr (dotted curves). Also shown are the data, and fitting\nfunction (dashed curves) for the LF from Pei (1995). The quality of our fits\nat different redshifts or in the OCDM model are similar. The upper labels show\nthe corresponding apparent magnitudes in the SDSS $g^\\prime$ band, assuming\nthat the intrinsic quasar spectrum is the same as the mean spectrum in the\nElvis et al. (1994) quasar sample. }\n\\label{fig:LFfits}\n\\end{figure}\n\n%########################## figure 2 ########################################\n\\clearpage\n\\newpage\n\\begin{figure}[t]\n\\special{psfile=fig2.eps hoffset=25 voffset=-400 hscale=70 vscale=70}\n\\vspace*{4.5in}\n\\caption{Bias parameter $b(L,z)$ of quasars as a function of their intrinsic\nB--band luminosity (lower labels) or apparent SDSS $g^\\prime$ magnitude (upper\nlabels), in the models with two different quasar lifetimes $t_Q=10^{6.5}$\n(solid curves) and $t_Q=10^8$ yr (dotted curves) as shown in\nFigure~\\ref{fig:LFfits}. For comparison, the bias parameter is also shown in\nthe OCDM model. Quasars are more highly biased in the long lifetime models,\nand in $\\Lambda$CDM.}\n\\label{fig:bias}\n\\end{figure}\n\n%########################## figure 3 ########################################\n\\clearpage\n\\newpage\n\\begin{figure}[t]\n\\special{psfile=fig3.eps hoffset=25 voffset=-400 hscale=70 vscale=70}\n\\vspace*{4.5in}\n\\caption{Correlation length $r_0$ in our models with two different quasar\nlifetimes $t_Q=10^{6.5}$ (solid curves) and $t_Q=10^8$ yr (dotted curves). An\napparent magnitude cut of $B<20.85$ was used, corresponding to the limits of\nthe 2dF survey (Croom et al. 1999). The open square shows a preliminary result\nfrom 2dF. The upper panel shows our results in the $\\Lambda$CDM model, and the\nlower panel in OCDM.}\n\\label{fig:r0}\n\\end{figure}\n\n%########################## figure 4 ########################################\n\\clearpage\n\\newpage\n\\begin{figure}[t]\n\\special{psfile=fig4.eps hoffset=25 voffset=-400 hscale=70 vscale=70}\n\\vspace*{4.5in}\n\\caption{Three--dimensional power spectrum $P_Q(k)$ of quasars in $\\Lambda$CDM\nat two different redshifts near the peak of the comoving quasar abundance.\nResults are shown for quasars with $B\\leq 20.4$ (or $g^\\prime\\lsim 19$), in the\nlong (dotted curves) and short lifetime (solid curves) models, together with\nthe expected $1\\sigma$ error bars from SDSS (crosses) with an assumed area of\n$\\pi$ steradians. The slightly lower curves in the lower panel refer to 2dF\n(open squares), with a magnitude cut of $B=20.5$, and show the expected error\nbars from an assumed area of 0.23 steradians.}\n\\label{fig:sdsslcdm}\n\\end{figure}\n\n%########################## figure 5 ########################################\n\\clearpage\n\\newpage\n\\begin{figure}[t]\n\\special{psfile=fig5.eps hoffset=25 voffset=-400 hscale=70 vscale=70}\n\\vspace*{4.5in}\n\\caption{Angular correlation function of the total XRB, $w_\\theta$ at $E = 1$\nkeV. The dashed lines in the upper right corner indicate $w_\\theta$ at $E =\n1.15$ keV with quoted $\\pm 1\\sigma$ uncertainties as measured from the ROSAT\nAll Sky Survey (Soltan et al. 1999), which can be considered an upper limit.}\n\\label{fig:xrb}\n\\end{figure}\n\n%########################## figure 6 ########################################\n\\newpage\n\\begin{figure}[t]\n\\special{psfile=fig6.eps hoffset=25 voffset=-400 hscale=70 vscale=70}\n\\vspace*{4.5in}\n\\caption{The ratio of the effective bias $b_{\\rm eff}^A (L)$ (in a model\nallowing multiple quasars per halo) to the original bias $b_0 (L)$ (for one\nquasar per halo) as a function of $z_1$ at fixed luminosity $L$, where $z_1$ is\nthe redshift when sub--halos are identified. The squares (open for $M_0 =\n10^{12.5} M_\\odot$ and solid for $M_0 = 10^{13.5} M_\\odot$) show this relation\nfor quasars at $z_0 = 3$, whereas the triangles are for $z_0 = 2$ (open for\n$M_0 = 10^{12} M_\\odot$ and solid for $M_0 = 10^{13} M_\\odot$). The model is\n$\\Lambda$CDM. See text for discussions.}\n\\label{fig:comparebiasPS}\n\\end{figure}\n\n%########################## App 1 ########################################\n\\clearpage\n\\newpage\n\\begin{figure}[t]\n\\special{psfile=figA1.eps hoffset=25 voffset=-400 hscale=70 vscale=70}\n\\vspace*{4.5in}\n\\caption{Fitting parameters $\\alpha(z)$ and $x_0(z)$ for the mean relation\nbetween B--band quasar luminosity $L_B$ and halo mass $M_{\\rm halo}$ given in\nequation \\ref{eq:params}, for two different quasar lifetimes $t_Q=10^{6.5}$\n(solid curves) and $t_Q=10^8$ yr (dotted curves). The filled dots correspond\nto a $\\Lambda$CDM and the open dots to an OCDM cosmology. In all cases, we\nassumed a scatter with $\\sigma=0.5$ (cf. eq.~\\ref{eq:scatter}) around the mean\n$L-M_{\\rm halo}$ relation.}\n\\label{fig:params}\n\\end{figure}\n\n%########################## App 2 ########################################\n\\clearpage\n\\newpage\n\\begin{figure}[t]\n\\special{psfile=figA2.eps hoffset=25 voffset=-400 hscale=70 vscale=70}\n\\vspace*{4.5in}\n\\caption{Same as Figure~\\ref{fig:params}, except the X--ray quasar luminosity\nis used at 1keV. Only the $\\Lambda$CDM case is shown.}\n\\label{fig:paramsx}\n\\end{figure}\n\n\\end{document}\n\n"
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"name": "astro-ph0002190.extracted_bib",
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"name": "ovm.astroph.tex",
"string": "\\documentclass[11pt]{article}\n\n\\newcommand{\\vcirc}{$\\rm v_{circ}$ }\n\\newcommand{\\elec}{$\\rm e^{-}$ }\n\\newcommand{\\rarr}{$\\rightarrow$ }\n\\newcommand{\\larr}{$\\leftarrow$ }\n\\newcommand{\\Delt}{$\\rm \\Delta$}\n\\newcommand{\\emo}{$\\rm \\mu _{814} (0)$}\n\\newcommand{\\emu}{$\\rm \\mu _{814}$}\n\\newcommand{\\tmo}{$\\rm \\mu _{300}$}\n\\newcommand{\\mo}{$\\rm \\mu _{0}$}\n\\newcommand{\\MgL}{\\rm $\\rm M_{gas}/L_T$ }\n\\newcommand{\\ML}{\\rm $\\rm M_T/L_T$ }\n\\newcommand{\\MgM}{\\rm $\\rm M_{gas}/M_T$ }\n\\newcommand{\\Lt}{\\rm $\\rm L_T$}\n\\newcommand{\\mss}{mag arcsec$^{-2}$}\n\\newcommand{\\Bmoi}{\\rm ${\\mu_{B_{i}}}$(0) }\n\\newcommand{\\plm}{$\\pm$ }\n\\newcommand{\\lb}{$\\langle \\:$}\n\\newcommand{\\gb}{$\\rangle \\:$}\n\\newcommand{\\lt}{$< \\:$}\n\\newcommand{\\gt}{$> \\:$}\n\\newcommand{\\lta}{$\\leq $}\n\\newcommand{\\gta}{$\\geq $}\n\\newcommand{\\Bmu}{\\rm $\\mu_B \\:$}\n\\newcommand{\\Rmu}{\\rm $\\mu_R \\:$}\n\\newcommand{\\Imu}{\\rm $\\mu_I \\:$}\n\\newcommand{\\Umu}{\\rm $\\mu_U \\:$}\n\\newcommand{\\Vmu}{\\rm $\\mu_V \\:$}\n\\newcommand{\\Bmo}{\\rm ${\\mu _B}$(0) }\n\\newcommand{\\Imo}{\\rm ${\\mu _I}$(0) }\n\\newcommand{\\Vmo}{\\rm ${\\mu _V}$(0) }\n\\newcommand{\\Ho}{\\rm H$_0$ }\n\\newcommand{\\Bmag}{\\rm B$\\rm _{mag}$ }\n\\newcommand{\\Bt}{\\rm B$\\rm _T$(0) }\n\\newcommand{\\mt}{\\rm m$\\rm _T$ }\n\\newcommand{\\muo}{\\rm ${\\mu}$(0) }\n\\newcommand{\\rts}{\\rm $\\rm r_{27}$ }\n\\newcommand{\\rtf}{\\rm $\\rm r_{25}$ }\n\\newcommand{\\Vc}{{V$_{circ}$\\ }}\n\\newcommand{\\Halp}{H$_{\\alpha}$\\ }\n\\newcommand{\\alp}{$\\alpha$\\ }\n\\newcommand{\\etal}{{\\it et.al.}}\n\\newcommand{\\degree}{$^{\\circ}$ }\n\\newcommand{\\arcs}{\\rm arcsec$^2$}\n\\newcommand{\\teff}{\\rm T$_{eff}$\\ }\n\\newcommand{\\kmsec}{km sec$^{-1}$\\ }\n\\newcommand{\\kms}{km sec$^{-1}$\\ }\n\\newcommand{\\app}{$\\sim$}\n\\newcommand{\\eg}{{\\em e.\\ g.\\ }}\n\\newcommand{\\ie}{{\\em i.\\ e.\\ }}\n\\newcommand{\\mn}{{\\em MNRAS\\ }}\n\\newcommand{\\solarm}{$M_{\\odot}$\\ }\n\\newcommand{\\Msol}{$M_{\\odot}$\\ }\n\\newcommand{\\Zsol}{$Z_{\\odot}$\\ }\n\\newcommand{\\Lsol}{$L_{\\odot}$\\ }\n\\newcommand{\\fivesixco}{$^{56}$Co\\ }\n\\newcommand{\\chisq}{${\\chi}^{2}$\\ }\n\\newcommand{\\chinusq}{${\\chi}_{\\nu}^{2}$\\ }\n\\newcommand{\\bvzero}{\\rm (B-V)$_{\\circ}$\\ }\n\\newcommand{\\feh}{\\rm [Fe/H]\\ }\n\\newcommand{\\lsb}{\\rm low surface brightness}\n\\newcommand{\\hsb}{\\rm high surface brightness}\n\\newcommand{\\lsbg}{\\rm low surface brightness galaxy}\n\\newcommand{\\lsbgs}{\\rm low surface brightness galaxies}\n\\newcommand{\\PMO}{\\rm Pine Mountain Observatory}\n\n\\usepackage{apjfonts}\n\\usepackage{float}\n\\usepackage{multicol}\n\\usepackage{epsfig}\n\n\\textwidth=17.5cm\n\\textheight=23.5cm\n\\voffset=-2.5cm\n\\hoffset=-2.54cm\n\n\\columnsep=7mm\n\\evensidemargin=25mm\n\\oddsidemargin=21mm\n\n\\renewcommand{\\baselinestretch}{0.87}\n\\renewcommand{\\topfraction}{0.99}\n\\renewcommand{\\bottomfraction}{0.99}\n\\renewcommand{\\textfraction}{0.01}\n\n\\begin{document}\n\n\\twocolumn[\n\\null\n\\vspace{-1cm}\n\n\\begin{center}\n\\noindent\n\n{\\Large \\bf Star Formation and Tidal Encounters with the Low Surface\nBrightness Galaxy UGC 12695 and Companions}\n\n\\vspace{1cm}\n\nK. O'Neil$^1$, M.A.W. Verheijen$^2$, S.S. McGaugh$^3$ \\\\\n\n\\end{center}\n\n\\vspace{1cm}\n\n$^1$Arecibo Observatory, HC03 Box 53995, Arecibo, PR 00612, email:koneil@naic.edu \\\\\n$^2$National Radio Astronomy Observatory, Box 0, Socorro, NM 87801, email:mverheij@nrao.edu \\\\\n$^3$Department of Astronomy, University of Maryland, College Park, MD 20742, email:ssm@astro.umd.edu \\\\\n\n\\vspace{0.5cm}\n\n\\begin{flushright}\n\n\\parbox{13.3cm}{{\\large\\noindent{\\bf\\sf ABSTRACT-- }}\nWe present VLA H I observations of the low surface brightness galaxy UGC\n12695 and its two companions, UGC 12687 and a newly discovered dwarf\ngalaxy 2333+1234. UGC 12695 shows solid body rotation but has a very\nlopsided morphology of the H I disk, with the majority of the H I lying\nin the southern arm of the galaxy. The H I column density distribution\nof this very blue, LSB galaxy coincides in detail with its light\ndistribution. Comparing the H I column density of UGC 12695 with the\nempirical (but not well understood) value of $\\Sigma_c$ = 10$^{21}$\natoms cm$^{-2}$ found in, i.e., Skillman's 1986 paper shows the star\nformation to be a local affair, occurring only in those regions where\nthe column density is above this star formation threshold. The low\nsurface brightness nature of this galaxy could thus be attributed to an\ninsufficient gas surface density, inhibiting star formation on a more\nglobal scale. Significantly, though, the Toomre criterion places a\nmuch lower critical density on the galaxy ($\\sim$10$^{20}$ atoms\ncm$^{-2}$), which is shown by the galaxy's low SFR to not be applicable.\n\nWithin a projected distance of 300 kpc/30 \\kms\\ of UGC 12695 lie two\ncompanion galaxies -- UGC 12687, a high surface brightness barred spiral\ngalaxy, and 2333+1234, a dwarf galaxy discovered during this\ninvestigation. The close proximity of the three galaxies, combined with\nUGC 12695's extremely blue color and regions of localized starburst and\nUGC 12687's UV excess bring to mind mutually induced star formation\nthrough tidal activity. } \n\\end{flushright} \n\n\\vspace{0.5cm}\n\n\\noindent\n{\\it Subject headings:} \ngalaxies: individual(UGC 12695, UGC 12687, 2333+1234) \n-- galaxies: spiral\n-- galaxies: evolution \n-- galaxies: interactions\n-- galaxies: kinematics and dynamics\n-- galaxies: structure\n\n\\null\n\\vspace{0.5cm}\n]\n\n\\setcounter{footnote}{0}\n\\footnotetext{To be published in The Astronomical Journal, May 2000}\n\n\\newpage\n\n\n\\begin{figure*}[t]\n\\begin{center}\n\\epsfig{file=ovm.fig1bmp.ps,width=17cm}\n\\caption{H I contours of all three galaxies overlaid on a POSS-II\nimage.}\n\\label{fig:Allposs2HI}\n\\end{center}\n\\end{figure*}\n\n\n\\section{Introduction}\n\nAttempts to understand star formation in low surface brightness (LSB)\ngalaxies has resulted in a large number of theories being discarded and\nfew alternatives being offered. As a result we have considerable\nknowledge on what these enigmatic systems are not. LSB galaxies are\n{\\em not}:\n\n\\begin{itemize}\n\n\\item simply the faded version of high surface brightness (HSB)\ngalaxies. Although some red LSB galaxies have been found which may be\nthe end product of the faint blue galaxies, the majority of LSB galaxies\nhave very blue colors and low metallicities (i.e. Ferguson \\& McGaugh\n1995; O'Neil, \\etal 1997a; McGaugh 1994; Schombert, \\etal 1990; De Blok\n\\& Van der Hulst 1998), arguing against any fading scenario. \n\n\\item lacking the neutral hydrogen necessary to form stars, as many LSB\ngalaxies contain more than 10$^9$ \\Msol of H I and LSB galaxies include\nsome of the highest M$_{HI}$/L$_B$ galaxies known (O'Neil, Bothun, \\&\nSchombert 1999). \n\n\\item a completely new type of galaxy. The transition from HSB to LSB\ngalaxies is smooth, with LSB galaxies covering the entire color and\nmorphological spectrum of HSB galaxies (i.e. O'Neil, \\etal 1997b;\nMatthews \\& Gallagher 1997)\n\n\\end{itemize}\n\nUGC 12695 is a relatively nearby (z=0.021) low surface brightness galaxy\nwith an absolute blue magnitude of M$_B$=$-$18.9. Previous studies of\nUGC 12695 (McGaugh, 1994; O'Neil \\etal, 1998) have shown it to be very\nremarkable. The galaxy is of an exceedingly transparent nature,\nevidenced by the many background galaxies seen through its elusive disk,\nand it contains a reasonably high gas fraction (M$_{HI}$/L$_B$ = 2.6\n\\Msol/\\Lsol) while having a very low metallicity and an extremely blue\ncolor for a galaxy ($U-I$ = $-0.2$) (Table 1). \n\nBecause UGC 12695 was thought to be fairly isolated, with the nearest\ngalaxy (UGC 12687) lying more than 277 kpc away\n(Figure~\\ref{fig:Allposs2HI}), it provides a good opportunity for\nstudying star formation and evolution in LSB galaxies. To this end, and\nwith the above points in mind, we undertook to observe UGC 12695 with\nthe Very Large Array (VLA) in the C configuration. The results of these\nobservations are described in this paper, as follows: Section 2\ndescribes the observations and data reduction; Section 3 examines the H\nI morphology and kinematics of UGC 12695 and its companions -- UGC\n12687, and 2333+1234; Section 4 looks at the dark and visible mass of\nUGC 12695; Section 5 examines the star formation potential of UGC\n12695; Finally, section 6 examines the possibility of a recent tidal\nencounter between the UGC galaxies. \n\n\\begin{table}[ht]\n\\begin{center}\n\\caption{Global properties of UGC~12695 and UGC~12687.}\n\\begin{tabular}{lccc}\n\\noalign{\\vspace{0.8mm}}\n\\hline\n\\hline\n\\noalign{\\vspace{0.8mm}}\n & & UGC~12695 & UGC~12687 \\\\\n\\hline\n\\noalign{\\vspace{0.8mm}}\nType & & Sm$^1$ & SBbc$^1$\\\\\nV$_{hel}$ & km s$^{-1}$& 6186$^2$& 6150$^2$\\\\\nM$_B$ & mag & -18.9$^3$& -20.3$^1$\\\\\n$B-V$ & & 0.26$^3$ & 0.70$^4$\\\\\n$\\mu_B(0)$ &mag/arcsec$^{2}$& 23.8$^3$ & - \\\\\nr$_{25}$ & kpc & 0.79$^1$ & 0.87$^1$\\\\\nM$_{HI}$ & M$_\\odot$ & 7.5$\\times$10$^9$ $^2$& 1.2$\\times$10$^{10}$ $^2$\\\\\nM$_{HI}$/L$_B$ & M$_\\odot$/L$_\\odot$ & 2.62$^2$ & 1.18$^2$ \\\\\n\\noalign{\\vspace{0.8mm}}\n\\hline\n\\multicolumn{4}{l}{$^1$De Vaucouleurs, \\etal 1991}\\\\\n\\multicolumn{4}{l}{$^2$This paper}\\\\\n\\multicolumn{4}{l}{$^3$O'Neil, \\etal 1998}\\\\\n\\multicolumn{4}{l}{$^4$Prugniel \\& Heraudeau 1998}\\\\\n\\noalign{\\vspace{0.8mm}}\n\\hline\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n\\begin{table}[ht]\n\\caption{VLA observing parameters}\n\\begin{tabular}{lr}\n\\noalign{\\vspace{0.8mm}}\n\\hline\n\\hline\n\\noalign{\\vspace{0.8mm}}\nConfiguration & C-short \\\\\nCorrelator mode & 2AC-normal \\\\\nTotal integration time \\hfill (hours) & 15.5 \\\\\nDates of observation & 15Jan99 \\\\\n\\multicolumn{2}{r}{16Jan99} \\\\\nField center, $\\alpha$(B1950) & 23:33:30 \\\\\n\\phantom{Field center, }$\\delta$(B1950) & 12:35:53 \\\\\nCentral frequency \\hfill (MHz) & 1391.64 \\\\\n$V_{\\rm hel}$ of central channel \\hfill (km$\\:$s$^{-1}$) & 6170 \\\\\nPrimary beam FWHM \\hfill (arcmin) & 32.4 \\\\\nSynthesized beam ($\\alpha$$\\times$$\\delta$) \\hfill (arcsec) & 16.2$\\times$14.1 \\\\\nBandwidth \\hfill (MHz) & 1.5625 \\\\\nNumber of channels & 256 \\\\\nChannel separation \\hfill (km$\\:$s$^{-1}$) & 1.31 \\\\\nVelocity resolution \\hfill (km$\\:$s$^{-1}$) & 1.58 \\\\\nrms noise in one channel \\hfill (K) & 2.63 \\\\\nK-mJy conversion, & \\\\\n\\phantom{K-}equiv. of 1mJy/beam \\hfill (K) & 2.76 \\\\\n\\noalign{\\vspace{0.8mm}}\n\\hline\n\\hline\n\\end{tabular}\n\\end{table}\n\n\\section{The Data -- Observations and Reduction} \n\nH I spectral line synthesis observations of UGC 12695 and its companions\nwere done in two runs with the VLA in its new C-short configuration and\nare specified in Table~2. The primary calibrator 3C48 was observed\nthree times per run and the secondary phase calibrator 2340+135 was\nobserved every 35 minutes. \n\nCalibration, flagging, concatenation and Fourier transformation of the\nUV data was done with the AIPS package. A robust R=0 weighting of the\nUV data points was applied and the entire primary beam was imaged with a\n512 x 512 map of 5 arcsecond pixels. The dirty maps and corresponding\nantenna patterns were exported into the GIPSY package which was used for\nfurther data reduction and analysis as described below. \n\nThe number of velocity channels was reduced by averaging adjacent pairs\nof channel maps which resulted in a data cube of 127 nearly independent\nchannels, each 2.68 \\kms\\ wide. The dirty maps were cleaned down to\nhalf the rms noise level with channel dependent search areas using the\nstandard H\\\"ogbom algorithm. The clean components were restored with a\nGaussian beam of FWHM 16.2$\\times$14.1 arcsec at a position angle of\n$-$54 degrees. The data cube was then Hanning smoothed in velocity\nwhich resulted in a velocity resolution of 5.3 \\kms. \n\nNo continuum emission was detected in the averaged line-free channels at\nthe positions of UGC 12695 and 2333+1234. Due to a steep rotation\ncurve, the line emission at the center of UGC 12687 spans the entire\nbandpass, leaving only 4 line-free continuum channels at the high\nvelocity end of the data cube while some line emission at the low\nvelocity edge of the bandpass is severely affected by the high noise\nlevel. No continuum emission could be detected in the line-free\nchannels at the position of the disk of UGC 12687. Therefore, no\ncontinuum map was subtracted to avoid the unnecessary addition of noise\nto the channel maps and the nuclear continuum emission of UGC 12687 was\nremoved at a later stage. \n\nThe areas of H I emission were isolated in each channel map and the\npixels outside these areas were set to zero. Global H I profiles were\nderived by measuring the total flux in the isolated areas, corrected for\nprimary beam attenuation. In the case of UGC 12687, a 2.9 mJy baseline\nwas subtracted from the global profile. \n\nIntegrated H I maps of the galaxies were constructed by summing the\nprimary beam corrected, isolated areas of H I emission. At the position\nof the nucleus of UGC 12687, 7 channels at the high velocity end of the\ndata cube are free from line emission and those were averaged to obtain\na map of the central continuum source. A Gaussian beam was fitted to\nthis source, giving a primary beam corrected flux density of 2.9$\\pm$0.2\nmJy at the position $23^{\\rm h}32^{\\rm m}45^{\\rm s}.4$ and $23^{\\rm\nd}32^\\prime53^{\\prime\\prime}$ (B1950). Subsequently, this fitted\nGaussian was subtracted from the integrated H I map.\n\nVelocity fields were constructed by fitting a single Gaussian to each\nprofile and rotation curves for UGC 12695 and UGC 12687 were derived by\nfitting tilted rings of 11 arcsec width to their velocity fields. \n\nOptical images were taken from the Hubble Space Telescope Wide Field\nPlanetary Camera-2 (WFPC2) images of O'Neil, \\etal (1998), the MDM 1.3m\nMcGraw Hill telescope (McGaugh, Schombert, \\& Bothun 1995), and from the\nSpace Telescope Science Institute Digital Sky Survey. The metallicity\nstudies of UGC 12695 are from McGaugh (1994). \n\nH$_0$ is 75 km s$^{-1}$ Mpc$^{-1}$ throughout this paper, and a \nVirgo-centric infall of 300 km s$^{-1}$ is assumed. B1950 coordinates\nare used throughout this paper.\n\n\n\n\\section{H I morphology and kinematics}\n\nThe following subsections contain detailed descriptions of the overall\nproperties of the neutral hydrogen gas in UGC 12695 and its companions\nUGC 12687 and 2333+1234 which are illustrated in\nFigures~\\ref{fig:U12695}, \\ref{fig:U12687}, \\ref{fig:2333},\nrespectively. The beam size is 16.2'' $\\times$ 14.1'', or 6.4 kpc\n$\\times$ 5.6 kpc at 82 Mpc. \n\n\\subsection{UGC 12695}\n\n\n\\begin{figure*}[p]\n\\epsfig{file=ovm.fig2bmp.ps,width=16cm}\n\\caption{UGC 12695. See section 3.1 for explanations.}\n\\label{fig:U12695}\n\\end{figure*}\n\n\nFigure~\\ref{fig:U12695} presents the data of UGC 12695. The upper left\npanel displays the HST WFPC2 F814W image of O'Neil, \\etal\\ (1998). It\nshows a relatively smooth triangular inner region and an irregular outer\ndisk dominated by several large star forming H$\\alpha$ regions. Several\nbackground galaxies can be seen through the disk, evidencing its\nextremely transparent nature. The southern spiral arm seems to be\nsharply outlined while the northern arm is extremely diffuse. Smoothing\nthe WFPC2 image to a 1$^{\\prime\\prime}$ resolution and fitting an\nellipse to the faintest isophotes indicates a position angle of\n88$^\\circ$, an inclination of 43$^\\circ$ and a central position at\n(23$^{\\rm h}$33$^{\\rm m}$30.4$^{\\rm s}$,\n12$^\\circ$36$^\\prime$1$^{\\prime\\prime}$).\n\nThe upper right panel shows the global H I profile obtained by measuring\nthe flux in the individual channel maps. The width at the 20\\% level of\nthe peak flux is 79.4 \\kms\\ and the width at the 50\\% level of the peak\nflux is 62.2 \\kms. The integrated flux density is 4.7 Jy km s$^{-1}$\nwhich corresponds to a total H I mass of 7.5$\\times$10$^9$ M$_\\odot$ for\na distance of 82 Mpc (v=6186 km s$^{-1}$ (Table 1) and H$_0$=75 km\ns$^{-1}$ Mpc$^{-1}$). The shape of the profile suggests a global\nlopsidedness of the H I distribution and or kinematics. The vertical\narrow indicates the systemic velocity as derived from the H I velocity\nfield. It should be noted that the H I profile of UGC 12695 was\npreviously determined both by Theureau, \\etal\\ (1998) using the\nNan\\c{c}ay telescope and Schneider, \\etal (1990) using the Arecibo\ntelescope. Although both of the earlier observations match our\nvelocity widths, the Nan\\c{c}ay result list a 40\\% smaller total flux. \nAs our results match those of Schneider, \\etal, we believe the data\ndifferences to be the result of uncertain beam shapes and primary beam\ncorrections in the Nan\\c{c}ay data.\n\nThe middle left panel presents the integrated H I column density map\nwith the size of the synthesized beam in the lower left corner. This H\nI map is at the same scale as the WFPC2 image above. Contour levels are\ndrawn at 0.5, 1, 2, 4, 6, 8, 10 and 12$\\times$10$^{20}$ atoms cm$^{-2}$.\n Overall, the neutral hydrogen distribution of UGC 12695 appears to\nmatch the optical morphology quite well, including the fact that the H I\ndistribution is very lopsided with a high column density ridge running\nthrough the southern part of the disk. The cross corresponds to the\nposition of the cross in the WFPC2 image and indicates the central\noptical concentration. Fitting an ellipse to the lowest H I contours\nindicates a position angle of 80$^\\circ$, an inclination of 37$^\\circ$\nafter a first order beam smearing correction, and puts the center of the\nH I disk at (23$^{\\rm h}$33$^{\\rm m}$30.0$^{\\rm s}$,\n12$^\\circ$36$^\\prime$4$^{\\prime\\prime}$), 7 arcseconds ($<$ 1 beam\nwidth) north of the central optical concentration. \n\nThe middle right panel shows the radial H I column density distribution,\nazimuthally averaged over the northern and southern sides separately.\nClearly, the H I surface density falls off more sharply at the southern\nedge, going from 10 to 0.5 x 10$^{20}$ atoms cm$^{-2}$ within two beam\nwidths. \n\nThe lower left panel shows the H I velocity field. Apart from some\nobvious wrinkles due to non-circular or streaming motions, the velocity\nfield is dominated by solid body rotation. This makes it impossible to\ndetermine the dynamical center and inclination from the velocity field\nand therefore the optical center (cross) was adopted as the dynamical\ncenter. The thick line indicates the adopted systemic isovelocity\ncontour at 6185.7 \\kms\\ while the black contours indicate the\napproaching side and the white contours the receding side of the galaxy.\n The isovelocity contour intervals are set at $\\pm$n$\\times$5 \\kms. \n\nThe lower right panel presents the position-velocity diagram along the\nkinematic major axis. Contours are drawn at -4, -2 (dashed), 2, 4, 8,\n12, 16 and 20 times the rms noise level. The vertical dashed line\ncorresponds to the position of the cross in the left panels, the\nhorizontal dashed line corresponds to the adopted systemic velocity. \nThe cross in the lower left corner indicates the beam. All profiles in\nthe vertical direction can be well described by single Gaussians. No\ndouble profiles are observed. The solid points show the derived\nrotation curve projected onto the position-velocity diagram. The\nrotation curve was derived by fitting full tilted rings to the velocity\nfield, effectively azimuthally averaging the wrinkles. Consequently,\nthis azimuthally averaged rotation curve might deviate locally from the\nposition-velocity slice. \n\nThe rotation curve of UGC 12695 is tabulated in Table~3. Fitting a\nsingle, galaxy wide ring to the entire velocity field gives a position\nangle of the kinematic major axis of 62 degree. The short thin lines\noutside the velocity field indicate this average kinematic major axis. \nNote the significant difference of 18 degrees between the kinematic and\nmorphological position angles of the outer H I disk. An inclination of\n40$^\\circ$ is adopted which is the average of the optical and H I\ninclinations. Given this rather face-on orientation of the disk, the\nuncertainty in the position of the dynamical center and the obvious\ndeviations from circular motions, we estimate the uncertainties in the\nrotation curve at some 20\\%. \n\n\n\\subsection {UGC 12687}\n\n\\begin{figure*}[p]\n\\epsfig{file=ovm.fig3.ps,width=16cm}\n\\caption{UGC 12687. See section 3.2 for explanations.}\n\\label{fig:U12687}\n\\end{figure*}\n\n\\begin{figure*}[p]\n\\epsfig{file=ovm.fig4.ps,width=16cm}\n\\caption{2333+1234. See section 3.3 for explanations.}\n\\label{fig:2333}\n\\end{figure*}\n\nThe upper left panel of Figure~\\ref{fig:U12687} shows the blue POSS-II\nimage of UGC 12687, a strongly barred two-armed spiral. The bar\ndynamics efficiently feeds gas to the nuclear region where a radio\ncontinuum source with a peak flux of 4.0$\\pm$0.6 mJy is found at 1.4 GHz\n(Condon {\\it et al}, 1998). An ultra-violet excess has been reported by\nKazarian \\& Kazarian (1985), suggesting a high level of star formation\nactivity. Nevertheless, the B$-$V=0.70 color from Prugniel \\& Heraudeau\n(1998) of UGC 12687 is considerably redder than that of UGC 12695. \n\nThe upper right panel shows the global H I profile which displays the\nclassical double-horned shape. Fluxes were measured in individual\nchannel maps including the central continuum source. Afterwards, a\n2.9~mJy/beam continuum baseline was subtracted from the global profile. \nUnfortunately, H I emission at the lower velocities is lost in the edge\nof the passband. To estimate total fluxes and line widths, the high\nvelocity edge was mirrored and, as an educated guess, put in place of\nthe missing low velocity side of the profile. This technique gives an\nintegrated flux density of 7.5 Jy km s$^{-1}$ or a total H I mass of\n1.2$\\times$10$^{10}$ M$_\\odot$. The inferred line widths are 296.7\n\\kms\\ at the 20\\% level and 255.4 \\kms\\ at the 50\\% level. Like UGC\n12695, UGC 12687 was imaged by Theureau, \\etal\\ (1998) with the\nNan\\c{c}ay telescope, with similar results -- the velocity widths of the\n Nan\\c{c}ay data matched ours well, but the total flux reported by \nTheureau, \\etal\\ was only 80\\% of our result. To check our data, we\nobtained a 5 minute ON/OFF pair with the Arecibo telescope using the\nL-narrow receiver. The Arecibo data and our VLA data again matched to\nwithin 5\\% in total flux.\n\nThe middle left panel displays the integrated column density map of UGC\n12687 constructed by adding the individual channel maps, including the\ncentral continuum source which was removed by subtracting a 2.9 mJy/beam\ncentral point source. Contour levels are drawn at 0.5, 1, 2, 4, 6, 8,\n10, 12, 14, 16 and 18$\\times$10$^{20}$ atoms cm$^{-2}$. The central\nhole in the H I map might be due to a slight overestimation of the\ncontinuum flux or might be caused by H I seen in absorption. \nFurthermore, the approaching south-eastern side of the galaxy is missing\nsome flux in the integrated H I map due to the bandpass effect mentioned\nabove. Nevertheless, it is clear that the H I gas in UGC 12687 is\nconcentrated near the tips of the bar and to some extent along both\noptically visible spiral arms. Fitting an ellipse to the outer H I\ncontours gives an axis ratio of (b/a)=0.72 and a position angle of 129.8\ndegrees centered on (23$^{\\rm h}$32$^{\\rm m}$45.2$^{\\rm s}$,\n12$^\\circ$38$^\\prime$54$^{\\prime\\prime}$). \n\nThe middle right panel shows the azimuthally averaged radial H I surface\ndensity profiles of the receding and approaching sides separately. Note\nthat the approaching side misses some flux around a radius of 1\narcminute. \n\nThe lower left panel shows the velocity field which suggests, at least\nin projection, a declining rotation curve in the inner regions. Fitting\ntilted rings gives a dynamical center at (23$^{\\rm h}$32$^{\\rm\nm}$45.4$^{\\rm s}$, 12$^\\circ$38$^\\prime$52$^{\\prime\\prime}$), a systemic\nvelocity of 6150.2 \\kms\\ (thick line), an inclination of 43$^\\circ$ and\na position angle of 297$^\\circ$. However, due to the strong bar,\nnon-circular motions are certainly present. No significant warp could\nbe detected. The isovelocity contours are plotted at intervals of\n$\\pm$n$\\times$20 \\kms. The inferred rotation curve of UGC 12687 is\ntabulated in Table~3.\n\nThe lower right panel shows the position-velocity diagram over the\nentire observed bandwidth along the kinematic major axis. The central\ncontinuum source has not been removed. Note how the low velocity gas is\nlost in the edge of the bandpass as well as the limited number of line\nfree channels at the high velocity side. Also note the occasional double\nprofiles. \n\n\\subsection{2333+1234}\n\nIn the VLA data cube, the H I emission of a tiny irregular dwarf low\nsurface brightness galaxy was discovered. Having discovered it first in\nH I, we were then able to discern the galaxy as a barely visible smudge\non the POSS-II plate (left panel of Figure~\\ref{fig:2333}). Fitting an\nellipse to the faintest POSS-II isophotes yields a size of\n17.5$\\times$7.2 arcsec and a position angle of 58$^\\circ$, centered on\n(23$^{\\rm h}$33$^{\\rm m}$8.9$^{\\rm s}$,\n12$^\\circ$34$^\\prime$39$^{\\prime\\prime}$). \n\nThe upper right panel shows the measured global H I profile with an\nintegrated flux of 0.33 Jy km s$^{-1}$ or a total H I mass of\n5.2$\\times$10$^8$ M$_\\odot$. The line widths are 92 \\kms\\ at the 20\\%\nlevel and 75 \\kms\\ at the 50\\% level.\n\nThe middle left panel shows the resolved integrated H I column density\nmap which seems to be slightly offset from the optical image. H I\ncontours are plotted at 0.5, 1, 2, 4 and 6$\\times$10$^{20}$ atoms\ncm$^{-2}$\n\nThe middle right panel shows the barely resolved radial H I surface\ndensity profile. No deconvolution attempt was made. \n\nThe lower left panel shows the velocity field which clearly indicates a\nvelocity gradient along the optical major axis. The optical center was\ntaken to be the dynamical center and a systemic velocity of 6192.5 \\kms\\\nwas inferred. Isovelocity contours are plotted in steps of\n$\\pm$n$\\times$10 \\kms. Obviously, trying to derive a rotation curve by\nfitting tilted rings is futile. \n\nThe lower right panel displays the position-velocity diagram through the\noptical center along the kinematic major axis, however, and the sign of\nsolid body rotation is evident. \n\n\n\\section{Dark and Visible Matter in UGC 12695}\n\n\\begin{table}[t]\n\\begin{center}\n\\caption{Inclination corrected rotation curves of UGC~12695 and\nUGC~12687.}\n\\begin{tabular}{ccccccc}\n\\noalign{\\vspace{0.8mm}}\n\\hline\n\\hline\n\\noalign{\\vspace{0.8mm}}\n &\\multicolumn{3}{c}{UGC~12695} & \\multicolumn{3}{c}{UGC~12687} \\\\\nR & V$_{\\rm rot}$ & incl. & P.A. & V$_{\\rm rot}$ & incl. & P.A. \\\\\n$\\prime\\prime$ & km/s & $\\circ$ & $\\circ$ & km/s & $\\circ$ & $\\circ$ \\\\\n\\hline\n\\noalign{\\vspace{0.8mm}}\n 10.7 & 17 & 40 & 62 & 195 & 43 & 297 \\\\\n 21.3 & 26 & 40 & 62 & 195 & 43 & 297 \\\\\n 32.0 & 32 & 40 & 62 & 195 & 43 & 297 \\\\\n 42.7 & 38 & 40 & 62 & 195 & 43 & 297 \\\\\n 53.3 & 45 & 40 & 62 & 179 & 43 & 297 \\\\\n 64.0 & 52 & 40 & 62 & 174 & 43 & 297 \\\\\n 74.7 & & & & 171 & 43 & 297 \\\\\n\\noalign{\\vspace{0.8mm}}\n\\hline\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\nPrevious studies of the dark and visible matter of LSB galaxies have\nshown them to be extremely dark matter dominated with respect to\n``normal'' HSB galaxies (i.e. Van Zee, \\etal 1997; De Blok \\& McGaugh\n1997, 1998). Thus, although the lack of any turn-over in UGC 12695's\nrotation curve makes it clear that we have not come close to determining\nthe full gravitational potential of the galaxy, it is still a worthwhile\nexercise to look at UGC 12695's total mass.\n\n\n\\begin{figure}[t]\n\\epsfig{file=ovm.fig5.ps,width=8.5cm}\n\\caption{LSB galaxy Tully-Fisher relation. The \nlines are the 1$\\sigma$ and 2$\\sigma$ fits to the data of Zwaan, \\etal\n(1995), and the circles are recent observations of LSB galaxies in the \nPegasus and Cancer groups from O'Neil, Bothun, \\& Schombert (1999). UGC \n12695 (using {\\it i} = 40\\degree) is shown as a diamond.}\n\\label{fig:tf}\n\\end{figure}\n\n\nClassic Newtonian mechanics states that the dynamical mass of a\nrotating, gravitationally bound object is simply\n\\[M_{dyn}\\:=\\:{{v^2\\:R}\\over{G\\:\\sin^2{\\it i}}}\\] where G is the\ngravitational constant. Using the maximum known velocity of UGC 12695\n(33/sin(40\\degree) km s$^{-1}$ at r=64''), this gives a total dynamical\nmass of 16 x 10$^{9}$\\Msol, while the determined H I flux gives a total\nH I mass of M$_{HI}$ = 7.5 x 10$^{9}$\\Msol. Although at first glance\nthese numbers hardly seem remarkable, they imply a considerable absence\nof dark matter for a LSB galaxy. Assuming a minimal disk scenario\n(M$_*$/L$_B$ = 0), and letting all the gas in the galaxy be neutral\nhydrogen and helium (M$_{gas}$ = 1.47$\\times$M$_{HI}$ =\n11$\\times$10$^9$\\Msol), gives a dark-to-total mass ratio of only\nM$_{DM}$/M$_{dyn}$ = 0.30. Using somewhat more realistic numbers by\nletting M$_*$/L$_B$ = 1, (a low-to-average LSB maximal disk value from\nVan Zee, \\etal\\ 1997 \\& De Blok \\& McGaugh 1997) reduces the dark matter\ncontribution to only 12\\% of the total dynamical mass of UGC 12695. \n(The luminosity value, L$_B$ = 2.86 $\\times$ 10$^9$ \\Msol, is derived\nfrom the value given in O'Neil, \\etal, 1998 which used integrated\naperatures. The error in L$_B$ is less than 1\\%.) For comparison, the\naverage M$_{DM}$/M$_{dyn}$ values for LSB galaxies from De Blok \\&\nMcGaugh is 0.6 for maximum disk scenarios, and for Van Zee, \\etal\\\n(1997) \\lb~M$_{DM}$/M$_{dyn}$\\gb = 0.7. Additionally, if the stellar\nmass-to-light ratio of UGC 12695 is increased to 1.7, a reasonable value\nfor both HSB and LSB galaxies, there is no need to invoke any dark\nmatter to explain the maximum {\\it observed} rotational velocity at the\nlast measured point of UGC 12695's rotation curve. It should be noted\nthat we were not able to observe any turn-over in UGC 12695's rotation\ncurve. Thus, unlike the Van Zee, \\etal\\ and De Blok \\& McGaugh samples\nwe are not determining the dynamical mass from the flat portion of the\nrotation curve but instead from the still rising portion. As such, it is\nextremely likely that dark matter will play a large role in UGC 12695's \nouter regions.\n\nIt should also be noted that the {\\it observed} velocity width of UGC\n12695 causes it to fall well off the standard Tully-Fisher relation,\nlying approximately 2.5 magnitudes (3$\\sigma$) above the LSB galaxy line\ndefined by Zwaan, \\etal\\ (1995) (Figure~\\ref{fig:tf}). This may be the\nconsequence of the apparent lack of dark matter in the observed portion\nof UGC 12695. On the other hand, it is quite likely that there is\nsignificant dark matter outside the observed radius (else the rotation\ncurve would show some turn over), and thus we are merely viewing a\nlower limit of the galaxy's rotational velocity. The uncertainty in UGC\n12695's inclination (see the next section) also makes the current\nlocation of UGC 12695 on the Tully-Fisher relation suspect and if the\ninclination is less than 40\\degree, UGC 12695 could move onto (or even\nto the right of) the Tully-Fisher relation of Zwaan, \\etal.\n\n\\section{Star Formation in UGC 12695}\n\n\\begin{figure*}[t] \n\\epsfig{file=ovm.fig6bmp.ps,width=17.5cm}\n\\caption{Left panel: HI contours of U12695 overlaid on the HST WFPC2\nF814W image. Right panel: HI contours of U12695 overlaid on the\nH$\\alpha$ image. The red contours indicate the critical HI column\ndensity of 1.6$\\times$10$^{20}$ and 6.0$\\times$10$^{20}$ cm$^{-2}$ above\nwhich star formation is expected based on Toomre's criterion (for {\\it\ni} = 40\\degree \\& 10\\degree, respectively), while the green contours are\nthe 10$^{21}$ cm$^{-2}$ level.}\n\\label{fig:U12695optHI}\n\\end{figure*} \n\nIt was demonstrated by Toomre (1964) that a thin, {\\it collisionless}\nstellar disk in circular motion becomes unstable if the surface mass\ndensity exceeds a critical value of \\[\\Sigma_c\\:=\\:\\alpha\\:{{\\kappa\n\\sigma}\\over{3.36 G}}\\] where $\\Sigma_c$ is the critical density,\n$\\sigma$ is the velocity dispersion, \\alp is a dimensionless constant\nnear 1, and $\\kappa$ is the epicyclic frequency of the gas, also written\nas \\[\\kappa\\:=\\:1.41\\:{V\\over R}\\:\\left(1\\:+\\:{R \\over\nV}{{dV}\\over{dR}}\\right)^{1/2}.\\] Cowie (1981) showed that this\ncriterion is also applicable to instabilities in a gaseous disk if\nembedded in a more massive stellar disk. Kennicutt (1989) determined an\nempirical value for \\alp of about 2/3. Typical HSB galaxies exceed this\ncritical surface density and form stars throughout most of their stellar\ndisks. \n\nAs an LSB galaxy which appears to be in the midst of considerable but\nlocalized star formation, UGC 12695 is an ideal case on which to test\nthis star formation threshold theory. Before this can be done, though,\n$\\kappa$ and $\\sigma$ must be determined. From the rotation curve of\nUGC 12695 it is apparent that its near solid body rotation makes\ndetermining $\\kappa$ relatively easy. Approximating the rotation curve\nas pure solid body with an inclination corrected amplitude of 57 \\kms\\ \nat a radius of 22 kpc yields $\\kappa$=5.2 \\kms\\ kpc$^{-1}$ (using the\nfact that for a gas disk in pure solid body rotation,\n${{dV}\\over{dR}}={V\\over R}$ and $\\kappa={{2V}\\over{R}}$). Due to beam\nsmearing the velocity dispersion is hard to measure from the data and a\ncanonical dispersion of $\\sim$8 \\kms\\ is assumed as an average estimate\n(8 \\kms\\ is also observed in several highly resolved face-on gas disks).\n This leads to a critical surface mass density of\n$\\Sigma_c\\:=\\:4.0\\times10^{-3}$ kg m$^{-2}$. Taking a 32\\% helium mass\nfraction into account, this corresponds to a critical H I column density\nof 1.6$\\times$10$^{20}$ atoms cm$^{-2}$ (i.e. between the 1st and 2nd\ncontours in Figure~\\ref{fig:U12695optHI}) above which star formation is\nto be expected. This implies that everywhere throughout the disk of UGC\n12695 star formation should occur. \n\n\\begin{figure*}[t]\n\\epsfig{file=ovm.fig7.ps,width=17.5cm}\n\\caption{The azimuthally averaged observed gas \ndensity, Toomre star formation threshold, and rotation curves of UGC\n12695 for an assumed galaxy inclination of 40\\degree, 25\\degree, and\n10\\degree (left to right).}\n\\label{fig:azav}\n\\end{figure*}\n\nHowever, we only observe star formation in a limited number of localized\nregions near the very peaks of the H I column density distribution where\nit reaches levels of 1$\\times$10$^{21}$ atoms cm$^{-2}$. This is\nillustrated in Figure~\\ref{fig:U12695optHI} which shows in the left\npanel the HI column density map overlaid on a false-color WFPC2 F814W\nimage and in the right panel the same H I contours overlaid on a\ngreyscale MDM-1.3m H$\\alpha$ image. The lower red contour indicates the\ncritical column density of 1.6$\\times$10$^{20}$ atoms/cm$^2$. Obviously,\nthe theoretically derived and empirically adjusted critical surface\ndensity is clearly not applicable to the low metallicity, irregular gas\ndisk of UGC 12695. \n\nOne of the more curious aspects of the Kennicutt-Cowie-Toomre star\nformation criterion is that it successfully works at all, considering\nthe number of physical processes which affect the value of $\\Sigma_c$. \nFor example, disks are not infinitely thin but have a certain thickness\nwhich could increase or decrease the column density thresholds and alter\nthe radial instabilities. That is, if the volume gas density is\nsignificantly different than the surface gas density of UGC 12695, a\nvolume-density dependent Schmidt law would be more appropriate than the\nKennicutt/Cowie/Toomre star formation criterion used above (i.e.\nFerguson, \\etal\\ 1998). Additionally, there is energy dissipation,\nmagnetic field lines, etc. which should also affect $\\Sigma_c$ (i.e.\nHunter, Elmegreen, \\& Hunter 1998). Thus it is not surprising that UGC\n12695, and in fact many LSB galaxies, do not adhere to the Toomre\ncriterion (i.e. Van Zee, \\etal\\ 1997; Van der Hulst, \\etal\\ 1993).\n\nWhat is interesting is that UGC 12695, like many LSB and dwarf galaxies,\nforms stars only where the local H I column density exceeds 10$^{21}$\natoms cm$^{-2}$. In fact, Skillman (1986) pointed out that the actually\nobserved {\\em local} H I column density threshold for star formation, at\na resolution of 500 pc, is about 1$\\times$10$^{21}$ atoms cm$^{-2}$ and\nroughly 5$\\times$10$^{21}$ atoms cm$^{-2}$ for star formation events of\nthe order of 30 Doradus. This local H I column density threshold\nappears to be in better agreement with the observations of UGC 12695\n(i.e. note the green contours in Figure~\\ref{fig:U12695optHI}), although\nthe beam size makes a detailed analysis impossible. (The H$\\alpha$ data\nof McGaugh 1994 is not photometric, making determination of UGC 12695's\nH II luminosity difficult. It should be noted, though, that attempts to\ndetect faint diffuse H-$\\alpha$ regions have not been successful,\nmaking it unlikely that any widespread component of faint star-forming\nregions has been missed.)\n\nUnlike our sample, a previous study by Van der Hulst, \\etal\\ (1993)\nfound their sample of low surface galaxies to be generally consistent\nwith the Kennicutt-Toomre criterion for star formation. Perhaps the\nmost important difference between this study of UGC 12695 and the Van\nder Hulst, \\etal\\ results is that Van Der Hulst, \\etal\\ used azimuthally\naveraged radial H I surface density profiles. Figure~\\ref{fig:azav}\nshows the results of applying Van der Hulst, \\etal's method to UGC 12695\nfor a variety of possible inclinations (see below). As can be seen, even\nby ignoring the extremely asymmetric nature of UGC 12695, only the most\nextreme case ({\\it i}=10\\degree) does UGC 12695 come close to falling\nbelow the critical density for star formation anywhere but in the\noutermost isophotes. This sort of study, though, disallows for any\nanalysis of the local star forming potential of UGC 12695 while hiding\nthe exceptionally asymmetric nature of galaxy.\n\n\n\\begin{figure*}[p]\n\\hspace{-1cm}\n\\epsfig{file=ovm.fig8bmp.ps,width=18.5cm}\n\\caption{Zooming in on the main star formation regions in in UGC~12695.\nThe upper row shows the star formation complexes in the eastern side of\nthe galaxy. Those in the western side are shown in the bottom row. The\nwhite contours are from the VLA H I map while the yellow contours are\nfrom the MDM-1.3m H$\\alpha$ image.}\n\\label{fig:U12695SFs}\n\\end{figure*}\n\n\nAt this point, it is important to consider the uncertainties involved\nin calculating $\\Sigma_C$. Most notably, we should take another look at\nUGC 12695's assumed inclination. It is certainly possible that UGC\n12695's shape truly is circular, thus validating the inclination value\nused in the previous calculations (40\\degree). If, however, UGC 12695\nhas recently tidally interacted with UGC 12687, as discussed below, the\nperceived inclination may be overestimated in that UGC 12695 may have\nbeen distorted (and `flattened') by the interaction (e.g. see Figure 2\nof Mihos, \\etal, 1997). In this case the true inclination of UGC 12695\nmay be considerably less than we have assumed, thereby raising the \nvalue of $\\Sigma_C$. As an example, if UGC 12695's true inclination is\n10\\degree, the critical density will increase to\n$\\Sigma_C\\:=\\:6\\times10^{20}$ atoms cm$^{-2}$. In this case, although\nthe critical density and the density at which star formation is observed\nstill would not precisely coincide, they would lie considerably closer \ntogether (i.e. the higher red contour in Figure~\\ref{fig:U12695optHI}). \nIf, in addition to the above correction to {\\it i}, our estimate of\n$\\kappa$ is off by a factor of 60\\% (3$\\sigma$) due to inclination\nuncertainties and the rotation curve shape, the critical density would\nreadily be raised to 10$^{21}$ atoms cm$^{-2}$, the observed local H I\ncolumn density threshold for star formation of Skillman (1986). Of\ncourse, if the inclination correction is off in the other direction, \nand {\\it i}=50\\degree, $\\Sigma_C$ would be reduced even more, raising\nagain the question of why UGC 12695 is LSB.\n\nIt is noteworthy to point out that the three local peaks in the neutral\nhydrogen of UGC 12695 lie near, but not on top, the primary star\nformation regions of the galaxy, as defined by the H-\\alp image of\nMcGaugh (1994). This is illustrated in Figure~\\ref{fig:U12695SFs} which\ndisplays in the left panels the white VLA H I contours on the color\nWFPC2 F814W image, in the middle panels the yellow MDM-1.3m H$\\alpha$\ncontours on the WFPC2 image and in the right panels the combined H I and\nH$\\alpha$ contours on the WFPC2 image.\n\nFigure~\\ref{fig:U12695SFs} shows that there seems to be a clear offset\nbetween the highest peaks in the H I column density at 1.2 x 10$^{21}$\ncm$^{-2}$ and the location of the primary H$\\alpha$ complexes. The\nlargest star clusters seem to surround the regions with the highest HI\ncolumn densities. However, the relatively poor spatial resolution of\nthe current H I observations is insufficient to draw any further\nconclusions on the relation between the H I peaks and the H$\\alpha$\nregions.\n \nThe colors of those regions, as provided by the WFPC2 images, also put\nthe star-formation peaks away from the H I peaks, with the left two H I\npeaks having F300W $-$ F814W = $-$0.06 and $-$2.82, versus $-$3.27 and\n$-$3.14 for the corresponding H-\\alp peaks (top and bottom,\nrespectively). (These colors roughly correspond to U $-$ I colors of\n1.42, $-$1.34, $-$1.79. and $-$1.66, respectively (i.e. O'Neil, \\etal\n1998).) The third H I peak, at the bottom right of\nFigure~\\ref{fig:U12695optHI}, lies in the extremely noisy PC chip of the\nWFPC2 image, making the determination of colors in that region extremely\ndifficult. Thus the neutral hydrogen is behaving as expected -- as star\nformation occurs the surrounding gas is ionized, shifting the peak in\nthe neutral hydrogen distribution to the edge of the star forming\nregions. \n\n\n\\section{Are UGC~12695 and UGC~12687 Ti-dally Interacting?}\n\nThe close proximity of UGC 12695 and UGC 12687 in redshift space, the\nlopsided morphology of UGC 12695 and its slightly skewed kinematics, \nimmediately brings to mind the possibility of a tidal interaction\n(Figure~\\ref{fig:Allposs2HI}). Additionally, the presence of 2333+1234\nlying between the two galaxies suggests it may have been formed as a\ntidal remnant. (Of course, 2333+1234 may simply be a naturally\noccurring representative of the faint-end of the luminosity function.) \n\nIn 1997 Mihos, McGaugh, \\& De Blok argued that LSB and HSB galaxies of\nthe same total mass are equally susceptible to local disk instabilities\nbut that LSB galaxies are far less responsive to global instabilities\nthan their HSB counterparts. This difference is mainly due to the\nstabilizing nature of the relatively more massive dark matter halo in\nwhich the LSB disk is embedded. To test their hypothesis, they modeled\na strong prograde tidal encounter between an LSB and an HSB disk galaxy\nof similar mass. After the encounter the HSB galaxy exhibited two\ndefinitive spiral arms, a central inflow of gas and an oval central\nregion. Presumably, the HSB system was in the midst of, or had recently\nundergone, a large burst of star formation in its core. Being more\nstable than its HSB counterpart, the LSB galaxy displayed a milder, yet\nsignificant response. Although the encounter strongly perturbed the LSB\ngalaxy, it did not result in a central gas inflow. However, it did\ninduce long-lived spiral arms, an overall lopsided distortion of the\ngalaxy, and possibly localized compressions and instabilities in the\ndisk. \n\nThe observed morphologies of UGC 12695 and UGC 12687 show a striking\nresemblance to the numerical simulations of Mihos \\etal\\ at the time\nstamp T=36 (see their Figure~2). Their HSB system (UGC 12687 in our\ncase) shows a strong bar from which two well defined spiral arms emerge.\n UGC~12687's observed morphology is in close agreement with their\nresults while its central continuum emission and UV-excess indicate a\nconsiderable nuclear star formation activity, hinting at well developed\nbar kinematics efficient in fueling H I to the central region. In the\ncase of the LSB galaxy, the numerical simulations display a sharp\nstellar edge on one side of the disk and a more diffuse gradient on the\nother side while a highly variable structure in the mass surface density\nhints at strong local instabilities. Observationally, UGC 12695's\nextremely blue colors, highly asymmetric gas and star distribution, and\nregions of intense local star formation also match the model predictions\nextremely well. In fact, without relying on some sort of external\ntrigger the observed morphology and color of UGC 12695 is extremely\ndifficult to explain. \n\nIn spite of the above assertions, a number of arguments against any\nmajor tidal encounter between these two galaxies must be considered. \nThe first, and perhaps most obvious of these is the apparently settled\nkinematics of both UGC 12695 and UGC 12687. At first glance it would\nseem that if the two galaxies have interacted recently enough for the\ntidally-induced star formation to be at, or near, its peak the galaxies\nwould still exhibit highly agitated kinematics. A study by V\\'azquez\nand Scalo (1989), though, has shown that starbursts do not typically\noccur during the gas compression stage but in fact occur well after the\ngas has re-established. In other words, the V\\'azquez and Scalo model\nsuggests that disks can have tidally induced star formation well after\nthe gas has kinematically re-settled. \n\nA second argument which could be put forward against the idea of the two\ngalaxies having recently undergone a tidal interaction is simply this --\nif UGC 12695 is experiencing a burst of localized star formation due to\na recent tidal encounter, should it not be experiencing a corresponding\nrise in central surface brightness? A recent paper by O'Neil, Bothun, \\&\nSchombert (1998) tested this idea through modeling a wide variety of LSB\ngalaxies experiencing localized starbursts. Their results were quite\ndefinitive -- if a galaxy forms as a LSB galaxy, due to a high angular\nmomentum giving rise to a low gas surface density etc., it will remain a\nLSB galaxy barring any major encounter catastrophe. Thus it is quite\nbelievable that UGC 12695 could be undergoing significant localized star\nformation activity and yet not be undergoing any significant change in\nits global surface brightness. \n\nThe final argument against UGC 12695 and UGC 12687 having undergone a\nsignificant tidal interaction in the recent past comes from examining\nthe smoothed data cube. Not a trace of extended H I gas above a minimal\ndetectable column density of 2$\\times$10$^{19}$ atoms cm$^{-2}$\n(3$\\sigma$) can be found besides the rotating gas disks of the three\nidentified galaxies. This leads to the conclusion that no major tidal\ntails were ever formed in any past interaction between the two systems. \n\n\n\\section{Conclusion}\n \nUGC 12695 is an intriguing low surface brightness galaxy of a very\ntransparent nature, having an extremely blue color, a highly asymmetric\nappearance and very localized bursts of star formation near the peaks in\nthe H I column density distribution.\n\nMany of the properties of both UGC 12687 and UGC 12695 can be explained\nas being induced by such a tidal interaction, including the bar of UGC\n12687 and its central radio continuum emission and UV excess as well as\nthe lopsided appearance of UGC 12695 and the offset between its\nmorphological and kinematic major axes. Furthermore, the localized\nbursts of star formation in UGC 12695 could very well be induced by such\nan interaction, giving rise to local instabilities in the LSB disk as\ndemonstrated by Mihos \\etal (1997). \n\nIt is likely that UGC 12695 could have been living a fairly quiescent\nexistence, its low surface gas density keeping its star formation rate\nquite low, and just now it is experiencing a period of localized but\nvigorous star formation triggered by a mild tidal interaction which\nmight lead to a major morphological transition. \n\nWithin all this, though, it is easy to overlook one important fact. \nAlthough many of the properties of UGC 12695 and UGC 12687 can readily\nbe explained through an ongoing tidal encounter, the two galaxies are\nstill fundamentally distinct. UGC 12695 is not simply a fainter, or\nmore `stretched-out', or more quickly rotating version of UGC 12687. \nWere any of these the case the behavior of the two galaxies after the\ntidal encounter would be similar, and UGC 12695 would have experienced a\ncentral gas inflow with the majority of its star formation now occurring\nnot in the outlying regions (as it is), but in the galaxy's core. Thus\nthe fundamental question of why UGC 12695 is an LSB galaxy, and UGC\n12687 is not remains unanswered. \n\n\n\\section{Acknowledgments}\n\nThe Very Large Array is a facility of the National Radio Astronomy\nObservatory, a facility of the National Science Foundation operated\nunder cooperative agreement by Associated Universities, Inc. The\nDigitized Sky Surveys were produced at the Space Telescope Science\nInstitute under U.S. Government grant NAG W-2166. The images of these\nsurveys are based on photographic data obtained using the Oschin Schmidt\nTelescope on Palomar Mountain and the UK Schmidt Telescope. The plates\nwere processed into the present compressed digital form with the\npermission of these institutions. \n\n\n\\section*{References}\n\n\\noindent\n Condon, \\etal, 1998, AJ, 115, 1693\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Cowie, L., 1981, ApJ, 245, 66\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n De Blok, W.J.G. \\& Van der Hulst, J.M., 1998, A\\&A, 336, 49\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n De Blok, W.J.G. \\& McGaugh, S., 1998, ApJ, 499, 41\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n De Blok, W.J.G. \\& McGaugh, S., 1997, MNRAS, 290, 533\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Ferguson, H., \\& McGaugh, S., 1995, ApJ, 440, 470\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Ferguson, A. \\etal, 1998, ApJ, 506, L19\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Kazarian, M.A. \\& Kazarian, E.S., 1985, Afz, 22, 431\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Kennicutt, R., 1989, ApJ, 344, 685\\\\ \n\n\\vspace{-3.5mm}\n\\noindent\n Hunter, D., Elmegreen, B. \\& Baker, A., 1998, ApJ, 493, 595\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Matthews, L., \\& Gallagher, J., 1997, AJ, 114, 1899\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n McGaugh, S., 1994, ApJ, 426, 135\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Mihos, C., McGaugh, S., \\& De Blok, W.J.G, 1997, ApJ, 477L, 79\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n O'Neil, K, Bothun, G., \\& Schombert, J., 1999, AJ, in press\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n O'Neil, K., Bothun, G., \\& Schombert, 1998, AJ, 116, 2776\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n O'Neil, K., \\etal, 1998, AJ, 116, 657\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n O'Neil, K., Bothun, G., \\& Cornell M., 1997b, AJ, 113, 1212\\\\ \n\n\\vspace{-3.5mm}\n\\noindent\n O'Neil, K., \\etal, 1997a, AJ, 113, 1212\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Prugniel, P. \\& Heraudeau, P., 1998, A\\&AS, 128, 299\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Schombert, J. \\etal, 1990, AJ, 100, 1533\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Skillman, E.D., 1986, in \"{\\it Star Formation in Galaxies}\", C.J. Lonsdale (ed), NASA Conference Publication 2466, 263\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Theureau, G., \\etal, 1998, A\\&AS, 130, 333\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Schneider, S., \\etal, 1990, ApJS, 72, 245\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Toomre, A., 1964, ApJ, 139, 1217\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n De Vaucouleurs, G. \\etal, 1991, {\\it The Third Reference Catalog of Bright Galaxies}, Springer-Verlag: New York\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Van der Hulst, J.M., \\etal, 1993, AJ, 106, 548\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Van Zee, L., \\etal, 1997, AJ, 113, 1618\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n V\\'azquez, E. \\& Scalo, J.M., 1989, ApJ, 343, 644\\\\\n\n\\vspace{-3.5mm}\n\\noindent\n Zwaan, M., Van der Hulst, J., De Blok, W., \\& McGaugh, S.S., 1995, MNRAS, 273, L35\\\\\n\n\n\\end{document}\n"
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astro-ph0002192
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Strong, Variable Circular Polarization in PKS~1519-273
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[
{
"author": "J-P Macquart\\altaffilmark{1}"
},
{
"author": "Lucyna Kedziora-Chudczer\\altaffilmark{1,2}"
},
{
"author": "David P. Rayner\\altaffilmark{2,3}"
},
{
"author": "David L. Jauncey\\altaffilmark{2}"
}
] |
We report strong variability in the circular and linear polarization of the intraday variable source PKS~1519-273. The circular polarization varies on a timescale of hours to days at frequencies between 1.4 and 8.6~GHz, and is strongly correlated with variations in the total intensity at 4.8 and 8.6~GHz. We argue that the variability is due to interstellar scintillation of a highly compact ($15-35 \mu$as) component of the source with $-3.8\pm 0.4$\% circular polarization at 4.8~GHz. We find that no simple model for the circular polarization can account for both the high magnitude and the frequency dependence in PKS~1519-273 at centimeter wavelengths.
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[
{
"name": "C1519em.tex",
"string": "\\documentclass[10pt]{article}\n\\usepackage[]{emulateapj}\n\\usepackage[]{psfig}\n\n%\\documentstyle[10pt,emulateapj,psfig]{article}\n%\\documentstyle[12pt,aasms4]{article}\n\n\n\\begin{document}\n\\submitted{}\n\n\\title{Strong, Variable Circular Polarization in PKS~1519-273}\n\n\\author{J-P Macquart\\altaffilmark{1}, \nLucyna Kedziora-Chudczer\\altaffilmark{1,2}, David P. Rayner\\altaffilmark{2,3}, \nDavid L. Jauncey\\altaffilmark{2}}\n\\affil{$^1$Special Research Centre for Theoretical Astrophysics, School of \nPhysics, University of Sydney, New South Wales 2006, Australia.}\n\\affil{$^2$Australia Telescope National Facility, CSIRO, Epping, New \nSouth Wales 2121, Australia.}\n\\affil{$^3$School of Mathematics and Physics, University of Tasmania, \nHobart, Tasmania 7001, Australia.}\n\n% \\altaffiltext{1}{jpm@physics.usyd.edu.au}\n% \\altaffiltext{2}{lkedzior@antf.csiro.au}\n% \\altaffiltext{3}{d_rayner@postoffice.utas.edu.au}\n% \\altaffiltext{4}{djauncey@antf.csiro.au}\n\n\\begin{abstract}\nWe report strong variability in the circular and linear \npolarization of the intraday variable source PKS~1519-273.\nThe circular polarization varies on \na timescale of hours to days at frequencies between 1.4 and 8.6~GHz, and \nis strongly correlated with variations in the total intensity at 4.8 \nand 8.6~GHz. We argue that the variability is due to \ninterstellar scintillation of a highly compact \n($15-35 \\mu$as) component of the \nsource with $-3.8\\pm 0.4$\\% circular polarization at 4.8~GHz.\nWe find that no simple model for the circular polarization \ncan account for both the high magnitude and the frequency \ndependence in PKS~1519-273 at centimeter wavelengths. \n\\end{abstract}\n\n\\keywords{BL Lacertae objects: individual (PKS~1519-273) --- polarization --- \nradiation mechanisms: non-thermal --- scattering}\n\n\n\\section{Introduction}\n\nCircular polarization (CP) in extragalactic sources is very small, typically \n0.05\\% to 0.1\\% of the total source flux density (e.g. \nRoberts et al. 1975, Seaquist et al. 1974, Weiler and de Pater \n1983)\\markcite{Roberts75,Seaquist74,Weiler83} and sometimes variable \n(Komesaroff et al., 1984). Recent measurements of \nCP in extragalactic sources have\nrekindled debate as to its characteristics and origin. \nWardle et al. (1998)\\markcite{Wardle98} detected CP \nin 3C~279 and attributed it to the presence of a relativistic pair plasma. \nNew evidence has emerged that Sgr A$^*$, the AGN-like object at the \ncore of our own Galaxy, is also weakly circularly polarized (Bower et al. \n1999, Sault \\& Macquart 1999)\\markcite{Bower99,Sault99}.\n\nWe present Australia Telescope Compact Array (ATCA) measurements of the \ntimescale and magnitude of the variability of the CP \nin the extragalactic, intraday variable (IDV) BL Lac object, \nPKS~1519-273 (White et al. 1988)\\markcite{White88}. \nPKS~1519-273, at Galactic co-ordinates $l=339.5^{\\circ}, \\, b=24.5^{\\circ}$,\nis identified with a $m_V=18.5$ star-like object with a \nfeatureless optical spectrum. The lower limit on its redshift is $z=0.2$ \n(Veron-Cetty \\& Veron 1993)\\markcite{Veron93}. \nPKS~1519-273 is a compact high brightness temperature \nradio source (Linfield et al. 1989)\\markcite{Linfield89}. The ATCA IDV\nSurvey data shows strong IDV (Kedziora-Chudczer \n1998)\\markcite{KedzioraPhD} and IDV of the total and polarized \nflux densities at GHz frequencies has been \nfound during each of the 5 epochs of ATCA observations over the \npast 7 years.\n\nPKS~1519-273 has not been seen to exhibit IDV at \neither optical (Heidt \\& Wagner 1996)\\markcite{Heidt96} or mm \nwavelengths (Steppe et al. 1988, \nSteppe et al. 1995)\\markcite{Steppe88,Steppe95}. However, it does have a \nhigh degree ($5-12$\\%) of variable optical linear polarization (Impey and Tapia \n1988)\\markcite{Impey96}. PKS~1519-273 is a weak, soft X-ray source \nwith a flux density at 1~keV of 0.39~$\\mu$Jy \n(Urry et al. 1996)\\markcite{Urry96}. Its $\\gamma $-ray \nenergy output is less than \n$0.7\\times 10^{-7}$photons~cm$^{-2}$sec$^{-1}$ for energies \n$E>100$~MeV (Fichtel et al. 1994)\\markcite{Fichtel94}.\n \n\n\\section{Observations and Results}\nWe base our present report on PKS~1519-273 on the data obtained with ATCA \nover 5 days starting on 1998 September 9. Data were collected simultaneously for two \nfrequencies centered on either 1.384 and 2.496 GHz, or 4.800 and \n8.640 GHz each with a 128 MHz bandwidth. \nTo ensure high quality amplitude and phase calibration\nwe frequently observed both the standard primary flux density calibrator, \nPKS~1934-638, and a secondary calibrator, PKS~1514-241. \nThe primary calibrator was used to determine accurately the flux \ndensity scale and the instrumental \npolarization leakages (e.g. Sault, Killeen \\& Kesteven 1991)\\markcite{Sault91}. The \ntotal and polarized flux density lightcurves of \nPKS~1519-273 are presented in fig. 1. The circularly polarized emission, is unresolved on all ATCA baselines and is strongly variable at 4.8 and \n8.6~GHz. Comparison of the 2.5, 4.8 and 8.6~GHz Stokes $V$ measurements for \nPKS~1519-273 and the strong calibrator source PKS~1514-241, extensive \ntesting and consistency checks demonstrate that the observed CP and its \nvariations are not instrumental effects. \n\nThe most striking features of the 4.8 and 8.6~GHz light curves in \nfig. 1 are the exceptionally high level of CP \nand the large amplitude variability in all four Stokes \nparameters. The fractional variability of both the circularly and \nlinearly polarized flux density exceeds that of the total flux \ndensity. The high degree of correlation between the fluctuations in $I$ and \n$V$ (see figs. 1 \\& 2) suggests that the mechanism of variability of the \nCP is strongly related to that in $I$. Comparison of the \nfluctuations in $V$ with those in $I$ implies that, although the \noverall CP is only $\\sim 1$\\%, the\nCP of the variable component, $\\Delta V/\\Delta I$, is \n$-2.4 \\pm 1.3$\\%, $-3.8 \\pm 0.4$\\% and $-2.6 \\pm 0.5$\\% at 2.4, 4.8 and \n8.6~GHz respectively (see figs. 2 \\& 3(c)). The CP is \nweaker, $< 1.3$\\% at 1.4~GHz and its variability is less well-established.\n\n\n\\placefigure{fig:HIGH.PS}\n\\begin{figure*}\n \\begin{center}\n\\begin{tabular}{c}\n \\psfig{file=HIGH.PS,angle=270,width=120mm} \\\\\n \\psfig{file=LOW.PS,angle=270,width=120mm}\n\\end{tabular}\n\\end{center}\n\\caption{Variability of PKS~1519-273 in the total intensity ($I$), \nCP ($V$), and magnitude of the linear polarization ($P$),\nfor the four bands of the ATCA over 5 days. Each point \nrepresents a 10~min average, and is plotted with $1\\,\\sigma$ error bars. \nFluctuations in $I$ and $V$ are strongly correlated ($r=-0.90$ at \n4.8~GHz and $r=-0.80$ at 8.6~GHz).}\n\\end{figure*}\n\n\\placefigure{fig:v_vs_i_2496.eps}\n\\begin{figure*}\n\\begin{tabular}{c}\n \\psfig{file=v_vs_i_2496.eps,angle=270,width=60mm} \n \\psfig{file=v_vs_i_4800.eps,angle=270,width=60mm} \n \\psfig{file=v_vs_i_8640.eps,angle=270,width=60mm}\n\\end{tabular}\n\\caption{Plot \nof the correlation between $V$ and $I$. The best fit lines give \na fractional CP of $-2.4\\pm 1.3$\\%, $-3.8 \\pm 0.4$\\% \nand $-2.6 \\pm 0.5$\\% respectively at 2.5, 4.8 and 8.6~GHz for the \nvariable component of the source. The fluctuations in $I$ and $V$ do \nnot appear to be correlated at 1.4~GHz, indicating that we detect \n{\\it no} CP associated with the variable component \nat this frequency. We place an upper limit on the CP of \nthis component of 1.3\\%.}\n\\end{figure*}\n\n\\section{Discussion}\n\\subsection{Scintillation}\n\nWe attribute the short-timescale variability of this source to \nInterstellar Scintillation (ISS) in our Galaxy. ISS has already been \ninvoked to explain radio source IDV (Heeschen \\&\nRickett 1997)\\markcite{Heeschen97}, \nincluding the rapid variability of PKS~0405-385 (Kedziora-Chudczer et \nal. 1997)\\markcite{Ked97}. If intrinsic to the source, the total intensity \nvariations observed at 4.8~GHz imply a brightness temperature of $T_B \\gtrsim 3 \n\\times 10^{17}$~K for $z \\gtrsim 0.2$, based simply on light travel \ntimes. However, assuming that the \nvariations are intrinsic implies a source size that is necessarily \nsufficiently small to exhibit variability due to \nISS (Rickett et al. 1995)\\markcite{Rickett95}. This suggests that an \nexplanation based on ISS should be sought first.\n\nThe increase in modulation index (the rms normalized by the mean intensity), shown in fig. 3, and\nthe short variability timescale from 8.6 to 4.8~GHz, shown in fig. 1, \nare consistent with \nscintillation in the regime of weak scattering \n(e.g., Narayan 1992)\\markcite{Narayan92}, while the decrease in \nmodulation indices and the increasingly longer \nvariability timescales from 4.8 to 1.4~GHz \nare characteristic of refractive scintillation.\n\nAssuming that the density \ninhomogeneities in the ISM are located on a thin screen, the refractive scintillation at 1.4~GHz may be used to place a \nconstraint upon the distance to the scattering screen. The physical \nextent of the scattering disk at 1.4~GHz is the product of the long-period,\nrefractive variability \ntimescale, $t_{1.4}$, no \nless than 4 days (see fig. 1), and \nthe scintillation speed, $v$, of order 50~km/s (see Rickett et al. 1995). VSOP\nobservations at 1.7~GHz\\footnote{See \nhttp://www.vsop.isas.ac.jp/general/pr/1519-273.gif} indicate that the \nsource is unresolved, so we assume an\nangular size of no more than 0.3~mas. This implies an observer-screen distance of \n$D \\geq 390 (v/50~{\\rm km/s}) (t_{1.4}/4~{\\rm days})$~pc, or 390~pc in the\npresent case.\n\nHaving obtained a lower limit to the distance to the \nscattering screen, we may constrain the angular diameter of the source \nfrom the scintillation parameters in the weak scattering regime where \nthe scattering is quite sensitive to source size effects. The \nscintillation timescale of $\\sim 12$~hours at 4.8~GHz can be explained \neither in terms a scattering screen at large distance ($> 15$~kpc), or \nby a partially resolved source. For weak \nscattering, the source is resolved if the angular diameter of the \nsource, $\\theta_S$, exceeds the angular diameter of \nthe first Fresnel zone $\\theta_F = (k D)^{-1/2}$, where $k$ is the \nwavenumber. The \nscintillation timescale is then $t_{4.8} \\approx \\theta_S D/v$ for $\\theta_S >\n\\theta_F$ (Narayan 1992).\nA screen in our own Galaxy implies $D \\ll 15$~kpc, so the source must be partially resolved. \nAssuming the asymptotic results of weak scattering to be valid \nbetween the weak and strong scattering regimes, the scintillation timescale \nthen yields an {\\it estimate} of the intrinsic angular source size of \n$$\n\\theta_S \\approx 14.4 \\left(\\frac{t_{4.8}}{12~{\\rm hours}} \\right) \n\\left( \\frac{v}{50~{\\rm km/s} } \\right) \n\\left( \\frac{D}{1~{\\rm kpc}}\\right)^{-1}~\\mu{\\rm as}. \\eqno(1)\n$$\n\nFor a scintillating source of flux density $I_0$, the root-mean-square \nfluctuation is $I_{\\rm rms} = I_0 m(\\theta_S)$, where \n$m(\\theta_S)=(kD \\theta_S^2)^{7/12}$ is the modulation index expected for \na source of size $\\theta_S > \\theta_F$ (e.g. Narayan 1992)\\markcite{Narayan92}, \nand we have assumed that 4.8~GHz is near the \ntransition frequency between weak and strong scattering.\nGiven $I_{\\rm rms} = 0.11$~Jy and with the derived angular size of the \nscintillating component of the source, we estimate $I_0$ and derive \nits brightness temperature:\n{\\small\n$$\nT_b \\approx 2.0 \\times 10^{14} \\left( \\frac{D}{1~{\\rm kpc}} \n\\right)^{17/12} \n\\left( \\frac{t_{4.8}}{12~{\\rm hours}} \\right)^{-5/6} \n\\left( \\frac{v}{50~{\\rm km/s}} \\right)^{-5/6}~{\\rm K}. \\eqno(2)\n$$}\nUsing the limit of the distance to the scattering screen, the maximum \npossible angular size of the source for $t_{4.8}=12$~hours and \n$v=50$~km/s is $37\\,\\mu$as, the minimum brightness \ntemperature is $T_b=5 \\times 10^{13}$~K, consistent with incoherent synchrotron \nemission subject to relativistic beaming with a Doppler \nboosting factor $\\delta \\gtrsim 200 (1+z)$ \n(Readhead 1994)\\markcite{Readhead94}.\n\nHowever, if the CP observed at \n4.8~GHz is entirely due to the variable component, we may further \nconstrain $T_b$. From fig. 2 we have \n$I_0 = 0.35 \\pm 0.04$~Jy, implying $m(\\theta_S) \\approx 0.32$ \n(consistent with the modulation index observed in $V$: $0.32$) and hence an \nangular size of $9.8 (D/1\\, {\\rm kpc})^{-1/2} \\,\\mu$as. Comparing with \nequation (1), we have $v = 34 \\,(D/1\\,{\\rm kpc})^{1/2}$~km/s, implying \na brightness temperature of \n$3 \\times 10^{14} (D/1\\,{\\rm kpc}) (t_{4.8}/12\\,{\\rm hours})^{-5/6}$~K. \nA scintillation speed exceeding $50$~km/s therefore implies \na brightness temperature $T_b \\gtrsim 6 \\times 10^{14}$~K.\n% comparable \n% to that derived for PKS~0405-385 \n% (Kedziora-Chudczer et al. 1997)\\markcite{Kedzioraetal}.\n\n\\subsection{Circular Polarization}\nWe consider the origin of the CP in terms of intrinsic synchrotron \n(Legg \\& Westfold 1968)\\markcite{Legg68}, partial conversion of the linear \npolarization into CP due to ellipticity of the \nnatural wave modes of the cold background plasma (Pacholczyk \n1973)\\markcite{Pac73} or \nof the relativistic electron gas itself (e.g. Sazonov 1969, \nJones \\& O'Dell 1977a,b)\\markcite{Saz69,Jones77a,Jones77b}.\n\nIf the CP in \nthe scintillating component is due to \nsynchrotron emission then, following Legg \\& Westfold~(1968)\\markcite{Leg68}, \nthe Lorentz factor of the particles responsible for a CP \nof $m_c$ in a {\\it uniform} magnetic field \nis $\\gamma \\approx \\cot \\theta/m_c$, where \n$\\theta$ is the angle between the magnetic field\nand the line of sight. For $30^\\circ < \\theta < 60^\\circ$ this \nimplies Lorentz factors in the range $\\approx 15-45$ to\nexplain the CP at 4.8~GHz. Indeed, the observed (low) \nlevel of linear polarization suggests a\nnon-uniform magnetic field, indicating that \neven higher Lorentz factors are required. The \nmaximum brightness temperature of such emission is $T_B \\leq \n5.9 \\times 10^9 \\gamma$~K$=2.7 \\times 10^{11}$~K in the rest frame. Bulk motion with a \nDoppler boosting factor $\\delta \\gtrsim 200$ would account for the difference \nbetween the rest-frame and scintillation-derived brightness \ntemperatures. Such a Doppler factor, although very high, cannot be \nentirely ruled out. However the observed frequency dependence of the degree of \nCP is far from \nthe $\\nu^{-1/2}$ expected from synchrotron theory (see fig 3c); the \nCP {\\it decreases} sharply between 8.6 and 1.4~GHz.\nIt is therefore unlikely that the CP is due to synchrotron emission.\n\nAlternatively, the CP could be due to propagation \nthrough a relativistic pair plasma, such as may be present within the \nsource itself. The \nbirefringence induced in a medium by the presence of a pair plasma \nmay convert linear polarization to CP as \nfollows:\n$$\nV(\\nu) = U_{0}(\\nu) \\sin ( c^3 {\\rm RRM}/\\nu^3), \\eqno(3)\n$$\nwhere the relativistic rotation measure, RRM, depends upon the \ndensity of relativistic particles, the path length, the magnetic \nfield, and the minimum Lorentz factor of the pairs (e.g. Kennett \\& Melrose \n1998)\\markcite{Ken98}.\nThis effect operates only when the direction of the incident linear \npolarization is at an oblique angle to the projection of the magnetic \nfield on the plane orthogonal to the ray direction. The axes used to \ndefine the Stokes parameters may be chosen such that synchrotron \nemission has $Q \\neq 0, U=0$. With this choice, the effect occurs \nonly if the incident radiation has $U_0 \\neq 0$, requiring either \nFaraday rotation or that it \noriginate from a region of the source where the magnetic field is in a \ndifferent direction to that where the polarization \nconversion takes place. \n\nA characteristic of this model is a strong frequency dependence on the \nsign of $V$. If ${\\rm RRM}$ is high enough to produce the CP \nobserved at high frequency, this model predicts rapid changes \nin $V$ at low frequency: in particular, equation (3) yields the lower limit \n$|{\\rm RRM}| \\geq 6.2 \\times 10^2 \\, (1+z)^3\n/f_U(8.6\\,{\\rm GHz})$~rad/m$^3$ \nto explain the $-2.6$\\% CP at 8.6~GHz, where we write $f_U(8.6\\,{\\rm GHz}) =\n|(U_0(8.6\\,{\\rm GHz})/I(8.6\\,{\\rm GHz})|$. \nFor this lower limit, $\\lambda^3 {\\rm RRM}$ will vary by \n$0.88/f_U(8.6\\,{\\rm GHz})$~rad across 64~MHz\nbandwidth at 1.4~GHz and $0.08/f_U(8.6\\,{\\rm GHz})$~rad at 2.5~GHz. We \nsearched for frequency-dependent variations in $V$\nat all four frequencies by selecting two adjacent 32~MHz sub-bands at each \nfrequency. None were found. Although the Faraday rotation \n(RM $\\approx$ 69 rad/m$^2$)\nacross the band was clearly detected at 1.4 and 2.5~GHz, the variations in $V$ \nbetween sub-bands were less than 4\\% and 0.8\\% at these frequencies\nrespectively. This result appears inconsistent with the derived lower \nlimit on RRM, although the null result at \n1.4~GHz may result from an absence\nof CP in the scintillating component (which in turn implies\n$|U_0| /I \\sim |V|/I < 0.01$ at 1.4~GHz).\n\nThe fact that all detections of the CP are of same sign also argues \nagainst this model. If (i) $V$ does not change sign at any frequencies intermediate to those of our \nmeasurements (i.e. the spectrum is well-sampled) and (ii) $U_0$ does not \nchange sign in the range 1.4$-$8.6~GHz then equation (3) implies \n$\\lambda^3 {\\rm RRM} < 2 \\pi$ for \nall frequencies above 1.4~GHz (even if $V(1.4~{\\rm GHz})$, whose sign \nis uncertain, is positive).\nAt 1.4~GHz one then has \n$|{\\rm RRM}| < 6.2 \\times 10^2 \\, (1+z)^{3}$~rad/m$^3$, requiring \n$f_U(8.6\\,{\\rm GHz}) \\geq 100$\\% to be \nconsistent with the lower limit on ${\\rm RRM}$ obtained above. While \ndifficult to exclude entirely, we therefore conclude that the production of \nCP by a pair-dominated plasma is implausible.\n\nPolarization conversion may also occur in a medium containing a \nmixture of\ncold and relativistic pair plasma, in which case the fractional CP \nvaries as $m_c \\propto \\nu^{-1}$ Pacholczyk (1973). \nThis model appears implausible in light of the observed \n$\\nu^{0.7_{-0.3}^{+1.4}}$ frequency \ndependence of the CP from 1.4 to 4.8~GHz. \n\nThe presence of several distinct sub-components may \nalter the spectral properties of the observed CP.\nHowever, the scintillation characteristics argue against the existence of \nmultiple circularly polarized components, each with distinct $U_0$, RRM and \n$\\gamma$. The presence of multiple components with different $V/I$ \nwould lead to substructure in the lightcurve of $V$ compared to the lightcurve\nof $I$ as the scintillation selectively amplifies and deamplifies\nparts of the source differently. This would result in a loss of correlation \nbetween $V$ and $I$, particularly at 4.8 and 8.6~GHz, where the \nscintillation is most sensitive to small-scale structure. This \nis not observed in fig. 1 where \nthe correlation coefficients are close to unity. However, it is more \ndifficult to ascertain the presence of substructure in the variability \nat 1.4 and 2.5~GHz due to the long timescale of the fluctuations.\n \nJones \\& O'Dell (1977a, 1977b)\\markcite{Jones77a,Jones77b} \npresented a model for the CP of inhomogeneous \nsynchrotron sources, incorporating optical depth effects, mode \ncoupling and mode conversion due to the birefringence of the \nplasma. Below the self-absorption turnover \nfrequency, $\\nu_{\\rm SSA}$, mode coupling dominates, and the \nCP is typically less than 0.05\\%, and certainly \nnot more than 2\\%. Mode conversion dominates above $\\nu_{\\rm SSA}$, with the \nCP as high as 10\\% near $\\nu_{\\rm SSA}$, and \ndecreasing to less than $10^{-3}$ at frequencies a decade above\n$\\nu_{\\rm SSA}$. This model is viable only if $\\nu_{\\rm SSA}$ is\nwithin a factor $\\sim 1.4$ of the frequency at which the high (3.8\\%) \nCP was observed, at 4.8~GHz. This is difficult to \nverify as we do not know the intrinsic spectrum of the \nscintillating component and the frequency range of our observations is limited.\n\n\\placefigure{fig:FIG3N.PS}\n\\begin{figure*}\n\\begin{tabular}{c}\n \\psfig{file=FIG3N.PS,angle=270,width=70mm}\n\\end{tabular}\n\\caption{Various quantities derived from the data in \nfig. 1. (a) Spectra of the \ntotal intensity (circles) and CP (squares) in PKS~1519-273 for the four \nbands of ATCA averaged over the duration of the observations.\n(b) Modulation indices derived from the intensity \nfluctuations over the 5 days of observations. The long timescale of \nvariability makes it difficult to compare these values with the \nensemble-average quantities predicted by scintillation theory. This \nis particularly relevant at 2.5 and 1.4~GHz because the timescale of \nvariability is comparable to or exceeds the period of observation.\n(c) The spectrum of circularly polarized component derived by \ncomparing the magnitude of the fluctuations in $I$ with those in $V$ \n(see fig. 2).}\n\\end{figure*}\n\n\n\\section{Conclusion}\nThe variability detected in PKS~1519-273 in all four Stokes \nparameters at frequencies from 1.4 to 8.6~GHz is remarkable, but has a natural \ninterpretation in terms of ISS. The \nscintillation properties at 4.8~GHz constrain the brightness \ntemperature of the scintillating component to $T_b \\geq 5 \\times \n10^{13}$~K, although there is strong evidence to suggest it may be as \nhigh as $6 \\times 10^{14}$~K. Comparison of the fluctuations in \n$I$ and $V$ imply that \nthis component is exceptionally highly circularly polarized at 8.6 and \n4.8~GHz. Simple applications of synchrotron theory and models of \ncircular repolarization encounter difficulties with the spectral \nbehavior and magnitude of the CP. \nThe strong correlation between the fluctuations in $I$ and $V$ at 4.8 \nand 8.6~GHz and the high sensitivity of the scintillation to source \nstructure at these frequencies argue against a complex source, with different $V/I$ in each component.\nInclusion of effects due to small-scale inhomogeneity, mode coupling \nand optical depth effects may reproduce \nthe observed characteristics of the CP. However, \nthis model is only viable if the frequency at which the\nsource is observed to become optically thin is in the range \n$3.4\\,{\\rm GHz} \\lesssim \\nu \\lesssim 6.7\\,{\\rm GHz}$. This possibility is \npresently difficult to confirm. Even if correct, the puzzle \nremains as to why so few sources exhibit such high \nlevels of CP. \n\nFinally, in light of the extremely high brightness temperature of \nPKS~1519-273, we advance the possibility that the observed emission \nis not due to synchrotron emission at all and that high CP \nmay be a characteristic of a new emission mechanism.\n\n\n\\acknowledgments\nWe thank Don Melrose, Ron Ekers, Mark Walker, Jim Lovell, Dick \nHunstead and Lawrence Cram for valuable discussions. The \nAustralia Telescope is funded by the Commonwealth Government for \noperation as a national facility by the CSIRO.\n\n\\begin{references}\n\n\\reference{Bower99}\nBower, G.C., Falcke, H. \\& Backer, D.C., \n{1999}, \\apj, 1999, 523, L29\n\n% \\reference{Cordes86}\n% Cordes, J.M., 1986, \\apj, {311}, 183\n\n\\reference{Fichtel94}\nFichtel, C.E. et al., 1994, \\apjs, 94, 551\n\n% \\reference{Frater92}\n% Frater, R.H., Brooks, J.W. \\& Whiteoak, J.B., 1992, JEEEA,12, 103\n% JEEEA = Jnl of Electrical and Electronics Engineering, Australia\n\n\n\\reference{Heidt96}\nHeidt, J. \\& Wagner, S.J., 1996, \\aap, {305}, 42\n\n\\reference{Heeschen97}\nHeeschen, D.S., Rickett, B.J., 1997, \\aj, 93, 589\n\n\\reference{Impey96} Impey, C.D. \\& Tapia, S., 1996, \\apj, 333, 666\n\n\\reference{Jones77a}\nJones, T.W., O'Dell, S.L.,\n{1977a},\n\\apj,\n{214},\n552\n\n\n\\reference{Jones77b}\nJones, T.W., O'Dell, S.L.,\n{1977b},\n\\apj,\n{215},\n236.\n\n\n\\reference\n{KedzioraPhD}\nKedziora-Chudczer, L., Jauncey, D.L., Wieringa, M.H., Reynolds, J.E., Tzioumis,\nA.K. {1998} in ASP Conf. 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Eksper Teor. Fiz.,\n{56},\n1074 (English transl. in Soviet Phys. -- JETP, {29}, 578).\n\n\\reference{Seaquist74}\nSeaquist, E.R, Gregory, P.C. \\& Clarke, T.R., 1974, \\aj, 79, 918\n\n\\reference{Steppe88}\nSteppe, H., Salter, C.J., Chini, R., Kreysa, E., Brunswig, W. \\& Lobato \nPerez, J., 1988, \\aaps, 75, 317\n\n\\reference{Steppe95}\nSteppe, H., Jeyakumar, S., Saikia, D.J. \\& Salter, C.J., 1995,\n\\aaps, 113, 409\n\n\\reference{Urry96}\nUrry, C.M., Sambruna, R.M., Worrall, D.M., Kollgaard, R.I., \nFeigelson, E.D., Perlman, E.S. \\& Stocke, J.T., 1996, \\apj, 463, 424\n\n\\reference{Veron93}\nVeron-Cetty, M.-P. \\& Veron, P., 1993, \\aaps, 100, 521\n\n% \\reference{Walker98}\n% Walker, M.A., 1998, \\mnras, 294, 307\n\n\\reference{Wardle98}\nWardle, J.F.C., Homan, D.C., Ojha, R. \\& Roberts, D.H.,\n{1998},\nNature,\n{395},\n457\n\n\\reference\n{Weiler83}\nWeiler, K. W \\& de Pater, I.,\n{1983},\n\\apjs,\n{52},\n293\n\n\\reference{White88} White, G.L., Jauncey, D.L., Savage, A., Wright, \nA.E, Batty, M.J., Peterson, B.A. \\& Gulkis, S., 1988, \\apj, 327, 561\n\n\\end{references}\n\n\n% \\figcaption[HIGH.PS,LOW.PS]{Variability of PKS~1519-273 in the total intensity ($I$), \n% CP ($V$), and magnitude of the linear polarization ($P$),\n% for the four bands of the ATCA over 5 days. Each point \n% represents a 10~min average, and is plotted with $1\\,\\sigma$ error bars. \n% Fluctuations in $I$ and $V$ are strongly correlated ($r=-0.90$ at \n% 4.8~GHz and $r=-0.80$ at 8.6~GHz).}\n% \\special{psfile=HIGH.PS angle=270 hscale=50 vscale=50}\n% \\vskip 2.8 in\n% \\special{psfile=LOW.PS angle=270 hscale=50 vscale=50}\n\n\n \n% \\figcaption[v_vs_i_2496.eps,v_vs_i_4800.eps,v_vs_i_8640.eps]{Plot \n% of the correlation between $V$ and $I$. The best fit lines give \n% a fractional CP of $-2.4\\pm 1.3$\\%, $-3.8 \\pm 0.4$\\% \n% and $-2.6 \\pm 0.5$\\% respectively at 2.5, 4.8 and 8.6~GHz for the \n% variable component of the source. The fluctuations in $I$ and $V$ do \n% not appear to be correlated at 1.4~GHz, indicating that we detect \n% {\\it no} CP associated with the variable component \n% at this frequency. We place an upper limit on the CP of \n% this component of 1.3\\%.}\n% \\special{psfile=v_vs_i_2496.eps angle=270 hscale=30 vscale=30}\n% \\vskip 2.2 in\n% \\special{psfile=v_vs_i_4800.eps angle=270 hscale=30 vscale=30}\n% \\vskip 2.2 in\n% \\special{psfile=v_vs_i_8640.eps angle=270 hscale=30 vscale=30}\n\n\n% \\figcaption[FIG3N.PS]{Various quantities derived from the data in \n% fig. 1. (a) Spectra of the \n% total intensity (circles) and CP (squares) in PKS~1519-273 for the four \n% bands of ATCA averaged over the duration of the observations.\n% (b) Modulation indices derived from the intensity \n% fluctuations over the 5 days of observations. The long timescale of \n% variability makes it difficult to compare these values with the \n% ensemble-average quantities predicted by scintillation theory. This \n% is particularly relevant at 2.5 and 1.4~GHz because the timescale of \n% variability is comparable to or exceeds the period of observation.\n% (c) The spectrum of circularly polarized component derived by \n% comparing the magnitude of the fluctuations in $I$ with those in $V$ \n% (see fig. 2).}\n% \\special{psfile=FIG3N.PS angle=270 hscale=80 vscale=80}\n\n\n\\end{document}\n\n\n"
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astro-ph0002193
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A Theoretical Review of Axion\footnote{Talk presented at cosmo-99, ICTP, Trieste, Italy, 28 September 1999.}
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"author": "Jihn E. Kim"
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It is emphasized that the existence of a very light axion is consistent with the strong CP invariance and cosmological and astrophysical constraints. The attempt to embed the very light axion in superstring models is discussed.
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"name": "c99lanl.tex",
"string": "%%UNIX --- UPDATED ON 13/8/97 \n%====================================================================%\n% sprocl.tex 27-Feb-1995 %\n% This latex file rewritten from various sources for use in the %\n% preparation of the standard proceedings Volume, latest version %\n% by Susan Hezlet with acknowledgments to Lukas Nellen. %\n% Some changes are due to David Cassel. %\n%====================================================================%\n\n\\documentstyle[epsf,sprocl]{article}\n\n\\font\\eightrm=cmr8\n\n\\input{psfig.sty}\n\n\\bibliographystyle{unsrt} %for BibTeX - sorted numerical labels by\n %order of first citation.\n\n\\arraycolsep1.5pt\n\n% A useful Journal macro\n\\def\\Journal#1#2#3#4{{#1} {\\bf #2}, #3 (#4)}\n\n% Some useful journal names\n\\def\\NCA{\\em Nuovo Cimento}\n\\def\\NIM{\\em Nucl. Instrum. Methods}\n\\def\\NIMA{{\\em Nucl. Instrum. Methods} A}\n\\def\\NPB{{\\em Nucl. Phys.} B}\n\\def\\PLB{{\\em Phys. Lett.} B}\n\\def\\PRL{\\em Phys. Rev. Lett.}\n\\def\\PRD{{\\em Phys. Rev.} D}\n\\def\\ZPC{{\\em Z. Phys.} C}\n\n% Some other macros used in the sample text\n\\def\\st{\\scriptstyle}\n\\def\\sst{\\scriptscriptstyle}\n\\def\\mco{\\multicolumn}\n\\def\\epp{\\epsilon^{\\prime}}\n\\def\\vep{\\varepsilon}\n\\def\\ra{\\rightarrow}\n\\def\\ppg{\\pi^+\\pi^-\\gamma}\n\\def\\vp{{\\bf p}}\n\\def\\ko{K^0}\n\\def\\kb{\\bar{K^0}}\n\\def\\al{\\alpha}\n\\def\\ab{\\bar{\\alpha}}\n\\def\\be{\\begin{equation}}\n\\def\\ee{\\end{equation}}\n\\def\\bea{\\begin{eqnarray}}\n\\def\\eea{\\end{eqnarray}}\n\\def\\CPbar{\\hbox{{\\rm CP}\\hskip-1.80em{/}}}%temp replacemt due to no font\n\\def\\Dslash{D{\\hskip -0.22cm}\\slash} \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%BEGINNING OF TEXT \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{document}\n\n\\title{A Theoretical Review of Axion\\footnote{Talk presented at cosmo-99,\nICTP, Trieste, Italy, 28 September 1999.}}\n\n\\author{Jihn E. Kim}\n\n\\address{Department of Physics and Center for Theoretical Physics \\\\\nSeoul National University, Seoul 151-742, Korea } \n\n\\maketitle\\abstracts{It is emphasized that the existence of a very light \naxion is consistent with the strong CP invariance and cosmological\nand astrophysical constraints. The attempt to embed the very light axion\nin superstring models is discussed.}\n\n\\section{The Strong CP Problem}\n\nThe standard model $SU(3)\\times SU(2)\\times U(1)$ describes the\nweak and electromagnetic interactions very successfully. The strong\ninteraction part, quantum chromodynamics, is proven to be successful\nat perturbative level, but the study of nonperturbative effects are not \nso successful. Because of the lack of a calculational tool of the\nnonperturbative effects, the frequently used method for the study\nof QCD at low energy is the symmetry principle. At energy scales below\nthe confinement and chiral symmetry breaking scale, some symmetries\nof QCD are manifest in strong interaction dynamics. Baryon number is\nknown to be conserved. Chiral symmetry is broken. \n\nDiscrete symmetries are believed to be conserved in the process of\nconfinement. Here we are interested in CP. If QCD conserves CP,\nthe CP symmetry will be preserved in strong interactions at low energy.\nIf QCD violates CP, its effect will be shown in low energy strong\ninteraction dynamics. QCD before 1975 was described by\n\\begin{equation}\n{\\cal L}= -\\frac{1}{2g^2}{\\rm Tr\\ }F_{\\mu\\nu}F^{\\mu\\nu}\n+\\bar q(i\\Dslash-M_q)q\n\\end{equation} \nwhere $q$ and $M_q$ are quark and quark mass matricies, respectively.\nAfter the discovery of the instanton solution in non-Abelian gauge\ntheories,\\cite{bpst} it is known that the $\\theta$-term must be\nconsidered,\\cite{theta}\n\\begin{equation}\n{\\cal L}_\\theta=\\frac{\\theta}{16\\pi^2}{\\rm Tr}\\ F_{\\mu\\nu}\\tilde F^{\\mu\\nu}.\n\\end{equation}\nNote that ${\\cal L}_\\theta$ is odd uner P or T discrete transformation.\nTherefore, this term violates the CP invariance. Thus QCD contains a\nterm violating CP symmetry. If QCD violates the CP symmetry, it must be\nrevealed in strong interaction dynamics. For example, we may expect a \nCP violating static property of neutron, the electric dipole moment\nof neutron $d_n$. The experimental upper limit of $d_n$ is known to\nbe $0.63\\times 10^{-25}\\ e\\cdot$cm.\\cite{dn} On the other hand, if\nstrong interaction violates the CP invariance at the full strength,\nthen we expect $d_n\\sim 10^{-14}\\ e\\cdot$cm. Therefore, the vacuum\nangle is restricted to a tiny region\n\\begin{equation}\n|\\theta|< 10^{-9}.\n\\end{equation}\nThe question, $\\lq\\lq$Why is the vacuum angle so small\", is the\nstrong CP problem. If we treat $\\theta$ as O(1) parameter, then the\nabove observation excludes QCD as the theory of strong interactions.\nIn this case, different $\\theta$'s describe different universes. Since \nQCD is known to be so successful except for the strong CP problem, it is\nbetter to keep QCD as the theory of strong interactions. It is\ndesirable to resolve the strong CP problem with QCD untouched.\n\nThere have been several attempts toward the solution of the strong\nCP problem, one even incorrectly asserting that there is no\nstrong CP problem.\\cite{marshak}\\footnote{This reference~[4]\nstarts with an assumption on CPT invariant $|n\\rangle$ vacua and obtains\nthe CPT odd $|\\theta\\rangle$ vacuum. But in Yang-Mills theories,\n$|n\\rangle$ vacua are not CPT invariant, and the $|\\theta\\rangle$\nvacuum is CPT invariant.} \n\nOne class of solutions employs CP\nsymmetry at the Lagrangian level, and require the induced vacuum \nangle (in the process of introducing weak CP violation) sufficiently\nsmall.\\cite{natural} These are called natural solutions.\nHere, the weak CP violation is through spontaneous symmetry\nbreaking or soft breaking. Namely, the Kobayashi-Maskawa type\nweak CP violation is not possible except for the Nelson-Barr type.\nThe reason for a possible Kobayashi-Maskawa weak CP violation in\nthe Nelson-Barr type strong CP solution is that the spontaneous CP\nviolation here is introduced at a super high energy scale and\nhence at the electroweak scale CP is already violated as in the\nKobayashi-Maskawa model. In this class of models, at tree level\n$\\theta=0$, which implies $Arg\\ Det\\ M_q=0$. This is attained by\nassuming a CP invariant Lagrangian including the $\\theta$ term\nand specific symmetries. Possible symmetries used for this purpose\nare: left-right symmetry, $U(1)$ gauge symmetry, permutation symmetry,\nand other discrete symmetries.\n\nThe other solutions are the $m_u=0$ solution and the axion solution.\n\nHere, the most attractive solution is the axion solution, making\n$\\theta$ a dynamical variable. A dynamical $\\theta$ is equivalent to\na pseudoscalar field which we call axion. If the axion has a potential,\nthen in the evolving universe the minimum of the vacuum will be\nchosen. The axion solution guarantees that $\\theta=0$ is the\nminimum of the $\\theta$ potential, which is discussed below.\n\n\\section{The Peccei-Quinn Solution}\n\nThe axion solution is a dynamical solution. Peccei and Quinn~\\cite{pq}\nshowed that $\\theta=0$ at the point $dV/d\\theta=0$, which has been\nshown later by Vafa and Witten,\\cite{vw}\n\\begin{equation}\n{\\cal L}=-\\frac{1}{4}F^2+\\bar q(i\\Dslash-M_q)q+\\theta\\frac{g^2}{32\\pi^2}\nF\\tilde F\n\\end{equation}\nwhere we suppressed the Greek indices for space-time in $F$. Let us treat\n$\\theta$ as a coupling. After integrating the quark fields out, the\ngenerating functional in the Euclidian space is given by\n\\begin{equation}\n\\int [dA_\\mu]\\prod_i{\\rm Det}(\\Dslash+m_i)\n\\exp{\\{-\\int d^4x[\\frac{1}{4g^2}F^2-i\\theta\\frac{1}{32\\pi^2}F\\tilde F]\\}}.\n\\end{equation}\nNote that the resulting functional has a specific form of the $\\theta$\ndependence. In the Euclidian space, corresponding to the eigenstate\n$\\psi$ of $i\\Dslash$, $i\\Dslash\\psi=\\lambda\\psi$, there corresponds to\nthe other eigenstate of $i\\Dslash$, $i\\Dslash(\\gamma_5\\psi)=-\\lambda\n(\\gamma_5\\psi)$. Thus, the nonzero real eigenvalues of $i\\Dslash$ are\npaired with opposite sign and the identical magnitude. For $N_0$ number\nof zero modes, we can show that\n\\begin{equation}\n{\\rm Det\\ }(\\Dslash+m_i)=\\prod_i (-i\\lambda+m_i)=m_i^{N_0}(m_i^2+\n\\lambda^2)>0.\n\\end{equation}\nThus, the generating functional is bounded by usung the\nSchwarz inequality in view of Eq.~(6),\n\\begin{eqnarray}\n&\\exp[-\\int d^4x V[\\theta]]\\equiv |\\int[dA_\\mu]\\prod {\\rm Det\\ }\n(\\Dslash+m_i)\\exp(-\\int d^4x{\\cal L})|\\nonumber\\\\\n&\\le \\int [dA_\\mu]|\\prod {\\rm Det}(\\Dslash+m_i)\\exp(-\\int d^4x{\\cal L})\n|\\nonumber\\\\\n&=|\\int[dA_\\mu]\\prod{\\rm Det\\ }(\\Dslash+m_i)\\exp[-\\int d^4x\n{\\cal L}(\\theta=0)] |\\\\\n&=\\exp(-\\int d^4x V[0])\\nonumber\n\\end{eqnarray}\nwhere ${\\cal L}=(1/4g^2)F^2-i\\theta\\{F\\tilde F\\}$, and the simplified\nnotation $\\{\\ \\ \\}$ includes a factor $1/32\\pi^2$. The above\ninequality guarantees\n\\begin{equation}\nV[\\theta]\\ge V[0].\n\\end{equation}\nInstanton solutions have integer values for $\\int d^4x\\{F\\tilde F\\}$,\nhence $V[\\theta]$ is periodic with the $\\theta$ period of $2\\pi$,\n$\\theta\\rightarrow \\theta+2n\\pi$. The above agument is for a nonzero\nup quark mass. If $m_u=0$, $\\theta$ is unphysical and there is no\nstrong CP problem.\n\nAs a coupling, any $\\theta$ defines a good theory (or universe). The \nshape of $V$ as a function of $\\theta$ is\n\n\\begin{figure}\n\\epsfxsize=60mm\n\\centerline{\\epsfbox{c99kim1.eps}}\n\\end{figure}\n\\centerline{Fig.~1.\n{\\it Shape of $V[\\theta]$. The KM weak CP introduces}~\\cite{gr} \n$|\\theta| \\simeq 10^{-16}$.}\n\\vskip 0.3cm\nHere, the axion solution of the strong CP problem is transparent. If\nwe identify $\\theta$ as a pseudoscalar field,\n\\begin{equation}\n\\theta=\\frac{a}{F_a}\n\\end{equation}\nthe vacuum angle is chosen at $\\theta\\simeq 0$, realizing the\nalmost CP invariant QCD vacuum. Note the key ingredients of this\naxion solution. Firstly, the theory introduces an axion coupling\n$a\\{F\\tilde F\\}$. Second, there is no axion potential except\nthat coming from the $F\\tilde F$ term, otherwise our proof does not\ngo through. Third, there necessarily appears a mass parameter $F_a$,\nthe so-called axion decay constant. One possible example for \nthe axion is to introduce a\nGoldstone boson, using a global $U(1)$ symmetry.~\\cite{pq} As explained\nabove Peccei-Quinn showed that $\\theta=0$ is the minimum of the\npotential, which is meaningful only if there is a dynamical field\n$a$. Later, Weinberg and Wilczek explicitly showed that the model\ncontains the axion.~\\cite{ww} It was immediately known that the\nPQWW axion does not exist,\\cite{peccei} and hence there soon \nappeared a flurry of natural solutions.~\\cite{natural} \n\nTo have the anomalous coupling, the global symmetry must have a\ntriangle anomaly in $U(1)_{\\rm global}\\times SU(3)_c\\times SU(3)_c$.\nThis anomalous coupling introduces an axion decay constant which\ncan be large for the very light axion models.\\cite{invisible,dfsz}\nSoon after the invention of the very light axion, it has been\nknown that the astrophysical and cosmological bounds restrict \nthe axion decay constant in the region, $10^9{\\ \\rm GeV}\\le F_a\n\\le 10^{12}\\ {\\rm GeV}$.\\cite{astro,cos}\nAlso, it was known that a more ambitious composite axion can be \nconstructed.\\cite{comp}\n\nAnother interesting possibility is that there results an axion with\nthe above properties from a more fundamental theory such as from\nthe string theory. This possibility introduces a nonrenormalizable\ninteraction $aF\\tilde F$. Indeed, superstring models have a host\nof moduli fields which do not have potentials at the compactification\nscale. But some of the moduli have the desired anomalous \ncouplings,\\cite{witten} and becomes the axion. In this case, the \nso-called superstring axions are expected to have the decay constant \nnear the Planck scale. But the exact magnitude depends on the details\nof the model. \n\nThe mass of the very light axion is an important parameter in the\nevolving universe. The allowed range of the decay constant gives\ntens of micro-eV axion mass,\n\\begin{equation} \nm_a=0.6\\times 10^7\\ \\frac{\\rm eV}{F_a^{\\rm GeV}}\n\\end{equation}\nwhere $F_a^{\\rm GeV}=F_a/{\\rm GeV}$.\n\nThe neutron electric dipole moment in the $\\theta$ vacuum is\ngiven by~\\cite{quint}\n\\begin{equation}\n\\frac{d_n}{e}=O(1)\\frac{m_u\\sin\\theta}{f_\\pi^2[2Z\\cos\\theta+(\n1+Z)^2]^{1/2}}\n\\end{equation}\nwhere $Z=m_u/m_d$ is the ratio of the current quark masses.\nFor $m_u<2\\times 10^{-13}$~GeV, the neutron electric dipole \nmoment is satisfied even for O(1) $\\theta$.\n\nThe very light axion physics is closely connected to the study\nof the evolution of the universe. The domain wall problem~\\cite{sikivie}\nmust be studied in specific models. Usually, inflation needed in\nsupergravity models with the condition on the reheating temperature\n$T_R<10^9$~GeV \\cite{ekn} does not lead to the axionic domain\nwall problem.\n\nTheoretically, the introduction of the Peccei-Quinn U(1) global\nsymmetry is ad hoc. It is better if the axion arises from a\nfundamental theory. In this spirit, it is most important to\ndraw a very light axion from superstring theory. If we cannot,\nhow can we understand the strong CP problem?\n\n\\section{Embedding the Very Light Axion in Superstring}\n\nThe pseudoscalar moduli fields in D=10 superstring is $B_{MN}\\\n(M,N=0,\\cdots,9)$ among the bosonic fields $G_{MN}, B_{MN}$ and\nthe dilaton. Upon compactification to D=4, $B_{\\mu\\nu}\\ (\\mu,\\nu\n=0,\\cdots,3)$ turns out to be a pseudoscalar field. Dual \ntransformation of $B_{\\mu\\nu}$ defines a pseudoscalar $a$ as\n\\begin{equation}\n\\partial^\\sigma a\\propto\\epsilon^{\\mu\\nu\\rho\\sigma}H_{\\mu\\nu\\rho};\nH_{\\mu\\nu\\rho}={\\rm field\\ strength\\ of\\ }B_{\\mu\\nu}\\propto\n\\epsilon_{\\mu\\nu\\rho\\sigma}\\partial^\\sigma a.\n\\end{equation}\nOf course, $B_{\\mu\\nu}$ does not have renormalzable couplings to \nmatter fields, hence there is no potential for $a$ since the\npossible derivative coupling $\\partial^\\mu a\\psi\\gamma_\\mu\\gamma_5\n\\psi$ does not lead to a potential term. If we consider a field\nstrenth \n$H_{\\mu\\nu\\rho}$ to obtain couplings, it is invariant under\na shift $a\\rightarrow a+c$. This consideration does not lead to\nan anomalous coupling needed for an axion. \n\nHowever, the gauge invariant D=10 field strength of $B_{MN}$ is\nnot $H=dB$,\\footnote{In this paragraph we use the differential form.}\nbut is~\\cite{green}\n\\begin{equation}\nH=dB+\\omega^0_{3Y}-\\omega^0_{3L}\n\\end{equation} \nwhere the Yang-Mills Chern-Simmons form is tr$(AF-A^3/3)$ and the\nLorentz Chern-Simmons form is tr$(\\omega R-\\omega^3/3)$. The \nChern-Simmons forms satisfy $d\\omega^0_{3Y}={\\rm tr\\ }F^2$ and\n$d\\omega^0_{3L}={\\rm tr}\\ R^2$. Therefore,\n\\begin{equation}\ndH=-{\\rm tr\\ }F^2+{\\rm tr\\ }R^2,\n\\end{equation}\nand the equation of motion for $a$ is\n\\begin{equation}\n\\Box a=-\\frac{1}{M}[{\\rm Tr\\ }F_{\\mu\\nu}\\tilde F^{\\mu\\nu}\n-{\\rm Tr\\ }R_{\\mu\\nu}\\tilde R^{\\mu\\nu}]\n\\end{equation}\nwhich implies $aF\\tilde F$ coupling which is needed for the\naxion interpretation of $a$.\\cite{witten} This is the so-called\nmodel-independent axion. Here, $M$ is about the compactification\nscale suppressed by a factor and corresponds to the axion decay\nconstant.\\cite{choikim} \n\nTo cancel the Yang-Mills anomaly, one\nshould introduce the Green-Schwarz term,\\cite{green} $S_{GS}\\sim\n\\int(B{\\rm tr}F^4+\\cdots)$. The Green-Schwarz term gives the \nneeded anomalous coupling for pseudoscalars $B_{ij}\\ (i,j=4,\\cdots,\n9)$\n\\begin{equation}\nB_{ij}\\epsilon^{\\mu\\nu\\rho\\sigma}F_{\\mu\\nu}F_{\\rho\\sigma}\n\\langle F_{kl}\\rangle\\langle F_{pq}\\rangle\\epsilon^{ijklpq}.\n\\end{equation}\nHere, we have model-dependent axions $a_k\\sim \\epsilon_{ijk}B_{ij}$,\nthe number of which is the second Betti number.\\cite{witten1}\nUnlike the model-independent axion, the model-dependent axions receive\nnonvanishing superpotential terms from the world-sheet instanton effect,\n\\begin{equation}\n\\int_{\\Sigma_J} d^2z \\omega^I_{ij}(\\partial X^i\\underline\n\\partial X^{\\underline j}-\\underline\\partial X^i\\partial X^{\\underline\nj})=2\\alpha^\\prime\\delta_{IJ} \n\\end{equation}\nwhere $\\alpha^\\prime$ is the string tension, and $\\omega=4\\pi^2 {\\rm Re}\n(T_I)\\omega^I$. The internal space volume is given by\\cite{mth}\n$V_6=(1/3!)\\int \\omega\\land\\omega\\land\\omega\\approx \n(1/6)(4\\pi^2{\\rm Re}T)^3\n(2\\alpha^\\prime)^3$. So the model-dependent\naxion cannot be a candidate for the low energy QCD axion unless\nthe potential is sufficiently suppressed.\\cite{wen}\n\nThus, the model-independent axion is a good candidate for\nthe QCD axion. However, it has two serious problems:\n\\\\\n\\indent (A) The decay constant problem-- $F_a$ is too large, $\\sim \n10^{16}$~GeV,\\cite{choikim} and\\\\\n\\indent (B) The hidden sector problem-- We need a hidden sector confining\nforce for \nsupersymmetry breaking around $10^{10-13}$~GeV. If so, the\ndominant contribution \nto the model-independent axion comes from\nthe hidden sector anomaly, \n\\newpage\n\\begin{figure}\n\\epsfxsize=80mm\n\\centerline{\\epsfbox{c99kim2.eps}}\n\\end{figure}\n\\centerline{Fig. 2. {\\it The almost flat axion potential.}}\n\\vskip 0.3cm\n\\noindent $m_a\\simeq \\Lambda_h^2/F_a$. Then, this \ncannot be the needed axion for the strong CP problem. With two confining\nforces with scales of $\\Lambda_h$ and $\\Lambda_{QCD}$, the potential can\nbe written as\n\\begin{equation}\nV\\sim -\\Lambda^4_{QCD}\\cos(\\theta+\\alpha)-\\Lambda^4_h\\cos(\\theta_h+\\beta)\n\\end{equation}\nwhere $\\alpha$ and $\\beta$ are constants, and $\\Lambda_h\\gg\\Lambda_{QCD}$.\nTo settle both $\\theta_h$ and $\\theta$ dynamically at zero, we need\ntwo axions. But as shown above, we have only one axion for this \npurpose, the model-independent axion.\n\nBoth of the above problems are difficult to circumvent.\\footnote{See, \nhowever, Lalak et al.\\cite{lalak}} \n\nThe approximate global symmetries may be a way out from this dilemma.\n\\cite{shafi} Discrete symmetries may forbid sufficiently many terms so that\nthe Peccei-Quinn symmetry violating terms can appear only at $d\\ge 9$.\nOne such example is $Z_N$ symmetry (e.g. $N=3$) in theories without\nhidden sector quarks.\\cite{gkn} \n\n\\section{Cosmology with Axion}\n\nIn the hot cores of stellar objects, the axion production can occur\nthrough $\\gamma+e({\\rm or\\ }Z)\\rightarrow a+\ne({\\rm or\\ }Z)$, $n+n\\rightarrow n+n+a$, $\\gamma+e\\rightarrow a+e$,\n$e^++e^-\\rightarrow a+\\gamma$, etc. For a sufficiently large $F_a$,\naxions produced in the stellar core can escape the star since the \nrescattering cross section is small. If its production rate is too\nlarge $(\\sim 1/F_a^2)$, it takes out too much energy from the core. \nThus, there results the upper bounds on $F_a$ from star evolutions.\nThe best bound is obtained from the study of supernovae.\n\\cite{kang,astro,choikang} \nThus, the solar axion search may not succeed which\nneeds $F_a\\sim 10^7$~GeV.\n\nThe lifetime of $a$ is extremely long and hence can be treated in most cases\nas a stable particle. The classical coherent states of $a$ will \noscillate around the minimum $\\langle a\\rangle=0$. When can this \nhappen? It is around $T_1\\simeq 1$~GeV, not around the axion scale of \n$F_a$ since the axion potential is extremely flat.\nIts existence is felt when the expansion rate is smaller than the\noscillation rate of the classical axion field, viz. \n$3H<m_a$.\\cite{cos} For $T<T_1$, \nthe classical axion field $\\langle a\\rangle$ begins\nto roll down the hill. After this happens, the Hubble expansion is \nnegligible and the $\\langle a\\rangle$ equation leads to a conserved\n$m_aA^2$ (where $A$ is the amplitude of the classical axion field)\nin the\ncomoving volume. \nThis coherent axion field carries energy\ndensity behaving \nlike nonrelativistic particles and its\n\\newpage \n\\begin{figure}\n\\epsfxsize=100mm\n\\centerline{\\epsfbox{c99kim3.eps}}\n\\end{figure}\n\\centerline{Fig. 3. {\\it Axion search experiments. The model predictions \nare shown.}\\cite{search}}\n\\vskip 0.3cm\n\\noindent contribution to cosmic energy is~\\cite{review}\n\\begin{equation}\n\\Omega_ah^2\\simeq 0.13\\times 10^{\\pm 0.4}\\Lambda_{200}^{-0.7}\nf(\\theta_1)\\left(\\frac{10^{-5}{\\rm eV}}{m_a}\\right)^{1.18}N^2_{DW}\n\\end{equation}\nwhere $\\theta_1$ is the $\\theta$ value at the cosmic temperature\n$T_1$. These considerations restrict $F_a$ as\n\\begin{equation}\n10^9\\ {\\rm GeV}\\le F_a\\le 10^{12}\\ {\\rm GeV}.\n\\end{equation}\nIn this scenario, cold axions are packed around us , for which the \naxion search experiments are performed. In this search one probes\nthe axion--electromagnetic coupling of $a{\\bf E\\cdot B}$.\\cite{sik83}\nThe current status is exhibited in Fig.~3.\n\nDepending on models, there can exist domain walls, but in supersymmetric\nmodels the requirement of $T_{RH}<10^9$~GeV gives a sufficient \ndilution of the dangerous domain walls. \nAlso there can exist hot axions produced by\nvibrations of axionic strings when they are formed around $T\\sim \nF_a$.\\cite{shellard} These hot axions are also diluted by inflation\nwith $T_{RH}<10^9$~GeV.\n\n\\vskip 0.2cm\n\\noindent {\\bf Quintessence idea}\n\\vskip 0.2cm\nRecently, there is an evidence that the cosmological constant\nis very tiny,\\cite{perl} which is another difficult problem for the\ncosmological constant. Since the axion potential is almost flat, there\nmay be a mechanism to have a very small cosmological constant within\nthe axion idea. We start with the assumption that at the minimum\nof the potential the cosmological constant is zero.\n\nWe note that the massless quark solution of the strong CP problem \nleads to a flat $\\theta_h$ direction. Eventually, we will identify\nthis $\\theta_h$ direction as the hidden sector(h-sector) axion \ndirection. If we break the global symmetry by a tiny h-sector quark\nmass, the degeneracy is broken feebly. A random value of $\\theta_h$\nwill give a generic value of the potential determined by the\nnonvanishing h-quark mass. This generic value of the potential \nenergy is expected to be $(0.003\\ {\\rm eV})^4$ so that it explains\nthe Type 1a data.\\cite{perl} If $\\theta_h$ is a coupling, then the\nrandom value of $\\theta_h$ gives a true cosmological constant, i.e.\nit is zero. If $\\theta_h$ is a dynamical field such as an axion, \nthen the cosmological constant is nonzero like in axion models.\nWe will call this dynamical $\\theta_h$ with a currently interesting\ncosmological constant a {\\it quintessence}. The axion quintessence\nneeds a potential height of order $10^{-47}$~GeV$^4$ and \n$F_a\\sim M_P$, i.e. $m_a\\sim 10^{-33}$~eV, for it to dominate the\nmass density of the universe recently. In terms of the known scales,\n$M_P=2.44\\times 10^{18}$~GeV and $v\\simeq 247$~GeV, we obtain\na small energy density $v^{n+4}/M_P^n$. For $n=3$, \n\\begin{equation}\n\\frac{v^7}{M_P^3}\\sim 4\\times 10^{-39}\\ {\\rm GeV}^4\n\\end{equation}\nwhich can be a reasonable candidate for the vacuum energy with\na further suppression by coupling constants. How can one forbid\n$n=1,2$ but allow $n=3$ in supergravity?\n\nWith a (almost) massless h-quark, the h-sector instanton potential\nis almost flat. Then the axion corresponding to the h-sector\ncan be a quintessence.\\cite{kim} For this idea to work, we must \nintroduce at least one model-dependent axion so that two axions\nsurvive. If two axions are present with $F_1$ and $F_2$ and two\nexplicit scales $\\Lambda_1$ and $\\Lambda_2$ break the\nsymmetries, the larger $F$ corresponds to the smaller $\\Lambda$.\nBecause the h-sector instanton potential is made almost\nflat by almost massless h-quark,\\cite{kim} the smaller symmetry\nbreaking scale $(v^7/M_P^3)^{1/4}$ corresponds to the larger $F$,\ni.e. the Planck scale decay constant. This solves the axion decay\nconstant problem by lowering the decay constant of the QCD axion to\n$10^{12}$~GeV. \n\nNow the problem is how to save a model-dependent axion. For this\nwe have to assume that many singlets do not develop vacuum\nexpectation values.\\cite{kim}\n\n\\section{Conclusion}\n\nWe have shown that:\n\n\\noindent\ni) The strong CP problem is a serious problem.\\\\\nii) But there are solutions, natural~\\cite{natural} and automatic.\n\\cite{pq,ww,invisible,dfsz}\\\\\niii) The very light axion solution is the most attractive one.\n\\cite{invisible,dfsz} Here, the\\\\\n\\indent\\hskip -0.3cm weak CP violation is of \nthe Kobayashi-Maskawa type.\\\\\niv) The very light axion can close the universe,\\cite{cos}\nand can be detected.\\\\\nv) Superstring models have two problems housing the very light\naxion. One\\\\\n\\indent\\hskip -0.3cm possible scenario with quintessence is also discussed.\n\n\\section*{Acknowledgments}\nThis work is supported in part by the Korea Research Foundation,\nKorea Science and Engineering Foundation, and the BK21 program\nof the Ministry of Education. \n\n\\section*{References}\n\\begin{thebibliography}{99}\n\\bibitem{bpst} A. A. Belavin, A. M. Polyakov, A. S. Shvarts and Yu. S.\n Tyupkin, Phys. Lett. {\\bf B59}, 85 (1975).\n\\bibitem{theta} C. G. Callan, R. Dashen and D. J. Gross, Phys. Lett.\n {\\bf 63}, 334 (1976); R. Jackiw and C. Rebbi, Phys. Rev. Lett. \n {\\bf 37}, 172 (1976). \n\\bibitem{dn} P. G. Harris et al, Phys. Rev. Lett. {\\bf 82}, 904 (1999). \n\\bibitem{marshak} S. Okubo and R. E. Marshak, Prog. Theor. Phys. {\\bf 87},\n 1059 (1992). \n\\bibitem{natural} M. A. B. Beg and H.-S. Tsao, Phys. Rev. Lett. {\\bf 41},\n 278 (1978); H. Georgi, Hadronic J. {\\bf 1}, 155 (1978); R. N. \n Mohapatra and G. Senjanovic, Phys. Lett. {\\bf B79}, 283 (1978);\n G. Segre and A. Weldon, Phys. Rev. Lett. {\\bf 42}, 1191 (1979);\n S. M. Barr and P. Langacker, Phys. Rev. Lett. {\\bf 42}, 1654 (1979);\n A. E. Nelson, Phys. Lett. {\\bf B136}, 387 (1984);\n S. M. Barr, Phys. Rev. Lett. {\\bf 53}, 329 (1984).\n\\bibitem{pq} R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. {\\bf 38}, 1448\n (1977).\n\\bibitem{vw} C. Vafa and E. Witten, Phys. Rev. Lett. {\\bf 53}, 535 (1983).\n\\bibitem{gr} H. Georgi and L. Randall, Nucl. Phys. {\\bf B276}, 241 (1986). \n\\bibitem{ww} S. Weinberg, Phys. Rev. Lett. {\\bf 40}, 223 (1978);\n F. Wilczek, Phys. Rev. Lett. {\\bf 40}, 279 (1978).\n\\bibitem{peccei} R. D. Peccei, in {\\it Proc. 19th ICHEP Meeting (Aug. 23--30,\n 1978)}, ed. H. Homma et al (Phys. Soc. of Japan, Tokyo, 1979), p.1045. \n\\bibitem{invisible} J. E. Kim, Phys. Rev. Lett. {\\bf 43}, 103 (1979); M. A.\n Shifman, A. I. Vainstein and V. I. Zakharov, Nucl. Phys. {\\bf B166},\n 493 (1980).\n\\bibitem{dfsz} M. Dine, W. Fischler and M. Srednicki, Phys. Lett. {\\bf B104},\n 199 (1981); A. P. Zhitnitskii, Sov. J. Nucl. Phys. {\\bf 31}, 260 (1980).\n\\bibitem{astro} G. Raffelt and D. Seckel, Phys. Rev. Lett. {\\bf 60}, 1793\n (1988); M. S. Turner, Phys. Rev. Lett. {\\bf 60}, 1797 (1988);\n Mayle et al, Phys. Lett. {\\bf B203}, 188 (1988). \n\\bibitem{cos} J. Preskill, M. B. Wise\n and F. Wilczek, Phys. Lett. {\\bf B120}, 127 (1983); L. F. Abbott and\n P. Sikivie, Phys. Lett. {\\bf B120}, 133 (1983); M. Dine and W. Fischler,\n Phys. Lett. {\\bf B120}, 137 (1983).\n\\bibitem{comp} J. E. Kim, Phys. Rev. {\\bf D31}, 1733 (1985); K. Choi and \n J. E. Kim, Phys. Rev. {\\bf D32}, 1828 (1985).\n\\bibitem{witten} E. Witten, Phys. Lett. {\\bf B149}, 351 (1984); Phys. Lett.\n {\\bf B153}, 243 (1985).\n\\bibitem{quint} J. E. Kim, JHEP {\\bf 9905}, 022 (1999). \n\\bibitem{sikivie} P. Sikivie, Phys. Rev. Lett. {\\bf 48}, 1156 (1982); K. Choi \n and J. E. Kim, Phys. Rev. Lett. {\\bf 55}, 2637 (1985).\n\\bibitem{ekn} J. Ellis, J. E. Kim and D. V. Nanopoulos, Phys. Lett. {\\bf B145},\n 181 (1984). \n\\bibitem{green} M. B. Green and J. H. Schwarz, Phys. Lett. {\\bf 149}, 117 \n (1984).\n\\bibitem{choikim} K. Choi and J. E. Kim, Phys. Lett. {\\bf B154}, 393 (1985). \n\\bibitem{witten1} E. Witten, Phys. Lett. {\\bf 153}, 243 (1985); K. Choi\n and J. E. Kim, Phys. Lett. {\\bf B165}, 71 (1985).\n\\bibitem{mth} K. Choi, Phys. Rev. {\\bf D56}, 6658 (1997).\n\\bibitem{wen} X. G. Wen and E. Witten, Phys. Lett. {\\bf B166}, 397 (1988).\n\\bibitem{lalak} Z. Lalak, S. Lavignac and H. P. Nilles, Nucl. Phys.\n {\\bf B559}, 48 (1999). \n\\bibitem{shafi} G. Lazarides, C. Panagiotakopoulos and Q. Shafi, \n Phys. Rev. Lett. {\\bf 58}, 1707 (1987).\n\\bibitem{gkn} H. Georgi, J. E. Kim and H. P. Nilles, Phys. Lett.\n {\\bf B437}, 325 (1998). \n\\bibitem{kang} A. Patziris and K. Kang, Phys. Rev. {\\bf D33}, 3509 (1986).\n\\bibitem{choikang} K. Choi, K. Kang and J. E. Kim, Phys. Rev. Lett. {\\bf 62},\n 849 (1989). \n\\bibitem{review} J. E. Kim, Phys. Rep. {\\bf 150}, 1 (1987). \n\\bibitem{sik83} P. Sikivie, Phys. Rev. Lett. {\\bf 51}, 1415 (1983);\n ibid 52, 695(E) (1984).\n\\bibitem{search} J. E. Kim, Phys. Rev. {\\bf D58}, 055006 (1998).\n\\bibitem{shellard} R. A. Battye and E. P. S. Shellard, Phys. Rev. Lett.\n {\\bf 73}, 2954 (1994).\n\\bibitem{perl} S. Perlmutter et al, Astrophys. J. {\\bf 483}, 565 (1997).\n\\bibitem{kim} J. E. Kim, hep-ph/9907528.\n\n\\end{thebibliography}\n\n\\end{document}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% End of sprocl.tex \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n"
}
] |
[
{
"name": "astro-ph0002193.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{bpst} A. A. Belavin, A. M. Polyakov, A. S. Shvarts and Yu. S.\n Tyupkin, Phys. Lett. {\\bf B59}, 85 (1975).\n\\bibitem{theta} C. G. Callan, R. Dashen and D. J. Gross, Phys. Lett.\n {\\bf 63}, 334 (1976); R. Jackiw and C. Rebbi, Phys. Rev. Lett. \n {\\bf 37}, 172 (1976). \n\\bibitem{dn} P. G. Harris et al, Phys. Rev. Lett. {\\bf 82}, 904 (1999). \n\\bibitem{marshak} S. Okubo and R. E. Marshak, Prog. Theor. Phys. {\\bf 87},\n 1059 (1992). \n\\bibitem{natural} M. A. B. Beg and H.-S. Tsao, Phys. Rev. Lett. {\\bf 41},\n 278 (1978); H. Georgi, Hadronic J. {\\bf 1}, 155 (1978); R. N. \n Mohapatra and G. Senjanovic, Phys. Lett. {\\bf B79}, 283 (1978);\n G. Segre and A. Weldon, Phys. Rev. Lett. {\\bf 42}, 1191 (1979);\n S. M. Barr and P. Langacker, Phys. Rev. Lett. {\\bf 42}, 1654 (1979);\n A. E. Nelson, Phys. Lett. {\\bf B136}, 387 (1984);\n S. M. Barr, Phys. Rev. Lett. {\\bf 53}, 329 (1984).\n\\bibitem{pq} R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. {\\bf 38}, 1448\n (1977).\n\\bibitem{vw} C. Vafa and E. Witten, Phys. Rev. Lett. {\\bf 53}, 535 (1983).\n\\bibitem{gr} H. Georgi and L. Randall, Nucl. Phys. {\\bf B276}, 241 (1986). \n\\bibitem{ww} S. Weinberg, Phys. Rev. Lett. {\\bf 40}, 223 (1978);\n F. Wilczek, Phys. Rev. Lett. {\\bf 40}, 279 (1978).\n\\bibitem{peccei} R. D. Peccei, in {\\it Proc. 19th ICHEP Meeting (Aug. 23--30,\n 1978)}, ed. H. Homma et al (Phys. Soc. of Japan, Tokyo, 1979), p.1045. \n\\bibitem{invisible} J. E. Kim, Phys. Rev. Lett. {\\bf 43}, 103 (1979); M. A.\n Shifman, A. I. Vainstein and V. I. Zakharov, Nucl. Phys. {\\bf B166},\n 493 (1980).\n\\bibitem{dfsz} M. Dine, W. Fischler and M. Srednicki, Phys. Lett. {\\bf B104},\n 199 (1981); A. P. Zhitnitskii, Sov. J. Nucl. Phys. {\\bf 31}, 260 (1980).\n\\bibitem{astro} G. Raffelt and D. Seckel, Phys. Rev. Lett. {\\bf 60}, 1793\n (1988); M. S. Turner, Phys. Rev. Lett. {\\bf 60}, 1797 (1988);\n Mayle et al, Phys. Lett. {\\bf B203}, 188 (1988). \n\\bibitem{cos} J. Preskill, M. B. Wise\n and F. Wilczek, Phys. Lett. {\\bf B120}, 127 (1983); L. F. Abbott and\n P. Sikivie, Phys. Lett. {\\bf B120}, 133 (1983); M. Dine and W. Fischler,\n Phys. Lett. {\\bf B120}, 137 (1983).\n\\bibitem{comp} J. E. Kim, Phys. Rev. {\\bf D31}, 1733 (1985); K. Choi and \n J. E. Kim, Phys. Rev. {\\bf D32}, 1828 (1985).\n\\bibitem{witten} E. Witten, Phys. Lett. {\\bf B149}, 351 (1984); Phys. Lett.\n {\\bf B153}, 243 (1985).\n\\bibitem{quint} J. E. Kim, JHEP {\\bf 9905}, 022 (1999). \n\\bibitem{sikivie} P. Sikivie, Phys. Rev. Lett. {\\bf 48}, 1156 (1982); K. Choi \n and J. E. Kim, Phys. Rev. Lett. {\\bf 55}, 2637 (1985).\n\\bibitem{ekn} J. Ellis, J. E. Kim and D. V. Nanopoulos, Phys. Lett. {\\bf B145},\n 181 (1984). \n\\bibitem{green} M. B. Green and J. H. Schwarz, Phys. Lett. {\\bf 149}, 117 \n (1984).\n\\bibitem{choikim} K. Choi and J. E. Kim, Phys. Lett. {\\bf B154}, 393 (1985). \n\\bibitem{witten1} E. Witten, Phys. Lett. {\\bf 153}, 243 (1985); K. Choi\n and J. E. Kim, Phys. Lett. {\\bf B165}, 71 (1985).\n\\bibitem{mth} K. Choi, Phys. Rev. {\\bf D56}, 6658 (1997).\n\\bibitem{wen} X. G. Wen and E. Witten, Phys. Lett. {\\bf B166}, 397 (1988).\n\\bibitem{lalak} Z. Lalak, S. Lavignac and H. P. Nilles, Nucl. Phys.\n {\\bf B559}, 48 (1999). \n\\bibitem{shafi} G. Lazarides, C. Panagiotakopoulos and Q. Shafi, \n Phys. Rev. Lett. {\\bf 58}, 1707 (1987).\n\\bibitem{gkn} H. Georgi, J. E. Kim and H. P. Nilles, Phys. Lett.\n {\\bf B437}, 325 (1998). \n\\bibitem{kang} A. Patziris and K. Kang, Phys. Rev. {\\bf D33}, 3509 (1986).\n\\bibitem{choikang} K. Choi, K. Kang and J. E. Kim, Phys. Rev. Lett. {\\bf 62},\n 849 (1989). \n\\bibitem{review} J. E. Kim, Phys. Rep. {\\bf 150}, 1 (1987). \n\\bibitem{sik83} P. Sikivie, Phys. Rev. Lett. {\\bf 51}, 1415 (1983);\n ibid 52, 695(E) (1984).\n\\bibitem{search} J. E. Kim, Phys. Rev. {\\bf D58}, 055006 (1998).\n\\bibitem{shellard} R. A. Battye and E. P. S. Shellard, Phys. Rev. Lett.\n {\\bf 73}, 2954 (1994).\n\\bibitem{perl} S. Perlmutter et al, Astrophys. J. {\\bf 483}, 565 (1997).\n\\bibitem{kim} J. E. Kim, hep-ph/9907528.\n\n\\end{thebibliography}"
}
] |
astro-ph0002194
|
Resonant inverse Compton scattering by secondary pulsar plasma
|
[
{
"author": "Y.E.~Lyubarskii"
},
{
"author": "S.A.~Petrova"
}
] |
We consider resonant inverse Compton scattering of thermal photons by secondary particles above the pulsar polar gap. At neutron star temperatures higher than $10^5$ K the process appears to be an essential energy loss mechanism for the particles. The distribution function of the secondary plasma particles is found to be strongly affected by the scattering. It becomes two-humped implying the development of two-stream instability. The resonantly upscattered Compton photons are found to gain energy of 1--10 MeV forming an additional component in the pulsar gamma-ray spectrum. The corresponding gamma-ray flux is estimated as well. %\keywords{plasmas---scattering---pulsars: general---gamma-rays: theory}
|
[
{
"name": "ms.tex",
"string": "\n\\documentstyle[graphicx]{article}\n%\\documentstyle{l-aa}\n%\\input aa_symb\n\n\\begin{document}\n%\\thesaurus{02.16.1, 02.19.2, 08.16.6, 13.07.3}\n\\title{Resonant inverse Compton scattering by secondary pulsar plasma}\n\\author{ Y.E.~Lyubarskii, S.A.~Petrova }\n\\date{Institute of Radio Astronomy, Chervonopraporna St.4, Kharkov, 310002 Ukraine}\n\n\\maketitle\n\\begin{abstract}\nWe consider resonant inverse Compton scattering of thermal photons by\nsecondary particles above the pulsar polar gap. At neutron star\ntemperatures higher than $10^5$ K the process appears to be an essential\nenergy loss mechanism for the particles. The distribution function of the\nsecondary plasma particles is found to be strongly affected by the scattering.\nIt becomes two-humped implying the development of two-stream instability. The\nresonantly upscattered Compton photons are found to gain energy of\n1--10 MeV forming an additional component in the pulsar gamma-ray spectrum. The\ncorresponding gamma-ray flux is estimated as well.\n%\\keywords{plasmas---scattering---pulsars: general---gamma-rays: theory}\n\\end{abstract}\n\n\\section{Introduction}\nRotation of a highly magnetized neutron star is known to induce a strong\nelectric field, which intensely accelerates charged particles. According to the\ncustomary polar gap models (Ruderman \\& Sutherland 1975, Arons \\& Scharlemann\n1979), the acceleration takes place near the neutron star surface above the polar\ncap, the Lorentz-factor of the primary particles increasing up to $\\sim 10^6$.\nThe particles move along the magnetic lines and emit curvature photons,\nwhich initiate pair-production cascade. The first electron-positron\npairs created screen the accelerating electric field, so that at higher altitudes the\nparticle energy remains unaltered; the typical Lorentz-factors of the secondary\nplasma are $\\sim 10-10^4$.\n\nRecent observations testify to thermal soft X-ray emission from some pulsars\nindicating that the neutron stars can be rather hot, $T\\sim 5\\cdot 10^5$ K,\nwhile the polar caps can have still higher temperatures scaling a few times\n$10^6$ K (Cordova {\\it et al.} 1989, Ogelman 1991, Halpern \\& Holt 1992, Finley\n{\\it et al.} 1992, Halpern \\& Ruderman 1993, Ogelman \\& Finley 1993,\nOgelman {\\it et al.} 1993, Yancopoulos {\\it et al.} 1994, Ogelman 1995,\nGreiveldinger {\\it et al.} 1996). Such high temperatures of the neutron star surface\nare also predicted theoretically (Alpar {\\it et al.} 1984, Shibazaki \\& Lamb\n1989, Van Riper 1991, Page \\& Applegate 1992, Umeda {\\it et al.} 1993, Halpern\n\\& Ruderman 1993). The thermal X-ray photons should suffer inverse Compton\nscattering off the primary particles in the polar gap. In the presence of a\nstrong magnetic field the scattering cross-section is essentially enhanced,\nif the photon energy in the particle rest frame equals the cyclotron energy\n(Herold 1979, Xia {\\it et al.} 1985). For the pulsars with hot polar caps the\nresonant Compton scattering in the polar gap was found to be rather efficient\n(Kardashev {\\it et al.} 1984, Xia {\\it et al.} 1985, Daugherty \\& Harding\n1989, Dermer 1990,\nSturner 1995, Chang 1995). Firstly, it was recognized as an essential mechanism\nfor energy loss of primary particles accelerating in the polar gap.\nSecondly, inverse Compton scattering was found to condition the gap formation,\nsince the pair production avalanche may be triggered by the upscattered\nCompton photons rather than by curvature photons (Zhang \\& Qiao 1996, Qiao\n\\& Zhang 1996, Luo 1996, Zhang {\\it et al.} 1997).\n\nAs shown by Sturner (1995), given typical values of neutron star temperature\nand surface magnetic field, the resonant Compton scattering is the\nstrongest for particle Lorentz-factors $\\sim 10^2-10^3$. Theoretical models\n(Van Riper 1991, Page \\& Applegate 1992, Umeda {\\it et al.} 1993) suggest\nthat the typical temperatures of the neutron star surface are as high as a few\ntimes $10^5$ K. Hence, the scattering is likely to be essential for the\nsecondary plasma in most of the pulsars. Daugherty \\&\nHarding (1989), Zhang {\\it et al.} (1997)\ntraced the evolution of the Lorentz-factor of secondary particles\non account of magnetic inverse Compton scattering above the polar gap. Our\naim is to investigate in more detail the influence of resonant inverse\nCompton scattering on the parameters of secondary plasma. For the resonant\ncharacter of the scattering, the evolution of particle Lorentz-factor with\nthe distance depends strongly on the initial particle energy. Since the\ndistribution function of the secondary plasma is generally believed to be\nrather broad (the Lorentz-factor ranges from $10$ to $10^4$), its evolution\non account of the Compton scattering is of a great interest. It will be\nshown that only particles with Lorentz-factors between 100 and 1000 are\nessentially decelerated in the course of\nthe resonant scattering forming a sharp peak at low energies. Particles with\nlarger Lorentz-factors are not decelerated at all. Thus,\nthe resultant distribution function of secondary particles becomes\ntwo-humped, giving rise to the two-stream instability.\n\nIn Sect. 2 we examine how the resonant inverse Compton scattering affects the\nLorentz-factor of a secondary particle at various pulsar parameters. Section 3\nis devoted to studying the evolution of the distribution function. The\nconditions for the development of the two-stream instability are also\ndiscussed. In Sect. 4 we estimate the gamma-ray luminosity caused by\nthe upscattered Compton photons. Section 5 contains a brief summary.\n\n\\section{Deceleration of secondary particles due to resonant inverse Compton\nscattering}\nConsider the flow of secondary plasma streaming along the open magnetic field\nlines above the polar gap. The neutron star is supposed to emit a blackbody\nradiation, which is scattered by the plasma particles. In a strong magnetic\nfield the scattering is particularly efficient, if the photon energy,\n$\\varepsilon mc^2$, satisfies the resonance condition:\n$$\n\\varepsilon\\gamma (1-\\beta\\cos\\theta)=\\varepsilon_B, \\eqno (1)$$\nwhere $\\gamma$ is the Lorentz-factor of the scattering particles, $\\beta$\nthe particle velocity in units of $c$, $\\theta$ the angle the photon makes\nwith the particle velocity, $\\varepsilon\\equiv B/B_{cr}$, with $B_{cr}=\nm^2 c^3/\\hbar e=4.414\\cdot 10^{13}$ G.\nAt the distance $z$ from the neutron star the rate of energy\nloss due to the resonant inverse Compton scattering can be written as\n(Sturner 1995):\n$$\n\\frac{d\\gamma}{dt}=4.92\\cdot 10^{11}\\frac{T_6B_{12}^2(z)}{\\beta\\gamma}\n$$$$\n\\times\\ln\\left[1-\\exp\\left(-\\frac{\\varepsilon_Bmc^2}\n{\\gamma (1-\\beta\\cos\\theta_c(z))kT}\\right)\\right]{\\rm s}^{-1}.\n\\eqno (2)$$\nHere $T_6$ is the neutron star temperature in units of $10^6$ K, $B_{12}(z)$\nthe magnetic field strength in units of $10^{12}$ G, $\\theta_c(z)$ the maximum\nincident angle of photons,\n$$\n\\cos\\theta_c=\\sqrt{1-\\frac{1}{(1+z/R)^2}}, \\eqno (3)$$\nwhere $R$ is the neutron star radius. Provided that the magnetic field is\ndipolar, $B_{12}(z)\\propto (1+z/R)^{-3}$.\n \nNumerical solutions of Eq. (2) are presented in Fig. 1.\n\n\n\n\n One can see that the\nresonant inverse Compton scattering is significant up to $z\\sim R$ and it\naffects the particle Lorentz-factor essentially. Note that the curves for\ndifferent initial Lorentz-factors are not similar to each other. In agreement\nwith Eq. (1), the larger the particle Lorentz-factor the lower is the energy\nof resonantly scattered photons. At $\\gamma_0=3000$ the energy of the resonant\nphotons is below $\\varepsilon_{max}=2.82kT/(mc^2)$, which corresponds to the\nmaximum in the photon distribution. As $\\gamma$ is decreasing with the altitude,\nthe resonant energy increases. Hence, the photon spectral density increases\nand the scattering becomes more efficient. However, at distances $z\\sim R$ it\nceases due to the essential shrinking of the solid angle subtended by the\nneutron star. If the initial Lorentz-factor is $100$, the energy of resonant\nphotons is above $\\varepsilon_{max}$ and further increases with the altitude,\nso that the scattering gradually ceases.\n\nTheoretical models predict that the polar cap region should be significantly\nhotter than the rest surface of the neutron star ({\\it e.g.} Cheng \\& Ruderman 1980,\nArons 1981, Alpar {\\it et al.} 1984, Umeda {\\it et al.} 1993, Luo 1996).\nHowever, the luminosities observed from the hot spots appear to be too small\n(Finley {\\it et al.} 1992, Halpern \\& Ruderman 1993, Becker \\& Trumper 1993,\nYancopoulos {\\it et al.} 1994, Greiveldinger {\\it et al.} 1996).\nThe latter is usually interpreted as a consequence of small hot spot radii\n({\\it e.g.} Yancopoulos {\\it et al.} 1994, Greiveldinger {\\it et al.} 1996).\nAs is evident from Fig.1, for typical hot spot parameters\nthe particle energy loss is mainly determined by the scattering\nof the photons from the whole neutron star rather than by the scattering\nof hot spot photons.\nSo hereafter we take into account only the photons from the whole neutron star\nsurface keeping in mind that the influence of hot spot photons can\nsomehow alter our quantitative results, while the qualitative picture should\nremain the same.\n\n\nIt should be pointed out that the evolution of Lorentz-factor with the\naltitude shown in Fig. 1 is somewhat different from that reported by\nZhang {\\it et al.}(1997)(see their Fig. 1). These authors claim that\nat distances $z\\sim{\\rm few} R$ the particles suffer severe nonresonant\nmagnetized scattering, which leads to the drastic decrease of the\nfinal Lorentz-factor. In fact, the rate of energy loss on account of\nnonresonant magnetic scattering increases with decreasing the field strength\nas $B_{12}^{-2}(z)$ (see Eq. (5) in Sturner 1995). However, this equation is\napplicable only if in the particle rest frame the cyclotron energy exceeds\nthe energy of most of photons, $\\varepsilon_B >\\varepsilon\\gamma (1-\\beta\\cos\n\\theta_c)$. For the photon energies at the peak of the Planck distribution,\n$\\varepsilon\\approx 2.82kT$, the latter condition can be rewritten as\n$4\\cdot 10^{-2}B_{12}(z)/(T_6\\gamma_3(1-\\beta\\cos\\theta_c))>1$, with\n$\\gamma_3\\equiv\\gamma/10^3$. Taking $T_6=0.5$, $\\gamma_3=3$, $B_{12}=0.1$\n(Zhang {\\it et al.} 1997, Fig. 1a), one can obtain that at $z=10R$ the\nleft-hand side of this inequality is $5\\cdot 10^{-5}$, while at $z=0$ it\nequals $3\\cdot 10^{-4}$. So even at the stellar surface most of the photons\nscatter in the Thomson regime rather than in the magnetic one. The rate of\nenergy loss out of the Thomson scattering is found to be\n$$\n\\frac{d\\gamma_T}{dt}=-30\\gamma T_6^4(1-\\beta\\cos\\theta_c)^3\\,{\\rm s}^{-1},\n\\eqno (4)$$\nshowing that this process is inefficient. Thus the resonant inverse Compton\nscattering is the only significant energy loss mechanism for the secondary\nparticles in pulsar magnetospheres.\n\nWe believe that the particles start deceleration just above the polar\ngap. In general the gap thickness is supposed to be of the order of the polar\ncap radius (Ruderman \\& Sutherland 1975) or even larger (Arons \\& Scharlemann\n1979). The energy loss of secondary particles due to the resonant\ninverse Compton scattering above the gap should certainly be influenced by\nthe adopted value of the gap height. In Fig. 2 we show the final\nLorentz-factors versus the gap height. One can see that the dependence is\nsufficiently weak, therefore, below we fix $z_0$ at $10^{-2}R$.\n\nIn contrast with the gap height, such pulsar parameters as the star temperature\nand magnetic field strength can influence particle deceleration essentially.\nIn Fig. 3 we present the dependences of the normalized final Lorentz-factor\non the neutron star temperature at various magnetic field strengths.\nApparently, at the temperatures $<10^5$ K the scattering is inefficient yet,\nwhile at higher temperatures it becomes significant. Note that at various\ninitial Lorentz-factors ($\\gamma_0=100$ and $3000$) the scattering efficiency\nversus magnetic field strength is essentially different. The particles with\n$\\gamma_0=100$ resonantly scatter the photons from the Wien region. Then the\nweaker the field strength, the lower is the energy of resonant photons and,\ncorrespondingly, the higher is the photon spectral density and the larger\nis the particle energy loss (see Fig. 3a). At $\\gamma_0=3000$ the resonant\nenergy lies in the Rayleigh-Jeans region. So the scattering is more efficient\nfor higher magnetic field strengths, since the photon spectral density\nincreases with the energy (see Fig. 3b).\n\nFor the resonant character of the scattering the particle energy loss\ndepends strongly on the initial Lorentz-factor. Figure 4 shows the final\nLorentz-factor versus the initial one for various neutron star temperatures\nand magnetic field strengths. At $\\gamma_0\\sim 10$ as well as at $\\gamma_0\n\\sim 10^4$ the resonant scattering appears to be inefficient. Provided that the\nscattering is intense ($\\gamma_0\\sim 10^2-10^3$), the final Lorentz-factor\nappears to be independent of the initial one. According to Fig. 4a, the length\nof the plateau increases with the star temperature. In fact, the higher\ntemperature implies the larger amount of photons at every energy, the\nscattering becoming more efficient. As can be seen from Fig. 4b, the increase\nof the magnetic field strength leads to the shift of the plateau toward a\nhigher energy; this is certainly consistent with the resonance condition (1).\n\n\\section{The distribution function of the secondary plasma as a result of\nresonant inverse Compton scattering}\nSince the energy loss depends essentially on the initial particle energy,\nwe are to investigate the evolution of the distribution function of\nsecondary particles as a result of the resonant inverse Compton scattering.\nConservation of the number of particles along a phase trajectory\nimplies that\n$$\nf(z,\\,\\gamma)d\\gamma=f(z_0,\\,\\gamma_0)d\\gamma_0\\,,$$\nwhere $f(z,\\,\\gamma)$ is the particle distribution function and the\nsubscript ''0'' refers to the initial values. So looking for the phase\ntrajectories of individual particles one can reconstruct the distribution\nfunction at any height $z$. We are particularly interested in the final\ndistribution function arising at distances, where the resonant scattering\nceases.\n\nLet us begin with the evolution of a waterbag distribution function:\n$$\nf(z_0,\\,\\gamma_0)=\n\\left\\{\n\\begin{array}{l}\n\\frac{1}{\\gamma_{max}-\\gamma_{min}},\\quad\\qquad\\qquad \\gamma_{min}\\leq\\gamma\\leq\n\\gamma_{max},\\\\\n0\\,,\\,\\quad\\qquad\\qquad\\qquad \\gamma <\\gamma_{min}\\,{\\rm and }\\,\\gamma >\\gamma_{max},\\\\\n\\end{array}\n\\right.$$\nwith $\\gamma_{min}=10$, $\\gamma_{max}=10^4$.\nThe final distribution functions\nat various pulsar\nparameters are plotted in Fig. 5. The particles with $\\gamma\\sim 10^2-10^3$\nare essentially decelerated due to the scattering, the final energies becoming\nequal (see also Fig. 4). These particles form the sharp peak at $\\gamma\n<10^2$. For the Lorentz-factors of a few thousand the scattering becomes\ninefficient and the distribution function remains almost unaltered. Thus,\nthe resonant inverse Compton scattering leads to the two-humped distribution\nfunction of the secondary plasma. At higher neutron star temperatures the\nmain peak of the function shifts towards the lower energies and the humps\nbecome more prominent. The magnetic field strength variation also results\nin the shift of the main peak. For the more realistic distribution function\nresembling that found by Arons (1980),\n$$\nf(\\gamma)=\n\\left\\{\n\\begin{array}{l}\n\\exp\\left(-10\\frac{\\gamma_m-\\gamma}{\\gamma_m}\\right),\\quad\\qquad\\qquad 10\\leq\\gamma\\leq\n\\gamma_m,\\\\\n(\\gamma/\\gamma_m)^{-3/2},\\,\\quad\\qquad\\qquad\\qquad \\gamma_m\\leq\\gamma\\leq\\gamma_c,\\\\\n(\\gamma_c/\\gamma_m)^{-3/2}\\exp\\left(-\\frac{\\gamma-\\gamma_c}{\\gamma_c}\\right),\n\\quad \\gamma_c\\leq\\gamma\\leq 10^4,\\\\\n\\end{array}\n\\right.\\eqno (5)$$\nwith $\\gamma_m=10^2$, $\\gamma_c=10^{3.5}$, the evolution on account of\nthe resonant inverse Compton scattering is qualitatively the same (see Fig. 6).\n\nWe next examine the dispersion properties of the plasma with the evolved\ndistribution function. For simplicity let us assume that the plasma consists\nof the two particle flows characterized by the number densities $n_a$,\n$n_b$ and by the Lorentz-factors $\\gamma_a$, $\\gamma_b$ ($\\gamma_a <\\gamma_b$).\nGiven the infinitely strong magnetic field, the dispersion relation is as\nfollows (see, {\\it e.g.} Lyubarskii 1995):\n$$\n\\frac{\\omega_{pa}^2}{(\\omega -kv_a)^2\\gamma_a^3}+\\frac{\\omega_{pb}^2}\n{(\\omega -kv_b)^2\\gamma_b^3}=1. \\eqno (6)$$\nHere $\\omega$ is the frequency, $k$ the wave number, $v_{a,b}$ are the\nparticle velocities, $\\omega_{pa,b}$ the plasma frequencies given by the\ncustomary expression:\n$$\n\\omega_{pa,b}=\\sqrt{\\frac{4\\pi n_{a,b}e^2}{m}}, \\eqno (7)$$\nwhere $e$ is the electron charge, $m$ the electron mass. As is evident from\nEq. (6), the dispersion properties of the plasma are mainly determined by one\nof the particle flows on condition that\n$$\n\\frac{n_a}{\\gamma_a^3}\\gg\\frac{n_b}{\\gamma_b^3}, \\eqno (8)$$\nrather than $n_a\\gg n_b$. This is because of the great inertia of the\nfast particles performing one-dimensional motion in the superstrong magnetic\nfield. For the distribution functions plotted in Fig. 5 and 6 $n_a$ and\n$n_b$ are comparable, while $\\gamma_a/\\gamma_b\\sim 10^{-1}-10^{-2}$. Therefore\nthe low-energy particles of the main peak almost completely determine the\ndispersion properties of the plasma.\n\nThe two-humped distribution function implies the possibility of the\ntwo-stream instability. Provided that the contribution of one of the plasma\nflows to the plasma dispersion is small ({\\it i.e.} Eq. (8) is valid), the\ngrowth rate of the instability takes the form (Lominadze \\& Mikhailovskii 1979,\nCheng \\& Ruderman 1980):\n$$\n{\\rm Im} \\omega\\approx\\left(\\frac{n_b}{n_a}\\right)^{1/3}\\frac{\\omega_{pa}}\n{\\gamma_a^{1/2}\\gamma_b}. \\eqno (9)$$\nThe two-stream instability results in an essential development of\ninitial perturbations on condition that\n$$\n\\frac{R_c}{c}{\\rm Im}\\omega> 10, \\eqno (10)$$\nwhere $R_c$ is the characteristic scale length for the increase of\nperturbations.\n\nIt is convenient to normalize the number density of the secondary plasma by\nthe Goldreich-Julian charge density:\n$$\nn=\\frac{\\kappa B}{Pce}, \\eqno (11)$$\nwhere $\\kappa$ is the multiplicity factor of the secondary plasma, $P$ the\npulsar period. The\nlatter equation can be rewritten as:\n$$\nn=6.25\\cdot 10^{13} P^{-1}\\kappa_3B_{12}(1+z/R)^{-3}\\, {\\rm cm^{-3}},\\eqno (12)$$\nwhere $\\kappa_3\\equiv\\kappa/10^3$. Using Eqs. (9) and (12) in Eq. (10) we\nreduce the condition for the efficient instability development to the form:\n$$\n\\frac{\\kappa_3B_{12}}{PR_{c7}\\gamma_{b3}^2\\gamma_{a2}}>4\\cdot 10^{-4}.\n\\eqno (13)$$\nHere $R_{c7}\\equiv R_c/10^7{\\rm cm}$, $\\gamma_{b3}\\equiv \\gamma_b/10^3$,\n$\\gamma_{a2}\\equiv\\gamma_a/10^2$ and it is assumed that $(n_b/n_a)^{1/3}\n\\approx 1$. As can be seen from Eq. (13), at typical pulsar parameters the\ntwo-stream instability can develop readily providing the increase of plasma\noscillations. The latter can be transformed into electromagnetic waves,\nthus giving rise to pulsar radio emission.\n\nIt should be mentioned that two-steram instability has always been one of\nthe most popular mechanisms for pulsar radio emission.\nFor more than two\ndecades a number of scenarios for the instability development were proposed.\nThe first and the most natural one involves the instability caused by\nthe flows of primary and secondary pulsar plasma (Ruderman \\& Sutherland 1975).\nHowever, the growth rate of this instability appears to be too small\nbecause of enormous inertia of the high-energy primary particles (Benford \\&\nBuschauer 1977). Cheng \\& Ruderman (1977) considered the two-stream\ninstability arising in the secondary plasma due to the difference in the\nvelocities of electrons and positrons moving along the curved magnetic lines.\nHowever, this difference is insufficient to cause the instability, since the\nparticle distribution functions are too broad (Buschauer \\& Benford 1977).\nLyubarskii (1993) suggested that current and charge density adjustment\nin pulsar\nmagnetosphere leads to the backward particle flow, which\ncauses intense two-stream instability. However, numerical simulations of the\nplasma flow in the open field line tube are necessary to prove this idea.\nGiven nonstationary generation of the secondary plasma the particles are\nconfined to the separate clouds, and the fastest particles of a cloud can\noutstrip the slower particles of the previous cloud giving rise to the\ntwo-stream instability (Usov 1987, Ursov \\& Usov 1988). Up to now it is not\nclear whether the instability initiated in such a way can account for pulsar\nradio emission, since the nonstationarity of plasma generation is not studied\nin detail yet.\nThe present\npaper suggests one more possibility of two-stream instability in pulsars,\nwhich is based on the selective energy loss of particles as a result of\nresonant inverse Compton scattering. Note that in this model the instability\narises naturally, with no additional assumptions being involved.\n\n\\section{Gamma-ray luminosity provided by resonantly\nupscattered Compton photons}\nThe photons produced by the resonant inverse Compton scattering have\nthe energies\n$$\nE\\sim\\gamma\\epsilon_Bmc^2\\sim B_{12}\\gamma_2\\,{\\rm MeV},\\eqno (14)$$\nso that typically $E\\sim 1-10$ MeV. Note that the curvature gamma-photons\nproduced in the polar gap as well as the photons upscattered by the primary\nparticles have essentially higher energies, $E\\sim 100$ MeV. Hence, the resonant\nscattering by secondary plasma results in an additional low-energy component in pulsar\ngamma-ray spectrum. The spectrum of this component in the case of some\nspecific distribution functions of the scattering particles is obtained\nby Daugherty \\& Harding (1989).\nIn general, the low-energy tail of this component spreads even to the\nX-ray band on account of the photons resonantly scattered at distances\n$z>R$, where the magnetic field strength decreases essentially. However,\nthese photons are very few, since at $z>R$ the scattering rate decreases\nsignificantly due to the shrinking of the solid angle subtended by the\nneutron star.\n\nGiven that the scattering is efficient, most of the energy of the secondary\nplasma should be transferred to the low-energy gamma-rays. The luminosity\nprovided by the upscattered photons can be estimated as follows:\n$$\nL=nSmc^3\\Delta\\gamma,\\eqno (15)$$\nwhere $S$ is the cross-sectional area of the open field line tube,\n$$\nS=\\frac{\\pi R^3}{R_L},\n\\eqno (16)$$\n$R_L$ is the light cylinder radius, $\\Delta\\gamma$ the difference between\nthe Lorentz-factors of the\nparticles, which mainly contribute to the final and initial plasma energy,\n$\\Delta\\gamma\\sim 10^2-10^3$. Substituting Eqs. (12) and (16) into Eq. (15)\nwe find:\n$$\nL=0.942\\cdot 10^{30}\\frac{B_{12}R_6^3\\kappa_3\\gamma_3}{P^2}\\, {\\rm ergs/s}.\n\\eqno (17)$$\n\nAlthough in the particle rest frame the photons are scattered in all\ndirections, in the laboratory frame they are beamed along the particle velocity.\nSo the opening angle of the gamma-ray beam is given by\n$\\varphi =3\\sqrt{R/R_L}.$\nThe averaged observed photon flux, $F$, is related to the luminosity as\n$$\nF=\\frac{L\\varphi}{2\\pi\\Omega d^2E\\Delta E},\\eqno (18)$$\nwhere $\\Omega =\\pi\\varphi^2/4$ is the solid angle occupied by the beam of\nupscattered photons,\n$d$ the distance to the pulsar, $\\Delta E$ the energy band. Taking into\naccount Eq. (17), Eq. (18) can be rewritten as\n$$\nF=3\\cdot 10^{-10}\\frac{B_{12}R_6^{5/2}\\gamma_3\\kappa_3}{P^{3/2}d_3^2 E_6^2}\\,\n{\\rm photons/(cm^2\\cdot s\\cdot keV)}, \\eqno (19)$$\nwhere $d_3\\equiv d/10^3\\,{\\rm pc}$, $E_6\\equiv E/1\\,{\\rm MeV}$.\n\nFor most pulsars the flux given by Eq. (19) is too low to be detected.\nAt present the detectors of the Compton gamma-ray observatory are the most\nsensitive to the low-energy gamma-ray emission (OSSE at 0.05--10 MeV and\nCOMPTEL at 1--30 MeV). At 1 MeV the source sensitivity of OSSE is only\n$2\\cdot 10^{-7}$ photons/(${\\rm cm^2\\cdot s\\cdot keV}$) (Gehrels \\&\nShrader 1996). In the observations reported by Kuiper {\\it et al.} (1996) the\nflux from Geminga in the band of 3--10 MeV was found to be $10^{-7}E_6^{-2}$\nphotons/(${\\rm cm^2\\cdot s\\cdot keV}$). Substituting Geminga parameters\n($P=0.237$ s, $B_{12}=3.3$, $d_3=0.15$) into Eq. (19) one can obtain the flux\nprovided by the upscattered Compton photons: $F=3.8\\cdot 10^{-7}\\kappa_3\n\\gamma_3R_6^{5/2}E_6^{-2}$ photons/(${\\rm cm^2\\cdot s\\cdot keV}$), which is\nconsistent with the one detected.\n\n\\section{Conclusions}\nWe have investigated resonant inverse Compton scattering by secondary\npulsar plasma. The process is found to cause the efficient energy loss of\nthe secondary particles given the neutron star temperatures $>10^5$ K, so\nthat our results are applicable to most pulsars. For the resonant\ncharacter of the scattering, the energy loss depends strongly on the initial\nparticle energy. At $\\gamma_0\\sim 10^2-10^3$ the scattering is the most\nessential, the final Lorentz-factors of the particles being independent of\nthe initial ones.\n \nThe distribution function of the secondary plasma is significantly altered by\nthe resonant inverse Compton scattering. It is shown that ultimately the\ndistribution function becomes two-humped. The main peak at $\\gamma\\sim 10^2$\nis very sharp. It is formed by particles which suffered severe energy\nloss on account of the scattering. Another hump is sufficiently broad. It is\nassociated with the particles, whose Lorentz-factors are almost unaltered by\nthe scattering. 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}
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[
{
"name": "astro-ph0002194.extracted_bib",
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}
] |
astro-ph0002195
|
ISO-SWS spectra of galaxies: continuum and features \thanks{Based on observations with ISO, an ESA project with instruments funded by ESA member states (especially the PI countries: France, Germany, the Netherlands and the United Kingdom) and with participation of ISAS and NASA.}
|
[
{
"author": "E. Sturm \\inst{1,}\\inst{2}"
},
{
"author": "{D. Lutz \\inst{1}}"
},
{
"author": "{D. Tran \\inst{1}}"
},
{
"author": "{H. Feuchtgruber \\inst{1}}"
},
{
"author": "{R. Genzel \\inst{1}}"
},
{
"author": "{D. Kunze \\inst{1}}"
},
{
"author": "{A.F.M. Moorwood \\inst{3}}"
},
{
"author": "{M.D. Thornley \\inst{4}}"
}
] |
We present an inventory of mid-infrared spectral features detected in high resolution (R$\sim$1500) ISO-SWS 2.4--45$\mu$m spectra of the galaxies \object{M\,82}, \object{NGC\,253}, \object{Circinus}, \object{NGC\,1068}, and a position in the \object{30\,Doradus} region of the Large Magellanic Cloud. We discuss their identifications and highlight possible relations between these features and the physical state of the interstellar medium in galaxies. The spectral features vary considerably from source to source in presence and relative strength. Emission features are largely absent in the intense radiation field close to an AGN. Compared to normal infrared-selected starbursts, they also seem to be weaker in a low metallicity, intensely star forming environment. The large number of features beyond 13$\mu$m is remarkable. Some of the features %are unambiguously detected for the first time in astronomical objects and have -- to our knowledge -- not been reported before in astronomical objects. In the 5--13$\mu$m region, emission from unidentified infrared bands (UIBs), usually ascribed to aromatic molecules, and apparent silicate absorption dominate the spectrum. The density of features makes it difficult to determine the continuum, particularly in ground-based data of limited wavelength coverage. In fact the apparent depth of the 9.7$\mu$m silicate absorption may be overestimated in the presence of UIB emission, as we demonstrate by comparing the spectrum of M\,82 to the (absorption free) spectrum of the reflection nebula \object{NGC\,7023}. No strong silicate absorption is present in M\,82. The (very small grain) dust continuum under the UIB emission in our starburst templates can be modeled by a simple power law, starting at wavelengths between 8 and 9$\mu$m. We find broad H$_2$O-ice absorption features at 3.0$\mu$m in M\,82 and NGC\,253. Their optical depths (relative to the visual extinction) indicate that the lines of sight towards these galaxies have similar properties as the line of sight towards the Galactic Center. %: a mixture of diffuse ISM and molecular cloud %extinction, with some %variance in the relative weight for different lines of sight. The active galaxy NGC\,1068 exhibits a clearly different spectrum of absorption features, indicating different physical conditions in the obscuring regions of this AGN compared to the starburst templates. The spectra are valuable templates for future mid-infrared missions. We smooth our data to simulate low resolution spectra as obtained with ISOCAM-CVF, ISOPHOT-S, and in the future with the low resolution mode of SIRTF-IRS, and use our high spectral resolution information to highlight possible identification problems at low resolving power that are caused by coincidences of lines and features. The spectra are available in electronic form from the authors. \keywords{ Infrared: ISM: continuum -- Infrared: ISM: lines and bands -- % Galaxies: ISM -- Galaxies: individual: M\,82 -- Galaxies: individual: NGC\,253 -- Galaxies: individual: Circinus -- Galaxies: individual: NGC\,1068 }
|
[
{
"name": "sturm.tex",
"string": "\\documentclass{aa}\n%\\documentclass[referee]{aa}\n\\usepackage{graphics}\n\n\\begin{document}\n\n \\thesaurus{03\n (13.09.3);\n (13.09.4);\n% 11\n% (11.09.4);\n (11.09.1 M\\,82);\n (11.09.1 NGC\\,253);\n (11.09.1 Circinus);\n (11.09.1 NGC\\,1068)} \n%\n \\title{ISO-SWS spectra of galaxies: continuum and features\n \\thanks{Based on observations with ISO, an ESA project with\n instruments funded by ESA member states (especially\n the PI countries: France, Germany, the Netherlands and\n the United Kingdom) and with participation of ISAS and\n NASA.} }\n\n \\author{E. Sturm \\inst{1,}\\inst{2}\n \\and{D. Lutz \\inst{1}}\n \\and{D. Tran \\inst{1}}\n \\and{H. Feuchtgruber \\inst{1}}\n \\and{R. Genzel \\inst{1}}\n \\and{D. Kunze \\inst{1}}\n \\and{A.F.M. Moorwood \\inst{3}}\n \\and{M.D. Thornley \\inst{4}}}\n\n \\offprints{sturm@mpe.mpg.de}\n\n \\institute{Max-Planck-Institut f\\\"ur extraterrestrische Physik,\n Postfach 1603, D-85740 Garching, Germany\n \\and Infrared Processing and Analysis Center, \n MS 100-22, Pasadena, CA 91125, USA\n \\and European Southern Observatory,\n Karl-Schwarzschild-Str. 2, D-85748 Garching, Germany \n \\and National Radio Astronomy Observatory,\n 520 Edgemont Road, Charlottesville, VA 22903, USA}\n \n \\date{Received 19 October 1999 / Accepted 26 January 2000}\n\n \\maketitle\n\n \\begin{abstract}\n\nWe present an inventory of mid-infrared spectral features detected in\nhigh resolution (R$\\sim$1500) ISO-SWS 2.4--45$\\mu$m spectra of the \ngalaxies \\object{M\\,82}, \\object{NGC\\,253}, \\object{Circinus},\n\\object{NGC\\,1068}, and a position in the \\object{30\\,Doradus} region of the \nLarge Magellanic Cloud.\nWe discuss their identifications and highlight possible relations between\nthese features and the physical state of the interstellar medium in\ngalaxies. The spectral features vary considerably from source to source in \npresence and relative strength. Emission features are largely absent in \nthe intense radiation field close to an AGN. Compared to normal \ninfrared-selected starbursts, they also seem to be weaker in a\nlow metallicity, intensely star forming environment.\nThe large number of features beyond 13$\\mu$m is remarkable. \nSome of the features \n%are unambiguously detected for the first time in astronomical objects and \nhave -- to our knowledge -- not been \nreported before in astronomical objects. \n\nIn the 5--13$\\mu$m region, emission from unidentified infrared bands (UIBs),\nusually ascribed to\naromatic molecules, and apparent\nsilicate absorption dominate the spectrum. The density \nof features makes it\ndifficult to determine the continuum, particularly in ground-based data of \nlimited wavelength coverage. In fact \nthe apparent depth of the 9.7$\\mu$m\nsilicate absorption may be overestimated in the presence of UIB emission, as\nwe demonstrate by comparing the spectrum of M\\,82 to the (absorption free)\nspectrum of the reflection nebula \\object{NGC\\,7023}. \nNo strong silicate absorption is \npresent in M\\,82.\nThe (very small grain) dust continuum \nunder the UIB emission in our starburst templates \ncan be modeled by a simple power law, starting at wavelengths\nbetween 8 and 9$\\mu$m.\n\nWe find broad H$_2$O-ice absorption features at 3.0$\\mu$m in M\\,82 and \nNGC\\,253. Their optical depths (relative to the visual extinction) \nindicate that the lines of sight towards these galaxies have similar \nproperties as the line of sight\ntowards the Galactic Center.\n%: a mixture of diffuse ISM and molecular cloud\n%extinction, with some \n%variance in the relative weight for different lines of sight.\nThe active galaxy NGC\\,1068 exhibits a clearly different spectrum of \nabsorption features, indicating different\nphysical conditions in the obscuring regions of this AGN compared to the\nstarburst templates.\n\n\nThe spectra are valuable templates for future\nmid-infrared missions. \nWe smooth our data to simulate low resolution spectra as obtained\nwith ISOCAM-CVF, ISOPHOT-S, and in the future with the low resolution mode of\nSIRTF-IRS, and use our \nhigh\nspectral resolution information to highlight possible identification problems\nat low resolving power that are caused by coincidences of lines and features. \nThe spectra are available in electronic form from the authors.\n \\keywords{\n Infrared: ISM: continuum --\n Infrared: ISM: lines and bands --\n% Galaxies: ISM --\n Galaxies: individual: M\\,82 --\n Galaxies: individual: NGC\\,253 --\n Galaxies: individual: Circinus --\n Galaxies: individual: NGC\\,1068\n}\n\n \\end{abstract}\n\n%\n%________________________________________________________________\n\n\\section{Introduction}\nMid-infrared spectra of galaxies are rich in emission lines, and\ndisplay prominent broader emission and absorption features due to the presence\nof various solids and/or large molecules in their interstellar medium\n(ISM). Significant variation from source to source suggests \nthat these features may provide important\ndiagnostics of the ISM conditions in galaxies. \n\nThe ground based and Kuiper Airborne Observatory spectra of the \nprototypical starburst M\\,82 by Gillett et al. (1975) and Willner et al. (1977) \nfully established the existence of the\nmid-infrared `unidentified infrared bands' (UIB) at 6.2, 7.7, 8.6, \nand 11.3$\\mu$m\nin galaxy spectra. These emission bands are characteristic of C-C and C-H bonds\nin aromatic molecules. In this paper we will refer to them as \n`PAH features' \naccording to one of the most popular interpretations of their carrier, \npolycyclic aromatic hydrocarbon molecules\n\\footnote{Other suggested carriers include small grains of\nhydrogenated amorphous carbon (HACs), quenched carbonaceous composites (QCCs),\nor coal.}. \nThese detections and\nrelated work using the IRAS LRS (Cohen \\& Volk 1989) form the basic pre-ISO\nknowledge of mid-infrared spectral features in galaxies.\n\nConsiderable work has also been\ndone from the ground but has been limited to the features\nfound in atmospheric windows, mainly silicate absorption and PAH feature\nemission in the N band (e.g. Roche et al. 1991, and references therein) \nand the companion PAH feature\nin the L band (e.g. Moorwood 1986).\n%(e.g. Bridger, Wright \\& Geballe 1994).\nThe restriction\nto atmospheric windows increases problems in establishing the `continuum' on\nwhich the features are superposed. This is a nontrivial task, even with full\nwavelength coverage, due to the crowding of mid-infrared \nemission and absorption features (especially in the 10$\\mu$m region).\n\nWith the Short Wavelength Spectrometer SWS (de~Graauw et al. 1996) on\nboard\nthe Infrared Space Observatory ISO (Kessler et al. 1996) high spectral\nresolution observations with good signal-to-noise (S/N) were\nobtained for a number of bright galaxies. Their main\nadvantages lie in continuous wavelength coverage from 2.4 to 45$\\mu$m\nand in the possibility to clearly separate features from nearby\nemission lines.\n\nThe interpretation of\ngalaxy-integrated spectra strongly benefits from comparisons to similar\nobservations of galactic\nsources, sometimes spatially resolved, allowing\nbetter isolation of the physical mechanisms at work. Recent ISO spectra\n%which have been recently observed in\nof many galactic template objects, such as reflection\nnebulae (e.g. Boulanger et al. 1996, Cesarsky et al. 1996a, Verstraete et al.\n1996, Moutou et al. 1998), planetary nebulae and circumstellar regions\n(e.g. Beintema et al. 1996), and HII regions (Roelfsema et al. 1996,\nCesarsky et al. 1996b) have clearly demonstrated the importance of such\ntemplate spectra. They\n%provide a wealth of information and\nprove that PAHs\nare an ubiquitous part of the ISM. Additional information on emission features \nof crystalline silicates comes from similar template observations with ISO of \ne.g. planetary nebulae (Waters et al. 1998), evolved\nstars (Waters et al. 1996), young stars (Waelkens et al. 1996), or LBVs in \nthe LMC (Voors et al. 1999).\nAbsorption features (silicates, ices) have been found e.g. in the Galactic\ncenter (Lutz et al. 1996, Chiar et al. 2000), young stellar objects\n(d'Hendecourt et al. 1996, Whittet et al. 1996, Dartois et al. 1999), and \nin dark clouds in the solar neighborhood (Whittet et al. 1998).\n\nIn this paper we present an inventory of mid-infrared spectral features \ndetected in high resolution (R$\\sim$1500) ISO-SWS 2.4--45$\\mu$m spectra of the \nstarburst galaxies M\\,82 and NGC\\,253, the Seyfert 2 galaxies \nCircinus and NGC\\,1068, \nand a position in the 30\\,Doradus star forming region of the Large Magellanic \nCloud (Sect. \\ref{s:inventory}). \nWe briefly discuss possible feature identifications (Sect. \\ref{s:ident}) \nand highlight possible relations \nbetween these features and the physical state of the interstellar medium in\ngalaxies (Sect. \\ref{s:PAH_var}). \nWe also address the issue of the continuum determination and the \napparent depth of the silicate absorption at 9.7$\\mu$m (Sect. \n\\ref{s:continuum}). \nFinally (Sects. \\ref{s:lowres} and \\ref{s:conclusions}) we demonstrate\nthe use of these ISO spectra as templates for future \ninfrared missions such as SIRTF, with particular emphasis on \npotential identification problems\nat low resolving power that are caused by coincidences of lines and features.\n\nAll the spectra shown here exhibit a large number of atomic, ionic and\nmolecular emission lines. These have been or will be discussed elsewhere, \nalong with more details on observations and data processing\n(Circinus: Moorwood et al. 1996; M\\,82: Lutz et al. 1998b, Schreiber 1998;\nNGC\\,1068: Lutz et al. 2000; 30\\,Dor: Thornley et al., in prep.). \n\n%--------------------------------------------------------------------\n\n\\section{Observations and data reduction}\n\nThe objects discussed here have been observed as part of the ISO guaranteed \ntime project on bright galactic nuclei. Here we concentrate on full grating \nscans obtained in SWS01 mode, speed 4. This mode provides a full \n2.4--45$\\mu$m scan at resolving power of approximately 1000--2000.\nFor NGC\\,253, Circinus, and NGC\\,1068 the observations were centered on the\nnuclei. In the case of M\\,82 the observation was centered on the \nsouthwestern star formation \nlobe. For 30\\,Dor the apertures were lying roughly parallel to an ionized\nshell region, about 0.5\\arcmin\\/ away from the central stellar cluster.\nTable \\ref{tab:positions} summarizes the positions.\nNote that different parts of an SWS full grating scan are observed with\ndifferent aperture sizes\\footnote{The aperture sizes are\n14\\arcsec$\\times$20\\arcsec\\/ for 2.4--12.0$\\mu$m, 14\\arcsec$\\times$27\\arcsec\\/ \nfor 12.0--27.5$\\mu$m, 20\\arcsec$\\times$27\\arcsec\\/ for 27.5--29.0$\\mu$m, and\n20\\arcsec$\\times$33\\arcsec\\/ for 29.0--45$\\mu$m, with some wavelength overlap\nbetween the bands.}, varying between 14\\arcsec$\\times$20\\arcsec\\/ and \n20\\arcsec$\\times$33\\arcsec.\n\nWe have processed the data using the SWS Interactive Analysis (IA) system\n(Lahuis et al. 1998, Wieprecht et al. 1998) and the ISO Spectral Analysis\nPackage ISAP (Sturm et al. 1998). Dark current subtraction, scan direction \nmatching, and flatfielding have been done interactively, and noisy \ndetectors have been eliminated. In ISAP we clipped outliers and\naveraged the data of all 12 detectors for each AOT band, retaining the \ninstrumental resolution. For those wavelength ranges affected by fringes, the \naveraged spectra were defringed using the FFT or iterative sine fitting \noptions of the defringe module within ISAP. \n%More details about the observations and the data processing can be found\n%elsewhere (M\\,82: Schreiber 1998????; NGC\\,253: Thornley, in prep.; 30\\,Dor:\n%Thornley, in prep.; Circinus: Moorwood et al. 1996; NGC\\,1068: Lutz et al. \n%2000????).\n\n\\begin{table}\n\\caption[]{\\label{tab:positions} Summary of observed positions (J2000), \nand position angles.}\n%\\begin{footnotesize}\n%{\\scriptsize\n\\begin{flushleft}\n\\begin{tabular}{lllll}\n%\\begin{tabular}{llll}\n\\hline\\noalign{\\smallskip}\nObject & RA & Decl. & PA & remark\\\\\n%Object & RA & Decl. & \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nM\\,82 & 09$^h$55$^m$50.7$^s$ & 69\\degr40\\arcmin44.4\\arcsec & 245\\degr & 1 \\\\\nNGC\\,253 & 00$^h$47$^m$33.2$^s$ & -25\\degr17\\arcmin17.2\\arcsec & 28\\degr & 2 \\\\\n30\\,Dor & 05$^h$38$^m$46.0$^s$ & -69\\degr05\\arcmin07.9\\arcsec & 230\\degr & 3 \\\\\nCircinus & 14$^h$13$^m$09.7$^s$ & -65\\degr20\\arcmin21.5\\arcsec & 19\\degr & 2 \\\\\nNGC\\,1068 & 02$^h$42$^m$40.8$^s$ & -00\\degr00\\arcmin47.3\\arcsec & -11\\degr & 2 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n1 = SW lobe\\\\\n2 = nucleus\\\\\n3 = ionized shell\n\\end{table}\n\n\\begin{figure*}\n \\setcounter{figure}{0}\n% \\resizebox{\\hsize}{!}{\\includegraphics{fig1.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig1.ps}}\n \\caption{The full SWS01 spectra of the five extragalactic templates. x-axis:\n wavelength in $\\mu$m; y-axis: flux density in Jansky.}\n \\label{fig:m82}\n\\end{figure*} \n\nTo reduce noise for display purposes (Fig. 1), we have smoothed the data \nwith a gaussian filter to a uniform resolution of 1000. This\nbroadens slightly the line widths of the narrow atomic and ionic emission\nlines, but does not affect the broad emission and\nabsorption features discussed in this paper.\nWe did not remove the flux jumps at detector band limits. Part of\nthese jumps may be real because the sources are extended and because\nthe aperture sizes\nchange at some band edges (at approximately 12.0, 27.5 and 29.0$\\mu$m).\nAnother part simply reflects the flux calibration\nuncertainty, which is of the order of 20 per cent.\n\nWe carefully checked the reality of the features in the final spectra \nagainst the possibility of residual instrumental features from the \nRelative Spectral Response Function (RSRF), which might be caused \ne.g. by an improper dark current subtraction.\nFor example, the detector RSRF exhibits absorption features \nat 11.05 and 34$\\mu$m\nwhich might appear in emission in the calibrated spectrum. This is, however,\nat most an effect of the order of a few per cent of the continuum level. \nThe features\nwe see at these wavelengths in our spectra (see below) are stronger, so\nthat they must be real.\nFurthermore, we checked whether a feature\n%listed in the next section\nappears in both scan directions and in the majority of all\ndetectors. Additional confirmation\nwas possible for those features that lie in the overlap\nregion of two different AOT bands and appear in both bands.\nAt this stage of instrument calibration, we do not believe that any\nof the broad structures in band 3E (appr. 27.5--29.5 $\\mu$m) are real\nfeatures.\nAlso, features at the end of band 4 (43--45 $\\mu$m, e.g. in Circinus)\ncannot be trusted.\n\n%--------------------------------------------------------------------\n\n\\section{An inventory of features}\n\\label{s:inventory}\n\n\\begin{table}\n\\caption[]{\\label{tab:inventory} Summary of observed broad emission features\n(approximate peak positions in $\\mu$m). Uncertain detections are given in\nparentheses, nondetections are marked by a dash.} \n%\\begin{footnotesize}\n%{\\scriptsize\n\\begin{flushleft}\n\\begin{tabular}{llllll}\n%\\begin{tabular}{lll}\n\\hline\\noalign{\\smallskip}\nM\\,82 & NGC & 30\\,Dor & Circinus & NGC & nearby\\\\\n%\\multicolumn{5}{c}{ } & ionic lines\\\\ \n & 253 & & & 1068 & lines\\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\n3.25 & 3.25 & -- & 3.25 & -- & \\\\\n3.3 & 3.3 & 3.3 & 3.3 & 3.3 & Pf$_{\\delta}$\\\\\n3.4 & 3.4 & 3.4 & -- & -- & \\\\\n3.5 & (3.5) & 3.5 & -- & -- & \\\\\n-- & 3.75 & -- & 3.75 & -- & \\\\\n5.25 & -- & -- & -- & -- & \\\\\n5.65 & 5.65 & -- & -- & -- & \\\\\n6.0 & 6.0 & 6.0 & (6.0) & -- & \\\\\n6.2 & 6.2 & 6.2 & 6.2 & (6.2) & \\\\\n6.3 & 6.3 & 6.3 & 6.3 & -- & \\\\\n7.0 & 7.0 & (7.0) & -- & -- & H$_2$+\\\\\n & & & & & [Ar II]\\\\\n7.6 & 7.6 & 7.6 & 7.6 &(7.6) & Pf$_{\\alpha}$+\\\\\n & & & & & [Ne VI]\\\\\n7.8 & 7.8 & 7.8 & 7.8 & 7.8 & \\\\\n8.3 & -- & -- & -- & -- & \\\\\n8.6 & 8.6 & 8.6 & 8.6 & 8.6 & \\\\\n(10.6)& -- & -- & -- & -- & [S IV]\\\\\n11.05 & 11.05& 11.05 & 11.05 & 11.05 & \\\\\n11.25 & 11.2 & 11.25 & 11.25 & 11.25 & \\\\\n12.0 & 12.0 & 12.0 & -- & -- & \\\\\n12.7 & 12.7 & -- & 12.7 & (12.7)& [Ne II]\\\\\n13.55 & 13.55& (13.5) & 13.6 & 13.4 & \\\\\n14.25 & 14.25& 14.25 & 14.25 & -- & [Ne V]+\\\\\n & & & & & [Cl II]\\\\\n(14.8)&(14.8)&(14.8) &(14.8) & -- & \\\\\n15.7 & 15.7 & 15.7 & 15.85 & 15.9 & [Ne III]\\\\\n16.5 & 16.5 & 16.5 & -- & -- & \\\\\n(17.4)&(17.4)& -- & -- & -- & \\\\\n(18.0)& -- &(18.0) & -- & -- & \\\\\n20.5 &(20.3)&(20.4) & 20.2 & -- & \\\\\n-- & -- & -- & 21.7 & -- & \\\\\n%(27.9)&(28.0)& (27.9) & (27.8)& -- & \\\\\n34 & 34 & 34 & 34 & -- & [Si II]+\\\\\n & & & & & [S III]\\\\\n%-- & 36 & -- & -- & (36) & [Ne III]\\\\\n% & & & (44) & & \\\\\n% & & & & \\\\\n%\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n%\\end{footnotesize}\n%}\n\\end{table}\n\n\\begin{table}\n\\caption[]{\\label{tab:invent_abs} Summary of observed absorption features.\nUncertain detections are given in parentheses.} \n%\\begin{footnotesize}\n%{\\scriptsize\n\\begin{flushleft}\n\\begin{tabular}{llllll}\n%\\begin{tabular}{lll}\n\\hline\\noalign{\\smallskip}\nM\\,82 & NGC & 30\\,Dor & Circinus & NGC & species\\\\\n & 253 & & & 1068 & \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\n3.0 & 3.0 & -- & -- & -- & H$_2$O ice \\\\\n--$^1$ & --$^1$& --$^1$& --$^1$ & 3.4 & hydrocarbon \\\\\n%(--) & (--) & -- & -- & -- & 7.7$\\mu$m CH$_4$ \\\\\n(9.7) & (9.7) & -- & (9.7) & 9.4 & silicate \\\\\n(18.0 )& (18.0)& -- & (18.0) & -- & silicate \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n$^1$ could be filled in by PAH emission\n\\end{table}\n\n\n\\begin{table}\n\\caption[]{\\label{tab:PAH_flux1} Approximate absolute and relative fluxes of the \nprominent PAHs at 3.3 and 6.2$\\mu$m (see text for details).}\n%\\begin{footnotesize}\n%{\\scriptsize\n\\begin{flushleft}\n\\begin{tabular}{lllll}\n\\hline\\noalign{\\smallskip}\nObject & \\multicolumn{2}{c}{3.3$\\mu$m} & \\multicolumn{2}{c}{6.2$\\mu$m} \\\\ \n & flux$^1$ & relative flux$^2$ & flux$^1$ & relative flux$^2$ \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nM\\,82 & 3.3 & 0.2 & 37 & 2.7 \\\\\nNGC\\,253 & 1.0 & 0.1 & 13 & 1.7 \\\\\n30\\,Dor & 0.3 & 0.04& 1.5 & 0.2 \\\\\nCircinus & 0.7 & 0.06& 6.3 & 0.6 \\\\\nNGC\\,1068 & 0.3 & 0.02& 1.0 & 0.05\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n$^1$ [10$^{-18}$ W/cm$^2$] \\\\\n$^2$ PAH flux/continuum(11.6--11.9$\\mu$m)\n\\end{table}\n\n\\begin{table}\n\\caption[]{\\label{tab:PAH_flux2} Approximate absolute and relative fluxes of the \nprominent PAHs at 7.7 and 11.3$\\mu$m (see text for details).}\n%\\begin{footnotesize}\n%{\\scriptsize\n\\begin{flushleft}\n\\begin{tabular}{lllll}\n\\hline\\noalign{\\smallskip}\nObject & \\multicolumn{2}{c}{7.6--7.8$\\mu$m} & \\multicolumn{2}{c}{11.3$\\mu$m} \\\\ \n & flux$^1$ & relative flux$^2$ & flux$^1$ & relative flux$^2$ \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nM\\,82 & 99 & 7.2 & 16 & 1.2 \\\\\nNGC\\,253 & 39 & 5.0 & 7.2 & 0.9 \\\\\n30\\,Dor & 0.3 & 0.04& 1.7 & 0.2 \\\\\nCircinus & 21 & 1.9 & 3.9 & 0.4 \\\\\nNGC\\,1068 & 2.1 & 0.1 & 1.1 & 0.06\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n$^1$ [10$^{-18}$ W/cm$^2$] \\\\\n$^2$ PAH flux/continuum(11.6--11.9$\\mu$m)\n\\end{table}\n\nIn Tables \\ref{tab:inventory} and \\ref{tab:invent_abs} \nwe give an inventory of features that we believe to be reliable detections. \nWe consider a detection reliable if the feature has an amplitude of at least\n3$\\sigma$ of the noise level and if it fulfills the criteria described above.\nWe also list a few uncertain detections in parantheses, e.g. features in\ncompliance with the above criteria but with an amplitude of less than\n3$\\sigma$ (but note that the definition of the local noise level is in many \ncases somewhat uncertain).\nMost of these features have been described before in reports of ISO-SWS\nobservations of galactic template sources (e.g. Moutou et al. 1996, \nVerstraete et al. 1996, \nRoelfsema et al. 1996, Beintema et al. 1996). Here we highlight \na few of their characteristics, source by source. In Sect. \\ref{s:ident}\nwe briefly discuss possible identifications. Please note that many of \nthe features are severely blended and thus the peak wavelengths given here are \napproximate. \n\nWe also list the fluxes of four of the most prominent PAHs in\nTables \\ref{tab:PAH_flux1} and \\ref{tab:PAH_flux2}. To measure these fluxes\nwe defined continua by a linear interpolation between the following points: \n2.50 and 3.65$\\mu$m for the 3.3$\\mu$m feature, 5.9 and 10.9$\\mu$m for the\nfeatures at 6.2 and 7.7$\\mu$m, and 10.9 and 11.8$\\mu$m for the 11.3$\\mu$m\nfeature. We then obtained the fluxes by integrating between the following band\nlimits: 3.10--3.35$\\mu$m, 6.0--6.5$\\mu$m, 7.3--8.2$\\mu$m, and\n11.1--11.7$\\mu$m. To give an indication of the relative contribution of these\nfeatures to the infrared luminosity we also list their ratio to the continuum\nflux in the range 11.6--11.9$\\mu$m. Due to the uncertainties involved in this\nmeasuring process (continuum shape, feature profile, etc.) \nall absolute and relative fluxes are only approximate.\nBy definition, these fluxes ignore a possible, PAH-related `plateau' or\n`continuum' in the 6--9 and 10--13$\\mu$m range (e.g. Boulanger et al. 1996).\\\\\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n% \\resizebox{\\hsize}{!}{\\includegraphics{fig2a.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig2a.ps}}\n \\vspace*{0.05cm} \\caption{Details of the spectra. Wavelength in $\\mu$m, flux \n density in\n Jansky.}\n \\label{fig:details}\n\\end{figure*} \n\\begin{figure*}\n\\setcounter{figure}{1}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig2b.ps}}\n% \\resizebox{\\hsize}{!}{\\includegraphics{h1809.f2b}}\n \\vspace*{0.05cm} \\caption{{\\it continued} }\n\\end{figure*} \n\n%{\\vspace*{0.3cm} \\noindent \\bf M\\,82:} \n{\\noindent \\bf M\\,82:} \nM\\,82 is a small galaxy undergoing a very powerful\nstarburst, and is considered to be\na prototype of starburst activity.\nDue to its proximity (3.63 Mpc, Freedman et al. 1994) it is the\nbrightest galaxy in the infrared, with the infrared luminosity arising mainly\nfrom warm dust in the central region.\n%On the whole it is considered to be the prototypical starburst galaxy.\nEmission features\nat 8.7 and 11.3$\\mu$m were first detected by Gillett et al (1975), and the\n3.3, 6.2 and 7.6$\\mu$m features by Willner et al. (1977).\n%For more information on M\\,82 see e.g. Schreiber 1998????\n\nThe main PAH features are clearly seen in the\nmid-infrared spectrum of M\\,82, shown in its entirety in Fig. 1\nand in detail in the top panels of Fig 2. In addition,\nthe spectrum shows a large number of weaker features\nwhich have previously been detected with ISO only in\ngalactic template sources.\n\nThe 3.3$\\mu$m feature has satellites at 3.4 and 3.5$\\mu$m.\nIt also shows a blue asymmetry, which might be due to a feature at 3.25$\\mu$m\n(see Beintema et al. 1996).\nTwo weak features at 5.25 and 5.65$\\mu$m, that have been observed e.g. in\nthe planetary nebula NGC\\,7027 (Beintema et al. 1996) and the\nphotodissociation front of M\\,17 (Verstraete et al. 1996), are also present\nin M\\,82.\nThe 6.2$\\mu$m band has a red shoulder and\nshows an additional feature at 6.0$\\mu$m.\nThe 7.7$\\mu$m feature consists of two bands at 7.6 and 7.8$\\mu$m.\nA significant contribution of 7.7$\\mu$m solid methane absorption \n(e.g. Whittet et al. 1996, Lutz et al. 1996) to this strong dip between \n7.6 and 7.8$\\mu$m is unlikely, since in M\\,82 related icy absorption features \nare shallower and extinction is lower (Sect. \\ref{s:continuum}) than in the \nsources with clear methane absorptions.\nA weak feature is present at 10.6$\\mu$m, which is confirmed\nin the average starburst spectrum of Lutz et al. 1998a\n(their Fig. 1, independent ISOPHOT-S data), and probably related\nto a feature seen by Beintema et al. (1996) in the spectrum of NGC\\,7027. \nThe 11.3$\\mu$m feature peaks at 11.2$\\mu$m and shows the\nwell-known asymmetric shape towards longer wavelengths (Witteborn et al.\n1989).\nThere is an additional component around 11.05$\\mu$m, much too strong to be\nrelated to artifacts from the RSRF correction known to exist at this wavelength.\nA weak feature may be present near 12.0$\\mu$m. \nThe 12.7$\\mu$m feature is very prominent in M\\,82.\nMoutou et al. (1998) found two emission features at 15.8 and 16.4$\\mu$m in\nthe spectrum of the galactic reflection nebula NGC\\,7023. On the basis\nof their laboratory work, they\nattributed these features to PAH molecules.\nThese two features are clearly seen in M\\,82, and in some of our other \ntemplate spectra.\nMore emission features can be found at still longer wavelenghts\n(20.5 and 33-34$\\mu$m).\n\nIn addition we find two features that -- to our knowledge --\nhave not been reported before: at 7.0 and 8.3$\\mu$m.\nA feature around 7.0$\\mu$m is also present in NGC\\,253 (most clearly), and \nperhaps in 30\\,Dor.\nWe found the same feature in ISO-SWS \nspectra of the cool, dusty envelopes of the planetary nebula He\\,2-113\n(see e.g. Waters et al. 1998, their Fig. 2).\nThe average ISOPHOT-S spectra of starburst and normal galaxies (Lutz et al.\n1998a, Helou et al. 2000) also show hints of a weak feature, blended with\nH$_2$ S(5) 6.91$\\mu$m and [Ar II] 6.99$\\mu$m (see also Sect. \\ref{s:lowres}). \nThe 8.3 feature is also visible in\nthe galactic template spectrum of NGC\\,7023 (Fig. \\ref{fig:m82vsngc7023}),\nand perhaps in some of the compact HII regions shown in Roelfsema et al. (1996).\nWe also want to mention here the 14.3$\\mu$m band. An astronomical observation \nof this band has been reported only recently for the first time \n(Tielens et al. 1999). It is present in all \nour template spectra, with the\nexception of NGC\\,1068, in NGC\\,7023, and perhaps also in some of\nthe circumstellar PAH spectra shown in Beintema et al. (1996).\n%It is weak but important because it can be confused with the [Ne V] fine\n%structure line in spectra of low resolution (see Sec. \\ref{s:lowres}).\nOn the other hand, our spectra do not show some of the \nemission features that have been detected before \nin astronomical observations,\ne.g. at 4.65$\\mu$m (Verstraete et al. 1996) and \n13.3$\\mu$m (Moutou et al. 1998).\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n% \\resizebox{\\hsize}{!}{\\includegraphics{fig2c.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig2c.ps}}\n \\vspace*{0.05cm} \\caption{{\\it continued} }\n\\end{figure*} \n\\begin{figure*}\n\\setcounter{figure}{1}\n% \\resizebox{\\hsize}{!}{\\includegraphics{fig2d.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig2d.ps}}\n \\vspace*{0.05cm} \\caption{{\\it continued}. Broad features between 27.5 and \n 29.5$\\mu$m, and longward of 40$\\mu$m cannot be trusted.}\n\\end{figure*} \n\nThere are very few absorption features in our spectrum of M\\,82. The\ntrough around 10$\\mu$m looks like a strong 9.7$\\mu$m silicate feature.\nIn\nSect. \\ref{s:continuum} we argue, however, that the trough is mainly due \nto the strong PAH emission at 8.7 and 11.3$\\mu$m. \nAlso, there is no clear signature \nof a corresponding silicate absorption feature at 18$\\mu$m.\nA broad absorption feature around 3.0$\\mu$m is probably due to H$_2$O-ice.\nIts optical depth ($\\tau\\sim$0.2) is relatively small \ncompared e.g. to the Galactic center ($\\tau$=0.5, Lutz et al. 1996, \nChiar et al. 2000). However, \nsince the overall extinction estimates differ in the same sense,\nthis is consistent with the M\\,82 line of sight having properties similar to that\ntowards the Galactic center: a mixture of diffuse ISM and molecular cloud\nextinction, with some \nvariance in the relative weight for different lines of sight\n(Chiar et al. 2000). These properties seem to be quite typical for \nstarburst galaxies, as we find similar conditions in NGC\\,253 (see below) \nand in NGC\\,4945 (Spoon et al., in prep.).\n\nThe M\\,82 spectrum has the highest S/N ratio and\nshows the largest number of features in our sample.\nCombined with the ISO-LWS long wavelength spectrum (Colbert\net al. 1999) it will be an important template for future missions.\\\\\n\n\n{\\noindent \\bf NGC\\,253:}\nNGC\\,253 is a nearby, almost edge-on barred spiral galaxy with a high level \nof circumnuclear \nstarburst activity. At optical wavelengths the galaxy is heavily obscured by\ndust lanes in the central regions.\n%The ionic emission lines in NGC\\,253 are quite different from their \n%counterparts in M\\,82. E.g. the different [Ne III]/[Ne II] \n%ratios point to differences in the average radiation field \n%in these two starburst galaxies (Thornley et al. 2000).\nThe ionic emission lines in NGC\\,253 are of lower excitation (e.g. lower\n[Ne III]/[Ne II] ratio) than in M\\,82, suggesting a softer average\nradiation field (Thornley et al., in prep.). \nDespite these differences between the two galaxies, their \nspectra of broad emission features are \nremarkably similar. This is demonstrated in Fig. \\ref{fig:m82vsngc253}.\nOnly beyond 9$\\mu$m does a difference in the underlying continuum \nbecome obvious. NGC\\,253\n%, which has the stronger radiation field,\nhas a stronger continuum at these longer wavelengths. \nIn starburst galaxies this underlying continuum is usually attributed to \nvery small grains (VSG) of dust (e.g. D\\'esert et al. 1990). \nIn Sect. \\ref{s:continuum} we will use the difference in the continua of\nM\\,82 and NGC\\,253 to characterise the shape of the VSG continuum.\n\nTable \\ref{tab:inventory} shows that nearly all features of M\\,82 are also seen\nin NGC\\,253. The very few exceptions may simply be due to the lower\n%are probably just an issue of\nS/N ratio of the NGC\\,253 spectrum.\nThe red shoulder of the 6.2$\\mu$m band seen in M\\,82\nis more prominent in NGC\\,253 and is probably due to an additional feature at\n6.35$\\mu$m.\nThe 3.0$\\mu$m ice absorption is also present, having an optical depth of\n$\\tau\\sim$0.25.\\\\\n\n{\\noindent \\bf 30\\,Dor:}\nThe 30\\,Dor region in the LMC is the largest, most\nmassive, and most luminous H II region in the Local Group.\nAs a local template for massive star\nformation and its interaction with the interstellar medium, it is\ninstructive to compare its spectrum to the galaxy spectra in\nour sample.\nA more detailed study of the mid-infrared fine structure emission lines in\n30\\,Dor will be presented in an upcoming paper (Thornley et al., in prep.).\n%For an introduction to 30\\,Dor, more details about the ISO-SWS\n%observation, and a study of its mid-infrared\n%fine structure emission lines see Thornley et al. 2000????\n\nAn inspection of Fig. \\ref{fig:details} and Table \\ref{tab:inventory} shows\nthat the 30\\,Dor spectrum exhibits most of the PAH features found in the\ngalaxy spectra. Lower S/N may contribute to\nthe non-detection of some of the weak features.\nCompared to the two starburst galaxies, the features in 30\\,Dor are\nmuch weaker relative to the continuum (see also Tables \\ref{tab:PAH_flux1}\nand \\ref{tab:PAH_flux2}) and show different ratios.\nNote, for instance, the high 6.2/7.7$\\mu$m feature ratio, \nthe unusually high 3.4/3.3 ratio ($\\approx$ 0.5, see also Sect. \n\\ref{s:PAH_var}), the shape of the 7.6/7.8$\\mu$m features, or the complete\nabsence of the 12.7$\\mu$m feature.\nThese differences may be partly due to the fact, that the SWS apertures \ncovered only part of the entire 30\\,Dor complex. Verstraete et al. (1996)\nuse the case of M17 to demonstrate the strong variations in PAH spectra going\nfrom the center of an H\\,II region to the surrounding photodissociation region. \nOn the other hand, the similarity of the 30\\, Dor \nspectrum to the integrated ISOPHOT-S spectrum of the dwarf galaxy NGC\\,5253 \n(Rigopoulou et al. 1999) strongly suggests that the weakness of the PAHs is not\nan aperture effect but reflecting an intrinsic property of very active\nstar formation in a low metallicity environment.\n\nSilicate absorption at 9.7 and 18$\\mu$m is, if at all present, very weak.\nNo other absorption features can be detected. \\\\\n\n{\\noindent \\bf NGC\\,1068:}\nThe nearby, prototypical Seyfert 2 galaxy NGC\\,1068 is a key object in\nthe investigation and modeling of active galactic nuclei (AGNs).\nThe ISO-SWS observations were centered on the active nucleus, with the\naperture\ncovering very little of the\ncircumnuclear star forming `ring', which has a radius of $\\approx$15\\arcsec.\nIn stark contrast to the starburst templates we have shown, this active\nnucleus spectrum shows very little PAH emission.\nThe weaker features (e.g. 3.3, 6.2 or 12.7$\\mu$m)\nare barely visible, if at all. \n\nThe continuum around 10$\\mu$m is strong because of a central warm component\nheated by the AGN. Silicate absorption is clearly present, although centered\nat 9.4$\\mu$m rather than \nat 9.7$\\mu$m, but again surrounding weak PAH emission complicates its\ninterpretation. \nHydrocarbon absorption is seen at 3.4$\\mu$m (see also\nBridger et al. 1994), in contrast to our starburst templates, where\nit is not observed.\nNote, however, that in M\\,82 and NGC\\,253 a similar absorption feature\ncould plausibly\nexist if the analogy to the Galactic center holds, but be filled in by \nthe 3.3/3.4 PAH emission. On the other hand\nM\\,82 and NGC\\,253 show an H$_2$O ice absorption at 3.0$\\mu$m which is\ndefinitely absent in NGC\\,1068. \nThese differences in absorption features are entirely plausible because of the\ndifferent physical conditions in the obscuring regions. For the starbursts,\nthey likely include diffuse ISM as well as molecular clouds that can host icy\ngrains. Conversely, infrared polarimetry suggests that most of the \nnear-infrared obscuration in NGC\\,1068 occurs within a few parsecs from the \nnucleus, possibly in the torus (e.g. Packham et al. 1997). Such an energetic \nenvironment will be much less favourable for the existence of icy grains.\\\\\n\n{\\noindent \\bf Circinus:}\nThe Circinus Galaxy is a nearby spiral galaxy which shows Seyfert 2 activity\n(e.g. Moorwood \\& Glass 1984, Oliva et al. 1994, Moorwood et al. 1996,\nOliva et al. 1998). Due to its proximity (5 times closer than NGC\\,1068)\nit has become another template object for the study of AGNs.\nThe AGN is surrounded by circumnuclear\nstar-forming regions, as is often the case in Seyfert nuclei residing in\nspirals.\nThe ISO-SWS observations were centered on the active nucleus, but contrary to\nthe observations of NGC\\,1068 the apertures covered a significant amount of\nthis circumnuclear star formation.\nHence, most of the dust emission features seen in\nthe starburst templates are also found in\nCircinus, but with weaker line-to-continuum ratio (see the discussion in\nSect. \\ref{s:PAH_var}). A peculiarity of the Circinus spectrum are the\nvery pronounced features in the 20--22$\\mu$m region.\n\n\nThe observation was performed very early in the mission, when the\nobserving strategy was not yet fully optimized. For instance, exposures of\nthe internal flux calibration lamps, preceeding observations of the scientific\ntarget, caused memory effects in the immediately following scans.\nThe low flux level of band 4 ($\\lambda \\ge$ 29$\\mu$m),\nrelative to the preceding bands, is due to such a memory effect and an incorrect\ndark current subtraction. The same might be true for the apparent features near\n44$\\mu$m (which are not visible in the overlapping LWS spectrum). We did not \nattempt to improve the dark current subtraction further since this would \ninvolve subjective assumptions about the true dark current.\n\n%--------------------------------------------------------------------\n\\section{Mid-infrared features and the physical state of the ISM}\n\n%--------------------------------------------------------------------\n\n\\subsection{Identification}\n\\label{s:ident}\n\n\\subsubsection{The 2-13$\\mu$m region:}\n\nThe emission features in this wavelength range\nhave been extensively studied with ISO in galactic objects during the last few\nyears. Comprehensive discussions of their identifications and characteristics\ncan be found e.g. in Beintema et al. (1996), Moutou et al. (1998), Roelfsema\net al. (1996), and Verstraete et al. (1996).\nThey are most often attributed to PAH molecules. This is supported by\nrecent laboratory studies (e.g. Roelfsema et al. 1996, Moutou et al. 1996).\nThe only features in this range, \n%in Table \\ref{tab:inventory}, \nwhich have not\nbeen addressed in the\nliterature so far, are the ones at 7.0 and 8.3$\\mu$m. \nIn our sample of galaxies \nthey are\nunambiguously detected only in M\\,82 and NGC\\,253 (the 8.3$\\mu$m feature only\nin M\\,82), but as mentioned in Sect.\n\\ref{s:inventory} they seem to be present in other published spectra as well.\n%Here we will not attempt to identify its carrier but \nIt seems likely that they can be attributed to a PAH modes, too.\n\n\\subsubsection{Features between 13 and 20$\\mu$m:}\n\nFeatures in this range have attracted less attention in the past, because\nthey are intrinsically weak (but see e.g. Beintema et al. 1996).\nThese bands, however, are more sensitive to the molecular structure of PAHs,\nsince they\n%are due to skeletal vibration. \ninvolve the motion of the molecule as a whole, therefore depending on the \nexact species (L\\'eger et al. 1989).\nHence, their observation could help to better\nconstrain the composition of the interstellar mixture.\nThe 13.6, 15.8, and 16.5$\\mu$m features are\nalso visible in the spectra of NGC\\,7023 and have been attributed to PAH bands\nin the past by Moutou et al. (1998), based on their laboratory work.\nThe band at 14.3$\\mu$m has been tentatively attributed to a phenyl bending \nmode by Tielens et al. (1999). \nMoutou et al. (1996) list a feature at this wavelength in their composite\nlaboratory spectrum of a mixture of PAHs. Although weak, it might cause\nconfusion with [Ne V] in low resolution spectra (see Sect. \\ref{s:lowres}).\nFinally, the weak feature at 14.8$\\mu$m (if real) could be due to the smallest \nPAH, benzene (Tielens et al. 1999). \n\n\n\\subsubsection{Features in the 20 to 45 $\\mu$m region:}\n\nThe number of modes in the laboratory PAH spectra of Moutou et al. (1996) \ndecreases\nwith increasing wavelength. Few species show emission beyond 20$\\mu$m, \ne.g. near 21, 28 and 40$\\mu$m.\nIn this wavelength range other sources must be taken into\naccount. A number of recent papers have reported the detection of crystalline\nsilicates (olivines, fosterite, pyroxene, etc.) in objects like \nLuminous Blue Variables (Voors et al. 1999),\ndusty circumstellar disks (Waelkens et al. 1996, Waters et al. 1996), or\nPlanetary Nebulae (Waters et al. 1998).\nIn particular the feature at 34$\\mu$m\n%and 43$\\mu$m\ncould be attributed to\nthese kind of sources. However, one would expect to see emission\nfeatures at e.g. 23, 28, 40 and 43$\\mu$m, as well; none of these features are\nclearly detected in our spectra.\nOn the other hand, even in some of the galactic templates, such as the\nplanetary nebula NGC\\,6543 (e.g. Waters et al. 1996), not all of\nthese features are present.\n\nA feature near 20.5$\\mu$m shows a striking variation in shape and central\nwavelength between the galaxies. This is particularly surprising since \nthe galaxy spectra include a mixture of many different regions, and may suggest\na carrier occuring only transiently in very special conditions.\nIn Circinus this feature is most prominent, and peaks at the bluest wavelength \n(20.2$\\mu$m). Circinus also shows a second peak at 21.7$\\mu$m which \nis absent in the other spectra. \nA bump around 20.5$\\mu$m is also seen in ISO-SWS spectra of M supergiants \n(Voors et al. 1999, Molster et al. 1999). \nIt could be due to PAHs or alternatively metal\noxides like FeO (Waters et al. 1996, Henning et al. 1995).\nIRAS-LRS and ISO-SWS spectroscopy have also detected a broad feature, centered\nat approximately 20.1$\\mu$m, in carbon rich stars (Volk et al. 1999,\nGarc\\'{\\i}a-Lario et al. 1999, Szczerba et al. 1999). Possible candidates \nthat have\nbeen proposed include large PAH clusters or hydrogenated amorphous carbon\ngrains, hydrogenated fullerenes, and nano-diamonds (see references in\nVolk et al. 1999). However, compared to these detections, the\nfeatures\nin our spectra are much narrower.\n\nA mixture of fullerene molecules of different degree of hydrogenation (Webster\n1995) might also explain the second peak in Circinus around 21.7$\\mu$m, \nsince the emission\npeak shifts from 23 for fully hydrogenated fullerene (C$_{60}$H$_{60}$)\nto 19$\\mu$m for non-hydrogentated fullerene (C$_{60}$).\n%This second feature is observed in our sample in\n%the Circinus Galaxy only (OR IS IT IN 1068, too????). \nNone of the other galaxies exhibit this feature, but\n%However, the\nthe SWS01 spectrum of NML Cyg (Voors et al. 1999) and of the galaxy\nNGC4945 (S. Lord, private communication) also\nshow a weak emission feature around 21.6--22$\\mu$m.\n\nThe broad plateau at 33--34$\\mu$m, i.e. under the strong lines of [Si II]\nand [S III], could be affected by detector memory effects. To remove such a\npossible instrumental effect we treated the two\ndifferent scan directions of the SWS01 mode separately. \nThe trailing wings of each line profile, i.e. the blue\nwing for the scan with increasing wavelength, and the red wing for the scan\ndecreasing in wavelength, are much more distorted by memory effects than\nthe leading wings. Therefore, we cut out these trailing wings, before we\naveraged the spectra of the two scan directions.\nWe are\nhence confident that most of the remaining plateau is real. Such a feature\nhas been observed in many\ngalactic targets and is generally attributed to crystalline silicates\n(olivine, e.g. Waters et al. 1998).\n\n%A 44 FEATURE COULD ALSO BE H2O ICE\n%Features at 21, 22: seen in NML Cyg (Voors et al.), metal oxides? (Waters 96,\n%Henning 95). Nano-diamonds?\\\\\n%Feature at 34, 43: NGC6543, Waters 1996, also \n%NML Cyg (Justtanot, Waters 1996).\n%A pyroxene at 34 would also show 23.5 and 40 (Waters 1998).\n%43: crystalline ice, 34: olivine (Waters 1996)\\\\ \n%Feature at 36: seen in HD100546 (Waelkens 1996), but this one also shows\n%23.5 and 27 features, no 43. Unidentified/fosterite? (Waters 1996 \n%table2/figure2).\n%NGC6543 shows 34 and 43 but no 40 (Waters 96). NML Cyg shows 33, 40 and 43 \n%(plus 21, 22).\\\\\n%33 also seen in AG Car (Lamers 96). \n%Molinari: 43 ice feature should be more at 44-45. If there is no 62 um \n%feature it is probably amorphous ice not crystalline.\n%Waelkens: According to Koike et al. (1993) a 28$\\mu$m peak is characteristic\n%for all olivines. \n\n%No 4.65 um feature? No 13.1/13.3? (Verstraete/Moutou). No others????\n\n\n\n\n%--------------------------------------------------------------------\n\\subsection{Variation of PAH features}\n\\label{s:PAH_var}\n\nPublished mid-IR spectra of galactic template sources show a significant\nvariation of intrinsic\nPAH ratios from source to source. For instance Roelfsema et al.\n(1996) see a drastic change in the relative intensities of the 7.7 and 8.6\nbands with increasing intensity or hardness of the radiation field.\nSimilar changes are seen e.g. in different regions of M17\n(Verstraete et al. 1996) or - for the 8.6/11.3 ratio - in the\nreflection nebula NGC\\,1333 (Joblin et al. 1996).\nPAHs exposed to intense and hard radiation fields can be ionized, lose\nhydrogen atoms, or be photodissociated; any of these effects may contribute to\n% which in turn can cause\nthe observed variations in PAH ratios.\nAccording to Joblin et al. (1996) the ionization is best traced by the 3.4/3.3\nand 8.6/11.3 ratios. A good hydrogenation indicator is the (12+12.7)/11.3\nratio. For instance, these authors find a high 3.4/3.3 ratio \nof 0.1 in radiation fields that are 10$^5$ times the standard.\n\n\nAnother important factor that can alter observed\nPAH ratios is extinction. Extinction\nwill suppress the 6.2, 8.6 and 11.3$\\mu$m features with respect to \nthe one at 7.7$\\mu$m. \nThe 12.7/11.3 ratio is similarly affected, since the 11.3 feature is\nstill in the wing of the 9.7$\\mu$m silicate absorption. Details will depend\non the applicable extinction law (see e.g. the Galactic center, Lutz et al. \n1996). While extinction\nclearly affects PAH spectra in highly obscured sources like Ultraluminous \nInfrared Galaxies (ULIRGs, Lutz et al. 1998a) or the edge-on galaxy \nNGC\\,4945 (Spoon et al., in prep.), its\neffect will be less pronounced in the lower extinction sources of our sample.\n\nFinally, in active galaxies, such as NGC\\,1068 or the Circinus Galaxy, PAH\nfeatures can be diluted by an AGN-powered hot dust continuum.\nGenzel et al. (1998) and Lutz et al. (1998a) have used this as a diagnostic \nof the power sources of ULIRGs.\n\nOur sample of galaxy spectra exhibits a similar trend in relative PAH\nstrengths as the galactic templates.\nM\\,82 and NGC\\,253 have high\n3.4/3.3 ratios, consistent with them being active starburst galaxies.\n30\\,Dor seems to have an even higher 3.4/3.3 ratio, but the S/N ratio is not\nsufficient for a detailed analysis. However, a strong and hard, highly ionizing\nradiation field in 30\\,Dor is consistent with the results of Thornley et\nal. (1998), which are based on the ratios of fine structure emission lines,\nlike [Ne III]/[Ne II]. In that context it is interesting to note again\nthe complete absence of the 12.7$\\mu$m feature in 30\\,Dor.\nIn the two starburst galaxies\nM\\,82 and NGC\\,253 we see well-separated 7.6/7.8 and 8.6 features. The\n8.6 band is much weaker than the 7.6/7.8 band, just as observed in `normal'\nHII regions. In the Seyfert galaxy NGC\\,1068, however, the 8.6 band is similar\nin strength to the 7.7 band, as it is seen in the\nultracompact HII regions in M\\,17 (Cesarsky 1996b) or IRAS\\,18323-0242\n(Roelfsema et al. 1996), where the UV radiation field is\nextremely strong.\n\nNGC\\,1068, like many AGNs, shows an\nadditional component of warm dust in the 10$\\mu$m region. Unified models for\nSeyfert galaxies predict a dusty torus which would emit at these mid-infrared\nwavelengths (e.g. Pier \\& Krolik 1992). Hence, an alternative interpretation\nof the weak emission features on both sides of the silicate absorption might\nbe self-absorbed silicate emission from the torus, i.e. the emissions we \nidentified as PAH might simply be wings of a wide silicate emission maximum, \nthe center of which is suppressed by absorption.\nHowever, the observed double peaks at 7.7/8.6 and 11.05/11.25, as well as\nthe distinct rise in flux near 7.3$\\mu$m are not reproduced by torus models\nand show that there must be some\nreal, although weak, PAH emission on top of the continuum.\nThe weakness of the PAH emission can be understood in terms of dilution by the\nhot dust continuum and destruction by the intense AGN radiation field.\n\n\\begin{figure*}\n\\setcounter{figure}{2}\n% \\resizebox{\\hsize}{!}{\\includegraphics{m82vsngc253.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig3.ps}}\n \\caption{M\\,82 (full) versus NGC\\,253 (dash-dotted). In both spectra narrow\n emission lines have been masked out. Both spectra have been smoothed and \n corrected for zodiacal light and for their red shift. The spectrum of NGC\\,253\n has been multiplied by 2.6 to normalize the 7.6$\\mu$m PAH to the one in \n M\\,82.}\n \\label{fig:m82vsngc253}\n\\end{figure*} \n\\begin{figure*}\n \\setcounter{figure}{3}\n% \\resizebox{\\hsize}{!}{\\includegraphics{m82vsngc7023.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig4.ps}}\n \\caption{M\\,82 (full) versus the galactic reflection nebulae NGC\\,7023\n (dash-dotted). Both spectra have been corrected\n for zodiacal light and for their red shift. The spectrum of NGC\\,7023 \n has been smoothed and multiplied by 3.25 to normalize the 7.6$\\mu$m PAH to \n the one in M\\,82.}\n \\label{fig:m82vsngc7023}\n\\end{figure*} \n\\begin{figure*}\n \\setcounter{figure}{4}\n% \\resizebox{\\hsize}{!}{\\includegraphics{m82sim.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig5.ps}}\n \\caption{M\\,82 (full) versus NGC\\,7023 x 3.25 + power law (dashed).\n The spectra of NGC\\,7023 (dash-dotted) and M\\,82 have been smoothed. \n The power law component (dash-dotted) takes into account the aperture \n change at 12$\\mu$m (x 1.3).}\n \\label{fig:m82sim}\n\\end{figure*} \n\nNGC\\,1068 has a circumnuclear starburst region, and\nsome of the PAH emission might be picked up from this region by the large\nSWS aperture. The match in shape with the (small-aperture)\nground-based data of Roche et al. (1984) in the 8-13$\\mu$m range, and\ncomparisons to ground-based CO maps,\nsuggest that this effect is of minor importance here.\n\nIn the Circinus Galaxy the 7.7/8.6 ratio is somewhere in\nbetween the two extrema M\\,82 and NGC\\,1068.\nThe feature/continuum ratio of the PAH features,\nhowever, is much higher in Circinus than in NGC\\,1068. We attribute this to\nthe fact that in the case of Circinus the large SWS aperture\nindeed picked up parts of the well-known circumnuclear star forming region.\n%in Circinus.\n\n%Cesarsky (M17): a broad, smooth emission instead of the usual well-defined \n%7.7 and 8.6 bands is similar to M17 ultracompact HII region or protoplanetary \n%nebulae like IRAS 22273+5435 where the UV radiation field is extremely strong.\n%==> NGC\\,1068 does not pick up starburst ring, but shows PAHs in high radiation \n%environment (see also 1068 publication by Lutz).\n%While there exists an underlying continuum... another continuum starts at 15um\n%in regions of high radiation fields (see also Boulanger). Visible in 1068?\n \n%Roelfsema: The most dramatic change in relative intensities is seen \n%between the 7.6 and 8.6 bands. Similar to 8.6/11.3 (Joblin).\n%Non-compact PAHs enhance 8.6 relative to 7.6: less stable, occurs in sources\n%with higher luminosity/excitation. See their lab work.\n\n%--------------------------------------------------------------------\n\\section{Continuum placement and the depth of the silicate feature}\n\\label{s:continuum}\n\nAn important diagnostic in many extragalactic studies is the depth of the\nsilicate absorption feature at 9.7$\\mu$m and the extinction derived from it.\nHowever, the presence of strong PAH bands\non both sides of the 9.7$\\mu$m\nsilicate feature makes it very difficult to estimate the continuum level\nand the true depth of the silicate absorption.\nIn particular ground-based 8--13$\\mu$m data suffer from this problem.\nBecause of their continuous wavelength coverage ISO-SWS01 spectra are\nwell suited to shed more light on this question.\nIn the following we will discuss this issue using the example of M\\,82.\n\nFirstly, evidence against a strong 9.7$\\mu$m absorption comes \nfrom the absence of a strong 18$\\mu$m silicate absorption (see Fig. 1).\nAccording to Draine \\& Lee (1984) the expected ratio \n$\\tau_{sil}$(18$\\mu$m) / $\\tau_{sil}$(9.7$\\mu$m) is 0.4.\nFurthermore an analysis of hydrogen recombination lines in the ISO range\nyields a moderate A$_V$(gas)$\\approx$ 5 mag (for a uniform screen \nmodel - see Schreiber 1998). \n\nNext we come back to the comparison of the M\\,82 spectrum to the spectrum of\nNGC\\,253 (Fig.\n%\\ref{fig:m82vsngc253}\n3). The two galaxies are similar\nin A$_V$ and exhibit a very similar PAH spectrum. The only distinction appears\nto be a stronger VSG continuum in NGC\\,253. A strong\nrise of the continuum in this range is typical for regions of intense\nUV flux\n(e.g. D\\'esert et al. 1990, Vigroux et al. 1996) \\footnote{The spectrum of \nNGC\\,253 indicates lower ionization\n(e.g. low [Ne III]/[[Ne II]), but due to the compactness of the starburst in\nNGC\\,253 the radiation field here is more intense than in M\\,82.}.\nThe difference between both spectra\ncan be well fit by a power-law continuum that begins to rise at approximately\n8--9$\\mu$m.\n \nFinally, we\ncompare our spectrum\nof M\\,82 to the SWS01 spectrum of the galactic reflection nebula NGC 7023.\nLittle extinction is expected in the line of sight to this nebula.\nThe continuum under the PAH bands\nin NGC 7023 is very weak and starts to grow only beyond 20$\\mu$m (Moutou et\nal. 1998).\nThe flux density around 10$\\mu$m is almost on the same level as the flux\ndensity shortward of the 6$\\mu$m PAH band and at 15--20$\\mu$m.\n%(A similar behaviour is observed in many compact HII regions, Roelfsema et\n%al. 1996). \nIt could be explained by an underlying PAH plateau, or by\nthe wings of the 7.7/8.6 and 11.3 PAH\nfeatures (which can be represented by Lorentz profiles - Boulanger et al. 1998,\nMattila et al. 1999).\nWe therefore assume that in NGC\\,7023 this region consists\nmainly of emission bands, with little or no continuum and silicate absorption.\nIn Fig.\n%\\ref{fig:m82vsngc7023}\n4 we overplot the (smoothed) NGC\\,7023 spectrum on that of M\\,82. The NGC\\,7023\nspectrum has been multiplied by a factor 3.25 in order to normalize the\nPAH emission feature at 7.6$\\mu$m to the one in M\\,82.\nThe 3.3 and 11.3$\\mu$m bands\nin M\\,82 are weaker compared to NGC\\,7023. This might be explained\ne.g.\nby the harder radiation field in M\\,82 (Joblin et al. 1996, see \nSect. \\ref{s:PAH_var}).\n%Also, there might be a bit higher extinction in M\\,82, as indicated by the\n%slightly different 6.2$\\mu$m features (????).\nApart from this the two spectra are remarkably similar.\n%in the range up to 11$\\mu$m.\nOnly \n%beyond approximately 9$\\mu$m \nat higher wavelengths\na component of hot, small dust grains starts to add to the M\\,82\ncontinuum, as expected due to the much harder radiation field in M\\,82.\n\nIn view of these arguments we constructed a toy model in order to reproduce\nthe observed\nspectrum of M\\,82. The model simply consists of the scaled spectrum of\nNGC\\,7023 plus a power-law continuum which starts at 8.5$\\mu$m \n($f\\propto(\\lambda - 8.5)^{\\alpha}$).\nWe use a power-law rather than a black body curve for sake\nof simplicity. A power-law produces a very good fit to the continuum up to \n20 -- 25$\\mu$m. A black-body curve would be more problematic, because\nthe dust may not have a single temperature, and might not be in thermal \nequilibrium.\nM\\,82 is an extended source for the SWS apertures. There is a flux jump\naround 12$\\mu$m by a factor of about 1.3, corresponding to a similar change\nin aperture size. \nWe hence multiplied the power law continuum by 1.3 longward of 12$\\mu$m\n\\footnote{A more accurate correction for the change in aperture size would have\nto assume a light distribution (as a function of wavelength) and a model of\nthe instrument beam profile. Such a correction tool is not yet available.}.\nThe free parameters - the scaling factors for the\nNGC\\,7023 spectrum and the power law, plus the power law index - were adjusted \nby hand; we did not pursue a formal fit.\n%, since it is not needed for our purposes.\nFig.\n%\\ref{fig:m82sim}\n5 shows, that this simple model matches the observed\nspectrum remarkably well. There is no need to invoke any kind of extinction.\nDue to the uncertainties in the spectra, however, there is room for a moderate\nextinction,\nin accordance with the results from the recombination line studies (A$_V$ \n$\\approx$ 5 mag).\nA slightly different power-law, modified by a modest amount of extinction,\ncould fit the spectrum equally well.\nHowever,\na strong overall extinction, as deduced from the ground based 8-13$\\mu$m data\n(A$_V$ = 15--60 mag, Gillett et al. 1975), is clearly incompatible\nwith the new ISO data. This is an example of the potential danger of\noverestimating the silicate absorption depth in baseline-limited data.\n\n%--------------------------------------------------------------------\n\\section{The interpretation of low resolution spectra}\n\\label{s:lowres}\n\\begin{figure*}\n\\setcounter{figure}{5}\n% \\resizebox{\\hsize}{!}{\\includegraphics{fig6.eps}}\n \\resizebox{\\hsize}{!}{\\includegraphics{sturm_fig6.ps}}\n% \\hfill\n% \\parbox[b]{55mm}{\n \\caption{The ISO-SWS spectra of M\\,82 and NGC\\,1068, \n smoothed to a resolution of 50 \n to simulate the ISOCAM-CVF and SIRTF-IRS (low resolution mode) spectrometers.\n Wavelength in $\\mu$m, flux density in\n Jansky.\n The feature at 14.3$\\mu$m in M\\,82 is NOT [Ne V] (see text).}\n \\label{fig:m82lowres}\n% }\n\\end{figure*} \n%\\begin{figure*}\n% \\setcounter{figure}{6}\n% \\resizebox{\\hsize}{!}{\\includegraphics{ngc1068lowres.eps}}\n% \\caption{The ISO-SWS spectrum of NGC\\,1068, smoothed to a resolution of 50 \n% to simulate the CAM-CVF and SIRTF-IRS (low resolution mode) spectrometer.}\n% \\label{fig:ngc1068lowres}\n%\\end{figure*} \nMany ISO spectra of galactic and extragalactic objects have been\ntaken in low resolution mode (ISOPHOT-S, ISOCAM-CVF). Also, surveys\nwith future mid- and far-infrared space missions, e.g. of galaxies at higher\nredshifts, will likely be\nperformed with a relatively low resolution. For example\nthe IRS spectrometer on board\nSIRTF will have a resolution of approximately 50--100 \n(plus a medium resolution mode of R=600) in a wavelength range similar to \nISO-SWS.\nIn this low resolution mode SIRTF-IRS, being much more sensitive \nthan ISO-SWS, will be a unique tool to detect emission features in spectra of \nfaint high-z galaxies.\nLow resolution spectra, however, suffer from possible identification\nand interpretation problems caused by coincidences of\natomic/ionic lines and solid state features.\nIn our high resolution SWS01 galaxy spectra lines and features are well\nseparated, and we can use these spectra as templates to identify and highlight\nthe importance of possible confusion problems.\nIn Fig. 6\n%\\ref{fig:m82lowres}\n%6 and\n%\\ref{fig:ngc1068lowres}\n%7 \nwe have smoothed and rebinned the M\\,82 and NGC\\,1068 spectra\nto a resolution of 50 to simulate e.g. an ISOCAM-CVF or a SIRTF-IRS spectrum.\n\n\\begin{table}\n\\caption[]{\\label{tab:ne2_vs_pah} The flux ratio of PAH 12.7 / [Ne II] 12.8}\n\\begin{flushleft}\n\\begin{tabular}{ll}\n\\hline\\noalign{\\smallskip}\nObject & PAH 12.7/[Ne II] 12.8\\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nM\\,82 & 0.96\\\\\nNGC\\,253 & 1.32\\\\\n30\\,Dor & 0.00\\\\\nCircinus & 6.17\\\\\nNGC\\,1068 & 0..1$^a$\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n\\begin{list}{}{}\n\\item[$^{\\rm a}$] exact value difficult to measure, due to the broad wing of \n the [Ne II] line and the relatively strong noise. \n\\end{list}\n\\end{table}\nIn Table \\ref{tab:inventory} we have indicated possible confusions with\nnearby molecular, atomic, and ionic lines. We want to mention three lines in \nparticular: \n[Ar II] at 6.99$\\mu$m, which might be \nconfused with the underlying PAH emission (and the nearby H$_2$ S(5) line), \n[Ne II] at 12.8$\\mu$m, which in \nfact has been confused in the past with the underlying 12.7$\\mu$m PAH feature,\nand [Ne V] at 14.3$\\mu$m, which also has been\nconfused in the past with the nearby PAH emission.\nTo get an indication of the relative contributions of the 12.7$\\mu$m \nPAH flux\nand the [Ne II] line flux to the combined (line plus feature) flux in low \nresolution spectra\nwe have measured both fluxes in our high resolution spectra.\nTable \\ref{tab:ne2_vs_pah} summarizes the ratios of\nPAH/[Ne II] in all 5 templates. The values\nvary widely: in 30\\,Dor\nthe flux is solely due to\n[Ne II], whereas in Circinus [Ne II] contributes \nonly about 15\\% of the combined flux. For the 7.0$\\mu$m feature,\nwe find that the broad feature contributes 25\\% of the combined flux of\nfeature, H$_2$, and [Ar II] in NGC\\,253.\n%varies in a wide range. In 30\\,Dor the flux is solely due to\n%[Ne II], whereas in Circinus [Ne II] contributes only about 15\\% to the\n%combined flux.\n%For the 7.0$\\mu$m feature we find a contribution of $\\approx$ 25\\% to the\n%combined flux of feature, H$_2$ and [Ar II] in NGC\\,253.\n\nIn the low resolution representation of\nM\\,82 in\nFig.\n%\\ref{fig:m82lowres}\n6 the shape of the 14.3$\\mu$m \nPAH resembles very much the shape of an unresolved\nline like the [Ne III] line\nat 15.5$\\mu$m and can be mistaken as [Ne V]. \nThe high resolution spectrum of M\\,82 (Fig. 2) clearly shows, that\nthere is no \\mbox{[Ne V]} at 14.32$\\mu$m but an \nemission feature plus a weak line of \\mbox{[Cl II]} 14.37$\\mu$m.\nOf all the strong fine structure emission lines\nonly few lines remain unambiguously detectable in low resolution\nspectra, like Br\\,$\\beta$, Br\\,$\\alpha$, [Ne III] 15$\\mu$m,\n\\mbox{[S III]} 18.7, 33.5$\\mu$m, and [Si II] 34.8$\\mu$m in M\\,82, or\n[O IV] 26$\\mu$m and perhaps [Ne V] 24$\\mu$m, and [S IV] 10.5$\\mu$m in \nNGC\\,1068.\nClearly, low resolution spectra are very well suited for PAH and continuum\nmeasurements. However, flux measurements of narrow lines, and -- in some cases\n-- even their identification, can be very difficult. For these purposes higher\nresolutions, as for instance provided by the R=600 mode of the SIRTF \nspectrometer, are definitely needed.\n\n\n%--------------------------------------------------------------------\n\\section{Conclusions}\n\\label{s:conclusions}\n\nWe have detected a large number of mid-infrared features in galaxy spectra, \nsome of them previously unobserved, and discussed the dependence of the\ndust features on ISM condition in galaxies.\nThe spectral features vary considerably from source to source in \npresence and relative strength. Emission features are largely absent in \nthe intense radiation field close to an AGN, and weak in a\nlow metallicity, intensely star forming environment.\nDifferences in the absorption spectra point to different\nphysical properties of the obscuring regions in starburst and active galaxies.\n\nThe spectra presented here will be valuable template spectra for future\nmid- and far-infrared space missions such as SIRTF, SOFIA or FIRST. \n%They can be used for simulations of observations and for estimating\n%exposure times.\nThey\nprovide important clues for the identification and interpretation of high\nredshift, dusty galaxies.\n%, which supposedly contain a large amount of dust.\nThe strongest PAH features can be used to provide redshift information in \nfar-infrared photometric\ngalaxy surveys (Simpson \\& Eisenhardt 1999, see also the example of\n21396+3623, Rigopoulou et al. 1999). Furthermore, they affect\ngalaxy number counts.\nFor instance, Xu et al. (1998) have constructed semi-empirical galaxy SEDs\nto model the considerable PAH effects on number counts and redshift distributions.\n%The improved data reductions\n%and additional sources presented here might help to further constrain, refine\n%and test this kind of models (e.g. Xu et al. assumed no 3.3 feature and no\n%features beyond 13$\\mu$m). \\\\\n%GEORGE: DO YOU THINK THIS IS RELEVANT???? DID YOU EVER TEST THESE MODELS\n%AGAINST CIRCINUS????\nFinally, the continuum and the PAH features can be used to distinguish \nbetween starburst activity and active nuclei in high redshift galaxies, as\nhas been demonstrated for local infrared bright galaxies (Genzel et al. 1998,\nLutz et al. 1998a, Rigopoulou et al. 1999).\n\nThe advantage of the wide wavelength coverage of the SWS spectra has been\nused to\nillustrate the problem of the continuum definition and the true depth of the\nsilicate absorption.\nWe find that in our starburst templates the hot VSG dust continuum begins to\nrise around 8 to 9$\\mu$m,\nand that it can be well fitted by a simple power-law up to 20...25$\\mu$m.\nFinally we have demonstrated possible line identification problems in low\nresolution spectra.\n\nThe spectra presented here are available in electronic form from the authors.\nWe want to note again, that different parts of the spectra were\nobserved through different aperture sizes, which should be taken into account\nfor a detailed use as template spectra.\n\n\n%--------------------------------------------------------------------\n\\begin{acknowledgements}\nWe wish to thank George Helou for very fruitful discussions, and Bernhard\nBrandl for support with the SIRTF-IRS simulations.\n SWS and the ISO Spectometer Data Center at MPE are supported by\n DLR under grants 50 QI 8610 8 and 50 QI 9402 3. \nThe ISO Spectral Analysis Package \n(ISAP) is a joint development by the LWS and SWS Instrument Teams and Data \nCenters. Contributing institutes are CESR,\nIAS, IPAC, MPE, RAL and SRON.\n\\end{acknowledgements}\n\n%--------------------------------------------------------------------\n\\begin{thebibliography}{}\n\n\\bibitem[Beintema et al. 1996]{1996A&A...315L.369B} Beintema D. A.,\nvan den Ancker M.E., Molster F.J., et al. 1996, A\\&A 315, L369 \n\n%\\bibitem[Bland-Hawthorn et al. 1997]{1997Ap&SS.248....9B} Bland-Hawthorn, \n%J., Gallimore, J. F., Tacconi, L. J., Brinks, E. , Baum, S. A., Antonucci, \n%R. R. J. \\& Cecil, G. N. 1997, Ap\\&SS, 248, 9 \n\n\\bibitem[Boulanger et al. 1996]{1996A&A...315L.325B} Boulanger F., Reach W. T.,\nAbergel, A., et al. 1996, A\\&A 315, L325 \n\n\\bibitem[Boulanger Boisssel Cesarsky \\& Ryter 1998]{1998A&A...339..194B} \nBoulanger F., Boisssel P., Cesarsky D., Ryter C. 1998, A\\&A 339, 194 \n\n\\bibitem[Bridger et al. 1996]{} Bridger A., Wright G. S., Geballe T. R. 1994,\nin: I. 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"string": "\\begin{thebibliography}{}\n\n\\bibitem[Beintema et al. 1996]{1996A&A...315L.369B} Beintema D. A.,\nvan den Ancker M.E., Molster F.J., et al. 1996, A\\&A 315, L369 \n\n%\\bibitem[Bland-Hawthorn et al. 1997]{1997Ap&SS.248....9B} Bland-Hawthorn, \n%J., Gallimore, J. F., Tacconi, L. J., Brinks, E. , Baum, S. A., Antonucci, \n%R. R. J. \\& Cecil, G. N. 1997, Ap\\&SS, 248, 9 \n\n\\bibitem[Boulanger et al. 1996]{1996A&A...315L.325B} Boulanger F., Reach W. T.,\nAbergel, A., et al. 1996, A\\&A 315, L325 \n\n\\bibitem[Boulanger Boisssel Cesarsky \\& Ryter 1998]{1998A&A...339..194B} \nBoulanger F., Boisssel P., Cesarsky D., Ryter C. 1998, A\\&A 339, 194 \n\n\\bibitem[Bridger et al. 1996]{} Bridger A., Wright G. S., Geballe T. R. 1994,\nin: I. McLean (ed.), Infrared Astronomy with Arays, Dordrecht, Kluwer, p. 537\n\n%\\bibitem[Carral et al. 1994]{1994ApJ...423..223C} Carral, P., Hollenbach, \n%D. J., Lord, S. D., Colgan, S. W. J., Haas, M. R., Rubin, R. H. \\& \n%Erickson, E. 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}
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astro-ph0002196
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Neutrino Pair Annihilation in the Gravitation of Gamma Ray Burst Sources
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[
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"author": "Katsuaki Asano and Takeshi Fukuyama"
}
] |
We study semianalytically the gravitational effects on neutrino pair annihilation near the neutrinosphere and around the thin accretion disk. For the disk case, we assume that the accretion disk is isothermal and that the gravitational field is dominated by the Schwarzschild black hole. General relativistic effects are studied only near the rotation axis. The energy deposition rate is enhanced by the effect of orbital bending toward the center. However, the effects of the redshift and gravitational trapping of the deposited energy reduce the effective energy of the gamma ray bursts' source. Although each effect is substantial, the effects partly cancel one another. As a result, the gravitational effects do not substantially change the energy deposition rate for either the spherical symmetric case or the disk case.
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[
{
"name": "paper.TEX",
"string": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\n%\t Neutrino Pair Annihilation as a Source of Gamma Ray Bursts\n%\n%\n%\n%\n%\t Katsuaki ASANO & Takeshi FUKUYAMA\n%\n% 12nd June 1999\n%\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\documentstyle[12pt,aasms4]{article}\n%\\setlength{\\textwidth}{19cm}\n%\\setlength{\\oddsidemargin}{-1cm}\n\\begin{document}\n\n\n\\vspace*{0.5cm}\n\n\\title{Neutrino Pair Annihilation in the Gravitation of Gamma Ray Burst Sources}\n\n\\author{Katsuaki Asano and Takeshi Fukuyama}\n\n\n\\vspace{2cm}\n\n\\affil{Department of Physics, Ritsumeikan University\\\\\nKusatsu, Shiga 525-8577, Japan}\n\n\\affil{\\footnotesize e-mail: sph10001@se.ritsumei.ac.jp}\n\n\\vspace{2cm}\n\n\\baselineskip=16pt\n\n\\abstract{We study semianalytically\nthe gravitational effects on neutrino pair annihilation\nnear the neutrinosphere and around the thin accretion disk.\nFor the disk case, we assume that the accretion disk is isothermal\nand that the gravitational field is dominated by the Schwarzschild black hole.\nGeneral relativistic effects are studied only near the rotation axis.\nThe energy deposition rate is enhanced by\nthe effect of orbital bending toward the center.\nHowever, the effects of the redshift and gravitational trapping\nof the deposited energy reduce the effective energy of the gamma ray bursts' source.\nAlthough each effect is substantial,\nthe effects partly cancel one another.\nAs a result, the gravitational effects do not substantially change the\nenergy deposition rate for either the spherical symmetric case or the disk case.}\n\n\\vspace{0.5cm}\n\n\\noindent{\\it Subject headings}: accretion, accretion disks---black hole physics---gamma rays: bursts\n\n\n\\newpage\n\n\n\\section{INTRODUCTION}\n\n\\indent\n\nThe relativistic fireball (Shemi \\& Piran 1990; Rees \\& M\\'esz\\'aros 1992;\nM\\'esz\\'aros \\& Rees 1993; Sari \\& Piran 1995; Sari, Narayan \\& Piran 1996)\nis one of the most promising models of gamma ray bursts (GRBs).\nHowever, even if the fraction of the baryon rest energy is only $10^{-3}$\nin the fireball, the relativistic bulk flow, which is\nindispensable to GRBs, cannot be realized.\nNotwithstanding the very high energy phenomenon ($10^{52}$ ergs), the baryon\ndensity in the fireball must be extremely small.\nThis is the famous baryon contamination problem and still remains unsolved.\nThus the central engine of GRBs is still beyond\ndeep mist.\nThe source of GRBs may be one super massive\n(failed) supernovae (Woosley 1993; Paczy\\'nski 1998)\nor may be a merger of two neutron stars or of a neutron star and a black hole\n(e.g. Eichler et al. 1989; Narayan, Paczy\\'nski \\& Piran 1992;\nM\\'esz\\'aros \\& Rees 1992a; Katz 1997; Ruffert \\& Janka 1998, 1999).\n\nIn these compact high energy objects,\nthe neutrino-antineutrino annihilation\ninto electrons and positrons\n(hereafter neutrino pair annihilation)\nis a possible and important candidate to explain the energy source of GRBs\n(Paczy\\'nski 1990; M\\'esz\\'aros \\& Rees 1992b; Janka \\& Ruffert 1996;\nRuffert et al. 1997; Ruffert \\& Janka 1998, 1999).\nMotivated by the delayed explosion of Type II supernovae,\nthe energy deposition rate due\nto the neutrino pair annihilation above the neutrinosphere\nhas been calculated\n(Goodman, Dar \\& Nussinov 1987; Cooperstein, Van Den Horn \\& Baron 1987;\nBerezinsky \\& Prilutsky 1987).\nThe energy deposition rate is proportional to $r^{-8}$ ($r$\nis the distance from the center of the neutrinosphere) for a large $r$,\nand almost all deposition occurs near the neutrinosphere.\nAs they themselves noted in their paper,\nGoodman et al. (1987) neglected the general\nrelativistic effects on the energy deposition rate, which may change\ntheir numerical value seriously.\nIn simulations of the neutrino pair annihilation rate,\nit is very important to confirm whether or not the energy deposition\nrate is altered or not by the gravitational effects.\nIn the recent study, Salmonson \\& Wilson (1999)\nconcluded that the energy deposition rate in Type II\nsupernovae is enhanced about 4 times as a result of the gravitational effects.\nWe must check whether or not their results can be applied to the central engine\nof GRBs.\n\n\nOne of the most probable candidates for the central engine of GRBs\nis the accretion disk around a black hole (Woosley 1993; Popham, Woosley \\& Fryer 1999;\nMacFadyen \\& Woosley 1999; Ruffert \\& Janka 1999).\nThe system of an accretion disk and a black hole may be formed\nby the merging of two neutron stars,\nthe merging of a black hole and a neutron star,\nor the failed supernovae.\nIn general, the baryon density has the lowest value along the rotation axis\njust above the black hole (e.g. see Ruffert \\& Janka 1999).\nThis region might be a key to resolving the baryon contamination problem.\nThe hot accretion disk emits neutrinos and antineutrinos.\nThe energy deposited in the lowest density region is a candidate for\nthe central engine of GRBs.\nUsing hydrodynamic simulations,\nRuffert \\& Janka (1999) showed that the neutrino pair annihilation deposits \nenergy in the vicinity of the torus at a rate of $(3-5)\\times 10^{50}$ ergs ${\\rm s^{-1}}$.\nThey concluded that the gravitational effect on the energy deposition rate\naround the accretion disk is small.\nWe must supplement their results from the analytical side.\n\nIn various arguments on the energy deposition in the central engine of GRBs,\nthe order estimation of the deposited energy is sufficient, at least at present.\nIn this article, based on simple models, we study semianalytically\nthe gravitational effects on the energy deposition rate for two cases.\nIn one case neutrinos are emitted spherically symmetrically.\nIn the other case the hot accretion disk emits neutrinos.\nWe have derived the gravitational effects on the former case independently of\nSalmonson \\& Wilson (1999).\nSome differences of our work from Salmonson \\& Wilson in the formulation,\nthe interpretation of the energy deposition, and the additional factor are\nmentioned.\nAs for the disk case, we assume that the accretion disk is isothermal\nand that the gravitational field is dominated solely by the central\nSchwarzschild black hole.\nThese assumptions enable us to treat the energy deposition around the disk\nsemianalytically.\nThus, in both two cases gravitation is described by the Schwarzschild metric,\nand the essential differences between the two cases\ncome from the shape of the neutrino emitters.\n\nThe gravitational effects consist of three factors:\nthey are the bending of neutrino\ntrajectories, the gravitational redshift, and the trapping of deposited\nenergy into the central gravitational source.\nWe show that the energy deposition rate is indeed enhanced rather crucially by\nthe effect of neutrino bending.\nHowever, it is also shown that the gravitational redshift and the trapping\nof the deposited energy reduce this enhancement.\nAs a result, the gravitational effects do not substantially change the\nenergy deposition rate for either the spherical symmetric case or the disk case.\n\n\n\nThis paper is organized as follows. In section two we investigate\nneutrino pair annihilation near the neutrinosphere.\nThe same process around the accretion disk is\ndiscussed in section three. The last section is devoted to conclusions.\n\n\n\\section{NEUTRINO PAIR ANNIHILATION NEAR THE NEUTRINOSPHERE}\n\n\\indent\n\nIn this section we study the general relativistic effects on\nneutrino pair annihilation near the neutrinosphere.\nThis study has been already done by Salmonson \\& Wilson (1999).\nUsing another method, we formulate the same problem independently of\nthe work of Salmonson \\& Wilson.\nSome alterations in the interpretation of the energy deposition\nin Salmonson \\& Wilson are mentioned.\n\nThe number of reaction, $\\nu+\\bar{\\nu} \\to e^+ +e^-$,\nper unit volume per unit time (Goodman, Dar \\& Nussinov 1987) is written as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\frac{dN(\\mbox{\\boldmath$r$})}{dt dV}=\n\\int \\int f_{\\nu}(\\mbox{\\boldmath$p$}_{\\nu}, \\mbox{\\boldmath$r$})\nf_{\\bar{\\nu}}(\\mbox{\\boldmath$p$}_{\\bar{\\nu}}, \\mbox{\\boldmath$r$})\n\\sigma \\left| \\mbox{\\boldmath$v$}_{\\nu}-\\mbox{\\boldmath$v$}_{\\bar{\\nu}} \\right|\nd^3 \\mbox{\\boldmath$p$}_{\\nu} d^3 \\mbox{\\boldmath$p$}_{\\bar{\\nu}}.\n\\label{first}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%%\nHere $f_{\\nu}$ ($f_{\\bar{\\nu}}$) is the number density of neutrinos\n(antineutrinos) in phase space,\n$\\mbox{\\boldmath$v$}_{\\nu}$ ($\\mbox{\\boldmath$v$}_{\\bar{\\nu}}$)\nis the velocity of neutrinos (antineutrinos),\nand $\\sigma$ is the rest-frame cross section.\nThe left handside of equation (\\ref{first}) is Lorentz invariant,\nsince both the numerator, $dN$, and denominator, $dt dV=\\sqrt{-g} d^4 x$,\nare Lorentz invariant.\nSince $f_{\\nu}$ and $d^3 \\mbox{\\boldmath$p$}_{\\nu}/\\varepsilon_{\\nu}$\n(where $\\varepsilon_{\\nu}$ is the proper energy of neutrinos) of the right handside\nare also Lorentz invariant,\n$\\varepsilon_{\\nu} \\varepsilon_{\\bar{\\nu}}\n| \\mbox{\\boldmath$v$}_{\\nu}-\\mbox{\\boldmath$v$}_{\\bar{\\nu}} | \\sigma$\nshould be Lorentz invariant.\nThe latter is written in a manifest Lorentz-invariant form as\n$ \\sigma c^3 (p_{\\nu} \\cdot p_{\\bar{\\nu}})$,\nwhere $(p_{\\nu} \\cdot p_{\\bar{\\nu}})$ is the inner product of the 4-momenta.\nThe standard model predicts that the cross section is expressed as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\sigma=2 c^2 K G_{\\rm F}^2 (p_{\\nu} \\cdot p_{\\bar{\\nu}}),\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%%\nwhere the dimensionless parameter $K$ is written as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{eqnarray}\nK(\\nu_\\mu \\bar{\\nu_\\mu})&=&K(\\nu_\\tau \\bar{\\nu_\\tau})=\n\\frac{1-4 \\sin^2{\\theta_{\\rm W}}+8\\sin^4{\\theta_{\\rm W}}}{6 \\pi}, \\nonumber \\\\\nK(\\nu_{\\rm e} \\bar{\\nu_{\\rm e}})&=&\n\\frac{1+4 \\sin^2{\\theta_{\\rm W}}+8\\sin^4{\\theta_{\\rm W}}}{6 \\pi}.\n\\end{eqnarray}\n%%%%%%%%%%%%%%%%%%%%%%%%\nHere the Fermi constant $G_{\\rm F}^2=5.29 \\times 10^{-44} {\\rm cm^2\\, MeV^{-2}}$ and\nthe Weinberg angle $\\sin^2{\\theta_{\\rm W}}=0.23$.\n\nLet us incorporate the effects of gravitational force due to the neutron star\nor black hole on the neutrino pair annihilation rate.\nWe assume that the gravitational field is described by the Schwarzschild\nmetric:\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\nds^2=g_{i j} dx^i dx^j=\n\\left( 1-\\frac{r_{g}}{r} \\right) c^2 dt^2-\\frac{1}{1-\\frac{r_{g}}{r}} dr^2\n-r^2 \\left( d\\theta^2-\\sin^2{\\theta} d\\varphi^2 \\right),\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere $r_{g}=2GM/c^2$ is the Schwarzschild radius.\nIn this field the eikonal for a massless particle \n(Landau \\& Lifshitz 1979) is written as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\psi=-\\omega_0 t+L \\varphi+\\psi_r(r),\n\\label{eikonal}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere $\\omega_0$ and $L$ are constants.\n$\\psi_r(r)$ satisfies the equation\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\frac{\\partial \\psi_r(r)}{\\partial r}=\n\\sqrt{\\frac{\\omega_0^2}{c^2} \\left( 1-\\frac{r_{g}}{r} \\right)^{-2}-\\frac{L^2}{r^2}\n\\frac{1}{1-\\frac{r_{g}}{r}}}.\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nFrom equation (\\ref{eikonal}),\nwe can obtain the momentum of a neutrino by\n$p_{i}=\\hbar \\frac{\\partial \\psi}{\\partial x^i}$.\n\nLet us consider a neutrino and an antineutrino moving on the same surface,\n$\\theta=\\pi/2$.\nIn this case, the inner product of the two particles is written by\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{eqnarray}\n(p_{\\nu} \\cdot p_{\\bar{\\nu}})&=&g^{ij} p_{\\nu i} p_{\\bar{\\nu} j} \\\\\n&=& \\frac{\\varepsilon_{\\nu} \\varepsilon_{\\bar{\\nu}}}{c^2}\n\\left( 1-\\sqrt{1-\\left( \\frac{\\rho_{\\nu}}{r}\n\\right)^2 \\left( 1-\\frac{r_{g}}{r} \\right)}\n\\sqrt{1-\\left( \\frac{\\rho_{\\bar{\\nu}}}{r} \\right)^2\n\\left( 1-\\frac{r_{g}}{r} \\right)} \\right. \\nonumber \\\\\n&& \\left. -\\frac{\\rho_{\\nu} \\rho_{\\bar{\\nu}}}{r^2}\n\\left(1-\\frac{r_{g}}{r} \\right) \\right),\n\\label{product}\n\\end{eqnarray}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\rho_{\\nu} \\equiv \\frac{c L_\\nu}{\\omega_{0 \\nu}}.\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%%\nThe proper energy of the neutrino has been written as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\varepsilon_{\\nu} = \\frac{\\hbar \\omega_{0 \\nu}}{\\sqrt{1-\\frac{r_{g}}{r}}}\n\\equiv \\frac{\\varepsilon_{0 \\nu}}{\\sqrt{1-\\frac{r_{g}}{r}}},\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere $\\varepsilon_{0 \\nu}$ is the energy observed at infinity.\nThus the proper energy is redshifted, as is well known.\nIf we define an angle $\\theta_{\\nu}$ as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\sin{\\theta_{\\nu}} = \\frac{\\rho_{\\nu}}{r} \\sqrt{1-\\frac{r_{g}}{r}},\n\\label{sin}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nequation (\\ref{product}) becomes a simple and natural form,\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n(p_{\\nu} \\cdot p_{\\bar{\\nu}})=\\frac{\\varepsilon_{\\nu} \\varepsilon_{\\bar{\\nu}}}{c^2} \n\\left( 1-\\cos{(\\theta{\\nu}-\\theta{\\bar{\\nu}})} \\right).\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nThe angle $\\theta_{\\nu}$ ($\\theta_{\\bar{\\nu}}$)\nrepresents the angle between $\\mbox{\\boldmath$p$}_{\\nu}$ ($\\mbox{\\boldmath$p$}_{\\bar{\\nu}}$)\nand the position vector $\\mbox{\\boldmath$r$}$ (see Figure 1).\nWe assume that the neutrinosphere emits neutrinos and antineutrinos isotropically.\nThen we can write the number densities as\n$f_{\\nu}(\\mbox{\\boldmath$p$}_{\\nu}, \\mbox{\\boldmath$r$})\nd^3 \\mbox{\\boldmath$p$}_{\\nu}=n(\\varepsilon_{\\nu})\n\\varepsilon_{\\nu}^2 d \\varepsilon_{\\nu} d \\Omega$.\nBecause $\\rho_{\\nu}$ is constant along a neutrino ray,\nthe maximum angle, $\\theta_{\\rm M}$, is obtained by\nsubstituting $\\pi/2$ for $\\theta_{\\nu}$ at the radius of the\nneutrinosphere, $R_{\\nu}$, in equation (\\ref{sin}).\nThus we obtain\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\sin{\\theta_{\\rm M}}=\\frac{R_{\\nu}}{r} \\sqrt{\\frac{1-\\frac{r_{g}}{r}}\n{1-\\frac{r_{g}}{R_{\\nu}}}}.\n\\label{sM}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%%\nThe effect of the orbital bending is apparent in this equation.\nUntil now we have discussed the maximum angle on the surface of $\\theta=\\pi/2$.\nIn general cases, the angles between $\\mbox{\\boldmath$p$}_{\\nu}$\nand $\\mbox{\\boldmath$r$}$ or the inner product, $(p_{\\nu} \\cdot p_{\\bar{\\nu}})$,\nare expressed by the two angles, $\\theta_{\\nu}$\nand $\\varphi_{\\nu}$.\nFrom the symmetry, the behaviour of $\\theta_{\\rm M}$ is obviously\nthe same as described in equation (\\ref{sM}),\nand $\\varphi_{\\nu}$ varies from $0$ to $2 \\pi$.\n\nUsing the effective temperature of the neutrinosphere,\n$T_{\\rm eff}=T_0/\\sqrt{g_{00}}$ with a constant $T_0$,\nwe can write the density\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\nn(\\varepsilon_{\\nu})=\\frac{g_{\\nu}}{(hc)^3} \\frac{1}{\\exp{\\left( \n\\frac{\\varepsilon_{\\nu}}{k T_{\\rm eff}}\\right)}+1},\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere $g_{\\nu}$ is a statistical factor\n($g_{\\nu}=1$ for a neutrino).\n$\\varepsilon_{\\nu}/(k T_{\\rm eff})$ is constant along a neutrino ray,\nsince the redshift is cancelled out.\nThus $n(\\varepsilon_{\\nu})$ is conserved along a neutrino ray\nin accordance with Liouville's theorem in curved spacetime\n(Misner, Thorne \\& Wheeler 1975).\nFrom the above formulation, one can find\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\frac{dN(\\mbox{\\boldmath$r$})}{dt dV}=\n2 c K G_{\\rm F}^2 F(r) \\int \\int d \\varepsilon_{\\nu} d \\varepsilon_{\\bar{\\nu}}\nn(\\varepsilon_{\\nu}) n(\\varepsilon_{\\bar{\\nu}})\n\\varepsilon_{\\nu}^3 \\varepsilon_{\\bar{\\nu}}^3,\n\\label{num}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere the dimensionless factor $F(r)$ is written by\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{eqnarray}\nF(r)&=&\\int_0^{\\theta_{\\rm M}} d \\theta_{\\nu} \\sin{\\theta_{\\nu}}\n\\int_0^{\\theta_{\\rm M}} d \\theta_{\\bar{\\nu}} \\sin{\\theta_{\\bar{\\nu}}}\n\\int_0^{2 \\pi} d \\varphi_{\\nu} \\int_0^{2 \\pi} d \\varphi_{\\bar{\\nu}} \\nonumber \\\\\n&& \\times \\left( 1-\\sin{\\theta_{\\nu}} \\sin{\\theta_{\\bar{\\nu}}}\n\\cos{(\\varphi_{\\nu}-\\varphi_{\\bar{\\nu}})}-\\cos{\\theta_{\\nu}} \\cos{\\theta_{\\bar{\\nu}}}\n\\right)^2 \\label{Fr} \\\\\n&=& \\frac{2 \\pi^2 (1-X)^4}{3} (X^2+4X+5),\n\\end{eqnarray}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\nX = \\sqrt{1-\\left( \\frac{R_{\\nu}}{r} \\right)^2\n\\frac{1-\\frac{r_{g}}{r}}{1-\\frac{r_{g}}{R_{\\nu}}}}.\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nIn our assumption, the energy deposited by the neutrino pair annihilation\nis propagated outward as a fireball or a shock wave,\nand observed as a GRB by a distant observer.\nThus the energy we need to calculate is $\\varepsilon_{0 \\nu}$,\nnot the proper energy $\\varepsilon_{\\nu}$.\nIn this case the energy deposition rate is obtained by putting a factor\n$(\\varepsilon_{0 \\nu}+\\varepsilon_{0 \\bar{\\nu}})$ in the integrand\nin equation (\\ref{num});\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{eqnarray}\n\\frac{dE_0 (\\mbox{\\boldmath$r$})}{dt dV}&=&\n\\frac{2 c K G_{\\rm F}^2}{\\left( 1-\\frac{r_{g}}{r} \\right)^4}\n\\int_0^{\\infty} \\int_0^{\\infty} d \\varepsilon_{0 \\nu} d \\varepsilon_{0 \\bar{\\nu}}\n\\nonumber \\label{depo} \\\\\n&& \\times n(\\varepsilon_{0 \\nu}) n(\\varepsilon_{0 \\bar{\\nu}})\n\\varepsilon_{0 \\nu}^3 \\varepsilon_{0 \\bar{\\nu}}^3\n(\\varepsilon_{0 \\nu}+\\varepsilon_{0 \\bar{\\nu}}) F(r) \\\\\n&=& \\frac{21 \\pi^4}{4} \\zeta(5) \\frac{K G_{\\rm F}^2 g_{\\nu}^2}{h^6 c^5}\n\\frac{\\left( 1-\\frac{r_{g}}{R_{\\nu}} \\right)^{\\frac{9}{2}}}\n{\\left( 1-\\frac{r_{g}}{r} \\right)^4} (k T_{\\rm eff})^9 F(r).\n\\label{depo2}\n\\end{eqnarray}\n%%%%%%%%%%%%%%%%%%%%%%%\nThe integrals for $\\varepsilon_{0 \\nu}$ and $\\varepsilon_{0 \\bar{\\nu}}$\nshould be defined in the range in which the total energy\nproduced by the pair annihilation is larger than the mass of created electrons,\nand smaller than the masses of weak bosons.\nHere we have approximated the integrals as expressed in equation (\\ref{depo})\nin the same manner as Salmonson \\& Wilson (1999) did.\nThis is because the cross section decreases with the energy of neutrinos,\nand the number of neutrinos whose energy is larger than the masses of weak bosons\nis also very small in our assumption ($k T_{\\rm eff}$ is of the order of several MeV).\nThe factor $( 1-r_{g}/R_{\\nu})^{9/2} /( 1-r_{g}/r )^4$ represents\nthe effect of the gravitational redshift,\nand $F(r)$ includes the effect of the orbital bending.\n\nAs is understood from the Lorentz invariant, $dtdV=\\sqrt{-g} d^4 x$,\nif we integrate equation (\\ref{depo2}) over proper volume,\n$dV'=\\sqrt{-g_{rr} g_{\\theta \\theta} g_{\\varphi \\varphi}} dr d\\theta d\\varphi$,\nwe can obtain the total energy deposition per unit proper time,\n$d \\tau=\\sqrt{g_{00}} dt$.\nIt is natural to evaluate the energy deposition rate\nby the world time $dt$ for a distant observer.\nWe integrate over the volume,\n$dV=\\sqrt{g_{\\theta \\theta} g_{\\varphi \\varphi}} dr d\\theta d\\varphi$.\nThus the energy deposition per unit world time is expressed as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\frac{dE_0}{dt}=\n\\frac{21 \\pi^4}{4} \\zeta(5) \\frac{K G_{\\rm F}^2 g_{\\nu}^2}{h^6 c^5} (k T_{\\rm eff})^9\n\\left( 1-\\frac{r_{g}}{R_{\\nu}} \\right)^{\\frac{9}{2}}\n\\int_{R_{\\nu}}^{\\infty} dr 4 \\pi r^2\n\\frac{F(r)}{\\left( 1-\\frac{r_{g}}{r} \\right)^4} C(r),\n\\label{result}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere we have put a factor,\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\nC(r)=\\frac{1}{2} \\left( 1+\\sqrt{1-\\frac{27}{4} \\left( \\frac{r_{g}}{r} \\right)^2\n\\left( 1-\\frac{r_{g}}{r} \\right) } \\right),\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nin the integrand.\nThis is the escape probability of the deposited energy at $r$\nfrom the gravitational attraction\n(Chandrasekhar 1983; Shapiro \\& Teukolsky 1983; Ruffert \\& Janka 1999).\nThe electrons, positrons and photons which are captured by the gravitational attraction\ncannot contribute to the energy source of GRBs.\nApart from $C(r)$,\nthe radial profile in the integrand of equation (\\ref{result}) \nis different from those of Salmonson \\& Wilson (1999),\nsince Salmonson \\& Wilson calculated the proper energy deposition per\nunit proper time.\nOf course, the results of Salmonson \\& Wilson are not mistakes for the estimate of\nthe energy deposition rate in supernovae.\nFor the source of GRBs, however,\nequation (\\ref{result}) is adequate.\n\nLet us investigate the effects of the redshift, orbital bending and gravitational capture.\nWe integrate equation (\\ref{result}) and obtain\nthe energy deposition rate for $\\nu_{e}$ as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\frac{dE_0}{dt}=1.27 \\times 10^{42} \\left( \\frac{k T_{\\rm eff}}{1 {\\rm MeV}} \\right)^9\n\\left( \\frac{R_{\\nu}}{10 {\\rm km}} \\right)^3 f \\quad \\mbox{ergs ${\\rm s^{-1}}$},\n\\label{Gf}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere the dimensionless factor $f$ expresses the effects of the general relativity\n($f=1$ when we neglect the gravitation).\nThe energy deposition rates for $\\nu_{\\mu}$ and $\\nu_{\\tau}$ are 0.64 times\nequation (\\ref{Gf}).\nWe numerically estimate $f$ including the effects of the redshift only,\nthe orbital bending only, or both redshift and orbital bending.\nLast, the total effects of the redshift, orbital bending, and gravitational capture\nare calculated.\nThe results are listed in Table 1.\nAs Table 1 or equation (\\ref{result}) indicates,\nthe effect of the redshift reduces the energy deposition rate,\nand the effect of the orbital bending increases it.\nAlthough each effect, that of the redshift and that of orbital bending, is substantial,\nthe effects partly cancel each other.\nAs a result, the order of the energy deposition rate for\nthe most probable case, $R_{\\nu}/r_g=2.5$, is not altered.\nWhen we neglect the general relativistic effects, the energy deposition rate\nincreases by 1.3 times as $R_{\\nu}$ becomes 10\\%\nlarger, and also increases by 2.4 times as the temperature becomes 10\\%\nhigher.\nTherefore, the gravitational effects are not so large in comparison with\nthe errors due to the uncertainties of $R_{\\nu}$ or $T_{\\rm eff}$,\nand are overwhelmed by them.\nThe effect of the gravitational capture becomes important\nas $R_{\\nu}/r_g$ decreases.\nAs is plotted in Figure 2, in the cases of both the presence and absence\nof gravitation, the energy deposition mainly occurs near the neutrinosphere.\n\n\nSalmonson \\& Wilson (1999) concluded that the effects of gravity\nenhance the energy deposition rate up to a factor of more than\n4 for $R_{\\nu} \\le 2.5 r_g$. However, our results\nshow that the gravitational effects reduce the energy deposition rate.\nThis discrepancy survives even if we omit the escape factor $C(r)$.\nThe proper energy deposition per unit proper time is enhanced\nby both the effects of the redshift and that of orbital bending.\nAdditionally, Salmonson \\& Wilson expressed the general relativistic\neffects with the fixed neutrino luminosity at infinity $L_{\\infty}$,\nwhereas we have done so with the local physical quantity $T_{\\rm eff}$.\nTherefore, an additional factor coming from the redshift of the luminosity\n($L(R_{\\nu}) \\propto T_{\\rm eff}^4$, $L_{\\infty}=(1-{r_g/R_{\\nu}})L(R_{\\nu})$)\nenhances the energy deposition rate in the work of Salmonson \\& Wilson.\nHowever, the quantity $L_{\\infty}$ of GRBs is not directly observable at present.\nIt is more natural to study the effects for the given local parameters,\n$T_{\\rm eff}$ or $L(R_{\\nu})$,\nwhich is restricted or provided by models of the central engine.\n\n\\section{NEUTRINO PAIR ANNIHILATION AROUND THE ACCRETION DISK}\n\n\\indent\n\n\nIn this section we investigate the energy deposition rate around the accretion disk.\nIn order to simplify our formulation,\nwe assume that the accretion disk is isothermal\nand that the gravitational field is dominated\nby the central Schwarzschild black hole.\nWe neglect the rotation of the black hole.\nThe accretion disk is assumed to be thin, and its self-gravitational effects\nare neglected.\nOf course, these idealizations may be far from the case of the realistic accretion disk.\nHowever, we consider that this simple method is sufficient for qualitatively studying\nthe gravitational effects on the energy deposition rate.\nIn this case the equation of the energy deposition rate is\nthe same as equation (\\ref{depo2}) provided that $F(r)$\nis replaced by $F(r,\\theta)$ (it will be given below).\nThe effect of the gravitational redshift can be easily incorporated,\nwhereas the formulation of the neutrino bending is difficult to do\nbecause the accretion disk emits neutrinos anisotropically.\n\nFirst, we calculate the dimensionless factor $F(r, \\theta)$\nwithout the effect of gravity.\nThe accretion disk is placed on the equatorial plane, $\\theta=\\pi/2$.\nThe black hole is at the origin, and we consider\na point $P=(r,\\theta,0)$ where pair annihilations occur (see Figure 3).\nA neutrino is emitted from an arbitrary point on the disk $S=(R,\\pi/2,\\varphi)$,\nwhere $R$ is limited in the range from $R_{\\rm in}$ to $R_{\\rm out}$.\nThe neutrino emitted from $S$ travels straight and arrives at the point $P$.\nLet us denote the angle components of the vector joining $S$ and $P$\nby $(\\theta_{\\nu}, \\varphi_{\\nu})$.\nThey are given by\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\cos{\\theta_{\\nu}}=\\frac{r \\cos{\\theta}}{\\sqrt{r^2+R^2-2 r R \\sin{\\theta} \\cos{\\varphi}}},\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%\n%\\begin{equation}\n%\\sin{\\theta_{\\nu}}=\\frac{\\sqrt{r^2 \\sin^2{\\theta}+R^2-2 r R \\sin{\\theta} \\cos{\\varphi}}}\n%{\\sqrt{r^2+R^2-2 r R \\sin{\\theta} \\cos{\\varphi}}},\n%\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%\n%\\begin{equation}\n%\\cos{\\varphi_{\\nu}}=\\frac{r \\sin{\\theta}-R \\cos{\\varphi}}\n%{\\sqrt{r^2 \\sin^2{\\theta}+R^2-2 r R \\sin{\\theta} \\cos{\\varphi}}},\n%\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\sin{\\varphi_{\\nu}}=\\frac{-R \\sin{\\varphi}}\n{\\sqrt{r^2 \\sin^2{\\theta}+R^2-2 r R \\sin{\\theta} \\cos{\\varphi}}}.\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nThus $\\theta_{\\nu}$ and $\\varphi_{\\nu}$ are functions of $R$ and $\\varphi$\nfor fixed $r$ and $\\theta$.\nThe Jacobian $J \\equiv \\partial (\\theta_{\\nu}, \\varphi_{\\nu})/\\partial (R, \\varphi)$ is\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\nJ=\\frac{r R \\cos{\\theta}}\n{\\sqrt{r^2 \\sin^2{\\theta}+R^2-2 r R \\sin{\\theta} \\cos{\\varphi}}\n( r^2+R^2-2 r R \\sin{\\theta} \\cos{\\varphi})}.\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nConsequently, we obtain $F(r,\\theta)$ as\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{eqnarray}\nF(r,\\theta)&=&\\int_{R_{\\rm in}}^{R_{\\rm out}} dR \\int_{R_{\\rm in}}^{R_{\\rm out}} dR'\n\\int_0^{2 \\pi} d \\varphi \\int_0^{2 \\pi} d \\varphi' J J' \\nonumber \\\\\n& \\times & \\sin{\\theta_{\\nu}} \\sin{\\theta_{\\bar{\\nu}}}\n\\left( 1-\\sin{\\theta_{\\nu}} \\sin{\\theta_{\\bar{\\nu}}}\n\\cos{(\\varphi_{\\nu}-\\varphi_{\\bar{\\nu}})}-\\cos{\\theta_{\\nu}} \\cos{\\theta_{\\bar{\\nu}}}\n\\right)^2.\n\\label{Frtheta}\n\\end{eqnarray}\n%%%%%%%%%%%%%%%%%%%%%%%\n\nIn equation (\\ref{Frtheta}) we adopt $R_{\\rm in}=3r_g$, the innermost stable orbit, and\n$R_{\\rm out}=10r_g$ as Woosely (1993) assumed. $F(r,\\theta)$ derived from\nthe numerical integral of equation (\\ref{Frtheta}) is plotted in Figure 4(a) and (b).\nAs is shown in these figures, the energy deposition rate is maximized in the\nvicinity of the accretion disk, where $F(r,\\theta) \\simeq 30-33$.\nThe simulation of a neutron star merger by Ruffert \\& Janka\n(1999) showed that the Paczy\\'nski-Wiita potential (Paczy\\'nski \\& Wiita 1980),\nwhich mimics the effects of the general relativity,\ngives a relatively more transparent disk for neutrinos than\nthat given by the Newtonian potential.\nThe profile of the energy deposition rate in the Paczy\\'nski-Wiita potential\nis similar to our analytical one depicted in Figure 4(a), which shows that the rate takes\nits maximum value on the surface of the disk.\nOn the other hand, the simulated deposition rate in the Newtonian potential\nis maximized near the rotation axis.\nLet us calculate the energy deposition rate near the rotation axis,\nwhere is the lowest baryon density region.\nThus we calculate in the region $\\theta \\leq \\pi/4$\nand obtain\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\frac{dE_0}{dt}=5.22 \\times 10^{43} \\left( \\frac{k T_{\\rm eff}}{1 {\\rm MeV}} \\right)^9\n\\left( \\frac{r_g}{10 {\\rm km}} \\right)^3 G f \\quad \\mbox{ergs ${\\rm s^{-1}}$},\n\\label{Gf2}\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nwhere the dimensionless quantity $G$ shows the relative contributions\nfrom various regions in the absence of gravitation.\n$G$ is normalized to unity when\nwe integrate over the volume for $\\theta \\leq \\pi /4$ and $r=2r_g-10r_g$.\nThe values of $G$ in the other regions are summarized in Table 2, from\nwhich we can obtain the energy deposition rate in the respective region.\nWe neglect the energy deposited inside $r=2 r_g$,\nsince the baryon density in this region is very high and\nthe energy contribution is small for the small volume and deposition rate.\nIn the case of the spherical emitter in section 2, the deposition rate decreases as\n$r^{-8}$.\nOn the other hand, around the accretion disk, as is seen from Table 2, there remains a\nmarginal deposition rate even at regions relatively distant from the center.\nOf course the deposition rate per unit volume at distant positions is small.\nHowever, large volume results in a non-negligible contribution at the regions\ndistant from the center.\n\nUntill now we have neglected the gravitational effects.\nIt is easy to incorporate the effects of the redshift and\ntrapping by the central gravitational source in the preceding arguments of this\nsection. However, the bending effect is difficult to treat, unlike the case\nof the neutrinosphere, since the accretion disk emits neutrinos anisotropically.\nThus we are forced to make some approximation.\nAs is shown in Figure 4(b), the $\\theta$ dependence of $F(r,\\theta)$ is weak for \nsmall $\\theta$.\nWe may set $F(r,\\theta) \\simeq F(r,0)$ for $\\theta \\leq \\pi/4$.\nIn the absence of gravitation if we adopt this\napproximation in the region $\\theta \\leq \\pi /4$ and $r=2r_g-10r_g$,\nwe obtain $G=0.81$.\nThe exact value of $G$ is unity, and this approximation is not\nnecessarily satisfactory. However, this approximation may be sufficient for the order\nestimate of the gravitational effects.\n\nWe can obtain $F(r,0)$ including the effect of orbital bending\nwith comparative ease,\nsince the geometry of this case maintain the symmetry.\nA neutrino is emitted from the disk at $R$ and $\\theta=\\pi/2$,\nand it arrives at a point at $r$ and $\\theta=0$.\nThe nearest distance, $r_0$,\nfrom the origin to the orbit of neutrinos (Landau \\& Lifshitz 1979)\nis numerically obtained from\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\pi/2=\\int_{\\rm C} \\frac{dr'}{r' \\sqrt{\\left( \\frac{r'}{r_0} \\right)^2\n\\left(1-\\frac{r_g}{r_0} \\right)-\\left(1-\\frac{r_g}{r'} \\right)}}.\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nHere, in the case in which a neutrino passes through $r_0$\nuntil it arrives at a point at $\\theta=0$,\nthe integration for $r'$ is performed from $r_0$ to $R$ and $r$.\nWhen the distance from the origin to the neutrino varies monotonically,\nthe integration is performed from the smaller\nto the larger of $r$ and $R$.\nWe can get $\\theta_{\\nu}$ at $\\theta=0$ numerically from $r_0$ and the following equation;\n%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation}\n\\sin{\\theta_{\\nu}}=\\frac{r_0}{r} \\sqrt{\\frac{1-\\frac{r_g}{r}}{1-\\frac{r_g}{r_0}}}.\n\\end{equation}\n%%%%%%%%%%%%%%%%%%%%%%%\nThe constant, $r_0$, or $\\theta_{\\nu}$, is a function of $r$ and $R$ in this case.\nAs is easily understood, a neutrino coming from $R_{\\rm in}$ forms $\\theta_{\\rm m}$,\nthe minimum value of $\\theta_{\\nu}$, at $\\theta=0$ and that from\n$R_{\\rm out}$ forms the maximum value of $\\theta$, $\\theta_{\\rm M}$.\nIntegrating equation (\\ref{Fr}) from $\\theta_{\\rm m}$ to $\\theta_{\\rm M}$,\nwe obtain $F(r,0)$ involving gravitational effects.\nIn Figure 5 we plot $F(r,0)$ for both the case when the bending is taken into\nconsideration and the case when it is not.\nIn comparison with the spherical case in Figure 2,\nthe deposited energy at distant regions in the disk case\nis marginally substantial.\nIn the presence of bending, the peak of the energy deposition rate is\nshifted to a little bit larger $r$ and the value of the rate at the peak\nis about twice as larger as values obtained in the absence of bending.\n\nAlthough the $\\theta$ dependence of the gravitational effects may not necessarily\nbe small, unlike $F(r,\\theta)$ in the absence of gravitation,\nwe assume it is small here. Using $F(r,0)$\nwith the bending effect, we calculate the energy deposition rate in the range\n$\\theta \\le \\pi/4$ and $r=2 r_g-10 r_g$.\nTable 3 lists the values of the factor $f$ that shows the gravitational effects.\nThe $\\theta$-dependence is neglected in our calculation\nexcept for the case involving the redshift only.\nThus $f$ is normalized to unity when $F(r,\\theta)$\n(in the case involving the effect of the redshift only)\nor $F(r,0)$ (in the other cases) is integrated over $r$ and $\\theta$\nin the absence of gravitation.\nAs is easily seen, the gravitational effects cancel one another out.\nThis is analogous to the neutrino sphere case in the previous section.\n%%%\nThis result strongly supports that of Ruffert \\& Janka (1999).\nThey treated the system of the accretion torus and a black hole unlike our\nsystem of the disk and a black hole.\nUsing an approximation similar to ours,\nthey analytically calculated\nthe energy deposition rate due to the neutrino pair annihilation.\nTheir result is that the gravitational effects reduce the deposition rate by a factor\nof $10-30\\%$.\nIt agrees well with our result.\n%%%\n\nIn order to circumvent the baryon contamination problem,\nthe energy fraction of baryonic matter in the fireball\nmust be less than about $10^{-5}$ (Shemi \\& Piran 1990).\nIf we adopt the duration time of the neutrino radiation to be $t_{\\rm\ndur}=0.1$s and $T_{\\rm eff}=10$MeV,\nthe highest mean mass densities $\\bar{\\rho}$ inside $\\theta=0-\\pi/3$ to resolve\nthe above problem are\n$10^6$g/${\\rm cm^3}$ for $r=2 r_g-5 r_g$,\n$10^5$g/${\\rm cm^3}$ for $r=5 r_g-10 r_g$ and\n$10^4$g/${\\rm cm^3}$ for $r=10 r_g-20 r_g$.\nSince some fraction of energy really\nescapes from the considered regions during the finite duration time,\nthe above restrictions may become more stringent.\n\n\n\n\n\\section{CONCLUSIONS}\n\n\\indent\n\nIn this article we have investigated semianalytically\nthe neutrino pair annihilation near\nthe neutrinosphere and around the thin accretion disk assuming that the\ngravitational sources in both cases are described by the Schwarzschild metric.\nThe accretion disk has been assumed to be a blackbody and isothermal.\nThese assumptions enable us to treat these two cases based in an almost\nunified fashion, which also clarifies the physical differences between these\ntwo cases.\nWe have studied the general relativistic effects only near the rotation axis,\nbecause that region is especially of interest to the source of GRBs\nand estimating the effect of orbital bending\nfor large $\\theta$ is difficult.\n\n\nThe general relativistic effects as a whole do not enhance the neutrino energy\ndeposition rate in either case.\nThe energy deposition rate is enhanced by\nthe effect of orbital bending toward the center.\nHowever, the enhancement is cancelled out by the effects of the redshift and\ncapture by the gravitational attraction.\nConsequently, numerical simulations of the neutrino energy\ndeposition rate in various models can correctly estimate\nthe order of the rate without considering the gravitational effects,\nsince it is supposed\nthat the thickness, shape, or temperature distribution of the disk or sphere\ndoes not greatly affect the gravitational effects themselves.\n%%%\nTaking into account also the results of Ruffert \\& Janka (1999), the\nconclusions mentioned above are strongly suggested to be valid in the following\ngeometrical forms of the neutrino source: sphere, thin disk and torus.\n%%%\nWe have also shown that the neutrinos emitted from the disk can\ndeposit energy at more distant regions than the neutrinos emitted\nfrom the sphere.\nThe importance in this article resides in\nthe qualitative properties of the general relativistic effects.\nThe quantitative calculations in this paper are not so important,\nand should be investigated on the basis of more sophisticated models and simulations.\n\n\n\n\n\n\n\n\n\n\\vspace{1.5cm}\n\n%We are grateful to A and the referee\n%for their helpful advice.\nWe appreciate the helpful advice of M. Ruffert.\nThis work was partly supported by a Research Fellowship of the Japan Society for\nthe Promotion of Science.\n%and\n%B\n%for C.\n%Lastly, we appreciate D for E.\n\n\\newpage\n\n\\begin{center}\n{\\bf \\LARGE References}\n\\end{center}\n\n\\medskip\n\n\\begin{description}\n\n\\item\nBerezinsky, V. S., \\& Prilutsky, O. F. 1987, A\\&A 175, 309\n\\item\nChandrasekhar, S. 1983, The Mathematical Theory of Black Holes\n(New York: Oxford)\n\\item\nCooperstein, J., Van Den Horn, L. J., \\& Baron, E. 1987, ApJ 321, L129\n\\item\nEichler, D., Livio, M., Piran, T., \\& Schramm, D. N. 1989, Nature 340, 126\n\\item\nGoodman, J., Dar, A., \\& Nussinov, S. 1987, ApJ 314, L7\n\\item\nJanka, H.-T., \\& Ruffert, M. 1996, A\\&A 307, L33\n\\item\nKatz, J. I. 1997, ApJ 490, 633\n\\item\nLandau, L. D., \\& Lifshitz, E. M. 1979, Classical Theory of Fields\n(London: Pergamon)\n\\item\nMacFadyen, A., \\& Woosley, S. E. 1999, ApJ 524, 262\n\\item\nM\\'esz\\'aros, P., \\& Rees, M. J. 1992a, ApJ 397, 570\n\\item\nM\\'esz\\'aros, P., \\& Rees, M. J. 1992b, MNRAS 257, 29p\n\\item\nM\\'esz\\'aros, P., \\& Rees, M. J. 1993, ApJ 405, 278\n\\item\nMisner, C. W., Thorne, K. S., \\& Wheeler, J. A. 1975,\nGravitation (New York: Freeman)\n\\item\nNarayan, R., Paczy\\'nski, B., \\& Piran, T. 1992, ApJ 395, L83\n\\item\nPaczy\\'nski, B. 1990, ApJ 363, 218\n\\item\nPaczy\\'nski, B. 1998, ApJ 494, L45\n\\item\nPaczy\\'nski, B., \\& Wiita, P. J. 1980, A\\&A 88, 23\n\\item\nPopham, R., Woosley, S. E., \\& Fryer, C. 1999, ApJ 518, 356\n\\item\nRees, M. J., \\& M\\'esz\\'aros, P. 1992, MNRAS 258, 41p\n\\item\nRuffert, M., \\& Janka, H.-T. 1998, A\\&A 338, 535\n\\item\nRuffert, M., \\& Janka, H.-T. 1999, A\\&A 344, 573\n\\item\nRuffert, M., Janka, H.-T., Takahashi, K., \\& Sch\\\"afer, G. 1997, A\\&A 319, 122\n\\item\nSalmonson, J. D., \\& Wilson, J. R. 1999, ApJ 517, 859\n\\item\nSari, R., Narayan, R., \\& Piran, T. 1996 ApJ 473, 204\n\\item\nSari, R., \\& Piran, T. 1995, ApJ 455, L143\n\\item\nShapiro, S. L., \\& Teukolsky, S. A. 1983, Black Holes, White Dwarfs and Neutron Stars\n(New York: Wiley)\n\\item\nShemi, A., \\& Piran, T. 1990, ApJ 365, L55\n\\item\nWoosley, S. E. 1993, ApJ 405, 273\n\n\n\n\n\\end{description}\n\\newpage\n\n\\begin{center}\n{\\bf \\large Figure captions}\n\\end{center}\n\n\n\\figcaption{Maximum angle $\\theta_{\\rm M}$ at a distance $r$ from the\ncenter formed by neutrinos emitted from the surface of the neutrinosphere.\nThe dashed line shows the orbit forming the maximum\nangle in the absence of gravitation.}\n\n\\figcaption{The plot of $F(r)$ against $r$ for $R_{\\nu}=2.5r_g$ when neutrinos are\nemitted isotropically.\nThe solid (dashed) line shows $F(r)$ for the case in the presence (absence) of\ngravitation. The origin is at $r=R_{\\nu}$.}\n\n\\figcaption{Geometry of neutrino's path.\nA neutrino is emitted from a point $S=(R,\\pi/2,\\varphi)$ on the disk and arrives at\n$P=(r,\\theta,0)$. The angular components of the vector joining $S$ and $P$ are\n$(\\theta_{\\nu}, \\varphi_{\\nu})$.\n$R$ (radius on the disk) is limited to the range from $R_{\\rm in}$ to $R_{\\rm out}$.}\n\n\\figcaption{Contour plot of $F(r,\\theta)$ where neutrinos are\nemitted from the disk. Here gravitation has been neglected.\n%%%\n(a) Plot in Cartesian coordinates $(r \\sin{\\theta},r \\cos{\\theta})$.\n(b) Plot in polar coordinates, $(r, \\theta)$.\n%%%\nThe contours\nare plotted at unit intervals except for the line of $F(r,\\theta)=0.1$;\n$\\theta=0$ and $\\theta=\\pi/2$ correspond to points on the rotation\naxis and on the disk, respectively.}\n\n\\figcaption{Diagram of $F(r,0)$ vs. $r$\nwhere neutrinos are emitted from the disk.\nThe solid (dashed) line shows $F(r,0)$ for the case in which we\nconsider (neglect) the effect of gravitational bending.}\n\n\n\n\\newpage\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline \\hline\n$R_{\\nu}/r_{g}$ & \\multicolumn{4}{c}{$f$} \\\\\n&Redshift Only & Bending Only & Redshift and Bending & Whole \\\\ \\hline\n1.5 & 0.32 & 4.7 & 0.97 & 0.57 \\\\\n2.5 & 0.60 & 1.6 & 0.87 & 0.73 \\\\\n5 & 0.81 & 1.2 & 0.93 & 0.89 \\\\ \\hline\n\\end{tabular}\n\\end{center}\n{\\footnotesize Table~1. The dimensionless factor $f$ represents\nthe general relativistic effects (see eq. [\\ref{Gf}])\nwhen neutrinos are emitted isotropically from the neutrinosphere;\n$f$ is normalized to unity in the absence of gravitation.\nThe column headings \"Redshift Only\" and so on indicate\nthe incorporated effects of gravitation;\n\"Whole\" over the last column means that we incorporate\nall gravitational effects, redshift, bending, and trapping.\nThe energy deposition rate is enhanced by orbital bending\nand reduced by the redshift and trapping.}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline \\hline\n$\\theta$ & $2 r_g-5 r_g$ & $5 r_g-10 r_g$ & $10 r_g-20 r_g$ \\\\ \\hline\n$0-\\pi/4$ & 0.35 & 0.65 & 0.22 \\\\\n$\\pi/4-\\pi/3$ & 0.32 & 0.77 & 0.17 \\\\ \\hline\n%$\\pi/3-\\pi/2$ & 2.27 & 0.21 \\\\ \\hline\n\\end{tabular}\n\\end{center}\n{\\footnotesize Table~2. The dimensionless factor $G$.\nIt represents the fraction of the energy deposition rate for each region\n(see eq. [\\ref{Gf2}])\nwhen neutrinos are emitted from the disk.\n$G$ is normalized to unity for the region surrounded by\n$r=2 r_g-10 r_g$ and $\\theta=0-\\pi/4$.\nHere we neglect the effects of gravitation.}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline \\hline\nrange & \\multicolumn{4}{c}{$f$} \\\\\n&redshift only & bending only & redshift and bending & whole \\\\ \\hline\n$2 r_g-5 r_g$ & 0.66 & 2.6 & 1.6 & 1.4 \\\\ \n$5 r_g-10 r_g$ & 0.31 & 2.5 & 0.78 & 0.75 \\\\ \\hline\n\\end{tabular}\n\\end{center}\n{\\footnotesize Table~3. The dimensionless factor $f$ for $\\theta=0-\\pi/4$\n(see equation [\\ref{Gf2}]).\nNeutrinos are emitted from the disk;\n$f$ is normalized to unity when $F(r,\\theta)$\n(in the case involving the effect of the redshift only)\nor $F(r,0)$ (in the other cases) is integrated over $r$ and $\\theta$\nin the absence of gravitation.}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\\begin{center}\n%\\begin{tabular}{cccc}\n%\\hline \\hline\n%$\\theta$ & $2 r_g-5 r_g$ & $5 r_g-10 r_g$ & $10 r_g-20 r_g$ \\\\ \\hline\n%$0-\\pi/4$ & $1.8 \\times 10^7$ & $2.5 \\times 10^6$ & $3.2 \\times 10^5$ \\\\\n%$\\pi/4-\\pi/3$ & $2.5 \\times 10^7$ & $3.4 \\times 10^6$ & $4.3 \\times 10^5$ \\\\ \\hline\n%\\end{tabular}\n%\\end{center}\n%{\\footnotesize Table~4. The highest mean density $\\bar{\\rho}$ for $\\eta \\geq 10^5$.\n%We assume $T_{\\rm eff}=10$ MeV.}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\end{document}"
}
] |
[] |
astro-ph0002197
|
First VLT spectra of white dwarfs in a globular cluster
|
[
{
"author": "S.~Moehler\\inst{1}\\fnmsep\\thanks{Based on observations collected at the European Southern Observatory (ESO~N$^{\\b{o}}$~63.H-0348)}"
},
{
"author": "U.~Heber\\inst{1}"
},
{
"author": "R. Napiwotzki\\inst{1}"
},
{
"author": "D. Koester\\inst{2}"
},
{
"author": "A. Renzini\\inst{3}"
}
] |
We present the first spectra obtained with the {\em Very Large Telescope} for white dwarfs in a globular cluster. Estimates of atmospheric parameters are obtained and compared to evolutionary tracks. We discuss possible implications for the distance scale of globular clusters and white dwarf evolution and demonstrate how white dwarfs might be used to establish an independent distance scale to globular clusters.
|
[
{
"name": "b1293.tex",
"string": "\\documentclass{aa}\n\\begin{document}\n\\newcommand\\bsec{\\hbox{$.\\!\\!{\\arcsec}$}}\n\\newcommand\\rsec{\\hbox{$.\\!\\!{^s}$}}\n\\newcommand\\RA[4]{#1$^{\\rm h}$#2$^{\\rm m}$#3\\rsec#4}\n\\newcommand\\DEC[3]{#1$^{\\circ}$#2\\arcmin#3\\arcsec}\n\\newcommand{\\magpt}[2]{\\mbox{$\\rm #1\\hspace{-0.25em}\\stackrel{m}{.}\n \\hspace{-1.0mm}#2$}} % magnitude \\magpt {}{}\n\\newcommand\\ebv{$E_{B-V}$} \n\\newcommand\\teff{$T_{\\rm eff}$} \n\\newcommand\\logt{$ \\log\\,T_{\\rm eff}$}\n\\newcommand\\logg{$ \\log\\,g$}\n\\newcommand\\loghe{$ \\log{\\frac{n_{\\rm He}}{n_{\\rm H}}}$}\n\\newcommand\\Msolar{${\\rm M_\\odot}$}\n\\thesaurus{01 (08.06.3, 08.16.3, 08.23.1, 10.07.3 NGC~6397)}\n\n\\title{First VLT spectra of white dwarfs in a globular cluster}\n\\author{S.~Moehler\\inst{1}\\fnmsep\\thanks{Based on observations collected at the \n European Southern Observatory (ESO~N$^{\\b{o}}$~63.H-0348)} \n \\and U.~Heber\\inst{1} \\and R. Napiwotzki\\inst{1} \\and\n D. Koester\\inst{2} \\and A. Renzini\\inst{3}}\n\\offprints{S.~Moehler}\n\\institute {Dr. Remeis-Sternwarte, Astronomisches Institut der Universit\\\"at\n Erlangen-N\\\"urnberg, Sternwartstr. 7, 96049 Bamberg, Germany \n (e-mail: moehler,heber,napiwotzki@sternwarte.uni-erlangen.de)\n\\and Institut f\\\"ur Theoretische Physik und Astrophysik, Abteilung \n Astrophysik, Leibnizstr. 15, D-24098 Kiel, Germany\n\\and European Southern Observatory, Karl Schwarzschild-Str. 2, D-85748 \nGarching bei M\\\"unchen, Germany\n}\n\\date{}\n%\\titlerunning{}\n\\maketitle\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% FOLLOWING TYPESETTING RULES SET OUT IN \"ASTRONOMY AND ASTROPHYSICS %%\n%% INSTRUCTIONS FOR AUTHORS\" -- ASTRON. ASTROPHYS. 341 (1) 1999 %% \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\begin{abstract}\nWe present the first spectra obtained with the {\\em Very Large Telescope}\nfor white dwarfs in a\nglobular cluster. Estimates of atmospheric parameters are obtained and\ncompared to evolutionary tracks. We discuss possible implications for the\ndistance scale of globular clusters and white dwarf evolution and\ndemonstrate how white dwarfs might be used to establish an independent\ndistance scale to globular clusters. \n\\end{abstract}\n\n\\keywords{Stars: fundamental parameters -- Stars: Population~II -- Stars: \n white dwarfs -- globular clusters: individual: NGC~6397}\n\n\\section{Introduction} \nWhite dwarfs are the final stage of all low-mass stars and therefore all\nsingle stars in a globular cluster that currently finish their\nnuclear-burning lifetimes are expected to evolve into white dwarfs. As this\nhas been the situation for many billions of years globular clusters should\ncontain many white dwarfs. However, these stars managed to evade detection\nuntil photometric white dwarf sequences in globular clusters were\ndiscovered recently by observations with the {\\em Hubble Space Telescope}\n(HST) (Paresce et al.\\ \\cite{pade95}, Richer et al.\\ \\cite{rifa95},\n\\cite{rifa97}, Cool et al.\\ \\cite{copi96}, Renzini et al.\\ \\cite{rebr96}).\nPhotometric observations contain only a limited amount of information: The\ntwo chemically distinct white dwarfs sequences (hydrogen-rich DA's and\nhelium-rich DB's) in principle can be distinguished by their photometric\nproperties alone in the temperature range $10,000\\,K \\leq T_{\\mathrm{eff}}\n\\leq 15,000$\\,K (see Bergeron et al.\\ \\cite{bewe95}). Renzini et al.\\\n(\\cite{rebr96}) classified two white dwarfs in NGC\\,6752 as DB's by this\nmethod. However, without a spectral classification, both stars can also be\nexplained as high mass DA white dwarfs, possibly a product of merging.\nRicher et al.\\ (\\cite{rifa97}) speculate that the brightest white dwarf in\nM\\,4 (V=22.08) might be a hot (27,000K) DB star. \n\\newline\\indent\nThe location of the white dwarf cooling sequence (and thus the brightness\nof the white dwarfs) is also sensitive to the white dwarf mass. Renzini et\nal.\\ (\\cite{rebr96}) argued that the white dwarf masses in globular\nclusters are constrained to the narrow range 0.51\\Msolar $\\leq {\\rm M_{WD}}\n\\leq$ 0.55\\Msolar, but some systematic differences between clusters are\nobvious: At a given metallicity some globular clusters (e.g.\\ NGC\\,6752)\npossess very blue horizontal branches (HB's) with HB star masses as low as\n0.50\\Msolar. Such extreme HB stars evolve directly to low-mass C/O white\ndwarfs (bypassing the AGB), shifting the mean white dwarf mass closer to\n0.51\\Msolar. Other clusters show only red HB stars, which will evolve to\nthe AGB and form preferably white dwarfs with masses of $\\approx$0.55\\Msolar. \n\\begin{figure}\n\\vspace{8cm}\n\\special{psfile=b1293.f1 hscale=100 vscale=100 hoffset=-130 voffset=-330\nangle=0}\n\\caption{Colour-magnitude diagram of NGC~6397 (King et al.\\ \\cite{kian98},\ntheir Fig.~2). Open circles mark the four white dwarfs for which spectra \ncould be obtained, the open square marks WF4-205 (see text).\\label{cmd}} \n\\end{figure}\nLow-mass white dwarfs (M$<$0.45\\Msolar) with a degenerate He core are\nproduced if the red giant branch evolution is terminated by binary\ninteraction before the helium core exceeds the minimum mass for helium\nburning. Recently, Cool et al.\\ (\\cite{cogr98}) found 3 faint UV-bright\nstars in NGC\\,6397 which they suggest could be He white dwarfs (supported\nby Edmonds et al.\\ \\cite{edgr99}). Massive white dwarfs may be produced\nfrom blue stragglers or by collisions of white dwarf-binaries with\nsubsequent merging (e.g. Marsh et al.\\ \\cite{madh95}). \n\\newline\\indent\nOnly a detailed spectroscopic investigation can provide masses and absolute\nluminosities of the individual globular cluster white dwarfs. This is also\nvery important for the use of white dwarfs as standard candles to derive\ndistances to globular clusters (Renzini et al.\\ \\cite{rebr96}): The basic\nidea is to fit the white dwarf cooling sequence of a globular cluster to an\nappropriate empirical cooling sequence of local white dwarfs with well\ndetermined trigonometric parallaxes. The procedure is analogous to the\nclassical main sequence fitting but avoids the complications with\nmetallicity -- white dwarfs have virtually metal free atmospheres. In\naddition they are locally much more abundant than metal-poor subdwarfs. The\narrival of the {\\sc Hipparcos} results as well as new metallicity\ndeterminations have rekindled the debate on globular cluster distances (see\nthe review by Reid \\cite{reid99} and references therein). A further check\non the distance is therefore urgently needed. \n\\newline\\indent\nWe started an observing programme at the ESO {\\em Very Large Telescope\n(VLT)} to obtain spectra of white dwarfs in globular clusters. The\nprogramme consists of two parts: First, low S/N ($\\approx 10$) spectra of\nthe white dwarf candidates are obtained to verify their spectral type and\nestimate their effective temperatures. In a second run we plan to observe\nhigher S/N ($\\approx 30$) spectra that will allow to derive \\logg\\ with an\ninternal error of $\\le 0.1$dex. Here we report on the very first results\nfor NGC~6397. \n\n\\begin{table}\n\\caption{Target coordinates and photometric data (Cool priv. comm.). \n\\label{targ}}\n\\begin{tabular}{lrrrr}\n\\hline\nStar & $\\alpha_{2000}$ & $\\delta_{2000}$ & $V$ & $V-I$\\\\\n\\hline\nWF4-358 & \\RA{17}{40}{58}{52} & \\DEC{$-$53}{42}{25.3} & \\magpt{22}{73} & \n\\magpt{+0}{02}\\\\\nWF2-479 & \\RA{17}{41}{07}{06} & \\DEC{$-$53}{44}{45.1} & \\magpt{23}{87} & \n\\magpt{+0}{22}\\\\\nWF4-205 & \\RA{17}{41}{01}{58} & \\DEC{$-$53}{43}{15.3} & \\magpt{23}{99} &\n\\magpt{+0}{30}\\\\\nWF2-51 & \\RA{17}{41}{04}{52} & \\DEC{$-$53}{43}{55.8} & \\magpt{24}{00} & \n\\magpt{+0}{28}\\\\\nWF2-846 & \\RA{17}{41}{01}{78} & \\DEC{$-$53}{44}{47.2} & \\magpt{24}{30} & \n\\magpt{+0}{33}\\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\\begin{figure}\n\\vspace{8.5cm}\n\\special{psfile=b1293.f2 hscale=43 vscale=43 hoffset=-10 voffset=-70\nangle=0}\n\\caption{Traces through the slits along the spatial axis. The lines mark \nthe white dwarf spectra (WF4-205 unfortunately lies on the wing of a much \nbrighter star).\\label{slits}} \n\\end{figure}\n\n\\begin{figure}\n\\vspace{8.5cm}\n\\special{psfile=b1293.f3 hscale=43 vscale=43 hoffset=-10 voffset=-70\nangle=0}\n\\caption{The (relatively flux-calibrated) spectra of the white dwarfs in \nNGC~6397. The spectra of the three faintest stars \nare offset from each other as they would otherwise overlap. WF4-358 has no \nadditional offset relative to WF2-479.\\label{spectra}} \n\\end{figure}\n\\section{Observations and Data Reduction}\nCool et al.\\ (\\cite{copi96}) discovered the white dwarfs using the {\\em\nWide Field and Planetary Camera~2} (WFPC2) onboard the HST to observe the\nglobular cluster NGC~6397. From the improved colour-magnitude diagram of\nKing et al.\\ (\\cite{kian98}) targets brighter than $V\\approx25^{\\rm m}$\nwere selected (see Fig.~\\ref{cmd}). The WFPC2 images were convolved to a\nseeing of 0\\bsec5 to select targets that are sufficiently uncrowded to be\nobservable from the ground (see Table~\\ref{targ} and Fig.~\\ref{slits}). The\nstars were observed with the {\\em FOcal Reducer/low dispersion\nSpectrograph} (FORS) at Unit Telescope 1 of the VLT using the high\nresolution collimator (0\\bsec1/pixel) to allow better extraction of the\nspectra and get a better handle on cosmic rays. We used the {\\em\nmulti-object spectroscopy} (MOS) mode with the grism 300V and a slit width\nof 0\\bsec8. The slit width was chosen to be larger than the required seeing\nto avoid slit losses due to imperfect pointing of the telescope. The data\nwere obtained in service mode under excellent conditions (seeing below\n0\\bsec55, no moon) with a total exposure time of 90 minutes. The final\nresolution as judged from a wavelength calibration spectrum obtained with a\n0\\bsec5 slit is $\\approx$11.5~\\AA. A trace along the spatial axis of the\nslitlets at about 4550~\\AA\\ is plotted in Fig.~\\ref{slits}. Unfortunately\nWF4-205 lies so close to a bright star that even at this excellent\nseeing its spectrum could not be extracted. \n\nDue to the use of slit blades instead of fibers or masks the MOS slitlets\nare very well defined and can be treated like long slits. The spectra were\ntherefore corrected for bias, flat-fielded, wavelength calibrated, and\nextracted as described by Moehler et al.\\ (\\cite{mohe97}). We find only a\ndiffuse and rather low sky background without any strong sky lines below\n5150~\\AA. The spectra were relatively flux calibrated using LTT~7987\n(Hamuy et al.\\ \\cite{hawa92}) and are plotted in Fig.~\\ref{spectra}. All\nfour stars display only strong broad Balmer lines, which is characteristic\nfor hydrogen-rich white dwarfs (DA stars). \n\n\\section{Atmospheric parameters}\nAlthough the white dwarf spectra have low signal-to-noise, they are\nsufficient for rough parameter estimates. The atmospheric parameters are\nobtained by simultaneously fitting profiles of the observed Balmer lines\nwith model spectra using the least-square algorithm of Bergeron et al.\\\n(\\cite{besa92}; see Napiwotzki et al.\\ 1999 for minor modifications).\nAnalyses were performed with Koester's LTE models as described in Finley et\nal.\\ (\\cite{fiko97}). As a check we repeated the analysis of the hottest\nstar in our sample (WF4-358) with the non-LTE grid described in Napiwotzki\net al.\\ (\\cite{nagr99}). Since the non-LTE code does not treat convection\nand ignores molecular opacities reliable atmospheric models cannot be\ncalculated for the three cooler white dwarfs. \n\n\\begin{figure}\n\\vspace{8.cm}\n\\special{psfile=b1293.f4 hscale=43 vscale=43 hoffset=-10 voffset=-10 angle=0}\n\\caption{Sample fits to the spectra of WF4-358 (\\teff\\ =\n18,200~K, \\logg\\ = 7.3) and WF2-479 (\\teff\\ = 11,000~K, \\logg\\= = 7.7).\n\\label{wd_fit}} \n\\end{figure}\n\n\\begin{table}[h]\n\\caption{Effective temperatures and $\\chi^2$ values for the white dwarfs\nfrom the fit of H$_\\delta$, H$_\\gamma$, H$_\\beta$ at fixed \\logg\\ (see text\nfor details). Also given are masses derived from theoretical tracks of\nBl\\\"ocker (\\cite{bloe95}) and Driebe et al.\\ (\\cite{drsch98}) and absolute\nmagnitudes (Bergeron et al.\\ \\cite{bewe95}). Using Bergeron et al.'s\n(\\cite{bewe95}) Table~3 we derived $T_{\\rm eff, (V-I)_0}$ from $(V-I)_0$,\nwhich was calculated from $V-I$ assuming $E_{V-I}$ = \\magpt{0}{225}.\n\\label{tab-results}} \n\\begin{tabular}{lrrrrr}\n\\hline\nstar & $\\chi^2$ & \\teff & $T_{\\rm eff, (V-I)_0}$ & M & $M_V$ \\\\\n & & [K] & [K] & [\\Msolar] & \\\\\n\\hline\n\\multicolumn{6}{c}{\\logg\\ = 7.5}\\\\\n\\hline\nWF4-358 & 1.04 & 18900 & & 0.42 & \\magpt{10}{0} \\\\\nWF2-479 & 1.15 & 10800 & & 0.39 & \\magpt{11}{1} \\\\\nWF2-51 & 1.46 & 10900 & & 0.39 & \\magpt{11}{1} \\\\\nWF2-846 & 0.71 & 10500 & & 0.38 & \\magpt{11}{2} \\\\\n\\hline\n\\multicolumn{6}{c}{\\logg\\ = 7.7}\\\\\n\\hline\nWF4-358 & 1.07 & 19500 & & 0.48 & \\magpt{10}{3} \\\\\nWF2-479 & 1.14 & 11000 & & 0.46 & \\magpt{11}{4} \\\\\nWF2-51 & 1.46 & 11100 & & 0.46 & \\magpt{11}{4} \\\\\nWF2-846 & 0.71 & 10600 & & 0.46 & \\magpt{11}{5} \\\\\n\\hline\n\\multicolumn{6}{c}{\\logg\\ = 8.0}\\\\\n\\hline\nWF4-358 & 1.13 & 20300 & 19400 & 0.62 & \\magpt{10}{7} \\\\\nWF2-479 & 1.14 & 11200 & 11500 & 0.59 & \\magpt{11}{8} \\\\\nWF2-51 & 1.47 & 11300 & 10800 & 0.59 & \\magpt{11}{8} \\\\\nWF2-846 & 0.71 & 10800 & 10300 & 0.59 & \\magpt{11}{9} \\\\\n\\hline\n\\end{tabular}\\\\\n\\end{table}\nFitting the lines H$_\\beta$ to H$_\\epsilon$ for WF4-358 (see\nFig.~\\ref{wd_fit}) gives 18,200$\\pm$1300~K and 7.30$\\pm$0.36 for \\teff\\ and\n\\logg, respectively ($\\chi^2$ = 0.93). The errors given here are 1$\\sigma$\nerrors obtained from the $\\chi^2$ fit. Omitting H$_\\epsilon$ from the fit\nresults in 17,800~K and 7.19 ($\\chi^2$ = 1.02) with more or less unchanged\nerrors. The results of the non-LTE analysis are essentially identical to\nthose obtained with Koester's models, differing only by small fractions of\nthe formal errors ($\\Delta$\\teff $\\approx$500\\,K, $\\Delta$\\logg $\\approx$\n0.07\\,dex). The surface gravity is surprisingly low and suggests that\nWF4-358 could be a bright ($M_V$=\\magpt{9}{7}) helium white dwarf of\n(0.36$\\pm$0.12)\\Msolar. Within the error bars, however, the derived\nparameters are also consistent with a low-mass C/O white dwarf. For the\nremaining three stars the S/N is too low to determine \\teff\\ and \\logg\\\nsimultaneously. We thus fitted H$_\\delta$, H$_\\gamma$, H$_\\beta$\n(H$_\\epsilon$ being too noisy) for WF2-51, WF2-479, and WF2-846 for three\nfixed values of \\logg\\ (8.0, 7.7, 7.5, see Fig.~\\ref{wd_fit} for an\nexample). These \\logg\\ values correspond to C/O white dwarfs of $\\approx$\n0.6\\Msolar, low-mass C/O white dwarfs of $\\approx$0.5\\Msolar, and He white\ndwarfs of $\\approx$0.4\\Msolar, respectively (see below). The formal errors\nare $\\approx$550~K (WF2-479), $\\approx$650~K (WF2-846, WF4-358), and\n$\\approx$790~K (WF2-51). The errors for the cooler stars are relatively\nsmall despite their low S/N because -- at fixed \\logg\\ -- the line profiles\nare much more sensitive to temperature variations at \\teff\n$\\approx$11,000~K than at \\teff $\\approx$18,000~K. The relatively large\n$\\chi^2$ value for WF2-51 suggests that either the noise in this spectrum\nhas been underestimated or that the spectrum contains additional features\nthat are not well described by the model spectra. The temperatures derived\nfrom the Balmer lines agree quite well with those obtained from $(V-I)_0$\nusing the theoretical colours of Bergeron et al.\\ (\\cite{bewe95}, \\logg\\ = \n8.0). \n\nThe masses given in Table~\\ref{tab-results} were derived by interpolation\nbetween the evolutionary tracks of C/O white dwarfs calculated by Bl\\\"ocker\n(\\cite{bloe95}) and the He white dwarf tracks of Driebe et al.\\\n(\\cite{drsch98}). Finally, absolute magnitudes $M_V$ were calculated for\neach parameter set with the photometric calibration of Bergeron et al.\\\n(\\cite{bewe95}). \n\n\\section{The distance to NGC\\,6397} \nThe old distance modulus to NGC\\,6397 was $(m-M)_0$ = \\magpt{11}{71} with a\nreddening of \\ebv\\ of \\magpt{0}{18} (Djorgovski \\cite{djor93}). Using local\nmetal-poor subdwarfs to fit the main sequence of NGC\\,6397 Reid \\& Gizis\n(\\cite{regi98}) obtained a mean distance modulus\nof $(m-M)_0$ = \\magpt{12}{20}$\\pm$\\magpt{0}{15} for\n\\ebv\\ = \\magpt{0}{19}. Thus NGC\\,6397 is a good example for the large\ndifferences between old and new distances to globular clusters. The\nabsolute magnitudes given in Table~\\ref{tab-results} for \\logg\\ = 7.5, 7.7,\n8.0 (M$_{\\rm WD}$ = 0.4\\Msolar, 0.5\\Msolar, 0.6\\Msolar) yield mean true\ndistance moduli (for \\ebv\\ = \\magpt{0}{18}) $(m-M)_0$ of \\magpt{12}{3},\n\\magpt{12}{0}, and \\magpt{11}{6}, respectively, with an r.m.s. error of\n\\magpt{0}{17}. Considering the error bars of the various distance\ndeterminations the long distance scale would be more consistent with white\ndwarf masses $\\le$0.5\\Msolar\\ and the short distance scale with masses\n$>$0.5\\Msolar. The longer distance moduli obtained for low-mass white\ndwarfs also result in masses for blue HB stars (Heber et al.\\\n\\cite{hemo97}) and a hot post-AGB star (ROB\\,162, Heber \\& Kudritzki\n\\cite{heku86}) that agree with canonical evolutionary theory. \n\nThe distance moduli derived for a given \\logg\\ from Tables~\\ref{targ} and\n\\ref{tab-results} show a systematic variation with the brightest star\n(WF4-358) yielding the smallest distance and the faintest star (WF2-846)\ngiving the largest distance. This variation could reflect the fact that the\nstars may not all have the same surface gravity: From their different\napparent magnitudes (i.e. different absolute magnitudes) it is plausible\nthat WF4-358 has the smallest \\logg\\ and WF2-846 the largest. The quality\nof the current data, however, does not allow to verify this idea. \n\n\\section{Conclusions} \nUsing VLT-FORS1 multi object spectroscopy we have confirmed four white\ndwarf candidates to be hydrogen-rich DA white dwarfs. The gravity\ndetermined for the brightest star, WF4-358, suggests that it could be a He\nwhite dwarf with a mass of (0.36$\\pm$0.12)\\Msolar, although the error bars\nare large enough to also accommodate a C/O white dwarf. Temperatures derived\nfor the three cooler and fainter stars for fixed \\logg\\ would put them near\nthe red edge of the ZZ Ceti instability strip, for which Bergeron et al.\\\n(\\cite{bewe95b}) determine a temperature range of 11,160~K to 12,460~K\nusing their preferred ML2/$\\alpha$=0.6 prescription for the treatment of\nconvection. Therefore, a search for photometric variability of WF2-479 and\nWF2-51 -- if successful -- could place important additional constraints on\nthese stars. The systematic variation of the distance moduli derived for a\ngiven \\logg\\ shows that the assumption of a constant mass for\nall white dwarfs in a globular cluster may bias a distance determination.\nHowever, due to the low S/N of the current data, these results are\npreliminary. Once higher quality spectra are available, which will allow\nmore accurate parameter (and thus mass) determinations, analyses of white\ndwarfs in globular clusters will become a powerful tool for independent\ndistance estimates. \n\n\\acknowledgements\nWe highly appreciate the work performed by the FORS team in building an\nexcellent instrument and the efforts of the staff at the ESO Paranal\nobservatory and ESO Garching that made these observations possible. We\nthank Dr.\\ A.\\ Cool for providing us with the photometry and coordinates of\nthe white dwarf candidates and an anonymous referee for valuable comments.\nS.M. acknowledges financial support from the DARA under grant\n50~OR~96029-ZA. \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% FOLLOWING TYPESETTING RULES SET OUT IN \"ASTRONOMY AND ASTROPHYSICS %%\n%% INSTRUCTIONS FOR AUTHORS\" -- ASTRON. ASTROPHYS. 341 (1) 1999; %%\n%% JOURNAL ACRONYMS CAN BE FOUND AT THE FOLLOWING TWO WEB SITES: %%\n%% http://adsdoc.harvard.edu/abs_doc/refereed.html %%\n%% http://adsdoc.harvard.edu/abs_doc/non_refereed.html %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{thebibliography}{}\n\\bibitem[1992]{besa92}\nBergeron P., Saffer R.A., Liebert J., 1992, ApJ 394, 228\n\\bibitem[1995a]{bewe95}\nBergeron P., Wesemael F., Beauchamp A., 1995a, PASP 107, 1047\n\\bibitem[1995b]{bewe95b}\nBergeron P., Wesemael F., Lamontagne R., et al., 1995b, ApJ 449, 258\n\\bibitem[1995]{bloe95}\nBl\\\"ocker T., 1995, A\\&A 299, 755\n\\bibitem[1996]{copi96}\nCool A.M., Piotto G., King I.R., 1996, ApJ 468, 655\n\\bibitem[1998]{cogr98}\nCool A.M., Grindlay J.E., Cohn H.N., Lugger P.M., Bailyn C.D., 1998, ApJ \n508, L75\n%\\bibitem[1995]{dbsc95}\n% de Boer K.S., Schmidt J.H.K., Heber U., 1995, A\\&A 303, 95 \n\\bibitem[1993]{djor93}\nDjorgovski S., 1993, in {\\it Structure and Dynamics of Globular Clusters},\n eds. S.G. Djorgovski \\& G. Meylan, ASP Conf. Ser. 50 (San Francisco),\n p. 373\n\\bibitem[1998]{drsch98}\nDriebe T., Sch\\\"onberner D., Bl\\\"ocker T., Herwig F., 1998, A\\&A 339, 123\n\\bibitem[1999]{edgr99}\nEdmonds P.D., Grindlay J.E., Cool A., et al., 1999, ApJ 516, 250\n\\bibitem[1997]{fiko97}\nFinley D.S., Koester D., Basri G., 1997, ApJ 488, 375\n\\bibitem[1992]{hawa92}\nHamuy M., Walker A.R., Suntzeff N.B., et al., 1992, PASP 104, 533\n\\bibitem[1986]{heku86}\nHeber U., Kudritzki R.P., 1986, A\\&A 169, 244\n\\bibitem[1997]{hemo97}\nHeber U., Moehler S., Reid I.N., 1997, ESA SP-402, p.461 \n\\bibitem[1998]{kian98}\nKing I.R., Anderson J., Cool A.M., Piotto G., 1998, ApJ 492, L37\n\\bibitem[1995]{madh95}\nMarsh T.R., Dhillon V.S., Duck S.R., 1995, MNRAS 275, 828\n\\bibitem[1997]{mohe97}\nMoehler S., Heber U., Rupprecht G., 1997, A\\&A 319, 109\n\\bibitem[1999]{nagr99}\nNapiwotzki R., Green P.J., Saffer R.A., 1999, ApJ 517,399\n\\bibitem[1995]{pade95}\nParesce F., de Marchi G., Romaniello M., 1995, ApJ 440, 216\n\\bibitem[1999]{reid99}\nReid I.N., 1999, ARAA 37, 191\n\\bibitem[1998]{regi98}\nReid I.N., Gizis J.E., 1998, AJ 116, 2929\n\\bibitem[1996]{rebr96}\nRenzini A., Bragaglia A., Ferraro F.R., et al., 1996, ApJ 465, L23\n\\bibitem[1995]{rifa95}\nRicher H.B., Fahlmann G.G., Ibata R.A., et al., 1995, ApJ 451, L17\n\\bibitem[1997]{rifa97}\nRicher H.B., Fahlmann G.G., Ibata R.A., et al., 1997, ApJ 484, 741\n\\end{thebibliography}{}\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002197.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[1992]{besa92}\nBergeron P., Saffer R.A., Liebert J., 1992, ApJ 394, 228\n\\bibitem[1995a]{bewe95}\nBergeron P., Wesemael F., Beauchamp A., 1995a, PASP 107, 1047\n\\bibitem[1995b]{bewe95b}\nBergeron P., Wesemael F., Lamontagne R., et al., 1995b, ApJ 449, 258\n\\bibitem[1995]{bloe95}\nBl\\\"ocker T., 1995, A\\&A 299, 755\n\\bibitem[1996]{copi96}\nCool A.M., Piotto G., King I.R., 1996, ApJ 468, 655\n\\bibitem[1998]{cogr98}\nCool A.M., Grindlay J.E., Cohn H.N., Lugger P.M., Bailyn C.D., 1998, ApJ \n508, L75\n%\\bibitem[1995]{dbsc95}\n% de Boer K.S., Schmidt J.H.K., Heber U., 1995, A\\&A 303, 95 \n\\bibitem[1993]{djor93}\nDjorgovski S., 1993, in {\\it Structure and Dynamics of Globular Clusters},\n eds. S.G. Djorgovski \\& G. Meylan, ASP Conf. Ser. 50 (San Francisco),\n p. 373\n\\bibitem[1998]{drsch98}\nDriebe T., Sch\\\"onberner D., Bl\\\"ocker T., Herwig F., 1998, A\\&A 339, 123\n\\bibitem[1999]{edgr99}\nEdmonds P.D., Grindlay J.E., Cool A., et al., 1999, ApJ 516, 250\n\\bibitem[1997]{fiko97}\nFinley D.S., Koester D., Basri G., 1997, ApJ 488, 375\n\\bibitem[1992]{hawa92}\nHamuy M., Walker A.R., Suntzeff N.B., et al., 1992, PASP 104, 533\n\\bibitem[1986]{heku86}\nHeber U., Kudritzki R.P., 1986, A\\&A 169, 244\n\\bibitem[1997]{hemo97}\nHeber U., Moehler S., Reid I.N., 1997, ESA SP-402, p.461 \n\\bibitem[1998]{kian98}\nKing I.R., Anderson J., Cool A.M., Piotto G., 1998, ApJ 492, L37\n\\bibitem[1995]{madh95}\nMarsh T.R., Dhillon V.S., Duck S.R., 1995, MNRAS 275, 828\n\\bibitem[1997]{mohe97}\nMoehler S., Heber U., Rupprecht G., 1997, A\\&A 319, 109\n\\bibitem[1999]{nagr99}\nNapiwotzki R., Green P.J., Saffer R.A., 1999, ApJ 517,399\n\\bibitem[1995]{pade95}\nParesce F., de Marchi G., Romaniello M., 1995, ApJ 440, 216\n\\bibitem[1999]{reid99}\nReid I.N., 1999, ARAA 37, 191\n\\bibitem[1998]{regi98}\nReid I.N., Gizis J.E., 1998, AJ 116, 2929\n\\bibitem[1996]{rebr96}\nRenzini A., Bragaglia A., Ferraro F.R., et al., 1996, ApJ 465, L23\n\\bibitem[1995]{rifa95}\nRicher H.B., Fahlmann G.G., Ibata R.A., et al., 1995, ApJ 451, L17\n\\bibitem[1997]{rifa97}\nRicher H.B., Fahlmann G.G., Ibata R.A., et al., 1997, ApJ 484, 741\n\\end{thebibliography}"
}
] |
astro-ph0002198
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Improving the Resolution of X-Ray Telescopes with Occulting Satellites
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[] |
One of the challenges of X-ray astronomy is how to both collect large numbers of photons yet attain high angular resolution. Because X-ray telescopes utilize grazing optics, to collect more photons requires a larger acceptance angle which in turn compromises the angular resolution. All X-ray telescopes thus have angular resolution far poorer than their diffraction limit. Although collecting more photons is a desirable goal, sometimes selective collecting fewer photons may yield more information. Natural (such as lunar) occultations have long been used to study sources on small angular scales. But natural occulters are of limited utility because of their large angular velocities relative to the telescope, and because of the serendipity of their transits. We describe here how one can make use of an X-ray Big Occulting Steerable Satellite (X-BOSS) to achieve very-high resolution of X-ray sources. An X-BOSS could significantly improve the resolution of existing X-ray facilities such as the Chandra telescope, or X-ray Multiple Mirror (XMM) satellite, and could vastly improve the resolution of some future X-ray telescopes, particularly Constellation X where sub-milliarcsecond resolution is possible for a wide range of sources. Similar occulting satellites could also be deployed in conjunction with planned space observatories for other wavebands.
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[
{
"name": "ms.tex",
"string": "%% For submission to apj use\n%\\documentclass{aastex}\n\\documentclass[preprint,12pt]{aastex}\n% To include figures\n\\usepackage{epsfig}\n% Include draftcopy to get ``draft date'' to appear on each page\n%\\usepackage{draftcopy}\n\n% $Id: ms.tex,v 1.9 2000/02/09 21:22:53 copi Exp $\n\n\\newcommand\\be{\\begin{equation}}\n\\newcommand\\ee{\\end{equation}}\n\n\\newcommand{\\mcommand}[1]{\\ifmmode #1\\else $#1$\\fi}\n\\newcommand{\\sci}[1]{\\mcommand{\\times 10^{#1}}}\n\n\\newcommand{\\unit}[1]{\\mcommand{\\;{\\rm #1}}}\n\\newcommand\\meter{\\unit{m}}\n\\newcommand\\second{\\unit{s}}\n\\newcommand\\as{\\unit{arcsecond}}\n\\newcommand\\mas{\\unit{mas}}\n\\newcommand\\parsec{\\unit{pc}}\n\\newcommand\\kpc{\\unit{kpc}}\n\\newcommand\\Mpc{\\unit{Mpc}}\n\\newcommand\\yr{\\unit{yr}}\n\\newcommand\\mps{\\unit{m\\;s^{-1}}}\n\\newcommand\\cm{\\unit{cm}}\n\\newcommand\\km{\\unit{km}}\n\\newcommand\\kmps{\\unit{km\\;s^{-1}}}\n\\newcommand\\pmsqs{\\unit{m^{-2}\\;s^{-1}}}\n\\newcommand\\gram{\\unit{g}}\n\\newcommand\\kg{\\unit{kg}}\n\\newcommand\\AU{\\unit{AU}}\n\\newcommand\\keV{\\unit{keV}}\n\n%\\def\\vec#1{\\mbox{\\boldmath$#1$\\unboldmath}}\n\n\\newcommand\\etal{et al.}\n\\newcommand\\etc{etc}\n\n\\newcommand\\ltsim{\\lesssim}\n\\newcommand\\gtsim{\\gtrsim}\n\n\n\\begin{document}\n\n\\title{Improving the Resolution of X-Ray Telescopes with Occulting Satellites}\n\\author{Craig J. Copi\\altaffilmark{1}\\email{cjc5@po.cwru.edu} \\and Glenn D. Starkman\\altaffilmark{1,2}\\email{gds6@po.cwru.edu}}\n\\affil{\nBOSS home page: \\tt\\url{http://boss.phys.cwru.edu/}}\n\\altaffiltext{1}{Department of Physics, Case Western Reserve\nUniversity, Cleveland, OH 44106-7079}\n\\altaffiltext{2}{Department of Astronomy, Case Western Reserve\nUniversity, Cleveland, OH 44106-7079}\n\\authoraddr{10900 Euclid Avenue\\\\ Cleveland, OH 44106-7079}\n\n\\shorttitle{Improving X-Ray Resolution with X-BOSS}\n\\shortauthors{Craig J. Copi and Glenn D. Starkman}\n\n\\begin{abstract}\nOne of the challenges of X-ray astronomy \nis how to both collect large numbers of photons yet \nattain high angular resolution. \nBecause X-ray telescopes utilize grazing optics, \nto collect more photons requires a larger acceptance angle \nwhich in turn compromises the angular resolution.\nAll X-ray telescopes thus have angular resolution\nfar poorer than their diffraction limit.\nAlthough collecting more photons is a desirable goal,\nsometimes selective collecting fewer photons may yield more information.\nNatural (such as lunar) occultations \nhave long been used to study sources on small angular scales.\nBut natural occulters are of limited utility because\nof their large angular velocities relative to the telescope,\nand because of the serendipity of their transits.\nWe describe here how one can make use of an \nX-ray Big Occulting Steerable Satellite (X-BOSS) \nto achieve very-high resolution of X-ray sources.\nAn X-BOSS could significantly improve the resolution of \nexisting X-ray facilities such as the Chandra telescope, \nor X-ray Multiple Mirror (XMM) satellite, \nand could vastly improve the resolution of some future\nX-ray telescopes, particularly Constellation X where sub-milliarcsecond\nresolution is possible for a wide range of sources.\nSimilar occulting satellites could also be deployed in conjunction \nwith planned space observatories for other wavebands.\n\\end{abstract} \n\n\\keywords{space vehicles---occultations---X-rays:general}\n\n\n\\slugcomment{\\small Preprint: {\\bf CWRU-P04-00}}\n% \\\\ Submitted to: \\em The Astrophysical Journal}\n\n\\section{Introduction}\n\nOne of the big challenges in doing X-ray astronomy\nis the relatively low photon fluxes from target sources.\nThe fact that X-ray mirrors operate only at grazing \nangles of incidence further exacerbates this problem.\nThus, while one might naively expect \nsuperb angular resolution from a $1.2\\meter$ aperture X-ray telescope \nsuch as the one on board the Chandra satellite,\nthe $0.5$ arcsecond reality is far from the \n0.3 milliarcsecond nominal diffraction limit,\nand considerably worse than what is routinely achieved in\nlonger wavelength bands. This situation is unlikely to \nchange in the near future. Indeed, current plans for\nfuture X-ray missions opt for increased acceptance\nangle (and thus increased photon count rate) at\nthe price of reduced angular resolution.\n\nBut it {\\em is} possible to achieve higher \nX-ray photon count rates and yet improve one's angular resolution. \nThe necessary step is to separate the collection of photons \nfrom the means of achieving high resolution.\nOne way to do this is well-known---occultation.\nWhen an astronomical body, such as the moon, transits the field\nof view of a telescope, it occults different sources within the\nfield of view at different times. By carefully measuring\nthe photon count rate as a function of time during the transit,\none can then reconstruct the projection of the surface brightness\nin the field of view onto the path of the occulter.\n\n\nNatural occulters {\\em have} been used to achieve high-resolution\nin X-ray observations; however, they have at least two distinct\ndisadvantages:\n\\begin{enumerate}\n\\item Although natural occultations can be predicted, they cannot be\n scheduled---target sources are therefore limited, and multiple\n occultations of the same source over the course of a few years\n are uncommon.\n\\item Natural occulters have large angular velocities relative to\n a telescope. The shorter the transit time, the fewer photons one\n collects, and so the lower the resolution. This is especially important\n for X-ray astronomy, where photon count rates are relatively low.\n\\end{enumerate}\nThere is however an alternative to natural occulters which can overcome\nboth of these disadvantages---a steerable occulting satellite. Deployment\nof large steerable occulting satellites has been discussed for optical and\nnear infra-red wavebands\n\\citep{Adams,Schneider,CS98,CS00},\nmostly for\nthe purpose of finding planet around nearby stars, but also for\nhigh-resolution astronomical observations. However, such satellites are\nnaturally well-suited for observations in the X-ray and far-UV\\@. In the\nlonger wavelength bands, minimization of diffractive losses pushes one to\nmake the satellite as large as feasible, and deploy it as far as possible\nfrom the telescope. In the X-ray waveband one is far into the geometric\noptic limit and diffraction of the X-ray photons around the satellite can\nessentially be neglected; thus the optimal size and placement of the satellite \nare determined by one's ability to accurately position the satellite with respect to the\ntelescope-star line-of-sight and to minimize the satellite's velocity\nperpendicular to that line-of-sight. The resolution delivered by the\ncombination of the X-ray telescope and the X-BOSS is determined by the\ncollecting area of the telescope (and thus the photon count rate for a\nsource) and by the accuracy with which one can match the X-BOSS and telescope\nvelocity. It is independent of the intrinsic resolution of the telescope.\n\nFor an X-ray telescope either in an eccentric high-Earth orbit (Chandra and XMM) or at the\nL2 point of the Earth-Sun system (Constellation-X) we discuss in section\n\\ref{sec:location} where to position X-BOSS relative to the satellite. In\nsection \\ref{sec:blocking} of this letter we discuss the X-ray blocking\nefficiency of a thick film and what it implies for the required thickness\nof the occulter. We also estimate in this section the required dimensions of an X-BOSS,\nwhich are determined mostly by limitations on telemetry.\nWe discuss the steering of the X-BOSS in section \\ref{sec:steer}. \nIn section \\ref{sec:resolve} we find the angular resolution that one\nobtains as a function of X-BOSS-telescope relative angular velocity, \nand of photon count rate. \nIn section~\\ref{sec:skycoverage} we discuss the the sky\ncoverage that one could obtain in each location. \nApplication of these techniques to specific sources is discussed briefly \nin section~\\ref{sec:results}. \nFinally, section~\\ref{sec:conclude} contains the conclusions.\n\n\\section{Locating an X-BOSS}\n\\label{sec:location}\n\nThe location of an X-BOSS is dictated by the location of the\ntelescope it is meant to occult. The Chandra X-ray telescope is\nin an elliptic orbit around the Earth with \nan apogee of $145,417\\km$ and a perigee of $16,026\\km$.\nThe X-ray Multiple Mirror (XMM) Telescope will also be inserted into\nan elliptic Earth orbit.\nOther X-ray telescopes, such as Constellation X, \nmay be located at the second Lagrangian point of the Earth-Sun system. \nThe orbital issues are entirely\ndifferent for these two locations; \nwe address each in turn below.\nFinally, some X-ray telescopes (Astro-E and XEUS) will be\nplaced in low earth orbit. Because orbital velocities\nare so high in low earth orbit, it is more difficult to make \nuse of the approach we advocate here; we will not discuss\nthese further.\n\n\\subsection{Eccentric high Earth-orbit}\n\\label{subsec:orbitearth}\n\nAs described above, the Chandra satellite is in an eccentric high altitude\nEarth orbit. The period of this orbit is 64 hours. The satellite\ntherefore has an average angular velocity of about 6 arcseconds per second. \nAn occulting satellite leading or following in Chandra's orbit would transit a source at\napproximately that rate. The planned X-ray Multiple Mirror Telescope (XMM)\nhas a similar orbit with a shorter 48 hour period.\nGiven that the attainable angular resolution is related to the angular \nvelocity of transit, \nthe resolution that one could achieve with these orbits is minimal.\n\nA great improvement is to place the X-BOSS in an orbit identical to that of\nthe telescope but slightly modified by shifting the apogee and perigee, by\nchanging the phase of the satellite in the orbit, or by rotating the orbit.\nIn all cases these modifications will put X-BOSS in an orbit with the same\nperiod as telescope. In such orbits the velocity perpendicular to the line\nof sight of X-BOSS and the telescope can be quite low. For example, consider\nplacing X-BOSS in an orbit identical to that of the telescope (in terms of\napogee, perigee, and orbital phase) but rotated about an axis through the center of the Earth\nin the plane of the orbit and perpendicular to the line connecting apogee and perigee. \nThe component of the relative velocity between X-BOSS and the telescope\nperpendicular to the line-of-sight between them is then zero throughout the\nentire orbit. Unfortunately, such an orbit intersects the telescope orbit at\ntwo points with disastrous consequences. The other orbital modifications\nmentioned above can alleviate this problem by enforcing a minimum\nseparation of, for example, $10\\km$ between the two spacecrafts. Although\n$10\\km$ may seem fairly close, note that each spacecraft is only a\nfew to tens of meters across; random errors therefore have a probability\nless than $10^{-9}$ per orbit crossing of causing catastrophic failure.\nThe importance of utilizing these orbit modifications is explained more\nfully in sections~\\ref{sec:steer} and \\ref{sec:skycoverage}.\n\n\\subsection{Orbit at L2}\n\\label{subsec:orbitL2}\n\nWe have previously discussed the orbital advantages of placing a large\nocculter at L2 in greater detail \\citep{CS00}. Here we will\nhighlight the important points.\nOrbits around L2, both in the plane of the ecliptic and oscillations\nperpendicular to this plane, have periods of about 6 months independent of\ntheir distance from L2 (for distances $\\ltsim 10^4\\km$). Therefore the\nlocal gravity is very small. Both the total velocity and acceleration of\norbits around L2 (relative to the L2 point) are on par with those we might attain\nthrough carefully \ntuning the orbit of X-BOSS relative to that of Chandra or XMM; \nthe relative velocity of the satellite and telescope due to the\nmotion of L2 about the Sun is of the same magnitude. If corrections are\nmade to the X-BOSS orbit to cancel these then the\nacceleration perpendicular to the line-of-sight is about\n$5\\sci{-10}\\meter\\second^{-2}$. Thus if the perpendicular velocity of\nX-BOSS relative to a particular line-of-sight between the telescope and some source\nis canceled by firing rockets, the perpendicular velocity will remain less than $10^{-4}\\mps$ for \nat least a day. Tuning the velocity of X-BOSS, therefore, can be done very \neasily at L2.\n\n\\section{Making an X-ray Occulter}\n\\label{sec:blocking}\n\n\\subsection{Thickness}\n\nThe attenuation length of X-ray photons in elemental matter\nis shown in figure~\\ref{fig:photonattenuation}.\nExcept in hydrogen, it is approximately $3\\times 10^{-4} \\gram \\cm^{-2}$ at\n$1\\keV$, and $10^{-2} \\gram\\cm^{-2}$ at $10\\keV$. \nThus a square $10\\meter$ on a side and one attenuation length\nthick has a mass of $0.3\\kg$ at $1\\keV$, and $10\\kg$ at $10\\keV$.\nAt a typical density of $3 \\gram \\cm^{-3}$, these represent thicknesses\nof just $1$ micron and $30$ microns respectively.\n\nA useful occulter would need to be $3\\hbox{--}5$ attenuation lengths thick,\nand so $3\\hbox{--}5$ microns and $1\\hbox{--}2\\kg$ to operate at $1\\keV$,\nand $100\\hbox{--}150$ microns and $30\\hbox{--}50\\kg$ to operate at $10\\keV$.\nEven at $100\\keV$ a $10\\meter\\times10\\meter$ lead film \n$0.6\\unit{mm}$ thick at a mass of $600\\kg$ would provide 3 attenuation \nlengths of occultation.\n\nIf positioning technology improved to the point where one could\nreduce the size of the occulter to $1\\hbox{--}2\\meter$, then even gamma ray\nocculters would be of reasonable mass.\n\n\\subsection{Size}\n\nThe size of the occulting satellite depend on\ntwo factors---the aperture of the telescope and \nthe accuracy with which one can position the occulter. \n\nThe apertures of typical X-ray satellites are about $1\\meter$.\nThis sets a lower bound on the dimensions of the occulter.\nOnce the occulter is larger than the aperture of the X-ray telescope,\nthere is essentially no effect on resolving power.\n\nNext we will estimate how well we can determine the position of X-BOSS \nin the plane perpendicular to the telescope-source line-of-sight \nit is meant to occult. \nConsider a telescope separated from the X-BOSS by a distance $r$. \nWe can mount a small diffraction-limited optical telescope of diameter $d$ \non the underside of the occulter. Using this telescope\nwe can establish the relative positions\nof the two satellite to within approximately\n\\be \n\\delta x = 1.2 r \\frac{\\lambda}{d} \n= 0.5 \\meter \\frac{r}{1000\\km} \\frac{\\lambda/400\\unit{nm}}{d/1\\meter}\n\\ee\nA $1\\meter$ positioning accuracy therefore requires\na $50\\unit{cm}$ finder scope at $1000\\unit{km}$ separation,\nproportionately smaller at smaller separations. \nThis is quite feasible, especially since the finder scope \nneed not have a full UV plane.\n\nAn important question is whether one will collect\nenough photons to reach the diffraction limit of the\nangular resolution. There are two principal\noptions---rely on reflected sunlight or \nshine a laser from the X-ray telescope onto the X-BOSS telescope.\nColumnation is not a significant problem, \nas seen by our calculation of the diffraction limit above. \nHowever, sunlight has an intensity of $1000\\unit{W}\\meter^{-2}$, \nwhich will be difficult to match with a laser anyway. \nAssuming isotropic scattering from the telescope,\nand a total reflecting area of $1\\meter^{2}$,\nthis results in a flux at the X-BOSS of $3\\sci{8}\\second^{-1}$,\nat $1000\\km$ (falling as $1/r^2$). Detailed studies\nof existing telescopes (Chandra, XMM) would be required\nto precisely quantify our ability to locate the\ntelescope relative to the X-BOSS, however, these\nestimates suggest that determining the relative\nposition to within $1\\hbox{--}3 \\meter$ is not unrealistic.\nIn the case of yet-to-be launched telescopes, \nthe mounting of a small reflector on\none or more corner of the telescope would be of\ndefinite benefit.\n\nAlthough we have argued that we can determine the\nrelative position of an X-BOSS and an X-ray telescope \nto within about a meter, we must also be able to reduce\nthe velocity to a fraction of a meter per second.\nThis can be done by a simple bootstrapping procedure.\nTwo position determinations each with error of $\\Delta x$,\nmade a time $t$ apart, determine the velocity within\n$\\Delta v \\simeq \\sqrt{2} \\Delta x/t$ (assuming the\nerror in $t$ to be negligible). If the relative velocity\ncan be canceled within errors by accurately firing rockets,\nthen the ability to reduce $\\Delta v$ is limited by \nthe time one can allow between position determinations, $t=\\Delta x/\\Delta v$.\nThis time is limited by the orbital accelerations, \nbut is thousands of seconds for the elliptic earth orbits of interest\n(cf.~subsection \\ref{subsec:earthorbit})\nand hundreds of thousands of seconds for orbits at L2.\n(cf.~subsection \\ref{subsec:L2orbits}).\nIn practice it may be desirable to gradually\nreduce the relative velocity using repeated position\ndeterminations and rocket firings.\n\n\n\\section{Steerability}\n\\label{sec:steer}\n\nIn order to successfully resolve objects it will be necessary\nto frequently change the velocity of the satellite. \nThese velocity changes will occur for two principal reasons:\nto move from one target source to another,\nand to match the velocity of the X-BOSS to that of the X-ray telescope.\nWhile solar radiation pressure might be used to some advantage,\nit will be necessary to make some velocity adjustments using rockets.\nThe number and size of such adjustments may be the limiting factor\non the useful lifetime of the X-BOSS.\n\n\nA change $\\Delta v$ in the satellite's velocity is related\nby momentum conservation to the mass of propellant ejected,\n$\\Delta m_{\\rm propellant}$, and the velocity of ejection $v_{\\rm ejection}$:\n\\be\n\\Delta v_{\\rm sat}\n= \\frac{\\Delta m_{\\rm propellant}{ v}_{\\rm ejection}}{m_{\\rm sat}} .\n\\ee\nIf $N$ is the number of desired major rocket-driven velocity changes,\nthen we must keep\n$(\\Delta m_{\\rm propellant}/m_{\\rm sat})\\leq N^{-1}$.\n(The mass of propellant ejected will of course vary on the particular\nmaneuver, but here $\\Delta m_{\\rm propellant}$ is taken to be some \ntypical mass of propellant expended per orbit reconfiguration.)\nWe therefore can accommodate only a limited number of such rocket firings:\n\\be\nN \\leq \\frac{v_{\\rm ejection}}{\\Delta{ v_{\\rm sat}}} .\n\\ee\nOff-the shelf, low-cost ion engines are currently available\nwith ejection velocities of $20 \\kmps$, and\nmore expensive systems with $30 \\kmps$ performance \nhave been developed, thus\n\\be\nN \\leq \\frac{30\\kmps}{\\Delta{ v_{\\rm sat}}} .\n\\label{eqn:Ncorrect}\n\\ee\n\nConsider first the need to match the velocities of the two spacecraft\nso that a long occultation can occur.\n$\\Delta{ v_{\\rm sat}}$ is then the relative velocity \nof the X-BOSS and the telescope in their orbits.\nIn determining the sky coverage for elliptic Earth orbits \nin section~\\ref{subsec:earthorbit} above, \nwe have considered only orbital configurations with relative velocities \nbetween the telescope and the X-BOSS of less than $10\\mps$.\n(Near L2, the relative velocities of relevance are typically \nconsiderably smaller than that.)\nIf $\\Delta{ v_{\\rm sat}}\\simeq 10\\mps$, then this implies \n$N\\leq 3000$,\nwhich is a reasonable quota of corrections for a mission with a 3--5 year\nlifetime, \ngiven the typical 2--3 day orbital period of Earth-orbiting\nX-ray telescopes. \n\nThe second type of velocity correction that will be required\nis target acquisition---the readjustment of the orbit\nof the occulter so as to allow the occultation of a new \ntarget source. \nFor satellites separated by $1000\\km$ near L2, relative velocities\nare only $v_{\\rm sat} = {\\cal O}(10^{-4}\\kmps)$,\nand the expression for\n$N$ (equation~\\ref{eqn:Ncorrect}) shows that any constraint on target\nchoice or order does not come from concerns about conserving\npropellant.\nFor telescopes in orbit about the Earth, \nthe matter is quite different.\nHere orbital velocities are $v_{\\rm sat} = {\\cal O}(1\\kmps)$,\nand so it is clear from the allowed number of orbital\ncorrections~(\\ref{eqn:Ncorrect}) that\none cannot indiscriminately rocket from one target to another on the sky.\nOne solution might have been to sail in the solar radiation pressure.\nHowever, the solar radiation pressure is approximately $P_{\\rm\n solar}=6\\times10^{-6}\\unit{Pa}$. \nFor an areal density of just $1.5\\times 10^{-3}\\gram\\cm^{-2}$\n(five attenuation lengths as $1\\keV$),\nthis results in an acceleration of only $4\\times10^{-4}\\meter\\second^{-2}$.\nAt this rate it takes about a month to change velocity by $1\\kmps$.\n\nClearly one cannot reposition randomly on the sky. \nHowever the velocity difference between two orbits which\nresult in occultation of target sources one degree apart are only\nof order $15\\mps$. Solar sailing can cause velocity changes\nof this order in under a day. \nMoreover, the allowed number of orbital corrections~(\\ref{eqn:Ncorrect})\nindicates that rocket driven\ncorrections of this magnitude can be made of order 1000 times.\nHow many corrections we can make, and how many sources we can\ntherefore target for occultation,\nclearly depends on exactly how we use the satellite. \nA reasonable program of observations certainly seems possible.\n\n\\section{Resolution}\n\\label{sec:resolve}\n\nWhen used in conjunction with an X-BOSS the telescope acts as a\nlight bucket. The angular resolution of the telescope itself is\nirrelevant; instead the collecting area is the important telescope\nparameter. The angular resolution of the system will come from probing the \nlightcurve as X-BOSS transits a source.\n\nTo study the angular resolution of X-BOSS we consider the simple case of\nidentifying a binary source. Let $f (\\vec x, t)$ be the normalized\nlightcurve (number of photons detected per second) generated as X-BOSS\nscans across a single source at a position\n$\\vec x$ in the plane of X-BOSS\\@. The lightcurve is the number of photons\ndetected as a function of time. It is normalized such that the value is\none (in the detector) when X-BOSS is not present. Since X-rays have\nextremely short\nwavelengths we can approximate the diffraction pattern produced by the\nsatellite simply by the geometric shadow projected on the telescope. This\nreduces the lightcurve to a calculation of the area of the telescope not\nunder the shadow of the occulter. We write the lightcurve of a single\nsource as\n\\be \nl_1 (\\vec x, t) = I_1 f (\\vec x, t)\n\\ee\nand the total lightcurve for two sources at $\\vec x_1$ and $\\vec x_2$\ncan be written as\n\\be\nl_2 (\\vec x_1, \\vec x_2, t) = I_2 \\left[ \\rho f (\\vec x_1, t) +\n (1-\\rho) f (\\vec x_2, t)\\right].\n\\ee\nHere $I_i$ is the total intensity of the system for $i=1$ or $2$ sources\nand $\\rho$ is\nthe intensity \nratio of the two sources. We would like to find the minimum separation of\ntwo sources that can be distinguished from a single source. An observation\nconsists of a sequence $\\left\\{O_j (\\vec x)\\slash j=1,...,n \\right\\}$\nof measurements of the integrated lightcurve between \ntimes $t_{j-1}$ and $t_j$:\n\\be \nO_j (\\vec x) = \\int_{t_{j-1}}^{t_j} dt\\; l_i (\\vec x, t).\n\\ee\nTo obtain\nlimits on the minimum separation we first evaluate the number of photons\nexpected between time $t_0$ and $t_k$\n\\be\nL_{i,k} (\\vec x) \\equiv \\int_{t_0}^{t_k} dt\\;l_i (\\vec x, t) =\n\\sum_{j=1}^k O_j (\\vec x)\n\\ee \nwhere $i$ is 1 or 2 as above.\nAssuming the counts in each time bin, $[t_{j-1},t_j)$, are Poisson distributed the\nlikelihood of a model with $i$ sources given an underlying model with 2\nsources is \n\\be \n{\\cal L}_i = \\prod_{k=1}^N \\left. e^{-L_{i,k}} \\left( L_{i,k} \\right)^{L_{2,k}}\n\\right/ \\left( L_{2,k}\\right)!.\n\\ee\nFinally the quantity\n\\be \nT = -2\\log \\left (\\frac{{\\cal L}_1}{{\\cal L}_2} \\right)\n\\ee\nis $\\chi^2$ distributed with 4 degrees of freedom ($t_0$, $x_2-x_1$, $I$,\nand $\\rho$) and allows us to\ncalculate the probability of misidentifying a binary source as a single source.\nThis probability depends on \n$\\mu_\\perp$, the angular velocity of X-BOSS as it transits the source.\nThe results for the 95\\% confidence limits as a function of the intensity\nin a $1.2\\meter$ aperture telescope for $\\rho=1$, $1/3$, and $1/10$ and for\n$\\mu_\\perp=10\\mas\\second^{-1}$, $\\mu_\\perp=1\\mas\\second^{-1}$, and\n$0.1\\mas\\second^{-1}$ are shown in figure~\\ref{fig:resolution}. In\nproducing figure~\\ref{fig:resolution} we assumed a uniform response over\nthe surface of the telescope. A more complicated response function may\nimprove resolution slightly.\n\nThe simple analysis employed here uses the edges of X-BOSS in a single\noccultation. In practice it would be necessary to obtain multiple\nprojections to resolve a source in two dimensions. This could be facilitated\nby putting slits at various angles in X-BOSS that allow for sources to be\nocculted by different regions of the satellite in different ways during a\nsingle transit.\n\n\n\\section{Sky Coverage}\n\\label{sec:skycoverage}\n\nThe issues of resolution and sky coverage are closely related. Here sky\ncoverage is the fraction of the sky for which a particular angular\nresolution can be obtained. While one can reposition X-BOSS to be in an\narbitrary direction on the sky relative to the X-ray telescope, this\nfrequently leads to large relative velocities and accelerations between the\nocculter and telescope perpendicular to the line-of-sight, thus leading to\npoor resolution (see figure~\\ref{fig:resolution}). Conversely, extremely\ngood resolution is possible if the relative velocity during the occultation\nis kept quite low; however this requires either special orbits (and thus\nvery little sky coverage) or expenditures of fuel. Here we will explore\nthe sky coverage that can be obtained subject to a number of constraints.\n\n\\subsection{Elliptic Earth Orbits}\n\\label{subsec:earthorbit}\n\nWe consider placing an X-BOSS in orbit around the Earth with nearly the\nsame orbital parameters as an X-ray telescope. As discussed in\nsection~\\ref{subsec:orbitearth} we then allow for small alterations in the\nX-BOSS orbit which change the direction of the line-of-sight from the\ntelescope to X-BOSS while keeping the X-BOSS period fixed.\nOur first constraint is that the\nminimum separation of the X-BOSS and telescope in their orbits must be larger than $10\\km$. \n(If this safety factor can be reduced then greater sky coverage may be possible.) \nWe then follow the two spacecrafts in their orbits to see what sky coverage \nthese orbits afford.\nTo limit the expenditure of propellant we \nconsider making observations only when the relative velocity of the\ntwo satellites perpendicular to the line-of-sight is sufficiently small,\nhere we require $v_\\perp^{\\rm orb} <\n10\\mps$ (see section~\\ref{sec:steer}). Prior to an observation this\nvelocity can be reduced to the desired range by firing the X-BOSS rockets\n(a small correction requiring acceptable use of consumables).\n\nAfter maneuvering to correct the perpendicular relative velocity between the\ntelescope and X-BOSS, they would still be accelerating relative to each\nother during the observation. The provides one limit on the total transit\ntime of the observation. There would also be some residual error in the\nvelocity correction, leaving X-BOSS with a component of its velocity perpendicular to the\nline-of-sight. This provides another limit on the total transit time of the\nobservation. Combining these two, the total transit time over which the\nobservation can made is\n\\be\nt_{\\rm obs} = \\min \\left(\\sqrt{\\frac{2w}{a_\\perp^{\\rm orb}}},\n \\frac{w}{\\mu_\\perp^{\\rm max} d} \\right).\n\\ee\nHere $a_\\perp^{\\rm orb}$ is the perpendicular linear acceleration, $w$ is the\nwidth of X-BOSS, $d$ is the distance between the two spacecrafts, and\n$\\mu_\\perp^{\\rm max}$ is the maximum angular velocity allowed to obtain a\nparticular resolution.\nIf we require that the angular velocity perpendicular to the line\nof sight at the end of the observation be less than the same maximum value,\n$\\mu_\\perp^{\\rm max}$, then we obtain the constraint\n\\be\na_\\perp^{\\rm orb} t_{\\rm obs} < \\mu_\\perp^{\\rm max} d.\n\\label{eqn:constraint1}\n\\ee\nOf course when we cancel $v_\\perp^{\\rm orb}$ before the observation we are\nalso making a small change to the orbit. This leads to an extra\nacceleration that must also be small. If we require that this acceleration\nalso not produce a large final velocity we obtain the constraint\n\\be\n\\frac{v_\\perp^{\\rm orb} t_{\\rm obs}^2}{r^3 d} < \\frac{\\mu_\\perp^{\\rm\n max}}{2g R_\\oplus^2},\n\\label{eqn:constraint2}\n\\ee\nwhere $r$ is the distance from X-BOSS to the (center of the) Earth,\n$g=9.8\\meter\\second^{-2}$, and $R_\\oplus$ is the radius of the Earth.\n\nThe sky coverage on each change of X-BOSS orbit is not large. To increase\nthe amount of sky\naccessible to observation we consider moving X-BOSS between orbits that are\nsimilar to the orbit of the X-ray telescope. Throughout we will consider\nmodifications of the X-BOSS orbit that leave the period unchanged. Over\nmany orbits this is a \ndesired feature since it prevents the times at which X-BOSS and the telescope\nachieve apogee and perigee from drifting apart, requiring a\nlarge expenditure of fuel to correct. The orbital modifications we\nconsider are increasing or decreasing the apogee distance (while preserving \nthe semi-major axis and thus the period), rotating the orbit\nabout all three axes, and introducing a phase shift (time of apogee) into the\norbit. For this study we taken the X-ray telescope to be the Chandra\nsatellite and allowed changes in apogee (and perigee) of\n$\\pm200\\km$, rotations about the two axes in the plane of the orbit of\n$\\pm1^\\circ$, rotations in the plane of the orbit of $\\pm0.4^\\circ$, and\ntime shifts of $\\pm100\\second$. All of these changes are relative to\nChandra's orbit. These changes can be accomplished using ion engines\nseveral thousand times before exhausting the supply of expendables (see\nsection~\\ref{sec:steer}). Since occultations are best done near apogee and \n1000 or so orbital periods is the Chandra mission lifetime, this rate of\nconsumption of expendable is acceptable.\n\nUsing Monte Carlo techniques,\nwe studied the orbits in this region of parameter space \nsubject to two constraints: the minimum separation of the X-BOSS and telescope \nmust be at least $10\\km$, and somewhere in the orbit the\nperpendicular velocity must be less than $10\\mps$. We generated $100,000$\norbits that satisfy these criteria. Next, for a variety of photon count rates\nand desired resolutions we used the resolution results show in \nfigure~(\\ref{fig:resolution}) to determine $\\mu_\\perp^{\\rm max}$. Finally\nwe checked which lines-of-sight satisfied the velocity and acceleration\nconstraints~(\\ref{eqn:constraint1}, \\ref{eqn:constraint2}) and thus which\nparts of the sky can be observed. The results are shown in\nfigure~\\ref{fig:skycoverage} assuming the width of X-BOSS is $10\\meter$. \nHere even for very intense sources (I=$10^5\\second^{-1}$) only 20\\%\nof the sky can be covered with a a resolution of\n$\\Delta\\theta=0.1\\as$. This tight constraint is due principally to the fact\nthat X-BOSS is accelerating during the time that both of the sources are\nocculted leading to a large velocity by the end of the observation which\noccurs when the transit is complete. \nTo counteract this we could use a narrower satellite, \nuse a satellite with slits in it so that we do not have to wait until the far\nedge starts unocculting the sources, or fire the rockets while both sources\nare occulted to cancel the velocity. To model these possibilities we have considered \na satellite that accelerates over only $2\\meter$ between the onset and end of\na transit. The results are shown in figure~\\ref{fig:skycoverage}b. \nHere we see a tremendous improvement in sky coverage and resolution. \nFor intense sources, $I=10^5\\second^{-1}$, we can obtain\n$\\Delta\\theta=0.1\\as$ over \n40\\% of the sky and $\\Delta\\theta=0.02\\as$ over 20\\% of the sky.\nLarger sky coverages would be obtained if we relaxed the criteria on the \norbital velocity difference between the Chandra and X-BOSS orbits.\nThis would be justified if the propellant velocities of ion engines\nrose about $30\\kmps$, or if we could make do with a smaller number of orbital \ncorrections.\n\n\\subsection{L2 Orbits}\n\\label{subsec:L2orbits}\n\nAs discussed above (section~\\ref{subsec:orbitL2}) the orbits at L2 are much \nsimpler to manage than orbits around the Earth. Full sky coverage can be\nobtained and the velocity perpendicular to the line-of-sight can be chosen\nas desired. Figure~\\ref{fig:resolution} best represents what can be\nachieved at L2. Since the perpendicular velocity can be chosen, extremely\nhigh angular resolution is possible. Even sub-milliarcsecond resolution is\npossible for many sources ($I\\gtsim 4\\sci{3}\\second^{-1}$) when\n$\\mu_\\perp=0.1\\mas\\second^{-1}$.\n\n\\section{Results}\n\\label{sec:results}\n\nThis is an exciting time for X-ray astronomy. Two new X-ray telescopes\n(the Chandra Advanced X-ray Astronomical Facility, and the X-ray Multiple\nMirror telescope (XMM)) have been successfully launched, while another\n(Astro-E) is being readied for launch. Of these three, Chandra and XMM are\nin highly elliptical high altitude earth orbits\n(cf.~Table~\\ref{tab:xray-telescopes}) while Astro-E is headed for a\ncircular low earth orbit. In addition, at least two major X-ray\nspace-observatories are being planned: Constellation X, with launch\nscheduled for 2003, and XEUS with a target date of 2007. Constellation X\nwill be placed at the L2 point of the Earth-Sun system, while XEUS, like\nAstro-E, will be placed in low Earth orbit.\n\nWhile this may seem a remarkable proliferation of X-ray telescopes, each\nmission has its own emphasis. In building an X-ray telescope there is a\ndirect competition between large effective area (and thus sensitivity) and\nsmall acceptance angle (and thus high angular resolution). Therefore one\nmust choose whether to build an instrument which aims for high\nangular-resolution or one which has a goal of achieving high sensitivity.\nChandra is the only high angular resolution instrument of the listed\nmissions, with a maximum resolution of $0.5\\as$ and thus has the relatively\nsmall effective area given above~(\\ref{eqn:AChandra}). The other\ninstruments all aim for large effective area, and so sacrifice angular\nresolution. XMM, which is already flying, has considerably larger\neffective area than Chandra (and thus much lower angular resolution).\nAstro-E will have even larger effective area. Constellation-X will consist\nof multiple X-ray telescopes flown in formation, with a total effective\narea considerably greater than either XMM or Astro-E; it too has relatively\nlow angular resolution compared to Chandra. Finally XEUS will have a huge\neffective area, and will be designed to be expandable. Its angular\nresolution is better than XMM, Astro-E, or Constellation-X but still not as\ngood as Chandra. The properties of the existing and planned\ntelescopes are shown in Table~\\ref{tab:xray-telescopes}.\n\nThroughout we have considered the photon rate in the detector, not at the\nsurface of the telescope. An X-ray telescope has an effective area, $\\cal\nA$, which includes the geometric collecting area (since grazing optics are\nused the collecting area is not the full beam) and the efficiency of the\nX-ray detector. As an example, with Chandra\n\\be \n {\\cal A}_{\\rm Chandra} \\approx 700 \\cm^2\n \\label{eqn:AChandra}\n\\ee\nfor $E\\approx 1\\keV$. This is the area to be used as the area of the\ntelescope, not the geometric area as in the case of optical telescopes.\nThe effective area for existing and planned X-ray telescopes is given in Table~\\ref{tab:xray-telescopes}.\n\nThe luminosity of X-ray sources varies greatly. Black holes in the cores\nof nearby galaxies have \n\\be \n{\\cal L}_{\\rm bh} \\approx 10^{38\\hbox{--}40}\\unit{erg}\\second^{-1} =\n6.2\\sci{46\\hbox{--}48} \\keV\\second^{-1}\n\\ee\nin the $0.2\\hbox{--}2.4\\keV$ energy range. This leads to a photon rate at\nthe surface of the detector of\n\\be\n\\Gamma_{\\rm bh} = (0.052\\hbox{--}5.2)\\sci{-2} \\left (\\frac{E}{\\keV}\\right) \n\\left ( \\frac{d}{1\\Mpc}\\right)^{-2}\n\\left (\\frac{\\cal A}{\\cm^2}\\right) \\second^ {-1},\n\\ee\nwhere the energy, $E$, we observe at is given in keV and $\\cal A$ is the\neffective area of the X-ray telescope as discussed above.\n\nAn active galactic nucleus (AGN), Seyfert galaxy, or the core of X-ray\nclusters can be much more luminous\n\\be \n{\\cal L}_{\\rm AGN} \\approx 10^{40\\hbox{--}44}\\unit{erg}\\second^{-1} =\n6.2\\sci{48\\hbox{--}52} \\keV\\second^{-1}.\n\\ee\nHowever, since they are approximately $100\\Mpc$ away the photon rate \nis only \n\\be\n\\Gamma_{\\rm AGN} = 5.2\\times (10^{-6}\\hbox{--}10^{-2})\\left\n (\\frac{E}{\\keV}\\right) \n\\left ( \\frac{d}{100\\Mpc}\\right)^{-2}\n\\left (\\frac{\\cal A}{\\cm^2}\\right) \\second^ {-1}.\n\\ee\nGalactic microquasars are somewhat less luminous\n\\be \n{\\cal L}_{\\rm microquasar} \\approx 10^{39}\\unit{erg}\\second^{-1} =\n6.2\\sci{47} \\keV\\second^{-1},\n\\ee\nsince they are in our own galaxy, though, the photon rate is fairly high\n\\be\n\\Gamma_{\\rm microquasar} = 52 \\left (\\frac{E}{\\keV} \\right) \n\\left ( \\frac{d}{10\\kpc}\\right)^{-2}\n\\left (\\frac{\\cal A}{\\cm^2}\\right) \\second^ {-1}.\n\\ee\n\nFor a $10\\meter$ X-BOSS employed in conjunction with Chandra we find\n(figure~\\ref{fig:skycoverage}a) that for the brightest sources (galactic \nmicroquasars) we can obtain $\\Delta\\theta=0.5\\as$ over about 30\\% of the\nsky with the sky coverage falling quickly until at $\\Delta\\theta=0.1\\as$\nvery little of the sky is accessible. This represents a modest gain over\nwhat can be obtained by Chandra without the aid of X-BOSS. For a $2\\meter$ \nX-BOSS (figure~\\ref{fig:skycoverage}b) the situation is much\nbetter. Here $\\Delta\\theta=0.5\\as$ can be obtained over about 50\\% of the\nsky, $\\Delta\\theta=0.1\\as$ over about 20\\% of the sky, and\n$\\Delta\\theta=0.05\\as$ over about 5\\% of the sky. Thus significant\nimprovements are attainable through the use of an X-BOSS with Chandra.\n\nFor an X-BOSS employed in conjunction with XMM the situation is similar.\nAlthough XMM has a shorter period than Chandra its has an effective area about\n$3$ times larger (Table~\\ref{tab:xray-telescopes}). For a $10\\meter$\nX-BOSS (figure~\\ref{fig:skycoverageXMM}a) the skycoverage that can be\nobtained for each incident photon rate, $\\Gamma$, is less than can be\nobtained by Chandra (compare to figure~\\ref{fig:skycoverage}a) even with\nthe factor of $3$ increase in effective area that XMM provides. For a\n$2\\meter$ X-BOSS (figure~\\ref{fig:skycoverageXMM}b) the sky coverage for\nXMM and Chandra are closer though Chandra is still superior. Note that for\nboth sizes of X-BOSS tremendous improvements over the nominal $15\\as$\nresolution for XMM are obtained.\n\nAt L2 the situation is even better. Since we can tune the velocity\nrelative to the line-of-sight more easily, great improvements in resolution \nare readily available (figure~\\ref{fig:resolution}). Sub-milliarcsecond\nresolution can be obtained for sources with photon rates $\\Gamma\\gtsim\n1000\\second^{-1}$. For a single Constellation X modules, which will have an \neffective area of about $15,000\\cm^2$, the brightest AGN's, X-ray cluster\ncores, and galactic black holes will have $\\Gamma\\approx 800\\second^{-1}$\nwe can obtain $\\Delta\\theta\\approx 2\\mas$.\n\n\\section{Conclusions}\n\\label{sec:conclude}\n\nWe have found that an X-BOSS used in conjunction with an X-ray telescope\ncan lead to tremendous improvements in angular resolution. \nThe trend of increasing the effective area of future X-ray telescopes at the\nexpense of angular resolution (Table~\\ref{tab:xray-telescopes}) meshes perfectly\nwith the benefits gained by including an X-BOSS in the mission. Indeed, an\nX-ray telescope to be used with an X-BOSS is treated as a light bucket with\nall the resolving power coming from the X-BOSS occulting the source. Thus\nan X-BOSS is an excellent addition to an X-ray telescope mission,\nparticularly one at L2, such as Constellation X where sub-milliarcsecond\nresolution can be attained for a wide range of sources.\n\nFor the Chandra X-ray telescope we found that moderate improvements in\nangular resolution over an appreciable fraction of the sky can be achieved\nthrough the use of an X-BOSS\\@. Similarly an X-BOSS employed in\nconjunction with XMM would provide tremendous improvements in the angular\nresolution that XMM could achieve allowing XMM to have angular resolution\ncomparable to Chandra. An X-BOSS launched for use with Chandra or XMM would\nalso provide an important test bed for the technology to be used with\nfuture missions.\n\n\\acknowledgements\nThe authors would like particularly to thank \nArt Chmielewski for financial and other support,\nA. Babul and M. Dragovan for many useful comments and suggestions,\nN. Choudhuri for helpful suggestions on statistical tests, and Paul\nGorenstein and William Zhang for comments on a preliminary version of the \nmanuscript.\nThis work was supported by \na CAREER grant to GDS from the National Science Foundation,\na DOE grant to the theoretical particle and astrophysics group at CWRU, \nby a grant from NASA's Jet Propulsion Laboratory,\nand by funds from CWRU.\n\n\\begin{thebibliography}{}\n\n\\bibitem[Adams \\etal (1988)]{Adams} Adams, D.J. \\etal~1988, \\apj, 327, L65\n\n\\bibitem[Copi \\& Starkman (1998)]{CS98} Copi, C.J. \\& Starkman, G.D.~1998, \nProceedings of SPIE, 3356, March 25, 1998, Kona, HI\n\n\\bibitem[Copi \\& Starkman (2000)]{CS00} Copi, C.J. \\& Starkman, G.D.~2000,\n \\apj, 534, too appear%,\n% preprint astro-ph/9904413\n \n\\bibitem[Schneider (1995)]{Schneider} Schneider, J.~1995, Proceeding of the\n workshop ``Detection and Study of Terrestrial Extra-solar Planets'', May\n 15--17, Boulder, CO\n\n\\end{thebibliography}\n\n\\begin{deluxetable}{lccl}\n\\tablecaption{Properties of existing and planned X-ray\n telescopes.\\label{tab:xray-telescopes}}\n\n\\tablehead{\n \\colhead{Satellite} & \\colhead{Effective} & \\colhead{Angular} &\n \\colhead{Orbit} \\\\ \n \\colhead{Name} & \\colhead{Area at $1\\keV$} & \\colhead{Resolution} &\n \\colhead{}\\\\ \n \\colhead{} & \\colhead{(cm$^2$)} & \\colhead{(arcsecond)} & \\colhead {}\n }\n\\startdata\nChandra (AXAF)\\tablenotemark{a} & \\phn\\phn\\phn\\phm{,}700 & 0.5 & eccentric\nhigh Earth orbit \\\\\nXMM & \\phn\\phn2,000 & 15 & eccentric high Earth orbit \\\\\nAstro-E & \\phn\\phn1,200 & 90 & low Earth orbit \\\\\nHETE-II\\tablenotemark{b} & \\phn\\phn\\phn\\phm{,}350 & 660 & low Earth orbit \\\\\nConstellation X & \\phn30,000\\tablenotemark{c} & 15 & L2 halo orbit \\\\\nXeus -- Phase I & \\phn60,000 & 2 & low Earth orbit \\\\\n\\phantom{Xeus}~-- Phase II& 300,000 & 2 & low Earth orbit \\\\\n\\enddata\n\\tablenotetext{a}{Effective area is for the AXAF CCD Imaging Spectrometer\n (ACIS)\\@. Angular resolution is for the High Resolution Camera (HRC)\\@.}\n\\tablenotetext{b}{These values are for the wide field X-ray monitor (WXM)\n instrument. The quoted effective area is for $2\\keV$ X-rays.}\n\\tablenotetext{c}{Total effective area for all modules.}\n\\tablerefs{\\\\\nChandra: http://asc.harvard.edu/\\\\\nXMM: http://xmm.vilspa.esa.es/\\\\\nHETE-II: http://space.mit.edu/HETE/\\\\\nAstro-E: http://heasarc.gsfc.nasa.gov/docs/astroe/overview.html\\\\\nConstellation X: http://constellation.gsfc.nasa.gov/\\\\\nXeus: http://astro.estec.esa.nl/SA-general/Projects/XEUS/web/mission.html\n}\n\n\\end{deluxetable}\n\n\\begin{figure}\n \\leavevmode\\center{\\epsfig{figure=photonattenuation.ps,height=5 in,width=8.5 in}}\n \\caption{The photon mass attenuation length $\\lambda=1/(\\mu/\\rho)$\nfor various elemental absorbers as a function of photon energy\n($\\rho$ is the density). The figure is obtained from the particle\ndata book, figure 23.11 (http://pdg.lbl.gov). \nThe data for $30{\\rm eV} < E < 1 {\\rm keV}$ are obtained from \nhttp://www-cxro.lbl.gov/optical\\_constants \n(courtesy of Eric M. Gullikson, LBNL).\nThe data for $1{\\rm keV} < E < 100 {\\rm GeV}$ are from \n\\protect\\url{http://physics.nist.gov/PhysRefData}, thru the courtesy of \nJohn H. Hubbel (NIST).\n}\n\\label{fig:photonattenuation}\n\\end{figure}\n\n\\begin{figure}\n \\leavevmode\\center{\\epsfig{figure=resolution.ps,height=6in,angle=-90}}\n \\caption{The minimum angular separation of two X-ray sources resolvable\n at the 95\\% confidence level. The limits are shown for intensity\n ratios, $\\rho=1$ (solid),\n $1/3$ (dashed), and $1/10$ (dashed-dotted). The upper set of three curves\n are for $\\mu_\\perp = 10\\mas\\second^{-1}$, the middle set of three curves are\n for $\\mu_\\perp = 1\\mas\\second^{-1}$, and the lower set of three curves\n are for $\\mu_\\perp = 0.1\\mas\\second^{-1}$. Note that the total photon\n rate is of photons detected in the telescope (without the presence\n X-BOSS), not photons incident on the telescope. Here $d$ is the\n distance between the telescope and X-BOSS in units of $10^3\\km$.\n }\n \\label{fig:resolution}\n\\end{figure}\n\n\\begin{figure}\n \\leavevmode\\center{\\epsfig{figure=skycoverage_10m.ps,height=4in,angle=-90}}\n \\leavevmode\\center{\\epsfig{figure=skycoverage_2m.ps,height=4in,angle=-90}}\n \\caption{The fraction of the sky that can be observed as a function of\n the desired resolution, $\\Delta\\theta$, and the photon rate in the\n detector (as in figure~\\protect\\ref{fig:resolution}), $\\Gamma$, for\n an X-BOSS used in conjunction with Chandra. (a) A satellite\n width of $10\\meter$ is assumed here. (b) A satellite\n width of $2\\meter$ is assumed here. A larger satellite can obtain\n these results if velocity corrections are made during the observation.\n See the text for details.\n }\n \\label{fig:skycoverage}\n\\end{figure}\n\n\\begin{figure}\n \\leavevmode\\center{\\epsfig{figure=skycoverage_XMM_10m.ps,height=4in,angle=-90}}\n \\leavevmode\\center{\\epsfig{figure=skycoverage_XMM_2m.ps,height=4in,angle=-90}}\n \\caption{\n The same as figure~\\protect\\ref{fig:skycoverage} for an X-BOSS used in\n conjunction with XMM\\@.\n }\n \\label{fig:skycoverageXMM}\n\\end{figure}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002198.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Adams \\etal (1988)]{Adams} Adams, D.J. \\etal~1988, \\apj, 327, L65\n\n\\bibitem[Copi \\& Starkman (1998)]{CS98} Copi, C.J. \\& Starkman, G.D.~1998, \nProceedings of SPIE, 3356, March 25, 1998, Kona, HI\n\n\\bibitem[Copi \\& Starkman (2000)]{CS00} Copi, C.J. \\& Starkman, G.D.~2000,\n \\apj, 534, too appear%,\n% preprint astro-ph/9904413\n \n\\bibitem[Schneider (1995)]{Schneider} Schneider, J.~1995, Proceeding of the\n workshop ``Detection and Study of Terrestrial Extra-solar Planets'', May\n 15--17, Boulder, CO\n\n\\end{thebibliography}"
}
] |
astro-ph0002199
|
The host galaxies of luminous radio-quiet quasars
|
[
{
"author": "W.J.Percival"
},
{
"author": "$^{1,2}$ L.Miller"
},
{
"author": "$^1$ R.J. McLure$^{2,1}$ and J.S. Dunlop$^2$"
},
{
"author": "$^1$ Dept. of Physics"
},
{
"author": "Nuclear \\& Astrophysics Laboratory"
},
{
"author": "Keble Road"
},
{
"author": "Oxford OX1 3RH"
},
{
"author": "U.K."
},
{
"author": "Royal Observatory"
},
{
"author": "Blackford Hill"
},
{
"author": "Edinburgh EH9 3HJ"
}
] |
We present the results of a deep $K$-band imaging study which reveals the host galaxies around a sample of luminous radio-quiet quasars. The $K$-band images, obtained at UKIRT, are of sufficient quality to allow accurate modelling of the underlying host galaxy. Initially, the basic structure of the hosts is revealed using a modified Clean deconvolution routine optimised for this analysis. 2 of the 14 quasars are shown to have host galaxies with violently disturbed morphologies which cannot be modelled by smooth elliptical profiles. For the remainder of our sample, 2D models of the host and nuclear component are fitted to the images using the $\chi^{2}$ statistic to determine goodness of fit. Host galaxies are detected around all of the quasars. The reliability of the modelling is extensively tested, and we find the host luminosity to be well constrained for 9 quasars. The derived average $K$-band absolute $K$-corrected host galaxy magnitude for these luminous radio-quiet quasars is $\langle M_K \rangle=-25.15\pm0.04$, slightly more luminous than an $L^*$ galaxy. The spread of derived host galaxy luminosities is small, although the spread of nuclear-to-host ratios is not. These host luminosities are shown to be comparable to those derived from samples of quasars of lower total luminosity and we conclude that there is no correlation between host and nuclear luminosity for these quasars. Nuclear-to-host ratios break the lower limit previously suggested from studies of lower nuclear luminosity quasars and Seyfert galaxies. Morphologies are less certain but, on the scales probed by these images, some hosts appear to be dominated by spheroids but others appear to have disk-dominated profiles.
|
[
{
"name": "ukirt_acc.tex",
"string": "\\documentstyle[epsf,graphics,epsfig]{mn}\n\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\def\\simlt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}}\n\\def\\simgt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}}\n\\newcommand{\\etal}{{\\it et~al.}}\n\\newcommand{\\msun}{\\thinspace\\hbox{$M_{\\odot}$}\\ }\n\n\\title[Quasar host galaxies]\n{The host galaxies of luminous radio-quiet quasars}\n\n\\author[W.J. Percival \\etal]{W.J.Percival,$^{1,2}$ L.Miller,$^1$\n\tR.J. McLure$^{2,1}$ and J.S. Dunlop$^2$\\\\\n $^1$ Dept. of Physics, University of Oxford, \n Nuclear \\& Astrophysics Laboratory, Keble Road, Oxford OX1 3RH, U.K.\\\\\n $^2$ Institute for Astronomy, University of Edinburgh, \n Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, U.K.\\\\}\n\n\\date{Submitted for publication in MNRAS}\n\\begin{document}\n\\maketitle\n\n\\begin{abstract} \nWe present the results of a deep $K$-band imaging study which reveals\nthe host galaxies around a sample of luminous radio-quiet quasars. The\n$K$-band images, obtained at UKIRT, are of sufficient quality to allow\naccurate modelling of the underlying host galaxy. Initially, the basic\nstructure of the hosts is revealed using a modified Clean\ndeconvolution routine optimised for this analysis. 2 of the 14 quasars\nare shown to have host galaxies with violently disturbed morphologies\nwhich cannot be modelled by smooth elliptical profiles. For the\nremainder of our sample, 2D models of the host and nuclear component\nare fitted to the images using the $\\chi^{2}$ statistic to determine\ngoodness of fit. Host galaxies are detected around all of the\nquasars. The reliability of the modelling is extensively tested, and\nwe find the host luminosity to be well constrained for 9 quasars. The\nderived average $K$-band absolute $K$-corrected host galaxy magnitude\nfor these luminous radio-quiet quasars is $\\langle M_K\n\\rangle=-25.15\\pm0.04$, slightly more luminous than an $L^*$\ngalaxy. The spread of derived host galaxy luminosities is small,\nalthough the spread of nuclear-to-host ratios is not. These host\nluminosities are shown to be comparable to those derived from samples\nof quasars of lower total luminosity and we conclude that there is no\ncorrelation between host and nuclear luminosity for these\nquasars. Nuclear-to-host ratios break the lower limit previously\nsuggested from studies of lower nuclear luminosity quasars and Seyfert\ngalaxies. Morphologies are less certain but, on the scales probed by\nthese images, some hosts appear to be dominated by spheroids but\nothers appear to have disk-dominated profiles.\n\\end{abstract}\n\n\\begin{keywords}\ngalaxies: active, quasars: general, infrared: galaxies\n\\end{keywords}\n\n\\section{Introduction}\nModels of the cosmological evolution of quasars often use galaxy\nmergers as the primary mechanism for quasar activation and require the\nmass of the structure within which a quasar is formed as a basic\nparameter \\cite{efrees,haehnelt,percival}. One step towards testing\nhypotheses about quasar initiation is to answer the question: Is a\nquasar's luminosity correlated with the luminosity of the structure\nwithin which it formed? Such a correlation has been shown to exist for\nlow redshift ($0<z<0.3$) Seyferts and quasars with luminosities\n$M_V\\simgt-25$ in that there appears to be a lower limit to the host\nluminosity which increases with quasar luminosity\n\\cite{mcleod95a,mcleod99}. However this limit is poorly defined,\nparticularly for high luminosity quasars when the strong nuclear\ncomponent makes it increasingly more difficult to find low luminosity\nhosts.\n\nRecent work has shown that the majority of nearby galaxies have\nmassive dark objects in their cores, which are suggested to be\nsuper-massive black holes potentially capable of powering AGN\n\\cite{kormendy,magorrian}. These studies have also found evidence for\na correlation between the mass of the compact object and the\nluminosity of the spheroidal component of the host. Assuming a link\nbetween nuclear luminosity and black hole mass, the average nuclear\nluminosity emitted by low redshift quasars is expected to increase\nwith host spheroidal luminosity. In light of this prediction there has\nbeen a resurgence of interest in host galaxy studies and recent work\n\\cite{mclure} has found weak evidence for a correlation in accord with\nthe relations of Magorrian \\etal\\ \\shortcite{magorrian}. However, this\ncorrelation relies on spheroid/disk decomposition for two quasars with\nlow nuclear luminosities, and only a small number of luminous\nradio-quiet quasars were observed.\n\nHost galaxy properties of AGN are known to be correlated with the\nradio power: radio galaxies tend to be large spheroidal galaxies,\nwhile disk galaxies tend to be radio-quiet. Recent evidence suggests\nthat the hosts of radio-loud quasars are also predominantly massive\nspheroidal galaxies regardless of the nuclear luminosity\n\\cite{dunlop93,taylor,mclure}. However, studies of radio-quiet quasars\nwith luminosities $M_V\\simgt-25$ have shown that the hosts can be\ndominated by either disk-like or spheroidal components or can be\ncomplex systems of gravitationally interacting components\n\\cite{taylor,bahcall,boyce,mclure}. There is therefore strong\njustification for studies to see if these luminosity and morphological\ntrends extend to the hosts of more luminous ($M_V\\simlt-25$)\nradio-quiet quasars.\n\nThere have been many recent detections of host galaxies in the optical\nthanks to results from HST \\cite{hooper,bahcall,boyce,mclure}, which\nadd to our knowledge from ground-based studies\n\\cite{malkan84a,malkan84b,hutchings92,veron-cetty}. However, quasar\nhosts often appear significantly disturbed, as if by interaction or\nmerger which can lead to strong bursts of star-formation and\nsignificant extended line and blue continuum emission at optical\nwavelengths which are not indicative of the mass of the underlying\nhost. The nuclear-to-host light ratio in the optical is also typically\nhigher than at longer wavebands.\n\nThese problems can be circumvented by observing in the infrared where\nthe contrast between host and nuclear component is improved and the\nemission associated with star bursting activity is largely absent: the\n$K$ magnitude is a better measurement of the long-lived stellar\npopulations in the host \\cite{bruzual}. Previous observations in the\ninfra-red have been successfully used to determine quasar host galaxy\nluminosities and morphologies (McLeod \\& Rieke 1994a;b; Dunlop \\etal\\\n1993; Taylor \\etal\\ 1996). However, recent advances in telescope\ndesign, in particular the advent of adaptive optics systems such as\nthe tip-tilt system on UKIRT produce clearer images of quasars and\nenable accurate point spread functions (psfs) to be more readily\nobtained as differences between successive observations are\nreduced. Such advances coupled with improved analysis techniques mean\nwe are now able to reveal the host galaxies of luminous quasars with\n$M_V\\simlt-25$ using infra-red observations.\n\nIn order to obtain enough luminous radio-quiet quasars our sample was\nforced to cover redshifts $0.26\\le z\\le0.46$. At such redshifts, with\ntypical seeing, the structure of the host galaxy is hidden in the\nwings of the psf from the nuclear component. There are two main ways\nof proceeding: either the psf can be deconvolved from the quasar light\nto directly observe the host galaxy, or known galaxy profiles can be\nused to model the hosts, a nuclear component can be added in and the\nprofiles can be fitted to the data. Because the host galaxies\nsometimes have disturbed morphologies indicative of violent mergers,\nit is difficult to assume a form for the galaxy. However without such\nmodelling, it is not easy to determine the contribution of the host to\nthe light from the centre of the quasar and deconvolution routines\ntend to produce biased solutions which may alter important features.\n\nFor the analysis of our quasar sample, an approach is adopted which\nuses both methods. Initially (Section~\\ref{sec:simple}) the images\nwere restored using a deconvolution algorithm, based on the Clean\nalgorithm \\cite{hogbom}, developed for this problem, which will be\ndescribed elsewhere \\cite{percival_clean}. This routine was used to\nreveal the extent to which the `nebulosity' around the point source is\ndisturbed. Deconvolution of the light from two of our quasars reveals\nviolently disturbed host galaxies indicative of close merger\nevents. In the remainder of our sample, the non-nuclear light is more\nuniformly distributed around the centre of the quasar. We should note\nthat the resolution provided by this deconvolution technique is\nprobably not sufficient to reveal evidence for weak mergers, where the\nhost galaxy is only slightly disturbed.\n\nWhere the image-restoration routine revealed approximate elliptical\nsymmetry in the non-nuclear component, 2D galaxy profiles were fitted\nto the hosts. Analysis of non-interacting, low redshift galaxies has\nshown that an empirical fit to both disk and spheroidal systems is\ngiven by:\n\\begin{equation}\n \\mu=\\mu_o\\exp\\left[-\\left(\\frac{r}{r_o}\\right)^{1/\\beta}\\right].\n \\label{eq:galprofile}\n\\end{equation}\nwhere $\\mu$ is the average surface brightness in concentric elliptical\nannuli around the core, and $r$ is the geometric average of the\nsemi-major and semi-minor axes.\n\nModel images were carefully created using this profile and were tested\nagainst the data using the $\\chi^2$ statistic to determine goodness of\nfit. Five host parameters were required, the half-light radius,\nintegrated luminosity, axial ratio, angle on the sky, and the\npower-law parameter of the galaxy $\\beta$, as well as the\nnuclear-to-host ratio. Section~\\ref{sec:model} describes the modelling\nprocedure in detail, and in Section~\\ref{sec:results} the best-fit\nparameters are presented for the host galaxies.\n\nMuch previous work has produced ambiguous results because of a lack of\nerror analysis and insufficient testing of the modelling. A detailed\nanalysis of the reliability of the 2D modelling method used in this\npaper has therefore been undertaken and is presented in\nSection~\\ref{sec:test}. Although hosts are detected in all of our\nsample, the upper limit of the host luminosity is only usefully\nconstrained for 9 of the 12 quasars modelled (see\nSection~\\ref{sec:calc_lum}). Similar analysis of the best-fit $\\beta$\nparameter which determines the morphology of the host reveals that\nthis parameter is, unsurprisingly, more poorly constrained than the\nluminosity. However, we have created Monte-Carlo simulations of images\nwith the same signal-to-noise as the original images\n(Sections~\\ref{sec:mock}~\\&~\\ref{sec:mock2}). By analysing these\nimages using exactly the same procedure as for the original data we\nfind that it is possible to distinguish between disk and spheroidal\nstructure.\n\nUnless stated otherwise we have adopted a flat, $\\Lambda=0$\ncosmological model with $H_0=50$km\\,s$^{-1}$Mpc$^{-1}$ and have\nconverted previously published data to this cosmology for ease of\ncomparison.\n\n\\section{The Sample and Observations}\n\n\\begin{table*}\n\\begin{minipage}{\\textwidth}\n \\centering\n \\begin{tabular}{ccccccccclc} \\hline\n quasar & \\multicolumn{2}{c}{J2000 coords} & V & z & $M_V$ \n & 1.4\\,GHz Flux density & Observing run &\n \\multicolumn{3}{c}{Integration time} \\\\ \n & & & & & & /W\\,Hz$^{-1}$Sr$^{-1}$ & & & /s & \\\\ \\hline \n 0043+039 & 00 45 47.3 & +04 10 22.5 & 16.0 & 0.384 & $-$26.0 & \n - & 09/1997 & & 2800 & \\\\\n 0137$-$010 & 01 40 17.0 & $-$00 50 03.0 & 16.4 & 0.335 & $-$25.3 & \n 1.46$\\times10^{23}$ & 09/1996 & & 11300 & \\\\\n 0244$-$012 & 02 46 51.8 & $-$00 59 32.3 & 16.5 & 0.467 & $-$25.9 & \n - & 09/1997 & & 10300 & \\\\\n 0316$-$346 & 03 18 06.5 & $-$34 26 37.1 & 15.1 & 0.265 & $-$26.0 & \n - & 09/1996 & & 6400 & \\\\\n 0956$-$073 & 09 59 16.7 & $-$07 35 18.9 & 16.5 & 0.327 & $-$25.1 & \n - & 05/1998 & & 8000 & \\\\\n 1214+180 & 12 16 49.1 & +17 48 04.1 & 16.7 & 0.374 & $-$25.2 & \n - & 05/1998 & & 7590 & \\\\\n 1216+069 & 12 19 20.9 & +06 38 38.4 & 15.7 & 0.334 & $-$26.0 & \n - & 05/1998 & & 7200 & \\\\\n 1354+213 & 13 56 32.9 & +21 03 51.2 & 15.9 & 0.300 & $-$25.5 & \n - & 05/1998 & & 8600 & \\\\\n 1543+489 & 15 45 30.2 & +48 46 08.9 & 16.1 & 0.400 & $-$26.0 & \n - & 05/1998 & & 14300 & \\\\\n 1636+384 & 16 38 17.6 & +38 22 49.0 & 17.0 & 0.360 & $-$24.8 & \n - & 05/1998 & & 7100 & \\\\\n 1700+518 & 17 01 24.9 & +51 49 20.4 & 15.1 & 0.290 & $-$26.2 & \n 7.18$\\times10^{23}$ & 09/1997 & & 3600 & \\\\\n 2112+059 & 21 14 52.6 & +06 07 42.5 & 15.5 & 0.466 & $-$26.7 & \n 2.95$\\times10^{23}$ & 09/1997 & & 15100 & \\\\\n 2233+134 & 22 36 07.7 & +13 43 55.0 & 16.7 & 0.325 & $-$26.9 & \n - & 09/1996 & & 6400 & \\\\\n 2245+004 & 22 47 41.6 & +00 54 57.3 & 18.5 & 0.364 & $-$23.4 & \n - & 09/1997 & & 11100 & \\\\ \\hline\n \\end{tabular}\n\n \\caption{The sample of 14 quasars observed. $M_V$ was calculated for\n each quasar from apparent magnitudes given in the catalogue of\n Hewitt \\& Burbidge \\protect\\shortcite{hewitt} assuming no\n $K$-correction. Radio fluxes were determined using the NVSS 1.4\\,GHz\n survey. Only 3 of the quasars were detected in this survey and their\n radio fluxes are below the radio-quiet/loud cutoff. We observed this\n sample in 3 observing runs at UKIRT. For the 09/1996 run, the\n tip-tilt system was not operational and the psf stars are not\n expected to be as well matched to the quasars as for the other runs\n (see Section~\\protect\\ref{sec:psf}). Note that coordinates given\n were determined using the original finding charts and the Digitised\n Sky Survey and may be different from those in the catalogue of\n Hewitt \\& Burbidge \\protect\\shortcite{hewitt} which are often\n inaccurate.} \\label{tab:quasars}\n\\end{minipage}\n\\end{table*}\n\nWe have selected 13 luminous ($M_V\\le-25.0$) quasars and one less\nluminous quasar within the redshift range $0.26\\le z\\le0.46$. The\nquasars were checked for radio loudness using the NVSS survey\n\\cite{condon}. Three of the 14 quasars were detected at 1.4\\,GHz in\nthis survey (see Table~\\ref{tab:quasars}) but their flux densities are\nall $<10^{24}$\\,W\\,Hz$^{-1}$Sr$^{-1}$ and they are considered part of\nthe radio-quiet population. Three quasars, 0137$-$010, 0316$-$346 and\n2233+134 were observed at UKIRT before the tip-tilt system was\noperational and so these data are not of the same quality as those\nfrom subsequent runs.\n\nOf the 13 luminous quasars selected, three, 0956$-$073, 1214+186 and\n1636+384 have not had previous attempts to measure host magnitudes and\nmorphologies. It is difficult to assess the significance of claimed\nhost detections for the other quasars and the associated parameters\ncalculated because of the lack of error analysis which abounds in this\nfield, and the great potential for systematic errors caused by the\nrequirement for accurate psf measurements. However, individual results\nfrom these studies are compared to the results of this paper in\nSection~\\ref{sec:results-quasars}.\n\nThe observations were all taken using the $256\\times256$\\,pixel InSb\narray camera IRCAM\\,3 on the 3.9\\,m UK Infrared Telescope (UKIRT). The\npixel scale is 0.281\\,arcsec\\,pixel$^{-1}$ which gives a field of view\nof $\\sim$72\\,arcsec. Our sample of quasars was observed during three\nobserving runs in 09/1996, 09/1997 and 05/1998. For the later two runs\nthe image quality was exceptional with consistent FWHM of 0.45\\,arcsec\nobserved. \n\nThe $K$-band quasar images were taken using a quadrant jitter pattern.\nThis cycled 2 or 4 times through a 4-point mosaic placing the quasar\nin each of the quadrants in turn. The actual position of the central\nvalue within each quadrant was shifted slightly for each image to\nreduce the effect of bad pixels. Each image consists of\n$\\sim$100\\,secs of integration time divided into exposures calculated\nto avoid saturation. The exposures varied between 5-10\\,secs for the\nquasars alone, down to 0.2\\,secs for the quasars with a bright star on\nthe chip which we hoped to use as a psf star. Standard stars from the\nsample of UKIRT faint standards \\cite{casali} were observed for\nphotometric calibration between observations of different quasars. All\nof the images were corrected for the non-linear response of IRCAM\\,3\nusing a formula supplied by the telescope support staff.\n\n\\section{Obtaining the correct PSF} \\label{sec:psf}\n\nObtaining an accurate psf is vital to the analysis of the images. With\nthese ground-based observations the psf varies with seeing conditions\nand telescope pointing. An experimental psf was therefore determined\nfor each of the quasars by observing a nearby bright star. This led to\nan unbiased, accurate psf without recourse to the quasar images. For\nthree of the quasars, 0956$-$073, 1214+180 and 1216+069 there was a\nnearby star which could be placed on the frame with the quasar. This\ngave an accurate psf measurement with no loss of integration time on\nthe quasar. If required, the position of the quasar for each\nobservation was altered slightly to allow both the quasar and psf to\nbe well within the boundaries of the chip. For the remaining quasars\nthe telescope was offset to a nearby bright star to use as the psf,\nbefore and after each quasar integration (which lasted a maximum of\n1600\\,secs). A number of psf measurements were therefore obtained for\neach night and each quasar. To ensure consistent adaptive optics\ncorrection, properties of the tip-tilt guiding were matched between\nquasar and psf measurements. To do this psf stars were selected to\nenable tip-tilt guiding from a star of a similar magnitude, distance\nfrom the object, and position angle to that used for the quasar\nimage. Magnitudes of the stars chosen to provide a psf measurement are\ngiven in Table~\\ref{tab:chisq}. By examining fine resolution contour\nplots of the psf images, it was found that the psf was stable over the\ncourse of each night, but varied between nights at the telescope and\nfor different telescope pointing. Because of this, the final stacking\nof psf images was performed with the same weighting between days as\nfor the quasar images (see Section~\\ref{sec:data}).\n\nAs a test of the effectiveness of this procedure to provide the\ncorrect psf, the fit between measured psf and image for quasar\n1543+489 has been compared to the fit between psfs measured for\ndifferent quasars and the same image. Fig.~\\ref{fig:psfquality} shows\nthe radial profile of $\\sigma^2({\\rm image}-{\\rm psf})$ calculated in\ncircular annuli of width 0.5\\,arcsec. Here the psf has been scaled so\nthe total intensity is the same for both quasar and psf. As can be\nseen, the psf observed with the quasar image matches the quasar close\nto its centre better than any other psf. As the core of the psf is\nundersampled and the sampling between psf and image has not been\nmatched (see Section~\\ref{sec:nuclear} for further discussion of\nthis), this result demonstrates the validity of the psf measuring\ntechnique.\n\n\\begin{figure}\n \\centering\n \\resizebox{\\columnwidth}{!}{\\includegraphics{psf.eps}}\n \\caption{ The radial profile of the variance (measured in annuli of\n width 0.5\\,arcsec) of the difference between the image of quasar\n 1543+489 and the scaled psf obtained using the procedure in\n Section~\\protect\\ref{sec:psf} (stars). For comparison, the profiles\n of the variance obtained using the 13 other psf measurements are\n also plotted (solid circles). The solid line is the best fit model\n to the variance, calculated as in Section~\\protect\\ref{sec:error}.}\n\\label{fig:psfquality}\n\\end{figure}\n\n\\section{The Data Reduction} \\label{sec:data}\n\nThe data reduction procedure was optimised to search for low surface\nbrightness extended objects. The same procedure was used for both\nimage and psf data so no extra differences between measured and actual\npsf were introduced. In calculating the flat-field for each mosaic, it\nwas decided to ignore all pixels within the quadrant containing the\nquasar. This ensured that the flat-fielding technique was not biased\nto remove or curtail extended emission which could occur if a routine\nbased on pixel values, such as a $\\sigma$-clipping routine, was\nused. Outside this quadrant, any areas occupied by bright stars were\nalso removed from the calculation. The sky background level, assumed\nto be spatially constant was also calculated ignoring these areas.\n\nAs the images were undersampled in the central regions we decided to\nuse a sub-pixel shifting routine to centralise the images before they\nwere median stacked to provide the final composite. Having replaced\nbad pixel values, the images were shifted using a bicubic spline\ninterpolation routine in order to equalise the intensity weighted\ncentres, and were median stacked. Because the psf quality was found to\nvary from day-to-day, the final stacking of psf images was performed\nwith the same weighting between days as for the quasar images.\n\nFinally, any nearby bright objects in the psf frame were replaced by the\naverage in an annulus of width 0.5\\,arcsec at the distance of the\nobject from the centre of the psf, around the centre. In the quasar\nframe any nearby objects were noted and blanked out of the error frame\nso they were not included when measuring $\\chi^2$ between image and\nmodel (see Section~\\ref{sec:model}).\n\n\\section{Determining Simple Morphology} \\label{sec:simple}\n\nBecause of the often disturbed morphology of quasar hosts it is not\npossible to immediately assume a form for the galaxy structure. For\ninstance if the host is involved in a close merger, modelling it with\na smooth profile will not provide the correct host luminosity. The\nextended wings of the psf from the intense nuclear component hide the\nhost galaxy sufficiently that direct observation cannot easily reveal\neven violently disturbed morphologies. Simply subtracting a multiple\nof the psf from the centre of the image will reveal some structure,\nbut a deconvolution routine will reveal more structure. The routine\nused was a modified Clean algorithm developed for this problem which\nwill be described elsewhere \\cite{percival_clean}. The results show\nthat this routine was of sufficient quality to reveal the approximate\nsymmetry of the host on a scale which includes most of the light\nimportant for modelling the galaxy.\n\nExamination of the deconvolved images revealed a clear distinction\nbetween disturbed and symmetric systems. Two of the quasars have\nmorphologies which showed no sign of elliptical symmetry and instead\nshow signs of recent merger. The deconvolved images of these quasars\nare shown in Fig.~\\ref{fig:disturbed}. From these images a value for\nthe non-nuclear luminosity was obtained by summing the residual light\nexcluding the central pixel. Unfortunately the non-nuclear structure\nrevealed was not of sufficient quality to be extrapolated into the\ncentral region so the amount of nuclear light which originates in the\nhost galaxy is unknown. Magnitudes obtained from these deconvolved\nimages should therefore be treated as approximate. The structure\nrevealed for these quasars is discussed in\nSection~\\ref{sec:results-quasars}. Deconvolving the remaining quasars\nrevealed host galaxies with approximate elliptical symmetry.\n\n\\begin{figure*}\n\\begin{minipage}{\\textwidth}\n \\begin{center}\n \\resizebox{8.0cm}{8.0cm}{\\includegraphics{cl_1636.eps}} \n \\hspace{1.0cm}\n \\resizebox{8.0cm}{8.0cm}{\\includegraphics{cl_1700.eps}}\n \\end{center}\n \\centering \n\n \\caption{The results of the deconvolution of quasars 1636+384 and\n 1700+518 revealing hosts with disturbed morphologies indicative of\n close merger events. The deconvolution output, obtained on the pixel\n scale, has been smoothed by convolving with a Gaussian with\n $\\sigma=0.5$\\,pixels and the residual frame remaining after the\n algorithm has finished had been added back in to preserve\n luminosity. Contours are shown at 0.0125\\%, 0.025\\%, 0.05\\% and 50\\%\n of the peak intensity. For quasar 1700+581 a contour is also\n included at 0.00625\\% of the peak intensity. The size of the images\n is 7.3$\\times$7.3\\,arcsec (26$\\times$26\\,pixels). See\n Section~\\ref{sec:results-quasars} for further discussion of the\n morphologies revealed.}\n\\label{fig:disturbed}\n\\end{minipage}\n\\end{figure*}\n\n\\section{Modelling the Quasar Images} \\label{sec:model}\n\nHaving determined that the extended structure around a quasar did not\nshow signs of a disturbed morphology indicative of a close merger and\nrevealed approximate elliptical symmetry, the luminosity and\nmorphology of the host galaxy were estimated by fitting model images\nto the data. A $\\chi^2$ minimisation technique described below was\nused to estimate the goodness of fit of the models.\n\n\\subsection{Producing a model galaxy} \\label{sec:galaxy}\n\nIn this Section we describe how the empirical galaxy surface\nbrightness profile given by Equation~\\ref{eq:galprofile} was used to\nestimate the contribution from the host to the counts in each\npixel. This had to be done carefully because of the poor sampling of\nthe images. The profile given by Equation~\\ref{eq:galprofile} has\nproved to be an excellent fit to many different types of galaxy\n\\cite{caon,baggett} and it is assumed that, if the hosts are not\nundergoing violent merger, this profile provides a good representation\nof the galaxy light.\n\nBefore the method is described, it is useful to revise how an image is\nobtained from the light emitted by the quasar. Initially, the\ncontinuous distribution of light is altered by the atmosphere and the\noptics of the telescope in a way approximately equivalent to\nconvolution with a continuous point spread function. The resulting\ncontinuous distribution is sampled by the detector which integrates\nthe light over each pixel. This is equivalent to convolving the light\nwith a square function of value 1 within a pixel and 0 otherwise, and\nsampling the resulting distribution assuming uniform response across\neach pixel. The dithering and subsequent stacking of the images will\nprovide another convolution, although by sub-pixel shifting the images\nprior to stacking, the effective smoothing width of this function is\nreduced to less than 1\\,pixel. The whole process can therefore be\nthought of as convolving the true psf, the quasar light and a narrow\nsmoothing function (of width $\\sim$1\\,pixel) and sampling the\nresulting continuous image on the pixel scale.\n\nBecause the psf measurements were obtained using exactly the same\nprocedure as the quasar images, the measured psf is the result of a\nconvolution of the true psf with the narrow smoothing function.\nConvolution is commutative and associative so this smoothing function\nis accounted for in the measured psf and further smoothing of the\nmodel galaxy is not required. For this reason the unconvolved model\ngalaxy should not be obtained by simply integrating the model profile\nover each pixel. Sampling the model galaxy profile onto a grid with\nspacing equivalent to the pixel scale and convolving with the psf will\nnot produce a correct model galaxy because of aliasing.\n\nIn order to limit the aliased signal, the procedure adopted was to\nextrapolate the psf onto a grid which was finer than the pixel scale\nusing a sinc function (so no extra high frequency components are\nintroduced). The surface brightness of the model galaxy was then\ncalculated at each point on a grid of the same size and was convolved\nwith the psf on this grid. To provide the final model, this\ndistribution was subsampled onto the pixel scale. Progressively finer\ngrids were used until the total counts in the sampled model galaxy\nconverged, when the majority of the aliased signal is assumed to have\nbeen removed. The algorithm adopted used a fine grid with 4$\\times$\nthe number of points at each successive step, and was stopped when the\naverage of all the counts differs from that of the previous step by a\nfactor less than 0.01.\n\nUnless stated otherwise, all model host luminosities and magnitudes\nwhich relate to a 2D profile should be assumed to have been integrated\nto infinite radius. For the large radius within which such models were\nfitted to the data, this makes only a small difference in the\nluminosity. The four parameters of the host galaxy are the geometric\nradius of the elliptical annulus which contains half of the integrated\nlight $R_{1/2}$, the total integrated host luminosity $L_{\\rm int}$,\nthe projected angle on the sky $\\alpha$, the axial ratio $a/b$ and the\npower law parameter $\\beta$. In this paper, the integrated host\nluminosity is quoted in counts /analogue data units (adu) detected in\na 1\\,sec exposure.\n\n\\subsection{The nuclear component} \\label{sec:nuclear}\n\nIn principle, adding in the nuclear light is simple - the correct\namount is added to the centre of the model galaxy to minimise $\\chi^2$\nbetween model and observed images. However, it is important to account\nfor all of the nuclear light. Differences between measured and true\npsf caused by undersampling, seeing variations or effects such as\ntelescope shake must be accounted for, even though the adopted\nobserving strategy has limited some of these. In particular, when a\nnearby star (as used in Section~\\ref{sec:star}) is deconvolved, the\nresulting light appears not only in the central pixel, but in the\nsurrounding pixels as well: if similar components from the nuclear\nlight are not accounted for in the quasar images, the host\nluminosities and morphologies derived will be wrong.\n\nBecause of the large peak in both the image and psf, trying to alter\nthe sampling of the images by extrapolating onto a fine grid and\nresampling without inducing unwarranted frequency components causes\n`ringing' in the images which is large enough to affect the results of\nthe modelling. It would be possible to use a different extrapolation\ntechnique, but this risks altering the image and measured psf in\ndifferent ways. Instead, a more simple correction to this problem is\nadopted: rather than only adding a multiple of the psf to the central\npixel, variable multiples of the psf are also added centred on the\nsurrounding 8 pixels. In the perfect case where the measured psf is\naccurate, while such free parameters make convergence to the minimum\n$\\chi^2$ value slower, they do not affect the position of the minimum:\nthe additional components make a negligible contribution to the\nmodel. However, suppose there is a discrepancy between measured and\ntrue psf so that the deconvolved image of the nuclear light consists\nof a central spike surrounded by corrective components which decrease\nin magnitude with distance away from the spike. Allowing the value of\nthe pixels close to the core to be free parameters in our model will\ncorrect these discrepancies and any light observed originating away\nfrom the core will be more likely to be from the host galaxy and not\nfrom escaping nuclear light. The opposite is also true, and these\nextra components will also correct psf measurement errors which cause\nlight from the galaxy to be wrongly ascribed to the core (as for\nquasar 0956$-$073: see below). Undersampling problems do not affect\nthe modelled galaxy to the same extent because the galaxy light is\nmore uniformly distributed and discrepancies are smoothed. In\nparticular, the total integrated light measured to be from the host\nwill only be minimally affected: see below.\n\nQuasar 0956$-$073 was modelled using different numbers of these extra\ncomponents, and the recovered host parameters are given in\nTable~\\ref{tab:nuc_param}. As expected, the $\\chi^2$ value decreases\nwith an increasing number of additive psf components showing that the\nfit between model and image is being improved. The recovered\nparameters for 1 or 9 additive components show moderate differences,\nbut allowing more components makes no further significant\nchange. Because the host luminosity increases for this quasar with\nincreasing numbers of added components, the sum of the extra psf\ncontributions must be negative which suggests that, for this quasar,\nthe psf has a slightly broader central profile than the quasar.\n\nFor all of the quasars modelled, the total light within the eight\nextra psf components was not found to be systematically positive or\nnegative. If adding 8 extra `psf components' around the core had\nalways resulted in a total positive (or negative) component being\nsubtracted from the quasar, this would have suggested that either\nthese components were removing host light in addition to `leaking'\nnuclear light, and that the host profile breaks down in a systematic\nway for these pixels, or that our observing strategy had produced a\nsystematically incorrect psf.\n\nFor all quasar host galaxy studies, there is no escaping the\nfundamental problem that the galaxy profile has to extrapolated into\nthe central region from some radius (to separate host and nuclear\nlight). By adding in these extra components, all we're doing is\nextrapolating from different distances, and arguing that simply\nextrapolating only into the central pixel is not necessarily correct\nfor these data. This is because the measured psf is incorrect for the\n(discrete) deconvolution problem we're trying to solve.\n\n\\begin{table}\n \\centering \\begin{tabular}{ccccccc} \\hline\n psf & $R_{1/2}$ & $L_{\\rm int}$ & a/b & $\\alpha$ & $\\beta$ & \n $\\chi^2$ \\\\\n cmpts & /kpc & /adu & & & & \\\\ \\hline\n 1 & 10.45 & 312.7 & 0.61 & 1.05 & 0.77 & 2840.3 \\\\\n 9 & 9.76 & 350.1 & 0.64 & 1.04 & 0.92 & 2814.2 \\\\\n 25 & 9.71 & 353.3 & 0.65 & 1.03 & 0.93 & 2799.9 \\\\\n \\hline\n \\end{tabular}\n\n \\caption{Recovered host galaxy parameters for quasar 0956$-$073\n modelled using different numbers of additive psf components.}\n \\label{tab:nuc_param}\n\\end{table}\n\n\\subsection{The error frame} \\label{sec:error}\n\nDetermining the fit between model and image requires an estimate of\nthe relative noise in each pixel, from both intrinsic noise in the\nimage and differences between measured and true psf. Ideally these\nerrors should be estimated without recourse to the images but,\nunfortunately, this is impractical for these data. Faced with a\nsimilar problem, Taylor \\etal\\ \\shortcite{taylor} estimated the radial\nerror profile by measuring the error in circular annuli of the image\nfrom which a multiple of the psf had been subtracted centred on the\nquasar with matched total luminosity. Using both the image and\nmeasured psf in this way allows the error from psf differences to be\nincluded in the error frame. However, this model assumes that the host\ngalaxies do not introduce any intrinsic variations in the annuli\nwithin which the variance is calculated. Such variations could result\nfrom either differences between the radial profile of the host\n(convolved with the psf) and the psf profile, or significant deviation\nfrom circular host profiles. These effects will be small because the\nhosts only contribute a small percentage of the light and deviations\nfrom circular hosts are small.\n\nIn order to reduce the number of parameters required to calculate the\nerror profile and hopefully alleviate any damage caused by calculating\nthe error frame from the data, Taylor \\etal\\ \\shortcite{taylor} showed\nthat a function of the form\n$\\log(\\sigma_i)=A\\exp^{-0.5(r/S)^{\\gamma}}-B$, where A,B,S and\n$\\gamma$ are four parameters, provides a good fit to the resulting\nprofile. This profile models both the error in the central regions of\nthe image and the Poisson background error outside the core. The four\nparameters are determined for each quasar by least-square fitting to\nthe observed error profile. Such a fitting procedure also enables the\nerror to be determined in the central regions where the gradient is\ntoo steep and there are too few points in each annulus to predict\nconfidently the error. In general this function fits the observed\nerror profiles very well, and is used here (without including a\ncontribution from the host) to estimate the errors in each pixel.\n\nFig.~\\ref{fig:epgal} shows the observed and fitted error profiles for\nquasars 0956$-$073 and 1543+489 with and without including the\nbest-fit model galaxy in the analysis. The best-fit host around quasar\n1543+489 has an axial ratio of 0.89 in contrast to 0.64 for\n0956$-$073. The deviation of the host around 0956$-$073 from circular\nsymmetry explains why the error profile changes when including this\nhost more than for quasar 1543+489.\n\n\\begin{figure}\n \\centering\n \\resizebox{\\columnwidth}{!}{\\includegraphics{epgal.eps}}\n \\caption{The calculated radial profile of the variance measured in\n annuli of width 0.3\\,arcsec of the difference between the image of\n the quasar and the scaled psf (open triangles). The best-fit model\n for this profile calculated as in Section~\\protect\\ref{sec:error} is\n also plotted (dashed line). For comparison the radial profile,\n calculated in the same way, for the difference between the image and\n best-fit model galaxy with one nuclear component is plotted (solid\n triangles) and the model of this profile (solid line). This solid\n line shows the radial error profile used to produce the simulated\n data of Section~\\ref{sec:mock}. The dotted line shows the Poisson\n noise level of the sky background. Top panel: quasar 0956$-$073,\n bottom panel: quasar 1543+489.} \\label{fig:epgal}\n\\end{figure}\n\n\\subsection{$\\chi^2$ minimisation} \\label{sec:minimise}\n\nThe algorithm used to find the global minimum in $\\chi^2$ was a\nmulti-dimensional direction set technique based on a method introduced\nby Powell in 1964 \\cite{nr}. This algorithm requires an initial `start\npoint' from which it works its way downwards until it finds the\nminimum position. Briefly, the algorithm minimises $\\chi^2$ by\nsequentially adjusting each parameter (i.e. minimising along the axes\nof the parameter space), and then it minimises $\\chi^2$ on the vector\nalong which the greatest change was made to $\\chi^2$ in the previous\nsteps. This procedure is repeated until the algorithm\nconverges. Additionally, for all the quasars it was ascertained that\nthe algorithm had found the correct minimum and not erroneously\nfinished early due to a numerical convergence problem by repeatedly\nre-running the algorithm starting from the previous best-fit\nparameters until the total host luminosity found for successive runs\ndiffered by less than 0.1\\,adu. The testing performed for this\nalgorithm is described in Section~\\ref{sec:minima}.\n\nFor all the results presented in Section~\\ref{sec:results}, the\nalgorithm was started from an initial position in parameter space\ncorresponding to a broad, low luminosity galaxy. This was chosen so\nthe algorithm avoided straying into a region of parameter space where\nall of the host light was in the core (i.e small $R_{1/2}$). This is a\nrelatively flat region for $\\chi^2$ in parameter space and it can\ntherefore take a long time for the algorithm to work its way out of\nthis region. \n\nAll pixels within a radius of 31\\,pixels (8.7\\,arcsec) measured from\nthe centre of the quasar were included in the calculation of\n$\\chi^2$. For all of the best-fit host galaxies, the difference\nbetween model host luminosity within this area and the integrated\nluminosity was negligible, which implies that this area contained all\nof the important signal.\n\n\\section{Testing the Modelling Procedure} \\label{sec:test}\n\n\\subsection{Robustness to the error profile}\n\nAs a test of the robustness of the best-fit host luminosities to the\ndetermination of the error profile, we have modelled our image of\nquasar 0956$-$073 using different error profiles. Quasar 0956$-$073\nwas chosen for this test because the derived axial ratio of the host\nis the lowest of any quasar (although the range of values is quite\nsmall: Section~\\ref{sec:axes}). If the galaxy is important in the\nerror frame calculation, the error profile calculated for this quasar\nas in Section~\\ref{sec:error} should be the most affected by the fact\nthat we are ignoring the host (see Fig.~\\ref{fig:epgal}). Using an\nerror profile calculated as in Section~\\ref{sec:error} but using the\nimage only (i.e. not subtracting the psf), the integrated host\nbrightness was found to drop from 350.1\\,adu to 316.6\\,adu,\ncorresponding to a variation of $\\sim$0.1\\,mag. We have also tried\nre-calculating the error frame from the image minus the best-fit model\nimage (galaxy and nuclear component convolved with the psf), again\nusing the above formula to fit the error frame. Radial profiles of the\ntwo error frames are shown in Fig.~\\ref{fig:epgal}. The best fit model\nparameters were used to calculate a new error frame, and we repeated\nthis process until the best-fit host luminosity converged (subsequent\niterations altered the integrated host luminosity by less than\n0.1\\,adu). The final best-fit luminosity was found to be 351.5\\,adu, a\nnegligible difference from the original minimum.\n\n\\subsection{Finding the minima} \\label{sec:minima}\n\nObvious tests to perform are that there is only one minimum for each\nquasar, and that the $\\chi^2$ function is well behaved around this\npoint. Obviously, it is impossible to cover every position in\nparameter space to check that $\\chi^2$ is well-behaved and that there\nare no local minima. However, we have examined the region of parameter\nspace of interest using a variety of techniques and have found no\npotential problems.\n\nThe minimisation algorithm is itself designed to cover a large region\nof parameter space; the algorithm sequentially searches for the\nminimum along a series of vectors (see Section~\\ref{sec:minimise} for\ndetails), and considers a large number of diverse values along each\nvector. Rerunning the algorithm starting at the best-fit location\npreviously found also tests any minimum along each axis in parameter\nspace, as does the calculation of the error bars, described in\nSection~\\ref{sec:bars}. The shapes of the surfaces around each minimum\nare also revealed by this calculation.\n\nA test for local minima has been performed for quasar 0956$-$073 over\na larger region of parameter space: the minimisation algorithm was\nstarted at a large number of diverse initial host parameters, and no\nsignificant change in the best-fit parameters was discovered. Quasar\n0956$-$073 was chosen for this test because it has average\nsignal-to-noise of any quasar. Fig.~\\ref{fig:smooth} shows a `slice'\nthrough parameter space revealing how smoothly the constrained\n$\\chi^2$ minimum varies with fixed host luminosity for quasar\n0956$-$073. To calculate each point of this curve, all of the\nparameters except the host luminosity were varied until the\nconstrained $\\chi^2$ minimum was reached. The remarkable smoothness of\nthis curve demonstrates both that the global minimum is well\npronounced and the function varies smoothly towards it, and that the\nminimisation routine is finding the correct minimum at each point: if\nit were not, a more rough surface would be expected, signifying that\nthe optimum position had not been reached for each host luminosity.\n\n\\begin{figure}\n \\centering \\resizebox{\\columnwidth}{!}{\\includegraphics{smooth.eps}}\n \\caption{The variation of $\\chi^2$ (normalised to the minimum value)\n versus fixed total host luminosity. For each point on the curve, all\n parameters other than the luminosity have been altered to obtain the\n local minimum in $\\chi^2$. The 68.3\\% confidence interval, found by\n a separate binary search is also shown (dotted line).}\n\\label{fig:smooth}\n\\end{figure}\n\n\\subsection{Using the $\\chi^2$ statistic} \\label{sec:chisq}\n\nUse of the $\\chi^2$ statistic is dependent on the error in each pixel\nbeing independent of the errors in the other pixels. This is expected\nif the errors in the images are dominated by Poisson shot noise. Any\nlarge-scale differences between actual and model host could provide\ncorrelated errors, although these would hopefully have been discovered\nby the analysis of Section~\\ref{sec:simple}. It is possible that\nsmall-scale discrepancies remain that extend across more than one\npixel. However, the relatively large pixel scale works to our\nadvantage by reducing the likelihood of this. The central limit\ntheorem then suggests that the error in each pixel should have\napproximately Gaussian distribution.\n\nThe minimum $\\chi^2$ values are highly dependent on the normalisation\nof the error frames, and cannot directly provide tests of the model\nfits. The position of these minima are unaffected by the normalisation\nof the error frame as they are only dependent on relative variations\nbetween pixels. Examining the reduced $\\chi^2$ values at the minima\ngiven in Table~\\ref{tab:errors}, we see that the reduced $\\chi^2$ is\nless than 1 for the majority of the quasars, and deduce that the\nprocedure outlined in Section~\\ref{sec:error} slightly over-estimates\nthe error in each pixel. This is as expected due to the effect of the\nhost galaxy. The confidence intervals calculated in\nSection~\\ref{sec:bars} will therefore be slightly too large, thus\nproviding a moderately pessimistic error analysis.\n\nAs any nearby companions were excluded when measuring $\\chi^2$, the\nnumber of pixels used, presented in Table~\\ref{tab:errors}, varies\nbetween quasars. For quasar 1214+180, a diffraction spike from a\nnearby star which ran close to the quasar was also\nexcluded. Unfortunately the position of the pixels which were not\nmodelled is more important than the number of such pixels and, for\nthis quasar the position of the diffraction spike was such that it\ncovered a highly important region of pixels. Even though the area\ncovered was small, the modelling suffered greatly.\n\n\\subsection{Calculating error bars on the parameters} \\label{sec:bars}\n\nProvided that the galaxy model is a good representation of the true\nunderlying host galaxy, the errors between the model and image are\nuncorrelated between separate pixels, and the procedure in\nSection~\\ref{sec:error} provides approximately the correct error frame\n(see Section~\\ref{sec:chisq}), it is possible to calculate error bars\non the true parameters using the $\\chi^2$ statistic. The procedure to\ndo this is to hold the chosen parameter fixed at a certain value, and\nminimise the remaining parameters to find the local minimum in\n$\\chi^2$. The end points of the 68.3\\% confidence intervals on the\nbest-fit parameter are given by the points for which\n$\\Delta\\chi^2=\\chi^2-\\chi_{\\rm min}^2=1$, where $\\chi_{\\rm min}^2$ is\nthe minimum value calculated allowing all parameters to vary\n\\cite{bevington}. A standard binary search has been used to find the\nrequired limits. As well as allowing error bars to be calculated, this\nprocedure enables the parameter space to be examined and any problems\nfor each quasar to be spotted.\n\nIn order to match the light from the host galaxies, the behaviour of\nthe integrated host luminosity, $\\beta$ and $R_{1/2}$ are coupled\n\\cite{abraham}. The determination of the error bars is therefore\ncomplicated by the question `what limits, if any should be placed on\nthe parameters being adjusted to find the constrained minima?'. In\nfinding the global minima, all of the parameters are effectively\nallowed to vary over all space: although bounds are placed on the\nparameters, they are not reached (except when modelling the star, see\nSection~\\ref{sec:star}). However, at fixed integrated host\nluminosity, these limits are often reached because the profiles\nrequired to optimally match the light do not necessarily have to be\nthose of galaxies. The philosophy adopted is that all the parameters\nshould be allowed to vary except $\\beta$, upon which limits of\n$0.25<\\beta<6.0$ should be set to provide some adherence to standard\ngalaxy profiles.\n\nFor quasar 0956$-$073, we have examined the required cut through\nparameter space for the integrated host luminosity, calculated by\nminimising all other parameters to obtain each point. The distribution\nof local $\\chi^2$ minima are shown in Fig.~\\ref{fig:smooth}: the curve\ndisplays simple structure, monotonically decreasing to the global\nminimum from both directions so we are justified in using the simple\n$\\Delta\\chi^2=1$ cut-off for the error bars. The resulting 68.3\\%\nconfidence interval for the luminosity is also shown.\n\nThe value of $\\chi^2$ depends on the error frame used, and it is\nexpected that the error bars do so as well. The effect of altering the\nerror frame for quasar 0956$-$073 has been tested by using the error\nframe calculated from the image only as in Section~\\ref{sec:error}.\nUsing this error frame, the 68.3\\% confidence interval on the host\nmagnitude changed slightly from $-25.11<M_{K}<-24.87$ to\n$-25.10<M_{K}<-24.66$.\n\n\\subsection{Fitting to a normal star} \\label{sec:star}\n\nOn the same frame as quasar 0043+039 we observed a star of similar\nsignal-to-noise as the quasar. As a test of the fitting procedure we\ndecided to see if we could fit a `galaxy' to the star. Starting from\nan initial position in parameter space corresponding to a broad, low\nluminosity galaxy as adopted in all of the modelling, the resulting\nbest-fit parameters are given in Table~\\ref{tab:chisq}. As can be\nseen, the fitting procedure rolled down the hill towards a host galaxy\nof very low luminosity. At such low total luminosity, the remaining\nfour galaxy parameters are poorly determined: altering these\nparameters results in a very small change in $\\chi^2$. Consequently it\nis no surprise to find that the best-fit $\\beta=6$ value is one of the\nlimits set in the modelling procedure.\n\n\\section{Results of the Analysis} \\label{sec:results}\n\n\\begin{table*}\n\\begin{minipage}{\\textwidth}\n \\centering \\begin{tabular}{cccccccccc} \\hline \n quasar & $R_{1/2}$ & $L_{\\rm int}$ & axial ratio & $\\alpha$ &\n $\\beta$ & nuc/host & $K_{\\rm host}$ & $K_{\\rm tot}$ & $K_{\\rm psf}$ \\\\\n & /kpc & /adu & & /radians & & ratio & & & \\\\ \\hline\n\n 0043+039 & 7.41 & 355.0 & 0.96 & 1.44 & 0.60 & 13.9 & 16.04 & 13.54 & 11.90 \\\\\n 0137$-$010 & 5.09 & 407.5 & 0.66 & 2.55 & 2.05 & 13.7 & 15.96 & 13.46 & 10.83 \\\\\n 0244$-$012 & 3.28 & 165.6 & 0.86 & 2.66 & 0.61 & 16.6 & 16.87 & 14.18 & 11.15 \\\\\n 0316$-$346 & 8.56 & 864.8 & 0.76 & 0.07 & 1.25 & 12.2 & 15.15 & 12.73 & 9.62 \\\\\n 0956$-$073 & 9.76 & 350.1 & 0.64 & 1.04 & 0.92 & 21.4 & 16.02 & 13.07 & 9.20 \\\\\n 1214+180 & 3.24 & 259.7 & 0.74 & 1.25 & 1.12 & 15.2 & 16.34 & 13.75 & 8.52 \\\\\n 1216+069 & 19.75 & 379.3 & 0.74 & 2.42 & 2.73 & 21.4 & 15.93 & 12.99 & 11.10 \\\\ \n 1354+213 & 11.55 & 481.4 & 0.69 & 1.38 & 0.73 & 6.79 & 15.67 & 13.82 & 9.21 \\\\\n 1543+489 & 7.75 & 320.1 & 0.89 & 3.00 & 0.67 & 25.9 & 16.12 & 12.98 & 9.92 \\\\\n 1636+384 & - & - & - & - & - & 24.1 & 17.65 & 14.11 & 10.07 \\\\\n 1700+518 & - & - & - & - & - & 14.8 & 15.86 & 11.82 & 10.23 \\\\\n 2112+059 & 5.59 & 169.1 & 0.93 & 0.49 & 2.13 & 67.0 & 16.85 & 12.72 & 11.08 \\\\\n 2233+134 & 8.01 & 175.0 & 0.80 & 1.54 & 0.64 & 28.5 & 16.88 & 13.64 & 10.17 \\\\\n 2245+004 & 5.16 & 572.9 & 0.81 & 1.93 & 3.16 & 1.25 & 15.52 & 14.87 & 10.02 \\\\\n star & 16.6 & 0.000031 & 0.16 & 2.26 & 6.0 & - & - & - & - \\\\ \n \\hline \\end{tabular}\n\n \\caption{Best-fit host galaxy parameters as determined by the 2D\n modelling described in Section~\\protect\\ref{sec:model}. Also\n included for comparison are the best-fit parameters for a nearby\n star found on the frame of quasar 0043+039 which had similar signal\n to noise as the quasar. For quasars 1636+384 and 1700+518\n deconvolution of the images revealed a highly disturbed morphology\n which extended close to the core of the quasar and model fitting was\n not attempted. Consequently host galaxy magnitudes presented for\n these quasars are the relatively inaccurate measurements calculated\n from the deconvolved images as described in\n Section~\\protect\\ref{sec:simple}. Nuclear-to-host ratios are\n calculated in the rest frame of the quasar from the derived absolute\n magnitudes in order that these values are consistent with\n Fig.~\\ref{fig:hostvnuc} (see Section~\\ref{sec:calc_lum} for\n details). The apparent magnitudes of the quasar, the host component,\n and the star used to give a psf measurement are also presented.}\n \\label{tab:chisq}\n\\end{minipage}\n\\end{table*}\n\n\\begin{table*}\n\\begin{minipage}{\\textwidth}\n \\centering \\begin{tabular}{ccccccccccc} \\hline \n\n quasar & $\\chi^2$ & number of & reduced & \n \\multicolumn{3}{c}{$L_{\\rm int}$ /adu} &\n \\multicolumn{3}{c}{$M_K$(host)} & $M_K$(tot) \\\\\n & & pixels modelled & $\\chi^2$ & \n min & best-fit & max & min & best-fit & max & \\\\ \n \\hline \n\n 0043+039 & 2639.79 & 2885 & 0.92 & 287.7 & 355.0 & 454.4 &\n $-$25.56 & $-$25.29 & $-$25.07 & $-$28.22 \\\\\n 0137$-$010 & 2661.25 & 2987 & 0.89 & 333.7 & 407.5 & - & \n - & $-$25.08 & $-$24.87 & $-$28.01 \\\\\n 0244$-$012 & 2985.64 & 2974 & 1.00 & 63.9 & 165.6 & 999.4 & \n $-$26.85 & $-$24.90 & $-$23.86 & $-$28.01 \\\\\n 0316$-$346 & 2674.08 & 2987 & 0.90 & 766.3 & 864.8 & 1009.7 & \n $-$25.61 & $-$25.44 & $-$25.31 & $-$28.24 \\\\\n 0956$-$073 & 2814.17 & 2987 & 0.94 & 315.8 & 350.1 & 394.4 & \n $-$25.11 & $-$24.98 & $-$24.87 & $-$28.36 \\\\\n 1214+180 & 2499.93 & 2509 & 1.00 & 112.7 & 259.7 & - & \n - & $-$24.94 & $-$24.03 & $-$27.96 \\\\\n 1216+069 & 2437.36 & 2625 & 0.93 & 290.2 & 379.3 & 604.0 & \n $-$25.62 & $-$25.11 & $-$24.82 & $-$28.49 \\\\\n 1354+213 & 2281.14 & 2987 & 0.76 & 462.4 & 481.4 & 502.1 & \n $-$25.20 & $-$25.16 & $-$25.11 & $-$27.38 \\\\\n 1543+489 & 2567.80 & 2874 & 0.89 & 263.6 & 320.1 & 402.3 & \n $-$25.56 & $-$25.31 & $-$25.10 & $-$28.89 \\\\\n 2112+059 & 2876.00 & 2945 & 0.98 & 37.7 & 169.1 & - & \n - & $-$24.91 & $-$23.29 & $-$29.50 \\\\\n 2233+134 & 2679.73 & 2941 & 0.91 & 108.7 & 175.0 & 269.2 & \n $-$24.58 & $-$24.11 & $-$23.59 & $-$27.78 \\\\\n 2245+004 & 2584.98 & 2987 & 0.87 & 438.1 & 572.9 & 941.6 & \n $-$26.24 & $-$25.70 & $-$25.41 & $-$26.48 \\\\\n star & 3055.42 & 2969 & 1.03 & - & 0.000031 & - & \n - & - & - & - \\\\ \\hline\n \\end{tabular}\n\n \\caption{Table showing the end points of the 68.3\\% confidence\n intervals calculated as in Section~\\protect\\ref{sec:bars} for the\n best-fit integrated host luminosities. To further aid comparison\n between model fits for different quasars, the $\\chi^2$ values for\n the best fit model are presented with the number of pixels used in\n this calculation. Note that the position of the un-modelled pixels\n is more important than the number of such pixels.}\n \\label{tab:errors}\n\\end{minipage}\n\\end{table*}\n\n\\subsection{Luminosities} \\label{sec:calc_lum}\n\nFor three of the quasars, analysis of how $\\chi^2$ varies within the\nparameter space revealed that the best-fit host luminosity was not\nwell constrained. A host galaxy was determined as being present in\nthat a lower limit was determined in all cases. However, the maximum\nlight which could have come from the host was not clear because the\nshape of the host was not sufficiently resolved. The morphology of the\nbest-fit galaxy at large $L_{\\rm int}$ could alter to place the\nmajority of the host light in the central region. This effect could\nhave been avoided by placing limits on $R_{1/2}$ or, for instance,\nusing the near-infrared Fundamental Plane \\cite{pahre}, although these\nupper limits would have been highly dependent on the criteria set.\nThe host luminosity is ultimately limited by the total light in the\nimage, and it is expected that the host luminosities for these quasars\ndo have upper bounds at high values of $L_{\\rm int}$, but these high\nvalues would not be of any use in determining the actual host light.\n\nFor the remaining nine quasars, the minima were sufficiently\nconstrained to provide 68.3\\% confidence intervals. Comparison of\ndifferent confidence intervals provided information on the depth of\nthe valleys within which each minimum was found and the quality of each\ndetermination.\n\n\\begin{figure*}\n \\centering \\resizebox{10cm}{!}{\\includegraphics{hostvnuc.eps}}\n \\caption{The top panel shows nuclear vs. integrated host absolute\n $K$-band magnitudes for our sample of quasars (solid circles) with\n error bars calculated as described in Section~\\ref{sec:bars}. The\n errors in the measured nuclear component are derived from these and\n consequently the errors are strongly correlated. Plotted for\n comparison are the calculated host magnitudes for the radio-quiet\n quasars imaged by Taylor \\etal\\ \\protect\\shortcite{taylor} (open\n triangles), McLeod \\& Rieke \\protect\\shortcite{mcleod94a} (crosses)\n and McLeod \\& Rieke \\protect\\shortcite{mcleod94b} (plus\n symbols). Details of the conversion of the McLeod \\& Rieke data from\n the $H$-band to the $K$-band can be found in\n Section~\\ref{sec:calc_lum}. The luminosity of an $L^*$ galaxy,\n $M_K^*=-24.6$ \\protect\\cite{gardner} is also plotted (dashed line),\n as is the locus of points with a rest-frame $K$-band nuclear-to-host\n ratio of 8 (dotted line). In order to compare with recent HST\n results, in the bottom panel we convert our data into the R-band\n (see Section~\\ref{sec:calc_lum} for details). Symbols for our data\n are as for the top panel. The $R$-band best-fit luminosities from\n disk or exponential galaxies \\protect\\cite{hooper} are also plotted\n (diamonds separated by dotted lines). No attempts were made to\n distinguish the best host morphology in this work. The derived\n $R$-band host luminosities of McLure \\etal\\\n \\protect\\shortcite{mclure} are also shown (radio-quiet sample: open\n squares, radio-loud sample: solid triangles). The luminosity of an\n $L^*$ galaxy, $M_R^*=-21.8$ \\protect\\cite{lin} is plotted for\n comparison (dashed line). }\n\\label{fig:hostvnuc}\n\\end{figure*}\n\nHost and nuclear luminosities for our quasars are compared with the\nresults of other studies in Fig.~\\ref{fig:hostvnuc}. In order to\ncompare with the $H$-band host galaxy studies undertaken by McLeod \\&\nRieke (1994a;b), we convert their total (nuclear + host) and host\nluminosities to the $K$-band by applying a single conversion factor to\nthe apparent magnitudes. This then sets the relative normalisation of\nthe $K$-band and $H$-band samples; conversion to absolute magnitudes\nis subsequently undertaken in exactly the same way for all of the\ninfra-red samples.\n\nIn a study of the energy distribution of the PG quasars (from which\nMcLeod \\& Rieke chose their samples), Neugebauer \\etal\\\n\\shortcite{neugebauer87} found $\\langle H-K\\rangle=0.90$ for the\nsample of Mcleod \\& Rieke \\shortcite{mcleod94a} and $\\langle\nH-K\\rangle=0.98$ for McLeod \\& Rieke \\shortcite{mcleod94b}. In the\nupper panel of Fig.~\\ref{fig:hostvnuc}, we adopt these values to\nconvert the total luminosities of the McLeod \\& Rieke quasars into the\n$K$-band.\n\nThe light from the galaxy component is assumed to be dominated by an\nevolved stellar population, the colour of which reddens with increasing\nredshift. For nearby galaxies, $H-K\\sim0.25$, which was used by McLeod\n\\& Rieke \\shortcite{mcleod95a} to convert galaxy absolute\nmagnitudes. However, the apparent $H-K$ is dependent on redshift and,\nat the redshifts of the quasars imaged by McLeod \\& Rieke (1994a;b),\n$H-K\\sim0.6$ is expected for an evolved stellar population\n\\cite{lilly}. This was adopted to convert the McLeod \\& Rieke galaxy\nluminosities into the $K$-band.\n\nWe have also checked the calibration of the McLeod \\& Rieke samples\nand our sample of modelled quasars (with 6 overlapping objects)\nagainst the data of Neugebauer \\etal\\ \\shortcite{neugebauer87}. The\naverage total quasar luminosity for the subsamples are in good\nagreement, although individual values vary by up to $0.7$\\,mag,\npresumably due to intrinsic quasar variability.\n\nOne quasar ($1354+213$) was imaged by McLeod \\& Rieke\n\\shortcite{mcleod94b}, Neugebauer \\etal\\ \\shortcite{neugebauer87} and\nin our study. Neugebauer \\etal\\ \\shortcite{neugebauer87} derived\n$H-K=1.0$ for this object, which is higher than $H-K=0.3$ derived\nby combining the McLeod \\& Rieke $H$-band and our $K$-band\nobservation. However, the McLeod \\& Rieke and our observations were\nundertaken at different epochs, and the luminosity is not expected to\nremain constant.\n\nThe study of Taylor \\etal\\ \\shortcite{taylor} was performed in the\n$K$-band, and the apparent $K$-band magnitudes of host and nuclear\ncomponents were taken directly from this work. The data from the\ndifferent infra-red samples were then converted to absolute\nmagnitudes, applying the $K$-correction of Glazebrook \\etal\\\n\\shortcite{glazebrook95} for the host galaxy and assuming the nuclear\ncomponent follows a standard power law spectrum $f(\\nu)=\\nu^{-0.5}$.\n\nUsing the error bars calculated in Section~\\ref{sec:bars} to weight\nthe data, the average integrated host galaxy magnitude for our quasars\nwas found to be $\\langle M_K \\rangle =-25.15\\pm0.04$. For comparison,\nwhen converted for cosmology exactly as our data, the sample of Taylor\n\\etal\\ \\shortcite{taylor} gives $\\langle M_K \\rangle =-25.68$, McLeod\n\\& Rieke \\shortcite{mcleod94a} $\\langle M_K \\rangle =-25.42$ and\nMcLeod \\& Rieke \\shortcite{mcleod94b} $\\langle M_K \\rangle =-25.68$.\n\nRecent determinations of the $K$-band luminosity of an $L^*$ galaxy\n\\cite{gardner} have resulted in $M_K^*=-24.6$, compared to previous\ndeterminations of $M_K^*=-24.3$ \\cite{glazebrook95} and $M_K^*=-25.1$\n\\cite{mobasher}. The Gardner \\etal\\ \\shortcite{gardner} value is\nplotted in the top panel of Fig.~\\ref{fig:hostvnuc}. This shows that\nthe average luminosity of our hosts is $\\sim1.6$ times that of an\n$L^*$ galaxy. Note that for all three values, the derived average\nluminosity is $1-2$ times that of an $L^*$ galaxy, and the conclusions\nof Section~\\ref{sec:discuss:lum} are not affected by this choice.\n\nWe compare our sample to recent HST $R$-band results in the lower\npanel of Fig.~\\ref{fig:hostvnuc} assuming an apparent $R-K=2.5$ for\nthe total light from our quasars based on the average value for the 6\nquasars which overlap our sample and the sample of Neugebauer \\etal\\\n\\shortcite{neugebauer87}. The $R-K$ colour of an evolved stellar\npopulation, assumed to dominate the host galaxies, is dependent on the\nredshift of the source and, for the redshifts of our sample\n($z\\sim0.35$), is expected to be $\\sim3.5$ \\cite{dunlop89}. All the\ndata (including our data after conversion to apparent $R$-band\nmagnitudes) presented in the bottom panel of Fig.~\\ref{fig:hostvnuc}\nwere adjusted for cosmology assuming that the nuclear component has a\nspectrum of the form $f(\\nu)\\propto\\nu^{-0.5}$, and the galaxy\ncomponent has $f(\\nu)\\propto\\nu^{-1.5}$.\n\n\\subsection{Morphologies} \\label{sec:morph}\n\nMorphologies are parametrised by the best-fit value of $\\beta$:\n$\\beta=1$ values correspond to disk-like, and $\\beta=4$ to spheroidal\nprofiles. The technique described in Section~\\ref{sec:bars} has been\nused to reveal how well the $\\beta$ parameter is constrained by the\nmodelling. The result of this analysis is presented in\nTable~\\ref{tab:beta}. As can be seen, the $\\beta$ parameter is well\nconstrained for fewer quasars than the luminosity and $\\chi^2$ error\nbars reveal a highly skewed distribution for the expected true value\ngiven the best-fit $\\beta$ value. In order to correctly determine the\ndifferential probability between disk and spheroidal profiles, we need\nto know the relative dispersion of $\\beta$ for each morphological\ntype. However, examining the best-fit parameters, the error bars on\n$\\beta$, and the shape of $\\chi^2$ surface, on which we have\ninformation from the binary search to find the error bars, we can\ninfer the best fit morphology for some of the quasars. The suggestion\nfrom this is that luminous radio-quiet quasars can exist in hosts\ndominated by either disk-like or spheroidal components. A histogram of\nthese data is plotted in Fig.~\\ref{fig:mock_beta}, where the\ndistribution is compared to that recovered from simulated data with\nexact $\\beta=1$ or $\\beta=4$ profiles.\n\n\\begin{table}\n \\centering \\begin{tabular}{ccccc} \\hline \n\n quasar & min $\\beta$ & $\\beta$ & max $\\beta$ & morphology? \\\\ \\hline \n 0043+039 & 0.42 & 0.60 & 0.86 & disk \\\\\n 0137$-$010 & 1.52 & 2.05 & $>$6.0 & spheroid \\\\\n 0244$-$012 & $<$0.25 & 0.61 & 1.62 & disk \\\\\n 0316$-$346 & 1.02 & 1.25 & 3.62 & ? \\\\\n 0956$-$073 & 0.71 & 0.92 & 1.21 & disk \\\\\n 1214+180 & $<$0.25 & 1.12 & $>$6.0 & ? \\\\\n 1216+069 & 1.44 & 2.73 & $>$6.0 & spheroid \\\\\n 1354+213 & 0.65 & 0.73 & 0.82 & disk \\\\\n 1543+489 & 0.49 & 0.67 & 0.90 & disk \\\\\n 2112+059 & $<$0.25 & 2.13 & $>$6.0 & ? \\\\\n 2233+134 & $<$0.25 & 0.64 & 1.21 & disk \\\\\n 2245+004 & 2.17 & 3.16 & 5.55 & spheroid \\\\\n \\hline \\end{tabular}\n\n \\caption{Table showing 68.3\\% confidence intervals for the best-fit\n host $\\beta$ parameters for the 12 quasars modelled using the 2D\n $\\chi^2$ minimising technique (Section~\\protect\\ref{sec:model}).\n Error bars were calculated as described in\n Section~\\protect\\ref{sec:bars} with $\\beta$ constrained to lie in\n the range $0.25<\\beta<6.0$. The morphology of the dominant\n contribution to the host galaxy is also presented, based on the best\n fit $\\beta$ parameter and associated confidence interval.}\n \\label{tab:beta}\n\\end{table}\n\n\\subsection{Axial ratios and angles} \\label{sec:axes}\n\nAnalysis of the parameter space reveals that the axial ratio and\nprojected angle of each host are better constrained than the other\nparameters. Fig.~\\ref{fig:histograms} shows histograms of these\nparameters for all quasars modelled. The distribution of axial ratios\nis small with $\\langle a/b\\rangle=0.79\\pm0.03$. This is in agreement\nwith those found by McLure \\etal\\ \\shortcite{mclure}, but higher than\nfound by Hooper, Impey \\& Foltz \\shortcite{hooper}. The projected\nangles are uniformly distributed as expected.\n\n\\begin{figure}\n \\centering \n \\resizebox{5.0cm}{5.0cm}{\\includegraphics{axis.eps}}\n \\vspace{5mm}\\\\\n \\resizebox{5.0cm}{5.0cm}{\\includegraphics{angle.eps}}\n \\caption{Histograms showing the distribution of axial ratios and\n projected angles of the host galaxies. These parameters were well\n constrained for all of the 12 quasars modelled, and are therefore\n plotted from all of the minima found. Axial ratios are tightly\n constrained with with $a/b>0.64$ for all hosts, and $\\langle\n a/b\\rangle=0.79\\pm0.03$. The distribution of projected angles is\n approximately uniformly distributed.}\n\\label{fig:histograms}\n\\end{figure}\n\n\\subsection{Highlighted results for selected quasars} \n \\label{sec:results-quasars}\n\n\\subsubsection{Quasar 0043+039}\nThe broad-absorption-line (BAL) quasar PG0043+039 has been subject to\n2 previous studies to determine host galaxy properties. It was\nobserved in the $i$ band by Veron-Cetty \\& Woltjer\n\\shortcite{veron-cetty} who determined $M_i=-23.9$ if the host is a\ndisk like ($\\beta=1$) galaxy, or $M_i=-24.7$ for a spheroidal\n($\\beta=4$) galaxy. This quasar was also observed using the wide-field\ncamera on HST by Boyce \\etal\\ \\shortcite{boyce}, who used a cross\ncorrelation technique to determine that the host was slightly better\nfit by a disk galaxy with $M_V=-21.6$. We also find that the dominant\nmorphology is disk-like and calculate $M_K=-25.29$. The old burst\nmodel of Bruzual \\& Charlot \\shortcite{bruzual} predicts $V-K=3.3$\nwhich is consistent with the derived $V-K=3.7$.\n\n\\subsubsection{Quasar 0316$-$346}\nThis quasar was previously observed using the wide field camera on HST\n\\cite{bahcall} and the host was found to reveal evidence of a merger,\nin particular tidal tails extending $\\sim20$\\,kpc west of the\nquasar. Bahcall \\etal\\ \\shortcite{bahcall} also provide a 2D fit to\nthe host properties and find that the best-fit host is disk galaxy\nwith $M_{V}=-22.3$. We also calculate a best-fit disk galaxy and find\n$M_K=-25.44$, giving $V-K=3.1$, again consistent with the old burst\nmodel of Bruzual \\& Charlot \\shortcite{bruzual} which predicts\n$V-K=3.3$.\n\n\\subsubsection{Quasar 1214+180}\nThere have been no previous attempts to determine the morphology of\nthe host galaxy around this quasar possibly due to the nearby star\nwhich was utilised in this work to obtain an accurate\npsf. Unfortunately in our images, a diffraction spike from this star\npassed close to the quasar reducing the area that could be used to\ncalculate $\\chi^2$. Although the modelling converged to give basic\ngalaxy parameters, further analysis of the parameter space revealed\nthat this minimum was not well constrained.\n\n\\subsubsection{Quasar 1216+069}\nOur analysis of this quasar benefited because the images were obtained\nusing the tip-tilt system and there is a nearby bright star which was\nplaced on the same frame as the quasar and used to obtain a psf\nmeasurement. Previously, `nebulosity' has been observed around this\nquasar \\cite{hutchings84}, and a more detailed HST study found a\nbest-fit spheroidal ($\\beta=4$) galaxy with $M_{V}=-22.3$\n\\cite{boyce}. We also find that the most likely host is a large\nspheroidal galaxy and obtain $M_K=-25.1$, giving $V-K=2.8$.\n\n\\subsubsection{Quasar 1354+213}\nUsing a psf subtraction technique, McLeod \\& Rieke\n\\shortcite{mcleod94b} found a residual host galaxy with $M_K=-25.6$\nwhen converted to our cosmology using the $K$-correction from\nGlazebrook \\etal\\ \\shortcite{glazebrook95} and the apparent colour\ncorrection $H-K=0.6$ (see Section~\\ref{sec:calc_lum}). Our best fit\nhost luminosity was $M_K=-25.2$. Analysis shows that the luminosity\nand the $\\beta$ parameter are both tightly constrained by the\nmodelling and the best-fit $\\beta=0.73$ suggests that the host is\ndominated by a disk component. The rest-frame nuclear-to-host ratio\nfor this quasar is only $6.8$ (the apparent nuclear-to-host ratio is\n$4.6$), which explains why the derived parameters have small error\nbars.\n\n\\subsubsection{Quasar 1636+384}\nWe are not aware of any previous attempts to determine the luminosity\nand morphology for the host galaxy of quasar 1636+384. Preliminary\ndeconvolution of the light revealed that the excess, non-central light\ndisplayed a morphology greatly disturbed from elliptical symmetry (as\nshown in Fig.~\\ref{fig:disturbed}). The structure includes an excess\nof light to the NW of the core which is interpreted as a merging\ncomponent as well as light around the central core which probably\noriginates from the host. From this image it was unclear how to\ndistinguish between the host and the interacting companion, so the\nluminosity of the host was estimated by summing pixel values excluding\nthe central pixel. This provided an approximate $K$-band absolute\nmagnitude of $M_K=-23.5$.\n\n\\subsubsection{Quasar 1700+518}\nQuasar 1700+518 is a bright BAL quasar of low redshift\n($z=0.29$). Such low redshift BAL objects are rare and hard to\ndiscover since the broad absorption lines are in the UV and\nconsequently quasar 1700+518 has received much interest: specific\nstudies of this quasar have been undertaken in many different\nwavebands \\cite{h92_1700,stockton,hines}. Because of the low redshift\nand the brightness of the quasar, 1700+518 has also been included in\nmany samples of quasars imaged to obtain details of their host\ngalaxies \\cite{neugebauer,mcleod94b}, although these have only\nprovided upper limits for the host magnitude. More recent imaging\nstudies have shown that the morphology of the underlying structure\nconsists of a disturbed host predominantly to the SW of the core\n\\cite{stockton} and a close interacting companion to the NE\n\\cite{h92_1700} which is most likely a ring galaxy \\cite{hines}.\nDeconvolution of the light from this quasar, as shown in\nFig.~\\ref{fig:disturbed}, confirms this picture of the structure. With\nthe disturbed morphology it is difficult to know how to split the\nlight in the central pixels into nuclear and host components. As for\nquasar 1636+384 the host luminosity was estimated by summing the\ncounts in the pixels surrounding the central one (ignoring those from\nthe NE companion). There will be errors caused by leakage of light\nfrom the nuclear component and from the contribution of the host to\nthe central pixel. An approximate $K$-band absolute magnitude of\n$-24.9$ was obtained for the host galaxy and $-24.4$ for the NE\ncompanion galaxy.\n\n\\subsubsection{Quasar 2233+134}\nBoth Smith \\etal\\ \\shortcite{smith} and Veron-Cetty \\& Woltjer\n\\shortcite{veron-cetty} included this quasar in their samples, but\nboth failed to resolve the host galaxy beyond obtaining upper limits\nfor the luminosity. Hutchings \\& Neff \\shortcite{hutchings92} did\nresolve the host galaxy and found the host to be best-fit by a\n$\\beta=4$ model, although they did not resolve further information\nabout the galaxy. However, we find that the most probable host has an\ndisk profile and calculate $M_K=-24.1$, the lowest luminosity host\nmodelled. If we constrain the host to have an elliptical profile, the\nbest fit luminosity becomes $M_K=-25.9$, although the half light\nradius is very small for this model ($R_{1/2}=1.5$\\,kpc) which places\nit a long way from the $K$-band Fundamental Plane of Pahre, Djorgovski\n\\& de Carvalho \\shortcite{pahre}. If the host parameters are\nconstrained to lie on this plane, then rerunning the modelling gives a\nbest fit host with $M_K=-24.6$. Neither of these changes would be\nsufficient to alter our conclusions.\n\n\\section{Simulated Data I - Single component galaxies} \\label{sec:mock}\n\nTrying to recover known host parameters from Monte-Carlo simulations\nof the actual data enables the distribution of recovered parameters\ngiven the true values to be determined. Note that the error bars\ncalculated using the $\\chi^2$ statistic are instead determined from\nthe distribution of possible true values given the data. These two\ndistributions are not necessarily equal. We need to determine the\ndistribution of recovered values in order to answer questions such as\n`Are our results biased towards low $\\beta$ values?'.\n\nIn view of the distribution of recovered $\\beta$ values, it was\ndecided to simulate data to match the images of quasars 0956$-$073 and\n1543+489. These quasars span the distribution of signal-to-noise of\nall the images, and 2D model fitting revealed evidence for disk\ndominated hosts in both cases. Verification of this result is\ninteresting as recent work has suggested that the hosts of luminous\nquasars should be dominated by the spheroidal component (see\nSection~\\ref{sec:discuss_morph}).\n\n\\subsection{Creating the mock data} \\label{sec:mock_noise}\n\n\\begin{table*}\n\\begin{minipage}{\\textwidth}\n \\centering \\begin{tabular}{ccccccccc} \\hline \n quasar & \\multicolumn{4}{c}{$\\beta$} & \n \\multicolumn{4}{c}{$L_{\\rm int}$ /adu} \\\\\n & true & min & average & max & true & min & average & max \\\\ \\hline\n\n 0956$-$073 & 1.0 & 0.74 & 1.14 & 2.28 & 300.0 & 262.1 & 323.7 & 510.0 \\\\\n 0956$-$073 & 4.0 & 1.93 & 3.77 & 7.42 & 300.0 & 213.6 & 288.3 & 463.1 \\\\\n 1543+489 & 1.0 & 0.79 & 1.08 & 1.69 & 300.0 & 260.1 & 324.7 & 512.2 \\\\\n 1543+489 & 4.0 & 2.13 & 4.04 & 7.25 & 300.0 & 209.6 & 302.2 & 469.8 \\\\\n \\hline \n \\end{tabular}\n\n \\caption{Table showing the mean and 68.3\\% confidence intervals for\n the recovered $\\beta$ and integrated host luminosity from the\n simulated data. 100 simulations were performed for each morphology\n for each quasar.} \\label{tab:mock_stat}\n\\end{minipage}\n\\end{table*}\n\n\\begin{figure*}\n\\begin{minipage}{\\textwidth}\n \\centering \\resizebox{10cm}{!}{\\includegraphics{mock_l.eps}}\n \\caption{The distribution of recovered luminosities from Monte-Carlo\n simulations of 100 $\\beta=1$ images and 100 $\\beta=4$ images. The\n $y$-axis gives the number of recovered values within each luminosity\n bin. Noise has been added to match observations of quasar (a)\n 0956$-$073 and (b) 1543+489, including a contribution from the error\n in the measured psf as described in\n Section~\\protect\\ref{sec:mock_noise}. The luminosity of each\n simulated galaxy, marked by the dotted line, was set at 300\\,adu.}\n \\label{fig:mock_lum}\n\\end{minipage}\n\\end{figure*}\n\nSimulated galaxies were created using the procedure outlined in\nSection~\\ref{sec:galaxy} and a single $\\delta$ function added to the\ncentre of each to create a `perfect unconvolved model'. The height of\nthe $\\delta$ function was chosen to match the total signal of the\noriginal images. These models were then convolved with the psf\nmeasured to match the quasar.\n\nGaussian noise was added with a radially dependent variance as given\nby the error profile calculated in Section~\\ref{sec:error} including\nthe best-fit host galaxy in the calculation. The error profiles used\nfor quasars 0956$-$073 and 1543+489 are given by the solid lines in\nFig.~\\ref{fig:epgal}. Differences between measured and true psf were\nincluded in this analysis, and are therefore included in the noise\nlevels added to the simulated data. This noise model assumes that the\nerrors in different pixels are independent (see\nSection~\\ref{sec:chisq}).\n\nWe have simulated 100 images with exact disk hosts, and 100 images\nwith exact spheroidal hosts for each of the two quasars chosen. The\ntrue integrated host luminosity was set at 300\\,adu for simulated data\nof both quasars. This conservative value is below the best-fit value\nobtained from the data for both quasars, providing a stringent test of\nthe modelling. This is particularly true for a $\\beta=4$ host:\nconstraining $\\beta=4$ when modelling the observed image would have\nresulted in a best-fit $L_{\\rm int}\\gg300$\\,adu. The simulated images\nwere analysed using exactly the same 2D modelling procedure described\nabove for the observed data. The range of recovered parameters is\nanalysed below.\n\n\\subsection{Results from the simulated data: luminosities}\n\nRecovered luminosities, presented in Fig.~\\ref{fig:mock_lum} reveal a\nskewed distribution, particularly for hosts with exact spheroidal\nprofiles where the recovered luminosity is biased towards a low\nvalue. This is consistent with the morphology being skewed towards a\nlow $\\beta$ value (see next Section): if $\\beta$ is decreased, the\nluminosity also has to decrease to keep the counts in the outer pixels\n(those most important for fitting the host) the same. The counts in\nthe centre of the galaxy are less important because of the additional\nnuclear component which is adjusted to match the data.\n\nThe mean and variance in the recovered luminosities are presented in\nTable~\\ref{tab:mock_stat}. Although the error bars reveal the extent\nof the skewed distribution, the mean is within 10\\% of the true value\nfor each quasar and morphology.\n\n\\subsection{Results from the simulated data: morphologies}\n\n\\begin{figure*}\n\\begin{minipage}{\\textwidth}\n \\centering \\resizebox{15cm}{!}{\\includegraphics{mock_b.eps}}\n\n \\caption{Evidence that the hosts of luminous radio-quiet quasars are\n not exclusively dominated by spheroidal components. The distribution\n of $\\beta$ values recovered from 2-D modelling of 100 simulated\n images created with hosts using exact disk or spheroidal profiles is\n presented. Noise has been added to these images to match\n observations of (a) quasar 0956$-$073 and (b) quasar 1543+489,\n including a contribution from the error in the measured psf as\n described in Section~\\protect\\ref{sec:mock_noise}. The dotted line\n shows the best-fit $\\beta$ value recovered from the images of these\n quasars. (c) For comparison the distribution of best-fit $\\beta$\n values obtained from all of our $K$-band images is also plotted. The\n probable morphology of the host was determined from the $\\chi^2$\n error bars derived for the true value given the data.}\n \\label{fig:mock_beta}\n\\end{minipage}\n\\end{figure*}\n\nThe skewed distribution observed in the error bars on the true host\n$\\beta$ value is mirrored by the distribution of $\\beta$ values\nrecovered using the standard modelling procedure described in\nSection~\\ref{sec:model}. Fig.~\\ref{fig:mock_beta} shows the relative\ndistribution of $\\beta$ values retrieved from the simulated images.\nLimits of $0.25<\\beta<8$ were placed on fitted $\\beta$ values. For\nquasar 0956$-$073, 16 of the simulated images created with exact\nspheroidal hosts, had recovered $\\beta>8$. For quasar 1543+489, this\nnumber was 14: these values are not included in\nFig.~\\ref{fig:mock_beta}. The distribution was used to calculate the\nmean and standard deviation given in Table~\\ref{tab:mock_stat},\nassuming all fits with $\\beta>8$ actually had $\\beta=8$.\n\nIf the host were a spheroidal galaxy with $\\beta=4$, the probability\nof recovering a best-fit value of $\\beta<1$ is $\\sim0.03$ for\n0956$-$073 and $\\sim0.01$ for 1543+489: the best-fit values from the\nimages were $\\beta=0.92$ and $\\beta=0.67$ respectively. The evidence\nfor the existence of hosts dominated by a disk component therefore\nappears to be strong. In Fig.~\\ref{fig:mock_beta}, the distribution of\nretrieved $\\beta$ values for the 12 quasars modelled is also\nshown. This distribution is inconsistent with the hypothesis that all\nthe hosts are dominated by spheroidal components on the scales probed\nby these measurements. The histogram is divided to show the probable\ndistribution of morphologies given the options $\\beta=1$ or\n$\\beta=4$. As can be seen, the modelling suggests that approximately\nhalf of the hosts are dominated by disk components.\n\n\\section{Simulated Data II - Two component galaxies} \\label{sec:mock2}\n\nIn order to constrain the potential importance of spheroidal cores in\nthe galaxies found to be dominated by disk-like profiles, we have\nanalysed synthetic quasars created with two host galaxy\ncomponents. Using the Fundamental-Plane (FP) relation between\n$R_{1/2}$ and $L_{\\rm int}$ found in the K-band by Pahre \\etal\\\n\\shortcite{pahre}, we have added extra spheroidal ($\\beta=4$)\ncomponents to the recovered best-fit host galaxy of quasar\n1543+489. Note that this best fit host had $\\beta=0.67$. We have tried\nthe same analysis using $\\beta=1$ and found no change in the effects\nproduced by the spheroidal core. After adding in the nuclear component\nand noise as described in Section~\\ref{sec:mock}, we have recovered\nthe best-fit host galaxy parameters using our single component\nmodelling. Spheroidal components were added with a variety of\ndifferent luminosities, and five different realisations of the\nadditional noise component were added to each. The resulting average\nrecovered $L_{\\rm int}$ \\& $\\beta$ are given in Table~\\ref{tab:2cmpt}.\n\n\\begin{table}\n \\centering\n \\begin{tabular}{cccccc} \\hline\n \\multicolumn{4}{c}{$L_{\\rm int}$ /adu} & $R_{1/2}$ & $\\beta$ \\\\\n spheroidal & total & recovered & diff & /kpc & \\\\ \\hline\n 0.0\t& 320.1 & 291.2 & -28.9 & 8.26 & 0.61 \t\\\\\n 40.0\t& 360.1 & 306.5 & -53.6 & 8.19 & 0.63 \t\\\\\n 80.0\t& 400.1 & 337.9 & -62.2 & 8.02 & 0.69\t\\\\\t\n 120.0\t& 440.1 & 382.7 & -57.4 & 7.71 & 0.81\t\\\\\n 160.0\t& 480.1 & 436.3 & -43.8 & 7.35 & 0.96\t\\\\\n 320.0\t& 640.1 & 785.8 & 145.7 & 5.45 & 1.93\t\\\\\n 480.0 & 800.1 & 1305.2 & 505.1 & 3.85 & 3.37 \t\\\\\n \\hline \\end{tabular}\n\n \\caption{Average recovered host parameters from single component\n fits to synthetic quasars with 2-component host\n galaxies. Uncorrelated Gaussian noise has been added to these models\n to match that of quasar 1543+489, and the average recovered values\n are given for 5 different realisations of this noise. The same noise\n was added to corresponding mock images created with different\n spheroidal luminosities, so there will be a systematic error because\n 5 realisations are not sufficient to fully sample the recovered\n parameters with the given noise level. The result of analysing a\n host with no spheroidal component shows that the results\n systematically underestimate $\\beta$ and $L_{\\rm int}$ and\n overestimate $R_{1/2}$ by small amounts. Note that the relative\n dependence of the recovered parameters on the spheroidal component\n will not be affected.} \\label{tab:2cmpt}\n\\end{table}\n\nBecause $R_{1/2}(\\rm spheroidal)$ and $L_{\\rm int}(\\rm spheroidal)$\nfollow a FP relation, the importance of this component is enhanced for\nlarge $L_{\\rm int}(\\rm spheroidal)$ and diminished for small $L_{\\rm\nint}(\\rm spheroidal)$. The recovered total luminosity for small\nspheroidal components is therefore very similar to that of the disk\nalone. For large spheroidal components, the modelling places an excess\nof host light in the core in order to simultaneously fit the outer\ndisk-like profile and the inner profile with a single, large $\\beta$\nvalue. This explains the behaviour of the difference between the\nactual and recovered $L_{\\rm int}$ values. Recovered $\\beta$\nmonotonically increases with the increasing luminosity of the\nspheroidal core, suggesting that the spheroidal core cannot be\ncompletely `hidden' without affecting the best fit galaxy. This adds\nto the evidence that the low $\\beta$ values recovered for some of the\nquasars implies that they do not contain strong spheroidal\ncomponents. Note that the recovered host luminosities are\napproximately correct for recovered values of $\\beta$ consistent with\na host dominated by a disk-like profile.\n\nFor the quasars which have best-fit hosts dominated by spheroidal\ncomponents, a disk-like profile at larger radii could have erroneously\nincreased the recovered total host luminosity. However, in order to\nsimultaneously fit these regions, small values of $R_{1/2}$ were\nrequired. For the quasars with hosts found to be dominated by\nspheroidal components, the relatively large values of $R_{1/2}$\nrecovered suggest that such a disk-like component is not present.\n\n\\section{Discussion}\n\n\\subsection{Luminosities} \\label{sec:discuss:lum}\n\nThe integrated host luminosities derived from our $K$-band images\nexhibit a low dispersion around a mean similar to that calculated in\nstudies of less luminous quasars. This is in accord with the work of\nMcLure \\etal\\ \\shortcite{mclure} who also found no evidence for an\nincreasing trend, although they had fewer data points at high nuclear\nluminosity.\n\nPrevious HST studies have found evidence that host luminosity\nincreases with nuclear luminosity \\cite{hooper}, although the trend\nobserved in this work could be due to incorrect nuclear component\nremoval: escaping nuclear light which increases in luminosity with the\ncore could be added to the host light. It has recently been stated\nthat the psf derived by packages such as {\\sc tinytim}, as used by\nHooper, Impey \\& Foltz \\shortcite{hooper} deviate from empirical\nWFPC~2 psfs at large radii ($\\ge2$ arcsec), due to scattering within\nthe camera \\cite{mclure}, and this could be the reason for an excess\nof nuclear light at larger radii which could be mistaken as host\nlight. This excess light could also be the reason the low axial ratios\nobserved in the Hooper, Impey \\& Foltz \\shortcite{hooper} work are not in\naccord with those derived in McLure \\etal\\ \\shortcite{mclure}, or in\nthis $K$-band study.\n\nThe triangular shape of the McLeod \\& Rieke points in\nFig.~\\ref{fig:hostvnuc} found for low redshift ($0<z<0.3$) Seyferts\nand quasars of lower luminosity than those in our sample, has been\nshown to be in accord with a lower limit to the host luminosity which\nincreases with nuclear luminosity \\cite{mcleod95a}. This cut-off in\nthe host luminosity is equivalent to there being an upper limit to\nallowed nuclear-to-host ratios. The triangular shape is {\\em not}\nfollowed by the results of the work presented in this paper which lie\nto the right of the McLeod \\& Rieke points. The relative positions of\nthe two data sets in this Figure are set by the empirical $H-K$\ncorrections applied to the apparent $H$-band data (see\nSection~\\ref{sec:calc_lum} for details). Quasar 1354+213 was included\nin both our sample and the sample of McLeod \\& Rieke\n\\shortcite{mcleod94b}, and the results of both studies independently\nsuggest a rest-frame nuclear-to-host ratio of $7-9$. This places\n1354+213 at the right of the triangular shape of the McLeod \\& Rieke\npoints in Fig.~\\ref{fig:hostvnuc}, but it has a nuclear-to-host ratio\nlower than most of the quasars in our sample, and is therefore to the\nleft of most of our points. We conclude that the limit suggested by\nMcLeod \\& Rieke \\shortcite{mcleod95a} must break down for quasars with\nthe highest nuclear luminosities.\n\nThis is in contrast to recent work by McLeod, Rieke \\&\nStorrie-Lombardi \\shortcite{mcleod99} who claim that the lower bound\non host luminosity extends to the highest luminosity quasars, partly\nbased on the discovery of one luminous quasar, 1821+643 which appears\nto be in a host at $\\sim25L^*$. What should we expect? The hosts of\nthe quasars known to date already extend to about $2L^*$. Should the\nhosts of quasars which are ten times more luminous be found in\ngalaxies at $20L^*$? Our analysis suggests not.\n\nThis result is highly important for recent quasar models. In\nparticular, the model of Kauffmann \\& Haehnelt \\shortcite{kauffmann}\npredicts that the upper limit to the nuclear-to-host ratio should\nextend to quasars such as those imaged in this work. However, this is\nclearly not the case. A possible fix to their model would be to invoke\nthe scatter of the Magorrian \\etal\\ \\shortcite{magorrian} relations to\nexplain high luminosity quasars (\\& high mass black holes) within low\nluminosity structures, and invoke a steeply-declining host mass\nfunction to explain the lack of really massive hosts. Further work on\nthis model would then be required, particularly with regard to the\nrevised slope of the high luminosity tail of the quasar luminosity\nfunction. Alternatively, factors other than black-hole mass, such as\nnuclear obscuration, accretion processes, etc. could be the cause of\ndiffering nuclear luminosities within reasonably similar galaxies\n(with similar black hole masses).\n\n\\subsection{Morphologies} \\label{sec:discuss_morph}\n\nRecent HST results suggest that luminous nuclear emission\npredominantly arises from hosts with large spheroidal components\n\\cite{mclure}. The two least luminous radio-quiet quasars imaged by\nMcLure \\etal\\ \\shortcite{mclure} have disk-like structure at radii\n$\\simgt3$\\,arcsec, while the more luminous quasars are completely\ndominated by spheroidal profiles. Could we be seeing a relationship\nbetween host morphology and nuclear luminosity? This is particularly\ninteresting when compared to the black hole mass-spheroid mass and\nspheroid mass-luminosity relations determined for nearby galaxies by\nMagorrian \\etal\\ \\shortcite{magorrian}: a large black hole,\npotentially capable of powering luminous AGN appears more likely to be\npresent in galaxies with large spheroidal components. Both the results\nof McLure \\etal\\ \\shortcite{mclure} and the relations of Magorrian\n\\etal\\ \\shortcite{magorrian} suggest that quasars with strong nuclear\nemission should predominantly exist in hosts with large spheroidal\ncomponents which dominate any disk-like structure.\n\nBy careful analysis we have provided evidence that a large fraction of\nthe host galaxies found in this work are dominated by disk-like\nprofiles. However, the most important light for this modelling comes\nfrom radii greater than those of the HST study, where the disk\ncomponent, if present, is expected to be strong. The $K$-band images\ndescribed here are not of sufficient quality for us to resolve the\ninner region and produce a 2-component fit to the host galaxy. This is\nin contrast to results from HST where the increased resolution enables\nthe inner region to be resolved, and the spheroidal core of the galaxy\nbecomes more important for modelling with a single $\\beta$\nparameter. By analysing synthetic data, we have been able to show that\nfor hosts where we find a dominant disk-like component, any additional\nspheroidal component will not result in a large change in the\nrecovered total host luminosities. We have also provided suggestive\nevidence that the spheroidal cores of these quasars are of relatively\nlow luminosity. Further analysis of both the regions and profiles\nprobed by different studies, and higher resolution data on the cores\nof the quasars analysed in this work would be very interesting, and\ncould help to explain the different morphological results of recent\nhost galaxy studies.\n\n\\section{Conclusions}\n\nWe have presented the results from a deep $K$-band imaging study\ndesigned to reveal the host galaxies of quasars with higher\nluminosities than targeted by previous studies. Extending host-galaxy\nstudies to these quasars was made possible by the stability provided\nby the tip-tilt adaptive optics system at UKIRT, which enabled\naccurate psf measurements to be obtained for the deep quasar\nimages. We have been able to resolve host galaxies for all of our\nsample.\n\nThe principle conclusion of this study is that the luminous quasars in\nthis sample have host galaxies with similar luminosities to quasars of\nlower total luminosity. Derived nuclear-to-host ratios are therefore\nlarger than those obtained by previous work, and place these quasars\nbeyond the upper limit suggested by studies of quasars with lower\ntotal luminosities. Host morphologies are less certain, but there is\nweak evidence that the hosts of these quasars can be dominated by\neither disk-like or spheroidal profiles on the scales probed by\nthese images.\n\n\\section{Acknowledgements}\nThe United Kingdom Infrared Telescope is operated by the Joint\nAstronomy Centre on behalf of the U.K. Particle Physics and Astronomy\nResearch Council.\n\n\\begin{thebibliography}{}\n \\bibitem[\\protect\\citename{Abraham, Crawford \\& McHardy }1992]{abraham} \n Abraham R.G., Crawford C.S., McHardy I.M., 1992, ApJ, 401, 474\n \\bibitem[\\protect\\citename{Baggett, Baggett \\& Anderson }1998]{baggett} \n Baggett W.E., Baggett S.M., Anderson K.S.J., \n 1998, AJ, 116, 1626 \n \\bibitem[\\protect\\citename{Bahcall \\etal\\ }1997]{bahcall} \n Bahcall J.N., Kirhakos S., Saxe D.H., Schneider D.P., \n 1997, ApJ, 479, 642\n \\bibitem[\\protect\\citename{Bevington \\& Robinson }1992]{bevington} \n Bevington P.R., Robinson D.K., 1992, Data reduction and error\n analysis for the physical sciences, 2nd ed. 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G., Charlot S., 1993, ApJ, 405, 538\n \\bibitem[\\protect\\citename{Caon, Capaccioli \\& D'Onofrio }1993]{caon} \n Caon N., Capaccioli M., D'Onofrio M., 1993, MNRAS 265, 1013\n \\bibitem[\\protect\\citename{Casali \\& Hawarden }1992]{casali} \n Casali M.M., Hawarden T.G., 1992, UKIRT newsletter, 3, 33\n \\bibitem[\\protect\\citename{Condon \\etal\\ }1998]{condon} \n Condon J.J., Cotton W.D., Greisen E.W., Yin Q.F., Perley R.A.,\n Taylor G.B., Broderick J.J., 1998, AJ, 115, 1693\n \\bibitem[\\protect\\citename{Dunlop \\etal\\ }1989]{dunlop89} \n Dunlop J.S., Guiderdoni B., Rocca-Volmerange B., Peacock J.A.,\n Longair M.S., 1989, MNRAS, 240, 257\n \\bibitem[\\protect\\citename{Dunlop \\etal\\ }1993]{dunlop93} \n Dunlop J.S., Taylor G.L., Hughes D.H., Robson E.I., 1993, \n MNRAS, 264, 455\n \\bibitem[\\protect\\citename{Efstathiou \\& Rees }1988]{efrees} \n Efstathiou G., Rees M.J., 1988, MNRAS, 230, 5p\n \\bibitem[\\protect\\citename{Gardner \\etal\\ }1997]{gardner} \n Gardner J.P., Sharples R.M., Frenk C.S., Carrasco B.E., 1997, \n ApJ, 480, L99\n \\bibitem[\\protect\\citename{Glazebrook \\etal\\ }1995]{glazebrook95} \n Glazebrook K., Peacock J.A., Miller L., Collins C.A., 1995, \n MNRAS, 275, 169\n \\bibitem[\\protect\\citename{Goldschmidt \\etal\\ }1992]{goldschmidt92}\n Goldschmidt P., Miller L., LaFranca F., Cristiani S., 1992, \n MNRAS, 256, L65\n \\bibitem[\\protect\\citename{Haehnelt \\& Rees }1993]{haehnelt} \n Haehnelt M.G., Rees M.J., 1993, MNRAS, 263, 168\n \\bibitem[\\protect\\citename{Hewitt \\& Burbidge }1993]{hewitt} \n Hewitt A., Burbidge G., 1993, AJS, 87, 451\n \\bibitem[\\protect\\citename{Hines \\etal\\ }1999]{hines} \n Hines D.C., Low F.J., Thompson R.I., Weymann R.J.,\n Storrie-Lombardi L.J., 1999, ApJ, 512, 140\n \\bibitem[\\protect\\citename{H\\\"{o}gbom }1974]{hogbom} \n H\\\"{o}gbom J.A., 1974, A\\&AS, 15, 417\n \\bibitem[\\protect\\citename{Hooper, Impey \\& Foltz }1997]{hooper} \n Hooper E.J., Impey C.D., Foltz C.B., 1997, ApJ, 480, L95\n \\bibitem[\\protect\\citename{Hutchings, Crampton \\& Campbell }1984]\n {hutchings84} Hutchings J.B., Crampton D., Campbell B., 1984, ApJ, 280, 41\n \\bibitem[\\protect\\citename{Hutchings \\& Neff }1992]{hutchings92} \n Hutchings J.B., Neff S.G., 1992, AJ, 104, 1\n \\bibitem[\\protect\\citename{Hutchings, Neff \\& Gower }1992]{h92_1700} \n Hutchings J.B., Neff S.G., Gower A.C., 1992, PASP, 104, 62\n \\bibitem[\\protect\\citename{Kauffmann \\& Haehnelt }1999]{kauffmann} \n Kauffmann G., Haehnelt M., 1999, MNRAS submitted, astro-ph/9906493\n \\bibitem[\\protect\\citename{Kormendy \\& Richstone }1995]{kormendy} \n Kormendy J., Richstone D., 1995, ARA\\&A, 33, 581 \n \\bibitem[\\protect\\citename{Lilly \\& Longair }1984]{lilly} \n Lilly S.J., Longair M.S., 1984, MNRAS, 211, 833\n \\bibitem[\\protect\\citename{Lin \\etal\\ }1996]{lin} \n Lin H., Kirshner R.P., Shectman S.A., Landy S.D., Oemler A.,\n Tucker D.L., Schechter P.L., 1996, ApJ, 464, 60 \n \\bibitem[\\protect\\citename{Magorrian \\etal\\ }1998]{magorrian} \n Magorrian J. \\etal, 1998, AJ, 115, 2285\n \\bibitem[\\protect\\citename{Malkan \\etal\\ }1984a]{malkan84a} \n Malkan M.A., Margon B., Chanan G.A., 1984a, ApJ, 280, 66\n \\bibitem[\\protect\\citename{Malkan }1984b]{malkan84b} \n Malkan M.A., 1984b, ApJ, 287, 555\n \\bibitem[\\protect\\citename{McLeod \\& Rieke }1994a]{mcleod94a} \n McLeod K.K., Rieke G.H., 1994a, ApJ, 420, 58\n \\bibitem[\\protect\\citename{McLeod \\& Rieke }1994b]{mcleod94b} \n McLeod K.K., Rieke G.H., 1994b, ApJ, 431, 137\n \\bibitem[\\protect\\citename{McLeod \\& Rieke }1995]{mcleod95a} \n McLeod K.K., Rieke G.H., 1995, ApJ, 441, 96\n \\bibitem[\\protect\\citename{McLeod, Rieke \\& Storrie-Lombardi \n }1999]{mcleod99} McLeod K.K., Rieke G.H., Storrie-Lombardi L.J., \n 1999, ApJ, 511, L67\n \\bibitem[\\protect\\citename{McLure \\etal\\ }1999]{mclure} \n McLure R.J., Dunlop J.S., Kukula M.J., Baum S.A., O'Dea C.P.,\n Hughes D.H., 1999, MNRAS, 308, 377\n \\bibitem[\\protect\\citename{Mobasher, Sharples \\& Ellis }1993]{mobasher} \n Mobasher B., Sharples R.M., Ellis R.S., 1993, MNRAS, 263, 560\n \\bibitem[\\protect\\citename{Neugebauer \\etal\\ }1985]{neugebauer} \n Neugebauer G., Matthews K., Soifer B.T., Elias J.H., 1985, ApJ, 298, 275\n \\bibitem[\\protect\\citename{Neugebauer \\etal\\ }1987]{neugebauer87} \n Neugebauer G., Green R.F., Matthews K., Schmidt M., Soifer B.T.,\n Bennett J., 1987, ApJs, 63, 615\n \\bibitem[\\protect\\citename{Pahre, Djorgovski \\& de Carvalho }1998]{pahre} \n Pahre M.A., Djorgovski S.G., de Carvalho R.R., 1998, AJ, 116, 1591\n \\bibitem[\\protect\\citename{Percival \\& Miller }1999]{percival} \n Percival W., Miller L., 1999, MNRAS, 309, 823\n \\bibitem[\\protect\\citename{Percival \\& Miller }2000]{percival_clean} \n Percival W., Miller L., 2000, in preparation\n \\bibitem[\\protect\\citename{Press \\etal\\ }1992]{nr}\n Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P., 1992,\n Numerical recipes in C, 2nd ed. Cambridge Univ. Press \n \\bibitem[\\protect\\citename{Smith \\etal\\ }1986]{smith} \n Smith E.P., Heckman T.M., Bothun G.D., Romanishin W., Balick B., \n 1986, ApJ, 306, 64\n \\bibitem[\\protect\\citename{Stockton, Canalizo \\& Close }1998]{stockton} \n Stockton A., Canalizo G., Close L.M., 1998, ApJ, 500, 121\n \\bibitem[\\protect\\citename{Taylor \\etal\\ }1996]{taylor} \n Taylor G.L., Dunlop J.S., Hughes D.H., Robson E.I., 1996, MNRAS, 283, 968\n \\bibitem[\\protect\\citename{Veron-Cetty \\& Woltjer }1990]{veron-cetty} \n Veron-Cetty M.P., Woltjer L., 1990, A\\&A, 236, 69\n\\end{thebibliography}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002199.extracted_bib",
"string": "\\begin{thebibliography}{}\n \\bibitem[\\protect\\citename{Abraham, Crawford \\& McHardy }1992]{abraham} \n Abraham R.G., Crawford C.S., McHardy I.M., 1992, ApJ, 401, 474\n \\bibitem[\\protect\\citename{Baggett, Baggett \\& Anderson }1998]{baggett} \n Baggett W.E., Baggett S.M., Anderson K.S.J., \n 1998, AJ, 116, 1626 \n \\bibitem[\\protect\\citename{Bahcall \\etal\\ }1997]{bahcall} \n Bahcall J.N., Kirhakos S., Saxe D.H., Schneider D.P., \n 1997, ApJ, 479, 642\n \\bibitem[\\protect\\citename{Bevington \\& Robinson }1992]{bevington} \n Bevington P.R., Robinson D.K., 1992, Data reduction and error\n analysis for the physical sciences, 2nd ed. McGraw-Hill\n \\bibitem[\\protect\\citename{Boyce \\etal\\ }1998]{boyce} \n Boyce P.J., Disney M.J., Blades J.C., Boksenberg A., Crane P.,\n Deharveng J.M., Macchetto F.D., Mackay C.D., Sparks W.B., \n 1998, MNRAS, 298, 121\n \\bibitem[\\protect\\citename{Bruzual \\& Charlot }1993]{bruzual} \n Bruzual A. G., Charlot S., 1993, ApJ, 405, 538\n \\bibitem[\\protect\\citename{Caon, Capaccioli \\& D'Onofrio }1993]{caon} \n Caon N., Capaccioli M., D'Onofrio M., 1993, MNRAS 265, 1013\n \\bibitem[\\protect\\citename{Casali \\& Hawarden }1992]{casali} \n Casali M.M., Hawarden T.G., 1992, UKIRT newsletter, 3, 33\n \\bibitem[\\protect\\citename{Condon \\etal\\ }1998]{condon} \n Condon J.J., Cotton W.D., Greisen E.W., Yin Q.F., Perley R.A.,\n Taylor G.B., Broderick J.J., 1998, AJ, 115, 1693\n \\bibitem[\\protect\\citename{Dunlop \\etal\\ }1989]{dunlop89} \n Dunlop J.S., Guiderdoni B., Rocca-Volmerange B., Peacock J.A.,\n Longair M.S., 1989, MNRAS, 240, 257\n \\bibitem[\\protect\\citename{Dunlop \\etal\\ }1993]{dunlop93} \n Dunlop J.S., Taylor G.L., Hughes D.H., Robson E.I., 1993, \n MNRAS, 264, 455\n \\bibitem[\\protect\\citename{Efstathiou \\& Rees }1988]{efrees} \n Efstathiou G., Rees M.J., 1988, MNRAS, 230, 5p\n \\bibitem[\\protect\\citename{Gardner \\etal\\ }1997]{gardner} \n Gardner J.P., Sharples R.M., Frenk C.S., Carrasco B.E., 1997, \n ApJ, 480, L99\n \\bibitem[\\protect\\citename{Glazebrook \\etal\\ }1995]{glazebrook95} \n Glazebrook K., Peacock J.A., Miller L., Collins C.A., 1995, \n MNRAS, 275, 169\n \\bibitem[\\protect\\citename{Goldschmidt \\etal\\ }1992]{goldschmidt92}\n Goldschmidt P., Miller L., LaFranca F., Cristiani S., 1992, \n MNRAS, 256, L65\n \\bibitem[\\protect\\citename{Haehnelt \\& Rees }1993]{haehnelt} \n Haehnelt M.G., Rees M.J., 1993, MNRAS, 263, 168\n \\bibitem[\\protect\\citename{Hewitt \\& Burbidge }1993]{hewitt} \n Hewitt A., Burbidge G., 1993, AJS, 87, 451\n \\bibitem[\\protect\\citename{Hines \\etal\\ }1999]{hines} \n Hines D.C., Low F.J., Thompson R.I., Weymann R.J.,\n Storrie-Lombardi L.J., 1999, ApJ, 512, 140\n \\bibitem[\\protect\\citename{H\\\"{o}gbom }1974]{hogbom} \n H\\\"{o}gbom J.A., 1974, A\\&AS, 15, 417\n \\bibitem[\\protect\\citename{Hooper, Impey \\& Foltz }1997]{hooper} \n Hooper E.J., Impey C.D., Foltz C.B., 1997, ApJ, 480, L95\n \\bibitem[\\protect\\citename{Hutchings, Crampton \\& Campbell }1984]\n {hutchings84} Hutchings J.B., Crampton D., Campbell B., 1984, ApJ, 280, 41\n \\bibitem[\\protect\\citename{Hutchings \\& Neff }1992]{hutchings92} \n Hutchings J.B., Neff S.G., 1992, AJ, 104, 1\n \\bibitem[\\protect\\citename{Hutchings, Neff \\& Gower }1992]{h92_1700} \n Hutchings J.B., Neff S.G., Gower A.C., 1992, PASP, 104, 62\n \\bibitem[\\protect\\citename{Kauffmann \\& Haehnelt }1999]{kauffmann} \n Kauffmann G., Haehnelt M., 1999, MNRAS submitted, astro-ph/9906493\n \\bibitem[\\protect\\citename{Kormendy \\& Richstone }1995]{kormendy} \n Kormendy J., Richstone D., 1995, ARA\\&A, 33, 581 \n \\bibitem[\\protect\\citename{Lilly \\& Longair }1984]{lilly} \n Lilly S.J., Longair M.S., 1984, MNRAS, 211, 833\n \\bibitem[\\protect\\citename{Lin \\etal\\ }1996]{lin} \n Lin H., Kirshner R.P., Shectman S.A., Landy S.D., Oemler A.,\n Tucker D.L., Schechter P.L., 1996, ApJ, 464, 60 \n \\bibitem[\\protect\\citename{Magorrian \\etal\\ }1998]{magorrian} \n Magorrian J. \\etal, 1998, AJ, 115, 2285\n \\bibitem[\\protect\\citename{Malkan \\etal\\ }1984a]{malkan84a} \n Malkan M.A., Margon B., Chanan G.A., 1984a, ApJ, 280, 66\n \\bibitem[\\protect\\citename{Malkan }1984b]{malkan84b} \n Malkan M.A., 1984b, ApJ, 287, 555\n \\bibitem[\\protect\\citename{McLeod \\& Rieke }1994a]{mcleod94a} \n McLeod K.K., Rieke G.H., 1994a, ApJ, 420, 58\n \\bibitem[\\protect\\citename{McLeod \\& Rieke }1994b]{mcleod94b} \n McLeod K.K., Rieke G.H., 1994b, ApJ, 431, 137\n \\bibitem[\\protect\\citename{McLeod \\& Rieke }1995]{mcleod95a} \n McLeod K.K., Rieke G.H., 1995, ApJ, 441, 96\n \\bibitem[\\protect\\citename{McLeod, Rieke \\& Storrie-Lombardi \n }1999]{mcleod99} McLeod K.K., Rieke G.H., Storrie-Lombardi L.J., \n 1999, ApJ, 511, L67\n \\bibitem[\\protect\\citename{McLure \\etal\\ }1999]{mclure} \n McLure R.J., Dunlop J.S., Kukula M.J., Baum S.A., O'Dea C.P.,\n Hughes D.H., 1999, MNRAS, 308, 377\n \\bibitem[\\protect\\citename{Mobasher, Sharples \\& Ellis }1993]{mobasher} \n Mobasher B., Sharples R.M., Ellis R.S., 1993, MNRAS, 263, 560\n \\bibitem[\\protect\\citename{Neugebauer \\etal\\ }1985]{neugebauer} \n Neugebauer G., Matthews K., Soifer B.T., Elias J.H., 1985, ApJ, 298, 275\n \\bibitem[\\protect\\citename{Neugebauer \\etal\\ }1987]{neugebauer87} \n Neugebauer G., Green R.F., Matthews K., Schmidt M., Soifer B.T.,\n Bennett J., 1987, ApJs, 63, 615\n \\bibitem[\\protect\\citename{Pahre, Djorgovski \\& de Carvalho }1998]{pahre} \n Pahre M.A., Djorgovski S.G., de Carvalho R.R., 1998, AJ, 116, 1591\n \\bibitem[\\protect\\citename{Percival \\& Miller }1999]{percival} \n Percival W., Miller L., 1999, MNRAS, 309, 823\n \\bibitem[\\protect\\citename{Percival \\& Miller }2000]{percival_clean} \n Percival W., Miller L., 2000, in preparation\n \\bibitem[\\protect\\citename{Press \\etal\\ }1992]{nr}\n Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P., 1992,\n Numerical recipes in C, 2nd ed. Cambridge Univ. Press \n \\bibitem[\\protect\\citename{Smith \\etal\\ }1986]{smith} \n Smith E.P., Heckman T.M., Bothun G.D., Romanishin W., Balick B., \n 1986, ApJ, 306, 64\n \\bibitem[\\protect\\citename{Stockton, Canalizo \\& Close }1998]{stockton} \n Stockton A., Canalizo G., Close L.M., 1998, ApJ, 500, 121\n \\bibitem[\\protect\\citename{Taylor \\etal\\ }1996]{taylor} \n Taylor G.L., Dunlop J.S., Hughes D.H., Robson E.I., 1996, MNRAS, 283, 968\n \\bibitem[\\protect\\citename{Veron-Cetty \\& Woltjer }1990]{veron-cetty} \n Veron-Cetty M.P., Woltjer L., 1990, A\\&A, 236, 69\n\\end{thebibliography}"
}
] |
astro-ph0002200
|
A local infrared perspective to deeper ISO surveys
|
[
{
"author": "D.M. Alexander\\inst{1}"
},
{
"author": "H. Aussel\\inst{2}"
}
] |
We present new techniques to produce IRAS 12 $\mu$m samples of galaxies and stars. We show that previous IRAS 12 $\mu$m samples are incompatible for detailed comparison with ISO surveys and review their problems. We provide a stellar infrared diagnostic diagram to distinguish galaxies from stars without using longer wavelength IRAS colour criteria and produce complete 12 $\mu$m samples of galaxies and stars. This new technique allows us to estimate the contribution of non-dusty galaxies to the IRAS 12 $\mu$m counts and produce a true local mid-infrared extragalactic sample compatible with ISO surveys. We present our initial analysis and results.
|
[
{
"name": "dma_ringberg.tex",
"string": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% This is a sample input file for your contribution to a multi-\n% author book to be published by Springer Verlag.\n%\n% Please use it as a template for your own input, and please\n% follow the instructions for the formal editing of your\n% manuscript as described in the file \"1readme\".\n%\n% Please send the Tex and figure files of your manuscript\n% together with any additional style files as well as the\n% PS file to the editor of your book.\n%\n% He or she will collect all contributions for the planned\n% book, possibly compile them all in one go and pass the\n% complete set of manuscripts on to Springer.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\n%RECOMMENDED%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\documentclass[runningheads]{cl2emult}\n\n\\usepackage{makeidx} % allows index generation\n\\usepackage{graphicx} % standard LaTeX graphics tool\n % for including eps-figure files\n\\usepackage{subeqnar} % subnumbers individual equations\n % within an array\n\\usepackage{multicol} % used for the two-column index\n\\usepackage{cropmark} % cropmarks for pages without\n % pagenumbers\n\\usepackage{lnp} % placeholder for figures\n\\makeindex % used for the subject index\n % please use the style sprmidx.sty with\n % your makeindex program\n\n%upright Greek letters (example below: upright \"mu\")\n\\newcommand{\\euler}[1]{{\\usefont{U}{eur}{m}{n}#1}}\n\\newcommand{\\eulerbold}[1]{{\\usefont{U}{eur}{b}{n}#1}}\n\\newcommand{\\umu}{\\mbox{\\euler{\\char22}}}\n\\newcommand{\\umub}{\\mbox{\\eulerbold{\\char22}}}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n%OPTIONAL%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\n%\\usepackage{amstex} % useful for coding complex math\n%\\mathindent\\parindent % needed in case \"Amstex\" is used\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%AUTHOR_STYLES_AND_DEFINITIONS%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\n%Please reduce your own definitions and macros to an absolute\n%minimum since otherwise it will become rather strenuous to\n%compile all individual contributions to a single book file\n%\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{document}\n%\n\\title*{A local infrared perspective to deeper ISO surveys}\n%\n%\n\\toctitle{A local infrared perspective to deeper ISO surveys}\n% allows explicit linebreak for the table of content\n%\n%\n\\titlerunning{A local infrared perspective}\n% allows abbreviation of title, if the full title is too long\n% to fit in the running head\n%\n\\author{D.M. Alexander\\inst{1}\n\\and H. Aussel\\inst{2}}\n%\n\\authorrunning{Alexander and Aussel}\n% if there are more than two authors,\n% please abbreviate author list for running head\n%\n%\n\\institute{International School for Advanced Studies, SISSA,\nTrieste, Italy\n\\and Osservatorio Astronomico di Padova, Padova, Italy}\n\n\\maketitle % typesets the title of the contribution\n\n\\begin{abstract}\n\nWe present new techniques to produce IRAS 12 $\\mu$m samples of galaxies and stars. We\nshow that previous IRAS 12 $\\mu$m samples are incompatible for detailed comparison\nwith ISO surveys and review their problems. We provide a stellar infrared diagnostic\ndiagram to distinguish galaxies from stars without using longer wavelength IRAS colour\ncriteria and produce complete 12 $\\mu$m samples of galaxies and stars. This new\ntechnique allows us to estimate the contribution of non-dusty galaxies to the IRAS 12\n$\\mu$m counts and produce a true local mid-infrared extragalactic sample compatible\nwith ISO surveys. We present our initial analysis and results.\n\n\\end{abstract}\n\n\\section{The importance of the local infrared picture} \n\nThe recent ISO mission has produced a number of deep mid-infrared extragalactic\nsurveys [1,2,3,4] many of which are presented elsewhere in these proceedings.\nIn order to accurately evaluate the apparent source evolution found in these surveys\nit is essential to have a stable and exact local infrared picture that is compatible\nwith ISO surveys. \n\n\n\\section{Previous work and problems}\n\nThere have been a number of previous IRAS 12 $\\mu$m extragalactic samples produced\nfrom either the Point Source Catalog, hereafter PSC, or the Faint Source Catalog,\nhereafter FSC. The FSC was constructed by co-adding the individual PSC scans and is\nconsequently deeper at 12 $\\mu$m by approximately one mag; the FSC is considered\ncomplete to $f_{12}$$>$0.2 Jy. Due to the greater depth of the FSC only those samples\nconstructed from it will be considered here [5,6 hereafter RMS and FSXH]. In essence\nnone of these samples are truly compatible with the deeper ISO surveys because they\napply longer wavelength IRAS colour selection criteria and do not objectively classify\ngalaxies. Some of these samples additionally suffer from inaccurate source flux\nestimation, no correction for the overdensity due to large scale structure and\ninaccurate K-correction. Due to the lack of space here these latter two points are not\nconsidered although we refer the interested reader to [6,14] for excellent coverage of\nthese problems.\n\n\n\\subsection{The colour selection problem}\n\nSelecting objects at 12 $\\mu$m without colour selection will produce an abundance of\nstars over galaxies due to the Jeans tail of stellar emission. Without exception every\nextragalactic 12 $\\mu$m sample to date has had (the majority of) stars removed by\napplying longer wavelength IRAS colour criteria. This technique is clearly\nincompatible with ISO surveys where no colour criterium is applied and will cause a\nbias towards dusty galaxies. This also enforces that every galaxy must have a longer\nwavelength flux, producing incompleteness even within the selection boundaries. For\nexample, in RMS the primary selection is $f_{12}$$>$0.22 Jy but every galaxy must also\nhave $f_{60}$$>$0.5$f_{12}$ or $f_{100}$$>$$f_{12}$. However due to the completeness\nof FSC ($f_{60}$$>$0.2 Jy and $f_{100}$$>$0.6 Jy) this sample cannot be complete for\n$f_{12}$$<$0.4 Jy or $f_{12}$$<$0.6Jy respectively. \n\n\n\\subsection{The classification problem}\n\nTo produce accurate extragalactic luminosity functions and understand the galaxy\ncontributions to fainter source counts it is necessary to classify galaxies in an\nobjective way, the most common technique is with optical line ratios [7,8]. To date\nthe only classified 12 $\\mu$m sample is RMS although their classification was taken\nfrom various catalogues which differ in the definition of extragalactic type and\ncompleteness. As a comparison to this classification we have obtained line ratios from\nthe literature for 349 of the 483 RMS galaxies with $\\delta$$>$0 degrees. This gives\ncompletenesses of 72\\%, 78\\% and 93\\% for objects $f_{12}$$>$0.22, 0.3 and 0.5 Jy\nrespectively. Due to the spectroscopic incompleteness at lower fluxes and the colour\nselection incompleteness we only consider those of $f_{12}$$>$0.5 Jy here, see table\n1; our classification follows that of [7,9]. \n\n\n\\begin{table}\n\\centering\n\\caption{Extragalactic classification}\n\\renewcommand{\\arraystretch}{1.4}\n\\setlength\\tabcolsep{5pt}\n\\begin{tabular}{llllll}\n\\hline\\noalign{\\smallskip}\n & AGN & LINER & HII \\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nRMS & 13\\% & 15\\% & - \\\\\nAA & 16\\% & 24\\% & 60\\% \\\\\n\\hline\n\\end{tabular}\n\\label{Tab1a}\n\\end{table}\n\n\nAll galaxies are found to show H$\\alpha$ emission although for some galaxies\nW$_{\\lambda}$(H$\\alpha$)$<$1 angstrom and they would appear as absorption line objects\nin lower resolution/signal to noise spectra. Of the HII galaxies, 50\\% show evidence\nfor significant star formation (W$_{\\lambda}$(H$\\alpha$)$>$10 angstroms). RMS\nclassified an object as an AGN if it is present in an AGN catalogue. We find a good\nagreement in classification for this object class, the principal reason for the\nconstruction of the RMS sample. LINERs were classified in the RMS sample if they were\npresent in an AGN catalgoue and consequently this sample is thought to be incomplete. \nWe confirm this here. RMS did not classify HII galaxies although they considered those\ngalaxies not classified as a LINER or AGN, but with high infrared luminosities, to be\nstarburst galaxies and all other objects to be normal galaxies. \n\n\\subsection{The source flux problem}\n\nThe FSC detection algorithm has been optimised for unresolved sources therefore fluxes\nfor extended sources need to be calculated from the coaddition of scans (the ADDSCAN\ntechnique nowadays accessed via XSCANPI) [10]. However, if a source is unresolved, the\nflux calculation using this technique leads erroneously to a larger flux than the FSC\nflux [10]. Whilst FSXH carefully calculate the fluxes of extended and unresolved\nsources seperately, RMS treat all sources as extended and consequently overestimate\nthe fluxes of unresolved galaxies; due to the large beamsize of IRAS a large number of\ngalaxies can be overestimated. The magnitude of this effect can be estimated from\nISOCAM observations. Unfortunately only a few observations are available for the lw10\nfilter (the closest to the IRAS 12 $\\mu$m band) therefore in order to predict the IRAS\n12 $\\mu$m fluxes we have used observations in the lw2 (6.7 $\\mu$m) and lw3 (14.3\n$\\mu$m) bands and a spectral decomposition technique similar to that described in\n[11]. In this simple model the mid-infrared emission is produced by two components:\nHII regions (using M17 [12]) and photo-dissociation regions (PDR) (using NGC7023\n[13]). The ratio of HII to PDR is calculated from the ratio of lw2 to lw3 fluxes, a\nsynthetic spectra is produced and the IRAS 12 $\\mu$m flux is calculated. This\ntechnique will be somewhat imprecise due to the uncertainty of the CAM photometry and\nthe ability of the model to reproduce the galactic spectrum. Overall we estimate an\nuncertainty of $\\sim$20\\%, roughly equal to the worst error in the FSC photometry. In\nfigure 1 we plot our predicted fluxes against the FSC and RMS fluxes divided by the\npredicted flux (i.e. the relative errors in flux).\n\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=.6\\textwidth]{dma_fig1.eps}\n\\caption[]{12 $\\mu$m flux comparison}\n\\label{eps1}\n\\end{figure}\n\n\nOnly those galaxies with z$>$2,500 kms$^{-1}$ have been plotted as they should all be\nunresolved in the IRAS beam. In general a good agreement between the predicted flux\nand FSC flux is found leading us to believe that the true fluxes for these objects are\nclose to the FSC flux. Consequently RMS may be overpredicting the source flux for\n$\\sim$50\\% of their objects. This will have the effect of shifting galaxies from faint\nflux/luminosity bins to higher bins causing unpredictable effects in the source count\nand luminosity function determinations. \n\n\n\\section{A new IRAS 12 $\\mu$m sample}\n\nOur new IRAS 12 $\\mu$m sample aims to address these problems and create a local\ninfrared sample that is compatible with ISO surveys. The sample definition is close to\nthat of RMS: sources are taken from the FSC for those objects with $|$b$|$$>$25\ndegrees, $f_{12}$$>$0.2 Jy and a moderate or good quality detection (S/N$>$3). This\nselection results in 31002 objects, by comparison the RMS colour selection bias\nproduces $\\sim$1100 objects. \n\nOur sample provides an interesting complement to the PSC-z extragalactic survey [15]\nwhich selects those objects from the PSC with $f_{60}$$>$0.6 Jy. As with our sample\nthey do not apply colour selection criteria, stars are identified on Schmidt plates.\nIn terms of the extragalactic objects we would expect many galaxies in common although\nour sample should have a higher fraction of quasars and early type galaxies. \n\n\n\\subsection{The stellar infrared diagnostic correlation}\n\nBy not applying colour selection to distinguish galaxies from stars we have had to\ndevise an alternative technique. The key assumption in our technique is that stars\nhave, in the majority, predictable properties and therefore with the large and\ncomplete optical stellar databases currently available (in particular the Guide Star\nCatalogue [16], hereafter GSC) it is possible to find the majority of stars in our\nsample through positional cross correlation. An important factor here is in\ndetermining the completeness of an optical stellar catalgoue in an infrared sample,\nrequiring an understanding of the general optical and infrared characteristics of\nstars.\n \nTo determine these characteristics for our stars we have used SIMBAD, which provides\nstellar classifications, and produced a large sample ($\\sim$9000 objects) of\nclassified stars. When cross correlationing to optical positions we consider a star\ncorrelated if its optical position falls within 5$\\sigma$ of the IRAS position (the\nmean major and minor error ellipse axes are 16.9\" and 2.0\" respectively). The\nproperties of our classified stellar sample are shown in figure 2. We have only\nplotted those stars for which there are at least 10 objects in a classified class and\nonly a subset of these classes are shown here for clarity. A clear correlation between\nstellar type and flux ratio is found. The predicted black body colours for the\ndifferent stellar types follows a straight line passing close to the A1V to K5III\npoints. The interesting deviation observed for stars beyond type MOIII is {\\it\npossibly} due to an increasing amount of stellar absorption in the V band.\n\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=.6\\textwidth]{dma_fig2.eps}\n\\caption[]{Stellar infrared diagnostic diagram}\n\\label{eps1}\n\\end{figure}\n\n\nThese optical-infrared flux correlations provide an essential tool, the ability to\npredict the IRAS 12 $\\mu$m flux of a star for a given spectral type or B-V colour. In\nthe cases where we find an IRAS source associated with both a galaxy and a star we\nwill be able to predict the flux from the star and therefore estimate the flux from\nthe galaxy.\n\n\n\\subsection{Cross correlating stars}\n\nThe GSC is considered complete for 6$<$V$<$15 mags over the whole sky. Based on our\nstellar infrared diagnostic correlation this corresponds to a depth of $f_{12}$$>$0.2\nJy and therefore any stars earlier than a type M6III in our sample should be in the\nGSC. However, to accurately cross correlate the positions between the GSC and our\nsample requires accounting for proper motion. The Schmidt plates for the GSC were\ntaken in 1975 and 1982, by comparison the mean IRAS observation epoch is 1983.5. By\nanalysing a sub-sample of Hipparcos stars ($\\sim$4000 objects, selected by sky area)\nwe find a mean proper motion of 0.03\"yr$^{-1}$, with a one $\\sigma$ maximum of\n0.13\"yr$^{-1}$ (the maximum in the whole catalogue is 6\"yr$^{-1}$). Taking into\naccount the different observation epochs and the mean IRAS error ellipse, virtually\nall our stars should fall within 5$\\sigma$ of their GSC position. \n\nWe initially searched for associations by selecting all objects within 2' of the IRAS\nposition (2' corresponds to $\\sim$5$\\sigma$ of the mean positional uncertainty in the\nmajor axis direction) although we only consider a star cross-correlated if it falls\nwithin 5$\\sigma$ of an IRAS source. From this cross correlation we find that over that\n29000 of our IRAS sources are stars. Of these a small ($\\sim$0.5\\%), but significant,\nfraction show a considerable infrared excess ($f_{25}$$>$$f_{12}$) and warrant further\nstudy.\n\n\n\\subsection{Cross correlating galaxies}\n\nOur extragalactic cross correlation is performed in a similar manner although the\nproblems associated with correlating galaxies are somewhat different. Proper motion is\nnot a problem although the extended size of galaxies is as the peak mid-infrared\nposition can vary from the peak optical position and therefore some positional\nuncertainty must be included when trying to correlate an infrared galaxy to an optical\nsource. Although a 5$\\sigma$ positional uncertainty can correspond to 2' if the galaxy\nlies along the major axis of the IRAS error ellipse it can also correspond to just 10\"\nif the galaxy lies perpendicular to this direction. Therefore we only consider a\ngalaxy cross correlated if it falls within 10$\\sigma$ of an IRAS source. Due to the\noften unknown incompleteness of extragalactic catalogues it is not possible to\naccurately determine the completeness of our sample in extragalactic catalogues and\ntherefore we have simply used the largest (and most appropriate) databases. In the\ncross correlation presented here we have used the QIGC sample [17], which has just\nbecome available in electronic form, NED, SIMBAD and the FSC 25 $\\mu$m sample [18].\n\nUsing these databases we find that over 700 of our sources, not confirmed as stars,\nfall within our 10$\\sigma$ threshold. From these confirmed galaxies we find $\\sim$50\nare elliptical or S0 systems (not all are active galaxies) and $\\sim$150 have\n$f_{12}$$>$$f_{25}$ and are most probably PDR dominated galaxies. A number of galaxies\nhave $f_{12}$$>$2$f_{60}$ and would therefore not be picked up by RMS. One of these\ngalaxies is NGC 3115, a nearby bulge dominated galaxy of Hubble type S0. This galaxy\nis only detected at 12 $\\mu$m, the 25, 60 and 100 $\\mu$m fluxes are upper limits,\nalthough with a V band mag of $\\sim$8.9 it is bright optical galaxy. In terms of it's\nB-V (1.0) and B/12 (2.5) colours it corresponds to a K0III star. As a comparison we\nhave plotted a sample of our {\\it normal} infrared galaxies, see figure 3. \n\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=.6\\textwidth]{dma_fig3.eps}\n\\caption[]{Stellar and galactic colour plot. All confirmed stars are plotted as dots\nand a selection of normal infrared galaxies are plotted as filled circles. NGC 3115 is\nnot plotted here but would correspond to the position of a K0III star, see figure 2}\n\\label{eps1} \n\\end{figure}\n\n\n\\subsection{Further improvements}\n\nAlthough our initial cross correlation has been successful we have $\\sim$500 objects\nfor which we do not have an optical identification. These objects do not have IRAS\nCirrus/Confused flags or low 12 $\\mu$m fluxes although approximately 75\\% have upper\nlimit 60 $\\mu$m IRAS fluxes. Visual inspection of a number of these objects with the\nDigital Sky Survey shows them to be nearby bright stars, suggesting incompleteness in\nthe GSC at bright fluxes. However there is also probably a substantial population of\nstars not yet accounted for: those with V$>$15 mags (e.g. M7III and M8III stars),\ndark molecular clouds and planetary nebulae. We are currently compiling a list of\nadditional stellar objects to cross correlate to our sample to allow us to produce a\ndefinitive list of unidentified extragalactic sources.\n\n\n\\section{Further work}\n\nOur primary aim is to construct complete 12 $\\mu$m FSC selected samples of galaxies\nand stars. From this we will create accurate extragalactic source counts and\nclassified luminosity functions with optical slit spectroscopy. As many of our\nextragalactic objects will be extended we also intend to obtain integrated spectra to\nprovide a classification which is compatible with the distant objects found in ISO\nsurveys where the observed slit spectra will be produced by the majority of the\ngalaxy. With our stellar sample we wish to create a complete list of high galactic\nlatitude stars and sources to help constrain galactic models and provide further\ndiagnostics in distinguishing stars from galaxies in faint surveys (e.g. the Hubble\nDeep Field [3]). Both our galactic and stellar samples show objects that deviate from\nthe norm (i.e. galaxies with stellar colours and stars with galactic colours) and\nwarrant further study in their own right.\n\\\\~\\\\ \n{\\bf Acknowledgements} We thank I.Matute for assistance in producing the initial\ncatalogue and M.Moshir for fruitful discussions. We are grateful to O.Laurent and\nH.Roussel for providing the ISOCAM fluxes for some of the RMS sample sources. We\nacknowledge and thank the EC TMR extragalactic networks for postdoctoral grant\nsupport. This research has made use of the NASA/IPAC Extragalactic Database (NED)\nwhich is operated by the Jet Propoulsion Laboratory, California Institute of\nTechnology, under contact with NASA.\n\n\n\n\\begin{thebibliography}{7}\n%\n\\addcontentsline{toc}{section}{References}\n\n\n\\bibitem{}\nElbaz, D., Cesarsky, C., Fadda, D., Aussel, H., D\\'esert, F.-X., et al. (1999) A\\&A,\n351, L37\n\n\\bibitem{}\nOliver, S., Rowan-Robinson, M., Alexander, D.M., Almaini, O., Balcells, M., et al. \n(1999), in press\n\n\\bibitem{}\nAussel, H., Cesarsky, C., Elbaz, D., Starck, J. (1999) A\\&A, 342, 313\n\n\\bibitem{}\nClements, D.L., D\\'esert, F.-X., Franceschini, A., Reach, W.T., Baker, A.C., Davies,\nJ.K., Cesarsky, C. (1999) A\\&A, 346, 383\n\n\\bibitem{}\nRush, B., Malkan, M.A., Spinoglio, L. (1993) ApJS, 89, 1 (RMS)\n\n\\bibitem{}\nFang, F., Shupe, D.L., Xu, C., Hacking, P.B. (1998) ApJ, 500, 693 (FSXH)\n\n\\bibitem{}\nBaldwin, J.A., Phillips, M.M., Terlevich, R. (1981) PASP, 93, 5\n\n\\bibitem{} \nPoggianti, B.M., Smail, I., Dressler, A., Couch, W.J., Barger, A.J., et al. (1999)\nApJ, 518, 576\n\n\\bibitem{}\nHo, L., Filippenko, A.V., Sargent, W.L.W. (1997) ApJS, 326, 653\n\n\\bibitem{}\nMoshir, M., et al. (1992) Explanatory Supplement to the IRAS Faint Source Survey, Version\n2, Pasadena, JPL\n\n\\bibitem{}\nTran, Q.D. (1998) PhD thesis, University of Paris, Orsay, France\n\n\\bibitem{}\nCesarsky, D., Lequeux, J., Abergel, A., Perault, M., Palazzi, E., Madden, S., Tran, D.\n(1996) A\\&A, 315, L309\n\n\\bibitem{}\nCesarsky, D., Lequeux, J., Abergel, A., Perault, M., Palazzi, E., Madden, S., Tran, D.\n(1996) A\\&A, 315, L305\n\n\\bibitem{}\nXu, C., Hacking, P.B., Fang, F., Shupe, D.L., Lonsdale, C.J., et al. (1998) ApJ, 508,\n576\n\n\\bibitem{}\nSaunders, W., Oliver, S., Keeble, O., Rowan-Robinson, M., Canavezes, A., et al. (1997)\nin Maddox, S., Aragon-Salamanca, A., Wide Field Spectroscopy and the Distant Universe,\nWorld Scientific Press, Singapore\n\n\\bibitem{}\nLasker, B.M., Sturch, C.R., McLean, B.J., Russel, J.L., Jenker, H., Shara, M.M. (1990)\nAJ, 99, 2019\n\n\\bibitem{}\nLawrence, A., Rowan-Robinson, M., Ellis, R.S., Frenk. C.S., Efstathiou. G., et al. \n(1999) MNRAS, 308, 897\n\n\\bibitem{}\nShupe, D.L., Fang, F., Hacking, P.B., Huchra, J.P. (1998) ApJ, 501, 597\n\n\n\n\\end{thebibliography}\n\n%INDEX%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\clearpage\n\\addcontentsline{toc}{section}{Index}\n\\flushbottom\n\\printindex\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002200.extracted_bib",
"string": "\\begin{thebibliography}{7}\n%\n\\addcontentsline{toc}{section}{References}\n\n\n\\bibitem{}\nElbaz, D., Cesarsky, C., Fadda, D., Aussel, H., D\\'esert, F.-X., et al. (1999) A\\&A,\n351, L37\n\n\\bibitem{}\nOliver, S., Rowan-Robinson, M., Alexander, D.M., Almaini, O., Balcells, M., et al. \n(1999), in press\n\n\\bibitem{}\nAussel, H., Cesarsky, C., Elbaz, D., Starck, J. (1999) A\\&A, 342, 313\n\n\\bibitem{}\nClements, D.L., D\\'esert, F.-X., Franceschini, A., Reach, W.T., Baker, A.C., Davies,\nJ.K., Cesarsky, C. (1999) A\\&A, 346, 383\n\n\\bibitem{}\nRush, B., Malkan, M.A., Spinoglio, L. (1993) ApJS, 89, 1 (RMS)\n\n\\bibitem{}\nFang, F., Shupe, D.L., Xu, C., Hacking, P.B. (1998) ApJ, 500, 693 (FSXH)\n\n\\bibitem{}\nBaldwin, J.A., Phillips, M.M., Terlevich, R. (1981) PASP, 93, 5\n\n\\bibitem{} \nPoggianti, B.M., Smail, I., Dressler, A., Couch, W.J., Barger, A.J., et al. (1999)\nApJ, 518, 576\n\n\\bibitem{}\nHo, L., Filippenko, A.V., Sargent, W.L.W. (1997) ApJS, 326, 653\n\n\\bibitem{}\nMoshir, M., et al. (1992) Explanatory Supplement to the IRAS Faint Source Survey, Version\n2, Pasadena, JPL\n\n\\bibitem{}\nTran, Q.D. (1998) PhD thesis, University of Paris, Orsay, France\n\n\\bibitem{}\nCesarsky, D., Lequeux, J., Abergel, A., Perault, M., Palazzi, E., Madden, S., Tran, D.\n(1996) A\\&A, 315, L309\n\n\\bibitem{}\nCesarsky, D., Lequeux, J., Abergel, A., Perault, M., Palazzi, E., Madden, S., Tran, D.\n(1996) A\\&A, 315, L305\n\n\\bibitem{}\nXu, C., Hacking, P.B., Fang, F., Shupe, D.L., Lonsdale, C.J., et al. (1998) ApJ, 508,\n576\n\n\\bibitem{}\nSaunders, W., Oliver, S., Keeble, O., Rowan-Robinson, M., Canavezes, A., et al. (1997)\nin Maddox, S., Aragon-Salamanca, A., Wide Field Spectroscopy and the Distant Universe,\nWorld Scientific Press, Singapore\n\n\\bibitem{}\nLasker, B.M., Sturch, C.R., McLean, B.J., Russel, J.L., Jenker, H., Shara, M.M. (1990)\nAJ, 99, 2019\n\n\\bibitem{}\nLawrence, A., Rowan-Robinson, M., Ellis, R.S., Frenk. C.S., Efstathiou. G., et al. \n(1999) MNRAS, 308, 897\n\n\\bibitem{}\nShupe, D.L., Fang, F., Hacking, P.B., Huchra, J.P. (1998) ApJ, 501, 597\n\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002201
|
\chandra~ uncovers a hidden Low-Luminosity AGN \\ in the radio galaxy Hydra~A (3C~218)
|
[
{
"author": "Rita M. Sambruna"
},
{
"author": "George Chartas"
},
{
"author": "and Michael Eracleous"
}
] |
We report the detection with \chandra ~of a Low-Luminosity AGN (LLAGN) in the Low Ionization Emission Line Region (LINER) hosted by Hydra~A, a nearby ($z$=0.0537) powerful FR~I radio galaxy with complex radio and optical morphology. In a 20 ks ACIS-S exposure during the calibration phase of the instrument, a point source is detected at energies $\gtrsim$ 2 keV at the position of the compact radio core, embedded in diffuse thermal X-ray emission ($kT \sim 1$ keV) at softer energies. The spectrum of the point source is well fitted by a heavily absorbed power law with intrinsic column density N$_H^{int} \sim 3 \times 10^{22}$ \nh~ and photon index $\Gamma \sim 1.7$. The intrinsic (absorption-corrected) luminosity is $L_{2-10~keV} \sim 1.3 \times 10^{42}$ \lum. These results provide strong evidence that an obscured AGN is present in the nuclear region of Hydra~A. We infer that the optical/UV emission of the AGN is mostly hidden by the heavy intrinsic reddening. In order to balance the photon budget of the nebula, we must either postulate that the ionizing spectrum includes a UV bump or invoke and additional power source (shocks in the cooling flow or interaction with the radio jets). Using an indirect estimate of the black hole mass and the X-ray luminosity, we infer that the accretion rate is low, suggesting that the accretion flow is advection dominated. %In this context, the %ionizing radiation from the AGN could power the LINER, if the spectral %energy distribution includes a ``UV bump''. Such a spectral feature %would not be inconsistent with an advection-dominated accretion flow. Finally, our results support current unification schemes for radio-loud sources, in particular the presence of the putative molecular torus in FR~Is. These observations underscore the power of the X-rays and of \chandra~in the quest for black holes.
|
[
{
"name": "hydra_rev.tex",
"string": "%\\documentstyle[12pt,aasms4]{article}\n%\\documentstyle[12pt,aasms4,flushrt]{article}\n\\documentstyle[11pt,aaspp4,flushrt]{article}\n% \\received{} \\accepted{~~}\n\n\\def\\oiii{[{\\sc O\\, iii}]}\n\\def\\oii{[{\\sc O\\, ii}]}\n\\def\\feka{Fe K$\\alpha$}\n\\def\\chandra{{\\it Chandra}} \n\\def\\asca{{\\it ASCA}} \n\\def\\rosat{{\\it ROSAT}} \n\\def\\lum{erg s$^{-1}$}\n\\def\\flux{erg cm$^{-2}$ s$^{-1}$}\n\\def\\nh{cm$^{-2}$}\n\n\\def\\cl{\\centerline}\n%\\input{psfig.tex}\n% in aasms4 use $\\gtrsim$ and $\\lesssim$\n\n\\begin{document}\n\n\\title{\\chandra~ uncovers a hidden Low-Luminosity AGN \\\\ \nin the radio galaxy Hydra~A (3C~218)}\n\n\\author{Rita M. Sambruna, George Chartas, and Michael Eracleous}\n\\affil{The Pennsylvania State University, Department of Astronomy and\nAstrophysics, 525 Davey Lab, State College, PA 16802 (email:\nrms@astro.psu.edu)} \n\n\\author{Richard F. Mushotzky}\n\\affil{NASA/GSFC, Code 662, Greenbelt, MD 20771}\n\n\\author{John A. Nousek} \n\\affil{The Pennsylvania State University, Department of Astronomy and\nAstrophysics, 525 Davey Lab, State College, PA 16802}\n\n\\begin{abstract}\n\nWe report the detection with \\chandra ~of a Low-Luminosity AGN (LLAGN)\nin the Low Ionization Emission Line Region (LINER) hosted by Hydra~A,\na nearby ($z$=0.0537) powerful FR~I radio galaxy with complex radio\nand optical morphology. In a 20 ks ACIS-S exposure during the\ncalibration phase of the instrument, a point source is detected at\nenergies $\\gtrsim$ 2 keV at the position of the compact radio core,\nembedded in diffuse thermal X-ray emission ($kT \\sim 1$ keV) at softer\nenergies. The spectrum of the point source is well fitted by a heavily\nabsorbed power law with intrinsic column density N$_H^{int} \\sim 3\n\\times 10^{22}$ \\nh~ and photon index $\\Gamma \\sim 1.7$. The intrinsic\n(absorption-corrected) luminosity is $L_{2-10~keV} \\sim 1.3 \\times\n10^{42}$ \\lum. These results provide strong evidence that an obscured\nAGN is present in the nuclear region of Hydra~A. We infer that the\noptical/UV emission of the AGN is mostly hidden by the heavy intrinsic\nreddening. In order to balance the photon budget of the nebula, we\nmust either postulate that the ionizing spectrum includes a UV bump or\ninvoke and additional power source (shocks in the cooling flow or\ninteraction with the radio jets). Using an indirect estimate of the\nblack hole mass and the X-ray luminosity, we infer that the accretion\nrate is low, suggesting that the accretion flow is advection\ndominated. %In this context, the\n%ionizing radiation from the AGN could power the LINER, if the spectral\n%energy distribution includes a ``UV bump''. Such a spectral feature\n%would not be inconsistent with an advection-dominated accretion flow.\nFinally, our results support current unification schemes for\nradio-loud sources, in particular the presence of the putative\nmolecular torus in FR~Is. These observations underscore the power of\nthe X-rays and of \\chandra~in the quest for black holes.\n\n\\end{abstract} \n\n\\noindent {\\underline{\\em Subject Headings:}} Galaxies: active --- \ngalaxies: individual (Hydra A, 3C~218) --- X-rays: galaxies. \n\n\\section{Introduction} \n\nRecent {\\it HST} and ground-based optical observations provided strong\nevidence that many nearby galaxies harbor supermassive black holes\n(e.g., Kormendy \\& Richstone 1995), possibly accreting at\nsub-Eddington luminosities (Fabian \\& Rees 1995). About 40\\% of nearby\nearly-type galaxies exhibit signs of mild nuclear activity, in the\nform of weak non-thermal radio cores (Sadler et al. 1989) and Low\nIonization Emission Lines (LINERs; Heckman 1986; Ho, Fillippenko, \\&\nSargent 1997a). These results collectively suggest that many nearby\ngalaxies may harbor weak nuclear activity in the form of a\nLow-Luminosity Active Galactic Nucleus (LLAGN; e.g., Ho 1999a).\n\nThanks to their high penetrating power, X-rays provide an optimal\nwindow to search for weak nuclear activity. Indeed, previous X-ray\n\\rosat~ images of a handful of galaxies show the presence of a central\nunresolved nucleus within the 5\\arcsec~ HRI resolution (e.g., Fabbiano\n1996). Indirect clues are provided by \\asca~ spectral constraints: a\nheavily absorbed power law component is often measured at energies\n$\\gtrsim 2$ keV, with intrinsic luminosities L$_{2-10~keV} \\sim\n10^{40-42}$ \\lum~, photon indices $\\Gamma_{2-10~keV} \\sim 1.5-1.7$,\nand a narrow Fe emission line at 6--7 keV in a few cases, suggestive\nof a LLAGN (Makishima et al. 1994; Ptak et al. 1999; Sambruna,\nEracleous, \\& Mushotzky 1999; Terashima et al. 1999). Within the\ncoarse angular resolution of these detectors, alternative scenarios\ncan not be ruled out in many cases (e.g., a starburst or X-ray\nbinaries). Unambiguous evidence for nuclear activity would be provided\nby the detection of a point source at the galaxy center. With its\nunprecedented angular resolution (0.5\\arcsec), wide-band coverage\n(0.2--10 keV), and high sensitivity, \\chandra~ is uniquely suited to\nthis task. \n\nIn this Letter, using recent \\chandra~calibration observations we\ndiscover a LLAGN in the LINER harbored by the nearby cD galaxy Hydra~A\n($z$=0.0537). Host of the powerful FR~I radio source 3C~218, Hydra~A\nis the dominant member of the poor cluster of galaxies A780, and\nfamous for its twin-jet radio morphology (Taylor et al. 1990).\n%and, in the local volume of space, is the second most powerful radio emitter\n%(second only to Cygnus~A). \nThe nuclear region contains a $\\sim$ 6\\arcsec~emission-line nebula\n(Baum et al. 1989; Heckman et al. 1989) and a disk of star formation\n%and lobes of excess blue light are present at $\\sim$ 2--3\\arcsec~on\n%either side of the core, probably due to active star formation\n(McNamara 1995; Melnick, Gopal-Krishna, \\& Terlevich 1997). At the\nposition of the nucleus, a LINER-like optical and UV spectrum is\nobserved (Hansen, J{\\o}rgensen, \\& N{\\o}rgaard-Nielsen 1995), which,\ntogether with the powerful lobe radio emission, led to the\nclassification of Hydra~A as a Weak Line Radio Galaxy (Tadhunter et\nal. 1998). The X-ray emission from Hydra~A in previous {\\it Einstein},\n\\rosat, and \\asca~ images is dominated by the cluster and the inner\n($\\lesssim$ 1.5\\arcmin) cooling flow, with $L^{cluster}_{0.5-4.5~keV}\n\\sim 2 \\times 10^{44}$ \\lum~ (David et al. 1990; Ikebe et al. 1997).\n\nIn the following, we assume a Friedman cosmology with $H_0=75$ km\ns$^{-1}$ Mpc$^{-1}$ and $q_0=0.5$. At the luminosity distance of\nHydra~A (217.46 Mpc), 1\\arcsec=0.95 kpc.\n\n\\section{Observations and Data analysis} \n\nHydra~A was observed with \\chandra~ ACIS-S for 20 ks on 1999 November\n11 at the aimpoint of S3 in faint telemetry mode with 5 CCDs turned\non. \n%For a description of the \\chandra~ payload and the ACIS\n%experiment, see O'Dell \\& Weisskopf (1998) and Lumb et al. (1993). \nThe data were analyzed using the \\verb+EventBrowser+ tool at Penn\nState, and the \\verb+CIAO+ software provided by the \\chandra~X-ray\nCenter. Only events for \\asca~ grades 0, 2, 3, 4, and 6 were\naccepted. The S3 background was rather stable during the observation.\n\nSpectral analysis was performed within \\verb+XSPEC+ v.10.0 using\nresponse files appropriate for the S3 aimpoint and for the epoch of\nthe present observation (\\verb+ccd7_c0.7.15.32.rmf+,\n\\verb+s3_c1_middle.arf+). The spectra were rebinned over the energy\nrange 0.2--6 keV to have a minimum of 20 counts in each bin, to\nvalidate the use of the $\\chi^2$ statistics. With a total count rate\nof $\\sim$ 0.02 c/s, pileup is not a concern. At this time of writing,\nthere appears to be an uncertainty of the order of 10\\% in the total\neffective area of the telescope mirror in the 1--2 keV energy\nrange. Fortunately, for the present analysis the energy range of\ninterest for the nuclear properties is restricted to energies above 2\nkeV, where the AGN component dominates. The errors in the on-axis\neffective area above 2 keV are of the order of 5\\% (Jerius et\nal. 2000). \n\nHydra~A was also observed with ACIS-I for 20 ks in 1999 October 30,\nafter the CCDs suffered radiation damage %due to exposure to collimated\n%high-energy protons from the Van Allen belts. \nresulting in a degradation of the gain and spectral resolution. \n%As a consequence of the increased Charge Transfer Inefficiency, the\n%gain and the spectral resolution of the ACIS-I CCDs were degraded,\n%making spectral analysis of these data difficult. \n%However, since the spectrum of the nucleus turned out to be\n%featureless in 2--6 keV in the ACIS-S data, \nTo improve the signal-to-noise ratio we extracted the ACIS-I spectrum\nof the nucleus in a region of similar size as for the ACIS-S\ndata, and analyzed the data using a position-dependent \n%Using calibration data, we built a position-dependent ACIS-I\nspectral response including an empirical CTI correction. The 2--6 keV\nACIS-I spectrum of the nucleus was fitted simultaneously to the ACIS-S\ndata leaving the intercalibration factors free to vary, giving a ratio\nof the two normalizations of $N_{ACIS-S}/N_{ACIS-I}=1.09 \\pm 0.22$.\n\n\\section{Results} \n\n%\\subsection{ACIS-S images} \n\nFigure 1 shows the S3 image of the central regions of Hydra~A in\n0.2--10 keV, with the VLA radio contours overlayed (Taylor et\nal. 1990). The ACIS-S data were adaptively smoothed using a Gaussian\nfunction with a kernel of 3.5\\arcsec~, and shifted by 3.6\\arcsec~to\nalign the X-ray and radio core and the other X-ray/radio morphology to\nbetter than 0.5\\arcsec. This shift is well within the range of\nuncertainties on the astrometry (0.5\\arcsec -- 5\\arcsec) measured in\nseveral other ACIS observations during the orbital activation and\ncheck-out phases. X-ray emission from the compact radio core is\nreadily apparent, embedded in diffuse soft X-ray emission. In the\n0.2--10 keV band, $\\sim$ 900 counts are detected within\n2.5\\arcsec~from the position of the radio core and the radial profile\nof the X-ray source is extended.\n%The presence of a diffuse soft component around the\n%nucleus in radio-loud sources is well established from previous\n%\\rosat~observations (Worrall \\& Birkinshaw 1994), extending from a few\n%kpc to cluster scales; a possible candidate is the halo of the host\n%galaxy. \nAt energies $\\gtrsim$ 2 keV, the radial profile is point-like and a\ntotal of $\\sim$ 150 counts are collected in 2--10 keV within\n1.5\\arcsec~ (or 80\\% of the total encircled energy). The hard X-ray\npoint source is also present in the 20 ks ACIS-I exposure. Thus, with\n\\chandra~we were able to detect a point-like X-ray source for the\nfirst time in Hydra~A at hard energies, indicating that the core radio\nemission is due to a hidden AGN. Interestingly, no X-ray emission is\ndetected from either the jets or lobes (Fig. 1). On the contrary, the\nextended radio structures appear to occupy regions relatively\ndeficient in X-ray photons. This is opposite to what recently detected\nwith \\chandra~ in the FR~II radio galaxy 3C~295 (Harris et al. 2000).\n\n%Also apparent in Figure 1 are two extended X-ray sources on the S-E\n%(source 1) and E (source 2) side of the nucleus, with source 1\n%matching faint radio emission. Source 1 has X-ray positions\n%$\\alpha^1_X$=09:18:6.2, $\\delta^1_X$=--12:05:47.3 (J2000), and $\\sim$\n%780 counts are detected in 0.2--10 keV within 2.5\\arcsec. Its optical\n%counterpart is a small nearby galaxy (Melnick et al. 1997). Note also\n%the embedded X-ray point source, most likely the ``second optical\n%nucleus'' reported by Ekers \\& Simkin (1983). Source 2 has\n%coordinates $\\alpha^2_X$=09:18:6.1, $\\delta^2_X$=--12:05:41.3 (J2000),\n%$\\sim$ 900 counts, and unclear optical counterpart.\n\nFigure 2 shows the inner 10\\arcsec~ region around the nucleus in\ncontour form, in 3.7--4.3 keV. The nuclear point source is apparent,\ntogether with extended faint emission elongated by $\\sim$ 3\\arcsec~ in\na N-W direction. Note the extension in the same direction in the radio\ncontours (Fig. 1). At roughly this distance, a spot of enhanced blue\nemission was observed in previous $B$ and $U$ band images, identified\nas the bluest edge of a star forming disk (McNamara 1995; Melnick et\nal. 1997). A total of $\\sim$ 260 counts are detected within 2\\arcsec~\nover the 0.2--10 keV band for this region. The study of the starburst\nand of the large-scale X-ray emission in Hydra~A are beyond the scope\nof this paper, and will not be discussed any further (see McNamara et\nal. 2000).\n \n%\\subsection{Nuclear X-ray spectrum} \n\nThe nuclear X-ray spectrum was extracted from a circular region with\nradius 1.5\\arcsec. The background was extracted in an annulus centered\non the nucleus with inner and outer radii 1\\arcmin~ and 1.3\\arcmin,\nrespectively. The cluster contribution in an area similar to the\nnuclear region is small, $\\sim$ 6\\%, while the instrumental and cosmic\nbackground is negligible, $\\sim 2 \\times 10^{-5}$ ph s$^{-1}$\narcsec$^{-2}$. The spectrum was fitted with a two-component model,\nincluding an absorbed power law at energies $\\gtrsim$ 2 keV, and a\nRaymond-Smith thermal plasma at softer energies. This model is a very\ngood description of the ACIS-S data, with $\\chi^2$=17 for 23 degrees\nof freedom. The data and residuals are shown in Figure 3. All\nspectral components in the fit were absorbed by the Galactic column\ndensity, N$_H^{Gal}=4.9 \\times 10^{20}$ cm$^{-2}$ (Dickey \\& Lockman\n1990).\n\n%In this small region, the X-ray contribution of the cooling flow is\n%small: converting from the \\rosat~surface brightness (Ikebe et\n%al. 1997), and assuming the gas is smoothly distributed in the inner\n%0.2\\arcmin~region, the ACIS-S surface brightness is $6.6 \\times\n%10^{-4}$ counts s$^{-1}$ arcsec$^{-2}$ in 0.2--10 keV, or $\\sim 4\n%\\times 10^{-3}$ counts s$^{-1}$ in a region of radius 1.5\\arcsec. This\n%is $\\sim$ 20\\% of the observed total ACIS-S count rate for the nuclear\n%region. \n\nThe fitted parameters of the absorbed power law are rest-frame column\ndensity N$_H^{int}=2.8^{+3.0}_{-1.4} \\times 10^{22}$ \\nh~ and photon\nindex $\\Gamma=1.75^{+1.14}_{-0.20}$ (uncertainties are 90\\% confidence\nfor one parameter of interest, $\\Delta\\chi^2$=2.7). This is the\nspectrum of the hard X-ray point source coincident with the radio core\nin Figure 1. The slope is consistent within 1$\\sigma$ with the average\nvalue measured with \\asca~for other Weak Line Radio Galaxies (WLRGs),\n$\\langle \\Gamma_{2-10~keV} \\rangle =1.49$ and dispersion\n$\\sigma_{\\Gamma}=0.30$ (Sambruna et al. 1999). The observed fluxes are\nF$_{0.2-2~keV} \\sim 9 \\times 10^{-15}$ and F$_{2-10~keV} \\sim 1.8\n\\times 10^{-13}$ \\flux. The intrinsic (absorption-corrected)\nluminosity is L$_{2-10~keV} \\sim 1.2 \\times 10^{42}$ \\lum, at the\nhigh-end of the distribution for WLRGs and LINERs.\n\nThe data require a thermal component at soft energies, with fitted\ntemperature $kT=1.05^{+0.32}_{-0.14}$ keV, consistent with the value\nmeasured for other radio sources with \\rosat~and \\asca~ (Worrall \\&\nBirkinshaw 1994; Sambruna et al. 1999). The abundance was fixed to the\nbest-fit value, 0.1 solar. The observed fluxes are F$_{0.2-2~keV}\n\\sim 3 \\times 10^{-14}$ and F$_{2-10~keV} \\sim 5 \\times 10^{-15}$\n\\flux. A possible origin of the thermal component is the halo of the\nhost galaxy. Indeed, the intrinsic luminosity is L$_{0.2-2~keV} \\sim 2\n\\times 10^{41}$ \\lum, consistent with the values measured for\nelliptical galaxies. Alternatively, the thermal component could be due\nto the cooling flow. \n%if the latter exhibits a local peak due to\n%small-scale ($\\lesssim$ 1.4 kpc) structures.\n\n%We also extracted the spectrum of the starburst component in Figure 2\n%and fitted it with a composite model including the same Raymond-Smith\n%model as for the nucleus, plus an additional thermal plasma component\n%described by \\verb+vmeka+ in \\verb+XSPEC+. The starburst spectrum is\n%very hot, $kT_{starb} \\gtrsim 5$ keV, and requires overabundant Ne\n%($A_{Ne} \\sim 34$ solar). This is similar to what measured with {\\it\n%SAX} for NGC~253 (Cappi et al. 1999). The spectral parameters are not\n%well determined as only $\\sim$ 260 counts were detected. The\n%absorption-corrected luminosities of the starburst are $L_{0.2-2~keV}\n%\\sim 1.5 \\times 10^{41}$ and $L_{2-10~keV} \\sim 2.7 \\times 10^{41}$\n%\\lum, respectively.\n\n\\section{Discussion and Conclusions}\n\nHydra~A is the second powerful radio galaxy observed with \\chandra,\nand the second instance where a nuclear X-ray point source is\ndetected. A luminous AGN was also discovered in an ACIS-S 20 ks image\nof the FR~II radio galaxy 3C~295 (Harris et al. 2000), with $\\Gamma\n\\sim 1.8$ and $L_{0.2-10~keV} \\sim 7 \\times 10^{43}$ \\lum. As in\nHydra~A, the AGN in 3C~295 resides in a cooling flow. These results\nconfirm that optically-weak, narrow-emission line radio sources harbor\ntrue AGNs as their brighter, broad-emission line Seyfert-like \ncounterparts. Thanks to \\chandra, a detailed study of the central\nengines of these systems becomes possible for the first time.\n\nThe large X-ray column density we measure in the nucleus of Hydra~A,\nN$_H^{int} \\sim 3 \\times 10^{22}$ \\nh, implies an optical extinction\n$A_V=10$, assuming galactic gas-to-dust ratios (Bohlin, Savage, \\&\nDrake 1978). This means that the optical and UV continuum from the AGN\nare strongly (factor $\\gtrsim 300$) suppressed, accounting for why the\nAGN was not previously detected at these wavelengths. The weak UV\ncontinuum detected in archival IUE spectra (Hansen et al. 1995 and our\nown inspection of an unpublished spectrum) cannot be due to the AGN;\nmost likely candidates are the starburst and/or the cooling flow.\nFuture {\\it HST} observations should detect only an extended thermal\ncomponent to the UV light.\n \nWe now turn to the issue of whether the LLAGN is capable of\nphotoionizing the emission-line nebula identified with the nucleus\n(Baum et al. 1989; Heckman et al. 1989). To make this assessment we\nfirst evaluate the total reddening to the nuclear emission-line\nsource, $E_{\\rm B-V}$. Since the nuclear spectrum resembles that of\nLINERs, we assume that the intrinsic Balmer decrement is\nH$\\alpha$/H$\\beta=3.1$ (e.g., Ho, Filippenko, \\& Sargent 1997b), leading\nto an estimate of $E_{\\rm B-V}\\approx 0.33$\\footnote{This is\nconsiderably higher than $E_{\\rm B-V}=0.15$ given by Hansen et\nal. (1995) based on the Ly$\\alpha$/H$\\beta$ ratio. Hansen et al. have\nprobably underestimated the reddening because the Ly$\\alpha$ flux was\nmeasured in the large IUE aperture which very likely includes a\ncontribution from the circumnuclear starburst region.}. With this\nvalue of the reddening and the H$\\beta$ flux measured by Hansen et\nal. (1995) we obtain the rate of emission of H$\\beta$ photons from the\nnebula as $Q_{\\rm H\\beta}=4.1\\times 10^{51}$~s$^{-1}$. If the H$\\beta$\nemission is the result of case~B recombination, then atomic physics\nimplies $Q_{\\rm H\\beta}=0.12\\; Q_{\\rm ion}$ (Osterbrock 1989), where\n$Q_{\\rm ion}$ is the ionizing photon rate from the active nucleus.\nThus, the observed H$\\beta$ flux requires that $Q_{\\rm ion}=(3.4\\times\n10^{52}/f_{\\rm c})$~s$^{-1}$, where $f_{\\rm c}$ is the covering\nfraction of the source by the nebula. In contrast, the observed\nionizing photon rate, assuming that the X-ray power-law spectrum\nextends all the way through the UV band, is $Q_{\\rm ion}=1.1\\times\n10^{52}$~s$^{-1}$, which falls short of the required rate by a\nconsiderable factor, even if $f_{\\rm c}=1$! In fact, if we model the\nspectral energy distribution (SED) of Hydra A after those observed in\nLINERs and other LLAGN, some of which are radio-loud (Ho 1999b), the\nproblem persists.\n\nIn order to balance the photon budget of the nebula, we must either\npostulate that the ionizing spectrum includes a UV bump or invoke and\nadditional power source. If we assume there is a UV bump, we can\nparameterize it following Mathews \\& Ferland (1987) and normalize the\nSED according to the \\chandra~ X-ray spectrum. We then find an\nionizing photon output rate of $Q_{\\rm ion}=6.4\\times\n10^{53}$~s$^{-1}$, which is more than enough to power the emission\nlines. \n% The UV bump may be somewhat weaker than the model of Mathews \\&\n% Ferland (1987) so as not to overproduce the rate of ionizing photons.\n% More specifically, if we adopt a covering factor for the\n% emission-line gas of $f_{\\rm c}=0.1$, then the UV bump must be about\n% a factor of 2 weaker than the model prescription. But even in this\n% case, the UV bump must be stronger than what is observed in the\n% LLAGNs of the Ho (1999b) collection. \nOn the other hand, one or more other power sources may contribute to\nthe ionization of the nebula. X-rays from shocks in the cooling flow\nare plausible (e.g., Heckman et al. 1989). Another possibility is\nmechanical interaction of the emission-line gas with the radio jets,\nwhich is particularly relevant since the images of Hansen et\nal. (1995) show superpositions of radio and emission-line knots.\n\nTo get a handle on the nature of the accretion flow, we compared the\nX-ray luminosity to the limiting Eddington luminosity through a rough\nestimate of the central black hole mass in Hydra~A, $M_{BH}$. The\napparent $V$ magnitude of the host galaxy in Hydra~A, $m_V=13.7$\n(Sandage 1973), and Figure 8 of Magorrian et al. (1998) imply $M_{BH}\n\\sim 4 \\times 10^9 M_{\\odot}$, consistent with the values dynamically\nmeasured in other giant ellipticals (e.g., Ford et al. 1994). The\nEddington luminosity is thus $L_{Edd} \\sim 5 \\times 10^{47}$\n\\lum. Assuming $L_X=0.1 L_{total}$, the luminosity relative to\nEddington is $L_{total}/L_{Edd} \\sim 2 \\times 10^{-5}$. This places\nHydra~A in the regime of an Advection-Dominated Accretion Flow (ADAF;\ne.g., Narayan, Mahadevan, \\& Quataert 1998), similar to other WLRGs\n(Sambruna et al. 1999). A powerful diagnostic of the accretion flow\nstructure in Hydra~A will be afforded by future higher-sensitivity\nX-ray observations, such as delivered by {\\it XMM}. The EPIC spectrum\nwill allow us to study in more detail the nuclear X-ray properties, in\nparticular whether an Fe line is present at 6--7 keV. The line energy\nand profile could allow us to discriminate between a standard\nSeyfert-like disk and an ADAF (e.g., Sambruna \\& Eracleous 1999).\n\n% The presence of an ADAF in Hydra~A does not preclude a modest UV\n% bump in the case where the transition radius between the ADAF and\n% the thin disk is rather small (of order a few tens of gravitational\n% radii; see the models of Gammie, Narayan \\& Blandford 1999). \n\nFinally, we note that the nuclear X-ray absorption in Hydra~A is much\nlarger (factor 10) than the optical/UV extinction to the emission-line\nnebula (see above), and consistent with the column measured in the\nradio toward the core (Taylor 1996). This suggests that the X-ray\nabsorber lies further in than the emission-line regions, close to the\ncentral black hole. A possible candidate is the molecular torus on\nparsec scales postulated by unification models (Urry \\& Padovani\n1995). Indeed, the radio and optical observations indicate an edge-on\ngeometry for Hydra~A (Taylor et al. 1990; Baum et al. 1989), such that\nthe torus intercepts the line of sight to the nucleus. Our results\nthus support current unification models for radio-loud sources and in\nparticular the presence of an obscuring torus in FR~I radio\ngalaxies. Clearly, large unbiased samples are needed to reach firmer\nconclusions, which we anticipate from \\chandra~in the next few years.\n\n%This result apparently contradicts a\n%recent claim, based on optical {\\it HST} data, that the nuclear\n%regions of FR~Is are not obscured (Chiaberge, Capetti, \\& Celotti\n%1999). Clearly, large unbiased samples are needed to reach firmer\n%conclusions, which we anticipate from \\chandra~in the next few years.\n\n%In conclusion, using \\chandra~data we discovered an obscured LLAGN in\n%the nearby LINER source Hydra~A. The AGN is bright enough to provide\n%at least half the photons needed to power the optical emission\n%lines. Our results support current unification models for radio-loud\n%sources and in particular the presence of an obscuring torus in FR~I\n%radio galaxies. \n\n% The present observations are a clear testimonial to the power of\n% X-rays in the quest for black holes. We can confidently anticipate\n% that in the next few years of operation, \\chandra~will truly\n% revolutionize our perception of nuclear activity in galaxies, with\n% profound implications for the AGN luminosity function, the origin of\n% the X-ray background, and the connection between AGNs and normal\n% galaxies.\n\n\\acknowledgements\n\nRMS acknowledges support from NASA contract NAS--38252. We are\ngrateful to Gordon Garmire and the ACIS team for making these\nobservations possible. We thank Joe Pesce for help with Figure 2, Niel\nBrandt for the \\verb+ASMOOTH+ routine, and Pat Broos and Scott Koch\nfor assistance with data retrieving and for the \\verb+TARA+ software.\nFinally, we are grateful to the referee, Yuichi Terashima, for his\nprompt and thoughtful comments and suggestions. \n\n\\newpage \n\n\\begin{references}\n\n\\reference {} Baum, S. A., Heckman, T. M., Bridle, A. H., van Breugel,\nW. J. M., \\& Miley, G. K. 1988, ApJS, 68, 833 \n\n\\reference {} Bohlin, R. 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M. \\& Birkinshaw, M. 1994, ApJ, 427, 134 \n\n\\end{references}\n\n\\newpage\n\n\\noindent{\\bf Figure Captions}\n\n\\begin{itemize}\n \n\\item\\noindent Figure 1: \\chandra~ACIS-S image in 0.2--10 keV of the\ncentral regions of Hydra~A, in a 20 ks calibration exposure. Radio VLA\ncontours at 6 cm are overlayed (Taylor et al. 1990). The ACIS-S image\nwas adaptively smoothed using a Gaussian function with a kernel of\n3.5\\arcsec, and shifted by 3.6\\arcsec~in declination to align the\nX-ray and radio core. X-ray emission from the compact radio core is\napparent, embedded in a diffuse halo, while the jets and lobes occupy\nregions deficient of X-rays. \n\n\\item\\noindent Figure 2: Contours of the inner region of Hydra~A at 4\nkeV. North is up and East is to the left. The intensity scale is\nlogarithmic with contour interval 0.4 or a factor 2.5 in\nintensity. The nuclear point source is apparent. A faint extended\nstructure is also present at $\\sim$ 3\\arcsec~ N-W of the nucleus,\nroughly at the position of the star formation region previously\ndetected in optical images (McNamara 1995; Melnick et al. 1997).\n\n\\item\\noindent Figure 3: The \\chandra~spectrum of the nuclear region\nin Hydra~A, extracted in a region of radius 1.5\\arcsec. The top panel\nshows the data convolved with the best-fit model, a highly absorbed\npower law at energies $\\gtrsim$ 2 keV and a soft thermal component\n(dotted lines). The bottom panel are the residuals in the form of\nratio of the data to the model. Crosses are ACIS-S data, asterisks are\nACIS-I data.\n\n\\end{itemize}\n\n\\end{document} \n\n\n"
}
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astro-ph0002202
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Recent Advances in Binary Star Formation Using SPH
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[
{
"author": "M. R. Bate"
}
] |
We review recent advances in the study of binary star formation that have been made using the smoothed particle hydrodynamics technique.
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[
{
"name": "proc.tex",
"string": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% %\n% Proceedings of 20 years of Numerical Astrophysics Template %\n% You can use it with the academic press style file which %\n% can be found at (http://www.apnet.com/www/journal/cp.htm). %\n% %\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\documentclass{cjour}\n\\usepackage{epsfig}\n\\textheight= 22.0cm\n\\voffset=2.0mm\n\n\\def\\simless{\\mathbin{\\lower 2pt\\hbox\n {$\\rlap{\\raise 5pt\\hbox{$\\char'074$}}\\mathchar\"7218$}}} % < or of order\n\\def\\simgreat{\\mathbin{\\lower 2pt\\hbox\n {$\\rlap{\\raise 5pt\\hbox{$\\char'076$}}\\mathchar\"7218$}}} % > or of order\n\n\\authorrunninghead{M. R. Bate}\n\\titlerunninghead{Recent Advances in Binary Star Formation Using SPH}\n\n\\begin{document}\n\n\\title{Recent Advances in Binary Star Formation Using SPH}\n\n%\\subtitle{This is a subtitle if you wish to include one.}\n\n\\author{Matthew R. Bate}\n\\affil{Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, United Kingdom}\n\\email{mbate@ast.cam.ac.uk}\n%\\and\n%\\author{While The Second Author is}\n%\\affil{From Somewhere else.}\n%\\email{secondauthor@somewhere.else}\n\n\\abstract{We review recent advances in the study of binary star formation that have been made using the smoothed particle hydrodynamics technique.}\n\n\\begin{article}\n\n%% Section headings:\n\\section{Introduction}\n \nThe Smoothed Particle Hydrodynamics (SPH) numerical method \nwas introduced by Lucy \\cite{Lucy77} and \nGingold and Monaghan \\cite{GinMon77}. Its first application\nwas in the field of star formation, where it was used to \nstudy whether or not a rapidly-rotating polytrope could undergo\nfission to form a close binary system \\cite{Lucy77, GinMon78}.\nSince this initial application, SPH has been widely used in the\nstudy of star formation, for example \\cite{GinMon81, \nMiyHayNar84, Lattanzioetal85, Durisenetal86, SigKla97, \nBonBas91, BatBonPri95, Heller93, NelPap93, ArtLub94,\nLarwoodetal96, Nelsonetal98, VanCam98, \nChapmanetal92}.\n\nSPH is has many attributes which make it particularly \nwell suited to the study of star formation.\nSPH is Lagrangian and does not require a computational grid.\nThus, it can efficiently follow problems with large density \ncontrasts since computational effort is not wasted simulating \nthe low-density regions. Also, recent SPH implementations \n\\cite{Evrard88, HerKat89, Benz90, Monaghan92} use spatially \nand temporally varying smoothing lengths so that the resolution \nincreases automatically with increasing density; the complex \nmulti-grid and adaptive-grid schemes that are used for \nfinite difference methods are avoided.\n\nIn this proceedings, we review some of the recent advances\nin the study of binary star formation that have been made using \nSPH. In Section \\ref{jeansmass}, we discuss the importance of\nalways resolving the Jeans mass in numerical studies of self-gravitating\ngas. While this has been demonstrated using various types of \nhydrodynamic code, we concentrate specifically on the problems\nthat can arise if this criterion is not obeyed with SPH.\nIn Section \\ref{collstellar}, we demonstrate that, for the first time, \nit is now possible to perform three-dimensional hydrodynamic \ncalculations which follow the collapse of a molecular cloud \ncore to stellar densities. These calculations are performed with\nSPH. Finally, in Section \\ref{accretion}, \nwe discuss how SPH has been used to study the evolution of a \nprotobinary system as it accretes from an infalling gaseous \nenvelope and how this work can lead to predictions\nof the properties of binary stars.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig01.eps, width=13cm}\n\\caption{\\label{bate.forces} The ratio of the gravitational force \nto pressure force between two SPH particles in a Jeans-mass\nclump of gas of radius $R=h$. The gravitational softening length\nis $\\epsilon$ and the hydrodynamic smoothing length is $h$.}\n\\end{center}\n\\end{figure}\n\n\\section{The Importance of Resolving the Jeans Mass}\n\\label{jeansmass}\n\nIt has recently been realised that it is important that the Jeans\nmass/length is always resolved during a hydrodynamical calculation. \nThis has been demonstrated both with SPH \\cite{BatBur97, Whitworth98}\nand with grid-based codes \\cite{Trueloveetal97, Trueloveetal98, Boss98}. \nIf this criterion is not obeyed, artificial \nfragmentation can be induced, or fragmentation can be inhibited. \nEssentially this is because when the resolution length/mass \napproaches the Jeans length/mass, collapse is artificially delayed\ndue to viscous forces, softening of gravitational forces, or a combination\nof both. A good example is the collapse of an isothermal \nfilament \\cite{Trueloveetal97}. Such a filament should collapse\nwithout limit to a filamentary singularity without fragmenting. \nHowever, if the collapse perpendicular to the major-axis is delayed, small\ndensity perturbations along the filament may have enough time to grow \nto non-linear amplitudes and fragments may\nform along the bar.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig02.eps, width=10cm}\n\\caption{\\label{bate.massden} Maximum density versus time for during the\ncollapse of a molecular cloud core [8]. Three calculations were \nperformed using SPH with $\\epsilon=h$. The smoothing\nlengths were allowed to vary with time and space freely (solid line) or \nsubject to\na minimum length of 5\\% (dotted line) or 10 \\% (dashed line) of the\ninitial cloud radius. When the minimum Jeans length in the \ncalculation is less than or approximately equal to the smoothing/softening\nlength, the collapse is delayed.\n}\n\\end{center}\n\\end{figure}\n\nBate \\& Burkert \\cite{BatBur97} first demonstrated the need for the\nJeans mass criterion using self-gravitating SPH calculations. With\nSPH, the problem can be understood by considering the \ngravitational and pressure forces between two particles \nwithin a marginally Jeans-stable clump of gas of radius $R\\approx h$\n(Figure \\ref{bate.forces}). SPH codes typically soften \nthe gravitational forces between neighbouring particles, using either \nthe Plummer force law or kernel softening \n\\cite{GinMon77, HerKat89, Benz90}. The\ncharacteristic gravitational softening length, $\\epsilon$, \nmay or may not be equal to the SPH hydrodynamic smoothing \nlength, $h$, depending on the specific implementation.\nIf $\\epsilon=h$, the ratio of the gravitational and \npressure forces between two particles is approximately \nconstant for particle with separations $\\simless h$.\nThus, a Jeans-unstable clump of gas will collapse, while a \nJeans-stable clump will be supported. However, although the\nratio of the gravitational and pressure forces is approximately \nindependent of the separation of the particles, the magnitude \nof the gravitational force decreases with separation due to \nthe softening. Thus, while a Jeans-unstable clump of gas with \na size much larger than the resolution length, $h$, \nwill collapse at the correct rate, the collapse of clumps with \na size $\\approx h$ will be delayed. This is demonstrated\nin Figure \\ref{bate.massden}. \n\nUnfortunately, the effect is not always limited to a simple delay of \nthe collapse. Given the right problem, artificial fragmentation\ncan be induced (such as with the filament described above), \nor inhibited. In Figure \\ref{bate.80000} we show how the collapse\nof a particular molecular cloud core with an initial $m=2$ \ndensity perturbation results in a binary protostellar system\nwith a bar of gas between them. This calculation was performed\nwith $8\\times 10^4$ particles, enough to resolved the Jeans mass/length\nuntil after the binary had formed. However, performing\nthe same calculation with $1\\times 10^4$ particles gives a different\nresult: a single, dense bar of gas without the binary. In this \ncalculation, the Jeans mass becomes unresolved before $t=1.20$\nand the collapse of each of the two over-dense regions resulting from the \noriginal $m=2$ density perturbation is delayed. The collapse of the\nlarger-scale elongated region, however, continues, leading to \nthe formation of a bar rather than a binary.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig03.eps, width=12.5cm}\n\\vspace{0.25truecm}\n\\caption{\\label{bate.80000} Collapse and fragmentation of a \nmolecular cloud core to form a binary [8]. The initial cloud had an initial\n10\\% $m=2$ density perturbation. The local Jeans mass/length is unresolved\ninside the thick density contour. The calculation was performed\nwith $8\\times 10^4$ particles.\n}\n\\vspace{-0.5truecm}\n\\end{center}\n\\end{figure}\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig04.eps, width=12.5cm}\n\\vspace{0.25truecm}\n\\caption{\\label{bate.10000} Same as Figure 3, except that the calculation\nwas performed with $1\\times 10^4$ particles. When $t \\simgreat 1.20$,\nthe region within which the binary formed in the $8\\times 10^4$-particle\ncalculation becomes unresolved, collapse of the two over-dense\nregions is delayed, and the calculation eventually produces a dense\nbar instead of a binary.\n}\n\\vspace{-1.0truecm}\n\\end{center}\n\\end{figure}\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig05.eps, width=12.5cm}\n\\vspace{0.25truecm}\n\\caption{\\label{bate.10000eh} Same as Figure 4, except that the calculation\nwas performed with $\\epsilon=1.0\\times 10^{14}$ cm (i.e.~$e<h$) \ninstead of $e=h$.\nWhen the local Jeans-mass becomes unresolved ($t \\simgreat 1.20$),\nthe calculation becomes susceptible to artificial fragmentation.\nInstead of a binary being formed, each of the two over-dense\nregions undergoes binary fragmentation \nso that the final result is a quadruple system.\n}\n\\end{center}\n\\end{figure}\n\nIt is important to note that, with SPH, the effect of not \nresolving a Jeans mass also depends on the way the\ngravitational softening and hydrodynamic smoothing are implemented!\nIf $\\epsilon < h$, the ratio of the gravitational to pressure forces\nbetween two particles increases with decreasing separation \n(Figure \\ref{bate.forces}). This\nmay lead to an instability in which a group of particles within\na Jeans-stable clump collapse artificially. As demonstrated in\nFigure \\ref{bate.10000eh}, this can lead to artificial \nfragmentation. Alternately, if $\\epsilon > h$, the pressure forces\nbetween particles within a Jeans-unstable clump may exceed the \ngravitational forces and the clump will be artificially supported\nagainst collapse.\n\nClearly, the best SPH implementation is one where $\\epsilon=h$ always.\nIn this case, collapse of Jeans-unstable clumps with a size \nsimilar to that of the resolution length will still be \ndelayed, but the possibilities of\nartificial collapse within Jeans-stable clumps or the supporting\nof Jeans-unstable clumps against collapse are eliminated. Then,\nin order to avoid the collapse of Jeans-unstable clumps being\ndelayed significantly, enough particles should be used so that\nthe Jeans length/mass is always resolved. \n\nHow many particles\nare necessary to ensure that the Jeans length/mass is resolved?\nWith SPH, the spatial resolution \nis given by the smoothing length which is usually variable in \ntime and space. The smoothing lengths are set by ensuring that \neach particle contains a certain number of neighbours, \n$N_{\\rm neigh}$, or equivalently a fixed mass, within two \nsmoothing lengths. Thus, in contrast to a grid-based code \nwhich has spatially-limited resolution, SPH has mass-limited \nresolution which {\\it automatically} gives greater spatial \nresolution in regions of higher density. Therefore, with SPH,\nit is necessary to ensure that the minimum resolvable mass is \nalways less than the Jeans mass. In practice, Bate \\& Burkert \nfound that a Jeans mass should always \nbe represented by at least $\\approx 2 N_{\\rm neigh}$ particles. \n\\newpage\n\n\\section{Collapse of a Molecular Cloud to Stellar Densities}\n\\label{collstellar}\n\nThe mass-limited resolution of SPH is ideal for studying the \ncollapse and fragmentation of molecular cloud cores because \nthere is a minimum Jeans mass in the problem \n(Figure \\ref{bate.tmr}). By contrast,\nthere is no minimum Jeans length. This is a problem \nfor grid-based codes which must resort to nested or \nadaptive grids \\cite{ BurBod93, Trueloveetal97, Trueloveetal98}. \nWith SPH, if the number of \nparticles used is sufficient to resolve the minimum Jeans mass, a \ncalculation can be followed to arbitrary densities with the required\nspatial resolution given automatically with increasing density.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig06.eps, width=12cm}\n\\caption{\\label{bate.tmr} The gas temperature $T$ (solid line), Jeans \nmass $M_{\\rm J}$ (dotted line), and Jeans radius $R_{\\rm J}$ (dashed \nline), as a function of density in a collapsing molecular cloud core \n(adapted from Tohline [36]). The minimum Jeans mass of \n$ \\approx 4 \\times 10^{-4}~{\\rm M}_{\\odot}$ occurs \nat a density of $\\sim 10^{-3} {\\rm \\ g \\ cm}^{-3}$.}\n\\end{center}\n\\end{figure}\n\n\nRecently, this ability of SPH was used to perform the first \nthree-dimensional calculations ever to follow the collapse of\na molecular cloud core to stellar densities \\cite{Bate98}.\nThe calculations followed the collapse of an initially \nuniform-density molecular cloud core of mass $M=1 {\\rm \\ M}_\\odot$ and\nradius $R=7 \\times 10^{16} {\\rm \\ cm}$.\n\nThe minimum resolvable mass in the SPH code was \n$\\approx 2 N_{\\rm neigh} = 100$ particles. Thus, to enable the\nminimum Jeans mass during the calculation\n($\\approx 4 \\times 10^{-4}\\ {\\rm M}_{\\odot}$)\nto be resolved, the calculation used $3 \\times 10^5$ \nequal-mass particles.\n\nThe code did not include radiative transfer. Instead, to model \nthe behaviour of the gas during the different phases of collapse,\na piece-wise polytropic equation of state, $P=K \\rho^{\\gamma}$, was\nused, where $P$ is the pressure, $\\rho$ is the density, $K$ \ngives the entropy of the gas, and the ratio of specific heats, \n$\\gamma$, was varied as\n\\begin{equation}\n\\label{polytropic}\n\\gamma = \\cases {\\begin{array}{lll}\n1 & & \\rho \\leq 1.0 \\times 10^{-13} \\cr\n7/5 & \\ 1.0 \\times 10^{-13} < \\hspace{-6pt} & \\rho \\leq 5.7 \\times 10^{-8} \n\\cr\n1.15 & \\ 5.7 \\times 10^{-8\\ } < \\hspace{-6pt} & \\rho < 1.0 \\times 10^{-3} \\cr\n5/3 & & \\rho > 1.0 \\times 10^{-3} \\cr\n\\end{array}}\n\\end{equation}\nwhere the densities are in ${\\rm g\\ cm}^{-3}$ \n(see Figure \\ref{bate.tmr}).\nThe values of $\\gamma$ and the transition densities \nwere derived from Tohline \\cite{Tohline82}. The variable value of $\\gamma$ \nmimics the following behaviour of the gas. The\ncollapse is isothermal ($\\gamma=1$) until the gas becomes optically thick \nto infrared radiation \nat $\\rho \\approx 10^{-13} {\\rm \\ g \\ cm}^{-3}$, beyond which $\\gamma=7/5$\n(appropriate for a diatomic gas).\nWhen the gas reaches a temperature of $\\approx$ 2000 K \n($\\rho = 5.7 \\times 10^{-8} {\\rm \\ g \\ cm}^{-3}$), molecular \nhydrogen begins to dissociate and the temperature only slowly increases\nwith density. In this phase $\\gamma = 1.15$ is used to \nmodel {\\it both} the decreasing mean molecular weight and the slow increase \nof temperature with density, the latter of which has an effective \n$\\gamma \\approx 1.10$.\nFinally, when the gas has fully dissociated\n($\\rho \\approx 10^{-3} {\\rm \\ g \\ cm}^{-3}$), the gas is monatomic and\n$\\gamma=5/3$. The value of $K$ is\ndefined such that when the gas is isothermal, $K = c_{\\rm s}^2$\nwith $c_{\\rm s} = 2.0 \\times 10^4 {\\rm \\ cm\\ s^{-1}}$, and when $\\gamma$\nchanges the pressure is continuous.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig07.eps, width=12.5cm}\n\\caption{\\label{bate.static} Radial density and velocity profiles of \nthe collapsing molecular cloud core with the one-dimensional grid \ncode (solid) and the three-dimensional SPH code (dotted). \nThe profiles are compared when the central density in each calculation \nis a) $10^{-14}$, b) $10^{-11}$, c) $10^{-9}$, d) $10^{-6}$, \ne) $10^{-3}$, and f) $10^{-1}$ g cm$^{-3}$.}\n\\end{center}\n\\end{figure}\n\n\\subsection{Collapse of an initially-static cloud}\n\nTo test that the above equation of state captures the important elements\nof the gas's behaviour, spherically-symmetric,\none-dimensional (1-D), finite-difference calculations were performed\nof the collapse of an initially-static molecular cloud core \nwith the above parameters and equation of state.\nThe results are shown in Figure \\ref{bate.static} (solid line). \nThese results \nare in good agreement with the results from 1-D calculations \nincorporating radiative transfer \n(e.g.\\ Larson 1969; Winkler \\& Newman 1980a, b).\n\nThe three-dimensional (3-D) SPH code was also tested on the same \nproblem to check that the SPH code can indeed accurately resolve the \ncollapse down to stellar densities \n(Figure \\ref{bate.static}, dotted line). \nThere is excellent agreement between the results from the 1-D \nfinite-difference code and those from the 3-D SPH code.\n\n\n\\subsection{Collapse of a rotating cloud}\n\nThree-dimensional calculations are required if the molecular\ncloud core is rotating. In Figures \\ref{bate.rotmassdens} to\n\\ref{bate.finalstate2} we present results from the collapse\nof a cloud core which is identical to that in the previous \nsection, but which is initially in solid-body rotation with\nangular frequency $\\Omega=7.6 \\times 10^{-14}$ rad s$^{-1}$.\nThus, the ratio of rotational energy to the magnitude of the \ngravitational potential energy is $\\beta=0.005$ (i.e.~the cloud\nis rotating quite slowly).\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig08.eps, width=12cm}\n\\caption{\\label{bate.rotmassdens} Maximum density (solid line) \nand maximum temperature (dotted line) versus time for the collapsing \nmolecular cloud core. Time is given in units of the initial free-fall \ntime ($t_{\\rm ff}=1.785 \\times 10^{12}$ s). The right graph has \nexpanded axes to show the second collapse phase in greater detail.}\n\\end{center}\n\\end{figure}\n\n\\begin{figure}[b]\n\\begin{center}\n\\vspace{8.4truecm}\n%\\epsfig{file=fig09.eps, width=12cm}\n\\caption{\\label{bate.bar} A time sequence showing the density in \nthe plane perpendicular to the rotation axis during the dynamic, \nrotational, bar instability of the first hydrostatic core. The\npanels cover the period from $t\\approx 1.023-1.030$ t$_{\\rm ff}$.\nSee also the MPEG animation on this CD-ROM: bate1.mpg.\n}\n\\end{center}\n\\end{figure}\n\nThe evolution of the calculation is as follows \n(Figure \\ref{bate.rotmassdens}). \nThe initial collapse is isothermal. When the density surpasses\n$10^{-13}$ g cm$^{-3}$, the gas in the center \nis assumed to become optically thick\nto infrared radiation and begins to heat ($t=1.009~t_{\\rm ff}$).\nThe heating stops the collapse at the center and the first hydrostatic core\nis formed ($t=1.015~t_{\\rm ff}$) with maximum density \n$\\approx 2 \\times 10^{-11}$ g cm$^{-3}$, mass \n$\\approx 0.01 {\\rm \\ M}_\\odot$ ($\\approx 3 \\times 10^3$ particles), and radius \n$\\approx 7$ AU. As the first core accretes, its maximum\ndensity only slowly increases at first.\nHowever, the first core is rapidly rotating, oblate, and has \n$\\beta \\approx 0.34 > 0.274$, making it dynamically unstable to the\ngrowth of non-axisymmetric perturbations \n\\cite{Durisenetal86, ImaDurPic99}. \nAt $t \\approx 1.023~t_{\\rm ff}$, after about 3 rotations, \nthe first core becomes violently bar-unstable\nand forms trailing spiral arms (Figure \\ref{bate.bar}). This leads\nto a rapid increase in maximum density (Figure \\ref{bate.rotmassdens})\nas angular momentum is removed from\nthe central regions of the first core (now a disc with spiral structure) \nby gravitational torques ($t=1.023-1.030~t_{\\rm ff}$). An MPEG animation of \nthis bar instability is provided on this CD-ROM (bate1.mpg).\nWhen the maximum temperature reaches 2000 K, molecular hydrogen begins to\ndissociate, resulting in a rapid second collapse to stellar densities\n($t=1.030~t_{\\rm ff}$). The collapse is again halted at a density of \n$\\approx 0.007$ g cm$^{-3}$ with the formation of the second hydrostatic, \nor stellar, core. The initial mass and radius of the stellar core are \n$\\approx 0.0015 {\\rm \\ M}_\\odot$ ($\\approx 5 \\times 10^2$ particles) \nand $\\approx 0.8 {\\rm \\ R}_\\odot$, \nrespectively. Finally,\nan inner circumstellar disc begins to form around the stellar \nobject, within the region undergoing second collapse. The \ncalculation is stopped when the stellar object has a mass of \n$\\approx 0.004 {\\rm \\ M}_\\odot$ ($\\approx 1.2 \\times 10^3$ particles), \nthe inner circumstellar disc has extended out to $\\approx 0.1$ AU, \nand the outer disc (the remnant of the first hydrostatic core) contains \n$\\approx 0.08 {\\rm \\ M}_\\odot$ ($\\approx 2.4 \\times 10^4$ particles) \nand extends out to $\\approx 70$ AU. Note that the massive outer \ndisc forms {\\it before} the stellar core.\nThis final state is illustrated in Figures \\ref{bate.finalstate}\nand \\ref{bate.finalstate2}.\nIf the calculation was evolved further, the inner circumstellar disc would \ncontinue to grow in radius as gas with higher angular momentum fell in.\nEventually, the inner disc would meet the outer disc with only a\nsmall molecular dissociation region between the two.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig10.eps, width=12cm}\n\\caption{\\label{bate.finalstate} The state of the system at the end of \nthe calculation. The left graph gives the density (solid line) and \nsmoothing length (dashed line) as a function of radius and the mass \nenclosed within radius $r$ of the center of the stellar core (dotted line). \nThe right graph gives the radial (solid line) and rotational (dotted line) \nvelocities as functions of radius from the center of the stellar core. \nThe densities, smoothing lengths and velocities are the mean values in \nthe plane perpendicular to the rotation axis and through the stellar core. \nThe stellar core ($r<0.004$ AU), inner circumstellar disc \n($0.004<r<0.1$ AU), region undergoing the second collapse ($0.1<r<1$ AU), \nouter circumstellar disc formed from the first core ($1<r<60$ AU), \nand isothermal collapse region ($r>60$ AU) are clearly visible.}\n\\end{center}\n\\end{figure}\n\n\\begin{figure}[t]\n\\begin{center}\n\\vspace{18.0truecm}\n%\\epsfig{file=fig11.eps, width=12.0cm}\n\\caption{\\label{bate.finalstate2} The state of the system at the end of \nthe calculation (not a time sequence). \nThe upper six panels give the density in the plane \nperpendicular to the rotation axis and through the stellar \ncore. The lower six panels give the density in a \nsection down the rotation axis. In each case, the six consecutive panels \ngive the structure on a spatial scale that is 10 times smaller than the \nprevious panel to resolve structure from 3000 AU to \n$\\approx 0.2~{\\rm R}_\\odot$. The remnant of the first hydrostatic \ncore (now a disc with spiral structure), the inner circumstellar disc, \nand the stellar core are all clearly visible. The logarithm of the \ndensity is plotted with the maximum and minimum \ndensities (in g~cm$^{-3}$) given under each panel. }\n\\vspace{-1.0truecm}\n\\end{center}\n\\end{figure}\n\n\n\\subsection{Close binary stellar systems}\n\nThe ability to perform three-dimensional calculations which follow\nthe collapse of molecular cloud cores to stellar densities allows\nus to study the formation of close ($\\simless 1$ AU) binary\nstellar systems. Currently, there is no accepted mechanism for \nforming close binaries; the proposal that close binary systems form\nvia the fission of a rapidly-rotating protostellar object \nhas been discredited by studies of rapidly-rotating \npolytropes \\cite{Durisenetal86}. Although fission\nitself appears not to operate, it is possible that fragmentation\ncan still occur due to the growth of non-axisymmetric perturbations\nin rotationally-supported objects. Only two studies have \nlooked at this possibility in detail \\cite{Boss87, BonBat94b}, and the\nlatter of these finds that fragmentation of a massive circumstellar\ndisc on scales ($\\simless 1$ AU) may be possible. However, in both\nthese studies, only the region inside the first hydrostatic\ncore was modelled and the initial conditions were chosen somewhat\nartificially. The ability to perform three-dimensional \ncalculations which follow the collapse of molecular cloud \ncores to stellar densities now allows us to study the formation of\nclose binaries from the collapse of larger-scale ($\\approx 10000$ AU)\nmolecular cloud cores.\n\n\n\\section{The evolution of an accreting protobinary system}\n\\label{accretion}\n\nThe favoured mechanism for the formation of most binary stellar\nsystems is the fragmentation of a collapsing molecular cloud core.\nFragmentation has been studied numerically for $\\approx 20$ years.\nThese calculations appear to show that it is possible to form binaries \nwith similar properties to those that are observed via fragmentation. \nHowever, they have not allowed us to predict the fundamental properties of \nstellar systems such as the fraction of stellar systems which \nare binary or the properties of binary \nsystems (e.g.~the distributions of mass ratios,\nseparations, and eccentricities and the properties of \ndiscs in pre-main-sequence systems).\n\n\nThere are two primary reasons for this lack of predictive power. \nFirst, the results of fragmentation calculations depend sensitively\non the initial conditions, which are poorly constrained.\nThe second problem is that of accretion. Fragmentation \ncalculations are typically stopped soon after the fragmentation\noccurs, when the binary or multiple protostellar system contains \nonly a small fraction of the total mass of the\noriginal cloud \\cite{Boss86, BonBat94b}. However, because much\nof the gas contained in the original cloud still has to fall on \nto the system and be accreted, \nthe final properties of the stellar system are \nunknown. Following the calculation significantly beyond the\npoint at which fragmentation occurs is extremely computationally \nintensive. Thus, it is impossible to perform the number of \ncalculations that are required to predict the statistical properties of \nbinary stellar systems -- even if we knew the distribution of the \ninitial conditions. On the other hand, if we can overcome this second\ndifficulty, we can make theoretical predictions about the properties\nof binary stars and, by comparing these predictions to the observed\nproperties of binary systems, we may be able to better constrain\nthe initial conditions for star formation.\n\n\\subsection{The Effects of Accretion on a Protobinary System}\n\nUsing SPH, Bate \\& Bonnell \\cite{BatBon97} studied and quantified how \nthe properties of a binary system are affected by the accretion \nof a small amount of gas from an infalling gaseous envelope. \nThey found that the effects depend primarily on the specific \nangular momentum of the gas and the binary's mass ratio \n(see also \\cite{Artymowicz83, Bate97}). Generally, accretion of gas \nwith low specific angular momentum decreases the mass ratio and \nseparation of the binary, while accretion of gas with high \nspecific angular momentum increases the separation and drives the \nmass ratio toward unity. From these results, they predicted \nthat closer binaries should have mass ratios that are biased \ntoward equal masses compared to wider systems, since the gas which\nfalls on to a closer system is likely to have more specific angular\nmomentum, relative to the binary, than for a wider system.\n\n\\begin{figure}[t]\n\\begin{center}\n\\vspace{9truecm}\n%\\epsfig{file=fig12.eps, width=13cm}\n\\caption{\\label{bate.accretion} The dependence of the \ndistribution of gas around an accreting protobinary system\non the specific angular momentum of the infalling gas \n(increasing from left-to-right and downward). For gas with low\nspecific angular momentum, only the primary forms a circumstellar\ndisc and the secondary accretes a small amount of gas via a\nBondi-Hoyle-type accretion stream. For gas with intermediate angular \nmomentum, both the primary and secondary form circumstellar discs.\nFor gas with high angular momentum, two circumstellar discs and\na circumbinary disc are formed. Finally, for the case with\nthe highest angular momentum, all the infalling gas settles into\na circumbinary disc. The\nbinary has a mass ratio of $q=0.6$ and the primary is on \nthe right.\n}\n\\end{center}\n\\end{figure}\n\nThey also studied the process of disc formation around an \naccreting protobinary system and found that for each protostar,\na circumstellar disc was only formed if the specific angular \nmomentum of the infalling gas was greater than the specific\norbital angular momentum of that protostar about the centre of\nmass of the binary (Figure \\ref{bate.accretion}). This is because,\nto be capture by one of the protostars, the gas much achieve the\nsame specific orbital angular momentum as that of the protostar.\nIf the gas has more specific angular momentum initially, some of its\nangular momentum goes into forming a disc around the protostar.\nHowever, if it has less specific angular momentum initially, there is\nno excess angular momentum to form a circumstellar\ndisc, and it must gain angular momentum even to be captured by\nthe protostar. In this case, the infalling gas gains angular \nmomentum as it falls on to the protostar in a Bondi-Hoyle-type accretion\nstream. In practice, \nthis means that a circumstellar disc is almost always formed around\nthe primary, but the secondary does not have a circumstellar disc\nunless the infalling gas has more specific angular momentum that\nsome critical value. In a similar way, the formation of a circumbinary \ndisc only begins when the specific angular momentum of the infalling\ngas is great enough for the gas to form a circular orbit at a radius\ngreater than that of the secondary from the centre of mass of the\nbinary.\n\n\n\\subsection{Development of a Protobinary Evolution Code}\n\nUsing the quantitative results of Bate \\& Bonnell \\cite{BatBon97}, \nBate \\cite{Bate2000} developed a protobinary evolution (PBE) code \nwhich follows the evolution of a protobinary system as it accretes \nfrom its initial to its final mass, but does so in far less time \nthan would be required for a full hydrodynamic calculation. \n\nThis code is based on the following model for the \nformation of binary stellar systems (Figure \\ref{bate.model}). \nThe model begins with a \nmolecular cloud core of known initial density and angular \nmomentum profile. It is assumed that this cloud begins to collapse\nand that a `seed' binary system\nis formed at the centre, presumably \nvia some sort of fragmentation. The `seed' binary has mass \nratio $q \\leq 1$,\nseparation $a$, and is assumed to have a circular orbit.\nIt initial consists of only a small fraction of the total mass of the core\nand is assumed to have formed from the gas that was originally\ncontained within a sphere of radius $r$, at the centre of the initial \ncloud (Figure \\ref{bate.model}). For the results presented in\nthis proceedings, the separation of the `seed' binary is set by assuming\nthat the angular momentum of the gas from which the binary \nforms is equal to the orbital angular momentum of the binary.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig13.eps, width=7cm}\n\\caption{\\label{bate.model} The model for studying the evolution of a \nprotobinary system that forms within a collapsing molecular cloud \ncore and is built up to its final mass by accreting the remaining \ngas as it falls on to the binary.}\n\\end{center}\n\\end{figure}\n\nSubsequently, the binary accretes the remainder of the initial \ncloud (which falls on to the binary) and the binary's \nproperties evolve due to the accretion. This evolution is calculated\nby taking a thin shell of gas of thickness d$r$ \n(Figure \\ref{bate.model}), surrounding the\nsphere from which the binary was formed, dividing the shell into \nsmall elements of gas, and calculating the effect that each \nelement of gas has on the protobinary when it is accreted\n(using the results of Bate \\& Bonnell \\cite{BatBon97}). \nThe binary's parameters (masses and separation) are updated,\nand the next shell of gas is considered until the whole cloud \nis accreted on to the binary. The amount of gas which settles \ninto a circumbinary disc is also recorded. In this way, the code\ncalculates the \nevolution of the binary from its initial to its final state when\nall of the original cloud's gas is contained\neither in one of the two stars or their surrounding discs.\n\n\n\\subsection{Testing the Protobinary Evolution Code}\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig14.eps, width=12.5cm}\n\\caption{\\label{bate.testcase1} First comparison of the results from \nthe protobinary evolution (PBE) code (solid lines) with those from a full SPH \ncalculation (dotted lines). \nThe graphs show the evolution of a protobinary system \nthat was formed in the centre of a collapsing molecular cloud core \nwhich initially had a uniform-density profile and was in solid-body \nrotation. The evolution of the (a; upper left) mass ratio, (b; upper \nright) separation, (c; lower) ratio of mass in a circumbinary disc \nto that of the binary are plotted \nas the binary accretes gas from the infalling envelope.}\n\\end{center}\n\\end{figure}\n\nTo test how accurately the PBE code describes the evolution \nof a `seed' binary as it accretes from its initial to \nits final mass, the PBE results were compared to those from \nfull SPH calculations. Two test cases were performed. The first \nfollowed the formation of a binary system from the collapse \nof an initially uniform-density, spherical molecular cloud \ncore in solid-body rotation. The `seed' binary was assumed \nto have a mass ratio of $q=0.6$ and a mass of $1/10$ the\ninitial cloud mass. The second test case was similar, except \nthat the progenitor cloud was centrally-condensed with a 1/r-density \ndistribution and the cloud had a total mass of only 5 times the\n`seed' binary's mass. A full discussion of the test cases\nis given by \\cite{Bate2000}.\n\n\n\\subsubsection{Test Case 1}\n\nThe evolution of the mass ratio, separation and amount of gas\nin the circumbinary disc are given for\nthe PBE code and for a full SPH calculation in Figure \n\\ref{bate.testcase1}. The curves are given as functions of the \namount of gas that has fallen on to the binary, $M_{\\rm acc}$, \nrelative to the binary's initial mass. \nIn addition, an MPEG animation of the\nSPH calculation is included on this CD-ROM as bate2.mpg.\nThe CPU time required to evolve the SPH\ncalculation until the entire cloud falls on to the binary in \nis prohibitively long, which, after all, is the reason that \nthe PBE code was developed in the first place. It takes \n$\\approx 60$ orbits for the binary to increase its mass by \na factor of 6 (i.e.~$\\approx 60$\\% of the total cloud was \naccreted). The SPH calculation took $\\approx 5$ months on \na 170 MHz Sun Ultra workstation with a GRAvity-PipE (GRAPE) board used\nto calculate the gravitational forces and neighbouring SPH particles. \nThe evolution with the PBE code took a few seconds!\n\nAlthough the SPH calculation did not run to completion, \nwe can compare the evolution as the binary's mass increases \nby a factor of 6 (Figure \\ref{bate.testcase1}). \nGenerally, there is good agreement \nbetween the PBE and SPH codes. The mass ratio is predicted \nto within 5\\% over the entire evolution and the separation \nto within 15\\%. In fact, as discussed in \\cite{Bate2000},\nthe small differences between the PBE and SPH results \nreflect unphysical treatment of the circumstellar discs\nby the SPH code rather than a problem with the PBE code.\nFor example, the slower rate of increase of the mass ratio\ninitially is due to the circumsecondary disc not being \nresolved correctly in the SPH calculation, and the larger\nseparation when $M_{\\rm acc}\\simgreat 3$ is due to \nunphysically-rapid viscous evolution of the \ncircumstellar discs which transfers angular momentum into\nthe binary's orbit too quickly. The greatest difference between\nthe PBE and SPH results is that the PBE code predicts that a \ncircumbinary disc should be formed around the binary whereas\nno circumbinary disc is formed in the SPH calculation. This is\ndue to the larger separation of the binary when $M_{\\rm acc}\\simgreat 3$ \nand the large shear viscosity in the SPH calculation.\n\n\n\\subsubsection{Test Case 2}\n\nUnlike test case 1, the PBE code predicts that a massive \ncircumbinary disc should be produced very early in the \nevolution of test case 2. Thus, test case 2 provides a \nbetter test of how well the PBE code predicts the formation\nof a circumbinary disc and its evolution. We note that,\nalthough the\nPBE code records the amount of gas which settles into a \ncircumbinary disc, it does not attempt to take account of the\ninteraction between the binary and the circumbinary disc. In\nreality, this interaction is expected to result in the \ntransfer of angular momentum from the orbit of the binary into\nthe gas of the circumbinary disc and, hence, in a smaller \nseparation. Furthermore, if the separation decreases, more \nof the infalling gas would be expected to settle into the \ncircumbinary disc and, for the same increase in the binary's\nmass, the mass ratio should increase more rapidly because the\ngas has a greater specific angular momentum relative to that of\nthe binary. Thus, if a massive circumbinary disc is formed, \nthe PBE code is expected to over-estimate the binary's separation, \nunder-estimate the mass in the circumbinary disc, and slightly\nunder-estimate the mass-ratio of the binary.\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig15.eps, width=12.5cm}\n\\caption{\\label{bate.testcase2} Same as Figure 14, except that the \nprotobinary system was formed from a molecular cloud core \nwhich initially had a density profile of $\\rho \\propto 1/r$.}\n\\end{center}\n\\end{figure}\n\nThe evolution of the mass ratio, separation and amount of gas\nin the circumbinary disc are given for test case 2 in Figure \n\\ref{bate.testcase2}. An MPEG animation of the\nSPH calculation is included on this CD-ROM as bate3.mpg.\nTo avoid the problems that occurred due to the large shear viscosity\nin the SPH calculation for test case 1, the SPH calculation here\nuses a formulation with less shear viscosity (see \\cite{Bate2000}).\nAs with test case 1, due to the computational cost, the SPH \ncalculations were stopped before all of the gas had fallen on \nto the binary. The SPH calculation took $\\approx 4$ months \non a 300 MHz Sun Ultra workstation (using a binary tree, \nnot a GRAPE board). During the evolution, the \nbinary performed $\\approx 40$ orbits and $\\approx 60$\\%\nof the total mass was accreted by the binary or settled \ninto a circumbinary disc.\n\nThe agreement for the evolution of the mass ratio is even \nbetter than it was with test case 1 with differences between the PBE\nand SPH results of $\\simless 3$\\%. The separation\nfollows the prediction of the PBE code to better than $3$\\%\nuntil the circumbinary disc begins to form. Once the circumbinary\ndisc attains approximately 5\\% of the binary's mass, however,\nthe separation is always smaller than predicted by the PBE code.\nAs described above, this is expected because the PBE code\nneglects the separation-decreasing effect of the interaction \nbetween the binary and the circumbinary disc. This also explains\nwhy the PBE code slightly under-estimates the binary's mass ratio.\nHowever, it is pleasing to see that even neglecting the \ninteraction between the binary and the circumbinary disc, \nthe PBE code still predicts the mass of the circumbinary disc to \nwithin a factor of 2 of that given by the SPH code during the\nentire evolution.\n\n\n\\subsection{The Evolution of Accreting Protobinary Systems}\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig16.eps, width=12cm}\n\\vspace{0.5truecm}\n\\caption{\\label{bate.uniform} The evolution of protobinary systems \nformed in the centre of collapsing molecular cloud cores as they \naccrete from the gaseous envelope. The initial cores have uniform-density \nprofiles and are in solid-body rotation. The evolution of the mass ratio \n(a; upper left), separation (b; upper right), and ratio of the \ncircumbinary disc mass to that of the binary (c; lower left), and the \nrelative accretion rate (d; lower right) are given as functions of the \namount of gas that has been accreted from the envelope. The evolutionary\ncurves\nare given for `seed' binary systems with initial mass ratios of $q=0.1$ to \n$q=1.0$, with various different line types and/or widths for each. The \ncurves are all given by a thin dotted lines once the circumbinary \ndisc mass exceeds 5\\% of the binary's mass. Beyond this point, \nthe binary's mass ratio and the mass in the circumbinary disc are likely \nto be under-estimated, and the separation is likely to be over-estimated. }\n\\end{center}\n\\end{figure}\n\nAs we have seen, the PBE code gives a relatively accurate \ndescription of the evolution of an accreting protobinary, but does\nso $\\sim 10^6$ times faster than a full hydrodynamic SPH calculation.\nThis allows us to perform many calculations to \nstudy how the evolution of a binary as it accretes\nto its final mass depends on its initial mass ratio and on the\nproperties of the molecular cloud core from which it formed.\n\nAs examples, we give the evolution of `seed' binaries that form\nfrom two types of molecular cloud core. A greater range of\nmolecular cloud cores is considered in \\cite{Bate2000}.\nFigure \\ref{bate.uniform} presents the evolution of\nbinaries formed from molecular cloud cores which had\nuniform-density and were in solid-body rotation before they began\nto collapse dynamically. In Figure \\ref{bate.1r}, the \nmolecular cloud cores had radial density profiles of $\\rho \\propto 1/r$\nwith solid-body rotation, initially. \nEvolutionary curves are provided for `seed' binaries\nwith initial mass ratios ranging from $q=0.1-1.0$. \n\nIn all cases, the long-term evolution is towards a mass ratio \nof unity, since the material that falls in later has higher \nspecific angular momentum relative to that of the binary. \nThus, the more the binary accretes relative to its initial mass, \nthe stronger the tendency is for the mass ratio to be \ndriven to unity. Similarly, the more the binary accretes \nrelative to its initial mass, the more likely it is to be surrounded\nby a circumbinary disc. Note that, in the previous sections,\nwe found that when a massive circumbinary disc is formed, the PBE\ncode tends to over-estimate the separation, and under-estimate \nthe mass of the circumbinary disc and the binary's mass ratio.\nThus, if anything, the evolutionary curves in Figures \\ref{bate.uniform}\nand \\ref{bate.1r} tend to under-estimate the binary's mass ratio and \nthe mass of the circumbinary disc.\n\n\n\\subsection{The Properties of Binary Stars}\n\n\\begin{figure}[t]\n\\begin{center}\n\\epsfig{file=fig17.eps, width=12cm}\n\\vspace{0.5truecm}\n\\caption{\\label{bate.1r} Same as Figure 16, except that the \nprotobinary systems were formed from a molecular cloud cores \nwhich initially had a density profiles of $\\rho \\propto 1/r$.}\n\\end{center}\n\\end{figure}\n\nThe aim of developing the PBE code was to make it possible to predict\nsome of the properties of binary stars and, by comparing\nthese to the observed properties of binary systems, to constrain \nthe initial conditions for binary star formation. \n\nIn order to obtain predictions about the properties of binaries we \nnote that, generally, the initial mass of a `seed' binary is smaller \nfor those binaries with smaller separations. This relationship\nbetween a `seed' binary's mass and its separation is observed from\nfragmentation calculations \\cite{Boss86, BonBat94b} and\nis easily understood from a Jeans-mass argument \\cite{Bate2000}. \nIn order for\nfragmentation to occur, the Jeans length at the time of fragmentation\nmust be less than or approximately equal to the separation of the\nbinary which is formed. However, for a constant temperature,\nthe Jeans mass depends linearly on the Jeans length. Thus, the\nsmaller the separation of the `seed' binary, the smaller its initial\nmass. Generally, `seed' binaries with separations $\\simless 10$\nAU are expected to have masses $\\approx 0.01 {\\rm M}_{\\odot}$, while\nfor larger separations, the `seed' mass is expected to increase\napproximately linearly (i.e. `seed' binaries with separations of\n100-1000 AU should have initial masses of \n$\\approx 0.1-1.0 {\\rm M}_{\\odot}$).\n\nThis dependence of the initial mass on the separation means that\nto form binaries with the same final total mass, the closer systems\nneed to accrete more material, relative to their initial mass.\nTherefore, from the evolutionary curves of Figures \\ref{bate.uniform}\nand \\ref{bate.1r}, closer systems are more likely to have equal-mass\ncomponents than wider systems.\n\nThis prediction is supported by surveys of main-sequence \nG-dwarf stellar systems. Duquennoy \\& Mayor \\cite{DuqMay91} \nfound that the mass-ratio distribution, averaged over \nbinaries with all separations, increases toward small mass \nratios. However, there is mounting evidence that\nthe mass-ratio distributions differ between short and long-period\nsystems with the distribution for close binary systems ($P <\n3000$ days; $a \\simless 5$ AU) consistent with\na uniform distribution \\cite{Mazehetal92, HalMayUdr98}.\nThus, relative to wide systems, the close systems are biased toward\nmass ratios of unity.\n\nThe fraction by which the mass of a `seed' binary must\nbe increased in order for its mass ratio to approach unity depends\non the conditions in the molecular cloud core. Generally,\nthe less centrally-condensed a core is, the easier it is to \nform a binary system with a low mass ratio \n(c.f.~Figures \\ref{bate.uniform} and \\ref{bate.1r}).\nWe can use this dependence of the evolutionary curves on the \ntype of molecular cloud core to attempt to constrain the initial\nconditions for binary star formation.\n\nDuquennoy \\& Mayor \\cite{DuqMay91} found that binaries containing\nG-dwarfs with\nseparations $\\simgreat 30$ AU generally have unequal masses\n(typically $q\\approx 0.3$). Such binaries are likely to have\naccreted from a few to ten times there initial mass. For uniform-density\ncores (Figure \\ref{bate.uniform}), the observed mass-ratio \ndistribution can easily be obtained. Cores with $\\rho \\propto 1/r$\nresult in higher mass ratios than uniform-density cores, but it is\nstill possible to envisage a spectrum of `seed' mass ratios which gives\na final mass-ratio distribution which is consistent with the\nobservations of wide binaries.\n\nHowever, close binaries ($\\simless 5$ AU) have initial masses\nof $\\approx 0.01 {\\rm M}_{\\odot}$. Thus, they are expected to\nhave to accrete up to 100 times their initial mass from the infalling\ngaseous envelope before systems with G-dwarf primaries are obtained,\nyet the observed mass-ratio distribution is approximately flat\n(i.e.~approximately 1/2 the binaries have $q<0.5$). \nIt is effectively impossible for cores in solid-body rotation \nto produce such a mass ratio distribution if they are \nsignificantly centrally-condensed (Figure \\ref{bate.1r}). \nEven with uniform-density cores most of the `seed' binaries \nwould need to have mass ratios $q<0.1$, which is unlikely.\n\nHowever, the PBE code only evolves circular binaries whereas \nmost binaries have significant eccentricity \\cite{DuqMay91}.\nFor the same semi-major axis, eccentric binaries have less \nangular momentum than circular binaries meaning that the \nclouds from which they formed may be rotating more slowly\nand, thus, the gas in the envelope may have less angular momentum.\nThis would result in slower evolution toward equal masses for\neccentric binaries.\nTaking the effects of eccentricity into account, it is quite \npossible that the observed binary mass ratios could be \nproduced by the collapse of molecular cloud cores\nwith radial density profiles less centrally-condensed than $\\rho \n\\propto 1/r$. However, even accounting for eccentric binaries, \nit seems virtually impossible that the observed G-dwarf binary \nsystems could have been formed from molecular cloud cores with\ndensity profiles that were more centrally-condensed \nthan $\\rho \\propto 1/r$.\n\nThe above conclusion that closer binaries should have mass ratios\nthat are biased toward unity compared to wider systems with the\nsame total mass is just one of many predictions that may be\nderived using the PBE code (see \\cite{Bate2000}). \nOthers include: closer binaries are \nmore likely to have circumbinary discs than wider binaries; \nbrown dwarf companions to solar-type stars\nshould be very rare at separations $\\simless 5$ AU, but their\nfrequency should increase at larger separations. \n\n\n\\section{Conclusions}\n\nThe Lagrangian nature of SPH and its inherent ability to\nprovide finer spatial resolution in regions of higher density \nmake it a powerful tool which is ideally suited for \nstudying star formation.\n\nRecent advances in the study of binary star formation that \nhave been made using SPH include: the realisation that it is\nessential that the Jeans mass is always resolved in numerical \nstudies of self-gravitating gas; the ability to perform \nthree-dimensional hydrodynamic calculations which follow the \ncollapse of a molecular cloud core to stellar densities;\nthe study of the effects of accretion on a protobinary systems\nand the development of a code which enables the evolution of\naccreting binary systems to be followed $\\sim 10^6$ times \nfaster than a full hydrodynamic calculation. 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}
] |
[
{
"name": "astro-ph0002202.extracted_bib",
"string": "\\bibitem{Artymowicz83}\n Artymowicz P., 1983, Acta Astronomica, 33, 223\n\n\n\\bibitem{ArtLub94}\n Artymowicz P., Lubow S. H., 1994, ApJ, 421, 651\n\n\n\\bibitem{Bate97}\n Bate M. R., 1997, MNRAS, 285, 16\n\n\n\\bibitem{Bate98}\n Bate M. R., 1998, ApJ, 508, L95\n\n\n\\bibitem{Bate2000}\n Bate M. R., 2000, MNRAS, submitted\n\n\n\\bibitem{BatBon97}\n Bate M. R., Bonnell I. A., 1997, MNRAS, 285, 33\n\n\n\\bibitem{BatBonPri95}\n Bate M. R., Bonnell I. A., Price N. M., 1995, MNRAS, 277, 362\n\n\n\\bibitem{BatBur97}\n Bate M. R., Burkert A., 1997, MNRAS, 288, 1060\n\n\n\\bibitem{Benz90}\n Benz W., 1990, in Buchler J. R., ed., The Numerical Modeling of Nonlinear Stellar Pulsations: Problems and Prospects. Kluwer, Dordrecht, p. 269\n\n\n\\bibitem{BonBas91}\n Bonnell I. A., Bastien P., 1991, ApJ, 374, 610\n\n\n\\bibitem{BonBat94b}\n Bonnell I. A., Bate M. R., 1994, MNRAS, 271, 999\n\n\n\\bibitem{Boss86}\n Boss A. P., 1986, ApJS, 62, 519\n\n\n\\bibitem{Boss87}\n Boss A. P., 1987, ApJ, 319, 149\n\n\n\\bibitem{Boss98}\n Boss A. P., 1998, ApJ, 501, 77\n\n\n\\bibitem{BurBod93}\n Burkert A., Bodenheimer P., 1993, MNRAS, 264, 798\n\n\n\\bibitem{Chapmanetal92}\n Chapman S., Pongracic H., Disney M., Nelson A., Turner J., Whitworth A., 1992, Nature, 359, 207\n\n\n\\bibitem{Durisenetal86}\n Durisen R. H., Gingold R.A., Tohline J.E., Boss A.P., 1986, ApJ, 305, 281\n\n\n\\bibitem{DuqMay91}\n Duquennoy A., Mayor M., 1991, A\\&A, 248, 485\n\n\n\\bibitem{Evrard88}\n Evrard A. E., 1988, MNRAS, 235, 911\n\n\n\\bibitem{Lucy77}\n Lucy L., 1977, AJ, 82, 1013\n\n\n\\bibitem{GinMon77}\n Gingold R. A., Monaghan J. J., 1977, MNRAS, 181, 375\n\n\n\\bibitem{GinMon78}\n Gingold R. A., Monaghan J. J., 1978, MNRAS, 184, 481\n\n\n\\bibitem{GinMon81}\n Gingold R. A., Monaghan J. J., 1981, MNRAS, 197, 461\n\n\n\\bibitem{HalMayUdr98}\n Halbwachs J. L., Mayor M., Udry S., 1998, in Rebolo R., Martin E. L., Zapatero Osorio M.R., eds., Brown Dwarfs and Extrasolar Planets (ASP Conf. Ser. 134). Brigham Young University, Provo, p. 308\n\n\n\\bibitem{Heller93}\n Heller, C. H., 1993, ApJ, 408, 337\n\n\n\\bibitem{HerKat89}\n Hernquist L., Katz N., 1989, ApJS, 70, 419\n\n\n\\bibitem{ImaDurPic99}\n Imamura J. N., Durisen R. H., Pickett B. K., 1999, ApJ, in press\n\n\n\\bibitem{Larwoodetal96}\n Larwood J. D., Nelson R. P., Papaloizou J. C. B., Terquem C., 1996, MNRAS, 282, 597\n\n\n\\bibitem{Lattanzioetal85}\n Lattanzio J. C., Monaghan J. J., Pongracic H., Schwarz M. P., 1985, MNRAS, 215, 125\n\n\n\\bibitem{Mazehetal92}\n Mazeh T., Goldberg D., Duquennoy A., Mayor M., 1992, ApJ, 401, 265\n\n\n\\bibitem{MiyHayNar84}\n Miyama S. M., Hayashi C., Narita S., 1984, ApJ, 279, 621\n\n\n\\bibitem{Monaghan92}\n Monaghan J. J., 1992, ARA\\&A, 30, 543\n\n\n\\bibitem{Nelsonetal98}\n Nelson A. F., Benz W., Adams F. C., Arnett D., ApJ, 502, 342\n\n\n\\bibitem{NelPap93}\n Nelson R., Papaloizou J. C., 1993, MNRAS, 265, 905\n\n\n\\bibitem{SigKla97}\n Sigalotti L. Di G., Klapp J., A\\&A, 319, 547\n\n\n\\bibitem{Tohline82}\n Tohline, J. E., 1982, Fund. Cos. Phys., 8, 1\n\n\n\\bibitem{Trueloveetal97}\n Truelove J. K., Klein R. I., McKee C. F., Holliman J. H. II, Howell L. H., Greenough J. A., 1997, ApJ, 489, L179\n\n\n\\bibitem{Trueloveetal98}\n Truelove J. K., Klein R. I., McKee C. F., Holliman J. H. II, Howell L. H. Greenough J. A., \\& Woods D. T., 1998, ApJ, 495, 821\n\n\n\\bibitem{VanCam98}\n Vanhala, H. A. T., Cameron A. G. W., 1998, ApJ, 508, 291\n\n\n\\bibitem{Whitworth98}\n Whitworth A. P., 1998, MNRAS, 296, 442\n\n"
}
] |